Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(27,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.27");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.16 | ||
Character | \(\chi\) | \(=\) | 76.27 |
Dual form | 76.4.f.a.31.16 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.147992 | + | 2.82455i | 0.0523231 | + | 0.998630i | ||||
\(3\) | −2.98979 | + | 5.17847i | −0.575386 | + | 0.996597i | 0.420614 | + | 0.907240i | \(0.361815\pi\) |
−0.996000 | + | 0.0893577i | \(0.971519\pi\) | |||||||
\(4\) | −7.95620 | + | 0.836024i | −0.994525 | + | 0.104503i | ||||
\(5\) | −1.90510 | + | 3.29973i | −0.170398 | + | 0.295137i | −0.938559 | − | 0.345119i | \(-0.887839\pi\) |
0.768161 | + | 0.640256i | \(0.221172\pi\) | |||||||
\(6\) | −15.0693 | − | 7.67845i | −1.02534 | − | 0.522453i | ||||
\(7\) | − | 2.74987i | − | 0.148479i | −0.997240 | − | 0.0742395i | \(-0.976347\pi\) | ||
0.997240 | − | 0.0742395i | \(-0.0236529\pi\) | |||||||
\(8\) | −3.53885 | − | 22.3490i | −0.156396 | − | 0.987694i | ||||
\(9\) | −4.37772 | − | 7.58243i | −0.162138 | − | 0.280831i | ||||
\(10\) | −9.60221 | − | 4.89273i | −0.303649 | − | 0.154722i | ||||
\(11\) | − | 15.1389i | − | 0.414958i | −0.978239 | − | 0.207479i | \(-0.933474\pi\) | ||
0.978239 | − | 0.207479i | \(-0.0665259\pi\) | |||||||
\(12\) | 19.4581 | − | 43.7005i | 0.468088 | − | 1.05127i | ||||
\(13\) | −24.8365 | + | 14.3394i | −0.529878 | + | 0.305925i | −0.740967 | − | 0.671542i | \(-0.765632\pi\) |
0.211089 | + | 0.977467i | \(0.432299\pi\) | |||||||
\(14\) | 7.76715 | − | 0.406959i | 0.148276 | − | 0.00776888i | ||||
\(15\) | −11.3917 | − | 19.7310i | −0.196089 | − | 0.339635i | ||||
\(16\) | 62.6021 | − | 13.3031i | 0.978158 | − | 0.207861i | ||||
\(17\) | −11.8965 | + | 20.6054i | −0.169725 | + | 0.293973i | −0.938323 | − | 0.345759i | \(-0.887621\pi\) |
0.768598 | + | 0.639732i | \(0.220955\pi\) | |||||||
\(18\) | 20.7691 | − | 13.4872i | 0.271962 | − | 0.176610i | ||||
\(19\) | −82.0880 | + | 10.9801i | −0.991172 | + | 0.132579i | ||||
\(20\) | 12.3987 | − | 27.8460i | 0.138622 | − | 0.311328i | ||||
\(21\) | 14.2401 | + | 8.22154i | 0.147974 | + | 0.0854327i | ||||
\(22\) | 42.7605 | − | 2.24043i | 0.414390 | − | 0.0217119i | ||||
\(23\) | −57.0658 | + | 32.9469i | −0.517349 | + | 0.298692i | −0.735849 | − | 0.677145i | \(-0.763217\pi\) |
0.218500 | + | 0.975837i | \(0.429884\pi\) | |||||||
\(24\) | 126.314 | + | 48.4930i | 1.07432 | + | 0.412441i | ||||
\(25\) | 55.2412 | + | 95.6805i | 0.441929 | + | 0.765444i | ||||
\(26\) | −44.1779 | − | 68.0300i | −0.333231 | − | 0.513145i | ||||
\(27\) | −109.095 | −0.777605 | ||||||||
\(28\) | 2.29895 | + | 21.8785i | 0.0155165 | + | 0.147666i | ||||
\(29\) | −144.532 | + | 83.4459i | −0.925483 | + | 0.534328i | −0.885380 | − | 0.464868i | \(-0.846102\pi\) |
−0.0401027 | + | 0.999196i | \(0.512769\pi\) | |||||||
\(30\) | 54.0455 | − | 35.0966i | 0.328910 | − | 0.213591i | ||||
\(31\) | 89.3278 | 0.517540 | 0.258770 | − | 0.965939i | \(-0.416683\pi\) | ||||
0.258770 | + | 0.965939i | \(0.416683\pi\) | |||||||
\(32\) | 46.8400 | + | 174.854i | 0.258757 | + | 0.965942i | ||||
\(33\) | 78.3962 | + | 45.2620i | 0.413546 | + | 0.238761i | ||||
\(34\) | −59.9616 | − | 30.5529i | −0.302451 | − | 0.154111i | ||||
\(35\) | 9.07383 | + | 5.23878i | 0.0438217 | + | 0.0253004i | ||||
\(36\) | 41.1691 | + | 56.6674i | 0.190598 | + | 0.262349i | ||||
\(37\) | 208.064i | 0.924475i | 0.886756 | + | 0.462238i | \(0.152953\pi\) | ||||
−0.886756 | + | 0.462238i | \(0.847047\pi\) | |||||||
\(38\) | −43.1623 | − | 230.237i | −0.184259 | − | 0.982878i | ||||
\(39\) | − | 171.487i | − | 0.704100i | ||||||
\(40\) | 80.4875 | + | 30.8998i | 0.318155 | + | 0.122142i | ||||
\(41\) | −30.2818 | − | 17.4832i | −0.115347 | − | 0.0665955i | 0.441217 | − | 0.897401i | \(-0.354547\pi\) |
−0.556563 | + | 0.830805i | \(0.687880\pi\) | |||||||
\(42\) | −21.1147 | + | 41.4387i | −0.0775732 | + | 0.152241i | ||||
\(43\) | 298.492 | + | 172.334i | 1.05859 | + | 0.611179i | 0.925043 | − | 0.379863i | \(-0.124029\pi\) |
0.133551 | + | 0.991042i | \(0.457362\pi\) | |||||||
\(44\) | 12.6564 | + | 120.448i | 0.0433643 | + | 0.412686i | ||||
\(45\) | 33.3600 | 0.110511 | ||||||||
\(46\) | −101.506 | − | 156.309i | −0.325352 | − | 0.501012i | ||||
\(47\) | 118.179 | − | 68.2307i | 0.366770 | − | 0.211755i | −0.305277 | − | 0.952264i | \(-0.598749\pi\) |
0.672046 | + | 0.740509i | \(0.265416\pi\) | |||||||
\(48\) | −118.277 | + | 363.957i | −0.355664 | + | 1.09443i | ||||
\(49\) | 335.438 | 0.977954 | ||||||||
\(50\) | −262.079 | + | 170.192i | −0.741272 | + | 0.481374i | ||||
\(51\) | −71.1363 | − | 123.212i | −0.195315 | − | 0.338296i | ||||
\(52\) | 185.616 | − | 134.851i | 0.495007 | − | 0.359624i | ||||
\(53\) | −224.708 | + | 129.735i | −0.582376 | + | 0.336235i | −0.762077 | − | 0.647486i | \(-0.775820\pi\) |
0.179701 | + | 0.983721i | \(0.442487\pi\) | |||||||
\(54\) | −16.1452 | − | 308.144i | −0.0406867 | − | 0.776540i | ||||
\(55\) | 49.9542 | + | 28.8411i | 0.122470 | + | 0.0707078i | ||||
\(56\) | −61.4567 | + | 9.73137i | −0.146652 | + | 0.0232216i | ||||
\(57\) | 188.566 | − | 457.919i | 0.438178 | − | 1.06408i | ||||
\(58\) | −257.087 | − | 395.890i | −0.582020 | − | 0.896257i | ||||
\(59\) | 26.4616 | − | 45.8329i | 0.0583900 | − | 0.101134i | −0.835353 | − | 0.549714i | \(-0.814737\pi\) |
0.893743 | + | 0.448580i | \(0.148070\pi\) | |||||||
\(60\) | 107.130 | + | 147.460i | 0.230508 | + | 0.317284i | ||||
\(61\) | −424.689 | − | 735.584i | −0.891408 | − | 1.54396i | −0.838188 | − | 0.545382i | \(-0.816385\pi\) |
−0.0532207 | − | 0.998583i | \(-0.516949\pi\) | |||||||
\(62\) | 13.2198 | + | 252.311i | 0.0270793 | + | 0.516831i | ||||
\(63\) | −20.8507 | + | 12.0381i | −0.0416974 | + | 0.0240740i | ||||
\(64\) | −486.953 | + | 158.179i | −0.951080 | + | 0.308944i | ||||
\(65\) | − | 109.272i | − | 0.208516i | ||||||
\(66\) | −116.243 | + | 228.133i | −0.216796 | + | 0.425472i | ||||
\(67\) | 239.349 | + | 414.565i | 0.436435 | + | 0.755927i | 0.997412 | − | 0.0719043i | \(-0.0229076\pi\) |
−0.560977 | + | 0.827832i | \(0.689574\pi\) | |||||||
\(68\) | 77.4245 | − | 173.886i | 0.138075 | − | 0.310100i | ||||
\(69\) | − | 394.018i | − | 0.687452i | ||||||
\(70\) | −13.4544 | + | 26.4048i | −0.0229729 | + | 0.0450854i | ||||
\(71\) | −8.16262 | + | 14.1381i | −0.0136440 | + | 0.0236321i | −0.872767 | − | 0.488137i | \(-0.837676\pi\) |
0.859123 | + | 0.511770i | \(0.171010\pi\) | |||||||
\(72\) | −153.967 | + | 124.671i | −0.252017 | + | 0.204063i | ||||
\(73\) | 332.179 | − | 575.350i | 0.532583 | − | 0.922461i | −0.466693 | − | 0.884419i | \(-0.654555\pi\) |
0.999276 | − | 0.0380415i | \(-0.0121119\pi\) | |||||||
\(74\) | −587.689 | + | 30.7919i | −0.923209 | + | 0.0483715i | ||||
\(75\) | −660.639 | −1.01712 | ||||||||
\(76\) | 643.929 | − | 155.987i | 0.971890 | − | 0.235434i | ||||
\(77\) | −41.6299 | −0.0616125 | ||||||||
\(78\) | 484.374 | − | 25.3787i | 0.703136 | − | 0.0368407i | ||||
\(79\) | −30.7967 | + | 53.3415i | −0.0438595 | + | 0.0759669i | −0.887122 | − | 0.461535i | \(-0.847299\pi\) |
0.843262 | + | 0.537502i | \(0.180632\pi\) | |||||||
\(80\) | −75.3667 | + | 231.914i | −0.105328 | + | 0.324110i | ||||
\(81\) | 444.370 | − | 769.671i | 0.609560 | − | 1.05579i | ||||
\(82\) | 44.9007 | − | 88.1198i | 0.0604689 | − | 0.118673i | ||||
\(83\) | 1045.75i | 1.38296i | 0.722397 | + | 0.691479i | \(0.243040\pi\) | ||||
−0.722397 | + | 0.691479i | \(0.756960\pi\) | |||||||
\(84\) | −120.171 | − | 53.5071i | −0.156091 | − | 0.0695012i | ||||
\(85\) | −45.3282 | − | 78.5107i | −0.0578415 | − | 0.100184i | ||||
\(86\) | −442.593 | + | 868.609i | −0.554953 | + | 1.08912i | ||||
\(87\) | − | 997.943i | − | 1.22978i | ||||||
\(88\) | −338.338 | + | 53.5741i | −0.409852 | + | 0.0648980i | ||||
\(89\) | −1197.64 | + | 691.455i | −1.42640 | + | 0.823530i | −0.996834 | − | 0.0795084i | \(-0.974665\pi\) |
−0.429561 | + | 0.903038i | \(0.641332\pi\) | |||||||
\(90\) | 4.93702 | + | 94.2271i | 0.00578231 | + | 0.110360i | ||||
\(91\) | 39.4314 | + | 68.2972i | 0.0454235 | + | 0.0786757i | ||||
\(92\) | 426.482 | − | 309.841i | 0.483302 | − | 0.351121i | ||||
\(93\) | −267.072 | + | 462.582i | −0.297785 | + | 0.515779i | ||||
\(94\) | 210.211 | + | 323.705i | 0.230655 | + | 0.355188i | ||||
\(95\) | 120.155 | − | 291.787i | 0.129764 | − | 0.315123i | ||||
\(96\) | −1045.52 | − | 280.218i | −1.11154 | − | 0.297913i | ||||
\(97\) | 729.386 | + | 421.111i | 0.763484 | + | 0.440798i | 0.830545 | − | 0.556951i | \(-0.188029\pi\) |
−0.0670613 | + | 0.997749i | \(0.521362\pi\) | |||||||
\(98\) | 49.6422 | + | 947.463i | 0.0511696 | + | 0.976614i | ||||
\(99\) | −114.789 | + | 66.2736i | −0.116533 | + | 0.0672803i | ||||
\(100\) | −519.501 | − | 715.070i | −0.519501 | − | 0.715070i | ||||
\(101\) | 400.538 | + | 693.753i | 0.394605 | + | 0.683475i | 0.993051 | − | 0.117688i | \(-0.0375483\pi\) |
−0.598446 | + | 0.801163i | \(0.704215\pi\) | |||||||
\(102\) | 337.490 | − | 219.162i | 0.327613 | − | 0.212748i | ||||
\(103\) | 1482.54 | 1.41824 | 0.709121 | − | 0.705087i | \(-0.249092\pi\) | ||||
0.709121 | + | 0.705087i | \(0.249092\pi\) | |||||||
\(104\) | 408.363 | + | 504.326i | 0.385032 | + | 0.475512i | ||||
\(105\) | −54.2578 | + | 31.3257i | −0.0504287 | + | 0.0291150i | ||||
\(106\) | −399.698 | − | 615.498i | −0.366246 | − | 0.563986i | ||||
\(107\) | 1297.07 | 1.17189 | 0.585946 | − | 0.810350i | \(-0.300723\pi\) | ||||
0.585946 | + | 0.810350i | \(0.300723\pi\) | |||||||
\(108\) | 867.981 | − | 91.2059i | 0.773347 | − | 0.0812620i | ||||
\(109\) | 824.748 | + | 476.169i | 0.724739 | + | 0.418428i | 0.816494 | − | 0.577353i | \(-0.195914\pi\) |
−0.0917554 | + | 0.995782i | \(0.529248\pi\) | |||||||
\(110\) | −74.0703 | + | 145.367i | −0.0642030 | + | 0.126001i | ||||
\(111\) | −1077.46 | − | 622.070i | −0.921330 | − | 0.531930i | ||||
\(112\) | −36.5819 | − | 172.148i | −0.0308631 | − | 0.145236i | ||||
\(113\) | 1956.01i | 1.62837i | 0.580605 | + | 0.814185i | \(0.302816\pi\) | ||||
−0.580605 | + | 0.814185i | \(0.697184\pi\) | |||||||
\(114\) | 1321.32 | + | 464.846i | 1.08555 | + | 0.381902i | ||||
\(115\) | − | 251.069i | − | 0.203585i | ||||||
\(116\) | 1080.17 | − | 784.744i | 0.864577 | − | 0.628118i | ||||
\(117\) | 217.455 | + | 125.547i | 0.171826 | + | 0.0992040i | ||||
\(118\) | 133.374 | + | 67.9594i | 0.104051 | + | 0.0530184i | ||||
\(119\) | 56.6621 | + | 32.7139i | 0.0436488 | + | 0.0252006i | ||||
\(120\) | −400.655 | + | 324.418i | −0.304788 | + | 0.246793i | ||||
\(121\) | 1101.81 | 0.827810 | ||||||||
\(122\) | 2014.84 | − | 1308.42i | 1.49521 | − | 0.970972i | ||||
\(123\) | 181.072 | − | 104.542i | 0.132738 | − | 0.0766362i | ||||
\(124\) | −710.710 | + | 74.6802i | −0.514707 | + | 0.0540845i | ||||
\(125\) | −897.236 | −0.642010 | ||||||||
\(126\) | −37.0881 | − | 57.1123i | −0.0262228 | − | 0.0403807i | ||||
\(127\) | −330.264 | − | 572.035i | −0.230758 | − | 0.399684i | 0.727274 | − | 0.686348i | \(-0.240787\pi\) |
−0.958031 | + | 0.286664i | \(0.907454\pi\) | |||||||
\(128\) | −518.851 | − | 1352.02i | −0.358284 | − | 0.933613i | ||||
\(129\) | −1784.86 | + | 1030.49i | −1.21820 | + | 0.703328i | ||||
\(130\) | 308.644 | − | 16.1714i | 0.208230 | − | 0.0109102i | ||||
\(131\) | −790.314 | − | 456.288i | −0.527099 | − | 0.304321i | 0.212735 | − | 0.977110i | \(-0.431763\pi\) |
−0.739835 | + | 0.672789i | \(0.765096\pi\) | |||||||
\(132\) | −661.575 | − | 294.573i | −0.436233 | − | 0.194237i | ||||
\(133\) | 30.1938 | + | 225.731i | 0.0196852 | + | 0.147168i | ||||
\(134\) | −1135.54 | + | 737.406i | −0.732056 | + | 0.475389i | ||||
\(135\) | 207.837 | − | 359.984i | 0.132502 | − | 0.229500i | ||||
\(136\) | 502.609 | + | 192.956i | 0.316900 | + | 0.121660i | ||||
\(137\) | −1098.42 | − | 1902.51i | −0.684993 | − | 1.18644i | −0.973439 | − | 0.228946i | \(-0.926472\pi\) |
0.288446 | − | 0.957496i | \(-0.406861\pi\) | |||||||
\(138\) | 1112.92 | − | 58.3116i | 0.686510 | − | 0.0359696i | ||||
\(139\) | −2444.82 | + | 1411.52i | −1.49185 | + | 0.861319i | −0.999956 | − | 0.00933765i | \(-0.997028\pi\) |
−0.491892 | + | 0.870656i | \(0.663694\pi\) | |||||||
\(140\) | −76.5730 | − | 34.0948i | −0.0462257 | − | 0.0205824i | ||||
\(141\) | 815.982i | 0.487362i | ||||||||
\(142\) | −41.1417 | − | 20.9634i | −0.0243137 | − | 0.0123888i | ||||
\(143\) | 217.082 | + | 375.997i | 0.126946 | + | 0.219877i | ||||
\(144\) | −374.924 | − | 416.439i | −0.216970 | − | 0.240995i | ||||
\(145\) | − | 635.892i | − | 0.364193i | ||||||
\(146\) | 1674.27 | + | 853.108i | 0.949064 | + | 0.483587i | ||||
\(147\) | −1002.89 | + | 1737.06i | −0.562701 | + | 0.974626i | ||||
\(148\) | −173.947 | − | 1655.40i | −0.0966104 | − | 0.919413i | ||||
\(149\) | −587.807 | + | 1018.11i | −0.323188 | + | 0.559779i | −0.981144 | − | 0.193278i | \(-0.938088\pi\) |
0.657956 | + | 0.753057i | \(0.271421\pi\) | |||||||
\(150\) | −97.7694 | − | 1866.01i | −0.0532189 | − | 1.01573i | ||||
\(151\) | −3239.21 | −1.74572 | −0.872859 | − | 0.487973i | \(-0.837736\pi\) | ||||
−0.872859 | + | 0.487973i | \(0.837736\pi\) | |||||||
\(152\) | 535.891 | + | 1795.73i | 0.285964 | + | 0.958240i | ||||
\(153\) | 208.318 | 0.110075 | ||||||||
\(154\) | −6.16090 | − | 117.586i | −0.00322376 | − | 0.0615281i | ||||
\(155\) | −170.179 | + | 294.758i | −0.0881876 | + | 0.152745i | ||||
\(156\) | 143.367 | + | 1364.38i | 0.0735805 | + | 0.700245i | ||||
\(157\) | 1652.44 | − | 2862.11i | 0.839995 | − | 1.45491i | −0.0499023 | − | 0.998754i | \(-0.515891\pi\) |
0.889898 | − | 0.456160i | \(-0.150776\pi\) | |||||||
\(158\) | −155.224 | − | 79.0928i | −0.0781577 | − | 0.0398246i | ||||
\(159\) | − | 1551.52i | − | 0.773860i | ||||||
\(160\) | −666.208 | − | 178.556i | −0.329177 | − | 0.0882254i | ||||
\(161\) | 90.5997 | + | 156.923i | 0.0443494 | + | 0.0768155i | ||||
\(162\) | 2239.74 | + | 1141.24i | 1.08624 | + | 0.553483i | ||||
\(163\) | 1552.61i | 0.746074i | 0.927817 | + | 0.373037i | \(0.121684\pi\) | ||||
−0.927817 | + | 0.373037i | \(0.878316\pi\) | |||||||
\(164\) | 255.544 | + | 113.783i | 0.121675 | + | 0.0541768i | ||||
\(165\) | −298.705 | + | 172.458i | −0.140934 | + | 0.0813686i | ||||
\(166\) | −2953.76 | + | 154.762i | −1.38106 | + | 0.0723607i | ||||
\(167\) | −589.142 | − | 1020.42i | −0.272989 | − | 0.472831i | 0.696637 | − | 0.717424i | \(-0.254679\pi\) |
−0.969626 | + | 0.244593i | \(0.921346\pi\) | |||||||
\(168\) | 133.349 | − | 347.347i | 0.0612388 | − | 0.159514i | ||||
\(169\) | −687.264 | + | 1190.38i | −0.312820 | + | 0.541819i | ||||
\(170\) | 215.049 | − | 139.651i | 0.0970208 | − | 0.0630043i | ||||
\(171\) | 442.614 | + | 574.359i | 0.197939 | + | 0.256856i | ||||
\(172\) | −2518.93 | − | 1121.58i | −1.11667 | − | 0.497207i | ||||
\(173\) | −2037.00 | − | 1176.06i | −0.895204 | − | 0.516846i | −0.0195628 | − | 0.999809i | \(-0.506227\pi\) |
−0.875641 | + | 0.482962i | \(0.839561\pi\) | |||||||
\(174\) | 2818.74 | − | 147.688i | 1.22809 | − | 0.0643459i | ||||
\(175\) | 263.109 | − | 151.906i | 0.113652 | − | 0.0656172i | ||||
\(176\) | −201.394 | − | 947.725i | −0.0862538 | − | 0.405895i | ||||
\(177\) | 158.230 | + | 274.062i | 0.0671936 | + | 0.116383i | ||||
\(178\) | −2130.29 | − | 3280.46i | −0.897035 | − | 1.38135i | ||||
\(179\) | 1491.91 | 0.622964 | 0.311482 | − | 0.950252i | \(-0.399175\pi\) | ||||
0.311482 | + | 0.950252i | \(0.399175\pi\) | |||||||
\(180\) | −265.419 | + | 27.8897i | −0.109906 | + | 0.0115488i | ||||
\(181\) | 2564.50 | − | 1480.62i | 1.05314 | − | 0.608030i | 0.129612 | − | 0.991565i | \(-0.458627\pi\) |
0.923526 | + | 0.383535i | \(0.125294\pi\) | |||||||
\(182\) | −187.073 | + | 121.484i | −0.0761913 | + | 0.0494778i | ||||
\(183\) | 5078.93 | 2.05161 | ||||||||
\(184\) | 938.277 | + | 1158.77i | 0.375928 | + | 0.464269i | ||||
\(185\) | −686.557 | − | 396.384i | −0.272847 | − | 0.157528i | ||||
\(186\) | −1346.11 | − | 685.899i | −0.530654 | − | 0.270390i | ||||
\(187\) | 311.942 | + | 180.100i | 0.121986 | + | 0.0704289i | ||||
\(188\) | −883.213 | + | 641.657i | −0.342633 | + | 0.248924i | ||||
\(189\) | 299.997i | 0.115458i | ||||||||
\(190\) | 841.949 | + | 296.201i | 0.321481 | + | 0.113098i | ||||
\(191\) | − | 4369.32i | − | 1.65525i | −0.561280 | − | 0.827626i | \(-0.689691\pi\) | ||
0.561280 | − | 0.827626i | \(-0.310309\pi\) | |||||||
\(192\) | 636.762 | − | 2994.60i | 0.239346 | − | 1.12561i | ||||
\(193\) | 273.691 | + | 158.016i | 0.102076 | + | 0.0589338i | 0.550169 | − | 0.835053i | \(-0.314563\pi\) |
−0.448093 | + | 0.893987i | \(0.647897\pi\) | |||||||
\(194\) | −1081.51 | + | 2122.51i | −0.400246 | + | 0.785502i | ||||
\(195\) | 565.862 | + | 326.700i | 0.207806 | + | 0.119977i | ||||
\(196\) | −2668.81 | + | 280.434i | −0.972599 | + | 0.102199i | ||||
\(197\) | 4041.91 | 1.46180 | 0.730898 | − | 0.682487i | \(-0.239101\pi\) | ||||
0.730898 | + | 0.682487i | \(0.239101\pi\) | |||||||
\(198\) | −204.181 | − | 314.421i | −0.0732855 | − | 0.112853i | ||||
\(199\) | 3883.42 | − | 2242.10i | 1.38336 | − | 0.798683i | 0.390804 | − | 0.920474i | \(-0.372197\pi\) |
0.992556 | + | 0.121791i | \(0.0388636\pi\) | |||||||
\(200\) | 1942.87 | − | 1573.18i | 0.686909 | − | 0.556204i | ||||
\(201\) | −2862.42 | −1.00447 | ||||||||
\(202\) | −1900.26 | + | 1234.01i | −0.661892 | + | 0.429826i | ||||
\(203\) | 229.465 | + | 397.445i | 0.0793364 | + | 0.137415i | ||||
\(204\) | 668.982 | + | 920.824i | 0.229599 | + | 0.316032i | ||||
\(205\) | 115.380 | − | 66.6145i | 0.0393096 | − | 0.0226954i | ||||
\(206\) | 219.404 | + | 4187.51i | 0.0742069 | + | 1.41630i | ||||
\(207\) | 499.635 | + | 288.465i | 0.167764 | + | 0.0968584i | ||||
\(208\) | −1364.06 | + | 1228.08i | −0.454715 | + | 0.409385i | ||||
\(209\) | 166.226 | + | 1242.72i | 0.0550149 | + | 0.411295i | ||||
\(210\) | −96.5109 | − | 148.618i | −0.0317137 | − | 0.0488362i | ||||
\(211\) | −720.358 | + | 1247.70i | −0.235031 | + | 0.407085i | −0.959282 | − | 0.282451i | \(-0.908852\pi\) |
0.724251 | + | 0.689536i | \(0.242186\pi\) | |||||||
\(212\) | 1679.36 | − | 1220.06i | 0.544050 | − | 0.395254i | ||||
\(213\) | −48.8091 | − | 84.5398i | −0.0157011 | − | 0.0271952i | ||||
\(214\) | 191.956 | + | 3663.64i | 0.0613171 | + | 1.17029i | ||||
\(215\) | −1137.31 | + | 656.628i | −0.360764 | + | 0.208287i | ||||
\(216\) | 386.070 | + | 2438.16i | 0.121615 | + | 0.768036i | ||||
\(217\) | − | 245.640i | − | 0.0768438i | ||||||
\(218\) | −1222.91 | + | 2400.01i | −0.379934 | + | 0.745640i | ||||
\(219\) | 1986.29 | + | 3440.35i | 0.612881 | + | 1.06154i | ||||
\(220\) | −421.557 | − | 187.702i | −0.129188 | − | 0.0575222i | ||||
\(221\) | − | 682.355i | − | 0.207693i | ||||||
\(222\) | 1597.61 | − | 3135.39i | 0.482994 | − | 0.947900i | ||||
\(223\) | −1613.13 | + | 2794.03i | −0.484410 | + | 0.839022i | −0.999840 | − | 0.0179097i | \(-0.994299\pi\) |
0.515430 | + | 0.856932i | \(0.327632\pi\) | |||||||
\(224\) | 480.826 | − | 128.804i | 0.143422 | − | 0.0384200i | ||||
\(225\) | 483.660 | − | 837.724i | 0.143307 | − | 0.248215i | ||||
\(226\) | −5524.85 | + | 289.474i | −1.62614 | + | 0.0852015i | ||||
\(227\) | −2678.71 | −0.783227 | −0.391614 | − | 0.920130i | \(-0.628083\pi\) | ||||
−0.391614 | + | 0.920130i | \(0.628083\pi\) | |||||||
\(228\) | −1117.44 | + | 3800.94i | −0.324579 | + | 1.10405i | ||||
\(229\) | 2791.09 | 0.805418 | 0.402709 | − | 0.915328i | \(-0.368069\pi\) | ||||
0.402709 | + | 0.915328i | \(0.368069\pi\) | |||||||
\(230\) | 709.158 | − | 37.1563i | 0.203306 | − | 0.0106522i | ||||
\(231\) | 124.465 | − | 215.579i | 0.0354510 | − | 0.0614029i | ||||
\(232\) | 2376.41 | + | 2934.85i | 0.672495 | + | 0.830527i | ||||
\(233\) | 21.1659 | − | 36.6605i | 0.00595119 | − | 0.0103078i | −0.863034 | − | 0.505145i | \(-0.831439\pi\) |
0.868986 | + | 0.494837i | \(0.164772\pi\) | |||||||
\(234\) | −322.434 | + | 632.792i | −0.0900776 | + | 0.176782i | ||||
\(235\) | 519.946i | 0.144330i | ||||||||
\(236\) | −172.217 | + | 386.778i | −0.0475014 | + | 0.106683i | ||||
\(237\) | −184.152 | − | 318.960i | −0.0504723 | − | 0.0874206i | ||||
\(238\) | −84.0165 | + | 164.886i | −0.0228823 | + | 0.0449076i | ||||
\(239\) | − | 2258.29i | − | 0.611200i | −0.952160 | − | 0.305600i | \(-0.901143\pi\) | ||
0.952160 | − | 0.305600i | \(-0.0988569\pi\) | |||||||
\(240\) | −975.631 | − | 1083.66i | −0.262403 | − | 0.291458i | ||||
\(241\) | 1695.77 | − | 979.056i | 0.453255 | − | 0.261687i | −0.255949 | − | 0.966690i | \(-0.582388\pi\) |
0.709204 | + | 0.705003i | \(0.249055\pi\) | |||||||
\(242\) | 163.060 | + | 3112.13i | 0.0433136 | + | 0.826676i | ||||
\(243\) | 1184.36 | + | 2051.38i | 0.312662 | + | 0.541547i | ||||
\(244\) | 3993.88 | + | 5497.40i | 1.04788 | + | 1.44236i | ||||
\(245\) | −639.044 | + | 1106.86i | −0.166641 | + | 0.288631i | ||||
\(246\) | 322.082 | + | 495.977i | 0.0834765 | + | 0.128546i | ||||
\(247\) | 1881.33 | − | 1449.80i | 0.484641 | − | 0.373476i | ||||
\(248\) | −316.118 | − | 1996.39i | −0.0809415 | − | 0.511172i | ||||
\(249\) | −5415.36 | − | 3126.56i | −1.37825 | − | 0.795734i | ||||
\(250\) | −132.784 | − | 2534.29i | −0.0335920 | − | 0.641130i | ||||
\(251\) | −4714.35 | + | 2721.83i | −1.18553 | + | 0.684464i | −0.957286 | − | 0.289141i | \(-0.906630\pi\) |
−0.228239 | + | 0.973605i | \(0.573297\pi\) | |||||||
\(252\) | 155.828 | − | 113.210i | 0.0389533 | − | 0.0282997i | ||||
\(253\) | 498.779 | + | 863.910i | 0.123945 | + | 0.214678i | ||||
\(254\) | 1566.87 | − | 1017.51i | 0.387062 | − | 0.251354i | ||||
\(255\) | 542.087 | 0.133125 | ||||||||
\(256\) | 3742.05 | − | 1665.61i | 0.913587 | − | 0.406643i | ||||
\(257\) | 3229.14 | − | 1864.35i | 0.783768 | − | 0.452509i | −0.0539961 | − | 0.998541i | \(-0.517196\pi\) |
0.837764 | + | 0.546033i | \(0.183863\pi\) | |||||||
\(258\) | −3174.81 | − | 4888.91i | −0.766105 | − | 1.17973i | ||||
\(259\) | 572.150 | 0.137265 | ||||||||
\(260\) | 91.3539 | + | 869.389i | 0.0217905 | + | 0.207374i | ||||
\(261\) | 1265.44 | + | 730.605i | 0.300111 | + | 0.173269i | ||||
\(262\) | 1171.85 | − | 2299.81i | 0.276325 | − | 0.542301i | ||||
\(263\) | −732.809 | − | 423.087i | −0.171813 | − | 0.0991965i | 0.411627 | − | 0.911352i | \(-0.364961\pi\) |
−0.583441 | + | 0.812156i | \(0.698294\pi\) | |||||||
\(264\) | 734.128 | − | 1912.25i | 0.171146 | − | 0.445799i | ||||
\(265\) | − | 988.633i | − | 0.229175i | ||||||
\(266\) | −633.121 | + | 118.691i | −0.145937 | + | 0.0273586i | ||||
\(267\) | − | 8269.23i | − | 1.89539i | ||||||
\(268\) | −2250.89 | − | 3098.26i | −0.513042 | − | 0.706180i | ||||
\(269\) | −7167.68 | − | 4138.26i | −1.62461 | − | 0.937971i | −0.985663 | − | 0.168723i | \(-0.946036\pi\) |
−0.638951 | − | 0.769248i | \(-0.720631\pi\) | |||||||
\(270\) | 1047.55 | + | 533.772i | 0.236119 | + | 0.120312i | ||||
\(271\) | −167.303 | − | 96.5926i | −0.0375017 | − | 0.0216516i | 0.481132 | − | 0.876648i | \(-0.340226\pi\) |
−0.518634 | + | 0.854997i | \(0.673559\pi\) | |||||||
\(272\) | −470.631 | + | 1448.20i | −0.104913 | + | 0.322831i | ||||
\(273\) | −471.567 | −0.104544 | ||||||||
\(274\) | 5211.19 | − | 3384.09i | 1.14898 | − | 0.746133i | ||||
\(275\) | 1448.49 | − | 836.288i | 0.317627 | − | 0.183382i | ||||
\(276\) | 329.408 | + | 3134.88i | 0.0718408 | + | 0.683688i | ||||
\(277\) | −120.448 | −0.0261264 | −0.0130632 | − | 0.999915i | \(-0.504158\pi\) | ||||
−0.0130632 | + | 0.999915i | \(0.504158\pi\) | |||||||
\(278\) | −4348.72 | − | 6696.63i | −0.938197 | − | 1.44474i | ||||
\(279\) | −391.052 | − | 677.322i | −0.0839128 | − | 0.145341i | ||||
\(280\) | 84.9704 | − | 221.330i | 0.0181356 | − | 0.0472393i | ||||
\(281\) | 740.923 | − | 427.772i | 0.157295 | − | 0.0908140i | −0.419287 | − | 0.907854i | \(-0.637720\pi\) |
0.576581 | + | 0.817040i | \(0.304386\pi\) | |||||||
\(282\) | −2304.79 | + | 120.759i | −0.486695 | + | 0.0255003i | ||||
\(283\) | 4122.48 | + | 2380.12i | 0.865923 | + | 0.499941i | 0.865991 | − | 0.500059i | \(-0.166688\pi\) |
−6.85577e−5 | 1.00000i | \(0.500022\pi\) | ||||||||
\(284\) | 53.1237 | − | 119.309i | 0.0110997 | − | 0.0249286i | ||||
\(285\) | 1151.77 | + | 1494.60i | 0.239386 | + | 0.310640i | ||||
\(286\) | −1029.90 | + | 668.804i | −0.212934 | + | 0.138277i | ||||
\(287\) | −48.0764 | + | 83.2708i | −0.00988802 | + | 0.0171266i | ||||
\(288\) | 1120.77 | − | 1120.62i | 0.229312 | − | 0.229283i | ||||
\(289\) | 2173.45 | + | 3764.52i | 0.442387 | + | 0.766236i | ||||
\(290\) | 1796.11 | − | 94.1070i | 0.363694 | − | 0.0190557i | ||||
\(291\) | −4361.43 | + | 2518.07i | −0.878596 | + | 0.507257i | ||||
\(292\) | −2161.87 | + | 4855.31i | −0.433267 | + | 0.973066i | ||||
\(293\) | 645.643i | 0.128733i | 0.997926 | + | 0.0643666i | \(0.0205027\pi\) | ||||
−0.997926 | + | 0.0643666i | \(0.979497\pi\) | |||||||
\(294\) | −5054.83 | − | 2575.65i | −1.00273 | − | 0.510935i | ||||
\(295\) | 100.824 | + | 174.633i | 0.0198990 | + | 0.0344661i | ||||
\(296\) | 4650.03 | − | 736.308i | 0.913099 | − | 0.144585i | ||||
\(297\) | 1651.57i | 0.322673i | ||||||||
\(298\) | −2962.70 | − | 1509.62i | −0.575922 | − | 0.293456i | ||||
\(299\) | 944.877 | − | 1636.57i | 0.182755 | − | 0.316540i | ||||
\(300\) | 5256.17 | − | 552.309i | 1.01155 | − | 0.106292i | ||||
\(301\) | 473.896 | − | 820.812i | 0.0907473 | − | 0.157179i | ||||
\(302\) | −479.378 | − | 9149.32i | −0.0913414 | − | 1.74333i | ||||
\(303\) | −4790.11 | −0.908199 | ||||||||
\(304\) | −4992.81 | + | 1779.41i | −0.941965 | + | 0.335710i | ||||
\(305\) | 3236.31 | 0.607575 | ||||||||
\(306\) | 30.8295 | + | 588.406i | 0.00575949 | + | 0.109925i | ||||
\(307\) | −2990.93 | + | 5180.44i | −0.556031 | + | 0.963074i | 0.441792 | + | 0.897118i | \(0.354343\pi\) |
−0.997823 | + | 0.0659559i | \(0.978990\pi\) | |||||||
\(308\) | 331.215 | − | 34.8036i | 0.0612752 | − | 0.00643869i | ||||
\(309\) | −4432.48 | + | 7677.29i | −0.816036 | + | 1.41342i | ||||
\(310\) | −857.745 | − | 437.057i | −0.157150 | − | 0.0800747i | ||||
\(311\) | − | 3531.15i | − | 0.643836i | −0.946768 | − | 0.321918i | \(-0.895672\pi\) | ||
0.946768 | − | 0.321918i | \(-0.104328\pi\) | |||||||
\(312\) | −3832.56 | + | 606.867i | −0.695436 | + | 0.110119i | ||||
\(313\) | 797.224 | + | 1380.83i | 0.143967 | + | 0.249359i | 0.928987 | − | 0.370112i | \(-0.120681\pi\) |
−0.785020 | + | 0.619470i | \(0.787347\pi\) | |||||||
\(314\) | 8328.74 | + | 4243.84i | 1.49687 | + | 0.762719i | ||||
\(315\) | − | 91.7356i | − | 0.0164086i | ||||||
\(316\) | 200.430 | − | 450.142i | 0.0356806 | − | 0.0801344i | ||||
\(317\) | 675.595 | − | 390.055i | 0.119701 | − | 0.0691093i | −0.438954 | − | 0.898509i | \(-0.644651\pi\) |
0.558655 | + | 0.829400i | \(0.311318\pi\) | |||||||
\(318\) | 4382.36 | − | 229.613i | 0.772800 | − | 0.0404908i | ||||
\(319\) | 1263.28 | + | 2188.06i | 0.221724 | + | 0.384037i | ||||
\(320\) | 405.746 | − | 1908.16i | 0.0708809 | − | 0.333342i | ||||
\(321\) | −3877.97 | + | 6716.84i | −0.674290 | + | 1.16790i | ||||
\(322\) | −429.830 | + | 279.127i | −0.0743897 | + | 0.0483079i | ||||
\(323\) | 750.312 | − | 1822.08i | 0.129252 | − | 0.313880i | ||||
\(324\) | −2892.03 | + | 6495.15i | −0.495890 | + | 1.11371i | ||||
\(325\) | −2744.00 | − | 1584.25i | −0.468337 | − | 0.270395i | ||||
\(326\) | −4385.44 | + | 229.775i | −0.745052 | + | 0.0390369i | ||||
\(327\) | −4931.65 | + | 2847.29i | −0.834009 | + | 0.481515i | ||||
\(328\) | −283.569 | + | 738.637i | −0.0477361 | + | 0.124343i | ||||
\(329\) | −187.625 | − | 324.977i | −0.0314411 | − | 0.0544576i | ||||
\(330\) | −531.322 | − | 818.187i | −0.0886312 | − | 0.136484i | ||||
\(331\) | 9635.61 | 1.60006 | 0.800032 | − | 0.599958i | \(-0.204816\pi\) | ||||
0.800032 | + | 0.599958i | \(0.204816\pi\) | |||||||
\(332\) | −874.268 | − | 8320.15i | −0.144523 | − | 1.37538i | ||||
\(333\) | 1577.63 | − | 910.847i | 0.259621 | − | 0.149892i | ||||
\(334\) | 2795.05 | − | 1815.08i | 0.457900 | − | 0.297355i | ||||
\(335\) | −1823.94 | −0.297470 | ||||||||
\(336\) | 1000.83 | + | 325.247i | 0.162500 | + | 0.0528086i | ||||
\(337\) | 1345.70 | + | 776.938i | 0.217522 | + | 0.125586i | 0.604802 | − | 0.796376i | \(-0.293252\pi\) |
−0.387281 | + | 0.921962i | \(0.626586\pi\) | |||||||
\(338\) | −3463.99 | − | 1765.05i | −0.557445 | − | 0.284041i | ||||
\(339\) | −10129.1 | − | 5848.06i | −1.62283 | − | 0.936941i | ||||
\(340\) | 426.277 | + | 586.751i | 0.0679944 | + | 0.0935913i | ||||
\(341\) | − | 1352.32i | − | 0.214758i | ||||||
\(342\) | −1556.80 | + | 1335.19i | −0.246147 | + | 0.211107i | ||||
\(343\) | − | 1865.62i | − | 0.293684i | ||||||
\(344\) | 2795.18 | − | 7280.84i | 0.438098 | − | 1.14115i | ||||
\(345\) | 1300.15 | + | 750.644i | 0.202893 | + | 0.117140i | ||||
\(346\) | 3020.39 | − | 5927.66i | 0.469298 | − | 0.921021i | ||||
\(347\) | −3460.70 | − | 1998.04i | −0.535390 | − | 0.309107i | 0.207819 | − | 0.978167i | \(-0.433364\pi\) |
−0.743208 | + | 0.669060i | \(0.766697\pi\) | |||||||
\(348\) | 834.304 | + | 7939.83i | 0.128515 | + | 1.22304i | ||||
\(349\) | −12255.5 | −1.87972 | −0.939860 | − | 0.341561i | \(-0.889044\pi\) | ||||
−0.939860 | + | 0.341561i | \(0.889044\pi\) | |||||||
\(350\) | 468.004 | + | 720.684i | 0.0714740 | + | 0.110063i | ||||
\(351\) | 2709.54 | − | 1564.35i | 0.412036 | − | 0.237889i | ||||
\(352\) | 2647.09 | − | 709.105i | 0.400826 | − | 0.107373i | ||||
\(353\) | 2540.72 | 0.383084 | 0.191542 | − | 0.981484i | \(-0.438651\pi\) | ||||
0.191542 | + | 0.981484i | \(0.438651\pi\) | |||||||
\(354\) | −750.685 | + | 487.487i | −0.112707 | + | 0.0731910i | ||||
\(355\) | −31.1013 | − | 53.8690i | −0.00464981 | − | 0.00805371i | ||||
\(356\) | 8950.55 | − | 6502.61i | 1.33252 | − | 0.968083i | ||||
\(357\) | −338.816 | + | 195.615i | −0.0502298 | + | 0.0290002i | ||||
\(358\) | 220.791 | + | 4213.97i | 0.0325954 | + | 0.622110i | ||||
\(359\) | 5373.03 | + | 3102.12i | 0.789910 | + | 0.456055i | 0.839931 | − | 0.542694i | \(-0.182596\pi\) |
−0.0500211 | + | 0.998748i | \(0.515929\pi\) | |||||||
\(360\) | −118.056 | − | 745.562i | −0.0172836 | − | 0.109152i | ||||
\(361\) | 6617.87 | − | 1802.67i | 0.964845 | − | 0.262818i | ||||
\(362\) | 4561.61 | + | 7024.45i | 0.662300 | + | 1.01988i | ||||
\(363\) | −3294.20 | + | 5705.72i | −0.476310 | + | 0.824993i | ||||
\(364\) | −370.822 | − | 510.420i | −0.0533966 | − | 0.0734981i | ||||
\(365\) | 1265.67 | + | 2192.20i | 0.181502 | + | 0.314370i | ||||
\(366\) | 751.643 | + | 14345.7i | 0.107347 | + | 2.04880i | ||||
\(367\) | −1966.29 | + | 1135.24i | −0.279671 | + | 0.161468i | −0.633275 | − | 0.773927i | \(-0.718290\pi\) |
0.353603 | + | 0.935395i | \(0.384956\pi\) | |||||||
\(368\) | −3134.14 | + | 2821.70i | −0.443963 | + | 0.399705i | ||||
\(369\) | 306.146i | 0.0431905i | ||||||||
\(370\) | 1018.00 | − | 1997.88i | 0.143036 | − | 0.280716i | ||||
\(371\) | 356.754 | + | 617.916i | 0.0499238 | + | 0.0864706i | ||||
\(372\) | 1738.15 | − | 3903.67i | 0.242254 | − | 0.544075i | ||||
\(373\) | 14152.4i | 1.96456i | 0.187409 | + | 0.982282i | \(0.439991\pi\) | ||||
−0.187409 | + | 0.982282i | \(0.560009\pi\) | |||||||
\(374\) | −462.536 | + | 907.750i | −0.0639497 | + | 0.125504i | ||||
\(375\) | 2682.55 | − | 4646.31i | 0.369403 | − | 0.639825i | ||||
\(376\) | −1943.10 | − | 2399.72i | −0.266510 | − | 0.329139i | ||||
\(377\) | 2393.12 | − | 4145.01i | 0.326929 | − | 0.566257i | ||||
\(378\) | −847.356 | + | 44.3972i | −0.115300 | + | 0.00604112i | ||||
\(379\) | 5749.56 | 0.779249 | 0.389624 | − | 0.920974i | \(-0.372605\pi\) | ||||
0.389624 | + | 0.920974i | \(0.372605\pi\) | |||||||
\(380\) | −712.033 | + | 2421.96i | −0.0961224 | + | 0.326958i | ||||
\(381\) | 3949.69 | 0.531099 | ||||||||
\(382\) | 12341.4 | − | 646.626i | 1.65299 | − | 0.0866080i | ||||
\(383\) | −4565.82 | + | 7908.22i | −0.609144 | + | 1.05507i | 0.382237 | + | 0.924064i | \(0.375154\pi\) |
−0.991382 | + | 0.131005i | \(0.958180\pi\) | |||||||
\(384\) | 8552.63 | + | 1355.39i | 1.13659 | + | 0.180122i | ||||
\(385\) | 79.3092 | − | 137.368i | 0.0104986 | − | 0.0181841i | ||||
\(386\) | −405.819 | + | 796.440i | −0.0535121 | + | 0.105020i | ||||
\(387\) | − | 3017.72i | − | 0.396381i | ||||||
\(388\) | −6155.20 | − | 2740.66i | −0.805368 | − | 0.358598i | ||||
\(389\) | −1323.99 | − | 2293.22i | −0.172568 | − | 0.298897i | 0.766749 | − | 0.641947i | \(-0.221873\pi\) |
−0.939317 | + | 0.343050i | \(0.888540\pi\) | |||||||
\(390\) | −839.039 | + | 1646.66i | −0.108940 | + | 0.213799i | ||||
\(391\) | − | 1567.82i | − | 0.202782i | ||||||
\(392\) | −1187.06 | − | 7496.70i | −0.152949 | − | 0.965920i | ||||
\(393\) | 4725.75 | − | 2728.41i | 0.606571 | − | 0.350204i | ||||
\(394\) | 598.170 | + | 11416.6i | 0.0764858 | + | 1.45979i | ||||
\(395\) | −117.342 | − | 203.242i | −0.0149471 | − | 0.0258891i | ||||
\(396\) | 857.880 | − | 623.253i | 0.108864 | − | 0.0790900i | ||||
\(397\) | 1107.92 | − | 1918.97i | 0.140062 | − | 0.242595i | −0.787458 | − | 0.616369i | \(-0.788603\pi\) |
0.927520 | + | 0.373774i | \(0.121936\pi\) | |||||||
\(398\) | 6907.64 | + | 10637.1i | 0.869971 | + | 1.33968i | ||||
\(399\) | −1259.22 | − | 518.531i | −0.157994 | − | 0.0650602i | ||||
\(400\) | 4731.07 | + | 5254.92i | 0.591383 | + | 0.656865i | ||||
\(401\) | 120.133 | + | 69.3586i | 0.0149604 | + | 0.00863742i | 0.507462 | − | 0.861674i | \(-0.330584\pi\) |
−0.492501 | + | 0.870312i | \(0.663917\pi\) | |||||||
\(402\) | −423.615 | − | 8085.04i | −0.0525572 | − | 1.00310i | ||||
\(403\) | −2218.59 | + | 1280.91i | −0.274233 | + | 0.158329i | ||||
\(404\) | −3766.76 | − | 5184.77i | −0.463869 | − | 0.638495i | ||||
\(405\) | 1693.14 | + | 2932.60i | 0.207735 | + | 0.359808i | ||||
\(406\) | −1088.65 | + | 706.955i | −0.133075 | + | 0.0864177i | ||||
\(407\) | 3149.86 | 0.383618 | ||||||||
\(408\) | −2501.91 | + | 2025.85i | −0.303586 | + | 0.245820i | ||||
\(409\) | −2742.74 | + | 1583.52i | −0.331588 | + | 0.191443i | −0.656546 | − | 0.754286i | \(-0.727983\pi\) |
0.324958 | + | 0.945729i | \(0.394650\pi\) | |||||||
\(410\) | 205.231 | + | 316.038i | 0.0247211 | + | 0.0380683i | ||||
\(411\) | 13136.1 | 1.57654 | ||||||||
\(412\) | −11795.4 | + | 1239.44i | −1.41048 | + | 0.148210i | ||||
\(413\) | −126.034 | − | 72.7660i | −0.0150163 | − | 0.00866969i | ||||
\(414\) | −740.842 | + | 1453.94i | −0.0879478 | + | 0.172602i | ||||
\(415\) | −3450.68 | − | 1992.25i | −0.408162 | − | 0.235652i | ||||
\(416\) | −3670.65 | − | 3671.12i | −0.432616 | − | 0.432671i | ||||
\(417\) | − | 16880.6i | − | 1.98236i | ||||||
\(418\) | −3485.52 | + | 653.427i | −0.407853 | + | 0.0764598i | ||||
\(419\) | − | 12356.2i | − | 1.44066i | −0.693629 | − | 0.720332i | \(-0.743989\pi\) | ||
0.693629 | − | 0.720332i | \(-0.256011\pi\) | |||||||
\(420\) | 405.496 | − | 294.594i | 0.0471100 | − | 0.0342256i | ||||
\(421\) | −8694.11 | − | 5019.55i | −1.00647 | − | 0.581088i | −0.0963160 | − | 0.995351i | \(-0.530706\pi\) |
−0.910157 | + | 0.414263i | \(0.864039\pi\) | |||||||
\(422\) | −3630.79 | − | 1850.04i | −0.418825 | − | 0.213409i | ||||
\(423\) | −1034.71 | − | 597.389i | −0.118934 | − | 0.0686668i | ||||
\(424\) | 3694.65 | + | 4562.87i | 0.423179 | + | 0.522624i | ||||
\(425\) | −2628.71 | −0.300026 | ||||||||
\(426\) | 231.564 | − | 150.375i | 0.0263364 | − | 0.0171026i | ||||
\(427\) | −2022.76 | + | 1167.84i | −0.229246 | + | 0.132355i | ||||
\(428\) | −10319.7 | + | 1084.38i | −1.16548 | + | 0.122466i | ||||
\(429\) | −2596.12 | −0.292172 | ||||||||
\(430\) | −2023.00 | − | 3115.23i | −0.226878 | − | 0.349371i | ||||
\(431\) | 7828.86 | + | 13560.0i | 0.874948 | + | 1.51545i | 0.856818 | + | 0.515619i | \(0.172438\pi\) |
0.0181304 | + | 0.999836i | \(0.494229\pi\) | |||||||
\(432\) | −6829.57 | + | 1451.30i | −0.760621 | + | 0.161634i | ||||
\(433\) | 69.4935 | − | 40.1221i | 0.00771280 | − | 0.00445299i | −0.496139 | − | 0.868243i | \(-0.665249\pi\) |
0.503851 | + | 0.863790i | \(0.331916\pi\) | |||||||
\(434\) | 693.822 | − | 36.3528i | 0.0767386 | − | 0.00402071i | ||||
\(435\) | 3292.95 | + | 1901.18i | 0.362953 | + | 0.209551i | ||||
\(436\) | −6959.95 | − | 3098.98i | −0.764498 | − | 0.340400i | ||||
\(437\) | 4322.65 | − | 3331.13i | 0.473182 | − | 0.364645i | ||||
\(438\) | −9423.51 | + | 6119.53i | −1.02802 | + | 0.667585i | ||||
\(439\) | −2528.56 | + | 4379.60i | −0.274901 | + | 0.476143i | −0.970110 | − | 0.242665i | \(-0.921978\pi\) |
0.695209 | + | 0.718808i | \(0.255312\pi\) | |||||||
\(440\) | 467.788 | − | 1218.49i | 0.0506839 | − | 0.132021i | ||||
\(441\) | −1468.45 | − | 2543.44i | −0.158563 | − | 0.274639i | ||||
\(442\) | 1927.35 | − | 100.983i | 0.207409 | − | 0.0108672i | ||||
\(443\) | 12056.5 | − | 6960.82i | 1.29305 | − | 0.746543i | 0.313856 | − | 0.949471i | \(-0.398379\pi\) |
0.979194 | + | 0.202928i | \(0.0650457\pi\) | |||||||
\(444\) | 9092.52 | + | 4048.53i | 0.971873 | + | 0.432736i | ||||
\(445\) | − | 5269.17i | − | 0.561310i | ||||||
\(446\) | −8130.61 | − | 4142.88i | −0.863219 | − | 0.439846i | ||||
\(447\) | −3514.84 | − | 6087.89i | −0.371916 | − | 0.644177i | ||||
\(448\) | 434.972 | + | 1339.06i | 0.0458716 | + | 0.141215i | ||||
\(449\) | 14729.2i | 1.54813i | 0.633103 | + | 0.774067i | \(0.281781\pi\) | ||||
−0.633103 | + | 0.774067i | \(0.718219\pi\) | |||||||
\(450\) | 2437.77 | + | 1242.15i | 0.255373 | + | 0.130123i | ||||
\(451\) | −264.675 | + | 458.431i | −0.0276343 | + | 0.0478641i | ||||
\(452\) | −1635.27 | − | 15562.4i | −0.170170 | − | 1.61945i | ||||
\(453\) | 9684.57 | − | 16774.2i | 1.00446 | − | 1.73978i | ||||
\(454\) | −396.429 | − | 7566.17i | −0.0409809 | − | 0.782154i | ||||
\(455\) | −300.483 | −0.0309602 | ||||||||
\(456\) | −10901.3 | − | 2593.75i | −1.11952 | − | 0.266367i | ||||
\(457\) | 384.104 | 0.0393165 | 0.0196582 | − | 0.999807i | \(-0.493742\pi\) | ||||
0.0196582 | + | 0.999807i | \(0.493742\pi\) | |||||||
\(458\) | 413.060 | + | 7883.59i | 0.0421420 | + | 0.804314i | ||||
\(459\) | 1297.85 | − | 2247.94i | 0.131979 | − | 0.228595i | ||||
\(460\) | 209.900 | + | 1997.56i | 0.0212753 | + | 0.202471i | ||||
\(461\) | 1493.52 | − | 2586.85i | 0.150890 | − | 0.261348i | −0.780665 | − | 0.624950i | \(-0.785120\pi\) |
0.931555 | + | 0.363601i | \(0.118453\pi\) | |||||||
\(462\) | 627.334 | + | 319.653i | 0.0631737 | + | 0.0321896i | ||||
\(463\) | − | 2290.11i | − | 0.229872i | −0.993373 | − | 0.114936i | \(-0.963334\pi\) | ||
0.993373 | − | 0.114936i | \(-0.0366662\pi\) | |||||||
\(464\) | −7937.95 | + | 7146.62i | −0.794203 | + | 0.715029i | ||||
\(465\) | −1017.60 | − | 1762.53i | −0.101484 | − | 0.175775i | ||||
\(466\) | 106.682 | + | 54.3588i | 0.0106050 | + | 0.00540370i | ||||
\(467\) | 6810.70i | 0.674864i | 0.941350 | + | 0.337432i | \(0.109558\pi\) | ||||
−0.941350 | + | 0.337432i | \(0.890442\pi\) | |||||||
\(468\) | −1835.07 | − | 817.083i | −0.181253 | − | 0.0807045i | ||||
\(469\) | 1140.00 | − | 658.178i | 0.112239 | − | 0.0648014i | ||||
\(470\) | −1468.61 | + | 76.9479i | −0.144132 | + | 0.00755179i | ||||
\(471\) | 9880.92 | + | 17114.3i | 0.966643 | + | 1.67427i | ||||
\(472\) | −1117.96 | − | 429.195i | −0.109022 | − | 0.0418544i | ||||
\(473\) | 2608.94 | − | 4518.82i | 0.253614 | − | 0.439272i | ||||
\(474\) | 873.666 | − | 567.349i | 0.0846599 | − | 0.0549773i | ||||
\(475\) | −5585.22 | − | 7247.67i | −0.539510 | − | 0.700096i | ||||
\(476\) | −478.164 | − | 212.907i | −0.0460433 | − | 0.0205012i | ||||
\(477\) | 1967.41 | + | 1135.89i | 0.188850 | + | 0.109033i | ||||
\(478\) | 6378.66 | − | 334.209i | 0.610362 | − | 0.0319799i | ||||
\(479\) | −15066.2 | + | 8698.45i | −1.43714 | + | 0.829733i | −0.997650 | − | 0.0685138i | \(-0.978174\pi\) |
−0.439490 | + | 0.898247i | \(0.644841\pi\) | |||||||
\(480\) | 2916.47 | − | 2916.09i | 0.277329 | − | 0.277293i | ||||
\(481\) | −2983.52 | − | 5167.60i | −0.282820 | − | 0.489859i | ||||
\(482\) | 3016.36 | + | 4644.91i | 0.285044 | + | 0.438942i | ||||
\(483\) | −1083.50 | −0.102072 | ||||||||
\(484\) | −8766.26 | + | 921.143i | −0.823277 | + | 0.0865086i | ||||
\(485\) | −2779.11 | + | 1604.52i | −0.260192 | + | 0.150222i | ||||
\(486\) | −5618.95 | + | 3648.89i | −0.524446 | + | 0.340570i | ||||
\(487\) | 7807.97 | 0.726516 | 0.363258 | − | 0.931689i | \(-0.381664\pi\) | ||||
0.363258 | + | 0.931689i | \(0.381664\pi\) | |||||||
\(488\) | −14936.6 | + | 12094.5i | −1.38555 | + | 1.12191i | ||||
\(489\) | −8040.16 | − | 4641.99i | −0.743535 | − | 0.429280i | ||||
\(490\) | −3220.95 | − | 1641.21i | −0.296954 | − | 0.151311i | ||||
\(491\) | 4149.86 | + | 2395.92i | 0.381427 | + | 0.220217i | 0.678439 | − | 0.734657i | \(-0.262657\pi\) |
−0.297012 | + | 0.954874i | \(0.595990\pi\) | |||||||
\(492\) | −1353.25 | + | 983.139i | −0.124002 | + | 0.0900880i | ||||
\(493\) | − | 3970.86i | − | 0.362756i | ||||||
\(494\) | 4373.45 | + | 5099.37i | 0.398322 | + | 0.464436i | ||||
\(495\) | − | 505.032i | − | 0.0458576i | ||||||
\(496\) | 5592.11 | − | 1188.34i | 0.506236 | − | 0.107577i | ||||
\(497\) | 38.8778 | + | 22.4461i | 0.00350887 | + | 0.00202585i | ||||
\(498\) | 8029.70 | − | 15758.7i | 0.722529 | − | 1.41800i | ||||
\(499\) | −10055.5 | − | 5805.55i | −0.902097 | − | 0.520826i | −0.0242170 | − | 0.999707i | \(-0.507709\pi\) |
−0.877880 | + | 0.478881i | \(0.841043\pi\) | |||||||
\(500\) | 7138.59 | − | 750.110i | 0.638494 | − | 0.0670919i | ||||
\(501\) | 7045.65 | 0.628296 | ||||||||
\(502\) | −8385.64 | − | 12913.1i | −0.745556 | − | 1.14809i | ||||
\(503\) | −4083.42 | + | 2357.56i | −0.361969 | + | 0.208983i | −0.669944 | − | 0.742411i | \(-0.733682\pi\) |
0.307975 | + | 0.951394i | \(0.400349\pi\) | |||||||
\(504\) | 342.828 | + | 423.390i | 0.0302991 | + | 0.0374192i | ||||
\(505\) | −3052.27 | −0.268959 | ||||||||
\(506\) | −2366.35 | + | 1536.68i | −0.207899 | + | 0.135007i | ||||
\(507\) | −4109.56 | − | 7117.96i | −0.359984 | − | 0.623510i | ||||
\(508\) | 3105.88 | + | 4275.11i | 0.271262 | + | 0.373381i | ||||
\(509\) | −6329.33 | + | 3654.24i | −0.551164 | + | 0.318215i | −0.749591 | − | 0.661901i | \(-0.769750\pi\) |
0.198427 | + | 0.980116i | \(0.436417\pi\) | |||||||
\(510\) | 80.2247 | + | 1531.15i | 0.00696551 | + | 0.132942i | ||||
\(511\) | −1582.14 | − | 913.447i | −0.136966 | − | 0.0790773i | ||||
\(512\) | 5258.40 | + | 10323.1i | 0.453888 | + | 0.891059i | ||||
\(513\) | 8955.38 | − | 1197.87i | 0.770740 | − | 0.103094i | ||||
\(514\) | 5743.83 | + | 8844.97i | 0.492898 | + | 0.759018i | ||||
\(515\) | −2824.39 | + | 4891.98i | −0.241665 | + | 0.418576i | ||||
\(516\) | 13339.2 | − | 9690.94i | 1.13803 | − | 0.826782i | ||||
\(517\) | −1032.93 | − | 1789.10i | −0.0878693 | − | 0.152194i | ||||
\(518\) | 84.6737 | + | 1616.07i | 0.00718214 | + | 0.137077i | ||||
\(519\) | 12180.4 | − | 7032.37i | 1.03018 | − | 0.594772i | ||||
\(520\) | −2442.12 | + | 386.697i | −0.205950 | + | 0.0326111i | ||||
\(521\) | 6588.33i | 0.554012i | 0.960868 | + | 0.277006i | \(0.0893422\pi\) | ||||
−0.960868 | + | 0.277006i | \(0.910658\pi\) | |||||||
\(522\) | −1876.36 | + | 3682.44i | −0.157329 | + | 0.308766i | ||||
\(523\) | −7428.10 | − | 12865.9i | −0.621048 | − | 1.07569i | −0.989291 | − | 0.145958i | \(-0.953374\pi\) |
0.368242 | − | 0.929730i | \(-0.379960\pi\) | |||||||
\(524\) | 6669.36 | + | 2969.60i | 0.556016 | + | 0.247571i | ||||
\(525\) | 1816.67i | 0.151021i | ||||||||
\(526\) | 1086.58 | − | 2132.47i | 0.0900708 | − | 0.176768i | ||||
\(527\) | −1062.69 | + | 1840.63i | −0.0878397 | + | 0.152143i | ||||
\(528\) | 5509.89 | + | 1790.59i | 0.454143 | + | 0.147586i | ||||
\(529\) | −3912.50 | + | 6776.65i | −0.321567 | + | 0.556970i | ||||
\(530\) | 2792.45 | − | 146.310i | 0.228861 | − | 0.0119911i | ||||
\(531\) | −463.366 | −0.0378689 | ||||||||
\(532\) | −428.945 | − | 1770.72i | −0.0349570 | − | 0.144305i | ||||
\(533\) | 1002.79 | 0.0814929 | ||||||||
\(534\) | 23356.9 | − | 1223.78i | 1.89279 | − | 0.0991727i | ||||
\(535\) | −2471.05 | + | 4279.98i | −0.199687 | + | 0.345869i | ||||
\(536\) | 8418.07 | − | 6816.28i | 0.678368 | − | 0.549289i | ||||
\(537\) | −4460.50 | + | 7725.81i | −0.358444 | + | 0.620844i | ||||
\(538\) | 10628.0 | − | 20857.9i | 0.851682 | − | 1.67147i | ||||
\(539\) | − | 5078.15i | − | 0.405810i | ||||||
\(540\) | −1352.64 | + | 3037.86i | −0.107793 | + | 0.242090i | ||||
\(541\) | 8293.82 | + | 14365.3i | 0.659111 | + | 1.14161i | 0.980846 | + | 0.194784i | \(0.0624005\pi\) |
−0.321735 | + | 0.946830i | \(0.604266\pi\) | |||||||
\(542\) | 248.071 | − | 486.852i | 0.0196597 | − | 0.0385832i | ||||
\(543\) | 17706.9i | 1.39941i | ||||||||
\(544\) | −4160.17 | − | 1115.00i | −0.327878 | − | 0.0878773i | ||||
\(545\) | −3142.46 | + | 1814.30i | −0.246987 | + | 0.142598i | ||||
\(546\) | −69.7882 | − | 1331.97i | −0.00547007 | − | 0.104401i | ||||
\(547\) | −2049.99 | − | 3550.69i | −0.160240 | − | 0.277544i | 0.774715 | − | 0.632311i | \(-0.217893\pi\) |
−0.934955 | + | 0.354767i | \(0.884560\pi\) | |||||||
\(548\) | 10329.8 | + | 14218.5i | 0.805229 | + | 1.10836i | ||||
\(549\) | −3718.34 | + | 6440.35i | −0.289062 | + | 0.500670i | ||||
\(550\) | 2576.51 | + | 3967.58i | 0.199750 | + | 0.307597i | ||||
\(551\) | 10948.1 | − | 8436.88i | 0.846472 | − | 0.652311i | ||||
\(552\) | −8805.90 | + | 1394.37i | −0.678992 | + | 0.107515i | ||||
\(553\) | 146.682 | + | 84.6869i | 0.0112795 | + | 0.00651221i | ||||
\(554\) | −17.8253 | − | 340.211i | −0.00136701 | − | 0.0260906i | ||||
\(555\) | 4105.33 | − | 2370.21i | 0.313985 | − | 0.181279i | ||||
\(556\) | 18271.4 | − | 13274.2i | 1.39367 | − | 1.01251i | ||||
\(557\) | −855.805 | − | 1482.30i | −0.0651017 | − | 0.112759i | 0.831637 | − | 0.555319i | \(-0.187404\pi\) |
−0.896739 | + | 0.442560i | \(0.854071\pi\) | |||||||
\(558\) | 1855.26 | − | 1204.79i | 0.140752 | − | 0.0914026i | ||||
\(559\) | −9884.66 | −0.747901 | ||||||||
\(560\) | 637.734 | + | 207.248i | 0.0481235 | + | 0.0156390i | ||||
\(561\) | −1865.28 | + | 1076.92i | −0.140378 | + | 0.0810475i | ||||
\(562\) | 1317.92 | + | 2029.47i | 0.0989198 | + | 0.152327i | ||||
\(563\) | −769.154 | −0.0575772 | −0.0287886 | − | 0.999586i | \(-0.509165\pi\) | ||||
−0.0287886 | + | 0.999586i | \(0.509165\pi\) | |||||||
\(564\) | −682.180 | − | 6492.12i | −0.0509308 | − | 0.484694i | ||||
\(565\) | −6454.31 | − | 3726.40i | −0.480593 | − | 0.277470i | ||||
\(566\) | −6112.67 | + | 11996.4i | −0.453948 | + | 0.890895i | ||||
\(567\) | −2116.49 | − | 1221.96i | −0.156763 | − | 0.0905069i | ||||
\(568\) | 344.858 | + | 132.394i | 0.0254752 | + | 0.00978013i | ||||
\(569\) | 10990.5i | 0.809748i | 0.914373 | + | 0.404874i | \(0.132685\pi\) | ||||
−0.914373 | + | 0.404874i | \(0.867315\pi\) | |||||||
\(570\) | −4051.12 | + | 3474.43i | −0.297689 | + | 0.255312i | ||||
\(571\) | − | 15340.0i | − | 1.12427i | −0.827045 | − | 0.562135i | \(-0.809980\pi\) | ||
0.827045 | − | 0.562135i | \(-0.190020\pi\) | |||||||
\(572\) | −2041.49 | − | 2810.02i | −0.149229 | − | 0.205407i | ||||
\(573\) | 22626.4 | + | 13063.4i | 1.64962 | + | 0.952409i | ||||
\(574\) | −242.318 | − | 123.471i | −0.0176205 | − | 0.00897836i | ||||
\(575\) | −6304.76 | − | 3640.05i | −0.457264 | − | 0.264001i | ||||
\(576\) | 3331.13 | + | 2999.82i | 0.240967 | + | 0.217001i | ||||
\(577\) | −7757.47 | −0.559701 | −0.279851 | − | 0.960044i | \(-0.590285\pi\) | ||||
−0.279851 | + | 0.960044i | \(0.590285\pi\) | |||||||
\(578\) | −10311.4 | + | 6696.13i | −0.742039 | + | 0.481873i | ||||
\(579\) | −1636.56 | + | 944.868i | −0.117466 | + | 0.0678193i | ||||
\(580\) | 531.620 | + | 5059.28i | 0.0380592 | + | 0.362198i | ||||
\(581\) | 2875.66 | 0.205340 | ||||||||
\(582\) | −7757.88 | − | 11946.4i | −0.552533 | − | 0.850851i | ||||
\(583\) | 1964.04 | + | 3401.82i | 0.139523 | + | 0.241662i | ||||
\(584\) | −14034.0 | − | 5387.77i | −0.994403 | − | 0.381760i | ||||
\(585\) | −828.547 | + | 478.362i | −0.0585576 | + | 0.0338082i | ||||
\(586\) | −1823.65 | + | 95.5501i | −0.128557 | + | 0.00673573i | ||||
\(587\) | 21859.4 | + | 12620.5i | 1.53702 | + | 0.887401i | 0.999011 | + | 0.0444643i | \(0.0141581\pi\) |
0.538013 | + | 0.842937i | \(0.319175\pi\) | |||||||
\(588\) | 6526.97 | − | 14658.8i | 0.457768 | − | 1.02809i | ||||
\(589\) | −7332.74 | + | 980.829i | −0.512972 | + | 0.0686152i | ||||
\(590\) | −478.338 | + | 310.628i | −0.0333777 | + | 0.0216751i | ||||
\(591\) | −12084.5 | + | 20930.9i | −0.841097 | + | 1.45682i | ||||
\(592\) | 2767.91 | + | 13025.3i | 0.192163 | + | 0.904283i | ||||
\(593\) | −4399.27 | − | 7619.75i | −0.304648 | − | 0.527666i | 0.672535 | − | 0.740065i | \(-0.265205\pi\) |
−0.977183 | + | 0.212400i | \(0.931872\pi\) | |||||||
\(594\) | −4664.95 | + | 244.420i | −0.322231 | + | 0.0168833i | ||||
\(595\) | −215.894 | + | 124.647i | −0.0148753 | + | 0.00858825i | ||||
\(596\) | 3825.55 | − | 8591.72i | 0.262920 | − | 0.590488i | ||||
\(597\) | 26813.6i | 1.83820i | ||||||||
\(598\) | 4762.43 | + | 2426.65i | 0.325669 | + | 0.165942i | ||||
\(599\) | −9011.57 | − | 15608.5i | −0.614696 | − | 1.06468i | −0.990438 | − | 0.137960i | \(-0.955945\pi\) |
0.375742 | − | 0.926724i | \(-0.377388\pi\) | |||||||
\(600\) | 2337.90 | + | 14764.6i | 0.159074 | + | 1.00460i | ||||
\(601\) | 13989.3i | 0.949474i | 0.880128 | + | 0.474737i | \(0.157457\pi\) | ||||
−0.880128 | + | 0.474737i | \(0.842543\pi\) | |||||||
\(602\) | 2388.56 | + | 1217.07i | 0.161712 | + | 0.0823989i | ||||
\(603\) | 2095.60 | − | 3629.69i | 0.141525 | − | 0.245129i | ||||
\(604\) | 25771.8 | − | 2708.06i | 1.73616 | − | 0.182433i | ||||
\(605\) | −2099.07 | + | 3635.70i | −0.141057 | + | 0.244317i | ||||
\(606\) | −708.898 | − | 13529.9i | −0.0475198 | − | 0.906955i | ||||
\(607\) | −2781.03 | −0.185961 | −0.0929805 | − | 0.995668i | \(-0.529639\pi\) | ||||
−0.0929805 | + | 0.995668i | \(0.529639\pi\) | |||||||
\(608\) | −5764.92 | − | 13839.1i | −0.384537 | − | 0.923110i | ||||
\(609\) | −2744.21 | −0.182596 | ||||||||
\(610\) | 478.948 | + | 9141.12i | 0.0317902 | + | 0.606743i | ||||
\(611\) | −1956.77 | + | 3389.23i | −0.129562 | + | 0.224408i | ||||
\(612\) | −1657.42 | + | 174.159i | −0.109473 | + | 0.0115032i | ||||
\(613\) | 13690.2 | − | 23712.0i | 0.902023 | − | 1.56235i | 0.0771582 | − | 0.997019i | \(-0.475415\pi\) |
0.824865 | − | 0.565330i | \(-0.191251\pi\) | |||||||
\(614\) | −15075.1 | − | 7681.38i | −0.990848 | − | 0.504878i | ||||
\(615\) | 796.654i | 0.0522345i | ||||||||
\(616\) | 147.322 | + | 930.385i | 0.00963598 | + | 0.0608543i | ||||
\(617\) | 9153.41 | + | 15854.2i | 0.597248 | + | 1.03446i | 0.993225 | + | 0.116204i | \(0.0370727\pi\) |
−0.395977 | + | 0.918260i | \(0.629594\pi\) | |||||||
\(618\) | −22340.9 | − | 11383.6i | −1.45418 | − | 0.740964i | ||||
\(619\) | 1584.70i | 0.102899i | 0.998676 | + | 0.0514495i | \(0.0163841\pi\) | ||||
−0.998676 | + | 0.0514495i | \(0.983616\pi\) | |||||||
\(620\) | 1107.55 | − | 2487.43i | 0.0717424 | − | 0.161125i | ||||
\(621\) | 6225.58 | − | 3594.34i | 0.402293 | − | 0.232264i | ||||
\(622\) | 9973.91 | − | 522.582i | 0.642954 | − | 0.0336875i | ||||
\(623\) | 1901.41 | + | 3293.34i | 0.122277 | + | 0.211790i | ||||
\(624\) | −2281.32 | − | 10735.5i | −0.146355 | − | 0.688721i | ||||
\(625\) | −5195.82 | + | 8999.42i | −0.332532 | + | 0.575963i | ||||
\(626\) | −3782.25 | + | 2456.15i | −0.241484 | + | 0.156817i | ||||
\(627\) | −6932.37 | − | 2854.67i | −0.441550 | − | 0.181826i | ||||
\(628\) | −10754.4 | + | 24153.0i | −0.683353 | + | 1.53473i | ||||
\(629\) | −4287.25 | − | 2475.24i | −0.271771 | − | 0.156907i | ||||
\(630\) | 259.112 | − | 13.5762i | 0.0163861 | − | 0.000858551i | ||||
\(631\) | 7046.41 | − | 4068.25i | 0.444554 | − | 0.256663i | −0.260974 | − | 0.965346i | \(-0.584044\pi\) |
0.705527 | + | 0.708683i | \(0.250710\pi\) | |||||||
\(632\) | 1301.11 | + | 499.508i | 0.0818916 | + | 0.0314388i | ||||
\(633\) | −4307.44 | − | 7460.70i | −0.270467 | − | 0.468462i | ||||
\(634\) | 1201.71 | + | 1850.53i | 0.0752778 | + | 0.115921i | ||||
\(635\) | 2516.75 | 0.157282 | ||||||||
\(636\) | 1297.11 | + | 12344.2i | 0.0808706 | + | 0.769623i | ||||
\(637\) | −8331.12 | + | 4809.98i | −0.518196 | + | 0.299181i | ||||
\(638\) | −5993.33 | + | 3892.00i | −0.371909 | + | 0.241514i | ||||
\(639\) | 142.935 | 0.00884883 | ||||||||
\(640\) | 5449.76 | + | 863.658i | 0.336595 | + | 0.0533423i | ||||
\(641\) | −13924.2 | − | 8039.12i | −0.857990 | − | 0.495361i | 0.00534868 | − | 0.999986i | \(-0.498297\pi\) |
−0.863339 | + | 0.504625i | \(0.831631\pi\) | |||||||
\(642\) | −19546.0 | − | 9959.49i | −1.20159 | − | 0.612258i | ||||
\(643\) | −10841.9 | − | 6259.59i | −0.664952 | − | 0.383910i | 0.129210 | − | 0.991617i | \(-0.458756\pi\) |
−0.794161 | + | 0.607707i | \(0.792089\pi\) | |||||||
\(644\) | −852.021 | − | 1172.77i | −0.0521340 | − | 0.0717602i | ||||
\(645\) | − | 7852.73i | − | 0.479381i | ||||||
\(646\) | 5257.60 | + | 1849.64i | 0.320213 | + | 0.112652i | ||||
\(647\) | 25082.4i | 1.52409i | 0.647522 | + | 0.762047i | \(0.275806\pi\) | ||||
−0.647522 | + | 0.762047i | \(0.724194\pi\) | |||||||
\(648\) | −18773.9 | − | 7207.46i | −1.13813 | − | 0.436938i | ||||
\(649\) | −693.858 | − | 400.599i | −0.0419666 | − | 0.0242294i | ||||
\(650\) | 4068.70 | − | 7985.02i | 0.245519 | − | 0.481844i | ||||
\(651\) | 1272.04 | + | 734.412i | 0.0765824 | + | 0.0442149i | ||||
\(652\) | −1298.02 | − | 12352.9i | −0.0779669 | − | 0.741989i | ||||
\(653\) | 25504.0 | 1.52841 | 0.764203 | − | 0.644976i | \(-0.223133\pi\) | ||||
0.764203 | + | 0.644976i | \(0.223133\pi\) | |||||||
\(654\) | −8772.17 | − | 13508.3i | −0.524494 | − | 0.807672i | ||||
\(655\) | 3011.26 | − | 1738.55i | 0.179633 | − | 0.103711i | ||||
\(656\) | −2128.28 | − | 691.642i | −0.126670 | − | 0.0411648i | ||||
\(657\) | −5816.73 | −0.345407 | ||||||||
\(658\) | 890.147 | − | 578.052i | 0.0527379 | − | 0.0342474i | ||||
\(659\) | −10482.3 | − | 18155.8i | −0.619623 | − | 1.07322i | −0.989555 | − | 0.144159i | \(-0.953952\pi\) |
0.369932 | − | 0.929059i | \(-0.379381\pi\) | |||||||
\(660\) | 2232.38 | − | 1621.83i | 0.131660 | − | 0.0956511i | ||||
\(661\) | −10964.6 | + | 6330.40i | −0.645193 | + | 0.372502i | −0.786612 | − | 0.617447i | \(-0.788167\pi\) |
0.141419 | + | 0.989950i | \(0.454834\pi\) | |||||||
\(662\) | 1426.00 | + | 27216.3i | 0.0837204 | + | 1.59787i | ||||
\(663\) | 3533.56 | + | 2040.10i | 0.206986 | + | 0.119504i | ||||
\(664\) | 23371.3 | − | 3700.73i | 1.36594 | − | 0.216290i | ||||
\(665\) | −802.375 | − | 330.409i | −0.0467891 | − | 0.0192673i | ||||
\(666\) | 2806.21 | + | 4321.31i | 0.163271 | + | 0.251423i | ||||
\(667\) | 5498.57 | − | 9523.80i | 0.319199 | − | 0.552868i | ||||
\(668\) | 5540.43 | + | 7626.16i | 0.320907 | + | 0.441714i | ||||
\(669\) | −9645.86 | − | 16707.1i | −0.557445 | − | 0.965523i | ||||
\(670\) | −269.928 | − | 5151.81i | −0.0155645 | − | 0.297062i | ||||
\(671\) | −11135.9 | + | 6429.31i | −0.640680 | + | 0.369897i | ||||
\(672\) | −770.563 | + | 2875.04i | −0.0442338 | + | 0.165040i | ||||
\(673\) | − | 10948.2i | − | 0.627078i | −0.949575 | − | 0.313539i | \(-0.898485\pi\) | ||
0.949575 | − | 0.313539i | \(-0.101515\pi\) | |||||||
\(674\) | −1995.35 | + | 3915.97i | −0.114033 | + | 0.223795i | ||||
\(675\) | −6026.53 | − | 10438.3i | −0.343646 | − | 0.595213i | ||||
\(676\) | 4472.83 | − | 10045.4i | 0.254485 | − | 0.571543i | ||||
\(677\) | − | 24797.2i | − | 1.40773i | −0.710335 | − | 0.703864i | \(-0.751456\pi\) | ||
0.710335 | − | 0.703864i | \(-0.248544\pi\) | |||||||
\(678\) | 15019.1 | − | 29475.8i | 0.850746 | − | 1.66963i | ||||
\(679\) | 1158.00 | − | 2005.72i | 0.0654492 | − | 0.113361i | ||||
\(680\) | −1594.22 | + | 1290.88i | −0.0899055 | + | 0.0727983i | ||||
\(681\) | 8008.80 | − | 13871.6i | 0.450658 | − | 0.780562i | ||||
\(682\) | 3819.70 | − | 200.133i | 0.214463 | − | 0.0112368i | ||||
\(683\) | 29592.3 | 1.65786 | 0.828929 | − | 0.559355i | \(-0.188951\pi\) | ||||
0.828929 | + | 0.559355i | \(0.188951\pi\) | |||||||
\(684\) | −4001.70 | − | 4199.67i | −0.223697 | − | 0.234764i | ||||
\(685\) | 8370.38 | 0.466884 | ||||||||
\(686\) | 5269.53 | − | 276.097i | 0.293282 | − | 0.0153665i | ||||
\(687\) | −8344.79 | + | 14453.6i | −0.463426 | + | 0.802677i | ||||
\(688\) | 20978.8 | + | 6817.61i | 1.16251 | + | 0.377789i | ||||
\(689\) | 3720.64 | − | 6444.33i | 0.205726 | − | 0.356327i | ||||
\(690\) | −1927.82 | + | 3783.44i | −0.106364 | + | 0.208744i | ||||
\(691\) | 9430.69i | 0.519190i | 0.965718 | + | 0.259595i | \(0.0835891\pi\) | ||||
−0.965718 | + | 0.259595i | \(0.916411\pi\) | |||||||
\(692\) | 17190.0 | + | 7654.01i | 0.944314 | + | 0.420465i | ||||
\(693\) | 182.244 | + | 315.656i | 0.00998971 | + | 0.0173027i | ||||
\(694\) | 5131.41 | − | 10070.6i | 0.280671 | − | 0.550830i | ||||
\(695\) | − | 10756.3i | − | 0.587066i | ||||||
\(696\) | −22303.0 | + | 3531.57i | −1.21465 | + | 0.192333i | ||||
\(697\) | 720.495 | − | 415.978i | 0.0391545 | − | 0.0226059i | ||||
\(698\) | −1813.72 | − | 34616.3i | −0.0983528 | − | 1.87714i | ||||
\(699\) | 126.563 | + | 219.214i | 0.00684846 | + | 0.0118619i | ||||
\(700\) | −1966.35 | + | 1428.56i | −0.106173 | + | 0.0771349i | ||||
\(701\) | −1225.58 | + | 2122.77i | −0.0660337 | + | 0.114374i | −0.897152 | − | 0.441722i | \(-0.854368\pi\) |
0.831118 | + | 0.556096i | \(0.187701\pi\) | |||||||
\(702\) | 4819.59 | + | 7421.73i | 0.259122 | + | 0.399024i | ||||
\(703\) | −2284.57 | − | 17079.6i | −0.122566 | − | 0.916314i | ||||
\(704\) | 2394.65 | + | 7371.91i | 0.128199 | + | 0.394658i | ||||
\(705\) | −2692.52 | − | 1554.53i | −0.143839 | − | 0.0830454i | ||||
\(706\) | 376.006 | + | 7176.39i | 0.0200442 | + | 0.382559i | ||||
\(707\) | 1907.73 | − | 1101.43i | 0.101482 | − | 0.0585905i | ||||
\(708\) | −1488.03 | − | 2048.20i | −0.0789880 | − | 0.108723i | ||||
\(709\) | −13931.2 | − | 24129.6i | −0.737938 | − | 1.27815i | −0.953422 | − | 0.301639i | \(-0.902466\pi\) |
0.215484 | − | 0.976507i | \(-0.430867\pi\) | |||||||
\(710\) | 147.553 | − | 95.8193i | 0.00779939 | − | 0.00506484i | ||||
\(711\) | 539.277 | 0.0284451 | ||||||||
\(712\) | 19691.6 | + | 24319.0i | 1.03648 | + | 1.28005i | ||||
\(713\) | −5097.56 | + | 2943.08i | −0.267749 | + | 0.154585i | ||||
\(714\) | −602.668 | − | 928.053i | −0.0315886 | − | 0.0486436i | ||||
\(715\) | −1654.25 | −0.0865252 | ||||||||
\(716\) | −11869.9 | + | 1247.27i | −0.619553 | + | 0.0651015i | ||||
\(717\) | 11694.5 | + | 6751.82i | 0.609120 | + | 0.351676i | ||||
\(718\) | −7966.93 | + | 15635.5i | −0.414099 | + | 0.812690i | ||||
\(719\) | −2315.74 | − | 1336.99i | −0.120115 | − | 0.0693483i | 0.438739 | − | 0.898615i | \(-0.355425\pi\) |
−0.558854 | + | 0.829266i | \(0.688759\pi\) | |||||||
\(720\) | 2088.41 | − | 443.793i | 0.108098 | − | 0.0229711i | ||||
\(721\) | − | 4076.79i | − | 0.210579i | ||||||
\(722\) | 6071.13 | + | 18425.8i | 0.312942 | + | 0.949772i | ||||
\(723\) | 11708.7i | 0.602284i | ||||||||
\(724\) | −19165.9 | + | 13924.1i | −0.983831 | + | 0.714756i | ||||
\(725\) | −15968.3 | − | 9219.29i | −0.817996 | − | 0.472270i | ||||
\(726\) | −16603.6 | − | 8460.23i | −0.848785 | − | 0.432491i | ||||
\(727\) | 17208.4 | + | 9935.30i | 0.877890 | + | 0.506850i | 0.869962 | − | 0.493119i | \(-0.164143\pi\) |
0.00792765 | + | 0.999969i | \(0.497477\pi\) | |||||||
\(728\) | 1386.83 | − | 1122.94i | 0.0706035 | − | 0.0571691i | ||||
\(729\) | 9831.95 | 0.499515 | ||||||||
\(730\) | −6004.68 | + | 3899.38i | −0.304443 | + | 0.197702i | ||||
\(731\) | −7102.02 | + | 4100.35i | −0.359340 | + | 0.207465i | ||||
\(732\) | −40409.0 | + | 4246.11i | −2.04038 | + | 0.214400i | ||||
\(733\) | 5928.83 | 0.298754 | 0.149377 | − | 0.988780i | \(-0.452273\pi\) | ||||
0.149377 | + | 0.988780i | \(0.452273\pi\) | |||||||
\(734\) | −3497.53 | − | 5385.88i | −0.175880 | − | 0.270840i | ||||
\(735\) | −3821.22 | − | 6618.54i | −0.191766 | − | 0.332148i | ||||
\(736\) | −8433.87 | − | 8434.95i | −0.422387 | − | 0.422441i | ||||
\(737\) | 6276.04 | − | 3623.47i | 0.313678 | − | 0.181102i | ||||
\(738\) | −864.725 | + | 45.3072i | −0.0431314 | + | 0.00225986i | ||||
\(739\) | 13991.3 | + | 8077.88i | 0.696453 | + | 0.402097i | 0.806025 | − | 0.591882i | \(-0.201615\pi\) |
−0.109572 | + | 0.993979i | \(0.534948\pi\) | |||||||
\(740\) | 5793.77 | + | 2579.73i | 0.287815 | + | 0.128152i | ||||
\(741\) | 1882.95 | + | 14077.0i | 0.0933492 | + | 0.697885i | ||||
\(742\) | −1692.54 | + | 1099.12i | −0.0837400 | + | 0.0543799i | ||||
\(743\) | −15384.9 | + | 26647.5i | −0.759648 | + | 1.31575i | 0.183382 | + | 0.983042i | \(0.441295\pi\) |
−0.943030 | + | 0.332707i | \(0.892038\pi\) | |||||||
\(744\) | 11283.4 | + | 4331.77i | 0.556005 | + | 0.213455i | ||||
\(745\) | −2239.67 | − | 3879.22i | −0.110141 | − | 0.190770i | ||||
\(746\) | −39974.1 | + | 2094.44i | −1.96187 | + | 0.102792i | ||||
\(747\) | 7929.29 | − | 4577.98i | 0.388377 | − | 0.224229i | ||||
\(748\) | −2632.44 | − | 1172.12i | −0.128678 | − | 0.0572953i | ||||
\(749\) | − | 3566.77i | − | 0.174001i | ||||||
\(750\) | 13520.7 | + | 6889.38i | 0.658277 | + | 0.335420i | ||||
\(751\) | −618.267 | − | 1070.87i | −0.0300411 | − | 0.0520327i | 0.850614 | − | 0.525791i | \(-0.176230\pi\) |
−0.880655 | + | 0.473758i | \(0.842897\pi\) | |||||||
\(752\) | 6490.58 | − | 5843.54i | 0.314743 | − | 0.283367i | ||||
\(753\) | − | 32550.8i | − | 1.57532i | ||||||
\(754\) | 12062.0 | + | 6146.07i | 0.582587 | + | 0.296853i | ||||
\(755\) | 6171.03 | − | 10688.5i | 0.297466 | − | 0.515226i | ||||
\(756\) | −250.804 | − | 2386.83i | −0.0120657 | − | 0.114826i | ||||
\(757\) | −13954.0 | + | 24169.0i | −0.669967 | + | 1.16042i | 0.307945 | + | 0.951404i | \(0.400359\pi\) |
−0.977913 | + | 0.209014i | \(0.932975\pi\) | |||||||
\(758\) | 850.891 | + | 16239.9i | 0.0407727 | + | 0.778181i | ||||
\(759\) | −5964.98 | −0.285264 | ||||||||
\(760\) | −6946.34 | − | 1652.74i | −0.331540 | − | 0.0788833i | ||||
\(761\) | 30436.9 | 1.44985 | 0.724924 | − | 0.688828i | \(-0.241875\pi\) | ||||
0.724924 | + | 0.688828i | \(0.241875\pi\) | |||||||
\(762\) | 584.523 | + | 11156.1i | 0.0277888 | + | 0.530371i | ||||
\(763\) | 1309.40 | − | 2267.95i | 0.0621278 | − | 0.107608i | ||||
\(764\) | 3652.86 | + | 34763.2i | 0.172979 | + | 1.64619i | ||||
\(765\) | −396.868 | + | 687.395i | −0.0187566 | + | 0.0324874i | ||||
\(766\) | −23012.9 | − | 11726.0i | −1.08550 | − | 0.553105i | ||||
\(767\) | 1517.77i | 0.0714519i | ||||||||
\(768\) | −2562.65 | + | 24357.9i | −0.120406 | + | 1.14446i | ||||
\(769\) | 2664.30 | + | 4614.71i | 0.124938 | + | 0.216399i | 0.921709 | − | 0.387883i | \(-0.126793\pi\) |
−0.796771 | + | 0.604282i | \(0.793460\pi\) | |||||||
\(770\) | 399.739 | + | 203.684i | 0.0187086 | + | 0.00953279i | ||||
\(771\) | 22296.0i | 1.04147i | ||||||||
\(772\) | −2309.65 | − | 1028.39i | −0.107676 | − | 0.0479438i | ||||
\(773\) | −4850.85 | + | 2800.64i | −0.225709 | + | 0.130313i | −0.608591 | − | 0.793484i | \(-0.708265\pi\) |
0.382882 | + | 0.923797i | \(0.374932\pi\) | |||||||
\(774\) | 8523.71 | − | 446.599i | 0.395838 | − | 0.0207399i | ||||
\(775\) | 4934.57 | + | 8546.93i | 0.228716 | + | 0.396148i | ||||
\(776\) | 6830.22 | − | 17791.3i | 0.315967 | − | 0.823028i | ||||
\(777\) | −1710.61 | + | 2962.86i | −0.0789804 | + | 0.136798i | ||||
\(778\) | 6281.38 | − | 4079.06i | 0.289458 | − | 0.187971i | ||||
\(779\) | 2677.74 | + | 1102.66i | 0.123158 | + | 0.0507150i | ||||
\(780\) | −4775.24 | − | 2126.22i | −0.219206 | − | 0.0976036i | ||||
\(781\) | 214.034 | + | 123.573i | 0.00980634 | + | 0.00566169i | ||||
\(782\) | 4428.38 | − | 232.024i | 0.202504 | − | 0.0106102i | ||||
\(783\) | 15767.8 | − | 9103.52i | 0.719660 | − | 0.415496i | ||||
\(784\) | 20999.1 | − | 4462.38i | 0.956594 | − | 0.203279i | ||||
\(785\) | 6296.14 | + | 10905.2i | 0.286266 | + | 0.495828i | ||||
\(786\) | 8405.92 | + | 12944.3i | 0.381462 | + | 0.587416i | ||||
\(787\) | −761.989 | −0.0345133 | −0.0172567 | − | 0.999851i | \(-0.505493\pi\) | ||||
−0.0172567 | + | 0.999851i | \(0.505493\pi\) | |||||||
\(788\) | −32158.2 | + | 3379.13i | −1.45379 | + | 0.152762i | ||||
\(789\) | 4381.89 | − | 2529.89i | 0.197718 | − | 0.114153i | ||||
\(790\) | 556.702 | − | 361.516i | 0.0250716 | − | 0.0162812i | ||||
\(791\) | 5378.77 | 0.241779 | ||||||||
\(792\) | 1887.37 | + | 2330.89i | 0.0846777 | + | 0.104577i | ||||
\(793\) | 21095.6 | + | 12179.6i | 0.944675 | + | 0.545409i | ||||
\(794\) | 5584.19 | + | 2845.38i | 0.249591 | + | 0.127177i | ||||
\(795\) | 5119.61 | + | 2955.81i | 0.228395 | + | 0.131864i | ||||
\(796\) | −29022.8 | + | 21085.2i | −1.29232 | + | 0.938875i | ||||
\(797\) | 29757.1i | 1.32252i | 0.750156 | + | 0.661261i | \(0.229978\pi\) | ||||
−0.750156 | + | 0.661261i | \(0.770022\pi\) | |||||||
\(798\) | 1278.27 | − | 3633.46i | 0.0567044 | − | 0.161182i | ||||
\(799\) | 3246.83i | 0.143760i | ||||||||
\(800\) | −14142.6 | + | 14140.8i | −0.625023 | + | 0.624942i | ||||
\(801\) | 10485.8 | + | 6053.99i | 0.462545 | + | 0.267050i | ||||
\(802\) | −178.128 | + | 349.586i | −0.00784281 | + | 0.0153919i | ||||
\(803\) | −8710.14 | − | 5028.80i | −0.382782 | − | 0.221000i | ||||
\(804\) | 22773.9 | − | 2393.05i | 0.998974 | − | 0.104970i | ||||
\(805\) | −690.407 | −0.0302281 | ||||||||
\(806\) | −3946.32 | − | 6076.97i | −0.172461 | − | 0.265573i | ||||
\(807\) | 42859.7 | − | 24745.1i | 1.86956 | − | 1.07939i | ||||
\(808\) | 14087.2 | − | 11406.7i | 0.613350 | − | 0.496642i | ||||
\(809\) | 16983.7 | 0.738091 | 0.369046 | − | 0.929411i | \(-0.379685\pi\) | ||||
0.369046 | + | 0.929411i | \(0.379685\pi\) | |||||||
\(810\) | −8032.72 | + | 5216.36i | −0.348446 | + | 0.226277i | ||||
\(811\) | −8683.03 | − | 15039.4i | −0.375959 | − | 0.651179i | 0.614511 | − | 0.788908i | \(-0.289353\pi\) |
−0.990470 | + | 0.137729i | \(0.956020\pi\) | |||||||
\(812\) | −2157.94 | − | 2970.31i | −0.0932623 | − | 0.128371i | ||||
\(813\) | 1000.40 | − | 577.584i | 0.0431559 | − | 0.0249161i | ||||
\(814\) | 466.155 | + | 8896.94i | 0.0200721 | + | 0.383093i | ||||
\(815\) | −5123.21 | − | 2957.89i | −0.220194 | − | 0.127129i | ||||
\(816\) | −6092.38 | − | 6766.97i | −0.261368 | − | 0.290308i | ||||
\(817\) | −26394.8 | − | 10869.1i | −1.13028 | − | 0.465436i | ||||
\(818\) | −4878.64 | − | 7512.65i | −0.208530 | − | 0.321117i | ||||
\(819\) | 345.239 | − | 597.972i | 0.0147297 | − | 0.0255126i | ||||
\(820\) | −862.292 | + | 626.458i | −0.0367226 | + | 0.0266791i | ||||
\(821\) | −7723.99 | − | 13378.3i | −0.328342 | − | 0.568706i | 0.653841 | − | 0.756632i | \(-0.273157\pi\) |
−0.982183 | + | 0.187927i | \(0.939823\pi\) | |||||||
\(822\) | 1944.05 | + | 37103.7i | 0.0824896 | + | 1.57438i | ||||
\(823\) | 18590.9 | − | 10733.4i | 0.787408 | − | 0.454610i | −0.0516410 | − | 0.998666i | \(-0.516445\pi\) |
0.839049 | + | 0.544055i | \(0.183112\pi\) | |||||||
\(824\) | −5246.48 | − | 33133.2i | −0.221808 | − | 1.40079i | ||||
\(825\) | 10001.3i | 0.422062i | ||||||||
\(826\) | 186.879 | − | 366.760i | 0.00787211 | − | 0.0154494i | ||||
\(827\) | 10977.5 | + | 19013.7i | 0.461580 | + | 0.799480i | 0.999040 | − | 0.0438092i | \(-0.0139494\pi\) |
−0.537460 | + | 0.843289i | \(0.680616\pi\) | |||||||
\(828\) | −4216.36 | − | 1877.37i | −0.176967 | − | 0.0787962i | ||||
\(829\) | 2566.58i | 0.107528i | 0.998554 | + | 0.0537642i | \(0.0171219\pi\) | ||||
−0.998554 | + | 0.0537642i | \(0.982878\pi\) | |||||||
\(830\) | 5116.55 | − | 10041.5i | 0.213973 | − | 0.419933i | ||||
\(831\) | 360.114 | − | 623.736i | 0.0150328 | − | 0.0260375i | ||||
\(832\) | 9826.03 | − | 10911.2i | 0.409443 | − | 0.454662i | ||||
\(833\) | −3990.55 | + | 6911.83i | −0.165984 | + | 0.287492i | ||||
\(834\) | 47680.1 | − | 2498.19i | 1.97965 | − | 0.103723i | ||||
\(835\) | 4489.51 | 0.186067 | ||||||||
\(836\) | −2361.47 | − | 9748.34i | −0.0976952 | − | 0.403294i | ||||
\(837\) | −9745.21 | −0.402442 | ||||||||
\(838\) | 34900.6 | − | 1828.62i | 1.43869 | − | 0.0753801i | ||||
\(839\) | 15521.0 | − | 26883.2i | 0.638672 | − | 1.10621i | −0.347052 | − | 0.937846i | \(-0.612817\pi\) |
0.985724 | − | 0.168367i | \(-0.0538494\pi\) | |||||||
\(840\) | 892.108 | + | 1101.75i | 0.0366436 | + | 0.0452547i | ||||
\(841\) | 1731.92 | − | 2999.77i | 0.0710123 | − | 0.122997i | ||||
\(842\) | 12891.3 | − | 25299.8i | 0.527630 | − | 1.03550i | ||||
\(843\) | 5115.80i | 0.209012i | ||||||||
\(844\) | 4688.20 | − | 10529.2i | 0.191202 | − | 0.429417i | ||||
\(845\) | −2618.62 | − | 4535.58i | −0.106607 | − | 0.184649i | ||||
\(846\) | 1534.23 | − | 3011.00i | 0.0623497 | − | 0.122364i | ||||
\(847\) | − | 3029.85i | − | 0.122912i | ||||||
\(848\) | −12341.3 | + | 11111.0i | −0.499766 | + | 0.449945i | ||||
\(849\) | −24650.7 | + | 14232.1i | −0.996479 | + | 0.575317i | ||||
\(850\) | −389.029 | − | 7424.93i | −0.0156983 | − | 0.299615i | ||||
\(851\) | −6855.09 | − | 11873.4i | −0.276133 | − | 0.478277i | ||||
\(852\) | 459.012 | + | 631.810i | 0.0184571 | + | 0.0254055i | ||||
\(853\) | −3057.82 | + | 5296.30i | −0.122741 | + | 0.212593i | −0.920848 | − | 0.389923i | \(-0.872502\pi\) |
0.798107 | + | 0.602516i | \(0.205835\pi\) | |||||||
\(854\) | −3597.98 | − | 5540.56i | −0.144169 | − | 0.222007i | ||||
\(855\) | −2738.45 | + | 366.296i | −0.109536 | + | 0.0146515i | ||||
\(856\) | −4590.13 | − | 28988.2i | −0.183280 | − | 1.15747i | ||||
\(857\) | −4662.53 | − | 2691.91i | −0.185845 | − | 0.107298i | 0.404191 | − | 0.914675i | \(-0.367553\pi\) |
−0.590036 | + | 0.807377i | \(0.700886\pi\) | |||||||
\(858\) | −384.205 | − | 7332.87i | −0.0152874 | − | 0.291772i | ||||
\(859\) | 27405.6 | − | 15822.6i | 1.08855 | − | 0.628476i | 0.155362 | − | 0.987858i | \(-0.450346\pi\) |
0.933191 | + | 0.359382i | \(0.117012\pi\) | |||||||
\(860\) | 8499.74 | − | 6175.09i | 0.337022 | − | 0.244847i | ||||
\(861\) | −287.477 | − | 497.925i | −0.0113789 | − | 0.0197088i | ||||
\(862\) | −37142.3 | + | 24119.8i | −1.46760 | + | 0.953043i | ||||
\(863\) | −39874.4 | −1.57282 | −0.786408 | − | 0.617707i | \(-0.788062\pi\) | ||||
−0.786408 | + | 0.617707i | \(0.788062\pi\) | |||||||
\(864\) | −5110.01 | − | 19075.7i | −0.201211 | − | 0.751121i | ||||
\(865\) | 7761.39 | − | 4481.04i | 0.305081 | − | 0.176139i | ||||
\(866\) | 123.611 | + | 190.350i | 0.00485045 | + | 0.00746924i | ||||
\(867\) | −25992.6 | −1.01817 | ||||||||
\(868\) | 205.361 | + | 1954.36i | 0.00803041 | + | 0.0764231i | ||||
\(869\) | 807.529 | + | 466.227i | 0.0315231 | + | 0.0181999i | ||||
\(870\) | −4882.66 | + | 9582.46i | −0.190273 | + | 0.373421i | ||||
\(871\) | −11889.2 | − | 6864.23i | −0.462514 | − | 0.267033i | ||||
\(872\) | 7723.22 | − | 20117.4i | 0.299933 | − | 0.781261i | ||||
\(873\) | − | 7374.02i | − | 0.285880i | ||||||
\(874\) | 10048.7 | + | 11716.6i | 0.388904 | + | 0.453454i | ||||
\(875\) | 2467.28i | 0.0953249i | ||||||||
\(876\) | −18679.5 | − | 25711.6i | −0.720460 | − | 0.991681i | ||||
\(877\) | −16934.3 | − | 9777.05i | −0.652032 | − | 0.376451i | 0.137202 | − | 0.990543i | \(-0.456189\pi\) |
−0.789234 | + | 0.614092i | \(0.789522\pi\) | |||||||
\(878\) | −12744.6 | − | 6493.91i | −0.489874 | − | 0.249611i | ||||
\(879\) | −3343.44 | − | 1930.34i | −0.128295 | − | 0.0740713i | ||||
\(880\) | 3510.92 | + | 1140.97i | 0.134492 | + | 0.0437067i | ||||
\(881\) | 17129.3 | 0.655052 | 0.327526 | − | 0.944842i | \(-0.393785\pi\) | ||||
0.327526 | + | 0.944842i | \(0.393785\pi\) | |||||||
\(882\) | 6966.75 | − | 4524.13i | 0.265967 | − | 0.172716i | ||||
\(883\) | −39394.1 | + | 22744.2i | −1.50138 | + | 0.866820i | −0.501378 | + | 0.865228i | \(0.667173\pi\) |
−0.999999 | + | 0.00159204i | \(0.999493\pi\) | |||||||
\(884\) | 570.465 | + | 5428.95i | 0.0217045 | + | 0.206556i | ||||
\(885\) | −1205.77 | −0.0457985 | ||||||||
\(886\) | 21445.5 | + | 33024.0i | 0.813176 | + | 1.25222i | ||||
\(887\) | 8136.62 | + | 14093.0i | 0.308006 | + | 0.533481i | 0.977926 | − | 0.208952i | \(-0.0670051\pi\) |
−0.669920 | + | 0.742433i | \(0.733672\pi\) | |||||||
\(888\) | −10089.7 | + | 26281.4i | −0.381292 | + | 0.993184i | ||||
\(889\) | −1573.02 | + | 908.183i | −0.0593446 | + | 0.0342626i | ||||
\(890\) | 14883.1 | − | 779.797i | 0.560541 | − | 0.0293695i | ||||
\(891\) | −11651.9 | − | 6727.25i | −0.438108 | − | 0.252942i | ||||
\(892\) | 10498.5 | − | 23578.4i | 0.394077 | − | 0.885050i | ||||
\(893\) | −8951.90 | + | 6898.54i | −0.335458 | + | 0.258511i | ||||
\(894\) | 16675.4 | − | 10828.8i | 0.623835 | − | 0.405112i | ||||
\(895\) | −2842.24 | + | 4922.90i | −0.106151 | + | 0.183860i | ||||
\(896\) | −3717.86 | + | 1426.77i | −0.138622 | + | 0.0531976i | ||||
\(897\) | 5649.97 | + | 9786.04i | 0.210309 | + | 0.364266i | ||||
\(898\) | −41603.3 | + | 2179.80i | −1.54601 | + | 0.0810033i | ||||
\(899\) | −12910.8 | + | 7454.04i | −0.478975 | + | 0.276536i | ||||
\(900\) | −3147.74 | + | 7069.45i | −0.116583 | + | 0.261832i | ||||
\(901\) | − | 6173.58i | − | 0.228270i | ||||||
\(902\) | −1334.03 | − | 679.745i | −0.0492444 | − | 0.0250921i | ||||
\(903\) | 2833.70 | + | 4908.12i | 0.104429 | + | 0.180877i | ||||
\(904\) | 43714.8 | − | 6922.02i | 1.60833 | − | 0.254671i | ||||
\(905\) | 11282.9i | 0.414427i | ||||||||
\(906\) | 48812.8 | + | 24872.1i | 1.78995 | + | 0.912054i | ||||
\(907\) | −21797.1 | + | 37753.7i | −0.797973 | + | 1.38213i | 0.122961 | + | 0.992412i | \(0.460761\pi\) |
−0.920934 | + | 0.389718i | \(0.872572\pi\) | |||||||
\(908\) | 21312.4 | − | 2239.47i | 0.778939 | − | 0.0818495i | ||||
\(909\) | 3506.89 | − | 6074.11i | 0.127961 | − | 0.221634i | ||||
\(910\) | −44.4692 | − | 848.731i | −0.00161993 | − | 0.0309178i | ||||
\(911\) | −47453.1 | −1.72579 | −0.862893 | − | 0.505386i | \(-0.831350\pi\) | ||||
−0.862893 | + | 0.505386i | \(0.831350\pi\) | |||||||
\(912\) | 5712.87 | − | 31175.2i | 0.207426 | − | 1.13192i | ||||
\(913\) | 15831.4 | 0.573869 | ||||||||
\(914\) | 56.8444 | + | 1084.92i | 0.00205716 | + | 0.0392626i | ||||
\(915\) | −9675.89 | + | 16759.1i | −0.349590 | + | 0.605508i | ||||
\(916\) | −22206.5 | + | 2333.42i | −0.801008 | + | 0.0841685i | ||||
\(917\) | −1254.73 | + | 2173.26i | −0.0451853 | + | 0.0782632i | ||||
\(918\) | 6541.50 | + | 3333.17i | 0.235187 | + | 0.119838i | ||||
\(919\) | − | 1142.19i | − | 0.0409984i | −0.999790 | − | 0.0204992i | \(-0.993474\pi\) | ||
0.999790 | − | 0.0204992i | \(-0.00652555\pi\) | |||||||
\(920\) | −5611.14 | + | 888.495i | −0.201080 | + | 0.0318400i | ||||
\(921\) | −17884.5 | − | 30976.9i | −0.639864 | − | 1.10828i | ||||
\(922\) | 7527.72 | + | 3835.69i | 0.268885 | + | 0.137008i | ||||
\(923\) | − | 468.188i | − | 0.0166962i | ||||||
\(924\) | −810.036 | + | 1819.25i | −0.0288401 | + | 0.0647714i | ||||
\(925\) | −19907.7 | + | 11493.7i | −0.707634 | + | 0.408553i | ||||
\(926\) | 6468.55 | − | 338.919i | 0.229557 | − | 0.0120276i | ||||
\(927\) | −6490.14 | − | 11241.2i | −0.229950 | − | 0.398286i | ||||
\(928\) | −21360.8 | − | 21363.5i | −0.755605 | − | 0.755702i | ||||
\(929\) | 23496.4 | − | 40696.9i | 0.829807 | − | 1.43727i | −0.0683826 | − | 0.997659i | \(-0.521784\pi\) |
0.898189 | − | 0.439609i | \(-0.144883\pi\) | |||||||
\(930\) | 4827.76 | − | 3135.10i | 0.170224 | − | 0.110542i | ||||
\(931\) | −27535.4 | + | 3683.15i | −0.969321 | + | 0.129657i | ||||
\(932\) | −137.751 | + | 309.373i | −0.00484141 | + | 0.0108732i | ||||
\(933\) | 18286.0 | + | 10557.4i | 0.641645 | + | 0.370454i | ||||
\(934\) | −19237.2 | + | 1007.93i | −0.673940 | + | 0.0353110i | ||||
\(935\) | −1188.56 | + | 686.217i | −0.0415724 | + | 0.0240018i | ||||
\(936\) | 2036.32 | − | 5304.18i | 0.0711102 | − | 0.185227i | ||||
\(937\) | 17443.6 | + | 30213.1i | 0.608171 | + | 1.05338i | 0.991542 | + | 0.129789i | \(0.0414300\pi\) |
−0.383370 | + | 0.923595i | \(0.625237\pi\) | |||||||
\(938\) | 2027.77 | + | 3122.58i | 0.0705853 | + | 0.108695i | ||||
\(939\) | −9534.13 | −0.331347 | ||||||||
\(940\) | −434.687 | − | 4136.79i | −0.0150829 | − | 0.143540i | ||||
\(941\) | −11616.2 | + | 6706.60i | −0.402419 | + | 0.232337i | −0.687527 | − | 0.726159i | \(-0.741304\pi\) |
0.285108 | + | 0.958495i | \(0.407970\pi\) | |||||||
\(942\) | −46877.8 | + | 30442.0i | −1.62140 | + | 1.05292i | ||||
\(943\) | 2304.07 | 0.0795661 | ||||||||
\(944\) | 1046.83 | − | 3221.26i | 0.0360927 | − | 0.111063i | ||||
\(945\) | −989.909 | − | 571.524i | −0.0340759 | − | 0.0196737i | ||||
\(946\) | 13149.8 | + | 6700.35i | 0.451940 | + | 0.230282i | ||||
\(947\) | 26116.5 | + | 15078.4i | 0.896170 | + | 0.517404i | 0.875956 | − | 0.482392i | \(-0.160232\pi\) |
0.0202144 | + | 0.999796i | \(0.493565\pi\) | |||||||
\(948\) | 1731.80 | + | 2383.75i | 0.0593316 | + | 0.0816674i | ||||
\(949\) | 19052.9i | 0.651722i | ||||||||
\(950\) | 19644.8 | − | 16848.3i | 0.670908 | − | 0.575403i | ||||
\(951\) | 4664.73i | 0.159058i | ||||||||
\(952\) | 530.603 | − | 1382.11i | 0.0180640 | − | 0.0470529i | ||||
\(953\) | −24482.8 | − | 14135.2i | −0.832189 | − | 0.480465i | 0.0224123 | − | 0.999749i | \(-0.492865\pi\) |
−0.854602 | + | 0.519284i | \(0.826199\pi\) | |||||||
\(954\) | −2917.21 | + | 5725.16i | −0.0990022 | + | 0.194297i | ||||
\(955\) | 14417.6 | + | 8324.01i | 0.488527 | + | 0.282051i | ||||
\(956\) | 1887.98 | + | 17967.4i | 0.0638722 | + | 0.607853i | ||||
\(957\) | −15107.7 | −0.510306 | ||||||||
\(958\) | −26798.9 | − | 41267.9i | −0.903793 | − | 1.39176i | ||||
\(959\) | −5231.66 | + | 3020.50i | −0.176162 | + | 0.101707i | ||||
\(960\) | 8668.27 | + | 7806.16i | 0.291424 | + | 0.262440i | ||||
\(961\) | −21811.5 | −0.732152 | ||||||||
\(962\) | 14154.6 | − | 9191.86i | 0.474390 | − | 0.308064i | ||||
\(963\) | −5678.20 | − | 9834.93i | −0.190008 | − | 0.329103i | ||||
\(964\) | −12673.4 | + | 9207.27i | −0.423426 | + | 0.307621i | ||||
\(965\) | −1042.82 | + | 602.072i | −0.0347871 | + | 0.0200843i | ||||
\(966\) | −160.349 | − | 3060.40i | −0.00534073 | − | 0.101932i | ||||
\(967\) | −22660.5 | − | 13083.1i | −0.753582 | − | 0.435081i | 0.0734047 | − | 0.997302i | \(-0.476614\pi\) |
−0.826987 | + | 0.562221i | \(0.809947\pi\) | |||||||
\(968\) | −3899.16 | − | 24624.4i | −0.129467 | − | 0.817623i | ||||
\(969\) | 7192.31 | + | 9333.11i | 0.238442 | + | 0.309415i | ||||
\(970\) | −4943.34 | − | 7612.29i | −0.163630 | − | 0.251975i | ||||
\(971\) | 19927.0 | − | 34514.5i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621784\pi\) | |||||||
\(972\) | −11138.0 | − | 15331.0i | −0.367544 | − | 0.505908i | ||||
\(973\) | 3881.49 | + | 6722.93i | 0.127888 | + | 0.221508i | ||||
\(974\) | 1155.52 | + | 22054.0i | 0.0380136 | + | 0.725520i | ||||
\(975\) | 16408.0 | − | 9473.15i | 0.538949 | − | 0.311163i | ||||
\(976\) | −36372.0 | − | 40399.4i | −1.19287 | − | 1.32495i | ||||
\(977\) | − | 4631.89i | − | 0.151676i | −0.997120 | − | 0.0758379i | \(-0.975837\pi\) | ||
0.997120 | − | 0.0758379i | \(-0.0241631\pi\) | |||||||
\(978\) | 11921.7 | − | 23396.8i | 0.389788 | − | 0.764978i | ||||
\(979\) | 10467.8 | + | 18130.8i | 0.341730 | + | 0.591894i | ||||
\(980\) | 4159.00 | − | 9340.63i | 0.135566 | − | 0.304465i | ||||
\(981\) | − | 8338.13i | − | 0.271372i | ||||||
\(982\) | −6153.26 | + | 12076.1i | −0.199958 | + | 0.392427i | ||||
\(983\) | 11953.8 | − | 20704.7i | 0.387862 | − | 0.671797i | −0.604300 | − | 0.796757i | \(-0.706547\pi\) |
0.992162 | + | 0.124960i | \(0.0398803\pi\) | |||||||
\(984\) | −2977.20 | − | 3676.82i | −0.0964528 | − | 0.119119i | ||||
\(985\) | −7700.24 | + | 13337.2i | −0.249086 | + | 0.431430i | ||||
\(986\) | 11215.9 | − | 587.657i | 0.362259 | − | 0.0189805i | ||||
\(987\) | 2243.84 | 0.0723631 | ||||||||
\(988\) | −13756.2 | + | 13107.7i | −0.442958 | + | 0.422077i | ||||
\(989\) | −22711.5 | −0.730217 | ||||||||
\(990\) | 1426.49 | − | 74.7408i | 0.0457948 | − | 0.00239941i | ||||
\(991\) | 22419.6 | − | 38831.9i | 0.718650 | − | 1.24474i | −0.242885 | − | 0.970055i | \(-0.578094\pi\) |
0.961535 | − | 0.274683i | \(-0.0885730\pi\) | |||||||
\(992\) | 4184.12 | + | 15619.4i | 0.133917 | + | 0.499914i | ||||
\(993\) | −28808.5 | + | 49897.7i | −0.920654 | + | 1.59462i | ||||
\(994\) | −57.6467 | + | 113.134i | −0.00183948 | + | 0.00361006i | ||||
\(995\) | 17085.7i | 0.544375i | ||||||||
\(996\) | 45699.6 | + | 20348.2i | 1.45386 | + | 0.647346i | ||||
\(997\) | −15019.0 | − | 26013.7i | −0.477088 | − | 0.826341i | 0.522567 | − | 0.852598i | \(-0.324974\pi\) |
−0.999655 | + | 0.0262574i | \(0.991641\pi\) | |||||||
\(998\) | 14909.9 | − | 29261.5i | 0.472912 | − | 0.928113i | ||||
\(999\) | − | 22698.8i | − | 0.718876i |
(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 | 76.4.f.a.27.16 | ✓ | 56 | |
4.3 | odd | 2 | inner | 76.4.f.a.27.25 | yes | 56 | |
19.12 | odd | 6 | inner | 76.4.f.a.31.25 | yes | 56 | |
76.31 | even | 6 | inner | 76.4.f.a.31.16 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.f.a.27.16 | ✓ | 56 | 1.1 | even | 1 | trivial | |
76.4.f.a.27.25 | yes | 56 | 4.3 | odd | 2 | inner | |
76.4.f.a.31.16 | yes | 56 | 76.31 | even | 6 | inner | |
76.4.f.a.31.25 | yes | 56 | 19.12 | odd | 6 | inner |