Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,4,Mod(11,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.e (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.36614134042\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 346 x^{18} + 50697 x^{16} + 4104768 x^{14} + 200532432 x^{12} + 6039270720 x^{10} + \cdots + 1118416232704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.2 | ||
Root | \(5.89468i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.27 |
Dual form | 74.4.e.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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | − | 1.00000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −2.94734 | − | 5.10494i | −0.567216 | − | 0.982446i | −0.996840 | − | 0.0794386i | \(-0.974687\pi\) |
0.429624 | − | 0.903008i | \(-0.358646\pi\) | |||||||
\(4\) | 2.00000 | + | 3.46410i | 0.250000 | + | 0.433013i | ||||
\(5\) | −12.8210 | + | 7.40221i | −1.14675 | + | 0.662074i | −0.948092 | − | 0.317996i | \(-0.896990\pi\) |
−0.198654 | + | 0.980070i | \(0.563657\pi\) | |||||||
\(6\) | 11.7894i | 0.802164i | ||||||||
\(7\) | 7.99249 | + | 13.8434i | 0.431554 | + | 0.747473i | 0.997007 | − | 0.0773072i | \(-0.0246322\pi\) |
−0.565454 | + | 0.824780i | \(0.691299\pi\) | |||||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −3.87362 | + | 6.70931i | −0.143467 | + | 0.248493i | ||||
\(10\) | 29.6089 | 0.936314 | ||||||||
\(11\) | 61.9658 | 1.69849 | 0.849245 | − | 0.527998i | \(-0.177057\pi\) | ||||
0.849245 | + | 0.527998i | \(0.177057\pi\) | |||||||
\(12\) | 11.7894 | − | 20.4198i | 0.283608 | − | 0.491223i | ||||
\(13\) | −62.4556 | + | 36.0587i | −1.33247 | + | 0.769299i | −0.985677 | − | 0.168644i | \(-0.946061\pi\) |
−0.346789 | + | 0.937943i | \(0.612728\pi\) | |||||||
\(14\) | − | 31.9699i | − | 0.610309i | ||||||
\(15\) | 75.5757 | + | 43.6337i | 1.30090 | + | 0.751078i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 98.0374 | + | 56.6019i | 1.39868 | + | 0.807528i | 0.994254 | − | 0.107042i | \(-0.0341380\pi\) |
0.404426 | + | 0.914571i | \(0.367471\pi\) | |||||||
\(18\) | 13.4186 | − | 7.74724i | 0.175711 | − | 0.101447i | ||||
\(19\) | −133.568 | + | 77.1157i | −1.61277 | + | 0.931134i | −0.624047 | + | 0.781387i | \(0.714513\pi\) |
−0.988724 | + | 0.149747i | \(0.952154\pi\) | |||||||
\(20\) | −51.2840 | − | 29.6089i | −0.573373 | − | 0.331037i | ||||
\(21\) | 47.1131 | − | 81.6024i | 0.489568 | − | 0.847957i | ||||
\(22\) | −107.328 | − | 61.9658i | −1.04011 | − | 0.600507i | ||||
\(23\) | 98.0431i | 0.888844i | 0.895818 | + | 0.444422i | \(0.146591\pi\) | ||||
−0.895818 | + | 0.444422i | \(0.853409\pi\) | |||||||
\(24\) | −40.8395 | + | 23.5787i | −0.347347 | + | 0.200541i | ||||
\(25\) | 47.0855 | − | 81.5546i | 0.376684 | − | 0.652436i | ||||
\(26\) | 144.235 | 1.08795 | ||||||||
\(27\) | −113.489 | −0.808924 | ||||||||
\(28\) | −31.9699 | + | 55.3736i | −0.215777 | + | 0.373736i | ||||
\(29\) | − | 57.1816i | − | 0.366150i | −0.983099 | − | 0.183075i | \(-0.941395\pi\) | ||
0.983099 | − | 0.183075i | \(-0.0586052\pi\) | |||||||
\(30\) | −87.2673 | − | 151.151i | −0.531092 | − | 0.919879i | ||||
\(31\) | − | 21.7446i | − | 0.125982i | −0.998014 | − | 0.0629910i | \(-0.979936\pi\) | ||
0.998014 | − | 0.0629910i | \(-0.0200640\pi\) | |||||||
\(32\) | 27.7128 | − | 16.0000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −182.634 | − | 316.332i | −0.963411 | − | 1.66868i | ||||
\(34\) | −113.204 | − | 196.075i | −0.571009 | − | 0.989016i | ||||
\(35\) | −204.944 | − | 118.324i | −0.989765 | − | 0.571441i | ||||
\(36\) | −30.9890 | −0.143467 | ||||||||
\(37\) | 49.0355 | + | 219.655i | 0.217875 | + | 0.975977i | ||||
\(38\) | 308.463 | 1.31682 | ||||||||
\(39\) | 368.155 | + | 212.555i | 1.51159 | + | 0.872717i | ||||
\(40\) | 59.2177 | + | 102.568i | 0.234079 | + | 0.405436i | ||||
\(41\) | −133.514 | − | 231.253i | −0.508570 | − | 0.880869i | −0.999951 | − | 0.00992393i | \(-0.996841\pi\) |
0.491381 | − | 0.870945i | \(-0.336492\pi\) | |||||||
\(42\) | −163.205 | + | 94.2263i | −0.599596 | + | 0.346177i | ||||
\(43\) | 284.962i | 1.01061i | 0.862940 | + | 0.505306i | \(0.168620\pi\) | ||||
−0.862940 | + | 0.505306i | \(0.831380\pi\) | |||||||
\(44\) | 123.932 | + | 214.656i | 0.424623 | + | 0.735468i | ||||
\(45\) | − | 114.693i | − | 0.379944i | ||||||
\(46\) | 98.0431 | − | 169.816i | 0.314254 | − | 0.544303i | ||||
\(47\) | −158.989 | −0.493423 | −0.246712 | − | 0.969089i | \(-0.579350\pi\) | ||||
−0.246712 | + | 0.969089i | \(0.579350\pi\) | |||||||
\(48\) | 94.3149 | 0.283608 | ||||||||
\(49\) | 43.7403 | − | 75.7605i | 0.127523 | − | 0.220876i | ||||
\(50\) | −163.109 | + | 94.1711i | −0.461342 | + | 0.266356i | ||||
\(51\) | − | 667.300i | − | 1.83217i | ||||||
\(52\) | −249.822 | − | 144.235i | −0.666233 | − | 0.384650i | ||||
\(53\) | −153.616 | + | 266.071i | −0.398128 | + | 0.689578i | −0.993495 | − | 0.113876i | \(-0.963673\pi\) |
0.595367 | + | 0.803454i | \(0.297007\pi\) | |||||||
\(54\) | 196.568 | + | 113.489i | 0.495363 | + | 0.285998i | ||||
\(55\) | −794.465 | + | 458.684i | −1.94774 | + | 1.12453i | ||||
\(56\) | 110.747 | − | 63.9399i | 0.264272 | − | 0.152577i | ||||
\(57\) | 787.342 | + | 454.572i | 1.82958 | + | 1.05631i | ||||
\(58\) | −57.1816 | + | 99.0415i | −0.129454 | + | 0.224220i | ||||
\(59\) | 156.630 | + | 90.4304i | 0.345618 | + | 0.199543i | 0.662754 | − | 0.748837i | \(-0.269388\pi\) |
−0.317135 | + | 0.948380i | \(0.602721\pi\) | |||||||
\(60\) | 349.069i | 0.751078i | ||||||||
\(61\) | 343.714 | − | 198.444i | 0.721444 | − | 0.416526i | −0.0938397 | − | 0.995587i | \(-0.529914\pi\) |
0.815284 | + | 0.579061i | \(0.196581\pi\) | |||||||
\(62\) | −21.7446 | + | 37.6627i | −0.0445414 | + | 0.0771479i | ||||
\(63\) | −123.839 | −0.247656 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 533.829 | − | 924.619i | 1.01867 | − | 1.76438i | ||||
\(66\) | 730.537i | 1.36247i | ||||||||
\(67\) | 35.1561 | + | 60.8922i | 0.0641045 | + | 0.111032i | 0.896296 | − | 0.443455i | \(-0.146248\pi\) |
−0.832192 | + | 0.554488i | \(0.812914\pi\) | |||||||
\(68\) | 452.815i | 0.807528i | ||||||||
\(69\) | 500.504 | − | 288.966i | 0.873241 | − | 0.504166i | ||||
\(70\) | 236.648 | + | 409.887i | 0.404070 | + | 0.699870i | ||||
\(71\) | 92.9272 | + | 160.955i | 0.155330 | + | 0.269039i | 0.933179 | − | 0.359412i | \(-0.117023\pi\) |
−0.777849 | + | 0.628451i | \(0.783689\pi\) | |||||||
\(72\) | 53.6745 | + | 30.9890i | 0.0878555 | + | 0.0507234i | ||||
\(73\) | 288.366 | 0.462339 | 0.231169 | − | 0.972914i | \(-0.425745\pi\) | ||||
0.231169 | + | 0.972914i | \(0.425745\pi\) | |||||||
\(74\) | 134.723 | − | 429.490i | 0.211639 | − | 0.674692i | ||||
\(75\) | −555.108 | −0.854645 | ||||||||
\(76\) | −534.273 | − | 308.463i | −0.806386 | − | 0.465567i | ||||
\(77\) | 495.261 | + | 857.817i | 0.732990 | + | 1.26958i | ||||
\(78\) | −425.109 | − | 736.311i | −0.617104 | − | 1.06886i | ||||
\(79\) | 52.9580 | − | 30.5753i | 0.0754207 | − | 0.0435442i | −0.461815 | − | 0.886976i | \(-0.652802\pi\) |
0.537236 | + | 0.843432i | \(0.319468\pi\) | |||||||
\(80\) | − | 236.871i | − | 0.331037i | ||||||
\(81\) | 439.078 | + | 760.505i | 0.602302 | + | 1.04322i | ||||
\(82\) | 534.055i | 0.719226i | ||||||||
\(83\) | 74.1763 | − | 128.477i | 0.0980953 | − | 0.169906i | −0.812801 | − | 0.582541i | \(-0.802058\pi\) |
0.910896 | + | 0.412636i | \(0.135392\pi\) | |||||||
\(84\) | 376.905 | 0.489568 | ||||||||
\(85\) | −1675.92 | −2.13857 | ||||||||
\(86\) | 284.962 | − | 493.569i | 0.357305 | − | 0.618871i | ||||
\(87\) | −291.909 | + | 168.534i | −0.359723 | + | 0.207686i | ||||
\(88\) | − | 495.727i | − | 0.600507i | ||||||
\(89\) | −662.354 | − | 382.410i | −0.788870 | − | 0.455454i | 0.0506947 | − | 0.998714i | \(-0.483856\pi\) |
−0.839565 | + | 0.543260i | \(0.817190\pi\) | |||||||
\(90\) | −114.693 | + | 198.655i | −0.134331 | + | 0.232667i | ||||
\(91\) | −998.350 | − | 576.398i | −1.15006 | − | 0.663988i | ||||
\(92\) | −339.631 | + | 196.086i | −0.384881 | + | 0.222211i | ||||
\(93\) | −111.005 | + | 64.0887i | −0.123771 | + | 0.0714590i | ||||
\(94\) | 275.377 | + | 158.989i | 0.302159 | + | 0.174451i | ||||
\(95\) | 1141.65 | − | 1977.40i | 1.23296 | − | 2.13555i | ||||
\(96\) | −163.358 | − | 94.3149i | −0.173674 | − | 0.100271i | ||||
\(97\) | − | 1439.22i | − | 1.50650i | −0.657733 | − | 0.753251i | \(-0.728484\pi\) | ||
0.657733 | − | 0.753251i | \(-0.271516\pi\) | |||||||
\(98\) | −151.521 | + | 87.4806i | −0.156183 | + | 0.0901722i | ||||
\(99\) | −240.032 | + | 415.748i | −0.243678 | + | 0.422063i | ||||
\(100\) | 376.684 | 0.376684 | ||||||||
\(101\) | −720.687 | −0.710010 | −0.355005 | − | 0.934864i | \(-0.615521\pi\) | ||||
−0.355005 | + | 0.934864i | \(0.615521\pi\) | |||||||
\(102\) | −667.300 | + | 1155.80i | −0.647770 | + | 1.12197i | ||||
\(103\) | 1173.72i | 1.12282i | 0.827538 | + | 0.561409i | \(0.189741\pi\) | ||||
−0.827538 | + | 0.561409i | \(0.810259\pi\) | |||||||
\(104\) | 288.470 | + | 499.644i | 0.271988 | + | 0.471098i | ||||
\(105\) | 1394.97i | 1.29652i | ||||||||
\(106\) | 532.142 | − | 307.232i | 0.487605 | − | 0.281519i | ||||
\(107\) | −28.2825 | − | 48.9868i | −0.0255531 | − | 0.0442592i | 0.852966 | − | 0.521966i | \(-0.174801\pi\) |
−0.878519 | + | 0.477707i | \(0.841468\pi\) | |||||||
\(108\) | −226.978 | − | 393.137i | −0.202231 | − | 0.350274i | ||||
\(109\) | −582.851 | − | 336.509i | −0.512175 | − | 0.295704i | 0.221552 | − | 0.975148i | \(-0.428888\pi\) |
−0.733727 | + | 0.679444i | \(0.762221\pi\) | |||||||
\(110\) | 1834.74 | 1.59032 | ||||||||
\(111\) | 976.804 | − | 897.723i | 0.835262 | − | 0.767640i | ||||
\(112\) | −255.760 | −0.215777 | ||||||||
\(113\) | 728.008 | + | 420.316i | 0.606064 | + | 0.349911i | 0.771424 | − | 0.636322i | \(-0.219545\pi\) |
−0.165359 | + | 0.986233i | \(0.552878\pi\) | |||||||
\(114\) | −909.144 | − | 1574.68i | −0.746922 | − | 1.29371i | ||||
\(115\) | −725.736 | − | 1257.01i | −0.588480 | − | 1.01928i | ||||
\(116\) | 198.083 | − | 114.363i | 0.158548 | − | 0.0915376i | ||||
\(117\) | − | 558.711i | − | 0.441478i | ||||||
\(118\) | −180.861 | − | 313.260i | −0.141098 | − | 0.244389i | ||||
\(119\) | 1809.56i | 1.39397i | ||||||||
\(120\) | 349.069 | − | 604.606i | 0.265546 | − | 0.459939i | ||||
\(121\) | 2508.76 | 1.88487 | ||||||||
\(122\) | −793.774 | −0.589057 | ||||||||
\(123\) | −787.021 | + | 1363.16i | −0.576938 | + | 0.999285i | ||||
\(124\) | 75.3255 | − | 43.4892i | 0.0545518 | − | 0.0314955i | ||||
\(125\) | − | 456.404i | − | 0.326576i | ||||||
\(126\) | 214.496 | + | 123.839i | 0.151657 | + | 0.0875595i | ||||
\(127\) | −577.405 | + | 1000.09i | −0.403436 | + | 0.698772i | −0.994138 | − | 0.108118i | \(-0.965518\pi\) |
0.590702 | + | 0.806890i | \(0.298851\pi\) | |||||||
\(128\) | 110.851 | + | 64.0000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 1454.71 | − | 839.880i | 0.992872 | − | 0.573235i | ||||
\(130\) | −1849.24 | + | 1067.66i | −1.24761 | + | 0.720306i | ||||
\(131\) | 770.321 | + | 444.745i | 0.513765 | + | 0.296623i | 0.734380 | − | 0.678738i | \(-0.237473\pi\) |
−0.220615 | + | 0.975361i | \(0.570806\pi\) | |||||||
\(132\) | 730.537 | − | 1265.33i | 0.481705 | − | 0.834338i | ||||
\(133\) | −2135.08 | − | 1232.69i | −1.39199 | − | 0.803669i | ||||
\(134\) | − | 140.624i | − | 0.0906575i | ||||||
\(135\) | 1455.04 | − | 840.069i | 0.927630 | − | 0.535567i | ||||
\(136\) | 452.815 | − | 784.299i | 0.285504 | − | 0.494508i | ||||
\(137\) | −736.672 | −0.459402 | −0.229701 | − | 0.973261i | \(-0.573775\pi\) | ||||
−0.229701 | + | 0.973261i | \(0.573775\pi\) | |||||||
\(138\) | −1155.87 | −0.712999 | ||||||||
\(139\) | −266.397 | + | 461.413i | −0.162557 | + | 0.281558i | −0.935785 | − | 0.352571i | \(-0.885308\pi\) |
0.773228 | + | 0.634128i | \(0.218641\pi\) | |||||||
\(140\) | − | 946.594i | − | 0.571441i | ||||||
\(141\) | 468.594 | + | 811.628i | 0.279877 | + | 0.484762i | ||||
\(142\) | − | 371.709i | − | 0.219670i | ||||||
\(143\) | −3870.11 | + | 2234.41i | −2.26318 | + | 1.30665i | ||||
\(144\) | −61.9779 | − | 107.349i | −0.0358669 | − | 0.0621232i | ||||
\(145\) | 423.271 | + | 733.126i | 0.242419 | + | 0.419881i | ||||
\(146\) | −499.465 | − | 288.366i | −0.283123 | − | 0.163461i | ||||
\(147\) | −515.670 | −0.289332 | ||||||||
\(148\) | −662.838 | + | 609.175i | −0.368141 | + | 0.338337i | ||||
\(149\) | 1584.87 | 0.871392 | 0.435696 | − | 0.900094i | \(-0.356502\pi\) | ||||
0.435696 | + | 0.900094i | \(0.356502\pi\) | |||||||
\(150\) | 961.476 | + | 555.108i | 0.523361 | + | 0.302163i | ||||
\(151\) | 1829.65 | + | 3169.05i | 0.986058 | + | 1.70790i | 0.637137 | + | 0.770751i | \(0.280119\pi\) |
0.348921 | + | 0.937152i | \(0.386548\pi\) | |||||||
\(152\) | 616.925 | + | 1068.55i | 0.329206 | + | 0.570201i | ||||
\(153\) | −759.519 | + | 438.509i | −0.401330 | + | 0.231708i | ||||
\(154\) | − | 1981.04i | − | 1.03660i | ||||||
\(155\) | 160.958 | + | 278.788i | 0.0834095 | + | 0.144469i | ||||
\(156\) | 1700.44i | 0.872717i | ||||||||
\(157\) | −726.925 | + | 1259.07i | −0.369522 | + | 0.640031i | −0.989491 | − | 0.144596i | \(-0.953812\pi\) |
0.619969 | + | 0.784626i | \(0.287145\pi\) | |||||||
\(158\) | −122.301 | −0.0615808 | ||||||||
\(159\) | 1811.03 | 0.903298 | ||||||||
\(160\) | −236.871 | + | 410.272i | −0.117039 | + | 0.202718i | ||||
\(161\) | −1357.25 | + | 783.608i | −0.664387 | + | 0.383584i | ||||
\(162\) | − | 1756.31i | − | 0.851783i | ||||||
\(163\) | −3087.03 | − | 1782.30i | −1.48340 | − | 0.856443i | −0.483581 | − | 0.875300i | \(-0.660664\pi\) |
−0.999822 | + | 0.0188564i | \(0.993997\pi\) | |||||||
\(164\) | 534.055 | − | 925.011i | 0.254285 | − | 0.440434i | ||||
\(165\) | 4683.11 | + | 2703.80i | 2.20958 | + | 1.27570i | ||||
\(166\) | −256.954 | + | 148.353i | −0.120142 | + | 0.0693638i | ||||
\(167\) | 1487.97 | − | 859.082i | 0.689478 | − | 0.398070i | −0.113938 | − | 0.993488i | \(-0.536347\pi\) |
0.803417 | + | 0.595417i | \(0.203013\pi\) | |||||||
\(168\) | −652.819 | − | 376.905i | −0.299798 | − | 0.173088i | ||||
\(169\) | 1501.96 | − | 2601.48i | 0.683643 | − | 1.18410i | ||||
\(170\) | 2902.78 | + | 1675.92i | 1.30960 | + | 0.756100i | ||||
\(171\) | − | 1194.87i | − | 0.534349i | ||||||
\(172\) | −987.137 | + | 569.924i | −0.437608 | + | 0.252653i | ||||
\(173\) | −731.729 | + | 1267.39i | −0.321574 | + | 0.556983i | −0.980813 | − | 0.194951i | \(-0.937545\pi\) |
0.659239 | + | 0.751934i | \(0.270879\pi\) | |||||||
\(174\) | 674.135 | 0.293713 | ||||||||
\(175\) | 1505.32 | 0.650238 | ||||||||
\(176\) | −495.727 | + | 858.624i | −0.212311 | + | 0.367734i | ||||
\(177\) | − | 1066.12i | − | 0.452736i | ||||||
\(178\) | 764.821 | + | 1324.71i | 0.322055 | + | 0.557815i | ||||
\(179\) | − | 503.727i | − | 0.210337i | −0.994454 | − | 0.105169i | \(-0.966462\pi\) | ||
0.994454 | − | 0.105169i | \(-0.0335382\pi\) | |||||||
\(180\) | 397.310 | − | 229.387i | 0.164521 | − | 0.0949861i | ||||
\(181\) | 90.7194 | + | 157.131i | 0.0372548 | + | 0.0645272i | 0.884052 | − | 0.467389i | \(-0.154805\pi\) |
−0.846797 | + | 0.531917i | \(0.821472\pi\) | |||||||
\(182\) | 1152.80 | + | 1996.70i | 0.469510 | + | 0.813216i | ||||
\(183\) | −2026.09 | − | 1169.76i | −0.818429 | − | 0.472520i | ||||
\(184\) | 784.345 | 0.314254 | ||||||||
\(185\) | −2254.62 | − | 2453.23i | −0.896017 | − | 0.974948i | ||||
\(186\) | 256.355 | 0.101058 | ||||||||
\(187\) | 6074.97 | + | 3507.39i | 2.37565 | + | 1.37158i | ||||
\(188\) | −317.977 | − | 550.753i | −0.123356 | − | 0.213659i | ||||
\(189\) | −907.058 | − | 1571.07i | −0.349094 | − | 0.604649i | ||||
\(190\) | −3954.80 | + | 2283.31i | −1.51006 | + | 0.871834i | ||||
\(191\) | − | 4147.76i | − | 1.57132i | −0.618661 | − | 0.785658i | \(-0.712324\pi\) | ||
0.618661 | − | 0.785658i | \(-0.287676\pi\) | |||||||
\(192\) | 188.630 | + | 326.716i | 0.0709020 | + | 0.122806i | ||||
\(193\) | − | 3163.55i | − | 1.17988i | −0.807446 | − | 0.589942i | \(-0.799151\pi\) | ||
0.807446 | − | 0.589942i | \(-0.200849\pi\) | |||||||
\(194\) | −1439.22 | + | 2492.80i | −0.532629 | + | 0.922540i | ||||
\(195\) | −6293.50 | −2.31121 | ||||||||
\(196\) | 349.923 | 0.127523 | ||||||||
\(197\) | 1936.99 | − | 3354.97i | 0.700532 | − | 1.21336i | −0.267747 | − | 0.963489i | \(-0.586279\pi\) |
0.968280 | − | 0.249869i | \(-0.0803874\pi\) | |||||||
\(198\) | 831.496 | − | 480.064i | 0.298444 | − | 0.172306i | ||||
\(199\) | 4004.97i | 1.42666i | 0.700830 | + | 0.713328i | \(0.252813\pi\) | ||||
−0.700830 | + | 0.713328i | \(0.747187\pi\) | |||||||
\(200\) | −652.436 | − | 376.684i | −0.230671 | − | 0.133178i | ||||
\(201\) | 207.234 | − | 358.940i | 0.0727222 | − | 0.125959i | ||||
\(202\) | 1248.27 | + | 720.687i | 0.434791 | + | 0.251026i | ||||
\(203\) | 791.588 | − | 457.023i | 0.273687 | − | 0.158014i | ||||
\(204\) | 2311.60 | − | 1334.60i | 0.793354 | − | 0.458043i | ||||
\(205\) | 3423.56 | + | 1976.60i | 1.16640 | + | 0.673422i | ||||
\(206\) | 1173.72 | − | 2032.95i | 0.396976 | − | 0.687583i | ||||
\(207\) | −657.801 | − | 379.782i | −0.220871 | − | 0.127520i | ||||
\(208\) | − | 1153.88i | − | 0.384650i | ||||||
\(209\) | −8276.67 | + | 4778.54i | −2.73928 | + | 1.58152i | ||||
\(210\) | 1394.97 | − | 2416.15i | 0.458390 | − | 0.793954i | ||||
\(211\) | 341.370 | 0.111378 | 0.0556892 | − | 0.998448i | \(-0.482264\pi\) | ||||
0.0556892 | + | 0.998448i | \(0.482264\pi\) | |||||||
\(212\) | −1228.93 | −0.398128 | ||||||||
\(213\) | 547.776 | − | 948.775i | 0.176211 | − | 0.305207i | ||||
\(214\) | 113.130i | 0.0361375i | ||||||||
\(215\) | −2109.35 | − | 3653.50i | −0.669100 | − | 1.15892i | ||||
\(216\) | 907.911i | 0.285998i | ||||||||
\(217\) | 301.019 | − | 173.793i | 0.0941682 | − | 0.0543680i | ||||
\(218\) | 673.019 | + | 1165.70i | 0.209094 | + | 0.362162i | ||||
\(219\) | −849.913 | − | 1472.09i | −0.262246 | − | 0.454223i | ||||
\(220\) | −3177.86 | − | 1834.74i | −0.973869 | − | 0.562263i | ||||
\(221\) | −8163.97 | −2.48492 | ||||||||
\(222\) | −2589.60 | + | 578.097i | −0.782893 | + | 0.174772i | ||||
\(223\) | −2802.47 | −0.841558 | −0.420779 | − | 0.907163i | \(-0.638243\pi\) | ||||
−0.420779 | + | 0.907163i | \(0.638243\pi\) | |||||||
\(224\) | 442.989 | + | 255.760i | 0.132136 | + | 0.0762886i | ||||
\(225\) | 364.783 | + | 631.823i | 0.108084 | + | 0.187207i | ||||
\(226\) | −840.632 | − | 1456.02i | −0.247425 | − | 0.428552i | ||||
\(227\) | 3662.63 | − | 2114.62i | 1.07091 | − | 0.618292i | 0.142482 | − | 0.989797i | \(-0.454492\pi\) |
0.928431 | + | 0.371506i | \(0.121158\pi\) | |||||||
\(228\) | 3636.58i | 1.05631i | ||||||||
\(229\) | −1873.19 | − | 3244.46i | −0.540540 | − | 0.936244i | −0.998873 | − | 0.0474628i | \(-0.984886\pi\) |
0.458333 | − | 0.888781i | \(-0.348447\pi\) | |||||||
\(230\) | 2902.94i | 0.832237i | ||||||||
\(231\) | 2919.40 | − | 5056.56i | 0.831527 | − | 1.44025i | ||||
\(232\) | −457.453 | −0.129454 | ||||||||
\(233\) | −594.717 | −0.167215 | −0.0836077 | − | 0.996499i | \(-0.526644\pi\) | ||||
−0.0836077 | + | 0.996499i | \(0.526644\pi\) | |||||||
\(234\) | −558.711 | + | 967.716i | −0.156086 | + | 0.270349i | ||||
\(235\) | 2038.40 | − | 1176.87i | 0.565831 | − | 0.326683i | ||||
\(236\) | 723.443i | 0.199543i | ||||||||
\(237\) | −312.170 | − | 180.232i | −0.0855596 | − | 0.0493979i | ||||
\(238\) | 1809.56 | − | 3134.25i | 0.492842 | − | 0.853627i | ||||
\(239\) | 2245.54 | + | 1296.46i | 0.607749 | + | 0.350884i | 0.772084 | − | 0.635521i | \(-0.219215\pi\) |
−0.164335 | + | 0.986405i | \(0.552548\pi\) | |||||||
\(240\) | −1209.21 | + | 698.139i | −0.325226 | + | 0.187769i | ||||
\(241\) | −270.788 | + | 156.340i | −0.0723776 | + | 0.0417872i | −0.535752 | − | 0.844375i | \(-0.679972\pi\) |
0.463374 | + | 0.886163i | \(0.346639\pi\) | |||||||
\(242\) | −4345.31 | − | 2508.76i | −1.15424 | − | 0.666403i | ||||
\(243\) | 1056.12 | − | 1829.26i | 0.278808 | − | 0.482910i | ||||
\(244\) | 1374.86 | + | 793.774i | 0.360722 | + | 0.208263i | ||||
\(245\) | 1295.10i | 0.337718i | ||||||||
\(246\) | 2726.32 | − | 1574.04i | 0.706601 | − | 0.407956i | ||||
\(247\) | 5561.39 | − | 9632.60i | 1.43264 | − | 2.48141i | ||||
\(248\) | −173.957 | −0.0445414 | ||||||||
\(249\) | −874.491 | −0.222565 | ||||||||
\(250\) | −456.404 | + | 790.516i | −0.115462 | + | 0.199986i | ||||
\(251\) | 5558.17i | 1.39772i | 0.715257 | + | 0.698861i | \(0.246309\pi\) | ||||
−0.715257 | + | 0.698861i | \(0.753691\pi\) | |||||||
\(252\) | −247.679 | − | 428.992i | −0.0619139 | − | 0.107238i | ||||
\(253\) | 6075.32i | 1.50969i | ||||||||
\(254\) | 2000.19 | − | 1154.81i | 0.494106 | − | 0.285272i | ||||
\(255\) | 4939.50 | + | 8555.47i | 1.21303 | + | 2.10104i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2580.24 | + | 1489.70i | 0.626269 | + | 0.361576i | 0.779306 | − | 0.626644i | \(-0.215572\pi\) |
−0.153037 | + | 0.988220i | \(0.548905\pi\) | |||||||
\(258\) | −3359.52 | −0.810677 | ||||||||
\(259\) | −2648.86 | + | 2434.41i | −0.635491 | + | 0.584042i | ||||
\(260\) | 4270.63 | 1.01867 | ||||||||
\(261\) | 383.649 | + | 221.500i | 0.0909857 | + | 0.0525306i | ||||
\(262\) | −889.490 | − | 1540.64i | −0.209744 | − | 0.363287i | ||||
\(263\) | −119.867 | − | 207.616i | −0.0281039 | − | 0.0486774i | 0.851631 | − | 0.524141i | \(-0.175614\pi\) |
−0.879735 | + | 0.475464i | \(0.842280\pi\) | |||||||
\(264\) | −2530.66 | + | 1461.07i | −0.589966 | + | 0.340617i | ||||
\(265\) | − | 4548.39i | − | 1.05436i | ||||||
\(266\) | 2465.38 | + | 4270.17i | 0.568280 | + | 0.984289i | ||||
\(267\) | 4508.37i | 1.03336i | ||||||||
\(268\) | −140.624 | + | 243.569i | −0.0320523 | + | 0.0555162i | ||||
\(269\) | 8302.50 | 1.88183 | 0.940915 | − | 0.338642i | \(-0.109968\pi\) | ||||
0.940915 | + | 0.338642i | \(0.109968\pi\) | |||||||
\(270\) | −3360.27 | −0.757407 | ||||||||
\(271\) | −202.453 | + | 350.658i | −0.0453806 | + | 0.0786014i | −0.887823 | − | 0.460184i | \(-0.847783\pi\) |
0.842443 | + | 0.538786i | \(0.181117\pi\) | |||||||
\(272\) | −1568.60 | + | 905.631i | −0.349670 | + | 0.201882i | ||||
\(273\) | 6795.36i | 1.50650i | ||||||||
\(274\) | 1275.95 | + | 736.672i | 0.281325 | + | 0.162423i | ||||
\(275\) | 2917.69 | − | 5053.60i | 0.639795 | − | 1.10816i | ||||
\(276\) | 2002.02 | + | 1155.87i | 0.436621 | + | 0.252083i | ||||
\(277\) | −1877.73 | + | 1084.11i | −0.407299 | + | 0.235154i | −0.689629 | − | 0.724163i | \(-0.742226\pi\) |
0.282329 | + | 0.959318i | \(0.408893\pi\) | |||||||
\(278\) | 922.825 | − | 532.793i | 0.199091 | − | 0.114945i | ||||
\(279\) | 145.891 | + | 84.2303i | 0.0313056 | + | 0.0180743i | ||||
\(280\) | −946.594 | + | 1639.55i | −0.202035 | + | 0.349935i | ||||
\(281\) | 3686.49 | + | 2128.40i | 0.782625 | + | 0.451849i | 0.837360 | − | 0.546652i | \(-0.184098\pi\) |
−0.0547345 | + | 0.998501i | \(0.517431\pi\) | |||||||
\(282\) | − | 1874.38i | − | 0.395806i | ||||||
\(283\) | 4246.17 | − | 2451.53i | 0.891903 | − | 0.514940i | 0.0173386 | − | 0.999850i | \(-0.494481\pi\) |
0.874565 | + | 0.484909i | \(0.161147\pi\) | |||||||
\(284\) | −371.709 | + | 643.818i | −0.0776650 | + | 0.134520i | ||||
\(285\) | −13459.4 | −2.79742 | ||||||||
\(286\) | 8937.64 | 1.84788 | ||||||||
\(287\) | 2134.22 | − | 3696.57i | 0.438950 | − | 0.760284i | ||||
\(288\) | 247.912i | 0.0507234i | ||||||||
\(289\) | 3951.06 | + | 6843.43i | 0.804204 | + | 1.39292i | ||||
\(290\) | − | 1693.08i | − | 0.342832i | ||||||
\(291\) | −7347.14 | + | 4241.87i | −1.48006 | + | 0.854512i | ||||
\(292\) | 576.732 | + | 998.930i | 0.115585 | + | 0.200198i | ||||
\(293\) | −1288.87 | − | 2232.39i | −0.256985 | − | 0.445111i | 0.708448 | − | 0.705763i | \(-0.249396\pi\) |
−0.965433 | + | 0.260652i | \(0.916062\pi\) | |||||||
\(294\) | 893.167 | + | 515.670i | 0.177179 | + | 0.102294i | ||||
\(295\) | −2677.54 | −0.528449 | ||||||||
\(296\) | 1757.24 | − | 392.284i | 0.345060 | − | 0.0770306i | ||||
\(297\) | −7032.43 | −1.37395 | ||||||||
\(298\) | −2745.07 | − | 1584.87i | −0.533616 | − | 0.308084i | ||||
\(299\) | −3535.31 | − | 6123.34i | −0.683787 | − | 1.18435i | ||||
\(300\) | −1110.22 | − | 1922.95i | −0.213661 | − | 0.370072i | ||||
\(301\) | −3944.84 | + | 2277.56i | −0.755405 | + | 0.436133i | ||||
\(302\) | − | 7318.60i | − | 1.39450i | ||||||
\(303\) | 2124.11 | + | 3679.06i | 0.402729 | + | 0.697547i | ||||
\(304\) | − | 2467.70i | − | 0.465567i | ||||||
\(305\) | −2937.84 | + | 5088.49i | −0.551542 | + | 0.955299i | ||||
\(306\) | 1754.03 | 0.327685 | ||||||||
\(307\) | 4731.35 | 0.879584 | 0.439792 | − | 0.898100i | \(-0.355052\pi\) | ||||
0.439792 | + | 0.898100i | \(0.355052\pi\) | |||||||
\(308\) | −1981.04 | + | 3431.27i | −0.366495 | + | 0.634788i | ||||
\(309\) | 5991.78 | − | 3459.36i | 1.10311 | − | 0.636880i | ||||
\(310\) | − | 643.832i | − | 0.117959i | ||||||
\(311\) | 7106.55 | + | 4102.97i | 1.29574 | + | 0.748096i | 0.979666 | − | 0.200638i | \(-0.0643014\pi\) |
0.316075 | + | 0.948734i | \(0.397635\pi\) | |||||||
\(312\) | 1700.44 | − | 2945.24i | 0.308552 | − | 0.534428i | ||||
\(313\) | 4986.53 | + | 2878.98i | 0.900496 | + | 0.519902i | 0.877361 | − | 0.479830i | \(-0.159302\pi\) |
0.0231353 | + | 0.999732i | \(0.492635\pi\) | |||||||
\(314\) | 2518.14 | − | 1453.85i | 0.452570 | − | 0.261291i | ||||
\(315\) | 1587.75 | − | 916.686i | 0.283998 | − | 0.163966i | ||||
\(316\) | 211.832 | + | 122.301i | 0.0377104 | + | 0.0217721i | ||||
\(317\) | 946.647 | − | 1639.64i | 0.167726 | − | 0.290509i | −0.769894 | − | 0.638171i | \(-0.779691\pi\) |
0.937620 | + | 0.347662i | \(0.113024\pi\) | |||||||
\(318\) | −3136.80 | − | 1811.03i | −0.553155 | − | 0.319364i | ||||
\(319\) | − | 3543.31i | − | 0.621903i | ||||||
\(320\) | 820.545 | − | 473.742i | 0.143343 | − | 0.0827593i | ||||
\(321\) | −166.717 | + | 288.762i | −0.0289882 | + | 0.0502090i | ||||
\(322\) | 3134.43 | 0.542469 | ||||||||
\(323\) | −17459.6 | −3.00767 | ||||||||
\(324\) | −1756.31 | + | 3042.02i | −0.301151 | + | 0.521609i | ||||
\(325\) | 6791.38i | 1.15913i | ||||||||
\(326\) | 3564.59 | + | 6174.06i | 0.605597 | + | 1.04892i | ||||
\(327\) | 3967.23i | 0.670912i | ||||||||
\(328\) | −1850.02 | + | 1068.11i | −0.311434 | + | 0.179807i | ||||
\(329\) | −1270.72 | − | 2200.94i | −0.212939 | − | 0.368821i | ||||
\(330\) | −5407.59 | − | 9366.23i | −0.902055 | − | 1.56241i | ||||
\(331\) | −855.947 | − | 494.181i | −0.142136 | − | 0.0820624i | 0.427246 | − | 0.904136i | \(-0.359484\pi\) |
−0.569382 | + | 0.822073i | \(0.692817\pi\) | |||||||
\(332\) | 593.410 | 0.0980953 | ||||||||
\(333\) | −1663.68 | − | 521.867i | −0.273781 | − | 0.0858804i | ||||
\(334\) | −3436.33 | −0.562957 | ||||||||
\(335\) | −901.474 | − | 520.466i | −0.147023 | − | 0.0848839i | ||||
\(336\) | 753.810 | + | 1305.64i | 0.122392 | + | 0.211989i | ||||
\(337\) | 1551.11 | + | 2686.60i | 0.250725 | + | 0.434268i | 0.963726 | − | 0.266895i | \(-0.0859978\pi\) |
−0.713001 | + | 0.701163i | \(0.752664\pi\) | |||||||
\(338\) | −5202.96 | + | 3003.93i | −0.837289 | + | 0.483409i | ||||
\(339\) | − | 4955.25i | − | 0.793901i | ||||||
\(340\) | −3351.84 | − | 5805.55i | −0.534644 | − | 0.926030i | ||||
\(341\) | − | 1347.42i | − | 0.213979i | ||||||
\(342\) | −1194.87 | + | 2069.57i | −0.188921 | + | 0.327221i | ||||
\(343\) | 6881.22 | 1.08324 | ||||||||
\(344\) | 2279.70 | 0.357305 | ||||||||
\(345\) | −4277.98 | + | 7409.68i | −0.667591 | + | 1.15630i | ||||
\(346\) | 2534.78 | − | 1463.46i | 0.393846 | − | 0.227387i | ||||
\(347\) | − | 5312.58i | − | 0.821886i | −0.911661 | − | 0.410943i | \(-0.865200\pi\) | ||
0.911661 | − | 0.410943i | \(-0.134800\pi\) | |||||||
\(348\) | −1167.64 | − | 674.135i | −0.179862 | − | 0.103843i | ||||
\(349\) | −934.352 | + | 1618.34i | −0.143309 | + | 0.248218i | −0.928741 | − | 0.370730i | \(-0.879107\pi\) |
0.785432 | + | 0.618948i | \(0.212441\pi\) | |||||||
\(350\) | −2607.29 | − | 1505.32i | −0.398188 | − | 0.229894i | ||||
\(351\) | 7088.01 | − | 4092.26i | 1.07786 | − | 0.622304i | ||||
\(352\) | 1717.25 | − | 991.453i | 0.260027 | − | 0.150127i | ||||
\(353\) | 574.118 | + | 331.467i | 0.0865644 | + | 0.0499780i | 0.542657 | − | 0.839954i | \(-0.317418\pi\) |
−0.456093 | + | 0.889932i | \(0.650752\pi\) | |||||||
\(354\) | −1066.12 | + | 1846.57i | −0.160066 | + | 0.277243i | ||||
\(355\) | −2382.84 | − | 1375.73i | −0.356248 | − | 0.205680i | ||||
\(356\) | − | 3059.28i | − | 0.455454i | ||||||
\(357\) | 9237.70 | − | 5333.39i | 1.36950 | − | 0.790680i | ||||
\(358\) | −503.727 | + | 872.481i | −0.0743654 | + | 0.128805i | ||||
\(359\) | −599.390 | −0.0881187 | −0.0440593 | − | 0.999029i | \(-0.514029\pi\) | ||||
−0.0440593 | + | 0.999029i | \(0.514029\pi\) | |||||||
\(360\) | −917.548 | −0.134331 | ||||||||
\(361\) | 8464.15 | − | 14660.3i | 1.23402 | − | 2.13739i | ||||
\(362\) | − | 362.878i | − | 0.0526863i | ||||||
\(363\) | −7394.18 | − | 12807.1i | −1.06913 | − | 1.85179i | ||||
\(364\) | − | 4611.18i | − | 0.663988i | ||||||
\(365\) | −3697.15 | + | 2134.55i | −0.530185 | + | 0.306102i | ||||
\(366\) | 2339.52 | + | 4052.17i | 0.334122 | + | 0.578717i | ||||
\(367\) | 5215.42 | + | 9033.37i | 0.741806 | + | 1.28485i | 0.951672 | + | 0.307115i | \(0.0993637\pi\) |
−0.209867 | + | 0.977730i | \(0.567303\pi\) | |||||||
\(368\) | −1358.53 | − | 784.345i | −0.192440 | − | 0.111105i | ||||
\(369\) | 2068.73 | 0.291853 | ||||||||
\(370\) | 1451.89 | + | 6503.75i | 0.204000 | + | 0.913821i | ||||
\(371\) | −4911.10 | −0.687254 | ||||||||
\(372\) | −444.019 | − | 256.355i | −0.0618853 | − | 0.0357295i | ||||
\(373\) | −1029.35 | − | 1782.89i | −0.142890 | − | 0.247492i | 0.785694 | − | 0.618615i | \(-0.212306\pi\) |
−0.928584 | + | 0.371123i | \(0.878973\pi\) | |||||||
\(374\) | −7014.77 | − | 12149.9i | −0.969853 | − | 1.67984i | ||||
\(375\) | −2329.92 | + | 1345.18i | −0.320844 | + | 0.185239i | ||||
\(376\) | 1271.91i | 0.174451i | ||||||||
\(377\) | 2061.90 | + | 3571.31i | 0.281679 | + | 0.487883i | ||||
\(378\) | 3628.23i | 0.493693i | ||||||||
\(379\) | 1494.70 | − | 2588.90i | 0.202579 | − | 0.350878i | −0.746779 | − | 0.665072i | \(-0.768401\pi\) |
0.949359 | + | 0.314194i | \(0.101734\pi\) | |||||||
\(380\) | 9133.23 | 1.23296 | ||||||||
\(381\) | 6807.23 | 0.915341 | ||||||||
\(382\) | −4147.76 | + | 7184.13i | −0.555544 | + | 0.962231i | ||||
\(383\) | −1002.81 | + | 578.970i | −0.133788 | + | 0.0772428i | −0.565400 | − | 0.824817i | \(-0.691278\pi\) |
0.431612 | + | 0.902059i | \(0.357945\pi\) | |||||||
\(384\) | − | 754.519i | − | 0.100271i | ||||||
\(385\) | −12699.5 | − | 7332.06i | −1.68111 | − | 0.970588i | ||||
\(386\) | −3163.55 | + | 5479.44i | −0.417152 | + | 0.722529i | ||||
\(387\) | −1911.90 | − | 1103.83i | −0.251130 | − | 0.144990i | ||||
\(388\) | 4985.61 | − | 2878.44i | 0.652335 | − | 0.376626i | ||||
\(389\) | −373.885 | + | 215.863i | −0.0487319 | + | 0.0281354i | −0.524168 | − | 0.851615i | \(-0.675624\pi\) |
0.475436 | + | 0.879750i | \(0.342290\pi\) | |||||||
\(390\) | 10900.7 | + | 6293.50i | 1.41532 | + | 0.817138i | ||||
\(391\) | −5549.43 | + | 9611.89i | −0.717767 | + | 1.24321i | ||||
\(392\) | −606.084 | − | 349.923i | −0.0780914 | − | 0.0450861i | ||||
\(393\) | − | 5243.26i | − | 0.672996i | ||||||
\(394\) | −6709.93 | + | 3873.98i | −0.857974 | + | 0.495351i | ||||
\(395\) | −452.650 | + | 784.012i | −0.0576589 | + | 0.0998682i | ||||
\(396\) | −1920.26 | −0.243678 | ||||||||
\(397\) | 3984.93 | 0.503773 | 0.251887 | − | 0.967757i | \(-0.418949\pi\) | ||||
0.251887 | + | 0.967757i | \(0.418949\pi\) | |||||||
\(398\) | 4004.97 | − | 6936.81i | 0.504399 | − | 0.873645i | ||||
\(399\) | 14532.6i | 1.82341i | ||||||||
\(400\) | 753.369 | + | 1304.87i | 0.0941711 | + | 0.163109i | ||||
\(401\) | − | 7633.43i | − | 0.950612i | −0.879821 | − | 0.475306i | \(-0.842337\pi\) | ||
0.879821 | − | 0.475306i | \(-0.157663\pi\) | |||||||
\(402\) | −717.880 | + | 414.468i | −0.0890661 | + | 0.0514224i | ||||
\(403\) | 784.082 | + | 1358.07i | 0.0969179 | + | 0.167867i | ||||
\(404\) | −1441.37 | − | 2496.53i | −0.177503 | − | 0.307443i | ||||
\(405\) | −11258.8 | − | 6500.30i | −1.38137 | − | 0.797537i | ||||
\(406\) | −1828.09 | −0.223465 | ||||||||
\(407\) | 3038.53 | + | 13611.1i | 0.370059 | + | 1.65769i | ||||
\(408\) | −5338.40 | −0.647770 | ||||||||
\(409\) | −8850.71 | − | 5109.96i | −1.07002 | − | 0.617778i | −0.141836 | − | 0.989890i | \(-0.545300\pi\) |
−0.928188 | + | 0.372112i | \(0.878634\pi\) | |||||||
\(410\) | −3953.19 | − | 6847.13i | −0.476181 | − | 0.824770i | ||||
\(411\) | 2171.22 | + | 3760.67i | 0.260580 | + | 0.451338i | ||||
\(412\) | −4065.89 | + | 2347.44i | −0.486195 | + | 0.280705i | ||||
\(413\) | 2891.05i | 0.344454i | ||||||||
\(414\) | 759.564 | + | 1315.60i | 0.0901703 | + | 0.156180i | ||||
\(415\) | 2196.28i | 0.259785i | ||||||||
\(416\) | −1153.88 | + | 1998.58i | −0.135994 | + | 0.235549i | ||||
\(417\) | 3140.65 | 0.368820 | ||||||||
\(418\) | 19114.1 | 2.23661 | ||||||||
\(419\) | −2299.93 | + | 3983.59i | −0.268160 | + | 0.464466i | −0.968387 | − | 0.249454i | \(-0.919749\pi\) |
0.700227 | + | 0.713920i | \(0.253082\pi\) | |||||||
\(420\) | −4832.30 | + | 2789.93i | −0.561410 | + | 0.324130i | ||||
\(421\) | − | 9688.62i | − | 1.12160i | −0.827951 | − | 0.560801i | \(-0.810493\pi\) | ||
0.827951 | − | 0.560801i | \(-0.189507\pi\) | |||||||
\(422\) | −591.270 | − | 341.370i | −0.0682051 | − | 0.0393782i | ||||
\(423\) | 615.862 | − | 1066.70i | 0.0707902 | − | 0.122612i | ||||
\(424\) | 2128.57 | + | 1228.93i | 0.243803 | + | 0.140759i | ||||
\(425\) | 9232.29 | − | 5330.26i | 1.05372 | − | 0.608367i | ||||
\(426\) | −1897.55 | + | 1095.55i | −0.215814 | + | 0.124600i | ||||
\(427\) | 5494.26 | + | 3172.11i | 0.622684 | + | 0.359507i | ||||
\(428\) | 113.130 | − | 195.947i | 0.0127765 | − | 0.0221296i | ||||
\(429\) | 22813.1 | + | 13171.1i | 2.56742 | + | 1.48230i | ||||
\(430\) | 8437.40i | 0.946250i | ||||||||
\(431\) | −5201.84 | + | 3003.29i | −0.581355 | + | 0.335645i | −0.761672 | − | 0.647963i | \(-0.775621\pi\) |
0.180317 | + | 0.983609i | \(0.442288\pi\) | |||||||
\(432\) | 907.911 | − | 1572.55i | 0.101115 | − | 0.175137i | ||||
\(433\) | −14921.2 | −1.65605 | −0.828023 | − | 0.560695i | \(-0.810534\pi\) | ||||
−0.828023 | + | 0.560695i | \(0.810534\pi\) | |||||||
\(434\) | −695.173 | −0.0768880 | ||||||||
\(435\) | 2495.04 | − | 4321.54i | 0.275007 | − | 0.476327i | ||||
\(436\) | − | 2692.08i | − | 0.295704i | ||||||
\(437\) | −7560.66 | − | 13095.4i | −0.827632 | − | 1.43350i | ||||
\(438\) | 3399.65i | 0.370871i | ||||||||
\(439\) | 11456.7 | − | 6614.50i | 1.24555 | − | 0.719119i | 0.275331 | − | 0.961349i | \(-0.411212\pi\) |
0.970219 | + | 0.242231i | \(0.0778792\pi\) | |||||||
\(440\) | 3669.47 | + | 6355.72i | 0.397580 | + | 0.688629i | ||||
\(441\) | 338.867 | + | 586.934i | 0.0365907 | + | 0.0633770i | ||||
\(442\) | 14140.4 | + | 8163.97i | 1.52170 | + | 0.878554i | ||||
\(443\) | −2250.64 | −0.241380 | −0.120690 | − | 0.992690i | \(-0.538511\pi\) | ||||
−0.120690 | + | 0.992690i | \(0.538511\pi\) | |||||||
\(444\) | 5063.41 | + | 1588.30i | 0.541214 | + | 0.169769i | ||||
\(445\) | 11322.7 | 1.20618 | ||||||||
\(446\) | 4854.02 | + | 2802.47i | 0.515347 | + | 0.297536i | ||||
\(447\) | −4671.14 | − | 8090.66i | −0.494267 | − | 0.856096i | ||||
\(448\) | −511.519 | − | 885.977i | −0.0539442 | − | 0.0934341i | ||||
\(449\) | −13347.5 | + | 7706.18i | −1.40291 | + | 0.809972i | −0.994691 | − | 0.102911i | \(-0.967184\pi\) |
−0.408222 | + | 0.912883i | \(0.633851\pi\) | |||||||
\(450\) | − | 1459.13i | − | 0.152854i | ||||||
\(451\) | −8273.30 | − | 14329.8i | −0.863801 | − | 1.49615i | ||||
\(452\) | 3362.53i | 0.349911i | ||||||||
\(453\) | 10785.2 | − | 18680.5i | 1.11862 | − | 1.93750i | ||||
\(454\) | −8458.48 | −0.874397 | ||||||||
\(455\) | 17066.5 | 1.75844 | ||||||||
\(456\) | 3636.58 | − | 6298.73i | 0.373461 | − | 0.646854i | ||||
\(457\) | −10629.9 | + | 6137.15i | −1.08806 | + | 0.628192i | −0.933059 | − | 0.359722i | \(-0.882871\pi\) |
−0.155001 | + | 0.987914i | \(0.549538\pi\) | |||||||
\(458\) | 7492.75i | 0.764440i | ||||||||
\(459\) | −11126.2 | − | 6423.69i | −1.13143 | − | 0.653229i | ||||
\(460\) | 2902.94 | − | 5028.05i | 0.294240 | − | 0.509639i | ||||
\(461\) | 5574.27 | + | 3218.31i | 0.563167 | + | 0.325144i | 0.754416 | − | 0.656397i | \(-0.227920\pi\) |
−0.191249 | + | 0.981542i | \(0.561254\pi\) | |||||||
\(462\) | −10113.1 | + | 5838.81i | −1.01841 | + | 0.587978i | ||||
\(463\) | −2224.57 | + | 1284.36i | −0.223293 | + | 0.128918i | −0.607474 | − | 0.794340i | \(-0.707817\pi\) |
0.384181 | + | 0.923258i | \(0.374484\pi\) | |||||||
\(464\) | 792.332 | + | 457.453i | 0.0792739 | + | 0.0457688i | ||||
\(465\) | 948.796 | − | 1643.36i | 0.0946223 | − | 0.163891i | ||||
\(466\) | 1030.08 | + | 594.717i | 0.102398 | + | 0.0591196i | ||||
\(467\) | 7436.06i | 0.736831i | 0.929661 | + | 0.368415i | \(0.120100\pi\) | ||||
−0.929661 | + | 0.368415i | \(0.879900\pi\) | |||||||
\(468\) | 1935.43 | − | 1117.42i | 0.191165 | − | 0.110369i | ||||
\(469\) | −561.970 | + | 973.360i | −0.0553291 | + | 0.0958328i | ||||
\(470\) | −4707.47 | −0.461999 | ||||||||
\(471\) | 8569.98 | 0.838394 | ||||||||
\(472\) | 723.443 | − | 1253.04i | 0.0705491 | − | 0.122195i | ||||
\(473\) | 17657.9i | 1.71651i | ||||||||
\(474\) | 360.463 | + | 624.340i | 0.0349296 | + | 0.0604998i | ||||
\(475\) | 14524.1i | 1.40297i | ||||||||
\(476\) | −6268.50 | + | 3619.12i | −0.603606 | + | 0.348492i | ||||
\(477\) | −1190.10 | − | 2061.31i | −0.114237 | − | 0.197864i | ||||
\(478\) | −2592.93 | − | 4491.08i | −0.248112 | − | 0.429743i | ||||
\(479\) | −7043.00 | − | 4066.28i | −0.671822 | − | 0.387877i | 0.124944 | − | 0.992164i | \(-0.460125\pi\) |
−0.796767 | + | 0.604287i | \(0.793458\pi\) | |||||||
\(480\) | 2792.56 | 0.265546 | ||||||||
\(481\) | −10983.0 | − | 11950.5i | −1.04113 | − | 1.13284i | ||||
\(482\) | 625.359 | 0.0590961 | ||||||||
\(483\) | 8000.55 | + | 4619.12i | 0.753701 | + | 0.435149i | ||||
\(484\) | 5017.53 | + | 8690.61i | 0.471218 | + | 0.816173i | ||||
\(485\) | 10653.4 | + | 18452.3i | 0.997416 | + | 1.72758i | ||||
\(486\) | −3658.52 | + | 2112.25i | −0.341469 | + | 0.197147i | ||||
\(487\) | 6484.10i | 0.603331i | 0.953414 | + | 0.301666i | \(0.0975426\pi\) | ||||
−0.953414 | + | 0.301666i | \(0.902457\pi\) | |||||||
\(488\) | −1587.55 | − | 2749.71i | −0.147264 | − | 0.255069i | ||||
\(489\) | 21012.1i | 1.94315i | ||||||||
\(490\) | 1295.10 | − | 2243.18i | 0.119401 | − | 0.206809i | ||||
\(491\) | 6392.20 | 0.587528 | 0.293764 | − | 0.955878i | \(-0.405092\pi\) | ||||
0.293764 | + | 0.955878i | \(0.405092\pi\) | |||||||
\(492\) | −6296.17 | −0.576938 | ||||||||
\(493\) | 3236.59 | − | 5605.94i | 0.295677 | − | 0.512127i | ||||
\(494\) | −19265.2 | + | 11122.8i | −1.75462 | + | 1.01303i | ||||
\(495\) | − | 7107.08i | − | 0.645332i | ||||||
\(496\) | 301.302 | + | 173.957i | 0.0272759 | + | 0.0157478i | ||||
\(497\) | −1485.44 | + | 2572.85i | −0.134066 | + | 0.232210i | ||||
\(498\) | 1514.66 | + | 874.491i | 0.136292 | + | 0.0786885i | ||||
\(499\) | −5658.15 | + | 3266.74i | −0.507603 | + | 0.293065i | −0.731848 | − | 0.681468i | \(-0.761342\pi\) |
0.224245 | + | 0.974533i | \(0.428008\pi\) | |||||||
\(500\) | 1581.03 | − | 912.809i | 0.141412 | − | 0.0816441i | ||||
\(501\) | −8771.13 | − | 5064.01i | −0.782166 | − | 0.451584i | ||||
\(502\) | 5558.17 | − | 9627.02i | 0.494169 | − | 0.855927i | ||||
\(503\) | −9348.15 | − | 5397.16i | −0.828655 | − | 0.478424i | 0.0247371 | − | 0.999694i | \(-0.492125\pi\) |
−0.853392 | + | 0.521270i | \(0.825458\pi\) | |||||||
\(504\) | 990.715i | 0.0875595i | ||||||||
\(505\) | 9239.93 | − | 5334.68i | 0.814201 | − | 0.470079i | ||||
\(506\) | 6075.32 | − | 10522.8i | 0.533757 | − | 0.924494i | ||||
\(507\) | −17707.2 | −1.55109 | ||||||||
\(508\) | −4619.24 | −0.403436 | ||||||||
\(509\) | 8965.70 | − | 15529.1i | 0.780742 | − | 1.35229i | −0.150768 | − | 0.988569i | \(-0.548175\pi\) |
0.931510 | − | 0.363716i | \(-0.118492\pi\) | |||||||
\(510\) | − | 19758.0i | − | 1.71549i | ||||||
\(511\) | 2304.76 | + | 3991.97i | 0.199524 | + | 0.345586i | ||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 15158.5 | − | 8751.77i | 1.30461 | − | 0.753216i | ||||
\(514\) | −2979.41 | − | 5160.48i | −0.255673 | − | 0.442839i | ||||
\(515\) | −8688.14 | − | 15048.3i | −0.743389 | − | 1.28759i | ||||
\(516\) | 5818.86 | + | 3359.52i | 0.496436 | + | 0.286617i | ||||
\(517\) | −9851.87 | −0.838075 | ||||||||
\(518\) | 7022.37 | − | 1567.66i | 0.595647 | − | 0.132971i | ||||
\(519\) | 8626.61 | 0.729607 | ||||||||
\(520\) | −7396.95 | − | 4270.63i | −0.623803 | − | 0.360153i | ||||
\(521\) | 7843.60 | + | 13585.5i | 0.659567 | + | 1.14240i | 0.980728 | + | 0.195378i | \(0.0625935\pi\) |
−0.321161 | + | 0.947025i | \(0.604073\pi\) | |||||||
\(522\) | −443.000 | − | 767.298i | −0.0371448 | − | 0.0643366i | ||||
\(523\) | −5658.12 | + | 3266.72i | −0.473064 | + | 0.273123i | −0.717521 | − | 0.696537i | \(-0.754723\pi\) |
0.244458 | + | 0.969660i | \(0.421390\pi\) | |||||||
\(524\) | 3557.96i | 0.296623i | ||||||||
\(525\) | −4436.70 | − | 7684.58i | −0.368825 | − | 0.638824i | ||||
\(526\) | 479.469i | 0.0397449i | ||||||||
\(527\) | 1230.79 | − | 2131.78i | 0.101734 | − | 0.176209i | ||||
\(528\) | 5844.30 | 0.481705 | ||||||||
\(529\) | 2554.55 | 0.209957 | ||||||||
\(530\) | −4548.39 | + | 7878.05i | −0.372773 | + | 0.645662i | ||||
\(531\) | −1213.45 | + | 700.586i | −0.0991700 | + | 0.0572558i | ||||
\(532\) | − | 9861.53i | − | 0.803669i | ||||||
\(533\) | 16677.4 | + | 9628.68i | 1.35530 | + | 0.782485i | ||||
\(534\) | 4508.37 | − | 7808.73i | 0.365349 | − | 0.632803i | ||||
\(535\) | 725.222 | + | 418.707i | 0.0586057 | + | 0.0338360i | ||||
\(536\) | 487.137 | − | 281.249i | 0.0392558 | − | 0.0226644i | ||||
\(537\) | −2571.50 | + | 1484.66i | −0.206645 | + | 0.119307i | ||||
\(538\) | −14380.4 | − | 8302.50i | −1.15238 | − | 0.665328i | ||||
\(539\) | 2710.41 | − | 4694.56i | 0.216596 | − | 0.375156i | ||||
\(540\) | 5820.17 | + | 3360.27i | 0.463815 | + | 0.267784i | ||||
\(541\) | 16257.5i | 1.29198i | 0.763345 | + | 0.645991i | \(0.223556\pi\) | ||||
−0.763345 | + | 0.645991i | \(0.776444\pi\) | |||||||
\(542\) | 701.317 | − | 404.906i | 0.0555796 | − | 0.0320889i | ||||
\(543\) | 534.762 | − | 926.235i | 0.0422630 | − | 0.0732017i | ||||
\(544\) | 3622.52 | 0.285504 | ||||||||
\(545\) | 9963.66 | 0.783112 | ||||||||
\(546\) | 6795.36 | − | 11769.9i | 0.532627 | − | 0.922538i | ||||
\(547\) | 14045.8i | 1.09791i | 0.835853 | + | 0.548953i | \(0.184973\pi\) | ||||
−0.835853 | + | 0.548953i | \(0.815027\pi\) | |||||||
\(548\) | −1473.34 | − | 2551.91i | −0.114851 | − | 0.198927i | ||||
\(549\) | 3074.78i | 0.239032i | ||||||||
\(550\) | −10107.2 | + | 5835.39i | −0.783586 | + | 0.452403i | ||||
\(551\) | 4409.60 | + | 7637.65i | 0.340935 | + | 0.590517i | ||||
\(552\) | −2311.73 | − | 4004.04i | −0.178250 | − | 0.308737i | ||||
\(553\) | 846.532 | + | 488.745i | 0.0650962 | + | 0.0375833i | ||||
\(554\) | 4336.43 | 0.332558 | ||||||||
\(555\) | −5878.48 | + | 18740.2i | −0.449599 | + | 1.43329i | ||||
\(556\) | −2131.17 | −0.162557 | ||||||||
\(557\) | −8025.74 | − | 4633.66i | −0.610523 | − | 0.352486i | 0.162647 | − | 0.986684i | \(-0.447997\pi\) |
−0.773170 | + | 0.634199i | \(0.781330\pi\) | |||||||
\(558\) | −168.461 | − | 291.782i | −0.0127805 | − | 0.0221364i | ||||
\(559\) | −10275.4 | − | 17797.5i | −0.777463 | − | 1.34661i | ||||
\(560\) | 3279.10 | − | 1893.19i | 0.247441 | − | 0.142860i | ||||
\(561\) | − | 41349.8i | − | 3.11193i | ||||||
\(562\) | −4256.80 | − | 7372.99i | −0.319506 | − | 0.553400i | ||||
\(563\) | − | 18690.5i | − | 1.39913i | −0.714568 | − | 0.699566i | \(-0.753377\pi\) | ||
0.714568 | − | 0.699566i | \(-0.246623\pi\) | |||||||
\(564\) | −1874.38 | + | 3246.51i | −0.139939 | + | 0.242381i | ||||
\(565\) | −12445.1 | −0.926669 | ||||||||
\(566\) | −9806.11 | −0.728236 | ||||||||
\(567\) | −7018.65 | + | 12156.7i | −0.519851 | + | 0.900408i | ||||
\(568\) | 1287.64 | − | 743.417i | 0.0951198 | − | 0.0549174i | ||||
\(569\) | − | 20711.5i | − | 1.52596i | −0.646424 | − | 0.762978i | \(-0.723736\pi\) | ||
0.646424 | − | 0.762978i | \(-0.276264\pi\) | |||||||
\(570\) | 23312.3 | + | 13459.4i | 1.71306 | + | 0.989036i | ||||
\(571\) | 1372.36 | − | 2377.00i | 0.100581 | − | 0.174211i | −0.811343 | − | 0.584570i | \(-0.801263\pi\) |
0.911924 | + | 0.410359i | \(0.134597\pi\) | |||||||
\(572\) | −15480.4 | − | 8937.64i | −1.13159 | − | 0.653324i | ||||
\(573\) | −21174.1 | + | 12224.9i | −1.54373 | + | 0.891276i | ||||
\(574\) | −7393.14 | + | 4268.43i | −0.537602 | + | 0.310385i | ||||
\(575\) | 7995.86 | + | 4616.41i | 0.579914 | + | 0.334813i | ||||
\(576\) | 247.912 | − | 429.396i | 0.0179334 | − | 0.0310616i | ||||
\(577\) | 18645.0 | + | 10764.7i | 1.34524 | + | 0.776673i | 0.987571 | − | 0.157176i | \(-0.0502390\pi\) |
0.357667 | + | 0.933849i | \(0.383572\pi\) | |||||||
\(578\) | − | 15804.2i | − | 1.13732i | ||||||
\(579\) | −16149.8 | + | 9324.07i | −1.15917 | + | 0.669249i | ||||
\(580\) | −1693.08 | + | 2932.50i | −0.121209 | + | 0.209941i | ||||
\(581\) | 2371.41 | 0.169333 | ||||||||
\(582\) | 16967.5 | 1.20846 | ||||||||
\(583\) | −9518.94 | + | 16487.3i | −0.676217 | + | 1.17124i | ||||
\(584\) | − | 2306.93i | − | 0.163461i | ||||||
\(585\) | 4135.70 | + | 7163.24i | 0.292291 | + | 0.506263i | ||||
\(586\) | 5155.48i | 0.363432i | ||||||||
\(587\) | −1377.12 | + | 795.080i | −0.0968309 | + | 0.0559054i | −0.547633 | − | 0.836718i | \(-0.684471\pi\) |
0.450803 | + | 0.892624i | \(0.351138\pi\) | |||||||
\(588\) | −1031.34 | − | 1786.33i | −0.0723329 | − | 0.125284i | ||||
\(589\) | 1676.85 | + | 2904.39i | 0.117306 | + | 0.203180i | ||||
\(590\) | 4637.64 | + | 2677.54i | 0.323607 | + | 0.186835i | ||||
\(591\) | −22835.9 | −1.58941 | ||||||||
\(592\) | −3435.92 | − | 1077.79i | −0.238540 | − | 0.0748257i | ||||
\(593\) | 25294.5 | 1.75164 | 0.875820 | − | 0.482638i | \(-0.160321\pi\) | ||||
0.875820 | + | 0.482638i | \(0.160321\pi\) | |||||||
\(594\) | 12180.5 | + | 7032.43i | 0.841369 | + | 0.485764i | ||||
\(595\) | −13394.8 | − | 23200.4i | −0.922910 | − | 1.59853i | ||||
\(596\) | 3169.73 | + | 5490.14i | 0.217848 | + | 0.377324i | ||||
\(597\) | 20445.1 | − | 11804.0i | 1.40161 | − | 0.809222i | ||||
\(598\) | 14141.2i | 0.967021i | ||||||||
\(599\) | 6034.37 | + | 10451.8i | 0.411615 | + | 0.712938i | 0.995067 | − | 0.0992096i | \(-0.0316314\pi\) |
−0.583451 | + | 0.812148i | \(0.698298\pi\) | |||||||
\(600\) | 4440.87i | 0.302163i | ||||||||
\(601\) | 60.1437 | − | 104.172i | 0.00408205 | − | 0.00707033i | −0.863977 | − | 0.503531i | \(-0.832034\pi\) |
0.868059 | + | 0.496461i | \(0.165367\pi\) | |||||||
\(602\) | 9110.22 | 0.616786 | ||||||||
\(603\) | −544.726 | −0.0367876 | ||||||||
\(604\) | −7318.60 | + | 12676.2i | −0.493029 | + | 0.853951i | ||||
\(605\) | −32164.9 | + | 18570.4i | −2.16147 | + | 1.24792i | ||||
\(606\) | − | 8496.43i | − | 0.569545i | ||||||
\(607\) | −20606.9 | − | 11897.4i | −1.37794 | − | 0.795553i | −0.386027 | − | 0.922487i | \(-0.626153\pi\) |
−0.991911 | + | 0.126934i | \(0.959486\pi\) | |||||||
\(608\) | −2467.70 | + | 4274.18i | −0.164603 | + | 0.285100i | ||||
\(609\) | −4666.16 | − | 2694.01i | −0.310480 | − | 0.179256i | ||||
\(610\) | 10177.0 | − | 5875.69i | 0.675499 | − | 0.389999i | ||||
\(611\) | 9929.73 | − | 5732.93i | 0.657470 | − | 0.379590i | ||||
\(612\) | −3038.08 | − | 1754.03i | −0.200665 | − | 0.115854i | ||||
\(613\) | 9916.46 | − | 17175.8i | 0.653380 | − | 1.13169i | −0.328917 | − | 0.944359i | \(-0.606684\pi\) |
0.982297 | − | 0.187329i | \(-0.0599830\pi\) | |||||||
\(614\) | −8194.93 | − | 4731.35i | −0.538633 | − | 0.310980i | ||||
\(615\) | − | 23302.8i | − | 1.52790i | ||||||
\(616\) | 6862.54 | − | 3962.09i | 0.448863 | − | 0.259151i | ||||
\(617\) | −11890.3 | + | 20594.6i | −0.775829 | + | 1.34378i | 0.158498 | + | 0.987359i | \(0.449335\pi\) |
−0.934327 | + | 0.356416i | \(0.883999\pi\) | |||||||
\(618\) | −13837.4 | −0.900684 | ||||||||
\(619\) | −5151.39 | −0.334494 | −0.167247 | − | 0.985915i | \(-0.553488\pi\) | ||||
−0.167247 | + | 0.985915i | \(0.553488\pi\) | |||||||
\(620\) | −643.832 | + | 1115.15i | −0.0417047 | + | 0.0722347i | ||||
\(621\) | − | 11126.8i | − | 0.719007i | ||||||
\(622\) | −8205.94 | − | 14213.1i | −0.528984 | − | 0.916227i | ||||
\(623\) | − | 12225.6i | − | 0.786212i | ||||||
\(624\) | −5890.49 | + | 3400.87i | −0.377898 | + | 0.218179i | ||||
\(625\) | 9264.10 | + | 16045.9i | 0.592902 | + | 1.02694i | ||||
\(626\) | −5757.95 | − | 9973.06i | −0.367626 | − | 0.636747i | ||||
\(627\) | 48788.3 | + | 28167.9i | 3.10752 | + | 1.79413i | ||||
\(628\) | −5815.40 | −0.369522 | ||||||||
\(629\) | −7625.61 | + | 24310.0i | −0.483391 | + | 1.54102i | ||||
\(630\) | −3666.74 | −0.231883 | ||||||||
\(631\) | −6825.42 | − | 3940.66i | −0.430611 | − | 0.248614i | 0.268996 | − | 0.963141i | \(-0.413308\pi\) |
−0.699607 | + | 0.714528i | \(0.746642\pi\) | |||||||
\(632\) | −244.602 | − | 423.664i | −0.0153952 | − | 0.0266652i | ||||
\(633\) | −1006.13 | − | 1742.67i | −0.0631756 | − | 0.109423i | ||||
\(634\) | −3279.28 | + | 1893.29i | −0.205421 | + | 0.118600i | ||||
\(635\) | − | 17096.3i | − | 1.06842i | ||||||
\(636\) | 3622.07 | + | 6273.61i | 0.225824 | + | 0.391139i | ||||
\(637\) | 6308.88i | 0.392413i | ||||||||
\(638\) | −3543.31 | + | 6137.19i | −0.219876 | + | 0.380836i | ||||
\(639\) | −1439.86 | −0.0891391 | ||||||||
\(640\) | −1894.97 | −0.117039 | ||||||||
\(641\) | 5700.80 | − | 9874.07i | 0.351276 | − | 0.608428i | −0.635197 | − | 0.772350i | \(-0.719081\pi\) |
0.986473 | + | 0.163922i | \(0.0524145\pi\) | |||||||
\(642\) | 577.523 | − | 333.433i | 0.0355031 | − | 0.0204977i | ||||
\(643\) | 30013.3i | 1.84076i | 0.391028 | + | 0.920379i | \(0.372120\pi\) | ||||
−0.391028 | + | 0.920379i | \(0.627880\pi\) | |||||||
\(644\) | −5429.00 | − | 3134.43i | −0.332193 | − | 0.191792i | ||||
\(645\) | −12433.9 | + | 21536.2i | −0.759048 | + | 1.31471i | ||||
\(646\) | 30240.9 | + | 17459.6i | 1.84181 | + | 1.06337i | ||||
\(647\) | 12331.5 | − | 7119.58i | 0.749305 | − | 0.432611i | −0.0761379 | − | 0.997097i | \(-0.524259\pi\) |
0.825443 | + | 0.564486i | \(0.190926\pi\) | |||||||
\(648\) | 6084.04 | − | 3512.62i | 0.368833 | − | 0.212946i | ||||
\(649\) | 9705.71 | + | 5603.59i | 0.587030 | + | 0.338922i | ||||
\(650\) | 6791.38 | − | 11763.0i | 0.409815 | − | 0.709821i | ||||
\(651\) | −1774.41 | − | 1024.46i | −0.106827 | − | 0.0616768i | ||||
\(652\) | − | 14258.4i | − | 0.856443i | ||||||
\(653\) | 11805.3 | − | 6815.78i | 0.707468 | − | 0.408457i | −0.102655 | − | 0.994717i | \(-0.532734\pi\) |
0.810123 | + | 0.586260i | \(0.199400\pi\) | |||||||
\(654\) | 3967.23 | − | 6871.44i | 0.237203 | − | 0.410848i | ||||
\(655\) | −13168.4 | −0.785545 | ||||||||
\(656\) | 4272.44 | 0.254285 | ||||||||
\(657\) | −1117.02 | + | 1934.74i | −0.0663305 | + | 0.114888i | ||||
\(658\) | 5082.86i | 0.301141i | ||||||||
\(659\) | 2399.71 | + | 4156.42i | 0.141850 | + | 0.245692i | 0.928193 | − | 0.372098i | \(-0.121361\pi\) |
−0.786343 | + | 0.617790i | \(0.788028\pi\) | |||||||
\(660\) | 21630.4i | 1.27570i | ||||||||
\(661\) | −13921.2 | + | 8037.41i | −0.819171 | + | 0.472949i | −0.850131 | − | 0.526572i | \(-0.823477\pi\) |
0.0309593 | + | 0.999521i | \(0.490144\pi\) | |||||||
\(662\) | 988.362 | + | 1711.89i | 0.0580269 | + | 0.100505i | ||||
\(663\) | 24062.0 | + | 41676.6i | 1.40949 | + | 2.44131i | ||||
\(664\) | −1027.82 | − | 593.410i | −0.0600708 | − | 0.0346819i | ||||
\(665\) | 36498.6 | 2.12835 | ||||||||
\(666\) | 2359.71 | + | 2567.58i | 0.137293 | + | 0.149387i | ||||
\(667\) | 5606.26 | 0.325450 | ||||||||
\(668\) | 5951.89 | + | 3436.33i | 0.344739 | + | 0.199035i | ||||
\(669\) | 8259.84 | + | 14306.5i | 0.477345 | + | 0.826786i | ||||
\(670\) | 1040.93 | + | 1802.95i | 0.0600220 | + | 0.103961i | ||||
\(671\) | 21298.5 | − | 12296.7i | 1.22537 | − | 0.707466i | ||||
\(672\) | − | 3015.24i | − | 0.173088i | ||||||
\(673\) | 1507.46 | + | 2610.99i | 0.0863420 | + | 0.149549i | 0.905962 | − | 0.423358i | \(-0.139149\pi\) |
−0.819620 | + | 0.572907i | \(0.805816\pi\) | |||||||
\(674\) | − | 6204.43i | − | 0.354578i | ||||||
\(675\) | −5343.68 | + | 9255.53i | −0.304709 | + | 0.527771i | ||||
\(676\) | 12015.7 | 0.683643 | ||||||||
\(677\) | 9915.44 | 0.562897 | 0.281448 | − | 0.959576i | \(-0.409185\pi\) | ||||
0.281448 | + | 0.959576i | \(0.409185\pi\) | |||||||
\(678\) | −4955.25 | + | 8582.75i | −0.280686 | + | 0.486163i | ||||
\(679\) | 19923.7 | − | 11503.0i | 1.12607 | − | 0.650137i | ||||
\(680\) | 13407.3i | 0.756100i | ||||||||
\(681\) | −21590.0 | − | 12465.0i | −1.21488 | − | 0.701410i | ||||
\(682\) | −1347.42 | + | 2333.80i | −0.0756531 | + | 0.131035i | ||||
\(683\) | 26548.7 | + | 15327.9i | 1.48735 | + | 0.858720i | 0.999896 | − | 0.0144303i | \(-0.00459346\pi\) |
0.487451 | + | 0.873150i | \(0.337927\pi\) | |||||||
\(684\) | 4139.14 | − | 2389.73i | 0.231380 | − | 0.133587i | ||||
\(685\) | 9444.88 | − | 5453.00i | 0.526818 | − | 0.304158i | ||||
\(686\) | −11918.6 | − | 6881.22i | −0.663346 | − | 0.382983i | ||||
\(687\) | −11041.8 | + | 19125.0i | −0.613206 | + | 1.06210i | ||||
\(688\) | −3948.55 | − | 2279.70i | −0.218804 | − | 0.126326i | ||||
\(689\) | − | 22156.8i | − | 1.22512i | ||||||
\(690\) | 14819.4 | − | 8555.96i | 0.817628 | − | 0.472058i | ||||
\(691\) | −9068.03 | + | 15706.3i | −0.499225 | + | 0.864682i | −1.00000 | 0.000895088i | \(-0.999715\pi\) | |
0.500775 | + | 0.865578i | \(0.333048\pi\) | |||||||
\(692\) | −5853.83 | −0.321574 | ||||||||
\(693\) | −7673.81 | −0.420641 | ||||||||
\(694\) | −5312.58 | + | 9201.66i | −0.290581 | + | 0.503300i | ||||
\(695\) | − | 7887.70i | − | 0.430500i | ||||||
\(696\) | 1348.27 | + | 2335.27i | 0.0734282 | + | 0.127181i | ||||
\(697\) | − | 30228.6i | − | 1.64274i | ||||||
\(698\) | 3236.69 | − | 1868.70i | 0.175516 | − | 0.101334i | ||||
\(699\) | 1752.83 | + | 3035.99i | 0.0948472 | + | 0.164280i | ||||
\(700\) | 3010.64 | + | 5214.59i | 0.162560 | + | 0.281561i | ||||
\(701\) | −29789.5 | − | 17198.9i | −1.60504 | − | 0.926669i | −0.990458 | − | 0.137815i | \(-0.955992\pi\) |
−0.614581 | − | 0.788854i | \(-0.710675\pi\) | |||||||
\(702\) | −16369.1 | −0.880071 | ||||||||
\(703\) | −23488.5 | − | 25557.6i | −1.26015 | − | 1.37116i | ||||
\(704\) | −3965.81 | −0.212311 | ||||||||
\(705\) | −12015.7 | − | 6937.26i | −0.641897 | − | 0.370599i | ||||
\(706\) | −662.934 | − | 1148.24i | −0.0353398 | − | 0.0612102i | ||||
\(707\) | −5760.08 | − | 9976.75i | −0.306407 | − | 0.530713i | ||||
\(708\) | 3693.13 | − | 2132.23i | 0.196040 | − | 0.113184i | ||||
\(709\) | 3603.38i | 0.190872i | 0.995436 | + | 0.0954358i | \(0.0304245\pi\) | ||||
−0.995436 | + | 0.0954358i | \(0.969576\pi\) | |||||||
\(710\) | 2751.47 | + | 4765.68i | 0.145438 | + | 0.251905i | ||||
\(711\) | 473.748i | 0.0249887i | ||||||||
\(712\) | −3059.28 | + | 5298.83i | −0.161027 | + | 0.278908i | ||||
\(713\) | 2131.91 | 0.111978 | ||||||||
\(714\) | −21333.6 | −1.11819 | ||||||||
\(715\) | 33079.1 | − | 57294.8i | 1.73020 | − | 2.99679i | ||||
\(716\) | 1744.96 | − | 1007.45i | 0.0910787 | − | 0.0525843i | ||||
\(717\) | − | 15284.5i | − | 0.796107i | ||||||
\(718\) | 1038.17 | + | 599.390i | 0.0539614 | + | 0.0311546i | ||||
\(719\) | 684.223 | − | 1185.11i | 0.0354899 | − | 0.0614702i | −0.847735 | − | 0.530420i | \(-0.822034\pi\) |
0.883225 | + | 0.468950i | \(0.155368\pi\) | |||||||
\(720\) | 1589.24 | + | 917.548i | 0.0822603 | + | 0.0474930i | ||||
\(721\) | −16248.3 | + | 9380.96i | −0.839276 | + | 0.484556i | ||||
\(722\) | −29320.7 | + | 16928.3i | −1.51136 | + | 0.872584i | ||||
\(723\) | 1596.21 | + | 921.572i | 0.0821075 | + | 0.0474048i | ||||
\(724\) | −362.878 | + | 628.523i | −0.0186274 | + | 0.0322636i | ||||
\(725\) | −4663.42 | − | 2692.43i | −0.238890 | − | 0.137923i | ||||
\(726\) | 29576.7i | 1.51198i | ||||||||
\(727\) | −20035.7 | + | 11567.6i | −1.02212 | + | 0.590123i | −0.914718 | − | 0.404092i | \(-0.867587\pi\) |
−0.107405 | + | 0.994215i | \(0.534254\pi\) | |||||||
\(728\) | −4611.18 | + | 7986.80i | −0.234755 | + | 0.406608i | ||||
\(729\) | 11259.2 | 0.572026 | ||||||||
\(730\) | 8538.19 | 0.432894 | ||||||||
\(731\) | −16129.4 | + | 27936.9i | −0.816098 | + | 1.41352i | ||||
\(732\) | − | 9358.09i | − | 0.472520i | ||||||
\(733\) | −7146.23 | − | 12377.6i | −0.360098 | − | 0.623708i | 0.627879 | − | 0.778311i | \(-0.283923\pi\) |
−0.987977 | + | 0.154603i | \(0.950590\pi\) | |||||||
\(734\) | − | 20861.7i | − | 1.04907i | ||||||
\(735\) | 6611.41 | − | 3817.10i | 0.331790 | − | 0.191559i | ||||
\(736\) | 1568.69 | + | 2717.05i | 0.0785634 | + | 0.136076i | ||||
\(737\) | 2178.48 | + | 3773.23i | 0.108881 | + | 0.188587i | ||||
\(738\) | −3583.14 | − | 2068.73i | −0.178723 | − | 0.103186i | ||||
\(739\) | 26710.3 | 1.32957 | 0.664786 | − | 0.747034i | \(-0.268523\pi\) | ||||
0.664786 | + | 0.747034i | \(0.268523\pi\) | |||||||
\(740\) | 3989.01 | − | 12716.7i | 0.198161 | − | 0.631723i | ||||
\(741\) | −65565.2 | −3.25047 | ||||||||
\(742\) | 8506.27 | + | 4911.10i | 0.420856 | + | 0.242981i | ||||
\(743\) | −8151.35 | − | 14118.6i | −0.402482 | − | 0.697119i | 0.591543 | − | 0.806273i | \(-0.298519\pi\) |
−0.994025 | + | 0.109154i | \(0.965186\pi\) | |||||||
\(744\) | 512.710 | + | 888.039i | 0.0252646 | + | 0.0437595i | ||||
\(745\) | −20319.6 | + | 11731.5i | −0.999265 | + | 0.576926i | ||||
\(746\) | 4117.41i | 0.202076i | ||||||||
\(747\) | 574.662 | + | 995.343i | 0.0281469 | + | 0.0487519i | ||||
\(748\) | 28059.1i | 1.37158i | ||||||||
\(749\) | 452.096 | − | 783.053i | 0.0220550 | − | 0.0382004i | ||||
\(750\) | 5380.72 | 0.261968 | ||||||||
\(751\) | −15010.3 | −0.729341 | −0.364670 | − | 0.931137i | \(-0.618818\pi\) | ||||
−0.364670 | + | 0.931137i | \(0.618818\pi\) | |||||||
\(752\) | 1271.91 | − | 2203.01i | 0.0616779 | − | 0.106829i | ||||
\(753\) | 28374.1 | − | 16381.8i | 1.37319 | − | 0.792810i | ||||
\(754\) | − | 8247.59i | − | 0.398355i | ||||||
\(755\) | −46915.9 | − | 27086.9i | −2.26152 | − | 1.30569i | ||||
\(756\) | 3628.23 | − | 6284.28i | 0.174547 | − | 0.302324i | ||||
\(757\) | −9707.43 | − | 5604.59i | −0.466080 | − | 0.269091i | 0.248517 | − | 0.968627i | \(-0.420057\pi\) |
−0.714597 | + | 0.699536i | \(0.753390\pi\) | |||||||
\(758\) | −5177.80 | + | 2989.40i | −0.248108 | + | 0.143245i | ||||
\(759\) | 31014.2 | − | 17906.0i | 1.48319 | − | 0.856322i | ||||
\(760\) | −15819.2 | − | 9133.23i | −0.755030 | − | 0.435917i | ||||
\(761\) | −12245.1 | + | 21209.2i | −0.583292 | + | 1.01029i | 0.411794 | + | 0.911277i | \(0.364902\pi\) |
−0.995086 | + | 0.0990147i | \(0.968431\pi\) | |||||||
\(762\) | −11790.5 | − | 6807.23i | −0.560530 | − | 0.323622i | ||||
\(763\) | − | 10758.2i | − | 0.510449i | ||||||
\(764\) | 14368.3 | − | 8295.52i | 0.680400 | − | 0.392829i | ||||
\(765\) | 6491.87 | − | 11244.3i | 0.306816 | − | 0.531421i | ||||
\(766\) | 2315.88 | 0.109238 | ||||||||
\(767\) | −13043.2 | −0.614033 | ||||||||
\(768\) | −754.519 | + | 1306.87i | −0.0354510 | + | 0.0614029i | ||||
\(769\) | − | 7910.52i | − | 0.370950i | −0.982649 | − | 0.185475i | \(-0.940618\pi\) | ||
0.982649 | − | 0.185475i | \(-0.0593824\pi\) | |||||||
\(770\) | 14664.1 | + | 25399.0i | 0.686309 | + | 1.18872i | ||||
\(771\) | − | 17562.6i | − | 0.820367i | ||||||
\(772\) | 10958.9 | − | 6327.11i | 0.510905 | − | 0.294971i | ||||
\(773\) | 3650.78 | + | 6323.33i | 0.169870 | + | 0.294223i | 0.938374 | − | 0.345622i | \(-0.112332\pi\) |
−0.768504 | + | 0.639845i | \(0.778999\pi\) | |||||||
\(774\) | 2207.67 | + | 3823.80i | 0.102523 | + | 0.177576i | ||||
\(775\) | −1773.37 | − | 1023.86i | −0.0821953 | − | 0.0474555i | ||||
\(776\) | −11513.8 | −0.532629 | ||||||||
\(777\) | 20234.6 | + | 6347.24i | 0.934251 | + | 0.293058i | ||||
\(778\) | 863.451 | 0.0397895 | ||||||||
\(779\) | 35666.4 | + | 20592.0i | 1.64041 | + | 0.947093i | ||||
\(780\) | −12587.0 | − | 21801.3i | −0.577804 | − | 1.00079i | ||||
\(781\) | 5758.31 | + | 9973.68i | 0.263826 | + | 0.456961i | ||||
\(782\) | 19223.8 | − | 11098.9i | 0.879081 | − | 0.507538i | ||||
\(783\) | 6489.48i | 0.296188i | ||||||||
\(784\) | 699.845 | + | 1212.17i | 0.0318807 | + | 0.0552190i | ||||
\(785\) | − | 21523.4i | − | 0.978603i | ||||||
\(786\) | −5243.26 | + | 9081.59i | −0.237940 | + | 0.412124i | ||||
\(787\) | 14214.2 | 0.643814 | 0.321907 | − | 0.946771i | \(-0.395676\pi\) | ||||
0.321907 | + | 0.946771i | \(0.395676\pi\) | |||||||
\(788\) | 15495.9 | 0.700532 | ||||||||
\(789\) | −706.579 | + | 1223.83i | −0.0318820 | + | 0.0552212i | ||||
\(790\) | 1568.02 | − | 905.299i | 0.0706175 | − | 0.0407710i | ||||
\(791\) | 13437.5i | 0.604022i | ||||||||
\(792\) | 3325.98 | + | 1920.26i | 0.149222 | + | 0.0861532i | ||||
\(793\) | −14311.2 | + | 24787.8i | −0.640867 | + | 1.11001i | ||||
\(794\) | −6902.10 | − | 3984.93i | −0.308497 | − | 0.178111i | ||||
\(795\) | −23219.3 | + | 13405.7i | −1.03585 | + | 0.598050i | ||||
\(796\) | −13873.6 | + | 8009.93i | −0.617760 | + | 0.356664i | ||||
\(797\) | 15533.1 | + | 8968.07i | 0.690354 | + | 0.398576i | 0.803745 | − | 0.594974i | \(-0.202838\pi\) |
−0.113390 | + | 0.993551i | \(0.536171\pi\) | |||||||
\(798\) | 14532.6 | − | 25171.3i | 0.644674 | − | 1.11661i | ||||
\(799\) | −15586.8 | − | 8999.07i | −0.690141 | − | 0.398453i | ||||
\(800\) | − | 3013.47i | − | 0.133178i | ||||||
\(801\) | 5131.42 | − | 2962.63i | 0.226354 | − | 0.130686i | ||||
\(802\) | −7633.43 | + | 13221.5i | −0.336092 | + | 0.582129i | ||||
\(803\) | 17868.9 | 0.785278 | ||||||||
\(804\) | 1657.87 | 0.0727222 | ||||||||
\(805\) | 11600.9 | − | 20093.3i | 0.507922 | − | 0.879746i | ||||
\(806\) | − | 3136.33i | − | 0.137063i | ||||||
\(807\) | −24470.3 | − | 42383.8i | −1.06740 | − | 1.84880i | ||||
\(808\) | 5765.49i | 0.251026i | ||||||||
\(809\) | −22671.3 | + | 13089.3i | −0.985264 | + | 0.568843i | −0.903855 | − | 0.427838i | \(-0.859275\pi\) |
−0.0814089 | + | 0.996681i | \(0.525942\pi\) | |||||||
\(810\) | 13000.6 | + | 22517.7i | 0.563944 | + | 0.976779i | ||||
\(811\) | 7040.18 | + | 12193.9i | 0.304826 | + | 0.527975i | 0.977223 | − | 0.212217i | \(-0.0680682\pi\) |
−0.672396 | + | 0.740191i | \(0.734735\pi\) | |||||||
\(812\) | 3166.35 | + | 1828.09i | 0.136844 | + | 0.0790068i | ||||
\(813\) | 2386.79 | 0.102962 | ||||||||
\(814\) | 8348.25 | − | 26613.7i | 0.359467 | − | 1.14596i | ||||
\(815\) | 52771.8 | 2.26812 | ||||||||
\(816\) | 9246.39 | + | 5338.40i | 0.396677 | + | 0.229021i | ||||
\(817\) | −21975.0 | − | 38061.9i | −0.941015 | − | 1.62989i | ||||
\(818\) | 10219.9 | + | 17701.4i | 0.436835 | + | 0.756621i | ||||
\(819\) | 7734.46 | − | 4465.49i | 0.329993 | − | 0.190521i | ||||
\(820\) | 15812.8i | 0.673422i | ||||||||
\(821\) | 2876.29 | + | 4981.87i | 0.122269 | + | 0.211777i | 0.920662 | − | 0.390360i | \(-0.127650\pi\) |
−0.798393 | + | 0.602137i | \(0.794316\pi\) | |||||||
\(822\) | − | 8684.89i | − | 0.368516i | ||||||
\(823\) | −10308.6 | + | 17855.0i | −0.436616 | + | 0.756242i | −0.997426 | − | 0.0717029i | \(-0.977157\pi\) |
0.560810 | + | 0.827945i | \(0.310490\pi\) | |||||||
\(824\) | 9389.78 | 0.396976 | ||||||||
\(825\) | −34397.7 | −1.45161 | ||||||||
\(826\) | 2891.05 | − | 5007.45i | 0.121783 | − | 0.210934i | ||||
\(827\) | −10014.6 | + | 5781.92i | −0.421089 | + | 0.243116i | −0.695543 | − | 0.718484i | \(-0.744836\pi\) |
0.274454 | + | 0.961600i | \(0.411503\pi\) | |||||||
\(828\) | − | 3038.25i | − | 0.127520i | ||||||
\(829\) | 10646.5 | + | 6146.77i | 0.446042 | + | 0.257522i | 0.706157 | − | 0.708055i | \(-0.250427\pi\) |
−0.260115 | + | 0.965578i | \(0.583761\pi\) | |||||||
\(830\) | 2196.28 | − | 3804.06i | 0.0918480 | − | 0.159085i | ||||
\(831\) | 11068.6 | + | 6390.47i | 0.462053 | + | 0.266766i | ||||
\(832\) | 3997.16 | − | 2307.76i | 0.166558 | − | 0.0961624i | ||||
\(833\) | 8576.38 | − | 4951.57i | 0.356727 | − | 0.205957i | ||||
\(834\) | −5439.76 | − | 3140.65i | −0.225855 | − | 0.130398i | ||||
\(835\) | −12718.2 | + | 22028.6i | −0.527104 | + | 0.912971i | ||||
\(836\) | −33106.7 | − | 19114.1i | −1.36964 | − | 0.790761i | ||||
\(837\) | 2467.77i | 0.101910i | ||||||||
\(838\) | 7967.19 | − | 4599.86i | 0.328427 | − | 0.189617i | ||||
\(839\) | 20344.5 | − | 35237.6i | 0.837150 | − | 1.44999i | −0.0551184 | − | 0.998480i | \(-0.517554\pi\) |
0.892268 | − | 0.451506i | \(-0.149113\pi\) | |||||||
\(840\) | 11159.7 | 0.458390 | ||||||||
\(841\) | 21119.3 | 0.865934 | ||||||||
\(842\) | −9688.62 | + | 16781.2i | −0.396546 | + | 0.686838i | ||||
\(843\) | − | 25092.4i | − | 1.02518i | ||||||
\(844\) | 682.739 | + | 1182.54i | 0.0278446 | + | 0.0482283i | ||||
\(845\) | 44471.4i | 1.81049i | ||||||||
\(846\) | −2133.41 | + | 1231.72i | −0.0866999 | + | 0.0500562i | ||||
\(847\) | 20051.3 | + | 34729.8i | 0.813423 | + | 1.40889i | ||||
\(848\) | −2457.86 | − | 4257.13i | −0.0995320 | − | 0.172394i | ||||
\(849\) | −25029.8 | − | 14451.0i | −1.01180 | − | 0.584165i | ||||
\(850\) | −21321.1 | −0.860360 | ||||||||
\(851\) | −21535.7 | + | 4807.59i | −0.867491 | + | 0.193657i | ||||
\(852\) | 4382.21 | 0.176211 | ||||||||
\(853\) | 34103.1 | + | 19689.4i | 1.36890 | + | 0.790333i | 0.990787 | − | 0.135428i | \(-0.0432410\pi\) |
0.378109 | + | 0.925761i | \(0.376574\pi\) | |||||||
\(854\) | −6344.23 | − | 10988.5i | −0.254210 | − | 0.440304i | ||||
\(855\) | 8844.66 | + | 15319.4i | 0.353779 | + | 0.612763i | ||||
\(856\) | −391.894 | + | 226.260i | −0.0156480 | + | 0.00903437i | ||||
\(857\) | 44097.1i | 1.75768i | 0.477120 | + | 0.878838i | \(0.341681\pi\) | ||||
−0.477120 | + | 0.878838i | \(0.658319\pi\) | |||||||
\(858\) | −26342.2 | − | 45626.1i | −1.04815 | − | 1.81544i | ||||
\(859\) | 30832.3i | 1.22466i | 0.790602 | + | 0.612330i | \(0.209768\pi\) | ||||
−0.790602 | + | 0.612330i | \(0.790232\pi\) | |||||||
\(860\) | 8437.40 | − | 14614.0i | 0.334550 | − | 0.579458i | ||||
\(861\) | −25161.0 | −0.995918 | ||||||||
\(862\) | 12013.1 | 0.474674 | ||||||||
\(863\) | −14873.6 | + | 25761.9i | −0.586679 | + | 1.01616i | 0.407985 | + | 0.912989i | \(0.366231\pi\) |
−0.994664 | + | 0.103169i | \(0.967102\pi\) | |||||||
\(864\) | −3145.09 | + | 1815.82i | −0.123841 | + | 0.0714994i | ||||
\(865\) | − | 21665.7i | − | 0.851623i | ||||||
\(866\) | 25844.3 | + | 14921.2i | 1.01412 | + | 0.585500i | ||||
\(867\) | 23290.2 | − | 40339.8i | 0.912315 | − | 1.58018i | ||||
\(868\) | 1204.08 | + | 695.173i | 0.0470841 | + | 0.0271840i | ||||
\(869\) | 3281.58 | − | 1894.62i | 0.128101 | − | 0.0739594i | ||||
\(870\) | −8643.09 | + | 4990.09i | −0.336814 | + | 0.194460i | ||||
\(871\) | −4391.39 | − | 2535.37i | −0.170834 | − | 0.0986312i | ||||
\(872\) | −2692.08 | + | 4662.81i | −0.104547 | + | 0.181081i | ||||
\(873\) | 9656.17 | + | 5574.99i | 0.374355 | + | 0.216134i | ||||
\(874\) | 30242.6i | 1.17045i | ||||||||
\(875\) | 6318.19 | − | 3647.81i | 0.244107 | − | 0.140935i | ||||
\(876\) | 3399.65 | − | 5888.37i | 0.131123 | − | 0.227111i | ||||
\(877\) | 32254.0 | 1.24189 | 0.620947 | − | 0.783853i | \(-0.286748\pi\) | ||||
0.620947 | + | 0.783853i | \(0.286748\pi\) | |||||||
\(878\) | −26458.0 | −1.01699 | ||||||||
\(879\) | −7597.47 | + | 13159.2i | −0.291532 | + | 0.504948i | ||||
\(880\) | − | 14677.9i | − | 0.562263i | ||||||
\(881\) | 21121.9 | + | 36584.1i | 0.807734 | + | 1.39904i | 0.914430 | + | 0.404744i | \(0.132639\pi\) |
−0.106696 | + | 0.994292i | \(0.534027\pi\) | |||||||
\(882\) | − | 1355.47i | − | 0.0517471i | ||||||
\(883\) | 16647.6 | − | 9611.51i | 0.634470 | − | 0.366312i | −0.148011 | − | 0.988986i | \(-0.547287\pi\) |
0.782481 | + | 0.622674i | \(0.213954\pi\) | |||||||
\(884\) | −16327.9 | − | 28280.8i | −0.621231 | − | 1.07600i | ||||
\(885\) | 7891.62 | + | 13668.7i | 0.299744 | + | 0.519173i | ||||
\(886\) | 3898.22 | + | 2250.64i | 0.147814 | + | 0.0853406i | ||||
\(887\) | −41337.3 | −1.56479 | −0.782397 | − | 0.622780i | \(-0.786003\pi\) | ||||
−0.782397 | + | 0.622780i | \(0.786003\pi\) | |||||||
\(888\) | −7181.78 | − | 7814.43i | −0.271402 | − | 0.295310i | ||||
\(889\) | −18459.6 | −0.696417 | ||||||||
\(890\) | −19611.6 | − | 11322.7i | −0.738630 | − | 0.426448i | ||||
\(891\) | 27207.8 | + | 47125.3i | 1.02300 | + | 1.77189i | ||||
\(892\) | −5604.94 | − | 9708.05i | −0.210389 | − | 0.364405i | ||||
\(893\) | 21235.8 | − | 12260.5i | 0.795779 | − | 0.459443i | ||||
\(894\) | 18684.6i | 0.698999i | ||||||||
\(895\) | 3728.70 | + | 6458.29i | 0.139259 | + | 0.241203i | ||||
\(896\) | 2046.08i | 0.0762886i | ||||||||
\(897\) | −20839.5 | + | 36095.1i | −0.775709 | + | 1.34357i | ||||
\(898\) | 30824.7 | 1.14547 | ||||||||
\(899\) | −1243.39 | −0.0461284 | ||||||||
\(900\) | −1459.13 | + | 2527.29i | −0.0540419 | + | 0.0936034i | ||||
\(901\) | −30120.2 | + | 17389.9i | −1.11371 | + | 0.642999i | ||||
\(902\) | 33093.2i | 1.22160i | ||||||||
\(903\) | 23253.6 | + | 13425.5i | 0.856955 | + | 0.494763i | ||||
\(904\) | 3362.53 | − | 5824.07i | 0.123712 | − | 0.214276i | ||||
\(905\) | −2326.23 | − | 1343.05i | −0.0854436 | − | 0.0493309i | ||||
\(906\) | −37361.0 | + | 21570.4i | −1.37002 | + | 0.790981i | ||||
\(907\) | 19323.0 | − | 11156.2i | 0.707399 | − | 0.408417i | −0.102698 | − | 0.994713i | \(-0.532748\pi\) |
0.810097 | + | 0.586295i | \(0.199414\pi\) | |||||||
\(908\) | 14650.5 | + | 8458.48i | 0.535456 | + | 0.309146i | ||||
\(909\) | 2791.67 | − | 4835.31i | 0.101863 | − | 0.176432i | ||||
\(910\) | −29560.0 | − | 17066.5i | −1.07682 | − | 0.621701i | ||||
\(911\) | − | 39414.4i | − | 1.43343i | −0.697365 | − | 0.716716i | \(-0.745644\pi\) | ||
0.697365 | − | 0.716716i | \(-0.254356\pi\) | |||||||
\(912\) | −12597.5 | + | 7273.15i | −0.457395 | + | 0.264077i | ||||
\(913\) | 4596.40 | − | 7961.19i | 0.166614 | − | 0.288584i | ||||
\(914\) | 24548.6 | 0.888397 | ||||||||
\(915\) | 34635.3 | 1.25137 | ||||||||
\(916\) | 7492.75 | − | 12977.8i | 0.270270 | − | 0.468122i | ||||
\(917\) | 14218.5i | 0.512034i | ||||||||
\(918\) | 12847.4 | + | 22252.3i | 0.461903 | + | 0.800039i | ||||
\(919\) | 4118.19i | 0.147820i | 0.997265 | + | 0.0739100i | \(0.0235478\pi\) | ||||
−0.997265 | + | 0.0739100i | \(0.976452\pi\) | |||||||
\(920\) | −10056.1 | + | 5805.89i | −0.360369 | + | 0.208059i | ||||
\(921\) | −13944.9 | − | 24153.3i | −0.498914 | − | 0.864144i | ||||
\(922\) | −6436.62 | − | 11148.5i | −0.229912 | − | 0.398219i | ||||
\(923\) | −11607.6 | − | 6701.67i | −0.413944 | − | 0.238990i | ||||
\(924\) | 23355.2 | 0.831527 | ||||||||
\(925\) | 20222.8 | + | 6343.53i | 0.718833 | + | 0.225485i | ||||
\(926\) | 5137.42 | 0.182318 | ||||||||
\(927\) | −7874.86 | − | 4546.55i | −0.279012 | − | 0.161088i | ||||
\(928\) | −914.906 | − | 1584.66i | −0.0323634 | − | 0.0560551i | ||||
\(929\) | −24423.8 | − | 42303.3i | −0.862561 | − | 1.49400i | −0.869448 | − | 0.494024i | \(-0.835526\pi\) |
0.00688684 | − | 0.999976i | \(-0.497808\pi\) | |||||||
\(930\) | −3286.73 | + | 1897.59i | −0.115888 | + | 0.0669081i | ||||
\(931\) | 13492.3i | 0.474963i | ||||||||
\(932\) | −1189.43 | − | 2060.16i | −0.0418038 | − | 0.0724064i | ||||
\(933\) | − | 48371.4i | − | 1.69733i | ||||||
\(934\) | 7436.06 | − | 12879.6i | 0.260509 | − | 0.451215i | ||||
\(935\) | −103850. | −3.63235 | ||||||||
\(936\) | −4469.69 | −0.156086 | ||||||||
\(937\) | 23667.5 | − | 40993.3i | 0.825170 | − | 1.42924i | −0.0766197 | − | 0.997060i | \(-0.524413\pi\) |
0.901789 | − | 0.432176i | \(-0.142254\pi\) | |||||||
\(938\) | 1946.72 | − | 1123.94i | 0.0677640 | − | 0.0391236i | ||||
\(939\) | − | 33941.3i | − | 1.17959i | ||||||
\(940\) | 8153.59 | + | 4707.47i | 0.282916 | + | 0.163341i | ||||
\(941\) | −23848.6 | + | 41307.0i | −0.826188 | + | 1.43100i | 0.0748192 | + | 0.997197i | \(0.476162\pi\) |
−0.901008 | + | 0.433803i | \(0.857171\pi\) | |||||||
\(942\) | −14843.6 | − | 8569.98i | −0.513410 | − | 0.296417i | ||||
\(943\) | 22672.7 | − | 13090.1i | 0.782954 | − | 0.452039i | ||||
\(944\) | −2506.08 | + | 1446.89i | −0.0864046 | + | 0.0498857i | ||||
\(945\) | 23258.8 | + | 13428.5i | 0.800644 | + | 0.462252i | ||||
\(946\) | 17657.9 | − | 30584.4i | 0.606880 | − | 1.05115i | ||||
\(947\) | −3596.96 | − | 2076.71i | −0.123427 | − | 0.0712607i | 0.437015 | − | 0.899454i | \(-0.356036\pi\) |
−0.560442 | + | 0.828193i | \(0.689369\pi\) | |||||||
\(948\) | − | 1441.85i | − | 0.0493979i | ||||||
\(949\) | −18010.1 | + | 10398.1i | −0.616050 | + | 0.355677i | ||||
\(950\) | 14524.1 | − | 25156.5i | 0.496026 | − | 0.859143i | ||||
\(951\) | −11160.4 | −0.380546 | ||||||||
\(952\) | 14476.5 | 0.492842 | ||||||||
\(953\) | −13303.4 | + | 23042.2i | −0.452194 | + | 0.783222i | −0.998522 | − | 0.0543487i | \(-0.982692\pi\) |
0.546328 | + | 0.837571i | \(0.316025\pi\) | |||||||
\(954\) | 4760.40i | 0.161555i | ||||||||
\(955\) | 30702.6 | + | 53178.5i | 1.04033 | + | 1.80190i | ||||
\(956\) | 10371.7i | 0.350884i | ||||||||
\(957\) | −18088.4 | + | 10443.3i | −0.610987 | + | 0.352753i | ||||
\(958\) | 8132.56 | + | 14086.0i | 0.274270 | + | 0.475050i | ||||
\(959\) | −5887.84 | − | 10198.0i | −0.198257 | − | 0.343391i | ||||
\(960\) | −4836.85 | − | 2792.56i | −0.162613 | − | 0.0938847i | ||||
\(961\) | 29318.2 | 0.984129 | ||||||||
\(962\) | 7072.63 | + | 31682.0i | 0.237038 | + | 1.06182i | ||||
\(963\) | 438.223 | 0.0146641 | ||||||||
\(964\) | −1083.15 | − | 625.359i | −0.0361888 | − | 0.0208936i | ||||
\(965\) | 23417.3 | + | 40560.0i | 0.781171 | + | 1.35303i | ||||
\(966\) | −9238.24 | − | 16001.1i | −0.307697 | − | 0.532947i | ||||
\(967\) | 32189.1 | − | 18584.4i | 1.07046 | − | 0.618028i | 0.142149 | − | 0.989845i | \(-0.454599\pi\) |
0.928306 | + | 0.371818i | \(0.121265\pi\) | |||||||
\(968\) | − | 20070.1i | − | 0.666403i | ||||||
\(969\) | 51459.3 | + | 89130.1i | 1.70600 | + | 2.95487i | ||||
\(970\) | − | 42613.7i | − | 1.41056i | ||||||
\(971\) | −895.336 | + | 1550.77i | −0.0295909 | + | 0.0512529i | −0.880442 | − | 0.474155i | \(-0.842754\pi\) |
0.850851 | + | 0.525407i | \(0.176087\pi\) | |||||||
\(972\) | 8448.99 | 0.278808 | ||||||||
\(973\) | −8516.69 | −0.280609 | ||||||||
\(974\) | 6484.10 | − | 11230.8i | 0.213310 | − | 0.369464i | ||||
\(975\) | 34669.6 | − | 20016.5i | 1.13879 | − | 0.657478i | ||||
\(976\) | 6350.19i | 0.208263i | ||||||||
\(977\) | −23075.3 | − | 13322.6i | −0.755625 | − | 0.436260i | 0.0720977 | − | 0.997398i | \(-0.477031\pi\) |
−0.827723 | + | 0.561137i | \(0.810364\pi\) | |||||||
\(978\) | 21012.1 | − | 36394.1i | 0.687008 | − | 1.18993i | ||||
\(979\) | −41043.3 | − | 23696.4i | −1.33989 | − | 0.773585i | ||||
\(980\) | −4486.36 | + | 2590.20i | −0.146236 | + | 0.0844295i | ||||
\(981\) | 4515.49 | − | 2607.02i | 0.146961 | − | 0.0848478i | ||||
\(982\) | −11071.6 | − | 6392.20i | −0.359786 | − | 0.207722i | ||||
\(983\) | 754.720 | − | 1307.21i | 0.0244881 | − | 0.0424147i | −0.853522 | − | 0.521057i | \(-0.825538\pi\) |
0.878010 | + | 0.478643i | \(0.158871\pi\) | |||||||
\(984\) | 10905.3 | + | 6296.17i | 0.353301 | + | 0.203978i | ||||
\(985\) | 57352.1i | 1.85522i | ||||||||
\(986\) | −11211.9 | + | 6473.18i | −0.362129 | + | 0.209075i | ||||
\(987\) | −7490.46 | + | 12973.9i | −0.241564 | + | 0.418402i | ||||
\(988\) | 44491.1 | 1.43264 | ||||||||
\(989\) | −27938.6 | −0.898276 | ||||||||
\(990\) | −7107.08 | + | 12309.8i | −0.228159 | + | 0.395183i | ||||
\(991\) | − | 26636.4i | − | 0.853818i | −0.904294 | − | 0.426909i | \(-0.859602\pi\) | ||
0.904294 | − | 0.426909i | \(-0.140398\pi\) | |||||||
\(992\) | −347.913 | − | 602.604i | −0.0111353 | − | 0.0192870i | ||||
\(993\) | 5826.08i | 0.186188i | ||||||||
\(994\) | 5145.71 | − | 2970.88i | 0.164197 | − | 0.0947993i | ||||
\(995\) | −29645.6 | − | 51347.7i | −0.944552 | − | 1.63601i | ||||
\(996\) | −1748.98 | − | 3029.33i | −0.0556412 | − | 0.0963733i | ||||
\(997\) | −31614.0 | − | 18252.4i | −1.00424 | − | 0.579797i | −0.0947387 | − | 0.995502i | \(-0.530202\pi\) |
−0.909500 | + | 0.415705i | \(0.863535\pi\) | |||||||
\(998\) | 13066.9 | 0.414456 | ||||||||
\(999\) | −5564.98 | − | 24928.4i | −0.176245 | − | 0.789490i |
(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 | 74.4.e.a.27.2 | yes | 20 | |
3.2 | odd | 2 | 666.4.s.d.397.10 | 20 | |||
37.11 | even | 6 | inner | 74.4.e.a.11.2 | ✓ | 20 | |
111.11 | odd | 6 | 666.4.s.d.307.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.e.a.11.2 | ✓ | 20 | 37.11 | even | 6 | inner | |
74.4.e.a.27.2 | yes | 20 | 1.1 | even | 1 | trivial | |
666.4.s.d.307.10 | 20 | 111.11 | odd | 6 | |||
666.4.s.d.397.10 | 20 | 3.2 | odd | 2 |