Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(25,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.l (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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 25.18 | ||
Character | \(\chi\) | \(=\) | 403.25 |
Dual form | 403.2.l.c.129.17 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0456796i | 0.0323003i | 0.999870 | + | 0.0161502i | \(0.00514098\pi\) | ||||
−0.999870 | + | 0.0161502i | \(0.994859\pi\) | |||||||
\(3\) | −1.38907 | − | 2.40594i | −0.801981 | − | 1.38907i | −0.918311 | − | 0.395860i | \(-0.870446\pi\) |
0.116330 | − | 0.993211i | \(-0.462887\pi\) | |||||||
\(4\) | 1.99791 | 0.998957 | ||||||||
\(5\) | 1.25901 | + | 0.726890i | 0.563046 | + | 0.325075i | 0.754367 | − | 0.656453i | \(-0.227944\pi\) |
−0.191321 | + | 0.981528i | \(0.561277\pi\) | |||||||
\(6\) | 0.109902 | − | 0.0634522i | 0.0448675 | − | 0.0259042i | ||||
\(7\) | 3.37083 | − | 1.94615i | 1.27405 | − | 0.735575i | 0.298305 | − | 0.954471i | \(-0.403579\pi\) |
0.975748 | + | 0.218896i | \(0.0702455\pi\) | |||||||
\(8\) | 0.182623i | 0.0645670i | ||||||||
\(9\) | −2.35904 | + | 4.08597i | −0.786346 | + | 1.36199i | ||||
\(10\) | −0.0332040 | + | 0.0575110i | −0.0105000 | + | 0.0181866i | ||||
\(11\) | 4.61476 | + | 2.66433i | 1.39140 | + | 0.803327i | 0.993471 | − | 0.114088i | \(-0.0363946\pi\) |
0.397932 | + | 0.917415i | \(0.369728\pi\) | |||||||
\(12\) | −2.77524 | − | 4.80686i | −0.801144 | − | 1.38762i | ||||
\(13\) | −2.43729 | + | 2.65700i | −0.675982 | + | 0.736918i | ||||
\(14\) | 0.0888992 | + | 0.153978i | 0.0237593 | + | 0.0411523i | ||||
\(15\) | − | 4.03881i | − | 1.04282i | ||||||
\(16\) | 3.98748 | 0.996871 | ||||||||
\(17\) | −0.180975 | − | 0.313457i | −0.0438928 | − | 0.0760246i | 0.843244 | − | 0.537530i | \(-0.180643\pi\) |
−0.887137 | + | 0.461506i | \(0.847309\pi\) | |||||||
\(18\) | −0.186645 | − | 0.107760i | −0.0439927 | − | 0.0253992i | ||||
\(19\) | −1.92657 | + | 1.11231i | −0.441986 | + | 0.255181i | −0.704440 | − | 0.709764i | \(-0.748802\pi\) |
0.262453 | + | 0.964945i | \(0.415468\pi\) | |||||||
\(20\) | 2.51539 | + | 1.45226i | 0.562459 | + | 0.324736i | ||||
\(21\) | −9.36464 | − | 5.40668i | −2.04353 | − | 1.17983i | ||||
\(22\) | −0.121706 | + | 0.210800i | −0.0259477 | + | 0.0449428i | ||||
\(23\) | 0.428612 | 0.0893718 | 0.0446859 | − | 0.999001i | \(-0.485771\pi\) | ||||
0.0446859 | + | 0.999001i | \(0.485771\pi\) | |||||||
\(24\) | 0.439380 | − | 0.253676i | 0.0896881 | − | 0.0517814i | ||||
\(25\) | −1.44326 | − | 2.49980i | −0.288653 | − | 0.499961i | ||||
\(26\) | −0.121370 | − | 0.111334i | −0.0238027 | − | 0.0218345i | ||||
\(27\) | 4.77305 | 0.918575 | ||||||||
\(28\) | 6.73462 | − | 3.88823i | 1.27272 | − | 0.734807i | ||||
\(29\) | −7.70065 | −1.42998 | −0.714988 | − | 0.699137i | \(-0.753568\pi\) | ||||
−0.714988 | + | 0.699137i | \(0.753568\pi\) | |||||||
\(30\) | 0.184491 | 0.0336833 | ||||||||
\(31\) | −5.49130 | − | 0.919550i | −0.986267 | − | 0.165156i | ||||
\(32\) | 0.547392i | 0.0967662i | ||||||||
\(33\) | − | 14.8038i | − | 2.57701i | ||||||
\(34\) | 0.0143186 | − | 0.00826685i | 0.00245562 | − | 0.00141775i | ||||
\(35\) | 5.65854 | 0.956468 | ||||||||
\(36\) | −4.71315 | + | 8.16342i | −0.785525 | + | 1.36057i | ||||
\(37\) | 5.16646 | − | 2.98286i | 0.849361 | − | 0.490379i | −0.0110742 | − | 0.999939i | \(-0.503525\pi\) |
0.860435 | + | 0.509560i | \(0.170192\pi\) | |||||||
\(38\) | −0.0508098 | − | 0.0880051i | −0.00824243 | − | 0.0142763i | ||||
\(39\) | 9.77814 | + | 2.17322i | 1.56576 | + | 0.347994i | ||||
\(40\) | −0.132747 | + | 0.229924i | −0.0209891 | + | 0.0363542i | ||||
\(41\) | 1.59673 | + | 0.921870i | 0.249367 | + | 0.143972i | 0.619474 | − | 0.785017i | \(-0.287346\pi\) |
−0.370108 | + | 0.928989i | \(0.620679\pi\) | |||||||
\(42\) | 0.246975 | − | 0.427773i | 0.0381090 | − | 0.0660067i | ||||
\(43\) | −4.68376 | − | 8.11250i | −0.714266 | − | 1.23715i | −0.963242 | − | 0.268636i | \(-0.913427\pi\) |
0.248976 | − | 0.968510i | \(-0.419906\pi\) | |||||||
\(44\) | 9.21989 | + | 5.32311i | 1.38995 | + | 0.802489i | ||||
\(45\) | −5.94010 | + | 3.42952i | −0.885498 | + | 0.511243i | ||||
\(46\) | 0.0195788i | 0.00288674i | ||||||||
\(47\) | 3.48799i | 0.508776i | 0.967102 | + | 0.254388i | \(0.0818741\pi\) | ||||
−0.967102 | + | 0.254388i | \(0.918126\pi\) | |||||||
\(48\) | −5.53890 | − | 9.59366i | −0.799471 | − | 1.38472i | ||||
\(49\) | 4.07498 | − | 7.05808i | 0.582140 | − | 1.00830i | ||||
\(50\) | 0.114190 | − | 0.0659276i | 0.0161489 | − | 0.00932357i | ||||
\(51\) | −0.502774 | + | 0.870829i | −0.0704024 | + | 0.121941i | ||||
\(52\) | −4.86949 | + | 5.30845i | −0.675277 | + | 0.736149i | ||||
\(53\) | −2.49130 | + | 4.31506i | −0.342206 | + | 0.592719i | −0.984842 | − | 0.173453i | \(-0.944507\pi\) |
0.642636 | + | 0.766172i | \(0.277841\pi\) | |||||||
\(54\) | 0.218031i | 0.0296703i | ||||||||
\(55\) | 3.87335 | + | 6.70884i | 0.522283 | + | 0.904620i | ||||
\(56\) | 0.355411 | + | 0.615590i | 0.0474938 | + | 0.0822617i | ||||
\(57\) | 5.35230 | + | 3.09015i | 0.708929 | + | 0.409300i | ||||
\(58\) | − | 0.351763i | − | 0.0461887i | ||||||
\(59\) | −12.0997 | + | 6.98577i | −1.57525 | + | 0.909470i | −0.579738 | + | 0.814803i | \(0.696845\pi\) |
−0.995509 | + | 0.0946669i | \(0.969821\pi\) | |||||||
\(60\) | − | 8.06918i | − | 1.04173i | ||||||
\(61\) | −11.3454 | −1.45263 | −0.726314 | − | 0.687363i | \(-0.758768\pi\) | ||||
−0.726314 | + | 0.687363i | \(0.758768\pi\) | |||||||
\(62\) | 0.0420047 | − | 0.250840i | 0.00533460 | − | 0.0318568i | ||||
\(63\) | 18.3641i | 2.31366i | ||||||||
\(64\) | 7.94996 | 0.993746 | ||||||||
\(65\) | −4.99991 | + | 1.57354i | −0.620163 | + | 0.195174i | ||||
\(66\) | 0.676231 | 0.0832383 | ||||||||
\(67\) | 9.07912 | + | 5.24183i | 1.10919 | + | 0.640392i | 0.938620 | − | 0.344954i | \(-0.112105\pi\) |
0.170571 | + | 0.985345i | \(0.445439\pi\) | |||||||
\(68\) | −0.361572 | − | 0.626261i | −0.0438470 | − | 0.0759453i | ||||
\(69\) | −0.595372 | − | 1.03122i | −0.0716744 | − | 0.124144i | ||||
\(70\) | 0.258480i | 0.0308942i | ||||||||
\(71\) | 1.24196 | + | 0.717045i | 0.147393 | + | 0.0850976i | 0.571883 | − | 0.820335i | \(-0.306213\pi\) |
−0.424490 | + | 0.905433i | \(0.639546\pi\) | |||||||
\(72\) | −0.746192 | − | 0.430814i | −0.0879396 | − | 0.0507719i | ||||
\(73\) | −11.8818 | − | 6.85998i | −1.39066 | − | 0.802900i | −0.397275 | − | 0.917700i | \(-0.630044\pi\) |
−0.993389 | + | 0.114800i | \(0.963377\pi\) | |||||||
\(74\) | 0.136256 | + | 0.236002i | 0.0158394 | + | 0.0274346i | ||||
\(75\) | −4.00959 | + | 6.94481i | −0.462987 | + | 0.801918i | ||||
\(76\) | −3.84913 | + | 2.22230i | −0.441525 | + | 0.254915i | ||||
\(77\) | 20.7407 | 2.36363 | ||||||||
\(78\) | −0.0992717 | + | 0.446661i | −0.0112403 | + | 0.0505744i | ||||
\(79\) | −1.88892 | − | 3.27171i | −0.212520 | − | 0.368096i | 0.739982 | − | 0.672626i | \(-0.234834\pi\) |
−0.952503 | + | 0.304530i | \(0.901500\pi\) | |||||||
\(80\) | 5.02028 | + | 2.89846i | 0.561285 | + | 0.324058i | ||||
\(81\) | 0.447000 | + | 0.774227i | 0.0496667 | + | 0.0860252i | ||||
\(82\) | −0.0421106 | + | 0.0729377i | −0.00465034 | + | 0.00805463i | ||||
\(83\) | 10.3146 | + | 5.95513i | 1.13217 | + | 0.653660i | 0.944480 | − | 0.328567i | \(-0.106566\pi\) |
0.187692 | + | 0.982228i | \(0.439899\pi\) | |||||||
\(84\) | −18.7097 | − | 10.8021i | −2.04140 | − | 1.17860i | ||||
\(85\) | − | 0.526195i | − | 0.0570738i | ||||||
\(86\) | 0.370576 | − | 0.213952i | 0.0399602 | − | 0.0230710i | ||||
\(87\) | 10.6968 | + | 18.5273i | 1.14681 | + | 1.98634i | ||||
\(88\) | −0.486568 | + | 0.842761i | −0.0518684 | + | 0.0898386i | ||||
\(89\) | 16.5238i | 1.75152i | 0.482747 | + | 0.875760i | \(0.339639\pi\) | ||||
−0.482747 | + | 0.875760i | \(0.660361\pi\) | |||||||
\(90\) | −0.156659 | − | 0.271341i | −0.0165133 | − | 0.0286019i | ||||
\(91\) | −3.04477 | + | 13.6996i | −0.319179 | + | 1.43611i | ||||
\(92\) | 0.856329 | 0.0892785 | ||||||||
\(93\) | 5.41543 | + | 14.4891i | 0.561554 | + | 1.50245i | ||||
\(94\) | −0.159330 | −0.0164336 | ||||||||
\(95\) | −3.23410 | −0.331812 | ||||||||
\(96\) | 1.31699 | − | 0.760367i | 0.134415 | − | 0.0776046i | ||||
\(97\) | − | 14.3360i | − | 1.45560i | −0.685788 | − | 0.727802i | \(-0.740542\pi\) | ||
0.685788 | − | 0.727802i | \(-0.259458\pi\) | |||||||
\(98\) | 0.322410 | + | 0.186143i | 0.0325683 | + | 0.0188033i | ||||
\(99\) | −21.7728 | + | 12.5705i | −2.18825 | + | 1.26338i | ||||
\(100\) | −2.88351 | − | 4.99439i | −0.288351 | − | 0.499439i | ||||
\(101\) | 12.5359 | 1.24737 | 0.623683 | − | 0.781677i | \(-0.285636\pi\) | ||||
0.623683 | + | 0.781677i | \(0.285636\pi\) | |||||||
\(102\) | −0.0397791 | − | 0.0229665i | −0.00393872 | − | 0.00227402i | ||||
\(103\) | −2.67855 | + | 4.63938i | −0.263925 | + | 0.457131i | −0.967281 | − | 0.253706i | \(-0.918350\pi\) |
0.703356 | + | 0.710837i | \(0.251684\pi\) | |||||||
\(104\) | −0.485228 | − | 0.445105i | −0.0475805 | − | 0.0436461i | ||||
\(105\) | −7.86011 | − | 13.6141i | −0.767069 | − | 1.32860i | ||||
\(106\) | −0.197110 | − | 0.113801i | −0.0191450 | − | 0.0110534i | ||||
\(107\) | −5.65905 | − | 9.80176i | −0.547081 | − | 0.947571i | −0.998473 | − | 0.0552458i | \(-0.982406\pi\) |
0.451392 | − | 0.892326i | \(-0.350928\pi\) | |||||||
\(108\) | 9.53615 | 0.917616 | ||||||||
\(109\) | 3.50754i | 0.335962i | 0.985790 | + | 0.167981i | \(0.0537247\pi\) | ||||
−0.985790 | + | 0.167981i | \(0.946275\pi\) | |||||||
\(110\) | −0.306457 | + | 0.176933i | −0.0292195 | + | 0.0168699i | ||||
\(111\) | −14.3532 | − | 8.28680i | −1.36234 | − | 0.786549i | ||||
\(112\) | 13.4411 | − | 7.76023i | 1.27007 | − | 0.733273i | ||||
\(113\) | 6.52165 | − | 11.2958i | 0.613505 | − | 1.06262i | −0.377140 | − | 0.926156i | \(-0.623092\pi\) |
0.990645 | − | 0.136466i | \(-0.0435743\pi\) | |||||||
\(114\) | −0.141157 | + | 0.244491i | −0.0132205 | + | 0.0228986i | ||||
\(115\) | 0.539627 | + | 0.311554i | 0.0503204 | + | 0.0290525i | ||||
\(116\) | −15.3852 | −1.42848 | ||||||||
\(117\) | −5.10675 | − | 16.2266i | −0.472119 | − | 1.50015i | ||||
\(118\) | −0.319107 | − | 0.552709i | −0.0293762 | − | 0.0508810i | ||||
\(119\) | −1.22007 | − | 0.704407i | −0.111844 | − | 0.0645729i | ||||
\(120\) | 0.737579 | 0.0673314 | ||||||||
\(121\) | 8.69734 | + | 15.0642i | 0.790668 | + | 1.36948i | ||||
\(122\) | − | 0.518253i | − | 0.0469204i | ||||||
\(123\) | − | 5.12217i | − | 0.461851i | ||||||
\(124\) | −10.9712 | − | 1.83718i | −0.985238 | − | 0.164984i | ||||
\(125\) | − | 11.4653i | − | 1.02548i | ||||||
\(126\) | −0.838866 | −0.0747321 | ||||||||
\(127\) | 0.152041 | + | 0.263343i | 0.0134915 | + | 0.0233679i | 0.872692 | − | 0.488271i | \(-0.162372\pi\) |
−0.859201 | + | 0.511638i | \(0.829039\pi\) | |||||||
\(128\) | 1.45794i | 0.128865i | ||||||||
\(129\) | −13.0121 | + | 22.5377i | −1.14566 | + | 1.98433i | ||||
\(130\) | −0.0718788 | − | 0.228394i | −0.00630418 | − | 0.0200315i | ||||
\(131\) | −2.18790 | − | 3.78955i | −0.191158 | − | 0.331095i | 0.754477 | − | 0.656327i | \(-0.227891\pi\) |
−0.945634 | + | 0.325232i | \(0.894557\pi\) | |||||||
\(132\) | − | 29.5767i | − | 2.57432i | ||||||
\(133\) | −4.32943 | + | 7.49880i | −0.375409 | + | 0.650228i | ||||
\(134\) | −0.239445 | + | 0.414730i | −0.0206849 | + | 0.0358272i | ||||
\(135\) | 6.00932 | + | 3.46948i | 0.517200 | + | 0.298606i | ||||
\(136\) | 0.0572445 | − | 0.0330501i | 0.00490868 | − | 0.00283403i | ||||
\(137\) | −5.51009 | − | 3.18125i | −0.470759 | − | 0.271793i | 0.245799 | − | 0.969321i | \(-0.420950\pi\) |
−0.716557 | + | 0.697528i | \(0.754283\pi\) | |||||||
\(138\) | 0.0471055 | − | 0.0271964i | 0.00400988 | − | 0.00231511i | ||||
\(139\) | 5.18457 | 0.439749 | 0.219875 | − | 0.975528i | \(-0.429435\pi\) | ||||
0.219875 | + | 0.975528i | \(0.429435\pi\) | |||||||
\(140\) | 11.3053 | 0.955470 | ||||||||
\(141\) | 8.39191 | − | 4.84507i | 0.706726 | − | 0.408029i | ||||
\(142\) | −0.0327543 | + | 0.0567321i | −0.00274868 | + | 0.00476085i | ||||
\(143\) | −18.3266 | + | 5.76765i | −1.53255 | + | 0.482315i | ||||
\(144\) | −9.40662 | + | 16.2928i | −0.783885 | + | 1.35773i | ||||
\(145\) | −9.69520 | − | 5.59753i | −0.805143 | − | 0.464849i | ||||
\(146\) | 0.313361 | − | 0.542757i | 0.0259339 | − | 0.0449189i | ||||
\(147\) | −22.6418 | −1.86746 | ||||||||
\(148\) | 10.3221 | − | 5.95949i | 0.848475 | − | 0.489867i | ||||
\(149\) | 13.3000 | − | 7.67878i | 1.08958 | − | 0.629070i | 0.156116 | − | 0.987739i | \(-0.450103\pi\) |
0.933465 | + | 0.358669i | \(0.116769\pi\) | |||||||
\(150\) | −0.317236 | − | 0.183156i | −0.0259022 | − | 0.0149546i | ||||
\(151\) | 0.418901i | 0.0340897i | 0.999855 | + | 0.0170449i | \(0.00542581\pi\) | ||||
−0.999855 | + | 0.0170449i | \(0.994574\pi\) | |||||||
\(152\) | −0.203133 | − | 0.351837i | −0.0164763 | − | 0.0285377i | ||||
\(153\) | 1.70770 | 0.138060 | ||||||||
\(154\) | 0.947428i | 0.0763459i | ||||||||
\(155\) | −6.24520 | − | 5.14930i | −0.501626 | − | 0.413601i | ||||
\(156\) | 19.5359 | + | 4.34191i | 1.56412 | + | 0.347631i | ||||
\(157\) | 2.15899 | 0.172306 | 0.0861530 | − | 0.996282i | \(-0.472543\pi\) | ||||
0.0861530 | + | 0.996282i | \(0.472543\pi\) | |||||||
\(158\) | 0.149450 | − | 0.0862851i | 0.0118896 | − | 0.00686447i | ||||
\(159\) | 13.8424 | 1.09777 | ||||||||
\(160\) | −0.397894 | + | 0.689173i | −0.0314563 | + | 0.0544839i | ||||
\(161\) | 1.44478 | − | 0.834142i | 0.113864 | − | 0.0657396i | ||||
\(162\) | −0.0353663 | + | 0.0204188i | −0.00277864 | + | 0.00160425i | ||||
\(163\) | 15.3206i | 1.20000i | 0.800000 | + | 0.600000i | \(0.204833\pi\) | ||||
−0.800000 | + | 0.600000i | \(0.795167\pi\) | |||||||
\(164\) | 3.19012 | + | 1.84182i | 0.249107 | + | 0.143822i | ||||
\(165\) | 10.7607 | − | 18.6381i | 0.837721 | − | 1.45098i | ||||
\(166\) | −0.272028 | + | 0.471166i | −0.0211134 | + | 0.0365696i | ||||
\(167\) | 17.2091 | − | 9.93568i | 1.33168 | − | 0.768846i | 0.346123 | − | 0.938189i | \(-0.387498\pi\) |
0.985557 | + | 0.169344i | \(0.0541648\pi\) | |||||||
\(168\) | 0.987383 | − | 1.71020i | 0.0761783 | − | 0.131945i | ||||
\(169\) | −1.11925 | − | 12.9517i | −0.0860958 | − | 0.996287i | ||||
\(170\) | 0.0240363 | 0.00184350 | ||||||||
\(171\) | − | 10.4959i | − | 0.802642i | ||||||
\(172\) | −9.35774 | − | 16.2081i | −0.713521 | − | 1.23585i | ||||
\(173\) | −1.91073 | + | 3.30947i | −0.145270 | + | 0.251615i | −0.929474 | − | 0.368889i | \(-0.879738\pi\) |
0.784204 | + | 0.620503i | \(0.213072\pi\) | |||||||
\(174\) | −0.846320 | + | 0.488623i | −0.0641594 | + | 0.0370424i | ||||
\(175\) | −9.72998 | − | 5.61760i | −0.735517 | − | 0.424651i | ||||
\(176\) | 18.4013 | + | 10.6240i | 1.38705 | + | 0.800813i | ||||
\(177\) | 33.6147 | + | 19.4075i | 2.52664 | + | 1.45875i | ||||
\(178\) | −0.754800 | −0.0565747 | ||||||||
\(179\) | 3.03131 | + | 5.25038i | 0.226571 | + | 0.392432i | 0.956790 | − | 0.290781i | \(-0.0939152\pi\) |
−0.730219 | + | 0.683213i | \(0.760582\pi\) | |||||||
\(180\) | −11.8678 | + | 6.85188i | −0.884574 | + | 0.510709i | ||||
\(181\) | 3.55562 | − | 6.15851i | 0.264287 | − | 0.457758i | −0.703090 | − | 0.711101i | \(-0.748197\pi\) |
0.967377 | + | 0.253343i | \(0.0815301\pi\) | |||||||
\(182\) | −0.625792 | − | 0.139084i | −0.0463868 | − | 0.0103096i | ||||
\(183\) | 15.7596 | + | 27.2964i | 1.16498 | + | 2.01780i | ||||
\(184\) | 0.0782744i | 0.00577046i | ||||||||
\(185\) | 8.67284 | 0.637640 | ||||||||
\(186\) | −0.661855 | + | 0.247374i | −0.0485296 | + | 0.0181384i | ||||
\(187\) | − | 1.92871i | − | 0.141041i | ||||||
\(188\) | 6.96871i | 0.508245i | ||||||||
\(189\) | 16.0891 | − | 9.28907i | 1.17031 | − | 0.675680i | ||||
\(190\) | − | 0.147732i | − | 0.0107176i | ||||||
\(191\) | −5.02568 | + | 8.70473i | −0.363645 | + | 0.629852i | −0.988558 | − | 0.150843i | \(-0.951801\pi\) |
0.624912 | + | 0.780695i | \(0.285135\pi\) | |||||||
\(192\) | −11.0431 | − | 19.1272i | −0.796965 | − | 1.38038i | ||||
\(193\) | 0.620882 | − | 0.358467i | 0.0446921 | − | 0.0258030i | −0.477487 | − | 0.878639i | \(-0.658452\pi\) |
0.522180 | + | 0.852836i | \(0.325119\pi\) | |||||||
\(194\) | 0.654864 | 0.0470165 | ||||||||
\(195\) | 10.7311 | + | 9.84374i | 0.768469 | + | 0.704925i | ||||
\(196\) | 8.14146 | − | 14.1014i | 0.581533 | − | 1.00724i | ||||
\(197\) | −4.76127 | − | 2.74892i | −0.339227 | − | 0.195853i | 0.320703 | − | 0.947180i | \(-0.396081\pi\) |
−0.659930 | + | 0.751327i | \(0.729414\pi\) | |||||||
\(198\) | −0.574216 | − | 0.994571i | −0.0408078 | − | 0.0706811i | ||||
\(199\) | 7.59611 | − | 13.1569i | 0.538474 | − | 0.932665i | −0.460512 | − | 0.887653i | \(-0.652334\pi\) |
0.998986 | − | 0.0450113i | \(-0.0143324\pi\) | |||||||
\(200\) | 0.456522 | − | 0.263573i | 0.0322810 | − | 0.0186374i | ||||
\(201\) | − | 29.1251i | − | 2.05433i | ||||||
\(202\) | 0.572633i | 0.0402903i | ||||||||
\(203\) | −25.9576 | + | 14.9866i | −1.82186 | + | 1.05185i | ||||
\(204\) | −1.00450 | + | 1.73984i | −0.0703289 | + | 0.121813i | ||||
\(205\) | 1.34020 | + | 2.32129i | 0.0936033 | + | 0.162126i | ||||
\(206\) | −0.211925 | − | 0.122355i | −0.0147655 | − | 0.00852486i | ||||
\(207\) | −1.01111 | + | 1.75130i | −0.0702771 | + | 0.121723i | ||||
\(208\) | −9.71865 | + | 10.5947i | −0.673867 | + | 0.734612i | ||||
\(209\) | −11.8542 | −0.819975 | ||||||||
\(210\) | 0.621887 | − | 0.359047i | 0.0429143 | − | 0.0247766i | ||||
\(211\) | 11.4894 | + | 19.9002i | 0.790962 | + | 1.36999i | 0.925372 | + | 0.379060i | \(0.123753\pi\) |
−0.134410 | + | 0.990926i | \(0.542914\pi\) | |||||||
\(212\) | −4.97740 | + | 8.62111i | −0.341849 | + | 0.592100i | ||||
\(213\) | − | 3.98411i | − | 0.272986i | ||||||
\(214\) | 0.447740 | − | 0.258503i | 0.0306069 | − | 0.0176709i | ||||
\(215\) | − | 13.6183i | − | 0.928760i | ||||||
\(216\) | 0.871669i | 0.0593096i | ||||||||
\(217\) | −20.2998 | + | 7.58725i | −1.37804 | + | 0.515056i | ||||
\(218\) | −0.160223 | −0.0108517 | ||||||||
\(219\) | 38.1160i | 2.57564i | ||||||||
\(220\) | 7.73862 | + | 13.4037i | 0.521738 | + | 0.903677i | ||||
\(221\) | 1.27394 | + | 0.283137i | 0.0856947 | + | 0.0190459i | ||||
\(222\) | 0.378538 | − | 0.655646i | 0.0254058 | − | 0.0440041i | ||||
\(223\) | 0.675531 | − | 0.390018i | 0.0452369 | − | 0.0261175i | −0.477211 | − | 0.878789i | \(-0.658352\pi\) |
0.522448 | + | 0.852671i | \(0.325019\pi\) | |||||||
\(224\) | 1.06531 | + | 1.84517i | 0.0711788 | + | 0.123285i | ||||
\(225\) | 13.6188 | 0.907923 | ||||||||
\(226\) | 0.515988 | + | 0.297906i | 0.0343230 | + | 0.0198164i | ||||
\(227\) | 3.25775 | + | 1.88086i | 0.216225 | + | 0.124837i | 0.604201 | − | 0.796832i | \(-0.293492\pi\) |
−0.387976 | + | 0.921669i | \(0.626826\pi\) | |||||||
\(228\) | 10.6934 | + | 6.17385i | 0.708189 | + | 0.408873i | ||||
\(229\) | −2.54141 | + | 1.46728i | −0.167941 | + | 0.0969608i | −0.581615 | − | 0.813464i | \(-0.697579\pi\) |
0.413674 | + | 0.910425i | \(0.364245\pi\) | |||||||
\(230\) | −0.0142316 | + | 0.0246499i | −0.000938406 | + | 0.00162537i | ||||
\(231\) | −28.8104 | − | 49.9010i | −1.89558 | − | 3.28325i | ||||
\(232\) | − | 1.40632i | − | 0.0923292i | ||||||
\(233\) | −9.22280 | −0.604205 | −0.302103 | − | 0.953275i | \(-0.597689\pi\) | ||||
−0.302103 | + | 0.953275i | \(0.597689\pi\) | |||||||
\(234\) | 0.741226 | − | 0.233274i | 0.0484555 | − | 0.0152496i | ||||
\(235\) | −2.53539 | + | 4.39142i | −0.165390 | + | 0.286465i | ||||
\(236\) | −24.1742 | + | 13.9570i | −1.57360 | + | 0.908521i | ||||
\(237\) | −5.24769 | + | 9.08927i | −0.340874 | + | 0.590411i | ||||
\(238\) | 0.0321770 | − | 0.0557322i | 0.00208573 | − | 0.00361258i | ||||
\(239\) | −5.22248 | − | 3.01520i | −0.337814 | − | 0.195037i | 0.321491 | − | 0.946913i | \(-0.395816\pi\) |
−0.659305 | + | 0.751876i | \(0.729149\pi\) | |||||||
\(240\) | − | 16.1047i | − | 1.03955i | ||||||
\(241\) | −7.07505 | + | 4.08478i | −0.455744 | + | 0.263124i | −0.710253 | − | 0.703946i | \(-0.751420\pi\) |
0.254509 | + | 0.967070i | \(0.418086\pi\) | |||||||
\(242\) | −0.688128 | + | 0.397291i | −0.0442345 | + | 0.0255388i | ||||
\(243\) | 8.40141 | − | 14.5517i | 0.538951 | − | 0.933490i | ||||
\(244\) | −22.6671 | −1.45111 | ||||||||
\(245\) | 10.2609 | − | 5.92413i | 0.655544 | − | 0.378479i | ||||
\(246\) | 0.233979 | 0.0149179 | ||||||||
\(247\) | 1.74022 | − | 7.82991i | 0.110728 | − | 0.498206i | ||||
\(248\) | 0.167931 | − | 1.00284i | 0.0106636 | − | 0.0636803i | ||||
\(249\) | − | 33.0884i | − | 2.09689i | ||||||
\(250\) | 0.523728 | 0.0331235 | ||||||||
\(251\) | 13.8774 | + | 24.0364i | 0.875934 | + | 1.51716i | 0.855765 | + | 0.517365i | \(0.173087\pi\) |
0.0201694 | + | 0.999797i | \(0.493579\pi\) | |||||||
\(252\) | 36.6900i | 2.31125i | ||||||||
\(253\) | 1.97794 | + | 1.14196i | 0.124352 | + | 0.0717947i | ||||
\(254\) | −0.0120294 | + | 0.00694518i | −0.000754792 | + | 0.000435779i | ||||
\(255\) | −1.26599 | + | 0.730922i | −0.0792796 | + | 0.0457721i | ||||
\(256\) | 15.8333 | 0.989583 | ||||||||
\(257\) | −4.00758 | + | 6.94133i | −0.249986 | + | 0.432988i | −0.963522 | − | 0.267630i | \(-0.913759\pi\) |
0.713536 | + | 0.700619i | \(0.247093\pi\) | |||||||
\(258\) | −1.02951 | − | 0.594389i | −0.0640946 | − | 0.0370050i | ||||
\(259\) | 11.6102 | − | 20.1094i | 0.721421 | − | 1.24954i | ||||
\(260\) | −9.98939 | + | 3.14380i | −0.619516 | + | 0.194970i | ||||
\(261\) | 18.1661 | − | 31.4647i | 1.12445 | − | 1.94761i | ||||
\(262\) | 0.173105 | − | 0.0999422i | 0.0106945 | − | 0.00617445i | ||||
\(263\) | 2.00561 | 0.123671 | 0.0618355 | − | 0.998086i | \(-0.480305\pi\) | ||||
0.0618355 | + | 0.998086i | \(0.480305\pi\) | |||||||
\(264\) | 2.70351 | 0.166390 | ||||||||
\(265\) | −6.27314 | + | 3.62180i | −0.385356 | + | 0.222485i | ||||
\(266\) | −0.342542 | − | 0.197767i | −0.0210026 | − | 0.0121258i | ||||
\(267\) | 39.7553 | − | 22.9527i | 2.43298 | − | 1.40468i | ||||
\(268\) | 18.1393 | + | 10.4727i | 1.10803 | + | 0.639724i | ||||
\(269\) | −6.12969 | + | 10.6169i | −0.373734 | + | 0.647326i | −0.990137 | − | 0.140105i | \(-0.955256\pi\) |
0.616403 | + | 0.787431i | \(0.288589\pi\) | |||||||
\(270\) | −0.158485 | + | 0.274503i | −0.00964506 | + | 0.0167057i | ||||
\(271\) | − | 15.2475i | − | 0.926219i | −0.886301 | − | 0.463110i | \(-0.846734\pi\) | ||
0.886301 | − | 0.463110i | \(-0.153266\pi\) | |||||||
\(272\) | −0.721634 | − | 1.24991i | −0.0437555 | − | 0.0757867i | ||||
\(273\) | 37.1898 | − | 11.7042i | 2.25083 | − | 0.708368i | ||||
\(274\) | 0.145318 | − | 0.251698i | 0.00877899 | − | 0.0152057i | ||||
\(275\) | − | 15.3813i | − | 0.927529i | ||||||
\(276\) | −1.18950 | − | 2.06028i | −0.0715996 | − | 0.124014i | ||||
\(277\) | −5.74669 | −0.345285 | −0.172643 | − | 0.984985i | \(-0.555231\pi\) | ||||
−0.172643 | + | 0.984985i | \(0.555231\pi\) | |||||||
\(278\) | 0.236829i | 0.0142040i | ||||||||
\(279\) | 16.7114 | − | 20.2681i | 1.00049 | − | 1.21342i | ||||
\(280\) | 1.03338i | 0.0617562i | ||||||||
\(281\) | − | 23.5073i | − | 1.40233i | −0.713000 | − | 0.701164i | \(-0.752664\pi\) | ||
0.713000 | − | 0.701164i | \(-0.247336\pi\) | |||||||
\(282\) | 0.221321 | + | 0.383339i | 0.0131795 | + | 0.0228275i | ||||
\(283\) | −6.94506 | −0.412841 | −0.206420 | − | 0.978463i | \(-0.566181\pi\) | ||||
−0.206420 | + | 0.978463i | \(0.566181\pi\) | |||||||
\(284\) | 2.48132 | + | 1.43259i | 0.147240 | + | 0.0850088i | ||||
\(285\) | 4.49240 | + | 7.78106i | 0.266107 | + | 0.460910i | ||||
\(286\) | −0.263464 | − | 0.837152i | −0.0155789 | − | 0.0495019i | ||||
\(287\) | 7.17638 | 0.423608 | ||||||||
\(288\) | −2.23663 | − | 1.29132i | −0.131795 | − | 0.0760917i | ||||
\(289\) | 8.43450 | − | 14.6090i | 0.496147 | − | 0.859352i | ||||
\(290\) | 0.255693 | − | 0.442873i | 0.0150148 | − | 0.0260064i | ||||
\(291\) | −34.4917 | + | 19.9138i | −2.02194 | + | 1.16737i | ||||
\(292\) | −23.7389 | − | 13.7056i | −1.38921 | − | 0.802062i | ||||
\(293\) | −11.2418 | + | 6.49047i | −0.656754 | + | 0.379177i | −0.791039 | − | 0.611766i | \(-0.790460\pi\) |
0.134285 | + | 0.990943i | \(0.457126\pi\) | |||||||
\(294\) | − | 1.03427i | − | 0.0603196i | ||||||
\(295\) | −20.3115 | −1.18258 | ||||||||
\(296\) | 0.544738 | + | 0.943514i | 0.0316623 | + | 0.0548407i | ||||
\(297\) | 22.0265 | + | 12.7170i | 1.27811 | + | 0.737915i | ||||
\(298\) | 0.350763 | + | 0.607540i | 0.0203192 | + | 0.0351938i | ||||
\(299\) | −1.04465 | + | 1.13882i | −0.0604137 | + | 0.0658596i | ||||
\(300\) | −8.01081 | + | 13.8751i | −0.462504 | + | 0.801081i | ||||
\(301\) | −31.5763 | − | 18.2306i | −1.82003 | − | 1.05079i | ||||
\(302\) | −0.0191352 | −0.00110111 | ||||||||
\(303\) | −17.4132 | − | 30.1606i | −1.00036 | − | 1.73268i | ||||
\(304\) | −7.68218 | + | 4.43531i | −0.440604 | + | 0.254383i | ||||
\(305\) | −14.2840 | − | 8.24685i | −0.817898 | − | 0.472213i | ||||
\(306\) | 0.0780072i | 0.00445937i | ||||||||
\(307\) | 13.7200 | − | 7.92122i | 0.783040 | − | 0.452088i | −0.0544669 | − | 0.998516i | \(-0.517346\pi\) |
0.837506 | + | 0.546427i | \(0.184013\pi\) | |||||||
\(308\) | 41.4382 | 2.36116 | ||||||||
\(309\) | 14.8828 | 0.846651 | ||||||||
\(310\) | 0.235218 | − | 0.285278i | 0.0133595 | − | 0.0162027i | ||||
\(311\) | −20.1613 | −1.14325 | −0.571623 | − | 0.820517i | \(-0.693686\pi\) | ||||
−0.571623 | + | 0.820517i | \(0.693686\pi\) | |||||||
\(312\) | −0.396880 | + | 1.78571i | −0.0224689 | + | 0.101096i | ||||
\(313\) | 7.60195 | + | 13.1670i | 0.429688 | + | 0.744241i | 0.996845 | − | 0.0793685i | \(-0.0252904\pi\) |
−0.567158 | + | 0.823609i | \(0.691957\pi\) | |||||||
\(314\) | 0.0986217i | 0.00556554i | ||||||||
\(315\) | −13.3487 | + | 23.1206i | −0.752114 | + | 1.30270i | ||||
\(316\) | −3.77390 | − | 6.53659i | −0.212299 | − | 0.367712i | ||||
\(317\) | −4.85475 | + | 2.80289i | −0.272670 | + | 0.157426i | −0.630100 | − | 0.776514i | \(-0.716986\pi\) |
0.357431 | + | 0.933940i | \(0.383653\pi\) | |||||||
\(318\) | 0.632313i | 0.0354584i | ||||||||
\(319\) | −35.5367 | − | 20.5171i | −1.98967 | − | 1.14874i | ||||
\(320\) | 10.0091 | + | 5.77875i | 0.559525 | + | 0.323042i | ||||
\(321\) | −15.7216 | + | 27.2307i | −0.877496 | + | 1.51987i | ||||
\(322\) | 0.0381033 | + | 0.0659968i | 0.00212341 | + | 0.00367786i | ||||
\(323\) | 0.697323 | + | 0.402599i | 0.0388001 | + | 0.0224012i | ||||
\(324\) | 0.893067 | + | 1.54684i | 0.0496149 | + | 0.0859355i | ||||
\(325\) | 10.1596 | + | 2.25800i | 0.563554 | + | 0.125251i | ||||
\(326\) | −0.699837 | −0.0387604 | ||||||||
\(327\) | 8.43895 | − | 4.87223i | 0.466675 | − | 0.269435i | ||||
\(328\) | −0.168355 | + | 0.291599i | −0.00929583 | + | 0.0161009i | ||||
\(329\) | 6.78815 | + | 11.7574i | 0.374243 | + | 0.648208i | ||||
\(330\) | 0.851381 | + | 0.491545i | 0.0468670 | + | 0.0270587i | ||||
\(331\) | 16.1012 | + | 9.29600i | 0.884999 | + | 0.510955i | 0.872304 | − | 0.488965i | \(-0.162625\pi\) |
0.0126958 | + | 0.999919i | \(0.495959\pi\) | |||||||
\(332\) | 20.6077 | + | 11.8978i | 1.13099 | + | 0.652978i | ||||
\(333\) | 28.1467i | 1.54243i | ||||||||
\(334\) | 0.453857 | + | 0.786104i | 0.0248340 | + | 0.0430137i | ||||
\(335\) | 7.62047 | + | 13.1990i | 0.416351 | + | 0.721141i | ||||
\(336\) | −37.3413 | − | 21.5590i | −2.03714 | − | 1.17614i | ||||
\(337\) | −1.60605 | −0.0874871 | −0.0437435 | − | 0.999043i | \(-0.513928\pi\) | ||||
−0.0437435 | + | 0.999043i | \(0.513928\pi\) | |||||||
\(338\) | 0.591629 | − | 0.0511267i | 0.0321804 | − | 0.00278092i | ||||
\(339\) | −36.2361 | −1.96808 | ||||||||
\(340\) | − | 1.05129i | − | 0.0570143i | ||||||
\(341\) | −22.8911 | − | 18.8742i | −1.23962 | − | 1.02209i | ||||
\(342\) | 0.479448 | 0.0259256 | ||||||||
\(343\) | − | 4.47601i | − | 0.241682i | ||||||
\(344\) | 1.48153 | − | 0.855361i | 0.0798787 | − | 0.0461180i | ||||
\(345\) | − | 1.73108i | − | 0.0931982i | ||||||
\(346\) | −0.151175 | − | 0.0872811i | −0.00812723 | − | 0.00469226i | ||||
\(347\) | 0.940923 | + | 1.62973i | 0.0505114 | + | 0.0874883i | 0.890176 | − | 0.455618i | \(-0.150582\pi\) |
−0.839664 | + | 0.543106i | \(0.817248\pi\) | |||||||
\(348\) | 21.3712 | + | 37.0160i | 1.14562 | + | 1.98427i | ||||
\(349\) | 23.6256i | 1.26465i | 0.774704 | + | 0.632324i | \(0.217899\pi\) | ||||
−0.774704 | + | 0.632324i | \(0.782101\pi\) | |||||||
\(350\) | 0.256610 | − | 0.444461i | 0.0137164 | − | 0.0237574i | ||||
\(351\) | −11.6333 | + | 12.6820i | −0.620940 | + | 0.676914i | ||||
\(352\) | −1.45844 | + | 2.52609i | −0.0777349 | + | 0.134641i | ||||
\(353\) | −17.0288 | + | 9.83158i | −0.906352 | + | 0.523282i | −0.879256 | − | 0.476350i | \(-0.841959\pi\) |
−0.0270963 | + | 0.999633i | \(0.508626\pi\) | |||||||
\(354\) | −0.886524 | + | 1.53550i | −0.0471182 | + | 0.0816112i | ||||
\(355\) | 1.04243 | + | 1.80553i | 0.0553262 | + | 0.0958278i | ||||
\(356\) | 33.0131i | 1.74969i | ||||||||
\(357\) | 3.91389i | 0.207145i | ||||||||
\(358\) | −0.239835 | + | 0.138469i | −0.0126757 | + | 0.00731831i | ||||
\(359\) | 6.07359 | + | 3.50659i | 0.320552 | + | 0.185071i | 0.651638 | − | 0.758530i | \(-0.274082\pi\) |
−0.331087 | + | 0.943600i | \(0.607415\pi\) | |||||||
\(360\) | −0.626309 | − | 1.08480i | −0.0330094 | − | 0.0571739i | ||||
\(361\) | −7.02554 | + | 12.1686i | −0.369765 | + | 0.640452i | ||||
\(362\) | 0.281318 | + | 0.162419i | 0.0147857 | + | 0.00853655i | ||||
\(363\) | 24.1625 | − | 41.8506i | 1.26820 | − | 2.19659i | ||||
\(364\) | −6.08319 | + | 27.3706i | −0.318846 | + | 1.43461i | ||||
\(365\) | −9.97290 | − | 17.2736i | −0.522005 | − | 0.904140i | ||||
\(366\) | −1.24689 | + | 0.719890i | −0.0651758 | + | 0.0376292i | ||||
\(367\) | 13.1443 | − | 22.7666i | 0.686126 | − | 1.18841i | −0.286955 | − | 0.957944i | \(-0.592643\pi\) |
0.973081 | − | 0.230462i | \(-0.0740236\pi\) | |||||||
\(368\) | 1.70908 | 0.0890921 | ||||||||
\(369\) | −7.53347 | + | 4.34945i | −0.392177 | + | 0.226423i | ||||
\(370\) | 0.396171i | 0.0205960i | ||||||||
\(371\) | 19.3937i | 1.00687i | ||||||||
\(372\) | 10.8196 | + | 28.9479i | 0.560968 | + | 1.50088i | ||||
\(373\) | −0.891291 | −0.0461493 | −0.0230747 | − | 0.999734i | \(-0.507346\pi\) | ||||
−0.0230747 | + | 0.999734i | \(0.507346\pi\) | |||||||
\(374\) | 0.0881025 | 0.00455567 | ||||||||
\(375\) | −27.5848 | + | 15.9261i | −1.42447 | + | 0.822419i | ||||
\(376\) | −0.636988 | −0.0328501 | ||||||||
\(377\) | 18.7687 | − | 20.4606i | 0.966638 | − | 1.05377i | ||||
\(378\) | 0.424321 | + | 0.734945i | 0.0218247 | + | 0.0378015i | ||||
\(379\) | −6.00363 | + | 3.46620i | −0.308386 | + | 0.178046i | −0.646204 | − | 0.763165i | \(-0.723644\pi\) |
0.337818 | + | 0.941211i | \(0.390311\pi\) | |||||||
\(380\) | −6.46145 | −0.331466 | ||||||||
\(381\) | 0.422392 | − | 0.731605i | 0.0216398 | − | 0.0374813i | ||||
\(382\) | −0.397628 | − | 0.229571i | −0.0203444 | − | 0.0117459i | ||||
\(383\) | −1.27372 | − | 0.735384i | −0.0650841 | − | 0.0375763i | 0.467105 | − | 0.884202i | \(-0.345297\pi\) |
−0.532189 | + | 0.846626i | \(0.678630\pi\) | |||||||
\(384\) | 3.50771 | − | 2.02518i | 0.179002 | − | 0.103347i | ||||
\(385\) | 26.1128 | + | 15.0762i | 1.33083 | + | 0.768356i | ||||
\(386\) | 0.0163746 | + | 0.0283616i | 0.000833445 | + | 0.00144357i | ||||
\(387\) | 44.1966 | 2.24664 | ||||||||
\(388\) | − | 28.6422i | − | 1.45408i | ||||||
\(389\) | −15.4827 | − | 26.8168i | −0.785002 | − | 1.35966i | −0.928998 | − | 0.370085i | \(-0.879329\pi\) |
0.143996 | − | 0.989578i | \(-0.454005\pi\) | |||||||
\(390\) | −0.449658 | + | 0.490191i | −0.0227693 | + | 0.0248218i | ||||
\(391\) | −0.0775679 | − | 0.134352i | −0.00392278 | − | 0.00679445i | ||||
\(392\) | 1.28897 | + | 0.744185i | 0.0651027 | + | 0.0375870i | ||||
\(393\) | −6.07829 | + | 10.5279i | −0.306609 | + | 0.531063i | ||||
\(394\) | 0.125570 | − | 0.217493i | 0.00632610 | − | 0.0109571i | ||||
\(395\) | − | 5.49215i | − | 0.276340i | ||||||
\(396\) | −43.5001 | + | 25.1148i | −2.18596 | + | 1.26207i | ||||
\(397\) | −11.8136 | + | 6.82056i | −0.592906 | + | 0.342314i | −0.766246 | − | 0.642548i | \(-0.777877\pi\) |
0.173340 | + | 0.984862i | \(0.444544\pi\) | |||||||
\(398\) | 0.600999 | + | 0.346987i | 0.0301254 | + | 0.0173929i | ||||
\(399\) | 24.0556 | 1.20428 | ||||||||
\(400\) | −5.75499 | − | 9.96793i | −0.287749 | − | 0.498397i | ||||
\(401\) | 18.9283i | 0.945235i | 0.881268 | + | 0.472617i | \(0.156691\pi\) | ||||
−0.881268 | + | 0.472617i | \(0.843309\pi\) | |||||||
\(402\) | 1.33042 | 0.0663554 | ||||||||
\(403\) | 15.8271 | − | 12.3492i | 0.788406 | − | 0.615155i | ||||
\(404\) | 25.0456 | 1.24607 | ||||||||
\(405\) | 1.29968i | 0.0645816i | ||||||||
\(406\) | −0.684582 | − | 1.18573i | −0.0339752 | − | 0.0588468i | ||||
\(407\) | 31.7893 | 1.57574 | ||||||||
\(408\) | −0.159033 | − | 0.0918180i | −0.00787333 | − | 0.00454567i | ||||
\(409\) | 23.6452 | − | 13.6515i | 1.16918 | − | 0.675025i | 0.215691 | − | 0.976462i | \(-0.430799\pi\) |
0.953486 | + | 0.301436i | \(0.0974661\pi\) | |||||||
\(410\) | −0.106035 | + | 0.0612196i | −0.00523672 | + | 0.00302342i | ||||
\(411\) | 17.6759i | 0.871890i | ||||||||
\(412\) | −5.35150 | + | 9.26907i | −0.263650 | + | 0.456654i | ||||
\(413\) | −27.1907 | + | 47.0956i | −1.33797 | + | 2.31742i | ||||
\(414\) | −0.0799984 | − | 0.0461871i | −0.00393171 | − | 0.00226997i | ||||
\(415\) | 8.65745 | + | 14.9951i | 0.424977 | + | 0.736082i | ||||
\(416\) | −1.45442 | − | 1.33415i | −0.0713088 | − | 0.0654123i | ||||
\(417\) | −7.20173 | − | 12.4738i | −0.352670 | − | 0.610843i | ||||
\(418\) | − | 0.541496i | − | 0.0264855i | ||||||
\(419\) | −7.67420 | −0.374909 | −0.187455 | − | 0.982273i | \(-0.560024\pi\) | ||||
−0.187455 | + | 0.982273i | \(0.560024\pi\) | |||||||
\(420\) | −15.7038 | − | 27.1998i | −0.766268 | − | 1.32722i | ||||
\(421\) | −9.77317 | − | 5.64254i | −0.476315 | − | 0.275001i | 0.242564 | − | 0.970135i | \(-0.422011\pi\) |
−0.718880 | + | 0.695135i | \(0.755345\pi\) | |||||||
\(422\) | −0.909032 | + | 0.524830i | −0.0442510 | + | 0.0255483i | ||||
\(423\) | −14.2518 | − | 8.22831i | −0.692948 | − | 0.400074i | ||||
\(424\) | −0.788028 | − | 0.454968i | −0.0382700 | − | 0.0220952i | ||||
\(425\) | −0.522388 | + | 0.904803i | −0.0253395 | + | 0.0438894i | ||||
\(426\) | 0.181992 | 0.00881755 | ||||||||
\(427\) | −38.2434 | + | 22.0798i | −1.85073 | + | 1.06852i | ||||
\(428\) | −11.3063 | − | 19.5831i | −0.546510 | − | 0.946583i | ||||
\(429\) | 39.3336 | + | 36.0811i | 1.89904 | + | 1.74201i | ||||
\(430\) | 0.622078 | 0.0299993 | ||||||||
\(431\) | 9.75404 | − | 5.63150i | 0.469836 | − | 0.271260i | −0.246335 | − | 0.969185i | \(-0.579226\pi\) |
0.716171 | + | 0.697925i | \(0.245893\pi\) | |||||||
\(432\) | 19.0325 | 0.915701 | ||||||||
\(433\) | 2.41491 | 0.116053 | 0.0580267 | − | 0.998315i | \(-0.481519\pi\) | ||||
0.0580267 | + | 0.998315i | \(0.481519\pi\) | |||||||
\(434\) | −0.346582 | − | 0.927287i | −0.0166365 | − | 0.0445112i | ||||
\(435\) | 31.1014i | 1.49120i | ||||||||
\(436\) | 7.00777i | 0.335611i | ||||||||
\(437\) | −0.825753 | + | 0.476749i | −0.0395011 | + | 0.0228060i | ||||
\(438\) | −1.74112 | −0.0831940 | ||||||||
\(439\) | 7.81146 | − | 13.5298i | 0.372821 | − | 0.645744i | −0.617178 | − | 0.786824i | \(-0.711724\pi\) |
0.989998 | + | 0.141079i | \(0.0450573\pi\) | |||||||
\(440\) | −1.22519 | + | 0.707363i | −0.0584086 | + | 0.0337222i | ||||
\(441\) | 19.2261 | + | 33.3005i | 0.915527 | + | 1.58574i | ||||
\(442\) | −0.0129336 | + | 0.0581931i | −0.000615188 | + | 0.00276797i | ||||
\(443\) | −5.53076 | + | 9.57956i | −0.262774 | + | 0.455138i | −0.966978 | − | 0.254859i | \(-0.917971\pi\) |
0.704204 | + | 0.709998i | \(0.251304\pi\) | |||||||
\(444\) | −28.6764 | − | 16.5563i | −1.36092 | − | 0.785728i | ||||
\(445\) | −12.0110 | + | 20.8036i | −0.569375 | + | 0.986187i | ||||
\(446\) | 0.0178159 | + | 0.0308580i | 0.000843605 | + | 0.00146117i | ||||
\(447\) | −36.9494 | − | 21.3327i | −1.74765 | − | 1.00900i | ||||
\(448\) | 26.7980 | − | 15.4718i | 1.26608 | − | 0.730974i | ||||
\(449\) | 10.7069i | 0.505290i | 0.967559 | + | 0.252645i | \(0.0813005\pi\) | ||||
−0.967559 | + | 0.252645i | \(0.918700\pi\) | |||||||
\(450\) | 0.622103i | 0.0293262i | ||||||||
\(451\) | 4.91234 | + | 8.50842i | 0.231313 | + | 0.400646i | ||||
\(452\) | 13.0297 | − | 22.5681i | 0.612865 | − | 1.06151i | ||||
\(453\) | 1.00785 | − | 0.581884i | 0.0473530 | − | 0.0273393i | ||||
\(454\) | −0.0859170 | + | 0.148813i | −0.00403229 | + | 0.00698412i | ||||
\(455\) | −13.7915 | + | 15.0347i | −0.646555 | + | 0.704838i | ||||
\(456\) | −0.564332 | + | 0.977452i | −0.0264273 | + | 0.0457734i | ||||
\(457\) | 20.3654i | 0.952653i | 0.879268 | + | 0.476327i | \(0.158032\pi\) | ||||
−0.879268 | + | 0.476327i | \(0.841968\pi\) | |||||||
\(458\) | −0.0670249 | − | 0.116091i | −0.00313187 | − | 0.00542455i | ||||
\(459\) | −0.863802 | − | 1.49615i | −0.0403188 | − | 0.0698343i | ||||
\(460\) | 1.07813 | + | 0.622457i | 0.0502679 | + | 0.0290222i | ||||
\(461\) | − | 19.4786i | − | 0.907209i | −0.891203 | − | 0.453604i | \(-0.850138\pi\) | ||
0.891203 | − | 0.453604i | \(-0.149862\pi\) | |||||||
\(462\) | 2.27946 | − | 1.31605i | 0.106050 | − | 0.0612280i | ||||
\(463\) | 3.83752i | 0.178345i | 0.996016 | + | 0.0891723i | \(0.0284222\pi\) | ||||
−0.996016 | + | 0.0891723i | \(0.971578\pi\) | |||||||
\(464\) | −30.7062 | −1.42550 | ||||||||
\(465\) | −3.71389 | + | 22.1783i | −0.172227 | + | 1.02849i | ||||
\(466\) | − | 0.421293i | − | 0.0195160i | ||||||
\(467\) | 20.8281 | 0.963809 | 0.481905 | − | 0.876224i | \(-0.339945\pi\) | ||||
0.481905 | + | 0.876224i | \(0.339945\pi\) | |||||||
\(468\) | −10.2028 | − | 32.4194i | −0.471627 | − | 1.49859i | ||||
\(469\) | 40.8055 | 1.88422 | ||||||||
\(470\) | −0.200598 | − | 0.115815i | −0.00925290 | − | 0.00534217i | ||||
\(471\) | −2.99899 | − | 5.19440i | −0.138186 | − | 0.239345i | ||||
\(472\) | −1.27576 | − | 2.20968i | −0.0587217 | − | 0.101709i | ||||
\(473\) | − | 49.9164i | − | 2.29516i | ||||||
\(474\) | −0.415194 | − | 0.239712i | −0.0190705 | − | 0.0110103i | ||||
\(475\) | 5.56110 | + | 3.21071i | 0.255161 | + | 0.147317i | ||||
\(476\) | −2.43759 | − | 1.40734i | −0.111727 | − | 0.0645055i | ||||
\(477\) | −11.7541 | − | 20.3588i | −0.538185 | − | 0.932163i | ||||
\(478\) | 0.137733 | − | 0.238561i | 0.00629976 | − | 0.0109115i | ||||
\(479\) | 10.8953 | − | 6.29038i | 0.497817 | − | 0.287415i | −0.229994 | − | 0.973192i | \(-0.573871\pi\) |
0.727812 | + | 0.685777i | \(0.240537\pi\) | |||||||
\(480\) | 2.21081 | 0.100909 | ||||||||
\(481\) | −4.66672 | + | 20.9973i | −0.212784 | + | 0.957397i | ||||
\(482\) | −0.186591 | − | 0.323185i | −0.00849899 | − | 0.0147207i | ||||
\(483\) | −4.01379 | − | 2.31737i | −0.182634 | − | 0.105444i | ||||
\(484\) | 17.3765 | + | 30.0970i | 0.789843 | + | 1.36805i | ||||
\(485\) | 10.4207 | − | 18.0492i | 0.473180 | − | 0.819572i | ||||
\(486\) | 0.664714 | + | 0.383773i | 0.0301520 | + | 0.0174083i | ||||
\(487\) | 21.1166 | + | 12.1917i | 0.956884 | + | 0.552457i | 0.895213 | − | 0.445639i | \(-0.147024\pi\) |
0.0616713 | + | 0.998097i | \(0.480357\pi\) | |||||||
\(488\) | − | 2.07193i | − | 0.0937918i | ||||||
\(489\) | 36.8604 | − | 21.2814i | 1.66689 | − | 0.962377i | ||||
\(490\) | 0.270612 | + | 0.468713i | 0.0122250 | + | 0.0211743i | ||||
\(491\) | 7.47672 | − | 12.9501i | 0.337420 | − | 0.584428i | −0.646527 | − | 0.762891i | \(-0.723779\pi\) |
0.983947 | + | 0.178463i | \(0.0571125\pi\) | |||||||
\(492\) | − | 10.2337i | − | 0.461369i | ||||||
\(493\) | 1.39362 | + | 2.41383i | 0.0627657 | + | 0.108713i | ||||
\(494\) | 0.357667 | + | 0.0794925i | 0.0160922 | + | 0.00357654i | ||||
\(495\) | −36.5495 | −1.64278 | ||||||||
\(496\) | −21.8965 | − | 3.66669i | −0.983182 | − | 0.164639i | ||||
\(497\) | 5.58190 | 0.250383 | ||||||||
\(498\) | 1.51146 | 0.0677303 | ||||||||
\(499\) | 36.5626 | − | 21.1094i | 1.63677 | − | 0.944988i | 0.654831 | − | 0.755776i | \(-0.272740\pi\) |
0.981936 | − | 0.189212i | \(-0.0605934\pi\) | |||||||
\(500\) | − | 22.9066i | − | 1.02441i | ||||||
\(501\) | −47.8093 | − | 27.6027i | −2.13596 | − | 1.23320i | ||||
\(502\) | −1.09797 | + | 0.633914i | −0.0490048 | + | 0.0282930i | ||||
\(503\) | −9.96985 | − | 17.2683i | −0.444534 | − | 0.769955i | 0.553486 | − | 0.832859i | \(-0.313297\pi\) |
−0.998020 | + | 0.0629034i | \(0.979964\pi\) | |||||||
\(504\) | −3.35371 | −0.149386 | ||||||||
\(505\) | 15.7828 | + | 9.11220i | 0.702325 | + | 0.405488i | ||||
\(506\) | −0.0521645 | + | 0.0903515i | −0.00231899 | + | 0.00401661i | ||||
\(507\) | −29.6064 | + | 20.6837i | −1.31487 | + | 0.918596i | ||||
\(508\) | 0.303765 | + | 0.526137i | 0.0134774 | + | 0.0233436i | ||||
\(509\) | 19.4167 | + | 11.2103i | 0.860631 | + | 0.496886i | 0.864224 | − | 0.503108i | \(-0.167810\pi\) |
−0.00359246 | + | 0.999994i | \(0.501144\pi\) | |||||||
\(510\) | −0.0333882 | − | 0.0578301i | −0.00147845 | − | 0.00256076i | ||||
\(511\) | −53.4021 | −2.36237 | ||||||||
\(512\) | 3.63913i | 0.160828i | ||||||||
\(513\) | −9.19564 | + | 5.30911i | −0.405998 | + | 0.234403i | ||||
\(514\) | −0.317077 | − | 0.183065i | −0.0139857 | − | 0.00807463i | ||||
\(515\) | −6.74463 | + | 3.89401i | −0.297204 | + | 0.171591i | ||||
\(516\) | −25.9971 | + | 45.0284i | −1.14446 | + | 1.98226i | ||||
\(517\) | −9.29318 | + | 16.0963i | −0.408714 | + | 0.707913i | ||||
\(518\) | 0.918588 | + | 0.530347i | 0.0403605 | + | 0.0233021i | ||||
\(519\) | 10.6165 | 0.466014 | ||||||||
\(520\) | −0.287365 | − | 0.913099i | −0.0126018 | − | 0.0400420i | ||||
\(521\) | −21.6959 | − | 37.5784i | −0.950514 | − | 1.64634i | −0.744314 | − | 0.667829i | \(-0.767224\pi\) |
−0.206200 | − | 0.978510i | \(-0.566110\pi\) | |||||||
\(522\) | 1.43729 | + | 0.829821i | 0.0629085 | + | 0.0363203i | ||||
\(523\) | 34.3881 | 1.50369 | 0.751844 | − | 0.659341i | \(-0.229165\pi\) | ||||
0.751844 | + | 0.659341i | \(0.229165\pi\) | |||||||
\(524\) | −4.37123 | − | 7.57119i | −0.190958 | − | 0.330749i | ||||
\(525\) | 31.2130i | 1.36225i | ||||||||
\(526\) | 0.0916152i | 0.00399461i | ||||||||
\(527\) | 0.705548 | + | 1.88771i | 0.0307341 | + | 0.0822298i | ||||
\(528\) | − | 59.0299i | − | 2.56895i | ||||||
\(529\) | −22.8163 | −0.992013 | ||||||||
\(530\) | −0.165442 | − | 0.286554i | −0.00718635 | − | 0.0124471i | ||||
\(531\) | − | 65.9187i | − | 2.86063i | ||||||
\(532\) | −8.64983 | + | 14.9819i | −0.375018 | + | 0.649550i | ||||
\(533\) | −6.34109 | + | 1.99563i | −0.274663 | + | 0.0864403i | ||||
\(534\) | 1.04847 | + | 1.81600i | 0.0453718 | + | 0.0785862i | ||||
\(535\) | − | 16.4540i | − | 0.711369i | ||||||
\(536\) | −0.957279 | + | 1.65806i | −0.0413482 | + | 0.0716171i | ||||
\(537\) | 8.42141 | − | 14.5863i | 0.363411 | − | 0.629446i | ||||
\(538\) | −0.484977 | − | 0.280002i | −0.0209088 | − | 0.0120717i | ||||
\(539\) | 37.6101 | − | 21.7142i | 1.61998 | − | 0.935298i | ||||
\(540\) | 12.0061 | + | 6.93173i | 0.516661 | + | 0.298294i | ||||
\(541\) | 22.7855 | − | 13.1552i | 0.979624 | − | 0.565586i | 0.0774674 | − | 0.996995i | \(-0.475317\pi\) |
0.902157 | + | 0.431409i | \(0.141983\pi\) | |||||||
\(542\) | 0.696499 | 0.0299172 | ||||||||
\(543\) | −19.7560 | −0.847812 | ||||||||
\(544\) | 0.171584 | − | 0.0990642i | 0.00735661 | − | 0.00424734i | ||||
\(545\) | −2.54960 | + | 4.41603i | −0.109213 | + | 0.189162i | ||||
\(546\) | 0.534641 | + | 1.69882i | 0.0228805 | + | 0.0727026i | ||||
\(547\) | 6.17850 | − | 10.7015i | 0.264174 | − | 0.457562i | −0.703173 | − | 0.711019i | \(-0.748234\pi\) |
0.967347 | + | 0.253456i | \(0.0815675\pi\) | |||||||
\(548\) | −11.0087 | − | 6.35586i | −0.470268 | − | 0.271509i | ||||
\(549\) | 26.7642 | − | 46.3570i | 1.14227 | − | 1.97847i | ||||
\(550\) | 0.702612 | 0.0299595 | ||||||||
\(551\) | 14.8359 | − | 8.56550i | 0.632030 | − | 0.364903i | ||||
\(552\) | 0.188324 | − | 0.108729i | 0.00801558 | − | 0.00462780i | ||||
\(553\) | −12.7345 | − | 7.35224i | −0.541524 | − | 0.312649i | ||||
\(554\) | − | 0.262507i | − | 0.0111528i | ||||||
\(555\) | −12.0472 | − | 20.8663i | −0.511375 | − | 0.885727i | ||||
\(556\) | 10.3583 | 0.439291 | ||||||||
\(557\) | 38.0150i | 1.61075i | 0.592766 | + | 0.805375i | \(0.298036\pi\) | ||||
−0.592766 | + | 0.805375i | \(0.701964\pi\) | |||||||
\(558\) | 0.925836 | + | 0.763372i | 0.0391938 | + | 0.0323161i | ||||
\(559\) | 32.9706 | + | 7.32780i | 1.39451 | + | 0.309933i | ||||
\(560\) | 22.5633 | 0.953475 | ||||||||
\(561\) | −4.64036 | + | 2.67911i | −0.195916 | + | 0.113112i | ||||
\(562\) | 1.07380 | 0.0452957 | ||||||||
\(563\) | −15.3956 | + | 26.6660i | −0.648848 | + | 1.12384i | 0.334550 | + | 0.942378i | \(0.391416\pi\) |
−0.983398 | + | 0.181460i | \(0.941918\pi\) | |||||||
\(564\) | 16.7663 | − | 9.68003i | 0.705989 | − | 0.407603i | ||||
\(565\) | 16.4216 | − | 9.48104i | 0.690864 | − | 0.398870i | ||||
\(566\) | − | 0.317247i | − | 0.0133349i | ||||||
\(567\) | 3.01352 | + | 1.73986i | 0.126556 | + | 0.0730671i | ||||
\(568\) | −0.130949 | + | 0.226810i | −0.00549449 | + | 0.00951674i | ||||
\(569\) | 13.0541 | − | 22.6104i | 0.547257 | − | 0.947876i | −0.451204 | − | 0.892421i | \(-0.649005\pi\) |
0.998461 | − | 0.0554558i | \(-0.0176612\pi\) | |||||||
\(570\) | −0.355435 | + | 0.205211i | −0.0148876 | + | 0.00859533i | ||||
\(571\) | −11.8892 | + | 20.5926i | −0.497546 | + | 0.861775i | −0.999996 | − | 0.00283159i | \(-0.999099\pi\) |
0.502450 | + | 0.864606i | \(0.332432\pi\) | |||||||
\(572\) | −36.6150 | + | 11.5233i | −1.53095 | + | 0.481812i | ||||
\(573\) | 27.9241 | 1.16655 | ||||||||
\(574\) | 0.327814i | 0.0136827i | ||||||||
\(575\) | −0.618600 | − | 1.07145i | −0.0257974 | − | 0.0446824i | ||||
\(576\) | −18.7543 | + | 32.4833i | −0.781428 | + | 1.35347i | ||||
\(577\) | 24.8238 | − | 14.3320i | 1.03343 | − | 0.596649i | 0.115462 | − | 0.993312i | \(-0.463165\pi\) |
0.917964 | + | 0.396663i | \(0.129832\pi\) | |||||||
\(578\) | 0.667332 | + | 0.385284i | 0.0277573 | + | 0.0160257i | ||||
\(579\) | −1.72490 | − | 0.995871i | −0.0716844 | − | 0.0413870i | ||||
\(580\) | −19.3702 | − | 11.1834i | −0.804303 | − | 0.464364i | ||||
\(581\) | 46.3582 | 1.92326 | ||||||||
\(582\) | −0.909652 | − | 1.57556i | −0.0377063 | − | 0.0653092i | ||||
\(583\) | −22.9935 | + | 13.2753i | −0.952293 | + | 0.549807i | ||||
\(584\) | 1.25279 | − | 2.16990i | 0.0518408 | − | 0.0897909i | ||||
\(585\) | 5.36553 | − | 24.1416i | 0.221837 | − | 0.998130i | ||||
\(586\) | −0.296482 | − | 0.513521i | −0.0122475 | − | 0.0212134i | ||||
\(587\) | − | 16.9101i | − | 0.697956i | −0.937131 | − | 0.348978i | \(-0.886529\pi\) | ||
0.937131 | − | 0.348978i | \(-0.113471\pi\) | |||||||
\(588\) | −45.2363 | −1.86551 | ||||||||
\(589\) | 11.6022 | − | 4.33644i | 0.478062 | − | 0.178680i | ||||
\(590\) | − | 0.927822i | − | 0.0381978i | ||||||
\(591\) | 15.2738i | 0.628280i | ||||||||
\(592\) | 20.6012 | − | 11.8941i | 0.846704 | − | 0.488845i | ||||
\(593\) | − | 18.8997i | − | 0.776118i | −0.921635 | − | 0.388059i | \(-0.873146\pi\) | ||
0.921635 | − | 0.388059i | \(-0.126854\pi\) | |||||||
\(594\) | −0.580907 | + | 1.00616i | −0.0238349 | + | 0.0412833i | ||||
\(595\) | −1.02405 | − | 1.77371i | −0.0419821 | − | 0.0727151i | ||||
\(596\) | 26.5723 | − | 15.3415i | 1.08844 | − | 0.628414i | ||||
\(597\) | −42.2062 | −1.72738 | ||||||||
\(598\) | −0.0520208 | − | 0.0477192i | −0.00212729 | − | 0.00195138i | ||||
\(599\) | −15.6563 | + | 27.1175i | −0.639700 | + | 1.10799i | 0.345799 | + | 0.938309i | \(0.387608\pi\) |
−0.985499 | + | 0.169684i | \(0.945725\pi\) | |||||||
\(600\) | −1.26828 | − | 0.732243i | −0.0517774 | − | 0.0298937i | ||||
\(601\) | −12.1642 | − | 21.0691i | −0.496189 | − | 0.859425i | 0.503801 | − | 0.863820i | \(-0.331934\pi\) |
−0.999990 | + | 0.00439478i | \(0.998601\pi\) | |||||||
\(602\) | 0.832764 | − | 1.44239i | 0.0339409 | − | 0.0587874i | ||||
\(603\) | −42.8360 | + | 24.7314i | −1.74442 | + | 1.00714i | ||||
\(604\) | 0.836929i | 0.0340541i | ||||||||
\(605\) | 25.2880i | 1.02810i | ||||||||
\(606\) | 1.37772 | − | 0.795429i | 0.0559662 | − | 0.0323121i | ||||
\(607\) | 19.0218 | − | 32.9467i | 0.772070 | − | 1.33727i | −0.164356 | − | 0.986401i | \(-0.552555\pi\) |
0.936426 | − | 0.350864i | \(-0.114112\pi\) | |||||||
\(608\) | −0.608869 | − | 1.05459i | −0.0246929 | − | 0.0427694i | ||||
\(609\) | 72.1138 | + | 41.6349i | 2.92220 | + | 1.68713i | ||||
\(610\) | 0.376713 | − | 0.652485i | 0.0152526 | − | 0.0264184i | ||||
\(611\) | −9.26758 | − | 8.50125i | −0.374926 | − | 0.343924i | ||||
\(612\) | 3.41185 | 0.137916 | ||||||||
\(613\) | −5.56881 | + | 3.21516i | −0.224922 | + | 0.129859i | −0.608227 | − | 0.793763i | \(-0.708119\pi\) |
0.383305 | + | 0.923622i | \(0.374786\pi\) | |||||||
\(614\) | 0.361838 | + | 0.626722i | 0.0146026 | + | 0.0252924i | ||||
\(615\) | 3.72326 | − | 6.44887i | 0.150136 | − | 0.260043i | ||||
\(616\) | 3.78774i | 0.152612i | ||||||||
\(617\) | −29.9548 | + | 17.2944i | −1.20593 | + | 0.696246i | −0.961869 | − | 0.273512i | \(-0.911815\pi\) |
−0.244066 | + | 0.969759i | \(0.578481\pi\) | |||||||
\(618\) | 0.679838i | 0.0273471i | ||||||||
\(619\) | 13.3254i | 0.535592i | 0.963476 | + | 0.267796i | \(0.0862953\pi\) | ||||
−0.963476 | + | 0.267796i | \(0.913705\pi\) | |||||||
\(620\) | −12.4774 | − | 10.2878i | −0.501103 | − | 0.413170i | ||||
\(621\) | 2.04579 | 0.0820946 | ||||||||
\(622\) | − | 0.920962i | − | 0.0369272i | ||||||
\(623\) | 32.1578 | + | 55.6989i | 1.28837 | + | 2.23153i | ||||
\(624\) | 38.9902 | + | 8.66568i | 1.56086 | + | 0.346905i | ||||
\(625\) | 1.11767 | − | 1.93587i | 0.0447070 | − | 0.0774347i | ||||
\(626\) | −0.601461 | + | 0.347254i | −0.0240392 | + | 0.0138790i | ||||
\(627\) | 16.4664 | + | 28.5206i | 0.657604 | + | 1.13900i | ||||
\(628\) | 4.31347 | 0.172126 | ||||||||
\(629\) | −1.87000 | − | 1.07964i | −0.0745617 | − | 0.0430482i | ||||
\(630\) | −1.05614 | − | 0.609763i | −0.0420776 | − | 0.0242935i | ||||
\(631\) | 15.0213 | + | 8.67253i | 0.597987 | + | 0.345248i | 0.768249 | − | 0.640151i | \(-0.221128\pi\) |
−0.170262 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(632\) | 0.597489 | − | 0.344960i | 0.0237668 | − | 0.0137218i | ||||
\(633\) | 31.9191 | − | 55.2856i | 1.26867 | − | 2.19740i | ||||
\(634\) | −0.128035 | − | 0.221763i | −0.00508491 | − | 0.00880732i | ||||
\(635\) | 0.442069i | 0.0175430i | ||||||||
\(636\) | 27.6558 | 1.09663 | ||||||||
\(637\) | 8.82137 | + | 28.0298i | 0.349515 | + | 1.11058i | ||||
\(638\) | 0.937213 | − | 1.62330i | 0.0371046 | − | 0.0642671i | ||||
\(639\) | −5.85965 | + | 3.38307i | −0.231804 | + | 0.133832i | ||||
\(640\) | −1.05976 | + | 1.83556i | −0.0418906 | + | 0.0725567i | ||||
\(641\) | 21.7575 | − | 37.6851i | 0.859369 | − | 1.48847i | −0.0131618 | − | 0.999913i | \(-0.504190\pi\) |
0.872531 | − | 0.488558i | \(-0.162477\pi\) | |||||||
\(642\) | −1.24389 | − | 0.718157i | −0.0490922 | − | 0.0283434i | ||||
\(643\) | 19.8059i | 0.781068i | 0.920589 | + | 0.390534i | \(0.127710\pi\) | ||||
−0.920589 | + | 0.390534i | \(0.872290\pi\) | |||||||
\(644\) | 2.88654 | − | 1.66654i | 0.113746 | − | 0.0656710i | ||||
\(645\) | −32.7648 | + | 18.9168i | −1.29011 | + | 0.744848i | ||||
\(646\) | −0.0183906 | + | 0.0318534i | −0.000723567 | + | 0.00125325i | ||||
\(647\) | −30.5580 | −1.20136 | −0.600679 | − | 0.799491i | \(-0.705103\pi\) | ||||
−0.600679 | + | 0.799491i | \(0.705103\pi\) | |||||||
\(648\) | −0.141392 | + | 0.0816325i | −0.00555439 | + | 0.00320683i | ||||
\(649\) | −74.4497 | −2.92240 | ||||||||
\(650\) | −0.103145 | + | 0.464087i | −0.00404566 | + | 0.0182030i | ||||
\(651\) | 46.4524 | + | 38.3010i | 1.82061 | + | 1.50113i | ||||
\(652\) | 30.6092i | 1.19875i | ||||||||
\(653\) | −27.9507 | −1.09379 | −0.546897 | − | 0.837200i | \(-0.684191\pi\) | ||||
−0.546897 | + | 0.837200i | \(0.684191\pi\) | |||||||
\(654\) | 0.222561 | + | 0.385487i | 0.00870284 | + | 0.0150738i | ||||
\(655\) | − | 6.36144i | − | 0.248562i | ||||||
\(656\) | 6.36692 | + | 3.67594i | 0.248586 | + | 0.143521i | ||||
\(657\) | 56.0594 | − | 32.3659i | 2.18708 | − | 1.26271i | ||||
\(658\) | −0.537074 | + | 0.310080i | −0.0209373 | + | 0.0120882i | ||||
\(659\) | −36.8074 | −1.43381 | −0.716906 | − | 0.697170i | \(-0.754442\pi\) | ||||
−0.716906 | + | 0.697170i | \(0.754442\pi\) | |||||||
\(660\) | 21.4990 | − | 37.2374i | 0.836847 | − | 1.44946i | ||||
\(661\) | −22.6262 | − | 13.0633i | −0.880059 | − | 0.508102i | −0.00938107 | − | 0.999956i | \(-0.502986\pi\) |
−0.870678 | + | 0.491854i | \(0.836319\pi\) | |||||||
\(662\) | −0.424637 | + | 0.735494i | −0.0165040 | + | 0.0285858i | ||||
\(663\) | −1.08838 | − | 3.45833i | −0.0422694 | − | 0.134310i | ||||
\(664\) | −1.08754 | + | 1.88368i | −0.0422049 | + | 0.0731010i | ||||
\(665\) | −10.9016 | + | 6.29404i | −0.422746 | + | 0.244072i | ||||
\(666\) | −1.28573 | −0.0498210 | ||||||||
\(667\) | −3.30059 | −0.127799 | ||||||||
\(668\) | 34.3823 | − | 19.8506i | 1.33029 | − | 0.768043i | ||||
\(669\) | −1.87672 | − | 1.08353i | −0.0725583 | − | 0.0418915i | ||||
\(670\) | −0.602926 | + | 0.348100i | −0.0232931 | + | 0.0134483i | ||||
\(671\) | −52.3563 | − | 30.2279i | −2.02119 | − | 1.16694i | ||||
\(672\) | 2.95957 | − | 5.12613i | 0.114168 | − | 0.197745i | ||||
\(673\) | 20.8683 | − | 36.1449i | 0.804413 | − | 1.39328i | −0.112274 | − | 0.993677i | \(-0.535814\pi\) |
0.916687 | − | 0.399606i | \(-0.130853\pi\) | |||||||
\(674\) | − | 0.0733636i | − | 0.00282586i | ||||||
\(675\) | −6.88877 | − | 11.9317i | −0.265149 | − | 0.459251i | ||||
\(676\) | −2.23616 | − | 25.8764i | −0.0860060 | − | 0.995247i | ||||
\(677\) | −19.4456 | + | 33.6807i | −0.747354 | + | 1.29445i | 0.201733 | + | 0.979441i | \(0.435343\pi\) |
−0.949087 | + | 0.315014i | \(0.897991\pi\) | |||||||
\(678\) | − | 1.65525i | − | 0.0635695i | ||||||
\(679\) | −27.9000 | − | 48.3243i | −1.07071 | − | 1.85452i | ||||
\(680\) | 0.0960952 | 0.00368508 | ||||||||
\(681\) | − | 10.4506i | − | 0.400468i | ||||||
\(682\) | 0.862164 | − | 1.04565i | 0.0330140 | − | 0.0400402i | ||||
\(683\) | − | 2.48961i | − | 0.0952622i | −0.998865 | − | 0.0476311i | \(-0.984833\pi\) | ||
0.998865 | − | 0.0476311i | \(-0.0151672\pi\) | |||||||
\(684\) | − | 20.9699i | − | 0.801804i | ||||||
\(685\) | −4.62484 | − | 8.01045i | −0.176706 | − | 0.306064i | ||||
\(686\) | 0.204462 | 0.00780640 | ||||||||
\(687\) | 7.06040 | + | 4.07632i | 0.269371 | + | 0.155521i | ||||
\(688\) | −18.6764 | − | 32.3485i | −0.712031 | − | 1.23327i | ||||
\(689\) | −5.39307 | − | 17.1364i | −0.205460 | − | 0.652845i | ||||
\(690\) | 0.0790750 | 0.00301033 | ||||||||
\(691\) | 33.3797 | + | 19.2718i | 1.26982 | + | 0.733132i | 0.974954 | − | 0.222406i | \(-0.0713909\pi\) |
0.294868 | + | 0.955538i | \(0.404724\pi\) | |||||||
\(692\) | −3.81746 | + | 6.61204i | −0.145118 | + | 0.251352i | ||||
\(693\) | −48.9282 | + | 84.7461i | −1.85863 | + | 3.21924i | ||||
\(694\) | −0.0744452 | + | 0.0429810i | −0.00282590 | + | 0.00163154i | ||||
\(695\) | 6.52742 | + | 3.76861i | 0.247599 | + | 0.142951i | ||||
\(696\) | −3.38351 | + | 1.95347i | −0.128252 | + | 0.0740462i | ||||
\(697\) | − | 0.667341i | − | 0.0252773i | ||||||
\(698\) | −1.07921 | −0.0408486 | ||||||||
\(699\) | 12.8111 | + | 22.1895i | 0.484561 | + | 0.839284i | ||||
\(700\) | −19.4397 | − | 11.2235i | −0.734750 | − | 0.424208i | ||||
\(701\) | 5.20190 | + | 9.00995i | 0.196473 | + | 0.340301i | 0.947382 | − | 0.320104i | \(-0.103718\pi\) |
−0.750909 | + | 0.660405i | \(0.770385\pi\) | |||||||
\(702\) | −0.579307 | − | 0.531405i | −0.0218645 | − | 0.0200566i | ||||
\(703\) | −6.63571 | + | 11.4934i | −0.250271 | + | 0.433482i | ||||
\(704\) | 36.6872 | + | 21.1814i | 1.38270 | + | 0.798302i | ||||
\(705\) | 14.0873 | 0.530560 | ||||||||
\(706\) | −0.449103 | − | 0.777868i | −0.0169022 | − | 0.0292755i | ||||
\(707\) | 42.2563 | − | 24.3967i | 1.58921 | − | 0.917531i | ||||
\(708\) | 67.1593 | + | 38.7744i | 2.52400 | + | 1.45723i | ||||
\(709\) | 26.4554i | 0.993555i | 0.867878 | + | 0.496778i | \(0.165484\pi\) | ||||
−0.867878 | + | 0.496778i | \(0.834516\pi\) | |||||||
\(710\) | −0.0824760 | + | 0.0476175i | −0.00309527 | + | 0.00178705i | ||||
\(711\) | 17.8241 | 0.668457 | ||||||||
\(712\) | −3.01763 | −0.113090 | ||||||||
\(713\) | −2.35364 | − | 0.394130i | −0.0881445 | − | 0.0147603i | ||||
\(714\) | −0.178785 | −0.00669085 | ||||||||
\(715\) | −27.2658 | − | 6.05991i | −1.01968 | − | 0.226628i | ||||
\(716\) | 6.05630 | + | 10.4898i | 0.226334 | + | 0.392023i | ||||
\(717\) | 16.7533i | 0.625664i | ||||||||
\(718\) | −0.160179 | + | 0.277439i | −0.00597784 | + | 0.0103539i | ||||
\(719\) | 20.5868 | + | 35.6573i | 0.767757 | + | 1.32979i | 0.938777 | + | 0.344526i | \(0.111960\pi\) |
−0.171020 | + | 0.985268i | \(0.554706\pi\) | |||||||
\(720\) | −23.6861 | + | 13.6752i | −0.882728 | + | 0.509643i | ||||
\(721\) | 20.8514i | 0.776546i | ||||||||
\(722\) | −0.555856 | − | 0.320924i | −0.0206868 | − | 0.0119435i | ||||
\(723\) | 19.6555 | + | 11.3481i | 0.730996 | + | 0.422041i | ||||
\(724\) | 7.10381 | − | 12.3042i | 0.264011 | − | 0.457281i | ||||
\(725\) | 11.1141 | + | 19.2501i | 0.412766 | + | 0.714932i | ||||
\(726\) | 1.91172 | + | 1.10373i | 0.0709505 | + | 0.0409633i | ||||
\(727\) | −8.85220 | − | 15.3325i | −0.328310 | − | 0.568650i | 0.653867 | − | 0.756610i | \(-0.273146\pi\) |
−0.982177 | + | 0.187960i | \(0.939812\pi\) | |||||||
\(728\) | −2.50186 | − | 0.556046i | −0.0927251 | − | 0.0206084i | ||||
\(729\) | −43.9986 | −1.62958 | ||||||||
\(730\) | 0.789049 | − | 0.455558i | 0.0292040 | − | 0.0168609i | ||||
\(731\) | −1.69528 | + | 2.93632i | −0.0627023 | + | 0.108604i | ||||
\(732\) | 31.4862 | + | 54.5358i | 1.16376 | + | 2.01570i | ||||
\(733\) | −18.9721 | − | 10.9536i | −0.700751 | − | 0.404579i | 0.106876 | − | 0.994272i | \(-0.465915\pi\) |
−0.807627 | + | 0.589693i | \(0.799249\pi\) | |||||||
\(734\) | 1.03997 | + | 0.600425i | 0.0383859 | + | 0.0221621i | ||||
\(735\) | −28.5062 | − | 16.4581i | −1.05147 | − | 0.607065i | ||||
\(736\) | 0.234619i | 0.00864817i | ||||||||
\(737\) | 27.9320 | + | 48.3796i | 1.02889 | + | 1.78209i | ||||
\(738\) | −0.198681 | − | 0.344126i | −0.00731355 | − | 0.0126674i | ||||
\(739\) | 31.9225 | + | 18.4305i | 1.17429 | + | 0.677977i | 0.954687 | − | 0.297613i | \(-0.0961904\pi\) |
0.219603 | + | 0.975589i | \(0.429524\pi\) | |||||||
\(740\) | 17.3276 | 0.636974 | ||||||||
\(741\) | −21.2556 | + | 6.68944i | −0.780844 | + | 0.245743i | ||||
\(742\) | −0.885898 | −0.0325223 | ||||||||
\(743\) | − | 5.05507i | − | 0.185452i | −0.995692 | − | 0.0927262i | \(-0.970442\pi\) | ||
0.995692 | − | 0.0927262i | \(-0.0295581\pi\) | |||||||
\(744\) | −2.64604 | + | 0.988981i | −0.0970085 | + | 0.0362578i | ||||
\(745\) | 22.3265 | 0.817980 | ||||||||
\(746\) | − | 0.0407138i | − | 0.00149064i | ||||||
\(747\) | −48.6650 | + | 28.0967i | −1.78056 | + | 1.02801i | ||||
\(748\) | − | 3.85339i | − | 0.140894i | ||||||
\(749\) | −38.1513 | − | 22.0267i | −1.39402 | − | 0.804837i | ||||
\(750\) | −0.727496 | − | 1.26006i | −0.0265644 | − | 0.0460109i | ||||
\(751\) | 9.58618 | + | 16.6037i | 0.349804 | + | 0.605879i | 0.986215 | − | 0.165472i | \(-0.0529147\pi\) |
−0.636410 | + | 0.771351i | \(0.719581\pi\) | |||||||
\(752\) | 13.9083i | 0.507184i | ||||||||
\(753\) | 38.5534 | − | 66.7764i | 1.40496 | − | 2.43347i | ||||
\(754\) | 0.934631 | + | 0.857347i | 0.0340373 | + | 0.0312227i | ||||
\(755\) | −0.304495 | + | 0.527401i | −0.0110817 | + | 0.0191941i | ||||
\(756\) | 32.1447 | − | 18.5588i | 1.16909 | − | 0.674975i | ||||
\(757\) | −13.6298 | + | 23.6075i | −0.495383 | + | 0.858029i | −0.999986 | − | 0.00532260i | \(-0.998306\pi\) |
0.504602 | + | 0.863352i | \(0.331639\pi\) | |||||||
\(758\) | −0.158334 | − | 0.274243i | −0.00575096 | − | 0.00996096i | ||||
\(759\) | − | 6.34508i | − | 0.230312i | ||||||
\(760\) | − | 0.590621i | − | 0.0214241i | ||||||
\(761\) | 35.2717 | − | 20.3641i | 1.27860 | − | 0.738198i | 0.302006 | − | 0.953306i | \(-0.402344\pi\) |
0.976590 | + | 0.215108i | \(0.0690103\pi\) | |||||||
\(762\) | 0.0334194 | + | 0.0192947i | 0.00121066 | + | 0.000698973i | ||||
\(763\) | 6.82620 | + | 11.8233i | 0.247125 | + | 0.428033i | ||||
\(764\) | −10.0409 | + | 17.3913i | −0.363266 | + | 0.629195i | ||||
\(765\) | 2.15002 | + | 1.24131i | 0.0777340 | + | 0.0448798i | ||||
\(766\) | 0.0335920 | − | 0.0581831i | 0.00121373 | − | 0.00210224i | ||||
\(767\) | 10.9293 | − | 49.1752i | 0.394635 | − | 1.77561i | ||||
\(768\) | −21.9936 | − | 38.0941i | −0.793626 | − | 1.37460i | ||||
\(769\) | −21.6531 | + | 12.5014i | −0.780832 | + | 0.450814i | −0.836725 | − | 0.547623i | \(-0.815533\pi\) |
0.0558929 | + | 0.998437i | \(0.482199\pi\) | |||||||
\(770\) | −0.688676 | + | 1.19282i | −0.0248182 | + | 0.0429863i | ||||
\(771\) | 22.2673 | 0.801936 | ||||||||
\(772\) | 1.24047 | − | 0.716185i | 0.0446455 | − | 0.0257761i | ||||
\(773\) | − | 29.0375i | − | 1.04441i | −0.852821 | − | 0.522204i | \(-0.825110\pi\) | ||
0.852821 | − | 0.522204i | \(-0.174890\pi\) | |||||||
\(774\) | 2.01888i | 0.0725672i | ||||||||
\(775\) | 5.62670 | + | 15.0543i | 0.202117 | + | 0.540768i | ||||
\(776\) | 2.61809 | 0.0939839 | ||||||||
\(777\) | −64.5094 | −2.31426 | ||||||||
\(778\) | 1.22498 | − | 0.707241i | 0.0439176 | − | 0.0253558i | ||||
\(779\) | −4.10161 | −0.146956 | ||||||||
\(780\) | 21.4398 | + | 19.6669i | 0.767667 | + | 0.704189i | ||||
\(781\) | 3.82089 | + | 6.61798i | 0.136722 | + | 0.236810i | ||||
\(782\) | 0.00613712 | − | 0.00354327i | 0.000219463 | − | 0.000126707i | ||||
\(783\) | −36.7556 | −1.31354 | ||||||||
\(784\) | 16.2489 | − | 28.1440i | 0.580319 | − | 1.00514i | ||||
\(785\) | 2.71819 | + | 1.56935i | 0.0970163 | + | 0.0560124i | ||||
\(786\) | −0.480910 | − | 0.277654i | −0.0171535 | − | 0.00990358i | ||||
\(787\) | −27.9699 | + | 16.1484i | −0.997018 | + | 0.575629i | −0.907365 | − | 0.420344i | \(-0.861909\pi\) |
−0.0896536 | + | 0.995973i | \(0.528576\pi\) | |||||||
\(788\) | −9.51261 | − | 5.49211i | −0.338873 | − | 0.195648i | ||||
\(789\) | −2.78593 | − | 4.82537i | −0.0991817 | − | 0.171788i | ||||
\(790\) | 0.250879 | 0.00892588 | ||||||||
\(791\) | − | 50.7684i | − | 1.80512i | ||||||
\(792\) | −2.29567 | − | 3.97621i | −0.0815729 | − | 0.141288i | ||||
\(793\) | 27.6520 | − | 30.1447i | 0.981951 | − | 1.07047i | ||||
\(794\) | −0.311560 | − | 0.539638i | −0.0110569 | − | 0.0191511i | ||||
\(795\) | 17.4277 | + | 10.0619i | 0.618096 | + | 0.356858i | ||||
\(796\) | 15.1764 | − | 26.2863i | 0.537912 | − | 0.931691i | ||||
\(797\) | 23.0278 | − | 39.8854i | 0.815688 | − | 1.41281i | −0.0931455 | − | 0.995653i | \(-0.529692\pi\) |
0.908833 | − | 0.417160i | \(-0.136974\pi\) | |||||||
\(798\) | 1.09885i | 0.0388988i | ||||||||
\(799\) | 1.09334 | − | 0.631239i | 0.0386795 | − | 0.0223316i | ||||
\(800\) | 1.36837 | − | 0.790031i | 0.0483793 | − | 0.0279318i | ||||
\(801\) | −67.5158 | − | 38.9803i | −2.38555 | − | 1.37730i | ||||
\(802\) | −0.864637 | −0.0305314 | ||||||||
\(803\) | −36.5545 | − | 63.3143i | −1.28998 | − | 2.23431i | ||||
\(804\) | − | 58.1895i | − | 2.05218i | ||||||
\(805\) | 2.42532 | 0.0854812 | ||||||||
\(806\) | 0.564104 | + | 0.722977i | 0.0198697 | + | 0.0254658i | ||||
\(807\) | 34.0583 | 1.19891 | ||||||||
\(808\) | 2.28934i | 0.0805387i | ||||||||
\(809\) | 13.5584 | + | 23.4838i | 0.476687 | + | 0.825646i | 0.999643 | − | 0.0267135i | \(-0.00850417\pi\) |
−0.522956 | + | 0.852360i | \(0.675171\pi\) | |||||||
\(810\) | −0.0593688 | −0.00208601 | ||||||||
\(811\) | 18.4126 | + | 10.6305i | 0.646552 | + | 0.373287i | 0.787134 | − | 0.616782i | \(-0.211564\pi\) |
−0.140582 | + | 0.990069i | \(0.544897\pi\) | |||||||
\(812\) | −51.8610 | + | 29.9419i | −1.81996 | + | 1.05076i | ||||
\(813\) | −36.6846 | + | 21.1799i | −1.28658 | + | 0.742810i | ||||
\(814\) | 1.45212i | 0.0508968i | ||||||||
\(815\) | −11.1364 | + | 19.2888i | −0.390090 | + | 0.675656i | ||||
\(816\) | −2.00480 | + | 3.47242i | −0.0701821 | + | 0.121559i | ||||
\(817\) | 18.0472 | + | 10.4196i | 0.631392 | + | 0.364534i | ||||
\(818\) | 0.623596 | + | 1.08010i | 0.0218035 | + | 0.0377648i | ||||
\(819\) | −48.7934 | − | 44.7587i | −1.70498 | − | 1.56400i | ||||
\(820\) | 2.67760 | + | 4.63773i | 0.0935057 | + | 0.161957i | ||||
\(821\) | 4.27210i | 0.149097i | 0.997217 | + | 0.0745486i | \(0.0237516\pi\) | ||||
−0.997217 | + | 0.0745486i | \(0.976248\pi\) | |||||||
\(822\) | −0.807429 | −0.0281623 | ||||||||
\(823\) | −10.1826 | − | 17.6367i | −0.354942 | − | 0.614778i | 0.632166 | − | 0.774833i | \(-0.282166\pi\) |
−0.987108 | + | 0.160055i | \(0.948833\pi\) | |||||||
\(824\) | −0.847257 | − | 0.489164i | −0.0295156 | − | 0.0170408i | ||||
\(825\) | −37.0066 | + | 21.3658i | −1.28840 | + | 0.743860i | ||||
\(826\) | −2.15131 | − | 1.24206i | −0.0748536 | − | 0.0432167i | ||||
\(827\) | −27.5966 | − | 15.9329i | −0.959626 | − | 0.554040i | −0.0635682 | − | 0.997977i | \(-0.520248\pi\) |
−0.896058 | + | 0.443937i | \(0.853581\pi\) | |||||||
\(828\) | −2.02011 | + | 3.49894i | −0.0702038 | + | 0.121597i | ||||
\(829\) | 32.3558 | 1.12376 | 0.561882 | − | 0.827217i | \(-0.310077\pi\) | ||||
0.561882 | + | 0.827217i | \(0.310077\pi\) | |||||||
\(830\) | −0.684971 | + | 0.395468i | −0.0237757 | + | 0.0137269i | ||||
\(831\) | 7.98257 | + | 13.8262i | 0.276912 | + | 0.479626i | ||||
\(832\) | −19.3764 | + | 21.1230i | −0.671754 | + | 0.732309i | ||||
\(833\) | −2.94988 | −0.102207 | ||||||||
\(834\) | 0.569796 | − | 0.328972i | 0.0197304 | − | 0.0113914i | ||||
\(835\) | 28.8886 | 0.999730 | ||||||||
\(836\) | −23.6837 | −0.819119 | ||||||||
\(837\) | −26.2103 | − | 4.38906i | −0.905960 | − | 0.151708i | ||||
\(838\) | − | 0.350554i | − | 0.0121097i | ||||||
\(839\) | − | 44.5019i | − | 1.53638i | −0.640224 | − | 0.768189i | \(-0.721158\pi\) | ||
0.640224 | − | 0.768189i | \(-0.278842\pi\) | |||||||
\(840\) | 2.48625 | − | 1.43544i | 0.0857838 | − | 0.0495273i | ||||
\(841\) | 30.3001 | 1.04483 | ||||||||
\(842\) | 0.257749 | − | 0.446434i | 0.00888262 | − | 0.0153851i | ||||
\(843\) | −56.5572 | + | 32.6533i | −1.94793 | + | 1.12464i | ||||
\(844\) | 22.9548 | + | 39.7589i | 0.790136 | + | 1.36856i | ||||
\(845\) | 8.00534 | − | 17.1199i | 0.275392 | − | 0.588943i | ||||
\(846\) | 0.375866 | − | 0.651018i | 0.0129225 | − | 0.0223825i | ||||
\(847\) | 58.6345 | + | 33.8526i | 2.01470 | + | 1.16319i | ||||
\(848\) | −9.93402 | + | 17.2062i | −0.341136 | + | 0.590864i | ||||
\(849\) | 9.64718 | + | 16.7094i | 0.331090 | + | 0.573465i | ||||
\(850\) | −0.0413310 | − | 0.0238625i | −0.00141764 | − | 0.000818476i | ||||
\(851\) | 2.21441 | − | 1.27849i | 0.0759089 | − | 0.0438260i | ||||
\(852\) | − | 7.95990i | − | 0.272702i | ||||||
\(853\) | − | 11.2789i | − | 0.386183i | −0.981181 | − | 0.193091i | \(-0.938149\pi\) | ||
0.981181 | − | 0.193091i | \(-0.0618514\pi\) | |||||||
\(854\) | −1.00860 | − | 1.74694i | −0.0345135 | − | 0.0597791i | ||||
\(855\) | 7.62937 | − | 13.2144i | 0.260919 | − | 0.451925i | ||||
\(856\) | 1.79003 | − | 1.03347i | 0.0611818 | − | 0.0353233i | ||||
\(857\) | −12.6143 | + | 21.8487i | −0.430898 | + | 0.746337i | −0.996951 | − | 0.0780321i | \(-0.975136\pi\) |
0.566053 | + | 0.824369i | \(0.308470\pi\) | |||||||
\(858\) | −1.64817 | + | 1.79674i | −0.0562676 | + | 0.0613398i | ||||
\(859\) | 2.10975 | − | 3.65420i | 0.0719838 | − | 0.124680i | −0.827787 | − | 0.561043i | \(-0.810400\pi\) |
0.899771 | + | 0.436363i | \(0.143734\pi\) | |||||||
\(860\) | − | 27.2082i | − | 0.927791i | ||||||
\(861\) | −9.96851 | − | 17.2660i | −0.339726 | − | 0.588422i | ||||
\(862\) | 0.257244 | + | 0.445560i | 0.00876178 | + | 0.0151758i | ||||
\(863\) | −15.3488 | − | 8.86161i | −0.522478 | − | 0.301653i | 0.215470 | − | 0.976510i | \(-0.430872\pi\) |
−0.737948 | + | 0.674858i | \(0.764205\pi\) | |||||||
\(864\) | 2.61273i | 0.0888870i | ||||||||
\(865\) | −4.81124 | + | 2.77777i | −0.163587 | + | 0.0944471i | ||||
\(866\) | 0.110312i | 0.00374856i | ||||||||
\(867\) | −46.8645 | −1.59160 | ||||||||
\(868\) | −40.5573 | + | 15.1587i | −1.37660 | + | 0.514518i | ||||
\(869\) | − | 20.1309i | − | 0.682893i | ||||||
\(870\) | −1.42070 | −0.0481663 | ||||||||
\(871\) | −36.0560 | + | 11.3473i | −1.22171 | + | 0.384489i | ||||
\(872\) | −0.640558 | −0.0216920 | ||||||||
\(873\) | 58.5766 | + | 33.8192i | 1.98252 | + | 1.14461i | ||||
\(874\) | −0.0217777 | − | 0.0377200i | −0.000736640 | − | 0.00127590i | ||||
\(875\) | −22.3131 | − | 38.6474i | −0.754321 | − | 1.30652i | ||||
\(876\) | 76.1525i | 2.57295i | ||||||||
\(877\) | −35.3362 | − | 20.4014i | −1.19322 | − | 0.688906i | −0.234185 | − | 0.972192i | \(-0.575242\pi\) |
−0.959035 | + | 0.283286i | \(0.908575\pi\) | |||||||
\(878\) | 0.618038 | + | 0.356824i | 0.0208578 | + | 0.0120422i | ||||
\(879\) | 31.2314 | + | 18.0314i | 1.05341 | + | 0.608185i | ||||
\(880\) | 15.4449 | + | 26.7514i | 0.520649 | + | 0.901790i | ||||
\(881\) | 2.03185 | − | 3.51927i | 0.0684549 | − | 0.118567i | −0.829766 | − | 0.558111i | \(-0.811526\pi\) |
0.898221 | + | 0.439543i | \(0.144860\pi\) | |||||||
\(882\) | −1.52115 | + | 0.878239i | −0.0512199 | + | 0.0295718i | ||||
\(883\) | −29.7726 | −1.00193 | −0.500963 | − | 0.865468i | \(-0.667021\pi\) | ||||
−0.500963 | + | 0.865468i | \(0.667021\pi\) | |||||||
\(884\) | 2.54523 | + | 0.565684i | 0.0856052 | + | 0.0190260i | ||||
\(885\) | 28.2142 | + | 48.8684i | 0.948409 | + | 1.64269i | ||||
\(886\) | −0.437590 | − | 0.252643i | −0.0147011 | − | 0.00848770i | ||||
\(887\) | −16.9824 | − | 29.4143i | −0.570212 | − | 0.987636i | −0.996544 | − | 0.0830692i | \(-0.973528\pi\) |
0.426332 | − | 0.904567i | \(-0.359806\pi\) | |||||||
\(888\) | 1.51336 | − | 2.62122i | 0.0507851 | − | 0.0879623i | ||||
\(889\) | 1.02501 | + | 0.591790i | 0.0343777 | + | 0.0198480i | ||||
\(890\) | −0.950301 | − | 0.548656i | −0.0318542 | − | 0.0183910i | ||||
\(891\) | 4.76383i | 0.159594i | ||||||||
\(892\) | 1.34965 | − | 0.779223i | 0.0451897 | − | 0.0260903i | ||||
\(893\) | −3.87972 | − | 6.71988i | −0.129830 | − | 0.224872i | ||||
\(894\) | 0.974470 | − | 1.68783i | 0.0325912 | − | 0.0564495i | ||||
\(895\) | 8.81372i | 0.294610i | ||||||||
\(896\) | 2.83736 | + | 4.91445i | 0.0947895 | + | 0.164180i | ||||
\(897\) | 4.19103 | + | 0.931468i | 0.139934 | + | 0.0311008i | ||||
\(898\) | −0.489087 | −0.0163210 | ||||||||
\(899\) | 42.2866 | + | 7.08114i | 1.41034 | + | 0.236169i | ||||
\(900\) | 27.2093 | 0.906975 | ||||||||
\(901\) | 1.80345 | 0.0600816 | ||||||||
\(902\) | −0.388661 | + | 0.224393i | −0.0129410 | + | 0.00747149i | ||||
\(903\) | 101.294i | 3.37086i | ||||||||
\(904\) | 2.06288 | + | 1.19100i | 0.0686103 | + | 0.0396122i | ||||
\(905\) | 8.95311 | − | 5.16908i | 0.297612 | − | 0.171826i | ||||
\(906\) | 0.0265802 | + | 0.0460383i | 0.000883068 | + | 0.00152952i | ||||
\(907\) | 37.9946 | 1.26159 | 0.630795 | − | 0.775949i | \(-0.282729\pi\) | ||||
0.630795 | + | 0.775949i | \(0.282729\pi\) | |||||||
\(908\) | 6.50870 | + | 3.75780i | 0.215999 | + | 0.124707i | ||||
\(909\) | −29.5726 | + | 51.2212i | −0.980861 | + | 1.69890i | ||||
\(910\) | −0.686779 | − | 0.629990i | −0.0227665 | − | 0.0208840i | ||||
\(911\) | 21.4030 | + | 37.0710i | 0.709112 | + | 1.22822i | 0.965187 | + | 0.261561i | \(0.0842373\pi\) |
−0.256075 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(912\) | 21.3422 | + | 12.3219i | 0.706711 | + | 0.408020i | ||||
\(913\) | 31.7329 | + | 54.9630i | 1.05021 | + | 1.81901i | ||||
\(914\) | −0.930283 | −0.0307710 | ||||||||
\(915\) | 45.8219i | 1.51482i | ||||||||
\(916\) | −5.07752 | + | 2.93151i | −0.167766 | + | 0.0968597i | ||||
\(917\) | −14.7501 | − | 8.51595i | −0.487090 | − | 0.281221i | ||||
\(918\) | 0.0683434 | − | 0.0394581i | 0.00225567 | − | 0.00130231i | ||||
\(919\) | −6.72087 | + | 11.6409i | −0.221701 | + | 0.383997i | −0.955325 | − | 0.295559i | \(-0.904494\pi\) |
0.733624 | + | 0.679556i | \(0.237828\pi\) | |||||||
\(920\) | −0.0568968 | + | 0.0985482i | −0.00187583 | + | 0.00324904i | ||||
\(921\) | −38.1160 | − | 22.0063i | −1.25597 | − | 0.725132i | ||||
\(922\) | 0.889774 | 0.0293031 | ||||||||
\(923\) | −4.93220 | + | 1.55223i | −0.162345 | + | 0.0510923i | ||||
\(924\) | −57.5606 | − | 99.6979i | −1.89361 | − | 3.27982i | ||||
\(925\) | −14.9131 | − | 8.61009i | −0.490340 | − | 0.283098i | ||||
\(926\) | −0.175296 | −0.00576059 | ||||||||
\(927\) | −12.6376 | − | 21.8889i | −0.415072 | − | 0.718927i | ||||
\(928\) | − | 4.21528i | − | 0.138373i | ||||||
\(929\) | 7.05767i | 0.231555i | 0.993275 | + | 0.115777i | \(0.0369359\pi\) | ||||
−0.993275 | + | 0.115777i | \(0.963064\pi\) | |||||||
\(930\) | −1.01310 | − | 0.169649i | −0.0332207 | − | 0.00556300i | ||||
\(931\) | 18.1305i | 0.594205i | ||||||||
\(932\) | −18.4263 | −0.603575 | ||||||||
\(933\) | 28.0055 | + | 48.5070i | 0.916860 | + | 1.58805i | ||||
\(934\) | 0.951418i | 0.0311314i | ||||||||
\(935\) | 1.40196 | − | 2.42826i | 0.0458489 | − | 0.0794127i | ||||
\(936\) | 2.96336 | − | 0.932610i | 0.0968604 | − | 0.0304833i | ||||
\(937\) | −20.9806 | − | 36.3395i | −0.685406 | − | 1.18716i | −0.973309 | − | 0.229499i | \(-0.926291\pi\) |
0.287903 | − | 0.957660i | \(-0.407042\pi\) | |||||||
\(938\) | 1.86398i | 0.0608611i | ||||||||
\(939\) | 21.1193 | − | 36.5797i | 0.689202 | − | 1.19373i | ||||
\(940\) | −5.06548 | + | 8.77368i | −0.165218 | + | 0.286166i | ||||
\(941\) | 42.4463 | + | 24.5064i | 1.38371 | + | 0.798885i | 0.992597 | − | 0.121458i | \(-0.0387571\pi\) |
0.391112 | + | 0.920343i | \(0.372090\pi\) | |||||||
\(942\) | 0.237278 | − | 0.136992i | 0.00773093 | − | 0.00446346i | ||||
\(943\) | 0.684376 | + | 0.395125i | 0.0222863 | + | 0.0128670i | ||||
\(944\) | −48.2474 | + | 27.8556i | −1.57032 | + | 0.906624i | ||||
\(945\) | 27.0085 | 0.878587 | ||||||||
\(946\) | 2.28016 | 0.0741343 | ||||||||
\(947\) | −26.7651 | + | 15.4528i | −0.869750 | + | 0.502150i | −0.867265 | − | 0.497847i | \(-0.834124\pi\) |
−0.00248455 | + | 0.999997i | \(0.500791\pi\) | |||||||
\(948\) | −10.4844 | + | 18.1596i | −0.340519 | + | 0.589795i | ||||
\(949\) | 47.1864 | − | 14.8502i | 1.53174 | − | 0.482059i | ||||
\(950\) | −0.146664 | + | 0.254029i | −0.00475840 | + | 0.00824178i | ||||
\(951\) | 13.4872 | + | 7.78682i | 0.437352 | + | 0.252505i | ||||
\(952\) | 0.128641 | − | 0.222813i | 0.00416928 | − | 0.00722140i | ||||
\(953\) | −40.7189 | −1.31901 | −0.659507 | − | 0.751699i | \(-0.729235\pi\) | ||||
−0.659507 | + | 0.751699i | \(0.729235\pi\) | |||||||
\(954\) | 0.929979 | − | 0.536924i | 0.0301092 | − | 0.0173835i | ||||
\(955\) | −12.6548 | + | 7.30623i | −0.409499 | + | 0.236424i | ||||
\(956\) | −10.4341 | − | 6.02411i | −0.337462 | − | 0.194834i | ||||
\(957\) | 113.999i | 3.68506i | ||||||||
\(958\) | 0.287342 | + | 0.497691i | 0.00928360 | + | 0.0160797i | ||||
\(959\) | −24.7647 | −0.799695 | ||||||||
\(960\) | − | 32.1084i | − | 1.03629i | ||||||
\(961\) | 29.3089 | + | 10.0991i | 0.945447 | + | 0.325776i | ||||
\(962\) | −0.959150 | − | 0.213174i | −0.0309242 | − | 0.00687300i | ||||
\(963\) | 53.3996 | 1.72078 | ||||||||
\(964\) | −14.1353 | + | 8.16104i | −0.455269 | + | 0.262850i | ||||
\(965\) | 1.04226 | 0.0335516 | ||||||||
\(966\) | 0.105856 | − | 0.183348i | 0.00340587 | − | 0.00589914i | ||||
\(967\) | −17.5975 | + | 10.1599i | −0.565897 | + | 0.326721i | −0.755509 | − | 0.655138i | \(-0.772610\pi\) |
0.189612 | + | 0.981859i | \(0.439277\pi\) | |||||||
\(968\) | −2.75108 | + | 1.58833i | −0.0884229 | + | 0.0510510i | ||||
\(969\) | − | 2.23696i | − | 0.0718614i | ||||||
\(970\) | 0.824480 | + | 0.476014i | 0.0264725 | + | 0.0152839i | ||||
\(971\) | 25.5597 | − | 44.2707i | 0.820250 | − | 1.42071i | −0.0852468 | − | 0.996360i | \(-0.527168\pi\) |
0.905496 | − | 0.424354i | \(-0.139499\pi\) | |||||||
\(972\) | 16.7853 | − | 29.0730i | 0.538388 | − | 0.932516i | ||||
\(973\) | 17.4763 | − | 10.0899i | 0.560264 | − | 0.323468i | ||||
\(974\) | −0.556910 | + | 0.964597i | −0.0178446 | + | 0.0309077i | ||||
\(975\) | −8.67980 | − | 27.5800i | −0.277976 | − | 0.883266i | ||||
\(976\) | −45.2396 | −1.44808 | ||||||||
\(977\) | 23.0780i | 0.738330i | 0.929364 | + | 0.369165i | \(0.120356\pi\) | ||||
−0.929364 | + | 0.369165i | \(0.879644\pi\) | |||||||
\(978\) | 0.972124 | + | 1.68377i | 0.0310851 | + | 0.0538410i | ||||
\(979\) | −44.0249 | + | 76.2534i | −1.40704 | + | 2.43707i | ||||
\(980\) | 20.5004 | − | 11.8359i | 0.654860 | − | 0.378084i | ||||
\(981\) | −14.3317 | − | 8.27443i | −0.457577 | − | 0.264182i | ||||
\(982\) | 0.591553 | + | 0.341534i | 0.0188772 | + | 0.0108988i | ||||
\(983\) | −16.5523 | − | 9.55649i | −0.527937 | − | 0.304805i | 0.212239 | − | 0.977218i | \(-0.431925\pi\) |
−0.740176 | + | 0.672413i | \(0.765258\pi\) | |||||||
\(984\) | 0.935426 | 0.0298203 | ||||||||
\(985\) | −3.99633 | − | 6.92184i | −0.127334 | − | 0.220548i | ||||
\(986\) | −0.110263 | + | 0.0636601i | −0.00351148 | + | 0.00202735i | ||||
\(987\) | 18.8585 | − | 32.6638i | 0.600271 | − | 1.03970i | ||||
\(988\) | 3.47681 | − | 15.6435i | 0.110612 | − | 0.497686i | ||||
\(989\) | −2.00751 | − | 3.47712i | −0.0638352 | − | 0.110566i | ||||
\(990\) | − | 1.66957i | − | 0.0530623i | ||||||
\(991\) | −3.32877 | −0.105742 | −0.0528709 | − | 0.998601i | \(-0.516837\pi\) | ||||
−0.0528709 | + | 0.998601i | \(0.516837\pi\) | |||||||
\(992\) | 0.503355 | − | 3.00590i | 0.0159815 | − | 0.0954374i | ||||
\(993\) | − | 51.6512i | − | 1.63910i | ||||||
\(994\) | 0.254979i | 0.00808744i | ||||||||
\(995\) | 19.1272 | − | 11.0431i | 0.606372 | − | 0.350089i | ||||
\(996\) | − | 66.1077i | − | 2.09470i | ||||||
\(997\) | 14.4702 | − | 25.0632i | 0.458277 | − | 0.793760i | −0.540593 | − | 0.841284i | \(-0.681800\pi\) |
0.998870 | + | 0.0475248i | \(0.0151333\pi\) | |||||||
\(998\) | 0.964269 | + | 1.67016i | 0.0305234 | + | 0.0528681i | ||||
\(999\) | 24.6598 | − | 14.2373i | 0.780201 | − | 0.450450i |
(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 | 403.2.l.c.25.18 | yes | 68 | |
13.12 | even | 2 | inner | 403.2.l.c.25.17 | ✓ | 68 | |
31.5 | even | 3 | inner | 403.2.l.c.129.18 | yes | 68 | |
403.129 | even | 6 | inner | 403.2.l.c.129.17 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.l.c.25.17 | ✓ | 68 | 13.12 | even | 2 | inner | |
403.2.l.c.25.18 | yes | 68 | 1.1 | even | 1 | trivial | |
403.2.l.c.129.17 | yes | 68 | 403.129 | even | 6 | inner | |
403.2.l.c.129.18 | yes | 68 | 31.5 | even | 3 | inner |