Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,6,Mod(9,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.9");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.24537347738\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{79})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 79x^{2} + 6241 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 9.2 | ||
Root | \(-4.44410 - 7.69740i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.9 |
Dual form | 14.6.c.a.11.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | + | 3.46410i | −0.353553 | + | 0.612372i | ||||
\(3\) | 5.38819 | + | 9.33263i | 0.345653 | + | 0.598688i | 0.985472 | − | 0.169837i | \(-0.0543242\pi\) |
−0.639819 | + | 0.768525i | \(0.720991\pi\) | |||||||
\(4\) | −8.00000 | − | 13.8564i | −0.250000 | − | 0.433013i | ||||
\(5\) | −53.0528 | + | 91.8901i | −0.949037 | + | 1.64378i | −0.201578 | + | 0.979473i | \(0.564607\pi\) |
−0.747459 | + | 0.664308i | \(0.768726\pi\) | |||||||
\(6\) | −43.1056 | −0.488827 | ||||||||
\(7\) | 124.435 | − | 36.3731i | 0.959835 | − | 0.280566i | ||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 63.4347 | − | 109.872i | 0.261048 | − | 0.452149i | ||||
\(10\) | −212.211 | − | 367.560i | −0.671070 | − | 1.16233i | ||||
\(11\) | 46.7174 | + | 80.9168i | 0.116412 | + | 0.201631i | 0.918343 | − | 0.395785i | \(-0.129527\pi\) |
−0.801931 | + | 0.597416i | \(0.796194\pi\) | |||||||
\(12\) | 86.2111 | − | 149.322i | 0.172826 | − | 0.299344i | ||||
\(13\) | 661.131 | 1.08500 | 0.542499 | − | 0.840057i | \(-0.317478\pi\) | ||||
0.542499 | + | 0.840057i | \(0.317478\pi\) | |||||||
\(14\) | −122.869 | + | 503.801i | −0.167542 | + | 0.686971i | ||||
\(15\) | −1143.43 | −1.31215 | ||||||||
\(16\) | −128.000 | + | 221.703i | −0.125000 | + | 0.216506i | ||||
\(17\) | −227.960 | − | 394.838i | −0.191309 | − | 0.331357i | 0.754375 | − | 0.656444i | \(-0.227940\pi\) |
−0.945684 | + | 0.325086i | \(0.894607\pi\) | |||||||
\(18\) | 253.739 | + | 439.489i | 0.184589 | + | 0.319717i | ||||
\(19\) | −553.140 | + | 958.066i | −0.351521 | + | 0.608851i | −0.986516 | − | 0.163664i | \(-0.947669\pi\) |
0.634996 | + | 0.772516i | \(0.281002\pi\) | |||||||
\(20\) | 1697.69 | 0.949037 | ||||||||
\(21\) | 1009.93 | + | 965.318i | 0.499741 | + | 0.477663i | ||||
\(22\) | −373.739 | −0.164631 | ||||||||
\(23\) | −374.195 | + | 648.125i | −0.147495 | + | 0.255470i | −0.930301 | − | 0.366797i | \(-0.880455\pi\) |
0.782806 | + | 0.622266i | \(0.213788\pi\) | |||||||
\(24\) | 344.844 | + | 597.288i | 0.122207 | + | 0.211668i | ||||
\(25\) | −4066.69 | − | 7043.72i | −1.30134 | − | 2.25399i | ||||
\(26\) | −1322.26 | + | 2290.22i | −0.383605 | + | 0.664423i | ||||
\(27\) | 3985.86 | 1.05223 | ||||||||
\(28\) | −1499.48 | − | 1433.23i | −0.361447 | − | 0.345479i | ||||
\(29\) | 2804.78 | 0.619304 | 0.309652 | − | 0.950850i | \(-0.399787\pi\) | ||||
0.309652 | + | 0.950850i | \(0.399787\pi\) | |||||||
\(30\) | 2286.87 | − | 3960.97i | 0.463915 | − | 0.803524i | ||||
\(31\) | 179.649 | + | 311.162i | 0.0335754 | + | 0.0581543i | 0.882325 | − | 0.470641i | \(-0.155977\pi\) |
−0.848749 | + | 0.528795i | \(0.822644\pi\) | |||||||
\(32\) | −512.000 | − | 886.810i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −503.444 | + | 871.991i | −0.0804761 | + | 0.139389i | ||||
\(34\) | 1823.68 | 0.270552 | ||||||||
\(35\) | −3259.28 | + | 13364.0i | −0.449730 | + | 1.84402i | ||||
\(36\) | −2029.91 | −0.261048 | ||||||||
\(37\) | 3406.41 | − | 5900.08i | 0.409066 | − | 0.708522i | −0.585720 | − | 0.810514i | \(-0.699188\pi\) |
0.994785 | + | 0.101991i | \(0.0325214\pi\) | |||||||
\(38\) | −2212.56 | − | 3832.26i | −0.248563 | − | 0.430523i | ||||
\(39\) | 3562.30 | + | 6170.08i | 0.375033 | + | 0.649575i | ||||
\(40\) | −3395.38 | + | 5880.97i | −0.335535 | + | 0.581164i | ||||
\(41\) | 2319.39 | 0.215484 | 0.107742 | − | 0.994179i | \(-0.465638\pi\) | ||||
0.107742 | + | 0.994179i | \(0.465638\pi\) | |||||||
\(42\) | −5363.83 | + | 1567.88i | −0.469193 | + | 0.137148i | ||||
\(43\) | −19965.7 | −1.64670 | −0.823349 | − | 0.567535i | \(-0.807897\pi\) | ||||
−0.823349 | + | 0.567535i | \(0.807897\pi\) | |||||||
\(44\) | 747.478 | − | 1294.67i | 0.0582058 | − | 0.100815i | ||||
\(45\) | 6730.78 | + | 11658.0i | 0.495489 | + | 0.858212i | ||||
\(46\) | −1496.78 | − | 2592.50i | −0.104295 | − | 0.180644i | ||||
\(47\) | 7104.77 | − | 12305.8i | 0.469143 | − | 0.812580i | −0.530234 | − | 0.847851i | \(-0.677896\pi\) |
0.999378 | + | 0.0352710i | \(0.0112294\pi\) | |||||||
\(48\) | −2758.76 | −0.172826 | ||||||||
\(49\) | 14161.0 | − | 9052.14i | 0.842566 | − | 0.538594i | ||||
\(50\) | 32533.6 | 1.84038 | ||||||||
\(51\) | 2456.58 | − | 4254.93i | 0.132253 | − | 0.229069i | ||||
\(52\) | −5289.04 | − | 9160.89i | −0.271249 | − | 0.469818i | ||||
\(53\) | −13072.1 | − | 22641.5i | −0.639228 | − | 1.10718i | −0.985602 | − | 0.169079i | \(-0.945921\pi\) |
0.346374 | − | 0.938096i | \(-0.387413\pi\) | |||||||
\(54\) | −7971.71 | + | 13807.4i | −0.372021 | + | 0.644359i | ||||
\(55\) | −9913.94 | −0.441916 | ||||||||
\(56\) | 7963.82 | − | 2327.88i | 0.339353 | − | 0.0991950i | ||||
\(57\) | −11921.7 | −0.486016 | ||||||||
\(58\) | −5609.56 | + | 9716.04i | −0.218957 | + | 0.379245i | ||||
\(59\) | −2452.18 | − | 4247.29i | −0.0917110 | − | 0.158848i | 0.816520 | − | 0.577317i | \(-0.195900\pi\) |
−0.908231 | + | 0.418469i | \(0.862567\pi\) | |||||||
\(60\) | 9147.48 | + | 15843.9i | 0.328037 | + | 0.568177i | ||||
\(61\) | 6601.64 | − | 11434.4i | 0.227158 | − | 0.393449i | −0.729807 | − | 0.683653i | \(-0.760390\pi\) |
0.956965 | + | 0.290205i | \(0.0937234\pi\) | |||||||
\(62\) | −1437.19 | −0.0474828 | ||||||||
\(63\) | 3897.09 | − | 15979.2i | 0.123706 | − | 0.507229i | ||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −35074.8 | + | 60751.4i | −1.02970 | + | 1.78350i | ||||
\(66\) | −2013.78 | − | 3487.97i | −0.0569052 | − | 0.0985626i | ||||
\(67\) | 29829.1 | + | 51665.5i | 0.811807 | + | 1.40609i | 0.911598 | + | 0.411082i | \(0.134849\pi\) |
−0.0997917 | + | 0.995008i | \(0.531818\pi\) | |||||||
\(68\) | −3647.36 | + | 6317.41i | −0.0956546 | + | 0.165679i | ||||
\(69\) | −8064.94 | −0.203929 | ||||||||
\(70\) | −39775.7 | − | 38018.5i | −0.970226 | − | 0.927363i | ||||
\(71\) | 8906.43 | 0.209680 | 0.104840 | − | 0.994489i | \(-0.466567\pi\) | ||||
0.104840 | + | 0.994489i | \(0.466567\pi\) | |||||||
\(72\) | 4059.82 | − | 7031.82i | 0.0922945 | − | 0.159859i | ||||
\(73\) | 5240.29 | + | 9076.46i | 0.115093 | + | 0.199347i | 0.917817 | − | 0.397004i | \(-0.129950\pi\) |
−0.802724 | + | 0.596351i | \(0.796617\pi\) | |||||||
\(74\) | 13625.6 | + | 23600.3i | 0.289253 | + | 0.501001i | ||||
\(75\) | 43824.3 | − | 75905.9i | 0.899625 | − | 1.55820i | ||||
\(76\) | 17700.5 | 0.351521 | ||||||||
\(77\) | 8756.46 | + | 8369.61i | 0.168307 | + | 0.160871i | ||||
\(78\) | −28498.4 | −0.530376 | ||||||||
\(79\) | 3615.01 | − | 6261.38i | 0.0651691 | − | 0.112876i | −0.831600 | − | 0.555375i | \(-0.812575\pi\) |
0.896769 | + | 0.442499i | \(0.145908\pi\) | |||||||
\(80\) | −13581.5 | − | 23523.9i | −0.237259 | − | 0.410945i | ||||
\(81\) | 6061.93 | + | 10499.6i | 0.102659 | + | 0.177811i | ||||
\(82\) | −4638.78 | + | 8034.61i | −0.0761850 | + | 0.131956i | ||||
\(83\) | −100461. | −1.60067 | −0.800336 | − | 0.599552i | \(-0.795345\pi\) | ||||
−0.800336 | + | 0.599552i | \(0.795345\pi\) | |||||||
\(84\) | 5296.36 | − | 21716.6i | 0.0818991 | − | 0.335810i | ||||
\(85\) | 48375.6 | 0.726238 | ||||||||
\(86\) | 39931.5 | − | 69163.3i | 0.582196 | − | 1.00839i | ||||
\(87\) | 15112.7 | + | 26176.0i | 0.214064 | + | 0.370770i | ||||
\(88\) | 2989.91 | + | 5178.68i | 0.0411577 | + | 0.0712873i | ||||
\(89\) | −10035.9 | + | 17382.7i | −0.134302 | + | 0.232617i | −0.925331 | − | 0.379162i | \(-0.876212\pi\) |
0.791029 | + | 0.611779i | \(0.209546\pi\) | |||||||
\(90\) | −53846.2 | −0.700727 | ||||||||
\(91\) | 82267.6 | − | 24047.3i | 1.04142 | − | 0.304413i | ||||
\(92\) | 11974.2 | 0.147495 | ||||||||
\(93\) | −1935.97 | + | 3353.20i | −0.0232109 | + | 0.0402024i | ||||
\(94\) | 28419.1 | + | 49223.3i | 0.331734 | + | 0.574581i | ||||
\(95\) | −58691.2 | − | 101656.i | −0.667212 | − | 1.15565i | ||||
\(96\) | 5517.51 | − | 9556.61i | 0.0611034 | − | 0.105834i | ||||
\(97\) | −23320.9 | −0.251662 | −0.125831 | − | 0.992052i | \(-0.540160\pi\) | ||||
−0.125831 | + | 0.992052i | \(0.540160\pi\) | |||||||
\(98\) | 3035.55 | + | 67159.4i | 0.0319280 | + | 0.706386i | ||||
\(99\) | 11854.0 | 0.121556 | ||||||||
\(100\) | −65067.1 | + | 112700.i | −0.650671 | + | 1.12700i | ||||
\(101\) | 34487.1 | + | 59733.4i | 0.336398 | + | 0.582658i | 0.983752 | − | 0.179531i | \(-0.0574581\pi\) |
−0.647355 | + | 0.762189i | \(0.724125\pi\) | |||||||
\(102\) | 9826.33 | + | 17019.7i | 0.0935171 | + | 0.161976i | ||||
\(103\) | −56862.6 | + | 98488.9i | −0.528121 | + | 0.914733i | 0.471341 | + | 0.881951i | \(0.343770\pi\) |
−0.999463 | + | 0.0327819i | \(0.989563\pi\) | |||||||
\(104\) | 42312.4 | 0.383605 | ||||||||
\(105\) | −142283. | + | 41590.2i | −1.25945 | + | 0.368144i | ||||
\(106\) | 104577. | 0.904005 | ||||||||
\(107\) | 60643.6 | − | 105038.i | 0.512066 | − | 0.886924i | −0.487836 | − | 0.872935i | \(-0.662214\pi\) |
0.999902 | − | 0.0139887i | \(-0.00445290\pi\) | |||||||
\(108\) | −31886.9 | − | 55229.7i | −0.263058 | − | 0.455631i | ||||
\(109\) | 30686.9 | + | 53151.3i | 0.247393 | + | 0.428497i | 0.962802 | − | 0.270209i | \(-0.0870928\pi\) |
−0.715409 | + | 0.698706i | \(0.753760\pi\) | |||||||
\(110\) | 19827.9 | − | 34342.9i | 0.156241 | − | 0.270617i | ||||
\(111\) | 73417.7 | 0.565579 | ||||||||
\(112\) | −7863.64 | + | 32243.2i | −0.0592351 | + | 0.242881i | ||||
\(113\) | −242939. | −1.78979 | −0.894893 | − | 0.446281i | \(-0.852748\pi\) | ||||
−0.894893 | + | 0.446281i | \(0.852748\pi\) | |||||||
\(114\) | 23843.4 | − | 41298.0i | 0.171833 | − | 0.297623i | ||||
\(115\) | −39704.2 | − | 68769.7i | −0.279957 | − | 0.484900i | ||||
\(116\) | −22438.2 | − | 38864.2i | −0.154826 | − | 0.268167i | ||||
\(117\) | 41938.6 | − | 72639.8i | 0.283237 | − | 0.490580i | ||||
\(118\) | 19617.4 | 0.129699 | ||||||||
\(119\) | −42727.6 | − | 40839.9i | −0.276593 | − | 0.264373i | ||||
\(120\) | −73179.8 | −0.463915 | ||||||||
\(121\) | 76160.5 | − | 131914.i | 0.472897 | − | 0.819081i | ||||
\(122\) | 26406.6 | + | 45737.5i | 0.160625 | + | 0.278210i | ||||
\(123\) | 12497.3 | + | 21646.0i | 0.0744826 | + | 0.129008i | ||||
\(124\) | 2874.39 | − | 4978.59i | 0.0167877 | − | 0.0290772i | ||||
\(125\) | 531418. | 3.04201 | ||||||||
\(126\) | 47559.5 | + | 45458.4i | 0.266877 | + | 0.255087i | ||||
\(127\) | 201922. | 1.11090 | 0.555448 | − | 0.831551i | \(-0.312547\pi\) | ||||
0.555448 | + | 0.831551i | \(0.312547\pi\) | |||||||
\(128\) | −8192.00 | + | 14189.0i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −107579. | − | 186333.i | −0.569186 | − | 0.985859i | ||||
\(130\) | −140299. | − | 243005.i | −0.728110 | − | 1.26112i | ||||
\(131\) | −141761. | + | 245536.i | −0.721734 | + | 1.25008i | 0.238571 | + | 0.971125i | \(0.423321\pi\) |
−0.960304 | + | 0.278954i | \(0.910012\pi\) | |||||||
\(132\) | 16110.2 | 0.0804761 | ||||||||
\(133\) | −33982.0 | + | 139336.i | −0.166579 | + | 0.683021i | ||||
\(134\) | −238633. | −1.14807 | ||||||||
\(135\) | −211461. | + | 366261.i | −0.998609 | + | 1.72964i | ||||
\(136\) | −14589.4 | − | 25269.6i | −0.0676380 | − | 0.117152i | ||||
\(137\) | −94235.3 | − | 163220.i | −0.428955 | − | 0.742972i | 0.567825 | − | 0.823149i | \(-0.307785\pi\) |
−0.996781 | + | 0.0801767i | \(0.974452\pi\) | |||||||
\(138\) | 16129.9 | − | 27937.8i | 0.0720997 | − | 0.124880i | ||||
\(139\) | −211579. | −0.928830 | −0.464415 | − | 0.885618i | \(-0.653735\pi\) | ||||
−0.464415 | + | 0.885618i | \(0.653735\pi\) | |||||||
\(140\) | 211251. | − | 61750.2i | 0.910919 | − | 0.266267i | ||||
\(141\) | 153128. | 0.648643 | ||||||||
\(142\) | −17812.9 | + | 30852.8i | −0.0741332 | + | 0.128402i | ||||
\(143\) | 30886.3 | + | 53496.6i | 0.126306 | + | 0.218769i | ||||
\(144\) | 16239.3 | + | 28127.3i | 0.0652621 | + | 0.113037i | ||||
\(145\) | −148801. | + | 257732.i | −0.587742 | + | 1.01800i | ||||
\(146\) | −41922.4 | −0.162766 | ||||||||
\(147\) | 160783. | + | 83384.6i | 0.613685 | + | 0.318268i | ||||
\(148\) | −109005. | −0.409066 | ||||||||
\(149\) | 146662. | − | 254026.i | 0.541192 | − | 0.937373i | −0.457644 | − | 0.889136i | \(-0.651306\pi\) |
0.998836 | − | 0.0482369i | \(-0.0153603\pi\) | |||||||
\(150\) | 175297. | + | 303624.i | 0.636131 | + | 1.10181i | ||||
\(151\) | 102238. | + | 177082.i | 0.364897 | + | 0.632020i | 0.988760 | − | 0.149514i | \(-0.0477708\pi\) |
−0.623863 | + | 0.781534i | \(0.714437\pi\) | |||||||
\(152\) | −35400.9 | + | 61316.2i | −0.124281 | + | 0.215262i | ||||
\(153\) | −57842.2 | −0.199764 | ||||||||
\(154\) | −46506.1 | + | 13594.0i | −0.158019 | + | 0.0461898i | ||||
\(155\) | −38123.6 | −0.127457 | ||||||||
\(156\) | 56996.8 | − | 98721.4i | 0.187516 | − | 0.324788i | ||||
\(157\) | −252957. | − | 438135.i | −0.819027 | − | 1.41860i | −0.906400 | − | 0.422421i | \(-0.861180\pi\) |
0.0873726 | − | 0.996176i | \(-0.472153\pi\) | |||||||
\(158\) | 14460.0 | + | 25045.5i | 0.0460815 | + | 0.0798155i | ||||
\(159\) | 140870. | − | 243994.i | 0.441902 | − | 0.765397i | ||||
\(160\) | 108652. | 0.335535 | ||||||||
\(161\) | −22988.6 | + | 94259.9i | −0.0698952 | + | 0.286591i | ||||
\(162\) | −48495.5 | −0.145182 | ||||||||
\(163\) | 142100. | − | 246124.i | 0.418914 | − | 0.725581i | −0.576916 | − | 0.816803i | \(-0.695744\pi\) |
0.995831 | + | 0.0912225i | \(0.0290775\pi\) | |||||||
\(164\) | −18555.1 | − | 32138.4i | −0.0538709 | − | 0.0933072i | ||||
\(165\) | −53418.3 | − | 92523.1i | −0.152750 | − | 0.264570i | ||||
\(166\) | 200922. | − | 348007.i | 0.565923 | − | 0.980207i | ||||
\(167\) | −13145.7 | −0.0364747 | −0.0182373 | − | 0.999834i | \(-0.505805\pi\) | ||||
−0.0182373 | + | 0.999834i | \(0.505805\pi\) | |||||||
\(168\) | 64635.8 | + | 61780.3i | 0.176685 | + | 0.168880i | ||||
\(169\) | 65800.6 | 0.177220 | ||||||||
\(170\) | −96751.2 | + | 167578.i | −0.256764 | + | 0.444728i | ||||
\(171\) | 70176.5 | + | 121549.i | 0.183528 | + | 0.317879i | ||||
\(172\) | 159726. | + | 276653.i | 0.411675 | + | 0.713041i | ||||
\(173\) | −25726.5 | + | 44559.6i | −0.0653530 | + | 0.113195i | −0.896851 | − | 0.442334i | \(-0.854151\pi\) |
0.831498 | + | 0.555528i | \(0.187484\pi\) | |||||||
\(174\) | −120902. | −0.302732 | ||||||||
\(175\) | −762240. | − | 728565.i | −1.88147 | − | 1.79835i | ||||
\(176\) | −23919.3 | −0.0582058 | ||||||||
\(177\) | 26425.6 | − | 45770.5i | 0.0634004 | − | 0.109813i | ||||
\(178\) | −40143.6 | − | 69530.8i | −0.0949657 | − | 0.164485i | ||||
\(179\) | 248867. | + | 431051.i | 0.580544 | + | 1.00553i | 0.995415 | + | 0.0956519i | \(0.0304936\pi\) |
−0.414870 | + | 0.909881i | \(0.636173\pi\) | |||||||
\(180\) | 107692. | − | 186529.i | 0.247744 | − | 0.429106i | ||||
\(181\) | −227120. | −0.515299 | −0.257650 | − | 0.966238i | \(-0.582948\pi\) | ||||
−0.257650 | + | 0.966238i | \(0.582948\pi\) | |||||||
\(182\) | −81232.7 | + | 333078.i | −0.181783 | + | 0.745362i | ||||
\(183\) | 142284. | 0.314071 | ||||||||
\(184\) | −23948.5 | + | 41480.0i | −0.0521475 | + | 0.0903221i | ||||
\(185\) | 361439. | + | 626031.i | 0.776437 | + | 1.34483i | ||||
\(186\) | −7743.88 | − | 13412.8i | −0.0164126 | − | 0.0284274i | ||||
\(187\) | 21299.4 | − | 36891.6i | 0.0445413 | − | 0.0771477i | ||||
\(188\) | −227353. | −0.469143 | ||||||||
\(189\) | 495979. | − | 144978.i | 1.00997 | − | 0.295221i | ||||
\(190\) | 469529. | 0.943580 | ||||||||
\(191\) | −251389. | + | 435419.i | −0.498612 | + | 0.863622i | −0.999999 | − | 0.00160157i | \(-0.999490\pi\) |
0.501386 | + | 0.865224i | \(0.332824\pi\) | |||||||
\(192\) | 22070.0 | + | 38226.4i | 0.0432066 | + | 0.0748360i | ||||
\(193\) | −70161.1 | − | 121523.i | −0.135582 | − | 0.234836i | 0.790237 | − | 0.612801i | \(-0.209957\pi\) |
−0.925820 | + | 0.377965i | \(0.876624\pi\) | |||||||
\(194\) | 46641.9 | − | 80786.1i | 0.0889758 | − | 0.154111i | ||||
\(195\) | −755960. | −1.42368 | ||||||||
\(196\) | −238718. | − | 123803.i | −0.443859 | − | 0.230193i | ||||
\(197\) | 378993. | 0.695769 | 0.347885 | − | 0.937537i | \(-0.386900\pi\) | ||||
0.347885 | + | 0.937537i | \(0.386900\pi\) | |||||||
\(198\) | −23708.0 | + | 41063.5i | −0.0429766 | + | 0.0744377i | ||||
\(199\) | 230511. | + | 399257.i | 0.412628 | + | 0.714693i | 0.995176 | − | 0.0981032i | \(-0.0312775\pi\) |
−0.582548 | + | 0.812796i | \(0.697944\pi\) | |||||||
\(200\) | −260268. | − | 450798.i | −0.460094 | − | 0.796906i | ||||
\(201\) | −321450. | + | 556767.i | −0.561207 | + | 0.972038i | ||||
\(202\) | −275897. | −0.475738 | ||||||||
\(203\) | 349012. | − | 102018.i | 0.594430 | − | 0.173756i | ||||
\(204\) | −78610.6 | −0.132253 | ||||||||
\(205\) | −123050. | + | 213129.i | −0.204502 | + | 0.354208i | ||||
\(206\) | −227450. | − | 393956.i | −0.373438 | − | 0.646814i | ||||
\(207\) | 47473.9 | + | 82227.3i | 0.0770068 | + | 0.133380i | ||||
\(208\) | −84624.7 | + | 146574.i | −0.135625 | + | 0.234909i | ||||
\(209\) | −103365. | −0.163684 | ||||||||
\(210\) | 140493. | − | 576063.i | 0.219840 | − | 0.901409i | ||||
\(211\) | 202139. | 0.312567 | 0.156284 | − | 0.987712i | \(-0.450049\pi\) | ||||
0.156284 | + | 0.987712i | \(0.450049\pi\) | |||||||
\(212\) | −209154. | + | 362265.i | −0.319614 | + | 0.553588i | ||||
\(213\) | 47989.6 | + | 83120.4i | 0.0724766 | + | 0.125533i | ||||
\(214\) | 242574. | + | 420151.i | 0.362085 | + | 0.627150i | ||||
\(215\) | 1.05924e6 | − | 1.83465e6i | 1.56278 | − | 2.70681i | ||||
\(216\) | 255095. | 0.372021 | ||||||||
\(217\) | 33672.5 | + | 32184.9i | 0.0485430 | + | 0.0463984i | ||||
\(218\) | −245495. | −0.349866 | ||||||||
\(219\) | −56471.5 | + | 97811.4i | −0.0795644 | + | 0.137810i | ||||
\(220\) | 79311.5 | + | 137372.i | 0.110479 | + | 0.191355i | ||||
\(221\) | −150711. | − | 261039.i | −0.207570 | − | 0.359522i | ||||
\(222\) | −146835. | + | 254326.i | −0.199962 | + | 0.346345i | ||||
\(223\) | 694340. | 0.934997 | 0.467498 | − | 0.883994i | \(-0.345155\pi\) | ||||
0.467498 | + | 0.883994i | \(0.345155\pi\) | |||||||
\(224\) | −95966.6 | − | 91726.9i | −0.127791 | − | 0.122145i | ||||
\(225\) | −1.03188e6 | −1.35885 | ||||||||
\(226\) | 485878. | − | 841565.i | 0.632785 | − | 1.09602i | ||||
\(227\) | −633487. | − | 1.09723e6i | −0.815968 | − | 1.41330i | −0.908630 | − | 0.417601i | \(-0.862871\pi\) |
0.0926620 | − | 0.995698i | \(-0.470462\pi\) | |||||||
\(228\) | 95373.6 | + | 165192.i | 0.121504 | + | 0.210451i | ||||
\(229\) | −428238. | + | 741730.i | −0.539631 | + | 0.934668i | 0.459293 | + | 0.888285i | \(0.348103\pi\) |
−0.998924 | + | 0.0463832i | \(0.985230\pi\) | |||||||
\(230\) | 317633. | 0.395919 | ||||||||
\(231\) | −30929.0 | + | 126818.i | −0.0381360 | + | 0.156369i | ||||
\(232\) | 179506. | 0.218957 | ||||||||
\(233\) | 142179. | − | 246261.i | 0.171571 | − | 0.297170i | −0.767398 | − | 0.641171i | \(-0.778449\pi\) |
0.938969 | + | 0.344001i | \(0.111782\pi\) | |||||||
\(234\) | 167755. | + | 290559.i | 0.200279 | + | 0.346893i | ||||
\(235\) | 753856. | + | 1.30572e6i | 0.890469 | + | 1.54234i | ||||
\(236\) | −39234.8 | + | 67956.7i | −0.0458555 | + | 0.0794241i | ||||
\(237\) | 77913.5 | 0.0901035 | ||||||||
\(238\) | 226929. | − | 66332.8i | 0.259685 | − | 0.0759077i | ||||
\(239\) | −427941. | −0.484606 | −0.242303 | − | 0.970201i | \(-0.577903\pi\) | ||||
−0.242303 | + | 0.970201i | \(0.577903\pi\) | |||||||
\(240\) | 146360. | − | 253502.i | 0.164019 | − | 0.284089i | ||||
\(241\) | −404791. | − | 701118.i | −0.448940 | − | 0.777586i | 0.549378 | − | 0.835574i | \(-0.314865\pi\) |
−0.998317 | + | 0.0579879i | \(0.981532\pi\) | |||||||
\(242\) | 304642. | + | 527655.i | 0.334388 | + | 0.579178i | ||||
\(243\) | 418956. | − | 725653.i | 0.455148 | − | 0.788339i | ||||
\(244\) | −211253. | −0.227158 | ||||||||
\(245\) | 80522.2 | + | 1.78150e6i | 0.0857038 | + | 1.89614i | ||||
\(246\) | −99978.7 | −0.105334 | ||||||||
\(247\) | −365697. | + | 633407.i | −0.381399 | + | 0.660602i | ||||
\(248\) | 11497.6 | + | 19914.4i | 0.0118707 | + | 0.0205607i | ||||
\(249\) | −541303. | − | 937565.i | −0.553277 | − | 0.958303i | ||||
\(250\) | −1.06284e6 | + | 1.84089e6i | −1.07551 | + | 1.86285i | ||||
\(251\) | −1.26305e6 | −1.26542 | −0.632711 | − | 0.774388i | \(-0.718058\pi\) | ||||
−0.632711 | + | 0.774388i | \(0.718058\pi\) | |||||||
\(252\) | −252591. | + | 73834.1i | −0.250563 | + | 0.0732412i | ||||
\(253\) | −69925.6 | −0.0686808 | ||||||||
\(254\) | −403843. | + | 699477.i | −0.392761 | + | 0.680283i | ||||
\(255\) | 260657. | + | 451471.i | 0.251026 | + | 0.434790i | ||||
\(256\) | −32768.0 | − | 56755.8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −28069.1 | + | 48617.1i | −0.0265091 | + | 0.0459152i | −0.878976 | − | 0.476867i | \(-0.841772\pi\) |
0.852466 | + | 0.522782i | \(0.175106\pi\) | |||||||
\(258\) | 860634. | 0.804951 | ||||||||
\(259\) | 209272. | − | 858076.i | 0.193848 | − | 0.794834i | ||||
\(260\) | 1.12239e6 | 1.02970 | ||||||||
\(261\) | 177920. | − | 308167.i | 0.161668 | − | 0.280018i | ||||
\(262\) | −567042. | − | 982146.i | −0.510343 | − | 0.883940i | ||||
\(263\) | −771376. | − | 1.33606e6i | −0.687664 | − | 1.19107i | −0.972592 | − | 0.232520i | \(-0.925303\pi\) |
0.284927 | − | 0.958549i | \(-0.408031\pi\) | |||||||
\(264\) | −32220.4 | + | 55807.4i | −0.0284526 | + | 0.0492813i | ||||
\(265\) | 2.77405e6 | 2.42660 | ||||||||
\(266\) | −414710. | − | 396389.i | −0.359369 | − | 0.343493i | ||||
\(267\) | −216302. | −0.185687 | ||||||||
\(268\) | 477265. | − | 826647.i | 0.405903 | − | 0.703045i | ||||
\(269\) | 602677. | + | 1.04387e6i | 0.507813 | + | 0.879558i | 0.999959 | + | 0.00904531i | \(0.00287925\pi\) |
−0.492146 | + | 0.870513i | \(0.663787\pi\) | |||||||
\(270\) | −845843. | − | 1.46504e6i | −0.706123 | − | 1.22304i | ||||
\(271\) | −882443. | + | 1.52844e6i | −0.729900 | + | 1.26422i | 0.227025 | + | 0.973889i | \(0.427100\pi\) |
−0.956925 | + | 0.290335i | \(0.906233\pi\) | |||||||
\(272\) | 116715. | 0.0956546 | ||||||||
\(273\) | 667699. | + | 638201.i | 0.542218 | + | 0.518264i | ||||
\(274\) | 753882. | 0.606634 | ||||||||
\(275\) | 379970. | − | 658128.i | 0.302983 | − | 0.524782i | ||||
\(276\) | 64519.6 | + | 111751.i | 0.0509822 | + | 0.0883038i | ||||
\(277\) | −741593. | − | 1.28448e6i | −0.580719 | − | 1.00584i | −0.995394 | − | 0.0958659i | \(-0.969438\pi\) |
0.414675 | − | 0.909970i | \(-0.363895\pi\) | |||||||
\(278\) | 423158. | − | 732932.i | 0.328391 | − | 0.568790i | ||||
\(279\) | 45584.0 | 0.0350592 | ||||||||
\(280\) | −208594. | + | 855297.i | −0.159004 | + | 0.651961i | ||||
\(281\) | −1.26812e6 | −0.958061 | −0.479031 | − | 0.877798i | \(-0.659012\pi\) | ||||
−0.479031 | + | 0.877798i | \(0.659012\pi\) | |||||||
\(282\) | −306255. | + | 530450.i | −0.229330 | + | 0.397211i | ||||
\(283\) | 723285. | + | 1.25277e6i | 0.536838 | + | 0.929831i | 0.999072 | + | 0.0430729i | \(0.0137148\pi\) |
−0.462234 | + | 0.886758i | \(0.652952\pi\) | |||||||
\(284\) | −71251.4 | − | 123411.i | −0.0524201 | − | 0.0907942i | ||||
\(285\) | 632479. | − | 1.09549e6i | 0.461247 | − | 0.798904i | ||||
\(286\) | −247090. | −0.178624 | ||||||||
\(287\) | 288613. | − | 84363.4i | 0.206829 | − | 0.0604574i | ||||
\(288\) | −129914. | −0.0922945 | ||||||||
\(289\) | 605997. | − | 1.04962e6i | 0.426802 | − | 0.739242i | ||||
\(290\) | −595206. | − | 1.03093e6i | −0.415597 | − | 0.719834i | ||||
\(291\) | −125658. | − | 217646.i | −0.0869875 | − | 0.150667i | ||||
\(292\) | 83844.7 | − | 145223.i | 0.0575465 | − | 0.0996734i | ||||
\(293\) | 367016. | 0.249756 | 0.124878 | − | 0.992172i | \(-0.460146\pi\) | ||||
0.124878 | + | 0.992172i | \(0.460146\pi\) | |||||||
\(294\) | −610418. | + | 390198.i | −0.411869 | + | 0.263279i | ||||
\(295\) | 520379. | 0.348149 | ||||||||
\(296\) | 218010. | − | 377605.i | 0.144627 | − | 0.250500i | ||||
\(297\) | 186209. | + | 322523.i | 0.122492 | + | 0.212163i | ||||
\(298\) | 586648. | + | 1.01610e6i | 0.382681 | + | 0.662823i | ||||
\(299\) | −247392. | + | 428495.i | −0.160032 | + | 0.277184i | ||||
\(300\) | −1.40238e6 | −0.899625 | ||||||||
\(301\) | −2.48443e6 | + | 726215.i | −1.58056 | + | 0.462007i | ||||
\(302\) | −817905. | −0.516042 | ||||||||
\(303\) | −371646. | + | 643710.i | −0.232554 | + | 0.402795i | ||||
\(304\) | −141604. | − | 245265.i | −0.0878801 | − | 0.152213i | ||||
\(305\) | 700471. | + | 1.21325e6i | 0.431162 | + | 0.746795i | ||||
\(306\) | 115684. | − | 200371.i | 0.0706271 | − | 0.122330i | ||||
\(307\) | −131281. | −0.0794979 | −0.0397490 | − | 0.999210i | \(-0.512656\pi\) | ||||
−0.0397490 | + | 0.999210i | \(0.512656\pi\) | |||||||
\(308\) | 45921.1 | − | 188290.i | 0.0275826 | − | 0.113097i | ||||
\(309\) | −1.22555e6 | −0.730186 | ||||||||
\(310\) | 76247.2 | − | 132064.i | 0.0450629 | − | 0.0780513i | ||||
\(311\) | 1.16736e6 | + | 2.02192e6i | 0.684389 | + | 1.18540i | 0.973629 | + | 0.228139i | \(0.0732641\pi\) |
−0.289240 | + | 0.957257i | \(0.593403\pi\) | |||||||
\(312\) | 227987. | + | 394885.i | 0.132594 | + | 0.229660i | ||||
\(313\) | 386400. | − | 669265.i | 0.222934 | − | 0.386133i | −0.732763 | − | 0.680483i | \(-0.761770\pi\) |
0.955698 | + | 0.294350i | \(0.0951031\pi\) | |||||||
\(314\) | 2.02366e6 | 1.15828 | ||||||||
\(315\) | 1.26158e6 | + | 1.20585e6i | 0.716372 | + | 0.684724i | ||||
\(316\) | −115680. | −0.0651691 | ||||||||
\(317\) | −262168. | + | 454088.i | −0.146532 | + | 0.253800i | −0.929943 | − | 0.367703i | \(-0.880144\pi\) |
0.783412 | + | 0.621503i | \(0.213478\pi\) | |||||||
\(318\) | 563480. | + | 975977.i | 0.312472 | + | 0.541217i | ||||
\(319\) | 131032. | + | 226954.i | 0.0720942 | + | 0.124871i | ||||
\(320\) | −217304. | + | 376382.i | −0.118630 | + | 0.205473i | ||||
\(321\) | 1.30704e6 | 0.707988 | ||||||||
\(322\) | −280549. | − | 268155.i | −0.150789 | − | 0.144127i | ||||
\(323\) | 504374. | 0.268996 | ||||||||
\(324\) | 96991.0 | − | 167993.i | 0.0513297 | − | 0.0889056i | ||||
\(325\) | −2.68862e6 | − | 4.65682e6i | −1.41195 | − | 2.44558i | ||||
\(326\) | 568400. | + | 984498.i | 0.296217 | + | 0.513063i | ||||
\(327\) | −330694. | + | 572779.i | −0.171024 | + | 0.296222i | ||||
\(328\) | 148441. | 0.0761850 | ||||||||
\(329\) | 436480. | − | 1.78969e6i | 0.222318 | − | 0.911568i | ||||
\(330\) | 427346. | 0.216020 | ||||||||
\(331\) | −315817. | + | 547012.i | −0.158440 | + | 0.274427i | −0.934306 | − | 0.356471i | \(-0.883980\pi\) |
0.775866 | + | 0.630898i | \(0.217313\pi\) | |||||||
\(332\) | 803688. | + | 1.39203e6i | 0.400168 | + | 0.693111i | ||||
\(333\) | −432170. | − | 748540.i | −0.213572 | − | 0.369917i | ||||
\(334\) | 26291.3 | − | 45537.9i | 0.0128957 | − | 0.0223361i | ||||
\(335\) | −6.33006e6 | −3.08174 | ||||||||
\(336\) | −343285. | + | 100344.i | −0.165885 | + | 0.0484892i | ||||
\(337\) | 3.33479e6 | 1.59954 | 0.799768 | − | 0.600309i | \(-0.204956\pi\) | ||||
0.799768 | + | 0.600309i | \(0.204956\pi\) | |||||||
\(338\) | −131601. | + | 227940.i | −0.0626568 | + | 0.108525i | ||||
\(339\) | −1.30900e6 | − | 2.26726e6i | −0.618645 | − | 1.07152i | ||||
\(340\) | −387005. | − | 670312.i | −0.181559 | − | 0.314470i | ||||
\(341\) | −16785.5 | + | 29073.3i | −0.00781714 | + | 0.0135397i | ||||
\(342\) | −561412. | −0.259547 | ||||||||
\(343\) | 1.43287e6 | − | 1.64148e6i | 0.657613 | − | 0.753356i | ||||
\(344\) | −1.27781e6 | −0.582196 | ||||||||
\(345\) | 427868. | − | 741089.i | 0.193536 | − | 0.335214i | ||||
\(346\) | −102906. | − | 178239.i | −0.0462116 | − | 0.0800408i | ||||
\(347\) | 325175. | + | 563220.i | 0.144975 | + | 0.251105i | 0.929364 | − | 0.369165i | \(-0.120356\pi\) |
−0.784388 | + | 0.620270i | \(0.787023\pi\) | |||||||
\(348\) | 241803. | − | 418816.i | 0.107032 | − | 0.185385i | ||||
\(349\) | −601041. | −0.264144 | −0.132072 | − | 0.991240i | \(-0.542163\pi\) | ||||
−0.132072 | + | 0.991240i | \(0.542163\pi\) | |||||||
\(350\) | 4.04830e6 | − | 1.18335e6i | 1.76646 | − | 0.516347i | ||||
\(351\) | 2.63517e6 | 1.14167 | ||||||||
\(352\) | 47838.6 | − | 82858.8i | 0.0205789 | − | 0.0356437i | ||||
\(353\) | 1.44444e6 | + | 2.50185e6i | 0.616970 | + | 1.06862i | 0.990036 | + | 0.140818i | \(0.0449732\pi\) |
−0.373066 | + | 0.927805i | \(0.621693\pi\) | |||||||
\(354\) | 105702. | + | 183082.i | 0.0448308 | + | 0.0776493i | ||||
\(355\) | −472511. | + | 818413.i | −0.198994 | + | 0.344668i | ||||
\(356\) | 321149. | 0.134302 | ||||||||
\(357\) | 150919. | − | 618814.i | 0.0626722 | − | 0.256974i | ||||
\(358\) | −1.99094e6 | −0.821014 | ||||||||
\(359\) | 48915.2 | − | 84723.7i | 0.0200313 | − | 0.0346951i | −0.855836 | − | 0.517247i | \(-0.826957\pi\) |
0.875867 | + | 0.482552i | \(0.160290\pi\) | |||||||
\(360\) | 430770. | + | 746115.i | 0.175182 | + | 0.303424i | ||||
\(361\) | 626123. | + | 1.08448e6i | 0.252867 | + | 0.437978i | ||||
\(362\) | 454240. | − | 786767.i | 0.182186 | − | 0.315555i | ||||
\(363\) | 1.64147e6 | 0.653832 | ||||||||
\(364\) | −991351. | − | 947554.i | −0.392169 | − | 0.374844i | ||||
\(365\) | −1.11205e6 | −0.436910 | ||||||||
\(366\) | −284567. | + | 492885.i | −0.111041 | + | 0.192328i | ||||
\(367\) | −1.07387e6 | − | 1.86001e6i | −0.416187 | − | 0.720857i | 0.579365 | − | 0.815068i | \(-0.303300\pi\) |
−0.995552 | + | 0.0942112i | \(0.969967\pi\) | |||||||
\(368\) | −95794.0 | − | 165920.i | −0.0368739 | − | 0.0638674i | ||||
\(369\) | 147130. | − | 254837.i | 0.0562516 | − | 0.0974307i | ||||
\(370\) | −2.89151e6 | −1.09805 | ||||||||
\(371\) | −2.45017e6 | − | 2.34192e6i | −0.924189 | − | 0.883360i | ||||
\(372\) | 61951.1 | 0.0232109 | ||||||||
\(373\) | −2.10229e6 | + | 3.64128e6i | −0.782386 | + | 1.35513i | 0.148163 | + | 0.988963i | \(0.452664\pi\) |
−0.930548 | + | 0.366169i | \(0.880669\pi\) | |||||||
\(374\) | 85197.4 | + | 147566.i | 0.0314954 | + | 0.0545517i | ||||
\(375\) | 2.86338e6 | + | 4.95952e6i | 1.05148 | + | 1.82122i | ||||
\(376\) | 454705. | − | 787573.i | 0.165867 | − | 0.287290i | ||||
\(377\) | 1.85433e6 | 0.671943 | ||||||||
\(378\) | −489740. | + | 2.00808e6i | −0.176293 | + | 0.722855i | ||||
\(379\) | −535586. | −0.191527 | −0.0957637 | − | 0.995404i | \(-0.530529\pi\) | ||||
−0.0957637 | + | 0.995404i | \(0.530529\pi\) | |||||||
\(380\) | −939059. | + | 1.62650e6i | −0.333606 | + | 0.577823i | ||||
\(381\) | 1.08799e6 | + | 1.88446e6i | 0.383985 | + | 0.665081i | ||||
\(382\) | −1.00556e6 | − | 1.74167e6i | −0.352572 | − | 0.610673i | ||||
\(383\) | 1.92349e6 | − | 3.33157e6i | 0.670027 | − | 1.16052i | −0.307870 | − | 0.951429i | \(-0.599616\pi\) |
0.977896 | − | 0.209091i | \(-0.0670506\pi\) | |||||||
\(384\) | −176560. | −0.0611034 | ||||||||
\(385\) | −1.23364e6 | + | 360601.i | −0.424166 | + | 0.123987i | ||||
\(386\) | 561289. | 0.191742 | ||||||||
\(387\) | −1.26652e6 | + | 2.19368e6i | −0.429868 | + | 0.744553i | ||||
\(388\) | 186568. | + | 323145.i | 0.0629154 | + | 0.108973i | ||||
\(389\) | 849163. | + | 1.47079e6i | 0.284523 | + | 0.492808i | 0.972493 | − | 0.232931i | \(-0.0748316\pi\) |
−0.687971 | + | 0.725739i | \(0.741498\pi\) | |||||||
\(390\) | 1.51192e6 | − | 2.61872e6i | 0.503347 | − | 0.871822i | ||||
\(391\) | 341206. | 0.112869 | ||||||||
\(392\) | 906304. | − | 579337.i | 0.297892 | − | 0.190422i | ||||
\(393\) | −3.05533e6 | −0.997877 | ||||||||
\(394\) | −757985. | + | 1.31287e6i | −0.245992 | + | 0.426070i | ||||
\(395\) | 383572. | + | 664367.i | 0.123696 | + | 0.214247i | ||||
\(396\) | −94832.1 | − | 164254.i | −0.0303891 | − | 0.0526354i | ||||
\(397\) | −1.81189e6 | + | 3.13828e6i | −0.576972 | + | 0.999346i | 0.418852 | + | 0.908055i | \(0.362433\pi\) |
−0.995824 | + | 0.0912910i | \(0.970901\pi\) | |||||||
\(398\) | −1.84409e6 | −0.583544 | ||||||||
\(399\) | −1.48347e6 | + | 433629.i | −0.466495 | + | 0.136360i | ||||
\(400\) | 2.08215e6 | 0.650671 | ||||||||
\(401\) | 1.39901e6 | − | 2.42315e6i | 0.434469 | − | 0.752522i | −0.562784 | − | 0.826604i | \(-0.690270\pi\) |
0.997252 | + | 0.0740827i | \(0.0236029\pi\) | |||||||
\(402\) | −1.28580e6 | − | 2.22707e6i | −0.396833 | − | 0.687335i | ||||
\(403\) | 118772. | + | 205719.i | 0.0364292 | + | 0.0630973i | ||||
\(404\) | 551793. | − | 955734.i | 0.168199 | − | 0.291329i | ||||
\(405\) | −1.28641e6 | −0.389710 | ||||||||
\(406\) | −344622. | + | 1.41305e6i | −0.103759 | + | 0.425444i | ||||
\(407\) | 636554. | 0.190480 | ||||||||
\(408\) | 157221. | − | 272315.i | 0.0467585 | − | 0.0809882i | ||||
\(409\) | 333141. | + | 577017.i | 0.0984735 | + | 0.170561i | 0.911053 | − | 0.412289i | \(-0.135271\pi\) |
−0.812579 | + | 0.582850i | \(0.801937\pi\) | |||||||
\(410\) | −492201. | − | 852517.i | −0.144605 | − | 0.250463i | ||||
\(411\) | 1.01552e6 | − | 1.75892e6i | 0.296539 | − | 0.513621i | ||||
\(412\) | 1.81960e6 | 0.528121 | ||||||||
\(413\) | −459623. | − | 439318.i | −0.132595 | − | 0.126737i | ||||
\(414\) | −379791. | −0.108904 | ||||||||
\(415\) | 5.32974e6 | − | 9.23137e6i | 1.51910 | − | 2.63115i | ||||
\(416\) | −338499. | − | 586297.i | −0.0959012 | − | 0.166106i | ||||
\(417\) | −1.14003e6 | − | 1.97459e6i | −0.321053 | − | 0.556079i | ||||
\(418\) | 206730. | − | 358066.i | 0.0578712 | − | 0.100236i | ||||
\(419\) | 2.89203e6 | 0.804762 | 0.402381 | − | 0.915472i | \(-0.368183\pi\) | ||||
0.402381 | + | 0.915472i | \(0.368183\pi\) | |||||||
\(420\) | 1.71455e6 | + | 1.63881e6i | 0.474273 | + | 0.453320i | ||||
\(421\) | 6.72027e6 | 1.84791 | 0.923956 | − | 0.382498i | \(-0.124936\pi\) | ||||
0.923956 | + | 0.382498i | \(0.124936\pi\) | |||||||
\(422\) | −404278. | + | 700229.i | −0.110509 | + | 0.191408i | ||||
\(423\) | −901379. | − | 1.56123e6i | −0.244938 | − | 0.424245i | ||||
\(424\) | −836615. | − | 1.44906e6i | −0.226001 | − | 0.391446i | ||||
\(425\) | −1.85409e6 | + | 3.21137e6i | −0.497917 | + | 0.862418i | ||||
\(426\) | −383917. | −0.102497 | ||||||||
\(427\) | 405570. | − | 1.66296e6i | 0.107646 | − | 0.441378i | ||||
\(428\) | −1.94060e6 | −0.512066 | ||||||||
\(429\) | −332843. | + | 576500.i | −0.0873163 | + | 0.151236i | ||||
\(430\) | 4.23695e6 | + | 7.33861e6i | 1.10505 | + | 1.91400i | ||||
\(431\) | −2.36149e6 | − | 4.09022e6i | −0.612341 | − | 1.06061i | −0.990845 | − | 0.135006i | \(-0.956895\pi\) |
0.378504 | − | 0.925600i | \(-0.376439\pi\) | |||||||
\(432\) | −510190. | + | 883674.i | −0.131529 | + | 0.227815i | ||||
\(433\) | −5.78136e6 | −1.48187 | −0.740935 | − | 0.671577i | \(-0.765617\pi\) | ||||
−0.740935 | + | 0.671577i | \(0.765617\pi\) | |||||||
\(434\) | −178837. | + | 52275.2i | −0.0455756 | + | 0.0133221i | ||||
\(435\) | −3.20708e6 | −0.812619 | ||||||||
\(436\) | 490991. | − | 850421.i | 0.123696 | − | 0.214249i | ||||
\(437\) | −413964. | − | 717007.i | −0.103695 | − | 0.179606i | ||||
\(438\) | −225886. | − | 391246.i | −0.0562605 | − | 0.0974461i | ||||
\(439\) | −2.68437e6 | + | 4.64946e6i | −0.664784 | + | 1.15144i | 0.314560 | + | 0.949237i | \(0.398143\pi\) |
−0.979344 | + | 0.202201i | \(0.935190\pi\) | |||||||
\(440\) | −634492. | −0.156241 | ||||||||
\(441\) | −96279.6 | − | 2.13012e6i | −0.0235743 | − | 0.521564i | ||||
\(442\) | 1.20569e6 | 0.293548 | ||||||||
\(443\) | −2.15756e6 | + | 3.73700e6i | −0.522339 | + | 0.904719i | 0.477323 | + | 0.878728i | \(0.341607\pi\) |
−0.999662 | + | 0.0259905i | \(0.991726\pi\) | |||||||
\(444\) | −587341. | − | 1.01730e6i | −0.141395 | − | 0.244903i | ||||
\(445\) | −1.06487e6 | − | 1.84440e6i | −0.254915 | − | 0.441525i | ||||
\(446\) | −1.38868e6 | + | 2.40526e6i | −0.330571 | + | 0.572566i | ||||
\(447\) | 3.16097e6 | 0.748259 | ||||||||
\(448\) | 509685. | − | 148984.i | 0.119979 | − | 0.0350707i | ||||
\(449\) | 4.75292e6 | 1.11261 | 0.556307 | − | 0.830977i | \(-0.312218\pi\) | ||||
0.556307 | + | 0.830977i | \(0.312218\pi\) | |||||||
\(450\) | 2.06376e6 | − | 3.57453e6i | 0.480427 | − | 0.832124i | ||||
\(451\) | 108356. | + | 187678.i | 0.0250848 | + | 0.0434482i | ||||
\(452\) | 1.94351e6 | + | 3.36626e6i | 0.447446 | + | 0.775000i | ||||
\(453\) | −1.10176e6 | + | 1.90830e6i | −0.252255 | + | 0.436919i | ||||
\(454\) | 5.06790e6 | 1.15395 | ||||||||
\(455\) | −2.15481e6 | + | 8.83536e6i | −0.487956 | + | 2.00076i | ||||
\(456\) | −762988. | −0.171833 | ||||||||
\(457\) | −1.06864e6 | + | 1.85093e6i | −0.239354 | + | 0.414573i | −0.960529 | − | 0.278180i | \(-0.910269\pi\) |
0.721175 | + | 0.692753i | \(0.243602\pi\) | |||||||
\(458\) | −1.71295e6 | − | 2.96692e6i | −0.381577 | − | 0.660910i | ||||
\(459\) | −908615. | − | 1.57377e6i | −0.201302 | − | 0.348665i | ||||
\(460\) | −635267. | + | 1.10031e6i | −0.139979 | + | 0.242450i | ||||
\(461\) | −1.72920e6 | −0.378959 | −0.189479 | − | 0.981885i | \(-0.560680\pi\) | ||||
−0.189479 | + | 0.981885i | \(0.560680\pi\) | |||||||
\(462\) | −377452. | − | 360777.i | −0.0822729 | − | 0.0786382i | ||||
\(463\) | −6.54367e6 | −1.41863 | −0.709315 | − | 0.704892i | \(-0.750996\pi\) | ||||
−0.709315 | + | 0.704892i | \(0.750996\pi\) | |||||||
\(464\) | −359012. | + | 621827.i | −0.0774130 | + | 0.134083i | ||||
\(465\) | −205417. | − | 355793.i | −0.0440559 | − | 0.0763071i | ||||
\(466\) | 568715. | + | 985044.i | 0.121319 | + | 0.210131i | ||||
\(467\) | 897094. | − | 1.55381e6i | 0.190347 | − | 0.329691i | −0.755018 | − | 0.655704i | \(-0.772372\pi\) |
0.945365 | + | 0.326013i | \(0.105705\pi\) | |||||||
\(468\) | −1.34204e6 | −0.283237 | ||||||||
\(469\) | 5.59100e6 | + | 5.34400e6i | 1.17370 | + | 1.12185i | ||||
\(470\) | −6.03085e6 | −1.25931 | ||||||||
\(471\) | 2.72597e6 | − | 4.72151e6i | 0.566198 | − | 0.980684i | ||||
\(472\) | −156939. | − | 271827.i | −0.0324247 | − | 0.0561613i | ||||
\(473\) | −932746. | − | 1.61556e6i | −0.191695 | − | 0.332025i | ||||
\(474\) | −155827. | + | 269900.i | −0.0318564 | + | 0.0551769i | ||||
\(475\) | 8.99780e6 | 1.82979 | ||||||||
\(476\) | −224074. | + | 918770.i | −0.0453288 | + | 0.185862i | ||||
\(477\) | −3.31690e6 | −0.667477 | ||||||||
\(478\) | 855882. | − | 1.48243e6i | 0.171334 | − | 0.296760i | ||||
\(479\) | −2.04701e6 | − | 3.54553e6i | −0.407645 | − | 0.706061i | 0.586981 | − | 0.809601i | \(-0.300316\pi\) |
−0.994625 | + | 0.103540i | \(0.966983\pi\) | |||||||
\(480\) | 585439. | + | 1.01401e6i | 0.115979 | + | 0.200881i | ||||
\(481\) | 2.25208e6 | − | 3.90072e6i | 0.443835 | − | 0.768745i | ||||
\(482\) | 3.23833e6 | 0.634897 | ||||||||
\(483\) | −1.00356e6 | + | 293347.i | −0.195738 | + | 0.0572155i | ||||
\(484\) | −2.43714e6 | −0.472897 | ||||||||
\(485\) | 1.23724e6 | − | 2.14296e6i | 0.238836 | − | 0.413676i | ||||
\(486\) | 1.67582e6 | + | 2.90261e6i | 0.321838 | + | 0.557440i | ||||
\(487\) | 2.22605e6 | + | 3.85563e6i | 0.425317 | + | 0.736670i | 0.996450 | − | 0.0841871i | \(-0.0268293\pi\) |
−0.571133 | + | 0.820857i | \(0.693496\pi\) | |||||||
\(488\) | 422505. | − | 731800.i | 0.0803124 | − | 0.139105i | ||||
\(489\) | 3.06265e6 | 0.579196 | ||||||||
\(490\) | −6.33233e6 | − | 3.28406e6i | −1.19144 | − | 0.617903i | ||||
\(491\) | 7.09674e6 | 1.32848 | 0.664240 | − | 0.747519i | \(-0.268755\pi\) | ||||
0.664240 | + | 0.747519i | \(0.268755\pi\) | |||||||
\(492\) | 199957. | − | 346336.i | 0.0372413 | − | 0.0645038i | ||||
\(493\) | −639377. | − | 1.10743e6i | −0.118479 | − | 0.205211i | ||||
\(494\) | −1.46279e6 | − | 2.53363e6i | −0.269690 | − | 0.467117i | ||||
\(495\) | −628888. | + | 1.08927e6i | −0.115361 | + | 0.199812i | ||||
\(496\) | −91980.4 | −0.0167877 | ||||||||
\(497\) | 1.10827e6 | − | 323954.i | 0.201258 | − | 0.0588291i | ||||
\(498\) | 4.33043e6 | 0.782451 | ||||||||
\(499\) | −4.70952e6 | + | 8.15712e6i | −0.846691 | + | 1.46651i | 0.0374536 | + | 0.999298i | \(0.488075\pi\) |
−0.884145 | + | 0.467213i | \(0.845258\pi\) | |||||||
\(500\) | −4.25134e6 | − | 7.36354e6i | −0.760503 | − | 1.31723i | ||||
\(501\) | −70831.4 | − | 122684.i | −0.0126076 | − | 0.0218370i | ||||
\(502\) | 2.52610e6 | − | 4.37533e6i | 0.447394 | − | 0.774910i | ||||
\(503\) | 957258. | 0.168698 | 0.0843489 | − | 0.996436i | \(-0.473119\pi\) | ||||
0.0843489 | + | 0.996436i | \(0.473119\pi\) | |||||||
\(504\) | 249414. | − | 1.02267e6i | 0.0437366 | − | 0.179333i | ||||
\(505\) | −7.31854e6 | −1.27702 | ||||||||
\(506\) | 139851. | − | 242230.i | 0.0242823 | − | 0.0420582i | ||||
\(507\) | 354546. | + | 614093.i | 0.0612567 | + | 0.106100i | ||||
\(508\) | −1.61537e6 | − | 2.79791e6i | −0.277724 | − | 0.481032i | ||||
\(509\) | 2.00727e6 | − | 3.47669e6i | 0.343408 | − | 0.594800i | −0.641655 | − | 0.766993i | \(-0.721752\pi\) |
0.985063 | + | 0.172193i | \(0.0550853\pi\) | |||||||
\(510\) | −2.08526e6 | −0.355005 | ||||||||
\(511\) | 982213. | + | 938821.i | 0.166400 | + | 0.159049i | ||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −2.20474e6 | + | 3.81871e6i | −0.369882 | + | 0.640654i | ||||
\(514\) | −112276. | − | 194468.i | −0.0187448 | − | 0.0324669i | ||||
\(515\) | −6.03344e6 | − | 1.04502e7i | −1.00241 | − | 1.73623i | ||||
\(516\) | −1.72127e6 | + | 2.98132e6i | −0.284593 | + | 0.492930i | ||||
\(517\) | 1.32766e6 | 0.218455 | ||||||||
\(518\) | 2.55392e6 | + | 2.44109e6i | 0.418199 | + | 0.399724i | ||||
\(519\) | −554478. | −0.0903578 | ||||||||
\(520\) | −2.24479e6 | + | 3.88809e6i | −0.364055 | + | 0.630562i | ||||
\(521\) | 2.15910e6 | + | 3.73967e6i | 0.348480 | + | 0.603585i | 0.985980 | − | 0.166865i | \(-0.0533646\pi\) |
−0.637500 | + | 0.770451i | \(0.720031\pi\) | |||||||
\(522\) | 711682. | + | 1.23267e6i | 0.114317 | + | 0.198002i | ||||
\(523\) | −672507. | + | 1.16482e6i | −0.107508 | + | 0.186210i | −0.914760 | − | 0.403997i | \(-0.867621\pi\) |
0.807252 | + | 0.590207i | \(0.200954\pi\) | |||||||
\(524\) | 4.53634e6 | 0.721734 | ||||||||
\(525\) | 2.69233e6 | − | 1.10394e7i | 0.426315 | − | 1.74802i | ||||
\(526\) | 6.17100e6 | 0.972504 | ||||||||
\(527\) | 81905.6 | − | 141865.i | 0.0128466 | − | 0.0222509i | ||||
\(528\) | −128882. | − | 223230.i | −0.0201190 | − | 0.0348472i | ||||
\(529\) | 2.93813e6 | + | 5.08899e6i | 0.456490 | + | 0.790664i | ||||
\(530\) | −5.54809e6 | + | 9.60958e6i | −0.857934 | + | 1.48599i | ||||
\(531\) | −622212. | −0.0957640 | ||||||||
\(532\) | 2.20255e6 | − | 643820.i | 0.337402 | − | 0.0986247i | ||||
\(533\) | 1.53342e6 | 0.233799 | ||||||||
\(534\) | 432603. | − | 749291.i | 0.0656503 | − | 0.113710i | ||||
\(535\) | 6.43462e6 | + | 1.11451e7i | 0.971938 | + | 1.68345i | ||||
\(536\) | 1.90906e6 | + | 3.30659e6i | 0.287017 | + | 0.497128i | ||||
\(537\) | −2.68189e6 | + | 4.64517e6i | −0.401334 | + | 0.695130i | ||||
\(538\) | −4.82141e6 | −0.718156 | ||||||||
\(539\) | 1.39404e6 | + | 722971.i | 0.206682 | + | 0.107189i | ||||
\(540\) | 6.76675e6 | 0.998609 | ||||||||
\(541\) | 3.53003e6 | − | 6.11419e6i | 0.518543 | − | 0.898144i | −0.481224 | − | 0.876597i | \(-0.659808\pi\) |
0.999768 | − | 0.0215461i | \(-0.00685888\pi\) | |||||||
\(542\) | −3.52977e6 | − | 6.11375e6i | −0.516117 | − | 0.893942i | ||||
\(543\) | −1.22377e6 | − | 2.11963e6i | −0.178115 | − | 0.308503i | ||||
\(544\) | −233431. | + | 404314.i | −0.0338190 | + | 0.0585762i | ||||
\(545\) | −6.51211e6 | −0.939140 | ||||||||
\(546\) | −3.54619e6 | + | 1.03657e6i | −0.509073 | + | 0.148805i | ||||
\(547\) | −1.23520e7 | −1.76510 | −0.882549 | − | 0.470221i | \(-0.844174\pi\) | ||||
−0.882549 | + | 0.470221i | \(0.844174\pi\) | |||||||
\(548\) | −1.50776e6 | + | 2.61152e6i | −0.214478 | + | 0.371486i | ||||
\(549\) | −837547. | − | 1.45067e6i | −0.118598 | − | 0.205418i | ||||
\(550\) | 1.51988e6 | + | 2.63251e6i | 0.214241 | + | 0.371077i | ||||
\(551\) | −1.55144e6 | + | 2.68716e6i | −0.217698 | + | 0.377064i | ||||
\(552\) | −516156. | −0.0720997 | ||||||||
\(553\) | 222087. | − | 910622.i | 0.0308823 | − | 0.126627i | ||||
\(554\) | 5.93275e6 | 0.821261 | ||||||||
\(555\) | −3.89501e6 | + | 6.74636e6i | −0.536755 | + | 0.929687i | ||||
\(556\) | 1.69263e6 | + | 2.93173e6i | 0.232207 | + | 0.402195i | ||||
\(557\) | 6.11254e6 | + | 1.05872e7i | 0.834803 | + | 1.44592i | 0.894191 | + | 0.447686i | \(0.147752\pi\) |
−0.0593878 | + | 0.998235i | \(0.518915\pi\) | |||||||
\(558\) | −91168.0 | + | 157908.i | −0.0123953 | + | 0.0214693i | ||||
\(559\) | −1.32000e7 | −1.78666 | ||||||||
\(560\) | −2.54565e6 | − | 2.43318e6i | −0.343027 | − | 0.327873i | ||||
\(561\) | 459060. | 0.0615832 | ||||||||
\(562\) | 2.53623e6 | − | 4.39288e6i | 0.338726 | − | 0.586690i | ||||
\(563\) | 406264. | + | 703669.i | 0.0540178 | + | 0.0935616i | 0.891770 | − | 0.452489i | \(-0.149464\pi\) |
−0.837752 | + | 0.546051i | \(0.816131\pi\) | |||||||
\(564\) | −1.22502e6 | − | 2.12180e6i | −0.162161 | − | 0.280871i | ||||
\(565\) | 1.28886e7 | − | 2.23237e7i | 1.69857 | − | 2.94201i | ||||
\(566\) | −5.78628e6 | −0.759204 | ||||||||
\(567\) | 1.13622e6 | + | 1.08602e6i | 0.148424 | + | 0.141867i | ||||
\(568\) | 570011. | 0.0741332 | ||||||||
\(569\) | 4.21941e6 | − | 7.30823e6i | 0.546350 | − | 0.946305i | −0.452171 | − | 0.891931i | \(-0.649350\pi\) |
0.998521 | − | 0.0543741i | \(-0.0173163\pi\) | |||||||
\(570\) | 2.52992e6 | + | 4.38194e6i | 0.326151 | + | 0.564910i | ||||
\(571\) | −1.85755e6 | − | 3.21738e6i | −0.238425 | − | 0.412963i | 0.721838 | − | 0.692062i | \(-0.243298\pi\) |
−0.960262 | + | 0.279099i | \(0.909964\pi\) | |||||||
\(572\) | 494180. | − | 855946.i | 0.0631532 | − | 0.109385i | ||||
\(573\) | −5.41813e6 | −0.689387 | ||||||||
\(574\) | −284982. | + | 1.16851e6i | −0.0361026 | + | 0.148031i | ||||
\(575\) | 6.08695e6 | 0.767768 | ||||||||
\(576\) | 259829. | − | 450036.i | 0.0326310 | − | 0.0565186i | ||||
\(577\) | −6.51875e6 | − | 1.12908e7i | −0.815126 | − | 1.41184i | −0.909237 | − | 0.416278i | \(-0.863334\pi\) |
0.0941114 | − | 0.995562i | \(-0.469999\pi\) | |||||||
\(578\) | 2.42399e6 | + | 4.19847e6i | 0.301794 | + | 0.522723i | ||||
\(579\) | 756084. | − | 1.30958e6i | 0.0937289 | − | 0.162343i | ||||
\(580\) | 4.76164e6 | 0.587742 | ||||||||
\(581\) | −1.25008e7 | + | 3.65407e6i | −1.53638 | + | 0.449094i | ||||
\(582\) | 1.00526e6 | 0.123019 | ||||||||
\(583\) | 1.22139e6 | − | 2.11551e6i | 0.148827 | − | 0.257776i | ||||
\(584\) | 335379. | + | 580893.i | 0.0406915 | + | 0.0704797i | ||||
\(585\) | 4.44992e6 | + | 7.70749e6i | 0.537604 | + | 0.931158i | ||||
\(586\) | −734031. | + | 1.27138e6i | −0.0883020 | + | 0.152944i | ||||
\(587\) | 1.15227e7 | 1.38026 | 0.690128 | − | 0.723687i | \(-0.257554\pi\) | ||||
0.690128 | + | 0.723687i | \(0.257554\pi\) | |||||||
\(588\) | −130849. | − | 2.89494e6i | −0.0156073 | − | 0.345300i | ||||
\(589\) | −397485. | −0.0472098 | ||||||||
\(590\) | −1.04076e6 | + | 1.80265e6i | −0.123089 | + | 0.213197i | ||||
\(591\) | 2.04209e6 | + | 3.53700e6i | 0.240495 | + | 0.416549i | ||||
\(592\) | 872042. | + | 1.51042e6i | 0.102266 | + | 0.177131i | ||||
\(593\) | 6.00513e6 | − | 1.04012e7i | 0.701271 | − | 1.21464i | −0.266749 | − | 0.963766i | \(-0.585950\pi\) |
0.968020 | − | 0.250871i | \(-0.0807171\pi\) | |||||||
\(594\) | −1.48967e6 | −0.173230 | ||||||||
\(595\) | 6.01960e6 | − | 1.75957e6i | 0.697068 | − | 0.203758i | ||||
\(596\) | −4.69318e6 | −0.541192 | ||||||||
\(597\) | −2.48408e6 | + | 4.30255e6i | −0.285252 | + | 0.494071i | ||||
\(598\) | −989567. | − | 1.71398e6i | −0.113160 | − | 0.195999i | ||||
\(599\) | 587299. | + | 1.01723e6i | 0.0668794 | + | 0.115838i | 0.897526 | − | 0.440961i | \(-0.145362\pi\) |
−0.830647 | + | 0.556800i | \(0.812029\pi\) | |||||||
\(600\) | 2.80475e6 | − | 4.85798e6i | 0.318066 | − | 0.550906i | ||||
\(601\) | −1.62934e7 | −1.84003 | −0.920014 | − | 0.391886i | \(-0.871823\pi\) | ||||
−0.920014 | + | 0.391886i | \(0.871823\pi\) | |||||||
\(602\) | 2.45318e6 | − | 1.00587e7i | 0.275891 | − | 1.13123i | ||||
\(603\) | 7.56879e6 | 0.847683 | ||||||||
\(604\) | 1.63581e6 | − | 2.83331e6i | 0.182449 | − | 0.316010i | ||||
\(605\) | 8.08105e6 | + | 1.39968e7i | 0.897593 | + | 1.55468i | ||||
\(606\) | −1.48658e6 | − | 2.57484e6i | −0.164440 | − | 0.284819i | ||||
\(607\) | 913146. | − | 1.58161e6i | 0.100593 | − | 0.174232i | −0.811336 | − | 0.584580i | \(-0.801259\pi\) |
0.911929 | + | 0.410348i | \(0.134593\pi\) | |||||||
\(608\) | 1.13283e6 | 0.124281 | ||||||||
\(609\) | 2.83265e6 | + | 2.70750e6i | 0.309492 | + | 0.295819i | ||||
\(610\) | −5.60377e6 | −0.609755 | ||||||||
\(611\) | 4.69718e6 | − | 8.13576e6i | 0.509019 | − | 0.881648i | ||||
\(612\) | 462738. | + | 801486.i | 0.0499409 | + | 0.0865002i | ||||
\(613\) | 2.55135e6 | + | 4.41907e6i | 0.274233 | + | 0.474985i | 0.969941 | − | 0.243339i | \(-0.0782428\pi\) |
−0.695709 | + | 0.718324i | \(0.744909\pi\) | |||||||
\(614\) | 262562. | − | 454771.i | 0.0281068 | − | 0.0486823i | ||||
\(615\) | −2.65207e6 | −0.282747 | ||||||||
\(616\) | 560413. | + | 535655.i | 0.0595054 | + | 0.0568766i | ||||
\(617\) | −8.03920e6 | −0.850158 | −0.425079 | − | 0.905156i | \(-0.639754\pi\) | ||||
−0.425079 | + | 0.905156i | \(0.639754\pi\) | |||||||
\(618\) | 2.45109e6 | − | 4.24542e6i | 0.258160 | − | 0.447146i | ||||
\(619\) | −4.30066e6 | − | 7.44896e6i | −0.451137 | − | 0.781392i | 0.547320 | − | 0.836923i | \(-0.315648\pi\) |
−0.998457 | + | 0.0555314i | \(0.982315\pi\) | |||||||
\(620\) | 304989. | + | 528256.i | 0.0318643 | + | 0.0551906i | ||||
\(621\) | −1.49149e6 | + | 2.58333e6i | −0.155200 | + | 0.268814i | ||||
\(622\) | −9.33886e6 | −0.967872 | ||||||||
\(623\) | −616553. | + | 2.52805e6i | −0.0636430 | + | 0.260955i | ||||
\(624\) | −1.82390e6 | −0.187516 | ||||||||
\(625\) | −1.54848e7 | + | 2.68204e7i | −1.58564 | + | 2.74641i | ||||
\(626\) | 1.54560e6 | + | 2.67706e6i | 0.157638 | + | 0.273038i | ||||
\(627\) | −556950. | − | 964666.i | −0.0565780 | − | 0.0979959i | ||||
\(628\) | −4.04732e6 | + | 7.01016e6i | −0.409514 | + | 0.709298i | ||||
\(629\) | −3.10610e6 | −0.313032 | ||||||||
\(630\) | −6.70034e6 | + | 1.95855e6i | −0.672582 | + | 0.196600i | ||||
\(631\) | 6.21151e6 | 0.621046 | 0.310523 | − | 0.950566i | \(-0.399496\pi\) | ||||
0.310523 | + | 0.950566i | \(0.399496\pi\) | |||||||
\(632\) | 231360. | − | 400728.i | 0.0230407 | − | 0.0399077i | ||||
\(633\) | 1.08916e6 | + | 1.88649e6i | 0.108040 | + | 0.187130i | ||||
\(634\) | −1.04867e6 | − | 1.81635e6i | −0.103614 | − | 0.179464i | ||||
\(635\) | −1.07125e7 | + | 1.85546e7i | −1.05428 | + | 1.82607i | ||||
\(636\) | −4.50784e6 | −0.441902 | ||||||||
\(637\) | 9.36227e6 | − | 5.98465e6i | 0.914182 | − | 0.584373i | ||||
\(638\) | −1.04826e6 | −0.101957 | ||||||||
\(639\) | 564977. | − | 978568.i | 0.0547367 | − | 0.0948067i | ||||
\(640\) | −869217. | − | 1.50553e6i | −0.0838838 | − | 0.145291i | ||||
\(641\) | −2.22571e6 | − | 3.85505e6i | −0.213956 | − | 0.370582i | 0.738993 | − | 0.673713i | \(-0.235302\pi\) |
−0.952949 | + | 0.303130i | \(0.901968\pi\) | |||||||
\(642\) | −2.61408e6 | + | 4.52771e6i | −0.250311 | + | 0.433552i | ||||
\(643\) | 1.58708e7 | 1.51381 | 0.756907 | − | 0.653523i | \(-0.226710\pi\) | ||||
0.756907 | + | 0.653523i | \(0.226710\pi\) | |||||||
\(644\) | 1.49001e6 | − | 435540.i | 0.141571 | − | 0.0413822i | ||||
\(645\) | 2.28295e7 | 2.16071 | ||||||||
\(646\) | −1.00875e6 | + | 1.74720e6i | −0.0951046 | + | 0.164726i | ||||
\(647\) | 1.82810e6 | + | 3.16635e6i | 0.171687 | + | 0.297371i | 0.939010 | − | 0.343890i | \(-0.111745\pi\) |
−0.767323 | + | 0.641261i | \(0.778411\pi\) | |||||||
\(648\) | 387964. | + | 671973.i | 0.0362956 | + | 0.0628658i | ||||
\(649\) | 229118. | − | 396845.i | 0.0213525 | − | 0.0369836i | ||||
\(650\) | 2.15089e7 | 1.99680 | ||||||||
\(651\) | −118936. | + | 487672.i | −0.0109992 | + | 0.0450998i | ||||
\(652\) | −4.54720e6 | −0.418914 | ||||||||
\(653\) | 2.07520e6 | − | 3.59435e6i | 0.190448 | − | 0.329866i | −0.754951 | − | 0.655781i | \(-0.772339\pi\) |
0.945399 | + | 0.325916i | \(0.105673\pi\) | |||||||
\(654\) | −1.32278e6 | − | 2.29112e6i | −0.120932 | − | 0.209461i | ||||
\(655\) | −1.50416e7 | − | 2.60528e7i | −1.36990 | − | 2.37274i | ||||
\(656\) | −296882. | + | 514215.i | −0.0269355 | + | 0.0466536i | ||||
\(657\) | 1.32967e6 | 0.120179 | ||||||||
\(658\) | 5.32672e6 | + | 5.09140e6i | 0.479618 | + | 0.458429i | ||||
\(659\) | −1.33739e7 | −1.19962 | −0.599810 | − | 0.800143i | \(-0.704757\pi\) | ||||
−0.599810 | + | 0.800143i | \(0.704757\pi\) | |||||||
\(660\) | −854692. | + | 1.48037e6i | −0.0763748 | + | 0.132285i | ||||
\(661\) | 4.91320e6 | + | 8.50992e6i | 0.437382 | + | 0.757568i | 0.997487 | − | 0.0708538i | \(-0.0225724\pi\) |
−0.560105 | + | 0.828422i | \(0.689239\pi\) | |||||||
\(662\) | −1.26327e6 | − | 2.18805e6i | −0.112034 | − | 0.194049i | ||||
\(663\) | 1.62412e6 | − | 2.81306e6i | 0.143494 | − | 0.248539i | ||||
\(664\) | −6.42950e6 | −0.565923 | ||||||||
\(665\) | −1.10008e7 | − | 1.05148e7i | −0.964648 | − | 0.922031i | ||||
\(666\) | 3.45736e6 | 0.302036 | ||||||||
\(667\) | −1.04954e6 | + | 1.81785e6i | −0.0913445 | + | 0.158213i | ||||
\(668\) | 105165. | + | 182152.i | 0.00911867 | + | 0.0157940i | ||||
\(669\) | 3.74124e6 | + | 6.48002e6i | 0.323184 | + | 0.559772i | ||||
\(670\) | 1.26601e7 | − | 2.19280e7i | 1.08956 | − | 1.88717i | ||||
\(671\) | 1.23365e6 | 0.105775 | ||||||||
\(672\) | 338967. | − | 1.38986e6i | 0.0289557 | − | 0.118727i | ||||
\(673\) | 401148. | 0.0341403 | 0.0170702 | − | 0.999854i | \(-0.494566\pi\) | ||||
0.0170702 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(674\) | −6.66958e6 | + | 1.15521e7i | −0.565521 | + | 0.979512i | ||||
\(675\) | −1.62093e7 | − | 2.80753e7i | −1.36932 | − | 2.37173i | ||||
\(676\) | −526405. | − | 911760.i | −0.0443050 | − | 0.0767386i | ||||
\(677\) | −1.03651e7 | + | 1.79529e7i | −0.869164 | + | 1.50544i | −0.00631194 | + | 0.999980i | \(0.502009\pi\) |
−0.862852 | + | 0.505456i | \(0.831324\pi\) | |||||||
\(678\) | 1.04720e7 | 0.874896 | ||||||||
\(679\) | −2.90194e6 | + | 848254.i | −0.241553 | + | 0.0706076i | ||||
\(680\) | 3.09604e6 | 0.256764 | ||||||||
\(681\) | 6.82671e6 | − | 1.18242e7i | 0.564084 | − | 0.977021i | ||||
\(682\) | −67141.9 | − | 116293.i | −0.00552755 | − | 0.00957400i | ||||
\(683\) | 9.59979e6 | + | 1.66273e7i | 0.787427 | + | 1.36386i | 0.927539 | + | 0.373727i | \(0.121920\pi\) |
−0.140112 | + | 0.990136i | \(0.544746\pi\) | |||||||
\(684\) | 1.12282e6 | − | 1.94479e6i | 0.0917638 | − | 0.158940i | ||||
\(685\) | 1.99978e7 | 1.62838 | ||||||||
\(686\) | 2.82052e6 | + | 8.24655e6i | 0.228833 | + | 0.669056i | ||||
\(687\) | −9.22972e6 | −0.746100 | ||||||||
\(688\) | 2.55561e6 | − | 4.42645e6i | 0.205837 | − | 0.356521i | ||||
\(689\) | −8.64237e6 | − | 1.49690e7i | −0.693561 | − | 1.20128i | ||||
\(690\) | 1.71147e6 | + | 2.96435e6i | 0.136851 | + | 0.237032i | ||||
\(691\) | 5.65465e6 | − | 9.79414e6i | 0.450517 | − | 0.780317i | −0.547902 | − | 0.836543i | \(-0.684573\pi\) |
0.998418 | + | 0.0562253i | \(0.0179065\pi\) | |||||||
\(692\) | 823248. | 0.0653530 | ||||||||
\(693\) | 1.47505e6 | − | 431167.i | 0.116674 | − | 0.0341045i | ||||
\(694\) | −2.60140e6 | −0.205026 | ||||||||
\(695\) | 1.12249e7 | − | 1.94420e7i | 0.881494 | − | 1.52679i | ||||
\(696\) | 967213. | + | 1.67526e6i | 0.0756831 | + | 0.131087i | ||||
\(697\) | −528728. | − | 915784.i | −0.0412240 | − | 0.0714021i | ||||
\(698\) | 1.20208e6 | − | 2.08207e6i | 0.0933890 | − | 0.161755i | ||||
\(699\) | 3.06435e6 | 0.237217 | ||||||||
\(700\) | −3.99738e6 | + | 1.63904e7i | −0.308340 | + | 1.26429i | ||||
\(701\) | −1.92159e7 | −1.47695 | −0.738473 | − | 0.674283i | \(-0.764453\pi\) | ||||
−0.738473 | + | 0.674283i | \(0.764453\pi\) | |||||||
\(702\) | −5.27034e6 | + | 9.12850e6i | −0.403642 | + | 0.699128i | ||||
\(703\) | 3.76844e6 | + | 6.52714e6i | 0.287590 | + | 0.498120i | ||||
\(704\) | 191354. | + | 331435.i | 0.0145515 | + | 0.0252039i | ||||
\(705\) | −8.12384e6 | + | 1.40709e7i | −0.615586 | + | 1.06623i | ||||
\(706\) | −1.15555e7 | −0.872527 | ||||||||
\(707\) | 6.46407e6 | + | 6.17850e6i | 0.486360 | + | 0.464873i | ||||
\(708\) | −845619. | −0.0634004 | ||||||||
\(709\) | −2.82240e6 | + | 4.88854e6i | −0.210864 | + | 0.365228i | −0.951985 | − | 0.306144i | \(-0.900961\pi\) |
0.741121 | + | 0.671371i | \(0.234294\pi\) | |||||||
\(710\) | −1.89004e6 | − | 3.27365e6i | −0.140710 | − | 0.243717i | ||||
\(711\) | −458634. | − | 794377.i | −0.0340245 | − | 0.0589322i | ||||
\(712\) | −642298. | + | 1.11249e6i | −0.0474828 | + | 0.0822427i | ||||
\(713\) | −268896. | −0.0198089 | ||||||||
\(714\) | 1.84180e6 | + | 1.76043e6i | 0.135206 | + | 0.129233i | ||||
\(715\) | −6.55441e6 | −0.479478 | ||||||||
\(716\) | 3.98188e6 | − | 6.89682e6i | 0.290272 | − | 0.502766i | ||||
\(717\) | −2.30583e6 | − | 3.99381e6i | −0.167506 | − | 0.290128i | ||||
\(718\) | 195661. | + | 338895.i | 0.0141642 | + | 0.0245332i | ||||
\(719\) | −2.21039e6 | + | 3.82850e6i | −0.159458 | + | 0.276189i | −0.934673 | − | 0.355508i | \(-0.884308\pi\) |
0.775215 | + | 0.631697i | \(0.217641\pi\) | |||||||
\(720\) | −3.44616e6 | −0.247744 | ||||||||
\(721\) | −3.49334e6 | + | 1.43237e7i | −0.250266 | + | 1.02617i | ||||
\(722\) | −5.00898e6 | −0.357607 | ||||||||
\(723\) | 4.36218e6 | − | 7.55552e6i | 0.310355 | − | 0.537550i | ||||
\(724\) | 1.81696e6 | + | 3.14707e6i | 0.128825 | + | 0.223131i | ||||
\(725\) | −1.14062e7 | − | 1.97561e7i | −0.805926 | − | 1.39591i | ||||
\(726\) | −3.28294e6 | + | 5.68622e6i | −0.231165 | + | 0.400389i | ||||
\(727\) | 1.92503e7 | 1.35083 | 0.675416 | − | 0.737437i | \(-0.263964\pi\) | ||||
0.675416 | + | 0.737437i | \(0.263964\pi\) | |||||||
\(728\) | 5.26513e6 | − | 1.53903e6i | 0.368197 | − | 0.107626i | ||||
\(729\) | 1.19758e7 | 0.834611 | ||||||||
\(730\) | 2.22410e6 | − | 3.85225e6i | 0.154471 | − | 0.267551i | ||||
\(731\) | 4.55138e6 | + | 7.88323e6i | 0.315029 | + | 0.545645i | ||||
\(732\) | −1.13827e6 | − | 1.97154e6i | −0.0785177 | − | 0.135997i | ||||
\(733\) | −6.50933e6 | + | 1.12745e7i | −0.447483 | + | 0.775063i | −0.998221 | − | 0.0596145i | \(-0.981013\pi\) |
0.550738 | + | 0.834678i | \(0.314346\pi\) | |||||||
\(734\) | 8.59100e6 | 0.588577 | ||||||||
\(735\) | −1.61922e7 | + | 1.03505e7i | −1.10557 | + | 0.706715i | ||||
\(736\) | 766352. | 0.0521475 | ||||||||
\(737\) | −2.78707e6 | + | 4.82735e6i | −0.189008 | + | 0.327371i | ||||
\(738\) | 588520. | + | 1.01935e6i | 0.0397759 | + | 0.0688939i | ||||
\(739\) | 8.54774e6 | + | 1.48051e7i | 0.575758 | + | 0.997242i | 0.995959 | + | 0.0898109i | \(0.0286263\pi\) |
−0.420201 | + | 0.907431i | \(0.638040\pi\) | |||||||
\(740\) | 5.78303e6 | − | 1.00165e7i | 0.388218 | − | 0.672414i | ||||
\(741\) | −7.88180e6 | −0.527327 | ||||||||
\(742\) | 1.30130e7 | − | 3.80378e6i | 0.867695 | − | 0.253633i | ||||
\(743\) | 2.36546e7 | 1.57197 | 0.785984 | − | 0.618247i | \(-0.212157\pi\) | ||||
0.785984 | + | 0.618247i | \(0.212157\pi\) | |||||||
\(744\) | −123902. | + | 214605.i | −0.00820628 | + | 0.0142137i | ||||
\(745\) | 1.55616e7 | + | 2.69536e7i | 1.02722 | + | 1.77920i | ||||
\(746\) | −8.40917e6 | − | 1.45651e7i | −0.553230 | − | 0.958223i | ||||
\(747\) | −6.37272e6 | + | 1.10379e7i | −0.417853 | + | 0.723742i | ||||
\(748\) | −681579. | −0.0445413 | ||||||||
\(749\) | 3.72562e6 | − | 1.52761e7i | 0.242658 | − | 0.994968i | ||||
\(750\) | −2.29071e7 | −1.48702 | ||||||||
\(751\) | 83281.8 | − | 144248.i | 0.00538828 | − | 0.00933277i | −0.863319 | − | 0.504659i | \(-0.831618\pi\) |
0.868707 | + | 0.495326i | \(0.164952\pi\) | |||||||
\(752\) | 1.81882e6 | + | 3.15029e6i | 0.117286 | + | 0.203145i | ||||
\(753\) | −6.80555e6 | − | 1.17876e7i | −0.437397 | − | 0.757593i | ||||
\(754\) | −3.70865e6 | + | 6.42357e6i | −0.237568 | + | 0.411480i | ||||
\(755\) | −2.16961e7 | −1.38520 | ||||||||
\(756\) | −5.97670e6 | − | 5.71266e6i | −0.380327 | − | 0.363525i | ||||
\(757\) | −4.63842e6 | −0.294192 | −0.147096 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147096 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(758\) | 1.07117e6 | − | 1.85532e6i | 0.0677152 | − | 0.117286i | ||||
\(759\) | −376773. | − | 652590.i | −0.0237397 | − | 0.0411184i | ||||
\(760\) | −3.75624e6 | − | 6.50599e6i | −0.235895 | − | 0.408582i | ||||
\(761\) | 3.48499e6 | − | 6.03619e6i | 0.218143 | − | 0.377834i | −0.736098 | − | 0.676875i | \(-0.763334\pi\) |
0.954240 | + | 0.299041i | \(0.0966669\pi\) | |||||||
\(762\) | −8.70395e6 | −0.543036 | ||||||||
\(763\) | 5.75180e6 | + | 5.49769e6i | 0.357678 | + | 0.341876i | ||||
\(764\) | 8.04445e6 | 0.498612 | ||||||||
\(765\) | 3.06869e6 | − | 5.31513e6i | 0.189583 | − | 0.328368i | ||||
\(766\) | 7.69394e6 | + | 1.33263e7i | 0.473780 | + | 0.820612i | ||||
\(767\) | −1.62121e6 | − | 2.80802e6i | −0.0995063 | − | 0.172350i | ||||
\(768\) | 353121. | − | 611623.i | 0.0216033 | − | 0.0374180i | ||||
\(769\) | 3.02590e6 | 0.184518 | 0.0922590 | − | 0.995735i | \(-0.470591\pi\) | ||||
0.0922590 | + | 0.995735i | \(0.470591\pi\) | |||||||
\(770\) | 1.21812e6 | − | 4.99465e6i | 0.0740395 | − | 0.303584i | ||||
\(771\) | −604967. | −0.0366518 | ||||||||
\(772\) | −1.12258e6 | + | 1.94436e6i | −0.0677912 | + | 0.117418i | ||||
\(773\) | −1.39269e7 | − | 2.41221e7i | −0.838314 | − | 1.45200i | −0.891304 | − | 0.453407i | \(-0.850208\pi\) |
0.0529900 | − | 0.998595i | \(-0.483125\pi\) | |||||||
\(774\) | −5.06608e6 | − | 8.77471e6i | −0.303962 | − | 0.526478i | ||||
\(775\) | 1.46116e6 | − | 2.53080e6i | 0.0873862 | − | 0.151357i | ||||
\(776\) | −1.49254e6 | −0.0889758 | ||||||||
\(777\) | 9.13571e6 | − | 2.67043e6i | 0.542862 | − | 0.158682i | ||||
\(778\) | −6.79330e6 | −0.402376 | ||||||||
\(779\) | −1.28295e6 | + | 2.22213e6i | −0.0757470 | + | 0.131198i | ||||
\(780\) | 6.04768e6 | + | 1.04749e7i | 0.355920 | + | 0.616471i | ||||
\(781\) | 416085. | + | 720680.i | 0.0244092 | + | 0.0422780i | ||||
\(782\) | −682411. | + | 1.18197e6i | −0.0399052 | + | 0.0691178i | ||||
\(783\) | 1.11795e7 | 0.651653 | ||||||||
\(784\) | 194275. | + | 4.29820e6i | 0.0112883 | + | 0.249745i | ||||
\(785\) | 5.36804e7 | 3.10915 | ||||||||
\(786\) | 6.11067e6 | − | 1.05840e7i | 0.352803 | − | 0.611073i | ||||
\(787\) | −1.43956e7 | − | 2.49340e7i | −0.828503 | − | 1.43501i | −0.899213 | − | 0.437512i | \(-0.855860\pi\) |
0.0707097 | − | 0.997497i | \(-0.477474\pi\) | |||||||
\(788\) | −3.03194e6 | − | 5.25148e6i | −0.173942 | − | 0.301277i | ||||
\(789\) | 8.31264e6 | − | 1.43979e7i | 0.475386 | − | 0.823393i | ||||
\(790\) | −3.06858e6 | −0.174932 | ||||||||
\(791\) | −3.02300e7 | + | 8.83644e6i | −1.71790 | + | 0.502153i | ||||
\(792\) | 758657. | 0.0429766 | ||||||||
\(793\) | 4.36455e6 | − | 7.55962e6i | 0.246466 | − | 0.426891i | ||||
\(794\) | −7.24755e6 | − | 1.25531e7i | −0.407981 | − | 0.706644i | ||||
\(795\) | 1.49471e7 | + | 2.58891e7i | 0.838763 | + | 1.45278i | ||||
\(796\) | 3.68818e6 | − | 6.38811e6i | 0.206314 | − | 0.357347i | ||||
\(797\) | −3.67489e6 | −0.204927 | −0.102463 | − | 0.994737i | \(-0.532672\pi\) | ||||
−0.102463 | + | 0.994737i | \(0.532672\pi\) | |||||||
\(798\) | 1.46481e6 | − | 6.00616e6i | 0.0814282 | − | 0.333879i | ||||
\(799\) | −6.47841e6 | −0.359006 | ||||||||
\(800\) | −4.16430e6 | + | 7.21277e6i | −0.230047 | + | 0.398453i | ||||
\(801\) | 1.27325e6 | + | 2.20533e6i | 0.0701185 | + | 0.121449i | ||||
\(802\) | 5.59602e6 | + | 9.69259e6i | 0.307216 | + | 0.532113i | ||||
\(803\) | −489625. | + | 848056.i | −0.0267963 | + | 0.0464126i | ||||
\(804\) | 1.02864e7 | 0.561207 | ||||||||
\(805\) | −7.44194e6 | − | 7.11317e6i | −0.404759 | − | 0.386878i | ||||
\(806\) | −950173. | −0.0515187 | ||||||||
\(807\) | −6.49468e6 | + | 1.12491e7i | −0.351054 | + | 0.608043i | ||||
\(808\) | 2.20717e6 | + | 3.82294e6i | 0.118935 | + | 0.206001i | ||||
\(809\) | 5.20061e6 | + | 9.00772e6i | 0.279372 | + | 0.483886i | 0.971229 | − | 0.238148i | \(-0.0765404\pi\) |
−0.691857 | + | 0.722035i | \(0.743207\pi\) | |||||||
\(810\) | 2.57282e6 | − | 4.45625e6i | 0.137783 | − | 0.238648i | ||||
\(811\) | −1.53749e7 | −0.820844 | −0.410422 | − | 0.911896i | \(-0.634619\pi\) | ||||
−0.410422 | + | 0.911896i | \(0.634619\pi\) | |||||||
\(812\) | −4.20571e6 | − | 4.01991e6i | −0.223846 | − | 0.213957i | ||||
\(813\) | −1.90191e7 | −1.00917 | ||||||||
\(814\) | −1.27311e6 | + | 2.20509e6i | −0.0673449 | + | 0.116645i | ||||
\(815\) | 1.50776e7 | + | 2.61152e7i | 0.795130 | + | 1.37721i | ||||
\(816\) | 628885. | + | 1.08926e6i | 0.0330633 | + | 0.0572673i | ||||
\(817\) | 1.10438e7 | − | 1.91285e7i | 0.578848 | − | 1.00259i | ||||
\(818\) | −2.66513e6 | −0.139263 | ||||||||
\(819\) | 2.57649e6 | − | 1.05644e7i | 0.134220 | − | 0.550343i | ||||
\(820\) | 3.93761e6 | 0.204502 | ||||||||
\(821\) | −9.56213e6 | + | 1.65621e7i | −0.495104 | + | 0.857546i | −0.999984 | − | 0.00564381i | \(-0.998204\pi\) |
0.504880 | + | 0.863190i | \(0.331537\pi\) | |||||||
\(822\) | 4.06206e6 | + | 7.03570e6i | 0.209685 | + | 0.363185i | ||||
\(823\) | −1.44448e6 | − | 2.50191e6i | −0.0743381 | − | 0.128757i | 0.826460 | − | 0.562995i | \(-0.190351\pi\) |
−0.900798 | + | 0.434238i | \(0.857018\pi\) | |||||||
\(824\) | −3.63921e6 | + | 6.30329e6i | −0.186719 | + | 0.323407i | ||||
\(825\) | 8.18942e6 | 0.418908 | ||||||||
\(826\) | 2.44109e6 | − | 713545.i | 0.124490 | − | 0.0363891i | ||||
\(827\) | −1.99201e7 | −1.01281 | −0.506406 | − | 0.862295i | \(-0.669026\pi\) | ||||
−0.506406 | + | 0.862295i | \(0.669026\pi\) | |||||||
\(828\) | 759583. | − | 1.31564e6i | 0.0385034 | − | 0.0666899i | ||||
\(829\) | 5.98630e6 | + | 1.03686e7i | 0.302532 | + | 0.524001i | 0.976709 | − | 0.214569i | \(-0.0688346\pi\) |
−0.674177 | + | 0.738570i | \(0.735501\pi\) | |||||||
\(830\) | 2.13189e7 | + | 3.69255e7i | 1.07416 | + | 1.86051i | ||||
\(831\) | 7.99170e6 | − | 1.38420e7i | 0.401455 | − | 0.695340i | ||||
\(832\) | 2.70799e6 | 0.135625 | ||||||||
\(833\) | −6.80227e6 | − | 3.52777e6i | −0.339657 | − | 0.176152i | ||||
\(834\) | 9.12024e6 | 0.454037 | ||||||||
\(835\) | 697414. | − | 1.20796e6i | 0.0346158 | − | 0.0599564i | ||||
\(836\) | 826919. | + | 1.43227e6i | 0.0409211 | + | 0.0708774i | ||||
\(837\) | 716056. | + | 1.24025e6i | 0.0353292 | + | 0.0611919i | ||||
\(838\) | −5.78406e6 | + | 1.00183e7i | −0.284526 | + | 0.492814i | ||||
\(839\) | −1.43453e7 | −0.703568 | −0.351784 | − | 0.936081i | \(-0.614425\pi\) | ||||
−0.351784 | + | 0.936081i | \(0.614425\pi\) | |||||||
\(840\) | −9.10611e6 | + | 2.66177e6i | −0.445282 | + | 0.130159i | ||||
\(841\) | −1.26444e7 | −0.616463 | ||||||||
\(842\) | −1.34405e7 | + | 2.32797e7i | −0.653336 | + | 1.13161i | ||||
\(843\) | −6.83286e6 | − | 1.18349e7i | −0.331157 | − | 0.573580i | ||||
\(844\) | −1.61711e6 | − | 2.80092e6i | −0.0781418 | − | 0.135346i | ||||
\(845\) | −3.49091e6 | + | 6.04643e6i | −0.168188 | + | 0.291311i | ||||
\(846\) | 7.21103e6 | 0.346395 | ||||||||
\(847\) | 4.67890e6 | − | 1.91848e7i | 0.224096 | − | 0.918861i | ||||
\(848\) | 6.69292e6 | 0.319614 | ||||||||
\(849\) | −7.79440e6 | + | 1.35003e7i | −0.371119 | + | 0.642797i | ||||
\(850\) | −7.41634e6 | − | 1.28455e7i | −0.352081 | − | 0.609822i | ||||
\(851\) | 2.54933e6 | + | 4.41556e6i | 0.120671 | + | 0.209008i | ||||
\(852\) | 767833. | − | 1.32993e6i | 0.0362383 | − | 0.0627666i | ||||
\(853\) | −1.41859e7 | −0.667551 | −0.333776 | − | 0.942653i | \(-0.608323\pi\) | ||||
−0.333776 | + | 0.942653i | \(0.608323\pi\) | |||||||
\(854\) | 4.94951e6 | + | 4.73085e6i | 0.232230 | + | 0.221970i | ||||
\(855\) | −1.48922e7 | −0.696698 | ||||||||
\(856\) | 3.88119e6 | − | 6.72242e6i | 0.181043 | − | 0.313575i | ||||
\(857\) | −1.20697e7 | − | 2.09053e7i | −0.561363 | − | 0.972309i | −0.997378 | − | 0.0723698i | \(-0.976944\pi\) |
0.436015 | − | 0.899939i | \(-0.356390\pi\) | |||||||
\(858\) | −1.33137e6 | − | 2.30600e6i | −0.0617420 | − | 0.106940i | ||||
\(859\) | −6.86713e6 | + | 1.18942e7i | −0.317536 | + | 0.549988i | −0.979973 | − | 0.199129i | \(-0.936189\pi\) |
0.662438 | + | 0.749117i | \(0.269522\pi\) | |||||||
\(860\) | −3.38956e7 | −1.56278 | ||||||||
\(861\) | 2.34243e6 | + | 2.23895e6i | 0.107686 | + | 0.102929i | ||||
\(862\) | 1.88919e7 | 0.865981 | ||||||||
\(863\) | −8.74523e6 | + | 1.51472e7i | −0.399709 | + | 0.692317i | −0.993690 | − | 0.112163i | \(-0.964222\pi\) |
0.593981 | + | 0.804479i | \(0.297556\pi\) | |||||||
\(864\) | −2.04076e6 | − | 3.53470e6i | −0.0930052 | − | 0.161090i | ||||
\(865\) | −2.72973e6 | − | 4.72802e6i | −0.124045 | − | 0.214852i | ||||
\(866\) | 1.15627e7 | − | 2.00272e7i | 0.523920 | − | 0.907456i | ||||
\(867\) | 1.30609e7 | 0.590101 | ||||||||
\(868\) | 176587. | − | 724060.i | 0.00795537 | − | 0.0326193i | ||||
\(869\) | 675534. | 0.0303458 | ||||||||
\(870\) | 6.41417e6 | − | 1.11097e7i | 0.287304 | − | 0.497626i | ||||
\(871\) | 1.97209e7 | + | 3.41576e7i | 0.880808 | + | 1.52560i | ||||
\(872\) | 1.96396e6 | + | 3.40168e6i | 0.0874666 | + | 0.151497i | ||||
\(873\) | −1.47936e6 | + | 2.56232e6i | −0.0656958 | + | 0.113788i | ||||
\(874\) | 3.31171e6 | 0.146647 | ||||||||
\(875\) | 6.61268e7 | − | 1.93293e7i | 2.91983 | − | 0.853485i | ||||
\(876\) | 1.80709e6 | 0.0795644 | ||||||||
\(877\) | 1.75610e7 | − | 3.04166e7i | 0.770995 | − | 1.33540i | −0.166024 | − | 0.986122i | \(-0.553093\pi\) |
0.937018 | − | 0.349280i | \(-0.113574\pi\) | |||||||
\(878\) | −1.07375e7 | − | 1.85978e7i | −0.470073 | − | 0.814190i | ||||
\(879\) | 1.97755e6 | + | 3.42522e6i | 0.0863288 | + | 0.149526i | ||||
\(880\) | 1.26898e6 | − | 2.19795e6i | 0.0552395 | − | 0.0956776i | ||||
\(881\) | −8.78528e6 | −0.381343 | −0.190672 | − | 0.981654i | \(-0.561067\pi\) | ||||
−0.190672 | + | 0.981654i | \(0.561067\pi\) | |||||||
\(882\) | 7.57151e6 | + | 3.92672e6i | 0.327726 | + | 0.169964i | ||||
\(883\) | 1.87501e7 | 0.809287 | 0.404643 | − | 0.914475i | \(-0.367396\pi\) | ||||
0.404643 | + | 0.914475i | \(0.367396\pi\) | |||||||
\(884\) | −2.41138e6 | + | 4.17663e6i | −0.103785 | + | 0.179761i | ||||
\(885\) | 2.80390e6 | + | 4.85650e6i | 0.120339 | + | 0.208432i | ||||
\(886\) | −8.63023e6 | − | 1.49480e7i | −0.369350 | − | 0.639733i | ||||
\(887\) | 1.36217e7 | − | 2.35935e7i | 0.581330 | − | 1.00689i | −0.413992 | − | 0.910281i | \(-0.635866\pi\) |
0.995322 | − | 0.0966131i | \(-0.0308009\pi\) | |||||||
\(888\) | 4.69873e6 | 0.199962 | ||||||||
\(889\) | 2.51261e7 | − | 7.34451e6i | 1.06628 | − | 0.311680i | ||||
\(890\) | 8.51892e6 | 0.360504 | ||||||||
\(891\) | −566395. | + | 981025.i | −0.0239015 | + | 0.0413986i | ||||
\(892\) | −5.55472e6 | − | 9.62106e6i | −0.233749 | − | 0.404865i | ||||
\(893\) | 7.85986e6 | + | 1.36137e7i | 0.329827 | + | 0.571277i | ||||
\(894\) | −6.32194e6 | + | 1.09499e7i | −0.264549 | + | 0.458213i | ||||
\(895\) | −5.28124e7 | −2.20383 | ||||||||
\(896\) | −503273. | + | 2.06357e6i | −0.0209428 | + | 0.0858714i | ||||
\(897\) | −5.33198e6 | −0.221262 | ||||||||
\(898\) | −9.50584e6 | + | 1.64646e7i | −0.393369 | + | 0.681334i | ||||
\(899\) | 503877. | + | 872740.i | 0.0207934 | + | 0.0360152i | ||||
\(900\) | 8.25503e6 | + | 1.42981e7i | 0.339713 | + | 0.588400i | ||||
\(901\) | −5.95983e6 | + | 1.03227e7i | −0.244580 | + | 0.423626i | ||||
\(902\) | −866847. | −0.0354753 | ||||||||
\(903\) | −2.01641e7 | − | 1.92733e7i | −0.822923 | − | 0.786568i | ||||
\(904\) | −1.55481e7 | −0.632785 | ||||||||
\(905\) | 1.20494e7 | − | 2.08701e7i | 0.489038 | − | 0.847038i | ||||
\(906\) | −4.40703e6 | − | 7.63320e6i | −0.178372 | − | 0.308949i | ||||
\(907\) | −1.45210e7 | − | 2.51511e7i | −0.586110 | − | 1.01517i | −0.994736 | − | 0.102470i | \(-0.967325\pi\) |
0.408626 | − | 0.912702i | \(-0.366008\pi\) | |||||||
\(908\) | −1.01358e7 | + | 1.75557e7i | −0.407984 | + | 0.706649i | ||||
\(909\) | 8.75071e6 | 0.351264 | ||||||||
\(910\) | −2.62970e7 | − | 2.51352e7i | −1.05269 | − | 1.00619i | ||||
\(911\) | 4.12057e7 | 1.64498 | 0.822491 | − | 0.568778i | \(-0.192583\pi\) | ||||
0.822491 | + | 0.568778i | \(0.192583\pi\) | |||||||
\(912\) | 1.52598e6 | − | 2.64307e6i | 0.0607520 | − | 0.105226i | ||||
\(913\) | −4.69327e6 | − | 8.12899e6i | −0.186337 | − | 0.322745i | ||||
\(914\) | −4.27455e6 | − | 7.40374e6i | −0.169249 | − | 0.293147i | ||||
\(915\) | −7.54855e6 | + | 1.30745e7i | −0.298065 | + | 0.516263i | ||||
\(916\) | 1.37036e7 | 0.539631 | ||||||||
\(917\) | −8.70902e6 | + | 3.57095e7i | −0.342016 | + | 1.40236i | ||||
\(918\) | 7.26892e6 | 0.284684 | ||||||||
\(919\) | −1.52384e7 | + | 2.63937e7i | −0.595184 | + | 1.03089i | 0.398337 | + | 0.917239i | \(0.369588\pi\) |
−0.993521 | + | 0.113650i | \(0.963746\pi\) | |||||||
\(920\) | −2.54107e6 | − | 4.40126e6i | −0.0989798 | − | 0.171438i | ||||
\(921\) | −707367. | − | 1.22520e6i | −0.0274787 | − | 0.0475945i | ||||
\(922\) | 3.45839e6 | − | 5.99011e6i | 0.133982 | − | 0.232064i | ||||
\(923\) | 5.88831e6 | 0.227503 | ||||||||
\(924\) | 2.00467e6 | − | 585978.i | 0.0772437 | − | 0.0225788i | ||||
\(925\) | −5.54114e7 | −2.12934 | ||||||||
\(926\) | 1.30873e7 | − | 2.26679e7i | 0.501561 | − | 0.868730i | ||||
\(927\) | 7.21413e6 | + | 1.24952e7i | 0.275730 | + | 0.477579i | ||||
\(928\) | −1.43605e6 | − | 2.48731e6i | −0.0547393 | − | 0.0948112i | ||||
\(929\) | 1.80320e7 | − | 3.12323e7i | 0.685495 | − | 1.18731i | −0.287786 | − | 0.957695i | \(-0.592919\pi\) |
0.973281 | − | 0.229618i | \(-0.0737476\pi\) | |||||||
\(930\) | 1.64334e6 | 0.0623045 | ||||||||
\(931\) | 839541. | + | 1.85743e7i | 0.0317445 | + | 0.702324i | ||||
\(932\) | −4.54972e6 | −0.171571 | ||||||||
\(933\) | −1.25799e7 | + | 2.17890e7i | −0.473122 | + | 0.819471i | ||||
\(934\) | 3.58838e6 | + | 6.21525e6i | 0.134596 | + | 0.233126i | ||||
\(935\) | 2.25998e6 | + | 3.91440e6i | 0.0845426 | + | 0.146432i | ||||
\(936\) | 2.68407e6 | − | 4.64895e6i | 0.100139 | − | 0.173446i | ||||
\(937\) | 4.80602e7 | 1.78828 | 0.894141 | − | 0.447785i | \(-0.147787\pi\) | ||||
0.894141 | + | 0.447785i | \(0.147787\pi\) | |||||||
\(938\) | −2.96942e7 | + | 8.67980e6i | −1.10196 | + | 0.322109i | ||||
\(939\) | 8.32800e6 | 0.308231 | ||||||||
\(940\) | 1.20617e7 | − | 2.08915e7i | 0.445234 | − | 0.771169i | ||||
\(941\) | 2.14289e7 | + | 3.71159e7i | 0.788906 | + | 1.36642i | 0.926638 | + | 0.375955i | \(0.122685\pi\) |
−0.137732 | + | 0.990470i | \(0.543981\pi\) | |||||||
\(942\) | 1.09039e7 | + | 1.88861e7i | 0.400363 | + | 0.693448i | ||||
\(943\) | −867905. | + | 1.50326e6i | −0.0317829 | + | 0.0550495i | ||||
\(944\) | 1.25551e6 | 0.0458555 | ||||||||
\(945\) | −1.29910e7 | + | 5.32670e7i | −0.473221 | + | 1.94035i | ||||
\(946\) | 7.46197e6 | 0.271098 | ||||||||
\(947\) | −2.16216e7 | + | 3.74497e7i | −0.783452 | + | 1.35698i | 0.146467 | + | 0.989216i | \(0.453210\pi\) |
−0.929919 | + | 0.367763i | \(0.880124\pi\) | |||||||
\(948\) | −623308. | − | 1.07960e6i | −0.0225259 | − | 0.0390160i | ||||
\(949\) | 3.46452e6 | + | 6.00072e6i | 0.124876 | + | 0.216291i | ||||
\(950\) | −1.79956e7 | + | 3.11693e7i | −0.646930 | + | 1.12052i | ||||
\(951\) | −5.65045e6 | −0.202596 | ||||||||
\(952\) | −2.73456e6 | − | 2.61376e6i | −0.0977903 | − | 0.0934701i | ||||
\(953\) | −2.81115e7 | −1.00265 | −0.501327 | − | 0.865258i | \(-0.667155\pi\) | ||||
−0.501327 | + | 0.865258i | \(0.667155\pi\) | |||||||
\(954\) | 6.63380e6 | − | 1.14901e7i | 0.235989 | − | 0.408745i | ||||
\(955\) | −2.66738e7 | − | 4.62003e7i | −0.946403 | − | 1.63922i | ||||
\(956\) | 3.42353e6 | + | 5.92973e6i | 0.121152 | + | 0.209841i | ||||
\(957\) | −1.41205e6 | + | 2.44574e6i | −0.0498391 | + | 0.0863239i | ||||
\(958\) | 1.63761e7 | 0.576497 | ||||||||
\(959\) | −1.76630e7 | − | 1.68826e7i | −0.620179 | − | 0.592780i | ||||
\(960\) | −4.68351e6 | −0.164019 | ||||||||
\(961\) | 1.42500e7 | − | 2.46818e7i | 0.497745 | − | 0.862120i | ||||
\(962\) | 9.00833e6 | + | 1.56029e7i | 0.313839 | + | 0.543585i | ||||
\(963\) | −7.69382e6 | − | 1.33261e7i | −0.267348 | − | 0.463060i | ||||
\(964\) | −6.47665e6 | + | 1.12179e7i | −0.224470 | + | 0.388793i | ||||
\(965\) | 1.48890e7 | 0.514691 | ||||||||
\(966\) | 990935. | − | 4.06312e6i | 0.0341667 | − | 0.140093i | ||||
\(967\) | 3.70437e7 | 1.27394 | 0.636968 | − | 0.770890i | \(-0.280188\pi\) | ||||
0.636968 | + | 0.770890i | \(0.280188\pi\) | |||||||
\(968\) | 4.87427e6 | − | 8.44248e6i | 0.167194 | − | 0.289589i | ||||
\(969\) | 2.71767e6 | + | 4.70714e6i | 0.0929794 | + | 0.161045i | ||||
\(970\) | 4.94896e6 | + | 8.57186e6i | 0.168883 | + | 0.292513i | ||||
\(971\) | 2.29070e7 | − | 3.96761e7i | 0.779686 | − | 1.35046i | −0.152436 | − | 0.988313i | \(-0.548712\pi\) |
0.932123 | − | 0.362143i | \(-0.117955\pi\) | |||||||
\(972\) | −1.34066e7 | −0.455148 | ||||||||
\(973\) | −2.63278e7 | + | 7.69579e6i | −0.891523 | + | 0.260598i | ||||
\(974\) | −1.78084e7 | −0.601489 | ||||||||
\(975\) | 2.89736e7 | − | 5.01837e7i | 0.976091 | − | 1.69064i | ||||
\(976\) | 1.69002e6 | + | 2.92720e6i | 0.0567894 | + | 0.0983622i | ||||
\(977\) | −587483. | − | 1.01755e6i | −0.0196906 | − | 0.0341051i | 0.856012 | − | 0.516956i | \(-0.172935\pi\) |
−0.875703 | + | 0.482851i | \(0.839601\pi\) | |||||||
\(978\) | −6.12530e6 | + | 1.06093e7i | −0.204777 | + | 0.354683i | ||||
\(979\) | −1.87540e6 | −0.0625372 | ||||||||
\(980\) | 2.40410e7 | − | 1.53677e7i | 0.799626 | − | 0.511145i | ||||
\(981\) | 7.78647e6 | 0.258326 | ||||||||
\(982\) | −1.41935e7 | + | 2.45838e7i | −0.469689 | + | 0.813525i | ||||
\(983\) | 1.31760e7 | + | 2.28215e7i | 0.434911 | + | 0.753288i | 0.997288 | − | 0.0735929i | \(-0.0234466\pi\) |
−0.562378 | + | 0.826881i | \(0.690113\pi\) | |||||||
\(984\) | 799829. | + | 1.38535e6i | 0.0263336 | + | 0.0456111i | ||||
\(985\) | −2.01066e7 | + | 3.48257e7i | −0.660311 | + | 1.14369i | ||||
\(986\) | 5.11502e6 | 0.167554 | ||||||||
\(987\) | 1.90544e7 | − | 5.56972e6i | 0.622590 | − | 0.181987i | ||||
\(988\) | 1.17023e7 | 0.381399 | ||||||||
\(989\) | 7.47108e6 | − | 1.29403e7i | 0.242881 | − | 0.420681i | ||||
\(990\) | −2.51555e6 | − | 4.35707e6i | −0.0815728 | − | 0.141288i | ||||
\(991\) | −1.91212e7 | − | 3.31189e7i | −0.618487 | − | 1.07125i | −0.989762 | − | 0.142728i | \(-0.954413\pi\) |
0.371275 | − | 0.928523i | \(-0.378921\pi\) | |||||||
\(992\) | 183961. | − | 318630.i | 0.00593535 | − | 0.0102803i | ||||
\(993\) | −6.80674e6 | −0.219062 | ||||||||
\(994\) | −1.09433e6 | + | 4.48706e6i | −0.0351303 | + | 0.144044i | ||||
\(995\) | −4.89170e7 | −1.56640 | ||||||||
\(996\) | −8.66085e6 | + | 1.50010e7i | −0.276638 | + | 0.479152i | ||||
\(997\) | −2.18459e7 | − | 3.78383e7i | −0.696038 | − | 1.20557i | −0.969830 | − | 0.243784i | \(-0.921611\pi\) |
0.273792 | − | 0.961789i | \(-0.411722\pi\) | |||||||
\(998\) | −1.88381e7 | − | 3.26285e7i | −0.598701 | − | 1.03698i | ||||
\(999\) | 1.35775e7 | − | 2.35169e7i | 0.430433 | − | 0.745531i |
(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 | 14.6.c.a.9.2 | ✓ | 4 | |
3.2 | odd | 2 | 126.6.g.j.37.2 | 4 | |||
4.3 | odd | 2 | 112.6.i.d.65.1 | 4 | |||
7.2 | even | 3 | 98.6.a.h.1.1 | 2 | |||
7.3 | odd | 6 | 98.6.c.e.67.1 | 4 | |||
7.4 | even | 3 | inner | 14.6.c.a.11.2 | yes | 4 | |
7.5 | odd | 6 | 98.6.a.g.1.2 | 2 | |||
7.6 | odd | 2 | 98.6.c.e.79.1 | 4 | |||
21.2 | odd | 6 | 882.6.a.ba.1.1 | 2 | |||
21.5 | even | 6 | 882.6.a.bi.1.2 | 2 | |||
21.11 | odd | 6 | 126.6.g.j.109.2 | 4 | |||
28.11 | odd | 6 | 112.6.i.d.81.1 | 4 | |||
28.19 | even | 6 | 784.6.a.bb.1.1 | 2 | |||
28.23 | odd | 6 | 784.6.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.a.9.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
14.6.c.a.11.2 | yes | 4 | 7.4 | even | 3 | inner | |
98.6.a.g.1.2 | 2 | 7.5 | odd | 6 | |||
98.6.a.h.1.1 | 2 | 7.2 | even | 3 | |||
98.6.c.e.67.1 | 4 | 7.3 | odd | 6 | |||
98.6.c.e.79.1 | 4 | 7.6 | odd | 2 | |||
112.6.i.d.65.1 | 4 | 4.3 | odd | 2 | |||
112.6.i.d.81.1 | 4 | 28.11 | odd | 6 | |||
126.6.g.j.37.2 | 4 | 3.2 | odd | 2 | |||
126.6.g.j.109.2 | 4 | 21.11 | odd | 6 | |||
784.6.a.s.1.2 | 2 | 28.23 | odd | 6 | |||
784.6.a.bb.1.1 | 2 | 28.19 | even | 6 | |||
882.6.a.ba.1.1 | 2 | 21.2 | odd | 6 | |||
882.6.a.bi.1.2 | 2 | 21.5 | even | 6 |