Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(311,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.t (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 311.3 | ||
Character | \(\chi\) | \(=\) | 630.311 |
Dual form | 630.2.t.b.551.3 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.790256 | + | 1.54126i | −0.456254 | + | 0.889849i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.45501 | − | 0.939646i | 0.594007 | − | 0.383609i | ||||
\(7\) | −1.82075 | + | 1.91960i | −0.688179 | + | 0.725541i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.75099 | − | 2.43599i | −0.583664 | − | 0.811995i | ||||
\(10\) | 0.866025 | + | 0.500000i | 0.273861 | + | 0.158114i | ||||
\(11\) | − | 3.07697i | − | 0.927743i | −0.885903 | − | 0.463871i | \(-0.846460\pi\) | ||
0.885903 | − | 0.463871i | \(-0.153540\pi\) | |||||||
\(12\) | −1.72990 | + | 0.0862508i | −0.499380 | + | 0.0248984i | ||||
\(13\) | −0.449846 | − | 0.259719i | −0.124765 | − | 0.0720330i | 0.436319 | − | 0.899792i | \(-0.356282\pi\) |
−0.561084 | + | 0.827759i | \(0.689615\pi\) | |||||||
\(14\) | 2.53662 | − | 0.752047i | 0.677939 | − | 0.200993i | ||||
\(15\) | 0.790256 | − | 1.54126i | 0.204043 | − | 0.397953i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.44423 | + | 4.23353i | −0.592813 | + | 1.02678i | 0.401039 | + | 0.916061i | \(0.368649\pi\) |
−0.993852 | + | 0.110721i | \(0.964684\pi\) | |||||||
\(18\) | 0.298411 | + | 2.98512i | 0.0703361 | + | 0.703600i | ||||
\(19\) | 0.713627 | − | 0.412013i | 0.163717 | − | 0.0945222i | −0.415903 | − | 0.909409i | \(-0.636534\pi\) |
0.579620 | + | 0.814887i | \(0.303201\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | −1.51975 | − | 4.32323i | −0.331637 | − | 0.943407i | ||||
\(22\) | −1.53849 | + | 2.66474i | −0.328007 | + | 0.568124i | ||||
\(23\) | − | 8.94137i | − | 1.86440i | −0.361939 | − | 0.932202i | \(-0.617885\pi\) | ||
0.361939 | − | 0.932202i | \(-0.382115\pi\) | |||||||
\(24\) | 1.54126 | + | 0.790256i | 0.314609 | + | 0.161310i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.259719 | + | 0.449846i | 0.0509350 | + | 0.0882220i | ||||
\(27\) | 5.13823 | − | 0.773690i | 0.988853 | − | 0.148897i | ||||
\(28\) | −2.57280 | − | 0.617016i | −0.486213 | − | 0.116605i | ||||
\(29\) | 5.55412 | − | 3.20667i | 1.03137 | − | 0.595464i | 0.113996 | − | 0.993481i | \(-0.463635\pi\) |
0.917378 | + | 0.398017i | \(0.130302\pi\) | |||||||
\(30\) | −1.45501 | + | 0.939646i | −0.265648 | + | 0.171555i | ||||
\(31\) | −0.784474 | + | 0.452916i | −0.140896 | + | 0.0813462i | −0.568791 | − | 0.822482i | \(-0.692589\pi\) |
0.427895 | + | 0.903828i | \(0.359255\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 4.74243 | + | 2.43160i | 0.825551 | + | 0.423287i | ||||
\(34\) | 4.23353 | − | 2.44423i | 0.726045 | − | 0.419182i | ||||
\(35\) | 1.82075 | − | 1.91960i | 0.307763 | − | 0.324472i | ||||
\(36\) | 1.23413 | − | 2.73440i | 0.205688 | − | 0.455733i | ||||
\(37\) | 2.53840 | + | 4.39664i | 0.417311 | + | 0.722804i | 0.995668 | − | 0.0929800i | \(-0.0296392\pi\) |
−0.578357 | + | 0.815784i | \(0.696306\pi\) | |||||||
\(38\) | −0.824025 | −0.133675 | ||||||||
\(39\) | 0.755788 | − | 0.488087i | 0.121023 | − | 0.0781565i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 2.18596 | − | 3.78619i | 0.341389 | − | 0.591304i | −0.643302 | − | 0.765613i | \(-0.722436\pi\) |
0.984691 | + | 0.174309i | \(0.0557692\pi\) | |||||||
\(42\) | −0.845472 | + | 4.50391i | −0.130459 | + | 0.694968i | ||||
\(43\) | −1.84515 | − | 3.19589i | −0.281383 | − | 0.487369i | 0.690343 | − | 0.723482i | \(-0.257460\pi\) |
−0.971726 | + | 0.236113i | \(0.924126\pi\) | |||||||
\(44\) | 2.66474 | − | 1.53849i | 0.401724 | − | 0.231936i | ||||
\(45\) | 1.75099 | + | 2.43599i | 0.261022 | + | 0.363135i | ||||
\(46\) | −4.47068 | + | 7.74345i | −0.659166 | + | 1.14171i | ||||
\(47\) | 1.89222 | − | 3.27742i | 0.276008 | − | 0.478060i | −0.694381 | − | 0.719608i | \(-0.744322\pi\) |
0.970389 | + | 0.241547i | \(0.0776549\pi\) | |||||||
\(48\) | −0.939646 | − | 1.45501i | −0.135626 | − | 0.210013i | ||||
\(49\) | −0.369732 | − | 6.99023i | −0.0528188 | − | 0.998604i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | −4.59342 | − | 7.11278i | −0.643208 | − | 0.995988i | ||||
\(52\) | − | 0.519437i | − | 0.0720330i | ||||||
\(53\) | 4.69700 | + | 2.71181i | 0.645182 | + | 0.372496i | 0.786608 | − | 0.617453i | \(-0.211835\pi\) |
−0.141426 | + | 0.989949i | \(0.545169\pi\) | |||||||
\(54\) | −4.83668 | − | 1.89908i | −0.658189 | − | 0.258432i | ||||
\(55\) | 3.07697i | 0.414899i | ||||||||
\(56\) | 1.91960 | + | 1.82075i | 0.256517 | + | 0.243308i | ||||
\(57\) | 0.0710728 | + | 1.42548i | 0.00941382 | + | 0.188810i | ||||
\(58\) | −6.41334 | −0.842113 | ||||||||
\(59\) | −5.29109 | − | 9.16443i | −0.688841 | − | 1.19311i | −0.972213 | − | 0.234097i | \(-0.924787\pi\) |
0.283372 | − | 0.959010i | \(-0.408547\pi\) | |||||||
\(60\) | 1.72990 | − | 0.0862508i | 0.223329 | − | 0.0111349i | ||||
\(61\) | −8.24872 | − | 4.76240i | −1.05614 | − | 0.609763i | −0.131779 | − | 0.991279i | \(-0.542069\pi\) |
−0.924362 | + | 0.381516i | \(0.875402\pi\) | |||||||
\(62\) | 0.905833 | 0.115041 | ||||||||
\(63\) | 7.86424 | + | 1.07412i | 0.990801 | + | 0.135326i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.449846 | + | 0.259719i | 0.0557965 | + | 0.0322141i | ||||
\(66\) | −2.89127 | − | 4.47704i | −0.355891 | − | 0.551086i | ||||
\(67\) | −3.95287 | − | 6.84657i | −0.482920 | − | 0.836442i | 0.516888 | − | 0.856053i | \(-0.327090\pi\) |
−0.999808 | + | 0.0196114i | \(0.993757\pi\) | |||||||
\(68\) | −4.88846 | −0.592813 | ||||||||
\(69\) | 13.7810 | + | 7.06596i | 1.65904 | + | 0.850642i | ||||
\(70\) | −2.53662 | + | 0.752047i | −0.303184 | + | 0.0898868i | ||||
\(71\) | − | 10.6760i | − | 1.26701i | −0.773741 | − | 0.633503i | \(-0.781617\pi\) | ||
0.773741 | − | 0.633503i | \(-0.218383\pi\) | |||||||
\(72\) | −2.43599 | + | 1.75099i | −0.287084 | + | 0.206356i | ||||
\(73\) | 5.78211 | + | 3.33830i | 0.676744 | + | 0.390719i | 0.798627 | − | 0.601826i | \(-0.205560\pi\) |
−0.121883 | + | 0.992544i | \(0.538893\pi\) | |||||||
\(74\) | − | 5.07681i | − | 0.590167i | ||||||
\(75\) | −0.790256 | + | 1.54126i | −0.0912509 | + | 0.177970i | ||||
\(76\) | 0.713627 | + | 0.412013i | 0.0818586 | + | 0.0472611i | ||||
\(77\) | 5.90656 | + | 5.60240i | 0.673115 | + | 0.638453i | ||||
\(78\) | −0.898575 | + | 0.0448019i | −0.101744 | + | 0.00507281i | ||||
\(79\) | −1.73049 | + | 2.99730i | −0.194696 | + | 0.337223i | −0.946801 | − | 0.321820i | \(-0.895705\pi\) |
0.752105 | + | 0.659043i | \(0.229039\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −2.86805 | + | 8.53078i | −0.318673 | + | 0.947865i | ||||
\(82\) | −3.78619 | + | 2.18596i | −0.418115 | + | 0.241399i | ||||
\(83\) | −3.32033 | − | 5.75098i | −0.364454 | − | 0.631252i | 0.624235 | − | 0.781237i | \(-0.285411\pi\) |
−0.988688 | + | 0.149985i | \(0.952078\pi\) | |||||||
\(84\) | 2.98415 | − | 3.47776i | 0.325598 | − | 0.379455i | ||||
\(85\) | 2.44423 | − | 4.23353i | 0.265114 | − | 0.459191i | ||||
\(86\) | 3.69030i | 0.397935i | ||||||||
\(87\) | 0.553156 | + | 11.0945i | 0.0593045 | + | 1.18945i | ||||
\(88\) | −3.07697 | −0.328007 | ||||||||
\(89\) | 0.771960 | + | 1.33707i | 0.0818276 | + | 0.141729i | 0.904035 | − | 0.427459i | \(-0.140591\pi\) |
−0.822207 | + | 0.569188i | \(0.807258\pi\) | |||||||
\(90\) | −0.298411 | − | 2.98512i | −0.0314553 | − | 0.314659i | ||||
\(91\) | 1.31761 | − | 0.390641i | 0.138123 | − | 0.0409503i | ||||
\(92\) | 7.74345 | − | 4.47068i | 0.807310 | − | 0.466101i | ||||
\(93\) | −0.0781288 | − | 1.56700i | −0.00810158 | − | 0.162491i | ||||
\(94\) | −3.27742 | + | 1.89222i | −0.338040 | + | 0.195167i | ||||
\(95\) | −0.713627 | + | 0.412013i | −0.0732166 | + | 0.0422716i | ||||
\(96\) | 0.0862508 | + | 1.72990i | 0.00880293 | + | 0.176557i | ||||
\(97\) | 1.93786 | − | 1.11882i | 0.196759 | − | 0.113599i | −0.398384 | − | 0.917219i | \(-0.630429\pi\) |
0.595143 | + | 0.803620i | \(0.297095\pi\) | |||||||
\(98\) | −3.17492 | + | 6.23858i | −0.320715 | + | 0.630192i | ||||
\(99\) | −7.49547 | + | 5.38776i | −0.753323 | + | 0.541490i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −4.19679 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(102\) | 0.421633 | + | 8.45656i | 0.0417479 | + | 0.837324i | ||||
\(103\) | − | 0.701137i | − | 0.0690851i | −0.999403 | − | 0.0345426i | \(-0.989003\pi\) | ||
0.999403 | − | 0.0345426i | \(-0.0109974\pi\) | |||||||
\(104\) | −0.259719 | + | 0.449846i | −0.0254675 | + | 0.0441110i | ||||
\(105\) | 1.51975 | + | 4.32323i | 0.148313 | + | 0.421904i | ||||
\(106\) | −2.71181 | − | 4.69700i | −0.263395 | − | 0.456213i | ||||
\(107\) | −17.8959 | + | 10.3322i | −1.73006 | + | 0.998851i | −0.841072 | + | 0.540924i | \(0.818075\pi\) |
−0.888990 | + | 0.457927i | \(0.848592\pi\) | |||||||
\(108\) | 3.23915 | + | 4.06299i | 0.311687 | + | 0.390962i | ||||
\(109\) | −0.903287 | + | 1.56454i | −0.0865192 | + | 0.149856i | −0.906038 | − | 0.423197i | \(-0.860908\pi\) |
0.819518 | + | 0.573053i | \(0.194241\pi\) | |||||||
\(110\) | 1.53849 | − | 2.66474i | 0.146689 | − | 0.254073i | ||||
\(111\) | −8.78238 | + | 0.437878i | −0.833587 | + | 0.0415616i | ||||
\(112\) | −0.752047 | − | 2.53662i | −0.0710618 | − | 0.239688i | ||||
\(113\) | −16.2514 | − | 9.38276i | −1.52881 | − | 0.882656i | −0.999412 | − | 0.0342794i | \(-0.989086\pi\) |
−0.529393 | − | 0.848377i | \(-0.677580\pi\) | |||||||
\(114\) | 0.651191 | − | 1.27004i | 0.0609896 | − | 0.118950i | ||||
\(115\) | 8.94137i | 0.833787i | ||||||||
\(116\) | 5.55412 | + | 3.20667i | 0.515687 | + | 0.297732i | ||||
\(117\) | 0.155006 | + | 1.55058i | 0.0143303 | + | 0.143351i | ||||
\(118\) | 10.5822i | 0.974168i | ||||||||
\(119\) | −3.67635 | − | 12.4002i | −0.337011 | − | 1.13672i | ||||
\(120\) | −1.54126 | − | 0.790256i | −0.140698 | − | 0.0721401i | ||||
\(121\) | 1.53223 | 0.139293 | ||||||||
\(122\) | 4.76240 | + | 8.24872i | 0.431168 | + | 0.746804i | ||||
\(123\) | 4.10805 | + | 6.36120i | 0.370411 | + | 0.573570i | ||||
\(124\) | −0.784474 | − | 0.452916i | −0.0704479 | − | 0.0406731i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −6.27357 | − | 4.86233i | −0.558894 | − | 0.433171i | ||||
\(127\) | 1.53891 | 0.136556 | 0.0682779 | − | 0.997666i | \(-0.478250\pi\) | ||||
0.0682779 | + | 0.997666i | \(0.478250\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 6.38386 | − | 0.318291i | 0.562067 | − | 0.0280240i | ||||
\(130\) | −0.259719 | − | 0.449846i | −0.0227788 | − | 0.0394541i | ||||
\(131\) | 10.5223 | 0.919335 | 0.459668 | − | 0.888091i | \(-0.347969\pi\) | ||||
0.459668 | + | 0.888091i | \(0.347969\pi\) | |||||||
\(132\) | 0.265391 | + | 5.32286i | 0.0230994 | + | 0.463296i | ||||
\(133\) | −0.508437 | + | 2.12005i | −0.0440871 | + | 0.183832i | ||||
\(134\) | 7.90574i | 0.682952i | ||||||||
\(135\) | −5.13823 | + | 0.773690i | −0.442228 | + | 0.0665887i | ||||
\(136\) | 4.23353 | + | 2.44423i | 0.363022 | + | 0.209591i | ||||
\(137\) | 0.00335499i | 0.000286636i | 1.00000 | 0.000143318i | \(4.56196e-5\pi\) | |||||
−1.00000 | 0.000143318i | \(0.999954\pi\) | ||||||||
\(138\) | −8.40172 | − | 13.0098i | −0.715202 | − | 1.10747i | ||||
\(139\) | 16.6324 | + | 9.60272i | 1.41074 | + | 0.814492i | 0.995458 | − | 0.0951995i | \(-0.0303489\pi\) |
0.415284 | + | 0.909692i | \(0.363682\pi\) | |||||||
\(140\) | 2.57280 | + | 0.617016i | 0.217441 | + | 0.0521474i | ||||
\(141\) | 3.55603 | + | 5.50641i | 0.299472 | + | 0.463723i | ||||
\(142\) | −5.33799 | + | 9.24567i | −0.447954 | + | 0.775879i | ||||
\(143\) | −0.799148 | + | 1.38416i | −0.0668281 | + | 0.115750i | ||||
\(144\) | 2.98512 | − | 0.298411i | 0.248760 | − | 0.0248676i | ||||
\(145\) | −5.55412 | + | 3.20667i | −0.461244 | + | 0.266300i | ||||
\(146\) | −3.33830 | − | 5.78211i | −0.276280 | − | 0.478530i | ||||
\(147\) | 11.0660 | + | 4.95421i | 0.912706 | + | 0.408617i | ||||
\(148\) | −2.53840 | + | 4.39664i | −0.208655 | + | 0.361402i | ||||
\(149\) | 12.0662i | 0.988502i | 0.869319 | + | 0.494251i | \(0.164558\pi\) | ||||
−0.869319 | + | 0.494251i | \(0.835442\pi\) | |||||||
\(150\) | 1.45501 | − | 0.939646i | 0.118801 | − | 0.0767218i | ||||
\(151\) | −14.6605 | −1.19305 | −0.596527 | − | 0.802593i | \(-0.703453\pi\) | ||||
−0.596527 | + | 0.802593i | \(0.703453\pi\) | |||||||
\(152\) | −0.412013 | − | 0.713627i | −0.0334186 | − | 0.0578828i | ||||
\(153\) | 14.5927 | − | 1.45877i | 1.17975 | − | 0.117934i | ||||
\(154\) | −2.31403 | − | 7.80511i | −0.186470 | − | 0.628953i | ||||
\(155\) | 0.784474 | − | 0.452916i | 0.0630105 | − | 0.0363791i | ||||
\(156\) | 0.800590 | + | 0.410488i | 0.0640985 | + | 0.0328654i | ||||
\(157\) | −0.502653 | + | 0.290207i | −0.0401161 | + | 0.0231610i | −0.519924 | − | 0.854213i | \(-0.674040\pi\) |
0.479808 | + | 0.877374i | \(0.340706\pi\) | |||||||
\(158\) | 2.99730 | − | 1.73049i | 0.238453 | − | 0.137671i | ||||
\(159\) | −7.89145 | + | 5.09629i | −0.625833 | + | 0.404162i | ||||
\(160\) | −0.866025 | + | 0.500000i | −0.0684653 | + | 0.0395285i | ||||
\(161\) | 17.1638 | + | 16.2800i | 1.35270 | + | 1.28304i | ||||
\(162\) | 6.74920 | − | 5.95385i | 0.530267 | − | 0.467779i | ||||
\(163\) | 0.0642633 | + | 0.111307i | 0.00503349 | + | 0.00871827i | 0.868531 | − | 0.495635i | \(-0.165064\pi\) |
−0.863498 | + | 0.504353i | \(0.831731\pi\) | |||||||
\(164\) | 4.37192 | 0.341389 | ||||||||
\(165\) | −4.74243 | − | 2.43160i | −0.369198 | − | 0.189300i | ||||
\(166\) | 6.64066i | 0.515415i | ||||||||
\(167\) | −12.6749 | + | 21.9535i | −0.980811 | + | 1.69881i | −0.321564 | + | 0.946888i | \(0.604209\pi\) |
−0.659247 | + | 0.751927i | \(0.729125\pi\) | |||||||
\(168\) | −4.32323 | + | 1.51975i | −0.333545 | + | 0.117252i | ||||
\(169\) | −6.36509 | − | 11.0247i | −0.489622 | − | 0.848051i | ||||
\(170\) | −4.23353 | + | 2.44423i | −0.324697 | + | 0.187464i | ||||
\(171\) | −2.25321 | − | 1.01695i | −0.172307 | − | 0.0777684i | ||||
\(172\) | 1.84515 | − | 3.19589i | 0.140691 | − | 0.243685i | ||||
\(173\) | 2.36631 | − | 4.09857i | 0.179907 | − | 0.311609i | −0.761941 | − | 0.647646i | \(-0.775754\pi\) |
0.941849 | + | 0.336037i | \(0.109087\pi\) | |||||||
\(174\) | 5.06818 | − | 9.88466i | 0.384218 | − | 0.749354i | ||||
\(175\) | −1.82075 | + | 1.91960i | −0.137636 | + | 0.145108i | ||||
\(176\) | 2.66474 | + | 1.53849i | 0.200862 | + | 0.115968i | ||||
\(177\) | 18.3061 | − | 0.912720i | 1.37597 | − | 0.0686043i | ||||
\(178\) | − | 1.54392i | − | 0.115722i | ||||||
\(179\) | −6.52127 | − | 3.76505i | −0.487422 | − | 0.281413i | 0.236082 | − | 0.971733i | \(-0.424137\pi\) |
−0.723504 | + | 0.690320i | \(0.757470\pi\) | |||||||
\(180\) | −1.23413 | + | 2.73440i | −0.0919866 | + | 0.203810i | ||||
\(181\) | 12.3791i | 0.920133i | 0.887884 | + | 0.460067i | \(0.152175\pi\) | ||||
−0.887884 | + | 0.460067i | \(0.847825\pi\) | |||||||
\(182\) | −1.33641 | − | 0.320501i | −0.0990611 | − | 0.0237571i | ||||
\(183\) | 13.8587 | − | 8.94995i | 1.02447 | − | 0.661599i | ||||
\(184\) | −8.94137 | −0.659166 | ||||||||
\(185\) | −2.53840 | − | 4.39664i | −0.186627 | − | 0.323248i | ||||
\(186\) | −0.715840 | + | 1.39613i | −0.0524879 | + | 0.102369i | ||||
\(187\) | 13.0265 | + | 7.52084i | 0.952590 | + | 0.549978i | ||||
\(188\) | 3.78444 | 0.276008 | ||||||||
\(189\) | −7.87026 | + | 11.2720i | −0.572477 | + | 0.819921i | ||||
\(190\) | 0.824025 | 0.0597811 | ||||||||
\(191\) | 16.6514 | + | 9.61366i | 1.20485 | + | 0.695620i | 0.961630 | − | 0.274351i | \(-0.0884630\pi\) |
0.243220 | + | 0.969971i | \(0.421796\pi\) | |||||||
\(192\) | 0.790256 | − | 1.54126i | 0.0570318 | − | 0.111231i | ||||
\(193\) | −11.8348 | − | 20.4985i | −0.851889 | − | 1.47551i | −0.879502 | − | 0.475896i | \(-0.842124\pi\) |
0.0276128 | − | 0.999619i | \(-0.491209\pi\) | |||||||
\(194\) | −2.23764 | −0.160653 | ||||||||
\(195\) | −0.755788 | + | 0.488087i | −0.0541231 | + | 0.0349527i | ||||
\(196\) | 5.86885 | − | 3.81531i | 0.419204 | − | 0.272522i | ||||
\(197\) | − | 5.93788i | − | 0.423057i | −0.977372 | − | 0.211528i | \(-0.932156\pi\) | ||
0.977372 | − | 0.211528i | \(-0.0678441\pi\) | |||||||
\(198\) | 9.18514 | − | 0.918202i | 0.652760 | − | 0.0652538i | ||||
\(199\) | −14.4039 | − | 8.31608i | −1.02106 | − | 0.589511i | −0.106652 | − | 0.994296i | \(-0.534013\pi\) |
−0.914412 | + | 0.404785i | \(0.867346\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 13.6762 | − | 0.681876i | 0.964641 | − | 0.0480958i | ||||
\(202\) | 3.63453 | + | 2.09840i | 0.255725 | + | 0.147643i | ||||
\(203\) | −3.95714 | + | 16.5002i | −0.277737 | + | 1.15809i | ||||
\(204\) | 3.86313 | − | 7.53441i | 0.270473 | − | 0.527514i | ||||
\(205\) | −2.18596 | + | 3.78619i | −0.152674 | + | 0.264439i | ||||
\(206\) | −0.350569 | + | 0.607203i | −0.0244253 | + | 0.0423058i | ||||
\(207\) | −21.7810 | + | 15.6563i | −1.51389 | + | 1.08819i | ||||
\(208\) | 0.449846 | − | 0.259719i | 0.0311912 | − | 0.0180082i | ||||
\(209\) | −1.26775 | − | 2.19581i | −0.0876923 | − | 0.151888i | ||||
\(210\) | 0.845472 | − | 4.50391i | 0.0583431 | − | 0.310799i | ||||
\(211\) | 10.7108 | − | 18.5516i | 0.737360 | − | 1.27714i | −0.216320 | − | 0.976322i | \(-0.569406\pi\) |
0.953680 | − | 0.300822i | \(-0.0972611\pi\) | |||||||
\(212\) | 5.42363i | 0.372496i | ||||||||
\(213\) | 16.4545 | + | 8.43675i | 1.12744 | + | 0.578077i | ||||
\(214\) | 20.6644 | 1.41259 | ||||||||
\(215\) | 1.84515 | + | 3.19589i | 0.125838 | + | 0.217958i | ||||
\(216\) | −0.773690 | − | 5.13823i | −0.0526430 | − | 0.349612i | ||||
\(217\) | 0.558914 | − | 2.33053i | 0.0379415 | − | 0.158206i | ||||
\(218\) | 1.56454 | − | 0.903287i | 0.105964 | − | 0.0611783i | ||||
\(219\) | −9.71455 | + | 6.27364i | −0.656448 | + | 0.423934i | ||||
\(220\) | −2.66474 | + | 1.53849i | −0.179657 | + | 0.103725i | ||||
\(221\) | 2.19905 | − | 1.26962i | 0.147924 | − | 0.0854042i | ||||
\(222\) | 7.82470 | + | 4.01198i | 0.525160 | + | 0.269266i | ||||
\(223\) | 23.0028 | − | 13.2807i | 1.54038 | − | 0.889340i | 0.541569 | − | 0.840657i | \(-0.317831\pi\) |
0.998814 | − | 0.0486838i | \(-0.0155027\pi\) | |||||||
\(224\) | −0.617016 | + | 2.57280i | −0.0412261 | + | 0.171902i | ||||
\(225\) | −1.75099 | − | 2.43599i | −0.116733 | − | 0.162399i | ||||
\(226\) | 9.38276 | + | 16.2514i | 0.624132 | + | 1.08103i | ||||
\(227\) | −26.7377 | −1.77464 | −0.887321 | − | 0.461152i | \(-0.847436\pi\) | ||||
−0.887321 | + | 0.461152i | \(0.847436\pi\) | |||||||
\(228\) | −1.19897 | + | 0.774292i | −0.0794036 | + | 0.0512788i | ||||
\(229\) | 7.93372i | 0.524275i | 0.965031 | + | 0.262137i | \(0.0844274\pi\) | ||||
−0.965031 | + | 0.262137i | \(0.915573\pi\) | |||||||
\(230\) | 4.47068 | − | 7.74345i | 0.294788 | − | 0.510588i | ||||
\(231\) | −13.3025 | + | 4.67624i | −0.875239 | + | 0.307674i | ||||
\(232\) | −3.20667 | − | 5.55412i | −0.210528 | − | 0.364646i | ||||
\(233\) | 24.2871 | − | 14.0222i | 1.59110 | − | 0.918623i | 0.597983 | − | 0.801509i | \(-0.295969\pi\) |
0.993118 | − | 0.117114i | \(-0.0373644\pi\) | |||||||
\(234\) | 0.641053 | − | 1.42035i | 0.0419069 | − | 0.0928510i | ||||
\(235\) | −1.89222 | + | 3.27742i | −0.123435 | + | 0.213795i | ||||
\(236\) | 5.29109 | − | 9.16443i | 0.344420 | − | 0.596554i | ||||
\(237\) | −3.25210 | − | 5.03578i | −0.211247 | − | 0.327109i | ||||
\(238\) | −3.01626 | + | 12.5770i | −0.195515 | + | 0.815247i | ||||
\(239\) | −24.5540 | − | 14.1762i | −1.58826 | − | 0.916985i | −0.993593 | − | 0.113016i | \(-0.963949\pi\) |
−0.594671 | − | 0.803969i | \(-0.702718\pi\) | |||||||
\(240\) | 0.939646 | + | 1.45501i | 0.0606539 | + | 0.0939207i | ||||
\(241\) | − | 0.954238i | − | 0.0614679i | −0.999528 | − | 0.0307339i | \(-0.990216\pi\) | ||
0.999528 | − | 0.0307339i | \(-0.00978446\pi\) | |||||||
\(242\) | −1.32695 | − | 0.766113i | −0.0852994 | − | 0.0492476i | ||||
\(243\) | −10.8817 | − | 11.1619i | −0.698061 | − | 0.716038i | ||||
\(244\) | − | 9.52480i | − | 0.609763i | ||||||
\(245\) | 0.369732 | + | 6.99023i | 0.0236213 | + | 0.446589i | ||||
\(246\) | −0.377081 | − | 7.56299i | −0.0240418 | − | 0.482198i | ||||
\(247\) | −0.428029 | −0.0272349 | ||||||||
\(248\) | 0.452916 | + | 0.784474i | 0.0287602 | + | 0.0498142i | ||||
\(249\) | 11.4877 | − | 0.572762i | 0.728003 | − | 0.0362973i | ||||
\(250\) | 0.866025 | + | 0.500000i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | 6.84608 | 0.432121 | 0.216060 | − | 0.976380i | \(-0.430679\pi\) | ||||
0.216060 | + | 0.976380i | \(0.430679\pi\) | |||||||
\(252\) | 3.00191 | + | 7.34769i | 0.189102 | + | 0.462861i | ||||
\(253\) | −27.5124 | −1.72969 | ||||||||
\(254\) | −1.33273 | − | 0.769453i | −0.0836230 | − | 0.0482798i | ||||
\(255\) | 4.59342 | + | 7.11278i | 0.287651 | + | 0.445419i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −26.4342 | −1.64892 | −0.824459 | − | 0.565922i | \(-0.808521\pi\) | ||||
−0.824459 | + | 0.565922i | \(0.808521\pi\) | |||||||
\(258\) | −5.68773 | − | 2.91628i | −0.354102 | − | 0.181560i | ||||
\(259\) | −13.0616 | − | 3.13247i | −0.811608 | − | 0.194642i | ||||
\(260\) | 0.519437i | 0.0322141i | ||||||||
\(261\) | −17.5366 | − | 7.91490i | −1.08549 | − | 0.489920i | ||||
\(262\) | −9.11256 | − | 5.26114i | −0.562976 | − | 0.325034i | ||||
\(263\) | − | 25.7323i | − | 1.58672i | −0.608750 | − | 0.793362i | \(-0.708329\pi\) | ||
0.608750 | − | 0.793362i | \(-0.291671\pi\) | |||||||
\(264\) | 2.43160 | − | 4.74243i | 0.149654 | − | 0.291877i | ||||
\(265\) | −4.69700 | − | 2.71181i | −0.288534 | − | 0.166585i | ||||
\(266\) | 1.50035 | − | 1.58180i | 0.0919921 | − | 0.0969864i | ||||
\(267\) | −2.67083 | + | 0.133164i | −0.163452 | + | 0.00814952i | ||||
\(268\) | 3.95287 | − | 6.84657i | 0.241460 | − | 0.418221i | ||||
\(269\) | −4.44806 | + | 7.70427i | −0.271203 | + | 0.469738i | −0.969170 | − | 0.246392i | \(-0.920755\pi\) |
0.697967 | + | 0.716130i | \(0.254088\pi\) | |||||||
\(270\) | 4.83668 | + | 1.89908i | 0.294351 | + | 0.115574i | ||||
\(271\) | 19.2172 | − | 11.0951i | 1.16736 | − | 0.673978i | 0.214306 | − | 0.976767i | \(-0.431251\pi\) |
0.953058 | + | 0.302789i | \(0.0979176\pi\) | |||||||
\(272\) | −2.44423 | − | 4.23353i | −0.148203 | − | 0.256696i | ||||
\(273\) | −0.439170 | + | 2.33950i | −0.0265798 | + | 0.141593i | ||||
\(274\) | 0.00167750 | − | 0.00290551i | 0.000101341 | − | 0.000175528i | ||||
\(275\) | − | 3.07697i | − | 0.185549i | ||||||
\(276\) | 0.771200 | + | 15.4677i | 0.0464208 | + | 0.931045i | ||||
\(277\) | 12.6086 | 0.757576 | 0.378788 | − | 0.925484i | \(-0.376341\pi\) | ||||
0.378788 | + | 0.925484i | \(0.376341\pi\) | |||||||
\(278\) | −9.60272 | − | 16.6324i | −0.575933 | − | 0.997545i | ||||
\(279\) | 2.47691 | + | 1.11792i | 0.148289 | + | 0.0669278i | ||||
\(280\) | −1.91960 | − | 1.82075i | −0.114718 | − | 0.108811i | ||||
\(281\) | −6.81401 | + | 3.93407i | −0.406490 | + | 0.234687i | −0.689280 | − | 0.724495i | \(-0.742073\pi\) |
0.282791 | + | 0.959182i | \(0.408740\pi\) | |||||||
\(282\) | −0.326410 | − | 6.54670i | −0.0194375 | − | 0.389850i | ||||
\(283\) | −25.5885 | + | 14.7735i | −1.52108 | + | 0.878193i | −0.521385 | + | 0.853322i | \(0.674584\pi\) |
−0.999691 | + | 0.0248719i | \(0.992082\pi\) | |||||||
\(284\) | 9.24567 | − | 5.33799i | 0.548629 | − | 0.316751i | ||||
\(285\) | −0.0710728 | − | 1.42548i | −0.00420999 | − | 0.0844383i | ||||
\(286\) | 1.38416 | − | 0.799148i | 0.0818474 | − | 0.0472546i | ||||
\(287\) | 3.28789 | + | 11.0899i | 0.194078 | + | 0.654615i | ||||
\(288\) | −2.73440 | − | 1.23413i | −0.161126 | − | 0.0727218i | ||||
\(289\) | −3.44853 | − | 5.97302i | −0.202854 | − | 0.351354i | ||||
\(290\) | 6.41334 | 0.376605 | ||||||||
\(291\) | 0.192998 | + | 3.87090i | 0.0113138 | + | 0.226916i | ||||
\(292\) | 6.67660i | 0.390719i | ||||||||
\(293\) | −3.97830 | + | 6.89061i | −0.232415 | + | 0.402554i | −0.958518 | − | 0.285031i | \(-0.907996\pi\) |
0.726104 | + | 0.687585i | \(0.241329\pi\) | |||||||
\(294\) | −7.10631 | − | 9.82346i | −0.414448 | − | 0.572916i | ||||
\(295\) | 5.29109 | + | 9.16443i | 0.308059 | + | 0.533574i | ||||
\(296\) | 4.39664 | − | 2.53840i | 0.255550 | − | 0.147542i | ||||
\(297\) | −2.38063 | − | 15.8102i | −0.138138 | − | 0.917401i | ||||
\(298\) | 6.03310 | − | 10.4496i | 0.349488 | − | 0.605332i | ||||
\(299\) | −2.32224 | + | 4.02224i | −0.134299 | + | 0.232612i | ||||
\(300\) | −1.72990 | + | 0.0862508i | −0.0998759 | + | 0.00497969i | ||||
\(301\) | 9.49440 | + | 2.27698i | 0.547248 | + | 0.131243i | ||||
\(302\) | 12.6964 | + | 7.33025i | 0.730593 | + | 0.421808i | ||||
\(303\) | 3.31654 | − | 6.46837i | 0.190530 | − | 0.371598i | ||||
\(304\) | 0.824025i | 0.0472611i | ||||||||
\(305\) | 8.24872 | + | 4.76240i | 0.472320 | + | 0.272694i | ||||
\(306\) | −13.3670 | − | 6.03299i | −0.764140 | − | 0.344883i | ||||
\(307\) | − | 33.8175i | − | 1.93006i | −0.262132 | − | 0.965032i | \(-0.584426\pi\) | ||
0.262132 | − | 0.965032i | \(-0.415574\pi\) | |||||||
\(308\) | −1.89854 | + | 7.91644i | −0.108180 | + | 0.451081i | ||||
\(309\) | 1.08064 | + | 0.554078i | 0.0614754 | + | 0.0315204i | ||||
\(310\) | −0.905833 | −0.0514479 | ||||||||
\(311\) | −11.6897 | − | 20.2471i | −0.662861 | − | 1.14811i | −0.979860 | − | 0.199684i | \(-0.936009\pi\) |
0.316999 | − | 0.948426i | \(-0.397325\pi\) | |||||||
\(312\) | −0.488087 | − | 0.755788i | −0.0276325 | − | 0.0427881i | ||||
\(313\) | 14.9966 | + | 8.65830i | 0.847659 | + | 0.489396i | 0.859860 | − | 0.510529i | \(-0.170551\pi\) |
−0.0122014 | + | 0.999926i | \(0.503884\pi\) | |||||||
\(314\) | 0.580414 | 0.0327546 | ||||||||
\(315\) | −7.86424 | − | 1.07412i | −0.443100 | − | 0.0605197i | ||||
\(316\) | −3.46099 | −0.194696 | ||||||||
\(317\) | 13.8006 | + | 7.96781i | 0.775121 | + | 0.447517i | 0.834699 | − | 0.550707i | \(-0.185642\pi\) |
−0.0595771 | + | 0.998224i | \(0.518975\pi\) | |||||||
\(318\) | 9.38234 | − | 0.467792i | 0.526136 | − | 0.0262325i | ||||
\(319\) | −9.86685 | − | 17.0899i | −0.552437 | − | 0.956850i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −1.78232 | − | 35.7474i | −0.0994794 | − | 1.99522i | ||||
\(322\) | −6.72433 | − | 22.6808i | −0.374732 | − | 1.26395i | ||||
\(323\) | 4.02822i | 0.224136i | ||||||||
\(324\) | −8.82190 | + | 1.78158i | −0.490106 | + | 0.0989769i | ||||
\(325\) | −0.449846 | − | 0.259719i | −0.0249530 | − | 0.0144066i | ||||
\(326\) | − | 0.128527i | − | 0.00711843i | ||||||
\(327\) | −1.69754 | − | 2.62859i | −0.0938743 | − | 0.145361i | ||||
\(328\) | −3.78619 | − | 2.18596i | −0.209057 | − | 0.120699i | ||||
\(329\) | 2.84607 | + | 9.59966i | 0.156909 | + | 0.529247i | ||||
\(330\) | 2.89127 | + | 4.47704i | 0.159159 | + | 0.246453i | ||||
\(331\) | −4.20318 | + | 7.28013i | −0.231028 | + | 0.400152i | −0.958111 | − | 0.286398i | \(-0.907542\pi\) |
0.727083 | + | 0.686550i | \(0.240876\pi\) | |||||||
\(332\) | 3.32033 | − | 5.75098i | 0.182227 | − | 0.315626i | ||||
\(333\) | 6.26544 | − | 13.8820i | 0.343344 | − | 0.760729i | ||||
\(334\) | 21.9535 | − | 12.6749i | 1.20124 | − | 0.693538i | ||||
\(335\) | 3.95287 | + | 6.84657i | 0.215968 | + | 0.374068i | ||||
\(336\) | 4.50391 | + | 0.845472i | 0.245708 | + | 0.0461243i | ||||
\(337\) | 7.68218 | − | 13.3059i | 0.418475 | − | 0.724820i | −0.577311 | − | 0.816524i | \(-0.695898\pi\) |
0.995786 | + | 0.0917044i | \(0.0292315\pi\) | |||||||
\(338\) | 12.7302i | 0.692431i | ||||||||
\(339\) | 27.3041 | − | 17.6330i | 1.48296 | − | 0.957691i | ||||
\(340\) | 4.88846 | 0.265114 | ||||||||
\(341\) | 1.39361 | + | 2.41381i | 0.0754684 | + | 0.130715i | ||||
\(342\) | 1.44286 | + | 2.00731i | 0.0780210 | + | 0.108543i | ||||
\(343\) | 14.0916 | + | 12.0177i | 0.760877 | + | 0.648896i | ||||
\(344\) | −3.19589 | + | 1.84515i | −0.172311 | + | 0.0994838i | ||||
\(345\) | −13.7810 | − | 7.06596i | −0.741945 | − | 0.380419i | ||||
\(346\) | −4.09857 | + | 2.36631i | −0.220341 | + | 0.127214i | ||||
\(347\) | −9.56913 | + | 5.52474i | −0.513698 | + | 0.296584i | −0.734352 | − | 0.678768i | \(-0.762514\pi\) |
0.220654 | + | 0.975352i | \(0.429181\pi\) | |||||||
\(348\) | −9.33150 | + | 6.02628i | −0.500221 | + | 0.323042i | ||||
\(349\) | 13.7644 | − | 7.94687i | 0.736791 | − | 0.425386i | −0.0841107 | − | 0.996456i | \(-0.526805\pi\) |
0.820901 | + | 0.571070i | \(0.193472\pi\) | |||||||
\(350\) | 2.53662 | − | 0.752047i | 0.135588 | − | 0.0401986i | ||||
\(351\) | −2.51235 | − | 0.986452i | −0.134099 | − | 0.0526529i | ||||
\(352\) | −1.53849 | − | 2.66474i | −0.0820017 | − | 0.142031i | ||||
\(353\) | −11.9879 | −0.638053 | −0.319026 | − | 0.947746i | \(-0.603356\pi\) | ||||
−0.319026 | + | 0.947746i | \(0.603356\pi\) | |||||||
\(354\) | −16.3099 | − | 8.36262i | −0.866863 | − | 0.444468i | ||||
\(355\) | 10.6760i | 0.566622i | ||||||||
\(356\) | −0.771960 | + | 1.33707i | −0.0409138 | + | 0.0708647i | ||||
\(357\) | 22.0172 | + | 4.13306i | 1.16527 | + | 0.218745i | ||||
\(358\) | 3.76505 | + | 6.52127i | 0.198989 | + | 0.344660i | ||||
\(359\) | −11.7767 | + | 6.79925i | −0.621548 | + | 0.358851i | −0.777471 | − | 0.628918i | \(-0.783498\pi\) |
0.155923 | + | 0.987769i | \(0.450165\pi\) | |||||||
\(360\) | 2.43599 | − | 1.75099i | 0.128388 | − | 0.0922854i | ||||
\(361\) | −9.16049 | + | 15.8664i | −0.482131 | + | 0.835076i | ||||
\(362\) | 6.18956 | − | 10.7206i | 0.325316 | − | 0.563464i | ||||
\(363\) | −1.21085 | + | 2.36157i | −0.0635532 | + | 0.123950i | ||||
\(364\) | 0.997112 | + | 0.945766i | 0.0522629 | + | 0.0495716i | ||||
\(365\) | −5.78211 | − | 3.33830i | −0.302649 | − | 0.174735i | ||||
\(366\) | −16.4770 | + | 0.821522i | −0.861265 | + | 0.0429416i | ||||
\(367\) | − | 5.63278i | − | 0.294029i | −0.989134 | − | 0.147014i | \(-0.953034\pi\) | ||
0.989134 | − | 0.147014i | \(-0.0469664\pi\) | |||||||
\(368\) | 7.74345 | + | 4.47068i | 0.403655 | + | 0.233050i | ||||
\(369\) | −13.0507 | + | 1.30463i | −0.679392 | + | 0.0679161i | ||||
\(370\) | 5.07681i | 0.263931i | ||||||||
\(371\) | −13.7577 | + | 4.07882i | −0.714262 | + | 0.211762i | ||||
\(372\) | 1.31800 | − | 0.851163i | 0.0683351 | − | 0.0441307i | ||||
\(373\) | 5.72999 | 0.296687 | 0.148344 | − | 0.988936i | \(-0.452606\pi\) | ||||
0.148344 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(374\) | −7.52084 | − | 13.0265i | −0.388893 | − | 0.673583i | ||||
\(375\) | 0.790256 | − | 1.54126i | 0.0408086 | − | 0.0795906i | ||||
\(376\) | −3.27742 | − | 1.89222i | −0.169020 | − | 0.0975837i | ||||
\(377\) | −3.33133 | −0.171572 | ||||||||
\(378\) | 12.4519 | − | 5.82675i | 0.640455 | − | 0.299696i | ||||
\(379\) | −12.0397 | −0.618437 | −0.309219 | − | 0.950991i | \(-0.600067\pi\) | ||||
−0.309219 | + | 0.950991i | \(0.600067\pi\) | |||||||
\(380\) | −0.713627 | − | 0.412013i | −0.0366083 | − | 0.0211358i | ||||
\(381\) | −1.21613 | + | 2.37186i | −0.0623042 | + | 0.121514i | ||||
\(382\) | −9.61366 | − | 16.6514i | −0.491878 | − | 0.851957i | ||||
\(383\) | 20.5060 | 1.04781 | 0.523903 | − | 0.851778i | \(-0.324475\pi\) | ||||
0.523903 | + | 0.851778i | \(0.324475\pi\) | |||||||
\(384\) | −1.45501 | + | 0.939646i | −0.0742509 | + | 0.0479511i | ||||
\(385\) | −5.90656 | − | 5.60240i | −0.301026 | − | 0.285525i | ||||
\(386\) | 23.6696i | 1.20475i | ||||||||
\(387\) | −4.55431 | + | 10.0907i | −0.231508 | + | 0.512941i | ||||
\(388\) | 1.93786 | + | 1.11882i | 0.0983797 | + | 0.0567995i | ||||
\(389\) | 25.8396i | 1.31012i | 0.755577 | + | 0.655060i | \(0.227357\pi\) | ||||
−0.755577 | + | 0.655060i | \(0.772643\pi\) | |||||||
\(390\) | 0.898575 | − | 0.0448019i | 0.0455011 | − | 0.00226863i | ||||
\(391\) | 37.8536 | + | 21.8548i | 1.91434 | + | 1.10524i | ||||
\(392\) | −6.99023 | + | 0.369732i | −0.353060 | + | 0.0186743i | ||||
\(393\) | −8.31529 | + | 16.2176i | −0.419451 | + | 0.818070i | ||||
\(394\) | −2.96894 | + | 5.14236i | −0.149573 | + | 0.259068i | ||||
\(395\) | 1.73049 | − | 2.99730i | 0.0870706 | − | 0.150811i | ||||
\(396\) | −8.41367 | − | 3.79739i | −0.422803 | − | 0.190826i | ||||
\(397\) | 5.58453 | − | 3.22423i | 0.280279 | − | 0.161819i | −0.353271 | − | 0.935521i | \(-0.614930\pi\) |
0.633550 | + | 0.773702i | \(0.281597\pi\) | |||||||
\(398\) | 8.31608 | + | 14.4039i | 0.416848 | + | 0.722001i | ||||
\(399\) | −2.86576 | − | 2.45902i | −0.143468 | − | 0.123105i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | − | 12.1434i | − | 0.606413i | −0.952925 | − | 0.303206i | \(-0.901943\pi\) | ||
0.952925 | − | 0.303206i | \(-0.0980571\pi\) | |||||||
\(402\) | −12.1848 | − | 6.24755i | −0.607724 | − | 0.311600i | ||||
\(403\) | 0.470523 | 0.0234384 | ||||||||
\(404\) | −2.09840 | − | 3.63453i | −0.104399 | − | 0.180825i | ||||
\(405\) | 2.86805 | − | 8.53078i | 0.142515 | − | 0.423898i | ||||
\(406\) | 11.6771 | − | 12.3111i | 0.579525 | − | 0.610988i | ||||
\(407\) | 13.5284 | − | 7.81060i | 0.670576 | − | 0.387157i | ||||
\(408\) | −7.11278 | + | 4.59342i | −0.352135 | + | 0.227408i | ||||
\(409\) | 19.2077 | − | 11.0896i | 0.949761 | − | 0.548345i | 0.0567546 | − | 0.998388i | \(-0.481925\pi\) |
0.893007 | + | 0.450043i | \(0.148591\pi\) | |||||||
\(410\) | 3.78619 | − | 2.18596i | 0.186987 | − | 0.107957i | ||||
\(411\) | −0.00517093 | − | 0.00265130i | −0.000255063 | − | 0.000130779i | ||||
\(412\) | 0.607203 | − | 0.350569i | 0.0299147 | − | 0.0172713i | ||||
\(413\) | 27.2258 | + | 6.52937i | 1.33969 | + | 0.321289i | ||||
\(414\) | 26.6911 | − | 2.66820i | 1.31179 | − | 0.131135i | ||||
\(415\) | 3.32033 | + | 5.75098i | 0.162989 | + | 0.282305i | ||||
\(416\) | −0.519437 | −0.0254675 | ||||||||
\(417\) | −27.9442 | + | 18.0463i | −1.36843 | + | 0.883732i | ||||
\(418\) | 2.53551i | 0.124016i | ||||||||
\(419\) | −7.31349 | + | 12.6673i | −0.357287 | + | 0.618840i | −0.987507 | − | 0.157577i | \(-0.949632\pi\) |
0.630219 | + | 0.776417i | \(0.282965\pi\) | |||||||
\(420\) | −2.98415 | + | 3.47776i | −0.145612 | + | 0.169697i | ||||
\(421\) | 17.6810 | + | 30.6243i | 0.861717 | + | 1.49254i | 0.870270 | + | 0.492575i | \(0.163944\pi\) |
−0.00855262 | + | 0.999963i | \(0.502722\pi\) | |||||||
\(422\) | −18.5516 | + | 10.7108i | −0.903078 | + | 0.521392i | ||||
\(423\) | −11.2970 | + | 1.12932i | −0.549279 | + | 0.0549092i | ||||
\(424\) | 2.71181 | − | 4.69700i | 0.131697 | − | 0.228106i | ||||
\(425\) | −2.44423 | + | 4.23353i | −0.118563 | + | 0.205356i | ||||
\(426\) | −10.0316 | − | 15.5337i | −0.486035 | − | 0.752610i | ||||
\(427\) | 24.1608 | − | 7.16310i | 1.16922 | − | 0.346647i | ||||
\(428\) | −17.8959 | − | 10.3322i | −0.865031 | − | 0.499426i | ||||
\(429\) | −1.50183 | − | 2.32554i | −0.0725091 | − | 0.112278i | ||||
\(430\) | − | 3.69030i | − | 0.177962i | ||||||
\(431\) | 14.2396 | + | 8.22125i | 0.685898 | + | 0.396003i | 0.802074 | − | 0.597225i | \(-0.203730\pi\) |
−0.116175 | + | 0.993229i | \(0.537063\pi\) | |||||||
\(432\) | −1.89908 | + | 4.83668i | −0.0913695 | + | 0.232705i | ||||
\(433\) | − | 22.0355i | − | 1.05896i | −0.848323 | − | 0.529479i | \(-0.822388\pi\) | ||
0.848323 | − | 0.529479i | \(-0.177612\pi\) | |||||||
\(434\) | −1.64930 | + | 1.73884i | −0.0791687 | + | 0.0834669i | ||||
\(435\) | −0.553156 | − | 11.0945i | −0.0265218 | − | 0.531938i | ||||
\(436\) | −1.80657 | −0.0865192 | ||||||||
\(437\) | −3.68396 | − | 6.38080i | −0.176228 | − | 0.305235i | ||||
\(438\) | 11.5499 | − | 0.575862i | 0.551874 | − | 0.0275157i | ||||
\(439\) | 21.4924 | + | 12.4087i | 1.02578 | + | 0.592233i | 0.915772 | − | 0.401697i | \(-0.131580\pi\) |
0.110006 | + | 0.993931i | \(0.464913\pi\) | |||||||
\(440\) | 3.07697 | 0.146689 | ||||||||
\(441\) | −16.3807 | + | 13.1405i | −0.780033 | + | 0.625738i | ||||
\(442\) | −2.53925 | −0.120780 | ||||||||
\(443\) | −14.3967 | − | 8.31193i | −0.684007 | − | 0.394912i | 0.117356 | − | 0.993090i | \(-0.462558\pi\) |
−0.801363 | + | 0.598178i | \(0.795891\pi\) | |||||||
\(444\) | −4.77040 | − | 7.38682i | −0.226393 | − | 0.350563i | ||||
\(445\) | −0.771960 | − | 1.33707i | −0.0365944 | − | 0.0633834i | ||||
\(446\) | −26.5614 | −1.25772 | ||||||||
\(447\) | −18.5972 | − | 9.53539i | −0.879618 | − | 0.451008i | ||||
\(448\) | 1.82075 | − | 1.91960i | 0.0860224 | − | 0.0906926i | ||||
\(449\) | 12.5154i | 0.590638i | 0.955399 | + | 0.295319i | \(0.0954260\pi\) | ||||
−0.955399 | + | 0.295319i | \(0.904574\pi\) | |||||||
\(450\) | 0.298411 | + | 2.98512i | 0.0140672 | + | 0.140720i | ||||
\(451\) | −11.6500 | − | 6.72614i | −0.548578 | − | 0.316721i | ||||
\(452\) | − | 18.7655i | − | 0.882656i | ||||||
\(453\) | 11.5855 | − | 22.5957i | 0.544336 | − | 1.06164i | ||||
\(454\) | 23.1555 | + | 13.3688i | 1.08674 | + | 0.627431i | ||||
\(455\) | −1.31761 | + | 0.390641i | −0.0617707 | + | 0.0183135i | ||||
\(456\) | 1.42548 | − | 0.0710728i | 0.0667544 | − | 0.00332829i | ||||
\(457\) | 16.3501 | − | 28.3193i | 0.764827 | − | 1.32472i | −0.175511 | − | 0.984478i | \(-0.556158\pi\) |
0.940338 | − | 0.340242i | \(-0.110509\pi\) | |||||||
\(458\) | 3.96686 | − | 6.87080i | 0.185359 | − | 0.321051i | ||||
\(459\) | −9.28358 | + | 23.6439i | −0.433320 | + | 1.10360i | ||||
\(460\) | −7.74345 | + | 4.47068i | −0.361040 | + | 0.208447i | ||||
\(461\) | 2.69005 | + | 4.65931i | 0.125288 | + | 0.217006i | 0.921846 | − | 0.387557i | \(-0.126681\pi\) |
−0.796557 | + | 0.604563i | \(0.793348\pi\) | |||||||
\(462\) | 13.8584 | + | 2.60150i | 0.644751 | + | 0.121033i | ||||
\(463\) | 5.41835 | − | 9.38485i | 0.251812 | − | 0.436151i | −0.712213 | − | 0.701964i | \(-0.752307\pi\) |
0.964025 | + | 0.265813i | \(0.0856402\pi\) | |||||||
\(464\) | 6.41334i | 0.297732i | ||||||||
\(465\) | 0.0781288 | + | 1.56700i | 0.00362314 | + | 0.0726680i | ||||
\(466\) | −28.0443 | −1.29913 | ||||||||
\(467\) | −2.76713 | − | 4.79281i | −0.128048 | − | 0.221785i | 0.794872 | − | 0.606777i | \(-0.207538\pi\) |
−0.922920 | + | 0.384992i | \(0.874204\pi\) | |||||||
\(468\) | −1.26534 | + | 0.909530i | −0.0584904 | + | 0.0420431i | ||||
\(469\) | 20.3399 | + | 4.87797i | 0.939208 | + | 0.225244i | ||||
\(470\) | 3.27742 | − | 1.89222i | 0.151176 | − | 0.0872815i | ||||
\(471\) | −0.0500611 | − | 1.00406i | −0.00230670 | − | 0.0462646i | ||||
\(472\) | −9.16443 | + | 5.29109i | −0.421827 | + | 0.243542i | ||||
\(473\) | −9.83368 | + | 5.67748i | −0.452153 | + | 0.261051i | ||||
\(474\) | 0.298513 | + | 5.98717i | 0.0137111 | + | 0.275000i | ||||
\(475\) | 0.713627 | − | 0.412013i | 0.0327434 | − | 0.0189044i | ||||
\(476\) | 8.90067 | − | 9.38389i | 0.407962 | − | 0.430110i | ||||
\(477\) | −1.61847 | − | 16.1902i | −0.0741046 | − | 0.741298i | ||||
\(478\) | 14.1762 | + | 24.5540i | 0.648406 | + | 1.12307i | ||||
\(479\) | 39.8255 | 1.81968 | 0.909838 | − | 0.414964i | \(-0.136206\pi\) | ||||
0.909838 | + | 0.414964i | \(0.136206\pi\) | |||||||
\(480\) | −0.0862508 | − | 1.72990i | −0.00393679 | − | 0.0789589i | ||||
\(481\) | − | 2.63708i | − | 0.120241i | ||||||
\(482\) | −0.477119 | + | 0.826394i | −0.0217322 | + | 0.0376412i | ||||
\(483\) | −38.6556 | + | 13.5887i | −1.75889 | + | 0.618306i | ||||
\(484\) | 0.766113 | + | 1.32695i | 0.0348233 | + | 0.0603158i | ||||
\(485\) | −1.93786 | + | 1.11882i | −0.0879935 | + | 0.0508031i | ||||
\(486\) | 3.84286 | + | 15.1074i | 0.174316 | + | 0.685284i | ||||
\(487\) | 19.7936 | − | 34.2835i | 0.896934 | − | 1.55354i | 0.0655411 | − | 0.997850i | \(-0.479123\pi\) |
0.831393 | − | 0.555685i | \(-0.187544\pi\) | |||||||
\(488\) | −4.76240 | + | 8.24872i | −0.215584 | + | 0.373402i | ||||
\(489\) | −0.222339 | + | 0.0110855i | −0.0100545 | + | 0.000501305i | ||||
\(490\) | 3.17492 | − | 6.23858i | 0.143428 | − | 0.281830i | ||||
\(491\) | 27.1823 | + | 15.6937i | 1.22672 | + | 0.708247i | 0.966342 | − | 0.257260i | \(-0.0828197\pi\) |
0.260377 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(492\) | −3.45493 | + | 6.73828i | −0.155760 | + | 0.303785i | ||||
\(493\) | 31.3514i | 1.41200i | ||||||||
\(494\) | 0.370684 | + | 0.214015i | 0.0166779 | + | 0.00962898i | ||||
\(495\) | 7.49547 | − | 5.38776i | 0.336896 | − | 0.242162i | ||||
\(496\) | − | 0.905833i | − | 0.0406731i | ||||||
\(497\) | 20.4936 | + | 19.4383i | 0.919264 | + | 0.871927i | ||||
\(498\) | −10.2350 | − | 5.24782i | −0.458642 | − | 0.235160i | ||||
\(499\) | −29.6748 | −1.32843 | −0.664214 | − | 0.747542i | \(-0.731234\pi\) | ||||
−0.664214 | + | 0.747542i | \(0.731234\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −23.8198 | − | 36.8842i | −1.06419 | − | 1.64787i | ||||
\(502\) | −5.92888 | − | 3.42304i | −0.264619 | − | 0.152778i | ||||
\(503\) | −31.4939 | −1.40424 | −0.702121 | − | 0.712058i | \(-0.747764\pi\) | ||||
−0.702121 | + | 0.712058i | \(0.747764\pi\) | |||||||
\(504\) | 1.07412 | − | 7.86424i | 0.0478450 | − | 0.350301i | ||||
\(505\) | 4.19679 | 0.186755 | ||||||||
\(506\) | 23.8264 | + | 13.7562i | 1.05921 | + | 0.611537i | ||||
\(507\) | 22.0220 | − | 1.09799i | 0.978030 | − | 0.0487634i | ||||
\(508\) | 0.769453 | + | 1.33273i | 0.0341390 | + | 0.0591304i | ||||
\(509\) | 12.4151 | 0.550290 | 0.275145 | − | 0.961403i | \(-0.411274\pi\) | ||||
0.275145 | + | 0.961403i | \(0.411274\pi\) | |||||||
\(510\) | −0.421633 | − | 8.45656i | −0.0186702 | − | 0.374463i | ||||
\(511\) | −16.9360 | + | 5.02112i | −0.749204 | + | 0.222121i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.34801 | − | 2.66914i | 0.147818 | − | 0.117846i | ||||
\(514\) | 22.8927 | + | 13.2171i | 1.00975 | + | 0.582981i | ||||
\(515\) | 0.701137i | 0.0308958i | ||||||||
\(516\) | 3.46758 | + | 5.36944i | 0.152652 | + | 0.236376i | ||||
\(517\) | −10.0845 | − | 5.82231i | −0.443517 | − | 0.256065i | ||||
\(518\) | 9.74544 | + | 9.24360i | 0.428190 | + | 0.406141i | ||||
\(519\) | 4.44699 | + | 6.88603i | 0.195201 | + | 0.302263i | ||||
\(520\) | 0.259719 | − | 0.449846i | 0.0113894 | − | 0.0197270i | ||||
\(521\) | 20.9931 | − | 36.3610i | 0.919722 | − | 1.59301i | 0.119886 | − | 0.992788i | \(-0.461747\pi\) |
0.799836 | − | 0.600218i | \(-0.204920\pi\) | |||||||
\(522\) | 11.2297 | + | 15.6228i | 0.491511 | + | 0.683792i | ||||
\(523\) | −20.1026 | + | 11.6062i | −0.879024 | + | 0.507505i | −0.870337 | − | 0.492457i | \(-0.836099\pi\) |
−0.00868774 | + | 0.999962i | \(0.502765\pi\) | |||||||
\(524\) | 5.26114 | + | 9.11256i | 0.229834 | + | 0.398084i | ||||
\(525\) | −1.51975 | − | 4.32323i | −0.0663275 | − | 0.188681i | ||||
\(526\) | −12.8662 | + | 22.2849i | −0.560992 | + | 0.971666i | ||||
\(527\) | − | 4.42813i | − | 0.192892i | ||||||
\(528\) | −4.47704 | + | 2.89127i | −0.194838 | + | 0.125826i | ||||
\(529\) | −56.9480 | −2.47600 | ||||||||
\(530\) | 2.71181 | + | 4.69700i | 0.117794 | + | 0.204025i | ||||
\(531\) | −13.0598 | + | 28.9359i | −0.566746 | + | 1.25571i | ||||
\(532\) | −2.09024 | + | 0.619706i | −0.0906233 | + | 0.0268677i | ||||
\(533\) | −1.96669 | + | 1.13547i | −0.0851867 | + | 0.0491826i | ||||
\(534\) | 2.37959 | + | 1.22009i | 0.102975 | + | 0.0527985i | ||||
\(535\) | 17.8959 | − | 10.3322i | 0.773707 | − | 0.446700i | ||||
\(536\) | −6.84657 | + | 3.95287i | −0.295727 | + | 0.170738i | ||||
\(537\) | 10.9564 | − | 7.07564i | 0.472804 | − | 0.305336i | ||||
\(538\) | 7.70427 | − | 4.44806i | 0.332155 | − | 0.191770i | ||||
\(539\) | −21.5088 | + | 1.13766i | −0.926448 | + | 0.0490023i | ||||
\(540\) | −3.23915 | − | 4.06299i | −0.139391 | − | 0.174843i | ||||
\(541\) | 3.91386 | + | 6.77900i | 0.168270 | + | 0.291452i | 0.937812 | − | 0.347145i | \(-0.112849\pi\) |
−0.769542 | + | 0.638596i | \(0.779515\pi\) | |||||||
\(542\) | −22.1902 | −0.953149 | ||||||||
\(543\) | −19.0795 | − | 9.78268i | −0.818780 | − | 0.419815i | ||||
\(544\) | 4.88846i | 0.209591i | ||||||||
\(545\) | 0.903287 | − | 1.56454i | 0.0386926 | − | 0.0670175i | ||||
\(546\) | 1.55008 | − | 1.80648i | 0.0663373 | − | 0.0773102i | ||||
\(547\) | 20.3459 | + | 35.2402i | 0.869930 | + | 1.50676i | 0.862068 | + | 0.506793i | \(0.169169\pi\) |
0.00786205 | + | 0.999969i | \(0.497497\pi\) | |||||||
\(548\) | −0.00290551 | + | 0.00167750i | −0.000124117 | + | 7.16591e-5i | ||||
\(549\) | 2.84230 | + | 28.4327i | 0.121307 | + | 1.21348i | ||||
\(550\) | −1.53849 | + | 2.66474i | −0.0656013 | + | 0.113625i | ||||
\(551\) | 2.64238 | − | 4.57674i | 0.112569 | − | 0.194975i | ||||
\(552\) | 7.06596 | − | 13.7810i | 0.300747 | − | 0.586559i | ||||
\(553\) | −2.60283 | − | 8.77920i | −0.110683 | − | 0.373330i | ||||
\(554\) | −10.9193 | − | 6.30428i | −0.463918 | − | 0.267843i | ||||
\(555\) | 8.78238 | − | 0.437878i | 0.372791 | − | 0.0185869i | ||||
\(556\) | 19.2054i | 0.814492i | ||||||||
\(557\) | 26.3951 | + | 15.2392i | 1.11840 | + | 0.645707i | 0.940991 | − | 0.338430i | \(-0.109896\pi\) |
0.177406 | + | 0.984138i | \(0.443229\pi\) | |||||||
\(558\) | −1.58611 | − | 2.20660i | −0.0671452 | − | 0.0934127i | ||||
\(559\) | 1.91688i | 0.0810754i | ||||||||
\(560\) | 0.752047 | + | 2.53662i | 0.0317798 | + | 0.107192i | ||||
\(561\) | −21.8858 | + | 14.1339i | −0.924021 | + | 0.596732i | ||||
\(562\) | 7.86814 | 0.331898 | ||||||||
\(563\) | 4.87559 | + | 8.44476i | 0.205481 | + | 0.355904i | 0.950286 | − | 0.311378i | \(-0.100791\pi\) |
−0.744805 | + | 0.667283i | \(0.767457\pi\) | |||||||
\(564\) | −2.99067 | + | 5.83282i | −0.125930 | + | 0.245606i | ||||
\(565\) | 16.2514 | + | 9.38276i | 0.683703 | + | 0.394736i | ||||
\(566\) | 29.5470 | 1.24195 | ||||||||
\(567\) | −11.1537 | − | 21.0379i | −0.468411 | − | 0.883511i | ||||
\(568\) | −10.6760 | −0.447954 | ||||||||
\(569\) | 28.8139 | + | 16.6357i | 1.20794 | + | 0.697405i | 0.962309 | − | 0.271958i | \(-0.0876711\pi\) |
0.245632 | + | 0.969363i | \(0.421004\pi\) | |||||||
\(570\) | −0.651191 | + | 1.27004i | −0.0272754 | + | 0.0531962i | ||||
\(571\) | 18.9605 | + | 32.8406i | 0.793473 | + | 1.37434i | 0.923804 | + | 0.382865i | \(0.125062\pi\) |
−0.130332 | + | 0.991470i | \(0.541604\pi\) | |||||||
\(572\) | −1.59830 | −0.0668281 | ||||||||
\(573\) | −27.9760 | + | 18.0669i | −1.16872 | + | 0.754755i | ||||
\(574\) | 2.69754 | − | 11.2481i | 0.112593 | − | 0.469485i | ||||
\(575\) | − | 8.94137i | − | 0.372881i | ||||||
\(576\) | 1.75099 | + | 2.43599i | 0.0729580 | + | 0.101499i | ||||
\(577\) | −11.5550 | − | 6.67129i | −0.481042 | − | 0.277730i | 0.239809 | − | 0.970820i | \(-0.422915\pi\) |
−0.720850 | + | 0.693091i | \(0.756249\pi\) | |||||||
\(578\) | 6.89705i | 0.286880i | ||||||||
\(579\) | 40.9461 | − | 2.04152i | 1.70166 | − | 0.0848428i | ||||
\(580\) | −5.55412 | − | 3.20667i | −0.230622 | − | 0.133150i | ||||
\(581\) | 17.0851 | + | 4.09740i | 0.708809 | + | 0.169989i | ||||
\(582\) | 1.76831 | − | 3.44880i | 0.0732988 | − | 0.142957i | ||||
\(583\) | 8.34418 | − | 14.4525i | 0.345581 | − | 0.598563i | ||||
\(584\) | 3.33830 | − | 5.78211i | 0.138140 | − | 0.239265i | ||||
\(585\) | −0.155006 | − | 1.55058i | −0.00640869 | − | 0.0641087i | ||||
\(586\) | 6.89061 | − | 3.97830i | 0.284649 | − | 0.164342i | ||||
\(587\) | −8.76612 | − | 15.1834i | −0.361817 | − | 0.626685i | 0.626443 | − | 0.779467i | \(-0.284510\pi\) |
−0.988260 | + | 0.152782i | \(0.951177\pi\) | |||||||
\(588\) | 1.24251 | + | 12.0605i | 0.0512403 | + | 0.497367i | ||||
\(589\) | −0.373215 | + | 0.646427i | −0.0153780 | + | 0.0266356i | ||||
\(590\) | − | 10.5822i | − | 0.435661i | ||||||
\(591\) | 9.15185 | + | 4.69245i | 0.376457 | + | 0.193021i | ||||
\(592\) | −5.07681 | −0.208655 | ||||||||
\(593\) | −13.1868 | − | 22.8403i | −0.541519 | − | 0.937938i | −0.998817 | − | 0.0486245i | \(-0.984516\pi\) |
0.457298 | − | 0.889313i | \(-0.348817\pi\) | |||||||
\(594\) | −5.84342 | + | 14.8824i | −0.239758 | + | 0.610630i | ||||
\(595\) | 3.67635 | + | 12.4002i | 0.150716 | + | 0.508357i | ||||
\(596\) | −10.4496 | + | 6.03310i | −0.428034 | + | 0.247126i | ||||
\(597\) | 24.2000 | − | 15.6284i | 0.990441 | − | 0.639626i | ||||
\(598\) | 4.02224 | − | 2.32224i | 0.164481 | − | 0.0949634i | ||||
\(599\) | 24.1184 | − | 13.9248i | 0.985452 | − | 0.568951i | 0.0815405 | − | 0.996670i | \(-0.474016\pi\) |
0.903912 | + | 0.427719i | \(0.140683\pi\) | |||||||
\(600\) | 1.54126 | + | 0.790256i | 0.0629219 | + | 0.0322621i | ||||
\(601\) | −23.8076 | + | 13.7453i | −0.971131 | + | 0.560683i | −0.899581 | − | 0.436754i | \(-0.856128\pi\) |
−0.0715503 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(602\) | −7.08390 | − | 6.71912i | −0.288718 | − | 0.273851i | ||||
\(603\) | −9.75671 | + | 21.6174i | −0.397324 | + | 0.880330i | ||||
\(604\) | −7.33025 | − | 12.6964i | −0.298263 | − | 0.516607i | ||||
\(605\) | −1.53223 | −0.0622938 | ||||||||
\(606\) | −6.10639 | + | 3.94350i | −0.248055 | + | 0.160194i | ||||
\(607\) | 39.3814i | 1.59844i | 0.601037 | + | 0.799221i | \(0.294754\pi\) | ||||
−0.601037 | + | 0.799221i | \(0.705246\pi\) | |||||||
\(608\) | 0.412013 | − | 0.713627i | 0.0167093 | − | 0.0289414i | ||||
\(609\) | −22.3041 | − | 19.1384i | −0.903807 | − | 0.775527i | ||||
\(610\) | −4.76240 | − | 8.24872i | −0.192824 | − | 0.333981i | ||||
\(611\) | −1.70241 | + | 0.982888i | −0.0688722 | + | 0.0397634i | ||||
\(612\) | 8.55966 | + | 11.9082i | 0.346004 | + | 0.481361i | ||||
\(613\) | −0.989576 | + | 1.71400i | −0.0399686 | + | 0.0692277i | −0.885318 | − | 0.464987i | \(-0.846059\pi\) |
0.845349 | + | 0.534214i | \(0.179392\pi\) | |||||||
\(614\) | −16.9087 | + | 29.2868i | −0.682381 | + | 1.18192i | ||||
\(615\) | −4.10805 | − | 6.36120i | −0.165653 | − | 0.256508i | ||||
\(616\) | 5.60240 | − | 5.90656i | 0.225727 | − | 0.237982i | ||||
\(617\) | −33.1061 | − | 19.1138i | −1.33280 | − | 0.769493i | −0.347072 | − | 0.937838i | \(-0.612824\pi\) |
−0.985728 | + | 0.168346i | \(0.946158\pi\) | |||||||
\(618\) | −0.658821 | − | 1.02016i | −0.0265017 | − | 0.0410370i | ||||
\(619\) | − | 26.6725i | − | 1.07206i | −0.844200 | − | 0.536028i | \(-0.819924\pi\) | ||
0.844200 | − | 0.536028i | \(-0.180076\pi\) | |||||||
\(620\) | 0.784474 | + | 0.452916i | 0.0315052 | + | 0.0181896i | ||||
\(621\) | −6.91785 | − | 45.9428i | −0.277604 | − | 1.84362i | ||||
\(622\) | 23.3794i | 0.937427i | ||||||||
\(623\) | −3.97219 | − | 0.952623i | −0.159143 | − | 0.0381661i | ||||
\(624\) | 0.0448019 | + | 0.898575i | 0.00179351 | + | 0.0359718i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.65830 | − | 14.9966i | −0.346055 | − | 0.599385i | ||||
\(627\) | 4.38618 | − | 0.218689i | 0.175167 | − | 0.00873361i | ||||
\(628\) | −0.502653 | − | 0.290207i | −0.0200580 | − | 0.0115805i | ||||
\(629\) | −24.8178 | −0.989549 | ||||||||
\(630\) | 6.27357 | + | 4.86233i | 0.249945 | + | 0.193720i | ||||
\(631\) | 8.55537 | 0.340584 | 0.170292 | − | 0.985394i | \(-0.445529\pi\) | ||||
0.170292 | + | 0.985394i | \(0.445529\pi\) | |||||||
\(632\) | 2.99730 | + | 1.73049i | 0.119226 | + | 0.0688353i | ||||
\(633\) | 20.1287 | + | 31.1686i | 0.800043 | + | 1.23884i | ||||
\(634\) | −7.96781 | − | 13.8006i | −0.316442 | − | 0.548094i | ||||
\(635\) | −1.53891 | −0.0610696 | ||||||||
\(636\) | −8.35924 | − | 4.28605i | −0.331466 | − | 0.169953i | ||||
\(637\) | −1.64917 | + | 3.24055i | −0.0653425 | + | 0.128395i | ||||
\(638\) | 19.7337i | 0.781265i | ||||||||
\(639\) | −26.0065 | + | 18.6936i | −1.02880 | + | 0.739505i | ||||
\(640\) | −0.866025 | − | 0.500000i | −0.0342327 | − | 0.0197642i | ||||
\(641\) | − | 24.1197i | − | 0.952672i | −0.879263 | − | 0.476336i | \(-0.841965\pi\) | ||
0.879263 | − | 0.476336i | \(-0.158035\pi\) | |||||||
\(642\) | −16.3302 | + | 31.8493i | −0.644500 | + | 1.25699i | ||||
\(643\) | 13.4384 | + | 7.75864i | 0.529957 | + | 0.305971i | 0.740999 | − | 0.671506i | \(-0.234352\pi\) |
−0.211042 | + | 0.977477i | \(0.567686\pi\) | |||||||
\(644\) | −5.51697 | + | 23.0043i | −0.217399 | + | 0.906498i | ||||
\(645\) | −6.38386 | + | 0.318291i | −0.251364 | + | 0.0125327i | ||||
\(646\) | 2.01411 | − | 3.48854i | 0.0792440 | − | 0.137255i | ||||
\(647\) | −3.88442 | + | 6.72802i | −0.152712 | + | 0.264506i | −0.932224 | − | 0.361883i | \(-0.882134\pi\) |
0.779511 | + | 0.626388i | \(0.215467\pi\) | |||||||
\(648\) | 8.53078 | + | 2.86805i | 0.335121 | + | 0.112668i | ||||
\(649\) | −28.1987 | + | 16.2805i | −1.10690 | + | 0.639067i | ||||
\(650\) | 0.259719 | + | 0.449846i | 0.0101870 | + | 0.0176444i | ||||
\(651\) | 3.15027 | + | 2.70314i | 0.123469 | + | 0.105945i | ||||
\(652\) | −0.0642633 | + | 0.111307i | −0.00251675 | + | 0.00435913i | ||||
\(653\) | 17.3302i | 0.678184i | 0.940753 | + | 0.339092i | \(0.110120\pi\) | ||||
−0.940753 | + | 0.339092i | \(0.889880\pi\) | |||||||
\(654\) | 0.155818 | + | 3.12520i | 0.00609298 | + | 0.122205i | ||||
\(655\) | −10.5223 | −0.411139 | ||||||||
\(656\) | 2.18596 | + | 3.78619i | 0.0853473 | + | 0.147826i | ||||
\(657\) | −1.99237 | − | 19.9305i | −0.0777297 | − | 0.777562i | ||||
\(658\) | 2.33506 | − | 9.73659i | 0.0910301 | − | 0.379572i | ||||
\(659\) | 3.46721 | − | 2.00179i | 0.135063 | − | 0.0779787i | −0.430946 | − | 0.902378i | \(-0.641820\pi\) |
0.566009 | + | 0.824399i | \(0.308487\pi\) | |||||||
\(660\) | −0.265391 | − | 5.32286i | −0.0103303 | − | 0.207192i | ||||
\(661\) | −33.8131 | + | 19.5220i | −1.31518 | + | 0.759317i | −0.982948 | − | 0.183882i | \(-0.941134\pi\) |
−0.332228 | + | 0.943199i | \(0.607800\pi\) | |||||||
\(662\) | 7.28013 | − | 4.20318i | 0.282950 | − | 0.163361i | ||||
\(663\) | 0.219012 | + | 4.39265i | 0.00850573 | + | 0.170596i | ||||
\(664\) | −5.75098 | + | 3.32033i | −0.223181 | + | 0.128854i | ||||
\(665\) | 0.508437 | − | 2.12005i | 0.0197163 | − | 0.0822121i | ||||
\(666\) | −12.3670 | + | 8.88945i | −0.479213 | + | 0.344459i | ||||
\(667\) | −28.6720 | − | 49.6614i | −1.11019 | − | 1.92290i | ||||
\(668\) | −25.3497 | −0.980811 | ||||||||
\(669\) | 2.29094 | + | 45.9486i | 0.0885728 | + | 1.77647i | ||||
\(670\) | − | 7.90574i | − | 0.305425i | ||||||
\(671\) | −14.6538 | + | 25.3811i | −0.565703 | + | 0.979827i | ||||
\(672\) | −3.47776 | − | 2.98415i | −0.134158 | − | 0.115116i | ||||
\(673\) | 5.02582 | + | 8.70498i | 0.193731 | + | 0.335552i | 0.946484 | − | 0.322751i | \(-0.104608\pi\) |
−0.752753 | + | 0.658303i | \(0.771274\pi\) | |||||||
\(674\) | −13.3059 | + | 7.68218i | −0.512525 | + | 0.295906i | ||||
\(675\) | 5.13823 | − | 0.773690i | 0.197771 | − | 0.0297794i | ||||
\(676\) | 6.36509 | − | 11.0247i | 0.244811 | − | 0.424026i | ||||
\(677\) | −11.3646 | + | 19.6840i | −0.436776 | + | 0.756519i | −0.997439 | − | 0.0715258i | \(-0.977213\pi\) |
0.560663 | + | 0.828044i | \(0.310547\pi\) | |||||||
\(678\) | −32.4625 | + | 1.61854i | −1.24672 | + | 0.0621597i | ||||
\(679\) | −1.38066 | + | 5.75700i | −0.0529849 | + | 0.220933i | ||||
\(680\) | −4.23353 | − | 2.44423i | −0.162349 | − | 0.0937320i | ||||
\(681\) | 21.1296 | − | 41.2098i | 0.809688 | − | 1.57916i | ||||
\(682\) | − | 2.78723i | − | 0.106728i | ||||||
\(683\) | −6.28399 | − | 3.62806i | −0.240450 | − | 0.138824i | 0.374933 | − | 0.927052i | \(-0.377666\pi\) |
−0.615384 | + | 0.788228i | \(0.710999\pi\) | |||||||
\(684\) | −0.245898 | − | 2.45982i | −0.00940215 | − | 0.0940534i | ||||
\(685\) | − | 0.00335499i | − | 0.000128188i | ||||||
\(686\) | −6.19485 | − | 17.4535i | −0.236520 | − | 0.666377i | ||||
\(687\) | −12.2280 | − | 6.26966i | −0.466526 | − | 0.239203i | ||||
\(688\) | 3.69030 | 0.140691 | ||||||||
\(689\) | −1.40862 | − | 2.43980i | −0.0536640 | − | 0.0929488i | ||||
\(690\) | 8.40172 | + | 13.0098i | 0.319848 | + | 0.495275i | ||||
\(691\) | −8.38246 | − | 4.83962i | −0.318884 | − | 0.184108i | 0.332011 | − | 0.943275i | \(-0.392273\pi\) |
−0.650895 | + | 0.759168i | \(0.725606\pi\) | |||||||
\(692\) | 4.73262 | 0.179907 | ||||||||
\(693\) | 3.30503 | − | 24.1981i | 0.125548 | − | 0.919209i | ||||
\(694\) | 11.0495 | 0.419433 | ||||||||
\(695\) | −16.6324 | − | 9.60272i | −0.630903 | − | 0.364252i | ||||
\(696\) | 11.0945 | − | 0.553156i | 0.420534 | − | 0.0209673i | ||||
\(697\) | 10.6860 | + | 18.5086i | 0.404760 | + | 0.701065i | ||||
\(698\) | −15.8937 | −0.601587 | ||||||||
\(699\) | 2.41885 | + | 48.5140i | 0.0914891 | + | 1.83497i | ||||
\(700\) | −2.57280 | − | 0.617016i | −0.0972426 | − | 0.0233210i | ||||
\(701\) | 5.56860i | 0.210323i | 0.994455 | + | 0.105162i | \(0.0335360\pi\) | ||||
−0.994455 | + | 0.105162i | \(0.966464\pi\) | |||||||
\(702\) | 1.68254 | + | 2.11047i | 0.0635032 | + | 0.0796545i | ||||
\(703\) | 3.62295 | + | 2.09171i | 0.136642 | + | 0.0788903i | ||||
\(704\) | 3.07697i | 0.115968i | ||||||||
\(705\) | −3.55603 | − | 5.50641i | −0.133928 | − | 0.207383i | ||||
\(706\) | 10.3818 | + | 5.99396i | 0.390726 | + | 0.225586i | ||||
\(707\) | 7.64132 | − | 8.05617i | 0.287381 | − | 0.302983i | ||||
\(708\) | 9.94350 | + | 15.3972i | 0.373700 | + | 0.578662i | ||||
\(709\) | −12.6267 | + | 21.8702i | −0.474207 | + | 0.821351i | −0.999564 | − | 0.0295310i | \(-0.990599\pi\) |
0.525357 | + | 0.850882i | \(0.323932\pi\) | |||||||
\(710\) | 5.33799 | − | 9.24567i | 0.200331 | − | 0.346984i | ||||
\(711\) | 10.3315 | − | 1.03280i | 0.387460 | − | 0.0387329i | ||||
\(712\) | 1.33707 | − | 0.771960i | 0.0501089 | − | 0.0289304i | ||||
\(713\) | 4.04969 | + | 7.01427i | 0.151662 | + | 0.262687i | ||||
\(714\) | −17.0009 | − | 14.5879i | −0.636243 | − | 0.545939i | ||||
\(715\) | 0.799148 | − | 1.38416i | 0.0298864 | − | 0.0517648i | ||||
\(716\) | − | 7.53011i | − | 0.281413i | ||||||
\(717\) | 41.2533 | − | 26.6413i | 1.54063 | − | 0.994938i | ||||
\(718\) | 13.5985 | 0.507492 | ||||||||
\(719\) | −3.56765 | − | 6.17935i | −0.133051 | − | 0.230451i | 0.791800 | − | 0.610780i | \(-0.209144\pi\) |
−0.924851 | + | 0.380329i | \(0.875811\pi\) | |||||||
\(720\) | −2.98512 | + | 0.298411i | −0.111249 | + | 0.0111211i | ||||
\(721\) | 1.34590 | + | 1.27660i | 0.0501241 | + | 0.0475429i | ||||
\(722\) | 15.8664 | − | 9.16049i | 0.590488 | − | 0.340918i | ||||
\(723\) | 1.47073 | + | 0.754092i | 0.0546971 | + | 0.0280450i | ||||
\(724\) | −10.7206 | + | 6.18956i | −0.398429 | + | 0.230033i | ||||
\(725\) | 5.55412 | − | 3.20667i | 0.206275 | − | 0.119093i | ||||
\(726\) | 2.22941 | − | 1.43975i | 0.0827412 | − | 0.0534342i | ||||
\(727\) | −7.48124 | + | 4.31930i | −0.277464 | + | 0.160194i | −0.632275 | − | 0.774744i | \(-0.717879\pi\) |
0.354811 | + | 0.934938i | \(0.384545\pi\) | |||||||
\(728\) | −0.390641 | − | 1.31761i | −0.0144781 | − | 0.0488340i | ||||
\(729\) | 25.8028 | − | 7.95080i | 0.955660 | − | 0.294474i | ||||
\(730\) | 3.33830 | + | 5.78211i | 0.123556 | + | 0.214005i | ||||
\(731\) | 18.0399 | 0.667229 | ||||||||
\(732\) | 14.6802 | + | 7.52703i | 0.542597 | + | 0.278207i | ||||
\(733\) | − | 36.2890i | − | 1.34037i | −0.742196 | − | 0.670183i | \(-0.766216\pi\) | ||
0.742196 | − | 0.670183i | \(-0.233784\pi\) | |||||||
\(734\) | −2.81639 | + | 4.87813i | −0.103955 | + | 0.180055i | ||||
\(735\) | −11.0660 | − | 4.95421i | −0.408175 | − | 0.182739i | ||||
\(736\) | −4.47068 | − | 7.74345i | −0.164792 | − | 0.285427i | ||||
\(737\) | −21.0667 | + | 12.1629i | −0.776003 | + | 0.448025i | ||||
\(738\) | 11.9546 | + | 5.39551i | 0.440053 | + | 0.198611i | ||||
\(739\) | 5.37054 | − | 9.30205i | 0.197558 | − | 0.342181i | −0.750178 | − | 0.661236i | \(-0.770032\pi\) |
0.947736 | + | 0.319055i | \(0.103365\pi\) | |||||||
\(740\) | 2.53840 | − | 4.39664i | 0.0933136 | − | 0.161624i | ||||
\(741\) | 0.338253 | − | 0.659707i | 0.0124260 | − | 0.0242349i | ||||
\(742\) | 13.9539 | + | 3.34647i | 0.512264 | + | 0.122853i | ||||
\(743\) | 9.06518 | + | 5.23379i | 0.332569 | + | 0.192009i | 0.656981 | − | 0.753907i | \(-0.271833\pi\) |
−0.324412 | + | 0.945916i | \(0.605166\pi\) | |||||||
\(744\) | −1.56700 | + | 0.0781288i | −0.0574491 | + | 0.00286434i | ||||
\(745\) | − | 12.0662i | − | 0.442072i | ||||||
\(746\) | −4.96231 | − | 2.86499i | −0.181683 | − | 0.104895i | ||||
\(747\) | −8.19544 | + | 18.1582i | −0.299855 | + | 0.664374i | ||||
\(748\) | 15.0417i | 0.549978i | ||||||||
\(749\) | 12.7503 | − | 53.1653i | 0.465885 | − | 1.94262i | ||||
\(750\) | −1.45501 | + | 0.939646i | −0.0531296 | + | 0.0343110i | ||||
\(751\) | 18.5461 | 0.676758 | 0.338379 | − | 0.941010i | \(-0.390121\pi\) | ||||
0.338379 | + | 0.941010i | \(0.390121\pi\) | |||||||
\(752\) | 1.89222 | + | 3.27742i | 0.0690021 | + | 0.119515i | ||||
\(753\) | −5.41016 | + | 10.5516i | −0.197157 | + | 0.384523i | ||||
\(754\) | 2.88502 | + | 1.66566i | 0.105066 | + | 0.0606599i | ||||
\(755\) | 14.6605 | 0.533550 | ||||||||
\(756\) | −13.6970 | − | 1.17982i | −0.498155 | − | 0.0429097i | ||||
\(757\) | −8.57410 | −0.311631 | −0.155816 | − | 0.987786i | \(-0.549801\pi\) | ||||
−0.155816 | + | 0.987786i | \(0.549801\pi\) | |||||||
\(758\) | 10.4267 | + | 6.01984i | 0.378714 | + | 0.218651i | ||||
\(759\) | 21.7418 | − | 42.4038i | 0.789177 | − | 1.53916i | ||||
\(760\) | 0.412013 | + | 0.713627i | 0.0149453 | + | 0.0258860i | ||||
\(761\) | −3.68978 | −0.133755 | −0.0668773 | − | 0.997761i | \(-0.521304\pi\) | ||||
−0.0668773 | + | 0.997761i | \(0.521304\pi\) | |||||||
\(762\) | 2.23913 | − | 1.44603i | 0.0811151 | − | 0.0523841i | ||||
\(763\) | −1.35863 | − | 4.58259i | −0.0491857 | − | 0.165901i | ||||
\(764\) | 19.2273i | 0.695620i | ||||||||
\(765\) | −14.5927 | + | 1.45877i | −0.527598 | + | 0.0527419i | ||||
\(766\) | −17.7587 | − | 10.2530i | −0.641648 | − | 0.370456i | ||||
\(767\) | 5.49677i | 0.198477i | ||||||||
\(768\) | 1.72990 | − | 0.0862508i | 0.0624225 | − | 0.00311231i | ||||
\(769\) | −1.09328 | − | 0.631204i | −0.0394246 | − | 0.0227618i | 0.480158 | − | 0.877182i | \(-0.340579\pi\) |
−0.519583 | + | 0.854420i | \(0.673913\pi\) | |||||||
\(770\) | 2.31403 | + | 7.80511i | 0.0833919 | + | 0.281276i | ||||
\(771\) | 20.8898 | − | 40.7420i | 0.752326 | − | 1.46729i | ||||
\(772\) | 11.8348 | − | 20.4985i | 0.425944 | − | 0.737757i | ||||
\(773\) | −1.80204 | + | 3.12123i | −0.0648150 | + | 0.112263i | −0.896612 | − | 0.442817i | \(-0.853979\pi\) |
0.831797 | + | 0.555080i | \(0.187312\pi\) | |||||||
\(774\) | 8.98952 | − | 6.46169i | 0.323122 | − | 0.232261i | ||||
\(775\) | −0.784474 | + | 0.452916i | −0.0281791 | + | 0.0162692i | ||||
\(776\) | −1.11882 | − | 1.93786i | −0.0401633 | − | 0.0695649i | ||||
\(777\) | 15.1500 | − | 17.6559i | 0.543502 | − | 0.633403i | ||||
\(778\) | 12.9198 | − | 22.3778i | 0.463197 | − | 0.802282i | ||||
\(779\) | − | 3.60257i | − | 0.129075i | ||||||
\(780\) | −0.800590 | − | 0.410488i | −0.0286657 | − | 0.0146978i | ||||
\(781\) | −32.8497 | −1.17546 | ||||||||
\(782\) | −21.8548 | − | 37.8536i | −0.781525 | − | 1.35364i | ||||
\(783\) | 26.0574 | − | 20.7738i | 0.931214 | − | 0.742395i | ||||
\(784\) | 6.23858 | + | 3.17492i | 0.222806 | + | 0.113390i | ||||
\(785\) | 0.502653 | − | 0.290207i | 0.0179405 | − | 0.0103579i | ||||
\(786\) | 15.3101 | − | 9.88722i | 0.546092 | − | 0.352665i | ||||
\(787\) | −12.5305 | + | 7.23448i | −0.446664 | + | 0.257882i | −0.706420 | − | 0.707793i | \(-0.749691\pi\) |
0.259756 | + | 0.965674i | \(0.416358\pi\) | |||||||
\(788\) | 5.14236 | − | 2.96894i | 0.183189 | − | 0.105764i | ||||
\(789\) | 39.6604 | + | 20.3351i | 1.41195 | + | 0.723950i | ||||
\(790\) | −2.99730 | + | 1.73049i | −0.106639 | + | 0.0615682i | ||||
\(791\) | 47.6010 | − | 14.1126i | 1.69249 | − | 0.501785i | ||||
\(792\) | 5.38776 | + | 7.49547i | 0.191446 | + | 0.266340i | ||||
\(793\) | 2.47377 | + | 4.28469i | 0.0878461 | + | 0.152154i | ||||
\(794\) | −6.44846 | −0.228847 | ||||||||
\(795\) | 7.89145 | − | 5.09629i | 0.279881 | − | 0.180747i | ||||
\(796\) | − | 16.6322i | − | 0.589511i | ||||||
\(797\) | −13.9972 | + | 24.2439i | −0.495808 | + | 0.858764i | −0.999988 | − | 0.00483393i | \(-0.998461\pi\) |
0.504180 | + | 0.863598i | \(0.331795\pi\) | |||||||
\(798\) | 1.25232 | + | 3.56245i | 0.0443315 | + | 0.126110i | ||||
\(799\) | 9.25003 | + | 16.0215i | 0.327243 | + | 0.566801i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | 1.90540 | − | 4.22169i | 0.0673239 | − | 0.149166i | ||||
\(802\) | −6.07170 | + | 10.5165i | −0.214399 | + | 0.371350i | ||||
\(803\) | 10.2719 | − | 17.7914i | 0.362486 | − | 0.627845i | ||||
\(804\) | 7.42860 | + | 11.5030i | 0.261986 | + | 0.405678i | ||||
\(805\) | −17.1638 | − | 16.2800i | −0.604946 | − | 0.573795i | ||||
\(806\) | −0.407485 | − | 0.235262i | −0.0143531 | − | 0.00828674i | ||||
\(807\) | −8.35922 | − | 12.9440i | −0.294258 | − | 0.455650i | ||||
\(808\) | 4.19679i | 0.147643i | ||||||||
\(809\) | 37.0756 | + | 21.4056i | 1.30351 | + | 0.752582i | 0.981004 | − | 0.193986i | \(-0.0621416\pi\) |
0.322505 | + | 0.946568i | \(0.395475\pi\) | |||||||
\(810\) | −6.74920 | + | 5.95385i | −0.237143 | + | 0.209197i | ||||
\(811\) | − | 7.75794i | − | 0.272418i | −0.990680 | − | 0.136209i | \(-0.956508\pi\) | ||
0.990680 | − | 0.136209i | \(-0.0434919\pi\) | |||||||
\(812\) | −16.2682 | + | 4.82314i | −0.570902 | + | 0.169259i | ||||
\(813\) | 1.91392 | + | 38.3868i | 0.0671240 | + | 1.34628i | ||||
\(814\) | −15.6212 | −0.547523 | ||||||||
\(815\) | −0.0642633 | − | 0.111307i | −0.00225105 | − | 0.00389893i | ||||
\(816\) | 8.45656 | − | 0.421633i | 0.296039 | − | 0.0147601i | ||||
\(817\) | −2.63350 | − | 1.52045i | −0.0921344 | − | 0.0531938i | ||||
\(818\) | −22.1792 | −0.775477 | ||||||||
\(819\) | −3.25873 | − | 2.52568i | −0.113869 | − | 0.0882543i | ||||
\(820\) | −4.37192 | −0.152674 | ||||||||
\(821\) | −21.1360 | − | 12.2029i | −0.737650 | − | 0.425883i | 0.0835640 | − | 0.996502i | \(-0.473370\pi\) |
−0.821214 | + | 0.570620i | \(0.806703\pi\) | |||||||
\(822\) | 0.00315251 | + | 0.00488156i | 0.000109956 | + | 0.000170264i | ||||
\(823\) | −11.5997 | − | 20.0913i | −0.404342 | − | 0.700340i | 0.589903 | − | 0.807474i | \(-0.299166\pi\) |
−0.994245 | + | 0.107134i | \(0.965833\pi\) | |||||||
\(824\) | −0.701137 | −0.0244253 | ||||||||
\(825\) | 4.74243 | + | 2.43160i | 0.165110 | + | 0.0846573i | ||||
\(826\) | −20.3135 | − | 19.2675i | −0.706799 | − | 0.670402i | ||||
\(827\) | − | 29.3259i | − | 1.01976i | −0.860245 | − | 0.509881i | \(-0.829689\pi\) | ||
0.860245 | − | 0.509881i | \(-0.170311\pi\) | |||||||
\(828\) | −24.4492 | − | 11.0348i | −0.849670 | − | 0.383486i | ||||
\(829\) | 26.1269 | + | 15.0844i | 0.907424 | + | 0.523901i | 0.879601 | − | 0.475712i | \(-0.157809\pi\) |
0.0278223 | + | 0.999613i | \(0.491143\pi\) | |||||||
\(830\) | − | 6.64066i | − | 0.230501i | ||||||
\(831\) | −9.96399 | + | 19.4331i | −0.345647 | + | 0.674128i | ||||
\(832\) | 0.449846 | + | 0.259719i | 0.0155956 | + | 0.00900412i | ||||
\(833\) | 30.4971 | + | 15.5205i | 1.05666 | + | 0.537752i | ||||
\(834\) | 33.2235 | − | 1.65648i | 1.15044 | − | 0.0573594i | ||||
\(835\) | 12.6749 | − | 21.9535i | 0.438632 | − | 0.759733i | ||||
\(836\) | 1.26775 | − | 2.19581i | 0.0438461 | − | 0.0759438i | ||||
\(837\) | −3.68039 | + | 2.93413i | −0.127213 | + | 0.101418i | ||||
\(838\) | 12.6673 | − | 7.31349i | 0.437586 | − | 0.252640i | ||||
\(839\) | −18.2437 | − | 31.5990i | −0.629843 | − | 1.09092i | −0.987583 | − | 0.157098i | \(-0.949786\pi\) |
0.357740 | − | 0.933821i | \(-0.383547\pi\) | |||||||
\(840\) | 4.32323 | − | 1.51975i | 0.149166 | − | 0.0524365i | ||||
\(841\) | 6.06549 | − | 10.5057i | 0.209155 | − | 0.362267i | ||||
\(842\) | − | 35.3619i | − | 1.21865i | ||||||
\(843\) | −0.678633 | − | 13.6111i | −0.0233734 | − | 0.468792i | ||||
\(844\) | 21.4215 | 0.737360 | ||||||||
\(845\) | 6.36509 | + | 11.0247i | 0.218966 | + | 0.379260i | ||||
\(846\) | 10.3481 | + | 4.67048i | 0.355777 | + | 0.160575i | ||||
\(847\) | −2.78980 | + | 2.94126i | −0.0958587 | + | 0.101063i | ||||
\(848\) | −4.69700 | + | 2.71181i | −0.161296 | + | 0.0931241i | ||||
\(849\) | −2.54845 | − | 51.1134i | −0.0874626 | − | 1.75421i | ||||
\(850\) | 4.23353 | − | 2.44423i | 0.145209 | − | 0.0838364i | ||||
\(851\) | 39.3120 | − | 22.6968i | 1.34760 | − | 0.778036i | ||||
\(852\) | 0.920811 | + | 18.4684i | 0.0315465 | + | 0.632717i | ||||
\(853\) | −2.99449 | + | 1.72887i | −0.102530 | + | 0.0591954i | −0.550388 | − | 0.834909i | \(-0.685520\pi\) |
0.447858 | + | 0.894104i | \(0.352187\pi\) | |||||||
\(854\) | −24.5054 | − | 5.87696i | −0.838558 | − | 0.201105i | ||||
\(855\) | 2.25321 | + | 1.01695i | 0.0770582 | + | 0.0347791i | ||||
\(856\) | 10.3322 | + | 17.8959i | 0.353147 | + | 0.611669i | ||||
\(857\) | −26.1122 | −0.891977 | −0.445989 | − | 0.895039i | \(-0.647148\pi\) | ||||
−0.445989 | + | 0.895039i | \(0.647148\pi\) | |||||||
\(858\) | 0.137854 | + | 2.76489i | 0.00470626 | + | 0.0943919i | ||||
\(859\) | 26.6217i | 0.908319i | 0.890920 | + | 0.454160i | \(0.150060\pi\) | ||||
−0.890920 | + | 0.454160i | \(0.849940\pi\) | |||||||
\(860\) | −1.84515 | + | 3.19589i | −0.0629191 | + | 0.108979i | ||||
\(861\) | −19.6907 | − | 3.69633i | −0.671057 | − | 0.125971i | ||||
\(862\) | −8.22125 | − | 14.2396i | −0.280017 | − | 0.485003i | ||||
\(863\) | 20.3839 | − | 11.7687i | 0.693877 | − | 0.400610i | −0.111186 | − | 0.993800i | \(-0.535465\pi\) |
0.805063 | + | 0.593189i | \(0.202131\pi\) | |||||||
\(864\) | 4.06299 | − | 3.23915i | 0.138226 | − | 0.110198i | ||||
\(865\) | −2.36631 | + | 4.09857i | −0.0804570 | + | 0.139356i | ||||
\(866\) | −11.0177 | + | 19.0833i | −0.374398 | + | 0.648476i | ||||
\(867\) | 11.9312 | − | 0.594876i | 0.405206 | − | 0.0202030i | ||||
\(868\) | 2.29775 | − | 0.681229i | 0.0779908 | − | 0.0231224i | ||||
\(869\) | 9.22263 | + | 5.32469i | 0.312856 | + | 0.180628i | ||||
\(870\) | −5.06818 | + | 9.88466i | −0.171827 | + | 0.335121i | ||||
\(871\) | 4.10653i | 0.139145i | ||||||||
\(872\) | 1.56454 | + | 0.903287i | 0.0529820 | + | 0.0305892i | ||||
\(873\) | −6.11860 | − | 2.76154i | −0.207083 | − | 0.0934640i | ||||
\(874\) | 7.36791i | 0.249223i | ||||||||
\(875\) | 1.82075 | − | 1.91960i | 0.0615526 | − | 0.0648943i | ||||
\(876\) | −10.2904 | − | 5.27622i | −0.347681 | − | 0.178267i | ||||
\(877\) | 7.21212 | 0.243536 | 0.121768 | − | 0.992559i | \(-0.461144\pi\) | ||||
0.121768 | + | 0.992559i | \(0.461144\pi\) | |||||||
\(878\) | −12.4087 | − | 21.4924i | −0.418772 | − | 0.725335i | ||||
\(879\) | −7.47639 | − | 11.5770i | −0.252172 | − | 0.390481i | ||||
\(880\) | −2.66474 | − | 1.53849i | −0.0898283 | − | 0.0518624i | ||||
\(881\) | −57.4455 | −1.93539 | −0.967694 | − | 0.252129i | \(-0.918869\pi\) | ||||
−0.967694 | + | 0.252129i | \(0.918869\pi\) | |||||||
\(882\) | 20.7564 | − | 3.18965i | 0.698903 | − | 0.107401i | ||||
\(883\) | 15.0734 | 0.507262 | 0.253631 | − | 0.967301i | \(-0.418375\pi\) | ||||
0.253631 | + | 0.967301i | \(0.418375\pi\) | |||||||
\(884\) | 2.19905 | + | 1.26962i | 0.0739622 | + | 0.0427021i | ||||
\(885\) | −18.3061 | + | 0.912720i | −0.615354 | + | 0.0306808i | ||||
\(886\) | 8.31193 | + | 14.3967i | 0.279245 | + | 0.483666i | ||||
\(887\) | 35.1323 | 1.17963 | 0.589814 | − | 0.807539i | \(-0.299201\pi\) | ||||
0.589814 | + | 0.807539i | \(0.299201\pi\) | |||||||
\(888\) | 0.437878 | + | 8.78238i | 0.0146942 | + | 0.294717i | ||||
\(889\) | −2.80197 | + | 2.95409i | −0.0939749 | + | 0.0990768i | ||||
\(890\) | 1.54392i | 0.0517523i | ||||||||
\(891\) | 26.2490 | + | 8.82493i | 0.879375 | + | 0.295646i | ||||
\(892\) | 23.0028 | + | 13.2807i | 0.770191 | + | 0.444670i | ||||
\(893\) | − | 3.11847i | − | 0.104356i | ||||||
\(894\) | 11.3380 | + | 17.5565i | 0.379198 | + | 0.587177i | ||||
\(895\) | 6.52127 | + | 3.76505i | 0.217982 | + | 0.125852i | ||||
\(896\) | −2.53662 | + | 0.752047i | −0.0847424 | + | 0.0251241i | ||||
\(897\) | −4.36417 | − | 6.75778i | −0.145715 | − | 0.225636i | ||||
\(898\) | 6.25770 | − | 10.8387i | 0.208822 | − | 0.361691i | ||||
\(899\) | −2.90471 | + | 5.03110i | −0.0968775 | + | 0.167797i | ||||
\(900\) | 1.23413 | − | 2.73440i | 0.0411377 | − | 0.0911466i | ||||
\(901\) | −22.9611 | + | 13.2566i | −0.764945 | + | 0.441641i | ||||
\(902\) | 6.72614 | + | 11.6500i | 0.223956 | + | 0.387903i | ||||
\(903\) | −11.0124 | + | 12.8340i | −0.366470 | + | 0.427088i | ||||
\(904\) | −9.38276 | + | 16.2514i | −0.312066 | + | 0.540514i | ||||
\(905\) | − | 12.3791i | − | 0.411496i | ||||||
\(906\) | −21.3312 | + | 13.7757i | −0.708682 | + | 0.457666i | ||||
\(907\) | 9.56489 | 0.317597 | 0.158799 | − | 0.987311i | \(-0.449238\pi\) | ||||
0.158799 | + | 0.987311i | \(0.449238\pi\) | |||||||
\(908\) | −13.3688 | − | 23.1555i | −0.443661 | − | 0.768443i | ||||
\(909\) | 7.34855 | + | 10.2233i | 0.243736 | + | 0.339086i | ||||
\(910\) | 1.33641 | + | 0.320501i | 0.0443015 | + | 0.0106245i | ||||
\(911\) | −10.5695 | + | 6.10232i | −0.350184 | + | 0.202179i | −0.664766 | − | 0.747051i | \(-0.731469\pi\) |
0.314582 | + | 0.949230i | \(0.398136\pi\) | |||||||
\(912\) | −1.27004 | − | 0.651191i | −0.0420553 | − | 0.0215631i | ||||
\(913\) | −17.6956 | + | 10.2166i | −0.585640 | + | 0.338119i | ||||
\(914\) | −28.3193 | + | 16.3501i | −0.936718 | + | 0.540814i | ||||
\(915\) | −13.8587 | + | 8.94995i | −0.458155 | + | 0.295876i | ||||
\(916\) | −6.87080 | + | 3.96686i | −0.227018 | + | 0.131069i | ||||
\(917\) | −19.1584 | + | 20.1986i | −0.632668 | + | 0.667015i | ||||
\(918\) | 19.8618 | − | 15.8345i | 0.655536 | − | 0.522615i | ||||
\(919\) | −5.75745 | − | 9.97219i | −0.189921 | − | 0.328952i | 0.755303 | − | 0.655376i | \(-0.227490\pi\) |
−0.945224 | + | 0.326424i | \(0.894156\pi\) | |||||||
\(920\) | 8.94137 | 0.294788 | ||||||||
\(921\) | 52.1216 | + | 26.7244i | 1.71747 | + | 0.880600i | ||||
\(922\) | − | 5.38010i | − | 0.177184i | ||||||
\(923\) | −2.77275 | + | 4.80254i | −0.0912662 | + | 0.158078i | ||||
\(924\) | −10.7010 | − | 9.18217i | −0.352037 | − | 0.302071i | ||||
\(925\) | 2.53840 | + | 4.39664i | 0.0834622 | + | 0.144561i | ||||
\(926\) | −9.38485 | + | 5.41835i | −0.308405 | + | 0.178058i | ||||
\(927\) | −1.70796 | + | 1.22769i | −0.0560968 | + | 0.0403225i | ||||
\(928\) | 3.20667 | − | 5.55412i | 0.105264 | − | 0.182323i | ||||
\(929\) | −7.79341 | + | 13.4986i | −0.255694 | + | 0.442874i | −0.965084 | − | 0.261942i | \(-0.915637\pi\) |
0.709390 | + | 0.704816i | \(0.248970\pi\) | |||||||
\(930\) | 0.715840 | − | 1.39613i | 0.0234733 | − | 0.0457808i | ||||
\(931\) | −3.14391 | − | 4.83608i | −0.103038 | − | 0.158496i | ||||
\(932\) | 24.2871 | + | 14.0222i | 0.795551 | + | 0.459311i | ||||
\(933\) | 40.4440 | − | 2.01649i | 1.32408 | − | 0.0660169i | ||||
\(934\) | 5.53426i | 0.181087i | ||||||||
\(935\) | −13.0265 | − | 7.52084i | −0.426011 | − | 0.245958i | ||||
\(936\) | 1.55058 | − | 0.155006i | 0.0506824 | − | 0.00506652i | ||||
\(937\) | − | 52.6446i | − | 1.71982i | −0.510442 | − | 0.859912i | \(-0.670518\pi\) | ||
0.510442 | − | 0.859912i | \(-0.329482\pi\) | |||||||
\(938\) | −15.1759 | − | 14.3944i | −0.495509 | − | 0.469993i | ||||
\(939\) | −25.1959 | + | 16.2715i | −0.822237 | + | 0.531000i | ||||
\(940\) | −3.78444 | −0.123435 | ||||||||
\(941\) | 1.60723 | + | 2.78380i | 0.0523942 | + | 0.0907494i | 0.891033 | − | 0.453939i | \(-0.149981\pi\) |
−0.838639 | + | 0.544688i | \(0.816648\pi\) | |||||||
\(942\) | −0.458675 | + | 0.894571i | −0.0149444 | + | 0.0291467i | ||||
\(943\) | −33.8537 | − | 19.5454i | −1.10243 | − | 0.636487i | ||||
\(944\) | 10.5822 | 0.344420 | ||||||||
\(945\) | 7.87026 | − | 11.2720i | 0.256020 | − | 0.366680i | ||||
\(946\) | 11.3550 | 0.369182 | ||||||||
\(947\) | 3.02017 | + | 1.74370i | 0.0981423 | + | 0.0566625i | 0.548268 | − | 0.836303i | \(-0.315287\pi\) |
−0.450126 | + | 0.892965i | \(0.648621\pi\) | |||||||
\(948\) | 2.73506 | − | 5.33430i | 0.0888308 | − | 0.173250i | ||||
\(949\) | −1.73404 | − | 3.00344i | −0.0562892 | − | 0.0974958i | ||||
\(950\) | −0.824025 | −0.0267349 | ||||||||
\(951\) | −23.1865 | + | 14.9738i | −0.751875 | + | 0.485560i | ||||
\(952\) | −12.4002 | + | 3.67635i | −0.401891 | + | 0.119151i | ||||
\(953\) | 45.7759i | 1.48283i | 0.671049 | + | 0.741413i | \(0.265844\pi\) | ||||
−0.671049 | + | 0.741413i | \(0.734156\pi\) | |||||||
\(954\) | −6.69346 | + | 14.8303i | −0.216709 | + | 0.480150i | ||||
\(955\) | −16.6514 | − | 9.61366i | −0.538825 | − | 0.311091i | ||||
\(956\) | − | 28.3525i | − | 0.916985i | ||||||
\(957\) | 34.1374 | − | 1.70205i | 1.10350 | − | 0.0550193i | ||||
\(958\) | −34.4899 | − | 19.9128i | −1.11432 | − | 0.643353i | ||||
\(959\) | −0.00644025 | − | 0.00610861i | −0.000207966 | − | 0.000197257i | ||||
\(960\) | −0.790256 | + | 1.54126i | −0.0255054 | + | 0.0497441i | ||||
\(961\) | −15.0897 | + | 26.1362i | −0.486766 | + | 0.843103i | ||||
\(962\) | −1.31854 | + | 2.28378i | −0.0425115 | + | 0.0736320i | ||||
\(963\) | 56.5047 | + | 25.5025i | 1.82084 | + | 0.821808i | ||||
\(964\) | 0.826394 | − | 0.477119i | 0.0266164 | − | 0.0153670i | ||||
\(965\) | 11.8348 | + | 20.4985i | 0.380976 | + | 0.659870i | ||||
\(966\) | 40.2711 | + | 7.55967i | 1.29570 | + | 0.243229i | ||||
\(967\) | −25.9697 | + | 44.9808i | −0.835129 | + | 1.44649i | 0.0587965 | + | 0.998270i | \(0.481274\pi\) |
−0.893925 | + | 0.448216i | \(0.852060\pi\) | |||||||
\(968\) | − | 1.53223i | − | 0.0492476i | ||||||
\(969\) | −6.20855 | − | 3.18332i | −0.199447 | − | 0.102263i | ||||
\(970\) | 2.23764 | 0.0718464 | ||||||||
\(971\) | −13.0616 | − | 22.6234i | −0.419167 | − | 0.726019i | 0.576688 | − | 0.816964i | \(-0.304345\pi\) |
−0.995856 | + | 0.0909448i | \(0.971011\pi\) | |||||||
\(972\) | 4.22566 | − | 15.0048i | 0.135538 | − | 0.481279i | ||||
\(973\) | −48.7169 | + | 14.4434i | −1.56179 | + | 0.463034i | ||||
\(974\) | −34.2835 | + | 19.7936i | −1.09852 | + | 0.634228i | ||||
\(975\) | 0.755788 | − | 0.488087i | 0.0242046 | − | 0.0156313i | ||||
\(976\) | 8.24872 | − | 4.76240i | 0.264035 | − | 0.152441i | ||||
\(977\) | 35.7603 | − | 20.6462i | 1.14407 | − | 0.660532i | 0.196638 | − | 0.980476i | \(-0.436998\pi\) |
0.947436 | + | 0.319944i | \(0.103664\pi\) | |||||||
\(978\) | 0.198094 | + | 0.101569i | 0.00633433 | + | 0.00324782i | ||||
\(979\) | 4.11414 | − | 2.37530i | 0.131489 | − | 0.0759149i | ||||
\(980\) | −5.86885 | + | 3.81531i | −0.187474 | + | 0.121876i | ||||
\(981\) | 5.39285 | − | 0.539101i | 0.172180 | − | 0.0172122i | ||||
\(982\) | −15.6937 | − | 27.1823i | −0.500806 | − | 0.867422i | ||||
\(983\) | 15.2552 | 0.486567 | 0.243283 | − | 0.969955i | \(-0.421776\pi\) | ||||
0.243283 | + | 0.969955i | \(0.421776\pi\) | |||||||
\(984\) | 6.36120 | − | 4.10805i | 0.202788 | − | 0.130960i | ||||
\(985\) | 5.93788i | 0.189197i | ||||||||
\(986\) | 15.6757 | − | 27.1511i | 0.499216 | − | 0.864667i | ||||
\(987\) | −17.0447 | − | 3.19963i | −0.542540 | − | 0.101845i | ||||
\(988\) | −0.214015 | − | 0.370684i | −0.00680872 | − | 0.0117930i | ||||
\(989\) | −28.5757 | + | 16.4982i | −0.908653 | + | 0.524611i | ||||
\(990\) | −9.18514 | + | 0.918202i | −0.291923 | + | 0.0291824i | ||||
\(991\) | 1.36395 | − | 2.36244i | 0.0433274 | − | 0.0750453i | −0.843548 | − | 0.537053i | \(-0.819537\pi\) |
0.886876 | + | 0.462008i | \(0.152871\pi\) | |||||||
\(992\) | −0.452916 | + | 0.784474i | −0.0143801 | + | 0.0249071i | ||||
\(993\) | −7.89901 | − | 12.2314i | −0.250668 | − | 0.388151i | ||||
\(994\) | −8.02884 | − | 27.0809i | −0.254659 | − | 0.858953i | ||||
\(995\) | 14.4039 | + | 8.31608i | 0.456634 | + | 0.263638i | ||||
\(996\) | 6.23987 | + | 9.66225i | 0.197718 | + | 0.306160i | ||||
\(997\) | − | 0.196236i | − | 0.00621485i | −0.999995 | − | 0.00310743i | \(-0.999011\pi\) | ||
0.999995 | − | 0.00310743i | \(-0.000989126\pi\) | |||||||
\(998\) | 25.6992 | + | 14.8374i | 0.813493 | + | 0.469670i | ||||
\(999\) | 16.4445 | + | 20.6270i | 0.520282 | + | 0.652610i |
(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 | 630.2.t.b.311.3 | ✓ | 28 | |
3.2 | odd | 2 | 1890.2.t.b.1151.12 | 28 | |||
7.5 | odd | 6 | 630.2.bk.b.131.12 | yes | 28 | ||
9.2 | odd | 6 | 630.2.bk.b.101.5 | yes | 28 | ||
9.7 | even | 3 | 1890.2.bk.b.521.11 | 28 | |||
21.5 | even | 6 | 1890.2.bk.b.341.11 | 28 | |||
63.47 | even | 6 | inner | 630.2.t.b.551.3 | yes | 28 | |
63.61 | odd | 6 | 1890.2.t.b.1601.12 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.3 | ✓ | 28 | 1.1 | even | 1 | trivial | |
630.2.t.b.551.3 | yes | 28 | 63.47 | even | 6 | inner | |
630.2.bk.b.101.5 | yes | 28 | 9.2 | odd | 6 | ||
630.2.bk.b.131.12 | yes | 28 | 7.5 | odd | 6 | ||
1890.2.t.b.1151.12 | 28 | 3.2 | odd | 2 | |||
1890.2.t.b.1601.12 | 28 | 63.61 | odd | 6 | |||
1890.2.bk.b.341.11 | 28 | 21.5 | even | 6 | |||
1890.2.bk.b.521.11 | 28 | 9.7 | even | 3 |