Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.2 | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.o.765.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32577 | − | 0.492271i | −0.937462 | − | 0.348088i | ||||
\(3\) | 0.221819 | + | 0.827840i | 0.128067 | + | 0.477954i | 0.999930 | − | 0.0117959i | \(-0.00375483\pi\) |
−0.871863 | + | 0.489750i | \(0.837088\pi\) | |||||||
\(4\) | 1.51534 | + | 1.30528i | 0.757669 | + | 0.652639i | ||||
\(5\) | 1.10095 | − | 4.10878i | 0.492358 | − | 1.83750i | −0.0519945 | − | 0.998647i | \(-0.516558\pi\) |
0.544352 | − | 0.838857i | \(-0.316775\pi\) | |||||||
\(6\) | 0.113440 | − | 1.20672i | 0.0463118 | − | 0.492642i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.36644 | − | 2.47646i | −0.483110 | − | 0.875560i | ||||
\(9\) | 1.96196 | − | 1.13274i | 0.653987 | − | 0.377579i | ||||
\(10\) | −3.48224 | + | 4.90534i | −1.10118 | + | 1.55121i | ||||
\(11\) | 1.18894 | − | 0.318576i | 0.358479 | − | 0.0960542i | −0.0750845 | − | 0.997177i | \(-0.523923\pi\) |
0.433564 | + | 0.901123i | \(0.357256\pi\) | |||||||
\(12\) | −0.744430 | + | 1.54399i | −0.214898 | + | 0.445713i | ||||
\(13\) | 1.73092 | − | 1.73092i | 0.480070 | − | 0.480070i | −0.425084 | − | 0.905154i | \(-0.639755\pi\) |
0.905154 | + | 0.425084i | \(0.139755\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.64563 | 0.941297 | ||||||||
\(16\) | 0.592502 | + | 3.95587i | 0.148125 | + | 0.988969i | ||||
\(17\) | 0.931914 | − | 1.61412i | 0.226022 | − | 0.391482i | −0.730603 | − | 0.682802i | \(-0.760761\pi\) |
0.956626 | + | 0.291320i | \(0.0940945\pi\) | |||||||
\(18\) | −3.15872 | + | 0.535936i | −0.744519 | + | 0.126321i | ||||
\(19\) | −3.69400 | − | 0.989804i | −0.847462 | − | 0.227077i | −0.191145 | − | 0.981562i | \(-0.561220\pi\) |
−0.656317 | + | 0.754485i | \(0.727887\pi\) | |||||||
\(20\) | 7.03141 | − | 4.78916i | 1.57227 | − | 1.07089i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.73309 | − | 0.162922i | −0.369496 | − | 0.0347352i | ||||
\(23\) | −1.23305 | + | 0.711901i | −0.257108 | + | 0.148442i | −0.623015 | − | 0.782210i | \(-0.714092\pi\) |
0.365906 | + | 0.930652i | \(0.380759\pi\) | |||||||
\(24\) | 1.74701 | − | 1.68052i | 0.356606 | − | 0.343035i | ||||
\(25\) | −11.3399 | − | 6.54709i | −2.26798 | − | 1.30942i | ||||
\(26\) | −3.14688 | + | 1.44272i | −0.617154 | + | 0.282941i | ||||
\(27\) | 3.19099 | + | 3.19099i | 0.614106 | + | 0.614106i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.181826 | + | 0.181826i | −0.0337642 | + | 0.0337642i | −0.723787 | − | 0.690023i | \(-0.757600\pi\) |
0.690023 | + | 0.723787i | \(0.257600\pi\) | |||||||
\(30\) | −4.83327 | − | 1.79464i | −0.882430 | − | 0.327654i | ||||
\(31\) | −3.23200 | + | 5.59799i | −0.580485 | + | 1.00543i | 0.414937 | + | 0.909850i | \(0.363804\pi\) |
−0.995422 | + | 0.0955792i | \(0.969530\pi\) | |||||||
\(32\) | 1.16184 | − | 5.53626i | 0.205386 | − | 0.978681i | ||||
\(33\) | 0.527459 | + | 0.913587i | 0.0918189 | + | 0.159035i | ||||
\(34\) | −2.03009 | + | 1.68120i | −0.348157 | + | 0.288324i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.45157 | + | 0.844420i | 0.741929 | + | 0.140737i | ||||
\(37\) | −0.0637719 | + | 0.238000i | −0.0104840 | + | 0.0391269i | −0.970970 | − | 0.239202i | \(-0.923114\pi\) |
0.960486 | + | 0.278329i | \(0.0897807\pi\) | |||||||
\(38\) | 4.41015 | + | 3.13070i | 0.715420 | + | 0.507867i | ||||
\(39\) | 1.81687 | + | 1.04897i | 0.290933 | + | 0.167970i | ||||
\(40\) | −11.6796 | + | 2.88797i | −1.84671 | + | 0.456628i | ||||
\(41\) | − | 0.440182i | − | 0.0687448i | −0.999409 | − | 0.0343724i | \(-0.989057\pi\) | ||
0.999409 | − | 0.0343724i | \(-0.0109432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.54503 | − | 5.54503i | −0.845609 | − | 0.845609i | 0.143972 | − | 0.989582i | \(-0.454012\pi\) |
−0.989582 | + | 0.143972i | \(0.954012\pi\) | |||||||
\(44\) | 2.21748 | + | 1.06915i | 0.334297 | + | 0.161180i | ||||
\(45\) | −2.49417 | − | 9.30835i | −0.371808 | − | 1.38761i | ||||
\(46\) | 1.98519 | − | 0.336824i | 0.292700 | − | 0.0496619i | ||||
\(47\) | 3.61427 | + | 6.26009i | 0.527195 | + | 0.913128i | 0.999498 | + | 0.0316918i | \(0.0100895\pi\) |
−0.472303 | + | 0.881436i | \(0.656577\pi\) | |||||||
\(48\) | −3.14340 | + | 1.36799i | −0.453711 | + | 0.197452i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 11.8112 | + | 14.2623i | 1.67035 | + | 2.01699i | ||||
\(51\) | 1.54295 | + | 0.413433i | 0.216056 | + | 0.0578921i | ||||
\(52\) | 4.88225 | − | 0.363599i | 0.677047 | − | 0.0504220i | ||||
\(53\) | 9.69274 | − | 2.59716i | 1.33140 | − | 0.356747i | 0.478163 | − | 0.878271i | \(-0.341303\pi\) |
0.853237 | + | 0.521524i | \(0.174636\pi\) | |||||||
\(54\) | −2.65969 | − | 5.80136i | −0.361938 | − | 0.789464i | ||||
\(55\) | − | 5.23583i | − | 0.706000i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.27760i | − | 0.434129i | ||||||
\(58\) | 0.330567 | − | 0.151552i | 0.0434056 | − | 0.0198998i | ||||
\(59\) | −1.63688 | + | 0.438601i | −0.213104 | + | 0.0571010i | −0.363791 | − | 0.931480i | \(-0.618518\pi\) |
0.150688 | + | 0.988581i | \(0.451851\pi\) | |||||||
\(60\) | 5.52436 | + | 4.75856i | 0.713192 | + | 0.614327i | ||||
\(61\) | 9.01647 | + | 2.41596i | 1.15444 | + | 0.309331i | 0.784743 | − | 0.619821i | \(-0.212795\pi\) |
0.369697 | + | 0.929152i | \(0.379461\pi\) | |||||||
\(62\) | 7.04063 | − | 5.83064i | 0.894161 | − | 0.740492i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.26567 | + | 6.76787i | −0.533209 | + | 0.845984i | ||||
\(65\) | −5.20632 | − | 9.01761i | −0.645765 | − | 1.11850i | ||||
\(66\) | −0.249558 | − | 1.47086i | −0.0307185 | − | 0.181050i | ||||
\(67\) | −2.57076 | − | 9.59422i | −0.314069 | − | 1.17212i | −0.924853 | − | 0.380324i | \(-0.875813\pi\) |
0.610785 | − | 0.791797i | \(-0.290854\pi\) | |||||||
\(68\) | 3.51904 | − | 1.22953i | 0.426746 | − | 0.149103i | ||||
\(69\) | −0.862854 | − | 0.862854i | −0.103875 | − | 0.103875i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.2912i | − | 1.34002i | −0.742352 | − | 0.670010i | \(-0.766290\pi\) | ||
0.742352 | − | 0.670010i | \(-0.233710\pi\) | |||||||
\(72\) | −5.48608 | − | 3.31089i | −0.646541 | − | 0.390192i | ||||
\(73\) | −8.13092 | − | 4.69439i | −0.951652 | − | 0.549437i | −0.0580583 | − | 0.998313i | \(-0.518491\pi\) |
−0.893594 | + | 0.448877i | \(0.851824\pi\) | |||||||
\(74\) | 0.201707 | − | 0.284140i | 0.0234480 | − | 0.0330306i | ||||
\(75\) | 2.90454 | − | 10.8399i | 0.335388 | − | 1.25168i | ||||
\(76\) | −4.30569 | − | 6.32158i | −0.493897 | − | 0.725135i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.89238 | − | 2.28509i | −0.214270 | − | 0.258736i | ||||
\(79\) | 6.52948 | + | 11.3094i | 0.734624 | + | 1.27241i | 0.954888 | + | 0.296966i | \(0.0959747\pi\) |
−0.220264 | + | 0.975440i | \(0.570692\pi\) | |||||||
\(80\) | 16.9061 | + | 1.92074i | 1.89016 | + | 0.214745i | ||||
\(81\) | 1.46441 | − | 2.53643i | 0.162712 | − | 0.281825i | ||||
\(82\) | −0.216689 | + | 0.583580i | −0.0239293 | + | 0.0644456i | ||||
\(83\) | 3.06926 | − | 3.06926i | 0.336895 | − | 0.336895i | −0.518302 | − | 0.855198i | \(-0.673436\pi\) |
0.855198 | + | 0.518302i | \(0.173436\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.60609 | − | 5.60609i | −0.608066 | − | 0.608066i | ||||
\(86\) | 4.62178 | + | 10.0811i | 0.498380 | + | 1.08707i | ||||
\(87\) | −0.190855 | − | 0.110190i | −0.0204618 | − | 0.0118137i | ||||
\(88\) | −2.41356 | − | 2.50904i | −0.257286 | − | 0.267465i | ||||
\(89\) | −5.66084 | + | 3.26829i | −0.600047 | + | 0.346438i | −0.769060 | − | 0.639176i | \(-0.779275\pi\) |
0.169013 | + | 0.985614i | \(0.445942\pi\) | |||||||
\(90\) | −1.27554 | + | 13.5686i | −0.134454 | + | 1.43025i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.79771 | − | 0.530699i | −0.291682 | − | 0.0553292i | ||||
\(93\) | −5.35117 | − | 1.43384i | −0.554890 | − | 0.148682i | ||||
\(94\) | −1.71003 | − | 10.0786i | −0.176376 | − | 1.03953i | ||||
\(95\) | −8.13378 | + | 14.0881i | −0.834508 | + | 1.44541i | ||||
\(96\) | 4.84085 | − | 0.266229i | 0.494068 | − | 0.0271719i | ||||
\(97\) | −1.70409 | −0.173024 | −0.0865122 | − | 0.996251i | \(-0.527572\pi\) | ||||
−0.0865122 | + | 0.996251i | \(0.527572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.97179 | − | 1.97179i | 0.198172 | − | 0.198172i | ||||
\(100\) | −8.63801 | − | 24.7228i | −0.863801 | − | 2.47228i | ||||
\(101\) | 2.36178 | − | 0.632838i | 0.235006 | − | 0.0629697i | −0.139394 | − | 0.990237i | \(-0.544515\pi\) |
0.374400 | + | 0.927267i | \(0.377849\pi\) | |||||||
\(102\) | −1.84208 | − | 1.30767i | −0.182393 | − | 0.129478i | ||||
\(103\) | 12.6328 | − | 7.29353i | 1.24474 | − | 0.718653i | 0.274687 | − | 0.961534i | \(-0.411426\pi\) |
0.970056 | + | 0.242881i | \(0.0780923\pi\) | |||||||
\(104\) | −6.65174 | − | 1.92134i | −0.652257 | − | 0.188403i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.1289 | − | 1.32821i | −1.37232 | − | 0.129007i | ||||
\(107\) | 1.28684 | − | 4.80256i | 0.124404 | − | 0.464281i | −0.875414 | − | 0.483374i | \(-0.839411\pi\) |
0.999818 | + | 0.0190927i | \(0.00607777\pi\) | |||||||
\(108\) | 0.670303 | + | 9.00056i | 0.0644999 | + | 0.866079i | ||||
\(109\) | 2.61683 | + | 9.76613i | 0.250647 | + | 0.935426i | 0.970461 | + | 0.241259i | \(0.0775604\pi\) |
−0.719814 | + | 0.694167i | \(0.755773\pi\) | |||||||
\(110\) | −2.57745 | + | 6.94152i | −0.245750 | + | 0.661848i | ||||
\(111\) | −0.211172 | −0.0200435 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.22780 | 0.491791 | 0.245895 | − | 0.969296i | \(-0.420918\pi\) | ||||
0.245895 | + | 0.969296i | \(0.420918\pi\) | |||||||
\(114\) | −1.61347 | + | 4.34535i | −0.151115 | + | 0.406979i | ||||
\(115\) | 1.56753 | + | 5.85009i | 0.146173 | + | 0.545524i | ||||
\(116\) | −0.512861 | + | 0.0381946i | −0.0476180 | + | 0.00354628i | ||||
\(117\) | 1.43532 | − | 5.35667i | 0.132695 | − | 0.495224i | ||||
\(118\) | 2.38604 | + | 0.224305i | 0.219653 | + | 0.0206489i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.98154 | − | 9.02824i | −0.454750 | − | 0.824162i | ||||
\(121\) | −8.21419 | + | 4.74247i | −0.746745 | + | 0.431133i | ||||
\(122\) | −10.7645 | − | 7.64155i | −0.974569 | − | 0.691834i | ||||
\(123\) | 0.364400 | − | 0.0976407i | 0.0328568 | − | 0.00880396i | ||||
\(124\) | −12.2045 | + | 4.26420i | −1.09600 | + | 0.382936i | ||||
\(125\) | −24.3460 | + | 24.3460i | −2.17757 | + | 2.17757i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.20463 | −0.106893 | −0.0534467 | − | 0.998571i | \(-0.517021\pi\) | ||||
−0.0534467 | + | 0.998571i | \(0.517021\pi\) | |||||||
\(128\) | 8.98693 | − | 6.87278i | 0.794340 | − | 0.607473i | ||||
\(129\) | 3.36041 | − | 5.82039i | 0.295867 | − | 0.512457i | ||||
\(130\) | 2.46328 | + | 14.5182i | 0.216044 | + | 1.27333i | ||||
\(131\) | −3.02113 | − | 0.809509i | −0.263957 | − | 0.0707272i | 0.124413 | − | 0.992231i | \(-0.460295\pi\) |
−0.388370 | + | 0.921503i | \(0.626962\pi\) | |||||||
\(132\) | −0.393204 | + | 2.07287i | −0.0342240 | + | 0.180421i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.31471 | + | 13.9853i | −0.113574 | + | 1.20814i | ||||
\(135\) | 16.6242 | − | 9.59798i | 1.43078 | − | 0.826063i | ||||
\(136\) | −5.27071 | − | 0.102240i | −0.451959 | − | 0.00876698i | ||||
\(137\) | −0.286357 | − | 0.165329i | −0.0244652 | − | 0.0141250i | 0.487718 | − | 0.873001i | \(-0.337830\pi\) |
−0.512183 | + | 0.858877i | \(0.671163\pi\) | |||||||
\(138\) | 0.719189 | + | 1.56870i | 0.0612214 | + | 0.133537i | ||||
\(139\) | 2.41295 | + | 2.41295i | 0.204663 | + | 0.204663i | 0.801995 | − | 0.597331i | \(-0.203772\pi\) |
−0.597331 | + | 0.801995i | \(0.703772\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.38064 | + | 4.38064i | −0.368917 | + | 0.368917i | ||||
\(142\) | −5.55834 | + | 14.9696i | −0.466445 | + | 1.25622i | ||||
\(143\) | 1.50653 | − | 2.60939i | 0.125982 | − | 0.218208i | ||||
\(144\) | 5.64344 | + | 7.09012i | 0.470286 | + | 0.590843i | ||||
\(145\) | 0.546903 | + | 0.947264i | 0.0454179 | + | 0.0786660i | ||||
\(146\) | 8.46883 | + | 10.2263i | 0.700885 | + | 0.846335i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.407292 | + | 0.277410i | −0.0334792 | + | 0.0228030i | ||||
\(149\) | 0.633381 | − | 2.36381i | 0.0518886 | − | 0.193651i | −0.935116 | − | 0.354341i | \(-0.884705\pi\) |
0.987005 | + | 0.160690i | \(0.0513719\pi\) | |||||||
\(150\) | −9.18692 | + | 12.9414i | −0.750109 | + | 1.05666i | ||||
\(151\) | −11.4320 | − | 6.60029i | −0.930326 | − | 0.537124i | −0.0434110 | − | 0.999057i | \(-0.513823\pi\) |
−0.886915 | + | 0.461934i | \(0.847156\pi\) | |||||||
\(152\) | 2.59643 | + | 10.5005i | 0.210598 | + | 0.851706i | ||||
\(153\) | − | 4.22246i | − | 0.341365i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.4427 | + | 19.4427i | 1.56167 | + | 1.56167i | ||||
\(156\) | 1.38398 | + | 3.96107i | 0.110807 | + | 0.317140i | ||||
\(157\) | −0.925585 | − | 3.45433i | −0.0738697 | − | 0.275685i | 0.919105 | − | 0.394013i | \(-0.128913\pi\) |
−0.992975 | + | 0.118327i | \(0.962247\pi\) | |||||||
\(158\) | −3.08931 | − | 18.2079i | −0.245772 | − | 1.44855i | ||||
\(159\) | 4.30007 | + | 7.44794i | 0.341018 | + | 0.590660i | ||||
\(160\) | −21.4682 | − | 10.8689i | −1.69721 | − | 0.859259i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.19008 | + | 2.64184i | −0.250636 | + | 0.207562i | ||||
\(163\) | 10.8521 | + | 2.90781i | 0.850001 | + | 0.227757i | 0.657420 | − | 0.753524i | \(-0.271648\pi\) |
0.192581 | + | 0.981281i | \(0.438314\pi\) | |||||||
\(164\) | 0.574559 | − | 0.667024i | 0.0448655 | − | 0.0520858i | ||||
\(165\) | 4.33443 | − | 1.16141i | 0.337435 | − | 0.0904155i | ||||
\(166\) | −5.58005 | + | 2.55823i | −0.433096 | + | 0.198557i | ||||
\(167\) | − | 11.7171i | − | 0.906693i | −0.891334 | − | 0.453346i | \(-0.850230\pi\) | ||
0.891334 | − | 0.453346i | \(-0.149770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00785i | 0.539065i | ||||||||
\(170\) | 4.67268 | + | 10.1921i | 0.358378 | + | 0.781699i | ||||
\(171\) | −8.36867 | + | 2.24238i | −0.639968 | + | 0.171479i | ||||
\(172\) | −1.16480 | − | 15.6404i | −0.0888148 | − | 1.19257i | ||||
\(173\) | 10.5772 | + | 2.83415i | 0.804169 | + | 0.215476i | 0.637413 | − | 0.770522i | \(-0.280004\pi\) |
0.166755 | + | 0.985998i | \(0.446671\pi\) | |||||||
\(174\) | 0.198787 | + | 0.240040i | 0.0150700 | + | 0.0181974i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.96469 | + | 4.51454i | 0.148094 | + | 0.340296i | ||||
\(177\) | −0.726183 | − | 1.25779i | −0.0545833 | − | 0.0945410i | ||||
\(178\) | 9.11386 | − | 1.54633i | 0.683112 | − | 0.115903i | ||||
\(179\) | 4.32641 | + | 16.1464i | 0.323371 | + | 1.20684i | 0.915939 | + | 0.401317i | \(0.131447\pi\) |
−0.592568 | + | 0.805520i | \(0.701886\pi\) | |||||||
\(180\) | 8.37048 | − | 17.3609i | 0.623899 | − | 1.29400i | ||||
\(181\) | 15.9791 | + | 15.9791i | 1.18772 | + | 1.18772i | 0.977696 | + | 0.210025i | \(0.0673544\pi\) |
0.210025 | + | 0.977696i | \(0.432646\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00010i | 0.591385i | ||||||||
\(184\) | 3.44788 | + | 2.08082i | 0.254181 | + | 0.153400i | ||||
\(185\) | 0.907680 | + | 0.524050i | 0.0667340 | + | 0.0385289i | ||||
\(186\) | 6.38858 | + | 4.53517i | 0.468434 | + | 0.332535i | ||||
\(187\) | 0.593770 | − | 2.21598i | 0.0434208 | − | 0.162048i | ||||
\(188\) | −2.69432 | + | 14.2038i | −0.196503 | + | 1.03592i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.7187 | − | 14.6736i | 1.28545 | − | 1.06454i | ||||
\(191\) | 4.97963 | + | 8.62497i | 0.360313 | + | 0.624081i | 0.988012 | − | 0.154375i | \(-0.0493364\pi\) |
−0.627699 | + | 0.778456i | \(0.716003\pi\) | |||||||
\(192\) | −6.54892 | − | 2.03005i | −0.472628 | − | 0.146506i | ||||
\(193\) | −4.02312 | + | 6.96824i | −0.289590 | + | 0.501585i | −0.973712 | − | 0.227783i | \(-0.926852\pi\) |
0.684122 | + | 0.729368i | \(0.260186\pi\) | |||||||
\(194\) | 2.25924 | + | 0.838876i | 0.162204 | + | 0.0602278i | ||||
\(195\) | 6.31028 | − | 6.31028i | 0.451889 | − | 0.451889i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.01951 | + | 6.01951i | 0.428873 | + | 0.428873i | 0.888244 | − | 0.459372i | \(-0.151925\pi\) |
−0.459372 | + | 0.888244i | \(0.651925\pi\) | |||||||
\(198\) | −3.58480 | + | 1.64349i | −0.254761 | + | 0.116798i | ||||
\(199\) | 12.7812 | + | 7.37922i | 0.906035 | + | 0.523099i | 0.879153 | − | 0.476539i | \(-0.158109\pi\) |
0.0268814 | + | 0.999639i | \(0.491442\pi\) | |||||||
\(200\) | −0.718278 | + | 37.0290i | −0.0507899 | + | 2.61834i | ||||
\(201\) | 7.37224 | − | 4.25636i | 0.519998 | − | 0.300221i | ||||
\(202\) | −3.44271 | − | 0.323639i | −0.242228 | − | 0.0227712i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.79845 | + | 2.64047i | 0.125917 | + | 0.184870i | ||||
\(205\) | −1.80861 | − | 0.484616i | −0.126319 | − | 0.0338470i | ||||
\(206\) | −20.3386 | + | 3.45081i | −1.41705 | + | 0.240429i | ||||
\(207\) | −1.61279 | + | 2.79344i | −0.112097 | + | 0.194158i | ||||
\(208\) | 7.87286 | + | 5.82172i | 0.545885 | + | 0.403664i | ||||
\(209\) | −4.70727 | −0.325609 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5016 | − | 14.5016i | 0.998329 | − | 0.998329i | −0.00166940 | − | 0.999999i | \(-0.500531\pi\) |
0.999999 | + | 0.00166940i | \(0.000531387\pi\) | |||||||
\(212\) | 18.0778 | + | 8.71613i | 1.24159 | + | 0.598626i | ||||
\(213\) | 9.34732 | − | 2.50461i | 0.640468 | − | 0.171613i | ||||
\(214\) | −4.07022 | + | 5.73363i | −0.278235 | + | 0.391943i | ||||
\(215\) | −28.8881 | + | 16.6786i | −1.97015 | + | 1.13747i | ||||
\(216\) | 3.54205 | − | 12.2627i | 0.241006 | − | 0.834368i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.33827 | − | 14.2358i | 0.0906391 | − | 0.964173i | ||||
\(219\) | 2.08261 | − | 7.77241i | 0.140730 | − | 0.525211i | ||||
\(220\) | 6.83422 | − | 7.93406i | 0.460763 | − | 0.534914i | ||||
\(221\) | −1.18085 | − | 4.40698i | −0.0794323 | − | 0.296445i | ||||
\(222\) | 0.279965 | + | 0.103954i | 0.0187900 | + | 0.00697691i | ||||
\(223\) | −4.72461 | −0.316383 | −0.158192 | − | 0.987408i | \(-0.550566\pi\) | ||||
−0.158192 | + | 0.987408i | \(0.550566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29.6646 | −1.97764 | ||||||||
\(226\) | −6.93087 | − | 2.57350i | −0.461035 | − | 0.171186i | ||||
\(227\) | 4.26257 | + | 15.9081i | 0.282917 | + | 1.05586i | 0.950348 | + | 0.311189i | \(0.100727\pi\) |
−0.667431 | + | 0.744671i | \(0.732606\pi\) | |||||||
\(228\) | 4.27818 | − | 4.96667i | 0.283329 | − | 0.328926i | ||||
\(229\) | −3.56601 | + | 13.3085i | −0.235649 | + | 0.879453i | 0.742207 | + | 0.670171i | \(0.233779\pi\) |
−0.977855 | + | 0.209282i | \(0.932887\pi\) | |||||||
\(230\) | 0.801648 | − | 8.52753i | 0.0528591 | − | 0.562289i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.698739 | + | 0.201830i | 0.0458745 | + | 0.0132508i | ||||
\(233\) | −12.0806 | + | 6.97475i | −0.791428 | + | 0.456931i | −0.840465 | − | 0.541866i | \(-0.817718\pi\) |
0.0490370 | + | 0.998797i | \(0.484385\pi\) | |||||||
\(234\) | −4.53983 | + | 6.39515i | −0.296778 | + | 0.418064i | ||||
\(235\) | 29.7005 | − | 7.95822i | 1.93745 | − | 0.519137i | ||||
\(236\) | −3.05293 | − | 1.47196i | −0.198729 | − | 0.0958161i | ||||
\(237\) | −7.91401 | + | 7.91401i | −0.514070 | + | 0.514070i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.1794 | −1.49935 | −0.749674 | − | 0.661807i | \(-0.769790\pi\) | ||||
−0.749674 | + | 0.661807i | \(0.769790\pi\) | |||||||
\(240\) | 2.16004 | + | 14.4216i | 0.139430 | + | 0.930913i | ||||
\(241\) | −2.09690 | + | 3.63195i | −0.135073 | + | 0.233954i | −0.925626 | − | 0.378441i | \(-0.876460\pi\) |
0.790552 | + | 0.612395i | \(0.209794\pi\) | |||||||
\(242\) | 13.2247 | − | 2.24382i | 0.850117 | − | 0.144238i | ||||
\(243\) | 15.5015 | + | 4.15362i | 0.994422 | + | 0.266455i | ||||
\(244\) | 10.5095 | + | 15.4300i | 0.672803 | + | 0.987804i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.531177 | − | 0.0499343i | −0.0338666 | − | 0.00318370i | ||||
\(247\) | −8.10728 | + | 4.68074i | −0.515854 | + | 0.297828i | ||||
\(248\) | 18.2795 | + | 0.354581i | 1.16075 | + | 0.0225159i | ||||
\(249\) | 3.22168 | + | 1.86004i | 0.204166 | + | 0.117875i | ||||
\(250\) | 44.2621 | − | 20.2924i | 2.79938 | − | 1.28340i | ||||
\(251\) | 16.5937 | + | 16.5937i | 1.04739 | + | 1.04739i | 0.998820 | + | 0.0485679i | \(0.0154657\pi\) |
0.0485679 | + | 0.998820i | \(0.484534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.23923 | + | 1.23923i | −0.0779095 | + | 0.0779095i | ||||
\(254\) | 1.59706 | + | 0.593003i | 0.100208 | + | 0.0372083i | ||||
\(255\) | 3.39741 | − | 5.88449i | 0.212754 | − | 0.368501i | ||||
\(256\) | −15.2979 | + | 4.68773i | −0.956118 | + | 0.292983i | ||||
\(257\) | −5.52727 | − | 9.57351i | −0.344782 | − | 0.597179i | 0.640532 | − | 0.767931i | \(-0.278714\pi\) |
−0.985314 | + | 0.170752i | \(0.945380\pi\) | |||||||
\(258\) | −7.32034 | + | 6.06228i | −0.455745 | + | 0.377421i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.88115 | − | 20.4604i | 0.240699 | − | 1.26890i | ||||
\(261\) | −0.150774 | + | 0.562697i | −0.00933269 | + | 0.0348301i | ||||
\(262\) | 3.60683 | + | 2.56044i | 0.222831 | + | 0.158184i | ||||
\(263\) | 14.1936 | + | 8.19466i | 0.875213 | + | 0.505304i | 0.869077 | − | 0.494677i | \(-0.164714\pi\) |
0.00613562 | + | 0.999981i | \(0.498047\pi\) | |||||||
\(264\) | 1.54171 | − | 2.55459i | 0.0948860 | − | 0.157224i | ||||
\(265\) | − | 42.6847i | − | 2.62210i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.96130 | − | 3.96130i | −0.242428 | − | 0.242428i | ||||
\(268\) | 8.62754 | − | 17.8941i | 0.527011 | − | 1.09305i | ||||
\(269\) | −0.333581 | − | 1.24494i | −0.0203388 | − | 0.0759055i | 0.955011 | − | 0.296572i | \(-0.0958435\pi\) |
−0.975349 | + | 0.220666i | \(0.929177\pi\) | |||||||
\(270\) | −26.7647 | + | 4.54112i | −1.62885 | + | 0.276364i | ||||
\(271\) | −10.0688 | − | 17.4397i | −0.611639 | − | 1.05939i | −0.990964 | − | 0.134126i | \(-0.957177\pi\) |
0.379326 | − | 0.925263i | \(-0.376156\pi\) | |||||||
\(272\) | 6.93742 | + | 2.73016i | 0.420643 | + | 0.165540i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.298258 | + | 0.360153i | 0.0180184 | + | 0.0217577i | ||||
\(275\) | −15.5682 | − | 4.17149i | −0.938798 | − | 0.251550i | ||||
\(276\) | −0.181252 | − | 2.43378i | −0.0109101 | − | 0.146496i | ||||
\(277\) | −31.1769 | + | 8.35382i | −1.87324 | + | 0.501932i | −0.873346 | + | 0.487100i | \(0.838055\pi\) |
−0.999890 | + | 0.0148319i | \(0.995279\pi\) | |||||||
\(278\) | −2.01119 | − | 4.38684i | −0.120623 | − | 0.263105i | ||||
\(279\) | 14.6441i | 0.876717i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.6466i | − | 0.814089i | −0.913408 | − | 0.407044i | \(-0.866559\pi\) | ||
0.913408 | − | 0.407044i | \(-0.133441\pi\) | |||||||
\(282\) | 7.96419 | − | 3.65127i | 0.474261 | − | 0.217430i | ||||
\(283\) | −18.1492 | + | 4.86306i | −1.07886 | + | 0.289079i | −0.754128 | − | 0.656728i | \(-0.771940\pi\) |
−0.324730 | + | 0.945807i | \(0.605273\pi\) | |||||||
\(284\) | 14.7382 | − | 17.1100i | 0.874549 | − | 1.01529i | ||||
\(285\) | −13.4669 | − | 3.60846i | −0.797713 | − | 0.213747i | ||||
\(286\) | −3.28184 | + | 2.71783i | −0.194059 | + | 0.160709i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.99164 | − | 12.1780i | −0.235210 | − | 0.717594i | ||||
\(289\) | 6.76307 | + | 11.7140i | 0.397828 | + | 0.689058i | ||||
\(290\) | −0.258758 | − | 1.52508i | −0.0151948 | − | 0.0895558i | ||||
\(291\) | −0.378000 | − | 1.41072i | −0.0221588 | − | 0.0826977i | ||||
\(292\) | −6.19362 | − | 17.7267i | −0.362454 | − | 1.03738i | ||||
\(293\) | −2.19433 | − | 2.19433i | −0.128194 | − | 0.128194i | 0.640099 | − | 0.768293i | \(-0.278893\pi\) |
−0.768293 | + | 0.640099i | \(0.778893\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.20847i | 0.419693i | ||||||||
\(296\) | 0.676537 | − | 0.167285i | 0.0393229 | − | 0.00972323i | ||||
\(297\) | 4.81047 | + | 2.77733i | 0.279132 | + | 0.161157i | ||||
\(298\) | −2.00335 | + | 2.82208i | −0.116051 | + | 0.163478i | ||||
\(299\) | −0.902063 | + | 3.36655i | −0.0521677 | + | 0.194692i | ||||
\(300\) | 18.5504 | − | 12.6349i | 1.07101 | − | 0.729475i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.9071 | + | 14.3781i | 0.685178 | + | 0.827368i | ||||
\(303\) | 1.04778 | + | 1.81480i | 0.0601932 | + | 0.104258i | ||||
\(304\) | 1.72684 | − | 15.1995i | 0.0990410 | − | 0.871749i | ||||
\(305\) | 19.8533 | − | 34.3869i | 1.13680 | − | 1.96899i | ||||
\(306\) | −2.07859 | + | 5.59801i | −0.118825 | + | 0.320017i | ||||
\(307\) | 8.28029 | − | 8.28029i | 0.472581 | − | 0.472581i | −0.430168 | − | 0.902749i | \(-0.641546\pi\) |
0.902749 | + | 0.430168i | \(0.141546\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.84007 | + | 8.84007i | 0.502894 | + | 0.502894i | ||||
\(310\) | −16.2055 | − | 35.3476i | −0.920410 | − | 2.00761i | ||||
\(311\) | −7.36500 | − | 4.25218i | −0.417631 | − | 0.241119i | 0.276432 | − | 0.961033i | \(-0.410848\pi\) |
−0.694063 | + | 0.719914i | \(0.744181\pi\) | |||||||
\(312\) | 0.115082 | − | 5.93277i | 0.00651525 | − | 0.335877i | ||||
\(313\) | −14.1001 | + | 8.14069i | −0.796984 | + | 0.460139i | −0.842415 | − | 0.538829i | \(-0.818867\pi\) |
0.0454317 | + | 0.998967i | \(0.485534\pi\) | |||||||
\(314\) | −0.473353 | + | 5.03529i | −0.0267128 | + | 0.284158i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.86752 | + | 25.6603i | −0.273819 | + | 1.44351i | ||||
\(317\) | 21.8574 | + | 5.85666i | 1.22763 | + | 0.328943i | 0.813657 | − | 0.581345i | \(-0.197474\pi\) |
0.413975 | + | 0.910288i | \(0.364140\pi\) | |||||||
\(318\) | −2.03450 | − | 11.9911i | −0.114089 | − | 0.672425i | ||||
\(319\) | −0.158255 | + | 0.274106i | −0.00886058 | + | 0.0153470i | ||||
\(320\) | 23.1114 | + | 24.9778i | 1.29197 | + | 1.39630i | ||||
\(321\) | 4.26120 | 0.237837 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.04015 | + | 5.04015i | −0.280442 | + | 0.280442i | ||||
\(324\) | 5.52982 | − | 1.93209i | 0.307212 | − | 0.107338i | ||||
\(325\) | −30.9609 | + | 8.29595i | −1.71740 | + | 0.460177i | ||||
\(326\) | −12.9560 | − | 9.19726i | −0.717564 | − | 0.509389i | ||||
\(327\) | −7.50434 | + | 4.33263i | −0.414991 | + | 0.239595i | ||||
\(328\) | −1.09009 | + | 0.601483i | −0.0601902 | + | 0.0332113i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.31820 | − | 0.593955i | −0.347805 | − | 0.0326961i | ||||
\(331\) | −3.00945 | + | 11.2314i | −0.165414 | + | 0.617334i | 0.832573 | + | 0.553915i | \(0.186867\pi\) |
−0.997987 | + | 0.0634183i | \(0.979800\pi\) | |||||||
\(332\) | 8.65721 | − | 0.644733i | 0.475126 | − | 0.0353843i | ||||
\(333\) | 0.144474 | + | 0.539183i | 0.00791711 | + | 0.0295470i | ||||
\(334\) | −5.76797 | + | 15.5341i | −0.315609 | + | 0.849990i | ||||
\(335\) | −42.2509 | −2.30841 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7590 | 0.858445 | 0.429223 | − | 0.903199i | \(-0.358788\pi\) | ||||
0.429223 | + | 0.903199i | \(0.358788\pi\) | |||||||
\(338\) | 3.44976 | − | 9.29080i | 0.187642 | − | 0.505353i | ||||
\(339\) | 1.15963 | + | 4.32779i | 0.0629823 | + | 0.235053i | ||||
\(340\) | −1.17762 | − | 15.8126i | −0.0638655 | − | 0.857560i | ||||
\(341\) | −2.05928 | + | 7.68532i | −0.111516 | + | 0.416183i | ||||
\(342\) | 12.1988 | + | 1.14677i | 0.659635 | + | 0.0620104i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.15506 | + | 21.3090i | −0.331859 | + | 1.14890i | ||||
\(345\) | −4.49523 | + | 2.59533i | −0.242015 | + | 0.139728i | ||||
\(346\) | −12.6278 | − | 8.96428i | −0.678873 | − | 0.481922i | ||||
\(347\) | −14.7478 | + | 3.95167i | −0.791706 | + | 0.212137i | −0.631939 | − | 0.775018i | \(-0.717741\pi\) |
−0.159766 | + | 0.987155i | \(0.551074\pi\) | |||||||
\(348\) | −0.145381 | − | 0.416095i | −0.00779327 | − | 0.0223050i | ||||
\(349\) | 6.62124 | − | 6.62124i | 0.354427 | − | 0.354427i | −0.507327 | − | 0.861754i | \(-0.669366\pi\) |
0.861754 | + | 0.507327i | \(0.169366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.0467 | 0.589628 | ||||||||
\(352\) | −0.382357 | − | 6.95241i | −0.0203797 | − | 0.370565i | ||||
\(353\) | 10.9032 | − | 18.8849i | 0.580319 | − | 1.00514i | −0.415123 | − | 0.909765i | \(-0.636261\pi\) |
0.995441 | − | 0.0953759i | \(-0.0304053\pi\) | |||||||
\(354\) | 0.343581 | + | 2.02502i | 0.0182611 | + | 0.107628i | ||||
\(355\) | −46.3931 | − | 12.4310i | −2.46229 | − | 0.659769i | ||||
\(356\) | −12.8441 | − | 2.43640i | −0.680736 | − | 0.129129i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.21257 | − | 23.5362i | 0.116938 | − | 1.24393i | ||||
\(359\) | −29.8216 | + | 17.2175i | −1.57392 | + | 0.908704i | −0.578241 | + | 0.815866i | \(0.696261\pi\) |
−0.995681 | + | 0.0928386i | \(0.970406\pi\) | |||||||
\(360\) | −19.6436 | + | 18.8960i | −1.03531 | + | 0.995908i | ||||
\(361\) | −3.78856 | − | 2.18733i | −0.199398 | − | 0.115123i | ||||
\(362\) | −13.3186 | − | 29.0508i | −0.700011 | − | 1.52687i | ||||
\(363\) | −5.74807 | − | 5.74807i | −0.301695 | − | 0.301695i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.2399 | + | 28.2399i | −1.47815 | + | 1.47815i | ||||
\(366\) | 3.93822 | − | 10.6063i | 0.205854 | − | 0.554400i | ||||
\(367\) | 1.65812 | − | 2.87195i | 0.0865533 | − | 0.149915i | −0.819499 | − | 0.573081i | \(-0.805748\pi\) |
0.906052 | + | 0.423166i | \(0.139081\pi\) | |||||||
\(368\) | −3.54677 | − | 4.45598i | −0.184888 | − | 0.232284i | ||||
\(369\) | −0.498611 | − | 0.863619i | −0.0259566 | − | 0.0449582i | ||||
\(370\) | −0.945402 | − | 1.14159i | −0.0491491 | − | 0.0593487i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.23727 | − | 9.15751i | −0.323387 | − | 0.474795i | ||||
\(373\) | 6.02667 | − | 22.4918i | 0.312049 | − | 1.16458i | −0.614656 | − | 0.788795i | \(-0.710705\pi\) |
0.926705 | − | 0.375789i | \(-0.122628\pi\) | |||||||
\(374\) | −1.87807 | + | 2.64559i | −0.0971124 | + | 0.136800i | ||||
\(375\) | −25.5550 | − | 14.7542i | −1.31966 | − | 0.761903i | ||||
\(376\) | 10.5642 | − | 17.5046i | 0.544805 | − | 0.902732i | ||||
\(377\) | 0.629452i | 0.0324184i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.77271 | + | 2.77271i | 0.142425 | + | 0.142425i | 0.774724 | − | 0.632299i | \(-0.217889\pi\) |
−0.632299 | + | 0.774724i | \(0.717889\pi\) | |||||||
\(380\) | −30.7143 | + | 10.7314i | −1.57561 | + | 0.550511i | ||||
\(381\) | −0.267209 | − | 0.997239i | −0.0136895 | − | 0.0510901i | ||||
\(382\) | −2.35603 | − | 13.8861i | −0.120545 | − | 0.710473i | ||||
\(383\) | 10.6953 | + | 18.5248i | 0.546504 | + | 0.946572i | 0.998511 | + | 0.0545578i | \(0.0173749\pi\) |
−0.452007 | + | 0.892014i | \(0.649292\pi\) | |||||||
\(384\) | 7.68304 | + | 5.91523i | 0.392073 | + | 0.301860i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.76400 | − | 7.25783i | 0.446076 | − | 0.369414i | ||||
\(387\) | −17.1602 | − | 4.59806i | −0.872302 | − | 0.233733i | ||||
\(388\) | −2.58228 | − | 2.22431i | −0.131095 | − | 0.112922i | ||||
\(389\) | 24.3067 | − | 6.51295i | 1.23240 | − | 0.330220i | 0.416885 | − | 0.908959i | \(-0.363122\pi\) |
0.815512 | + | 0.578740i | \(0.196455\pi\) | |||||||
\(390\) | −11.4724 | + | 5.25962i | −0.580925 | + | 0.266331i | ||||
\(391\) | 2.65372i | 0.134204i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.68058i | − | 0.135217i | ||||||
\(394\) | −5.01727 | − | 10.9437i | −0.252766 | − | 0.551337i | ||||
\(395\) | 53.6564 | − | 14.3772i | 2.69975 | − | 0.723395i | ||||
\(396\) | 5.56167 | − | 0.414197i | 0.279484 | − | 0.0208142i | ||||
\(397\) | 0.377699 | + | 0.101204i | 0.0189562 | + | 0.00507929i | 0.268285 | − | 0.963340i | \(-0.413543\pi\) |
−0.249328 | + | 0.968419i | \(0.580210\pi\) | |||||||
\(398\) | −13.3124 | − | 16.0750i | −0.667288 | − | 0.805765i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.1806 | − | 48.7384i | 0.959028 | − | 2.43692i | ||||
\(401\) | −9.92701 | − | 17.1941i | −0.495731 | − | 0.858631i | 0.504257 | − | 0.863554i | \(-0.331766\pi\) |
−0.999988 | + | 0.00492242i | \(0.998433\pi\) | |||||||
\(402\) | −11.8692 | + | 2.01383i | −0.591981 | + | 0.100440i | ||||
\(403\) | 4.09534 | + | 15.2840i | 0.204003 | + | 0.761350i | ||||
\(404\) | 4.40493 | + | 2.12382i | 0.219153 | + | 0.105664i | ||||
\(405\) | −8.80940 | − | 8.80940i | −0.437743 | − | 0.437743i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.303284i | 0.0150332i | ||||||||
\(408\) | −1.08451 | − | 4.38598i | −0.0536910 | − | 0.217138i | ||||
\(409\) | 30.4501 | + | 17.5804i | 1.50566 | + | 0.869295i | 0.999978 | + | 0.00657643i | \(0.00209336\pi\) |
0.505685 | + | 0.862718i | \(0.331240\pi\) | |||||||
\(410\) | 2.15924 | + | 1.53282i | 0.106637 | + | 0.0757004i | ||||
\(411\) | 0.0733461 | − | 0.273731i | 0.00361789 | − | 0.0135022i | ||||
\(412\) | 28.6630 | + | 5.43710i | 1.41212 | + | 0.267866i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.51333 | − | 2.90953i | 0.172671 | − | 0.142996i | ||||
\(415\) | −9.23185 | − | 15.9900i | −0.453174 | − | 0.784920i | ||||
\(416\) | −7.57175 | − | 11.5939i | −0.371236 | − | 0.568435i | ||||
\(417\) | −1.46230 | + | 2.53277i | −0.0716089 | + | 0.124030i | ||||
\(418\) | 6.24077 | + | 2.31725i | 0.305246 | + | 0.113341i | ||||
\(419\) | 17.1877 | − | 17.1877i | 0.839673 | − | 0.839673i | −0.149142 | − | 0.988816i | \(-0.547651\pi\) |
0.988816 | + | 0.149142i | \(0.0476513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.9543 | + | 12.9543i | 0.631352 | + | 0.631352i | 0.948407 | − | 0.317055i | \(-0.102694\pi\) |
−0.317055 | + | 0.948407i | \(0.602694\pi\) | |||||||
\(422\) | −26.3645 | + | 12.0871i | −1.28340 | + | 0.588389i | ||||
\(423\) | 14.1821 | + | 8.18803i | 0.689557 | + | 0.398116i | ||||
\(424\) | −19.6763 | − | 20.4548i | −0.955566 | − | 0.993371i | ||||
\(425\) | −21.1356 | + | 12.2026i | −1.02523 | + | 0.591915i | ||||
\(426\) | −13.6254 | − | 1.28088i | −0.660150 | − | 0.0620588i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.21868 | − | 5.59782i | 0.397265 | − | 0.270581i | ||||
\(429\) | 2.49433 | + | 0.668354i | 0.120427 | + | 0.0322685i | ||||
\(430\) | 46.5094 | − | 7.89117i | 2.24288 | − | 0.380546i | ||||
\(431\) | 2.85225 | − | 4.94025i | 0.137388 | − | 0.237963i | −0.789119 | − | 0.614240i | \(-0.789463\pi\) |
0.926507 | + | 0.376277i | \(0.122796\pi\) | |||||||
\(432\) | −10.7325 | + | 14.5138i | −0.516367 | + | 0.698297i | ||||
\(433\) | 8.09187 | 0.388870 | 0.194435 | − | 0.980915i | \(-0.437713\pi\) | ||||
0.194435 | + | 0.980915i | \(0.437713\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.662870 | + | 0.662870i | −0.0317822 | + | 0.0317822i | ||||
\(436\) | −8.78213 | + | 18.2147i | −0.420588 | + | 0.872325i | ||||
\(437\) | 5.25952 | − | 1.40928i | 0.251597 | − | 0.0674152i | ||||
\(438\) | −6.58719 | + | 9.27922i | −0.314748 | + | 0.443378i | ||||
\(439\) | 6.11379 | − | 3.52980i | 0.291795 | − | 0.168468i | −0.346956 | − | 0.937881i | \(-0.612785\pi\) |
0.638751 | + | 0.769413i | \(0.279451\pi\) | |||||||
\(440\) | −12.9663 | + | 7.15446i | −0.618145 | + | 0.341076i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.603895 | + | 6.42394i | −0.0287244 | + | 0.305556i | ||||
\(443\) | 3.95466 | − | 14.7590i | 0.187891 | − | 0.701221i | −0.806102 | − | 0.591777i | \(-0.798427\pi\) |
0.993993 | − | 0.109443i | \(-0.0349068\pi\) | |||||||
\(444\) | −0.319997 | − | 0.275638i | −0.0151864 | − | 0.0130812i | ||||
\(445\) | 7.19641 | + | 26.8574i | 0.341142 | + | 1.27316i | ||||
\(446\) | 6.26375 | + | 2.32579i | 0.296597 | + | 0.110129i | ||||
\(447\) | 2.09735 | 0.0992014 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5020 | 0.920356 | 0.460178 | − | 0.887827i | \(-0.347786\pi\) | ||||
0.460178 | + | 0.887827i | \(0.347786\pi\) | |||||||
\(450\) | 39.3284 | + | 14.6030i | 1.85396 | + | 0.688392i | ||||
\(451\) | −0.140231 | − | 0.523350i | −0.00660322 | − | 0.0246436i | ||||
\(452\) | 7.92189 | + | 6.82374i | 0.372615 | + | 0.320962i | ||||
\(453\) | 2.92814 | − | 10.9280i | 0.137576 | − | 0.513441i | ||||
\(454\) | 2.17992 | − | 23.1889i | 0.102309 | − | 1.08831i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.11683 | + | 4.47865i | −0.380105 | + | 0.209732i | ||||
\(457\) | 8.72578 | − | 5.03783i | 0.408175 | − | 0.235660i | −0.281830 | − | 0.959464i | \(-0.590942\pi\) |
0.690005 | + | 0.723804i | \(0.257608\pi\) | |||||||
\(458\) | 11.2791 | − | 15.8886i | 0.527039 | − | 0.742427i | ||||
\(459\) | 8.12437 | − | 2.17692i | 0.379213 | − | 0.101610i | ||||
\(460\) | −5.26066 | + | 10.9109i | −0.245279 | + | 0.508725i | ||||
\(461\) | 15.9419 | − | 15.9419i | 0.742487 | − | 0.742487i | −0.230569 | − | 0.973056i | \(-0.574059\pi\) |
0.973056 | + | 0.230569i | \(0.0740587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.23452 | −0.382690 | −0.191345 | − | 0.981523i | \(-0.561285\pi\) | ||||
−0.191345 | + | 0.981523i | \(0.561285\pi\) | |||||||
\(464\) | −0.827013 | − | 0.611549i | −0.0383931 | − | 0.0283904i | ||||
\(465\) | −11.7827 | + | 20.4082i | −0.546409 | + | 0.946408i | ||||
\(466\) | 19.4496 | − | 3.29998i | 0.900986 | − | 0.152869i | ||||
\(467\) | 33.3801 | + | 8.94417i | 1.54465 | + | 0.413887i | 0.927764 | − | 0.373169i | \(-0.121729\pi\) |
0.616882 | + | 0.787055i | \(0.288395\pi\) | |||||||
\(468\) | 9.16693 | − | 6.24368i | 0.423741 | − | 0.288614i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −43.2936 | − | 4.06991i | −1.99699 | − | 0.187731i | ||||
\(471\) | 2.65432 | − | 1.53247i | 0.122305 | − | 0.0706126i | ||||
\(472\) | 3.32288 | + | 3.45434i | 0.152948 | + | 0.158999i | ||||
\(473\) | −8.35922 | − | 4.82620i | −0.384357 | − | 0.221909i | ||||
\(474\) | 14.3880 | − | 6.59633i | 0.660863 | − | 0.302979i | ||||
\(475\) | 35.4092 | + | 35.4092i | 1.62469 | + | 1.62469i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.0749 | − | 16.0749i | 0.736017 | − | 0.736017i | ||||
\(478\) | 30.7305 | + | 11.4105i | 1.40558 | + | 0.521905i | ||||
\(479\) | −3.70229 | + | 6.41255i | −0.169162 | + | 0.292997i | −0.938125 | − | 0.346296i | \(-0.887439\pi\) |
0.768964 | + | 0.639293i | \(0.220773\pi\) | |||||||
\(480\) | 4.23564 | − | 20.1831i | 0.193330 | − | 0.921230i | ||||
\(481\) | 0.301574 | + | 0.522342i | 0.0137506 | + | 0.0238167i | ||||
\(482\) | 4.56792 | − | 3.78288i | 0.208063 | − | 0.172306i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.6375 | − | 3.53536i | −0.847160 | − | 0.160698i | ||||
\(485\) | −1.87611 | + | 7.00175i | −0.0851899 | + | 0.317933i | ||||
\(486\) | −18.5068 | − | 13.1377i | −0.839483 | − | 0.595938i | ||||
\(487\) | 29.4458 | + | 17.0005i | 1.33432 | + | 0.770368i | 0.985958 | − | 0.166993i | \(-0.0534056\pi\) |
0.348359 | + | 0.937361i | \(0.386739\pi\) | |||||||
\(488\) | −6.33747 | − | 25.6302i | −0.286884 | − | 1.16022i | ||||
\(489\) | 9.62880i | 0.435429i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.03871 | + | 2.03871i | 0.0920055 | + | 0.0920055i | 0.751612 | − | 0.659606i | \(-0.229277\pi\) |
−0.659606 | + | 0.751612i | \(0.729277\pi\) | |||||||
\(492\) | 0.679638 | + | 0.327684i | 0.0306404 | + | 0.0147732i | ||||
\(493\) | 0.124043 | + | 0.462935i | 0.00558662 | + | 0.0208496i | ||||
\(494\) | 13.0526 | − | 2.21461i | 0.587264 | − | 0.0996401i | ||||
\(495\) | −5.93083 | − | 10.2725i | −0.266571 | − | 0.461714i | ||||
\(496\) | −24.0599 | − | 9.46858i | −1.08032 | − | 0.425152i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.35557 | − | 4.05193i | −0.150367 | − | 0.181571i | ||||
\(499\) | 13.8956 | + | 3.72332i | 0.622053 | + | 0.166679i | 0.556061 | − | 0.831141i | \(-0.312312\pi\) |
0.0659922 | + | 0.997820i | \(0.478979\pi\) | |||||||
\(500\) | −68.6707 | + | 5.11415i | −3.07105 | + | 0.228712i | ||||
\(501\) | 9.69985 | − | 2.59907i | 0.433357 | − | 0.116118i | ||||
\(502\) | −13.8309 | − | 30.1681i | −0.617303 | − | 1.34647i | ||||
\(503\) | − | 27.2980i | − | 1.21716i | −0.793494 | − | 0.608579i | \(-0.791740\pi\) | ||
0.793494 | − | 0.608579i | \(-0.208260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.4008i | − | 0.462828i | ||||||
\(506\) | 2.25297 | − | 1.03290i | 0.100157 | − | 0.0459178i | ||||
\(507\) | −5.80138 | + | 1.55447i | −0.257648 | + | 0.0690366i | ||||
\(508\) | −1.82542 | − | 1.57237i | −0.0809898 | − | 0.0697627i | ||||
\(509\) | 19.9523 | + | 5.34620i | 0.884370 | + | 0.236966i | 0.672292 | − | 0.740286i | \(-0.265310\pi\) |
0.212078 | + | 0.977253i | \(0.431977\pi\) | |||||||
\(510\) | −7.40095 | + | 6.12904i | −0.327720 | + | 0.271398i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.5891 | + | 1.31585i | 0.998308 | + | 0.0581530i | ||||
\(513\) | −8.62906 | − | 14.9460i | −0.380982 | − | 0.659881i | ||||
\(514\) | 2.61513 | + | 15.4132i | 0.115349 | + | 0.679847i | ||||
\(515\) | −16.0596 | − | 59.9351i | −0.707669 | − | 2.64106i | ||||
\(516\) | 12.6894 | − | 4.43361i | 0.558619 | − | 0.195179i | ||||
\(517\) | 6.29146 | + | 6.29146i | 0.276698 | + | 0.276698i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.38489i | 0.411951i | ||||||||
\(520\) | −15.2176 | + | 25.2153i | −0.667335 | + | 1.10576i | ||||
\(521\) | −9.46400 | − | 5.46404i | −0.414625 | − | 0.239384i | 0.278150 | − | 0.960538i | \(-0.410279\pi\) |
−0.692775 | + | 0.721154i | \(0.743612\pi\) | |||||||
\(522\) | 0.476891 | − | 0.671785i | 0.0208730 | − | 0.0294033i | ||||
\(523\) | 3.18796 | − | 11.8976i | 0.139400 | − | 0.520247i | −0.860541 | − | 0.509381i | \(-0.829875\pi\) |
0.999941 | − | 0.0108660i | \(-0.00345883\pi\) | |||||||
\(524\) | −3.52140 | − | 5.17009i | −0.153833 | − | 0.225857i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.7834 | − | 17.8513i | −0.644588 | − | 0.778354i | ||||
\(527\) | 6.02390 | + | 10.4337i | 0.262405 | + | 0.454499i | ||||
\(528\) | −3.30151 | + | 2.62787i | −0.143680 | + | 0.114363i | ||||
\(529\) | −10.4864 | + | 18.1630i | −0.455930 | + | 0.789694i | ||||
\(530\) | −21.0124 | + | 56.5901i | −0.912722 | + | 2.45812i | ||||
\(531\) | −2.71468 | + | 2.71468i | −0.117807 | + | 0.117807i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.761918 | − | 0.761918i | −0.0330023 | − | 0.0330023i | ||||
\(534\) | 3.30174 | + | 7.20181i | 0.142880 | + | 0.311653i | ||||
\(535\) | −18.3160 | − | 10.5747i | −0.791868 | − | 0.457185i | ||||
\(536\) | −20.2469 | + | 19.4763i | −0.874532 | + | 0.841249i | ||||
\(537\) | −12.4069 | + | 7.16316i | −0.535399 | + | 0.309113i | ||||
\(538\) | −0.170597 | + | 1.81472i | −0.00735494 | + | 0.0782382i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 37.7193 | + | 7.15499i | 1.62318 | + | 0.307902i | ||||
\(541\) | −16.2057 | − | 4.34231i | −0.696739 | − | 0.186691i | −0.106969 | − | 0.994262i | \(-0.534115\pi\) |
−0.589769 | + | 0.807572i | \(0.700781\pi\) | |||||||
\(542\) | 4.76390 | + | 28.0777i | 0.204627 | + | 1.20604i | ||||
\(543\) | −9.68370 | + | 16.7727i | −0.415567 | + | 0.719784i | ||||
\(544\) | −7.85345 | − | 7.03466i | −0.336714 | − | 0.301609i | ||||
\(545\) | 43.0079 | 1.84226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.2429 | + | 23.2429i | −0.993797 | + | 0.993797i | −0.999981 | − | 0.00618416i | \(-0.998032\pi\) |
0.00618416 | + | 0.999981i | \(0.498032\pi\) | |||||||
\(548\) | −0.218129 | − | 0.624305i | −0.00931800 | − | 0.0266690i | ||||
\(549\) | 20.4266 | − | 5.47329i | 0.871786 | − | 0.233594i | ||||
\(550\) | 18.5864 | + | 13.1942i | 0.792526 | + | 0.562603i | ||||
\(551\) | 0.851637 | − | 0.491693i | 0.0362810 | − | 0.0209468i | ||||
\(552\) | −0.957780 | + | 3.31586i | −0.0407658 | + | 0.141132i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 45.4457 | + | 4.27222i | 1.93080 | + | 0.181509i | ||||
\(555\) | −0.232488 | + | 0.867659i | −0.00986858 | + | 0.0368301i | ||||
\(556\) | 0.506866 | + | 6.80599i | 0.0214959 | + | 0.288638i | ||||
\(557\) | 6.10578 | + | 22.7871i | 0.258710 | + | 0.965519i | 0.965989 | + | 0.258584i | \(0.0832560\pi\) |
−0.707279 | + | 0.706935i | \(0.750077\pi\) | |||||||
\(558\) | 7.20884 | − | 19.4147i | 0.305175 | − | 0.821888i | ||||
\(559\) | −19.1960 | −0.811904 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.96619 | 0.0830125 | ||||||||
\(562\) | −6.71783 | + | 18.0923i | −0.283375 | + | 0.763177i | ||||
\(563\) | −10.0847 | − | 37.6366i | −0.425020 | − | 1.58620i | −0.763880 | − | 0.645358i | \(-0.776708\pi\) |
0.338860 | − | 0.940837i | \(-0.389959\pi\) | |||||||
\(564\) | −12.3561 | + | 0.920203i | −0.520286 | + | 0.0387475i | ||||
\(565\) | 5.75553 | − | 21.4799i | 0.242137 | − | 0.903667i | ||||
\(566\) | 26.4556 | + | 2.48701i | 1.11201 | + | 0.104537i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.9622 | + | 15.4288i | −1.17327 | + | 0.647377i | ||||
\(569\) | −10.2086 | + | 5.89395i | −0.427968 | + | 0.247087i | −0.698481 | − | 0.715629i | \(-0.746140\pi\) |
0.270513 | + | 0.962716i | \(0.412807\pi\) | |||||||
\(570\) | 16.0778 | + | 11.4134i | 0.673423 | + | 0.478054i | ||||
\(571\) | 2.73214 | − | 0.732074i | 0.114336 | − | 0.0306363i | −0.201197 | − | 0.979551i | \(-0.564483\pi\) |
0.315534 | + | 0.948914i | \(0.397817\pi\) | |||||||
\(572\) | 5.68888 | − | 1.98766i | 0.237864 | − | 0.0831084i | ||||
\(573\) | −6.03552 | + | 6.03552i | −0.252138 | + | 0.252138i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.6435 | 0.777489 | ||||||||
\(576\) | −0.702857 | + | 18.1102i | −0.0292857 | + | 0.754591i | ||||
\(577\) | −21.6020 | + | 37.4157i | −0.899302 | + | 1.55764i | −0.0709133 | + | 0.997482i | \(0.522591\pi\) |
−0.828389 | + | 0.560154i | \(0.810742\pi\) | |||||||
\(578\) | −3.19983 | − | 18.8593i | −0.133095 | − | 0.784445i | ||||
\(579\) | −6.66100 | − | 1.78481i | −0.276822 | − | 0.0741741i | ||||
\(580\) | −0.407699 | + | 2.14929i | −0.0169288 | + | 0.0892443i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.193313 | + | 2.05637i | −0.00801308 | + | 0.0852391i | ||||
\(583\) | 10.6967 | − | 6.17574i | 0.443012 | − | 0.255773i | ||||
\(584\) | −0.515019 | + | 26.5505i | −0.0213116 | + | 1.09867i | ||||
\(585\) | −20.4292 | − | 11.7948i | −0.844643 | − | 0.487655i | ||||
\(586\) | 1.82897 | + | 3.98938i | 0.0755542 | + | 0.164800i | ||||
\(587\) | −28.1127 | − | 28.1127i | −1.16034 | − | 1.16034i | −0.984402 | − | 0.175935i | \(-0.943705\pi\) |
−0.175935 | − | 0.984402i | \(-0.556295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.4799 | − | 17.4799i | 0.720248 | − | 0.720248i | ||||
\(590\) | 3.54852 | − | 9.55678i | 0.146090 | − | 0.393446i | ||||
\(591\) | −3.64795 | + | 6.31844i | −0.150057 | + | 0.259906i | ||||
\(592\) | −0.979282 | − | 0.111258i | −0.0402483 | − | 0.00457268i | ||||
\(593\) | −8.44544 | − | 14.6279i | −0.346812 | − | 0.600697i | 0.638869 | − | 0.769316i | \(-0.279403\pi\) |
−0.985681 | + | 0.168619i | \(0.946069\pi\) | |||||||
\(594\) | −5.01038 | − | 6.05015i | −0.205579 | − | 0.248241i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.04521 | − | 2.75523i | 0.165698 | − | 0.112859i | ||||
\(597\) | −3.27371 | + | 12.2176i | −0.133984 | + | 0.500035i | ||||
\(598\) | 2.85318 | − | 4.01921i | 0.116675 | − | 0.164358i | ||||
\(599\) | −25.7194 | − | 14.8491i | −1.05087 | − | 0.606718i | −0.127975 | − | 0.991777i | \(-0.540848\pi\) |
−0.922892 | + | 0.385059i | \(0.874181\pi\) | |||||||
\(600\) | −30.8134 | + | 7.61912i | −1.25795 | + | 0.311049i | ||||
\(601\) | 30.4663i | 1.24275i | 0.783515 | + | 0.621373i | \(0.213425\pi\) | ||||
−0.783515 | + | 0.621373i | \(0.786575\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.9115 | − | 15.9115i | −0.647966 | − | 0.647966i | ||||
\(604\) | −8.70819 | − | 24.9236i | −0.354331 | − | 1.01413i | ||||
\(605\) | 10.4424 | + | 38.9715i | 0.424544 | + | 1.58442i | ||||
\(606\) | −0.495738 | − | 2.92180i | −0.0201380 | − | 0.118690i | ||||
\(607\) | 16.6272 | + | 28.7992i | 0.674879 | + | 1.16892i | 0.976504 | + | 0.215498i | \(0.0691373\pi\) |
−0.301626 | + | 0.953426i | \(0.597529\pi\) | |||||||
\(608\) | −9.77165 | + | 19.3009i | −0.396293 | + | 0.782756i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −43.2486 | + | 35.8160i | −1.75108 | + | 1.45015i | ||||
\(611\) | 17.0917 | + | 4.57971i | 0.691456 | + | 0.185275i | ||||
\(612\) | 5.51148 | − | 6.39845i | 0.222788 | − | 0.258642i | ||||
\(613\) | 19.7780 | − | 5.29950i | 0.798827 | − | 0.214045i | 0.163758 | − | 0.986501i | \(-0.447638\pi\) |
0.635069 | + | 0.772456i | \(0.280972\pi\) | |||||||
\(614\) | −15.0539 | + | 6.90162i | −0.607526 | + | 0.278527i | ||||
\(615\) | − | 1.60474i | − | 0.0647093i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.64884i | 0.106638i | 0.998578 | + | 0.0533192i | \(0.0169801\pi\) | ||||
−0.998578 | + | 0.0533192i | \(0.983020\pi\) | |||||||
\(618\) | −7.36820 | − | 16.0716i | −0.296392 | − | 0.646495i | ||||
\(619\) | −36.1940 | + | 9.69816i | −1.45476 | + | 0.389802i | −0.897677 | − | 0.440654i | \(-0.854747\pi\) |
−0.557084 | + | 0.830456i | \(0.688080\pi\) | |||||||
\(620\) | 4.08415 | + | 54.8404i | 0.164024 | + | 2.20244i | ||||
\(621\) | −6.20631 | − | 1.66298i | −0.249051 | − | 0.0667330i | ||||
\(622\) | 7.67108 | + | 9.26300i | 0.307582 | + | 0.371412i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.07310 | + | 7.80884i | −0.123023 | + | 0.312604i | ||||
\(625\) | 40.4934 | + | 70.1366i | 1.61974 | + | 2.80546i | ||||
\(626\) | 22.7009 | − | 3.85163i | 0.907311 | − | 0.153942i | ||||
\(627\) | −1.04416 | − | 3.89687i | −0.0416999 | − | 0.155626i | ||||
\(628\) | 3.10628 | − | 6.44262i | 0.123954 | − | 0.257089i | ||||
\(629\) | 0.324731 | + | 0.324731i | 0.0129479 | + | 0.0129479i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.0919i | − | 0.401753i | −0.979617 | − | 0.200877i | \(-0.935621\pi\) | ||
0.979617 | − | 0.200877i | \(-0.0643791\pi\) | |||||||
\(632\) | 19.0851 | − | 31.6236i | 0.759163 | − | 1.25792i | ||||
\(633\) | 15.2217 | + | 8.78826i | 0.605009 | + | 0.349302i | ||||
\(634\) | −26.0948 | − | 18.5243i | −1.03636 | − | 0.735695i | ||||
\(635\) | −1.32623 | + | 4.94955i | −0.0526298 | + | 0.196417i | ||||
\(636\) | −3.20556 | + | 16.8989i | −0.127109 | + | 0.670086i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.344744 | − | 0.285497i | 0.0136486 | − | 0.0113029i | ||||
\(639\) | −12.7900 | − | 22.1529i | −0.505964 | − | 0.876355i | ||||
\(640\) | −18.3446 | − | 44.4919i | −0.725136 | − | 1.75870i | ||||
\(641\) | −15.3814 | + | 26.6413i | −0.607528 | + | 1.05227i | 0.384118 | + | 0.923284i | \(0.374505\pi\) |
−0.991646 | + | 0.128986i | \(0.958828\pi\) | |||||||
\(642\) | −5.64938 | − | 2.09767i | −0.222963 | − | 0.0827883i | ||||
\(643\) | −22.2297 | + | 22.2297i | −0.876653 | + | 0.876653i | −0.993187 | − | 0.116533i | \(-0.962822\pi\) |
0.116533 | + | 0.993187i | \(0.462822\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.2151 | − | 20.2151i | −0.795970 | − | 0.795970i | ||||
\(646\) | 9.16321 | − | 4.20097i | 0.360522 | − | 0.165285i | ||||
\(647\) | −14.3410 | − | 8.27978i | −0.563803 | − | 0.325512i | 0.190867 | − | 0.981616i | \(-0.438870\pi\) |
−0.754670 | + | 0.656104i | \(0.772203\pi\) | |||||||
\(648\) | −8.28238 | − | 0.160659i | −0.325363 | − | 0.00631129i | ||||
\(649\) | −1.80643 | + | 1.04294i | −0.0709085 | + | 0.0409390i | ||||
\(650\) | 45.1309 | + | 4.24263i | 1.77018 | + | 0.166409i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.6491 | + | 18.5713i | 0.495377 | + | 0.727308i | ||||
\(653\) | 36.1075 | + | 9.67497i | 1.41300 | + | 0.378611i | 0.882993 | − | 0.469385i | \(-0.155524\pi\) |
0.530002 | + | 0.847996i | \(0.322191\pi\) | |||||||
\(654\) | 12.0819 | − | 2.04991i | 0.472438 | − | 0.0801578i | ||||
\(655\) | −6.65220 | + | 11.5219i | −0.259923 | + | 0.450200i | ||||
\(656\) | 1.74130 | − | 0.260808i | 0.0679865 | − | 0.0101829i | ||||
\(657\) | −21.2701 | −0.829824 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.8808 | + | 14.8808i | −0.579674 | + | 0.579674i | −0.934813 | − | 0.355139i | \(-0.884433\pi\) |
0.355139 | + | 0.934813i | \(0.384433\pi\) | |||||||
\(660\) | 8.08410 | + | 3.89771i | 0.314673 | + | 0.151718i | ||||
\(661\) | −11.0651 | + | 2.96488i | −0.430382 | + | 0.115321i | −0.467506 | − | 0.883990i | \(-0.654847\pi\) |
0.0371232 | + | 0.999311i | \(0.488181\pi\) | |||||||
\(662\) | 9.51873 | − | 13.4088i | 0.369956 | − | 0.521148i | ||||
\(663\) | 3.38634 | − | 1.95510i | 0.131515 | − | 0.0759299i | ||||
\(664\) | −11.7949 | − | 3.40693i | −0.457730 | − | 0.132214i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0738851 | − | 0.785953i | 0.00286299 | − | 0.0304551i | ||||
\(667\) | 0.0947582 | − | 0.353642i | 0.00366905 | − | 0.0136931i | ||||
\(668\) | 15.2940 | − | 17.7553i | 0.591743 | − | 0.686973i | ||||
\(669\) | −1.04801 | − | 3.91122i | −0.0405183 | − | 0.151217i | ||||
\(670\) | 56.0150 | + | 20.7989i | 2.16405 | + | 0.803530i | ||||
\(671\) | 11.4897 | 0.443555 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7704 | 0.800639 | 0.400319 | − | 0.916376i | \(-0.368899\pi\) | ||||
0.400319 | + | 0.916376i | \(0.368899\pi\) | |||||||
\(674\) | −20.8928 | − | 7.75768i | −0.804759 | − | 0.298815i | ||||
\(675\) | −15.2938 | − | 57.0772i | −0.588658 | − | 2.19690i | ||||
\(676\) | −9.14719 | + | 10.6193i | −0.351815 | + | 0.408433i | ||||
\(677\) | 7.11687 | − | 26.5605i | 0.273524 | − | 1.02080i | −0.683301 | − | 0.730137i | \(-0.739456\pi\) |
0.956824 | − | 0.290667i | \(-0.0938772\pi\) | |||||||
\(678\) | 0.593044 | − | 6.30851i | 0.0227757 | − | 0.242277i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.22284 | + | 21.5436i | −0.238635 | + | 0.826161i | ||||
\(681\) | −12.2239 | + | 7.05746i | −0.468420 | + | 0.270442i | ||||
\(682\) | 6.51339 | − | 9.17525i | 0.249410 | − | 0.351339i | ||||
\(683\) | 2.08533 | − | 0.558762i | 0.0797928 | − | 0.0213804i | −0.218702 | − | 0.975792i | \(-0.570182\pi\) |
0.298495 | + | 0.954411i | \(0.403516\pi\) | |||||||
\(684\) | −15.6083 | − | 7.52547i | −0.596798 | − | 0.287744i | ||||
\(685\) | −0.994563 | + | 0.994563i | −0.0380003 | + | 0.0380003i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.8083 | −0.450517 | ||||||||
\(688\) | 18.6500 | − | 25.2209i | 0.711025 | − | 0.961537i | ||||
\(689\) | 12.2819 | − | 21.2728i | 0.467902 | − | 0.810429i | ||||
\(690\) | 7.23726 | − | 1.22793i | 0.275518 | − | 0.0467466i | ||||
\(691\) | −2.35594 | − | 0.631272i | −0.0896242 | − | 0.0240147i | 0.213728 | − | 0.976893i | \(-0.431439\pi\) |
−0.303352 | + | 0.952878i | \(0.598106\pi\) | |||||||
\(692\) | 12.3287 | + | 18.1009i | 0.468666 | + | 0.688091i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.4976 | + | 2.02092i | 0.816036 | + | 0.0767131i | ||||
\(695\) | 12.5708 | − | 7.25775i | 0.476837 | − | 0.275302i | ||||
\(696\) | −0.0120889 | + | 0.623214i | −0.000458230 | + | 0.0236229i | ||||
\(697\) | −0.710506 | − | 0.410211i | −0.0269124 | − | 0.0155379i | ||||
\(698\) | −12.0377 | + | 5.51880i | −0.455633 | + | 0.208890i | ||||
\(699\) | −8.45369 | − | 8.45369i | −0.319748 | − | 0.319748i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.81795 | − | 6.81795i | 0.257510 | − | 0.257510i | −0.566530 | − | 0.824041i | \(-0.691715\pi\) |
0.824041 | + | 0.566530i | \(0.191715\pi\) | |||||||
\(702\) | −14.6454 | − | 5.43796i | −0.552754 | − | 0.205243i | ||||
\(703\) | 0.471146 | − | 0.816049i | 0.0177696 | − | 0.0307779i | ||||
\(704\) | −2.91555 | + | 9.40553i | −0.109884 | + | 0.354484i | ||||
\(705\) | 13.1763 | + | 22.8220i | 0.496247 | + | 0.859525i | ||||
\(706\) | −23.7516 | + | 19.6697i | −0.893904 | + | 0.740280i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.541347 | − | 2.85384i | 0.0203450 | − | 0.107254i | ||||
\(709\) | −3.04470 | + | 11.3630i | −0.114346 | + | 0.426745i | −0.999237 | − | 0.0390527i | \(-0.987566\pi\) |
0.884891 | + | 0.465798i | \(0.154233\pi\) | |||||||
\(710\) | 55.3873 | + | 39.3187i | 2.07865 | + | 1.47560i | ||||
\(711\) | 25.6212 | + | 14.7924i | 0.960869 | + | 0.554758i | ||||
\(712\) | 15.8290 | + | 9.55289i | 0.593216 | + | 0.358010i | ||||
\(713\) | − | 9.20346i | − | 0.344672i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.06280 | − | 9.06280i | −0.338929 | − | 0.338929i | ||||
\(716\) | −14.5195 | + | 30.1144i | −0.542621 | + | 1.12543i | ||||
\(717\) | −5.14163 | − | 19.1888i | −0.192018 | − | 0.716619i | ||||
\(718\) | 48.0123 | − | 8.14616i | 1.79180 | − | 0.304012i | ||||
\(719\) | 16.4827 | + | 28.5490i | 0.614703 | + | 1.06470i | 0.990437 | + | 0.137969i | \(0.0440573\pi\) |
−0.375734 | + | 0.926728i | \(0.622609\pi\) | |||||||
\(720\) | 35.3449 | − | 15.3818i | 1.31723 | − | 0.573247i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.94601 | + | 4.76490i | 0.146855 | + | 0.177331i | ||||
\(723\) | −3.47180 | − | 0.930267i | −0.129118 | − | 0.0345970i | ||||
\(724\) | 3.35660 | + | 45.0710i | 0.124747 | + | 1.67505i | ||||
\(725\) | 3.25232 | − | 0.871457i | 0.120788 | − | 0.0323651i | ||||
\(726\) | 4.79102 | + | 10.4502i | 0.177811 | + | 0.387844i | ||||
\(727\) | 13.8871i | 0.515045i | 0.966272 | + | 0.257523i | \(0.0829062\pi\) | ||||
−0.966272 | + | 0.257523i | \(0.917094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.96768i | 0.183988i | ||||||||
\(730\) | 51.3414 | − | 23.5380i | 1.90023 | − | 0.871180i | ||||
\(731\) | −14.1178 | + | 3.78286i | −0.522167 | + | 0.139914i | ||||
\(732\) | −10.4424 | + | 12.1229i | −0.385960 | + | 0.448074i | ||||
\(733\) | −10.6925 | − | 2.86505i | −0.394936 | − | 0.105823i | 0.0558846 | − | 0.998437i | \(-0.482202\pi\) |
−0.450821 | + | 0.892614i | \(0.648869\pi\) | |||||||
\(734\) | −3.61207 | + | 2.99131i | −0.133324 | + | 0.110411i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.50866 | + | 7.65359i | 0.0924704 | + | 0.282115i | ||||
\(737\) | −6.11297 | − | 10.5880i | −0.225174 | − | 0.390013i | ||||
\(738\) | 0.235909 | + | 1.39041i | 0.00868393 | + | 0.0511818i | ||||
\(739\) | −2.88999 | − | 10.7856i | −0.106310 | − | 0.396754i | 0.892181 | − | 0.451679i | \(-0.149175\pi\) |
−0.998490 | + | 0.0549249i | \(0.982508\pi\) | |||||||
\(740\) | 0.691413 | + | 1.97889i | 0.0254169 | + | 0.0727453i | ||||
\(741\) | −5.67325 | − | 5.67325i | −0.208412 | − | 0.208412i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 49.5292i | − | 1.81705i | −0.417832 | − | 0.908524i | \(-0.637210\pi\) | ||
0.417832 | − | 0.908524i | \(-0.362790\pi\) | |||||||
\(744\) | 3.76121 | + | 15.2112i | 0.137893 | + | 0.557669i | ||||
\(745\) | −9.01507 | − | 5.20485i | −0.330287 | − | 0.190691i | ||||
\(746\) | −19.0621 | + | 26.8523i | −0.697912 | + | 0.983132i | ||||
\(747\) | 2.54510 | − | 9.49845i | 0.0931204 | − | 0.347530i | ||||
\(748\) | 3.79223 | − | 2.58292i | 0.138658 | − | 0.0944411i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 26.6170 | + | 32.1407i | 0.971917 | + | 1.17361i | ||||
\(751\) | 0.523146 | + | 0.906116i | 0.0190899 | + | 0.0330646i | 0.875413 | − | 0.483377i | \(-0.160590\pi\) |
−0.856323 | + | 0.516441i | \(0.827256\pi\) | |||||||
\(752\) | −22.6227 | + | 18.0067i | −0.824964 | + | 0.656637i | ||||
\(753\) | −10.0562 | + | 17.4178i | −0.366467 | + | 0.634739i | ||||
\(754\) | 0.309861 | − | 0.834509i | 0.0112845 | − | 0.0303910i | ||||
\(755\) | −39.7052 | + | 39.7052i | −1.44502 | + | 1.44502i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.5274 | − | 29.5274i | −1.07319 | − | 1.07319i | −0.997101 | − | 0.0760892i | \(-0.975757\pi\) |
−0.0760892 | − | 0.997101i | \(-0.524243\pi\) | |||||||
\(758\) | −2.31106 | − | 5.04091i | −0.0839414 | − | 0.183094i | ||||
\(759\) | −1.30077 | − | 0.750998i | −0.0472148 | − | 0.0272595i | ||||
\(760\) | 46.0030 | + | 0.892353i | 1.66870 | + | 0.0323690i | ||||
\(761\) | 33.9144 | − | 19.5805i | 1.22940 | − | 0.709793i | 0.262493 | − | 0.964934i | \(-0.415455\pi\) |
0.966904 | + | 0.255141i | \(0.0821220\pi\) | |||||||
\(762\) | −0.136653 | + | 1.45365i | −0.00495043 | + | 0.0526602i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.71216 | + | 19.5696i | −0.134301 | + | 0.708002i | ||||
\(765\) | −17.3492 | − | 4.64869i | −0.627260 | − | 0.168074i | ||||
\(766\) | −5.06029 | − | 29.8246i | −0.182836 | − | 1.07761i | ||||
\(767\) | −2.07412 | + | 3.59249i | −0.0748923 | + | 0.129717i | ||||
\(768\) | −7.27405 | − | 11.6244i | −0.262480 | − | 0.419459i | ||||
\(769\) | −28.7025 | −1.03504 | −0.517519 | − | 0.855672i | \(-0.673144\pi\) | ||||
−0.517519 | + | 0.855672i | \(0.673144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.69929 | − | 6.69929i | 0.241269 | − | 0.241269i | ||||
\(772\) | −15.1919 | + | 5.30796i | −0.546768 | + | 0.191038i | ||||
\(773\) | 14.5617 | − | 3.90180i | 0.523748 | − | 0.140338i | 0.0127485 | − | 0.999919i | \(-0.495942\pi\) |
0.511000 | + | 0.859581i | \(0.329275\pi\) | |||||||
\(774\) | 20.4870 | + | 14.5434i | 0.736390 | + | 0.522753i | ||||
\(775\) | 73.3012 | − | 42.3205i | 2.63306 | − | 1.52020i | ||||
\(776\) | 2.32854 | + | 4.22011i | 0.0835899 | + | 0.151493i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.4312 | − | 3.33078i | −1.27027 | − | 0.119414i | ||||
\(779\) | −0.435693 | + | 1.62603i | −0.0156103 | + | 0.0582586i | ||||
\(780\) | 17.7989 | − | 1.32555i | 0.637302 | − | 0.0474621i | ||||
\(781\) | −3.59710 | − | 13.4246i | −0.128715 | − | 0.480369i | ||||
\(782\) | 1.30635 | − | 3.51823i | 0.0467150 | − | 0.125811i | ||||
\(783\) | −1.16041 | −0.0414697 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.2121 | −0.542944 | ||||||||
\(786\) | −1.31957 | + | 3.55383i | −0.0470675 | + | 0.126761i | ||||
\(787\) | 6.06728 | + | 22.6434i | 0.216275 | + | 0.807150i | 0.985714 | + | 0.168429i | \(0.0538695\pi\) |
−0.769438 | + | 0.638721i | \(0.779464\pi\) | |||||||
\(788\) | 1.26447 | + | 16.9787i | 0.0450447 | + | 0.604842i | ||||
\(789\) | −3.63546 | + | 13.5677i | −0.129426 | + | 0.483024i | ||||
\(790\) | −78.2136 | − | 7.35263i | −2.78272 | − | 0.261595i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.57739 | − | 2.18872i | −0.269251 | − | 0.0777727i | ||||
\(793\) | 19.7886 | − | 11.4249i | 0.702713 | − | 0.405712i | ||||
\(794\) | −0.450923 | − | 0.320104i | −0.0160027 | − | 0.0113601i | ||||
\(795\) | 35.3361 | − | 9.46828i | 1.25324 | − | 0.335805i | ||||
\(796\) | 9.73590 | + | 27.8650i | 0.345080 | + | 0.987649i | ||||
\(797\) | −3.81531 | + | 3.81531i | −0.135145 | + | 0.135145i | −0.771443 | − | 0.636298i | \(-0.780465\pi\) |
0.636298 | + | 0.771443i | \(0.280465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4727 | 0.476631 | ||||||||
\(800\) | −49.4215 | + | 55.1739i | −1.74732 | + | 1.95069i | ||||
\(801\) | −7.40422 | + | 12.8245i | −0.261615 | + | 0.453131i | ||||
\(802\) | 4.69679 | + | 27.6822i | 0.165850 | + | 0.977492i | ||||
\(803\) | −11.1627 | − | 2.99104i | −0.393923 | − | 0.105551i | ||||
\(804\) | 16.7272 | + | 3.17298i | 0.589922 | + | 0.111903i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.09439 | − | 22.2791i | 0.0737718 | − | 0.784748i | ||||
\(807\) | 0.956619 | − | 0.552304i | 0.0336746 | − | 0.0194420i | ||||
\(808\) | −4.79443 | − | 4.98411i | −0.168668 | − | 0.175341i | ||||
\(809\) | 24.7881 | + | 14.3114i | 0.871505 | + | 0.503164i | 0.867848 | − | 0.496830i | \(-0.165503\pi\) |
0.00365682 | + | 0.999993i | \(0.498836\pi\) | |||||||
\(810\) | 7.34264 | + | 16.0159i | 0.257994 | + | 0.562740i | ||||
\(811\) | −9.30808 | − | 9.30808i | −0.326851 | − | 0.326851i | 0.524537 | − | 0.851388i | \(-0.324238\pi\) |
−0.851388 | + | 0.524537i | \(0.824238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2039 | − | 12.2039i | 0.428008 | − | 0.428008i | ||||
\(814\) | 0.149298 | − | 0.402085i | 0.00523288 | − | 0.0140931i | ||||
\(815\) | 23.8951 | − | 41.3875i | 0.837009 | − | 1.44974i | ||||
\(816\) | −0.721286 | + | 6.34868i | −0.0252500 | + | 0.222248i | ||||
\(817\) | 14.9948 | + | 25.9718i | 0.524603 | + | 0.908639i | ||||
\(818\) | −31.7156 | − | 38.2973i | −1.10891 | − | 1.33903i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.10810 | − | 3.09510i | −0.0736180 | − | 0.108085i | ||||
\(821\) | 4.31850 | − | 16.1169i | 0.150717 | − | 0.562482i | −0.848718 | − | 0.528846i | \(-0.822625\pi\) |
0.999434 | − | 0.0336357i | \(-0.0107086\pi\) | |||||||
\(822\) | −0.231990 | + | 0.326799i | −0.00809158 | + | 0.0113984i | ||||
\(823\) | −9.41497 | − | 5.43573i | −0.328185 | − | 0.189478i | 0.326850 | − | 0.945076i | \(-0.394013\pi\) |
−0.655035 | + | 0.755598i | \(0.727346\pi\) | |||||||
\(824\) | −35.3241 | − | 21.3183i | −1.23057 | − | 0.742658i | ||||
\(825\) | − | 13.8133i | − | 0.480918i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.97483 | + | 9.97483i | 0.346859 | + | 0.346859i | 0.858938 | − | 0.512079i | \(-0.171125\pi\) |
−0.512079 | + | 0.858938i | \(0.671125\pi\) | |||||||
\(828\) | −6.09015 | + | 2.12787i | −0.211647 | + | 0.0739485i | ||||
\(829\) | 6.68921 | + | 24.9645i | 0.232326 | + | 0.867052i | 0.979336 | + | 0.202240i | \(0.0648220\pi\) |
−0.747010 | + | 0.664813i | \(0.768511\pi\) | |||||||
\(830\) | 4.36789 | + | 25.7437i | 0.151612 | + | 0.893577i | ||||
\(831\) | −13.8312 | − | 23.9564i | −0.479801 | − | 0.831039i | ||||
\(832\) | 4.33109 | + | 19.0982i | 0.150154 | + | 0.662109i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.18548 | − | 2.63803i | 0.110304 | − | 0.0913475i | ||||
\(835\) | −48.1428 | − | 12.8998i | −1.66605 | − | 0.446417i | ||||
\(836\) | −7.13311 | − | 6.14430i | −0.246704 | − | 0.212505i | ||||
\(837\) | −28.1764 | + | 7.54985i | −0.973920 | + | 0.260961i | ||||
\(838\) | −31.2479 | + | 14.3259i | −1.07944 | + | 0.494881i | ||||
\(839\) | 35.9931i | 1.24262i | 0.783565 | + | 0.621310i | \(0.213399\pi\) | ||||
−0.783565 | + | 0.621310i | \(0.786601\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9339i | 0.997720i | ||||||||
\(842\) | −10.7974 | − | 23.5514i | −0.372102 | − | 0.811634i | ||||
\(843\) | 11.2972 | − | 3.02708i | 0.389097 | − | 0.104258i | ||||
\(844\) | 40.9034 | − | 3.04622i | 1.40795 | − | 0.104855i | ||||
\(845\) | 28.7937 | + | 7.71526i | 0.990535 | + | 0.265413i | ||||
\(846\) | −14.7715 | − | 17.8369i | −0.507854 | − | 0.613245i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.0170 | + | 36.8044i | 0.550026 | + | 1.26387i | ||||
\(849\) | −8.05167 | − | 13.9459i | −0.276333 | − | 0.478622i | ||||
\(850\) | 34.0280 | − | 5.77347i | 1.16715 | − | 0.198029i | ||||
\(851\) | −0.0907985 | − | 0.338864i | −0.00311253 | − | 0.0116161i | ||||
\(852\) | 17.4336 | + | 8.40552i | 0.597264 | + | 0.287968i | ||||
\(853\) | −11.5045 | − | 11.5045i | −0.393906 | − | 0.393906i | 0.482171 | − | 0.876077i | \(-0.339848\pi\) |
−0.876077 | + | 0.482171i | \(0.839848\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.8538i | 1.26037i | ||||||||
\(856\) | −13.6517 | + | 3.37561i | −0.466607 | + | 0.115376i | ||||
\(857\) | −46.8795 | − | 27.0659i | −1.60137 | − | 0.924554i | −0.991213 | − | 0.132276i | \(-0.957771\pi\) |
−0.610161 | − | 0.792277i | \(-0.708895\pi\) | |||||||
\(858\) | −2.97790 | − | 2.11397i | −0.101664 | − | 0.0721698i | ||||
\(859\) | −1.84230 | + | 6.87557i | −0.0628586 | + | 0.234591i | −0.990207 | − | 0.139608i | \(-0.955416\pi\) |
0.927348 | + | 0.374199i | \(0.122082\pi\) | |||||||
\(860\) | −65.5454 | − | 12.4333i | −2.23508 | − | 0.423973i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.21337 | + | 5.14555i | −0.211628 | + | 0.175258i | ||||
\(863\) | −8.29596 | − | 14.3690i | −0.282398 | − | 0.489127i | 0.689577 | − | 0.724212i | \(-0.257796\pi\) |
−0.971975 | + | 0.235085i | \(0.924463\pi\) | |||||||
\(864\) | 21.3736 | − | 13.9587i | 0.727143 | − | 0.474885i | ||||
\(865\) | 23.2898 | − | 40.3391i | 0.791877 | − | 1.37157i | ||||
\(866\) | −10.7280 | − | 3.98339i | −0.364551 | − | 0.135361i | ||||
\(867\) | −8.19713 | + | 8.19713i | −0.278389 | + | 0.278389i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3661 | + | 11.3661i | 0.385567 | + | 0.385567i | ||||
\(870\) | 1.20513 | − | 0.552502i | 0.0408576 | − | 0.0187316i | ||||
\(871\) | −21.0566 | − | 12.1570i | −0.713475 | − | 0.411925i | ||||
\(872\) | 20.6097 | − | 19.8253i | 0.697931 | − | 0.671370i | ||||
\(873\) | −3.34336 | + | 1.93029i | −0.113156 | + | 0.0653305i | ||||
\(874\) | −7.66667 | − | 0.720721i | −0.259329 | − | 0.0243788i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.3010 | − | 9.05944i | 0.449399 | − | 0.306090i | ||||
\(877\) | 29.3202 | + | 7.85634i | 0.990074 | + | 0.265290i | 0.717282 | − | 0.696783i | \(-0.245386\pi\) |
0.272793 | + | 0.962073i | \(0.412053\pi\) | |||||||
\(878\) | −9.84311 | + | 1.67006i | −0.332189 | + | 0.0563619i | ||||
\(879\) | 1.32981 | − | 2.30330i | 0.0448534 | − | 0.0776883i | ||||
\(880\) | 20.7123 | − | 3.10224i | 0.698212 | − | 0.104577i | ||||
\(881\) | 48.7213 | 1.64146 | 0.820731 | − | 0.571314i | \(-0.193566\pi\) | ||||
0.820731 | + | 0.571314i | \(0.193566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.32744 | − | 2.32744i | 0.0783247 | − | 0.0783247i | −0.666859 | − | 0.745184i | \(-0.732362\pi\) |
0.745184 | + | 0.666859i | \(0.232362\pi\) | |||||||
\(884\) | 3.96295 | − | 8.21939i | 0.133288 | − | 0.276448i | ||||
\(885\) | −5.96746 | + | 1.59898i | −0.200594 | + | 0.0537490i | ||||
\(886\) | −12.5084 | + | 17.6203i | −0.420228 | + | 0.591965i | ||||
\(887\) | −45.9577 | + | 26.5337i | −1.54311 | + | 0.890914i | −0.544467 | + | 0.838782i | \(0.683268\pi\) |
−0.998640 | + | 0.0521315i | \(0.983399\pi\) | |||||||
\(888\) | 0.288554 | + | 0.522957i | 0.00968323 | + | 0.0175493i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.68031 | − | 39.1493i | 0.123364 | − | 1.31229i | ||||
\(891\) | 0.933049 | − | 3.48219i | 0.0312583 | − | 0.116658i | ||||
\(892\) | −7.15938 | − | 6.16692i | −0.239714 | − | 0.206484i | ||||
\(893\) | −7.15483 | − | 26.7022i | −0.239427 | − | 0.893555i | ||||
\(894\) | −2.78061 | − | 1.03247i | −0.0929975 | − | 0.0345308i | ||||
\(895\) | 71.1052 | 2.37678 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.98706 | −0.0997350 | ||||||||
\(898\) | −25.8552 | − | 9.60026i | −0.862798 | − | 0.320365i | ||||
\(899\) | −0.430199 | − | 1.60552i | −0.0143479 | − | 0.0535472i | ||||
\(900\) | −44.9519 | − | 38.7205i | −1.49840 | − | 1.29068i | ||||
\(901\) | 4.84066 | − | 18.0656i | 0.161266 | − | 0.601852i | ||||
\(902\) | −0.0717155 | + | 0.762874i | −0.00238786 | + | 0.0254009i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.14349 | − | 12.9464i | −0.237589 | − | 0.430592i | ||||
\(905\) | 83.2470 | − | 48.0627i | 2.76723 | − | 1.59766i | ||||
\(906\) | −9.26156 | + | 13.0465i | −0.307695 | + | 0.433442i | ||||
\(907\) | −53.9154 | + | 14.4466i | −1.79023 | + | 0.479691i | −0.992385 | − | 0.123172i | \(-0.960693\pi\) |
−0.797845 | + | 0.602863i | \(0.794027\pi\) | |||||||
\(908\) | −14.3053 | + | 29.6701i | −0.474738 | + | 0.984635i | ||||
\(909\) | 3.91688 | − | 3.91688i | 0.129915 | − | 0.129915i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.7554 | −1.48281 | −0.741406 | − | 0.671057i | \(-0.765841\pi\) | ||||
−0.741406 | + | 0.671057i | \(0.765841\pi\) | |||||||
\(912\) | 12.9658 | − | 1.94198i | 0.429340 | − | 0.0643055i | ||||
\(913\) | 2.67138 | − | 4.62696i | 0.0884097 | − | 0.153130i | ||||
\(914\) | −14.0484 | + | 2.38356i | −0.464678 | + | 0.0788412i | ||||
\(915\) | 32.8707 | + | 8.80768i | 1.08667 | + | 0.291173i | ||||
\(916\) | −22.7750 | + | 15.5123i | −0.752509 | + | 0.512541i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.8427 | − | 1.11330i | −0.390867 | − | 0.0367443i | ||||
\(919\) | −19.8098 | + | 11.4372i | −0.653464 | + | 0.377277i | −0.789782 | − | 0.613388i | \(-0.789806\pi\) |
0.136318 | + | 0.990665i | \(0.456473\pi\) | |||||||
\(920\) | 12.3456 | − | 11.8757i | 0.407021 | − | 0.391531i | ||||
\(921\) | 8.69148 | + | 5.01803i | 0.286394 | + | 0.165350i | ||||
\(922\) | −28.9830 | + | 13.2876i | −0.954504 | + | 0.437602i | ||||
\(923\) | −19.5442 | − | 19.5442i | −0.643304 | − | 0.643304i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.28137 | − | 2.28137i | 0.0750111 | − | 0.0750111i | ||||
\(926\) | 10.9171 | + | 4.05361i | 0.358758 | + | 0.133210i | ||||
\(927\) | 16.5233 | − | 28.6192i | 0.542697 | − | 0.939979i | ||||
\(928\) | 0.795383 | + | 1.21789i | 0.0261097 | + | 0.0399791i | ||||
\(929\) | −13.2871 | − | 23.0139i | −0.435935 | − | 0.755062i | 0.561436 | − | 0.827520i | \(-0.310249\pi\) |
−0.997371 | + | 0.0724577i | \(0.976916\pi\) | |||||||
\(930\) | 25.6675 | − | 21.2563i | 0.841671 | − | 0.697023i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −27.4102 | − | 5.19946i | −0.897852 | − | 0.170314i | ||||
\(933\) | 1.88643 | − | 7.04026i | 0.0617590 | − | 0.230488i | ||||
\(934\) | −39.8514 | − | 28.2900i | −1.30398 | − | 0.925676i | ||||
\(935\) | −8.45127 | − | 4.87934i | −0.276386 | − | 0.159572i | ||||
\(936\) | −15.2268 | + | 3.76508i | −0.497705 | + | 0.123066i | ||||
\(937\) | 11.8582i | 0.387391i | 0.981062 | + | 0.193696i | \(0.0620474\pi\) | ||||
−0.981062 | + | 0.193696i | \(0.937953\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.86686 | − | 9.86686i | −0.321993 | − | 0.321993i | ||||
\(940\) | 55.3939 | + | 26.7080i | 1.80675 | + | 0.871118i | ||||
\(941\) | −0.548049 | − | 2.04535i | −0.0178659 | − | 0.0666764i | 0.956417 | − | 0.292003i | \(-0.0943217\pi\) |
−0.974283 | + | 0.225327i | \(0.927655\pi\) | |||||||
\(942\) | −4.27341 | + | 0.725063i | −0.139235 | + | 0.0236238i | ||||
\(943\) | 0.313366 | + | 0.542765i | 0.0102046 | + | 0.0176749i | ||||
\(944\) | −2.70491 | − | 6.21542i | −0.0880372 | − | 0.202295i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.70662 | + | 10.5134i | 0.283077 | + | 0.341821i | ||||
\(947\) | −5.18291 | − | 1.38876i | −0.168422 | − | 0.0451285i | 0.173623 | − | 0.984812i | \(-0.444453\pi\) |
−0.342045 | + | 0.939684i | \(0.611119\pi\) | |||||||
\(948\) | −22.3224 | + | 1.66243i | −0.724997 | + | 0.0539931i | ||||
\(949\) | −22.1995 | + | 5.94835i | −0.720628 | + | 0.193092i | ||||
\(950\) | −29.5136 | − | 64.3755i | −0.957548 | − | 2.08862i | ||||
\(951\) | 19.3935i | 0.628878i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.43130i | 0.111151i | 0.998454 | + | 0.0555753i | \(0.0176993\pi\) | ||||
−0.998454 | + | 0.0555753i | \(0.982301\pi\) | |||||||
\(954\) | −29.2248 | + | 13.3984i | −0.946187 | + | 0.433789i | ||||
\(955\) | 40.9205 | − | 10.9646i | 1.32415 | − | 0.354806i | ||||
\(956\) | −35.1246 | − | 30.2555i | −1.13601 | − | 0.978533i | ||||
\(957\) | −0.262020 | − | 0.0702080i | −0.00846989 | − | 0.00226950i | ||||
\(958\) | 8.06510 | − | 6.67905i | 0.260572 | − | 0.215790i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15.5511 | + | 24.6731i | −0.501908 | + | 0.796322i | ||||
\(961\) | −5.39169 | − | 9.33869i | −0.173926 | − | 0.301248i | ||||
\(962\) | −0.142685 | − | 0.840962i | −0.00460034 | − | 0.0271137i | ||||
\(963\) | −2.91531 | − | 10.8801i | −0.0939446 | − | 0.350606i | ||||
\(964\) | −7.91822 | + | 2.76658i | −0.255029 | + | 0.0891057i | ||||
\(965\) | 24.2018 | + | 24.2018i | 0.779083 | + | 0.779083i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.4110i | 0.624217i | 0.950046 | + | 0.312108i | \(0.101035\pi\) | ||||
−0.950046 | + | 0.312108i | \(0.898965\pi\) | |||||||
\(968\) | 22.9687 | + | 13.8618i | 0.738243 | + | 0.445535i | ||||
\(969\) | −5.29044 | − | 3.05444i | −0.169954 | − | 0.0981227i | ||||
\(970\) | 5.93406 | − | 8.35916i | 0.190531 | − | 0.268397i | ||||
\(971\) | 5.21341 | − | 19.4567i | 0.167306 | − | 0.624396i | −0.830428 | − | 0.557125i | \(-0.811904\pi\) |
0.997735 | − | 0.0672705i | \(-0.0214291\pi\) | |||||||
\(972\) | 18.0684 | + | 26.5279i | 0.579545 | + | 0.850883i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −30.6695 | − | 37.0342i | −0.982715 | − | 1.18665i | ||||
\(975\) | −13.7354 | − | 23.7905i | −0.439886 | − | 0.761905i | ||||
\(976\) | −4.21494 | + | 37.0995i | −0.134917 | + | 1.18753i | ||||
\(977\) | −8.78731 | + | 15.2201i | −0.281131 | + | 0.486933i | −0.971664 | − | 0.236368i | \(-0.924043\pi\) |
0.690533 | + | 0.723301i | \(0.257376\pi\) | |||||||
\(978\) | 4.73998 | − | 12.7656i | 0.151568 | − | 0.408199i | ||||
\(979\) | −5.68920 | + | 5.68920i | −0.181828 | + | 0.181828i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1966 | + | 16.1966i | 0.517117 | + | 0.517117i | ||||
\(982\) | −1.69926 | − | 3.70645i | −0.0542256 | − | 0.118278i | ||||
\(983\) | 47.7497 | + | 27.5683i | 1.52298 | + | 0.879292i | 0.999631 | + | 0.0271723i | \(0.00865028\pi\) |
0.523347 | + | 0.852119i | \(0.324683\pi\) | |||||||
\(984\) | −0.739734 | − | 0.769000i | −0.0235819 | − | 0.0245148i | ||||
\(985\) | 31.3600 | − | 18.1057i | 0.999214 | − | 0.576896i | ||||
\(986\) | 0.0634368 | − | 0.674809i | 0.00202024 | − | 0.0214903i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.3949 | − | 3.48934i | −0.585221 | − | 0.111011i | ||||
\(989\) | 10.7848 | + | 2.88978i | 0.342937 | + | 0.0918896i | ||||
\(990\) | 2.80607 | + | 16.5386i | 0.0891828 | + | 0.525630i | ||||
\(991\) | 18.4719 | − | 31.9943i | 0.586781 | − | 1.01633i | −0.407870 | − | 0.913040i | \(-0.633728\pi\) |
0.994651 | − | 0.103294i | \(-0.0329382\pi\) | |||||||
\(992\) | 27.2369 | + | 24.3972i | 0.864771 | + | 0.774611i | ||||
\(993\) | −9.96536 | −0.316241 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.3910 | − | 44.3910i | 1.40729 | − | 1.40729i | ||||
\(996\) | 2.45407 | + | 7.02378i | 0.0777602 | + | 0.222557i | ||||
\(997\) | −3.58236 | + | 0.959891i | −0.113455 | + | 0.0304001i | −0.315100 | − | 0.949059i | \(-0.602038\pi\) |
0.201645 | + | 0.979459i | \(0.435371\pi\) | |||||||
\(998\) | −16.5895 | − | 11.7767i | −0.525132 | − | 0.372784i | ||||
\(999\) | −0.962950 | + | 0.555960i | −0.0304664 | + | 0.0175898i |
(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 | 784.2.x.o.165.2 | 48 | ||
7.2 | even | 3 | inner | 784.2.x.o.373.7 | 48 | ||
7.3 | odd | 6 | 784.2.m.j.197.9 | 24 | |||
7.4 | even | 3 | 784.2.m.k.197.9 | 24 | |||
7.5 | odd | 6 | 112.2.w.c.37.7 | ✓ | 48 | ||
7.6 | odd | 2 | 112.2.w.c.53.2 | yes | 48 | ||
16.13 | even | 4 | inner | 784.2.x.o.557.7 | 48 | ||
28.19 | even | 6 | 448.2.ba.c.177.6 | 48 | |||
28.27 | even | 2 | 448.2.ba.c.305.7 | 48 | |||
56.5 | odd | 6 | 896.2.ba.f.737.6 | 48 | |||
56.13 | odd | 2 | 896.2.ba.f.865.7 | 48 | |||
56.19 | even | 6 | 896.2.ba.e.737.7 | 48 | |||
56.27 | even | 2 | 896.2.ba.e.865.6 | 48 | |||
112.5 | odd | 12 | 896.2.ba.f.289.7 | 48 | |||
112.13 | odd | 4 | 112.2.w.c.109.7 | yes | 48 | ||
112.19 | even | 12 | 448.2.ba.c.401.7 | 48 | |||
112.27 | even | 4 | 896.2.ba.e.417.7 | 48 | |||
112.45 | odd | 12 | 784.2.m.j.589.9 | 24 | |||
112.61 | odd | 12 | 112.2.w.c.93.2 | yes | 48 | ||
112.69 | odd | 4 | 896.2.ba.f.417.6 | 48 | |||
112.75 | even | 12 | 896.2.ba.e.289.6 | 48 | |||
112.83 | even | 4 | 448.2.ba.c.81.6 | 48 | |||
112.93 | even | 12 | inner | 784.2.x.o.765.2 | 48 | ||
112.109 | even | 12 | 784.2.m.k.589.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.7 | ✓ | 48 | 7.5 | odd | 6 | ||
112.2.w.c.53.2 | yes | 48 | 7.6 | odd | 2 | ||
112.2.w.c.93.2 | yes | 48 | 112.61 | odd | 12 | ||
112.2.w.c.109.7 | yes | 48 | 112.13 | odd | 4 | ||
448.2.ba.c.81.6 | 48 | 112.83 | even | 4 | |||
448.2.ba.c.177.6 | 48 | 28.19 | even | 6 | |||
448.2.ba.c.305.7 | 48 | 28.27 | even | 2 | |||
448.2.ba.c.401.7 | 48 | 112.19 | even | 12 | |||
784.2.m.j.197.9 | 24 | 7.3 | odd | 6 | |||
784.2.m.j.589.9 | 24 | 112.45 | odd | 12 | |||
784.2.m.k.197.9 | 24 | 7.4 | even | 3 | |||
784.2.m.k.589.9 | 24 | 112.109 | even | 12 | |||
784.2.x.o.165.2 | 48 | 1.1 | even | 1 | trivial | ||
784.2.x.o.373.7 | 48 | 7.2 | even | 3 | inner | ||
784.2.x.o.557.7 | 48 | 16.13 | even | 4 | inner | ||
784.2.x.o.765.2 | 48 | 112.93 | even | 12 | inner | ||
896.2.ba.e.289.6 | 48 | 112.75 | even | 12 | |||
896.2.ba.e.417.7 | 48 | 112.27 | even | 4 | |||
896.2.ba.e.737.7 | 48 | 56.19 | even | 6 | |||
896.2.ba.e.865.6 | 48 | 56.27 | even | 2 | |||
896.2.ba.f.289.7 | 48 | 112.5 | odd | 12 | |||
896.2.ba.f.417.6 | 48 | 112.69 | odd | 4 | |||
896.2.ba.f.737.6 | 48 | 56.5 | odd | 6 | |||
896.2.ba.f.865.7 | 48 | 56.13 | odd | 2 |