Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (of order \(4\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 643.2 | ||
Character | \(\chi\) | \(=\) | 690.643 |
Dual form | 690.2.j.a.367.2 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.899538 | + | 2.04715i | −0.402286 | + | 0.915514i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.80902 | − | 1.80902i | −0.683744 | − | 0.683744i | 0.277098 | − | 0.960842i | \(-0.410627\pi\) |
−0.960842 | + | 0.277098i | \(0.910627\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −0.811485 | − | 2.08362i | −0.256614 | − | 0.658900i | ||||
\(11\) | − | 4.16725i | − | 1.25647i | −0.778022 | − | 0.628236i | \(-0.783777\pi\) | ||
0.778022 | − | 0.628236i | \(-0.216223\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | −3.18894 | − | 3.18894i | −0.884454 | − | 0.884454i | 0.109530 | − | 0.993984i | \(-0.465066\pi\) |
−0.993984 | + | 0.109530i | \(0.965066\pi\) | |||||||
\(14\) | 2.55834 | 0.683744 | ||||||||
\(15\) | −2.08362 | + | 0.811485i | −0.537990 | + | 0.209525i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.68449 | − | 1.68449i | −0.408549 | − | 0.408549i | 0.472683 | − | 0.881232i | \(-0.343285\pi\) |
−0.881232 | + | 0.472683i | \(0.843285\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | −5.24101 | −1.20237 | −0.601185 | − | 0.799110i | \(-0.705304\pi\) | ||||
−0.601185 | + | 0.799110i | \(0.705304\pi\) | |||||||
\(20\) | 2.04715 | + | 0.899538i | 0.457757 | + | 0.201143i | ||||
\(21\) | − | 2.55834i | − | 0.558275i | ||||||
\(22\) | 2.94669 | + | 2.94669i | 0.628236 | + | 0.628236i | ||||
\(23\) | 4.36621 | + | 1.98398i | 0.910418 | + | 0.413689i | ||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −3.38166 | − | 3.68298i | −0.676332 | − | 0.736597i | ||||
\(26\) | 4.50985 | 0.884454 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −1.80902 | + | 1.80902i | −0.341872 | + | 0.341872i | ||||
\(29\) | − | 3.48107i | − | 0.646418i | −0.946328 | − | 0.323209i | \(-0.895238\pi\) | ||
0.946328 | − | 0.323209i | \(-0.104762\pi\) | |||||||
\(30\) | 0.899538 | − | 2.04715i | 0.164232 | − | 0.373757i | ||||
\(31\) | 7.27142 | 1.30599 | 0.652993 | − | 0.757364i | \(-0.273513\pi\) | ||||
0.652993 | + | 0.757364i | \(0.273513\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 2.94669 | − | 2.94669i | 0.512953 | − | 0.512953i | ||||
\(34\) | 2.38223 | 0.408549 | ||||||||
\(35\) | 5.33061 | − | 2.07605i | 0.901038 | − | 0.350917i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.46339 | − | 5.46339i | −0.898175 | − | 0.898175i | 0.0970994 | − | 0.995275i | \(-0.469044\pi\) |
−0.995275 | + | 0.0970994i | \(0.969044\pi\) | |||||||
\(38\) | 3.70595 | − | 3.70595i | 0.601185 | − | 0.601185i | ||||
\(39\) | − | 4.50985i | − | 0.722154i | ||||||
\(40\) | −2.08362 | + | 0.811485i | −0.329450 | + | 0.128307i | ||||
\(41\) | 4.53754 | 0.708645 | 0.354322 | − | 0.935123i | \(-0.384712\pi\) | ||||
0.354322 | + | 0.935123i | \(0.384712\pi\) | |||||||
\(42\) | 1.80902 | + | 1.80902i | 0.279137 | + | 0.279137i | ||||
\(43\) | −6.37868 | + | 6.37868i | −0.972739 | + | 0.972739i | −0.999638 | − | 0.0268989i | \(-0.991437\pi\) |
0.0268989 | + | 0.999638i | \(0.491437\pi\) | |||||||
\(44\) | −4.16725 | −0.628236 | ||||||||
\(45\) | −2.04715 | − | 0.899538i | −0.305171 | − | 0.134095i | ||||
\(46\) | −4.49027 | + | 1.68449i | −0.662054 | + | 0.248365i | ||||
\(47\) | −9.09342 | + | 9.09342i | −1.32641 | + | 1.32641i | −0.417935 | + | 0.908477i | \(0.637246\pi\) |
−0.908477 | + | 0.417935i | \(0.862754\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 0.454913i | − | 0.0649875i | ||||||
\(50\) | 4.99546 | + | 0.213067i | 0.706464 | + | 0.0301322i | ||||
\(51\) | − | 2.38223i | − | 0.333579i | ||||||
\(52\) | −3.18894 | + | 3.18894i | −0.442227 | + | 0.442227i | ||||
\(53\) | 6.56472 | − | 6.56472i | 0.901734 | − | 0.901734i | −0.0938519 | − | 0.995586i | \(-0.529918\pi\) |
0.995586 | + | 0.0938519i | \(0.0299180\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 8.53099 | + | 3.74860i | 1.15032 | + | 0.505461i | ||||
\(56\) | − | 2.55834i | − | 0.341872i | ||||||
\(57\) | −3.70595 | − | 3.70595i | −0.490865 | − | 0.490865i | ||||
\(58\) | 2.46149 | + | 2.46149i | 0.323209 | + | 0.323209i | ||||
\(59\) | − | 6.80402i | − | 0.885808i | −0.896569 | − | 0.442904i | \(-0.853948\pi\) | ||
0.896569 | − | 0.442904i | \(-0.146052\pi\) | |||||||
\(60\) | 0.811485 | + | 2.08362i | 0.104762 | + | 0.268995i | ||||
\(61\) | 0.759260i | 0.0972133i | 0.998818 | + | 0.0486066i | \(0.0154781\pi\) | ||||
−0.998818 | + | 0.0486066i | \(0.984522\pi\) | |||||||
\(62\) | −5.14167 | + | 5.14167i | −0.652993 | + | 0.652993i | ||||
\(63\) | 1.80902 | − | 1.80902i | 0.227915 | − | 0.227915i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 9.39683 | − | 3.65967i | 1.16553 | − | 0.453927i | ||||
\(66\) | 4.16725i | 0.512953i | ||||||||
\(67\) | −2.02126 | − | 2.02126i | −0.246937 | − | 0.246937i | 0.572776 | − | 0.819712i | \(-0.305867\pi\) |
−0.819712 | + | 0.572776i | \(0.805867\pi\) | |||||||
\(68\) | −1.68449 | + | 1.68449i | −0.204275 | + | 0.204275i | ||||
\(69\) | 1.68449 | + | 4.49027i | 0.202789 | + | 0.540565i | ||||
\(70\) | −2.30132 | + | 5.23730i | −0.275061 | + | 0.625978i | ||||
\(71\) | −9.56406 | −1.13504 | −0.567522 | − | 0.823358i | \(-0.692098\pi\) | ||||
−0.567522 | + | 0.823358i | \(0.692098\pi\) | |||||||
\(72\) | −0.707107 | + | 0.707107i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | −5.78239 | − | 5.78239i | −0.676778 | − | 0.676778i | 0.282492 | − | 0.959270i | \(-0.408839\pi\) |
−0.959270 | + | 0.282492i | \(0.908839\pi\) | |||||||
\(74\) | 7.72640 | 0.898175 | ||||||||
\(75\) | 0.213067 | − | 4.99546i | 0.0246029 | − | 0.576826i | ||||
\(76\) | 5.24101i | 0.601185i | ||||||||
\(77\) | −7.53863 | + | 7.53863i | −0.859106 | + | 0.859106i | ||||
\(78\) | 3.18894 | + | 3.18894i | 0.361077 | + | 0.361077i | ||||
\(79\) | 6.84964 | 0.770645 | 0.385322 | − | 0.922782i | \(-0.374090\pi\) | ||||
0.385322 | + | 0.922782i | \(0.374090\pi\) | |||||||
\(80\) | 0.899538 | − | 2.04715i | 0.100571 | − | 0.228879i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −3.20853 | + | 3.20853i | −0.354322 | + | 0.354322i | ||||
\(83\) | 2.40890 | − | 2.40890i | 0.264411 | − | 0.264411i | −0.562432 | − | 0.826843i | \(-0.690134\pi\) |
0.826843 | + | 0.562432i | \(0.190134\pi\) | |||||||
\(84\) | −2.55834 | −0.279137 | ||||||||
\(85\) | 4.96367 | − | 1.93314i | 0.538386 | − | 0.209679i | ||||
\(86\) | − | 9.02081i | − | 0.972739i | ||||||
\(87\) | 2.46149 | − | 2.46149i | 0.263899 | − | 0.263899i | ||||
\(88\) | 2.94669 | − | 2.94669i | 0.314118 | − | 0.314118i | ||||
\(89\) | 3.58782 | 0.380308 | 0.190154 | − | 0.981754i | \(-0.439101\pi\) | ||||
0.190154 | + | 0.981754i | \(0.439101\pi\) | |||||||
\(90\) | 2.08362 | − | 0.811485i | 0.219633 | − | 0.0855381i | ||||
\(91\) | 11.5377i | 1.20948i | ||||||||
\(92\) | 1.98398 | − | 4.36621i | 0.206844 | − | 0.455209i | ||||
\(93\) | 5.14167 | + | 5.14167i | 0.533166 | + | 0.533166i | ||||
\(94\) | − | 12.8600i | − | 1.32641i | ||||||
\(95\) | 4.71449 | − | 10.7291i | 0.483696 | − | 1.10079i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.03278 | − | 4.03278i | −0.409467 | − | 0.409467i | 0.472086 | − | 0.881553i | \(-0.343501\pi\) |
−0.881553 | + | 0.472086i | \(0.843501\pi\) | |||||||
\(98\) | 0.321672 | + | 0.321672i | 0.0324938 | + | 0.0324938i | ||||
\(99\) | 4.16725 | 0.418824 | ||||||||
\(100\) | −3.68298 | + | 3.38166i | −0.368298 | + | 0.338166i | ||||
\(101\) | 6.36488 | 0.633329 | 0.316665 | − | 0.948538i | \(-0.397437\pi\) | ||||
0.316665 | + | 0.948538i | \(0.397437\pi\) | |||||||
\(102\) | 1.68449 | + | 1.68449i | 0.166789 | + | 0.166789i | ||||
\(103\) | −1.99918 | + | 1.99918i | −0.196985 | + | 0.196985i | −0.798706 | − | 0.601721i | \(-0.794482\pi\) |
0.601721 | + | 0.798706i | \(0.294482\pi\) | |||||||
\(104\) | − | 4.50985i | − | 0.442227i | ||||||
\(105\) | 5.23730 | + | 2.30132i | 0.511109 | + | 0.224586i | ||||
\(106\) | 9.28392i | 0.901734i | ||||||||
\(107\) | −6.26821 | − | 6.26821i | −0.605971 | − | 0.605971i | 0.335920 | − | 0.941891i | \(-0.390953\pi\) |
−0.941891 | + | 0.335920i | \(0.890953\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −1.53597 | −0.147119 | −0.0735595 | − | 0.997291i | \(-0.523436\pi\) | ||||
−0.0735595 | + | 0.997291i | \(0.523436\pi\) | |||||||
\(110\) | −8.68298 | + | 3.38166i | −0.827890 | + | 0.322429i | ||||
\(111\) | − | 7.72640i | − | 0.733357i | ||||||
\(112\) | 1.80902 | + | 1.80902i | 0.170936 | + | 0.170936i | ||||
\(113\) | −14.0619 | + | 14.0619i | −1.32283 | + | 1.32283i | −0.411360 | + | 0.911473i | \(0.634946\pi\) |
−0.911473 | + | 0.411360i | \(0.865054\pi\) | |||||||
\(114\) | 5.24101 | 0.490865 | ||||||||
\(115\) | −7.98909 | + | 7.15363i | −0.744986 | + | 0.667080i | ||||
\(116\) | −3.48107 | −0.323209 | ||||||||
\(117\) | 3.18894 | − | 3.18894i | 0.294818 | − | 0.294818i | ||||
\(118\) | 4.81117 | + | 4.81117i | 0.442904 | + | 0.442904i | ||||
\(119\) | 6.09455i | 0.558686i | ||||||||
\(120\) | −2.04715 | − | 0.899538i | −0.186879 | − | 0.0821162i | ||||
\(121\) | −6.36597 | −0.578724 | ||||||||
\(122\) | −0.536878 | − | 0.536878i | −0.0486066 | − | 0.0486066i | ||||
\(123\) | 3.20853 | + | 3.20853i | 0.289303 | + | 0.289303i | ||||
\(124\) | − | 7.27142i | − | 0.652993i | ||||||
\(125\) | 10.5816 | − | 3.60979i | 0.946444 | − | 0.322869i | ||||
\(126\) | 2.55834i | 0.227915i | ||||||||
\(127\) | −7.12493 | + | 7.12493i | −0.632235 | + | 0.632235i | −0.948628 | − | 0.316393i | \(-0.897528\pi\) |
0.316393 | + | 0.948628i | \(0.397528\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −9.02081 | −0.794238 | ||||||||
\(130\) | −4.05678 | + | 9.23234i | −0.355803 | + | 0.809730i | ||||
\(131\) | 1.98524 | 0.173451 | 0.0867257 | − | 0.996232i | \(-0.472360\pi\) | ||||
0.0867257 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(132\) | −2.94669 | − | 2.94669i | −0.256476 | − | 0.256476i | ||||
\(133\) | 9.48107 | + | 9.48107i | 0.822113 | + | 0.822113i | ||||
\(134\) | 2.85850 | 0.246937 | ||||||||
\(135\) | −0.811485 | − | 2.08362i | −0.0698415 | − | 0.179330i | ||||
\(136\) | − | 2.38223i | − | 0.204275i | ||||||
\(137\) | 13.6901 | + | 13.6901i | 1.16962 | + | 1.16962i | 0.982298 | + | 0.187325i | \(0.0599819\pi\) |
0.187325 | + | 0.982298i | \(0.440018\pi\) | |||||||
\(138\) | −4.36621 | − | 1.98398i | −0.371677 | − | 0.168888i | ||||
\(139\) | − | 19.4321i | − | 1.64821i | −0.566438 | − | 0.824104i | \(-0.691679\pi\) | ||
0.566438 | − | 0.824104i | \(-0.308321\pi\) | |||||||
\(140\) | −2.07605 | − | 5.33061i | −0.175458 | − | 0.450519i | ||||
\(141\) | −12.8600 | −1.08301 | ||||||||
\(142\) | 6.76281 | − | 6.76281i | 0.567522 | − | 0.567522i | ||||
\(143\) | −13.2891 | + | 13.2891i | −1.11129 | + | 1.11129i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 7.12628 | + | 3.13136i | 0.591805 | + | 0.260045i | ||||
\(146\) | 8.17754 | 0.676778 | ||||||||
\(147\) | 0.321672 | − | 0.321672i | 0.0265310 | − | 0.0265310i | ||||
\(148\) | −5.46339 | + | 5.46339i | −0.449088 | + | 0.449088i | ||||
\(149\) | −3.37276 | −0.276307 | −0.138154 | − | 0.990411i | \(-0.544117\pi\) | ||||
−0.138154 | + | 0.990411i | \(0.544117\pi\) | |||||||
\(150\) | 3.38166 | + | 3.68298i | 0.276111 | + | 0.300714i | ||||
\(151\) | −18.7035 | −1.52207 | −0.761035 | − | 0.648710i | \(-0.775309\pi\) | ||||
−0.761035 | + | 0.648710i | \(0.775309\pi\) | |||||||
\(152\) | −3.70595 | − | 3.70595i | −0.300592 | − | 0.300592i | ||||
\(153\) | 1.68449 | − | 1.68449i | 0.136183 | − | 0.136183i | ||||
\(154\) | − | 10.6612i | − | 0.859106i | ||||||
\(155\) | −6.54092 | + | 14.8857i | −0.525379 | + | 1.19565i | ||||
\(156\) | −4.50985 | −0.361077 | ||||||||
\(157\) | 11.8389 | + | 11.8389i | 0.944844 | + | 0.944844i | 0.998556 | − | 0.0537126i | \(-0.0171055\pi\) |
−0.0537126 | + | 0.998556i | \(0.517105\pi\) | |||||||
\(158\) | −4.84343 | + | 4.84343i | −0.385322 | + | 0.385322i | ||||
\(159\) | 9.28392 | 0.736263 | ||||||||
\(160\) | 0.811485 | + | 2.08362i | 0.0641535 | + | 0.164725i | ||||
\(161\) | −4.30950 | − | 11.4876i | −0.339636 | − | 0.905351i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −8.37789 | − | 8.37789i | −0.656207 | − | 0.656207i | 0.298274 | − | 0.954480i | \(-0.403589\pi\) |
−0.954480 | + | 0.298274i | \(0.903589\pi\) | |||||||
\(164\) | − | 4.53754i | − | 0.354322i | ||||||
\(165\) | 3.38166 | + | 8.68298i | 0.263262 | + | 0.675969i | ||||
\(166\) | 3.40670i | 0.264411i | ||||||||
\(167\) | −13.2847 | + | 13.2847i | −1.02800 | + | 1.02800i | −0.0284037 | + | 0.999597i | \(0.509042\pi\) |
−0.999597 | + | 0.0284037i | \(0.990958\pi\) | |||||||
\(168\) | 1.80902 | − | 1.80902i | 0.139569 | − | 0.139569i | ||||
\(169\) | 7.33872i | 0.564517i | ||||||||
\(170\) | −2.14291 | + | 4.87679i | −0.164354 | + | 0.374033i | ||||
\(171\) | − | 5.24101i | − | 0.400790i | ||||||
\(172\) | 6.37868 | + | 6.37868i | 0.486370 | + | 0.486370i | ||||
\(173\) | 13.3807 | + | 13.3807i | 1.01732 | + | 1.01732i | 0.999847 | + | 0.0174703i | \(0.00556124\pi\) |
0.0174703 | + | 0.999847i | \(0.494439\pi\) | |||||||
\(174\) | 3.48107i | 0.263899i | ||||||||
\(175\) | −0.545097 | + | 12.7801i | −0.0412055 | + | 0.966082i | ||||
\(176\) | 4.16725i | 0.314118i | ||||||||
\(177\) | 4.81117 | − | 4.81117i | 0.361630 | − | 0.361630i | ||||
\(178\) | −2.53697 | + | 2.53697i | −0.190154 | + | 0.190154i | ||||
\(179\) | − | 17.1255i | − | 1.28002i | −0.768367 | − | 0.640010i | \(-0.778930\pi\) | ||
0.768367 | − | 0.640010i | \(-0.221070\pi\) | |||||||
\(180\) | −0.899538 | + | 2.04715i | −0.0670476 | + | 0.152586i | ||||
\(181\) | 7.02770i | 0.522365i | 0.965289 | + | 0.261183i | \(0.0841124\pi\) | ||||
−0.965289 | + | 0.261183i | \(0.915888\pi\) | |||||||
\(182\) | −8.15839 | − | 8.15839i | −0.604740 | − | 0.604740i | ||||
\(183\) | −0.536878 | + | 0.536878i | −0.0396872 | + | 0.0396872i | ||||
\(184\) | 1.68449 | + | 4.49027i | 0.124182 | + | 0.331027i | ||||
\(185\) | 16.0989 | − | 6.26986i | 1.18362 | − | 0.460969i | ||||
\(186\) | −7.27142 | −0.533166 | ||||||||
\(187\) | −7.01970 | + | 7.01970i | −0.513331 | + | 0.513331i | ||||
\(188\) | 9.09342 | + | 9.09342i | 0.663206 | + | 0.663206i | ||||
\(189\) | 2.55834 | 0.186092 | ||||||||
\(190\) | 4.25300 | + | 10.9203i | 0.308545 | + | 0.792241i | ||||
\(191\) | 22.3085i | 1.61419i | 0.590422 | + | 0.807094i | \(0.298961\pi\) | ||||
−0.590422 | + | 0.807094i | \(0.701039\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −12.5386 | − | 12.5386i | −0.902550 | − | 0.902550i | 0.0931061 | − | 0.995656i | \(-0.470320\pi\) |
−0.995656 | + | 0.0931061i | \(0.970320\pi\) | |||||||
\(194\) | 5.70322 | 0.409467 | ||||||||
\(195\) | 9.23234 | + | 4.05678i | 0.661142 | + | 0.290512i | ||||
\(196\) | −0.454913 | −0.0324938 | ||||||||
\(197\) | −2.02769 | + | 2.02769i | −0.144467 | + | 0.144467i | −0.775641 | − | 0.631174i | \(-0.782573\pi\) |
0.631174 | + | 0.775641i | \(0.282573\pi\) | |||||||
\(198\) | −2.94669 | + | 2.94669i | −0.209412 | + | 0.209412i | ||||
\(199\) | −4.87669 | −0.345699 | −0.172850 | − | 0.984948i | \(-0.555297\pi\) | ||||
−0.172850 | + | 0.984948i | \(0.555297\pi\) | |||||||
\(200\) | 0.213067 | − | 4.99546i | 0.0150661 | − | 0.353232i | ||||
\(201\) | − | 2.85850i | − | 0.201623i | ||||||
\(202\) | −4.50065 | + | 4.50065i | −0.316665 | + | 0.316665i | ||||
\(203\) | −6.29731 | + | 6.29731i | −0.441985 | + | 0.441985i | ||||
\(204\) | −2.38223 | −0.166789 | ||||||||
\(205\) | −4.08169 | + | 9.28903i | −0.285078 | + | 0.648774i | ||||
\(206\) | − | 2.82727i | − | 0.196985i | ||||||
\(207\) | −1.98398 | + | 4.36621i | −0.137896 | + | 0.303473i | ||||
\(208\) | 3.18894 | + | 3.18894i | 0.221113 | + | 0.221113i | ||||
\(209\) | 21.8406i | 1.51074i | ||||||||
\(210\) | −5.33061 | + | 2.07605i | −0.367847 | + | 0.143261i | ||||
\(211\) | −10.4399 | −0.718710 | −0.359355 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359355 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(212\) | −6.56472 | − | 6.56472i | −0.450867 | − | 0.450867i | ||||
\(213\) | −6.76281 | − | 6.76281i | −0.463380 | − | 0.463380i | ||||
\(214\) | 8.86459 | 0.605971 | ||||||||
\(215\) | −7.32026 | − | 18.7960i | −0.499237 | − | 1.28188i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −13.1541 | − | 13.1541i | −0.892960 | − | 0.892960i | ||||
\(218\) | 1.08609 | − | 1.08609i | 0.0735595 | − | 0.0735595i | ||||
\(219\) | − | 8.17754i | − | 0.552587i | ||||||
\(220\) | 3.74860 | − | 8.53099i | 0.252731 | − | 0.575159i | ||||
\(221\) | 10.7435i | 0.722686i | ||||||||
\(222\) | 5.46339 | + | 5.46339i | 0.366679 | + | 0.366679i | ||||
\(223\) | 11.9073 | + | 11.9073i | 0.797373 | + | 0.797373i | 0.982681 | − | 0.185308i | \(-0.0593282\pi\) |
−0.185308 | + | 0.982681i | \(0.559328\pi\) | |||||||
\(224\) | −2.55834 | −0.170936 | ||||||||
\(225\) | 3.68298 | − | 3.38166i | 0.245532 | − | 0.225444i | ||||
\(226\) | − | 19.8865i | − | 1.32283i | ||||||
\(227\) | −0.242263 | − | 0.242263i | −0.0160796 | − | 0.0160796i | 0.699021 | − | 0.715101i | \(-0.253619\pi\) |
−0.715101 | + | 0.699021i | \(0.753619\pi\) | |||||||
\(228\) | −3.70595 | + | 3.70595i | −0.245433 | + | 0.245433i | ||||
\(229\) | 5.80623 | 0.383687 | 0.191843 | − | 0.981426i | \(-0.438553\pi\) | ||||
0.191843 | + | 0.981426i | \(0.438553\pi\) | |||||||
\(230\) | 0.590758 | − | 10.7075i | 0.0389534 | − | 0.706033i | ||||
\(231\) | −10.6612 | −0.701457 | ||||||||
\(232\) | 2.46149 | − | 2.46149i | 0.161605 | − | 0.161605i | ||||
\(233\) | −11.2922 | − | 11.2922i | −0.739779 | − | 0.739779i | 0.232756 | − | 0.972535i | \(-0.425226\pi\) |
−0.972535 | + | 0.232756i | \(0.925226\pi\) | |||||||
\(234\) | 4.50985i | 0.294818i | ||||||||
\(235\) | −10.4357 | − | 26.7955i | −0.680752 | − | 1.74795i | ||||
\(236\) | −6.80402 | −0.442904 | ||||||||
\(237\) | 4.84343 | + | 4.84343i | 0.314614 | + | 0.314614i | ||||
\(238\) | −4.30950 | − | 4.30950i | −0.279343 | − | 0.279343i | ||||
\(239\) | − | 0.457589i | − | 0.0295990i | −0.999890 | − | 0.0147995i | \(-0.995289\pi\) | ||
0.999890 | − | 0.0147995i | \(-0.00471099\pi\) | |||||||
\(240\) | 2.08362 | − | 0.811485i | 0.134497 | − | 0.0523811i | ||||
\(241\) | − | 22.2609i | − | 1.43395i | −0.697098 | − | 0.716976i | \(-0.745526\pi\) | ||
0.697098 | − | 0.716976i | \(-0.254474\pi\) | |||||||
\(242\) | 4.50142 | − | 4.50142i | 0.289362 | − | 0.289362i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0.759260 | 0.0486066 | ||||||||
\(245\) | 0.931275 | + | 0.409211i | 0.0594970 | + | 0.0261436i | ||||
\(246\) | −4.53754 | −0.289303 | ||||||||
\(247\) | 16.7133 | + | 16.7133i | 1.06344 | + | 1.06344i | ||||
\(248\) | 5.14167 | + | 5.14167i | 0.326496 | + | 0.326496i | ||||
\(249\) | 3.40670 | 0.215891 | ||||||||
\(250\) | −4.92979 | + | 10.0348i | −0.311787 | + | 0.634656i | ||||
\(251\) | 26.7068i | 1.68572i | 0.538135 | + | 0.842858i | \(0.319129\pi\) | ||||
−0.538135 | + | 0.842858i | \(0.680871\pi\) | |||||||
\(252\) | −1.80902 | − | 1.80902i | −0.113957 | − | 0.113957i | ||||
\(253\) | 8.26775 | − | 18.1951i | 0.519789 | − | 1.14392i | ||||
\(254\) | − | 10.0762i | − | 0.632235i | ||||||
\(255\) | 4.87679 | + | 2.14291i | 0.305396 | + | 0.134194i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.33827 | + | 5.33827i | −0.332992 | + | 0.332992i | −0.853722 | − | 0.520729i | \(-0.825660\pi\) |
0.520729 | + | 0.853722i | \(0.325660\pi\) | |||||||
\(258\) | 6.37868 | − | 6.37868i | 0.397119 | − | 0.397119i | ||||
\(259\) | 19.7667i | 1.22824i | ||||||||
\(260\) | −3.65967 | − | 9.39683i | −0.226963 | − | 0.582767i | ||||
\(261\) | 3.48107 | 0.215473 | ||||||||
\(262\) | −1.40378 | + | 1.40378i | −0.0867257 | + | 0.0867257i | ||||
\(263\) | 19.5204 | − | 19.5204i | 1.20368 | − | 1.20368i | 0.230639 | − | 0.973039i | \(-0.425918\pi\) |
0.973039 | − | 0.230639i | \(-0.0740817\pi\) | |||||||
\(264\) | 4.16725 | 0.256476 | ||||||||
\(265\) | 7.53377 | + | 19.3442i | 0.462796 | + | 1.18831i | ||||
\(266\) | −13.4083 | −0.822113 | ||||||||
\(267\) | 2.53697 | + | 2.53697i | 0.155260 | + | 0.155260i | ||||
\(268\) | −2.02126 | + | 2.02126i | −0.123468 | + | 0.123468i | ||||
\(269\) | − | 4.38872i | − | 0.267585i | −0.991009 | − | 0.133793i | \(-0.957284\pi\) | ||
0.991009 | − | 0.133793i | \(-0.0427156\pi\) | |||||||
\(270\) | 2.04715 | + | 0.899538i | 0.124586 | + | 0.0547442i | ||||
\(271\) | 18.9023 | 1.14823 | 0.574117 | − | 0.818773i | \(-0.305345\pi\) | ||||
0.574117 | + | 0.818773i | \(0.305345\pi\) | |||||||
\(272\) | 1.68449 | + | 1.68449i | 0.102137 | + | 0.102137i | ||||
\(273\) | −8.15839 | + | 8.15839i | −0.493768 | + | 0.493768i | ||||
\(274\) | −19.3607 | −1.16962 | ||||||||
\(275\) | −15.3479 | + | 14.0922i | −0.925514 | + | 0.849793i | ||||
\(276\) | 4.49027 | − | 1.68449i | 0.270282 | − | 0.101394i | ||||
\(277\) | 2.44423 | − | 2.44423i | 0.146860 | − | 0.146860i | −0.629854 | − | 0.776714i | \(-0.716885\pi\) |
0.776714 | + | 0.629854i | \(0.216885\pi\) | |||||||
\(278\) | 13.7406 | + | 13.7406i | 0.824104 | + | 0.824104i | ||||
\(279\) | 7.27142i | 0.435328i | ||||||||
\(280\) | 5.23730 | + | 2.30132i | 0.312989 | + | 0.137530i | ||||
\(281\) | 2.33823i | 0.139487i | 0.997565 | + | 0.0697436i | \(0.0222181\pi\) | ||||
−0.997565 | + | 0.0697436i | \(0.977782\pi\) | |||||||
\(282\) | 9.09342 | − | 9.09342i | 0.541505 | − | 0.541505i | ||||
\(283\) | 21.6132 | − | 21.6132i | 1.28477 | − | 1.28477i | 0.346850 | − | 0.937921i | \(-0.387251\pi\) |
0.937921 | − | 0.346850i | \(-0.112749\pi\) | |||||||
\(284\) | 9.56406i | 0.567522i | ||||||||
\(285\) | 10.9203 | − | 4.25300i | 0.646862 | − | 0.251926i | ||||
\(286\) | − | 18.7937i | − | 1.11129i | ||||||
\(287\) | −8.20849 | − | 8.20849i | −0.484532 | − | 0.484532i | ||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 11.3250i | − | 0.666175i | ||||||
\(290\) | −7.25324 | + | 2.82484i | −0.425925 | + | 0.165880i | ||||
\(291\) | − | 5.70322i | − | 0.334328i | ||||||
\(292\) | −5.78239 | + | 5.78239i | −0.338389 | + | 0.338389i | ||||
\(293\) | 21.4487 | − | 21.4487i | 1.25305 | − | 1.25305i | 0.298699 | − | 0.954347i | \(-0.403447\pi\) |
0.954347 | − | 0.298699i | \(-0.0965528\pi\) | |||||||
\(294\) | 0.454913i | 0.0265310i | ||||||||
\(295\) | 13.9289 | + | 6.12048i | 0.810970 | + | 0.356348i | ||||
\(296\) | − | 7.72640i | − | 0.449088i | ||||||
\(297\) | 2.94669 | + | 2.94669i | 0.170984 | + | 0.170984i | ||||
\(298\) | 2.38490 | − | 2.38490i | 0.138154 | − | 0.138154i | ||||
\(299\) | −7.59680 | − | 20.2504i | −0.439334 | − | 1.17111i | ||||
\(300\) | −4.99546 | − | 0.213067i | −0.288413 | − | 0.0123014i | ||||
\(301\) | 23.0783 | 1.33021 | ||||||||
\(302\) | 13.2254 | − | 13.2254i | 0.761035 | − | 0.761035i | ||||
\(303\) | 4.50065 | + | 4.50065i | 0.258556 | + | 0.258556i | ||||
\(304\) | 5.24101 | 0.300592 | ||||||||
\(305\) | −1.55432 | − | 0.682984i | −0.0890001 | − | 0.0391075i | ||||
\(306\) | 2.38223i | 0.136183i | ||||||||
\(307\) | 12.0002 | − | 12.0002i | 0.684889 | − | 0.684889i | −0.276209 | − | 0.961098i | \(-0.589078\pi\) |
0.961098 | + | 0.276209i | \(0.0890781\pi\) | |||||||
\(308\) | 7.53863 | + | 7.53863i | 0.429553 | + | 0.429553i | ||||
\(309\) | −2.82727 | −0.160838 | ||||||||
\(310\) | −5.90065 | − | 15.1509i | −0.335134 | − | 0.860514i | ||||
\(311\) | 1.56616 | 0.0888087 | 0.0444043 | − | 0.999014i | \(-0.485861\pi\) | ||||
0.0444043 | + | 0.999014i | \(0.485861\pi\) | |||||||
\(312\) | 3.18894 | − | 3.18894i | 0.180538 | − | 0.180538i | ||||
\(313\) | −8.94733 | + | 8.94733i | −0.505733 | + | 0.505733i | −0.913214 | − | 0.407481i | \(-0.866407\pi\) |
0.407481 | + | 0.913214i | \(0.366407\pi\) | |||||||
\(314\) | −16.7427 | −0.944844 | ||||||||
\(315\) | 2.07605 | + | 5.33061i | 0.116972 | + | 0.300346i | ||||
\(316\) | − | 6.84964i | − | 0.385322i | ||||||
\(317\) | 8.43391 | − | 8.43391i | 0.473695 | − | 0.473695i | −0.429413 | − | 0.903108i | \(-0.641279\pi\) |
0.903108 | + | 0.429413i | \(0.141279\pi\) | |||||||
\(318\) | −6.56472 | + | 6.56472i | −0.368131 | + | 0.368131i | ||||
\(319\) | −14.5065 | −0.812207 | ||||||||
\(320\) | −2.04715 | − | 0.899538i | −0.114439 | − | 0.0502857i | ||||
\(321\) | − | 8.86459i | − | 0.494773i | ||||||
\(322\) | 11.1702 | + | 5.07570i | 0.622493 | + | 0.282857i | ||||
\(323\) | 8.82843 | + | 8.82843i | 0.491227 | + | 0.491227i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −0.960900 | + | 22.5288i | −0.0533011 | + | 1.24967i | ||||
\(326\) | 11.8481 | 0.656207 | ||||||||
\(327\) | −1.08609 | − | 1.08609i | −0.0600611 | − | 0.0600611i | ||||
\(328\) | 3.20853 | + | 3.20853i | 0.177161 | + | 0.177161i | ||||
\(329\) | 32.9003 | 1.81385 | ||||||||
\(330\) | −8.53099 | − | 3.74860i | −0.469616 | − | 0.206354i | ||||
\(331\) | 12.9490 | 0.711741 | 0.355870 | − | 0.934535i | \(-0.384184\pi\) | ||||
0.355870 | + | 0.934535i | \(0.384184\pi\) | |||||||
\(332\) | −2.40890 | − | 2.40890i | −0.132206 | − | 0.132206i | ||||
\(333\) | 5.46339 | − | 5.46339i | 0.299392 | − | 0.299392i | ||||
\(334\) | − | 18.7874i | − | 1.02800i | ||||||
\(335\) | 5.95604 | − | 2.31963i | 0.325413 | − | 0.126735i | ||||
\(336\) | 2.55834i | 0.139569i | ||||||||
\(337\) | −4.75471 | − | 4.75471i | −0.259006 | − | 0.259006i | 0.565644 | − | 0.824650i | \(-0.308628\pi\) |
−0.824650 | + | 0.565644i | \(0.808628\pi\) | |||||||
\(338\) | −5.18926 | − | 5.18926i | −0.282259 | − | 0.282259i | ||||
\(339\) | −19.8865 | −1.08009 | ||||||||
\(340\) | −1.93314 | − | 4.96367i | −0.104839 | − | 0.269193i | ||||
\(341\) | − | 30.3018i | − | 1.64094i | ||||||
\(342\) | 3.70595 | + | 3.70595i | 0.200395 | + | 0.200395i | ||||
\(343\) | −13.4861 | + | 13.4861i | −0.728179 | + | 0.728179i | ||||
\(344\) | −9.02081 | −0.486370 | ||||||||
\(345\) | −10.7075 | − | 0.590758i | −0.576474 | − | 0.0318053i | ||||
\(346\) | −18.9232 | −1.01732 | ||||||||
\(347\) | −3.12333 | + | 3.12333i | −0.167669 | + | 0.167669i | −0.785954 | − | 0.618285i | \(-0.787828\pi\) |
0.618285 | + | 0.785954i | \(0.287828\pi\) | |||||||
\(348\) | −2.46149 | − | 2.46149i | −0.131950 | − | 0.131950i | ||||
\(349\) | − | 16.1446i | − | 0.864201i | −0.901825 | − | 0.432101i | \(-0.857773\pi\) | ||
0.901825 | − | 0.432101i | \(-0.142227\pi\) | |||||||
\(350\) | −8.65143 | − | 9.42231i | −0.462438 | − | 0.503644i | ||||
\(351\) | 4.50985 | 0.240718 | ||||||||
\(352\) | −2.94669 | − | 2.94669i | −0.157059 | − | 0.157059i | ||||
\(353\) | −10.2236 | − | 10.2236i | −0.544146 | − | 0.544146i | 0.380596 | − | 0.924742i | \(-0.375719\pi\) |
−0.924742 | + | 0.380596i | \(0.875719\pi\) | |||||||
\(354\) | 6.80402i | 0.361630i | ||||||||
\(355\) | 8.60324 | − | 19.5791i | 0.456612 | − | 1.03915i | ||||
\(356\) | − | 3.58782i | − | 0.190154i | ||||||
\(357\) | −4.30950 | + | 4.30950i | −0.228083 | + | 0.228083i | ||||
\(358\) | 12.1096 | + | 12.1096i | 0.640010 | + | 0.640010i | ||||
\(359\) | −18.2877 | −0.965188 | −0.482594 | − | 0.875844i | \(-0.660305\pi\) | ||||
−0.482594 | + | 0.875844i | \(0.660305\pi\) | |||||||
\(360\) | −0.811485 | − | 2.08362i | −0.0427690 | − | 0.109817i | ||||
\(361\) | 8.46813 | 0.445691 | ||||||||
\(362\) | −4.96934 | − | 4.96934i | −0.261183 | − | 0.261183i | ||||
\(363\) | −4.50142 | − | 4.50142i | −0.236263 | − | 0.236263i | ||||
\(364\) | 11.5377 | 0.604740 | ||||||||
\(365\) | 17.0389 | − | 6.63595i | 0.891858 | − | 0.347341i | ||||
\(366\) | − | 0.759260i | − | 0.0396872i | ||||||
\(367\) | 7.66636 | + | 7.66636i | 0.400181 | + | 0.400181i | 0.878297 | − | 0.478116i | \(-0.158680\pi\) |
−0.478116 | + | 0.878297i | \(0.658680\pi\) | |||||||
\(368\) | −4.36621 | − | 1.98398i | −0.227605 | − | 0.103422i | ||||
\(369\) | 4.53754i | 0.236215i | ||||||||
\(370\) | −6.95019 | + | 15.8171i | −0.361323 | + | 0.822292i | ||||
\(371\) | −23.7514 | −1.23311 | ||||||||
\(372\) | 5.14167 | − | 5.14167i | 0.266583 | − | 0.266583i | ||||
\(373\) | 18.9572 | − | 18.9572i | 0.981564 | − | 0.981564i | −0.0182689 | − | 0.999833i | \(-0.505815\pi\) |
0.999833 | + | 0.0182689i | \(0.00581550\pi\) | |||||||
\(374\) | − | 9.92735i | − | 0.513331i | ||||||
\(375\) | 10.0348 | + | 4.92979i | 0.518195 | + | 0.254573i | ||||
\(376\) | −12.8600 | −0.663206 | ||||||||
\(377\) | −11.1009 | + | 11.1009i | −0.571727 | + | 0.571727i | ||||
\(378\) | −1.80902 | + | 1.80902i | −0.0930458 | + | 0.0930458i | ||||
\(379\) | 21.8702 | 1.12340 | 0.561699 | − | 0.827341i | \(-0.310148\pi\) | ||||
0.561699 | + | 0.827341i | \(0.310148\pi\) | |||||||
\(380\) | −10.7291 | − | 4.71449i | −0.550393 | − | 0.241848i | ||||
\(381\) | −10.0762 | −0.516218 | ||||||||
\(382\) | −15.7745 | − | 15.7745i | −0.807094 | − | 0.807094i | ||||
\(383\) | −20.5841 | + | 20.5841i | −1.05180 | + | 1.05180i | −0.0532143 | + | 0.998583i | \(0.516947\pi\) |
−0.998583 | + | 0.0532143i | \(0.983053\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −8.65143 | − | 22.2140i | −0.440918 | − | 1.13213i | ||||
\(386\) | 17.7323 | 0.902550 | ||||||||
\(387\) | −6.37868 | − | 6.37868i | −0.324246 | − | 0.324246i | ||||
\(388\) | −4.03278 | + | 4.03278i | −0.204734 | + | 0.204734i | ||||
\(389\) | −2.71068 | −0.137437 | −0.0687184 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687184 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(390\) | −9.39683 | + | 3.65967i | −0.475827 | + | 0.185315i | ||||
\(391\) | −4.01285 | − | 10.6968i | −0.202938 | − | 0.540963i | ||||
\(392\) | 0.321672 | − | 0.321672i | 0.0162469 | − | 0.0162469i | ||||
\(393\) | 1.40378 | + | 1.40378i | 0.0708113 | + | 0.0708113i | ||||
\(394\) | − | 2.86759i | − | 0.144467i | ||||||
\(395\) | −6.16152 | + | 14.0223i | −0.310020 | + | 0.705536i | ||||
\(396\) | − | 4.16725i | − | 0.209412i | ||||||
\(397\) | 26.9536 | − | 26.9536i | 1.35276 | − | 1.35276i | 0.470203 | − | 0.882558i | \(-0.344181\pi\) |
0.882558 | − | 0.470203i | \(-0.155819\pi\) | |||||||
\(398\) | 3.44834 | − | 3.44834i | 0.172850 | − | 0.172850i | ||||
\(399\) | 13.4083i | 0.671252i | ||||||||
\(400\) | 3.38166 | + | 3.68298i | 0.169083 | + | 0.184149i | ||||
\(401\) | − | 9.86390i | − | 0.492580i | −0.969196 | − | 0.246290i | \(-0.920788\pi\) | ||
0.969196 | − | 0.246290i | \(-0.0792115\pi\) | |||||||
\(402\) | 2.02126 | + | 2.02126i | 0.100812 | + | 0.100812i | ||||
\(403\) | −23.1881 | − | 23.1881i | −1.15508 | − | 1.15508i | ||||
\(404\) | − | 6.36488i | − | 0.316665i | ||||||
\(405\) | 0.899538 | − | 2.04715i | 0.0446984 | − | 0.101724i | ||||
\(406\) | − | 8.90575i | − | 0.441985i | ||||||
\(407\) | −22.7673 | + | 22.7673i | −1.12853 | + | 1.12853i | ||||
\(408\) | 1.68449 | − | 1.68449i | 0.0833947 | − | 0.0833947i | ||||
\(409\) | 30.0925i | 1.48798i | 0.668191 | + | 0.743990i | \(0.267069\pi\) | ||||
−0.668191 | + | 0.743990i | \(0.732931\pi\) | |||||||
\(410\) | −3.68215 | − | 9.45453i | −0.181848 | − | 0.466926i | ||||
\(411\) | 19.3607i | 0.954993i | ||||||||
\(412\) | 1.99918 | + | 1.99918i | 0.0984926 | + | 0.0984926i | ||||
\(413\) | −12.3086 | + | 12.3086i | −0.605666 | + | 0.605666i | ||||
\(414\) | −1.68449 | − | 4.49027i | −0.0827882 | − | 0.220685i | ||||
\(415\) | 2.76449 | + | 7.09828i | 0.135703 | + | 0.348441i | ||||
\(416\) | −4.50985 | −0.221113 | ||||||||
\(417\) | 13.7406 | − | 13.7406i | 0.672878 | − | 0.672878i | ||||
\(418\) | −15.4436 | − | 15.4436i | −0.755372 | − | 0.755372i | ||||
\(419\) | 7.59626 | 0.371102 | 0.185551 | − | 0.982635i | \(-0.440593\pi\) | ||||
0.185551 | + | 0.982635i | \(0.440593\pi\) | |||||||
\(420\) | 2.30132 | − | 5.23730i | 0.112293 | − | 0.255554i | ||||
\(421\) | − | 23.4653i | − | 1.14363i | −0.820382 | − | 0.571816i | \(-0.806239\pi\) | ||
0.820382 | − | 0.571816i | \(-0.193761\pi\) | |||||||
\(422\) | 7.38210 | − | 7.38210i | 0.359355 | − | 0.359355i | ||||
\(423\) | −9.09342 | − | 9.09342i | −0.442137 | − | 0.442137i | ||||
\(424\) | 9.28392 | 0.450867 | ||||||||
\(425\) | −0.507575 | + | 11.9003i | −0.0246210 | + | 0.577251i | ||||
\(426\) | 9.56406 | 0.463380 | ||||||||
\(427\) | 1.37351 | − | 1.37351i | 0.0664690 | − | 0.0664690i | ||||
\(428\) | −6.26821 | + | 6.26821i | −0.302985 | + | 0.302985i | ||||
\(429\) | −18.7937 | −0.907366 | ||||||||
\(430\) | 18.4670 | + | 8.11457i | 0.890557 | + | 0.391319i | ||||
\(431\) | 21.7988i | 1.05001i | 0.851099 | + | 0.525005i | \(0.175937\pi\) | ||||
−0.851099 | + | 0.525005i | \(0.824063\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 17.0890 | − | 17.0890i | 0.821245 | − | 0.821245i | −0.165041 | − | 0.986287i | \(-0.552776\pi\) |
0.986287 | + | 0.165041i | \(0.0527757\pi\) | |||||||
\(434\) | 18.6027 | 0.892960 | ||||||||
\(435\) | 2.82484 | + | 7.25324i | 0.135441 | + | 0.347766i | ||||
\(436\) | 1.53597i | 0.0735595i | ||||||||
\(437\) | −22.8833 | − | 10.3981i | −1.09466 | − | 0.497407i | ||||
\(438\) | 5.78239 | + | 5.78239i | 0.276293 | + | 0.276293i | ||||
\(439\) | 18.6384i | 0.889563i | 0.895639 | + | 0.444781i | \(0.146719\pi\) | ||||
−0.895639 | + | 0.444781i | \(0.853281\pi\) | |||||||
\(440\) | 3.38166 | + | 8.68298i | 0.161214 | + | 0.413945i | ||||
\(441\) | 0.454913 | 0.0216625 | ||||||||
\(442\) | −7.59680 | − | 7.59680i | −0.361343 | − | 0.361343i | ||||
\(443\) | 7.32527 | + | 7.32527i | 0.348034 | + | 0.348034i | 0.859377 | − | 0.511343i | \(-0.170852\pi\) |
−0.511343 | + | 0.859377i | \(0.670852\pi\) | |||||||
\(444\) | −7.72640 | −0.366679 | ||||||||
\(445\) | −3.22738 | + | 7.34481i | −0.152993 | + | 0.348177i | ||||
\(446\) | −16.8395 | −0.797373 | ||||||||
\(447\) | −2.38490 | − | 2.38490i | −0.112802 | − | 0.112802i | ||||
\(448\) | 1.80902 | − | 1.80902i | 0.0854680 | − | 0.0854680i | ||||
\(449\) | − | 12.9705i | − | 0.612116i | −0.952013 | − | 0.306058i | \(-0.900990\pi\) | ||
0.952013 | − | 0.306058i | \(-0.0990102\pi\) | |||||||
\(450\) | −0.213067 | + | 4.99546i | −0.0100441 | + | 0.235488i | ||||
\(451\) | − | 18.9091i | − | 0.890393i | ||||||
\(452\) | 14.0619 | + | 14.0619i | 0.661417 | + | 0.661417i | ||||
\(453\) | −13.2254 | − | 13.2254i | −0.621383 | − | 0.621383i | ||||
\(454\) | 0.342612 | 0.0160796 | ||||||||
\(455\) | −23.6194 | − | 10.3786i | −1.10730 | − | 0.486557i | ||||
\(456\) | − | 5.24101i | − | 0.245433i | ||||||
\(457\) | −27.4401 | − | 27.4401i | −1.28360 | − | 1.28360i | −0.938607 | − | 0.344988i | \(-0.887883\pi\) |
−0.344988 | − | 0.938607i | \(-0.612117\pi\) | |||||||
\(458\) | −4.10563 | + | 4.10563i | −0.191843 | + | 0.191843i | ||||
\(459\) | 2.38223 | 0.111193 | ||||||||
\(460\) | 7.15363 | + | 7.98909i | 0.333540 | + | 0.372493i | ||||
\(461\) | 10.2068 | 0.475376 | 0.237688 | − | 0.971342i | \(-0.423610\pi\) | ||||
0.237688 | + | 0.971342i | \(0.423610\pi\) | |||||||
\(462\) | 7.53863 | − | 7.53863i | 0.350729 | − | 0.350729i | ||||
\(463\) | −8.13895 | − | 8.13895i | −0.378249 | − | 0.378249i | 0.492221 | − | 0.870470i | \(-0.336185\pi\) |
−0.870470 | + | 0.492221i | \(0.836185\pi\) | |||||||
\(464\) | 3.48107i | 0.161605i | ||||||||
\(465\) | −15.1509 | + | 5.90065i | −0.702607 | + | 0.273636i | ||||
\(466\) | 15.9696 | 0.739779 | ||||||||
\(467\) | −20.9496 | − | 20.9496i | −0.969434 | − | 0.969434i | 0.0301128 | − | 0.999547i | \(-0.490413\pi\) |
−0.999547 | + | 0.0301128i | \(0.990413\pi\) | |||||||
\(468\) | −3.18894 | − | 3.18894i | −0.147409 | − | 0.147409i | ||||
\(469\) | 7.31300i | 0.337683i | ||||||||
\(470\) | 26.3265 | + | 11.5681i | 1.21435 | + | 0.533597i | ||||
\(471\) | 16.7427i | 0.771462i | ||||||||
\(472\) | 4.81117 | − | 4.81117i | 0.221452 | − | 0.221452i | ||||
\(473\) | 26.5815 | + | 26.5815i | 1.22222 | + | 1.22222i | ||||
\(474\) | −6.84964 | −0.314614 | ||||||||
\(475\) | 17.7233 | + | 19.3025i | 0.813201 | + | 0.885661i | ||||
\(476\) | 6.09455 | 0.279343 | ||||||||
\(477\) | 6.56472 | + | 6.56472i | 0.300578 | + | 0.300578i | ||||
\(478\) | 0.323564 | + | 0.323564i | 0.0147995 | + | 0.0147995i | ||||
\(479\) | 23.4064 | 1.06947 | 0.534733 | − | 0.845021i | \(-0.320412\pi\) | ||||
0.534733 | + | 0.845021i | \(0.320412\pi\) | |||||||
\(480\) | −0.899538 | + | 2.04715i | −0.0410581 | + | 0.0934393i | ||||
\(481\) | 34.8449i | 1.58879i | ||||||||
\(482\) | 15.7409 | + | 15.7409i | 0.716976 | + | 0.716976i | ||||
\(483\) | 5.07570 | − | 11.1702i | 0.230952 | − | 0.508264i | ||||
\(484\) | 6.36597i | 0.289362i | ||||||||
\(485\) | 11.8834 | − | 4.62808i | 0.539596 | − | 0.210150i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 22.9383 | − | 22.9383i | 1.03943 | − | 1.03943i | 0.0402440 | − | 0.999190i | \(-0.487186\pi\) |
0.999190 | − | 0.0402440i | \(-0.0128135\pi\) | |||||||
\(488\) | −0.536878 | + | 0.536878i | −0.0243033 | + | 0.0243033i | ||||
\(489\) | − | 11.8481i | − | 0.535791i | ||||||
\(490\) | −0.947867 | + | 0.369155i | −0.0428203 | + | 0.0166767i | ||||
\(491\) | 30.8377 | 1.39169 | 0.695844 | − | 0.718193i | \(-0.255031\pi\) | ||||
0.695844 | + | 0.718193i | \(0.255031\pi\) | |||||||
\(492\) | 3.20853 | − | 3.20853i | 0.144651 | − | 0.144651i | ||||
\(493\) | −5.86383 | + | 5.86383i | −0.264094 | + | 0.264094i | ||||
\(494\) | −23.6361 | −1.06344 | ||||||||
\(495\) | −3.74860 | + | 8.53099i | −0.168487 | + | 0.383440i | ||||
\(496\) | −7.27142 | −0.326496 | ||||||||
\(497\) | 17.3015 | + | 17.3015i | 0.776080 | + | 0.776080i | ||||
\(498\) | −2.40890 | + | 2.40890i | −0.107945 | + | 0.107945i | ||||
\(499\) | 25.4897i | 1.14107i | 0.821272 | + | 0.570537i | \(0.193265\pi\) | ||||
−0.821272 | + | 0.570537i | \(0.806735\pi\) | |||||||
\(500\) | −3.60979 | − | 10.5816i | −0.161435 | − | 0.473222i | ||||
\(501\) | −18.7874 | −0.839359 | ||||||||
\(502\) | −18.8845 | − | 18.8845i | −0.842858 | − | 0.842858i | ||||
\(503\) | 3.49872 | − | 3.49872i | 0.156000 | − | 0.156000i | −0.624792 | − | 0.780792i | \(-0.714816\pi\) |
0.780792 | + | 0.624792i | \(0.214816\pi\) | |||||||
\(504\) | 2.55834 | 0.113957 | ||||||||
\(505\) | −5.72545 | + | 13.0299i | −0.254779 | + | 0.579822i | ||||
\(506\) | 7.01970 | + | 18.7121i | 0.312064 | + | 0.831852i | ||||
\(507\) | −5.18926 | + | 5.18926i | −0.230463 | + | 0.230463i | ||||
\(508\) | 7.12493 | + | 7.12493i | 0.316117 | + | 0.316117i | ||||
\(509\) | 26.2453i | 1.16330i | 0.813439 | + | 0.581651i | \(0.197593\pi\) | ||||
−0.813439 | + | 0.581651i | \(0.802407\pi\) | |||||||
\(510\) | −4.96367 | + | 1.93314i | −0.219795 | + | 0.0856011i | ||||
\(511\) | 20.9209i | 0.925486i | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 3.70595 | − | 3.70595i | 0.163622 | − | 0.163622i | ||||
\(514\) | − | 7.54946i | − | 0.332992i | ||||||
\(515\) | −2.29429 | − | 5.89097i | −0.101098 | − | 0.259587i | ||||
\(516\) | 9.02081i | 0.397119i | ||||||||
\(517\) | 37.8946 | + | 37.8946i | 1.66660 | + | 1.66660i | ||||
\(518\) | −13.9772 | − | 13.9772i | −0.614122 | − | 0.614122i | ||||
\(519\) | 18.9232i | 0.830636i | ||||||||
\(520\) | 9.23234 | + | 4.05678i | 0.404865 | + | 0.177902i | ||||
\(521\) | − | 16.1892i | − | 0.709263i | −0.935006 | − | 0.354631i | \(-0.884606\pi\) | ||
0.935006 | − | 0.354631i | \(-0.115394\pi\) | |||||||
\(522\) | −2.46149 | + | 2.46149i | −0.107736 | + | 0.107736i | ||||
\(523\) | 1.41722 | − | 1.41722i | 0.0619705 | − | 0.0619705i | −0.675442 | − | 0.737413i | \(-0.736047\pi\) |
0.737413 | + | 0.675442i | \(0.236047\pi\) | |||||||
\(524\) | − | 1.98524i | − | 0.0867257i | ||||||
\(525\) | −9.42231 | + | 8.65143i | −0.411223 | + | 0.377579i | ||||
\(526\) | 27.6060i | 1.20368i | ||||||||
\(527\) | −12.2486 | − | 12.2486i | −0.533559 | − | 0.533559i | ||||
\(528\) | −2.94669 | + | 2.94669i | −0.128238 | + | 0.128238i | ||||
\(529\) | 15.1276 | + | 17.3250i | 0.657723 | + | 0.753260i | ||||
\(530\) | −19.0056 | − | 8.35125i | −0.825551 | − | 0.362755i | ||||
\(531\) | 6.80402 | 0.295269 | ||||||||
\(532\) | 9.48107 | − | 9.48107i | 0.411056 | − | 0.411056i | ||||
\(533\) | −14.4700 | − | 14.4700i | −0.626764 | − | 0.626764i | ||||
\(534\) | −3.58782 | −0.155260 | ||||||||
\(535\) | 18.4705 | − | 7.19348i | 0.798548 | − | 0.311001i | ||||
\(536\) | − | 2.85850i | − | 0.123468i | ||||||
\(537\) | 12.1096 | − | 12.1096i | 0.522566 | − | 0.522566i | ||||
\(538\) | 3.10329 | + | 3.10329i | 0.133793 | + | 0.133793i | ||||
\(539\) | −1.89573 | −0.0816551 | ||||||||
\(540\) | −2.08362 | + | 0.811485i | −0.0896649 | + | 0.0349208i | ||||
\(541\) | −3.67997 | −0.158214 | −0.0791072 | − | 0.996866i | \(-0.525207\pi\) | ||||
−0.0791072 | + | 0.996866i | \(0.525207\pi\) | |||||||
\(542\) | −13.3660 | + | 13.3660i | −0.574117 | + | 0.574117i | ||||
\(543\) | −4.96934 | + | 4.96934i | −0.213255 | + | 0.213255i | ||||
\(544\) | −2.38223 | −0.102137 | ||||||||
\(545\) | 1.38166 | − | 3.14436i | 0.0591839 | − | 0.134689i | ||||
\(546\) | − | 11.5377i | − | 0.493768i | ||||||
\(547\) | −4.37686 | + | 4.37686i | −0.187141 | + | 0.187141i | −0.794459 | − | 0.607318i | \(-0.792245\pi\) |
0.607318 | + | 0.794459i | \(0.292245\pi\) | |||||||
\(548\) | 13.6901 | − | 13.6901i | 0.584812 | − | 0.584812i | ||||
\(549\) | −0.759260 | −0.0324044 | ||||||||
\(550\) | 0.887903 | − | 20.8173i | 0.0378603 | − | 0.887653i | ||||
\(551\) | 18.2443i | 0.777233i | ||||||||
\(552\) | −1.98398 | + | 4.36621i | −0.0844439 | + | 0.185838i | ||||
\(553\) | −12.3911 | − | 12.3911i | −0.526924 | − | 0.526924i | ||||
\(554\) | 3.45666i | 0.146860i | ||||||||
\(555\) | 15.8171 | + | 6.95019i | 0.671399 | + | 0.295019i | ||||
\(556\) | −19.4321 | −0.824104 | ||||||||
\(557\) | 3.04302 | + | 3.04302i | 0.128937 | + | 0.128937i | 0.768630 | − | 0.639693i | \(-0.220939\pi\) |
−0.639693 | + | 0.768630i | \(0.720939\pi\) | |||||||
\(558\) | −5.14167 | − | 5.14167i | −0.217664 | − | 0.217664i | ||||
\(559\) | 40.6825 | 1.72069 | ||||||||
\(560\) | −5.33061 | + | 2.07605i | −0.225260 | + | 0.0877292i | ||||
\(561\) | −9.92735 | −0.419133 | ||||||||
\(562\) | −1.65338 | − | 1.65338i | −0.0697436 | − | 0.0697436i | ||||
\(563\) | −27.0816 | + | 27.0816i | −1.14135 | + | 1.14135i | −0.153151 | + | 0.988203i | \(0.548942\pi\) |
−0.988203 | + | 0.153151i | \(0.951058\pi\) | |||||||
\(564\) | 12.8600i | 0.541505i | ||||||||
\(565\) | −16.1376 | − | 41.4361i | −0.678915 | − | 1.74323i | ||||
\(566\) | 30.5657i | 1.28477i | ||||||||
\(567\) | 1.80902 | + | 1.80902i | 0.0759716 | + | 0.0759716i | ||||
\(568\) | −6.76281 | − | 6.76281i | −0.283761 | − | 0.283761i | ||||
\(569\) | 34.6663 | 1.45329 | 0.726644 | − | 0.687014i | \(-0.241079\pi\) | ||||
0.726644 | + | 0.687014i | \(0.241079\pi\) | |||||||
\(570\) | −4.71449 | + | 10.7291i | −0.197468 | + | 0.449394i | ||||
\(571\) | 9.50431i | 0.397743i | 0.980026 | + | 0.198871i | \(0.0637276\pi\) | ||||
−0.980026 | + | 0.198871i | \(0.936272\pi\) | |||||||
\(572\) | 13.2891 | + | 13.2891i | 0.555646 | + | 0.555646i | ||||
\(573\) | −15.7745 | + | 15.7745i | −0.658990 | + | 0.658990i | ||||
\(574\) | 11.6086 | 0.484532 | ||||||||
\(575\) | −7.45808 | − | 22.7898i | −0.311023 | − | 0.950402i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −5.16579 | + | 5.16579i | −0.215054 | + | 0.215054i | −0.806411 | − | 0.591356i | \(-0.798593\pi\) |
0.591356 | + | 0.806411i | \(0.298593\pi\) | |||||||
\(578\) | 8.00797 | + | 8.00797i | 0.333088 | + | 0.333088i | ||||
\(579\) | − | 17.7323i | − | 0.736929i | ||||||
\(580\) | 3.13136 | − | 7.12628i | 0.130022 | − | 0.295903i | ||||
\(581\) | −8.71549 | −0.361579 | ||||||||
\(582\) | 4.03278 | + | 4.03278i | 0.167164 | + | 0.167164i | ||||
\(583\) | −27.3568 | − | 27.3568i | −1.13300 | − | 1.13300i | ||||
\(584\) | − | 8.17754i | − | 0.338389i | ||||||
\(585\) | 3.65967 | + | 9.39683i | 0.151309 | + | 0.388511i | ||||
\(586\) | 30.3330i | 1.25305i | ||||||||
\(587\) | −3.80896 | + | 3.80896i | −0.157213 | + | 0.157213i | −0.781330 | − | 0.624118i | \(-0.785459\pi\) |
0.624118 | + | 0.781330i | \(0.285459\pi\) | |||||||
\(588\) | −0.321672 | − | 0.321672i | −0.0132655 | − | 0.0132655i | ||||
\(589\) | −38.1095 | −1.57028 | ||||||||
\(590\) | −14.1770 | + | 5.52136i | −0.583659 | + | 0.227311i | ||||
\(591\) | −2.86759 | −0.117957 | ||||||||
\(592\) | 5.46339 | + | 5.46339i | 0.224544 | + | 0.224544i | ||||
\(593\) | −1.75845 | − | 1.75845i | −0.0722109 | − | 0.0722109i | 0.670079 | − | 0.742290i | \(-0.266260\pi\) |
−0.742290 | + | 0.670079i | \(0.766260\pi\) | |||||||
\(594\) | −4.16725 | −0.170984 | ||||||||
\(595\) | −12.4765 | − | 5.48228i | −0.511485 | − | 0.224752i | ||||
\(596\) | 3.37276i | 0.138154i | ||||||||
\(597\) | −3.44834 | − | 3.44834i | −0.141131 | − | 0.141131i | ||||
\(598\) | 19.6910 | + | 8.94746i | 0.805223 | + | 0.365889i | ||||
\(599\) | − | 36.0972i | − | 1.47489i | −0.675407 | − | 0.737445i | \(-0.736032\pi\) | ||
0.675407 | − | 0.737445i | \(-0.263968\pi\) | |||||||
\(600\) | 3.68298 | − | 3.38166i | 0.150357 | − | 0.138056i | ||||
\(601\) | 24.9687 | 1.01849 | 0.509247 | − | 0.860620i | \(-0.329924\pi\) | ||||
0.509247 | + | 0.860620i | \(0.329924\pi\) | |||||||
\(602\) | −16.3188 | + | 16.3188i | −0.665105 | + | 0.665105i | ||||
\(603\) | 2.02126 | − | 2.02126i | 0.0823122 | − | 0.0823122i | ||||
\(604\) | 18.7035i | 0.761035i | ||||||||
\(605\) | 5.72643 | − | 13.0321i | 0.232813 | − | 0.529830i | ||||
\(606\) | −6.36488 | −0.258556 | ||||||||
\(607\) | −25.6608 | + | 25.6608i | −1.04154 | + | 1.04154i | −0.0424416 | + | 0.999099i | \(0.513514\pi\) |
−0.999099 | + | 0.0424416i | \(0.986486\pi\) | |||||||
\(608\) | −3.70595 | + | 3.70595i | −0.150296 | + | 0.150296i | ||||
\(609\) | −8.90575 | −0.360879 | ||||||||
\(610\) | 1.58201 | − | 0.616128i | 0.0640538 | − | 0.0249463i | ||||
\(611\) | 57.9968 | 2.34630 | ||||||||
\(612\) | −1.68449 | − | 1.68449i | −0.0680915 | − | 0.0680915i | ||||
\(613\) | 27.1716 | − | 27.1716i | 1.09745 | − | 1.09745i | 0.102742 | − | 0.994708i | \(-0.467238\pi\) |
0.994708 | − | 0.102742i | \(-0.0327615\pi\) | |||||||
\(614\) | 16.9709i | 0.684889i | ||||||||
\(615\) | −9.45453 | + | 3.68215i | −0.381243 | + | 0.148478i | ||||
\(616\) | −10.6612 | −0.429553 | ||||||||
\(617\) | 20.6665 | + | 20.6665i | 0.832002 | + | 0.832002i | 0.987790 | − | 0.155789i | \(-0.0497919\pi\) |
−0.155789 | + | 0.987790i | \(0.549792\pi\) | |||||||
\(618\) | 1.99918 | − | 1.99918i | 0.0804189 | − | 0.0804189i | ||||
\(619\) | −44.8826 | −1.80398 | −0.901991 | − | 0.431754i | \(-0.857895\pi\) | ||||
−0.901991 | + | 0.431754i | \(0.857895\pi\) | |||||||
\(620\) | 14.8857 | + | 6.54092i | 0.597824 | + | 0.262690i | ||||
\(621\) | −4.49027 | + | 1.68449i | −0.180188 | + | 0.0675963i | ||||
\(622\) | −1.10744 | + | 1.10744i | −0.0444043 | + | 0.0444043i | ||||
\(623\) | −6.49043 | − | 6.49043i | −0.260033 | − | 0.260033i | ||||
\(624\) | 4.50985i | 0.180538i | ||||||||
\(625\) | −2.12873 | + | 24.9092i | −0.0851494 | + | 0.996368i | ||||
\(626\) | − | 12.6534i | − | 0.505733i | ||||||
\(627\) | −15.4436 | + | 15.4436i | −0.616759 | + | 0.616759i | ||||
\(628\) | 11.8389 | − | 11.8389i | 0.472422 | − | 0.472422i | ||||
\(629\) | 18.4061i | 0.733897i | ||||||||
\(630\) | −5.23730 | − | 2.30132i | −0.208659 | − | 0.0916869i | ||||
\(631\) | − | 39.6759i | − | 1.57947i | −0.613448 | − | 0.789735i | \(-0.710218\pi\) | ||
0.613448 | − | 0.789735i | \(-0.289782\pi\) | |||||||
\(632\) | 4.84343 | + | 4.84343i | 0.192661 | + | 0.192661i | ||||
\(633\) | −7.38210 | − | 7.38210i | −0.293412 | − | 0.293412i | ||||
\(634\) | 11.9273i | 0.473695i | ||||||||
\(635\) | −8.17666 | − | 20.9949i | −0.324481 | − | 0.833159i | ||||
\(636\) | − | 9.28392i | − | 0.368131i | ||||||
\(637\) | −1.45069 | + | 1.45069i | −0.0574785 | + | 0.0574785i | ||||
\(638\) | 10.2576 | − | 10.2576i | 0.406104 | − | 0.406104i | ||||
\(639\) | − | 9.56406i | − | 0.378348i | ||||||
\(640\) | 2.08362 | − | 0.811485i | 0.0823625 | − | 0.0320768i | ||||
\(641\) | 20.9245i | 0.826466i | 0.910625 | + | 0.413233i | \(0.135601\pi\) | ||||
−0.910625 | + | 0.413233i | \(0.864399\pi\) | |||||||
\(642\) | 6.26821 | + | 6.26821i | 0.247387 | + | 0.247387i | ||||
\(643\) | −19.5758 | + | 19.5758i | −0.771994 | + | 0.771994i | −0.978455 | − | 0.206461i | \(-0.933805\pi\) |
0.206461 | + | 0.978455i | \(0.433805\pi\) | |||||||
\(644\) | −11.4876 | + | 4.30950i | −0.452675 | + | 0.169818i | ||||
\(645\) | 8.11457 | − | 18.4670i | 0.319511 | − | 0.727136i | ||||
\(646\) | −12.4853 | −0.491227 | ||||||||
\(647\) | 27.6953 | − | 27.6953i | 1.08881 | − | 1.08881i | 0.0931635 | − | 0.995651i | \(-0.470302\pi\) |
0.995651 | − | 0.0931635i | \(-0.0296979\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | −28.3541 | −1.11299 | ||||||||
\(650\) | −15.2508 | − | 16.6097i | −0.598185 | − | 0.651486i | ||||
\(651\) | − | 18.6027i | − | 0.729099i | ||||||
\(652\) | −8.37789 | + | 8.37789i | −0.328103 | + | 0.328103i | ||||
\(653\) | −22.7542 | − | 22.7542i | −0.890442 | − | 0.890442i | 0.104122 | − | 0.994564i | \(-0.466797\pi\) |
−0.994564 | + | 0.104122i | \(0.966797\pi\) | |||||||
\(654\) | 1.53597 | 0.0600611 | ||||||||
\(655\) | −1.78580 | + | 4.06409i | −0.0697771 | + | 0.158797i | ||||
\(656\) | −4.53754 | −0.177161 | ||||||||
\(657\) | 5.78239 | − | 5.78239i | 0.225593 | − | 0.225593i | ||||
\(658\) | −23.2640 | + | 23.2640i | −0.906927 | + | 0.906927i | ||||
\(659\) | −16.1643 | −0.629673 | −0.314837 | − | 0.949146i | \(-0.601950\pi\) | ||||
−0.314837 | + | 0.949146i | \(0.601950\pi\) | |||||||
\(660\) | 8.68298 | − | 3.38166i | 0.337985 | − | 0.131631i | ||||
\(661\) | 20.0621i | 0.780326i | 0.920746 | + | 0.390163i | \(0.127581\pi\) | ||||
−0.920746 | + | 0.390163i | \(0.872419\pi\) | |||||||
\(662\) | −9.15632 | + | 9.15632i | −0.355870 | + | 0.355870i | ||||
\(663\) | −7.59680 | + | 7.59680i | −0.295035 | + | 0.295035i | ||||
\(664\) | 3.40670 | 0.132206 | ||||||||
\(665\) | −27.9378 | + | 10.8806i | −1.08338 | + | 0.421932i | ||||
\(666\) | 7.72640i | 0.299392i | ||||||||
\(667\) | 6.90638 | − | 15.1991i | 0.267416 | − | 0.588511i | ||||
\(668\) | 13.2847 | + | 13.2847i | 0.514000 | + | 0.514000i | ||||
\(669\) | 16.8395i | 0.651052i | ||||||||
\(670\) | −2.57133 | + | 5.85178i | −0.0993391 | + | 0.226074i | ||||
\(671\) | 3.16403 | 0.122146 | ||||||||
\(672\) | −1.80902 | − | 1.80902i | −0.0697844 | − | 0.0697844i | ||||
\(673\) | −24.4850 | − | 24.4850i | −0.943829 | − | 0.943829i | 0.0546752 | − | 0.998504i | \(-0.482588\pi\) |
−0.998504 | + | 0.0546752i | \(0.982588\pi\) | |||||||
\(674\) | 6.72418 | 0.259006 | ||||||||
\(675\) | 4.99546 | + | 0.213067i | 0.192275 | + | 0.00820095i | ||||
\(676\) | 7.33872 | 0.282259 | ||||||||
\(677\) | 13.9941 | + | 13.9941i | 0.537836 | + | 0.537836i | 0.922893 | − | 0.385057i | \(-0.125818\pi\) |
−0.385057 | + | 0.922893i | \(0.625818\pi\) | |||||||
\(678\) | 14.0619 | − | 14.0619i | 0.540044 | − | 0.540044i | ||||
\(679\) | 14.5907i | 0.559942i | ||||||||
\(680\) | 4.87679 | + | 2.14291i | 0.187016 | + | 0.0821768i | ||||
\(681\) | − | 0.342612i | − | 0.0131289i | ||||||
\(682\) | 21.4266 | + | 21.4266i | 0.820468 | + | 0.820468i | ||||
\(683\) | 2.28231 | + | 2.28231i | 0.0873303 | + | 0.0873303i | 0.749422 | − | 0.662092i | \(-0.230331\pi\) |
−0.662092 | + | 0.749422i | \(0.730331\pi\) | |||||||
\(684\) | −5.24101 | −0.200395 | ||||||||
\(685\) | −40.3405 | + | 15.7109i | −1.54133 | + | 0.600284i | ||||
\(686\) | − | 19.0722i | − | 0.728179i | ||||||
\(687\) | 4.10563 | + | 4.10563i | 0.156639 | + | 0.156639i | ||||
\(688\) | 6.37868 | − | 6.37868i | 0.243185 | − | 0.243185i | ||||
\(689\) | −41.8691 | −1.59508 | ||||||||
\(690\) | 7.98909 | − | 7.15363i | 0.304139 | − | 0.272334i | ||||
\(691\) | 15.2845 | 0.581450 | 0.290725 | − | 0.956807i | \(-0.406103\pi\) | ||||
0.290725 | + | 0.956807i | \(0.406103\pi\) | |||||||
\(692\) | 13.3807 | − | 13.3807i | 0.508659 | − | 0.508659i | ||||
\(693\) | −7.53863 | − | 7.53863i | −0.286369 | − | 0.286369i | ||||
\(694\) | − | 4.41705i | − | 0.167669i | ||||||
\(695\) | 39.7805 | + | 17.4799i | 1.50896 | + | 0.663051i | ||||
\(696\) | 3.48107 | 0.131950 | ||||||||
\(697\) | −7.64345 | − | 7.64345i | −0.289516 | − | 0.289516i | ||||
\(698\) | 11.4160 | + | 11.4160i | 0.432101 | + | 0.432101i | ||||
\(699\) | − | 15.9696i | − | 0.604027i | ||||||
\(700\) | 12.7801 | + | 0.545097i | 0.483041 | + | 0.0206027i | ||||
\(701\) | − | 16.4549i | − | 0.621493i | −0.950493 | − | 0.310746i | \(-0.899421\pi\) | ||
0.950493 | − | 0.310746i | \(-0.100579\pi\) | |||||||
\(702\) | −3.18894 | + | 3.18894i | −0.120359 | + | 0.120359i | ||||
\(703\) | 28.6336 | + | 28.6336i | 1.07994 | + | 1.07994i | ||||
\(704\) | 4.16725 | 0.157059 | ||||||||
\(705\) | 11.5681 | − | 26.3265i | 0.435680 | − | 0.991512i | ||||
\(706\) | 14.4583 | 0.544146 | ||||||||
\(707\) | −11.5142 | − | 11.5142i | −0.433035 | − | 0.433035i | ||||
\(708\) | −4.81117 | − | 4.81117i | −0.180815 | − | 0.180815i | ||||
\(709\) | −45.9132 | −1.72431 | −0.862153 | − | 0.506648i | \(-0.830884\pi\) | ||||
−0.862153 | + | 0.506648i | \(0.830884\pi\) | |||||||
\(710\) | 7.76109 | + | 19.9279i | 0.291269 | + | 0.747881i | ||||
\(711\) | 6.84964i | 0.256882i | ||||||||
\(712\) | 2.53697 | + | 2.53697i | 0.0950770 | + | 0.0950770i | ||||
\(713\) | 31.7486 | + | 14.4264i | 1.18899 | + | 0.540272i | ||||
\(714\) | − | 6.09455i | − | 0.228083i | ||||||
\(715\) | −15.2508 | − | 39.1589i | −0.570347 | − | 1.46446i | ||||
\(716\) | −17.1255 | −0.640010 | ||||||||
\(717\) | 0.323564 | − | 0.323564i | 0.0120837 | − | 0.0120837i | ||||
\(718\) | 12.9314 | − | 12.9314i | 0.482594 | − | 0.482594i | ||||
\(719\) | 30.7995i | 1.14863i | 0.818635 | + | 0.574314i | \(0.194731\pi\) | ||||
−0.818635 | + | 0.574314i | \(0.805269\pi\) | |||||||
\(720\) | 2.04715 | + | 0.899538i | 0.0762928 | + | 0.0335238i | ||||
\(721\) | 7.23311 | 0.269375 | ||||||||
\(722\) | −5.98787 | + | 5.98787i | −0.222846 | + | 0.222846i | ||||
\(723\) | 15.7409 | − | 15.7409i | 0.585409 | − | 0.585409i | ||||
\(724\) | 7.02770 | 0.261183 | ||||||||
\(725\) | −12.8207 | + | 11.7718i | −0.476150 | + | 0.437194i | ||||
\(726\) | 6.36597 | 0.236263 | ||||||||
\(727\) | 14.2480 | + | 14.2480i | 0.528429 | + | 0.528429i | 0.920104 | − | 0.391674i | \(-0.128104\pi\) |
−0.391674 | + | 0.920104i | \(0.628104\pi\) | |||||||
\(728\) | −8.15839 | + | 8.15839i | −0.302370 | + | 0.302370i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −7.35601 | + | 16.7407i | −0.272258 | + | 0.619600i | ||||
\(731\) | 21.4897 | 0.794824 | ||||||||
\(732\) | 0.536878 | + | 0.536878i | 0.0198436 | + | 0.0198436i | ||||
\(733\) | 4.70374 | − | 4.70374i | 0.173737 | − | 0.173737i | −0.614882 | − | 0.788619i | \(-0.710797\pi\) |
0.788619 | + | 0.614882i | \(0.210797\pi\) | |||||||
\(734\) | −10.8419 | −0.400181 | ||||||||
\(735\) | 0.369155 | + | 0.947867i | 0.0136165 | + | 0.0349626i | ||||
\(736\) | 4.49027 | − | 1.68449i | 0.165513 | − | 0.0620912i | ||||
\(737\) | −8.42311 | + | 8.42311i | −0.310269 | + | 0.310269i | ||||
\(738\) | −3.20853 | − | 3.20853i | −0.118107 | − | 0.118107i | ||||
\(739\) | 35.3216i | 1.29932i | 0.760223 | + | 0.649662i | \(0.225090\pi\) | ||||
−0.760223 | + | 0.649662i | \(0.774910\pi\) | |||||||
\(740\) | −6.26986 | − | 16.0989i | −0.230484 | − | 0.591808i | ||||
\(741\) | 23.6361i | 0.868295i | ||||||||
\(742\) | 16.7948 | − | 16.7948i | 0.616556 | − | 0.616556i | ||||
\(743\) | 18.5881 | − | 18.5881i | 0.681932 | − | 0.681932i | −0.278503 | − | 0.960435i | \(-0.589838\pi\) |
0.960435 | + | 0.278503i | \(0.0898383\pi\) | |||||||
\(744\) | 7.27142i | 0.266583i | ||||||||
\(745\) | 3.03393 | − | 6.90455i | 0.111155 | − | 0.252963i | ||||
\(746\) | 26.8095i | 0.981564i | ||||||||
\(747\) | 2.40890 | + | 2.40890i | 0.0881371 | + | 0.0881371i | ||||
\(748\) | 7.01970 | + | 7.01970i | 0.256665 | + | 0.256665i | ||||
\(749\) | 22.6786i | 0.828658i | ||||||||
\(750\) | −10.5816 | + | 3.60979i | −0.386384 | + | 0.131811i | ||||
\(751\) | − | 23.3137i | − | 0.850727i | −0.905022 | − | 0.425364i | \(-0.860146\pi\) | ||
0.905022 | − | 0.425364i | \(-0.139854\pi\) | |||||||
\(752\) | 9.09342 | − | 9.09342i | 0.331603 | − | 0.331603i | ||||
\(753\) | −18.8845 | + | 18.8845i | −0.688191 | + | 0.688191i | ||||
\(754\) | − | 15.6991i | − | 0.571727i | ||||||
\(755\) | 16.8245 | − | 38.2889i | 0.612307 | − | 1.39348i | ||||
\(756\) | − | 2.55834i | − | 0.0930458i | ||||||
\(757\) | −3.52220 | − | 3.52220i | −0.128016 | − | 0.128016i | 0.640196 | − | 0.768212i | \(-0.278853\pi\) |
−0.768212 | + | 0.640196i | \(0.778853\pi\) | |||||||
\(758\) | −15.4646 | + | 15.4646i | −0.561699 | + | 0.561699i | ||||
\(759\) | 18.7121 | − | 7.01970i | 0.679205 | − | 0.254799i | ||||
\(760\) | 10.9203 | − | 4.25300i | 0.396120 | − | 0.154272i | ||||
\(761\) | −14.8262 | −0.537449 | −0.268724 | − | 0.963217i | \(-0.586602\pi\) | ||||
−0.268724 | + | 0.963217i | \(0.586602\pi\) | |||||||
\(762\) | 7.12493 | − | 7.12493i | 0.258109 | − | 0.258109i | ||||
\(763\) | 2.77859 | + | 2.77859i | 0.100592 | + | 0.100592i | ||||
\(764\) | 22.3085 | 0.807094 | ||||||||
\(765\) | 1.93314 | + | 4.96367i | 0.0698930 | + | 0.179462i | ||||
\(766\) | − | 29.1103i | − | 1.05180i | ||||||
\(767\) | −21.6976 | + | 21.6976i | −0.783456 | + | 0.783456i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −14.2891 | −0.515277 | −0.257638 | − | 0.966241i | \(-0.582944\pi\) | ||||
−0.257638 | + | 0.966241i | \(0.582944\pi\) | |||||||
\(770\) | 21.8252 | + | 9.59018i | 0.786524 | + | 0.345606i | ||||
\(771\) | −7.54946 | −0.271887 | ||||||||
\(772\) | −12.5386 | + | 12.5386i | −0.451275 | + | 0.451275i | ||||
\(773\) | 0.499292 | − | 0.499292i | 0.0179583 | − | 0.0179583i | −0.698071 | − | 0.716029i | \(-0.745958\pi\) |
0.716029 | + | 0.698071i | \(0.245958\pi\) | |||||||
\(774\) | 9.02081 | 0.324246 | ||||||||
\(775\) | −24.5895 | − | 26.7805i | −0.883280 | − | 0.961985i | ||||
\(776\) | − | 5.70322i | − | 0.204734i | ||||||
\(777\) | −13.9772 | + | 13.9772i | −0.501429 | + | 0.501429i | ||||
\(778\) | 1.91674 | − | 1.91674i | 0.0687184 | − | 0.0687184i | ||||
\(779\) | −23.7813 | −0.852052 | ||||||||
\(780\) | 4.05678 | − | 9.23234i | 0.145256 | − | 0.330571i | ||||
\(781\) | 39.8558i | 1.42615i | ||||||||
\(782\) | 10.4013 | + | 4.72630i | 0.371951 | + | 0.169012i | ||||
\(783\) | 2.46149 | + | 2.46149i | 0.0879664 | + | 0.0879664i | ||||
\(784\) | 0.454913i | 0.0162469i | ||||||||
\(785\) | −34.8855 | + | 13.5864i | −1.24512 | + | 0.484921i | ||||
\(786\) | −1.98524 | −0.0708113 | ||||||||
\(787\) | 3.26984 | + | 3.26984i | 0.116557 | + | 0.116557i | 0.762980 | − | 0.646422i | \(-0.223736\pi\) |
−0.646422 | + | 0.762980i | \(0.723736\pi\) | |||||||
\(788\) | 2.02769 | + | 2.02769i | 0.0722335 | + | 0.0722335i | ||||
\(789\) | 27.6060 | 0.982799 | ||||||||
\(790\) | −5.55838 | − | 14.2721i | −0.197758 | − | 0.507778i | ||||
\(791\) | 50.8765 | 1.80896 | ||||||||
\(792\) | 2.94669 | + | 2.94669i | 0.104706 | + | 0.104706i | ||||
\(793\) | 2.42124 | − | 2.42124i | 0.0859807 | − | 0.0859807i | ||||
\(794\) | 38.1181i | 1.35276i | ||||||||
\(795\) | −8.35125 | + | 19.0056i | −0.296188 | + | 0.674059i | ||||
\(796\) | 4.87669i | 0.172850i | ||||||||
\(797\) | −8.95785 | − | 8.95785i | −0.317303 | − | 0.317303i | 0.530427 | − | 0.847730i | \(-0.322032\pi\) |
−0.847730 | + | 0.530427i | \(0.822032\pi\) | |||||||
\(798\) | −9.48107 | − | 9.48107i | −0.335626 | − | 0.335626i | ||||
\(799\) | 30.6356 | 1.08381 | ||||||||
\(800\) | −4.99546 | − | 0.213067i | −0.176616 | − | 0.00753306i | ||||
\(801\) | 3.58782i | 0.126769i | ||||||||
\(802\) | 6.97483 | + | 6.97483i | 0.246290 | + | 0.246290i | ||||
\(803\) | −24.0967 | + | 24.0967i | −0.850353 | + | 0.850353i | ||||
\(804\) | −2.85850 | −0.100812 | ||||||||
\(805\) | 27.3934 | + | 1.51136i | 0.965492 | + | 0.0532683i | ||||
\(806\) | 32.7930 | 1.15508 | ||||||||
\(807\) | 3.10329 | − | 3.10329i | 0.109241 | − | 0.109241i | ||||
\(808\) | 4.50065 | + | 4.50065i | 0.158332 | + | 0.158332i | ||||
\(809\) | − | 24.1346i | − | 0.848529i | −0.905538 | − | 0.424264i | \(-0.860533\pi\) | ||
0.905538 | − | 0.424264i | \(-0.139467\pi\) | |||||||
\(810\) | 0.811485 | + | 2.08362i | 0.0285127 | + | 0.0732111i | ||||
\(811\) | −32.8187 | −1.15242 | −0.576210 | − | 0.817302i | \(-0.695469\pi\) | ||||
−0.576210 | + | 0.817302i | \(0.695469\pi\) | |||||||
\(812\) | 6.29731 | + | 6.29731i | 0.220992 | + | 0.220992i | ||||
\(813\) | 13.3660 | + | 13.3660i | 0.468765 | + | 0.468765i | ||||
\(814\) | − | 32.1978i | − | 1.12853i | ||||||
\(815\) | 24.6870 | − | 9.61458i | 0.864749 | − | 0.336784i | ||||
\(816\) | 2.38223i | 0.0833947i | ||||||||
\(817\) | 33.4307 | − | 33.4307i | 1.16959 | − | 1.16959i | ||||
\(818\) | −21.2786 | − | 21.2786i | −0.743990 | − | 0.743990i | ||||
\(819\) | −11.5377 | −0.403160 | ||||||||
\(820\) | 9.28903 | + | 4.08169i | 0.324387 | + | 0.142539i | ||||
\(821\) | −25.3607 | −0.885096 | −0.442548 | − | 0.896745i | \(-0.645925\pi\) | ||||
−0.442548 | + | 0.896745i | \(0.645925\pi\) | |||||||
\(822\) | −13.6901 | − | 13.6901i | −0.477497 | − | 0.477497i | ||||
\(823\) | −1.68756 | − | 1.68756i | −0.0588246 | − | 0.0588246i | 0.677083 | − | 0.735907i | \(-0.263244\pi\) |
−0.735907 | + | 0.677083i | \(0.763244\pi\) | |||||||
\(824\) | −2.82727 | −0.0984926 | ||||||||
\(825\) | −20.8173 | − | 0.887903i | −0.724766 | − | 0.0309128i | ||||
\(826\) | − | 17.4070i | − | 0.605666i | ||||||
\(827\) | −31.5597 | − | 31.5597i | −1.09744 | − | 1.09744i | −0.994709 | − | 0.102728i | \(-0.967243\pi\) |
−0.102728 | − | 0.994709i | \(-0.532757\pi\) | |||||||
\(828\) | 4.36621 | + | 1.98398i | 0.151736 | + | 0.0689482i | ||||
\(829\) | 25.2130i | 0.875684i | 0.899052 | + | 0.437842i | \(0.144257\pi\) | ||||
−0.899052 | + | 0.437842i | \(0.855743\pi\) | |||||||
\(830\) | −6.97403 | − | 3.06446i | −0.242072 | − | 0.106369i | ||||
\(831\) | 3.45666 | 0.119910 | ||||||||
\(832\) | 3.18894 | − | 3.18894i | 0.110557 | − | 0.110557i | ||||
\(833\) | −0.766297 | + | 0.766297i | −0.0265506 | + | 0.0265506i | ||||
\(834\) | 19.4321i | 0.672878i | ||||||||
\(835\) | −15.2457 | − | 39.1459i | −0.527599 | − | 1.35470i | ||||
\(836\) | 21.8406 | 0.755372 | ||||||||
\(837\) | −5.14167 | + | 5.14167i | −0.177722 | + | 0.177722i | ||||
\(838\) | −5.37137 | + | 5.37137i | −0.185551 | + | 0.185551i | ||||
\(839\) | −3.96404 | −0.136854 | −0.0684270 | − | 0.997656i | \(-0.521798\pi\) | ||||
−0.0684270 | + | 0.997656i | \(0.521798\pi\) | |||||||
\(840\) | 2.07605 | + | 5.33061i | 0.0716306 | + | 0.183924i | ||||
\(841\) | 16.8822 | 0.582143 | ||||||||
\(842\) | 16.5925 | + | 16.5925i | 0.571816 | + | 0.571816i | ||||
\(843\) | −1.65338 | + | 1.65338i | −0.0569454 | + | 0.0569454i | ||||
\(844\) | 10.4399i | 0.359355i | ||||||||
\(845\) | −15.0235 | − | 6.60146i | −0.516824 | − | 0.227097i | ||||
\(846\) | 12.8600 | 0.442137 | ||||||||
\(847\) | 11.5161 | + | 11.5161i | 0.395699 | + | 0.395699i | ||||
\(848\) | −6.56472 | + | 6.56472i | −0.225434 | + | 0.225434i | ||||
\(849\) | 30.5657 | 1.04901 | ||||||||
\(850\) | −8.05590 | − | 8.77372i | −0.276315 | − | 0.300936i | ||||
\(851\) | −13.0150 | − | 34.6936i | −0.446150 | − | 1.18928i | ||||
\(852\) | −6.76281 | + | 6.76281i | −0.231690 | + | 0.231690i | ||||
\(853\) | −1.04985 | − | 1.04985i | −0.0359460 | − | 0.0359460i | 0.688905 | − | 0.724851i | \(-0.258092\pi\) |
−0.724851 | + | 0.688905i | \(0.758092\pi\) | |||||||
\(854\) | 1.94244i | 0.0664690i | ||||||||
\(855\) | 10.7291 | + | 4.71449i | 0.366929 | + | 0.161232i | ||||
\(856\) | − | 8.86459i | − | 0.302985i | ||||||
\(857\) | 38.2391 | − | 38.2391i | 1.30622 | − | 1.30622i | 0.382104 | − | 0.924119i | \(-0.375200\pi\) |
0.924119 | − | 0.382104i | \(-0.124800\pi\) | |||||||
\(858\) | 13.2891 | − | 13.2891i | 0.453683 | − | 0.453683i | ||||
\(859\) | − | 0.796740i | − | 0.0271844i | −0.999908 | − | 0.0135922i | \(-0.995673\pi\) | ||
0.999908 | − | 0.0135922i | \(-0.00432667\pi\) | |||||||
\(860\) | −18.7960 | + | 7.32026i | −0.640938 | + | 0.249619i | ||||
\(861\) | − | 11.6086i | − | 0.395619i | ||||||
\(862\) | −15.4141 | − | 15.4141i | −0.525005 | − | 0.525005i | ||||
\(863\) | −16.3964 | − | 16.3964i | −0.558140 | − | 0.558140i | 0.370637 | − | 0.928778i | \(-0.379139\pi\) |
−0.928778 | + | 0.370637i | \(0.879139\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | −39.4289 | + | 15.3559i | −1.34062 | + | 0.522116i | ||||
\(866\) | 24.1675i | 0.821245i | ||||||||
\(867\) | 8.00797 | − | 8.00797i | 0.271965 | − | 0.271965i | ||||
\(868\) | −13.1541 | + | 13.1541i | −0.446480 | + | 0.446480i | ||||
\(869\) | − | 28.5442i | − | 0.968295i | ||||||
\(870\) | −7.12628 | − | 3.13136i | −0.241603 | − | 0.106163i | ||||
\(871\) | 12.8914i | 0.436808i | ||||||||
\(872\) | −1.08609 | − | 1.08609i | −0.0367797 | − | 0.0367797i | ||||
\(873\) | 4.03278 | − | 4.03278i | 0.136489 | − | 0.136489i | ||||
\(874\) | 23.5335 | − | 8.82843i | 0.796033 | − | 0.298626i | ||||
\(875\) | −25.6724 | − | 12.6121i | −0.867885 | − | 0.426365i | ||||
\(876\) | −8.17754 | −0.276293 | ||||||||
\(877\) | 29.9674 | − | 29.9674i | 1.01193 | − | 1.01193i | 0.0119983 | − | 0.999928i | \(-0.496181\pi\) |
0.999928 | − | 0.0119983i | \(-0.00381927\pi\) | |||||||
\(878\) | −13.1793 | − | 13.1793i | −0.444781 | − | 0.444781i | ||||
\(879\) | 30.3330 | 1.02311 | ||||||||
\(880\) | −8.53099 | − | 3.74860i | −0.287580 | − | 0.126365i | ||||
\(881\) | − | 5.14908i | − | 0.173477i | −0.996231 | − | 0.0867384i | \(-0.972356\pi\) | ||
0.996231 | − | 0.0867384i | \(-0.0276444\pi\) | |||||||
\(882\) | −0.321672 | + | 0.321672i | −0.0108313 | + | 0.0108313i | ||||
\(883\) | 24.2836 | + | 24.2836i | 0.817207 | + | 0.817207i | 0.985702 | − | 0.168495i | \(-0.0538908\pi\) |
−0.168495 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(884\) | 10.7435 | 0.361343 | ||||||||
\(885\) | 5.52136 | + | 14.1770i | 0.185599 | + | 0.476556i | ||||
\(886\) | −10.3595 | −0.348034 | ||||||||
\(887\) | −11.6259 | + | 11.6259i | −0.390358 | + | 0.390358i | −0.874815 | − | 0.484457i | \(-0.839017\pi\) |
0.484457 | + | 0.874815i | \(0.339017\pi\) | |||||||
\(888\) | 5.46339 | − | 5.46339i | 0.183339 | − | 0.183339i | ||||
\(889\) | 25.7782 | 0.864574 | ||||||||
\(890\) | −2.91146 | − | 7.47567i | −0.0975924 | − | 0.250585i | ||||
\(891\) | 4.16725i | 0.139608i | ||||||||
\(892\) | 11.9073 | − | 11.9073i | 0.398686 | − | 0.398686i | ||||
\(893\) | 47.6587 | − | 47.6587i | 1.59484 | − | 1.59484i | ||||
\(894\) | 3.37276 | 0.112802 | ||||||||
\(895\) | 35.0585 | + | 15.4050i | 1.17188 | + | 0.514934i | ||||
\(896\) | 2.55834i | 0.0854680i | ||||||||
\(897\) | 8.94746 | − | 19.6910i | 0.298747 | − | 0.657462i | ||||
\(898\) | 9.17153 | + | 9.17153i | 0.306058 | + | 0.306058i | ||||
\(899\) | − | 25.3123i | − | 0.844213i | ||||||
\(900\) | −3.38166 | − | 3.68298i | −0.112722 | − | 0.122766i | ||||
\(901\) | −22.1164 | −0.736806 | ||||||||
\(902\) | 13.3707 | + | 13.3707i | 0.445196 | + | 0.445196i | ||||
\(903\) | 16.3188 | + | 16.3188i | 0.543056 | + | 0.543056i | ||||
\(904\) | −19.8865 | −0.661417 | ||||||||
\(905\) | −14.3868 | − | 6.32169i | −0.478233 | − | 0.210140i | ||||
\(906\) | 18.7035 | 0.621383 | ||||||||
\(907\) | 5.83912 | + | 5.83912i | 0.193885 | + | 0.193885i | 0.797372 | − | 0.603488i | \(-0.206223\pi\) |
−0.603488 | + | 0.797372i | \(0.706223\pi\) | |||||||
\(908\) | −0.242263 | + | 0.242263i | −0.00803978 | + | 0.00803978i | ||||
\(909\) | 6.36488i | 0.211110i | ||||||||
\(910\) | 24.0403 | − | 9.36268i | 0.796927 | − | 0.310370i | ||||
\(911\) | 34.0829i | 1.12922i | 0.825359 | + | 0.564608i | \(0.190973\pi\) | ||||
−0.825359 | + | 0.564608i | \(0.809027\pi\) | |||||||
\(912\) | 3.70595 | + | 3.70595i | 0.122716 | + | 0.122716i | ||||
\(913\) | −10.0385 | − | 10.0385i | −0.332225 | − | 0.332225i | ||||
\(914\) | 38.8062 | 1.28360 | ||||||||
\(915\) | −0.616128 | − | 1.58201i | −0.0203686 | − | 0.0522997i | ||||
\(916\) | − | 5.80623i | − | 0.191843i | ||||||
\(917\) | −3.59134 | − | 3.59134i | −0.118596 | − | 0.118596i | ||||
\(918\) | −1.68449 | + | 1.68449i | −0.0555965 | + | 0.0555965i | ||||
\(919\) | −19.5882 | −0.646154 | −0.323077 | − | 0.946373i | \(-0.604717\pi\) | ||||
−0.323077 | + | 0.946373i | \(0.604717\pi\) | |||||||
\(920\) | −10.7075 | − | 0.590758i | −0.353017 | − | 0.0194767i | ||||
\(921\) | 16.9709 | 0.559210 | ||||||||
\(922\) | −7.21726 | + | 7.21726i | −0.237688 | + | 0.237688i | ||||
\(923\) | 30.4992 | + | 30.4992i | 1.00389 | + | 1.00389i | ||||
\(924\) | 10.6612i | 0.350729i | ||||||||
\(925\) | −1.64624 | + | 38.5969i | −0.0541280 | + | 1.26906i | ||||
\(926\) | 11.5102 | 0.378249 | ||||||||
\(927\) | −1.99918 | − | 1.99918i | −0.0656617 | − | 0.0656617i | ||||
\(928\) | −2.46149 | − | 2.46149i | −0.0808023 | − | 0.0808023i | ||||
\(929\) | − | 1.07470i | − | 0.0352599i | −0.999845 | − | 0.0176300i | \(-0.994388\pi\) | ||
0.999845 | − | 0.0176300i | \(-0.00561208\pi\) | |||||||
\(930\) | 6.54092 | − | 14.8857i | 0.214485 | − | 0.488121i | ||||
\(931\) | 2.38420i | 0.0781390i | ||||||||
\(932\) | −11.2922 | + | 11.2922i | −0.369890 | + | 0.369890i | ||||
\(933\) | 1.10744 | + | 1.10744i | 0.0362560 | + | 0.0362560i | ||||
\(934\) | 29.6273 | 0.969434 | ||||||||
\(935\) | −8.05590 | − | 20.6849i | −0.263456 | − | 0.676467i | ||||
\(936\) | 4.50985 | 0.147409 | ||||||||
\(937\) | 29.4635 | + | 29.4635i | 0.962529 | + | 0.962529i | 0.999323 | − | 0.0367936i | \(-0.0117144\pi\) |
−0.0367936 | + | 0.999323i | \(0.511714\pi\) | |||||||
\(938\) | −5.17107 | − | 5.17107i | −0.168842 | − | 0.168842i | ||||
\(939\) | −12.6534 | −0.412929 | ||||||||
\(940\) | −26.7955 | + | 10.4357i | −0.873973 | + | 0.340376i | ||||
\(941\) | 6.28427i | 0.204861i | 0.994740 | + | 0.102431i | \(0.0326620\pi\) | ||||
−0.994740 | + | 0.102431i | \(0.967338\pi\) | |||||||
\(942\) | −11.8389 | − | 11.8389i | −0.385731 | − | 0.385731i | ||||
\(943\) | 19.8119 | + | 9.00240i | 0.645163 | + | 0.293158i | ||||
\(944\) | 6.80402i | 0.221452i | ||||||||
\(945\) | −2.30132 | + | 5.23730i | −0.0748620 | + | 0.170370i | ||||
\(946\) | −37.5920 | −1.22222 | ||||||||
\(947\) | 5.48123 | − | 5.48123i | 0.178116 | − | 0.178116i | −0.612418 | − | 0.790534i | \(-0.709803\pi\) |
0.790534 | + | 0.612418i | \(0.209803\pi\) | |||||||
\(948\) | 4.84343 | − | 4.84343i | 0.157307 | − | 0.157307i | ||||
\(949\) | 36.8794i | 1.19716i | ||||||||
\(950\) | −26.1812 | − | 1.11669i | −0.849431 | − | 0.0362301i | ||||
\(951\) | 11.9273 | 0.386771 | ||||||||
\(952\) | −4.30950 | + | 4.30950i | −0.139672 | + | 0.139672i | ||||
\(953\) | −13.7402 | + | 13.7402i | −0.445088 | + | 0.445088i | −0.893718 | − | 0.448630i | \(-0.851912\pi\) |
0.448630 | + | 0.893718i | \(0.351912\pi\) | |||||||
\(954\) | −9.28392 | −0.300578 | ||||||||
\(955\) | −45.6690 | − | 20.0674i | −1.47781 | − | 0.649365i | ||||
\(956\) | −0.457589 | −0.0147995 | ||||||||
\(957\) | −10.2576 | − | 10.2576i | −0.331582 | − | 0.331582i | ||||
\(958\) | −16.5508 | + | 16.5508i | −0.534733 | + | 0.534733i | ||||
\(959\) | − | 49.5312i | − | 1.59945i | ||||||
\(960\) | −0.811485 | − | 2.08362i | −0.0261906 | − | 0.0672487i | ||||
\(961\) | 21.8735 | 0.705598 | ||||||||
\(962\) | −24.6390 | − | 24.6390i | −0.794395 | − | 0.794395i | ||||
\(963\) | 6.26821 | − | 6.26821i | 0.201990 | − | 0.201990i | ||||
\(964\) | −22.2609 | −0.716976 | ||||||||
\(965\) | 36.9474 | − | 14.3895i | 1.18938 | − | 0.463214i | ||||
\(966\) | 4.30950 | + | 11.4876i | 0.138656 | + | 0.369608i | ||||
\(967\) | −15.7735 | + | 15.7735i | −0.507243 | + | 0.507243i | −0.913679 | − | 0.406436i | \(-0.866771\pi\) |
0.406436 | + | 0.913679i | \(0.366771\pi\) | |||||||
\(968\) | −4.50142 | − | 4.50142i | −0.144681 | − | 0.144681i | ||||
\(969\) | 12.4853i | 0.401085i | ||||||||
\(970\) | −5.13026 | + | 11.6753i | −0.164723 | + | 0.374873i | ||||
\(971\) | − | 45.2891i | − | 1.45340i | −0.686957 | − | 0.726698i | \(-0.741054\pi\) | ||
0.686957 | − | 0.726698i | \(-0.258946\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −35.1530 | + | 35.1530i | −1.12695 | + | 1.12695i | ||||
\(974\) | 32.4397i | 1.03943i | ||||||||
\(975\) | −16.6097 | + | 15.2508i | −0.531936 | + | 0.488416i | ||||
\(976\) | − | 0.759260i | − | 0.0243033i | ||||||
\(977\) | −35.2043 | − | 35.2043i | −1.12629 | − | 1.12629i | −0.990776 | − | 0.135511i | \(-0.956732\pi\) |
−0.135511 | − | 0.990776i | \(-0.543268\pi\) | |||||||
\(978\) | 8.37789 | + | 8.37789i | 0.267895 | + | 0.267895i | ||||
\(979\) | − | 14.9513i | − | 0.477847i | ||||||
\(980\) | 0.409211 | − | 0.931275i | 0.0130718 | − | 0.0297485i | ||||
\(981\) | − | 1.53597i | − | 0.0490396i | ||||||
\(982\) | −21.8056 | + | 21.8056i | −0.695844 | + | 0.695844i | ||||
\(983\) | 15.7468 | − | 15.7468i | 0.502245 | − | 0.502245i | −0.409890 | − | 0.912135i | \(-0.634433\pi\) |
0.912135 | + | 0.409890i | \(0.134433\pi\) | |||||||
\(984\) | 4.53754i | 0.144651i | ||||||||
\(985\) | −2.32701 | − | 5.97498i | −0.0741446 | − | 0.190379i | ||||
\(986\) | − | 8.29271i | − | 0.264094i | ||||||
\(987\) | 23.2640 | + | 23.2640i | 0.740503 | + | 0.740503i | ||||
\(988\) | 16.7133 | − | 16.7133i | 0.531720 | − | 0.531720i | ||||
\(989\) | −40.5059 | + | 15.1955i | −1.28801 | + | 0.483188i | ||||
\(990\) | −3.38166 | − | 8.68298i | −0.107476 | − | 0.275963i | ||||
\(991\) | 8.94505 | 0.284149 | 0.142074 | − | 0.989856i | \(-0.454623\pi\) | ||||
0.142074 | + | 0.989856i | \(0.454623\pi\) | |||||||
\(992\) | 5.14167 | − | 5.14167i | 0.163248 | − | 0.163248i | ||||
\(993\) | 9.15632 | + | 9.15632i | 0.290567 | + | 0.290567i | ||||
\(994\) | −24.4681 | −0.776080 | ||||||||
\(995\) | 4.38677 | − | 9.98332i | 0.139070 | − | 0.316493i | ||||
\(996\) | − | 3.40670i | − | 0.107945i | ||||||
\(997\) | −0.677346 | + | 0.677346i | −0.0214518 | + | 0.0214518i | −0.717751 | − | 0.696300i | \(-0.754829\pi\) |
0.696300 | + | 0.717751i | \(0.254829\pi\) | |||||||
\(998\) | −18.0239 | − | 18.0239i | −0.570537 | − | 0.570537i | ||||
\(999\) | 7.72640 | 0.244452 |
(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 | 690.2.j.a.643.2 | yes | 24 | |
5.2 | odd | 4 | inner | 690.2.j.a.367.5 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.a.643.5 | yes | 24 | |
115.22 | even | 4 | inner | 690.2.j.a.367.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.a.367.2 | ✓ | 24 | 115.22 | even | 4 | inner | |
690.2.j.a.367.5 | yes | 24 | 5.2 | odd | 4 | inner | |
690.2.j.a.643.2 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.a.643.5 | yes | 24 | 23.22 | odd | 2 | inner |