Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(379,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.17 | ||
Character | \(\chi\) | \(=\) | 380.379 |
Dual form | 380.2.d.b.379.20 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.440015 | − | 1.34402i | −0.311137 | − | 0.950365i | ||||
\(3\) | − | 0.562756i | − | 0.324908i | −0.986716 | − | 0.162454i | \(-0.948059\pi\) | ||
0.986716 | − | 0.162454i | \(-0.0519408\pi\) | |||||||
\(4\) | −1.61277 | + | 1.18278i | −0.806387 | + | 0.591388i | ||||
\(5\) | 1.40743 | − | 1.73757i | 0.629421 | − | 0.777065i | ||||
\(6\) | −0.756355 | + | 0.247621i | −0.308781 | + | 0.101091i | ||||
\(7\) | 3.12767 | 1.18215 | 0.591075 | − | 0.806617i | \(-0.298704\pi\) | ||||
0.591075 | + | 0.806617i | \(0.298704\pi\) | |||||||
\(8\) | 2.29932 | + | 1.64716i | 0.812932 | + | 0.582359i | ||||
\(9\) | 2.68331 | 0.894435 | ||||||||
\(10\) | −2.95462 | − | 1.12705i | −0.934331 | − | 0.356405i | ||||
\(11\) | 3.83819i | 1.15726i | 0.815591 | + | 0.578629i | \(0.196412\pi\) | ||||
−0.815591 | + | 0.578629i | \(0.803588\pi\) | |||||||
\(12\) | 0.665615 | + | 0.907599i | 0.192147 | + | 0.262001i | ||||
\(13\) | 2.34421 | 0.650166 | 0.325083 | − | 0.945685i | \(-0.394608\pi\) | ||||
0.325083 | + | 0.945685i | \(0.394608\pi\) | |||||||
\(14\) | −1.37622 | − | 4.20365i | −0.367811 | − | 1.12347i | ||||
\(15\) | −0.977829 | − | 0.792039i | −0.252474 | − | 0.204504i | ||||
\(16\) | 1.20208 | − | 3.81510i | 0.300520 | − | 0.953775i | ||||
\(17\) | − | 0.296420i | − | 0.0718924i | −0.999354 | − | 0.0359462i | \(-0.988556\pi\) | ||
0.999354 | − | 0.0359462i | \(-0.0114445\pi\) | |||||||
\(18\) | −1.18069 | − | 3.60641i | −0.278292 | − | 0.850040i | ||||
\(19\) | −4.35567 | + | 0.167855i | −0.999258 | + | 0.0385086i | ||||
\(20\) | −0.214705 | + | 4.46698i | −0.0480096 | + | 0.998847i | ||||
\(21\) | − | 1.76012i | − | 0.384089i | ||||||
\(22\) | 5.15860 | − | 1.68886i | 1.09982 | − | 0.360066i | ||||
\(23\) | −5.14271 | −1.07233 | −0.536164 | − | 0.844114i | \(-0.680127\pi\) | ||||
−0.536164 | + | 0.844114i | \(0.680127\pi\) | |||||||
\(24\) | 0.926950 | − | 1.29396i | 0.189213 | − | 0.264128i | ||||
\(25\) | −1.03830 | − | 4.89101i | −0.207660 | − | 0.978201i | ||||
\(26\) | −1.03149 | − | 3.15066i | −0.202291 | − | 0.617895i | ||||
\(27\) | − | 3.19832i | − | 0.615516i | ||||||
\(28\) | −5.04423 | + | 3.69934i | −0.953270 | + | 0.699109i | ||||
\(29\) | − | 6.81132i | − | 1.26483i | −0.774630 | − | 0.632415i | \(-0.782064\pi\) | ||
0.774630 | − | 0.632415i | \(-0.217936\pi\) | |||||||
\(30\) | −0.634256 | + | 1.66273i | −0.115799 | + | 0.303571i | ||||
\(31\) | 4.76184 | 0.855251 | 0.427626 | − | 0.903956i | \(-0.359350\pi\) | ||||
0.427626 | + | 0.903956i | \(0.359350\pi\) | |||||||
\(32\) | −5.65650 | + | 0.0630825i | −0.999938 | + | 0.0111515i | ||||
\(33\) | 2.15997 | 0.376002 | ||||||||
\(34\) | −0.398394 | + | 0.130429i | −0.0683240 | + | 0.0223684i | ||||
\(35\) | 4.40197 | − | 5.43455i | 0.744069 | − | 0.918607i | ||||
\(36\) | −4.32756 | + | 3.17375i | −0.721261 | + | 0.528958i | ||||
\(37\) | 1.81573 | 0.298503 | 0.149252 | − | 0.988799i | \(-0.452314\pi\) | ||||
0.149252 | + | 0.988799i | \(0.452314\pi\) | |||||||
\(38\) | 2.14216 | + | 5.78024i | 0.347504 | + | 0.937679i | ||||
\(39\) | − | 1.31922i | − | 0.211244i | ||||||
\(40\) | 6.09818 | − | 1.67697i | 0.964207 | − | 0.265152i | ||||
\(41\) | 12.0637i | 1.88403i | 0.335571 | + | 0.942015i | \(0.391071\pi\) | ||||
−0.335571 | + | 0.942015i | \(0.608929\pi\) | |||||||
\(42\) | −2.36563 | + | 0.774478i | −0.365025 | + | 0.119505i | ||||
\(43\) | 0.171877 | 0.0262110 | 0.0131055 | − | 0.999914i | \(-0.495828\pi\) | ||||
0.0131055 | + | 0.999914i | \(0.495828\pi\) | |||||||
\(44\) | −4.53972 | − | 6.19014i | −0.684389 | − | 0.933198i | ||||
\(45\) | 3.77656 | − | 4.66243i | 0.562976 | − | 0.695034i | ||||
\(46\) | 2.26287 | + | 6.91190i | 0.333642 | + | 1.01910i | ||||
\(47\) | −6.96079 | −1.01534 | −0.507668 | − | 0.861553i | \(-0.669492\pi\) | ||||
−0.507668 | + | 0.861553i | \(0.669492\pi\) | |||||||
\(48\) | −2.14697 | − | 0.676478i | −0.309889 | − | 0.0976412i | ||||
\(49\) | 2.78234 | 0.397477 | ||||||||
\(50\) | −6.11674 | + | 3.54761i | −0.865037 | + | 0.501707i | ||||
\(51\) | −0.166812 | −0.0233584 | ||||||||
\(52\) | −3.78068 | + | 2.77267i | −0.524285 | + | 0.384501i | ||||
\(53\) | −11.1028 | −1.52508 | −0.762542 | − | 0.646939i | \(-0.776049\pi\) | ||||
−0.762542 | + | 0.646939i | \(0.776049\pi\) | |||||||
\(54\) | −4.29860 | + | 1.40731i | −0.584965 | + | 0.191510i | ||||
\(55\) | 6.66913 | + | 5.40198i | 0.899265 | + | 0.728402i | ||||
\(56\) | 7.19152 | + | 5.15178i | 0.961007 | + | 0.688435i | ||||
\(57\) | 0.0944615 | + | 2.45118i | 0.0125117 | + | 0.324667i | ||||
\(58\) | −9.15454 | + | 2.99708i | −1.20205 | + | 0.393536i | ||||
\(59\) | −7.33191 | −0.954534 | −0.477267 | − | 0.878758i | \(-0.658373\pi\) | ||||
−0.477267 | + | 0.878758i | \(0.658373\pi\) | |||||||
\(60\) | 2.51382 | + | 0.120827i | 0.324533 | + | 0.0155987i | ||||
\(61\) | 3.27261 | 0.419015 | 0.209507 | − | 0.977807i | \(-0.432814\pi\) | ||||
0.209507 | + | 0.977807i | \(0.432814\pi\) | |||||||
\(62\) | −2.09528 | − | 6.40000i | −0.266101 | − | 0.812801i | ||||
\(63\) | 8.39250 | 1.05736 | ||||||||
\(64\) | 2.57373 | + | 7.57469i | 0.321716 | + | 0.946836i | ||||
\(65\) | 3.29930 | − | 4.07322i | 0.409228 | − | 0.505221i | ||||
\(66\) | −0.950418 | − | 2.90304i | −0.116988 | − | 0.357339i | ||||
\(67\) | 9.46955i | 1.15689i | 0.815722 | + | 0.578445i | \(0.196340\pi\) | ||||
−0.815722 | + | 0.578445i | \(0.803660\pi\) | |||||||
\(68\) | 0.350598 | + | 0.478058i | 0.0425163 | + | 0.0579731i | ||||
\(69\) | 2.89409i | 0.348408i | ||||||||
\(70\) | −9.24107 | − | 3.52505i | −1.10452 | − | 0.421324i | ||||
\(71\) | 9.45438 | 1.12203 | 0.561014 | − | 0.827806i | \(-0.310411\pi\) | ||||
0.561014 | + | 0.827806i | \(0.310411\pi\) | |||||||
\(72\) | 6.16977 | + | 4.41983i | 0.727115 | + | 0.520882i | ||||
\(73\) | − | 8.23306i | − | 0.963606i | −0.876279 | − | 0.481803i | \(-0.839982\pi\) | ||
0.876279 | − | 0.481803i | \(-0.160018\pi\) | |||||||
\(74\) | −0.798946 | − | 2.44037i | −0.0928756 | − | 0.283687i | ||||
\(75\) | −2.75245 | + | 0.584309i | −0.317825 | + | 0.0674702i | ||||
\(76\) | 6.82617 | − | 5.42249i | 0.783015 | − | 0.622002i | ||||
\(77\) | 12.0046i | 1.36805i | ||||||||
\(78\) | −1.77305 | + | 0.580475i | −0.200759 | + | 0.0657259i | ||||
\(79\) | 7.49873 | 0.843673 | 0.421836 | − | 0.906672i | \(-0.361386\pi\) | ||||
0.421836 | + | 0.906672i | \(0.361386\pi\) | |||||||
\(80\) | −4.93717 | − | 7.45818i | −0.551992 | − | 0.833849i | ||||
\(81\) | 6.25004 | 0.694449 | ||||||||
\(82\) | 16.2138 | − | 5.30820i | 1.79052 | − | 0.586192i | ||||
\(83\) | −6.37747 | −0.700018 | −0.350009 | − | 0.936746i | \(-0.613821\pi\) | ||||
−0.350009 | + | 0.936746i | \(0.613821\pi\) | |||||||
\(84\) | 2.08183 | + | 2.83867i | 0.227146 | + | 0.309725i | ||||
\(85\) | −0.515050 | − | 0.417189i | −0.0558650 | − | 0.0452505i | ||||
\(86\) | −0.0756284 | − | 0.231006i | −0.00815522 | − | 0.0249100i | ||||
\(87\) | −3.83311 | −0.410953 | ||||||||
\(88\) | −6.32212 | + | 8.82523i | −0.673940 | + | 0.940772i | ||||
\(89\) | − | 3.49224i | − | 0.370176i | −0.982722 | − | 0.185088i | \(-0.940743\pi\) | ||
0.982722 | − | 0.185088i | \(-0.0592571\pi\) | |||||||
\(90\) | −7.92814 | − | 3.02423i | −0.835699 | − | 0.318781i | ||||
\(91\) | 7.33191 | 0.768594 | ||||||||
\(92\) | 8.29403 | − | 6.08267i | 0.864712 | − | 0.634163i | ||||
\(93\) | − | 2.67975i | − | 0.277878i | ||||||
\(94\) | 3.06285 | + | 9.35543i | 0.315909 | + | 0.964939i | ||||
\(95\) | −5.83862 | + | 7.80452i | −0.599030 | + | 0.800727i | ||||
\(96\) | 0.0355001 | + | 3.18323i | 0.00362321 | + | 0.324887i | ||||
\(97\) | −11.9154 | −1.20983 | −0.604913 | − | 0.796292i | \(-0.706792\pi\) | ||||
−0.604913 | + | 0.796292i | \(0.706792\pi\) | |||||||
\(98\) | −1.22427 | − | 3.73952i | −0.123670 | − | 0.377749i | ||||
\(99\) | 10.2990i | 1.03509i | ||||||||
\(100\) | 7.45951 | + | 6.66001i | 0.745951 | + | 0.666001i | ||||
\(101\) | −6.01740 | −0.598754 | −0.299377 | − | 0.954135i | \(-0.596779\pi\) | ||||
−0.299377 | + | 0.954135i | \(0.596779\pi\) | |||||||
\(102\) | 0.0733998 | + | 0.224199i | 0.00726767 | + | 0.0221990i | ||||
\(103\) | 0.989632i | 0.0975113i | 0.998811 | + | 0.0487557i | \(0.0155256\pi\) | ||||
−0.998811 | + | 0.0487557i | \(0.984474\pi\) | |||||||
\(104\) | 5.39008 | + | 3.86128i | 0.528541 | + | 0.378630i | ||||
\(105\) | −3.05833 | − | 2.47724i | −0.298462 | − | 0.241754i | ||||
\(106\) | 4.88539 | + | 14.9223i | 0.474511 | + | 1.44939i | ||||
\(107\) | − | 9.95699i | − | 0.962578i | −0.876562 | − | 0.481289i | \(-0.840169\pi\) | ||
0.876562 | − | 0.481289i | \(-0.159831\pi\) | |||||||
\(108\) | 3.78289 | + | 5.15816i | 0.364009 | + | 0.496344i | ||||
\(109\) | 13.9205i | 1.33334i | 0.745351 | + | 0.666672i | \(0.232282\pi\) | ||||
−0.745351 | + | 0.666672i | \(0.767718\pi\) | |||||||
\(110\) | 4.32584 | − | 11.3404i | 0.412453 | − | 1.08126i | ||||
\(111\) | − | 1.02181i | − | 0.0969860i | ||||||
\(112\) | 3.75971 | − | 11.9324i | 0.355260 | − | 1.12751i | ||||
\(113\) | 18.4958 | 1.73993 | 0.869967 | − | 0.493110i | \(-0.164140\pi\) | ||||
0.869967 | + | 0.493110i | \(0.164140\pi\) | |||||||
\(114\) | 3.25287 | − | 1.20551i | 0.304659 | − | 0.112907i | ||||
\(115\) | −7.23799 | + | 8.93581i | −0.674946 | + | 0.833269i | ||||
\(116\) | 8.05627 | + | 10.9851i | 0.748006 | + | 1.01994i | ||||
\(117\) | 6.29022 | 0.581531 | ||||||||
\(118\) | 3.22615 | + | 9.85423i | 0.296991 | + | 0.907156i | ||||
\(119\) | − | 0.927105i | − | 0.0849875i | ||||||
\(120\) | −0.943725 | − | 3.43179i | −0.0861499 | − | 0.313278i | ||||
\(121\) | −3.73173 | −0.339248 | ||||||||
\(122\) | −1.44000 | − | 4.39845i | −0.130371 | − | 0.398217i | ||||
\(123\) | 6.78891 | 0.612136 | ||||||||
\(124\) | −7.67977 | + | 5.63219i | −0.689664 | + | 0.505785i | ||||
\(125\) | −9.95979 | − | 5.07962i | −0.890831 | − | 0.454335i | ||||
\(126\) | −3.69283 | − | 11.2797i | −0.328983 | − | 1.00487i | ||||
\(127\) | 7.85899i | 0.697372i | 0.937240 | + | 0.348686i | \(0.113372\pi\) | ||||
−0.937240 | + | 0.348686i | \(0.886628\pi\) | |||||||
\(128\) | 9.04805 | − | 6.79212i | 0.799742 | − | 0.600344i | ||||
\(129\) | − | 0.0967248i | − | 0.00851615i | ||||||
\(130\) | −6.92623 | − | 2.64204i | −0.607471 | − | 0.231723i | ||||
\(131\) | − | 16.0686i | − | 1.40392i | −0.712216 | − | 0.701960i | \(-0.752308\pi\) | ||
0.712216 | − | 0.701960i | \(-0.247692\pi\) | |||||||
\(132\) | −3.48354 | + | 2.55476i | −0.303203 | + | 0.222363i | ||||
\(133\) | −13.6231 | + | 0.524996i | −1.18127 | + | 0.0455229i | ||||
\(134\) | 12.7273 | − | 4.16674i | 1.09947 | − | 0.359952i | ||||
\(135\) | −5.55730 | − | 4.50140i | −0.478296 | − | 0.387419i | ||||
\(136\) | 0.488251 | − | 0.681564i | 0.0418672 | − | 0.0584436i | ||||
\(137\) | 18.8105i | 1.60709i | 0.595247 | + | 0.803543i | \(0.297054\pi\) | ||||
−0.595247 | + | 0.803543i | \(0.702946\pi\) | |||||||
\(138\) | 3.88971 | − | 1.27344i | 0.331114 | − | 0.108403i | ||||
\(139\) | − | 15.2280i | − | 1.29162i | −0.763498 | − | 0.645810i | \(-0.776520\pi\) | ||
0.763498 | − | 0.645810i | \(-0.223480\pi\) | |||||||
\(140\) | −0.671529 | + | 13.9713i | −0.0567545 | + | 1.18079i | ||||
\(141\) | 3.91723i | 0.329890i | ||||||||
\(142\) | −4.16007 | − | 12.7069i | −0.349105 | − | 1.06634i | ||||
\(143\) | 8.99752i | 0.752410i | ||||||||
\(144\) | 3.22555 | − | 10.2371i | 0.268796 | − | 0.853090i | ||||
\(145\) | −11.8351 | − | 9.58644i | −0.982855 | − | 0.796110i | ||||
\(146\) | −11.0654 | + | 3.62267i | −0.915778 | + | 0.299814i | ||||
\(147\) | − | 1.56578i | − | 0.129143i | ||||||
\(148\) | −2.92836 | + | 2.14760i | −0.240709 | + | 0.176531i | ||||
\(149\) | −18.8032 | −1.54041 | −0.770207 | − | 0.637794i | \(-0.779847\pi\) | ||||
−0.770207 | + | 0.637794i | \(0.779847\pi\) | |||||||
\(150\) | 1.99644 | + | 3.44223i | 0.163009 | + | 0.281057i | ||||
\(151\) | 8.71133 | 0.708918 | 0.354459 | − | 0.935072i | \(-0.384665\pi\) | ||||
0.354459 | + | 0.935072i | \(0.384665\pi\) | |||||||
\(152\) | −10.2915 | − | 6.78853i | −0.834755 | − | 0.550622i | ||||
\(153\) | − | 0.795385i | − | 0.0643031i | ||||||
\(154\) | 16.1344 | − | 5.28221i | 1.30015 | − | 0.425652i | ||||
\(155\) | 6.70194 | − | 8.27403i | 0.538313 | − | 0.664586i | ||||
\(156\) | 1.56034 | + | 2.12760i | 0.124927 | + | 0.170344i | ||||
\(157\) | 12.8390i | 1.02466i | 0.858788 | + | 0.512332i | \(0.171218\pi\) | ||||
−0.858788 | + | 0.512332i | \(0.828782\pi\) | |||||||
\(158\) | −3.29955 | − | 10.0784i | −0.262498 | − | 0.801797i | ||||
\(159\) | 6.24816i | 0.495511i | ||||||||
\(160\) | −7.85150 | + | 9.91735i | −0.620716 | + | 0.784036i | ||||
\(161\) | −16.0847 | −1.26765 | ||||||||
\(162\) | −2.75011 | − | 8.40018i | −0.216069 | − | 0.659980i | ||||
\(163\) | 0.411443 | 0.0322267 | 0.0161133 | − | 0.999870i | \(-0.494871\pi\) | ||||
0.0161133 | + | 0.999870i | \(0.494871\pi\) | |||||||
\(164\) | −14.2686 | − | 19.4560i | −1.11419 | − | 1.51926i | ||||
\(165\) | 3.04000 | − | 3.75309i | 0.236663 | − | 0.292178i | ||||
\(166\) | 2.80618 | + | 8.57144i | 0.217802 | + | 0.665273i | ||||
\(167\) | − | 1.56210i | − | 0.120879i | −0.998172 | − | 0.0604396i | \(-0.980750\pi\) | ||
0.998172 | − | 0.0604396i | \(-0.0192503\pi\) | |||||||
\(168\) | 2.89920 | − | 4.04707i | 0.223678 | − | 0.312238i | ||||
\(169\) | −7.50469 | −0.577284 | ||||||||
\(170\) | −0.334081 | + | 0.875807i | −0.0256228 | + | 0.0671713i | ||||
\(171\) | −11.6876 | + | 0.450406i | −0.893772 | + | 0.0344434i | ||||
\(172\) | −0.277199 | + | 0.203292i | −0.0211362 | + | 0.0155009i | ||||
\(173\) | 11.3997 | 0.866705 | 0.433352 | − | 0.901225i | \(-0.357331\pi\) | ||||
0.433352 | + | 0.901225i | \(0.357331\pi\) | |||||||
\(174\) | 1.68663 | + | 5.15178i | 0.127863 | + | 0.390555i | ||||
\(175\) | −3.24746 | − | 15.2975i | −0.245485 | − | 1.15638i | ||||
\(176\) | 14.6431 | + | 4.61382i | 1.10377 | + | 0.347779i | ||||
\(177\) | 4.12608i | 0.310135i | ||||||||
\(178\) | −4.69363 | + | 1.53664i | −0.351803 | + | 0.115176i | ||||
\(179\) | −8.31107 | −0.621199 | −0.310599 | − | 0.950541i | \(-0.600530\pi\) | ||||
−0.310599 | + | 0.950541i | \(0.600530\pi\) | |||||||
\(180\) | −0.576120 | + | 11.9863i | −0.0429415 | + | 0.893404i | ||||
\(181\) | − | 1.46224i | − | 0.108687i | −0.998522 | − | 0.0543437i | \(-0.982693\pi\) | ||
0.998522 | − | 0.0543437i | \(-0.0173067\pi\) | |||||||
\(182\) | −3.22615 | − | 9.85423i | −0.239138 | − | 0.730444i | ||||
\(183\) | − | 1.84168i | − | 0.136141i | ||||||
\(184\) | −11.8247 | − | 8.47086i | −0.871730 | − | 0.624480i | ||||
\(185\) | 2.55550 | − | 3.15495i | 0.187884 | − | 0.231957i | ||||
\(186\) | −3.60164 | + | 1.17913i | −0.264085 | + | 0.0864581i | ||||
\(187\) | 1.13772 | 0.0831981 | ||||||||
\(188\) | 11.2262 | − | 8.23306i | 0.818753 | − | 0.600457i | ||||
\(189\) | − | 10.0033i | − | 0.727632i | ||||||
\(190\) | 13.0585 | + | 4.41312i | 0.947363 | + | 0.320161i | ||||
\(191\) | − | 4.43480i | − | 0.320891i | −0.987045 | − | 0.160445i | \(-0.948707\pi\) | ||
0.987045 | − | 0.160445i | \(-0.0512930\pi\) | |||||||
\(192\) | 4.26271 | − | 1.44838i | 0.307634 | − | 0.104528i | ||||
\(193\) | −6.39281 | −0.460164 | −0.230082 | − | 0.973171i | \(-0.573899\pi\) | ||||
−0.230082 | + | 0.973171i | \(0.573899\pi\) | |||||||
\(194\) | 5.24295 | + | 16.0145i | 0.376422 | + | 1.14978i | ||||
\(195\) | −2.29223 | − | 1.85670i | −0.164150 | − | 0.132961i | ||||
\(196\) | −4.48729 | + | 3.29089i | −0.320521 | + | 0.235063i | ||||
\(197\) | 22.3795i | 1.59447i | 0.603668 | + | 0.797235i | \(0.293705\pi\) | ||||
−0.603668 | + | 0.797235i | \(0.706295\pi\) | |||||||
\(198\) | 13.8421 | − | 4.53173i | 0.983716 | − | 0.322056i | ||||
\(199\) | 0.591395i | 0.0419229i | 0.999780 | + | 0.0209614i | \(0.00667272\pi\) | ||||
−0.999780 | + | 0.0209614i | \(0.993327\pi\) | |||||||
\(200\) | 5.66889 | − | 12.9562i | 0.400851 | − | 0.916143i | ||||
\(201\) | 5.32905 | 0.375882 | ||||||||
\(202\) | 2.64775 | + | 8.08750i | 0.186295 | + | 0.569035i | ||||
\(203\) | − | 21.3036i | − | 1.49522i | ||||||
\(204\) | 0.269030 | − | 0.197302i | 0.0188359 | − | 0.0138139i | ||||
\(205\) | 20.9615 | + | 16.9787i | 1.46401 | + | 1.18585i | ||||
\(206\) | 1.33008 | − | 0.435453i | 0.0926713 | − | 0.0303394i | ||||
\(207\) | −13.7995 | −0.959128 | ||||||||
\(208\) | 2.81793 | − | 8.94339i | 0.195388 | − | 0.620112i | ||||
\(209\) | −0.644260 | − | 16.7179i | −0.0445644 | − | 1.15640i | ||||
\(210\) | −1.98375 | + | 5.20047i | −0.136891 | + | 0.358867i | ||||
\(211\) | −18.8494 | −1.29765 | −0.648824 | − | 0.760938i | \(-0.724739\pi\) | ||||
−0.648824 | + | 0.760938i | \(0.724739\pi\) | |||||||
\(212\) | 17.9063 | − | 13.1321i | 1.22981 | − | 0.901916i | ||||
\(213\) | − | 5.32052i | − | 0.364556i | ||||||
\(214\) | −13.3824 | + | 4.38122i | −0.914801 | + | 0.299494i | ||||
\(215\) | 0.241904 | − | 0.298648i | 0.0164977 | − | 0.0203676i | ||||
\(216\) | 5.26814 | − | 7.35395i | 0.358451 | − | 0.500373i | ||||
\(217\) | 14.8935 | 1.01103 | ||||||||
\(218\) | 18.7094 | − | 6.12523i | 1.26716 | − | 0.414853i | ||||
\(219\) | −4.63321 | −0.313083 | ||||||||
\(220\) | −17.1451 | − | 0.824081i | −1.15592 | − | 0.0555595i | ||||
\(221\) | − | 0.694870i | − | 0.0467420i | ||||||
\(222\) | −1.37333 | + | 0.449612i | −0.0921721 | + | 0.0301760i | ||||
\(223\) | 15.5731i | 1.04285i | 0.853296 | + | 0.521427i | \(0.174600\pi\) | ||||
−0.853296 | + | 0.521427i | \(0.825400\pi\) | |||||||
\(224\) | −17.6917 | + | 0.197302i | −1.18208 | + | 0.0131828i | ||||
\(225\) | −2.78607 | − | 13.1241i | −0.185738 | − | 0.874937i | ||||
\(226\) | −8.13840 | − | 24.8586i | −0.541359 | − | 1.65357i | ||||
\(227\) | − | 23.0220i | − | 1.52803i | −0.645201 | − | 0.764013i | \(-0.723227\pi\) | ||
0.645201 | − | 0.764013i | \(-0.276773\pi\) | |||||||
\(228\) | −3.05154 | − | 3.84147i | −0.202093 | − | 0.254408i | ||||
\(229\) | 14.0599 | 0.929102 | 0.464551 | − | 0.885546i | \(-0.346216\pi\) | ||||
0.464551 | + | 0.885546i | \(0.346216\pi\) | |||||||
\(230\) | 15.1947 | + | 5.79610i | 1.00191 | + | 0.382184i | ||||
\(231\) | 6.75567 | 0.444491 | ||||||||
\(232\) | 11.2193 | − | 15.6614i | 0.736585 | − | 1.02822i | ||||
\(233\) | 18.3115i | 1.19963i | 0.800140 | + | 0.599813i | \(0.204758\pi\) | ||||
−0.800140 | + | 0.599813i | \(0.795242\pi\) | |||||||
\(234\) | −2.76779 | − | 8.45418i | −0.180936 | − | 0.552667i | ||||
\(235\) | −9.79680 | + | 12.0949i | −0.639073 | + | 0.788981i | ||||
\(236\) | 11.8247 | − | 8.67202i | 0.769724 | − | 0.564500i | ||||
\(237\) | − | 4.21996i | − | 0.274116i | ||||||
\(238\) | −1.24605 | + | 0.407940i | −0.0807692 | + | 0.0264428i | ||||
\(239\) | − | 7.19400i | − | 0.465341i | −0.972556 | − | 0.232671i | \(-0.925254\pi\) | ||
0.972556 | − | 0.232671i | \(-0.0747464\pi\) | |||||||
\(240\) | −4.19714 | + | 2.77842i | −0.270924 | + | 0.179346i | ||||
\(241\) | − | 2.45499i | − | 0.158140i | −0.996869 | − | 0.0790698i | \(-0.974805\pi\) | ||
0.996869 | − | 0.0790698i | \(-0.0251950\pi\) | |||||||
\(242\) | 1.64201 | + | 5.01551i | 0.105553 | + | 0.322409i | ||||
\(243\) | − | 13.1122i | − | 0.841148i | ||||||
\(244\) | −5.27798 | + | 3.87077i | −0.337888 | + | 0.247800i | ||||
\(245\) | 3.91594 | − | 4.83451i | 0.250180 | − | 0.308866i | ||||
\(246\) | −2.98722 | − | 9.12443i | −0.190458 | − | 0.581752i | ||||
\(247\) | −10.2106 | + | 0.393487i | −0.649684 | + | 0.0250370i | ||||
\(248\) | 10.9490 | + | 7.84351i | 0.695261 | + | 0.498063i | ||||
\(249\) | 3.58896i | 0.227441i | ||||||||
\(250\) | −2.44465 | + | 15.6213i | −0.154613 | + | 0.987975i | ||||
\(251\) | 14.3768i | 0.907455i | 0.891140 | + | 0.453728i | \(0.149906\pi\) | ||||
−0.891140 | + | 0.453728i | \(0.850094\pi\) | |||||||
\(252\) | −13.5352 | + | 9.92645i | −0.852638 | + | 0.625308i | ||||
\(253\) | − | 19.7387i | − | 1.24096i | ||||||
\(254\) | 10.5626 | − | 3.45807i | 0.662758 | − | 0.216979i | ||||
\(255\) | −0.234776 | + | 0.289848i | −0.0147022 | + | 0.0181510i | ||||
\(256\) | −13.1100 | − | 9.17212i | −0.819375 | − | 0.573257i | ||||
\(257\) | −13.3686 | −0.833913 | −0.416956 | − | 0.908927i | \(-0.636903\pi\) | ||||
−0.416956 | + | 0.908927i | \(0.636903\pi\) | |||||||
\(258\) | −0.130000 | + | 0.0425603i | −0.00809345 | + | 0.00264969i | ||||
\(259\) | 5.67900 | 0.352876 | ||||||||
\(260\) | −0.503314 | + | 10.4715i | −0.0312142 | + | 0.649416i | ||||
\(261\) | − | 18.2769i | − | 1.13131i | ||||||
\(262\) | −21.5965 | + | 7.07042i | −1.33424 | + | 0.436812i | ||||
\(263\) | 18.3342 | 1.13053 | 0.565267 | − | 0.824908i | \(-0.308773\pi\) | ||||
0.565267 | + | 0.824908i | \(0.308773\pi\) | |||||||
\(264\) | 4.96645 | + | 3.55781i | 0.305664 | + | 0.218968i | ||||
\(265\) | −15.6263 | + | 19.2918i | −0.959919 | + | 1.18509i | ||||
\(266\) | 6.69997 | + | 18.0787i | 0.410801 | + | 1.10848i | ||||
\(267\) | −1.96528 | −0.120273 | ||||||||
\(268\) | −11.2004 | − | 15.2722i | −0.684171 | − | 0.932901i | ||||
\(269\) | 3.91723i | 0.238838i | 0.992844 | + | 0.119419i | \(0.0381031\pi\) | ||||
−0.992844 | + | 0.119419i | \(0.961897\pi\) | |||||||
\(270\) | −3.60467 | + | 9.44980i | −0.219373 | + | 0.575096i | ||||
\(271\) | 32.0793i | 1.94868i | 0.225079 | + | 0.974341i | \(0.427736\pi\) | ||||
−0.225079 | + | 0.974341i | \(0.572264\pi\) | |||||||
\(272\) | −1.13087 | − | 0.356320i | −0.0685692 | − | 0.0216051i | ||||
\(273\) | − | 4.12608i | − | 0.249722i | ||||||
\(274\) | 25.2816 | − | 8.27688i | 1.52732 | − | 0.500024i | ||||
\(275\) | 18.7726 | − | 3.98519i | 1.13203 | − | 0.240316i | ||||
\(276\) | −3.42306 | − | 4.66752i | −0.206044 | − | 0.280951i | ||||
\(277\) | 6.15489i | 0.369812i | 0.982756 | + | 0.184906i | \(0.0591980\pi\) | ||||
−0.982756 | + | 0.184906i | \(0.940802\pi\) | |||||||
\(278\) | −20.4667 | + | 6.70054i | −1.22751 | + | 0.401872i | ||||
\(279\) | 12.7775 | 0.764967 | ||||||||
\(280\) | 19.0731 | − | 5.24501i | 1.13984 | − | 0.313449i | ||||
\(281\) | 6.21318i | 0.370647i | 0.982678 | + | 0.185323i | \(0.0593333\pi\) | ||||
−0.982678 | + | 0.185323i | \(0.940667\pi\) | |||||||
\(282\) | 5.26483 | − | 1.72364i | 0.313516 | − | 0.102641i | ||||
\(283\) | 13.4604 | 0.800136 | 0.400068 | − | 0.916485i | \(-0.368986\pi\) | ||||
0.400068 | + | 0.916485i | \(0.368986\pi\) | |||||||
\(284\) | −15.2478 | + | 11.1824i | −0.904790 | + | 0.663555i | ||||
\(285\) | 4.39204 | + | 3.28572i | 0.260162 | + | 0.194629i | ||||
\(286\) | 12.0928 | − | 3.95904i | 0.715064 | − | 0.234103i | ||||
\(287\) | 37.7312i | 2.22720i | ||||||||
\(288\) | −15.1781 | + | 0.169270i | −0.894379 | + | 0.00997431i | ||||
\(289\) | 16.9121 | 0.994831 | ||||||||
\(290\) | −7.67672 | + | 20.1248i | −0.450792 | + | 1.18177i | ||||
\(291\) | 6.70547i | 0.393081i | ||||||||
\(292\) | 9.73786 | + | 13.2781i | 0.569865 | + | 0.777040i | ||||
\(293\) | −10.3893 | −0.606949 | −0.303475 | − | 0.952840i | \(-0.598147\pi\) | ||||
−0.303475 | + | 0.952840i | \(0.598147\pi\) | |||||||
\(294\) | −2.10444 | + | 0.688967i | −0.122733 | + | 0.0401814i | ||||
\(295\) | −10.3191 | + | 12.7397i | −0.600803 | + | 0.741735i | ||||
\(296\) | 4.17493 | + | 2.99079i | 0.242663 | + | 0.173836i | ||||
\(297\) | 12.2758 | 0.712312 | ||||||||
\(298\) | 8.27367 | + | 25.2718i | 0.479281 | + | 1.46396i | ||||
\(299\) | −12.0556 | −0.697192 | ||||||||
\(300\) | 3.74797 | − | 4.19788i | 0.216389 | − | 0.242365i | ||||
\(301\) | 0.537575 | 0.0309853 | ||||||||
\(302\) | −3.83311 | − | 11.7082i | −0.220571 | − | 0.673731i | ||||
\(303\) | 3.38633i | 0.194540i | ||||||||
\(304\) | −4.59548 | + | 16.8191i | −0.263569 | + | 0.964641i | ||||
\(305\) | 4.60596 | − | 5.68639i | 0.263737 | − | 0.325602i | ||||
\(306\) | −1.06901 | + | 0.349981i | −0.0611114 | + | 0.0200071i | ||||
\(307\) | − | 11.5192i | − | 0.657434i | −0.944428 | − | 0.328717i | \(-0.893384\pi\) | ||
0.944428 | − | 0.328717i | \(-0.106616\pi\) | |||||||
\(308\) | −14.1988 | − | 19.3607i | −0.809050 | − | 1.10318i | ||||
\(309\) | 0.556922 | 0.0316822 | ||||||||
\(310\) | −14.0694 | − | 5.36684i | −0.799088 | − | 0.304816i | ||||
\(311\) | − | 19.4638i | − | 1.10369i | −0.833946 | − | 0.551847i | \(-0.813923\pi\) | ||
0.833946 | − | 0.551847i | \(-0.186077\pi\) | |||||||
\(312\) | 2.17296 | − | 3.03330i | 0.123020 | − | 0.171727i | ||||
\(313\) | − | 14.3879i | − | 0.813255i | −0.913594 | − | 0.406628i | \(-0.866705\pi\) | ||
0.913594 | − | 0.406628i | \(-0.133295\pi\) | |||||||
\(314\) | 17.2559 | − | 5.64935i | 0.973804 | − | 0.318811i | ||||
\(315\) | 11.8118 | − | 14.5826i | 0.665522 | − | 0.821634i | ||||
\(316\) | −12.0938 | + | 8.86932i | −0.680327 | + | 0.498938i | ||||
\(317\) | −11.3099 | −0.635230 | −0.317615 | − | 0.948220i | \(-0.602882\pi\) | ||||
−0.317615 | + | 0.948220i | \(0.602882\pi\) | |||||||
\(318\) | 8.39764 | − | 2.74928i | 0.470917 | − | 0.154172i | ||||
\(319\) | 26.1432 | 1.46374 | ||||||||
\(320\) | 16.7839 | + | 6.18879i | 0.938248 | + | 0.345964i | ||||
\(321\) | −5.60336 | −0.312749 | ||||||||
\(322\) | 7.07751 | + | 21.6182i | 0.394414 | + | 1.20473i | ||||
\(323\) | 0.0497555 | + | 1.29111i | 0.00276847 | + | 0.0718390i | ||||
\(324\) | −10.0799 | + | 7.39240i | −0.559995 | + | 0.410689i | ||||
\(325\) | −2.43399 | − | 11.4655i | −0.135013 | − | 0.635993i | ||||
\(326\) | −0.181041 | − | 0.552987i | −0.0100269 | − | 0.0306271i | ||||
\(327\) | 7.83386 | 0.433214 | ||||||||
\(328\) | −19.8708 | + | 27.7382i | −1.09718 | + | 1.53159i | ||||
\(329\) | −21.7711 | −1.20028 | ||||||||
\(330\) | −6.38187 | − | 2.43440i | −0.351311 | − | 0.134009i | ||||
\(331\) | −8.54452 | −0.469649 | −0.234825 | − | 0.972038i | \(-0.575452\pi\) | ||||
−0.234825 | + | 0.972038i | \(0.575452\pi\) | |||||||
\(332\) | 10.2854 | − | 7.54312i | 0.564486 | − | 0.413982i | ||||
\(333\) | 4.87215 | 0.266992 | ||||||||
\(334\) | −2.09950 | + | 0.687349i | −0.114879 | + | 0.0376101i | ||||
\(335\) | 16.4540 | + | 13.3277i | 0.898978 | + | 0.728170i | ||||
\(336\) | −6.71503 | − | 2.11580i | −0.366335 | − | 0.115427i | ||||
\(337\) | −9.77305 | −0.532372 | −0.266186 | − | 0.963922i | \(-0.585764\pi\) | ||||
−0.266186 | + | 0.963922i | \(0.585764\pi\) | |||||||
\(338\) | 3.30218 | + | 10.0864i | 0.179615 | + | 0.548631i | ||||
\(339\) | − | 10.4086i | − | 0.565318i | ||||||
\(340\) | 1.32410 | + | 0.0636430i | 0.0718095 | + | 0.00345152i | ||||
\(341\) | 18.2769i | 0.989747i | ||||||||
\(342\) | 5.74806 | + | 15.5101i | 0.310820 | + | 0.838693i | ||||
\(343\) | −13.1915 | −0.712272 | ||||||||
\(344\) | 0.395200 | + | 0.283109i | 0.0213077 | + | 0.0152642i | ||||
\(345\) | 5.02869 | + | 4.07322i | 0.270735 | + | 0.219295i | ||||
\(346\) | −5.01605 | − | 15.3214i | −0.269664 | − | 0.823686i | ||||
\(347\) | −32.2557 | −1.73158 | −0.865789 | − | 0.500408i | \(-0.833183\pi\) | ||||
−0.865789 | + | 0.500408i | \(0.833183\pi\) | |||||||
\(348\) | 6.18195 | − | 4.53372i | 0.331387 | − | 0.243033i | ||||
\(349\) | 12.2964 | 0.658212 | 0.329106 | − | 0.944293i | \(-0.393253\pi\) | ||||
0.329106 | + | 0.944293i | \(0.393253\pi\) | |||||||
\(350\) | −19.1312 | + | 11.0958i | −1.02260 | + | 0.593093i | ||||
\(351\) | − | 7.49752i | − | 0.400188i | ||||||
\(352\) | −0.242123 | − | 21.7107i | −0.0129052 | − | 1.15719i | ||||
\(353\) | − | 9.48559i | − | 0.504867i | −0.967614 | − | 0.252434i | \(-0.918769\pi\) | ||
0.967614 | − | 0.252434i | \(-0.0812309\pi\) | |||||||
\(354\) | 5.54553 | − | 1.81554i | 0.294742 | − | 0.0964947i | ||||
\(355\) | 13.3064 | − | 16.4277i | 0.706228 | − | 0.871889i | ||||
\(356\) | 4.13053 | + | 5.63219i | 0.218918 | + | 0.298505i | ||||
\(357\) | −0.521734 | −0.0276131 | ||||||||
\(358\) | 3.65699 | + | 11.1702i | 0.193278 | + | 0.590365i | ||||
\(359\) | 11.7875i | 0.622118i | 0.950391 | + | 0.311059i | \(0.100684\pi\) | ||||
−0.950391 | + | 0.311059i | \(0.899316\pi\) | |||||||
\(360\) | 16.3633 | − | 4.49982i | 0.862420 | − | 0.237161i | ||||
\(361\) | 18.9436 | − | 1.46224i | 0.997034 | − | 0.0769600i | ||||
\(362\) | −1.96528 | + | 0.643407i | −0.103293 | + | 0.0338167i | ||||
\(363\) | 2.10005i | 0.110224i | ||||||||
\(364\) | −11.8247 | + | 8.67202i | −0.619784 | + | 0.454537i | ||||
\(365\) | −14.3055 | − | 11.5874i | −0.748785 | − | 0.606514i | ||||
\(366\) | −2.47526 | + | 0.810368i | −0.129384 | + | 0.0423586i | ||||
\(367\) | 27.6424 | 1.44292 | 0.721460 | − | 0.692457i | \(-0.243472\pi\) | ||||
0.721460 | + | 0.692457i | \(0.243472\pi\) | |||||||
\(368\) | −6.18195 | + | 19.6200i | −0.322256 | + | 1.02276i | ||||
\(369\) | 32.3705i | 1.68514i | ||||||||
\(370\) | −5.36477 | − | 2.04642i | −0.278901 | − | 0.106388i | ||||
\(371\) | −34.7259 | −1.80288 | ||||||||
\(372\) | 3.16955 | + | 4.32184i | 0.164334 | + | 0.224077i | ||||
\(373\) | 15.2573 | 0.789991 | 0.394996 | − | 0.918683i | \(-0.370746\pi\) | ||||
0.394996 | + | 0.918683i | \(0.370746\pi\) | |||||||
\(374\) | −0.500612 | − | 1.52911i | −0.0258860 | − | 0.0790685i | ||||
\(375\) | −2.85859 | + | 5.60494i | −0.147617 | + | 0.289438i | ||||
\(376\) | −16.0051 | − | 11.4655i | −0.825398 | − | 0.591290i | ||||
\(377\) | − | 15.9671i | − | 0.822350i | ||||||
\(378\) | −13.4446 | + | 4.40160i | −0.691516 | + | 0.226394i | ||||
\(379\) | 29.8592 | 1.53376 | 0.766882 | − | 0.641788i | \(-0.221807\pi\) | ||||
0.766882 | + | 0.641788i | \(0.221807\pi\) | |||||||
\(380\) | 0.185381 | − | 19.4927i | 0.00950982 | − | 0.999955i | ||||
\(381\) | 4.42269 | 0.226582 | ||||||||
\(382\) | −5.96045 | + | 1.95138i | −0.304963 | + | 0.0998411i | ||||
\(383\) | 24.1703i | 1.23504i | 0.786554 | + | 0.617521i | \(0.211863\pi\) | ||||
−0.786554 | + | 0.617521i | \(0.788137\pi\) | |||||||
\(384\) | −3.82231 | − | 5.09185i | −0.195056 | − | 0.259842i | ||||
\(385\) | 20.8589 | + | 16.8956i | 1.06307 | + | 0.861081i | ||||
\(386\) | 2.81293 | + | 8.59205i | 0.143174 | + | 0.437324i | ||||
\(387\) | 0.461198 | 0.0234440 | ||||||||
\(388\) | 19.2168 | − | 14.0933i | 0.975588 | − | 0.715477i | ||||
\(389\) | 14.6644 | 0.743513 | 0.371757 | − | 0.928330i | \(-0.378756\pi\) | ||||
0.371757 | + | 0.928330i | \(0.378756\pi\) | |||||||
\(390\) | −1.48683 | + | 3.89778i | −0.0752884 | + | 0.197372i | ||||
\(391\) | 1.52440i | 0.0770923i | ||||||||
\(392\) | 6.39749 | + | 4.58296i | 0.323122 | + | 0.231475i | ||||
\(393\) | −9.04271 | −0.456144 | ||||||||
\(394\) | 30.0784 | − | 9.84730i | 1.51533 | − | 0.496100i | ||||
\(395\) | 10.5539 | − | 13.0296i | 0.531025 | − | 0.655588i | ||||
\(396\) | −12.1815 | − | 16.6100i | −0.612142 | − | 0.834685i | ||||
\(397\) | − | 10.8320i | − | 0.543643i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) | ||
0.962348 | − | 0.271821i | \(-0.0876260\pi\) | |||||||
\(398\) | 0.794846 | − | 0.260222i | 0.0398420 | − | 0.0130438i | ||||
\(399\) | 0.295445 | + | 7.66649i | 0.0147907 | + | 0.383804i | ||||
\(400\) | −19.9078 | − | 1.91817i | −0.995390 | − | 0.0959085i | ||||
\(401\) | − | 24.3653i | − | 1.21675i | −0.793652 | − | 0.608373i | \(-0.791823\pi\) | ||
0.793652 | − | 0.608373i | \(-0.208177\pi\) | |||||||
\(402\) | −2.34486 | − | 7.16234i | −0.116951 | − | 0.357225i | ||||
\(403\) | 11.1627 | 0.556055 | ||||||||
\(404\) | 9.70471 | − | 7.11724i | 0.482827 | − | 0.354096i | ||||
\(405\) | 8.79648 | − | 10.8599i | 0.437101 | − | 0.539632i | ||||
\(406\) | −28.6324 | + | 9.37389i | −1.42100 | + | 0.465218i | ||||
\(407\) | 6.96911i | 0.345446i | ||||||||
\(408\) | −0.383554 | − | 0.274766i | −0.0189888 | − | 0.0136030i | ||||
\(409\) | − | 14.3876i | − | 0.711422i | −0.934596 | − | 0.355711i | \(-0.884239\pi\) | ||
0.934596 | − | 0.355711i | \(-0.115761\pi\) | |||||||
\(410\) | 13.5964 | − | 35.6435i | 0.671478 | − | 1.76031i | ||||
\(411\) | 10.5857 | 0.522154 | ||||||||
\(412\) | −1.17051 | − | 1.59605i | −0.0576670 | − | 0.0786319i | ||||
\(413\) | −22.9318 | −1.12840 | ||||||||
\(414\) | 6.07196 | + | 18.5467i | 0.298421 | + | 0.911522i | ||||
\(415\) | −8.97582 | + | 11.0813i | −0.440606 | + | 0.543959i | ||||
\(416\) | −13.2600 | + | 0.147878i | −0.650126 | + | 0.00725034i | ||||
\(417\) | −8.56965 | −0.419657 | ||||||||
\(418\) | −22.1857 | + | 8.22201i | −1.08514 | + | 0.402152i | ||||
\(419\) | 25.9927i | 1.26983i | 0.772583 | + | 0.634914i | \(0.218965\pi\) | ||||
−0.772583 | + | 0.634914i | \(0.781035\pi\) | |||||||
\(420\) | 7.86241 | + | 0.377907i | 0.383646 | + | 0.0184400i | ||||
\(421\) | − | 22.3672i | − | 1.09011i | −0.838400 | − | 0.545056i | \(-0.816508\pi\) | ||
0.838400 | − | 0.545056i | \(-0.183492\pi\) | |||||||
\(422\) | 8.29403 | + | 25.3340i | 0.403747 | + | 1.23324i | ||||
\(423\) | −18.6779 | −0.908151 | ||||||||
\(424\) | −25.5288 | − | 18.2880i | −1.23979 | − | 0.888146i | ||||
\(425\) | −1.44979 | + | 0.307772i | −0.0703252 | + | 0.0149291i | ||||
\(426\) | −7.15087 | + | 2.34111i | −0.346461 | + | 0.113427i | ||||
\(427\) | 10.2357 | 0.495338 | ||||||||
\(428\) | 11.7769 | + | 16.0584i | 0.569258 | + | 0.776211i | ||||
\(429\) | 5.06341 | 0.244464 | ||||||||
\(430\) | −0.507830 | − | 0.193714i | −0.0244897 | − | 0.00934173i | ||||
\(431\) | 25.7719 | 1.24139 | 0.620695 | − | 0.784052i | \(-0.286851\pi\) | ||||
0.620695 | + | 0.784052i | \(0.286851\pi\) | |||||||
\(432\) | −12.2019 | − | 3.84463i | −0.587064 | − | 0.184975i | ||||
\(433\) | 17.9384 | 0.862062 | 0.431031 | − | 0.902337i | \(-0.358150\pi\) | ||||
0.431031 | + | 0.902337i | \(0.358150\pi\) | |||||||
\(434\) | −6.55335 | − | 20.0171i | −0.314571 | − | 0.960852i | ||||
\(435\) | −5.39483 | + | 6.66030i | −0.258662 | + | 0.319337i | ||||
\(436\) | −16.4649 | − | 22.4507i | −0.788524 | − | 1.07519i | ||||
\(437\) | 22.3999 | − | 0.863229i | 1.07153 | − | 0.0412938i | ||||
\(438\) | 2.03868 | + | 6.22712i | 0.0974118 | + | 0.297543i | ||||
\(439\) | −22.9968 | −1.09758 | −0.548790 | − | 0.835960i | \(-0.684911\pi\) | ||||
−0.548790 | + | 0.835960i | \(0.684911\pi\) | |||||||
\(440\) | 6.43653 | + | 23.4060i | 0.306849 | + | 1.11584i | ||||
\(441\) | 7.46587 | 0.355518 | ||||||||
\(442\) | −0.933918 | + | 0.305753i | −0.0444219 | + | 0.0145432i | ||||
\(443\) | −24.3789 | −1.15828 | −0.579138 | − | 0.815230i | \(-0.696611\pi\) | ||||
−0.579138 | + | 0.815230i | \(0.696611\pi\) | |||||||
\(444\) | 1.20857 | + | 1.64795i | 0.0573564 | + | 0.0782083i | ||||
\(445\) | −6.06801 | − | 4.91507i | −0.287651 | − | 0.232997i | ||||
\(446\) | 20.9306 | − | 6.85241i | 0.991092 | − | 0.324471i | ||||
\(447\) | 10.5816i | 0.500492i | ||||||||
\(448\) | 8.04978 | + | 23.6912i | 0.380317 | + | 1.11930i | ||||
\(449\) | 35.0227i | 1.65283i | 0.563065 | + | 0.826413i | \(0.309622\pi\) | ||||
−0.563065 | + | 0.826413i | \(0.690378\pi\) | |||||||
\(450\) | −16.4131 | + | 9.51931i | −0.773720 | + | 0.448745i | ||||
\(451\) | −46.3027 | −2.18031 | ||||||||
\(452\) | −29.8295 | + | 21.8763i | −1.40306 | + | 1.02898i | ||||
\(453\) | − | 4.90236i | − | 0.230333i | ||||||
\(454\) | −30.9420 | + | 10.1300i | −1.45218 | + | 0.475426i | ||||
\(455\) | 10.3191 | − | 12.7397i | 0.483769 | − | 0.597247i | ||||
\(456\) | −3.82029 | + | 5.79163i | −0.178901 | + | 0.271218i | ||||
\(457\) | 1.73993i | 0.0813904i | 0.999172 | + | 0.0406952i | \(0.0129573\pi\) | ||||
−0.999172 | + | 0.0406952i | \(0.987043\pi\) | |||||||
\(458\) | −6.18655 | − | 18.8967i | −0.289078 | − | 0.882986i | ||||
\(459\) | −0.948045 | −0.0442509 | ||||||||
\(460\) | 1.10417 | − | 22.9724i | 0.0514821 | − | 1.07109i | ||||
\(461\) | 20.9737 | 0.976845 | 0.488422 | − | 0.872607i | \(-0.337573\pi\) | ||||
0.488422 | + | 0.872607i | \(0.337573\pi\) | |||||||
\(462\) | −2.97260 | − | 9.07975i | −0.138298 | − | 0.422428i | ||||
\(463\) | 4.36243 | 0.202740 | 0.101370 | − | 0.994849i | \(-0.467677\pi\) | ||||
0.101370 | + | 0.994849i | \(0.467677\pi\) | |||||||
\(464\) | −25.9859 | − | 8.18775i | −1.20636 | − | 0.380107i | ||||
\(465\) | −4.65626 | − | 3.77156i | −0.215929 | − | 0.174902i | ||||
\(466\) | 24.6110 | − | 8.05732i | 1.14008 | − | 0.373248i | ||||
\(467\) | 11.5244 | 0.533287 | 0.266643 | − | 0.963795i | \(-0.414085\pi\) | ||||
0.266643 | + | 0.963795i | \(0.414085\pi\) | |||||||
\(468\) | −10.1447 | + | 7.43993i | −0.468939 | + | 0.343911i | ||||
\(469\) | 29.6177i | 1.36762i | ||||||||
\(470\) | 20.5665 | + | 7.84517i | 0.948660 | + | 0.361871i | ||||
\(471\) | 7.22523 | 0.332921 | ||||||||
\(472\) | −16.8584 | − | 12.0768i | −0.775971 | − | 0.555881i | ||||
\(473\) | 0.659697i | 0.0303329i | ||||||||
\(474\) | −5.67170 | + | 1.85684i | −0.260510 | + | 0.0852876i | ||||
\(475\) | 5.34346 | + | 21.1293i | 0.245175 | + | 0.969479i | ||||
\(476\) | 1.09656 | + | 1.49521i | 0.0502606 | + | 0.0685328i | ||||
\(477\) | −29.7921 | −1.36409 | ||||||||
\(478\) | −9.66887 | + | 3.16547i | −0.442244 | + | 0.144785i | ||||
\(479\) | − | 11.7269i | − | 0.535817i | −0.963444 | − | 0.267908i | \(-0.913668\pi\) | ||
0.963444 | − | 0.267908i | \(-0.0863324\pi\) | |||||||
\(480\) | 5.58105 | + | 4.41848i | 0.254739 | + | 0.201675i | ||||
\(481\) | 4.25644 | 0.194077 | ||||||||
\(482\) | −3.29955 | + | 1.08023i | −0.150290 | + | 0.0492032i | ||||
\(483\) | 9.05178i | 0.411870i | ||||||||
\(484\) | 6.01843 | − | 4.41380i | 0.273565 | − | 0.200627i | ||||
\(485\) | −16.7701 | + | 20.7038i | −0.761489 | + | 0.940113i | ||||
\(486\) | −17.6230 | + | 5.76956i | −0.799398 | + | 0.261713i | ||||
\(487\) | − | 36.4267i | − | 1.65065i | −0.564656 | − | 0.825327i | \(-0.690991\pi\) | ||
0.564656 | − | 0.825327i | \(-0.309009\pi\) | |||||||
\(488\) | 7.52477 | + | 5.39051i | 0.340631 | + | 0.244017i | ||||
\(489\) | − | 0.231542i | − | 0.0104707i | ||||||
\(490\) | −8.22075 | − | 3.13585i | −0.371376 | − | 0.141663i | ||||
\(491\) | − | 7.95871i | − | 0.359171i | −0.983742 | − | 0.179586i | \(-0.942524\pi\) | ||
0.983742 | − | 0.179586i | \(-0.0574757\pi\) | |||||||
\(492\) | −10.9490 | + | 8.02976i | −0.493618 | + | 0.362010i | ||||
\(493\) | −2.01901 | −0.0909317 | ||||||||
\(494\) | 5.02166 | + | 13.5501i | 0.225935 | + | 0.609647i | ||||
\(495\) | 17.8953 | + | 14.4952i | 0.804334 | + | 0.651509i | ||||
\(496\) | 5.72411 | − | 18.1669i | 0.257020 | − | 0.815718i | ||||
\(497\) | 29.5702 | 1.32641 | ||||||||
\(498\) | 4.82363 | − | 1.57920i | 0.216152 | − | 0.0707655i | ||||
\(499\) | − | 25.3695i | − | 1.13569i | −0.823134 | − | 0.567847i | \(-0.807776\pi\) | ||
0.823134 | − | 0.567847i | \(-0.192224\pi\) | |||||||
\(500\) | 22.0709 | − | 3.58793i | 0.987043 | − | 0.160457i | ||||
\(501\) | −0.879084 | −0.0392746 | ||||||||
\(502\) | 19.3227 | − | 6.32600i | 0.862414 | − | 0.282343i | ||||
\(503\) | −8.43511 | −0.376103 | −0.188052 | − | 0.982159i | \(-0.560217\pi\) | ||||
−0.188052 | + | 0.982159i | \(0.560217\pi\) | |||||||
\(504\) | 19.2970 | + | 13.8238i | 0.859558 | + | 0.615761i | ||||
\(505\) | −8.46906 | + | 10.4557i | −0.376868 | + | 0.465271i | ||||
\(506\) | −26.5292 | + | 8.68532i | −1.17937 | + | 0.386110i | ||||
\(507\) | 4.22331i | 0.187564i | ||||||||
\(508\) | −9.29542 | − | 12.6748i | −0.412418 | − | 0.562352i | ||||
\(509\) | − | 38.3457i | − | 1.69965i | −0.527069 | − | 0.849823i | \(-0.676709\pi\) | ||
0.527069 | − | 0.849823i | \(-0.323291\pi\) | |||||||
\(510\) | 0.492866 | + | 0.188006i | 0.0218245 | + | 0.00832505i | ||||
\(511\) | − | 25.7503i | − | 1.13913i | ||||||
\(512\) | −6.55890 | + | 21.6560i | −0.289865 | + | 0.957067i | ||||
\(513\) | 0.536853 | + | 13.9308i | 0.0237027 | + | 0.615060i | ||||
\(514\) | 5.88240 | + | 17.9677i | 0.259461 | + | 0.792521i | ||||
\(515\) | 1.71955 | + | 1.39283i | 0.0757726 | + | 0.0613756i | ||||
\(516\) | 0.114404 | + | 0.155995i | 0.00503635 | + | 0.00686731i | ||||
\(517\) | − | 26.7168i | − | 1.17501i | ||||||
\(518\) | −2.49884 | − | 7.63268i | −0.109793 | − | 0.335361i | ||||
\(519\) | − | 6.41527i | − | 0.281599i | ||||||
\(520\) | 14.2954 | − | 3.93116i | 0.626894 | − | 0.172393i | ||||
\(521\) | − | 26.1113i | − | 1.14396i | −0.820269 | − | 0.571979i | \(-0.806176\pi\) | ||
0.820269 | − | 0.571979i | \(-0.193824\pi\) | |||||||
\(522\) | −24.5644 | + | 8.04208i | −1.07516 | + | 0.351992i | ||||
\(523\) | − | 5.15443i | − | 0.225387i | −0.993630 | − | 0.112694i | \(-0.964052\pi\) | ||
0.993630 | − | 0.112694i | \(-0.0359479\pi\) | |||||||
\(524\) | 19.0056 | + | 25.9150i | 0.830262 | + | 1.13210i | ||||
\(525\) | −8.60875 | + | 1.82753i | −0.375717 | + | 0.0797598i | ||||
\(526\) | −8.06730 | − | 24.6415i | −0.351751 | − | 1.07442i | ||||
\(527\) | − | 1.41150i | − | 0.0614860i | ||||||
\(528\) | 2.59645 | − | 8.24050i | 0.112996 | − | 0.358622i | ||||
\(529\) | 3.44744 | 0.149889 | ||||||||
\(530\) | 32.8044 | + | 12.5134i | 1.42493 | + | 0.543548i | ||||
\(531\) | −19.6738 | −0.853769 | ||||||||
\(532\) | 21.3500 | − | 16.9598i | 0.925641 | − | 0.735300i | ||||
\(533\) | 28.2798i | 1.22493i | ||||||||
\(534\) | 0.864752 | + | 2.64137i | 0.0374215 | + | 0.114303i | ||||
\(535\) | −17.3010 | − | 14.0137i | −0.747986 | − | 0.605867i | ||||
\(536\) | −15.5979 | + | 21.7735i | −0.673725 | + | 0.940472i | ||||
\(537\) | 4.67711i | 0.201832i | ||||||||
\(538\) | 5.26483 | − | 1.72364i | 0.226983 | − | 0.0743113i | ||||
\(539\) | 10.6792i | 0.459984i | ||||||||
\(540\) | 14.2868 | + | 0.686696i | 0.614807 | + | 0.0295507i | ||||
\(541\) | −8.68410 | −0.373359 | −0.186679 | − | 0.982421i | \(-0.559773\pi\) | ||||
−0.186679 | + | 0.982421i | \(0.559773\pi\) | |||||||
\(542\) | 43.1152 | − | 14.1154i | 1.85196 | − | 0.606308i | ||||
\(543\) | −0.822885 | −0.0353134 | ||||||||
\(544\) | 0.0186989 | + | 1.67670i | 0.000801709 | + | 0.0718879i | ||||
\(545\) | 24.1879 | + | 19.5921i | 1.03609 | + | 0.839234i | ||||
\(546\) | −5.54553 | + | 1.81554i | −0.237327 | + | 0.0776978i | ||||
\(547\) | − | 1.22724i | − | 0.0524731i | −0.999656 | − | 0.0262365i | \(-0.991648\pi\) | ||
0.999656 | − | 0.0262365i | \(-0.00835231\pi\) | |||||||
\(548\) | −22.2486 | − | 30.3370i | −0.950411 | − | 1.29593i | ||||
\(549\) | 8.78142 | 0.374782 | ||||||||
\(550\) | −13.6164 | − | 23.4772i | −0.580605 | − | 1.00107i | ||||
\(551\) | 1.14331 | + | 29.6678i | 0.0487068 | + | 1.26389i | ||||
\(552\) | −4.76703 | + | 6.65444i | −0.202898 | + | 0.283232i | ||||
\(553\) | 23.4536 | 0.997347 | ||||||||
\(554\) | 8.27229 | − | 2.70824i | 0.351456 | − | 0.115062i | ||||
\(555\) | −1.77547 | − | 1.43813i | −0.0753644 | − | 0.0610450i | ||||
\(556\) | 18.0113 | + | 24.5593i | 0.763849 | + | 1.04155i | ||||
\(557\) | − | 10.1755i | − | 0.431151i | −0.976487 | − | 0.215575i | \(-0.930837\pi\) | ||
0.976487 | − | 0.215575i | \(-0.0691627\pi\) | |||||||
\(558\) | −5.62227 | − | 17.1732i | −0.238010 | − | 0.726998i | ||||
\(559\) | 0.402915 | 0.0170415 | ||||||||
\(560\) | −15.4418 | − | 23.3267i | −0.652537 | − | 0.985735i | ||||
\(561\) | − | 0.640257i | − | 0.0270317i | ||||||
\(562\) | 8.35063 | − | 2.73389i | 0.352250 | − | 0.115322i | ||||
\(563\) | − | 44.1373i | − | 1.86017i | −0.367348 | − | 0.930084i | \(-0.619734\pi\) | ||
0.367348 | − | 0.930084i | \(-0.380266\pi\) | |||||||
\(564\) | −4.63321 | − | 6.31760i | −0.195093 | − | 0.266019i | ||||
\(565\) | 26.0314 | − | 32.1377i | 1.09515 | − | 1.35204i | ||||
\(566\) | −5.92276 | − | 18.0910i | −0.248952 | − | 0.760422i | ||||
\(567\) | 19.5481 | 0.820943 | ||||||||
\(568\) | 21.7386 | + | 15.5729i | 0.912133 | + | 0.653424i | ||||
\(569\) | − | 15.7494i | − | 0.660248i | −0.943938 | − | 0.330124i | \(-0.892910\pi\) | ||
0.943938 | − | 0.330124i | \(-0.107090\pi\) | |||||||
\(570\) | 2.48351 | − | 7.34875i | 0.104023 | − | 0.307805i | ||||
\(571\) | − | 29.5903i | − | 1.23832i | −0.785266 | − | 0.619158i | \(-0.787474\pi\) | ||
0.785266 | − | 0.619158i | \(-0.212526\pi\) | |||||||
\(572\) | −10.6421 | − | 14.5110i | −0.444967 | − | 0.606734i | ||||
\(573\) | −2.49571 | −0.104260 | ||||||||
\(574\) | 50.7115 | − | 16.6023i | 2.11666 | − | 0.692967i | ||||
\(575\) | 5.33966 | + | 25.1530i | 0.222679 | + | 1.04895i | ||||
\(576\) | 6.90610 | + | 20.3252i | 0.287754 | + | 0.846883i | ||||
\(577\) | − | 24.8985i | − | 1.03654i | −0.855218 | − | 0.518269i | \(-0.826577\pi\) | ||
0.855218 | − | 0.518269i | \(-0.173423\pi\) | |||||||
\(578\) | −7.44159 | − | 22.7302i | −0.309529 | − | 0.945453i | ||||
\(579\) | 3.59759i | 0.149511i | ||||||||
\(580\) | 30.4260 | + | 1.46243i | 1.26337 | + | 0.0607240i | ||||
\(581\) | −19.9466 | −0.827526 | ||||||||
\(582\) | 9.01228 | − | 2.95050i | 0.373571 | − | 0.122302i | ||||
\(583\) | − | 42.6146i | − | 1.76492i | ||||||
\(584\) | 13.5612 | − | 18.9304i | 0.561165 | − | 0.783346i | ||||
\(585\) | 8.85303 | − | 10.9297i | 0.366028 | − | 0.451888i | ||||
\(586\) | 4.57144 | + | 13.9634i | 0.188845 | + | 0.576823i | ||||
\(587\) | 41.6137 | 1.71758 | 0.858790 | − | 0.512327i | \(-0.171217\pi\) | ||||
0.858790 | + | 0.512327i | \(0.171217\pi\) | |||||||
\(588\) | 1.85197 | + | 2.52525i | 0.0763739 | + | 0.104140i | ||||
\(589\) | −20.7410 | + | 0.799298i | −0.854617 | + | 0.0329345i | ||||
\(590\) | 21.6630 | + | 8.26345i | 0.891851 | + | 0.340201i | ||||
\(591\) | 12.5942 | 0.518056 | ||||||||
\(592\) | 2.18265 | − | 6.92718i | 0.0897063 | − | 0.284705i | ||||
\(593\) | 34.0574i | 1.39857i | 0.714843 | + | 0.699285i | \(0.246498\pi\) | ||||
−0.714843 | + | 0.699285i | \(0.753502\pi\) | |||||||
\(594\) | −5.40151 | − | 16.4988i | −0.221627 | − | 0.676956i | ||||
\(595\) | −1.61091 | − | 1.30483i | −0.0660408 | − | 0.0534929i | ||||
\(596\) | 30.3252 | − | 22.2399i | 1.24217 | − | 0.910983i | ||||
\(597\) | 0.332811 | 0.0136211 | ||||||||
\(598\) | 5.30463 | + | 16.2029i | 0.216922 | + | 0.662587i | ||||
\(599\) | −45.2260 | −1.84789 | −0.923943 | − | 0.382530i | \(-0.875053\pi\) | ||||
−0.923943 | + | 0.382530i | \(0.875053\pi\) | |||||||
\(600\) | −7.29120 | − | 3.19021i | −0.297662 | − | 0.130240i | ||||
\(601\) | − | 13.7934i | − | 0.562645i | −0.959613 | − | 0.281322i | \(-0.909227\pi\) | ||
0.959613 | − | 0.281322i | \(-0.0907730\pi\) | |||||||
\(602\) | −0.236541 | − | 0.722511i | −0.00964068 | − | 0.0294473i | ||||
\(603\) | 25.4097i | 1.03476i | ||||||||
\(604\) | −14.0494 | + | 10.3036i | −0.571662 | + | 0.419246i | ||||
\(605\) | −5.25213 | + | 6.48413i | −0.213530 | + | 0.263618i | ||||
\(606\) | 4.55130 | − | 1.49004i | 0.184884 | − | 0.0605286i | ||||
\(607\) | − | 6.05673i | − | 0.245835i | −0.992417 | − | 0.122918i | \(-0.960775\pi\) | ||
0.992417 | − | 0.122918i | \(-0.0392251\pi\) | |||||||
\(608\) | 24.6272 | − | 1.22424i | 0.998767 | − | 0.0496494i | ||||
\(609\) | −11.9887 | −0.485808 | ||||||||
\(610\) | −9.66931 | − | 3.68840i | −0.391499 | − | 0.149339i | ||||
\(611\) | −16.3175 | −0.660137 | ||||||||
\(612\) | 0.940762 | + | 1.28278i | 0.0380281 | + | 0.0518532i | ||||
\(613\) | − | 17.6797i | − | 0.714074i | −0.934090 | − | 0.357037i | \(-0.883787\pi\) | ||
0.934090 | − | 0.357037i | \(-0.116213\pi\) | |||||||
\(614\) | −15.4820 | + | 5.06861i | −0.624802 | + | 0.204552i | ||||
\(615\) | 9.55490 | − | 11.7962i | 0.385291 | − | 0.475669i | ||||
\(616\) | −19.7735 | + | 27.6024i | −0.796698 | + | 1.11213i | ||||
\(617\) | − | 20.4490i | − | 0.823245i | −0.911355 | − | 0.411622i | \(-0.864962\pi\) | ||
0.911355 | − | 0.411622i | \(-0.135038\pi\) | |||||||
\(618\) | −0.245054 | − | 0.748513i | −0.00985751 | − | 0.0301096i | ||||
\(619\) | 41.3733i | 1.66293i | 0.555576 | + | 0.831466i | \(0.312498\pi\) | ||||
−0.555576 | + | 0.831466i | \(0.687502\pi\) | |||||||
\(620\) | −1.02239 | + | 21.2710i | −0.0410603 | + | 0.854265i | ||||
\(621\) | 16.4480i | 0.660036i | ||||||||
\(622\) | −26.1598 | + | 8.56438i | −1.04891 | + | 0.343400i | ||||
\(623\) | − | 10.9226i | − | 0.437604i | ||||||
\(624\) | −5.03295 | − | 1.58581i | −0.201479 | − | 0.0634830i | ||||
\(625\) | −22.8439 | + | 10.1566i | −0.913755 | + | 0.406266i | ||||
\(626\) | −19.3377 | + | 6.33091i | −0.772889 | + | 0.253034i | ||||
\(627\) | −9.40810 | + | 0.362561i | −0.375723 | + | 0.0144793i | ||||
\(628\) | −15.1857 | − | 20.7064i | −0.605974 | − | 0.826275i | ||||
\(629\) | − | 0.538217i | − | 0.0214601i | ||||||
\(630\) | −24.7966 | − | 9.45879i | −0.987921 | − | 0.376847i | ||||
\(631\) | − | 8.70064i | − | 0.346367i | −0.984890 | − | 0.173183i | \(-0.944595\pi\) | ||
0.984890 | − | 0.173183i | \(-0.0554054\pi\) | |||||||
\(632\) | 17.2420 | + | 12.3516i | 0.685848 | + | 0.491320i | ||||
\(633\) | 10.6076i | 0.421616i | ||||||||
\(634\) | 4.97654 | + | 15.2008i | 0.197644 | + | 0.603700i | ||||
\(635\) | 13.6555 | + | 11.0609i | 0.541903 | + | 0.438940i | ||||
\(636\) | −7.39017 | − | 10.0769i | −0.293039 | − | 0.399574i | ||||
\(637\) | 6.52239 | 0.258426 | ||||||||
\(638\) | −11.5034 | − | 35.1369i | −0.455423 | − | 1.39108i | ||||
\(639\) | 25.3690 | 1.00358 | ||||||||
\(640\) | 0.932694 | − | 25.2810i | 0.0368680 | − | 0.999320i | ||||
\(641\) | 21.0321i | 0.830718i | 0.909658 | + | 0.415359i | \(0.136344\pi\) | ||||
−0.909658 | + | 0.415359i | \(0.863656\pi\) | |||||||
\(642\) | 2.46556 | + | 7.53102i | 0.0973079 | + | 0.297226i | ||||
\(643\) | −28.6196 | −1.12865 | −0.564323 | − | 0.825554i | \(-0.690863\pi\) | ||||
−0.564323 | + | 0.825554i | \(0.690863\pi\) | |||||||
\(644\) | 25.9410 | − | 19.0246i | 1.02222 | − | 0.749675i | ||||
\(645\) | −0.168066 | − | 0.136133i | −0.00661760 | − | 0.00536024i | ||||
\(646\) | 1.71338 | − | 0.634978i | 0.0674119 | − | 0.0249829i | ||||
\(647\) | −15.6384 | −0.614808 | −0.307404 | − | 0.951579i | \(-0.599460\pi\) | ||||
−0.307404 | + | 0.951579i | \(0.599460\pi\) | |||||||
\(648\) | 14.3708 | + | 10.2948i | 0.564540 | + | 0.404419i | ||||
\(649\) | − | 28.1413i | − | 1.10464i | ||||||
\(650\) | −14.3389 | + | 8.31632i | −0.562418 | + | 0.326193i | ||||
\(651\) | − | 8.38140i | − | 0.328493i | ||||||
\(652\) | −0.663564 | + | 0.486645i | −0.0259872 | + | 0.0190585i | ||||
\(653\) | 21.3458i | 0.835324i | 0.908602 | + | 0.417662i | \(0.137150\pi\) | ||||
−0.908602 | + | 0.417662i | \(0.862850\pi\) | |||||||
\(654\) | −3.44701 | − | 10.5289i | −0.134789 | − | 0.411711i | ||||
\(655\) | −27.9203 | − | 22.6154i | −1.09094 | − | 0.883656i | ||||
\(656\) | 46.0242 | + | 14.5015i | 1.79694 | + | 0.566189i | ||||
\(657\) | − | 22.0918i | − | 0.861883i | ||||||
\(658\) | 9.57959 | + | 29.2607i | 0.373451 | + | 1.14070i | ||||
\(659\) | 27.8535 | 1.08502 | 0.542510 | − | 0.840049i | \(-0.317474\pi\) | ||||
0.542510 | + | 0.840049i | \(0.317474\pi\) | |||||||
\(660\) | −0.463757 | + | 9.64853i | −0.0180517 | + | 0.375569i | ||||
\(661\) | 18.3813i | 0.714949i | 0.933923 | + | 0.357474i | \(0.116362\pi\) | ||||
−0.933923 | + | 0.357474i | \(0.883638\pi\) | |||||||
\(662\) | 3.75971 | + | 11.4840i | 0.146125 | + | 0.446338i | ||||
\(663\) | −0.391042 | −0.0151868 | ||||||||
\(664\) | −14.6638 | − | 10.5047i | −0.569067 | − | 0.407662i | ||||
\(665\) | −18.2613 | + | 24.4100i | −0.708143 | + | 0.946579i | ||||
\(666\) | −2.14382 | − | 6.54826i | −0.0830712 | − | 0.253740i | ||||
\(667\) | 35.0286i | 1.35631i | ||||||||
\(668\) | 1.84762 | + | 2.51932i | 0.0714866 | + | 0.0974755i | ||||
\(669\) | 8.76388 | 0.338831 | ||||||||
\(670\) | 10.6727 | − | 27.9789i | 0.412322 | − | 1.08092i | ||||
\(671\) | 12.5609i | 0.484909i | ||||||||
\(672\) | 0.111033 | + | 9.95611i | 0.00428318 | + | 0.384065i | ||||
\(673\) | −40.0610 | −1.54424 | −0.772119 | − | 0.635478i | \(-0.780803\pi\) | ||||
−0.772119 | + | 0.635478i | \(0.780803\pi\) | |||||||
\(674\) | 4.30029 | + | 13.1352i | 0.165641 | + | 0.505948i | ||||
\(675\) | −15.6430 | + | 3.32080i | −0.602099 | + | 0.127818i | ||||
\(676\) | 12.1034 | − | 8.87637i | 0.465514 | − | 0.341399i | ||||
\(677\) | 27.5660 | 1.05945 | 0.529723 | − | 0.848171i | \(-0.322296\pi\) | ||||
0.529723 | + | 0.848171i | \(0.322296\pi\) | |||||||
\(678\) | −13.9894 | + | 4.57994i | −0.537258 | + | 0.175892i | ||||
\(679\) | −37.2675 | −1.43019 | ||||||||
\(680\) | −0.497087 | − | 1.80762i | −0.0190624 | − | 0.0693191i | ||||
\(681\) | −12.9558 | −0.496467 | ||||||||
\(682\) | 24.5644 | − | 8.04208i | 0.940621 | − | 0.307947i | ||||
\(683\) | 27.6266i | 1.05710i | 0.848901 | + | 0.528552i | \(0.177265\pi\) | ||||
−0.848901 | + | 0.528552i | \(0.822735\pi\) | |||||||
\(684\) | 18.3167 | − | 14.5502i | 0.700356 | − | 0.556341i | ||||
\(685\) | 32.6845 | + | 26.4743i | 1.24881 | + | 1.01153i | ||||
\(686\) | 5.80444 | + | 17.7296i | 0.221614 | + | 0.676918i | ||||
\(687\) | − | 7.91228i | − | 0.301872i | ||||||
\(688\) | 0.206610 | − | 0.655728i | 0.00787692 | − | 0.0249994i | ||||
\(689\) | −26.0272 | −0.991558 | ||||||||
\(690\) | 3.26179 | − | 8.55093i | 0.124174 | − | 0.325528i | ||||
\(691\) | 16.1536i | 0.614513i | 0.951627 | + | 0.307256i | \(0.0994109\pi\) | ||||
−0.951627 | + | 0.307256i | \(0.900589\pi\) | |||||||
\(692\) | −18.3852 | + | 13.4833i | −0.698900 | + | 0.512559i | ||||
\(693\) | 32.2120i | 1.22363i | ||||||||
\(694\) | 14.1930 | + | 43.3523i | 0.538759 | + | 1.64563i | ||||
\(695\) | −26.4597 | − | 21.4323i | −1.00367 | − | 0.812973i | ||||
\(696\) | −8.81355 | − | 6.31375i | −0.334077 | − | 0.239322i | ||||
\(697\) | 3.57591 | 0.135447 | ||||||||
\(698\) | −5.41060 | − | 16.5266i | −0.204794 | − | 0.625541i | ||||
\(699\) | 10.3049 | 0.389767 | ||||||||
\(700\) | 23.3309 | + | 20.8303i | 0.881825 | + | 0.787313i | ||||
\(701\) | −10.8798 | −0.410923 | −0.205461 | − | 0.978665i | \(-0.565869\pi\) | ||||
−0.205461 | + | 0.978665i | \(0.565869\pi\) | |||||||
\(702\) | −10.0768 | + | 3.29902i | −0.380324 | + | 0.124513i | ||||
\(703\) | −7.90869 | + | 0.304779i | −0.298282 | + | 0.0114949i | ||||
\(704\) | −29.0731 | + | 9.87847i | −1.09573 | + | 0.372309i | ||||
\(705\) | 6.80646 | + | 5.51321i | 0.256346 | + | 0.207640i | ||||
\(706\) | −12.7488 | + | 4.17380i | −0.479808 | + | 0.157083i | ||||
\(707\) | −18.8205 | −0.707817 | ||||||||
\(708\) | −4.88023 | − | 6.65444i | −0.183410 | − | 0.250089i | ||||
\(709\) | −45.2518 | −1.69947 | −0.849734 | − | 0.527212i | \(-0.823237\pi\) | ||||
−0.849734 | + | 0.527212i | \(0.823237\pi\) | |||||||
\(710\) | −27.9341 | − | 10.6556i | −1.04835 | − | 0.399897i | ||||
\(711\) | 20.1214 | 0.754610 | ||||||||
\(712\) | 5.75227 | − | 8.02976i | 0.215576 | − | 0.300928i | ||||
\(713\) | −24.4887 | −0.917110 | ||||||||
\(714\) | 0.229571 | + | 0.701220i | 0.00859147 | + | 0.0262425i | ||||
\(715\) | 15.6338 | + | 12.6634i | 0.584672 | + | 0.473583i | ||||
\(716\) | 13.4039 | − | 9.83014i | 0.500926 | − | 0.367369i | ||||
\(717\) | −4.04847 | −0.151193 | ||||||||
\(718\) | 15.8426 | − | 5.18666i | 0.591240 | − | 0.193564i | ||||
\(719\) | − | 36.6480i | − | 1.36674i | −0.730073 | − | 0.683369i | \(-0.760514\pi\) | ||
0.730073 | − | 0.683369i | \(-0.239486\pi\) | |||||||
\(720\) | −13.2479 | − | 20.0126i | −0.493721 | − | 0.745824i | ||||
\(721\) | 3.09525i | 0.115273i | ||||||||
\(722\) | −10.3008 | − | 24.8172i | −0.383355 | − | 0.923601i | ||||
\(723\) | −1.38156 | −0.0513808 | ||||||||
\(724\) | 1.72950 | + | 2.35826i | 0.0642765 | + | 0.0876442i | ||||
\(725\) | −33.3142 | + | 7.07218i | −1.23726 | + | 0.262654i | ||||
\(726\) | 2.82251 | − | 0.924054i | 0.104753 | − | 0.0342949i | ||||
\(727\) | 29.9330 | 1.11015 | 0.555077 | − | 0.831799i | \(-0.312689\pi\) | ||||
0.555077 | + | 0.831799i | \(0.312689\pi\) | |||||||
\(728\) | 16.8584 | + | 12.0768i | 0.624814 | + | 0.447597i | ||||
\(729\) | 11.3712 | 0.421154 | ||||||||
\(730\) | −9.27909 | + | 24.3255i | −0.343434 | + | 0.900328i | ||||
\(731\) | − | 0.0509477i | − | 0.00188437i | ||||||
\(732\) | 2.17830 | + | 2.97022i | 0.0805123 | + | 0.109782i | ||||
\(733\) | 11.4917i | 0.424456i | 0.977220 | + | 0.212228i | \(0.0680719\pi\) | ||||
−0.977220 | + | 0.212228i | \(0.931928\pi\) | |||||||
\(734\) | −12.1630 | − | 37.1518i | −0.448946 | − | 1.37130i | ||||
\(735\) | −2.72065 | − | 2.20372i | −0.100353 | − | 0.0812855i | ||||
\(736\) | 29.0897 | − | 0.324415i | 1.07226 | − | 0.0119581i | ||||
\(737\) | −36.3460 | −1.33882 | ||||||||
\(738\) | 43.5066 | − | 14.2435i | 1.60150 | − | 0.524311i | ||||
\(739\) | − | 10.5334i | − | 0.387477i | −0.981053 | − | 0.193739i | \(-0.937939\pi\) | ||
0.981053 | − | 0.193739i | \(-0.0620613\pi\) | |||||||
\(740\) | −0.389846 | + | 8.11081i | −0.0143310 | + | 0.298159i | ||||
\(741\) | 0.221437 | + | 5.74607i | 0.00813470 | + | 0.211087i | ||||
\(742\) | 15.2799 | + | 46.6722i | 0.560942 | + | 1.71339i | ||||
\(743\) | 0.681568i | 0.0250043i | 0.999922 | + | 0.0125022i | \(0.00397966\pi\) | ||||
−0.999922 | + | 0.0125022i | \(0.996020\pi\) | |||||||
\(744\) | 4.41398 | − | 6.16161i | 0.161825 | − | 0.225896i | ||||
\(745\) | −26.4641 | + | 32.6718i | −0.969569 | + | 1.19700i | ||||
\(746\) | −6.71342 | − | 20.5061i | −0.245796 | − | 0.750780i | ||||
\(747\) | −17.1127 | −0.626121 | ||||||||
\(748\) | −1.83488 | + | 1.34566i | −0.0670898 | + | 0.0492024i | ||||
\(749\) | − | 31.1422i | − | 1.13791i | ||||||
\(750\) | 8.79096 | + | 1.37574i | 0.321001 | + | 0.0502350i | ||||
\(751\) | −4.02795 | −0.146982 | −0.0734910 | − | 0.997296i | \(-0.523414\pi\) | ||||
−0.0734910 | + | 0.997296i | \(0.523414\pi\) | |||||||
\(752\) | −8.36743 | + | 26.5561i | −0.305129 | + | 0.968402i | ||||
\(753\) | 8.09063 | 0.294839 | ||||||||
\(754\) | −21.4601 | + | 7.02578i | −0.781532 | + | 0.255864i | ||||
\(755\) | 12.2606 | − | 15.1365i | 0.446208 | − | 0.550875i | ||||
\(756\) | 11.8317 | + | 16.1330i | 0.430313 | + | 0.586753i | ||||
\(757\) | 11.3612i | 0.412930i | 0.978454 | + | 0.206465i | \(0.0661960\pi\) | ||||
−0.978454 | + | 0.206465i | \(0.933804\pi\) | |||||||
\(758\) | −13.1385 | − | 40.1313i | −0.477211 | − | 1.45764i | ||||
\(759\) | −11.1081 | −0.403198 | ||||||||
\(760\) | −26.2801 | + | 8.32792i | −0.953281 | + | 0.302086i | ||||
\(761\) | −33.0747 | −1.19896 | −0.599479 | − | 0.800390i | \(-0.704626\pi\) | ||||
−0.599479 | + | 0.800390i | \(0.704626\pi\) | |||||||
\(762\) | −1.94605 | − | 5.94419i | −0.0704980 | − | 0.215335i | ||||
\(763\) | 43.5388i | 1.57621i | ||||||||
\(764\) | 5.24537 | + | 7.15232i | 0.189771 | + | 0.258762i | ||||
\(765\) | −1.38204 | − | 1.11945i | −0.0499676 | − | 0.0404737i | ||||
\(766\) | 32.4853 | − | 10.6353i | 1.17374 | − | 0.384268i | ||||
\(767\) | −17.1875 | −0.620606 | ||||||||
\(768\) | −5.16167 | + | 7.37774i | −0.186256 | + | 0.266221i | ||||
\(769\) | 9.24948 | 0.333545 | 0.166772 | − | 0.985995i | \(-0.446665\pi\) | ||||
0.166772 | + | 0.985995i | \(0.446665\pi\) | |||||||
\(770\) | 13.5298 | − | 35.4690i | 0.487581 | − | 1.27821i | ||||
\(771\) | 7.52329i | 0.270945i | ||||||||
\(772\) | 10.3102 | − | 7.56126i | 0.371071 | − | 0.272136i | ||||
\(773\) | 40.5301 | 1.45777 | 0.728884 | − | 0.684638i | \(-0.240040\pi\) | ||||
0.728884 | + | 0.684638i | \(0.240040\pi\) | |||||||
\(774\) | −0.202934 | − | 0.619859i | −0.00729431 | − | 0.0222804i | ||||
\(775\) | −4.94421 | − | 23.2902i | −0.177601 | − | 0.836608i | ||||
\(776\) | −27.3973 | − | 19.6266i | −0.983506 | − | 0.704553i | ||||
\(777\) | − | 3.19589i | − | 0.114652i | ||||||
\(778\) | −6.45254 | − | 19.7092i | −0.231335 | − | 0.706609i | ||||
\(779\) | −2.02495 | − | 52.5453i | −0.0725513 | − | 1.88263i | ||||
\(780\) | 5.89292 | + | 0.283243i | 0.211000 | + | 0.0101417i | ||||
\(781\) | 36.2878i | 1.29848i | ||||||||
\(782\) | 2.04882 | − | 0.670759i | 0.0732658 | − | 0.0239863i | ||||
\(783\) | −21.7848 | −0.778524 | ||||||||
\(784\) | 3.34460 | − | 10.6149i | 0.119450 | − | 0.379104i | ||||
\(785\) | 22.3086 | + | 18.0699i | 0.796230 | + | 0.644944i | ||||
\(786\) | 3.97893 | + | 12.1536i | 0.141924 | + | 0.433504i | ||||
\(787\) | − | 31.2567i | − | 1.11418i | −0.830452 | − | 0.557090i | \(-0.811918\pi\) | ||
0.830452 | − | 0.557090i | \(-0.188082\pi\) | |||||||
\(788\) | −26.4699 | − | 36.0930i | −0.942951 | − | 1.28576i | ||||
\(789\) | − | 10.3177i | − | 0.367319i | ||||||
\(790\) | −22.1559 | − | 8.45146i | −0.788270 | − | 0.300689i | ||||
\(791\) | 57.8487 | 2.05686 | ||||||||
\(792\) | −16.9642 | + | 23.6808i | −0.602796 | + | 0.841460i | ||||
\(793\) | 7.67168 | 0.272429 | ||||||||
\(794\) | −14.5584 | + | 4.76624i | −0.516659 | + | 0.169148i | ||||
\(795\) | 10.8566 | + | 8.79383i | 0.385044 | + | 0.311885i | ||||
\(796\) | −0.699488 | − | 0.953786i | −0.0247927 | − | 0.0338060i | ||||
\(797\) | −2.60336 | −0.0922156 | −0.0461078 | − | 0.998936i | \(-0.514682\pi\) | ||||
−0.0461078 | + | 0.998936i | \(0.514682\pi\) | |||||||
\(798\) | 10.1739 | − | 3.77045i | 0.360152 | − | 0.133473i | ||||
\(799\) | 2.06332i | 0.0729949i | ||||||||
\(800\) | 6.18167 | + | 27.6005i | 0.218555 | + | 0.975825i | ||||
\(801\) | − | 9.37074i | − | 0.331099i | ||||||
\(802\) | −32.7474 | + | 10.7211i | −1.15635 | + | 0.378575i | ||||
\(803\) | 31.6001 | 1.11514 | ||||||||
\(804\) | −8.59455 | + | 6.30307i | −0.303106 | + | 0.222292i | ||||
\(805\) | −22.6381 | + | 27.9483i | −0.797887 | + | 0.985048i | ||||
\(806\) | −4.91177 | − | 15.0029i | −0.173010 | − | 0.528456i | ||||
\(807\) | 2.20445 | 0.0776002 | ||||||||
\(808\) | −13.8359 | − | 9.91163i | −0.486746 | − | 0.348690i | ||||
\(809\) | 32.4459 | 1.14074 | 0.570368 | − | 0.821389i | \(-0.306800\pi\) | ||||
0.570368 | + | 0.821389i | \(0.306800\pi\) | |||||||
\(810\) | −18.4665 | − | 7.04413i | −0.648846 | − | 0.247505i | ||||
\(811\) | 36.2431 | 1.27267 | 0.636333 | − | 0.771414i | \(-0.280450\pi\) | ||||
0.636333 | + | 0.771414i | \(0.280450\pi\) | |||||||
\(812\) | 25.1974 | + | 34.3579i | 0.884255 | + | 1.20572i | ||||
\(813\) | 18.0529 | 0.633141 | ||||||||
\(814\) | 9.36661 | − | 3.06651i | 0.328300 | − | 0.107481i | ||||
\(815\) | 0.579075 | − | 0.714910i | 0.0202841 | − | 0.0250422i | ||||
\(816\) | −0.200522 | + | 0.636405i | −0.00701966 | + | 0.0222786i | ||||
\(817\) | −0.748638 | + | 0.0288504i | −0.0261915 | + | 0.00100935i | ||||
\(818\) | −19.3372 | + | 6.33077i | −0.676111 | + | 0.221350i | ||||
\(819\) | 19.6738 | 0.687457 | ||||||||
\(820\) | −53.8882 | − | 2.59014i | −1.88186 | − | 0.0904515i | ||||
\(821\) | −9.80103 | −0.342058 | −0.171029 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171029 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(822\) | −4.65787 | − | 14.2274i | −0.162462 | − | 0.496237i | ||||
\(823\) | 47.5409 | 1.65717 | 0.828586 | − | 0.559862i | \(-0.189146\pi\) | ||||
0.828586 | + | 0.559862i | \(0.189146\pi\) | |||||||
\(824\) | −1.63008 | + | 2.27548i | −0.0567866 | + | 0.0792700i | ||||
\(825\) | −2.24269 | − | 10.5644i | −0.0780804 | − | 0.367806i | ||||
\(826\) | 10.0903 | + | 30.8208i | 0.351088 | + | 1.07239i | ||||
\(827\) | 29.7178i | 1.03339i | 0.856169 | + | 0.516695i | \(0.172838\pi\) | ||||
−0.856169 | + | 0.516695i | \(0.827162\pi\) | |||||||
\(828\) | 22.2554 | − | 16.3217i | 0.773429 | − | 0.567217i | ||||
\(829\) | 26.6191i | 0.924521i | 0.886744 | + | 0.462260i | \(0.152961\pi\) | ||||
−0.886744 | + | 0.462260i | \(0.847039\pi\) | |||||||
\(830\) | 18.8430 | + | 7.18774i | 0.654049 | + | 0.249490i | ||||
\(831\) | 3.46371 | 0.120155 | ||||||||
\(832\) | 6.03335 | + | 17.7566i | 0.209169 | + | 0.615601i | ||||
\(833\) | − | 0.824741i | − | 0.0285756i | ||||||
\(834\) | 3.77077 | + | 11.5178i | 0.130571 | + | 0.398828i | ||||
\(835\) | −2.71427 | − | 2.19855i | −0.0939310 | − | 0.0760839i | ||||
\(836\) | 20.8126 | + | 26.2002i | 0.719818 | + | 0.906151i | ||||
\(837\) | − | 15.2299i | − | 0.526421i | ||||||
\(838\) | 34.9347 | − | 11.4372i | 1.20680 | − | 0.395091i | ||||
\(839\) | −42.7153 | −1.47470 | −0.737348 | − | 0.675513i | \(-0.763922\pi\) | ||||
−0.737348 | + | 0.675513i | \(0.763922\pi\) | |||||||
\(840\) | −2.95166 | − | 10.7335i | −0.101842 | − | 0.370341i | ||||
\(841\) | −17.3941 | −0.599796 | ||||||||
\(842\) | −30.0620 | + | 9.84191i | −1.03600 | + | 0.339175i | ||||
\(843\) | 3.49650 | 0.120426 | ||||||||
\(844\) | 30.3999 | − | 22.2947i | 1.04641 | − | 0.767414i | ||||
\(845\) | −10.5623 | + | 13.0399i | −0.363354 | + | 0.448587i | ||||
\(846\) | 8.21856 | + | 25.1035i | 0.282560 | + | 0.863075i | ||||
\(847\) | −11.6716 | −0.401042 | ||||||||
\(848\) | −13.3464 | + | 42.3582i | −0.458318 | + | 1.45459i | ||||
\(849\) | − | 7.57491i | − | 0.259970i | ||||||
\(850\) | 1.05158 | + | 1.81312i | 0.0360689 | + | 0.0621896i | ||||
\(851\) | −9.33775 | −0.320094 | ||||||||
\(852\) | 6.29298 | + | 8.58079i | 0.215594 | + | 0.293973i | ||||
\(853\) | − | 25.3286i | − | 0.867236i | −0.901097 | − | 0.433618i | \(-0.857237\pi\) | ||
0.901097 | − | 0.433618i | \(-0.142763\pi\) | |||||||
\(854\) | −4.50384 | − | 13.7569i | −0.154118 | − | 0.470752i | ||||
\(855\) | −15.6668 | + | 20.9419i | −0.535793 | + | 0.716198i | ||||
\(856\) | 16.4008 | − | 22.8943i | 0.560566 | − | 0.782511i | ||||
\(857\) | −20.9648 | −0.716146 | −0.358073 | − | 0.933694i | \(-0.616566\pi\) | ||||
−0.358073 | + | 0.933694i | \(0.616566\pi\) | |||||||
\(858\) | −2.22798 | − | 6.80532i | −0.0760618 | − | 0.232330i | ||||
\(859\) | 32.2246i | 1.09949i | 0.835333 | + | 0.549745i | \(0.185275\pi\) | ||||
−0.835333 | + | 0.549745i | \(0.814725\pi\) | |||||||
\(860\) | −0.0369029 | + | 0.767770i | −0.00125838 | + | 0.0261808i | ||||
\(861\) | 21.2335 | 0.723636 | ||||||||
\(862\) | −11.3400 | − | 34.6379i | −0.386243 | − | 1.17977i | ||||
\(863\) | 52.0944i | 1.77331i | 0.462428 | + | 0.886657i | \(0.346978\pi\) | ||||
−0.462428 | + | 0.886657i | \(0.653022\pi\) | |||||||
\(864\) | 0.201758 | + | 18.0913i | 0.00686394 | + | 0.615478i | ||||
\(865\) | 16.0443 | − | 19.8078i | 0.545522 | − | 0.673486i | ||||
\(866\) | −7.89314 | − | 24.1095i | −0.268220 | − | 0.819274i | ||||
\(867\) | − | 9.51741i | − | 0.323228i | ||||||
\(868\) | −24.0198 | + | 17.6156i | −0.815285 | + | 0.597914i | ||||
\(869\) | 28.7816i | 0.976348i | ||||||||
\(870\) | 11.3254 | + | 4.32012i | 0.383966 | + | 0.146466i | ||||
\(871\) | 22.1986i | 0.752170i | ||||||||
\(872\) | −22.9293 | + | 32.0077i | −0.776485 | + | 1.08392i | ||||
\(873\) | −31.9727 | −1.08211 | ||||||||
\(874\) | −11.0165 | − | 29.7261i | −0.372638 | − | 1.00550i | ||||
\(875\) | −31.1510 | − | 15.8874i | −1.05310 | − | 0.537092i | ||||
\(876\) | 7.47231 | − | 5.48005i | 0.252466 | − | 0.185154i | ||||
\(877\) | −6.22331 | −0.210146 | −0.105073 | − | 0.994465i | \(-0.533508\pi\) | ||||
−0.105073 | + | 0.994465i | \(0.533508\pi\) | |||||||
\(878\) | 10.1190 | + | 30.9082i | 0.341498 | + | 1.04310i | ||||
\(879\) | 5.84664i | 0.197202i | ||||||||
\(880\) | 28.6259 | − | 18.9498i | 0.964980 | − | 0.638797i | ||||
\(881\) | 22.3999 | 0.754672 | 0.377336 | − | 0.926076i | \(-0.376840\pi\) | ||||
0.377336 | + | 0.926076i | \(0.376840\pi\) | |||||||
\(882\) | −3.28509 | − | 10.0343i | −0.110615 | − | 0.337872i | ||||
\(883\) | 13.1166 | 0.441410 | 0.220705 | − | 0.975341i | \(-0.429164\pi\) | ||||
0.220705 | + | 0.975341i | \(0.429164\pi\) | |||||||
\(884\) | 0.821875 | + | 1.12067i | 0.0276427 | + | 0.0376921i | ||||
\(885\) | 7.16936 | + | 5.80716i | 0.240995 | + | 0.195206i | ||||
\(886\) | 10.7271 | + | 32.7657i | 0.360383 | + | 1.10078i | ||||
\(887\) | − | 8.90724i | − | 0.299076i | −0.988756 | − | 0.149538i | \(-0.952221\pi\) | ||
0.988756 | − | 0.149538i | \(-0.0477786\pi\) | |||||||
\(888\) | 1.68309 | − | 2.34947i | 0.0564807 | − | 0.0788430i | ||||
\(889\) | 24.5803i | 0.824398i | ||||||||
\(890\) | −3.93593 | + | 10.3182i | −0.131933 | + | 0.345867i | ||||
\(891\) | 23.9889i | 0.803657i | ||||||||
\(892\) | −18.4195 | − | 25.1160i | −0.616732 | − | 0.840944i | ||||
\(893\) | 30.3189 | − | 1.16840i | 1.01458 | − | 0.0390991i | ||||
\(894\) | 14.2219 | − | 4.65606i | 0.475650 | − | 0.155722i | ||||
\(895\) | −11.6972 | + | 14.4411i | −0.390995 | + | 0.482712i | ||||
\(896\) | 28.2993 | − | 21.2435i | 0.945415 | − | 0.709696i | ||||
\(897\) | 6.78435i | 0.226523i | ||||||||
\(898\) | 47.0712 | − | 15.4105i | 1.57079 | − | 0.514256i | ||||
\(899\) | − | 32.4344i | − | 1.08175i | ||||||
\(900\) | 20.0161 | + | 17.8708i | 0.667204 | + | 0.595695i | ||||
\(901\) | 3.29108i | 0.109642i | ||||||||
\(902\) | 20.3739 | + | 62.2317i | 0.678376 | + | 2.07209i | ||||
\(903\) | − | 0.302524i | − | 0.0100674i | ||||||
\(904\) | 42.5276 | + | 30.4655i | 1.41445 | + | 1.01327i | ||||
\(905\) | −2.54074 | − | 2.05800i | −0.0844572 | − | 0.0684101i | ||||
\(906\) | −6.58886 | + | 2.15711i | −0.218900 | + | 0.0716652i | ||||
\(907\) | 33.0139i | 1.09621i | 0.836410 | + | 0.548105i | \(0.184650\pi\) | ||||
−0.836410 | + | 0.548105i | \(0.815350\pi\) | |||||||
\(908\) | 27.2299 | + | 37.1293i | 0.903656 | + | 1.23218i | ||||
\(909\) | −16.1465 | −0.535547 | ||||||||
\(910\) | −21.6630 | − | 8.26345i | −0.718121 | − | 0.273931i | ||||
\(911\) | 39.2354 | 1.29993 | 0.649963 | − | 0.759966i | \(-0.274784\pi\) | ||||
0.649963 | + | 0.759966i | \(0.274784\pi\) | |||||||
\(912\) | 9.46505 | + | 2.58613i | 0.313419 | + | 0.0856354i | ||||
\(913\) | − | 24.4780i | − | 0.810102i | ||||||
\(914\) | 2.33850 | − | 0.765594i | 0.0773506 | − | 0.0253236i | ||||
\(915\) | −3.20005 | − | 2.59203i | −0.105790 | − | 0.0856900i | ||||
\(916\) | −22.6754 | + | 16.6297i | −0.749215 | + | 0.549460i | ||||
\(917\) | − | 50.2574i | − | 1.65964i | ||||||
\(918\) | 0.417154 | + | 1.27419i | 0.0137681 | + | 0.0420545i | ||||
\(919\) | 6.07612i | 0.200433i | 0.994966 | + | 0.100216i | \(0.0319535\pi\) | ||||
−0.994966 | + | 0.100216i | \(0.968047\pi\) | |||||||
\(920\) | −31.3611 | + | 8.62416i | −1.03395 | + | 0.284330i | ||||
\(921\) | −6.48249 | −0.213605 | ||||||||
\(922\) | −9.22876 | − | 28.1891i | −0.303933 | − | 0.928359i | ||||
\(923\) | 22.1630 | 0.729505 | ||||||||
\(924\) | −10.8954 | + | 7.99045i | −0.358432 | + | 0.262867i | ||||
\(925\) | −1.88526 | − | 8.88073i | −0.0619871 | − | 0.291996i | ||||
\(926\) | −1.91954 | − | 5.86319i | −0.0630798 | − | 0.192677i | ||||
\(927\) | 2.65548i | 0.0872175i | ||||||||
\(928\) | 0.429675 | + | 38.5283i | 0.0141048 | + | 1.26475i | ||||
\(929\) | 4.15684 | 0.136382 | 0.0681908 | − | 0.997672i | \(-0.478277\pi\) | ||||
0.0681908 | + | 0.997672i | \(0.478277\pi\) | |||||||
\(930\) | −3.02022 | + | 7.91764i | −0.0990370 | + | 0.259630i | ||||
\(931\) | −12.1190 | + | 0.467030i | −0.397183 | + | 0.0153063i | ||||
\(932\) | −21.6584 | − | 29.5323i | −0.709444 | − | 0.967362i | ||||
\(933\) | −10.9534 | −0.358598 | ||||||||
\(934\) | −5.07091 | − | 15.4890i | −0.165925 | − | 0.506817i | ||||
\(935\) | 1.60125 | − | 1.97686i | 0.0523666 | − | 0.0646503i | ||||
\(936\) | 14.4632 | + | 10.3610i | 0.472745 | + | 0.338660i | ||||
\(937\) | − | 37.0667i | − | 1.21091i | −0.795878 | − | 0.605457i | \(-0.792990\pi\) | ||
0.795878 | − | 0.605457i | \(-0.207010\pi\) | |||||||
\(938\) | 39.8067 | − | 13.0322i | 1.29973 | − | 0.425517i | ||||
\(939\) | −8.09691 | −0.264233 | ||||||||
\(940\) | 1.49452 | − | 31.0937i | 0.0487458 | − | 1.01416i | ||||
\(941\) | − | 21.6239i | − | 0.704920i | −0.935827 | − | 0.352460i | \(-0.885345\pi\) | ||
0.935827 | − | 0.352460i | \(-0.114655\pi\) | |||||||
\(942\) | −3.17921 | − | 9.71084i | −0.103584 | − | 0.316396i | ||||
\(943\) | − | 62.0400i | − | 2.02030i | ||||||
\(944\) | −8.81355 | + | 27.9720i | −0.286857 | + | 0.910411i | ||||
\(945\) | −17.3814 | − | 14.0789i | −0.565417 | − | 0.457987i | ||||
\(946\) | 0.886645 | − | 0.290276i | 0.0288273 | − | 0.00943769i | ||||
\(947\) | 4.46662 | 0.145146 | 0.0725729 | − | 0.997363i | \(-0.476879\pi\) | ||||
0.0725729 | + | 0.997363i | \(0.476879\pi\) | |||||||
\(948\) | 4.99127 | + | 6.80584i | 0.162109 | + | 0.221043i | ||||
\(949\) | − | 19.3000i | − | 0.626504i | ||||||
\(950\) | 26.0470 | − | 16.4789i | 0.845076 | − | 0.534647i | ||||
\(951\) | 6.36474i | 0.206391i | ||||||||
\(952\) | 1.52709 | − | 2.13171i | 0.0494933 | − | 0.0690891i | ||||
\(953\) | −47.8624 | −1.55041 | −0.775207 | − | 0.631707i | \(-0.782355\pi\) | ||||
−0.775207 | + | 0.631707i | \(0.782355\pi\) | |||||||
\(954\) | 13.1090 | + | 40.0412i | 0.424419 | + | 1.29638i | ||||
\(955\) | −7.70577 | − | 6.24165i | −0.249353 | − | 0.201975i | ||||
\(956\) | 8.50889 | + | 11.6023i | 0.275197 | + | 0.375245i | ||||
\(957\) | − | 14.7122i | − | 0.475579i | ||||||
\(958\) | −15.7612 | + | 5.16002i | −0.509221 | + | 0.166713i | ||||
\(959\) | 58.8330i | 1.89982i | ||||||||
\(960\) | 3.48278 | − | 9.44524i | 0.112406 | − | 0.304844i | ||||
\(961\) | −8.32490 | −0.268545 | ||||||||
\(962\) | −1.87290 | − | 5.72073i | −0.0603846 | − | 0.184444i | ||||
\(963\) | − | 26.7176i | − | 0.860964i | ||||||
\(964\) | 2.90370 | + | 3.95934i | 0.0935219 | + | 0.127522i | ||||
\(965\) | −8.99741 | + | 11.1079i | −0.289637 | + | 0.357577i | ||||
\(966\) | 12.1658 | − | 3.98291i | 0.391427 | − | 0.128148i | ||||
\(967\) | −23.9769 | −0.771044 | −0.385522 | − | 0.922699i | \(-0.625979\pi\) | ||||
−0.385522 | + | 0.922699i | \(0.625979\pi\) | |||||||
\(968\) | −8.58042 | − | 6.14675i | −0.275785 | − | 0.197564i | ||||
\(969\) | 0.726578 | − | 0.0280003i | 0.0233411 | − | 0.000899498i | ||||
\(970\) | 35.2054 | + | 13.4293i | 1.13038 | + | 0.431188i | ||||
\(971\) | −24.6952 | −0.792508 | −0.396254 | − | 0.918141i | \(-0.629690\pi\) | ||||
−0.396254 | + | 0.918141i | \(0.629690\pi\) | |||||||
\(972\) | 15.5088 | + | 21.1470i | 0.497445 | + | 0.678291i | ||||
\(973\) | − | 47.6282i | − | 1.52689i | ||||||
\(974\) | −48.9582 | + | 16.0283i | −1.56872 | + | 0.513580i | ||||
\(975\) | −6.45230 | + | 1.36974i | −0.206639 | + | 0.0438668i | ||||
\(976\) | 3.93394 | − | 12.4853i | 0.125922 | − | 0.399646i | ||||
\(977\) | 4.34630 | 0.139051 | 0.0695253 | − | 0.997580i | \(-0.477852\pi\) | ||||
0.0695253 | + | 0.997580i | \(0.477852\pi\) | |||||||
\(978\) | −0.311197 | + | 0.101882i | −0.00995098 | + | 0.00325782i | ||||
\(979\) | 13.4039 | 0.428390 | ||||||||
\(980\) | −0.597384 | + | 12.4287i | −0.0190827 | + | 0.397019i | ||||
\(981\) | 37.3530i | 1.19259i | ||||||||
\(982\) | −10.6967 | + | 3.50195i | −0.341344 | + | 0.111752i | ||||
\(983\) | − | 10.7314i | − | 0.342277i | −0.985247 | − | 0.171139i | \(-0.945255\pi\) | ||
0.985247 | − | 0.171139i | \(-0.0547446\pi\) | |||||||
\(984\) | 15.6099 | + | 11.1824i | 0.497624 | + | 0.356483i | ||||
\(985\) | 38.8859 | + | 31.4975i | 1.23901 | + | 1.00359i | ||||
\(986\) | 0.888394 | + | 2.71359i | 0.0282922 | + | 0.0864183i | ||||
\(987\) | 12.2518i | 0.389979i | ||||||||
\(988\) | 16.0020 | − | 12.7114i | 0.509090 | − | 0.404405i | ||||
\(989\) | −0.883913 | −0.0281068 | ||||||||
\(990\) | 11.6076 | − | 30.4297i | 0.368913 | − | 0.967120i | ||||
\(991\) | 12.0344 | 0.382286 | 0.191143 | − | 0.981562i | \(-0.438781\pi\) | ||||
0.191143 | + | 0.981562i | \(0.438781\pi\) | |||||||
\(992\) | −26.9353 | + | 0.300389i | −0.855198 | + | 0.00953735i | ||||
\(993\) | 4.80848i | 0.152593i | ||||||||
\(994\) | −13.0113 | − | 39.7429i | −0.412695 | − | 1.26057i | ||||
\(995\) | 1.02759 | + | 0.832345i | 0.0325768 | + | 0.0263871i | ||||
\(996\) | −4.24494 | − | 5.78818i | −0.134506 | − | 0.183406i | ||||
\(997\) | 34.6145i | 1.09625i | 0.836396 | + | 0.548126i | \(0.184659\pi\) | ||||
−0.836396 | + | 0.548126i | \(0.815341\pi\) | |||||||
\(998\) | −34.0971 | + | 11.1630i | −1.07932 | + | 0.353357i | ||||
\(999\) | − | 5.80727i | − | 0.183734i |
(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 | 380.2.d.b.379.17 | ✓ | 40 | |
4.3 | odd | 2 | inner | 380.2.d.b.379.19 | yes | 40 | |
5.4 | even | 2 | inner | 380.2.d.b.379.24 | yes | 40 | |
19.18 | odd | 2 | inner | 380.2.d.b.379.23 | yes | 40 | |
20.19 | odd | 2 | inner | 380.2.d.b.379.22 | yes | 40 | |
76.75 | even | 2 | inner | 380.2.d.b.379.21 | yes | 40 | |
95.94 | odd | 2 | inner | 380.2.d.b.379.18 | yes | 40 | |
380.379 | even | 2 | inner | 380.2.d.b.379.20 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.d.b.379.17 | ✓ | 40 | 1.1 | even | 1 | trivial | |
380.2.d.b.379.18 | yes | 40 | 95.94 | odd | 2 | inner | |
380.2.d.b.379.19 | yes | 40 | 4.3 | odd | 2 | inner | |
380.2.d.b.379.20 | yes | 40 | 380.379 | even | 2 | inner | |
380.2.d.b.379.21 | yes | 40 | 76.75 | even | 2 | inner | |
380.2.d.b.379.22 | yes | 40 | 20.19 | odd | 2 | inner | |
380.2.d.b.379.23 | yes | 40 | 19.18 | odd | 2 | inner | |
380.2.d.b.379.24 | yes | 40 | 5.4 | even | 2 | inner |