Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.39");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.b (of order \(2\), degree \(1\), 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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.8 | ||
Root | \(0.645572 - 1.89294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.3.b.b.39.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.645572 | + | 1.89294i | 0.322786 | + | 0.946472i | ||||
\(3\) | 0.820457i | 0.273486i | 0.990607 | + | 0.136743i | \(0.0436634\pi\) | ||||
−0.990607 | + | 0.136743i | \(0.956337\pi\) | |||||||
\(4\) | −3.16647 | + | 2.44406i | −0.791618 | + | 0.611016i | ||||
\(5\) | −2.38184 | −0.476367 | −0.238184 | − | 0.971220i | \(-0.576552\pi\) | ||||
−0.238184 | + | 0.971220i | \(0.576552\pi\) | |||||||
\(6\) | −1.55308 | + | 0.529664i | −0.258846 | + | 0.0882773i | ||||
\(7\) | 12.3764i | 1.76806i | 0.467427 | + | 0.884032i | \(0.345181\pi\) | ||||
−0.467427 | + | 0.884032i | \(0.654819\pi\) | |||||||
\(8\) | −6.67066 | − | 4.41614i | −0.833833 | − | 0.552017i | ||||
\(9\) | 8.32685 | 0.925206 | ||||||||
\(10\) | −1.53765 | − | 4.50868i | −0.153765 | − | 0.450868i | ||||
\(11\) | − | 9.15034i | − | 0.831849i | −0.909399 | − | 0.415925i | \(-0.863458\pi\) | ||
0.909399 | − | 0.415925i | \(-0.136542\pi\) | |||||||
\(12\) | −2.00525 | − | 2.59795i | −0.167104 | − | 0.216496i | ||||
\(13\) | 0.940214 | 0.0723242 | 0.0361621 | − | 0.999346i | \(-0.488487\pi\) | ||||
0.0361621 | + | 0.999346i | \(0.488487\pi\) | |||||||
\(14\) | −23.4279 | + | 7.98989i | −1.67342 | + | 0.570706i | ||||
\(15\) | − | 1.95419i | − | 0.130280i | ||||||
\(16\) | 4.05310 | − | 15.4781i | 0.253319 | − | 0.967383i | ||||
\(17\) | 27.1792 | 1.59878 | 0.799388 | − | 0.600814i | \(-0.205157\pi\) | ||||
0.799388 | + | 0.600814i | \(0.205157\pi\) | |||||||
\(18\) | 5.37558 | + | 15.7623i | 0.298644 | + | 0.875681i | ||||
\(19\) | − | 4.35890i | − | 0.229416i | ||||||
\(20\) | 7.54202 | − | 5.82136i | 0.377101 | − | 0.291068i | ||||
\(21\) | −10.1543 | −0.483540 | ||||||||
\(22\) | 17.3211 | − | 5.90721i | 0.787322 | − | 0.268509i | ||||
\(23\) | 13.8004i | 0.600018i | 0.953936 | + | 0.300009i | \(0.0969898\pi\) | ||||
−0.953936 | + | 0.300009i | \(0.903010\pi\) | |||||||
\(24\) | 3.62325 | − | 5.47299i | 0.150969 | − | 0.228041i | ||||
\(25\) | −19.3269 | −0.773074 | ||||||||
\(26\) | 0.606976 | + | 1.77977i | 0.0233452 | + | 0.0684528i | ||||
\(27\) | 14.2159i | 0.526516i | ||||||||
\(28\) | −30.2488 | − | 39.1897i | −1.08032 | − | 1.39963i | ||||
\(29\) | 49.8488 | 1.71892 | 0.859462 | − | 0.511200i | \(-0.170799\pi\) | ||||
0.859462 | + | 0.511200i | \(0.170799\pi\) | |||||||
\(30\) | 3.69918 | − | 1.26157i | 0.123306 | − | 0.0420525i | ||||
\(31\) | − | 24.6752i | − | 0.795974i | −0.917391 | − | 0.397987i | \(-0.869709\pi\) | ||
0.917391 | − | 0.397987i | \(-0.130291\pi\) | |||||||
\(32\) | 31.9158 | − | 2.31995i | 0.997369 | − | 0.0724986i | ||||
\(33\) | 7.50746 | 0.227499 | ||||||||
\(34\) | 17.5461 | + | 51.4487i | 0.516063 | + | 1.51320i | ||||
\(35\) | − | 29.4787i | − | 0.842248i | ||||||
\(36\) | −26.3667 | + | 20.3514i | −0.732410 | + | 0.565315i | ||||
\(37\) | −27.3757 | −0.739883 | −0.369942 | − | 0.929055i | \(-0.620622\pi\) | ||||
−0.369942 | + | 0.929055i | \(0.620622\pi\) | |||||||
\(38\) | 8.25115 | − | 2.81398i | 0.217136 | − | 0.0740522i | ||||
\(39\) | 0.771405i | 0.0197796i | ||||||||
\(40\) | 15.8884 | + | 10.5185i | 0.397211 | + | 0.262963i | ||||
\(41\) | −38.4024 | −0.936644 | −0.468322 | − | 0.883558i | \(-0.655141\pi\) | ||||
−0.468322 | + | 0.883558i | \(0.655141\pi\) | |||||||
\(42\) | −6.55536 | − | 19.2216i | −0.156080 | − | 0.457657i | ||||
\(43\) | − | 41.2108i | − | 0.958391i | −0.877708 | − | 0.479195i | \(-0.840929\pi\) | ||
0.877708 | − | 0.479195i | \(-0.159071\pi\) | |||||||
\(44\) | 22.3640 | + | 28.9743i | 0.508273 | + | 0.658507i | ||||
\(45\) | −19.8332 | −0.440738 | ||||||||
\(46\) | −26.1234 | + | 8.90917i | −0.567901 | + | 0.193678i | ||||
\(47\) | 45.1842i | 0.961367i | 0.876894 | + | 0.480683i | \(0.159611\pi\) | ||||
−0.876894 | + | 0.480683i | \(0.840389\pi\) | |||||||
\(48\) | 12.6991 | + | 3.32539i | 0.264565 | + | 0.0692790i | ||||
\(49\) | −104.176 | −2.12605 | ||||||||
\(50\) | −12.4769 | − | 36.5846i | −0.249538 | − | 0.731693i | ||||
\(51\) | 22.2994i | 0.437242i | ||||||||
\(52\) | −2.97716 | + | 2.29794i | −0.0572531 | + | 0.0441912i | ||||
\(53\) | −19.9964 | −0.377291 | −0.188646 | − | 0.982045i | \(-0.560410\pi\) | ||||
−0.188646 | + | 0.982045i | \(0.560410\pi\) | |||||||
\(54\) | −26.9100 | + | 9.17741i | −0.498333 | + | 0.169952i | ||||
\(55\) | 21.7946i | 0.396266i | ||||||||
\(56\) | 54.6561 | − | 82.5591i | 0.976001 | − | 1.47427i | ||||
\(57\) | 3.57629 | 0.0627419 | ||||||||
\(58\) | 32.1810 | + | 94.3610i | 0.554845 | + | 1.62691i | ||||
\(59\) | − | 34.7054i | − | 0.588228i | −0.955770 | − | 0.294114i | \(-0.904976\pi\) | ||
0.955770 | − | 0.294114i | \(-0.0950245\pi\) | |||||||
\(60\) | 4.77618 | + | 6.18790i | 0.0796029 | + | 0.103132i | ||||
\(61\) | 33.2008 | 0.544276 | 0.272138 | − | 0.962258i | \(-0.412269\pi\) | ||||
0.272138 | + | 0.962258i | \(0.412269\pi\) | |||||||
\(62\) | 46.7088 | − | 15.9296i | 0.753367 | − | 0.256929i | ||||
\(63\) | 103.057i | 1.63582i | ||||||||
\(64\) | 24.9955 | + | 58.9171i | 0.390555 | + | 0.920580i | ||||
\(65\) | −2.23944 | −0.0344529 | ||||||||
\(66\) | 4.84661 | + | 14.2112i | 0.0734334 | + | 0.215321i | ||||
\(67\) | 3.48192i | 0.0519690i | 0.999662 | + | 0.0259845i | \(0.00827205\pi\) | ||||
−0.999662 | + | 0.0259845i | \(0.991728\pi\) | |||||||
\(68\) | −86.0622 | + | 66.4277i | −1.26562 | + | 0.976878i | ||||
\(69\) | −11.3226 | −0.164096 | ||||||||
\(70\) | 55.8015 | − | 19.0306i | 0.797164 | − | 0.271866i | ||||
\(71\) | − | 88.8887i | − | 1.25195i | −0.779842 | − | 0.625977i | \(-0.784700\pi\) | ||
0.779842 | − | 0.625977i | \(-0.215300\pi\) | |||||||
\(72\) | −55.5456 | − | 36.7725i | −0.771467 | − | 0.510729i | ||||
\(73\) | −19.8573 | −0.272018 | −0.136009 | − | 0.990708i | \(-0.543428\pi\) | ||||
−0.136009 | + | 0.990708i | \(0.543428\pi\) | |||||||
\(74\) | −17.6730 | − | 51.8206i | −0.238824 | − | 0.700279i | ||||
\(75\) | − | 15.8568i | − | 0.211425i | ||||||
\(76\) | 10.6534 | + | 13.8023i | 0.140177 | + | 0.181610i | ||||
\(77\) | 113.249 | 1.47076 | ||||||||
\(78\) | −1.46023 | + | 0.497998i | −0.0187208 | + | 0.00638458i | ||||
\(79\) | − | 51.7431i | − | 0.654976i | −0.944855 | − | 0.327488i | \(-0.893798\pi\) | ||
0.944855 | − | 0.327488i | \(-0.106202\pi\) | |||||||
\(80\) | −9.65383 | + | 36.8664i | −0.120673 | + | 0.460830i | ||||
\(81\) | 63.2781 | 0.781211 | ||||||||
\(82\) | −24.7915 | − | 72.6936i | −0.302336 | − | 0.886507i | ||||
\(83\) | − | 6.62943i | − | 0.0798727i | −0.999202 | − | 0.0399363i | \(-0.987284\pi\) | ||
0.999202 | − | 0.0399363i | \(-0.0127155\pi\) | |||||||
\(84\) | 32.1534 | − | 24.8178i | 0.382779 | − | 0.295451i | ||||
\(85\) | −64.7365 | −0.761605 | ||||||||
\(86\) | 78.0097 | − | 26.6046i | 0.907090 | − | 0.309355i | ||||
\(87\) | 40.8988i | 0.470101i | ||||||||
\(88\) | −40.4091 | + | 61.0388i | −0.459195 | + | 0.693623i | ||||
\(89\) | 31.5105 | 0.354051 | 0.177025 | − | 0.984206i | \(-0.443353\pi\) | ||||
0.177025 | + | 0.984206i | \(0.443353\pi\) | |||||||
\(90\) | −12.8038 | − | 37.5431i | −0.142264 | − | 0.417146i | ||||
\(91\) | 11.6365i | 0.127874i | ||||||||
\(92\) | −33.7291 | − | 43.6987i | −0.366621 | − | 0.474986i | ||||
\(93\) | 20.2449 | 0.217687 | ||||||||
\(94\) | −85.5312 | + | 29.1697i | −0.909907 | + | 0.310316i | ||||
\(95\) | 10.3822i | 0.109286i | ||||||||
\(96\) | 1.90342 | + | 26.1855i | 0.0198273 | + | 0.272766i | ||||
\(97\) | 159.282 | 1.64208 | 0.821039 | − | 0.570873i | \(-0.193395\pi\) | ||||
0.821039 | + | 0.570873i | \(0.193395\pi\) | |||||||
\(98\) | −67.2534 | − | 197.200i | −0.686259 | − | 2.01225i | ||||
\(99\) | − | 76.1935i | − | 0.769632i | ||||||
\(100\) | 61.1980 | − | 47.2361i | 0.611980 | − | 0.472361i | ||||
\(101\) | 35.1573 | 0.348092 | 0.174046 | − | 0.984738i | \(-0.444316\pi\) | ||||
0.174046 | + | 0.984738i | \(0.444316\pi\) | |||||||
\(102\) | −42.2114 | + | 14.3958i | −0.413838 | + | 0.141136i | ||||
\(103\) | 117.214i | 1.13800i | 0.822339 | + | 0.568998i | \(0.192669\pi\) | ||||
−0.822339 | + | 0.568998i | \(0.807331\pi\) | |||||||
\(104\) | −6.27185 | − | 4.15211i | −0.0603063 | − | 0.0399242i | ||||
\(105\) | 24.1860 | 0.230343 | ||||||||
\(106\) | −12.9092 | − | 37.8522i | −0.121784 | − | 0.357096i | ||||
\(107\) | − | 191.832i | − | 1.79282i | −0.443228 | − | 0.896409i | \(-0.646167\pi\) | ||
0.443228 | − | 0.896409i | \(-0.353833\pi\) | |||||||
\(108\) | −34.7446 | − | 45.0144i | −0.321710 | − | 0.416800i | ||||
\(109\) | −183.807 | −1.68630 | −0.843152 | − | 0.537675i | \(-0.819303\pi\) | ||||
−0.843152 | + | 0.537675i | \(0.819303\pi\) | |||||||
\(110\) | −41.2560 | + | 14.0700i | −0.375055 | + | 0.127909i | ||||
\(111\) | − | 22.4606i | − | 0.202347i | ||||||
\(112\) | 191.564 | + | 50.1630i | 1.71039 | + | 0.447884i | ||||
\(113\) | 72.9718 | 0.645768 | 0.322884 | − | 0.946439i | \(-0.395348\pi\) | ||||
0.322884 | + | 0.946439i | \(0.395348\pi\) | |||||||
\(114\) | 2.30875 | + | 6.76971i | 0.0202522 | + | 0.0593834i | ||||
\(115\) | − | 32.8704i | − | 0.285829i | ||||||
\(116\) | −157.845 | + | 121.834i | −1.36073 | + | 1.05029i | ||||
\(117\) | 7.82902 | 0.0669147 | ||||||||
\(118\) | 65.6954 | − | 22.4049i | 0.556741 | − | 0.189872i | ||||
\(119\) | 336.382i | 2.82674i | ||||||||
\(120\) | −8.62999 | + | 13.0358i | −0.0719166 | + | 0.108631i | ||||
\(121\) | 37.2713 | 0.308027 | ||||||||
\(122\) | 21.4335 | + | 62.8473i | 0.175685 | + | 0.515142i | ||||
\(123\) | − | 31.5075i | − | 0.256159i | ||||||
\(124\) | 60.3078 | + | 78.1334i | 0.486353 | + | 0.630108i | ||||
\(125\) | 105.579 | 0.844635 | ||||||||
\(126\) | −195.081 | + | 66.5306i | −1.54826 | + | 0.528021i | ||||
\(127\) | 11.4215i | 0.0899331i | 0.998988 | + | 0.0449665i | \(0.0143181\pi\) | ||||
−0.998988 | + | 0.0449665i | \(0.985682\pi\) | |||||||
\(128\) | −95.3904 | + | 85.3503i | −0.745237 | + | 0.666799i | ||||
\(129\) | 33.8117 | 0.262106 | ||||||||
\(130\) | −1.44572 | − | 4.23913i | −0.0111209 | − | 0.0326087i | ||||
\(131\) | 36.9512i | 0.282070i | 0.990005 | + | 0.141035i | \(0.0450430\pi\) | ||||
−0.990005 | + | 0.141035i | \(0.954957\pi\) | |||||||
\(132\) | −23.7722 | + | 18.3487i | −0.180092 | + | 0.139005i | ||||
\(133\) | 53.9477 | 0.405622 | ||||||||
\(134\) | −6.59108 | + | 2.24783i | −0.0491872 | + | 0.0167749i | ||||
\(135\) | − | 33.8600i | − | 0.250815i | ||||||
\(136\) | −181.303 | − | 120.027i | −1.33311 | − | 0.882552i | ||||
\(137\) | −162.786 | −1.18822 | −0.594109 | − | 0.804385i | \(-0.702495\pi\) | ||||
−0.594109 | + | 0.804385i | \(0.702495\pi\) | |||||||
\(138\) | −7.30959 | − | 21.4331i | −0.0529680 | − | 0.155313i | ||||
\(139\) | 229.233i | 1.64916i | 0.565744 | + | 0.824581i | \(0.308589\pi\) | ||||
−0.565744 | + | 0.824581i | \(0.691411\pi\) | |||||||
\(140\) | 72.0478 | + | 93.3434i | 0.514627 | + | 0.666739i | ||||
\(141\) | −37.0717 | −0.262920 | ||||||||
\(142\) | 168.261 | − | 57.3841i | 1.18494 | − | 0.404113i | ||||
\(143\) | − | 8.60328i | − | 0.0601628i | ||||||
\(144\) | 33.7496 | − | 128.884i | 0.234372 | − | 0.895028i | ||||
\(145\) | −118.732 | −0.818839 | ||||||||
\(146\) | −12.8193 | − | 37.5887i | −0.0878035 | − | 0.257457i | ||||
\(147\) | − | 85.4722i | − | 0.581444i | ||||||
\(148\) | 86.6844 | − | 66.9079i | 0.585705 | − | 0.452081i | ||||
\(149\) | −110.328 | −0.740459 | −0.370229 | − | 0.928940i | \(-0.620721\pi\) | ||||
−0.370229 | + | 0.928940i | \(0.620721\pi\) | |||||||
\(150\) | 30.0161 | − | 10.2367i | 0.200107 | − | 0.0682449i | ||||
\(151\) | 104.737i | 0.693621i | 0.937935 | + | 0.346810i | \(0.112735\pi\) | ||||
−0.937935 | + | 0.346810i | \(0.887265\pi\) | |||||||
\(152\) | −19.2495 | + | 29.0767i | −0.126641 | + | 0.191294i | ||||
\(153\) | 226.317 | 1.47920 | ||||||||
\(154\) | 73.1102 | + | 214.373i | 0.474742 | + | 1.39204i | ||||
\(155\) | 58.7723i | 0.379176i | ||||||||
\(156\) | −1.88536 | − | 2.44263i | −0.0120857 | − | 0.0156579i | ||||
\(157\) | −147.695 | −0.940732 | −0.470366 | − | 0.882471i | \(-0.655878\pi\) | ||||
−0.470366 | + | 0.882471i | \(0.655878\pi\) | |||||||
\(158\) | 97.9468 | − | 33.4039i | 0.619917 | − | 0.211417i | ||||
\(159\) | − | 16.4062i | − | 0.103184i | ||||||
\(160\) | −76.0182 | + | 5.52575i | −0.475114 | + | 0.0345360i | ||||
\(161\) | −170.800 | −1.06087 | ||||||||
\(162\) | 40.8506 | + | 119.782i | 0.252164 | + | 0.739394i | ||||
\(163\) | − | 183.104i | − | 1.12334i | −0.827363 | − | 0.561668i | \(-0.810160\pi\) | ||
0.827363 | − | 0.561668i | \(-0.189840\pi\) | |||||||
\(164\) | 121.600 | − | 93.8580i | 0.741465 | − | 0.572305i | ||||
\(165\) | −17.8815 | −0.108373 | ||||||||
\(166\) | 12.5491 | − | 4.27978i | 0.0755973 | − | 0.0257818i | ||||
\(167\) | − | 214.501i | − | 1.28444i | −0.766522 | − | 0.642218i | \(-0.778014\pi\) | ||
0.766522 | − | 0.642218i | \(-0.221986\pi\) | |||||||
\(168\) | 67.7362 | + | 44.8429i | 0.403191 | + | 0.266922i | ||||
\(169\) | −168.116 | −0.994769 | ||||||||
\(170\) | −41.7921 | − | 122.542i | −0.245836 | − | 0.720838i | ||||
\(171\) | − | 36.2959i | − | 0.212257i | ||||||
\(172\) | 100.722 | + | 130.493i | 0.585592 | + | 0.758680i | ||||
\(173\) | 27.1849 | 0.157138 | 0.0785692 | − | 0.996909i | \(-0.474965\pi\) | ||||
0.0785692 | + | 0.996909i | \(0.474965\pi\) | |||||||
\(174\) | −77.4191 | + | 26.4031i | −0.444937 | + | 0.151742i | ||||
\(175\) | − | 239.198i | − | 1.36684i | ||||||
\(176\) | −141.630 | − | 37.0873i | −0.804717 | − | 0.210723i | ||||
\(177\) | 28.4743 | 0.160872 | ||||||||
\(178\) | 20.3423 | + | 59.6476i | 0.114283 | + | 0.335099i | ||||
\(179\) | − | 185.284i | − | 1.03511i | −0.855651 | − | 0.517553i | \(-0.826843\pi\) | ||
0.855651 | − | 0.517553i | \(-0.173157\pi\) | |||||||
\(180\) | 62.8013 | − | 48.4736i | 0.348896 | − | 0.269298i | ||||
\(181\) | 17.0150 | 0.0940053 | 0.0470026 | − | 0.998895i | \(-0.485033\pi\) | ||||
0.0470026 | + | 0.998895i | \(0.485033\pi\) | |||||||
\(182\) | −22.0273 | + | 7.51221i | −0.121029 | + | 0.0412759i | ||||
\(183\) | 27.2398i | 0.148852i | ||||||||
\(184\) | 60.9445 | − | 92.0580i | 0.331220 | − | 0.500315i | ||||
\(185\) | 65.2044 | 0.352456 | ||||||||
\(186\) | 13.0696 | + | 38.3225i | 0.0702665 | + | 0.206035i | ||||
\(187\) | − | 248.699i | − | 1.32994i | ||||||
\(188\) | −110.433 | − | 143.075i | −0.587411 | − | 0.761036i | ||||
\(189\) | −175.943 | −0.930914 | ||||||||
\(190\) | −19.6529 | + | 6.70245i | −0.103436 | + | 0.0352761i | ||||
\(191\) | 2.41797i | 0.0126595i | 0.999980 | + | 0.00632976i | \(0.00201484\pi\) | ||||
−0.999980 | + | 0.00632976i | \(0.997985\pi\) | |||||||
\(192\) | −48.3389 | + | 20.5077i | −0.251765 | + | 0.106811i | ||||
\(193\) | −150.712 | −0.780892 | −0.390446 | − | 0.920626i | \(-0.627679\pi\) | ||||
−0.390446 | + | 0.920626i | \(0.627679\pi\) | |||||||
\(194\) | 102.828 | + | 301.511i | 0.530040 | + | 1.55418i | ||||
\(195\) | − | 1.83736i | − | 0.00942236i | ||||||
\(196\) | 329.872 | − | 254.614i | 1.68302 | − | 1.29905i | ||||
\(197\) | 268.203 | 1.36144 | 0.680718 | − | 0.732545i | \(-0.261668\pi\) | ||||
0.680718 | + | 0.732545i | \(0.261668\pi\) | |||||||
\(198\) | 144.230 | − | 49.1884i | 0.728435 | − | 0.248426i | ||||
\(199\) | 308.615i | 1.55083i | 0.631452 | + | 0.775415i | \(0.282459\pi\) | ||||
−0.631452 | + | 0.775415i | \(0.717541\pi\) | |||||||
\(200\) | 128.923 | + | 85.3500i | 0.644615 | + | 0.426750i | ||||
\(201\) | −2.85676 | −0.0142128 | ||||||||
\(202\) | 22.6966 | + | 66.5507i | 0.112359 | + | 0.329459i | ||||
\(203\) | 616.951i | 3.03917i | ||||||||
\(204\) | −54.5011 | − | 70.6103i | −0.267162 | − | 0.346129i | ||||
\(205\) | 91.4683 | 0.446187 | ||||||||
\(206\) | −221.879 | + | 75.6698i | −1.07708 | + | 0.367329i | ||||
\(207\) | 114.914i | 0.555140i | ||||||||
\(208\) | 3.81078 | − | 14.5528i | 0.0183211 | − | 0.0699652i | ||||
\(209\) | −39.8854 | −0.190839 | ||||||||
\(210\) | 15.6138 | + | 45.7827i | 0.0743514 | + | 0.218013i | ||||
\(211\) | − | 334.011i | − | 1.58299i | −0.611176 | − | 0.791495i | \(-0.709303\pi\) | ||
0.611176 | − | 0.791495i | \(-0.290697\pi\) | |||||||
\(212\) | 63.3182 | − | 48.8726i | 0.298671 | − | 0.230531i | ||||
\(213\) | 72.9293 | 0.342391 | ||||||||
\(214\) | 363.126 | − | 123.841i | 1.69685 | − | 0.578697i | ||||
\(215\) | 98.1574i | 0.456546i | ||||||||
\(216\) | 62.7795 | − | 94.8297i | 0.290646 | − | 0.439026i | ||||
\(217\) | 305.391 | 1.40733 | ||||||||
\(218\) | −118.661 | − | 347.937i | −0.544316 | − | 1.59604i | ||||
\(219\) | − | 16.2920i | − | 0.0743929i | ||||||
\(220\) | −53.2675 | − | 69.0121i | −0.242125 | − | 0.313691i | ||||
\(221\) | 25.5543 | 0.115630 | ||||||||
\(222\) | 42.5166 | − | 14.4999i | 0.191516 | − | 0.0653149i | ||||
\(223\) | − | 290.142i | − | 1.30108i | −0.759470 | − | 0.650542i | \(-0.774542\pi\) | ||
0.759470 | − | 0.650542i | \(-0.225458\pi\) | |||||||
\(224\) | 28.7128 | + | 395.004i | 0.128182 | + | 1.76341i | ||||
\(225\) | −160.932 | −0.715252 | ||||||||
\(226\) | 47.1086 | + | 138.132i | 0.208445 | + | 0.611202i | ||||
\(227\) | − | 76.2561i | − | 0.335930i | −0.985793 | − | 0.167965i | \(-0.946280\pi\) | ||
0.985793 | − | 0.167965i | \(-0.0537195\pi\) | |||||||
\(228\) | −11.3242 | + | 8.74068i | −0.0496676 | + | 0.0383363i | ||||
\(229\) | −212.780 | −0.929169 | −0.464585 | − | 0.885529i | \(-0.653796\pi\) | ||||
−0.464585 | + | 0.885529i | \(0.653796\pi\) | |||||||
\(230\) | 62.2218 | − | 21.2202i | 0.270529 | − | 0.0922617i | ||||
\(231\) | 92.9156i | 0.402232i | ||||||||
\(232\) | −332.525 | − | 220.139i | −1.43330 | − | 0.948875i | ||||
\(233\) | −108.504 | −0.465680 | −0.232840 | − | 0.972515i | \(-0.574802\pi\) | ||||
−0.232840 | + | 0.972515i | \(0.574802\pi\) | |||||||
\(234\) | 5.05420 | + | 14.8199i | 0.0215991 | + | 0.0633329i | ||||
\(235\) | − | 107.622i | − | 0.457964i | ||||||
\(236\) | 84.8223 | + | 109.894i | 0.359416 | + | 0.465652i | ||||
\(237\) | 42.4530 | 0.179127 | ||||||||
\(238\) | −636.752 | + | 217.159i | −2.67543 | + | 0.912432i | ||||
\(239\) | − | 14.5126i | − | 0.0607222i | −0.999539 | − | 0.0303611i | \(-0.990334\pi\) | ||
0.999539 | − | 0.0303611i | \(-0.00966573\pi\) | |||||||
\(240\) | −30.2473 | − | 7.92055i | −0.126030 | − | 0.0330023i | ||||
\(241\) | −278.238 | −1.15451 | −0.577257 | − | 0.816563i | \(-0.695877\pi\) | ||||
−0.577257 | + | 0.816563i | \(0.695877\pi\) | |||||||
\(242\) | 24.0613 | + | 70.5524i | 0.0994268 | + | 0.291539i | ||||
\(243\) | 179.860i | 0.740166i | ||||||||
\(244\) | −105.130 | + | 81.1449i | −0.430859 | + | 0.332561i | ||||
\(245\) | 248.131 | 1.01278 | ||||||||
\(246\) | 59.6419 | − | 20.3404i | 0.242447 | − | 0.0826845i | ||||
\(247\) | − | 4.09830i | − | 0.0165923i | ||||||
\(248\) | −108.969 | + | 164.600i | −0.439391 | + | 0.663710i | ||||
\(249\) | 5.43916 | 0.0218440 | ||||||||
\(250\) | 68.1591 | + | 199.856i | 0.272636 | + | 0.799423i | ||||
\(251\) | 344.252i | 1.37152i | 0.727828 | + | 0.685760i | \(0.240530\pi\) | ||||
−0.727828 | + | 0.685760i | \(0.759470\pi\) | |||||||
\(252\) | −251.877 | − | 326.327i | −0.999514 | − | 1.29495i | ||||
\(253\) | 126.279 | 0.499125 | ||||||||
\(254\) | −21.6203 | + | 7.37340i | −0.0851191 | + | 0.0290291i | ||||
\(255\) | − | 53.1134i | − | 0.208288i | ||||||
\(256\) | −223.145 | − | 125.469i | −0.871659 | − | 0.490113i | ||||
\(257\) | 50.0048 | 0.194571 | 0.0972856 | − | 0.995257i | \(-0.468984\pi\) | ||||
0.0972856 | + | 0.995257i | \(0.468984\pi\) | |||||||
\(258\) | 21.8279 | + | 64.0036i | 0.0846042 | + | 0.248076i | ||||
\(259\) | − | 338.814i | − | 1.30816i | ||||||
\(260\) | 7.09112 | − | 5.47333i | 0.0272735 | − | 0.0210513i | ||||
\(261\) | 415.084 | 1.59036 | ||||||||
\(262\) | −69.9465 | + | 23.8546i | −0.266971 | + | 0.0910483i | ||||
\(263\) | 155.273i | 0.590391i | 0.955437 | + | 0.295195i | \(0.0953848\pi\) | ||||
−0.955437 | + | 0.295195i | \(0.904615\pi\) | |||||||
\(264\) | −50.0797 | − | 33.1539i | −0.189696 | − | 0.125583i | ||||
\(265\) | 47.6283 | 0.179729 | ||||||||
\(266\) | 34.8271 | + | 102.120i | 0.130929 | + | 0.383909i | ||||
\(267\) | 25.8530i | 0.0968277i | ||||||||
\(268\) | −8.51004 | − | 11.0254i | −0.0317539 | − | 0.0411396i | ||||
\(269\) | −457.281 | −1.69993 | −0.849964 | − | 0.526840i | \(-0.823377\pi\) | ||||
−0.849964 | + | 0.526840i | \(0.823377\pi\) | |||||||
\(270\) | 64.0951 | − | 21.8591i | 0.237389 | − | 0.0809596i | ||||
\(271\) | 349.279i | 1.28885i | 0.764666 | + | 0.644427i | \(0.222904\pi\) | ||||
−0.764666 | + | 0.644427i | \(0.777096\pi\) | |||||||
\(272\) | 110.160 | − | 420.683i | 0.405000 | − | 1.54663i | ||||
\(273\) | −9.54725 | −0.0349716 | ||||||||
\(274\) | −105.090 | − | 308.144i | −0.383540 | − | 1.12461i | ||||
\(275\) | 176.847i | 0.643081i | ||||||||
\(276\) | 35.8529 | − | 27.6733i | 0.129902 | − | 0.100266i | ||||
\(277\) | −108.548 | −0.391870 | −0.195935 | − | 0.980617i | \(-0.562774\pi\) | ||||
−0.195935 | + | 0.980617i | \(0.562774\pi\) | |||||||
\(278\) | −433.926 | + | 147.987i | −1.56089 | + | 0.532326i | ||||
\(279\) | − | 205.467i | − | 0.736440i | ||||||
\(280\) | −130.182 | + | 196.642i | −0.464935 | + | 0.702294i | ||||
\(281\) | 190.452 | 0.677767 | 0.338883 | − | 0.940828i | \(-0.389951\pi\) | ||||
0.338883 | + | 0.940828i | \(0.389951\pi\) | |||||||
\(282\) | −23.9325 | − | 70.1747i | −0.0848669 | − | 0.248846i | ||||
\(283\) | 289.950i | 1.02456i | 0.858819 | + | 0.512279i | \(0.171198\pi\) | ||||
−0.858819 | + | 0.512279i | \(0.828802\pi\) | |||||||
\(284\) | 217.250 | + | 281.464i | 0.764964 | + | 0.991069i | ||||
\(285\) | −8.51813 | −0.0298882 | ||||||||
\(286\) | 16.2855 | − | 5.55404i | 0.0569424 | − | 0.0194197i | ||||
\(287\) | − | 475.285i | − | 1.65605i | ||||||
\(288\) | 265.758 | − | 19.3179i | 0.922771 | − | 0.0670761i | ||||
\(289\) | 449.709 | 1.55609 | ||||||||
\(290\) | −76.6499 | − | 224.752i | −0.264310 | − | 0.775009i | ||||
\(291\) | 130.684i | 0.449084i | ||||||||
\(292\) | 62.8776 | − | 48.5325i | 0.215334 | − | 0.166207i | ||||
\(293\) | −177.881 | −0.607102 | −0.303551 | − | 0.952815i | \(-0.598172\pi\) | ||||
−0.303551 | + | 0.952815i | \(0.598172\pi\) | |||||||
\(294\) | 161.794 | − | 55.1785i | 0.550320 | − | 0.187682i | ||||
\(295\) | 82.6627i | 0.280212i | ||||||||
\(296\) | 182.614 | + | 120.895i | 0.616939 | + | 0.408428i | ||||
\(297\) | 130.081 | 0.437982 | ||||||||
\(298\) | −71.2249 | − | 208.845i | −0.239010 | − | 0.700823i | ||||
\(299\) | 12.9754i | 0.0433958i | ||||||||
\(300\) | 38.7551 | + | 50.2103i | 0.129184 | + | 0.167368i | ||||
\(301\) | 510.043 | 1.69450 | ||||||||
\(302\) | −198.261 | + | 67.6151i | −0.656492 | + | 0.223891i | ||||
\(303\) | 28.8450i | 0.0951981i | ||||||||
\(304\) | −67.4676 | − | 17.6671i | −0.221933 | − | 0.0581153i | ||||
\(305\) | −79.0790 | −0.259275 | ||||||||
\(306\) | 146.104 | + | 428.406i | 0.477464 | + | 1.40002i | ||||
\(307\) | 554.295i | 1.80552i | 0.430143 | + | 0.902761i | \(0.358463\pi\) | ||||
−0.430143 | + | 0.902761i | \(0.641537\pi\) | |||||||
\(308\) | −358.599 | + | 276.787i | −1.16428 | + | 0.898659i | ||||
\(309\) | −96.1686 | −0.311225 | ||||||||
\(310\) | −111.253 | + | 37.9418i | −0.358880 | + | 0.122393i | ||||
\(311\) | − | 67.7563i | − | 0.217866i | −0.994049 | − | 0.108933i | \(-0.965257\pi\) | ||
0.994049 | − | 0.108933i | \(-0.0347434\pi\) | |||||||
\(312\) | 3.40663 | − | 5.14578i | 0.0109187 | − | 0.0164929i | ||||
\(313\) | 447.248 | 1.42891 | 0.714454 | − | 0.699683i | \(-0.246675\pi\) | ||||
0.714454 | + | 0.699683i | \(0.246675\pi\) | |||||||
\(314\) | −95.3477 | − | 279.578i | −0.303655 | − | 0.890376i | ||||
\(315\) | − | 245.465i | − | 0.779253i | ||||||
\(316\) | 126.463 | + | 163.843i | 0.400201 | + | 0.518491i | ||||
\(317\) | 67.2154 | 0.212036 | 0.106018 | − | 0.994364i | \(-0.466190\pi\) | ||||
0.106018 | + | 0.994364i | \(0.466190\pi\) | |||||||
\(318\) | 31.0560 | − | 10.5914i | 0.0976605 | − | 0.0333063i | ||||
\(319\) | − | 456.133i | − | 1.42989i | ||||||
\(320\) | −59.5352 | − | 140.331i | −0.186048 | − | 0.438534i | ||||
\(321\) | 157.389 | 0.490310 | ||||||||
\(322\) | −110.264 | − | 323.315i | −0.342434 | − | 1.00408i | ||||
\(323\) | − | 118.471i | − | 0.366785i | ||||||
\(324\) | −200.368 | + | 154.656i | −0.618421 | + | 0.477333i | ||||
\(325\) | −18.1714 | −0.0559119 | ||||||||
\(326\) | 346.605 | − | 118.207i | 1.06321 | − | 0.362597i | ||||
\(327\) | − | 150.806i | − | 0.461180i | ||||||
\(328\) | 256.170 | + | 169.590i | 0.781005 | + | 0.517043i | ||||
\(329\) | −559.220 | −1.69976 | ||||||||
\(330\) | −11.5438 | − | 33.8488i | −0.0349813 | − | 0.102572i | ||||
\(331\) | 178.449i | 0.539122i | 0.962983 | + | 0.269561i | \(0.0868785\pi\) | ||||
−0.962983 | + | 0.269561i | \(0.913121\pi\) | |||||||
\(332\) | 16.2028 | + | 20.9919i | 0.0488035 | + | 0.0632287i | ||||
\(333\) | −227.953 | −0.684544 | ||||||||
\(334\) | 406.038 | − | 138.476i | 1.21568 | − | 0.414598i | ||||
\(335\) | − | 8.29337i | − | 0.0247563i | ||||||
\(336\) | −41.1566 | + | 157.170i | −0.122490 | + | 0.467768i | ||||
\(337\) | −280.146 | −0.831292 | −0.415646 | − | 0.909526i | \(-0.636445\pi\) | ||||
−0.415646 | + | 0.909526i | \(0.636445\pi\) | |||||||
\(338\) | −108.531 | − | 318.234i | −0.321098 | − | 0.941521i | ||||
\(339\) | 59.8702i | 0.176608i | ||||||||
\(340\) | 204.986 | − | 158.220i | 0.602901 | − | 0.465353i | ||||
\(341\) | −225.787 | −0.662131 | ||||||||
\(342\) | 68.7061 | − | 23.4316i | 0.200895 | − | 0.0685135i | ||||
\(343\) | − | 682.888i | − | 1.99093i | ||||||
\(344\) | −181.992 | + | 274.903i | −0.529048 | + | 0.799138i | ||||
\(345\) | 26.9687 | 0.0781702 | ||||||||
\(346\) | 17.5498 | + | 51.4596i | 0.0507221 | + | 0.148727i | ||||
\(347\) | 89.6003i | 0.258214i | 0.991631 | + | 0.129107i | \(0.0412111\pi\) | ||||
−0.991631 | + | 0.129107i | \(0.958789\pi\) | |||||||
\(348\) | −99.9592 | − | 129.505i | −0.287239 | − | 0.372140i | ||||
\(349\) | 5.38420 | 0.0154275 | 0.00771376 | − | 0.999970i | \(-0.497545\pi\) | ||||
0.00771376 | + | 0.999970i | \(0.497545\pi\) | |||||||
\(350\) | 452.788 | − | 154.419i | 1.29368 | − | 0.441198i | ||||
\(351\) | 13.3660i | 0.0380798i | ||||||||
\(352\) | −21.2284 | − | 292.040i | −0.0603079 | − | 0.829660i | ||||
\(353\) | 357.844 | 1.01372 | 0.506861 | − | 0.862028i | \(-0.330806\pi\) | ||||
0.506861 | + | 0.862028i | \(0.330806\pi\) | |||||||
\(354\) | 18.3822 | + | 53.9002i | 0.0519272 | + | 0.152261i | ||||
\(355\) | 211.718i | 0.596390i | ||||||||
\(356\) | −99.7772 | + | 77.0137i | −0.280273 | + | 0.216331i | ||||
\(357\) | −275.987 | −0.773072 | ||||||||
\(358\) | 350.732 | − | 119.614i | 0.979699 | − | 0.334118i | ||||
\(359\) | − | 415.792i | − | 1.15820i | −0.815258 | − | 0.579098i | \(-0.803405\pi\) | ||
0.815258 | − | 0.579098i | \(-0.196595\pi\) | |||||||
\(360\) | 132.301 | + | 87.5861i | 0.367502 | + | 0.243295i | ||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 10.9844 | + | 32.2084i | 0.0303436 | + | 0.0889734i | ||||
\(363\) | 30.5795i | 0.0842409i | ||||||||
\(364\) | −28.4404 | − | 36.8467i | −0.0781329 | − | 0.101227i | ||||
\(365\) | 47.2968 | 0.129580 | ||||||||
\(366\) | −51.5635 | + | 17.5853i | −0.140884 | + | 0.0480472i | ||||
\(367\) | 262.695i | 0.715789i | 0.933762 | + | 0.357894i | \(0.116505\pi\) | ||||
−0.933762 | + | 0.357894i | \(0.883495\pi\) | |||||||
\(368\) | 213.605 | + | 55.9345i | 0.580448 | + | 0.151996i | ||||
\(369\) | −319.771 | −0.866588 | ||||||||
\(370\) | 42.0942 | + | 123.428i | 0.113768 | + | 0.333590i | ||||
\(371\) | − | 247.485i | − | 0.667075i | ||||||
\(372\) | −64.1050 | + | 49.4799i | −0.172325 | + | 0.133011i | ||||
\(373\) | 158.344 | 0.424516 | 0.212258 | − | 0.977214i | \(-0.431918\pi\) | ||||
0.212258 | + | 0.977214i | \(0.431918\pi\) | |||||||
\(374\) | 470.773 | − | 160.553i | 1.25875 | − | 0.429287i | ||||
\(375\) | 86.6233i | 0.230995i | ||||||||
\(376\) | 199.540 | − | 301.409i | 0.530691 | − | 0.801619i | ||||
\(377\) | 46.8685 | 0.124320 | ||||||||
\(378\) | −113.584 | − | 333.050i | −0.300486 | − | 0.881084i | ||||
\(379\) | 539.136i | 1.42252i | 0.702928 | + | 0.711261i | \(0.251876\pi\) | ||||
−0.702928 | + | 0.711261i | \(0.748124\pi\) | |||||||
\(380\) | −25.3747 | − | 32.8749i | −0.0667756 | − | 0.0865129i | ||||
\(381\) | −9.37084 | −0.0245954 | ||||||||
\(382\) | −4.57708 | + | 1.56097i | −0.0119819 | + | 0.00408631i | ||||
\(383\) | − | 422.810i | − | 1.10394i | −0.833863 | − | 0.551971i | \(-0.813876\pi\) | ||
0.833863 | − | 0.551971i | \(-0.186124\pi\) | |||||||
\(384\) | −70.0262 | − | 78.2637i | −0.182360 | − | 0.203812i | ||||
\(385\) | −269.740 | −0.700623 | ||||||||
\(386\) | −97.2956 | − | 285.290i | −0.252061 | − | 0.739092i | ||||
\(387\) | − | 343.156i | − | 0.886709i | ||||||
\(388\) | −504.361 | + | 389.294i | −1.29990 | + | 1.00334i | ||||
\(389\) | −487.091 | −1.25216 | −0.626081 | − | 0.779758i | \(-0.715342\pi\) | ||||
−0.626081 | + | 0.779758i | \(0.715342\pi\) | |||||||
\(390\) | 3.47802 | − | 1.18615i | 0.00891800 | − | 0.00304141i | ||||
\(391\) | 375.085i | 0.959296i | ||||||||
\(392\) | 694.926 | + | 460.057i | 1.77277 | + | 1.17362i | ||||
\(393\) | −30.3168 | −0.0771420 | ||||||||
\(394\) | 173.144 | + | 507.693i | 0.439453 | + | 1.28856i | ||||
\(395\) | 123.244i | 0.312009i | ||||||||
\(396\) | 186.222 | + | 241.265i | 0.470257 | + | 0.609254i | ||||
\(397\) | −646.684 | −1.62893 | −0.814464 | − | 0.580215i | \(-0.802969\pi\) | ||||
−0.814464 | + | 0.580215i | \(0.802969\pi\) | |||||||
\(398\) | −584.191 | + | 199.233i | −1.46782 | + | 0.500586i | ||||
\(399\) | 44.2617i | 0.110932i | ||||||||
\(400\) | −78.3337 | + | 299.143i | −0.195834 | + | 0.747859i | ||||
\(401\) | −14.0555 | −0.0350512 | −0.0175256 | − | 0.999846i | \(-0.505579\pi\) | ||||
−0.0175256 | + | 0.999846i | \(0.505579\pi\) | |||||||
\(402\) | −1.84425 | − | 5.40770i | −0.00458768 | − | 0.0134520i | ||||
\(403\) | − | 23.2000i | − | 0.0575682i | ||||||
\(404\) | −111.325 | + | 85.9266i | −0.275556 | + | 0.212690i | ||||
\(405\) | −150.718 | −0.372144 | ||||||||
\(406\) | −1167.85 | + | 398.286i | −2.87649 | + | 0.981001i | ||||
\(407\) | 250.497i | 0.615471i | ||||||||
\(408\) | 98.4770 | − | 148.752i | 0.241365 | − | 0.364587i | ||||
\(409\) | 143.668 | 0.351266 | 0.175633 | − | 0.984456i | \(-0.443803\pi\) | ||||
0.175633 | + | 0.984456i | \(0.443803\pi\) | |||||||
\(410\) | 59.0494 | + | 173.144i | 0.144023 | + | 0.422303i | ||||
\(411\) | − | 133.559i | − | 0.324960i | ||||||
\(412\) | −286.477 | − | 371.153i | −0.695333 | − | 0.900858i | ||||
\(413\) | 429.530 | 1.04002 | ||||||||
\(414\) | −217.526 | + | 74.1853i | −0.525425 | + | 0.179192i | ||||
\(415\) | 15.7902i | 0.0380488i | ||||||||
\(416\) | 30.0077 | − | 2.18125i | 0.0721338 | − | 0.00524340i | ||||
\(417\) | −188.076 | −0.451022 | ||||||||
\(418\) | −25.7489 | − | 75.5008i | −0.0616003 | − | 0.180624i | ||||
\(419\) | − | 572.449i | − | 1.36623i | −0.730312 | − | 0.683114i | \(-0.760625\pi\) | ||
0.730312 | − | 0.683114i | \(-0.239375\pi\) | |||||||
\(420\) | −76.5842 | + | 59.1121i | −0.182343 | + | 0.140743i | ||||
\(421\) | 718.562 | 1.70680 | 0.853399 | − | 0.521258i | \(-0.174537\pi\) | ||||
0.853399 | + | 0.521258i | \(0.174537\pi\) | |||||||
\(422\) | 632.264 | − | 215.628i | 1.49825 | − | 0.510967i | ||||
\(423\) | 376.242i | 0.889462i | ||||||||
\(424\) | 133.390 | + | 88.3070i | 0.314598 | + | 0.208271i | ||||
\(425\) | −525.289 | −1.23597 | ||||||||
\(426\) | 47.0811 | + | 138.051i | 0.110519 | + | 0.324064i | ||||
\(427\) | 410.908i | 0.962314i | ||||||||
\(428\) | 468.849 | + | 607.429i | 1.09544 | + | 1.41923i | ||||
\(429\) | 7.05862 | 0.0164537 | ||||||||
\(430\) | −185.807 | + | 63.3677i | −0.432108 | + | 0.147367i | ||||
\(431\) | − | 252.198i | − | 0.585147i | −0.956243 | − | 0.292573i | \(-0.905488\pi\) | ||
0.956243 | − | 0.292573i | \(-0.0945116\pi\) | |||||||
\(432\) | 220.036 | + | 57.6186i | 0.509342 | + | 0.133376i | ||||
\(433\) | 239.008 | 0.551982 | 0.275991 | − | 0.961160i | \(-0.410994\pi\) | ||||
0.275991 | + | 0.961160i | \(0.410994\pi\) | |||||||
\(434\) | 197.152 | + | 578.089i | 0.454268 | + | 1.33200i | ||||
\(435\) | − | 97.4142i | − | 0.223941i | ||||||
\(436\) | 582.021 | − | 449.237i | 1.33491 | − | 1.03036i | ||||
\(437\) | 60.1547 | 0.137654 | ||||||||
\(438\) | 30.8399 | − | 10.5177i | 0.0704108 | − | 0.0240130i | ||||
\(439\) | 17.2750i | 0.0393508i | 0.999806 | + | 0.0196754i | \(0.00626327\pi\) | ||||
−0.999806 | + | 0.0196754i | \(0.993737\pi\) | |||||||
\(440\) | 96.2480 | − | 145.385i | 0.218745 | − | 0.330420i | ||||
\(441\) | −867.461 | −1.96703 | ||||||||
\(442\) | 16.4971 | + | 48.3728i | 0.0373238 | + | 0.109441i | ||||
\(443\) | 161.249i | 0.363993i | 0.983299 | + | 0.181997i | \(0.0582560\pi\) | ||||
−0.983299 | + | 0.181997i | \(0.941744\pi\) | |||||||
\(444\) | 54.8950 | + | 71.1208i | 0.123637 | + | 0.160182i | ||||
\(445\) | −75.0529 | −0.168658 | ||||||||
\(446\) | 549.222 | − | 187.307i | 1.23144 | − | 0.419972i | ||||
\(447\) | − | 90.5196i | − | 0.202505i | ||||||
\(448\) | −729.184 | + | 309.355i | −1.62764 | + | 0.690525i | ||||
\(449\) | 561.952 | 1.25156 | 0.625782 | − | 0.779998i | \(-0.284780\pi\) | ||||
0.625782 | + | 0.779998i | \(0.284780\pi\) | |||||||
\(450\) | −103.893 | − | 304.635i | −0.230874 | − | 0.676966i | ||||
\(451\) | 351.395i | 0.779147i | ||||||||
\(452\) | −231.063 | + | 178.348i | −0.511202 | + | 0.394575i | ||||
\(453\) | −85.9319 | −0.189695 | ||||||||
\(454\) | 144.349 | − | 49.2288i | 0.317948 | − | 0.108434i | ||||
\(455\) | − | 27.7163i | − | 0.0609149i | ||||||
\(456\) | −23.8562 | − | 15.7934i | −0.0523162 | − | 0.0346346i | ||||
\(457\) | −107.375 | −0.234957 | −0.117479 | − | 0.993075i | \(-0.537481\pi\) | ||||
−0.117479 | + | 0.993075i | \(0.537481\pi\) | |||||||
\(458\) | −137.365 | − | 402.780i | −0.299923 | − | 0.879433i | ||||
\(459\) | 386.378i | 0.841781i | ||||||||
\(460\) | 80.3373 | + | 104.083i | 0.174646 | + | 0.226268i | ||||
\(461\) | 666.303 | 1.44534 | 0.722672 | − | 0.691191i | \(-0.242914\pi\) | ||||
0.722672 | + | 0.691191i | \(0.242914\pi\) | |||||||
\(462\) | −175.884 | + | 59.9838i | −0.380701 | + | 0.129835i | ||||
\(463\) | − | 272.358i | − | 0.588246i | −0.955768 | − | 0.294123i | \(-0.904972\pi\) | ||
0.955768 | − | 0.294123i | \(-0.0950276\pi\) | |||||||
\(464\) | 202.042 | − | 771.566i | 0.435436 | − | 1.66286i | ||||
\(465\) | −48.2201 | −0.103699 | ||||||||
\(466\) | −70.0469 | − | 205.391i | −0.150315 | − | 0.440753i | ||||
\(467\) | 703.386i | 1.50618i | 0.657917 | + | 0.753090i | \(0.271438\pi\) | ||||
−0.657917 | + | 0.753090i | \(0.728562\pi\) | |||||||
\(468\) | −24.7904 | + | 19.1346i | −0.0529709 | + | 0.0408860i | ||||
\(469\) | −43.0938 | −0.0918844 | ||||||||
\(470\) | 203.721 | − | 69.4775i | 0.433450 | − | 0.147824i | ||||
\(471\) | − | 121.177i | − | 0.257277i | ||||||
\(472\) | −153.264 | + | 231.508i | −0.324712 | + | 0.490484i | ||||
\(473\) | −377.093 | −0.797237 | ||||||||
\(474\) | 27.4065 | + | 80.3611i | 0.0578196 | + | 0.169538i | ||||
\(475\) | 84.2438i | 0.177355i | ||||||||
\(476\) | −822.139 | − | 1065.14i | −1.72718 | − | 2.23770i | ||||
\(477\) | −166.507 | −0.349072 | ||||||||
\(478\) | 27.4716 | − | 9.36894i | 0.0574719 | − | 0.0196003i | ||||
\(479\) | − | 451.971i | − | 0.943572i | −0.881713 | − | 0.471786i | \(-0.843609\pi\) | ||
0.881713 | − | 0.471786i | \(-0.156391\pi\) | |||||||
\(480\) | −4.53364 | − | 62.3697i | −0.00944509 | − | 0.129937i | ||||
\(481\) | −25.7390 | −0.0535114 | ||||||||
\(482\) | −179.623 | − | 526.689i | −0.372661 | − | 1.09272i | ||||
\(483\) | − | 140.134i | − | 0.290133i | ||||||
\(484\) | −118.018 | + | 91.0934i | −0.243840 | + | 0.188209i | ||||
\(485\) | −379.383 | −0.782232 | ||||||||
\(486\) | −340.465 | + | 116.113i | −0.700546 | + | 0.238915i | ||||
\(487\) | 293.894i | 0.603478i | 0.953391 | + | 0.301739i | \(0.0975671\pi\) | ||||
−0.953391 | + | 0.301739i | \(0.902433\pi\) | |||||||
\(488\) | −221.472 | − | 146.619i | −0.453835 | − | 0.300449i | ||||
\(489\) | 150.229 | 0.307216 | ||||||||
\(490\) | 160.187 | + | 469.699i | 0.326912 | + | 0.958568i | ||||
\(491\) | − | 91.3499i | − | 0.186049i | −0.995664 | − | 0.0930243i | \(-0.970347\pi\) | ||
0.995664 | − | 0.0930243i | \(-0.0296534\pi\) | |||||||
\(492\) | 77.0064 | + | 99.7677i | 0.156517 | + | 0.202780i | ||||
\(493\) | 1354.85 | 2.74818 | ||||||||
\(494\) | 7.75785 | − | 2.64575i | 0.0157041 | − | 0.00535576i | ||||
\(495\) | 181.481i | 0.366627i | ||||||||
\(496\) | −381.926 | − | 100.011i | −0.770012 | − | 0.201635i | ||||
\(497\) | 1100.13 | 2.21353 | ||||||||
\(498\) | 3.51137 | + | 10.2960i | 0.00705095 | + | 0.0206748i | ||||
\(499\) | − | 758.796i | − | 1.52063i | −0.649553 | − | 0.760316i | \(-0.725044\pi\) | ||
0.649553 | − | 0.760316i | \(-0.274956\pi\) | |||||||
\(500\) | −334.314 | + | 258.043i | −0.668628 | + | 0.516085i | ||||
\(501\) | 175.989 | 0.351275 | ||||||||
\(502\) | −651.649 | + | 222.239i | −1.29811 | + | 0.442708i | ||||
\(503\) | − | 55.4556i | − | 0.110250i | −0.998479 | − | 0.0551248i | \(-0.982444\pi\) | ||
0.998479 | − | 0.0551248i | \(-0.0175557\pi\) | |||||||
\(504\) | 455.113 | − | 687.457i | 0.903002 | − | 1.36400i | ||||
\(505\) | −83.7389 | −0.165820 | ||||||||
\(506\) | 81.5220 | + | 239.038i | 0.161111 | + | 0.472408i | ||||
\(507\) | − | 137.932i | − | 0.272055i | ||||||
\(508\) | −27.9149 | − | 36.1659i | −0.0549505 | − | 0.0711927i | ||||
\(509\) | −479.828 | −0.942688 | −0.471344 | − | 0.881949i | \(-0.656231\pi\) | ||||
−0.471344 | + | 0.881949i | \(0.656231\pi\) | |||||||
\(510\) | 100.541 | − | 34.2886i | 0.197139 | − | 0.0672325i | ||||
\(511\) | − | 245.763i | − | 0.480945i | ||||||
\(512\) | 93.4494 | − | 503.400i | 0.182518 | − | 0.983202i | ||||
\(513\) | 61.9658 | 0.120791 | ||||||||
\(514\) | 32.2817 | + | 94.6563i | 0.0628049 | + | 0.184156i | ||||
\(515\) | − | 279.184i | − | 0.542104i | ||||||
\(516\) | −107.064 | + | 82.6379i | −0.207488 | + | 0.160151i | ||||
\(517\) | 413.451 | 0.799712 | ||||||||
\(518\) | 641.355 | − | 218.729i | 1.23814 | − | 0.422256i | ||||
\(519\) | 22.3041i | 0.0429751i | ||||||||
\(520\) | 14.9385 | + | 9.88966i | 0.0287279 | + | 0.0190186i | ||||
\(521\) | 29.8875 | 0.0573656 | 0.0286828 | − | 0.999589i | \(-0.490869\pi\) | ||||
0.0286828 | + | 0.999589i | \(0.490869\pi\) | |||||||
\(522\) | 267.966 | + | 785.730i | 0.513346 | + | 1.50523i | ||||
\(523\) | − | 324.051i | − | 0.619600i | −0.950802 | − | 0.309800i | \(-0.899738\pi\) | ||
0.950802 | − | 0.309800i | \(-0.100262\pi\) | |||||||
\(524\) | −90.3110 | − | 117.005i | −0.172349 | − | 0.223292i | ||||
\(525\) | 196.251 | 0.373812 | ||||||||
\(526\) | −293.923 | + | 100.240i | −0.558788 | + | 0.190570i | ||||
\(527\) | − | 670.652i | − | 1.27259i | ||||||
\(528\) | 30.4285 | − | 116.201i | 0.0576297 | − | 0.220078i | ||||
\(529\) | 338.548 | 0.639978 | ||||||||
\(530\) | 30.7475 | + | 90.1577i | 0.0580141 | + | 0.170109i | ||||
\(531\) | − | 288.987i | − | 0.544232i | ||||||
\(532\) | −170.824 | + | 131.852i | −0.321097 | + | 0.247841i | ||||
\(533\) | −36.1065 | −0.0677420 | ||||||||
\(534\) | −48.9383 | + | 16.6900i | −0.0916447 | + | 0.0312546i | ||||
\(535\) | 456.912i | 0.854040i | ||||||||
\(536\) | 15.3766 | − | 23.2267i | 0.0286878 | − | 0.0433334i | ||||
\(537\) | 152.018 | 0.283087 | ||||||||
\(538\) | −295.208 | − | 865.607i | −0.548713 | − | 1.60893i | ||||
\(539\) | 953.250i | 1.76855i | ||||||||
\(540\) | 82.7561 | + | 107.217i | 0.153252 | + | 0.198550i | ||||
\(541\) | −584.274 | −1.07999 | −0.539994 | − | 0.841669i | \(-0.681574\pi\) | ||||
−0.539994 | + | 0.841669i | \(0.681574\pi\) | |||||||
\(542\) | −661.166 | + | 225.485i | −1.21986 | + | 0.416024i | ||||
\(543\) | 13.9600i | 0.0257091i | ||||||||
\(544\) | 867.446 | − | 63.0545i | 1.59457 | − | 0.115909i | ||||
\(545\) | 437.799 | 0.803301 | ||||||||
\(546\) | −6.16344 | − | 18.0724i | −0.0112884 | − | 0.0330996i | ||||
\(547\) | 173.706i | 0.317562i | 0.987314 | + | 0.158781i | \(0.0507564\pi\) | ||||
−0.987314 | + | 0.158781i | \(0.949244\pi\) | |||||||
\(548\) | 515.457 | − | 397.859i | 0.940614 | − | 0.726020i | ||||
\(549\) | 276.458 | 0.503567 | ||||||||
\(550\) | −334.762 | + | 114.168i | −0.608658 | + | 0.207578i | ||||
\(551\) | − | 217.286i | − | 0.394348i | ||||||
\(552\) | 75.5296 | + | 50.0024i | 0.136829 | + | 0.0905840i | ||||
\(553\) | 640.396 | 1.15804 | ||||||||
\(554\) | −70.0755 | − | 205.475i | −0.126490 | − | 0.370894i | ||||
\(555\) | 53.4974i | 0.0963917i | ||||||||
\(556\) | −560.261 | − | 725.862i | −1.00766 | − | 1.30551i | ||||
\(557\) | −590.355 | −1.05988 | −0.529942 | − | 0.848034i | \(-0.677786\pi\) | ||||
−0.529942 | + | 0.848034i | \(0.677786\pi\) | |||||||
\(558\) | 388.937 | − | 132.644i | 0.697020 | − | 0.237713i | ||||
\(559\) | − | 38.7470i | − | 0.0693148i | ||||||
\(560\) | −456.275 | − | 119.480i | −0.814776 | − | 0.213357i | ||||
\(561\) | 204.047 | 0.363720 | ||||||||
\(562\) | 122.951 | + | 360.516i | 0.218774 | + | 0.641487i | ||||
\(563\) | 1015.03i | 1.80290i | 0.432882 | + | 0.901450i | \(0.357497\pi\) | ||||
−0.432882 | + | 0.901450i | \(0.642503\pi\) | |||||||
\(564\) | 117.387 | − | 90.6056i | 0.208132 | − | 0.160648i | ||||
\(565\) | −173.807 | −0.307623 | ||||||||
\(566\) | −548.859 | + | 187.183i | −0.969715 | + | 0.330713i | ||||
\(567\) | 783.158i | 1.38123i | ||||||||
\(568\) | −392.545 | + | 592.947i | −0.691100 | + | 1.04392i | ||||
\(569\) | −98.2869 | −0.172736 | −0.0863681 | − | 0.996263i | \(-0.527526\pi\) | ||||
−0.0863681 | + | 0.996263i | \(0.527526\pi\) | |||||||
\(570\) | −5.49907 | − | 16.1244i | −0.00964749 | − | 0.0282883i | ||||
\(571\) | 366.213i | 0.641354i | 0.947189 | + | 0.320677i | \(0.103910\pi\) | ||||
−0.947189 | + | 0.320677i | \(0.896090\pi\) | |||||||
\(572\) | 21.0270 | + | 27.2421i | 0.0367604 | + | 0.0476260i | ||||
\(573\) | −1.98384 | −0.00346219 | ||||||||
\(574\) | 899.689 | − | 306.831i | 1.56740 | − | 0.534549i | ||||
\(575\) | − | 266.719i | − | 0.463859i | ||||||
\(576\) | 208.134 | + | 490.594i | 0.361343 | + | 0.851726i | ||||
\(577\) | −267.138 | −0.462977 | −0.231489 | − | 0.972838i | \(-0.574360\pi\) | ||||
−0.231489 | + | 0.972838i | \(0.574360\pi\) | |||||||
\(578\) | 290.320 | + | 851.275i | 0.502284 | + | 1.47279i | ||||
\(579\) | − | 123.653i | − | 0.213563i | ||||||
\(580\) | 375.961 | − | 290.188i | 0.648208 | − | 0.500324i | ||||
\(581\) | 82.0488 | 0.141220 | ||||||||
\(582\) | −247.377 | + | 84.3657i | −0.425046 | + | 0.144958i | ||||
\(583\) | 182.974i | 0.313850i | ||||||||
\(584\) | 132.461 | + | 87.6925i | 0.226817 | + | 0.150158i | ||||
\(585\) | −18.6475 | −0.0318760 | ||||||||
\(586\) | −114.835 | − | 336.719i | −0.195964 | − | 0.574605i | ||||
\(587\) | 245.452i | 0.418147i | 0.977900 | + | 0.209074i | \(0.0670448\pi\) | ||||
−0.977900 | + | 0.209074i | \(0.932955\pi\) | |||||||
\(588\) | 208.900 | + | 270.645i | 0.355271 | + | 0.460281i | ||||
\(589\) | −107.557 | −0.182609 | ||||||||
\(590\) | −156.476 | + | 53.3647i | −0.265213 | + | 0.0904487i | ||||
\(591\) | 220.049i | 0.372333i | ||||||||
\(592\) | −110.956 | + | 423.724i | −0.187426 | + | 0.715750i | ||||
\(593\) | 33.3697 | 0.0562726 | 0.0281363 | − | 0.999604i | \(-0.491043\pi\) | ||||
0.0281363 | + | 0.999604i | \(0.491043\pi\) | |||||||
\(594\) | 83.9764 | + | 246.235i | 0.141374 | + | 0.414537i | ||||
\(595\) | − | 801.207i | − | 1.34657i | ||||||
\(596\) | 349.352 | − | 269.649i | 0.586160 | − | 0.452432i | ||||
\(597\) | −253.205 | −0.424129 | ||||||||
\(598\) | −24.5616 | + | 8.37653i | −0.0410729 | + | 0.0140076i | ||||
\(599\) | − | 427.260i | − | 0.713288i | −0.934240 | − | 0.356644i | \(-0.883921\pi\) | ||
0.934240 | − | 0.356644i | \(-0.116079\pi\) | |||||||
\(600\) | −70.0260 | + | 105.776i | −0.116710 | + | 0.176293i | ||||
\(601\) | −316.625 | −0.526831 | −0.263415 | − | 0.964683i | \(-0.584849\pi\) | ||||
−0.263415 | + | 0.964683i | \(0.584849\pi\) | |||||||
\(602\) | 329.270 | + | 965.483i | 0.546960 | + | 1.60379i | ||||
\(603\) | 28.9934i | 0.0480820i | ||||||||
\(604\) | −255.983 | − | 331.646i | −0.423813 | − | 0.549083i | ||||
\(605\) | −88.7741 | −0.146734 | ||||||||
\(606\) | −54.6020 | + | 18.6215i | −0.0901023 | + | 0.0307286i | ||||
\(607\) | − | 467.840i | − | 0.770741i | −0.922762 | − | 0.385370i | \(-0.874074\pi\) | ||
0.922762 | − | 0.385370i | \(-0.125926\pi\) | |||||||
\(608\) | −10.1124 | − | 139.118i | −0.0166323 | − | 0.228812i | ||||
\(609\) | −506.181 | −0.831168 | ||||||||
\(610\) | −51.0512 | − | 149.692i | −0.0836905 | − | 0.245397i | ||||
\(611\) | 42.4829i | 0.0695300i | ||||||||
\(612\) | −716.627 | + | 553.134i | −1.17096 | + | 0.903813i | ||||
\(613\) | −636.118 | −1.03771 | −0.518856 | − | 0.854861i | \(-0.673642\pi\) | ||||
−0.518856 | + | 0.854861i | \(0.673642\pi\) | |||||||
\(614\) | −1049.25 | + | 357.838i | −1.70888 | + | 0.582797i | ||||
\(615\) | 75.0458i | 0.122026i | ||||||||
\(616\) | −755.444 | − | 500.122i | −1.22637 | − | 0.811886i | ||||
\(617\) | 331.487 | 0.537256 | 0.268628 | − | 0.963244i | \(-0.413430\pi\) | ||||
0.268628 | + | 0.963244i | \(0.413430\pi\) | |||||||
\(618\) | −62.0838 | − | 182.042i | −0.100459 | − | 0.294566i | ||||
\(619\) | − | 479.724i | − | 0.774999i | −0.921870 | − | 0.387500i | \(-0.873339\pi\) | ||
0.921870 | − | 0.387500i | \(-0.126661\pi\) | |||||||
\(620\) | −143.643 | − | 186.101i | −0.231683 | − | 0.300163i | ||||
\(621\) | −196.186 | −0.315919 | ||||||||
\(622\) | 128.259 | − | 43.7416i | 0.206204 | − | 0.0703241i | ||||
\(623\) | 389.988i | 0.625984i | ||||||||
\(624\) | 11.9399 | + | 3.12658i | 0.0191345 | + | 0.00501055i | ||||
\(625\) | 231.698 | 0.370718 | ||||||||
\(626\) | 288.731 | + | 846.615i | 0.461231 | + | 1.35242i | ||||
\(627\) | − | 32.7242i | − | 0.0521918i | ||||||
\(628\) | 467.672 | − | 360.976i | 0.744700 | − | 0.574802i | ||||
\(629\) | −744.049 | −1.18291 | ||||||||
\(630\) | 464.651 | − | 158.465i | 0.737541 | − | 0.251532i | ||||
\(631\) | 389.892i | 0.617896i | 0.951079 | + | 0.308948i | \(0.0999768\pi\) | ||||
−0.951079 | + | 0.308948i | \(0.900023\pi\) | |||||||
\(632\) | −228.505 | + | 345.161i | −0.361558 | + | 0.546141i | ||||
\(633\) | 274.041 | 0.432925 | ||||||||
\(634\) | 43.3924 | + | 127.235i | 0.0684423 | + | 0.200686i | ||||
\(635\) | − | 27.2042i | − | 0.0428412i | ||||||
\(636\) | 40.0978 | + | 51.9498i | 0.0630469 | + | 0.0816821i | ||||
\(637\) | −97.9481 | −0.153765 | ||||||||
\(638\) | 863.435 | − | 294.467i | 1.35335 | − | 0.461547i | ||||
\(639\) | − | 740.163i | − | 1.15831i | ||||||
\(640\) | 227.204 | − | 203.291i | 0.355007 | − | 0.317642i | ||||
\(641\) | −170.264 | −0.265623 | −0.132811 | − | 0.991141i | \(-0.542400\pi\) | ||||
−0.132811 | + | 0.991141i | \(0.542400\pi\) | |||||||
\(642\) | 101.606 | + | 297.929i | 0.158265 | + | 0.464064i | ||||
\(643\) | − | 420.651i | − | 0.654200i | −0.944990 | − | 0.327100i | \(-0.893929\pi\) | ||
0.944990 | − | 0.327100i | \(-0.106071\pi\) | |||||||
\(644\) | 540.834 | − | 417.447i | 0.839805 | − | 0.648209i | ||||
\(645\) | −80.5339 | −0.124859 | ||||||||
\(646\) | 224.260 | − | 76.4819i | 0.347151 | − | 0.118393i | ||||
\(647\) | 178.658i | 0.276133i | 0.990423 | + | 0.138067i | \(0.0440888\pi\) | ||||
−0.990423 | + | 0.138067i | \(0.955911\pi\) | |||||||
\(648\) | −422.107 | − | 279.445i | −0.651400 | − | 0.431242i | ||||
\(649\) | −317.566 | −0.489317 | ||||||||
\(650\) | −11.7309 | − | 34.3974i | −0.0180476 | − | 0.0529191i | ||||
\(651\) | 250.560i | 0.384885i | ||||||||
\(652\) | 447.517 | + | 579.793i | 0.686376 | + | 0.889253i | ||||
\(653\) | −950.370 | −1.45539 | −0.727696 | − | 0.685900i | \(-0.759409\pi\) | ||||
−0.727696 | + | 0.685900i | \(0.759409\pi\) | |||||||
\(654\) | 285.467 | − | 97.3561i | 0.436494 | − | 0.148862i | ||||
\(655\) | − | 88.0117i | − | 0.134369i | ||||||
\(656\) | −155.649 | + | 594.397i | −0.237270 | + | 0.906094i | ||||
\(657\) | −165.349 | −0.251672 | ||||||||
\(658\) | −361.017 | − | 1058.57i | −0.548658 | − | 1.60877i | ||||
\(659\) | − | 327.948i | − | 0.497645i | −0.968549 | − | 0.248823i | \(-0.919956\pi\) | ||
0.968549 | − | 0.248823i | \(-0.0800436\pi\) | |||||||
\(660\) | 56.6214 | − | 43.7036i | 0.0857900 | − | 0.0662176i | ||||
\(661\) | 256.403 | 0.387902 | 0.193951 | − | 0.981011i | \(-0.437870\pi\) | ||||
0.193951 | + | 0.981011i | \(0.437870\pi\) | |||||||
\(662\) | −337.794 | + | 115.202i | −0.510264 | + | 0.174021i | ||||
\(663\) | 20.9662i | 0.0316232i | ||||||||
\(664\) | −29.2765 | + | 44.2227i | −0.0440911 | + | 0.0666005i | ||||
\(665\) | −128.495 | −0.193225 | ||||||||
\(666\) | −147.160 | − | 431.503i | −0.220961 | − | 0.647902i | ||||
\(667\) | 687.935i | 1.03139i | ||||||||
\(668\) | 524.254 | + | 679.211i | 0.784811 | + | 1.01678i | ||||
\(669\) | 238.049 | 0.355828 | ||||||||
\(670\) | 15.6989 | − | 5.35397i | 0.0234312 | − | 0.00799100i | ||||
\(671\) | − | 303.799i | − | 0.452755i | ||||||
\(672\) | −324.084 | + | 23.5576i | −0.482267 | + | 0.0350560i | ||||
\(673\) | −624.347 | −0.927707 | −0.463853 | − | 0.885912i | \(-0.653534\pi\) | ||||
−0.463853 | + | 0.885912i | \(0.653534\pi\) | |||||||
\(674\) | −180.854 | − | 530.300i | −0.268330 | − | 0.786795i | ||||
\(675\) | − | 274.749i | − | 0.407036i | ||||||
\(676\) | 532.335 | − | 410.886i | 0.787477 | − | 0.607820i | ||||
\(677\) | −135.259 | −0.199791 | −0.0998955 | − | 0.994998i | \(-0.531851\pi\) | ||||
−0.0998955 | + | 0.994998i | \(0.531851\pi\) | |||||||
\(678\) | −113.331 | + | 38.6505i | −0.167155 | + | 0.0570067i | ||||
\(679\) | 1971.34i | 2.90330i | ||||||||
\(680\) | 431.835 | + | 285.885i | 0.635052 | + | 0.420419i | ||||
\(681\) | 62.5648 | 0.0918720 | ||||||||
\(682\) | −145.762 | − | 427.401i | −0.213727 | − | 0.626688i | ||||
\(683\) | 84.9635i | 0.124398i | 0.998064 | + | 0.0621988i | \(0.0198113\pi\) | ||||
−0.998064 | + | 0.0621988i | \(0.980189\pi\) | |||||||
\(684\) | 88.7095 | + | 114.930i | 0.129692 | + | 0.168026i | ||||
\(685\) | 387.729 | 0.566028 | ||||||||
\(686\) | 1292.67 | − | 440.853i | 1.88436 | − | 0.642644i | ||||
\(687\) | − | 174.577i | − | 0.254114i | ||||||
\(688\) | −637.866 | − | 167.032i | −0.927131 | − | 0.242778i | ||||
\(689\) | −18.8009 | −0.0272873 | ||||||||
\(690\) | 17.4103 | + | 51.0503i | 0.0252322 | + | 0.0739859i | ||||
\(691\) | − | 673.647i | − | 0.974887i | −0.873155 | − | 0.487443i | \(-0.837930\pi\) | ||
0.873155 | − | 0.487443i | \(-0.162070\pi\) | |||||||
\(692\) | −86.0804 | + | 66.4418i | −0.124394 | + | 0.0960141i | ||||
\(693\) | 943.005 | 1.36076 | ||||||||
\(694\) | −169.608 | + | 57.8435i | −0.244392 | + | 0.0833479i | ||||
\(695\) | − | 545.997i | − | 0.785607i | ||||||
\(696\) | 180.615 | − | 272.822i | 0.259504 | − | 0.391986i | ||||
\(697\) | −1043.75 | −1.49749 | ||||||||
\(698\) | 3.47589 | + | 10.1920i | 0.00497979 | + | 0.0146017i | ||||
\(699\) | − | 89.0225i | − | 0.127357i | ||||||
\(700\) | 584.615 | + | 757.413i | 0.835164 | + | 1.08202i | ||||
\(701\) | 406.227 | 0.579496 | 0.289748 | − | 0.957103i | \(-0.406429\pi\) | ||||
0.289748 | + | 0.957103i | \(0.406429\pi\) | |||||||
\(702\) | −25.3011 | + | 8.62873i | −0.0360415 | + | 0.0122916i | ||||
\(703\) | 119.328i | 0.169741i | ||||||||
\(704\) | 539.112 | − | 228.717i | 0.765784 | − | 0.324883i | ||||
\(705\) | 88.2988 | 0.125246 | ||||||||
\(706\) | 231.014 | + | 677.378i | 0.327215 | + | 0.959459i | ||||
\(707\) | 435.122i | 0.615448i | ||||||||
\(708\) | −90.1631 | + | 69.5930i | −0.127349 | + | 0.0982952i | ||||
\(709\) | 668.985 | 0.943561 | 0.471780 | − | 0.881716i | \(-0.343611\pi\) | ||||
0.471780 | + | 0.881716i | \(0.343611\pi\) | |||||||
\(710\) | −400.771 | + | 136.680i | −0.564466 | + | 0.192506i | ||||
\(711\) | − | 430.857i | − | 0.605988i | ||||||
\(712\) | −210.196 | − | 139.155i | −0.295219 | − | 0.195442i | ||||
\(713\) | 340.528 | 0.477599 | ||||||||
\(714\) | −178.169 | − | 522.428i | −0.249537 | − | 0.731691i | ||||
\(715\) | 20.4916i | 0.0286596i | ||||||||
\(716\) | 452.846 | + | 586.697i | 0.632467 | + | 0.819409i | ||||
\(717\) | 11.9070 | 0.0166066 | ||||||||
\(718\) | 787.072 | − | 268.424i | 1.09620 | − | 0.373850i | ||||
\(719\) | − | 357.444i | − | 0.497140i | −0.968614 | − | 0.248570i | \(-0.920039\pi\) | ||
0.968614 | − | 0.248570i | \(-0.0799606\pi\) | |||||||
\(720\) | −80.3860 | + | 306.981i | −0.111647 | + | 0.426362i | ||||
\(721\) | −1450.69 | −2.01205 | ||||||||
\(722\) | −12.2659 | − | 35.9659i | −0.0169887 | − | 0.0498143i | ||||
\(723\) | − | 228.282i | − | 0.315743i | ||||||
\(724\) | −53.8774 | + | 41.5857i | −0.0744163 | + | 0.0574387i | ||||
\(725\) | −963.420 | −1.32886 | ||||||||
\(726\) | −57.8852 | + | 19.7412i | −0.0797317 | + | 0.0271918i | ||||
\(727\) | − | 931.519i | − | 1.28132i | −0.767825 | − | 0.640659i | \(-0.778661\pi\) | ||
0.767825 | − | 0.640659i | \(-0.221339\pi\) | |||||||
\(728\) | 51.3884 | − | 77.6232i | 0.0705885 | − | 0.106625i | ||||
\(729\) | 421.935 | 0.578787 | ||||||||
\(730\) | 30.5335 | + | 89.5303i | 0.0418267 | + | 0.122644i | ||||
\(731\) | − | 1120.08i | − | 1.53225i | ||||||
\(732\) | −66.5759 | − | 86.2542i | −0.0909507 | − | 0.117834i | ||||
\(733\) | −342.315 | −0.467006 | −0.233503 | − | 0.972356i | \(-0.575019\pi\) | ||||
−0.233503 | + | 0.972356i | \(0.575019\pi\) | |||||||
\(734\) | −497.266 | + | 169.588i | −0.677474 | + | 0.231047i | ||||
\(735\) | 203.581i | 0.276981i | ||||||||
\(736\) | 32.0164 | + | 440.451i | 0.0435005 | + | 0.598440i | ||||
\(737\) | 31.8608 | 0.0432303 | ||||||||
\(738\) | −206.435 | − | 605.309i | −0.279723 | − | 0.820202i | ||||
\(739\) | 233.486i | 0.315949i | 0.987443 | + | 0.157975i | \(0.0504964\pi\) | ||||
−0.987443 | + | 0.157975i | \(0.949504\pi\) | |||||||
\(740\) | −206.468 | + | 159.364i | −0.279011 | + | 0.215356i | ||||
\(741\) | 3.36248 | 0.00453775 | ||||||||
\(742\) | 468.475 | − | 159.769i | 0.631368 | − | 0.215323i | ||||
\(743\) | 684.601i | 0.921401i | 0.887556 | + | 0.460701i | \(0.152402\pi\) | ||||
−0.887556 | + | 0.460701i | \(0.847598\pi\) | |||||||
\(744\) | −135.047 | − | 89.4044i | −0.181515 | − | 0.120167i | ||||
\(745\) | 262.784 | 0.352730 | ||||||||
\(746\) | 102.223 | + | 299.737i | 0.137028 | + | 0.401792i | ||||
\(747\) | − | 55.2023i | − | 0.0738987i | ||||||
\(748\) | 607.836 | + | 787.499i | 0.812615 | + | 1.05281i | ||||
\(749\) | 2374.19 | 3.16982 | ||||||||
\(750\) | −163.973 | + | 55.9216i | −0.218631 | + | 0.0745621i | ||||
\(751\) | 985.017i | 1.31161i | 0.754931 | + | 0.655804i | \(0.227670\pi\) | ||||
−0.754931 | + | 0.655804i | \(0.772330\pi\) | |||||||
\(752\) | 699.367 | + | 183.136i | 0.930010 | + | 0.243532i | ||||
\(753\) | −282.444 | −0.375091 | ||||||||
\(754\) | 30.2570 | + | 88.7195i | 0.0401287 | + | 0.117665i | ||||
\(755\) | − | 249.466i | − | 0.330418i | ||||||
\(756\) | 557.118 | − | 430.015i | 0.736928 | − | 0.568803i | ||||
\(757\) | 1162.89 | 1.53619 | 0.768094 | − | 0.640338i | \(-0.221206\pi\) | ||||
0.768094 | + | 0.640338i | \(0.221206\pi\) | |||||||
\(758\) | −1020.55 | + | 348.051i | −1.34638 | + | 0.459171i | ||||
\(759\) | 103.606i | 0.136503i | ||||||||
\(760\) | 45.8491 | − | 69.2561i | 0.0603278 | − | 0.0911264i | ||||
\(761\) | −460.254 | −0.604802 | −0.302401 | − | 0.953181i | \(-0.597788\pi\) | ||||
−0.302401 | + | 0.953181i | \(0.597788\pi\) | |||||||
\(762\) | −6.04956 | − | 17.7385i | −0.00793905 | − | 0.0232788i | ||||
\(763\) | − | 2274.88i | − | 2.98149i | ||||||
\(764\) | −5.90967 | − | 7.65643i | −0.00773516 | − | 0.0100215i | ||||
\(765\) | −539.051 | −0.704642 | ||||||||
\(766\) | 800.356 | − | 272.954i | 1.04485 | − | 0.356337i | ||||
\(767\) | − | 32.6305i | − | 0.0425431i | ||||||
\(768\) | 102.942 | − | 183.081i | 0.134039 | − | 0.238386i | ||||
\(769\) | 757.145 | 0.984584 | 0.492292 | − | 0.870430i | \(-0.336159\pi\) | ||||
0.492292 | + | 0.870430i | \(0.336159\pi\) | |||||||
\(770\) | −174.137 | − | 510.603i | −0.226151 | − | 0.663120i | ||||
\(771\) | 41.0268i | 0.0532124i | ||||||||
\(772\) | 477.226 | − | 368.350i | 0.618168 | − | 0.477138i | ||||
\(773\) | 1071.48 | 1.38614 | 0.693068 | − | 0.720872i | \(-0.256258\pi\) | ||||
0.693068 | + | 0.720872i | \(0.256258\pi\) | |||||||
\(774\) | 649.575 | − | 221.532i | 0.839245 | − | 0.286217i | ||||
\(775\) | 476.894i | 0.615347i | ||||||||
\(776\) | −1062.51 | − | 703.409i | −1.36922 | − | 0.906455i | ||||
\(777\) | 277.982 | 0.357763 | ||||||||
\(778\) | −314.452 | − | 922.036i | −0.404180 | − | 1.18514i | ||||
\(779\) | 167.392i | 0.214881i | ||||||||
\(780\) | 4.49063 | + | 5.81795i | 0.00575721 | + | 0.00745891i | ||||
\(781\) | −813.362 | −1.04144 | ||||||||
\(782\) | −710.014 | + | 242.144i | −0.907946 | + | 0.309647i | ||||
\(783\) | 708.647i | 0.905041i | ||||||||
\(784\) | −422.238 | + | 1612.46i | −0.538568 | + | 2.05670i | ||||
\(785\) | 351.785 | 0.448134 | ||||||||
\(786\) | −19.5717 | − | 57.3880i | −0.0249004 | − | 0.0730128i | ||||
\(787\) | − | 625.691i | − | 0.795033i | −0.917595 | − | 0.397517i | \(-0.869872\pi\) | ||
0.917595 | − | 0.397517i | \(-0.130128\pi\) | |||||||
\(788\) | −849.257 | + | 655.505i | −1.07774 | + | 0.831859i | ||||
\(789\) | −127.395 | −0.161463 | ||||||||
\(790\) | −233.293 | + | 79.5627i | −0.295308 | + | 0.100712i | ||||
\(791\) | 903.132i | 1.14176i | ||||||||
\(792\) | −336.481 | + | 508.261i | −0.424850 | + | 0.641744i | ||||
\(793\) | 31.2159 | 0.0393643 | ||||||||
\(794\) | −417.481 | − | 1224.14i | −0.525795 | − | 1.54173i | ||||
\(795\) | 39.0769i | 0.0491534i | ||||||||
\(796\) | −754.275 | − | 977.221i | −0.947582 | − | 1.22766i | ||||
\(797\) | −549.357 | −0.689281 | −0.344641 | − | 0.938735i | \(-0.611999\pi\) | ||||
−0.344641 | + | 0.938735i | \(0.611999\pi\) | |||||||
\(798\) | −83.7850 | + | 28.5741i | −0.104994 | + | 0.0358072i | ||||
\(799\) | 1228.07i | 1.53701i | ||||||||
\(800\) | −616.832 | + | 44.8374i | −0.771040 | + | 0.0560468i | ||||
\(801\) | 262.383 | 0.327570 | ||||||||
\(802\) | −9.07386 | − | 26.6063i | −0.0113140 | − | 0.0331750i | ||||
\(803\) | 181.701i | 0.226278i | ||||||||
\(804\) | 9.04587 | − | 6.98212i | 0.0112511 | − | 0.00868422i | ||||
\(805\) | 406.818 | 0.505364 | ||||||||
\(806\) | 43.9162 | − | 14.9773i | 0.0544867 | − | 0.0185822i | ||||
\(807\) | − | 375.179i | − | 0.464906i | ||||||
\(808\) | −234.522 | − | 155.259i | −0.290250 | − | 0.192153i | ||||
\(809\) | −7.38519 | −0.00912879 | −0.00456440 | − | 0.999990i | \(-0.501453\pi\) | ||||
−0.00456440 | + | 0.999990i | \(0.501453\pi\) | |||||||
\(810\) | −97.2995 | − | 285.301i | −0.120123 | − | 0.352223i | ||||
\(811\) | − | 1100.76i | − | 1.35729i | −0.734466 | − | 0.678645i | \(-0.762567\pi\) | ||
0.734466 | − | 0.678645i | \(-0.237433\pi\) | |||||||
\(812\) | −1507.87 | − | 1953.56i | −1.85698 | − | 2.40586i | ||||
\(813\) | −286.569 | −0.352483 | ||||||||
\(814\) | −474.176 | + | 161.714i | −0.582526 | + | 0.198666i | ||||
\(815\) | 436.123i | 0.535121i | ||||||||
\(816\) | 345.152 | + | 90.3816i | 0.422981 | + | 0.110762i | ||||
\(817\) | −179.634 | −0.219870 | ||||||||
\(818\) | 92.7479 | + | 271.955i | 0.113384 | + | 0.332463i | ||||
\(819\) | 96.8955i | 0.118309i | ||||||||
\(820\) | −289.632 | + | 223.554i | −0.353210 | + | 0.272627i | ||||
\(821\) | 80.5795 | 0.0981480 | 0.0490740 | − | 0.998795i | \(-0.484373\pi\) | ||||
0.0490740 | + | 0.998795i | \(0.484373\pi\) | |||||||
\(822\) | 252.819 | − | 86.2218i | 0.307566 | − | 0.104893i | ||||
\(823\) | − | 980.615i | − | 1.19151i | −0.803165 | − | 0.595756i | \(-0.796852\pi\) | ||
0.803165 | − | 0.595756i | \(-0.203148\pi\) | |||||||
\(824\) | 517.631 | − | 781.892i | 0.628193 | − | 0.948898i | ||||
\(825\) | −145.096 | −0.175873 | ||||||||
\(826\) | 277.293 | + | 813.076i | 0.335705 | + | 0.984353i | ||||
\(827\) | 1517.68i | 1.83516i | 0.397553 | + | 0.917579i | \(0.369859\pi\) | ||||
−0.397553 | + | 0.917579i | \(0.630141\pi\) | |||||||
\(828\) | −280.857 | − | 363.872i | −0.339200 | − | 0.439459i | ||||
\(829\) | −229.487 | −0.276823 | −0.138412 | − | 0.990375i | \(-0.544200\pi\) | ||||
−0.138412 | + | 0.990375i | \(0.544200\pi\) | |||||||
\(830\) | −29.8900 | + | 10.1937i | −0.0360121 | + | 0.0122816i | ||||
\(831\) | − | 89.0589i | − | 0.107171i | ||||||
\(832\) | 23.5011 | + | 55.3947i | 0.0282465 | + | 0.0665802i | ||||
\(833\) | −2831.43 | −3.39908 | ||||||||
\(834\) | −121.417 | − | 356.018i | −0.145584 | − | 0.426880i | ||||
\(835\) | 510.906i | 0.611863i | ||||||||
\(836\) | 126.296 | − | 97.4825i | 0.151072 | − | 0.116606i | ||||
\(837\) | 350.781 | 0.419093 | ||||||||
\(838\) | 1083.61 | − | 369.557i | 1.29310 | − | 0.440999i | ||||
\(839\) | 949.272i | 1.13143i | 0.824600 | + | 0.565716i | \(0.191400\pi\) | ||||
−0.824600 | + | 0.565716i | \(0.808600\pi\) | |||||||
\(840\) | −161.337 | − | 106.809i | −0.192067 | − | 0.127153i | ||||
\(841\) | 1643.90 | 1.95470 | ||||||||
\(842\) | 463.884 | + | 1360.20i | 0.550931 | + | 1.61544i | ||||
\(843\) | 156.258i | 0.185359i | ||||||||
\(844\) | 816.344 | + | 1057.64i | 0.967232 | + | 1.25312i | ||||
\(845\) | 400.425 | 0.473876 | ||||||||
\(846\) | −712.206 | + | 242.892i | −0.841851 | + | 0.287106i | ||||
\(847\) | 461.286i | 0.544611i | ||||||||
\(848\) | −81.0476 | + | 309.508i | −0.0955750 | + | 0.364985i | ||||
\(849\) | −237.891 | −0.280202 | ||||||||
\(850\) | −339.112 | − | 994.342i | −0.398955 | − | 1.16981i | ||||
\(851\) | − | 377.796i | − | 0.443944i | ||||||
\(852\) | −230.929 | + | 178.244i | −0.271043 | + | 0.209207i | ||||
\(853\) | 245.110 | 0.287350 | 0.143675 | − | 0.989625i | \(-0.454108\pi\) | ||||
0.143675 | + | 0.989625i | \(0.454108\pi\) | |||||||
\(854\) | −777.826 | + | 265.271i | −0.910803 | + | 0.310622i | ||||
\(855\) | 86.4509i | 0.101112i | ||||||||
\(856\) | −847.154 | + | 1279.64i | −0.989666 | + | 1.49491i | ||||
\(857\) | 659.731 | 0.769814 | 0.384907 | − | 0.922955i | \(-0.374234\pi\) | ||||
0.384907 | + | 0.922955i | \(0.374234\pi\) | |||||||
\(858\) | 4.55685 | + | 13.3616i | 0.00531101 | + | 0.0155729i | ||||
\(859\) | − | 1240.81i | − | 1.44449i | −0.691639 | − | 0.722244i | \(-0.743111\pi\) | ||
0.691639 | − | 0.722244i | \(-0.256889\pi\) | |||||||
\(860\) | −239.903 | − | 310.813i | −0.278957 | − | 0.361410i | ||||
\(861\) | 389.951 | 0.452905 | ||||||||
\(862\) | 477.397 | − | 162.812i | 0.553825 | − | 0.188877i | ||||
\(863\) | 1063.44i | 1.23226i | 0.787646 | + | 0.616129i | \(0.211300\pi\) | ||||
−0.787646 | + | 0.616129i | \(0.788700\pi\) | |||||||
\(864\) | 32.9803 | + | 453.713i | 0.0381717 | + | 0.525130i | ||||
\(865\) | −64.7501 | −0.0748556 | ||||||||
\(866\) | 154.297 | + | 452.429i | 0.178172 | + | 0.522435i | ||||
\(867\) | 368.967i | 0.425568i | ||||||||
\(868\) | −967.013 | + | 746.396i | −1.11407 | + | 0.859903i | ||||
\(869\) | −473.467 | −0.544841 | ||||||||
\(870\) | 184.400 | − | 62.8879i | 0.211954 | − | 0.0722850i | ||||
\(871\) | 3.27375i | 0.00375861i | ||||||||
\(872\) | 1226.12 | + | 811.718i | 1.40610 | + | 0.930869i | ||||
\(873\) | 1326.31 | 1.51926 | ||||||||
\(874\) | 38.8342 | + | 113.869i | 0.0444327 | + | 0.130285i | ||||
\(875\) | 1306.70i | 1.49337i | ||||||||
\(876\) | 39.8188 | + | 51.5883i | 0.0454553 | + | 0.0588908i | ||||
\(877\) | −867.685 | −0.989379 | −0.494689 | − | 0.869070i | \(-0.664718\pi\) | ||||
−0.494689 | + | 0.869070i | \(0.664718\pi\) | |||||||
\(878\) | −32.7006 | + | 11.1522i | −0.0372444 | + | 0.0127019i | ||||
\(879\) | − | 145.944i | − | 0.166034i | ||||||
\(880\) | 337.340 | + | 88.3358i | 0.383341 | + | 0.100382i | ||||
\(881\) | 1540.22 | 1.74826 | 0.874132 | − | 0.485688i | \(-0.161431\pi\) | ||||
0.874132 | + | 0.485688i | \(0.161431\pi\) | |||||||
\(882\) | −560.009 | − | 1642.06i | −0.634931 | − | 1.86174i | ||||
\(883\) | 590.651i | 0.668914i | 0.942411 | + | 0.334457i | \(0.108553\pi\) | ||||
−0.942411 | + | 0.334457i | \(0.891447\pi\) | |||||||
\(884\) | −80.9169 | + | 62.4563i | −0.0915350 | + | 0.0706519i | ||||
\(885\) | −67.8211 | −0.0766341 | ||||||||
\(886\) | −305.235 | + | 104.098i | −0.344509 | + | 0.117492i | ||||
\(887\) | − | 336.467i | − | 0.379332i | −0.981849 | − | 0.189666i | \(-0.939259\pi\) | ||
0.981849 | − | 0.189666i | \(-0.0607405\pi\) | |||||||
\(888\) | −99.1889 | + | 149.827i | −0.111699 | + | 0.168724i | ||||
\(889\) | −141.358 | −0.159007 | ||||||||
\(890\) | −48.4521 | − | 142.071i | −0.0544405 | − | 0.159630i | ||||
\(891\) | − | 579.016i | − | 0.649850i | ||||||
\(892\) | 709.125 | + | 918.726i | 0.794983 | + | 1.02996i | ||||
\(893\) | 196.954 | 0.220553 | ||||||||
\(894\) | 171.349 | − | 58.4369i | 0.191665 | − | 0.0653657i | ||||
\(895\) | 441.316i | 0.493091i | ||||||||
\(896\) | −1056.33 | − | 1180.59i | −1.17894 | − | 1.31763i | ||||
\(897\) | −10.6457 | −0.0118681 | ||||||||
\(898\) | 362.781 | + | 1063.74i | 0.403987 | + | 1.18457i | ||||
\(899\) | − | 1230.03i | − | 1.36822i | ||||||
\(900\) | 509.586 | − | 393.328i | 0.566207 | − | 0.437031i | ||||
\(901\) | −543.488 | −0.603205 | ||||||||
\(902\) | −665.171 | + | 226.851i | −0.737440 | + | 0.251498i | ||||
\(903\) | 418.468i | 0.463420i | ||||||||
\(904\) | −486.770 | − | 322.253i | −0.538463 | − | 0.356475i | ||||
\(905\) | −40.5269 | −0.0447811 | ||||||||
\(906\) | −55.4753 | − | 162.664i | −0.0612310 | − | 0.179541i | ||||
\(907\) | − | 850.338i | − | 0.937528i | −0.883323 | − | 0.468764i | \(-0.844699\pi\) | ||
0.883323 | − | 0.468764i | \(-0.155301\pi\) | |||||||
\(908\) | 186.375 | + | 241.463i | 0.205259 | + | 0.265928i | ||||
\(909\) | 292.749 | 0.322056 | ||||||||
\(910\) | 52.4653 | − | 17.8929i | 0.0576542 | − | 0.0196625i | ||||
\(911\) | − | 1658.66i | − | 1.82070i | −0.413837 | − | 0.910351i | \(-0.635812\pi\) | ||
0.413837 | − | 0.910351i | \(-0.364188\pi\) | |||||||
\(912\) | 14.4951 | − | 55.3542i | 0.0158937 | − | 0.0606954i | ||||
\(913\) | −60.6616 | −0.0664420 | ||||||||
\(914\) | −69.3186 | − | 203.256i | −0.0758409 | − | 0.222380i | ||||
\(915\) | − | 64.8809i | − | 0.0709080i | ||||||
\(916\) | 673.761 | − | 520.047i | 0.735547 | − | 0.567737i | ||||
\(917\) | −457.324 | −0.498718 | ||||||||
\(918\) | −731.391 | + | 249.435i | −0.796723 | + | 0.271715i | ||||
\(919\) | 684.608i | 0.744948i | 0.928043 | + | 0.372474i | \(0.121490\pi\) | ||||
−0.928043 | + | 0.372474i | \(0.878510\pi\) | |||||||
\(920\) | −145.160 | + | 219.267i | −0.157783 | + | 0.238334i | ||||
\(921\) | −454.775 | −0.493784 | ||||||||
\(922\) | 430.147 | + | 1261.27i | 0.466537 | + | 1.36798i | ||||
\(923\) | − | 83.5744i | − | 0.0905465i | ||||||
\(924\) | −227.092 | − | 294.215i | −0.245770 | − | 0.318414i | ||||
\(925\) | 529.086 | 0.571985 | ||||||||
\(926\) | 515.558 | − | 175.827i | 0.556758 | − | 0.189878i | ||||
\(927\) | 976.020i | 1.05288i | ||||||||
\(928\) | 1590.96 | − | 115.647i | 1.71440 | − | 0.124620i | ||||
\(929\) | −191.705 | −0.206356 | −0.103178 | − | 0.994663i | \(-0.532901\pi\) | ||||
−0.103178 | + | 0.994663i | \(0.532901\pi\) | |||||||
\(930\) | −31.1296 | − | 91.2780i | −0.0334727 | − | 0.0981484i | ||||
\(931\) | 454.094i | 0.487749i | ||||||||
\(932\) | 343.574 | − | 265.190i | 0.368641 | − | 0.284538i | ||||
\(933\) | 55.5911 | 0.0595832 | ||||||||
\(934\) | −1331.47 | + | 454.087i | −1.42556 | + | 0.486174i | ||||
\(935\) | 592.361i | 0.633541i | ||||||||
\(936\) | −52.2248 | − | 34.5740i | −0.0557957 | − | 0.0369381i | ||||
\(937\) | 1030.61 | 1.09990 | 0.549951 | − | 0.835197i | \(-0.314646\pi\) | ||||
0.549951 | + | 0.835197i | \(0.314646\pi\) | |||||||
\(938\) | −27.8202 | − | 81.5742i | −0.0296590 | − | 0.0869660i | ||||
\(939\) | 366.948i | 0.390785i | ||||||||
\(940\) | 263.034 | + | 340.781i | 0.279823 | + | 0.362533i | ||||
\(941\) | −551.115 | −0.585669 | −0.292835 | − | 0.956163i | \(-0.594599\pi\) | ||||
−0.292835 | + | 0.956163i | \(0.594599\pi\) | |||||||
\(942\) | 229.382 | − | 78.2287i | 0.243505 | − | 0.0830453i | ||||
\(943\) | − | 529.970i | − | 0.562004i | ||||||
\(944\) | −537.175 | − | 140.665i | −0.569041 | − | 0.149009i | ||||
\(945\) | 419.067 | 0.443457 | ||||||||
\(946\) | −243.441 | − | 713.816i | −0.257337 | − | 0.754562i | ||||
\(947\) | 1465.05i | 1.54704i | 0.633773 | + | 0.773519i | \(0.281506\pi\) | ||||
−0.633773 | + | 0.773519i | \(0.718494\pi\) | |||||||
\(948\) | −134.426 | + | 103.758i | −0.141800 | + | 0.109449i | ||||
\(949\) | −18.6701 | −0.0196734 | ||||||||
\(950\) | −159.469 | + | 54.3855i | −0.167862 | + | 0.0572478i | ||||
\(951\) | 55.1473i | 0.0579888i | ||||||||
\(952\) | 1485.51 | − | 2243.89i | 1.56041 | − | 2.35703i | ||||
\(953\) | −572.440 | −0.600671 | −0.300336 | − | 0.953834i | \(-0.597099\pi\) | ||||
−0.300336 | + | 0.953834i | \(0.597099\pi\) | |||||||
\(954\) | −107.493 | − | 315.189i | −0.112676 | − | 0.330387i | ||||
\(955\) | − | 5.75920i | − | 0.00603058i | ||||||
\(956\) | 35.4697 | + | 45.9538i | 0.0371022 | + | 0.0480688i | ||||
\(957\) | 374.238 | 0.391053 | ||||||||
\(958\) | 855.556 | − | 291.780i | 0.893065 | − | 0.304572i | ||||
\(959\) | − | 2014.71i | − | 2.10084i | ||||||
\(960\) | 115.135 | − | 48.8460i | 0.119933 | − | 0.0508813i | ||||
\(961\) | 352.134 | 0.366425 | ||||||||
\(962\) | −16.6164 | − | 48.7225i | −0.0172727 | − | 0.0506471i | ||||
\(963\) | − | 1597.35i | − | 1.65873i | ||||||
\(964\) | 881.033 | − | 680.031i | 0.913934 | − | 0.705426i | ||||
\(965\) | 358.972 | 0.371992 | ||||||||
\(966\) | 265.266 | − | 90.4667i | 0.274603 | − | 0.0936509i | ||||
\(967\) | − | 228.290i | − | 0.236080i | −0.993009 | − | 0.118040i | \(-0.962339\pi\) | ||
0.993009 | − | 0.118040i | \(-0.0376612\pi\) | |||||||
\(968\) | −248.624 | − | 164.595i | −0.256843 | − | 0.170036i | ||||
\(969\) | 97.2007 | 0.100310 | ||||||||
\(970\) | −244.919 | − | 718.150i | −0.252494 | − | 0.740361i | ||||
\(971\) | 1338.46i | 1.37843i | 0.724555 | + | 0.689217i | \(0.242045\pi\) | ||||
−0.724555 | + | 0.689217i | \(0.757955\pi\) | |||||||
\(972\) | −439.590 | − | 569.523i | −0.452253 | − | 0.585929i | ||||
\(973\) | −2837.10 | −2.91582 | ||||||||
\(974\) | −556.324 | + | 189.730i | −0.571175 | + | 0.194794i | ||||
\(975\) | − | 14.9088i | − | 0.0152911i | ||||||
\(976\) | 134.566 | − | 513.887i | 0.137875 | − | 0.526523i | ||||
\(977\) | 396.018 | 0.405341 | 0.202671 | − | 0.979247i | \(-0.435038\pi\) | ||||
0.202671 | + | 0.979247i | \(0.435038\pi\) | |||||||
\(978\) | 96.9835 | + | 284.374i | 0.0991651 | + | 0.290771i | ||||
\(979\) | − | 288.332i | − | 0.294517i | ||||||
\(980\) | −785.701 | + | 606.449i | −0.801736 | + | 0.618825i | ||||
\(981\) | −1530.54 | −1.56018 | ||||||||
\(982\) | 172.920 | − | 58.9729i | 0.176090 | − | 0.0600539i | ||||
\(983\) | − | 169.385i | − | 0.172315i | −0.996282 | − | 0.0861573i | \(-0.972541\pi\) | ||
0.996282 | − | 0.0861573i | \(-0.0274588\pi\) | |||||||
\(984\) | −139.141 | + | 210.176i | −0.141404 | + | 0.213593i | ||||
\(985\) | −638.816 | −0.648544 | ||||||||
\(986\) | 874.654 | + | 2564.66i | 0.887073 | + | 2.60107i | ||||
\(987\) | − | 458.816i | − | 0.464859i | ||||||
\(988\) | 10.0165 | + | 12.9772i | 0.0101382 | + | 0.0131348i | ||||
\(989\) | 568.727 | 0.575052 | ||||||||
\(990\) | −343.533 | + | 117.159i | −0.347003 | + | 0.118342i | ||||
\(991\) | − | 899.988i | − | 0.908161i | −0.890961 | − | 0.454080i | \(-0.849968\pi\) | ||
0.890961 | − | 0.454080i | \(-0.150032\pi\) | |||||||
\(992\) | −57.2454 | − | 787.529i | −0.0577070 | − | 0.793880i | ||||
\(993\) | −146.410 | −0.147442 | ||||||||
\(994\) | 710.211 | + | 2082.48i | 0.714498 | + | 2.09505i | ||||
\(995\) | − | 735.071i | − | 0.738765i | ||||||
\(996\) | −17.2230 | + | 13.2937i | −0.0172921 | + | 0.0133471i | ||||
\(997\) | −1265.57 | −1.26938 | −0.634689 | − | 0.772768i | \(-0.718872\pi\) | ||||
−0.634689 | + | 0.772768i | \(0.718872\pi\) | |||||||
\(998\) | 1436.36 | − | 489.857i | 1.43924 | − | 0.490839i | ||||
\(999\) | − | 389.171i | − | 0.389560i |
(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 | 76.3.b.b.39.8 | yes | 14 | |
3.2 | odd | 2 | 684.3.g.b.343.7 | 14 | |||
4.3 | odd | 2 | inner | 76.3.b.b.39.7 | ✓ | 14 | |
8.3 | odd | 2 | 1216.3.d.d.191.9 | 14 | |||
8.5 | even | 2 | 1216.3.d.d.191.6 | 14 | |||
12.11 | even | 2 | 684.3.g.b.343.8 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.b.b.39.7 | ✓ | 14 | 4.3 | odd | 2 | inner | |
76.3.b.b.39.8 | yes | 14 | 1.1 | even | 1 | trivial | |
684.3.g.b.343.7 | 14 | 3.2 | odd | 2 | |||
684.3.g.b.343.8 | 14 | 12.11 | even | 2 | |||
1216.3.d.d.191.6 | 14 | 8.5 | even | 2 | |||
1216.3.d.d.191.9 | 14 | 8.3 | odd | 2 |