Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (of order \(3\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 8 x^{10} - 3 x^{9} + 42 x^{8} - 15 x^{7} + 101 x^{6} + 6 x^{5} + 150 x^{4} - 28 x^{3} + 40 x^{2} + 8 x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.3 | ||
Root | \(-0.144978 - 0.251110i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.415 |
Dual form | 483.2.i.f.277.3 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.144978 | + | 0.251110i | −0.102515 | + | 0.177562i | −0.912720 | − | 0.408585i | \(-0.866022\pi\) |
0.810205 | + | 0.586147i | \(0.199356\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.957963 | + | 1.65924i | 0.478981 | + | 0.829620i | ||||
\(5\) | −1.16311 | + | 2.01456i | −0.520157 | + | 0.900938i | 0.479569 | + | 0.877504i | \(0.340793\pi\) |
−0.999725 | + | 0.0234334i | \(0.992540\pi\) | |||||||
\(6\) | −0.289957 | −0.118374 | ||||||||
\(7\) | 2.35341 | + | 1.20891i | 0.889505 | + | 0.456926i | ||||
\(8\) | −1.13545 | −0.401442 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.337250 | − | 0.584135i | −0.106648 | − | 0.184720i | ||||
\(11\) | −0.365486 | − | 0.633040i | −0.110198 | − | 0.190869i | 0.805652 | − | 0.592389i | \(-0.201815\pi\) |
−0.915850 | + | 0.401521i | \(0.868482\pi\) | |||||||
\(12\) | −0.957963 | + | 1.65924i | −0.276540 | + | 0.478981i | ||||
\(13\) | −0.115233 | −0.0319599 | −0.0159800 | − | 0.999872i | \(-0.505087\pi\) | ||||
−0.0159800 | + | 0.999872i | \(0.505087\pi\) | |||||||
\(14\) | −0.644763 | + | 0.415698i | −0.172320 | + | 0.111100i | ||||
\(15\) | −2.32621 | −0.600625 | ||||||||
\(16\) | −1.75131 | + | 3.03336i | −0.437827 | + | 0.758339i | ||||
\(17\) | −0.394511 | − | 0.683313i | −0.0956830 | − | 0.165728i | 0.814210 | − | 0.580570i | \(-0.197170\pi\) |
−0.909893 | + | 0.414842i | \(0.863837\pi\) | |||||||
\(18\) | −0.144978 | − | 0.251110i | −0.0341717 | − | 0.0591872i | ||||
\(19\) | 3.46171 | − | 5.99586i | 0.794170 | − | 1.37554i | −0.129194 | − | 0.991619i | \(-0.541239\pi\) |
0.923365 | − | 0.383924i | \(-0.125428\pi\) | |||||||
\(20\) | −4.45685 | −0.996581 | ||||||||
\(21\) | 0.129755 | + | 2.64257i | 0.0283149 | + | 0.576656i | ||||
\(22\) | 0.211950 | 0.0451879 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | −0.567725 | − | 0.983328i | −0.115886 | − | 0.200721i | ||||
\(25\) | −0.205629 | − | 0.356160i | −0.0411258 | − | 0.0712320i | ||||
\(26\) | 0.0167063 | − | 0.0289362i | 0.00327638 | − | 0.00567486i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.248601 | + | 5.06296i | 0.0469812 | + | 0.956810i | ||||
\(29\) | −6.26700 | −1.16375 | −0.581877 | − | 0.813277i | \(-0.697681\pi\) | ||||
−0.581877 | + | 0.813277i | \(0.697681\pi\) | |||||||
\(30\) | 0.337250 | − | 0.584135i | 0.0615732 | − | 0.106648i | ||||
\(31\) | −0.747919 | − | 1.29543i | −0.134330 | − | 0.232667i | 0.791011 | − | 0.611802i | \(-0.209555\pi\) |
−0.925341 | + | 0.379135i | \(0.876222\pi\) | |||||||
\(32\) | −1.64325 | − | 2.84620i | −0.290489 | − | 0.503142i | ||||
\(33\) | 0.365486 | − | 0.633040i | 0.0636229 | − | 0.110198i | ||||
\(34\) | 0.228782 | 0.0392358 | ||||||||
\(35\) | −5.17269 | + | 3.33498i | −0.874344 | + | 0.563715i | ||||
\(36\) | −1.91593 | −0.319321 | ||||||||
\(37\) | −2.07147 | + | 3.58789i | −0.340548 | + | 0.589846i | −0.984535 | − | 0.175191i | \(-0.943946\pi\) |
0.643987 | + | 0.765037i | \(0.277279\pi\) | |||||||
\(38\) | 1.00375 | + | 1.73854i | 0.162829 | + | 0.282028i | ||||
\(39\) | −0.0576166 | − | 0.0997949i | −0.00922604 | − | 0.0159800i | ||||
\(40\) | 1.32065 | − | 2.28743i | 0.208813 | − | 0.361674i | ||||
\(41\) | 8.20805 | 1.28188 | 0.640941 | − | 0.767590i | \(-0.278544\pi\) | ||||
0.640941 | + | 0.767590i | \(0.278544\pi\) | |||||||
\(42\) | −0.682387 | − | 0.350532i | −0.105295 | − | 0.0540883i | ||||
\(43\) | 1.50333 | 0.229256 | 0.114628 | − | 0.993408i | \(-0.463432\pi\) | ||||
0.114628 | + | 0.993408i | \(0.463432\pi\) | |||||||
\(44\) | 0.700243 | − | 1.21286i | 0.105566 | − | 0.182845i | ||||
\(45\) | −1.16311 | − | 2.01456i | −0.173386 | − | 0.300313i | ||||
\(46\) | 0.144978 | + | 0.251110i | 0.0213759 | + | 0.0370241i | ||||
\(47\) | 1.89394 | − | 3.28039i | 0.276259 | − | 0.478494i | −0.694193 | − | 0.719789i | \(-0.744239\pi\) |
0.970452 | + | 0.241294i | \(0.0775719\pi\) | |||||||
\(48\) | −3.50262 | −0.505559 | ||||||||
\(49\) | 4.07706 | + | 5.69013i | 0.582437 | + | 0.812876i | ||||
\(50\) | 0.119247 | 0.0168641 | ||||||||
\(51\) | 0.394511 | − | 0.683313i | 0.0552426 | − | 0.0956830i | ||||
\(52\) | −0.110389 | − | 0.191200i | −0.0153082 | − | 0.0265146i | ||||
\(53\) | 3.40867 | + | 5.90399i | 0.468217 | + | 0.810976i | 0.999340 | − | 0.0363187i | \(-0.0115631\pi\) |
−0.531123 | + | 0.847295i | \(0.678230\pi\) | |||||||
\(54\) | 0.144978 | − | 0.251110i | 0.0197291 | − | 0.0341717i | ||||
\(55\) | 1.70039 | 0.229281 | ||||||||
\(56\) | −2.67218 | − | 1.37266i | −0.357084 | − | 0.183429i | ||||
\(57\) | 6.92342 | 0.917029 | ||||||||
\(58\) | 0.908580 | − | 1.57371i | 0.119302 | − | 0.206638i | ||||
\(59\) | 3.09423 | + | 5.35936i | 0.402834 | + | 0.697729i | 0.994067 | − | 0.108772i | \(-0.0346918\pi\) |
−0.591233 | + | 0.806501i | \(0.701359\pi\) | |||||||
\(60\) | −2.22842 | − | 3.85974i | −0.287688 | − | 0.498291i | ||||
\(61\) | 1.19537 | − | 2.07044i | 0.153051 | − | 0.265093i | −0.779296 | − | 0.626656i | \(-0.784423\pi\) |
0.932348 | + | 0.361563i | \(0.117757\pi\) | |||||||
\(62\) | 0.433729 | 0.0550836 | ||||||||
\(63\) | −2.22365 | + | 1.43366i | −0.280154 | + | 0.180624i | ||||
\(64\) | −6.05229 | −0.756537 | ||||||||
\(65\) | 0.134028 | − | 0.232144i | 0.0166242 | − | 0.0287939i | ||||
\(66\) | 0.105975 | + | 0.183554i | 0.0130446 | + | 0.0225940i | ||||
\(67\) | 4.18603 | + | 7.25042i | 0.511405 | + | 0.885779i | 0.999913 | + | 0.0132197i | \(0.00420809\pi\) |
−0.488508 | + | 0.872560i | \(0.662459\pi\) | |||||||
\(68\) | 0.755854 | − | 1.30918i | 0.0916607 | − | 0.158761i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −0.0875200 | − | 1.78241i | −0.0104606 | − | 0.213039i | ||||
\(71\) | −1.53737 | −0.182452 | −0.0912260 | − | 0.995830i | \(-0.529079\pi\) | ||||
−0.0912260 | + | 0.995830i | \(0.529079\pi\) | |||||||
\(72\) | 0.567725 | − | 0.983328i | 0.0669070 | − | 0.115886i | ||||
\(73\) | −4.95047 | − | 8.57447i | −0.579409 | − | 1.00357i | −0.995547 | − | 0.0942645i | \(-0.969950\pi\) |
0.416138 | − | 0.909301i | \(-0.363383\pi\) | |||||||
\(74\) | −0.600637 | − | 1.04033i | −0.0698226 | − | 0.120936i | ||||
\(75\) | 0.205629 | − | 0.356160i | 0.0237440 | − | 0.0411258i | ||||
\(76\) | 13.2647 | 1.52157 | ||||||||
\(77\) | −0.0948473 | − | 1.93164i | −0.0108089 | − | 0.220131i | ||||
\(78\) | 0.0334127 | 0.00378324 | ||||||||
\(79\) | −0.241983 | + | 0.419128i | −0.0272253 | + | 0.0471556i | −0.879317 | − | 0.476237i | \(-0.842000\pi\) |
0.852092 | + | 0.523392i | \(0.175334\pi\) | |||||||
\(80\) | −4.07392 | − | 7.05623i | −0.455478 | − | 0.788910i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.18999 | + | 2.06112i | −0.131412 | + | 0.227613i | ||||
\(83\) | −1.84208 | −0.202195 | −0.101097 | − | 0.994877i | \(-0.532235\pi\) | ||||
−0.101097 | + | 0.994877i | \(0.532235\pi\) | |||||||
\(84\) | −4.26035 | + | 2.74678i | −0.464843 | + | 0.299698i | ||||
\(85\) | 1.83543 | 0.199081 | ||||||||
\(86\) | −0.217951 | + | 0.377501i | −0.0235022 | + | 0.0407070i | ||||
\(87\) | −3.13350 | − | 5.42738i | −0.335947 | − | 0.581877i | ||||
\(88\) | 0.414990 | + | 0.718784i | 0.0442381 | + | 0.0766227i | ||||
\(89\) | −1.53229 | + | 2.65400i | −0.162422 | + | 0.281323i | −0.935737 | − | 0.352699i | \(-0.885264\pi\) |
0.773315 | + | 0.634022i | \(0.218597\pi\) | |||||||
\(90\) | 0.674501 | 0.0710986 | ||||||||
\(91\) | −0.271191 | − | 0.139307i | −0.0284285 | − | 0.0146033i | ||||
\(92\) | 1.91593 | 0.199749 | ||||||||
\(93\) | 0.747919 | − | 1.29543i | 0.0775556 | − | 0.134330i | ||||
\(94\) | 0.549160 | + | 0.951172i | 0.0566415 | + | 0.0981059i | ||||
\(95\) | 8.05266 | + | 13.9476i | 0.826186 | + | 1.43100i | ||||
\(96\) | 1.64325 | − | 2.84620i | 0.167714 | − | 0.290489i | ||||
\(97\) | 14.8351 | 1.50628 | 0.753140 | − | 0.657860i | \(-0.228538\pi\) | ||||
0.753140 | + | 0.657860i | \(0.228538\pi\) | |||||||
\(98\) | −2.01993 | + | 0.198845i | −0.204044 | + | 0.0200864i | ||||
\(99\) | 0.730971 | 0.0734654 | ||||||||
\(100\) | 0.393970 | − | 0.682376i | 0.0393970 | − | 0.0682376i | ||||
\(101\) | −5.42346 | − | 9.39371i | −0.539654 | − | 0.934709i | −0.998922 | − | 0.0464109i | \(-0.985222\pi\) |
0.459268 | − | 0.888298i | \(-0.348112\pi\) | |||||||
\(102\) | 0.114391 | + | 0.198131i | 0.0113264 | + | 0.0196179i | ||||
\(103\) | 4.69962 | − | 8.13998i | 0.463067 | − | 0.802056i | −0.536045 | − | 0.844189i | \(-0.680082\pi\) |
0.999112 | + | 0.0421338i | \(0.0134156\pi\) | |||||||
\(104\) | 0.130841 | 0.0128301 | ||||||||
\(105\) | −5.47452 | − | 2.81219i | −0.534259 | − | 0.274441i | ||||
\(106\) | −1.97674 | −0.191998 | ||||||||
\(107\) | 8.87488 | − | 15.3718i | 0.857967 | − | 1.48604i | −0.0158970 | − | 0.999874i | \(-0.505060\pi\) |
0.873864 | − | 0.486170i | \(-0.161606\pi\) | |||||||
\(108\) | −0.957963 | − | 1.65924i | −0.0921800 | − | 0.159660i | ||||
\(109\) | 4.88652 | + | 8.46370i | 0.468043 | + | 0.810675i | 0.999333 | − | 0.0365152i | \(-0.0116257\pi\) |
−0.531290 | + | 0.847190i | \(0.678292\pi\) | |||||||
\(110\) | −0.246520 | + | 0.426986i | −0.0235048 | + | 0.0407115i | ||||
\(111\) | −4.14294 | −0.393231 | ||||||||
\(112\) | −7.78861 | + | 5.02155i | −0.735954 | + | 0.474492i | ||||
\(113\) | −3.68270 | −0.346440 | −0.173220 | − | 0.984883i | \(-0.555417\pi\) | ||||
−0.173220 | + | 0.984883i | \(0.555417\pi\) | |||||||
\(114\) | −1.00375 | + | 1.73854i | −0.0940094 | + | 0.162829i | ||||
\(115\) | 1.16311 | + | 2.01456i | 0.108460 | + | 0.187858i | ||||
\(116\) | −6.00355 | − | 10.3985i | −0.557416 | − | 0.965473i | ||||
\(117\) | 0.0576166 | − | 0.0997949i | 0.00532666 | − | 0.00922604i | ||||
\(118\) | −1.79438 | −0.165186 | ||||||||
\(119\) | −0.102380 | − | 2.08504i | −0.00938514 | − | 0.191136i | ||||
\(120\) | 2.64129 | 0.241116 | ||||||||
\(121\) | 5.23284 | − | 9.06355i | 0.475713 | − | 0.823959i | ||||
\(122\) | 0.346606 | + | 0.600339i | 0.0313802 | + | 0.0543521i | ||||
\(123\) | 4.10403 | + | 7.10838i | 0.370048 | + | 0.640941i | ||||
\(124\) | 1.43296 | − | 2.48196i | 0.128683 | − | 0.222886i | ||||
\(125\) | −10.6744 | −0.954746 | ||||||||
\(126\) | −0.0376234 | − | 0.766231i | −0.00335176 | − | 0.0682612i | ||||
\(127\) | −3.53396 | −0.313588 | −0.156794 | − | 0.987631i | \(-0.550116\pi\) | ||||
−0.156794 | + | 0.987631i | \(0.550116\pi\) | |||||||
\(128\) | 4.16396 | − | 7.21219i | 0.368045 | − | 0.637473i | ||||
\(129\) | 0.751665 | + | 1.30192i | 0.0661804 | + | 0.114628i | ||||
\(130\) | 0.0388624 | + | 0.0673117i | 0.00340846 | + | 0.00590363i | ||||
\(131\) | 2.17610 | − | 3.76912i | 0.190127 | − | 0.329310i | −0.755165 | − | 0.655535i | \(-0.772443\pi\) |
0.945292 | + | 0.326225i | \(0.105777\pi\) | |||||||
\(132\) | 1.40049 | 0.121897 | ||||||||
\(133\) | 15.3953 | − | 9.92579i | 1.33494 | − | 0.860675i | ||||
\(134\) | −2.42754 | −0.209707 | ||||||||
\(135\) | 1.16311 | − | 2.01456i | 0.100104 | − | 0.173386i | ||||
\(136\) | 0.447947 | + | 0.775867i | 0.0384112 | + | 0.0665301i | ||||
\(137\) | 8.55769 | + | 14.8223i | 0.731133 | + | 1.26636i | 0.956399 | + | 0.292062i | \(0.0943413\pi\) |
−0.225267 | + | 0.974297i | \(0.572325\pi\) | |||||||
\(138\) | −0.144978 | + | 0.251110i | −0.0123414 | + | 0.0213759i | ||||
\(139\) | 5.41785 | 0.459536 | 0.229768 | − | 0.973245i | \(-0.426203\pi\) | ||||
0.229768 | + | 0.973245i | \(0.426203\pi\) | |||||||
\(140\) | −10.4888 | − | 5.38794i | −0.886464 | − | 0.455364i | ||||
\(141\) | 3.78787 | 0.318996 | ||||||||
\(142\) | 0.222885 | − | 0.386048i | 0.0187041 | − | 0.0323965i | ||||
\(143\) | 0.0421161 | + | 0.0729472i | 0.00352192 | + | 0.00610015i | ||||
\(144\) | −1.75131 | − | 3.03336i | −0.145942 | − | 0.252780i | ||||
\(145\) | 7.28919 | − | 12.6252i | 0.605334 | − | 1.04847i | ||||
\(146\) | 2.87085 | 0.237593 | ||||||||
\(147\) | −2.88927 | + | 6.37590i | −0.238303 | + | 0.525876i | ||||
\(148\) | −7.93756 | −0.652464 | ||||||||
\(149\) | 7.61206 | − | 13.1845i | 0.623604 | − | 1.08011i | −0.365204 | − | 0.930927i | \(-0.619001\pi\) |
0.988809 | − | 0.149187i | \(-0.0476657\pi\) | |||||||
\(150\) | 0.0596236 | + | 0.103271i | 0.00486824 | + | 0.00843205i | ||||
\(151\) | −7.19027 | − | 12.4539i | −0.585136 | − | 1.01349i | −0.994858 | − | 0.101275i | \(-0.967708\pi\) |
0.409722 | − | 0.912210i | \(-0.365626\pi\) | |||||||
\(152\) | −3.93059 | + | 6.80799i | −0.318813 | + | 0.552201i | ||||
\(153\) | 0.789022 | 0.0637887 | ||||||||
\(154\) | 0.498805 | + | 0.256229i | 0.0401949 | + | 0.0206475i | ||||
\(155\) | 3.47964 | 0.279491 | ||||||||
\(156\) | 0.110389 | − | 0.191200i | 0.00883820 | − | 0.0153082i | ||||
\(157\) | 2.23320 | + | 3.86802i | 0.178229 | + | 0.308702i | 0.941274 | − | 0.337644i | \(-0.109630\pi\) |
−0.763045 | + | 0.646345i | \(0.776297\pi\) | |||||||
\(158\) | −0.0701648 | − | 0.121529i | −0.00558201 | − | 0.00966832i | ||||
\(159\) | −3.40867 | + | 5.90399i | −0.270325 | + | 0.468217i | ||||
\(160\) | 7.64511 | 0.604399 | ||||||||
\(161\) | 2.22365 | − | 1.43366i | 0.175248 | − | 0.112988i | ||||
\(162\) | 0.289957 | 0.0227812 | ||||||||
\(163\) | −0.392861 | + | 0.680455i | −0.0307713 | + | 0.0532974i | −0.881001 | − | 0.473115i | \(-0.843130\pi\) |
0.850230 | + | 0.526412i | \(0.176463\pi\) | |||||||
\(164\) | 7.86301 | + | 13.6191i | 0.613998 | + | 1.06348i | ||||
\(165\) | 0.850197 | + | 1.47258i | 0.0661877 | + | 0.114640i | ||||
\(166\) | 0.267062 | − | 0.462565i | 0.0207280 | − | 0.0359020i | ||||
\(167\) | 5.52754 | 0.427734 | 0.213867 | − | 0.976863i | \(-0.431394\pi\) | ||||
0.213867 | + | 0.976863i | \(0.431394\pi\) | |||||||
\(168\) | −0.147331 | − | 3.00050i | −0.0113668 | − | 0.231494i | ||||
\(169\) | −12.9867 | −0.998979 | ||||||||
\(170\) | −0.266098 | + | 0.460895i | −0.0204088 | + | 0.0353491i | ||||
\(171\) | 3.46171 | + | 5.99586i | 0.264723 | + | 0.458514i | ||||
\(172\) | 1.44013 | + | 2.49439i | 0.109809 | + | 0.190195i | ||||
\(173\) | 4.97558 | − | 8.61796i | 0.378286 | − | 0.655211i | −0.612527 | − | 0.790450i | \(-0.709847\pi\) |
0.990813 | + | 0.135239i | \(0.0431801\pi\) | |||||||
\(174\) | 1.81716 | 0.137759 | ||||||||
\(175\) | −0.0533629 | − | 1.08678i | −0.00403386 | − | 0.0821527i | ||||
\(176\) | 2.56031 | 0.192991 | ||||||||
\(177\) | −3.09423 | + | 5.35936i | −0.232576 | + | 0.402834i | ||||
\(178\) | −0.444297 | − | 0.769544i | −0.0333014 | − | 0.0576798i | ||||
\(179\) | 8.74582 | + | 15.1482i | 0.653693 | + | 1.13223i | 0.982220 | + | 0.187735i | \(0.0601147\pi\) |
−0.328526 | + | 0.944495i | \(0.606552\pi\) | |||||||
\(180\) | 2.22842 | − | 3.85974i | 0.166097 | − | 0.287688i | ||||
\(181\) | −19.8587 | −1.47608 | −0.738042 | − | 0.674754i | \(-0.764250\pi\) | ||||
−0.738042 | + | 0.674754i | \(0.764250\pi\) | |||||||
\(182\) | 0.0742981 | − | 0.0479022i | 0.00550735 | − | 0.00355075i | ||||
\(183\) | 2.39074 | 0.176729 | ||||||||
\(184\) | −0.567725 | + | 0.983328i | −0.0418532 | + | 0.0724919i | ||||
\(185\) | −4.81868 | − | 8.34620i | −0.354276 | − | 0.613624i | ||||
\(186\) | 0.216864 | + | 0.375620i | 0.0159013 | + | 0.0275418i | ||||
\(187\) | −0.288376 | + | 0.499482i | −0.0210882 | + | 0.0365258i | ||||
\(188\) | 7.25728 | 0.529291 | ||||||||
\(189\) | −2.35341 | − | 1.20891i | −0.171185 | − | 0.0879354i | ||||
\(190\) | −4.66985 | −0.338787 | ||||||||
\(191\) | −7.05493 | + | 12.2195i | −0.510477 | + | 0.884172i | 0.489450 | + | 0.872032i | \(0.337198\pi\) |
−0.999926 | + | 0.0121400i | \(0.996136\pi\) | |||||||
\(192\) | −3.02615 | − | 5.24144i | −0.218393 | − | 0.378268i | ||||
\(193\) | 6.36241 | + | 11.0200i | 0.457976 | + | 0.793238i | 0.998854 | − | 0.0478631i | \(-0.0152411\pi\) |
−0.540878 | + | 0.841101i | \(0.681908\pi\) | |||||||
\(194\) | −2.15078 | + | 3.72525i | −0.154417 | + | 0.267458i | ||||
\(195\) | 0.268057 | 0.0191959 | ||||||||
\(196\) | −5.53562 | + | 12.2158i | −0.395401 | + | 0.872554i | ||||
\(197\) | −14.1582 | −1.00873 | −0.504364 | − | 0.863491i | \(-0.668273\pi\) | ||||
−0.504364 | + | 0.863491i | \(0.668273\pi\) | |||||||
\(198\) | −0.105975 | + | 0.183554i | −0.00753132 | + | 0.0130446i | ||||
\(199\) | 2.11973 | + | 3.67147i | 0.150263 | + | 0.260264i | 0.931324 | − | 0.364191i | \(-0.118654\pi\) |
−0.781061 | + | 0.624455i | \(0.785321\pi\) | |||||||
\(200\) | 0.233481 | + | 0.404402i | 0.0165096 | + | 0.0285955i | ||||
\(201\) | −4.18603 | + | 7.25042i | −0.295260 | + | 0.511405i | ||||
\(202\) | 3.14514 | 0.221291 | ||||||||
\(203\) | −14.7488 | − | 7.57626i | −1.03516 | − | 0.531749i | ||||
\(204\) | 1.51171 | 0.105841 | ||||||||
\(205\) | −9.54683 | + | 16.5356i | −0.666780 | + | 1.15490i | ||||
\(206\) | 1.36269 | + | 2.36024i | 0.0949428 | + | 0.164446i | ||||
\(207\) | 0.500000 | + | 0.866025i | 0.0347524 | + | 0.0601929i | ||||
\(208\) | 0.201809 | − | 0.349543i | 0.0139929 | − | 0.0242365i | ||||
\(209\) | −5.06082 | −0.350064 | ||||||||
\(210\) | 1.49986 | − | 0.967002i | 0.103500 | − | 0.0667294i | ||||
\(211\) | −26.3917 | −1.81688 | −0.908440 | − | 0.418015i | \(-0.862726\pi\) | ||||
−0.908440 | + | 0.418015i | \(0.862726\pi\) | |||||||
\(212\) | −6.53076 | + | 11.3116i | −0.448535 | + | 0.776885i | ||||
\(213\) | −0.768684 | − | 1.33140i | −0.0526693 | − | 0.0912260i | ||||
\(214\) | 2.57333 | + | 4.45714i | 0.175909 | + | 0.304684i | ||||
\(215\) | −1.74853 | + | 3.02855i | −0.119249 | + | 0.206545i | ||||
\(216\) | 1.13545 | 0.0772575 | ||||||||
\(217\) | −0.194093 | − | 3.95285i | −0.0131759 | − | 0.268337i | ||||
\(218\) | −2.83376 | −0.191926 | ||||||||
\(219\) | 4.95047 | − | 8.57447i | 0.334522 | − | 0.579409i | ||||
\(220\) | 1.62891 | + | 2.82136i | 0.109821 | + | 0.190216i | ||||
\(221\) | 0.0454608 | + | 0.0787404i | 0.00305802 | + | 0.00529665i | ||||
\(222\) | 0.600637 | − | 1.04033i | 0.0403121 | − | 0.0698226i | ||||
\(223\) | −9.57370 | −0.641102 | −0.320551 | − | 0.947231i | \(-0.603868\pi\) | ||||
−0.320551 | + | 0.947231i | \(0.603868\pi\) | |||||||
\(224\) | −0.426442 | − | 8.68482i | −0.0284928 | − | 0.580279i | ||||
\(225\) | 0.411258 | 0.0274172 | ||||||||
\(226\) | 0.533913 | − | 0.924764i | 0.0355153 | − | 0.0615144i | ||||
\(227\) | 11.4297 | + | 19.7968i | 0.758614 | + | 1.31396i | 0.943558 | + | 0.331209i | \(0.107456\pi\) |
−0.184944 | + | 0.982749i | \(0.559210\pi\) | |||||||
\(228\) | 6.63237 | + | 11.4876i | 0.439240 | + | 0.760785i | ||||
\(229\) | 1.04031 | − | 1.80187i | 0.0687458 | − | 0.119071i | −0.829604 | − | 0.558353i | \(-0.811434\pi\) |
0.898349 | + | 0.439282i | \(0.144767\pi\) | |||||||
\(230\) | −0.674501 | −0.0444753 | ||||||||
\(231\) | 1.62543 | − | 1.04796i | 0.106945 | − | 0.0689507i | ||||
\(232\) | 7.11586 | 0.467179 | ||||||||
\(233\) | −2.50851 | + | 4.34486i | −0.164338 | + | 0.284642i | −0.936420 | − | 0.350881i | \(-0.885882\pi\) |
0.772082 | + | 0.635523i | \(0.219215\pi\) | |||||||
\(234\) | 0.0167063 | + | 0.0289362i | 0.00109213 | + | 0.00189162i | ||||
\(235\) | 4.40569 | + | 7.63089i | 0.287396 | + | 0.497784i | ||||
\(236\) | −5.92831 | + | 10.2681i | −0.385900 | + | 0.668398i | ||||
\(237\) | −0.483967 | −0.0314370 | ||||||||
\(238\) | 0.538418 | + | 0.276578i | 0.0349005 | + | 0.0179279i | ||||
\(239\) | 20.5640 | 1.33018 | 0.665089 | − | 0.746764i | \(-0.268394\pi\) | ||||
0.665089 | + | 0.746764i | \(0.268394\pi\) | |||||||
\(240\) | 4.07392 | − | 7.05623i | 0.262970 | − | 0.455478i | ||||
\(241\) | −13.3130 | − | 23.0587i | −0.857563 | − | 1.48534i | −0.874247 | − | 0.485482i | \(-0.838644\pi\) |
0.0166841 | − | 0.999861i | \(-0.494689\pi\) | |||||||
\(242\) | 1.51730 | + | 2.62804i | 0.0975356 | + | 0.168937i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 4.58048 | 0.293235 | ||||||||
\(245\) | −16.2051 | + | 1.59526i | −1.03531 | + | 0.101917i | ||||
\(246\) | −2.37998 | −0.151742 | ||||||||
\(247\) | −0.398904 | + | 0.690922i | −0.0253816 | + | 0.0439623i | ||||
\(248\) | 0.849224 | + | 1.47090i | 0.0539258 | + | 0.0934022i | ||||
\(249\) | −0.921040 | − | 1.59529i | −0.0583686 | − | 0.101097i | ||||
\(250\) | 1.54756 | − | 2.68044i | 0.0978760 | − | 0.169526i | ||||
\(251\) | −1.18435 | −0.0747552 | −0.0373776 | − | 0.999301i | \(-0.511900\pi\) | ||||
−0.0373776 | + | 0.999301i | \(0.511900\pi\) | |||||||
\(252\) | −4.50895 | − | 2.31619i | −0.284037 | − | 0.145906i | ||||
\(253\) | −0.730971 | −0.0459558 | ||||||||
\(254\) | 0.512347 | − | 0.887412i | 0.0321475 | − | 0.0556811i | ||||
\(255\) | 0.917716 | + | 1.58953i | 0.0574696 | + | 0.0995403i | ||||
\(256\) | −4.84492 | − | 8.39166i | −0.302808 | − | 0.524478i | ||||
\(257\) | 4.60903 | − | 7.98307i | 0.287503 | − | 0.497970i | −0.685710 | − | 0.727875i | \(-0.740508\pi\) |
0.973213 | + | 0.229905i | \(0.0738415\pi\) | |||||||
\(258\) | −0.435901 | −0.0271380 | ||||||||
\(259\) | −9.21246 | + | 5.93955i | −0.572435 | + | 0.369066i | ||||
\(260\) | 0.513577 | 0.0318507 | ||||||||
\(261\) | 3.13350 | − | 5.42738i | 0.193959 | − | 0.335947i | ||||
\(262\) | 0.630976 | + | 1.09288i | 0.0389818 | + | 0.0675185i | ||||
\(263\) | 11.0508 | + | 19.1406i | 0.681422 | + | 1.18026i | 0.974547 | + | 0.224183i | \(0.0719714\pi\) |
−0.293125 | + | 0.956074i | \(0.594695\pi\) | |||||||
\(264\) | −0.414990 | + | 0.718784i | −0.0255409 | + | 0.0442381i | ||||
\(265\) | −15.8586 | −0.974185 | ||||||||
\(266\) | 0.260483 | + | 5.30493i | 0.0159712 | + | 0.325266i | ||||
\(267\) | −3.06457 | −0.187549 | ||||||||
\(268\) | −8.02012 | + | 13.8913i | −0.489907 | + | 0.848543i | ||||
\(269\) | −14.6763 | − | 25.4201i | −0.894829 | − | 1.54989i | −0.834016 | − | 0.551741i | \(-0.813964\pi\) |
−0.0608136 | − | 0.998149i | \(-0.519370\pi\) | |||||||
\(270\) | 0.337250 | + | 0.584135i | 0.0205244 | + | 0.0355493i | ||||
\(271\) | −7.92265 | + | 13.7224i | −0.481266 | + | 0.833578i | −0.999769 | − | 0.0214982i | \(-0.993156\pi\) |
0.518502 | + | 0.855076i | \(0.326490\pi\) | |||||||
\(272\) | 2.76364 | 0.167571 | ||||||||
\(273\) | −0.0149521 | − | 0.304512i | −0.000904943 | − | 0.0184299i | ||||
\(274\) | −4.96272 | −0.299809 | ||||||||
\(275\) | −0.150309 | + | 0.260343i | −0.00906397 | + | 0.0156993i | ||||
\(276\) | 0.957963 | + | 1.65924i | 0.0576626 | + | 0.0998745i | ||||
\(277\) | −12.2189 | − | 21.1637i | −0.734160 | − | 1.27160i | −0.955091 | − | 0.296313i | \(-0.904243\pi\) |
0.220931 | − | 0.975289i | \(-0.429090\pi\) | |||||||
\(278\) | −0.785472 | + | 1.36048i | −0.0471095 | + | 0.0815960i | ||||
\(279\) | 1.49584 | 0.0895535 | ||||||||
\(280\) | 5.87332 | − | 3.78671i | 0.350998 | − | 0.226299i | ||||
\(281\) | −9.53666 | −0.568910 | −0.284455 | − | 0.958689i | \(-0.591813\pi\) | ||||
−0.284455 | + | 0.958689i | \(0.591813\pi\) | |||||||
\(282\) | −0.549160 | + | 0.951172i | −0.0327020 | + | 0.0566415i | ||||
\(283\) | −2.11423 | − | 3.66195i | −0.125678 | − | 0.217680i | 0.796320 | − | 0.604876i | \(-0.206777\pi\) |
−0.921998 | + | 0.387195i | \(0.873444\pi\) | |||||||
\(284\) | −1.47274 | − | 2.55086i | −0.0873911 | − | 0.151366i | ||||
\(285\) | −8.05266 | + | 13.9476i | −0.476999 | + | 0.826186i | ||||
\(286\) | −0.0244237 | −0.00144420 | ||||||||
\(287\) | 19.3169 | + | 9.92282i | 1.14024 | + | 0.585725i | ||||
\(288\) | 3.28651 | 0.193659 | ||||||||
\(289\) | 8.18872 | − | 14.1833i | 0.481690 | − | 0.834311i | ||||
\(290\) | 2.11355 | + | 3.66077i | 0.124112 | + | 0.214968i | ||||
\(291\) | 7.41757 | + | 12.8476i | 0.434826 | + | 0.753140i | ||||
\(292\) | 9.48474 | − | 16.4280i | 0.555052 | − | 0.961379i | ||||
\(293\) | 30.9919 | 1.81057 | 0.905283 | − | 0.424809i | \(-0.139659\pi\) | ||||
0.905283 | + | 0.424809i | \(0.139659\pi\) | |||||||
\(294\) | −1.18217 | − | 1.64989i | −0.0689457 | − | 0.0962236i | ||||
\(295\) | −14.3956 | −0.838147 | ||||||||
\(296\) | 2.35205 | − | 4.07387i | 0.136710 | − | 0.236789i | ||||
\(297\) | 0.365486 | + | 0.633040i | 0.0212076 | + | 0.0367327i | ||||
\(298\) | 2.20717 | + | 3.82293i | 0.127858 | + | 0.221456i | ||||
\(299\) | −0.0576166 | + | 0.0997949i | −0.00333205 | + | 0.00577129i | ||||
\(300\) | 0.787940 | 0.0454917 | ||||||||
\(301\) | 3.53795 | + | 1.81740i | 0.203924 | + | 0.104753i | ||||
\(302\) | 4.16974 | 0.239941 | ||||||||
\(303\) | 5.42346 | − | 9.39371i | 0.311570 | − | 0.539654i | ||||
\(304\) | 12.1250 | + | 21.0012i | 0.695419 | + | 1.20450i | ||||
\(305\) | 2.78068 | + | 4.81628i | 0.159221 | + | 0.275780i | ||||
\(306\) | −0.114391 | + | 0.198131i | −0.00653931 | + | 0.0113264i | ||||
\(307\) | −15.9601 | −0.910888 | −0.455444 | − | 0.890264i | \(-0.650520\pi\) | ||||
−0.455444 | + | 0.890264i | \(0.650520\pi\) | |||||||
\(308\) | 3.11419 | − | 2.00781i | 0.177448 | − | 0.114406i | ||||
\(309\) | 9.39923 | 0.534704 | ||||||||
\(310\) | −0.504472 | + | 0.873771i | −0.0286521 | + | 0.0496269i | ||||
\(311\) | 7.66126 | + | 13.2697i | 0.434430 | + | 0.752455i | 0.997249 | − | 0.0741253i | \(-0.0236165\pi\) |
−0.562819 | + | 0.826580i | \(0.690283\pi\) | |||||||
\(312\) | 0.0654207 | + | 0.113312i | 0.00370372 | + | 0.00641503i | ||||
\(313\) | 8.38668 | − | 14.5262i | 0.474043 | − | 0.821067i | −0.525515 | − | 0.850784i | \(-0.676127\pi\) |
0.999558 | + | 0.0297173i | \(0.00946072\pi\) | |||||||
\(314\) | −1.29507 | −0.0730848 | ||||||||
\(315\) | −0.301838 | − | 6.14717i | −0.0170067 | − | 0.346354i | ||||
\(316\) | −0.927244 | −0.0521616 | ||||||||
\(317\) | −16.2005 | + | 28.0601i | −0.909912 | + | 1.57601i | −0.0957284 | + | 0.995407i | \(0.530518\pi\) |
−0.814184 | + | 0.580607i | \(0.802815\pi\) | |||||||
\(318\) | −0.988368 | − | 1.71190i | −0.0554249 | − | 0.0959988i | ||||
\(319\) | 2.29050 | + | 3.96726i | 0.128243 | + | 0.222124i | ||||
\(320\) | 7.03946 | − | 12.1927i | 0.393518 | − | 0.681592i | ||||
\(321\) | 17.7498 | 0.990695 | ||||||||
\(322\) | 0.0376234 | + | 0.766231i | 0.00209667 | + | 0.0427004i | ||||
\(323\) | −5.46273 | −0.303954 | ||||||||
\(324\) | 0.957963 | − | 1.65924i | 0.0532201 | − | 0.0921800i | ||||
\(325\) | 0.0236953 | + | 0.0410415i | 0.00131438 | + | 0.00227657i | ||||
\(326\) | −0.113913 | − | 0.197303i | −0.00630904 | − | 0.0109276i | ||||
\(327\) | −4.88652 | + | 8.46370i | −0.270225 | + | 0.468043i | ||||
\(328\) | −9.31983 | −0.514601 | ||||||||
\(329\) | 8.42291 | − | 5.43050i | 0.464370 | − | 0.299393i | ||||
\(330\) | −0.493041 | −0.0271410 | ||||||||
\(331\) | −12.9793 | + | 22.4807i | −0.713404 | + | 1.23565i | 0.250167 | + | 0.968203i | \(0.419514\pi\) |
−0.963572 | + | 0.267450i | \(0.913819\pi\) | |||||||
\(332\) | −1.76464 | − | 3.05645i | −0.0968474 | − | 0.167745i | ||||
\(333\) | −2.07147 | − | 3.58789i | −0.113516 | − | 0.196615i | ||||
\(334\) | −0.801374 | + | 1.38802i | −0.0438492 | + | 0.0759491i | ||||
\(335\) | −19.4752 | −1.06404 | ||||||||
\(336\) | −8.24309 | − | 4.23436i | −0.449698 | − | 0.231003i | ||||
\(337\) | 19.2372 | 1.04791 | 0.523957 | − | 0.851744i | \(-0.324455\pi\) | ||||
0.523957 | + | 0.851744i | \(0.324455\pi\) | |||||||
\(338\) | 1.88279 | − | 3.26110i | 0.102411 | − | 0.177380i | ||||
\(339\) | −1.84135 | − | 3.18932i | −0.100009 | − | 0.173220i | ||||
\(340\) | 1.75827 | + | 3.04542i | 0.0953558 | + | 0.165161i | ||||
\(341\) | −0.546707 | + | 0.946925i | −0.0296059 | + | 0.0512789i | ||||
\(342\) | −2.00749 | −0.108553 | ||||||||
\(343\) | 2.71612 | + | 18.3200i | 0.146657 | + | 0.989187i | ||||
\(344\) | −1.70696 | −0.0920329 | ||||||||
\(345\) | −1.16311 | + | 2.01456i | −0.0626195 | + | 0.108460i | ||||
\(346\) | 1.44270 | + | 2.49884i | 0.0775602 | + | 0.134338i | ||||
\(347\) | −10.8583 | − | 18.8071i | −0.582905 | − | 1.00962i | −0.995133 | − | 0.0985400i | \(-0.968583\pi\) |
0.412228 | − | 0.911081i | \(-0.364751\pi\) | |||||||
\(348\) | 6.00355 | − | 10.3985i | 0.321824 | − | 0.557416i | ||||
\(349\) | −33.3948 | −1.78758 | −0.893792 | − | 0.448482i | \(-0.851965\pi\) | ||||
−0.893792 | + | 0.448482i | \(0.851965\pi\) | |||||||
\(350\) | 0.280637 | + | 0.144159i | 0.0150007 | + | 0.00770564i | ||||
\(351\) | 0.115233 | 0.00615069 | ||||||||
\(352\) | −1.20117 | + | 2.08049i | −0.0640226 | + | 0.110890i | ||||
\(353\) | −13.7712 | − | 23.8524i | −0.732967 | − | 1.26954i | −0.955609 | − | 0.294637i | \(-0.904801\pi\) |
0.222642 | − | 0.974900i | \(-0.428532\pi\) | |||||||
\(354\) | −0.897192 | − | 1.55398i | −0.0476852 | − | 0.0825932i | ||||
\(355\) | 1.78812 | − | 3.09712i | 0.0949036 | − | 0.164378i | ||||
\(356\) | −5.87149 | −0.311188 | ||||||||
\(357\) | 1.75451 | − | 1.13119i | 0.0928586 | − | 0.0598687i | ||||
\(358\) | −5.07182 | −0.268054 | ||||||||
\(359\) | 6.57045 | − | 11.3804i | 0.346775 | − | 0.600632i | −0.638899 | − | 0.769290i | \(-0.720610\pi\) |
0.985675 | + | 0.168658i | \(0.0539434\pi\) | |||||||
\(360\) | 1.32065 | + | 2.28743i | 0.0696042 | + | 0.120558i | ||||
\(361\) | −14.4669 | − | 25.0573i | −0.761413 | − | 1.31881i | ||||
\(362\) | 2.87908 | − | 4.98672i | 0.151321 | − | 0.262096i | ||||
\(363\) | 10.4657 | 0.549306 | ||||||||
\(364\) | −0.0286471 | − | 0.583421i | −0.00150152 | − | 0.0305796i | ||||
\(365\) | 23.0317 | 1.20553 | ||||||||
\(366\) | −0.346606 | + | 0.600339i | −0.0181174 | + | 0.0313802i | ||||
\(367\) | 14.9919 | + | 25.9668i | 0.782572 | + | 1.35545i | 0.930439 | + | 0.366448i | \(0.119426\pi\) |
−0.147866 | + | 0.989007i | \(0.547241\pi\) | |||||||
\(368\) | 1.75131 | + | 3.03336i | 0.0912933 | + | 0.158125i | ||||
\(369\) | −4.10403 | + | 7.10838i | −0.213647 | + | 0.370048i | ||||
\(370\) | 2.79442 | 0.145275 | ||||||||
\(371\) | 0.884586 | + | 18.0153i | 0.0459254 | + | 0.935308i | ||||
\(372\) | 2.86591 | 0.148591 | ||||||||
\(373\) | −7.72460 | + | 13.3794i | −0.399965 | + | 0.692759i | −0.993721 | − | 0.111885i | \(-0.964311\pi\) |
0.593756 | + | 0.804645i | \(0.297644\pi\) | |||||||
\(374\) | −0.0836166 | − | 0.144828i | −0.00432371 | − | 0.00748889i | ||||
\(375\) | −5.33719 | − | 9.24429i | −0.275611 | − | 0.477373i | ||||
\(376\) | −2.15047 | + | 3.72472i | −0.110902 | + | 0.192088i | ||||
\(377\) | 0.722167 | 0.0371935 | ||||||||
\(378\) | 0.644763 | − | 0.415698i | 0.0331631 | − | 0.0213812i | ||||
\(379\) | −28.0665 | −1.44168 | −0.720840 | − | 0.693101i | \(-0.756244\pi\) | ||||
−0.720840 | + | 0.693101i | \(0.756244\pi\) | |||||||
\(380\) | −15.4283 | + | 26.7226i | −0.791455 | + | 1.37084i | ||||
\(381\) | −1.76698 | − | 3.06050i | −0.0905250 | − | 0.156794i | ||||
\(382\) | −2.04562 | − | 3.54313i | −0.104663 | − | 0.181282i | ||||
\(383\) | 10.4320 | − | 18.0688i | 0.533051 | − | 0.923271i | −0.466204 | − | 0.884677i | \(-0.654379\pi\) |
0.999255 | − | 0.0385937i | \(-0.0122878\pi\) | |||||||
\(384\) | 8.32792 | 0.424982 | ||||||||
\(385\) | 4.00172 | + | 2.05563i | 0.203947 | + | 0.104764i | ||||
\(386\) | −3.68965 | −0.187798 | ||||||||
\(387\) | −0.751665 | + | 1.30192i | −0.0382093 | + | 0.0661804i | ||||
\(388\) | 14.2115 | + | 24.6151i | 0.721480 | + | 1.24964i | ||||
\(389\) | −1.53651 | − | 2.66131i | −0.0779039 | − | 0.134934i | 0.824441 | − | 0.565947i | \(-0.191489\pi\) |
−0.902345 | + | 0.431014i | \(0.858156\pi\) | |||||||
\(390\) | −0.0388624 | + | 0.0673117i | −0.00196788 | + | 0.00340846i | ||||
\(391\) | −0.789022 | −0.0399026 | ||||||||
\(392\) | −4.62930 | − | 6.46085i | −0.233815 | − | 0.326322i | ||||
\(393\) | 4.35221 | 0.219540 | ||||||||
\(394\) | 2.05263 | − | 3.55526i | 0.103410 | − | 0.179111i | ||||
\(395\) | −0.562905 | − | 0.974980i | −0.0283228 | − | 0.0490565i | ||||
\(396\) | 0.700243 | + | 1.21286i | 0.0351885 | + | 0.0609483i | ||||
\(397\) | 17.2427 | − | 29.8652i | 0.865385 | − | 1.49889i | −0.00127899 | − | 0.999999i | \(-0.500407\pi\) |
0.866664 | − | 0.498892i | \(-0.166260\pi\) | |||||||
\(398\) | −1.22926 | −0.0616171 | ||||||||
\(399\) | 16.2936 | + | 8.36981i | 0.815702 | + | 0.419014i | ||||
\(400\) | 1.44048 | 0.0720240 | ||||||||
\(401\) | 16.9713 | − | 29.3952i | 0.847508 | − | 1.46793i | −0.0359181 | − | 0.999355i | \(-0.511436\pi\) |
0.883426 | − | 0.468571i | \(-0.155231\pi\) | |||||||
\(402\) | −1.21377 | − | 2.10231i | −0.0605372 | − | 0.104854i | ||||
\(403\) | 0.0861851 | + | 0.149277i | 0.00429319 | + | 0.00743602i | ||||
\(404\) | 10.3909 | − | 17.9976i | 0.516969 | − | 0.895416i | ||||
\(405\) | 2.32621 | 0.115590 | ||||||||
\(406\) | 4.04073 | − | 2.60518i | 0.200538 | − | 0.129293i | ||||
\(407\) | 3.02837 | 0.150111 | ||||||||
\(408\) | −0.447947 | + | 0.775867i | −0.0221767 | + | 0.0384112i | ||||
\(409\) | −7.16031 | − | 12.4020i | −0.354055 | − | 0.613241i | 0.632901 | − | 0.774233i | \(-0.281864\pi\) |
−0.986956 | + | 0.160992i | \(0.948531\pi\) | |||||||
\(410\) | −2.76817 | − | 4.79461i | −0.136710 | − | 0.236789i | ||||
\(411\) | −8.55769 | + | 14.8223i | −0.422120 | + | 0.731133i | ||||
\(412\) | 18.0082 | 0.887202 | ||||||||
\(413\) | 0.802984 | + | 16.3534i | 0.0395123 | + | 0.804699i | ||||
\(414\) | −0.289957 | −0.0142506 | ||||||||
\(415\) | 2.14253 | − | 3.71098i | 0.105173 | − | 0.182165i | ||||
\(416\) | 0.189357 | + | 0.327977i | 0.00928401 | + | 0.0160804i | ||||
\(417\) | 2.70893 | + | 4.69200i | 0.132657 | + | 0.229768i | ||||
\(418\) | 0.733709 | − | 1.27082i | 0.0358869 | − | 0.0621579i | ||||
\(419\) | 14.0322 | 0.685520 | 0.342760 | − | 0.939423i | \(-0.388638\pi\) | ||||
0.342760 | + | 0.939423i | \(0.388638\pi\) | |||||||
\(420\) | −0.578299 | − | 11.7775i | −0.0282181 | − | 0.574684i | ||||
\(421\) | −33.9644 | −1.65532 | −0.827662 | − | 0.561227i | \(-0.810329\pi\) | ||||
−0.827662 | + | 0.561227i | \(0.810329\pi\) | |||||||
\(422\) | 3.82623 | − | 6.62722i | 0.186258 | − | 0.322608i | ||||
\(423\) | 1.89394 | + | 3.28039i | 0.0920863 | + | 0.159498i | ||||
\(424\) | −3.87037 | − | 6.70369i | −0.187962 | − | 0.325560i | ||||
\(425\) | −0.162246 | + | 0.281018i | −0.00787008 | + | 0.0136314i | ||||
\(426\) | 0.445770 | 0.0215976 | ||||||||
\(427\) | 5.31617 | − | 3.42750i | 0.257268 | − | 0.165868i | ||||
\(428\) | 34.0072 | 1.64380 | ||||||||
\(429\) | −0.0421161 | + | 0.0729472i | −0.00203338 | + | 0.00352192i | ||||
\(430\) | −0.506999 | − | 0.878148i | −0.0244497 | − | 0.0423481i | ||||
\(431\) | −11.4813 | − | 19.8861i | −0.553033 | − | 0.957882i | −0.998054 | − | 0.0623614i | \(-0.980137\pi\) |
0.445020 | − | 0.895521i | \(-0.353196\pi\) | |||||||
\(432\) | 1.75131 | − | 3.03336i | 0.0842599 | − | 0.145942i | ||||
\(433\) | 19.1710 | 0.921299 | 0.460650 | − | 0.887582i | \(-0.347616\pi\) | ||||
0.460650 | + | 0.887582i | \(0.347616\pi\) | |||||||
\(434\) | 1.02074 | + | 0.524340i | 0.0489971 | + | 0.0251691i | ||||
\(435\) | 14.5784 | 0.698979 | ||||||||
\(436\) | −9.36220 | + | 16.2158i | −0.448368 | + | 0.776596i | ||||
\(437\) | −3.46171 | − | 5.99586i | −0.165596 | − | 0.286821i | ||||
\(438\) | 1.43542 | + | 2.48623i | 0.0685872 | + | 0.118796i | ||||
\(439\) | 14.7613 | − | 25.5673i | 0.704518 | − | 1.22026i | −0.262347 | − | 0.964974i | \(-0.584496\pi\) |
0.966865 | − | 0.255288i | \(-0.0821703\pi\) | |||||||
\(440\) | −1.93071 | −0.0920430 | ||||||||
\(441\) | −6.96633 | + | 0.685774i | −0.331730 | + | 0.0326559i | ||||
\(442\) | −0.0263633 | −0.00125398 | ||||||||
\(443\) | 6.13803 | − | 10.6314i | 0.291627 | − | 0.505112i | −0.682568 | − | 0.730822i | \(-0.739137\pi\) |
0.974195 | + | 0.225710i | \(0.0724702\pi\) | |||||||
\(444\) | −3.96878 | − | 6.87413i | −0.188350 | − | 0.326232i | ||||
\(445\) | −3.56442 | − | 6.17376i | −0.168970 | − | 0.292664i | ||||
\(446\) | 1.38798 | − | 2.40405i | 0.0657227 | − | 0.113835i | ||||
\(447\) | 15.2241 | 0.720076 | ||||||||
\(448\) | −14.2435 | − | 7.31669i | −0.672943 | − | 0.345681i | ||||
\(449\) | 33.5155 | 1.58169 | 0.790847 | − | 0.612014i | \(-0.209640\pi\) | ||||
0.790847 | + | 0.612014i | \(0.209640\pi\) | |||||||
\(450\) | −0.0596236 | + | 0.103271i | −0.00281068 | + | 0.00486824i | ||||
\(451\) | −2.99993 | − | 5.19602i | −0.141261 | − | 0.244671i | ||||
\(452\) | −3.52789 | − | 6.11049i | −0.165938 | − | 0.287413i | ||||
\(453\) | 7.19027 | − | 12.4539i | 0.337828 | − | 0.585136i | ||||
\(454\) | −6.62822 | −0.311078 | ||||||||
\(455\) | 0.596065 | − | 0.384301i | 0.0279440 | − | 0.0180163i | ||||
\(456\) | −7.86119 | −0.368134 | ||||||||
\(457\) | 13.4390 | − | 23.2770i | 0.628650 | − | 1.08885i | −0.359172 | − | 0.933271i | \(-0.616941\pi\) |
0.987823 | − | 0.155583i | \(-0.0497257\pi\) | |||||||
\(458\) | 0.301646 | + | 0.522466i | 0.0140950 | + | 0.0244132i | ||||
\(459\) | 0.394511 | + | 0.683313i | 0.0184142 | + | 0.0318943i | ||||
\(460\) | −2.22842 | + | 3.85974i | −0.103901 | + | 0.179961i | ||||
\(461\) | −33.3536 | −1.55343 | −0.776715 | − | 0.629852i | \(-0.783115\pi\) | ||||
−0.776715 | + | 0.629852i | \(0.783115\pi\) | |||||||
\(462\) | 0.0275016 | + | 0.560092i | 0.00127949 | + | 0.0260579i | ||||
\(463\) | −15.9403 | −0.740806 | −0.370403 | − | 0.928871i | \(-0.620780\pi\) | ||||
−0.370403 | + | 0.928871i | \(0.620780\pi\) | |||||||
\(464\) | 10.9755 | − | 19.0101i | 0.509523 | − | 0.882520i | ||||
\(465\) | 1.73982 | + | 3.01345i | 0.0806821 | + | 0.139746i | ||||
\(466\) | −0.727359 | − | 1.25982i | −0.0336943 | − | 0.0583602i | ||||
\(467\) | −1.86261 | + | 3.22613i | −0.0861912 | + | 0.149287i | −0.905898 | − | 0.423496i | \(-0.860803\pi\) |
0.819707 | + | 0.572783i | \(0.194136\pi\) | |||||||
\(468\) | 0.220778 | 0.0102055 | ||||||||
\(469\) | 1.08632 | + | 22.1237i | 0.0501615 | + | 1.02158i | ||||
\(470\) | −2.55492 | −0.117850 | ||||||||
\(471\) | −2.23320 | + | 3.86802i | −0.102901 | + | 0.178229i | ||||
\(472\) | −3.51334 | − | 6.08528i | −0.161714 | − | 0.280098i | ||||
\(473\) | −0.549446 | − | 0.951668i | −0.0252635 | − | 0.0437577i | ||||
\(474\) | 0.0701648 | − | 0.121529i | 0.00322277 | − | 0.00558201i | ||||
\(475\) | −2.84731 | −0.130644 | ||||||||
\(476\) | 3.36151 | − | 2.16727i | 0.154075 | − | 0.0993365i | ||||
\(477\) | −6.81735 | −0.312145 | ||||||||
\(478\) | −2.98134 | + | 5.16384i | −0.136363 | + | 0.236188i | ||||
\(479\) | −0.512438 | − | 0.887569i | −0.0234139 | − | 0.0405541i | 0.854081 | − | 0.520140i | \(-0.174120\pi\) |
−0.877495 | + | 0.479586i | \(0.840787\pi\) | |||||||
\(480\) | 3.82255 | + | 6.62086i | 0.174475 | + | 0.302199i | ||||
\(481\) | 0.238702 | − | 0.413444i | 0.0108839 | − | 0.0188514i | ||||
\(482\) | 7.72036 | 0.351653 | ||||||||
\(483\) | 2.35341 | + | 1.20891i | 0.107084 | + | 0.0550074i | ||||
\(484\) | 20.0515 | 0.911430 | ||||||||
\(485\) | −17.2548 | + | 29.8863i | −0.783502 | + | 1.35706i | ||||
\(486\) | 0.144978 | + | 0.251110i | 0.00657635 | + | 0.0113906i | ||||
\(487\) | −4.06377 | − | 7.03866i | −0.184147 | − | 0.318952i | 0.759142 | − | 0.650925i | \(-0.225619\pi\) |
−0.943289 | + | 0.331973i | \(0.892286\pi\) | |||||||
\(488\) | −1.35728 | + | 2.35088i | −0.0614412 | + | 0.106419i | ||||
\(489\) | −0.785722 | −0.0355316 | ||||||||
\(490\) | 1.94881 | − | 4.30055i | 0.0880384 | − | 0.194279i | ||||
\(491\) | −3.42514 | −0.154574 | −0.0772871 | − | 0.997009i | \(-0.524626\pi\) | ||||
−0.0772871 | + | 0.997009i | \(0.524626\pi\) | |||||||
\(492\) | −7.86301 | + | 13.6191i | −0.354492 | + | 0.613998i | ||||
\(493\) | 2.47240 | + | 4.28233i | 0.111351 | + | 0.192866i | ||||
\(494\) | −0.115665 | − | 0.200337i | −0.00520401 | − | 0.00901361i | ||||
\(495\) | −0.850197 | + | 1.47258i | −0.0382135 | + | 0.0661877i | ||||
\(496\) | 5.23935 | 0.235254 | ||||||||
\(497\) | −3.61805 | − | 1.85854i | −0.162292 | − | 0.0833670i | ||||
\(498\) | 0.534124 | 0.0239347 | ||||||||
\(499\) | 2.98901 | − | 5.17711i | 0.133806 | − | 0.231759i | −0.791334 | − | 0.611383i | \(-0.790613\pi\) |
0.925141 | + | 0.379624i | \(0.123947\pi\) | |||||||
\(500\) | −10.2257 | − | 17.7114i | −0.457305 | − | 0.792076i | ||||
\(501\) | 2.76377 | + | 4.78699i | 0.123476 | + | 0.213867i | ||||
\(502\) | 0.171705 | − | 0.297401i | 0.00766355 | − | 0.0132737i | ||||
\(503\) | 30.6662 | 1.36734 | 0.683669 | − | 0.729793i | \(-0.260383\pi\) | ||||
0.683669 | + | 0.729793i | \(0.260383\pi\) | |||||||
\(504\) | 2.52485 | − | 1.62784i | 0.112466 | − | 0.0725099i | ||||
\(505\) | 25.2322 | 1.12282 | ||||||||
\(506\) | 0.105975 | − | 0.183554i | 0.00471116 | − | 0.00815998i | ||||
\(507\) | −6.49336 | − | 11.2468i | −0.288380 | − | 0.499489i | ||||
\(508\) | −3.38540 | − | 5.86368i | −0.150203 | − | 0.260159i | ||||
\(509\) | −21.6478 | + | 37.4952i | −0.959523 | + | 1.66194i | −0.235864 | + | 0.971786i | \(0.575792\pi\) |
−0.723659 | + | 0.690157i | \(0.757541\pi\) | |||||||
\(510\) | −0.532196 | −0.0235660 | ||||||||
\(511\) | −1.28470 | − | 26.1639i | −0.0568318 | − | 1.15742i | ||||
\(512\) | 19.4655 | 0.860260 | ||||||||
\(513\) | −3.46171 | + | 5.99586i | −0.152838 | + | 0.264723i | ||||
\(514\) | 1.33642 | + | 2.31475i | 0.0589469 | + | 0.102099i | ||||
\(515\) | 10.9323 | + | 18.9353i | 0.481735 | + | 0.834389i | ||||
\(516\) | −1.44013 | + | 2.49439i | −0.0633984 | + | 0.109809i | ||||
\(517\) | −2.76882 | −0.121773 | ||||||||
\(518\) | −0.155872 | − | 3.17445i | −0.00684861 | − | 0.139477i | ||||
\(519\) | 9.95116 | 0.436808 | ||||||||
\(520\) | −0.152182 | + | 0.263588i | −0.00667364 | + | 0.0115591i | ||||
\(521\) | −19.9488 | − | 34.5524i | −0.873974 | − | 1.51377i | −0.857852 | − | 0.513898i | \(-0.828201\pi\) |
−0.0161226 | − | 0.999870i | \(-0.505132\pi\) | |||||||
\(522\) | 0.908580 | + | 1.57371i | 0.0397675 | + | 0.0688793i | ||||
\(523\) | −9.28460 | + | 16.0814i | −0.405987 | + | 0.703191i | −0.994436 | − | 0.105344i | \(-0.966406\pi\) |
0.588449 | + | 0.808535i | \(0.299739\pi\) | |||||||
\(524\) | 8.33850 | 0.364269 | ||||||||
\(525\) | 0.914496 | − | 0.589602i | 0.0399119 | − | 0.0257324i | ||||
\(526\) | −6.40851 | −0.279424 | ||||||||
\(527\) | −0.590125 | + | 1.02213i | −0.0257062 | + | 0.0445245i | ||||
\(528\) | 1.28016 | + | 2.21730i | 0.0557117 | + | 0.0964954i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 2.29915 | − | 3.98225i | 0.0998688 | − | 0.172978i | ||||
\(531\) | −6.18845 | −0.268556 | ||||||||
\(532\) | 31.2174 | + | 16.0359i | 1.35344 | + | 0.695245i | ||||
\(533\) | −0.945840 | −0.0409689 | ||||||||
\(534\) | 0.444297 | − | 0.769544i | 0.0192266 | − | 0.0333014i | ||||
\(535\) | 20.6449 | + | 35.7579i | 0.892555 | + | 1.54595i | ||||
\(536\) | −4.75302 | − | 8.23248i | −0.205299 | − | 0.355589i | ||||
\(537\) | −8.74582 | + | 15.1482i | −0.377410 | + | 0.653693i | ||||
\(538\) | 8.51098 | 0.366934 | ||||||||
\(539\) | 2.11197 | − | 4.66060i | 0.0909690 | − | 0.200746i | ||||
\(540\) | 4.45685 | 0.191792 | ||||||||
\(541\) | 20.5298 | − | 35.5587i | 0.882646 | − | 1.52879i | 0.0342589 | − | 0.999413i | \(-0.489093\pi\) |
0.848388 | − | 0.529376i | \(-0.177574\pi\) | |||||||
\(542\) | −2.29723 | − | 3.97891i | −0.0986743 | − | 0.170909i | ||||
\(543\) | −9.92934 | − | 17.1981i | −0.426109 | − | 0.738042i | ||||
\(544\) | −1.29656 | + | 2.24571i | −0.0555897 | + | 0.0962842i | ||||
\(545\) | −22.7341 | −0.973824 | ||||||||
\(546\) | 0.0786336 | + | 0.0403930i | 0.00336521 | + | 0.00172866i | ||||
\(547\) | 13.7117 | 0.586268 | 0.293134 | − | 0.956071i | \(-0.405302\pi\) | ||||
0.293134 | + | 0.956071i | \(0.405302\pi\) | |||||||
\(548\) | −16.3959 | + | 28.3985i | −0.700398 | + | 1.21312i | ||||
\(549\) | 1.19537 | + | 2.07044i | 0.0510171 | + | 0.0883643i | ||||
\(550\) | −0.0435831 | − | 0.0754882i | −0.00185839 | − | 0.00321883i | ||||
\(551\) | −21.6945 | + | 37.5760i | −0.924218 | + | 1.60079i | ||||
\(552\) | −1.13545 | −0.0483279 | ||||||||
\(553\) | −1.07617 | + | 0.693842i | −0.0457636 | + | 0.0295052i | ||||
\(554\) | 7.08588 | 0.301050 | ||||||||
\(555\) | 4.81868 | − | 8.34620i | 0.204541 | − | 0.354276i | ||||
\(556\) | 5.19010 | + | 8.98952i | 0.220109 | + | 0.381240i | ||||
\(557\) | 0.0463551 | + | 0.0802894i | 0.00196413 | + | 0.00340197i | 0.867006 | − | 0.498298i | \(-0.166041\pi\) |
−0.865042 | + | 0.501700i | \(0.832708\pi\) | |||||||
\(558\) | −0.216864 | + | 0.375620i | −0.00918060 | + | 0.0159013i | ||||
\(559\) | −0.173234 | −0.00732700 | ||||||||
\(560\) | −1.05722 | − | 21.5312i | −0.0446759 | − | 0.909859i | ||||
\(561\) | −0.576752 | −0.0243505 | ||||||||
\(562\) | 1.38261 | − | 2.39475i | 0.0583219 | − | 0.101016i | ||||
\(563\) | −20.7489 | − | 35.9382i | −0.874464 | − | 1.51462i | −0.857333 | − | 0.514762i | \(-0.827880\pi\) |
−0.0171307 | − | 0.999853i | \(-0.505453\pi\) | |||||||
\(564\) | 3.62864 | + | 6.28499i | 0.152793 | + | 0.264646i | ||||
\(565\) | 4.28337 | − | 7.41902i | 0.180203 | − | 0.312121i | ||||
\(566\) | 1.22607 | 0.0515355 | ||||||||
\(567\) | −0.129755 | − | 2.64257i | −0.00544921 | − | 0.110977i | ||||
\(568\) | 1.74560 | 0.0732439 | ||||||||
\(569\) | −7.47013 | + | 12.9386i | −0.313164 | + | 0.542416i | −0.979046 | − | 0.203642i | \(-0.934722\pi\) |
0.665881 | + | 0.746058i | \(0.268056\pi\) | |||||||
\(570\) | −2.33493 | − | 4.04421i | −0.0977993 | − | 0.169393i | ||||
\(571\) | −12.2330 | − | 21.1882i | −0.511935 | − | 0.886698i | −0.999904 | − | 0.0138372i | \(-0.995595\pi\) |
0.487969 | − | 0.872861i | \(-0.337738\pi\) | |||||||
\(572\) | −0.0806912 | + | 0.139761i | −0.00337387 | + | 0.00584371i | ||||
\(573\) | −14.1099 | −0.589448 | ||||||||
\(574\) | −5.29225 | + | 3.41207i | −0.220894 | + | 0.142417i | ||||
\(575\) | −0.411258 | −0.0171507 | ||||||||
\(576\) | 3.02615 | − | 5.24144i | 0.126089 | − | 0.218393i | ||||
\(577\) | 6.96129 | + | 12.0573i | 0.289802 | + | 0.501953i | 0.973762 | − | 0.227567i | \(-0.0730771\pi\) |
−0.683960 | + | 0.729520i | \(0.739744\pi\) | |||||||
\(578\) | 2.37438 | + | 4.11254i | 0.0987610 | + | 0.171059i | ||||
\(579\) | −6.36241 | + | 11.0200i | −0.264413 | + | 0.457976i | ||||
\(580\) | 27.9311 | 1.15977 | ||||||||
\(581\) | −4.33517 | − | 2.22691i | −0.179853 | − | 0.0923880i | ||||
\(582\) | −4.30155 | −0.178305 | ||||||||
\(583\) | 2.49164 | − | 4.31565i | 0.103193 | − | 0.178736i | ||||
\(584\) | 5.62101 | + | 9.73588i | 0.232599 | + | 0.402873i | ||||
\(585\) | 0.134028 | + | 0.232144i | 0.00554139 | + | 0.00959797i | ||||
\(586\) | −4.49316 | + | 7.78237i | −0.185611 | + | 0.321487i | ||||
\(587\) | −16.3231 | −0.673728 | −0.336864 | − | 0.941553i | \(-0.609366\pi\) | ||||
−0.336864 | + | 0.941553i | \(0.609366\pi\) | |||||||
\(588\) | −13.3470 | + | 1.31389i | −0.550419 | + | 0.0541840i | ||||
\(589\) | −10.3563 | −0.426725 | ||||||||
\(590\) | 2.08706 | − | 3.61489i | 0.0859228 | − | 0.148823i | ||||
\(591\) | −7.07908 | − | 12.2613i | −0.291195 | − | 0.504364i | ||||
\(592\) | −7.25557 | − | 12.5670i | −0.298202 | − | 0.516501i | ||||
\(593\) | −21.8493 | + | 37.8441i | −0.897244 | + | 1.55407i | −0.0662422 | + | 0.997804i | \(0.521101\pi\) |
−0.831002 | + | 0.556269i | \(0.812232\pi\) | |||||||
\(594\) | −0.211950 | −0.00869642 | ||||||||
\(595\) | 4.31952 | + | 2.21888i | 0.177083 | + | 0.0909651i | ||||
\(596\) | 29.1683 | 1.19478 | ||||||||
\(597\) | −2.11973 | + | 3.67147i | −0.0867546 | + | 0.150263i | ||||
\(598\) | −0.0167063 | − | 0.0289362i | −0.000683173 | − | 0.00118329i | ||||
\(599\) | −5.51281 | − | 9.54847i | −0.225247 | − | 0.390140i | 0.731146 | − | 0.682221i | \(-0.238986\pi\) |
−0.956394 | + | 0.292081i | \(0.905652\pi\) | |||||||
\(600\) | −0.233481 | + | 0.404402i | −0.00953184 | + | 0.0165096i | ||||
\(601\) | −6.86484 | −0.280023 | −0.140011 | − | 0.990150i | \(-0.544714\pi\) | ||||
−0.140011 | + | 0.990150i | \(0.544714\pi\) | |||||||
\(602\) | −0.969293 | + | 0.624932i | −0.0395054 | + | 0.0254703i | ||||
\(603\) | −8.37206 | −0.340937 | ||||||||
\(604\) | 13.7760 | − | 23.8608i | 0.560538 | − | 0.970881i | ||||
\(605\) | 12.1727 | + | 21.0837i | 0.494890 | + | 0.857175i | ||||
\(606\) | 1.57257 | + | 2.72377i | 0.0638812 | + | 0.110646i | ||||
\(607\) | −9.32609 | + | 16.1533i | −0.378534 | + | 0.655641i | −0.990849 | − | 0.134973i | \(-0.956905\pi\) |
0.612315 | + | 0.790614i | \(0.290238\pi\) | |||||||
\(608\) | −22.7539 | −0.922791 | ||||||||
\(609\) | −0.813177 | − | 16.5610i | −0.0329516 | − | 0.671085i | ||||
\(610\) | −1.61256 | −0.0652905 | ||||||||
\(611\) | −0.218244 | + | 0.378010i | −0.00882922 | + | 0.0152927i | ||||
\(612\) | 0.755854 | + | 1.30918i | 0.0305536 | + | 0.0529203i | ||||
\(613\) | −8.03007 | − | 13.9085i | −0.324331 | − | 0.561758i | 0.657045 | − | 0.753851i | \(-0.271806\pi\) |
−0.981377 | + | 0.192093i | \(0.938473\pi\) | |||||||
\(614\) | 2.31386 | − | 4.00773i | 0.0933799 | − | 0.161739i | ||||
\(615\) | −19.0937 | −0.769931 | ||||||||
\(616\) | 0.107694 | + | 2.19328i | 0.00433913 | + | 0.0883698i | ||||
\(617\) | 11.5349 | 0.464376 | 0.232188 | − | 0.972671i | \(-0.425412\pi\) | ||||
0.232188 | + | 0.972671i | \(0.425412\pi\) | |||||||
\(618\) | −1.36269 | + | 2.36024i | −0.0548153 | + | 0.0949428i | ||||
\(619\) | 10.1264 | + | 17.5395i | 0.407015 | + | 0.704971i | 0.994554 | − | 0.104225i | \(-0.0332364\pi\) |
−0.587539 | + | 0.809196i | \(0.699903\pi\) | |||||||
\(620\) | 3.33336 | + | 5.77355i | 0.133871 | + | 0.231871i | ||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | −4.44287 | −0.178143 | ||||||||
\(623\) | −6.81454 | + | 4.39354i | −0.273019 | + | 0.176023i | ||||
\(624\) | 0.403618 | 0.0161577 | ||||||||
\(625\) | 13.4436 | − | 23.2850i | 0.537743 | − | 0.931398i | ||||
\(626\) | 2.43178 | + | 4.21196i | 0.0971933 | + | 0.168344i | ||||
\(627\) | −2.53041 | − | 4.38280i | −0.101055 | − | 0.175032i | ||||
\(628\) | −4.27865 | + | 7.41084i | −0.170737 | + | 0.295725i | ||||
\(629\) | 3.26887 | 0.130338 | ||||||||
\(630\) | 1.58738 | + | 0.815412i | 0.0632426 | + | 0.0324868i | ||||
\(631\) | 9.38947 | 0.373789 | 0.186894 | − | 0.982380i | \(-0.440158\pi\) | ||||
0.186894 | + | 0.982380i | \(0.440158\pi\) | |||||||
\(632\) | 0.274760 | − | 0.475898i | 0.0109294 | − | 0.0189302i | ||||
\(633\) | −13.1959 | − | 22.8559i | −0.524488 | − | 0.908440i | ||||
\(634\) | −4.69745 | − | 8.13623i | −0.186560 | − | 0.323131i | ||||
\(635\) | 4.11036 | − | 7.11936i | 0.163115 | − | 0.282523i | ||||
\(636\) | −13.0615 | −0.517923 | ||||||||
\(637\) | −0.469813 | − | 0.655692i | −0.0186147 | − | 0.0259795i | ||||
\(638\) | −1.32829 | −0.0525876 | ||||||||
\(639\) | 0.768684 | − | 1.33140i | 0.0304087 | − | 0.0526693i | ||||
\(640\) | 9.68625 | + | 16.7771i | 0.382883 | + | 0.663172i | ||||
\(641\) | −1.01696 | − | 1.76142i | −0.0401674 | − | 0.0695719i | 0.845243 | − | 0.534382i | \(-0.179456\pi\) |
−0.885410 | + | 0.464811i | \(0.846122\pi\) | |||||||
\(642\) | −2.57333 | + | 4.45714i | −0.101561 | + | 0.175909i | ||||
\(643\) | −11.7666 | −0.464029 | −0.232015 | − | 0.972712i | \(-0.574532\pi\) | ||||
−0.232015 | + | 0.972712i | \(0.574532\pi\) | |||||||
\(644\) | 4.50895 | + | 2.31619i | 0.177678 | + | 0.0912705i | ||||
\(645\) | −3.49706 | −0.137697 | ||||||||
\(646\) | 0.791978 | − | 1.37175i | 0.0311599 | − | 0.0539706i | ||||
\(647\) | 6.07993 | + | 10.5307i | 0.239027 | + | 0.414006i | 0.960435 | − | 0.278503i | \(-0.0898383\pi\) |
−0.721409 | + | 0.692510i | \(0.756505\pi\) | |||||||
\(648\) | 0.567725 | + | 0.983328i | 0.0223023 | + | 0.0386288i | ||||
\(649\) | 2.26179 | − | 3.91754i | 0.0887830 | − | 0.153777i | ||||
\(650\) | −0.0137412 | −0.000538975 | ||||||||
\(651\) | 3.32623 | − | 2.14452i | 0.130365 | − | 0.0840502i | ||||
\(652\) | −1.50538 | −0.0589554 | ||||||||
\(653\) | 16.9183 | − | 29.3034i | 0.662065 | − | 1.14673i | −0.318007 | − | 0.948088i | \(-0.603014\pi\) |
0.980072 | − | 0.198642i | \(-0.0636530\pi\) | |||||||
\(654\) | −1.41688 | − | 2.45411i | −0.0554043 | − | 0.0959631i | ||||
\(655\) | 5.06208 | + | 8.76777i | 0.197792 | + | 0.342585i | ||||
\(656\) | −14.3748 | + | 24.8980i | −0.561243 | + | 0.972102i | ||||
\(657\) | 9.90095 | 0.386273 | ||||||||
\(658\) | 0.142513 | + | 2.90238i | 0.00555572 | + | 0.113147i | ||||
\(659\) | 15.7293 | 0.612727 | 0.306363 | − | 0.951915i | \(-0.400888\pi\) | ||||
0.306363 | + | 0.951915i | \(0.400888\pi\) | |||||||
\(660\) | −1.62891 | + | 2.82136i | −0.0634053 | + | 0.109821i | ||||
\(661\) | −15.5879 | − | 26.9990i | −0.606297 | − | 1.05014i | −0.991845 | − | 0.127450i | \(-0.959321\pi\) |
0.385548 | − | 0.922688i | \(-0.374013\pi\) | |||||||
\(662\) | −3.76342 | − | 6.51844i | −0.146270 | − | 0.253346i | ||||
\(663\) | −0.0454608 | + | 0.0787404i | −0.00176555 | + | 0.00305802i | ||||
\(664\) | 2.09159 | 0.0811694 | ||||||||
\(665\) | 2.08975 | + | 42.5594i | 0.0810371 | + | 1.65038i | ||||
\(666\) | 1.20127 | 0.0465484 | ||||||||
\(667\) | −3.13350 | + | 5.42738i | −0.121330 | + | 0.210149i | ||||
\(668\) | 5.29518 | + | 9.17151i | 0.204876 | + | 0.354856i | ||||
\(669\) | −4.78685 | − | 8.29107i | −0.185070 | − | 0.320551i | ||||
\(670\) | 2.82348 | − | 4.89041i | 0.109081 | − | 0.188933i | ||||
\(671\) | −1.74756 | −0.0674639 | ||||||||
\(672\) | 7.30805 | − | 4.71172i | 0.281914 | − | 0.181758i | ||||
\(673\) | 9.23484 | 0.355977 | 0.177988 | − | 0.984033i | \(-0.443041\pi\) | ||||
0.177988 | + | 0.984033i | \(0.443041\pi\) | |||||||
\(674\) | −2.78897 | + | 4.83064i | −0.107427 | + | 0.186069i | ||||
\(675\) | 0.205629 | + | 0.356160i | 0.00791467 | + | 0.0137086i | ||||
\(676\) | −12.4408 | − | 21.5481i | −0.478492 | − | 0.828772i | ||||
\(677\) | −22.7702 | + | 39.4391i | −0.875128 | + | 1.51577i | −0.0185021 | + | 0.999829i | \(0.505890\pi\) |
−0.856626 | + | 0.515938i | \(0.827444\pi\) | |||||||
\(678\) | 1.06783 | 0.0410096 | ||||||||
\(679\) | 34.9131 | + | 17.9344i | 1.33984 | + | 0.688259i | ||||
\(680\) | −2.08404 | −0.0799193 | ||||||||
\(681\) | −11.4297 | + | 19.7968i | −0.437986 | + | 0.758614i | ||||
\(682\) | −0.158522 | − | 0.274567i | −0.00607010 | − | 0.0105137i | ||||
\(683\) | −6.11461 | − | 10.5908i | −0.233969 | − | 0.405247i | 0.725003 | − | 0.688745i | \(-0.241838\pi\) |
−0.958973 | + | 0.283499i | \(0.908505\pi\) | |||||||
\(684\) | −6.63237 | + | 11.4876i | −0.253595 | + | 0.439240i | ||||
\(685\) | −39.8140 | −1.52121 | ||||||||
\(686\) | −4.99412 | − | 1.97396i | −0.190676 | − | 0.0753662i | ||||
\(687\) | 2.08062 | 0.0793808 | ||||||||
\(688\) | −2.63280 | + | 4.56014i | −0.100374 | + | 0.173854i | ||||
\(689\) | −0.392792 | − | 0.680336i | −0.0149642 | − | 0.0259187i | ||||
\(690\) | −0.337250 | − | 0.584135i | −0.0128389 | − | 0.0222376i | ||||
\(691\) | 11.2393 | − | 19.4670i | 0.427562 | − | 0.740558i | −0.569094 | − | 0.822272i | \(-0.692706\pi\) |
0.996656 | + | 0.0817139i | \(0.0260394\pi\) | |||||||
\(692\) | 19.0657 | 0.724769 | ||||||||
\(693\) | 1.72027 | + | 0.883680i | 0.0653478 | + | 0.0335682i | ||||
\(694\) | 6.29688 | 0.239026 | ||||||||
\(695\) | −6.30154 | + | 10.9146i | −0.239031 | + | 0.414014i | ||||
\(696\) | 3.55793 | + | 6.16252i | 0.134863 | + | 0.233590i | ||||
\(697\) | −3.23817 | − | 5.60867i | −0.122654 | − | 0.212444i | ||||
\(698\) | 4.84153 | − | 8.38577i | 0.183255 | − | 0.317406i | ||||
\(699\) | −5.01702 | −0.189761 | ||||||||
\(700\) | 1.75211 | − | 1.12963i | 0.0662233 | − | 0.0426962i | ||||
\(701\) | −27.0133 | −1.02028 | −0.510139 | − | 0.860092i | \(-0.670406\pi\) | ||||
−0.510139 | + | 0.860092i | \(0.670406\pi\) | |||||||
\(702\) | −0.0167063 | + | 0.0289362i | −0.000630540 | + | 0.00109213i | ||||
\(703\) | 14.3417 | + | 24.8405i | 0.540906 | + | 0.936876i | ||||
\(704\) | 2.21203 | + | 3.83134i | 0.0833688 | + | 0.144399i | ||||
\(705\) | −4.40569 | + | 7.63089i | −0.165928 | + | 0.287396i | ||||
\(706\) | 7.98611 | 0.300561 | ||||||||
\(707\) | −1.40744 | − | 28.6637i | −0.0529324 | − | 1.07801i | ||||
\(708\) | −11.8566 | −0.445599 | ||||||||
\(709\) | −13.3487 | + | 23.1207i | −0.501322 | + | 0.868316i | 0.498676 | + | 0.866788i | \(0.333820\pi\) |
−0.999999 | + | 0.00152776i | \(0.999514\pi\) | |||||||
\(710\) | 0.518478 | + | 0.898030i | 0.0194581 | + | 0.0337025i | ||||
\(711\) | −0.241983 | − | 0.419128i | −0.00907509 | − | 0.0157185i | ||||
\(712\) | 1.73983 | − | 3.01348i | 0.0652030 | − | 0.112935i | ||||
\(713\) | −1.49584 | −0.0560196 | ||||||||
\(714\) | 0.0296857 | + | 0.604573i | 0.00111096 | + | 0.0226256i | ||||
\(715\) | −0.195942 | −0.00732781 | ||||||||
\(716\) | −16.7563 | + | 29.0228i | −0.626214 | + | 1.08463i | ||||
\(717\) | 10.2820 | + | 17.8090i | 0.383989 | + | 0.665089i | ||||
\(718\) | 1.90515 | + | 3.29981i | 0.0710995 | + | 0.123148i | ||||
\(719\) | −17.3681 | + | 30.0824i | −0.647720 | + | 1.12188i | 0.335946 | + | 0.941881i | \(0.390944\pi\) |
−0.983666 | + | 0.180002i | \(0.942389\pi\) | |||||||
\(720\) | 8.14783 | 0.303652 | ||||||||
\(721\) | 20.9006 | − | 13.4753i | 0.778380 | − | 0.501845i | ||||
\(722\) | 8.38953 | 0.312226 | ||||||||
\(723\) | 13.3130 | − | 23.0587i | 0.495114 | − | 0.857563i | ||||
\(724\) | −19.0239 | − | 32.9503i | −0.707017 | − | 1.22459i | ||||
\(725\) | 1.28868 | + | 2.23206i | 0.0478603 | + | 0.0828965i | ||||
\(726\) | −1.51730 | + | 2.62804i | −0.0563122 | + | 0.0975356i | ||||
\(727\) | 6.54111 | 0.242596 | 0.121298 | − | 0.992616i | \(-0.461294\pi\) | ||||
0.121298 | + | 0.992616i | \(0.461294\pi\) | |||||||
\(728\) | 0.307923 | + | 0.158176i | 0.0114124 | + | 0.00586239i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.33910 | + | 5.78349i | −0.123586 | + | 0.214056i | ||||
\(731\) | −0.593081 | − | 1.02725i | −0.0219359 | − | 0.0379941i | ||||
\(732\) | 2.29024 | + | 3.96681i | 0.0846497 | + | 0.146618i | ||||
\(733\) | −25.9000 | + | 44.8600i | −0.956637 | + | 1.65694i | −0.226060 | + | 0.974113i | \(0.572584\pi\) |
−0.730577 | + | 0.682830i | \(0.760749\pi\) | |||||||
\(734\) | −8.69402 | −0.320902 | ||||||||
\(735\) | −9.48411 | − | 13.2364i | −0.349827 | − | 0.488234i | ||||
\(736\) | −3.28651 | −0.121142 | ||||||||
\(737\) | 3.05987 | − | 5.29984i | 0.112712 | − | 0.195222i | ||||
\(738\) | −1.18999 | − | 2.06112i | −0.0438042 | − | 0.0758710i | ||||
\(739\) | 20.2376 | + | 35.0525i | 0.744451 | + | 1.28943i | 0.950451 | + | 0.310875i | \(0.100622\pi\) |
−0.206000 | + | 0.978552i | \(0.566045\pi\) | |||||||
\(740\) | 9.23223 | − | 15.9907i | 0.339383 | − | 0.587829i | ||||
\(741\) | −0.797808 | −0.0293082 | ||||||||
\(742\) | −4.65207 | − | 2.38970i | −0.170783 | − | 0.0877287i | ||||
\(743\) | −41.4092 | −1.51916 | −0.759579 | − | 0.650415i | \(-0.774595\pi\) | ||||
−0.759579 | + | 0.650415i | \(0.774595\pi\) | |||||||
\(744\) | −0.849224 | + | 1.47090i | −0.0311341 | + | 0.0539258i | ||||
\(745\) | 17.7073 | + | 30.6699i | 0.648744 | + | 1.12366i | ||||
\(746\) | −2.23980 | − | 3.87945i | −0.0820050 | − | 0.142037i | ||||
\(747\) | 0.921040 | − | 1.59529i | 0.0336991 | − | 0.0583686i | ||||
\(748\) | −1.10501 | −0.0404033 | ||||||||
\(749\) | 39.4693 | − | 25.4470i | 1.44218 | − | 0.929815i | ||||
\(750\) | 3.09511 | 0.113017 | ||||||||
\(751\) | −12.7550 | + | 22.0924i | −0.465438 | + | 0.806162i | −0.999221 | − | 0.0394594i | \(-0.987436\pi\) |
0.533783 | + | 0.845621i | \(0.320770\pi\) | |||||||
\(752\) | 6.63373 | + | 11.4900i | 0.241907 | + | 0.418996i | ||||
\(753\) | −0.592173 | − | 1.02567i | −0.0215800 | − | 0.0373776i | ||||
\(754\) | −0.104699 | + | 0.181343i | −0.00381290 | + | 0.00660413i | ||||
\(755\) | 33.4522 | 1.21745 | ||||||||
\(756\) | −0.248601 | − | 5.06296i | −0.00904154 | − | 0.184138i | ||||
\(757\) | 45.9268 | 1.66924 | 0.834619 | − | 0.550827i | \(-0.185688\pi\) | ||||
0.834619 | + | 0.550827i | \(0.185688\pi\) | |||||||
\(758\) | 4.06904 | − | 7.04778i | 0.147794 | − | 0.255987i | ||||
\(759\) | −0.365486 | − | 0.633040i | −0.0132663 | − | 0.0229779i | ||||
\(760\) | −9.14339 | − | 15.8368i | −0.331666 | − | 0.574462i | ||||
\(761\) | −4.09191 | + | 7.08739i | −0.148331 | + | 0.256918i | −0.930611 | − | 0.366010i | \(-0.880724\pi\) |
0.782279 | + | 0.622928i | \(0.214057\pi\) | |||||||
\(762\) | 1.02469 | 0.0371208 | ||||||||
\(763\) | 1.26810 | + | 25.8259i | 0.0459084 | + | 0.934960i | ||||
\(764\) | −27.0334 | −0.978035 | ||||||||
\(765\) | −0.917716 | + | 1.58953i | −0.0331801 | + | 0.0574696i | ||||
\(766\) | 3.02483 | + | 5.23916i | 0.109292 | + | 0.189299i | ||||
\(767\) | −0.356558 | − | 0.617576i | −0.0128746 | − | 0.0222994i | ||||
\(768\) | 4.84492 | − | 8.39166i | 0.174826 | − | 0.302808i | ||||
\(769\) | 15.3794 | 0.554596 | 0.277298 | − | 0.960784i | \(-0.410561\pi\) | ||||
0.277298 | + | 0.960784i | \(0.410561\pi\) | |||||||
\(770\) | −1.09635 | + | 0.706850i | −0.0395098 | + | 0.0254731i | ||||
\(771\) | 9.21806 | 0.331980 | ||||||||
\(772\) | −12.1899 | + | 21.1135i | −0.438724 | + | 0.759893i | ||||
\(773\) | 0.100858 | + | 0.174691i | 0.00362760 | + | 0.00628319i | 0.867834 | − | 0.496855i | \(-0.165512\pi\) |
−0.864206 | + | 0.503138i | \(0.832179\pi\) | |||||||
\(774\) | −0.217951 | − | 0.377501i | −0.00783407 | − | 0.0135690i | ||||
\(775\) | −0.307588 | + | 0.532758i | −0.0110489 | + | 0.0191372i | ||||
\(776\) | −16.8446 | −0.604684 | ||||||||
\(777\) | −9.75003 | − | 5.00845i | −0.349780 | − | 0.179677i | ||||
\(778\) | 0.891041 | 0.0319454 | ||||||||
\(779\) | 28.4139 | − | 49.2143i | 1.01803 | − | 1.76329i | ||||
\(780\) | 0.256788 | + | 0.444770i | 0.00919450 | + | 0.0159253i | ||||
\(781\) | 0.561886 | + | 0.973214i | 0.0201058 | + | 0.0348244i | ||||
\(782\) | 0.114391 | − | 0.198131i | 0.00409062 | − | 0.00708516i | ||||
\(783\) | 6.26700 | 0.223964 | ||||||||
\(784\) | −24.4004 | + | 2.40201i | −0.871442 | + | 0.0857859i | ||||
\(785\) | −10.3898 | −0.370828 | ||||||||
\(786\) | −0.630976 | + | 1.09288i | −0.0225062 | + | 0.0389818i | ||||
\(787\) | 18.1360 | + | 31.4124i | 0.646478 | + | 1.11973i | 0.983958 | + | 0.178399i | \(0.0570919\pi\) |
−0.337481 | + | 0.941332i | \(0.609575\pi\) | |||||||
\(788\) | −13.5630 | − | 23.4918i | −0.483162 | − | 0.836860i | ||||
\(789\) | −11.0508 | + | 19.1406i | −0.393419 | + | 0.681422i | ||||
\(790\) | 0.326436 | 0.0116141 | ||||||||
\(791\) | −8.66691 | − | 4.45207i | −0.308160 | − | 0.158297i | ||||
\(792\) | −0.829981 | −0.0294921 | ||||||||
\(793\) | −0.137746 | + | 0.238584i | −0.00489151 | + | 0.00847235i | ||||
\(794\) | 4.99963 | + | 8.65962i | 0.177430 | + | 0.307318i | ||||
\(795\) | −7.92929 | − | 13.7339i | −0.281223 | − | 0.487093i | ||||
\(796\) | −4.06124 | + | 7.03427i | −0.143947 | + | 0.249323i | ||||
\(797\) | 25.4967 | 0.903138 | 0.451569 | − | 0.892236i | \(-0.350864\pi\) | ||||
0.451569 | + | 0.892236i | \(0.350864\pi\) | |||||||
\(798\) | −4.46397 | + | 2.87805i | −0.158023 | + | 0.101882i | ||||
\(799\) | −2.98871 | −0.105733 | ||||||||
\(800\) | −0.675801 | + | 1.17052i | −0.0238932 | + | 0.0413842i | ||||
\(801\) | −1.53229 | − | 2.65400i | −0.0541406 | − | 0.0937743i | ||||
\(802\) | 4.92095 | + | 8.52334i | 0.173765 | + | 0.300970i | ||||
\(803\) | −3.61865 | + | 6.26769i | −0.127699 | + | 0.221182i | ||||
\(804\) | −16.0402 | −0.565696 | ||||||||
\(805\) | 0.301838 | + | 6.14717i | 0.0106384 | + | 0.216659i | ||||
\(806\) | −0.0499799 | −0.00176047 | ||||||||
\(807\) | 14.6763 | − | 25.4201i | 0.516630 | − | 0.894829i | ||||
\(808\) | 6.15806 | + | 10.6661i | 0.216640 | + | 0.375231i | ||||
\(809\) | −8.26215 | − | 14.3105i | −0.290482 | − | 0.503129i | 0.683442 | − | 0.730005i | \(-0.260482\pi\) |
−0.973924 | + | 0.226876i | \(0.927149\pi\) | |||||||
\(810\) | −0.337250 | + | 0.584135i | −0.0118498 | + | 0.0205244i | ||||
\(811\) | −35.0068 | −1.22925 | −0.614627 | − | 0.788818i | \(-0.710694\pi\) | ||||
−0.614627 | + | 0.788818i | \(0.710694\pi\) | |||||||
\(812\) | −1.55799 | − | 31.7296i | −0.0546746 | − | 1.11349i | ||||
\(813\) | −15.8453 | −0.555719 | ||||||||
\(814\) | −0.439048 | + | 0.760454i | −0.0153886 | + | 0.0266539i | ||||
\(815\) | −0.913878 | − | 1.58288i | −0.0320117 | − | 0.0554460i | ||||
\(816\) | 1.38182 | + | 2.39339i | 0.0483734 | + | 0.0837853i | ||||
\(817\) | 5.20409 | − | 9.01375i | 0.182068 | − | 0.315351i | ||||
\(818\) | 4.15236 | 0.145184 | ||||||||
\(819\) | 0.256239 | − | 0.165205i | 0.00895370 | − | 0.00577272i | ||||
\(820\) | −36.5820 | −1.27750 | ||||||||
\(821\) | −17.4817 | + | 30.2792i | −0.610116 | + | 1.05675i | 0.381104 | + | 0.924532i | \(0.375544\pi\) |
−0.991220 | + | 0.132220i | \(0.957789\pi\) | |||||||
\(822\) | −2.48136 | − | 4.29784i | −0.0865474 | − | 0.149904i | ||||
\(823\) | 14.8624 | + | 25.7424i | 0.518069 | + | 0.897323i | 0.999780 | + | 0.0209920i | \(0.00668246\pi\) |
−0.481710 | + | 0.876331i | \(0.659984\pi\) | |||||||
\(824\) | −5.33618 | + | 9.24253i | −0.185895 | + | 0.321979i | ||||
\(825\) | −0.300618 | −0.0104662 | ||||||||
\(826\) | −4.22292 | − | 2.16925i | −0.146934 | − | 0.0754780i | ||||
\(827\) | 8.29301 | 0.288376 | 0.144188 | − | 0.989550i | \(-0.453943\pi\) | ||||
0.144188 | + | 0.989550i | \(0.453943\pi\) | |||||||
\(828\) | −0.957963 | + | 1.65924i | −0.0332915 | + | 0.0576626i | ||||
\(829\) | −0.882235 | − | 1.52808i | −0.0306413 | − | 0.0530723i | 0.850298 | − | 0.526301i | \(-0.176422\pi\) |
−0.880939 | + | 0.473229i | \(0.843088\pi\) | |||||||
\(830\) | 0.621242 | + | 1.07602i | 0.0215636 | + | 0.0373493i | ||||
\(831\) | 12.2189 | − | 21.1637i | 0.423867 | − | 0.734160i | ||||
\(832\) | 0.697425 | 0.0241789 | ||||||||
\(833\) | 2.27969 | − | 5.03073i | 0.0789867 | − | 0.174304i | ||||
\(834\) | −1.57094 | −0.0543973 | ||||||||
\(835\) | −6.42911 | + | 11.1355i | −0.222489 | + | 0.385362i | ||||
\(836\) | −4.84807 | − | 8.39711i | −0.167674 | − | 0.290420i | ||||
\(837\) | 0.747919 | + | 1.29543i | 0.0258519 | + | 0.0447768i | ||||
\(838\) | −2.03437 | + | 3.52363i | −0.0702762 | + | 0.121722i | ||||
\(839\) | −25.9251 | −0.895035 | −0.447517 | − | 0.894275i | \(-0.647692\pi\) | ||||
−0.447517 | + | 0.894275i | \(0.647692\pi\) | |||||||
\(840\) | 6.21604 | + | 3.19309i | 0.214474 | + | 0.110172i | ||||
\(841\) | 10.2753 | 0.354321 | ||||||||
\(842\) | 4.92411 | − | 8.52880i | 0.169696 | − | 0.293922i | ||||
\(843\) | −4.76833 | − | 8.25899i | −0.164230 | − | 0.284455i | ||||
\(844\) | −25.2823 | − | 43.7902i | −0.870251 | − | 1.50732i | ||||
\(845\) | 15.1049 | − | 26.1625i | 0.519625 | − | 0.900017i | ||||
\(846\) | −1.09832 | −0.0377610 | ||||||||
\(847\) | 23.2720 | − | 15.0042i | 0.799637 | − | 0.515550i | ||||
\(848\) | −23.8786 | −0.819993 | ||||||||
\(849\) | 2.11423 | − | 3.66195i | 0.0725601 | − | 0.125678i | ||||
\(850\) | −0.0470443 | − | 0.0814831i | −0.00161361 | − | 0.00279485i | ||||
\(851\) | 2.07147 | + | 3.58789i | 0.0710091 | + | 0.122991i | ||||
\(852\) | 1.47274 | − | 2.55086i | 0.0504553 | − | 0.0873911i | ||||
\(853\) | 23.2110 | 0.794729 | 0.397365 | − | 0.917661i | \(-0.369925\pi\) | ||||
0.397365 | + | 0.917661i | \(0.369925\pi\) | |||||||
\(854\) | 0.0899478 | + | 1.83186i | 0.00307795 | + | 0.0626849i | ||||
\(855\) | −16.1053 | −0.550791 | ||||||||
\(856\) | −10.0770 | + | 17.4538i | −0.344424 | + | 0.596560i | ||||
\(857\) | 6.21562 | + | 10.7658i | 0.212322 | + | 0.367752i | 0.952441 | − | 0.304724i | \(-0.0985642\pi\) |
−0.740119 | + | 0.672476i | \(0.765231\pi\) | |||||||
\(858\) | −0.0122118 | − | 0.0211515i | −0.000416905 | − | 0.000722101i | ||||
\(859\) | −2.97290 | + | 5.14922i | −0.101434 | + | 0.175689i | −0.912276 | − | 0.409577i | \(-0.865676\pi\) |
0.810842 | + | 0.585266i | \(0.199010\pi\) | |||||||
\(860\) | −6.70011 | −0.228472 | ||||||||
\(861\) | 1.06504 | + | 21.6903i | 0.0362964 | + | 0.739205i | ||||
\(862\) | 6.65815 | 0.226777 | ||||||||
\(863\) | −23.1256 | + | 40.0547i | −0.787204 | + | 1.36348i | 0.140469 | + | 0.990085i | \(0.455139\pi\) |
−0.927673 | + | 0.373393i | \(0.878194\pi\) | |||||||
\(864\) | 1.64325 | + | 2.84620i | 0.0559046 | + | 0.0968296i | ||||
\(865\) | 11.5743 | + | 20.0472i | 0.393536 | + | 0.681625i | ||||
\(866\) | −2.77938 | + | 4.81403i | −0.0944472 | + | 0.163587i | ||||
\(867\) | 16.3774 | 0.556207 | ||||||||
\(868\) | 6.37280 | − | 4.10873i | 0.216307 | − | 0.139460i | ||||
\(869\) | 0.353766 | 0.0120007 | ||||||||
\(870\) | −2.11355 | + | 3.66077i | −0.0716560 | + | 0.124112i | ||||
\(871\) | −0.482370 | − | 0.835489i | −0.0163445 | − | 0.0283095i | ||||
\(872\) | −5.54839 | − | 9.61010i | −0.187892 | − | 0.325439i | ||||
\(873\) | −7.41757 | + | 12.8476i | −0.251047 | + | 0.434826i | ||||
\(874\) | 2.00749 | 0.0679044 | ||||||||
\(875\) | −25.1212 | − | 12.9044i | −0.849251 | − | 0.436248i | ||||
\(876\) | 18.9695 | 0.640919 | ||||||||
\(877\) | 6.36556 | − | 11.0255i | 0.214950 | − | 0.372304i | −0.738307 | − | 0.674464i | \(-0.764375\pi\) |
0.953257 | + | 0.302161i | \(0.0977080\pi\) | |||||||
\(878\) | 4.28014 | + | 7.41342i | 0.144448 | + | 0.250191i | ||||
\(879\) | 15.4959 | + | 26.8398i | 0.522665 | + | 0.905283i | ||||
\(880\) | −2.97791 | + | 5.15790i | −0.100385 | + | 0.173873i | ||||
\(881\) | 22.2712 | 0.750334 | 0.375167 | − | 0.926957i | \(-0.377585\pi\) | ||||
0.375167 | + | 0.926957i | \(0.377585\pi\) | |||||||
\(882\) | 0.837762 | − | 1.84874i | 0.0282089 | − | 0.0622502i | ||||
\(883\) | 39.1941 | 1.31899 | 0.659493 | − | 0.751711i | \(-0.270771\pi\) | ||||
0.659493 | + | 0.751711i | \(0.270771\pi\) | |||||||
\(884\) | −0.0870994 | + | 0.150861i | −0.00292947 | + | 0.00507399i | ||||
\(885\) | −7.19782 | − | 12.4670i | −0.241952 | − | 0.419074i | ||||
\(886\) | 1.77976 | + | 3.08264i | 0.0597923 | + | 0.103563i | ||||
\(887\) | 3.77303 | − | 6.53508i | 0.126686 | − | 0.219426i | −0.795705 | − | 0.605685i | \(-0.792899\pi\) |
0.922391 | + | 0.386258i | \(0.126233\pi\) | |||||||
\(888\) | 4.70410 | 0.157859 | ||||||||
\(889\) | −8.31684 | − | 4.27224i | −0.278938 | − | 0.143286i | ||||
\(890\) | 2.06706 | 0.0692879 | ||||||||
\(891\) | −0.365486 | + | 0.633040i | −0.0122442 | + | 0.0212076i | ||||
\(892\) | −9.17124 | − | 15.8851i | −0.307076 | − | 0.531871i | ||||
\(893\) | −13.1125 | − | 22.7115i | −0.438793 | − | 0.760012i | ||||
\(894\) | −2.20717 | + | 3.82293i | −0.0738188 | + | 0.127858i | ||||
\(895\) | −40.6892 | −1.36009 | ||||||||
\(896\) | 18.5184 | − | 11.9394i | 0.618656 | − | 0.398866i | ||||
\(897\) | −0.115233 | −0.00384752 | ||||||||
\(898\) | −4.85902 | + | 8.41607i | −0.162148 | + | 0.280848i | ||||
\(899\) | 4.68721 | + | 8.11849i | 0.156327 | + | 0.270767i | ||||
\(900\) | 0.393970 | + | 0.682376i | 0.0131323 | + | 0.0227459i | ||||
\(901\) | 2.68952 | − | 4.65838i | 0.0896008 | − | 0.155193i | ||||
\(902\) | 1.73970 | 0.0579256 | ||||||||
\(903\) | 0.195065 | + | 3.97265i | 0.00649136 | + | 0.132202i | ||||
\(904\) | 4.18152 | 0.139075 | ||||||||
\(905\) | 23.0978 | − | 40.0065i | 0.767795 | − | 1.32986i | ||||
\(906\) | 2.08487 | + | 3.61110i | 0.0692651 | + | 0.119971i | ||||
\(907\) | −8.74635 | − | 15.1491i | −0.290418 | − | 0.503018i | 0.683491 | − | 0.729959i | \(-0.260461\pi\) |
−0.973909 | + | 0.226941i | \(0.927128\pi\) | |||||||
\(908\) | −21.8984 | + | 37.9291i | −0.726724 | + | 1.25872i | ||||
\(909\) | 10.8469 | 0.359770 | ||||||||
\(910\) | 0.0100852 | + | 0.205393i | 0.000334322 | + | 0.00680872i | ||||
\(911\) | 1.76174 | 0.0583691 | 0.0291846 | − | 0.999574i | \(-0.490709\pi\) | ||||
0.0291846 | + | 0.999574i | \(0.490709\pi\) | |||||||
\(912\) | −12.1250 | + | 21.0012i | −0.401500 | + | 0.695419i | ||||
\(913\) | 0.673254 | + | 1.16611i | 0.0222814 | + | 0.0385926i | ||||
\(914\) | 3.89673 | + | 6.74934i | 0.128892 | + | 0.223248i | ||||
\(915\) | −2.78068 | + | 4.81628i | −0.0919265 | + | 0.159221i | ||||
\(916\) | 3.98632 | 0.131712 | ||||||||
\(917\) | 9.67780 | − | 6.23956i | 0.319589 | − | 0.206049i | ||||
\(918\) | −0.228782 | −0.00755094 | ||||||||
\(919\) | 9.97936 | − | 17.2848i | 0.329189 | − | 0.570171i | −0.653162 | − | 0.757218i | \(-0.726558\pi\) |
0.982351 | + | 0.187046i | \(0.0598915\pi\) | |||||||
\(920\) | −1.32065 | − | 2.28743i | −0.0435405 | − | 0.0754143i | ||||
\(921\) | −7.98003 | − | 13.8218i | −0.262951 | − | 0.455444i | ||||
\(922\) | 4.83555 | − | 8.37541i | 0.159250 | − | 0.275829i | ||||
\(923\) | 0.177156 | 0.00583115 | ||||||||
\(924\) | 3.29592 | + | 1.69306i | 0.108428 | + | 0.0556977i | ||||
\(925\) | 1.70382 | 0.0560212 | ||||||||
\(926\) | 2.31099 | − | 4.00276i | 0.0759439 | − | 0.131539i | ||||
\(927\) | 4.69962 | + | 8.13998i | 0.154356 | + | 0.267352i | ||||
\(928\) | 10.2983 | + | 17.8371i | 0.338057 | + | 0.585533i | ||||
\(929\) | 8.47000 | − | 14.6705i | 0.277892 | − | 0.481322i | −0.692969 | − | 0.720967i | \(-0.743698\pi\) |
0.970861 | + | 0.239645i | \(0.0770311\pi\) | |||||||
\(930\) | −1.00894 | −0.0330846 | ||||||||
\(931\) | 48.2308 | − | 4.74790i | 1.58070 | − | 0.155606i | ||||
\(932\) | −9.61223 | −0.314859 | ||||||||
\(933\) | −7.66126 | + | 13.2697i | −0.250818 | + | 0.434430i | ||||
\(934\) | −0.540075 | − | 0.935438i | −0.0176718 | − | 0.0306085i | ||||
\(935\) | −0.670824 | − | 1.16190i | −0.0219383 | − | 0.0379982i | ||||
\(936\) | −0.0654207 | + | 0.113312i | −0.00213834 | + | 0.00370372i | ||||
\(937\) | −2.54779 | −0.0832327 | −0.0416163 | − | 0.999134i | \(-0.513251\pi\) | ||||
−0.0416163 | + | 0.999134i | \(0.513251\pi\) | |||||||
\(938\) | −5.71298 | − | 2.93468i | −0.186536 | − | 0.0958206i | ||||
\(939\) | 16.7734 | 0.547378 | ||||||||
\(940\) | −8.44098 | + | 14.6202i | −0.275314 | + | 0.476859i | ||||
\(941\) | 21.5008 | + | 37.2405i | 0.700906 | + | 1.21401i | 0.968149 | + | 0.250376i | \(0.0805543\pi\) |
−0.267242 | + | 0.963629i | \(0.586112\pi\) | |||||||
\(942\) | −0.647533 | − | 1.12156i | −0.0210978 | − | 0.0365424i | ||||
\(943\) | 4.10403 | − | 7.10838i | 0.133646 | − | 0.231481i | ||||
\(944\) | −21.6758 | −0.705487 | ||||||||
\(945\) | 5.17269 | − | 3.33498i | 0.168268 | − | 0.108487i | ||||
\(946\) | 0.318631 | 0.0103596 | ||||||||
\(947\) | 23.2147 | − | 40.2091i | 0.754377 | − | 1.30662i | −0.191306 | − | 0.981530i | \(-0.561272\pi\) |
0.945683 | − | 0.325090i | \(-0.105394\pi\) | |||||||
\(948\) | −0.463622 | − | 0.803017i | −0.0150577 | − | 0.0260808i | ||||
\(949\) | 0.570459 | + | 0.988064i | 0.0185179 | + | 0.0320739i | ||||
\(950\) | 0.412799 | − | 0.714989i | 0.0133930 | − | 0.0231973i | ||||
\(951\) | −32.4011 | −1.05068 | ||||||||
\(952\) | 0.116247 | + | 2.36746i | 0.00376759 | + | 0.0767299i | ||||
\(953\) | −23.0858 | −0.747824 | −0.373912 | − | 0.927464i | \(-0.621984\pi\) | ||||
−0.373912 | + | 0.927464i | \(0.621984\pi\) | |||||||
\(954\) | 0.988368 | − | 1.71190i | 0.0319996 | − | 0.0554249i | ||||
\(955\) | −16.4113 | − | 28.4251i | −0.531056 | − | 0.919815i | ||||
\(956\) | 19.6996 | + | 34.1207i | 0.637130 | + | 1.10354i | ||||
\(957\) | −2.29050 | + | 3.96726i | −0.0740413 | + | 0.128243i | ||||
\(958\) | 0.297170 | 0.00960112 | ||||||||
\(959\) | 2.22081 | + | 45.2285i | 0.0717137 | + | 1.46051i | ||||
\(960\) | 14.0789 | 0.454395 | ||||||||
\(961\) | 14.3812 | − | 24.9090i | 0.463911 | − | 0.803517i | ||||
\(962\) | 0.0692133 | + | 0.119881i | 0.00223153 | + | 0.00386512i | ||||
\(963\) | 8.87488 | + | 15.3718i | 0.285989 | + | 0.495348i | ||||
\(964\) | 25.5066 | − | 44.1788i | 0.821513 | − | 1.42290i | ||||
\(965\) | −29.6006 | −0.952878 | ||||||||
\(966\) | −0.644763 | + | 0.415698i | −0.0207449 | + | 0.0133749i | ||||
\(967\) | −6.48746 | −0.208623 | −0.104311 | − | 0.994545i | \(-0.533264\pi\) | ||||
−0.104311 | + | 0.994545i | \(0.533264\pi\) | |||||||
\(968\) | −5.94162 | + | 10.2912i | −0.190971 | + | 0.330772i | ||||
\(969\) | −2.73136 | − | 4.73086i | −0.0877441 | − | 0.151977i | ||||
\(970\) | −5.00316 | − | 8.66572i | −0.160642 | − | 0.278240i | ||||
\(971\) | −11.8178 | + | 20.4689i | −0.379250 | + | 0.656880i | −0.990953 | − | 0.134207i | \(-0.957151\pi\) |
0.611704 | + | 0.791087i | \(0.290485\pi\) | |||||||
\(972\) | 1.91593 | 0.0614533 | ||||||||
\(973\) | 12.7504 | + | 6.54971i | 0.408760 | + | 0.209974i | ||||
\(974\) | 2.35664 | 0.0755116 | ||||||||
\(975\) | −0.0236953 | + | 0.0410415i | −0.000758857 | + | 0.00131438i | ||||
\(976\) | 4.18692 | + | 7.25197i | 0.134020 | + | 0.232130i | ||||
\(977\) | −4.81215 | − | 8.33489i | −0.153954 | − | 0.266657i | 0.778723 | − | 0.627367i | \(-0.215868\pi\) |
−0.932678 | + | 0.360711i | \(0.882534\pi\) | |||||||
\(978\) | 0.113913 | − | 0.197303i | 0.00364253 | − | 0.00630904i | ||||
\(979\) | 2.24011 | 0.0715943 | ||||||||
\(980\) | −18.1708 | − | 25.3600i | −0.580446 | − | 0.810096i | ||||
\(981\) | −9.77303 | −0.312029 | ||||||||
\(982\) | 0.496571 | − | 0.860086i | 0.0158462 | − | 0.0274465i | ||||
\(983\) | −15.8658 | − | 27.4804i | −0.506041 | − | 0.876489i | −0.999976 | − | 0.00698980i | \(-0.997775\pi\) |
0.493934 | − | 0.869499i | \(-0.335558\pi\) | |||||||
\(984\) | −4.65991 | − | 8.07121i | −0.148553 | − | 0.257301i | ||||
\(985\) | 16.4674 | − | 28.5224i | 0.524696 | − | 0.908801i | ||||
\(986\) | −1.43378 | −0.0456608 | ||||||||
\(987\) | 8.91441 | + | 4.57920i | 0.283749 | + | 0.145758i | ||||
\(988\) | −1.52854 | −0.0486293 | ||||||||
\(989\) | 0.751665 | − | 1.30192i | 0.0239016 | − | 0.0413987i | ||||
\(990\) | −0.246520 | − | 0.426986i | −0.00783493 | − | 0.0135705i | ||||
\(991\) | −2.23075 | − | 3.86376i | −0.0708620 | − | 0.122737i | 0.828417 | − | 0.560111i | \(-0.189242\pi\) |
−0.899279 | + | 0.437375i | \(0.855908\pi\) | |||||||
\(992\) | −2.45804 | + | 4.25745i | −0.0780429 | + | 0.135174i | ||||
\(993\) | −25.9585 | −0.823768 | ||||||||
\(994\) | 0.991238 | − | 0.639081i | 0.0314402 | − | 0.0202704i | ||||
\(995\) | −9.86186 | −0.312642 | ||||||||
\(996\) | 1.76464 | − | 3.05645i | 0.0559149 | − | 0.0968474i | ||||
\(997\) | 12.7458 | + | 22.0764i | 0.403664 | + | 0.699166i | 0.994165 | − | 0.107870i | \(-0.0344032\pi\) |
−0.590501 | + | 0.807037i | \(0.701070\pi\) | |||||||
\(998\) | 0.866683 | + | 1.50114i | 0.0274344 | + | 0.0475177i | ||||
\(999\) | 2.07147 | − | 3.58789i | 0.0655384 | − | 0.113516i |
(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 | 483.2.i.f.415.3 | yes | 12 | |
7.2 | even | 3 | 3381.2.a.bc.1.4 | 6 | |||
7.4 | even | 3 | inner | 483.2.i.f.277.3 | ✓ | 12 | |
7.5 | odd | 6 | 3381.2.a.bd.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.f.277.3 | ✓ | 12 | 7.4 | even | 3 | inner | |
483.2.i.f.415.3 | yes | 12 | 1.1 | even | 1 | trivial | |
3381.2.a.bc.1.4 | 6 | 7.2 | even | 3 | |||
3381.2.a.bd.1.4 | 6 | 7.5 | odd | 6 |