Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(44,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.44");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.o (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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 44.18 | ||
Character | \(\chi\) | \(=\) | 105.44 |
Dual form | 105.3.o.b.74.18 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.60486 | − | 2.77971i | 0.802432 | − | 1.38985i | −0.115579 | − | 0.993298i | \(-0.536872\pi\) |
0.918011 | − | 0.396555i | \(-0.129794\pi\) | |||||||
\(3\) | 2.69226 | + | 1.32352i | 0.897421 | + | 0.441174i | ||||
\(4\) | −3.15118 | − | 5.45800i | −0.787795 | − | 1.36450i | ||||
\(5\) | −1.12712 | − | 4.87130i | −0.225423 | − | 0.974261i | ||||
\(6\) | 7.99972 | − | 5.35963i | 1.33329 | − | 0.893272i | ||||
\(7\) | −6.02754 | + | 3.55932i | −0.861077 | + | 0.508474i | ||||
\(8\) | −7.38994 | −0.923743 | ||||||||
\(9\) | 5.49658 | + | 7.12655i | 0.610731 | + | 0.791838i | ||||
\(10\) | −15.3497 | − | 4.68473i | −1.53497 | − | 0.468473i | ||||
\(11\) | 10.5523 | − | 6.09236i | 0.959298 | − | 0.553851i | 0.0633411 | − | 0.997992i | \(-0.479824\pi\) |
0.895957 | + | 0.444141i | \(0.146491\pi\) | |||||||
\(12\) | −1.26002 | − | 18.8650i | −0.105002 | − | 1.57209i | ||||
\(13\) | 8.47270i | 0.651746i | 0.945414 | + | 0.325873i | \(0.105658\pi\) | ||||
−0.945414 | + | 0.325873i | \(0.894342\pi\) | |||||||
\(14\) | 0.220467 | + | 22.4670i | 0.0157477 | + | 1.60479i | ||||
\(15\) | 3.41279 | − | 14.6066i | 0.227519 | − | 0.973774i | ||||
\(16\) | 0.744857 | − | 1.29013i | 0.0465536 | − | 0.0806332i | ||||
\(17\) | 5.29476 | + | 9.17080i | 0.311457 | + | 0.539459i | 0.978678 | − | 0.205401i | \(-0.0658498\pi\) |
−0.667221 | + | 0.744859i | \(0.732516\pi\) | |||||||
\(18\) | 28.6310 | − | 3.84173i | 1.59061 | − | 0.213429i | ||||
\(19\) | −10.0823 | + | 17.4631i | −0.530649 | + | 0.919111i | 0.468711 | + | 0.883351i | \(0.344718\pi\) |
−0.999360 | + | 0.0357599i | \(0.988615\pi\) | |||||||
\(20\) | −23.0359 | + | 21.5022i | −1.15179 | + | 1.07511i | ||||
\(21\) | −20.9386 | + | 1.60503i | −0.997075 | + | 0.0764301i | ||||
\(22\) | − | 39.1096i | − | 1.77771i | ||||||
\(23\) | −15.2706 | + | 26.4494i | −0.663939 | + | 1.14998i | 0.315633 | + | 0.948881i | \(0.397783\pi\) |
−0.979572 | + | 0.201094i | \(0.935550\pi\) | |||||||
\(24\) | −19.8957 | − | 9.78076i | −0.828987 | − | 0.407532i | ||||
\(25\) | −22.4592 | + | 10.9810i | −0.898369 | + | 0.439242i | ||||
\(26\) | 23.5516 | + | 13.5975i | 0.905832 | + | 0.522982i | ||||
\(27\) | 5.36609 | + | 26.4614i | 0.198744 | + | 0.980051i | ||||
\(28\) | 38.4206 | + | 21.6823i | 1.37217 | + | 0.774368i | ||||
\(29\) | − | 42.8910i | − | 1.47900i | −0.673157 | − | 0.739499i | \(-0.735062\pi\) | ||
0.673157 | − | 0.739499i | \(-0.264938\pi\) | |||||||
\(30\) | −35.1250 | − | 32.9282i | −1.17083 | − | 1.09761i | ||||
\(31\) | −6.11033 | − | 10.5834i | −0.197107 | − | 0.341400i | 0.750482 | − | 0.660891i | \(-0.229821\pi\) |
−0.947589 | + | 0.319491i | \(0.896488\pi\) | |||||||
\(32\) | −17.1707 | − | 29.7405i | −0.536584 | − | 0.929390i | ||||
\(33\) | 36.4729 | − | 2.43607i | 1.10524 | − | 0.0738203i | ||||
\(34\) | 33.9895 | 0.999691 | ||||||||
\(35\) | 24.1323 | + | 25.3502i | 0.689493 | + | 0.724292i | ||||
\(36\) | 21.5760 | − | 52.4573i | 0.599333 | − | 1.45715i | ||||
\(37\) | 28.8063 | + | 16.6313i | 0.778550 | + | 0.449496i | 0.835916 | − | 0.548857i | \(-0.184937\pi\) |
−0.0573663 | + | 0.998353i | \(0.518270\pi\) | |||||||
\(38\) | 32.3616 | + | 56.0519i | 0.851620 | + | 1.47505i | ||||
\(39\) | −11.2138 | + | 22.8108i | −0.287534 | + | 0.584891i | ||||
\(40\) | 8.32932 | + | 35.9987i | 0.208233 | + | 0.899967i | ||||
\(41\) | − | 6.40934i | − | 0.156325i | −0.996941 | − | 0.0781627i | \(-0.975095\pi\) | ||
0.996941 | − | 0.0781627i | \(-0.0249054\pi\) | |||||||
\(42\) | −29.1420 | + | 60.7790i | −0.693858 | + | 1.44712i | ||||
\(43\) | − | 20.0231i | − | 0.465653i | −0.972518 | − | 0.232827i | \(-0.925203\pi\) | ||
0.972518 | − | 0.232827i | \(-0.0747975\pi\) | |||||||
\(44\) | −66.5042 | − | 38.3962i | −1.51146 | − | 0.872642i | ||||
\(45\) | 28.5203 | − | 34.8079i | 0.633784 | − | 0.773510i | ||||
\(46\) | 49.0144 | + | 84.8955i | 1.06553 | + | 1.84555i | ||||
\(47\) | −11.8740 | + | 20.5664i | −0.252639 | + | 0.437583i | −0.964251 | − | 0.264989i | \(-0.914632\pi\) |
0.711613 | + | 0.702572i | \(0.247965\pi\) | |||||||
\(48\) | 3.71287 | − | 2.48754i | 0.0773514 | − | 0.0518237i | ||||
\(49\) | 23.6625 | − | 42.9079i | 0.482909 | − | 0.875671i | ||||
\(50\) | −5.51992 | + | 80.0531i | −0.110398 | + | 1.60106i | ||||
\(51\) | 2.11714 | + | 31.6979i | 0.0415126 | + | 0.621528i | ||||
\(52\) | 46.2440 | − | 26.6990i | 0.889308 | − | 0.513442i | ||||
\(53\) | −43.9372 | − | 76.1014i | −0.829003 | − | 1.43588i | −0.898821 | − | 0.438316i | \(-0.855575\pi\) |
0.0698177 | − | 0.997560i | \(-0.477758\pi\) | |||||||
\(54\) | 82.1667 | + | 27.5508i | 1.52161 | + | 0.510199i | ||||
\(55\) | −41.5714 | − | 44.5366i | −0.755843 | − | 0.809756i | ||||
\(56\) | 44.5432 | − | 26.3032i | 0.795414 | − | 0.469699i | ||||
\(57\) | −50.2571 | + | 33.6711i | −0.881704 | + | 0.590722i | ||||
\(58\) | −119.224 | − | 68.8342i | −2.05559 | − | 1.18680i | ||||
\(59\) | −41.9905 | + | 24.2432i | −0.711703 | + | 0.410902i | −0.811691 | − | 0.584087i | \(-0.801453\pi\) |
0.0999885 | + | 0.994989i | \(0.468119\pi\) | |||||||
\(60\) | −90.4772 | + | 27.4010i | −1.50795 | + | 0.456684i | ||||
\(61\) | 10.4973 | − | 18.1819i | 0.172087 | − | 0.298063i | −0.767062 | − | 0.641573i | \(-0.778282\pi\) |
0.939149 | + | 0.343509i | \(0.111616\pi\) | |||||||
\(62\) | −39.2250 | −0.632662 | ||||||||
\(63\) | −58.4965 | − | 23.3915i | −0.928515 | − | 0.371294i | ||||
\(64\) | −104.268 | −1.62918 | ||||||||
\(65\) | 41.2731 | − | 9.54971i | 0.634971 | − | 0.146919i | ||||
\(66\) | 51.7625 | − | 105.294i | 0.784280 | − | 1.59536i | ||||
\(67\) | 19.6174 | − | 11.3261i | 0.292798 | − | 0.169047i | −0.346405 | − | 0.938085i | \(-0.612598\pi\) |
0.639203 | + | 0.769038i | \(0.279264\pi\) | |||||||
\(68\) | 33.3695 | − | 57.7976i | 0.490728 | − | 0.849965i | ||||
\(69\) | −76.1189 | + | 50.9979i | −1.10317 | + | 0.739100i | ||||
\(70\) | 109.195 | − | 26.3969i | 1.55993 | − | 0.377098i | ||||
\(71\) | − | 2.44145i | − | 0.0343867i | −0.999852 | − | 0.0171933i | \(-0.994527\pi\) | ||
0.999852 | − | 0.0171933i | \(-0.00547308\pi\) | |||||||
\(72\) | −40.6194 | − | 52.6648i | −0.564158 | − | 0.731455i | ||||
\(73\) | −76.5611 | + | 44.2026i | −1.04878 | + | 0.605515i | −0.922308 | − | 0.386455i | \(-0.873699\pi\) |
−0.126474 | + | 0.991970i | \(0.540366\pi\) | |||||||
\(74\) | 92.4605 | − | 53.3821i | 1.24947 | − | 0.721380i | ||||
\(75\) | −74.9998 | − | 0.161411i | −0.999998 | − | 0.00215215i | ||||
\(76\) | 127.085 | 1.67217 | ||||||||
\(77\) | −41.9197 | + | 74.2809i | −0.544411 | + | 0.964686i | ||||
\(78\) | 45.4106 | + | 67.7793i | 0.582187 | + | 0.868965i | ||||
\(79\) | −3.20270 | + | 5.54725i | −0.0405406 | + | 0.0702183i | −0.885584 | − | 0.464480i | \(-0.846241\pi\) |
0.845043 | + | 0.534698i | \(0.179575\pi\) | |||||||
\(80\) | −7.12416 | − | 2.17430i | −0.0890520 | − | 0.0271788i | ||||
\(81\) | −20.5753 | + | 78.3432i | −0.254016 | + | 0.967200i | ||||
\(82\) | −17.8161 | − | 10.2861i | −0.217269 | − | 0.125440i | ||||
\(83\) | 103.557 | 1.24768 | 0.623839 | − | 0.781553i | \(-0.285572\pi\) | ||||
0.623839 | + | 0.781553i | \(0.285572\pi\) | |||||||
\(84\) | 74.7415 | + | 109.225i | 0.889779 | + | 1.30030i | ||||
\(85\) | 38.7059 | − | 36.1289i | 0.455364 | − | 0.425046i | ||||
\(86\) | −55.6583 | − | 32.1344i | −0.647190 | − | 0.373655i | ||||
\(87\) | 56.7672 | − | 115.474i | 0.652496 | − | 1.32729i | ||||
\(88\) | −77.9808 | + | 45.0222i | −0.886145 | + | 0.511616i | ||||
\(89\) | −54.2968 | − | 31.3483i | −0.610077 | − | 0.352228i | 0.162919 | − | 0.986639i | \(-0.447909\pi\) |
−0.772995 | + | 0.634412i | \(0.781242\pi\) | |||||||
\(90\) | −50.9846 | − | 135.140i | −0.566496 | − | 1.50156i | ||||
\(91\) | −30.1570 | − | 51.0696i | −0.331396 | − | 0.561204i | ||||
\(92\) | 192.481 | 2.09219 | ||||||||
\(93\) | −2.44325 | − | 36.5805i | −0.0262716 | − | 0.393339i | ||||
\(94\) | 38.1124 | + | 66.0126i | 0.405451 | + | 0.702262i | ||||
\(95\) | 96.4321 | + | 29.4312i | 1.01507 | + | 0.309802i | ||||
\(96\) | −6.86580 | − | 102.795i | −0.0715188 | − | 1.07078i | ||||
\(97\) | 140.539i | 1.44886i | 0.689348 | + | 0.724430i | \(0.257897\pi\) | ||||
−0.689348 | + | 0.724430i | \(0.742103\pi\) | |||||||
\(98\) | −81.2961 | − | 134.636i | −0.829552 | − | 1.37384i | ||||
\(99\) | 101.419 | + | 41.7142i | 1.02443 | + | 0.421355i | ||||
\(100\) | 130.708 | + | 87.9792i | 1.30708 | + | 0.879792i | ||||
\(101\) | 132.859 | − | 76.7059i | 1.31543 | − | 0.759465i | 0.332442 | − | 0.943124i | \(-0.392128\pi\) |
0.982990 | + | 0.183659i | \(0.0587942\pi\) | |||||||
\(102\) | 91.5087 | + | 44.9859i | 0.897144 | + | 0.441038i | ||||
\(103\) | −123.005 | − | 71.0169i | −1.19422 | − | 0.689485i | −0.234961 | − | 0.972005i | \(-0.575496\pi\) |
−0.959261 | + | 0.282520i | \(0.908830\pi\) | |||||||
\(104\) | − | 62.6128i | − | 0.602046i | ||||||
\(105\) | 31.4188 | + | 100.189i | 0.299227 | + | 0.954182i | ||||
\(106\) | −282.053 | −2.66088 | ||||||||
\(107\) | 28.5434 | − | 49.4386i | 0.266761 | − | 0.462043i | −0.701263 | − | 0.712903i | \(-0.747380\pi\) |
0.968023 | + | 0.250860i | \(0.0807134\pi\) | |||||||
\(108\) | 127.517 | − | 112.673i | 1.18071 | − | 1.04327i | ||||
\(109\) | −88.6354 | − | 153.521i | −0.813169 | − | 1.40845i | −0.910635 | − | 0.413211i | \(-0.864407\pi\) |
0.0974665 | − | 0.995239i | \(-0.468926\pi\) | |||||||
\(110\) | −190.515 | + | 44.0811i | −1.73195 | + | 0.400737i | ||||
\(111\) | 55.5423 | + | 82.9018i | 0.500381 | + | 0.746863i | ||||
\(112\) | 0.102324 | + | 10.4275i | 0.000913610 | + | 0.0931027i | ||||
\(113\) | 8.70089 | 0.0769990 | 0.0384995 | − | 0.999259i | \(-0.487742\pi\) | ||||
0.0384995 | + | 0.999259i | \(0.487742\pi\) | |||||||
\(114\) | 12.9400 | + | 193.738i | 0.113509 | + | 1.69945i | ||||
\(115\) | 146.055 | + | 44.5761i | 1.27004 | + | 0.387618i | ||||
\(116\) | −234.099 | + | 135.157i | −2.01809 | + | 1.16515i | ||||
\(117\) | −60.3811 | + | 46.5708i | −0.516078 | + | 0.398041i | ||||
\(118\) | 155.628i | 1.31888i | ||||||||
\(119\) | −64.5562 | − | 36.4316i | −0.542489 | − | 0.306148i | ||||
\(120\) | −25.2203 | + | 107.942i | −0.210169 | + | 0.899517i | ||||
\(121\) | 13.7337 | − | 23.7875i | 0.113502 | − | 0.196591i | ||||
\(122\) | −33.6935 | − | 58.3588i | −0.276176 | − | 0.478351i | ||||
\(123\) | 8.48290 | − | 17.2556i | 0.0689667 | − | 0.140290i | ||||
\(124\) | −38.5095 | + | 66.7004i | −0.310560 | + | 0.537907i | ||||
\(125\) | 78.8061 | + | 97.0288i | 0.630449 | + | 0.776231i | ||||
\(126\) | −158.900 | + | 125.063i | −1.26111 | + | 0.992562i | ||||
\(127\) | 58.7503i | 0.462601i | 0.972882 | + | 0.231300i | \(0.0742980\pi\) | ||||
−0.972882 | + | 0.231300i | \(0.925702\pi\) | |||||||
\(128\) | −98.6526 | + | 170.871i | −0.770724 | + | 1.33493i | ||||
\(129\) | 26.5010 | − | 53.9075i | 0.205434 | − | 0.417887i | ||||
\(130\) | 39.6923 | − | 130.053i | 0.305326 | − | 1.00041i | ||||
\(131\) | 69.7084 | + | 40.2462i | 0.532125 | + | 0.307223i | 0.741881 | − | 0.670531i | \(-0.233934\pi\) |
−0.209756 | + | 0.977754i | \(0.567267\pi\) | |||||||
\(132\) | −128.229 | − | 191.393i | −0.971430 | − | 1.44994i | ||||
\(133\) | −1.38505 | − | 141.146i | −0.0104139 | − | 1.06125i | ||||
\(134\) | − | 72.7076i | − | 0.542594i | ||||||
\(135\) | 122.853 | − | 55.9649i | 0.910024 | − | 0.414555i | ||||
\(136\) | −39.1280 | − | 67.7717i | −0.287706 | − | 0.498321i | ||||
\(137\) | 5.95720 | + | 10.3182i | 0.0434832 | + | 0.0753151i | 0.886948 | − | 0.461870i | \(-0.152821\pi\) |
−0.843465 | + | 0.537185i | \(0.819488\pi\) | |||||||
\(138\) | 19.5987 | + | 293.433i | 0.142020 | + | 2.12633i | ||||
\(139\) | 126.136 | 0.907450 | 0.453725 | − | 0.891142i | \(-0.350095\pi\) | ||||
0.453725 | + | 0.891142i | \(0.350095\pi\) | |||||||
\(140\) | 62.3166 | − | 211.597i | 0.445119 | − | 1.51141i | ||||
\(141\) | −59.1881 | + | 39.6547i | −0.419774 | + | 0.281239i | ||||
\(142\) | −6.78652 | − | 3.91820i | −0.0477924 | − | 0.0275930i | ||||
\(143\) | 51.6187 | + | 89.4063i | 0.360970 | + | 0.625219i | ||||
\(144\) | 13.2883 | − | 1.78304i | 0.0922801 | − | 0.0123822i | ||||
\(145\) | −208.935 | + | 48.3431i | −1.44093 | + | 0.333400i | ||||
\(146\) | 283.757i | 1.94354i | ||||||||
\(147\) | 120.495 | − | 84.2014i | 0.819696 | − | 0.572799i | ||||
\(148\) | − | 209.633i | − | 1.41644i | ||||||
\(149\) | −99.8945 | − | 57.6741i | −0.670433 | − | 0.387074i | 0.125808 | − | 0.992055i | \(-0.459848\pi\) |
−0.796241 | + | 0.604980i | \(0.793181\pi\) | |||||||
\(150\) | −120.813 | + | 208.218i | −0.805421 | + | 1.38812i | ||||
\(151\) | 139.800 | + | 242.140i | 0.925827 | + | 1.60358i | 0.790226 | + | 0.612815i | \(0.209963\pi\) |
0.135600 | + | 0.990764i | \(0.456704\pi\) | |||||||
\(152\) | 74.5079 | − | 129.051i | 0.490184 | − | 0.849023i | ||||
\(153\) | −36.2530 | + | 88.1413i | −0.236948 | + | 0.576087i | ||||
\(154\) | 139.204 | + | 235.735i | 0.903920 | + | 1.53075i | ||||
\(155\) | −44.6679 | + | 41.6940i | −0.288180 | + | 0.268994i | ||||
\(156\) | 159.838 | − | 10.6758i | 1.02460 | − | 0.0684344i | ||||
\(157\) | −23.3925 | + | 13.5057i | −0.148997 | + | 0.0860235i | −0.572645 | − | 0.819803i | \(-0.694083\pi\) |
0.423648 | + | 0.905827i | \(0.360749\pi\) | |||||||
\(158\) | 10.2798 | + | 17.8052i | 0.0650621 | + | 0.112691i | ||||
\(159\) | −17.5686 | − | 263.037i | −0.110494 | − | 1.65432i | ||||
\(160\) | −125.522 | + | 117.165i | −0.784510 | + | 0.732279i | ||||
\(161\) | −2.09779 | − | 213.778i | −0.0130297 | − | 1.32781i | ||||
\(162\) | 184.751 | + | 182.924i | 1.14044 | + | 1.12916i | ||||
\(163\) | 238.591 | + | 137.750i | 1.46375 | + | 0.845094i | 0.999182 | − | 0.0404450i | \(-0.0128776\pi\) |
0.464565 | + | 0.885539i | \(0.346211\pi\) | |||||||
\(164\) | −34.9822 | + | 20.1970i | −0.213306 | + | 0.123152i | ||||
\(165\) | −52.9760 | − | 174.925i | −0.321067 | − | 1.06015i | ||||
\(166\) | 166.195 | − | 287.859i | 1.00118 | − | 1.73409i | ||||
\(167\) | 8.17643 | 0.0489607 | 0.0244803 | − | 0.999700i | \(-0.492207\pi\) | ||||
0.0244803 | + | 0.999700i | \(0.492207\pi\) | |||||||
\(168\) | 154.735 | − | 11.8611i | 0.921041 | − | 0.0706018i | ||||
\(169\) | 97.2133 | 0.575227 | ||||||||
\(170\) | −38.3101 | − | 165.573i | −0.225353 | − | 0.973960i | ||||
\(171\) | −179.870 | + | 24.1351i | −1.05187 | + | 0.141141i | ||||
\(172\) | −109.286 | + | 63.0964i | −0.635384 | + | 0.366839i | ||||
\(173\) | 42.5110 | − | 73.6312i | 0.245728 | − | 0.425614i | −0.716608 | − | 0.697476i | \(-0.754306\pi\) |
0.962336 | + | 0.271862i | \(0.0876395\pi\) | |||||||
\(174\) | −229.880 | − | 343.116i | −1.32115 | − | 1.97193i | ||||
\(175\) | 96.2889 | − | 146.128i | 0.550222 | − | 0.835018i | ||||
\(176\) | − | 18.1518i | − | 0.103135i | ||||||
\(177\) | −145.136 | + | 9.69379i | −0.819976 | + | 0.0547672i | ||||
\(178\) | −174.278 | + | 100.619i | −0.979090 | + | 0.565278i | ||||
\(179\) | 107.239 | − | 61.9145i | 0.599101 | − | 0.345891i | −0.169587 | − | 0.985515i | \(-0.554243\pi\) |
0.768688 | + | 0.639624i | \(0.220910\pi\) | |||||||
\(180\) | −279.854 | − | 45.9778i | −1.55475 | − | 0.255432i | ||||
\(181\) | −169.201 | −0.934815 | −0.467407 | − | 0.884042i | \(-0.654812\pi\) | ||||
−0.467407 | + | 0.884042i | \(0.654812\pi\) | |||||||
\(182\) | −190.356 | + | 1.86795i | −1.04591 | + | 0.0102635i | ||||
\(183\) | 52.3256 | − | 35.0570i | 0.285932 | − | 0.191568i | ||||
\(184\) | 112.849 | − | 195.460i | 0.613309 | − | 1.06228i | ||||
\(185\) | 48.5483 | − | 159.070i | 0.262423 | − | 0.859837i | ||||
\(186\) | −105.604 | − | 51.9152i | −0.567764 | − | 0.279114i | ||||
\(187\) | 111.744 | + | 64.5152i | 0.597559 | + | 0.345001i | ||||
\(188\) | 149.669 | 0.796110 | ||||||||
\(189\) | −126.529 | − | 140.398i | −0.669465 | − | 0.742844i | ||||
\(190\) | 236.570 | − | 220.820i | 1.24511 | − | 1.16221i | ||||
\(191\) | 110.601 | + | 63.8554i | 0.579062 | + | 0.334322i | 0.760761 | − | 0.649033i | \(-0.224826\pi\) |
−0.181699 | + | 0.983354i | \(0.558159\pi\) | |||||||
\(192\) | −280.716 | − | 138.000i | −1.46206 | − | 0.718753i | ||||
\(193\) | 107.040 | − | 61.7995i | 0.554611 | − | 0.320205i | −0.196369 | − | 0.980530i | \(-0.562915\pi\) |
0.750980 | + | 0.660325i | \(0.229582\pi\) | |||||||
\(194\) | 390.658 | + | 225.547i | 2.01370 | + | 1.16261i | ||||
\(195\) | 123.757 | + | 28.9155i | 0.634653 | + | 0.148285i | ||||
\(196\) | −308.756 | + | 6.06019i | −1.57529 | + | 0.0309193i | ||||
\(197\) | −22.5579 | −0.114507 | −0.0572536 | − | 0.998360i | \(-0.518234\pi\) | ||||
−0.0572536 | + | 0.998360i | \(0.518234\pi\) | |||||||
\(198\) | 278.717 | − | 214.969i | 1.40766 | − | 1.08570i | ||||
\(199\) | 17.2597 | + | 29.8946i | 0.0867319 | + | 0.150224i | 0.906128 | − | 0.423004i | \(-0.139024\pi\) |
−0.819396 | + | 0.573228i | \(0.805691\pi\) | |||||||
\(200\) | 165.972 | − | 81.1493i | 0.829862 | − | 0.405747i | ||||
\(201\) | 67.8057 | − | 4.52883i | 0.337342 | − | 0.0225315i | ||||
\(202\) | − | 492.411i | − | 2.43768i | ||||||
\(203\) | 152.663 | + | 258.527i | 0.752032 | + | 1.27353i | ||||
\(204\) | 166.336 | − | 111.441i | 0.815372 | − | 0.546281i | ||||
\(205\) | −31.2218 | + | 7.22406i | −0.152302 | + | 0.0352393i | ||||
\(206\) | −394.812 | + | 227.945i | −1.91657 | + | 1.10653i | ||||
\(207\) | −272.429 | + | 36.5548i | −1.31608 | + | 0.176593i | ||||
\(208\) | 10.9309 | + | 6.31095i | 0.0525524 | + | 0.0303411i | ||||
\(209\) | 245.701i | 1.17560i | ||||||||
\(210\) | 328.919 | + | 73.4549i | 1.56628 | + | 0.349785i | ||||
\(211\) | 76.0725 | 0.360533 | 0.180267 | − | 0.983618i | \(-0.442304\pi\) | ||||
0.180267 | + | 0.983618i | \(0.442304\pi\) | |||||||
\(212\) | −276.908 | + | 479.618i | −1.30617 | + | 2.26235i | ||||
\(213\) | 3.23132 | − | 6.57304i | 0.0151705 | − | 0.0308593i | ||||
\(214\) | −91.6165 | − | 158.684i | −0.428114 | − | 0.741516i | ||||
\(215\) | −97.5386 | + | 22.5683i | −0.453668 | + | 0.104969i | ||||
\(216\) | −39.6551 | − | 195.548i | −0.183589 | − | 0.905316i | ||||
\(217\) | 74.5000 | + | 42.0433i | 0.343318 | + | 0.193748i | ||||
\(218\) | −568.991 | −2.61005 | ||||||||
\(219\) | −264.626 | + | 17.6747i | −1.20834 | + | 0.0807063i | ||||
\(220\) | −112.082 | + | 367.239i | −0.509463 | + | 1.66927i | ||||
\(221\) | −77.7014 | + | 44.8609i | −0.351590 | + | 0.202991i | ||||
\(222\) | 319.581 | − | 21.3452i | 1.43955 | − | 0.0961494i | ||||
\(223\) | − | 312.738i | − | 1.40241i | −0.712959 | − | 0.701206i | \(-0.752645\pi\) | ||
0.712959 | − | 0.701206i | \(-0.247355\pi\) | |||||||
\(224\) | 209.353 | + | 118.146i | 0.934611 | + | 0.527438i | ||||
\(225\) | −201.706 | − | 99.6985i | −0.896470 | − | 0.443105i | ||||
\(226\) | 13.9638 | − | 24.1859i | 0.0617865 | − | 0.107017i | ||||
\(227\) | −34.4570 | − | 59.6813i | −0.151793 | − | 0.262913i | 0.780094 | − | 0.625663i | \(-0.215171\pi\) |
−0.931887 | + | 0.362750i | \(0.881838\pi\) | |||||||
\(228\) | 342.146 | + | 168.200i | 1.50064 | + | 0.737718i | ||||
\(229\) | −172.075 | + | 298.043i | −0.751419 | + | 1.30150i | 0.195716 | + | 0.980661i | \(0.437297\pi\) |
−0.947135 | + | 0.320835i | \(0.896036\pi\) | |||||||
\(230\) | 358.307 | − | 334.451i | 1.55786 | − | 1.45414i | ||||
\(231\) | −211.171 | + | 144.502i | −0.914161 | + | 0.625550i | ||||
\(232\) | 316.962i | 1.36622i | ||||||||
\(233\) | 20.0104 | − | 34.6590i | 0.0858816 | − | 0.148751i | −0.819885 | − | 0.572528i | \(-0.805963\pi\) |
0.905767 | + | 0.423777i | \(0.139296\pi\) | |||||||
\(234\) | 32.5498 | + | 242.582i | 0.139102 | + | 1.03667i | ||||
\(235\) | 113.569 | + | 34.6613i | 0.483271 | + | 0.147495i | ||||
\(236\) | 264.639 | + | 152.789i | 1.12135 | + | 0.647412i | ||||
\(237\) | −15.9644 | + | 10.6958i | −0.0673605 | + | 0.0451300i | ||||
\(238\) | −204.873 | + | 120.979i | −0.860811 | + | 0.508317i | ||||
\(239\) | 341.734i | 1.42985i | 0.699201 | + | 0.714925i | \(0.253539\pi\) | ||||
−0.699201 | + | 0.714925i | \(0.746461\pi\) | |||||||
\(240\) | −16.3024 | − | 15.2828i | −0.0679266 | − | 0.0636782i | ||||
\(241\) | −64.0475 | − | 110.934i | −0.265757 | − | 0.460305i | 0.702004 | − | 0.712173i | \(-0.252289\pi\) |
−0.967762 | + | 0.251867i | \(0.918955\pi\) | |||||||
\(242\) | −44.0815 | − | 76.3514i | −0.182155 | − | 0.315502i | ||||
\(243\) | −159.083 | + | 183.689i | −0.654663 | + | 0.755921i | ||||
\(244\) | −132.316 | −0.542277 | ||||||||
\(245\) | −235.688 | − | 66.9053i | −0.961991 | − | 0.273083i | ||||
\(246\) | −34.3517 | − | 51.2729i | −0.139641 | − | 0.208427i | ||||
\(247\) | −147.960 | − | 85.4246i | −0.599027 | − | 0.345849i | ||||
\(248\) | 45.1550 | + | 78.2108i | 0.182077 | + | 0.315366i | ||||
\(249\) | 278.803 | + | 137.060i | 1.11969 | + | 0.550443i | ||||
\(250\) | 396.185 | − | 63.3399i | 1.58474 | − | 0.253360i | ||||
\(251\) | − | 201.118i | − | 0.801266i | −0.916239 | − | 0.400633i | \(-0.868790\pi\) | ||
0.916239 | − | 0.400633i | \(-0.131210\pi\) | |||||||
\(252\) | 56.6620 | + | 392.985i | 0.224849 | + | 1.55946i | ||||
\(253\) | 372.136i | 1.47089i | ||||||||
\(254\) | 163.309 | + | 94.2863i | 0.642947 | + | 0.371206i | ||||
\(255\) | 152.024 | − | 46.0405i | 0.596173 | − | 0.180551i | ||||
\(256\) | 108.113 | + | 187.257i | 0.422316 | + | 0.731473i | ||||
\(257\) | 126.605 | − | 219.286i | 0.492626 | − | 0.853253i | −0.507338 | − | 0.861747i | \(-0.669371\pi\) |
0.999964 | + | 0.00849432i | \(0.00270386\pi\) | |||||||
\(258\) | −107.316 | − | 160.179i | −0.415955 | − | 0.620850i | ||||
\(259\) | −232.828 | + | 2.28472i | −0.898949 | + | 0.00882132i | ||||
\(260\) | −182.181 | − | 195.176i | −0.700697 | − | 0.750676i | ||||
\(261\) | 305.664 | − | 235.753i | 1.17113 | − | 0.903270i | ||||
\(262\) | 223.745 | − | 129.179i | 0.853989 | − | 0.493051i | ||||
\(263\) | −90.9512 | − | 157.532i | −0.345822 | − | 0.598982i | 0.639681 | − | 0.768641i | \(-0.279067\pi\) |
−0.985503 | + | 0.169659i | \(0.945733\pi\) | |||||||
\(264\) | −269.533 | + | 18.0024i | −1.02096 | + | 0.0681910i | ||||
\(265\) | −321.191 | + | 299.806i | −1.21204 | + | 1.13134i | ||||
\(266\) | −394.567 | − | 222.670i | −1.48333 | − | 0.837105i | ||||
\(267\) | −104.691 | − | 156.261i | −0.392102 | − | 0.585247i | ||||
\(268\) | −123.636 | − | 71.3814i | −0.461329 | − | 0.266348i | ||||
\(269\) | −224.807 | + | 129.792i | −0.835714 | + | 0.482499i | −0.855805 | − | 0.517299i | \(-0.826938\pi\) |
0.0200914 | + | 0.999798i | \(0.493604\pi\) | |||||||
\(270\) | 41.5968 | − | 431.312i | 0.154062 | − | 1.59745i | ||||
\(271\) | −17.7512 | + | 30.7460i | −0.0655026 | + | 0.113454i | −0.896917 | − | 0.442199i | \(-0.854198\pi\) |
0.831414 | + | 0.555653i | \(0.187532\pi\) | |||||||
\(272\) | 15.7754 | 0.0579977 | ||||||||
\(273\) | −13.5990 | − | 177.406i | −0.0498131 | − | 0.649840i | ||||
\(274\) | 38.2420 | 0.139569 | ||||||||
\(275\) | −170.095 | + | 252.705i | −0.618529 | + | 0.918926i | ||||
\(276\) | 518.211 | + | 254.753i | 1.87758 | + | 0.923020i | ||||
\(277\) | 310.160 | − | 179.071i | 1.11971 | − | 0.646466i | 0.178385 | − | 0.983961i | \(-0.442913\pi\) |
0.941327 | + | 0.337495i | \(0.109579\pi\) | |||||||
\(278\) | 202.431 | − | 350.620i | 0.728167 | − | 1.26122i | ||||
\(279\) | 41.8372 | − | 101.718i | 0.149954 | − | 0.364581i | ||||
\(280\) | −178.336 | − | 187.337i | −0.636914 | − | 0.669060i | ||||
\(281\) | − | 193.923i | − | 0.690117i | −0.938581 | − | 0.345058i | \(-0.887859\pi\) | ||
0.938581 | − | 0.345058i | \(-0.112141\pi\) | |||||||
\(282\) | 15.2395 | + | 228.166i | 0.0540407 | + | 0.809099i | ||||
\(283\) | −111.089 | + | 64.1371i | −0.392539 | + | 0.226633i | −0.683260 | − | 0.730175i | \(-0.739438\pi\) |
0.290720 | + | 0.956808i | \(0.406105\pi\) | |||||||
\(284\) | −13.3255 | + | 7.69345i | −0.0469206 | + | 0.0270896i | ||||
\(285\) | 220.668 | + | 206.867i | 0.774273 | + | 0.725848i | ||||
\(286\) | 331.364 | 1.15862 | ||||||||
\(287\) | 22.8129 | + | 38.6326i | 0.0794873 | + | 0.134608i | ||||
\(288\) | 117.567 | − | 285.838i | 0.408219 | − | 0.992495i | ||||
\(289\) | 88.4310 | − | 153.167i | 0.305990 | − | 0.529990i | ||||
\(290\) | −200.933 | + | 658.362i | −0.692872 | + | 2.27021i | ||||
\(291\) | −186.007 | + | 378.369i | −0.639200 | + | 1.30024i | ||||
\(292\) | 482.516 | + | 278.581i | 1.65245 | + | 0.954043i | ||||
\(293\) | −430.914 | −1.47070 | −0.735348 | − | 0.677689i | \(-0.762981\pi\) | ||||
−0.735348 | + | 0.677689i | \(0.762981\pi\) | |||||||
\(294\) | −40.6766 | − | 470.073i | −0.138356 | − | 1.59889i | ||||
\(295\) | 165.424 | + | 177.223i | 0.560760 | + | 0.600757i | ||||
\(296\) | −212.877 | − | 122.905i | −0.719180 | − | 0.415219i | ||||
\(297\) | 217.837 | + | 246.536i | 0.733457 | + | 0.830087i | ||||
\(298\) | −320.634 | + | 185.118i | −1.07595 | + | 0.621202i | ||||
\(299\) | −224.098 | − | 129.383i | −0.749492 | − | 0.432719i | ||||
\(300\) | 235.457 | + | 409.858i | 0.784856 | + | 1.36619i | ||||
\(301\) | 71.2685 | + | 120.690i | 0.236773 | + | 0.400964i | ||||
\(302\) | 897.439 | 2.97165 | ||||||||
\(303\) | 459.213 | − | 30.6713i | 1.51555 | − | 0.101226i | ||||
\(304\) | 15.0198 | + | 26.0151i | 0.0494072 | + | 0.0855758i | ||||
\(305\) | −100.401 | − | 30.6425i | −0.329184 | − | 0.100467i | ||||
\(306\) | 186.826 | + | 242.228i | 0.610542 | + | 0.791594i | ||||
\(307\) | − | 204.653i | − | 0.666622i | −0.942817 | − | 0.333311i | \(-0.891834\pi\) | ||
0.942817 | − | 0.333311i | \(-0.108166\pi\) | |||||||
\(308\) | 537.521 | − | 5.27466i | 1.74520 | − | 0.0171255i | ||||
\(309\) | −237.169 | − | 353.996i | −0.767538 | − | 1.14562i | ||||
\(310\) | 44.2111 | + | 191.077i | 0.142616 | + | 0.616377i | ||||
\(311\) | 338.495 | − | 195.430i | 1.08841 | − | 0.628393i | 0.155257 | − | 0.987874i | \(-0.450379\pi\) |
0.933153 | + | 0.359481i | \(0.117046\pi\) | |||||||
\(312\) | 82.8694 | − | 168.570i | 0.265607 | − | 0.540289i | ||||
\(313\) | −222.263 | − | 128.323i | −0.710104 | − | 0.409979i | 0.100996 | − | 0.994887i | \(-0.467797\pi\) |
−0.811100 | + | 0.584908i | \(0.801131\pi\) | |||||||
\(314\) | 86.6992i | 0.276112i | ||||||||
\(315\) | −48.0149 | + | 311.319i | −0.152428 | + | 0.988315i | ||||
\(316\) | 40.3692 | 0.127751 | ||||||||
\(317\) | −159.906 | + | 276.965i | −0.504435 | + | 0.873707i | 0.495552 | + | 0.868578i | \(0.334966\pi\) |
−0.999987 | + | 0.00512853i | \(0.998368\pi\) | |||||||
\(318\) | −759.361 | − | 373.303i | −2.38793 | − | 1.17391i | ||||
\(319\) | −261.307 | − | 452.597i | −0.819145 | − | 1.41880i | ||||
\(320\) | 117.522 | + | 507.919i | 0.367255 | + | 1.58725i | ||||
\(321\) | 142.279 | − | 95.3239i | 0.443238 | − | 0.296959i | ||||
\(322\) | −597.607 | − | 337.253i | −1.85592 | − | 1.04737i | ||||
\(323\) | −213.534 | −0.661097 | ||||||||
\(324\) | 492.434 | − | 134.573i | 1.51986 | − | 0.415350i | ||||
\(325\) | −93.0391 | − | 190.290i | −0.286274 | − | 0.585509i | ||||
\(326\) | 765.811 | − | 442.141i | 2.34911 | − | 1.35626i | ||||
\(327\) | −35.4414 | − | 530.630i | −0.108384 | − | 1.62272i | ||||
\(328\) | 47.3647i | 0.144404i | ||||||||
\(329\) | −1.63119 | − | 166.228i | −0.00495801 | − | 0.505253i | ||||
\(330\) | −571.259 | − | 133.473i | −1.73109 | − | 0.404464i | ||||
\(331\) | −144.224 | + | 249.804i | −0.435723 | + | 0.754694i | −0.997354 | − | 0.0726932i | \(-0.976841\pi\) |
0.561631 | + | 0.827388i | \(0.310174\pi\) | |||||||
\(332\) | −326.327 | − | 565.215i | −0.982914 | − | 1.70246i | ||||
\(333\) | 39.8122 | + | 296.705i | 0.119556 | + | 0.891007i | ||||
\(334\) | 13.1221 | − | 22.7281i | 0.0392876 | − | 0.0680482i | ||||
\(335\) | −77.2842 | − | 82.7967i | −0.230699 | − | 0.247154i | ||||
\(336\) | −13.5255 | + | 28.2090i | −0.0402546 | + | 0.0839554i | ||||
\(337\) | 380.518i | 1.12913i | 0.825387 | + | 0.564567i | \(0.190957\pi\) | ||||
−0.825387 | + | 0.564567i | \(0.809043\pi\) | |||||||
\(338\) | 156.014 | − | 270.225i | 0.461581 | − | 0.799481i | ||||
\(339\) | 23.4251 | + | 11.5158i | 0.0691006 | + | 0.0339700i | ||||
\(340\) | −319.161 | − | 97.4083i | −0.938709 | − | 0.286495i | ||||
\(341\) | −128.956 | − | 74.4527i | −0.378170 | − | 0.218336i | ||||
\(342\) | −221.578 | + | 538.719i | −0.647890 | + | 1.57520i | ||||
\(343\) | 10.0957 | + | 342.851i | 0.0294336 | + | 0.999567i | ||||
\(344\) | 147.970i | 0.430144i | ||||||||
\(345\) | 334.221 | + | 313.318i | 0.968757 | + | 0.908167i | ||||
\(346\) | −136.449 | − | 236.336i | −0.394361 | − | 0.683053i | ||||
\(347\) | −85.3529 | − | 147.836i | −0.245974 | − | 0.426039i | 0.716431 | − | 0.697658i | \(-0.245774\pi\) |
−0.962405 | + | 0.271619i | \(0.912441\pi\) | |||||||
\(348\) | −809.140 | + | 54.0434i | −2.32511 | + | 0.155297i | ||||
\(349\) | 549.147 | 1.57349 | 0.786744 | − | 0.617280i | \(-0.211765\pi\) | ||||
0.786744 | + | 0.617280i | \(0.211765\pi\) | |||||||
\(350\) | −251.663 | − | 502.171i | −0.719037 | − | 1.43477i | ||||
\(351\) | −224.199 | + | 45.4653i | −0.638745 | + | 0.129531i | ||||
\(352\) | −362.380 | − | 209.220i | −1.02949 | − | 0.594375i | ||||
\(353\) | 153.623 | + | 266.082i | 0.435192 | + | 0.753775i | 0.997311 | − | 0.0732815i | \(-0.0233472\pi\) |
−0.562119 | + | 0.827056i | \(0.690014\pi\) | |||||||
\(354\) | −205.977 | + | 418.992i | −0.581857 | + | 1.18359i | ||||
\(355\) | −11.8931 | + | 2.75180i | −0.0335016 | + | 0.00775155i | ||||
\(356\) | 395.136i | 1.10993i | ||||||||
\(357\) | −125.584 | − | 183.525i | −0.351776 | − | 0.514076i | ||||
\(358\) | − | 397.457i | − | 1.11022i | ||||||
\(359\) | 94.3043 | + | 54.4466i | 0.262686 | + | 0.151662i | 0.625559 | − | 0.780177i | \(-0.284871\pi\) |
−0.362873 | + | 0.931839i | \(0.618204\pi\) | |||||||
\(360\) | −210.763 | + | 257.229i | −0.585454 | + | 0.714524i | ||||
\(361\) | −22.8069 | − | 39.5027i | −0.0631770 | − | 0.109426i | ||||
\(362\) | −271.545 | + | 470.330i | −0.750125 | + | 1.29926i | ||||
\(363\) | 68.4581 | − | 45.8653i | 0.188590 | − | 0.126351i | ||||
\(364\) | −183.708 | + | 325.526i | −0.504691 | + | 0.894303i | ||||
\(365\) | 301.618 | + | 323.131i | 0.826349 | + | 0.885291i | ||||
\(366\) | −13.4726 | − | 201.712i | −0.0368103 | − | 0.551124i | ||||
\(367\) | 99.8081 | − | 57.6242i | 0.271957 | − | 0.157014i | −0.357820 | − | 0.933791i | \(-0.616480\pi\) |
0.629776 | + | 0.776776i | \(0.283146\pi\) | |||||||
\(368\) | 22.7488 | + | 39.4021i | 0.0618174 | + | 0.107071i | ||||
\(369\) | 45.6764 | − | 35.2294i | 0.123784 | − | 0.0954727i | ||||
\(370\) | −364.254 | − | 390.236i | −0.984471 | − | 1.05469i | ||||
\(371\) | 535.702 | + | 302.318i | 1.44394 | + | 0.814874i | ||||
\(372\) | −191.957 | + | 128.607i | −0.516014 | + | 0.345718i | ||||
\(373\) | −77.4504 | − | 44.7160i | −0.207642 | − | 0.119882i | 0.392573 | − | 0.919721i | \(-0.371585\pi\) |
−0.600215 | + | 0.799839i | \(0.704918\pi\) | |||||||
\(374\) | 358.667 | − | 207.076i | 0.959002 | − | 0.553680i | ||||
\(375\) | 83.7472 | + | 365.529i | 0.223326 | + | 0.974744i | ||||
\(376\) | 87.7484 | − | 151.985i | 0.233373 | − | 0.404214i | ||||
\(377\) | 363.402 | 0.963932 | ||||||||
\(378\) | −593.325 | + | 126.394i | −1.56964 | + | 0.334376i | ||||
\(379\) | 221.030 | 0.583193 | 0.291596 | − | 0.956541i | \(-0.405814\pi\) | ||||
0.291596 | + | 0.956541i | \(0.405814\pi\) | |||||||
\(380\) | −143.239 | − | 619.070i | −0.376946 | − | 1.62913i | ||||
\(381\) | −77.7574 | + | 158.171i | −0.204088 | + | 0.415148i | ||||
\(382\) | 354.999 | − | 204.959i | 0.929316 | − | 0.536541i | ||||
\(383\) | 93.5845 | − | 162.093i | 0.244346 | − | 0.423220i | −0.717602 | − | 0.696454i | \(-0.754760\pi\) |
0.961948 | + | 0.273234i | \(0.0880934\pi\) | |||||||
\(384\) | −491.751 | + | 329.462i | −1.28060 | + | 0.857974i | ||||
\(385\) | 409.093 | + | 120.480i | 1.06258 | + | 0.312936i | ||||
\(386\) | − | 396.719i | − | 1.02777i | ||||||
\(387\) | 142.696 | − | 110.058i | 0.368722 | − | 0.284389i | ||||
\(388\) | 767.065 | − | 442.865i | 1.97697 | − | 1.14140i | ||||
\(389\) | −183.652 | + | 106.032i | −0.472113 | + | 0.272575i | −0.717124 | − | 0.696946i | \(-0.754542\pi\) |
0.245011 | + | 0.969520i | \(0.421209\pi\) | |||||||
\(390\) | 278.991 | − | 297.604i | 0.715360 | − | 0.763086i | ||||
\(391\) | −323.416 | −0.827152 | ||||||||
\(392\) | −174.865 | + | 317.087i | −0.446084 | + | 0.808895i | ||||
\(393\) | 134.407 | + | 200.614i | 0.342002 | + | 0.510468i | ||||
\(394\) | −36.2024 | + | 62.7044i | −0.0918843 | + | 0.159148i | ||||
\(395\) | 30.6321 | + | 9.34896i | 0.0775497 | + | 0.0236683i | ||||
\(396\) | −91.9131 | − | 684.993i | −0.232104 | − | 1.72978i | ||||
\(397\) | −514.877 | − | 297.264i | −1.29692 | − | 0.748776i | −0.317048 | − | 0.948410i | \(-0.602692\pi\) |
−0.979871 | + | 0.199634i | \(0.936025\pi\) | |||||||
\(398\) | 110.798 | 0.278386 | ||||||||
\(399\) | 183.081 | − | 381.835i | 0.458849 | − | 0.956980i | ||||
\(400\) | −2.56193 | + | 37.1546i | −0.00640483 | + | 0.0928866i | ||||
\(401\) | −400.309 | − | 231.118i | −0.998277 | − | 0.576355i | −0.0905387 | − | 0.995893i | \(-0.528859\pi\) |
−0.907738 | + | 0.419538i | \(0.862192\pi\) | |||||||
\(402\) | 96.2302 | − | 195.748i | 0.239379 | − | 0.486936i | ||||
\(403\) | 89.6700 | − | 51.7710i | 0.222506 | − | 0.128464i | ||||
\(404\) | −837.322 | − | 483.428i | −2.07258 | − | 1.19660i | ||||
\(405\) | 404.824 | + | 11.9267i | 0.999566 | + | 0.0294487i | ||||
\(406\) | 963.632 | − | 9.45606i | 2.37348 | − | 0.0232908i | ||||
\(407\) | 405.297 | 0.995815 | ||||||||
\(408\) | −15.6456 | − | 234.246i | −0.0383470 | − | 0.574132i | ||||
\(409\) | −105.366 | − | 182.500i | −0.257620 | − | 0.446211i | 0.707984 | − | 0.706228i | \(-0.249605\pi\) |
−0.965604 | + | 0.260018i | \(0.916272\pi\) | |||||||
\(410\) | −30.0260 | + | 98.3812i | −0.0732343 | + | 0.239954i | ||||
\(411\) | 2.38202 | + | 35.6637i | 0.00579567 | + | 0.0867730i | ||||
\(412\) | 895.148i | 2.17269i | ||||||||
\(413\) | 166.810 | − | 295.584i | 0.403898 | − | 0.715700i | ||||
\(414\) | −335.600 | + | 815.938i | −0.810628 | + | 1.97087i | ||||
\(415\) | −116.721 | − | 504.459i | −0.281255 | − | 1.21556i | ||||
\(416\) | 251.982 | − | 145.482i | 0.605727 | − | 0.349716i | ||||
\(417\) | 339.590 | + | 166.943i | 0.814365 | + | 0.400344i | ||||
\(418\) | 682.976 | + | 394.317i | 1.63391 | + | 0.943341i | ||||
\(419\) | − | 97.7368i | − | 0.233262i | −0.993175 | − | 0.116631i | \(-0.962791\pi\) | ||
0.993175 | − | 0.116631i | \(-0.0372095\pi\) | |||||||
\(420\) | 447.826 | − | 487.198i | 1.06625 | − | 1.15999i | ||||
\(421\) | 576.919 | 1.37035 | 0.685177 | − | 0.728376i | \(-0.259725\pi\) | ||||
0.685177 | + | 0.728376i | \(0.259725\pi\) | |||||||
\(422\) | 122.086 | − | 211.459i | 0.289303 | − | 0.501088i | ||||
\(423\) | −211.834 | + | 28.4241i | −0.500789 | + | 0.0671964i | ||||
\(424\) | 324.693 | + | 562.385i | 0.765786 | + | 1.32638i | ||||
\(425\) | −219.621 | − | 147.827i | −0.516756 | − | 0.347828i | ||||
\(426\) | −13.0853 | − | 19.5309i | −0.0307166 | − | 0.0458473i | ||||
\(427\) | 1.44206 | + | 146.955i | 0.00337719 | + | 0.344157i | ||||
\(428\) | −359.781 | −0.840610 | ||||||||
\(429\) | 20.6401 | + | 309.024i | 0.0481121 | + | 0.720336i | ||||
\(430\) | −93.8029 | + | 307.348i | −0.218146 | + | 0.714762i | ||||
\(431\) | −146.182 | + | 84.3983i | −0.339170 | + | 0.195820i | −0.659905 | − | 0.751349i | \(-0.729403\pi\) |
0.320735 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(432\) | 38.1356 | + | 12.7870i | 0.0882769 | + | 0.0295995i | ||||
\(433\) | − | 328.967i | − | 0.759739i | −0.925040 | − | 0.379870i | \(-0.875969\pi\) | ||
0.925040 | − | 0.379870i | \(-0.124031\pi\) | |||||||
\(434\) | 236.430 | − | 139.614i | 0.544771 | − | 0.321692i | ||||
\(435\) | −626.491 | − | 146.378i | −1.44021 | − | 0.336501i | ||||
\(436\) | −558.612 | + | 967.544i | −1.28122 | + | 2.21914i | ||||
\(437\) | −307.926 | − | 533.344i | −0.704637 | − | 1.22047i | ||||
\(438\) | −375.558 | + | 763.948i | −0.857439 | + | 1.74417i | ||||
\(439\) | 110.035 | − | 190.586i | 0.250649 | − | 0.434136i | −0.713056 | − | 0.701107i | \(-0.752689\pi\) |
0.963705 | + | 0.266971i | \(0.0860228\pi\) | |||||||
\(440\) | 307.210 | + | 329.123i | 0.698205 | + | 0.748006i | ||||
\(441\) | 435.848 | − | 67.2142i | 0.988317 | − | 0.152413i | ||||
\(442\) | 287.983i | 0.651545i | ||||||||
\(443\) | −98.0040 | + | 169.748i | −0.221228 | + | 0.383178i | −0.955181 | − | 0.296022i | \(-0.904340\pi\) |
0.733953 | + | 0.679200i | \(0.237673\pi\) | |||||||
\(444\) | 277.455 | − | 564.389i | 0.624898 | − | 1.27115i | ||||
\(445\) | −91.5083 | + | 299.829i | −0.205637 | + | 0.673774i | ||||
\(446\) | −869.319 | − | 501.902i | −1.94915 | − | 1.12534i | ||||
\(447\) | −192.609 | − | 287.487i | −0.430893 | − | 0.643147i | ||||
\(448\) | 628.477 | − | 371.121i | 1.40285 | − | 0.828396i | ||||
\(449\) | 434.253i | 0.967156i | 0.875301 | + | 0.483578i | \(0.160663\pi\) | ||||
−0.875301 | + | 0.483578i | \(0.839337\pi\) | |||||||
\(450\) | −600.843 | + | 400.680i | −1.33521 | + | 0.890400i | ||||
\(451\) | −39.0480 | − | 67.6331i | −0.0865809 | − | 0.149963i | ||||
\(452\) | −27.4181 | − | 47.4895i | −0.0606594 | − | 0.105065i | ||||
\(453\) | 55.8998 | + | 836.934i | 0.123399 | + | 1.84754i | ||||
\(454\) | −221.195 | −0.487214 | ||||||||
\(455\) | −214.785 | + | 204.465i | −0.472055 | + | 0.449374i | ||||
\(456\) | 371.397 | − | 248.828i | 0.814468 | − | 0.545675i | ||||
\(457\) | 18.5054 | + | 10.6841i | 0.0404932 | + | 0.0233787i | 0.520110 | − | 0.854099i | \(-0.325891\pi\) |
−0.479617 | + | 0.877478i | \(0.659224\pi\) | |||||||
\(458\) | 552.314 | + | 956.636i | 1.20593 | + | 2.08872i | ||||
\(459\) | −214.260 | + | 189.318i | −0.466797 | + | 0.412458i | ||||
\(460\) | −216.949 | − | 937.636i | −0.471628 | − | 2.03834i | ||||
\(461\) | − | 759.274i | − | 1.64702i | −0.567305 | − | 0.823508i | \(-0.692014\pi\) | ||
0.567305 | − | 0.823508i | \(-0.307986\pi\) | |||||||
\(462\) | 62.7723 | + | 818.900i | 0.135871 | + | 1.77251i | ||||
\(463\) | 242.225i | 0.523164i | 0.965181 | + | 0.261582i | \(0.0842443\pi\) | ||||
−0.965181 | + | 0.261582i | \(0.915756\pi\) | |||||||
\(464\) | −55.3349 | − | 31.9476i | −0.119256 | − | 0.0688527i | ||||
\(465\) | −175.441 | + | 53.1323i | −0.377292 | + | 0.114263i | ||||
\(466\) | −64.2280 | − | 111.246i | −0.137828 | − | 0.238726i | ||||
\(467\) | −207.939 | + | 360.160i | −0.445265 | + | 0.771221i | −0.998071 | − | 0.0620891i | \(-0.980224\pi\) |
0.552806 | + | 0.833310i | \(0.313557\pi\) | |||||||
\(468\) | 444.455 | + | 182.807i | 0.949691 | + | 0.390613i | ||||
\(469\) | −77.9317 | + | 138.093i | −0.166166 | + | 0.294442i | ||||
\(470\) | 278.610 | − | 260.061i | 0.592788 | − | 0.553321i | ||||
\(471\) | −80.8540 | + | 5.40033i | −0.171665 | + | 0.0114657i | ||||
\(472\) | 310.307 | − | 179.156i | 0.657430 | − | 0.379568i | ||||
\(473\) | −121.988 | − | 211.289i | −0.257903 | − | 0.446700i | ||||
\(474\) | 4.11045 | + | 61.5418i | 0.00867183 | + | 0.129835i | ||||
\(475\) | 34.6781 | − | 502.923i | 0.0730066 | − | 1.05878i | ||||
\(476\) | 4.58411 | + | 467.150i | 0.00963049 | + | 0.981408i | ||||
\(477\) | 300.836 | − | 731.417i | 0.630684 | − | 1.53337i | ||||
\(478\) | 949.921 | + | 548.437i | 1.98728 | + | 1.14736i | ||||
\(479\) | 45.1496 | − | 26.0672i | 0.0942581 | − | 0.0544199i | −0.452130 | − | 0.891952i | \(-0.649336\pi\) |
0.546388 | + | 0.837532i | \(0.316002\pi\) | |||||||
\(480\) | −493.007 | + | 149.307i | −1.02710 | + | 0.311057i | ||||
\(481\) | −140.912 | + | 244.067i | −0.292957 | + | 0.507417i | ||||
\(482\) | −411.150 | −0.853009 | ||||||||
\(483\) | 277.292 | − | 578.323i | 0.574104 | − | 1.19736i | ||||
\(484\) | −173.110 | −0.357664 | ||||||||
\(485\) | 684.610 | − | 158.404i | 1.41157 | − | 0.326606i | ||||
\(486\) | 255.294 | + | 737.000i | 0.525296 | + | 1.51646i | ||||
\(487\) | −728.584 | + | 420.648i | −1.49607 | + | 0.863754i | −0.999990 | − | 0.00452596i | \(-0.998559\pi\) |
−0.496075 | + | 0.868280i | \(0.665226\pi\) | |||||||
\(488\) | −77.5745 | + | 134.363i | −0.158964 | + | 0.275334i | ||||
\(489\) | 460.033 | + | 686.641i | 0.940764 | + | 1.40417i | ||||
\(490\) | −564.224 | + | 547.769i | −1.15148 | + | 1.11790i | ||||
\(491\) | 842.285i | 1.71545i | 0.514110 | + | 0.857724i | \(0.328122\pi\) | ||||
−0.514110 | + | 0.857724i | \(0.671878\pi\) | |||||||
\(492\) | −120.912 | + | 8.07589i | −0.245757 | + | 0.0164144i | ||||
\(493\) | 393.344 | − | 227.097i | 0.797859 | − | 0.460644i | ||||
\(494\) | −474.911 | + | 274.190i | −0.961358 | + | 0.555040i | ||||
\(495\) | 88.8916 | − | 541.059i | 0.179579 | − | 1.09305i | ||||
\(496\) | −18.2053 | −0.0367042 | ||||||||
\(497\) | 8.68990 | + | 14.7160i | 0.0174847 | + | 0.0296096i | ||||
\(498\) | 828.429 | − | 555.028i | 1.66351 | − | 1.11451i | ||||
\(499\) | −430.078 | + | 744.916i | −0.861879 | + | 1.49282i | 0.00823367 | + | 0.999966i | \(0.497379\pi\) |
−0.870113 | + | 0.492852i | \(0.835954\pi\) | |||||||
\(500\) | 281.251 | − | 735.879i | 0.562502 | − | 1.47176i | ||||
\(501\) | 22.0131 | + | 10.8217i | 0.0439384 | + | 0.0216002i | ||||
\(502\) | −559.048 | − | 322.767i | −1.11364 | − | 0.642961i | ||||
\(503\) | −639.911 | −1.27219 | −0.636095 | − | 0.771611i | \(-0.719451\pi\) | ||||
−0.636095 | + | 0.771611i | \(0.719451\pi\) | |||||||
\(504\) | 432.286 | + | 172.862i | 0.857710 | + | 0.342980i | ||||
\(505\) | −523.405 | − | 560.738i | −1.03645 | − | 1.11037i | ||||
\(506\) | 1034.43 | + | 597.227i | 2.04432 | + | 1.18029i | ||||
\(507\) | 261.724 | + | 128.664i | 0.516221 | + | 0.253775i | ||||
\(508\) | 320.659 | − | 185.133i | 0.631219 | − | 0.364435i | ||||
\(509\) | 627.238 | + | 362.136i | 1.23230 | + | 0.711466i | 0.967508 | − | 0.252841i | \(-0.0813649\pi\) |
0.264787 | + | 0.964307i | \(0.414698\pi\) | |||||||
\(510\) | 115.999 | − | 496.471i | 0.227449 | − | 0.973473i | ||||
\(511\) | 304.144 | − | 538.938i | 0.595195 | − | 1.05467i | ||||
\(512\) | −95.1944 | −0.185927 | ||||||||
\(513\) | −516.201 | − | 173.084i | −1.00624 | − | 0.337395i | ||||
\(514\) | −406.367 | − | 703.848i | −0.790597 | − | 1.36935i | ||||
\(515\) | −207.304 | + | 679.239i | −0.402533 | + | 1.31891i | ||||
\(516\) | −377.737 | + | 25.2295i | −0.732048 | + | 0.0488943i | ||||
\(517\) | 289.363i | 0.559697i | ||||||||
\(518\) | −367.306 | + | 650.859i | −0.709085 | + | 1.25649i | ||||
\(519\) | 211.903 | − | 141.970i | 0.408292 | − | 0.273546i | ||||
\(520\) | −305.006 | + | 70.5718i | −0.586550 | + | 0.135715i | ||||
\(521\) | −426.309 | + | 246.130i | −0.818251 | + | 0.472418i | −0.849813 | − | 0.527084i | \(-0.823285\pi\) |
0.0315618 | + | 0.999502i | \(0.489952\pi\) | |||||||
\(522\) | −164.776 | − | 1228.01i | −0.315662 | − | 2.35251i | ||||
\(523\) | −51.6590 | − | 29.8254i | −0.0987744 | − | 0.0570274i | 0.449799 | − | 0.893130i | \(-0.351496\pi\) |
−0.548574 | + | 0.836102i | \(0.684829\pi\) | |||||||
\(524\) | − | 507.291i | − | 0.968113i | ||||||
\(525\) | 452.639 | − | 265.975i | 0.862170 | − | 0.506619i | ||||
\(526\) | −583.858 | −1.11000 | ||||||||
\(527\) | 64.7055 | − | 112.073i | 0.122781 | − | 0.212663i | ||||
\(528\) | 24.0243 | − | 48.8693i | 0.0455005 | − | 0.0925555i | ||||
\(529\) | −201.882 | − | 349.669i | −0.381629 | − | 0.661001i | ||||
\(530\) | 317.906 | + | 1373.97i | 0.599823 | + | 2.59239i | ||||
\(531\) | −403.574 | − | 165.992i | −0.760026 | − | 0.312603i | ||||
\(532\) | −766.010 | + | 452.336i | −1.43987 | + | 0.850255i | ||||
\(533\) | 54.3044 | 0.101884 | ||||||||
\(534\) | −602.375 | + | 40.2333i | −1.12804 | + | 0.0753433i | ||||
\(535\) | −273.002 | − | 83.3205i | −0.510284 | − | 0.155739i | ||||
\(536\) | −144.972 | + | 83.6995i | −0.270470 | + | 0.156156i | ||||
\(537\) | 370.661 | − | 24.7569i | 0.690244 | − | 0.0461022i | ||||
\(538\) | 833.196i | 1.54869i | ||||||||
\(539\) | −11.7165 | − | 596.936i | −0.0217375 | − | 1.10749i | ||||
\(540\) | −692.589 | − | 494.178i | −1.28257 | − | 0.915144i | ||||
\(541\) | 276.972 | − | 479.729i | 0.511962 | − | 0.886745i | −0.487941 | − | 0.872876i | \(-0.662252\pi\) |
0.999904 | − | 0.0138685i | \(-0.00441463\pi\) | |||||||
\(542\) | 56.9766 | + | 98.6863i | 0.105123 | + | 0.182078i | ||||
\(543\) | −455.535 | − | 223.942i | −0.838923 | − | 0.412416i | ||||
\(544\) | 181.829 | − | 314.938i | 0.334245 | − | 0.578929i | ||||
\(545\) | −647.945 | + | 604.806i | −1.18889 | + | 1.10974i | ||||
\(546\) | −514.962 | − | 246.912i | −0.943154 | − | 0.452220i | ||||
\(547\) | 109.968i | 0.201039i | 0.994935 | + | 0.100520i | \(0.0320505\pi\) | ||||
−0.994935 | + | 0.100520i | \(0.967949\pi\) | |||||||
\(548\) | 37.5444 | − | 65.0288i | 0.0685117 | − | 0.118666i | ||||
\(549\) | 187.273 | − | 25.1285i | 0.341117 | − | 0.0457714i | ||||
\(550\) | 429.465 | + | 878.372i | 0.780845 | + | 1.59704i | ||||
\(551\) | 749.010 | + | 432.441i | 1.35936 | + | 0.784830i | ||||
\(552\) | 562.514 | − | 376.872i | 1.01905 | − | 0.682739i | ||||
\(553\) | −0.439970 | − | 44.8357i | −0.000795605 | − | 0.0810772i | ||||
\(554\) | − | 1149.54i | − | 2.07498i | ||||||
\(555\) | 341.237 | − | 364.004i | 0.614842 | − | 0.655862i | ||||
\(556\) | −397.476 | − | 688.448i | −0.714885 | − | 1.23822i | ||||
\(557\) | 226.708 | + | 392.669i | 0.407015 | + | 0.704971i | 0.994554 | − | 0.104225i | \(-0.0332362\pi\) |
−0.587538 | + | 0.809196i | \(0.699903\pi\) | |||||||
\(558\) | −215.603 | − | 279.539i | −0.386386 | − | 0.500966i | ||||
\(559\) | 169.650 | 0.303488 | ||||||||
\(560\) | 50.6802 | − | 12.2514i | 0.0905003 | − | 0.0218776i | ||||
\(561\) | 215.456 | + | 321.587i | 0.384057 | + | 0.573239i | ||||
\(562\) | −539.049 | − | 311.220i | −0.959161 | − | 0.553772i | ||||
\(563\) | 25.2929 | + | 43.8087i | 0.0449253 | + | 0.0778129i | 0.887614 | − | 0.460589i | \(-0.152362\pi\) |
−0.842688 | + | 0.538402i | \(0.819028\pi\) | |||||||
\(564\) | 402.948 | + | 198.090i | 0.714446 | + | 0.351223i | ||||
\(565\) | −9.80691 | − | 42.3847i | −0.0173574 | − | 0.0750172i | ||||
\(566\) | 411.725i | 0.727430i | ||||||||
\(567\) | −154.830 | − | 545.451i | −0.273068 | − | 0.961995i | ||||
\(568\) | 18.0422i | 0.0317644i | ||||||||
\(569\) | −767.186 | − | 442.935i | −1.34831 | − | 0.778445i | −0.360297 | − | 0.932838i | \(-0.617325\pi\) |
−0.988010 | + | 0.154392i | \(0.950658\pi\) | |||||||
\(570\) | 929.170 | − | 281.399i | 1.63012 | − | 0.493683i | ||||
\(571\) | −479.840 | − | 831.107i | −0.840350 | − | 1.45553i | −0.889599 | − | 0.456742i | \(-0.849016\pi\) |
0.0492497 | − | 0.998786i | \(-0.484317\pi\) | |||||||
\(572\) | 325.320 | − | 563.470i | 0.568741 | − | 0.985088i | ||||
\(573\) | 213.253 | + | 318.298i | 0.372169 | + | 0.555495i | ||||
\(574\) | 143.999 | − | 1.41305i | 0.250869 | − | 0.00246176i | ||||
\(575\) | 52.5231 | − | 761.721i | 0.0913446 | − | 1.32473i | ||||
\(576\) | −573.115 | − | 743.068i | −0.994991 | − | 1.29005i | ||||
\(577\) | 265.694 | − | 153.399i | 0.460476 | − | 0.265856i | −0.251769 | − | 0.967787i | \(-0.581012\pi\) |
0.712244 | + | 0.701932i | \(0.247679\pi\) | |||||||
\(578\) | −283.840 | − | 491.624i | −0.491072 | − | 0.850561i | ||||
\(579\) | 369.973 | − | 24.7109i | 0.638986 | − | 0.0426786i | ||||
\(580\) | 922.248 | + | 988.030i | 1.59008 | + | 1.70350i | ||||
\(581\) | −624.195 | + | 368.593i | −1.07435 | + | 0.634411i | ||||
\(582\) | 753.240 | + | 1124.28i | 1.29423 | + | 1.93175i | ||||
\(583\) | −927.274 | − | 535.362i | −1.59052 | − | 0.918288i | ||||
\(584\) | 565.783 | − | 326.655i | 0.968806 | − | 0.559340i | ||||
\(585\) | 294.917 | + | 241.644i | 0.504132 | + | 0.413067i | ||||
\(586\) | −691.559 | + | 1197.81i | −1.18013 | + | 2.04405i | ||||
\(587\) | −336.767 | −0.573708 | −0.286854 | − | 0.957974i | \(-0.592610\pi\) | ||||
−0.286854 | + | 0.957974i | \(0.592610\pi\) | |||||||
\(588\) | −839.274 | − | 392.330i | −1.42734 | − | 0.667228i | ||||
\(589\) | 246.426 | 0.418380 | ||||||||
\(590\) | 758.112 | − | 175.411i | 1.28494 | − | 0.297307i | ||||
\(591\) | −60.7319 | − | 29.8559i | −0.102761 | − | 0.0505176i | ||||
\(592\) | 42.9132 | − | 24.7760i | 0.0724885 | − | 0.0418513i | ||||
\(593\) | 556.222 | − | 963.405i | 0.937980 | − | 1.62463i | 0.168748 | − | 0.985659i | \(-0.446028\pi\) |
0.769232 | − | 0.638970i | \(-0.220639\pi\) | |||||||
\(594\) | 1034.90 | − | 209.866i | 1.74225 | − | 0.353310i | ||||
\(595\) | −104.707 | + | 355.535i | −0.175979 | + | 0.597538i | ||||
\(596\) | 726.966i | 1.21974i | ||||||||
\(597\) | 6.90138 | + | 103.328i | 0.0115601 | + | 0.173078i | ||||
\(598\) | −719.294 | + | 415.285i | −1.20283 | + | 0.694456i | ||||
\(599\) | 514.713 | − | 297.170i | 0.859287 | − | 0.496110i | −0.00448642 | − | 0.999990i | \(-0.501428\pi\) |
0.863773 | + | 0.503880i | \(0.168095\pi\) | |||||||
\(600\) | 554.245 | + | 1.19282i | 0.923741 | + | 0.00198803i | ||||
\(601\) | 434.293 | 0.722617 | 0.361309 | − | 0.932446i | \(-0.382330\pi\) | ||||
0.361309 | + | 0.932446i | \(0.382330\pi\) | |||||||
\(602\) | 449.859 | − | 4.41444i | 0.747275 | − | 0.00733295i | ||||
\(603\) | 188.545 | + | 77.5496i | 0.312678 | + | 0.128606i | ||||
\(604\) | 881.069 | − | 1526.06i | 1.45872 | − | 2.52658i | ||||
\(605\) | −131.356 | − | 40.0899i | −0.217117 | − | 0.0662642i | ||||
\(606\) | 651.716 | − | 1325.70i | 1.07544 | − | 2.18762i | ||||
\(607\) | 783.964 | + | 452.622i | 1.29154 | + | 0.745670i | 0.978927 | − | 0.204211i | \(-0.0654628\pi\) |
0.312612 | + | 0.949881i | \(0.398796\pi\) | |||||||
\(608\) | 692.482 | 1.13895 | ||||||||
\(609\) | 68.8414 | + | 898.076i | 0.113040 | + | 1.47467i | ||||
\(610\) | −246.307 | + | 229.908i | −0.403782 | + | 0.376899i | ||||
\(611\) | −174.253 | − | 100.605i | −0.285193 | − | 0.164656i | ||||
\(612\) | 595.315 | − | 79.8800i | 0.972738 | − | 0.130523i | ||||
\(613\) | 595.512 | − | 343.819i | 0.971472 | − | 0.560879i | 0.0717871 | − | 0.997420i | \(-0.477130\pi\) |
0.899685 | + | 0.436541i | \(0.143796\pi\) | |||||||
\(614\) | −568.875 | − | 328.440i | −0.926507 | − | 0.534919i | ||||
\(615\) | −93.6187 | − | 21.8737i | −0.152225 | − | 0.0355670i | ||||
\(616\) | 309.784 | − | 548.931i | 0.502896 | − | 0.891122i | ||||
\(617\) | −205.651 | −0.333308 | −0.166654 | − | 0.986015i | \(-0.553296\pi\) | ||||
−0.166654 | + | 0.986015i | \(0.553296\pi\) | |||||||
\(618\) | −1364.63 | + | 91.1452i | −2.20814 | + | 0.147484i | ||||
\(619\) | 428.521 | + | 742.221i | 0.692280 | + | 1.19906i | 0.971089 | + | 0.238718i | \(0.0767271\pi\) |
−0.278809 | + | 0.960347i | \(0.589940\pi\) | |||||||
\(620\) | 368.323 | + | 112.412i | 0.594069 | + | 0.181310i | ||||
\(621\) | −781.832 | − | 262.151i | −1.25899 | − | 0.422143i | ||||
\(622\) | − | 1254.56i | − | 2.01697i | ||||||
\(623\) | 438.855 | − | 4.30645i | 0.704422 | − | 0.00691244i | ||||
\(624\) | 21.0762 | + | 31.4580i | 0.0337759 | + | 0.0504135i | ||||
\(625\) | 383.833 | − | 493.251i | 0.614133 | − | 0.789202i | ||||
\(626\) | −713.402 | + | 411.883i | −1.13962 | + | 0.657960i | ||||
\(627\) | −325.191 | + | 661.492i | −0.518645 | + | 1.05501i | ||||
\(628\) | 147.428 | + | 85.1177i | 0.234758 | + | 0.135538i | ||||
\(629\) | 352.236i | 0.559994i | ||||||||
\(630\) | 788.318 | + | 633.092i | 1.25130 | + | 1.00491i | ||||
\(631\) | −464.352 | −0.735899 | −0.367949 | − | 0.929846i | \(-0.619940\pi\) | ||||
−0.367949 | + | 0.929846i | \(0.619940\pi\) | |||||||
\(632\) | 23.6678 | − | 40.9938i | 0.0374491 | − | 0.0648637i | ||||
\(633\) | 204.807 | + | 100.684i | 0.323550 | + | 0.159058i | ||||
\(634\) | 513.254 | + | 888.983i | 0.809550 | + | 1.40218i | ||||
\(635\) | 286.191 | − | 66.2184i | 0.450694 | − | 0.104281i | ||||
\(636\) | −1380.29 | + | 924.766i | −2.17027 | + | 1.45403i | ||||
\(637\) | 363.545 | + | 200.486i | 0.570715 | + | 0.314734i | ||||
\(638\) | −1677.45 | −2.62923 | ||||||||
\(639\) | 17.3991 | − | 13.4196i | 0.0272287 | − | 0.0210010i | ||||
\(640\) | 943.559 | + | 287.975i | 1.47431 | + | 0.449961i | ||||
\(641\) | 144.334 | − | 83.3312i | 0.225170 | − | 0.130002i | −0.383172 | − | 0.923677i | \(-0.625168\pi\) |
0.608342 | + | 0.793675i | \(0.291835\pi\) | |||||||
\(642\) | −36.6334 | − | 548.477i | −0.0570614 | − | 0.854325i | ||||
\(643\) | 643.063i | 1.00010i | 0.865997 | + | 0.500049i | \(0.166685\pi\) | ||||
−0.865997 | + | 0.500049i | \(0.833315\pi\) | |||||||
\(644\) | −1160.19 | + | 685.102i | −1.80154 | + | 1.06382i | ||||
\(645\) | −292.469 | − | 68.3346i | −0.453441 | − | 0.105945i | ||||
\(646\) | −342.693 | + | 593.562i | −0.530485 | + | 0.918827i | ||||
\(647\) | −86.4616 | − | 149.756i | −0.133635 | − | 0.231462i | 0.791440 | − | 0.611246i | \(-0.209332\pi\) |
−0.925075 | + | 0.379784i | \(0.875998\pi\) | |||||||
\(648\) | 152.050 | − | 578.952i | 0.234646 | − | 0.893444i | ||||
\(649\) | −295.397 | + | 511.642i | −0.455157 | + | 0.788354i | ||||
\(650\) | −678.266 | − | 46.7687i | −1.04349 | − | 0.0719518i | ||||
\(651\) | 144.928 | + | 211.794i | 0.222624 | + | 0.325337i | ||||
\(652\) | − | 1736.30i | − | 2.66304i | ||||||
\(653\) | −514.097 | + | 890.443i | −0.787285 | + | 1.36362i | 0.140339 | + | 0.990104i | \(0.455181\pi\) |
−0.927624 | + | 0.373515i | \(0.878153\pi\) | |||||||
\(654\) | −1531.87 | − | 753.073i | −2.34232 | − | 1.15149i | ||||
\(655\) | 117.482 | − | 384.933i | 0.179362 | − | 0.587684i | ||||
\(656\) | −8.26888 | − | 4.77404i | −0.0126050 | − | 0.00727750i | ||||
\(657\) | −735.836 | − | 302.653i | −1.11999 | − | 0.460660i | ||||
\(658\) | −464.684 | − | 262.240i | −0.706206 | − | 0.398540i | ||||
\(659\) | − | 494.948i | − | 0.751059i | −0.926810 | − | 0.375530i | \(-0.877461\pi\) | ||
0.926810 | − | 0.375530i | \(-0.122539\pi\) | |||||||
\(660\) | −787.804 | + | 840.363i | −1.19364 | + | 1.27328i | ||||
\(661\) | 190.532 | + | 330.011i | 0.288248 | + | 0.499261i | 0.973392 | − | 0.229147i | \(-0.0735938\pi\) |
−0.685143 | + | 0.728408i | \(0.740260\pi\) | |||||||
\(662\) | 462.921 | + | 801.803i | 0.699276 | + | 1.21118i | ||||
\(663\) | −268.567 | + | 17.9379i | −0.405079 | + | 0.0270557i | ||||
\(664\) | −765.282 | −1.15253 | ||||||||
\(665\) | −686.003 | + | 165.835i | −1.03158 | + | 0.249375i | ||||
\(666\) | 888.646 | + | 365.505i | 1.33430 | + | 0.548807i | ||||
\(667\) | 1134.44 | + | 654.970i | 1.70081 | + | 0.981964i | ||||
\(668\) | −25.7654 | − | 44.6270i | −0.0385710 | − | 0.0668069i | ||||
\(669\) | 413.915 | − | 841.973i | 0.618708 | − | 1.25855i | ||||
\(670\) | −354.181 | + | 81.9499i | −0.528628 | + | 0.122313i | ||||
\(671\) | − | 255.813i | − | 0.381242i | ||||||
\(672\) | 407.264 | + | 595.164i | 0.606048 | + | 0.885661i | ||||
\(673\) | − | 617.578i | − | 0.917649i | −0.888527 | − | 0.458825i | \(-0.848271\pi\) | ||
0.888527 | − | 0.458825i | \(-0.151729\pi\) | |||||||
\(674\) | 1057.73 | + | 610.680i | 1.56933 | + | 0.906053i | ||||
\(675\) | −411.092 | − | 535.377i | −0.609025 | − | 0.793151i | ||||
\(676\) | −306.337 | − | 530.591i | −0.453161 | − | 0.784897i | ||||
\(677\) | 150.968 | − | 261.485i | 0.222996 | − | 0.386241i | −0.732720 | − | 0.680530i | \(-0.761750\pi\) |
0.955716 | + | 0.294289i | \(0.0950829\pi\) | |||||||
\(678\) | 69.6047 | − | 46.6336i | 0.102662 | − | 0.0687811i | ||||
\(679\) | −500.224 | − | 847.107i | −0.736707 | − | 1.24758i | ||||
\(680\) | −286.035 | + | 266.991i | −0.420639 | + | 0.392634i | ||||
\(681\) | −13.7778 | − | 206.282i | −0.0202318 | − | 0.302911i | ||||
\(682\) | −413.913 | + | 238.973i | −0.606911 | + | 0.350400i | ||||
\(683\) | −45.4093 | − | 78.6511i | −0.0664850 | − | 0.115155i | 0.830867 | − | 0.556471i | \(-0.187845\pi\) |
−0.897352 | + | 0.441316i | \(0.854512\pi\) | |||||||
\(684\) | 698.532 | + | 905.677i | 1.02125 | + | 1.32409i | ||||
\(685\) | 43.5485 | − | 40.6491i | 0.0635744 | − | 0.0593417i | ||||
\(686\) | 969.229 | + | 522.167i | 1.41287 | + | 0.761176i | ||||
\(687\) | −857.737 | + | 574.664i | −1.24853 | + | 0.836484i | ||||
\(688\) | −25.8324 | − | 14.9143i | −0.0375471 | − | 0.0216778i | ||||
\(689\) | 644.784 | − | 372.266i | 0.935827 | − | 0.540300i | ||||
\(690\) | 1407.31 | − | 426.204i | 2.03958 | − | 0.617687i | ||||
\(691\) | −492.003 | + | 852.173i | −0.712015 | + | 1.23325i | 0.252084 | + | 0.967705i | \(0.418884\pi\) |
−0.964099 | + | 0.265541i | \(0.914449\pi\) | |||||||
\(692\) | −535.839 | −0.774334 | ||||||||
\(693\) | −759.781 | + | 109.548i | −1.09636 | + | 0.158078i | ||||
\(694\) | −547.919 | −0.789509 | ||||||||
\(695\) | −142.169 | − | 614.445i | −0.204560 | − | 0.884093i | ||||
\(696\) | −419.506 | + | 853.345i | −0.602739 | + | 1.22607i | ||||
\(697\) | 58.7787 | − | 33.9359i | 0.0843310 | − | 0.0486886i | ||||
\(698\) | 881.307 | − | 1526.47i | 1.26262 | − | 2.18692i | ||||
\(699\) | 99.7454 | − | 66.8271i | 0.142697 | − | 0.0956039i | ||||
\(700\) | −1100.99 | − | 65.0690i | −1.57285 | − | 0.0929557i | ||||
\(701\) | − | 446.823i | − | 0.637408i | −0.947854 | − | 0.318704i | \(-0.896752\pi\) | ||
0.947854 | − | 0.318704i | \(-0.103248\pi\) | |||||||
\(702\) | −233.429 | + | 696.174i | −0.332521 | + | 0.991701i | ||||
\(703\) | −580.870 | + | 335.366i | −0.826274 | + | 0.477049i | ||||
\(704\) | −1100.26 | + | 635.236i | −1.56287 | + | 0.902323i | ||||
\(705\) | 259.882 | + | 243.628i | 0.368627 | + | 0.345572i | ||||
\(706\) | 986.175 | 1.39685 | ||||||||
\(707\) | −527.790 | + | 935.234i | −0.746521 | + | 1.32282i | ||||
\(708\) | 510.258 | + | 761.605i | 0.720703 | + | 1.07571i | ||||
\(709\) | −574.318 | + | 994.748i | −0.810040 | + | 1.40303i | 0.102796 | + | 0.994702i | \(0.467221\pi\) |
−0.912836 | + | 0.408327i | \(0.866112\pi\) | |||||||
\(710\) | −11.4376 | + | 37.4755i | −0.0161092 | + | 0.0527824i | ||||
\(711\) | −57.1366 | + | 7.66665i | −0.0803609 | + | 0.0107829i | ||||
\(712\) | 401.250 | + | 231.662i | 0.563554 | + | 0.325368i | ||||
\(713\) | 373.233 | 0.523469 | ||||||||
\(714\) | −711.692 | + | 54.5543i | −0.996767 | + | 0.0764065i | ||||
\(715\) | 377.345 | − | 352.222i | 0.527755 | − | 0.492618i | ||||
\(716\) | −675.859 | − | 390.207i | −0.943937 | − | 0.544982i | ||||
\(717\) | −452.293 | + | 920.039i | −0.630813 | + | 1.28318i | ||||
\(718\) | 302.691 | − | 174.759i | 0.421576 | − | 0.243397i | ||||
\(719\) | 867.476 | + | 500.837i | 1.20650 | + | 0.696575i | 0.961994 | − | 0.273072i | \(-0.0880397\pi\) |
0.244510 | + | 0.969647i | \(0.421373\pi\) | |||||||
\(720\) | −23.6632 | − | 62.7219i | −0.0328656 | − | 0.0871137i | ||||
\(721\) | 994.189 | − | 9.75591i | 1.37890 | − | 0.0135311i | ||||
\(722\) | −146.408 | −0.202781 | ||||||||
\(723\) | −25.6098 | − | 383.431i | −0.0354216 | − | 0.530333i | ||||
\(724\) | 533.184 | + | 923.502i | 0.736442 | + | 1.27556i | ||||
\(725\) | 470.988 | + | 963.298i | 0.649638 | + | 1.32869i | ||||
\(726\) | −17.6263 | − | 263.901i | −0.0242786 | − | 0.363500i | ||||
\(727\) | − | 160.419i | − | 0.220659i | −0.993895 | − | 0.110330i | \(-0.964809\pi\) | ||
0.993895 | − | 0.110330i | \(-0.0351906\pi\) | |||||||
\(728\) | 222.859 | + | 377.401i | 0.306125 | + | 0.518408i | ||||
\(729\) | −671.410 | + | 283.989i | −0.921001 | + | 0.389559i | ||||
\(730\) | 1382.27 | − | 319.826i | 1.89351 | − | 0.438118i | ||||
\(731\) | 183.628 | − | 106.018i | 0.251201 | − | 0.145031i | ||||
\(732\) | −356.228 | − | 175.123i | −0.486651 | − | 0.239238i | ||||
\(733\) | −336.580 | − | 194.325i | −0.459181 | − | 0.265109i | 0.252519 | − | 0.967592i | \(-0.418741\pi\) |
−0.711700 | + | 0.702484i | \(0.752074\pi\) | |||||||
\(734\) | − | 369.916i | − | 0.503973i | ||||||
\(735\) | −545.983 | − | 492.065i | −0.742834 | − | 0.669476i | ||||
\(736\) | 1048.83 | 1.42503 | ||||||||
\(737\) | 138.006 | − | 239.033i | 0.187253 | − | 0.324332i | ||||
\(738\) | −24.6230 | − | 183.506i | −0.0333644 | − | 0.248653i | ||||
\(739\) | 599.057 | + | 1037.60i | 0.810631 | + | 1.40405i | 0.912423 | + | 0.409249i | \(0.134209\pi\) |
−0.101792 | + | 0.994806i | \(0.532457\pi\) | |||||||
\(740\) | −1021.19 | + | 236.281i | −1.37998 | + | 0.319299i | ||||
\(741\) | −285.285 | − | 425.814i | −0.385001 | − | 0.574647i | ||||
\(742\) | 1700.09 | − | 1003.92i | 2.29122 | − | 1.35299i | ||||
\(743\) | 592.907 | 0.797990 | 0.398995 | − | 0.916953i | \(-0.369359\pi\) | ||||
0.398995 | + | 0.916953i | \(0.369359\pi\) | |||||||
\(744\) | 18.0555 | + | 270.328i | 0.0242682 | + | 0.363344i | ||||
\(745\) | −168.356 | + | 551.622i | −0.225981 | + | 0.740432i | ||||
\(746\) | −248.595 | + | 143.526i | −0.333237 | + | 0.192394i | ||||
\(747\) | 569.210 | + | 738.005i | 0.761995 | + | 0.987959i | ||||
\(748\) | − | 813.196i | − | 1.08716i | ||||||
\(749\) | 3.92113 | + | 399.588i | 0.00523515 | + | 0.533495i | ||||
\(750\) | 1150.47 | + | 353.832i | 1.53395 | + | 0.471776i | ||||
\(751\) | −86.7806 | + | 150.308i | −0.115553 | + | 0.200144i | −0.918001 | − | 0.396578i | \(-0.870197\pi\) |
0.802447 | + | 0.596723i | \(0.203531\pi\) | |||||||
\(752\) | 17.6889 | + | 30.6381i | 0.0235225 | + | 0.0407421i | ||||
\(753\) | 266.184 | − | 541.462i | 0.353498 | − | 0.719073i | ||||
\(754\) | 583.211 | − | 1010.15i | 0.773490 | − | 1.33972i | ||||
\(755\) | 1021.97 | − | 953.928i | 1.35360 | − | 1.26348i | ||||
\(756\) | −367.575 | + | 1133.01i | −0.486210 | + | 1.49869i | ||||
\(757\) | 560.146i | 0.739956i | 0.929041 | + | 0.369978i | \(0.120635\pi\) | ||||
−0.929041 | + | 0.369978i | \(0.879365\pi\) | |||||||
\(758\) | 354.723 | − | 614.399i | 0.467973 | − | 0.810553i | ||||
\(759\) | −492.530 | + | 1001.89i | −0.648920 | + | 1.32001i | ||||
\(760\) | −712.628 | − | 217.495i | −0.937668 | − | 0.286177i | ||||
\(761\) | −450.545 | − | 260.123i | −0.592044 | − | 0.341817i | 0.173861 | − | 0.984770i | \(-0.444376\pi\) |
−0.765905 | + | 0.642953i | \(0.777709\pi\) | |||||||
\(762\) | 314.880 | + | 469.986i | 0.413228 | + | 0.616780i | ||||
\(763\) | 1080.68 | + | 609.873i | 1.41636 | + | 0.799309i | ||||
\(764\) | − | 804.880i | − | 1.05351i | ||||||
\(765\) | 470.225 | + | 77.2541i | 0.614673 | + | 0.100986i | ||||
\(766\) | −300.381 | − | 520.275i | −0.392142 | − | 0.679210i | ||||
\(767\) | −205.405 | − | 355.773i | −0.267804 | − | 0.463849i | ||||
\(768\) | 43.2296 | + | 647.236i | 0.0562886 | + | 0.842755i | ||||
\(769\) | 67.9595 | 0.0883739 | 0.0441869 | − | 0.999023i | \(-0.485930\pi\) | ||||
0.0441869 | + | 0.999023i | \(0.485930\pi\) | |||||||
\(770\) | 991.439 | − | 943.804i | 1.28758 | − | 1.22572i | ||||
\(771\) | 631.083 | − | 422.811i | 0.818526 | − | 0.548394i | ||||
\(772\) | −674.604 | − | 389.483i | −0.873839 | − | 0.504511i | ||||
\(773\) | 108.399 | + | 187.753i | 0.140232 | + | 0.242889i | 0.927584 | − | 0.373615i | \(-0.121882\pi\) |
−0.787352 | + | 0.616504i | \(0.788549\pi\) | |||||||
\(774\) | −76.9233 | − | 573.281i | −0.0993842 | − | 0.740673i | ||||
\(775\) | 253.450 | + | 170.597i | 0.327032 | + | 0.220125i | ||||
\(776\) | − | 1038.58i | − | 1.33837i | ||||||
\(777\) | −629.858 | − | 302.002i | −0.810627 | − | 0.388676i | ||||
\(778\) | 680.665i | 0.874891i | ||||||||
\(779\) | 111.927 | + | 64.6211i | 0.143680 | + | 0.0829539i | ||||
\(780\) | −232.161 | − | 766.586i | −0.297642 | − | 0.982803i | ||||
\(781\) | −14.8742 | − | 25.7629i | −0.0190451 | − | 0.0329871i | ||||
\(782\) | −519.040 | + | 899.003i | −0.663733 | + | 1.14962i | ||||
\(783\) | 1134.95 | − | 230.157i | 1.44949 | − | 0.293942i | ||||
\(784\) | −37.7315 | − | 62.4880i | −0.0481270 | − | 0.0797041i | ||||
\(785\) | 92.1564 | + | 98.7297i | 0.117397 | + | 0.125770i | ||||
\(786\) | 773.352 | − | 51.6531i | 0.983909 | − | 0.0657165i | ||||
\(787\) | −260.838 | + | 150.595i | −0.331434 | + | 0.191353i | −0.656478 | − | 0.754346i | \(-0.727954\pi\) |
0.325044 | + | 0.945699i | \(0.394621\pi\) | |||||||
\(788\) | 71.0841 | + | 123.121i | 0.0902082 | + | 0.156245i | ||||
\(789\) | −36.3674 | − | 544.494i | −0.0460931 | − | 0.690107i | ||||
\(790\) | 75.1478 | − | 70.1446i | 0.0951238 | − | 0.0887906i | ||||
\(791\) | −52.4450 | + | 30.9692i | −0.0663021 | + | 0.0391520i | ||||
\(792\) | −749.480 | − | 308.265i | −0.946313 | − | 0.389224i | ||||
\(793\) | 154.049 | + | 88.9405i | 0.194262 | + | 0.112157i | ||||
\(794\) | −1652.61 | + | 954.137i | −2.08138 | + | 1.20168i | ||||
\(795\) | −1261.53 | + | 382.055i | −1.58683 | + | 0.480572i | ||||
\(796\) | 108.777 | − | 188.406i | 0.136654 | − | 0.236692i | ||||
\(797\) | 170.307 | 0.213685 | 0.106842 | − | 0.994276i | \(-0.465926\pi\) | ||||
0.106842 | + | 0.994276i | \(0.465926\pi\) | |||||||
\(798\) | −767.570 | − | 1121.70i | −0.961867 | − | 1.40564i | ||||
\(799\) | −251.480 | −0.314744 | ||||||||
\(800\) | 712.222 | + | 479.396i | 0.890277 | + | 0.599245i | ||||
\(801\) | −75.0416 | − | 559.257i | −0.0936849 | − | 0.698198i | ||||
\(802\) | −1284.88 | + | 741.828i | −1.60210 | + | 0.924972i | ||||
\(803\) | −538.596 | + | 932.876i | −0.670730 | + | 1.16174i | ||||
\(804\) | −238.386 | − | 355.813i | −0.296500 | − | 0.442553i | ||||
\(805\) | −1039.01 | + | 251.171i | −1.29070 | + | 0.312014i | ||||
\(806\) | − | 332.342i | − | 0.412335i | ||||||
\(807\) | −777.023 | + | 51.8983i | −0.962854 | + | 0.0643101i | ||||
\(808\) | −981.818 | + | 566.853i | −1.21512 | + | 0.701550i | ||||
\(809\) | 746.188 | − | 430.812i | 0.922359 | − | 0.532524i | 0.0379720 | − | 0.999279i | \(-0.487910\pi\) |
0.884387 | + | 0.466755i | \(0.154577\pi\) | |||||||
\(810\) | 682.841 | − | 1106.15i | 0.843014 | − | 1.36562i | ||||
\(811\) | −1511.93 | −1.86428 | −0.932140 | − | 0.362099i | \(-0.882060\pi\) | ||||
−0.932140 | + | 0.362099i | \(0.882060\pi\) | |||||||
\(812\) | 929.975 | − | 1647.90i | 1.14529 | − | 2.02943i | ||||
\(813\) | −88.4840 | + | 59.2822i | −0.108836 | + | 0.0729179i | ||||
\(814\) | 650.446 | − | 1126.61i | 0.799074 | − | 1.38404i | ||||
\(815\) | 402.105 | − | 1317.51i | 0.493380 | − | 1.61657i | ||||
\(816\) | 42.4715 | + | 20.8791i | 0.0520483 | + | 0.0255871i | ||||
\(817\) | 349.666 | + | 201.880i | 0.427987 | + | 0.247099i | ||||
\(818\) | −676.396 | −0.826890 | ||||||||
\(819\) | 198.189 | − | 495.623i | 0.241989 | − | 0.605156i | ||||
\(820\) | 137.815 | + | 147.645i | 0.168067 | + | 0.180054i | ||||
\(821\) | 155.662 | + | 89.8715i | 0.189600 | + | 0.109466i | 0.591795 | − | 0.806088i | \(-0.298419\pi\) |
−0.402195 | + | 0.915554i | \(0.631753\pi\) | |||||||
\(822\) | 102.957 | + | 50.6141i | 0.125252 | + | 0.0615743i | ||||
\(823\) | −302.773 | + | 174.806i | −0.367889 | + | 0.212401i | −0.672536 | − | 0.740065i | \(-0.734795\pi\) |
0.304647 | + | 0.952465i | \(0.401462\pi\) | |||||||
\(824\) | 909.000 | + | 524.811i | 1.10315 | + | 0.636907i | ||||
\(825\) | −792.402 | + | 455.223i | −0.960488 | + | 0.551785i | ||||
\(826\) | −553.930 | − | 938.056i | −0.670617 | − | 1.13566i | ||||
\(827\) | 104.693 | 0.126594 | 0.0632968 | − | 0.997995i | \(-0.479839\pi\) | ||||
0.0632968 | + | 0.997995i | \(0.479839\pi\) | |||||||
\(828\) | 1057.99 | + | 1371.73i | 1.27776 | + | 1.65668i | ||||
\(829\) | 309.970 | + | 536.884i | 0.373909 | + | 0.647629i | 0.990163 | − | 0.139918i | \(-0.0446840\pi\) |
−0.616254 | + | 0.787547i | \(0.711351\pi\) | |||||||
\(830\) | −1589.57 | − | 485.138i | −1.91514 | − | 0.584504i | ||||
\(831\) | 1072.04 | − | 71.6027i | 1.29006 | − | 0.0861645i | ||||
\(832\) | − | 883.428i | − | 1.06181i | ||||||
\(833\) | 518.787 | − | 10.1826i | 0.622793 | − | 0.0122240i | ||||
\(834\) | 1009.05 | − | 676.040i | 1.20989 | − | 0.810600i | ||||
\(835\) | −9.21578 | − | 39.8299i | −0.0110369 | − | 0.0477005i | ||||
\(836\) | 1341.04 | − | 774.247i | 1.60411 | − | 0.926133i | ||||
\(837\) | 247.263 | − | 218.479i | 0.295416 | − | 0.261027i | ||||
\(838\) | −271.680 | − | 156.854i | −0.324200 | − | 0.187177i | ||||
\(839\) | − | 137.648i | − | 0.164062i | −0.996630 | − | 0.0820309i | \(-0.973859\pi\) | ||
0.996630 | − | 0.0820309i | \(-0.0261406\pi\) | |||||||
\(840\) | −232.183 | − | 740.392i | −0.276408 | − | 0.881419i | ||||
\(841\) | −998.635 | −1.18744 | ||||||||
\(842\) | 925.877 | − | 1603.67i | 1.09962 | − | 1.90459i | ||||
\(843\) | 256.661 | − | 522.092i | 0.304462 | − | 0.619326i | ||||
\(844\) | −239.718 | − | 415.204i | −0.284026 | − | 0.491948i | ||||
\(845\) | −109.571 | − | 473.556i | −0.129669 | − | 0.560421i | ||||
\(846\) | −260.954 | + | 634.453i | −0.308456 | + | 0.749944i | ||||
\(847\) | 1.88666 | + | 192.263i | 0.00222746 | + | 0.226993i | ||||
\(848\) | −130.908 | −0.154372 | ||||||||
\(849\) | −383.967 | + | 25.6456i | −0.452258 | + | 0.0302068i | ||||
\(850\) | −763.378 | + | 373.240i | −0.898091 | + | 0.439106i | ||||
\(851\) | −879.779 | + | 507.941i | −1.03382 | + | 0.596875i | ||||
\(852\) | −46.0581 | + | 3.07628i | −0.0540588 | + | 0.00361065i | ||||
\(853\) | 193.568i | 0.226926i | 0.993542 | + | 0.113463i | \(0.0361943\pi\) | ||||
−0.993542 | + | 0.113463i | \(0.963806\pi\) | |||||||
\(854\) | 410.806 | + | 231.835i | 0.481038 | + | 0.271469i | ||||
\(855\) | 320.304 | + | 848.999i | 0.374624 | + | 0.992981i | ||||
\(856\) | −210.934 | + | 365.348i | −0.246418 | + | 0.426809i | ||||
\(857\) | −206.116 | − | 357.004i | −0.240509 | − | 0.416574i | 0.720350 | − | 0.693610i | \(-0.243981\pi\) |
−0.960859 | + | 0.277036i | \(0.910648\pi\) | |||||||
\(858\) | 892.120 | + | 438.568i | 1.03977 | + | 0.511152i | ||||
\(859\) | 694.910 | − | 1203.62i | 0.808975 | − | 1.40119i | −0.104599 | − | 0.994514i | \(-0.533356\pi\) |
0.913574 | − | 0.406672i | \(-0.133311\pi\) | |||||||
\(860\) | 430.540 | + | 461.249i | 0.500628 | + | 0.536336i | ||||
\(861\) | 10.2872 | + | 134.202i | 0.0119480 | + | 0.155868i | ||||
\(862\) | 541.791i | 0.628528i | ||||||||
\(863\) | −352.319 | + | 610.235i | −0.408250 | + | 0.707109i | −0.994694 | − | 0.102881i | \(-0.967194\pi\) |
0.586444 | + | 0.809990i | \(0.300527\pi\) | |||||||
\(864\) | 694.835 | − | 613.950i | 0.804207 | − | 0.710591i | ||||
\(865\) | −406.595 | − | 124.093i | −0.470052 | − | 0.143460i | ||||
\(866\) | −914.432 | − | 527.948i | −1.05593 | − | 0.609639i | ||||
\(867\) | 440.800 | − | 295.326i | 0.508419 | − | 0.340629i | ||||
\(868\) | −5.29022 | − | 539.107i | −0.00609472 | − | 0.621091i | ||||
\(869\) | 78.0481i | 0.0898137i | ||||||||
\(870\) | −1412.32 | + | 1506.55i | −1.62336 | + | 1.73166i | ||||
\(871\) | 95.9629 | + | 166.213i | 0.110176 | + | 0.190830i | ||||
\(872\) | 655.011 | + | 1134.51i | 0.751159 | + | 1.30105i | ||||
\(873\) | −1001.56 | + | 772.486i | −1.14726 | + | 0.884863i | ||||
\(874\) | −1976.72 | −2.26169 | ||||||||
\(875\) | −820.364 | − | 304.349i | −0.937558 | − | 0.347828i | ||||
\(876\) | 930.352 | + | 1388.63i | 1.06205 | + | 1.58520i | ||||
\(877\) | 202.147 | + | 116.710i | 0.230499 | + | 0.133079i | 0.610802 | − | 0.791783i | \(-0.290847\pi\) |
−0.380303 | + | 0.924862i | \(0.624180\pi\) | |||||||
\(878\) | −353.182 | − | 611.728i | −0.402257 | − | 0.696729i | ||||
\(879\) | −1160.13 | − | 570.324i | −1.31983 | − | 0.648833i | ||||
\(880\) | −88.4227 | + | 20.4591i | −0.100480 | + | 0.0232490i | ||||
\(881\) | − | 160.437i | − | 0.182107i | −0.995846 | − | 0.0910537i | \(-0.970977\pi\) | ||
0.995846 | − | 0.0910537i | \(-0.0290235\pi\) | |||||||
\(882\) | 512.641 | − | 1319.40i | 0.581225 | − | 1.49592i | ||||
\(883\) | − | 1106.33i | − | 1.25293i | −0.779451 | − | 0.626463i | \(-0.784502\pi\) | ||
0.779451 | − | 0.626463i | \(-0.215498\pi\) | |||||||
\(884\) | 489.702 | + | 282.730i | 0.553962 | + | 0.319830i | ||||
\(885\) | 210.806 | + | 696.075i | 0.238199 | + | 0.786525i | ||||
\(886\) | 314.566 | + | 544.845i | 0.355041 | + | 0.614949i | ||||
\(887\) | −572.741 | + | 992.017i | −0.645706 | + | 1.11840i | 0.338432 | + | 0.940991i | \(0.390104\pi\) |
−0.984138 | + | 0.177405i | \(0.943230\pi\) | |||||||
\(888\) | −410.455 | − | 612.640i | −0.462224 | − | 0.689910i | ||||
\(889\) | −209.111 | − | 354.120i | −0.235220 | − | 0.398335i | ||||
\(890\) | 686.580 | + | 735.552i | 0.771438 | + | 0.826463i | ||||
\(891\) | 260.179 | + | 952.051i | 0.292008 | + | 1.06852i | ||||
\(892\) | −1706.92 | + | 985.493i | −1.91359 | + | 1.10481i | ||||
\(893\) | −239.436 | − | 414.715i | −0.268125 | − | 0.464406i | ||||
\(894\) | −1108.24 | + | 74.0207i | −1.23964 | + | 0.0827972i | ||||
\(895\) | −422.475 | − | 452.609i | −0.472039 | − | 0.505709i | ||||
\(896\) | −13.5523 | − | 1381.07i | −0.0151254 | − | 1.54137i | ||||
\(897\) | −432.090 | − | 644.932i | −0.481706 | − | 0.718988i | ||||
\(898\) | 1207.10 | + | 696.917i | 1.34421 | + | 0.776077i | ||||
\(899\) | −453.932 | + | 262.078i | −0.504930 | + | 0.291522i | ||||
\(900\) | 91.4562 | + | 1415.08i | 0.101618 | + | 1.57231i | ||||
\(901\) | 465.274 | − | 805.878i | 0.516397 | − | 0.894426i | ||||
\(902\) | −250.667 | −0.277901 | ||||||||
\(903\) | 32.1377 | + | 419.255i | 0.0355900 | + | 0.464291i | ||||
\(904\) | −64.2991 | −0.0711273 | ||||||||
\(905\) | 190.710 | + | 824.232i | 0.210729 | + | 0.910754i | ||||
\(906\) | 2416.14 | + | 1187.78i | 2.66682 | + | 1.31102i | ||||
\(907\) | 460.354 | − | 265.785i | 0.507557 | − | 0.293038i | −0.224272 | − | 0.974527i | \(-0.572000\pi\) |
0.731829 | + | 0.681489i | \(0.238667\pi\) | |||||||
\(908\) | −217.160 | + | 376.133i | −0.239163 | + | 0.414243i | ||||
\(909\) | 1276.92 | + | 525.203i | 1.40475 | + | 0.577781i | ||||
\(910\) | 223.653 | + | 925.178i | 0.245772 | + | 1.01668i | ||||
\(911\) | 996.269i | 1.09360i | 0.837263 | + | 0.546800i | \(0.184154\pi\) | ||||
−0.837263 | + | 0.546800i | \(0.815846\pi\) | |||||||
\(912\) | 6.00576 | + | 89.9184i | 0.00658526 | + | 0.0985948i | ||||
\(913\) | 1092.76 | − | 630.908i | 1.19689 | − | 0.691027i | ||||
\(914\) | 59.3972 | − | 34.2930i | 0.0649860 | − | 0.0375197i | ||||
\(915\) | −229.750 | − | 215.381i | −0.251093 | − | 0.235389i | ||||
\(916\) | 2168.96 | 2.36786 | ||||||||
\(917\) | −563.419 | + | 5.52879i | −0.614416 | + | 0.00602922i | ||||
\(918\) | 182.391 | + | 899.409i | 0.198683 | + | 0.979749i | ||||
\(919\) | 230.450 | − | 399.151i | 0.250761 | − | 0.434331i | −0.712974 | − | 0.701190i | \(-0.752652\pi\) |
0.963736 | + | 0.266859i | \(0.0859857\pi\) | |||||||
\(920\) | −1079.34 | − | 329.415i | −1.17319 | − | 0.358060i | ||||
\(921\) | 270.863 | − | 550.980i | 0.294097 | − | 0.598241i | ||||
\(922\) | −2110.56 | − | 1218.53i | −2.28911 | − | 1.32162i | ||||
\(923\) | 20.6857 | 0.0224114 | ||||||||
\(924\) | 1454.13 | + | 697.221i | 1.57373 | + | 0.754568i | ||||
\(925\) | −829.598 | − | 57.2034i | −0.896862 | − | 0.0618416i | ||||
\(926\) | 673.315 | + | 388.738i | 0.727122 | + | 0.419804i | ||||
\(927\) | −170.001 | − | 1266.95i | −0.183388 | − | 1.36672i | ||||
\(928\) | −1275.60 | + | 736.467i | −1.37457 | + | 0.793607i | ||||
\(929\) | −671.881 | − | 387.911i | −0.723230 | − | 0.417557i | 0.0927101 | − | 0.995693i | \(-0.470447\pi\) |
−0.815941 | + | 0.578136i | \(0.803780\pi\) | |||||||
\(930\) | −133.867 | + | 572.944i | −0.143943 | + | 0.616069i | ||||
\(931\) | 510.731 | + | 845.833i | 0.548584 | + | 0.908521i | ||||
\(932\) | −252.226 | −0.270628 | ||||||||
\(933\) | 1169.98 | − | 78.1440i | 1.25399 | − | 0.0837557i | ||||
\(934\) | 667.426 | + | 1156.02i | 0.714589 | + | 1.23770i | ||||
\(935\) | 188.325 | − | 617.053i | 0.201417 | − | 0.659950i | ||||
\(936\) | 446.213 | − | 344.156i | 0.476723 | − | 0.367688i | ||||
\(937\) | 1641.61i | 1.75198i | 0.482328 | + | 0.875991i | \(0.339791\pi\) | ||||
−0.482328 | + | 0.875991i | \(0.660209\pi\) | |||||||
\(938\) | 258.789 | + | 438.248i | 0.275895 | + | 0.467216i | ||||
\(939\) | −428.551 | − | 639.650i | −0.456390 | − | 0.681203i | ||||
\(940\) | −168.694 | − | 729.082i | −0.179462 | − | 0.775619i | ||||
\(941\) | −183.452 | + | 105.916i | −0.194954 | + | 0.112557i | −0.594300 | − | 0.804244i | \(-0.702571\pi\) |
0.399345 | + | 0.916801i | \(0.369237\pi\) | |||||||
\(942\) | −114.748 | + | 233.417i | −0.121814 | + | 0.247789i | ||||
\(943\) | 169.523 | + | 97.8744i | 0.179770 | + | 0.103790i | ||||
\(944\) | 72.2309i | 0.0765158i | ||||||||
\(945\) | −541.307 | + | 774.605i | −0.572811 | + | 0.819687i | ||||
\(946\) | −783.096 | −0.827797 | ||||||||
\(947\) | 326.915 | − | 566.234i | 0.345211 | − | 0.597924i | −0.640181 | − | 0.768224i | \(-0.721141\pi\) |
0.985392 | + | 0.170301i | \(0.0544739\pi\) | |||||||
\(948\) | 108.685 | + | 53.4295i | 0.114646 | + | 0.0563603i | ||||
\(949\) | −374.515 | − | 648.680i | −0.394642 | − | 0.683540i | ||||
\(950\) | −1342.32 | − | 903.517i | −1.41297 | − | 0.951071i | ||||
\(951\) | −797.078 | + | 534.024i | −0.838148 | + | 0.561540i | ||||
\(952\) | 477.066 | + | 269.228i | 0.501120 | + | 0.282802i | ||||
\(953\) | 1579.73 | 1.65764 | 0.828819 | − | 0.559516i | \(-0.189013\pi\) | ||||
0.828819 | + | 0.559516i | \(0.189013\pi\) | |||||||
\(954\) | −1550.32 | − | 2010.06i | −1.62508 | − | 2.10698i | ||||
\(955\) | 186.399 | − | 610.743i | 0.195183 | − | 0.639521i | ||||
\(956\) | 1865.19 | − | 1076.87i | 1.95103 | − | 1.12643i | ||||
\(957\) | −104.485 | − | 1564.36i | −0.109180 | − | 1.63465i | ||||
\(958\) | − | 167.337i | − | 0.174673i | ||||||
\(959\) | −72.6329 | − | 40.9896i | −0.0757381 | − | 0.0427421i | ||||
\(960\) | −355.843 | + | 1523.00i | −0.370670 | + | 1.58645i | ||||
\(961\) | 405.828 | − | 702.914i | 0.422297 | − | 0.731440i | ||||
\(962\) | 452.291 | + | 783.390i | 0.470157 | + | 0.814335i | ||||
\(963\) | 509.217 | − | 68.3272i | 0.528782 | − | 0.0709525i | ||||
\(964\) | −403.650 | + | 699.143i | −0.418724 | + | 0.725252i | ||||
\(965\) | −421.691 | − | 451.769i | −0.436985 | − | 0.468154i | ||||
\(966\) | −1162.55 | − | 1698.92i | −1.20347 | − | 1.75872i | ||||
\(967\) | − | 823.369i | − | 0.851467i | −0.904849 | − | 0.425734i | \(-0.860016\pi\) | ||
0.904849 | − | 0.425734i | \(-0.139984\pi\) | |||||||
\(968\) | −101.491 | + | 175.788i | −0.104846 | + | 0.181599i | ||||
\(969\) | −574.891 | − | 282.617i | −0.593282 | − | 0.291659i | ||||
\(970\) | 658.390 | − | 2157.23i | 0.678752 | − | 2.22395i | ||||
\(971\) | −872.614 | − | 503.804i | −0.898676 | − | 0.518851i | −0.0219055 | − | 0.999760i | \(-0.506973\pi\) |
−0.876770 | + | 0.480909i | \(0.840307\pi\) | |||||||
\(972\) | 1503.87 | + | 289.440i | 1.54719 | + | 0.297778i | ||||
\(973\) | −760.288 | + | 448.956i | −0.781385 | + | 0.461415i | ||||
\(974\) | 2700.33i | 2.77241i | ||||||||
\(975\) | 1.36759 | − | 635.451i | 0.00140265 | − | 0.651745i | ||||
\(976\) | −15.6380 | − | 27.0858i | −0.0160225 | − | 0.0277518i | ||||
\(977\) | −296.872 | − | 514.197i | −0.303860 | − | 0.526302i | 0.673147 | − | 0.739509i | \(-0.264942\pi\) |
−0.977007 | + | 0.213208i | \(0.931609\pi\) | |||||||
\(978\) | 2646.95 | − | 176.793i | 2.70649 | − | 0.180770i | ||||
\(979\) | −763.940 | −0.780327 | ||||||||
\(980\) | 377.525 | + | 1497.21i | 0.385229 | + | 1.52777i | ||||
\(981\) | 606.883 | − | 1475.50i | 0.618637 | − | 1.50408i | ||||
\(982\) | 2341.31 | + | 1351.75i | 2.38422 | + | 1.37653i | ||||
\(983\) | −396.614 | − | 686.956i | −0.403473 | − | 0.698836i | 0.590669 | − | 0.806914i | \(-0.298864\pi\) |
−0.994142 | + | 0.108078i | \(0.965530\pi\) | |||||||
\(984\) | −62.6882 | + | 127.518i | −0.0637075 | + | 0.129592i | ||||
\(985\) | 25.4254 | + | 109.887i | 0.0258126 | + | 0.111560i | ||||
\(986\) | − | 1457.84i | − | 1.47854i | ||||||
\(987\) | 215.615 | − | 449.689i | 0.218455 | − | 0.455612i | ||||
\(988\) | 1076.75i | 1.08983i | ||||||||
\(989\) | 529.600 | + | 305.764i | 0.535490 | + | 0.309165i | ||||
\(990\) | −1361.33 | − | 1115.42i | −1.37508 | − | 1.12669i | ||||
\(991\) | 835.228 | + | 1446.66i | 0.842813 | + | 1.45979i | 0.887507 | + | 0.460794i | \(0.152435\pi\) |
−0.0446942 | + | 0.999001i | \(0.514231\pi\) | |||||||
\(992\) | −209.837 | + | 363.449i | −0.211529 | + | 0.366380i | ||||
\(993\) | −718.911 | + | 481.654i | −0.723979 | + | 0.485049i | ||||
\(994\) | 54.8522 | − | 0.538260i | 0.0551833 | − | 0.000541510i | ||||
\(995\) | 126.172 | − | 117.772i | 0.126806 | − | 0.118364i | ||||
\(996\) | −130.484 | − | 1953.61i | −0.131008 | − | 1.96146i | ||||
\(997\) | −963.425 | + | 556.234i | −0.966324 | + | 0.557907i | −0.898114 | − | 0.439764i | \(-0.855062\pi\) |
−0.0682102 | + | 0.997671i | \(0.521729\pi\) | |||||||
\(998\) | 1380.43 | + | 2390.98i | 1.38320 | + | 2.39577i | ||||
\(999\) | −285.511 | + | 851.501i | −0.285797 | + | 0.852353i |
(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 | 105.3.o.b.44.18 | yes | 40 | |
3.2 | odd | 2 | inner | 105.3.o.b.44.4 | yes | 40 | |
5.4 | even | 2 | inner | 105.3.o.b.44.3 | ✓ | 40 | |
7.4 | even | 3 | inner | 105.3.o.b.74.17 | yes | 40 | |
15.14 | odd | 2 | inner | 105.3.o.b.44.17 | yes | 40 | |
21.11 | odd | 6 | inner | 105.3.o.b.74.3 | yes | 40 | |
35.4 | even | 6 | inner | 105.3.o.b.74.4 | yes | 40 | |
105.74 | odd | 6 | inner | 105.3.o.b.74.18 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.o.b.44.3 | ✓ | 40 | 5.4 | even | 2 | inner | |
105.3.o.b.44.4 | yes | 40 | 3.2 | odd | 2 | inner | |
105.3.o.b.44.17 | yes | 40 | 15.14 | odd | 2 | inner | |
105.3.o.b.44.18 | yes | 40 | 1.1 | even | 1 | trivial | |
105.3.o.b.74.3 | yes | 40 | 21.11 | odd | 6 | inner | |
105.3.o.b.74.4 | yes | 40 | 35.4 | even | 6 | inner | |
105.3.o.b.74.17 | yes | 40 | 7.4 | even | 3 | inner | |
105.3.o.b.74.18 | yes | 40 | 105.74 | odd | 6 | inner |