Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,2,Mod(19,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.o (of order \(6\), degree \(2\), 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: | \(4.69520363885\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.562828176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-1.33790 + 0.458297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.19 |
Dual form | 588.2.o.d.31.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.06584 | + | 0.929502i | −0.753666 | + | 0.657257i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.272050 | − | 1.98141i | 0.136025 | − | 0.990705i | ||||
\(5\) | −2.12403 | − | 1.22631i | −0.949894 | − | 0.548422i | −0.0568460 | − | 0.998383i | \(-0.518104\pi\) |
−0.893048 | + | 0.449961i | \(0.851438\pi\) | |||||||
\(6\) | −1.33790 | − | 0.458297i | −0.546193 | − | 0.187099i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.55176 | + | 2.36475i | 0.548631 | + | 0.836065i | ||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 3.40374 | − | 0.667235i | 1.07636 | − | 0.210998i | ||||
\(11\) | −1.09586 | + | 0.632697i | −0.330415 | + | 0.190765i | −0.656025 | − | 0.754739i | \(-0.727764\pi\) |
0.325610 | + | 0.945504i | \(0.394430\pi\) | |||||||
\(12\) | 1.85198 | − | 0.755103i | 0.534620 | − | 0.217979i | ||||
\(13\) | 2.99744i | 0.831342i | 0.909515 | + | 0.415671i | \(0.136453\pi\) | ||||
−0.909515 | + | 0.415671i | \(0.863547\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.45262i | − | 0.633263i | ||||||
\(16\) | −3.85198 | − | 1.07809i | −0.962994 | − | 0.269522i | ||||
\(17\) | −1.58759 | + | 0.916595i | −0.385047 | + | 0.222307i | −0.680012 | − | 0.733201i | \(-0.738025\pi\) |
0.294965 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(18\) | −0.272050 | − | 1.38780i | −0.0641229 | − | 0.327108i | ||||
\(19\) | 2.07993 | − | 3.60254i | 0.477168 | − | 0.826479i | −0.522490 | − | 0.852646i | \(-0.674997\pi\) |
0.999658 | + | 0.0261665i | \(0.00833000\pi\) | |||||||
\(20\) | −3.00766 | + | 3.87495i | −0.672534 | + | 0.866466i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.579927 | − | 1.69296i | 0.123641 | − | 0.360941i | ||||
\(23\) | −5.83564 | − | 3.36921i | −1.21682 | − | 0.702529i | −0.252580 | − | 0.967576i | \(-0.581279\pi\) |
−0.964236 | + | 0.265047i | \(0.914613\pi\) | |||||||
\(24\) | −1.27205 | + | 2.52624i | −0.259656 | + | 0.515667i | ||||
\(25\) | 0.507662 | + | 0.879296i | 0.101532 | + | 0.175859i | ||||
\(26\) | −2.78613 | − | 3.19481i | −0.546406 | − | 0.626554i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.42323 | −1.74985 | −0.874925 | − | 0.484258i | \(-0.839090\pi\) | ||||
−0.874925 | + | 0.484258i | \(0.839090\pi\) | |||||||
\(30\) | 2.27971 | + | 2.61411i | 0.416217 | + | 0.477269i | ||||
\(31\) | −4.71989 | − | 8.17509i | −0.847717 | − | 1.46829i | −0.883240 | − | 0.468921i | \(-0.844643\pi\) |
0.0355228 | − | 0.999369i | \(-0.488690\pi\) | |||||||
\(32\) | 5.10769 | − | 2.43135i | 0.902921 | − | 0.429806i | ||||
\(33\) | −1.09586 | − | 0.632697i | −0.190765 | − | 0.110138i | ||||
\(34\) | 0.840146 | − | 2.45262i | 0.144084 | − | 0.420620i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.57993 | + | 1.22631i | 0.263321 | + | 0.204385i | ||||
\(37\) | −3.75572 | + | 6.50509i | −0.617436 | + | 1.06943i | 0.372516 | + | 0.928026i | \(0.378495\pi\) |
−0.989952 | + | 0.141405i | \(0.954838\pi\) | |||||||
\(38\) | 1.13169 | + | 5.77304i | 0.183584 | + | 0.936512i | ||||
\(39\) | −2.59586 | + | 1.49872i | −0.415671 | + | 0.239988i | ||||
\(40\) | −0.396078 | − | 6.92573i | −0.0626254 | − | 1.09505i | ||||
\(41\) | − | 1.08966i | − | 0.170176i | −0.996373 | − | 0.0850880i | \(-0.972883\pi\) | ||
0.996373 | − | 0.0850880i | \(-0.0271171\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.27176i | − | 0.956435i | −0.878241 | − | 0.478218i | \(-0.841283\pi\) | ||
0.878241 | − | 0.478218i | \(-0.158717\pi\) | |||||||
\(44\) | 0.955503 | + | 2.34348i | 0.144047 | + | 0.353293i | ||||
\(45\) | 2.12403 | − | 1.22631i | 0.316631 | − | 0.182807i | ||||
\(46\) | 9.35158 | − | 1.83319i | 1.37882 | − | 0.270289i | ||||
\(47\) | −3.67579 | + | 6.36666i | −0.536169 | + | 0.928672i | 0.462937 | + | 0.886391i | \(0.346796\pi\) |
−0.999106 | + | 0.0422808i | \(0.986538\pi\) | |||||||
\(48\) | −0.992338 | − | 3.87495i | −0.143232 | − | 0.559301i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.35840 | − | 0.465320i | −0.192106 | − | 0.0658063i | ||||
\(51\) | −1.58759 | − | 0.916595i | −0.222307 | − | 0.128349i | ||||
\(52\) | 5.93917 | + | 0.815456i | 0.823615 | + | 0.113083i | ||||
\(53\) | 0.0358262 | + | 0.0620528i | 0.00492111 | + | 0.00852361i | 0.868475 | − | 0.495732i | \(-0.165100\pi\) |
−0.863554 | + | 0.504256i | \(0.831767\pi\) | |||||||
\(54\) | 1.06584 | − | 0.929502i | 0.145043 | − | 0.126489i | ||||
\(55\) | 3.10353 | 0.418479 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.15985 | 0.550986 | ||||||||
\(58\) | 10.0437 | − | 8.75892i | 1.31880 | − | 1.15010i | ||||
\(59\) | −1.68345 | − | 2.91583i | −0.219167 | − | 0.379608i | 0.735387 | − | 0.677648i | \(-0.237001\pi\) |
−0.954553 | + | 0.298040i | \(0.903667\pi\) | |||||||
\(60\) | −4.85964 | − | 0.667235i | −0.627377 | − | 0.0861397i | ||||
\(61\) | 9.61496 | + | 5.55120i | 1.23107 | + | 0.710758i | 0.967253 | − | 0.253815i | \(-0.0816853\pi\) |
0.263817 | + | 0.964573i | \(0.415019\pi\) | |||||||
\(62\) | 12.6294 | + | 4.32623i | 1.60394 | + | 0.549432i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.18406 | + | 7.33906i | −0.398008 | + | 0.917382i | ||||
\(65\) | 3.67579 | − | 6.36666i | 0.455926 | − | 0.789686i | ||||
\(66\) | 1.75611 | − | 0.344251i | 0.216163 | − | 0.0423744i | ||||
\(67\) | −2.43151 | + | 1.40383i | −0.297056 | + | 0.171505i | −0.641120 | − | 0.767441i | \(-0.721530\pi\) |
0.344064 | + | 0.938946i | \(0.388196\pi\) | |||||||
\(68\) | 1.38425 | + | 3.39503i | 0.167865 | + | 0.411707i | ||||
\(69\) | − | 6.73842i | − | 0.811211i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.92285i | − | 0.346878i | −0.984845 | − | 0.173439i | \(-0.944512\pi\) | ||
0.984845 | − | 0.173439i | \(-0.0554880\pi\) | |||||||
\(72\) | −2.82381 | + | 0.161492i | −0.332790 | + | 0.0190320i | ||||
\(73\) | −7.01910 | + | 4.05248i | −0.821523 | + | 0.474307i | −0.850941 | − | 0.525261i | \(-0.823968\pi\) |
0.0294183 | + | 0.999567i | \(0.490635\pi\) | |||||||
\(74\) | −2.04349 | − | 10.4244i | −0.237551 | − | 1.21181i | ||||
\(75\) | −0.507662 | + | 0.879296i | −0.0586198 | + | 0.101532i | ||||
\(76\) | −6.57226 | − | 5.10126i | −0.753890 | − | 0.585155i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.37372 | − | 4.01027i | 0.155543 | − | 0.454073i | ||||
\(79\) | −1.54471 | − | 0.891841i | −0.173794 | − | 0.100340i | 0.410580 | − | 0.911825i | \(-0.365326\pi\) |
−0.584374 | + | 0.811485i | \(0.698660\pi\) | |||||||
\(80\) | 6.85964 | + | 7.01360i | 0.766931 | + | 0.784144i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.01284 | + | 1.16141i | 0.111849 | + | 0.128256i | ||||
\(83\) | 5.33626 | 0.585730 | 0.292865 | − | 0.956154i | \(-0.405391\pi\) | ||||
0.292865 | + | 0.956154i | \(0.405391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.49611 | 0.487672 | ||||||||
\(86\) | 5.82962 | + | 6.68473i | 0.628624 | + | 0.720833i | ||||
\(87\) | −4.71162 | − | 8.16076i | −0.505138 | − | 0.874925i | ||||
\(88\) | −3.19669 | − | 1.60964i | −0.340768 | − | 0.171589i | ||||
\(89\) | −7.42323 | − | 4.28581i | −0.786861 | − | 0.454294i | 0.0519952 | − | 0.998647i | \(-0.483442\pi\) |
−0.838856 | + | 0.544353i | \(0.816775\pi\) | |||||||
\(90\) | −1.12403 | + | 3.28134i | −0.118483 | + | 0.345884i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.26338 | + | 10.6462i | −0.861517 | + | 1.10994i | ||||
\(93\) | 4.71989 | − | 8.17509i | 0.489430 | − | 0.847717i | ||||
\(94\) | −2.00000 | − | 10.2025i | −0.206284 | − | 1.05231i | ||||
\(95\) | −8.83564 | + | 5.10126i | −0.906518 | + | 0.523378i | ||||
\(96\) | 4.65946 | + | 3.20772i | 0.475554 | + | 0.327386i | ||||
\(97\) | − | 7.10394i | − | 0.721296i | −0.932702 | − | 0.360648i | \(-0.882556\pi\) | ||
0.932702 | − | 0.360648i | \(-0.117444\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.26539i | − | 0.127177i | ||||||
\(100\) | 1.88036 | − | 0.766674i | 0.188036 | − | 0.0766674i | ||||
\(101\) | −0.808273 | + | 0.466657i | −0.0804262 | + | 0.0464341i | −0.539674 | − | 0.841874i | \(-0.681452\pi\) |
0.459248 | + | 0.888308i | \(0.348119\pi\) | |||||||
\(102\) | 2.54410 | − | 0.498720i | 0.251904 | − | 0.0493806i | ||||
\(103\) | −2.06460 | + | 3.57600i | −0.203431 | + | 0.352353i | −0.949632 | − | 0.313368i | \(-0.898543\pi\) |
0.746200 | + | 0.665721i | \(0.231876\pi\) | |||||||
\(104\) | −7.08820 | + | 4.65132i | −0.695055 | + | 0.456100i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0958634 | − | 0.0328381i | −0.00931108 | − | 0.00318952i | ||||
\(107\) | 11.9878 | + | 6.92118i | 1.15891 | + | 0.669096i | 0.951042 | − | 0.309062i | \(-0.100015\pi\) |
0.207866 | + | 0.978157i | \(0.433348\pi\) | |||||||
\(108\) | −0.272050 | + | 1.98141i | −0.0261781 | + | 0.190661i | ||||
\(109\) | 0.492338 | + | 0.852754i | 0.0471574 | + | 0.0816791i | 0.888641 | − | 0.458604i | \(-0.151650\pi\) |
−0.841483 | + | 0.540283i | \(0.818317\pi\) | |||||||
\(110\) | −3.30788 | + | 2.88473i | −0.315394 | + | 0.275049i | ||||
\(111\) | −7.51143 | −0.712954 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.03187 | 0.473359 | 0.236679 | − | 0.971588i | \(-0.423941\pi\) | ||||
0.236679 | + | 0.971588i | \(0.423941\pi\) | |||||||
\(114\) | −4.43376 | + | 3.86659i | −0.415260 | + | 0.362140i | ||||
\(115\) | 8.26338 | + | 14.3126i | 0.770564 | + | 1.33466i | ||||
\(116\) | −2.56359 | + | 18.6713i | −0.238024 | + | 1.73359i | ||||
\(117\) | −2.59586 | − | 1.49872i | −0.239988 | − | 0.138557i | ||||
\(118\) | 4.50457 | + | 1.54304i | 0.414679 | + | 0.142049i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.79982 | − | 3.80588i | 0.529449 | − | 0.347428i | ||||
\(121\) | −4.69939 | + | 8.13958i | −0.427217 | + | 0.739962i | ||||
\(122\) | −15.4079 | + | 3.02041i | −1.39497 | + | 0.273455i | ||||
\(123\) | 0.943672 | − | 0.544829i | 0.0850880 | − | 0.0491256i | ||||
\(124\) | −17.4823 | + | 7.12801i | −1.56995 | + | 0.640114i | ||||
\(125\) | 9.77288i | 0.874113i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.38337i | − | 0.566433i | −0.959056 | − | 0.283216i | \(-0.908599\pi\) | ||
0.959056 | − | 0.283216i | \(-0.0914015\pi\) | |||||||
\(128\) | −3.42795 | − | 10.7819i | −0.302991 | − | 0.952993i | ||||
\(129\) | 5.43151 | − | 3.13588i | 0.478218 | − | 0.276099i | ||||
\(130\) | 2.00000 | + | 10.2025i | 0.175412 | + | 0.894820i | ||||
\(131\) | 1.93601 | − | 3.35327i | 0.169150 | − | 0.292976i | −0.768971 | − | 0.639283i | \(-0.779231\pi\) |
0.938121 | + | 0.346307i | \(0.112564\pi\) | |||||||
\(132\) | −1.55176 | + | 1.99923i | −0.135064 | + | 0.174011i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.28674 | − | 3.75636i | 0.111158 | − | 0.324500i | ||||
\(135\) | 2.12403 | + | 1.22631i | 0.182807 | + | 0.105544i | ||||
\(136\) | −4.63108 | − | 2.33191i | −0.397112 | − | 0.199960i | ||||
\(137\) | 7.35158 | + | 12.7333i | 0.628088 | + | 1.08788i | 0.987935 | + | 0.154869i | \(0.0494955\pi\) |
−0.359847 | + | 0.933011i | \(0.617171\pi\) | |||||||
\(138\) | 6.26338 | + | 7.18211i | 0.533174 | + | 0.611382i | ||||
\(139\) | −2.01655 | −0.171041 | −0.0855207 | − | 0.996336i | \(-0.527255\pi\) | ||||
−0.0855207 | + | 0.996336i | \(0.527255\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.35158 | −0.619115 | ||||||||
\(142\) | 2.71679 | + | 3.11530i | 0.227988 | + | 0.261430i | ||||
\(143\) | −1.89647 | − | 3.28479i | −0.158591 | − | 0.274688i | ||||
\(144\) | 2.85964 | − | 2.79687i | 0.238303 | − | 0.233072i | ||||
\(145\) | 20.0152 | + | 11.5558i | 1.66217 | + | 0.959656i | ||||
\(146\) | 3.71448 | − | 10.8436i | 0.307413 | − | 0.897421i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.8675 | + | 9.21133i | 0.975504 | + | 0.757167i | ||||
\(149\) | 0.248055 | − | 0.429644i | 0.0203215 | − | 0.0351978i | −0.855686 | − | 0.517496i | \(-0.826864\pi\) |
0.876007 | + | 0.482298i | \(0.160198\pi\) | |||||||
\(150\) | −0.276219 | − | 1.40907i | −0.0225532 | − | 0.115050i | ||||
\(151\) | −11.4636 | + | 6.61849i | −0.932891 | + | 0.538605i | −0.887725 | − | 0.460374i | \(-0.847715\pi\) |
−0.0451665 | + | 0.998979i | \(0.514382\pi\) | |||||||
\(152\) | 11.7466 | − | 0.671783i | 0.952779 | − | 0.0544888i | ||||
\(153\) | − | 1.83319i | − | 0.148205i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.1522i | 1.85963i | ||||||||
\(156\) | 2.26338 | + | 5.55120i | 0.181215 | + | 0.444452i | ||||
\(157\) | −4.38345 | + | 2.53079i | −0.349838 | + | 0.201979i | −0.664614 | − | 0.747187i | \(-0.731404\pi\) |
0.314776 | + | 0.949166i | \(0.398071\pi\) | |||||||
\(158\) | 2.47539 | − | 0.485251i | 0.196932 | − | 0.0386045i | ||||
\(159\) | −0.0358262 | + | 0.0620528i | −0.00284120 | + | 0.00492111i | ||||
\(160\) | −13.8305 | − | 1.09935i | −1.09339 | − | 0.0869115i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.33790 | + | 0.458297i | 0.105115 | + | 0.0360072i | ||||
\(163\) | 10.4232 | + | 6.01786i | 0.816411 | + | 0.471355i | 0.849177 | − | 0.528108i | \(-0.177098\pi\) |
−0.0327665 | + | 0.999463i | \(0.510432\pi\) | |||||||
\(164\) | −2.15906 | − | 0.296442i | −0.168594 | − | 0.0231482i | ||||
\(165\) | 1.55176 | + | 2.68773i | 0.120805 | + | 0.209240i | ||||
\(166\) | −5.68762 | + | 4.96006i | −0.441445 | + | 0.384976i | ||||
\(167\) | 7.46424 | 0.577600 | 0.288800 | − | 0.957389i | \(-0.406744\pi\) | ||||
0.288800 | + | 0.957389i | \(0.406744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.01532 | 0.308871 | ||||||||
\(170\) | −4.79216 | + | 4.17915i | −0.367542 | + | 0.320526i | ||||
\(171\) | 2.07993 | + | 3.60254i | 0.159056 | + | 0.275493i | ||||
\(172\) | −12.4269 | − | 1.70624i | −0.947545 | − | 0.130099i | ||||
\(173\) | −3.77932 | − | 2.18199i | −0.287336 | − | 0.165894i | 0.349404 | − | 0.936972i | \(-0.386384\pi\) |
−0.636740 | + | 0.771079i | \(0.719717\pi\) | |||||||
\(174\) | 12.6073 | + | 4.31864i | 0.955757 | + | 0.327396i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.90334 | − | 1.25570i | 0.369603 | − | 0.0946518i | ||||
\(177\) | 1.68345 | − | 2.91583i | 0.126536 | − | 0.219167i | ||||
\(178\) | 11.8957 | − | 2.33191i | 0.891619 | − | 0.174784i | ||||
\(179\) | 21.2754 | − | 12.2834i | 1.59020 | − | 0.918102i | 0.596928 | − | 0.802295i | \(-0.296388\pi\) |
0.993272 | − | 0.115808i | \(-0.0369457\pi\) | |||||||
\(180\) | −1.85198 | − | 4.54219i | −0.138038 | − | 0.338555i | ||||
\(181\) | 11.7182i | 0.871011i | 0.900186 | + | 0.435505i | \(0.143430\pi\) | ||||
−0.900186 | + | 0.435505i | \(0.856570\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.1024i | 0.820713i | ||||||||
\(184\) | −1.08820 | − | 19.0280i | −0.0802233 | − | 1.40277i | ||||
\(185\) | 15.9545 | − | 9.21133i | 1.17300 | − | 0.677231i | ||||
\(186\) | 2.56810 | + | 13.1005i | 0.188302 | + | 0.960577i | ||||
\(187\) | 1.15985 | − | 2.00893i | 0.0848169 | − | 0.146907i | ||||
\(188\) | 11.6150 | + | 9.01530i | 0.847108 | + | 0.657508i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.67579 | − | 13.6499i | 0.339217 | − | 0.990268i | ||||
\(191\) | −13.7628 | − | 7.94594i | −0.995839 | − | 0.574948i | −0.0888244 | − | 0.996047i | \(-0.528311\pi\) |
−0.907014 | + | 0.421099i | \(0.861644\pi\) | |||||||
\(192\) | −7.94784 | + | 0.912047i | −0.573586 | + | 0.0658213i | ||||
\(193\) | −9.86690 | − | 17.0900i | −0.710235 | − | 1.23016i | −0.964769 | − | 0.263100i | \(-0.915255\pi\) |
0.254533 | − | 0.967064i | \(-0.418078\pi\) | |||||||
\(194\) | 6.60313 | + | 7.57170i | 0.474077 | + | 0.543616i | ||||
\(195\) | 7.35158 | 0.526458 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.998775 | 0.0711598 | 0.0355799 | − | 0.999367i | \(-0.488672\pi\) | ||||
0.0355799 | + | 0.999367i | \(0.488672\pi\) | |||||||
\(198\) | 1.17619 | + | 1.34871i | 0.0835880 | + | 0.0958489i | ||||
\(199\) | 1.35158 | + | 2.34101i | 0.0958110 | + | 0.165950i | 0.909947 | − | 0.414725i | \(-0.136122\pi\) |
−0.814136 | + | 0.580675i | \(0.802789\pi\) | |||||||
\(200\) | −1.29154 | + | 2.56495i | −0.0913259 | + | 0.181370i | ||||
\(201\) | −2.43151 | − | 1.40383i | −0.171505 | − | 0.0990186i | ||||
\(202\) | 0.427735 | − | 1.24868i | 0.0300953 | − | 0.0878565i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.24806 | + | 2.89631i | −0.157395 | + | 0.202782i | ||||
\(205\) | −1.33626 | + | 2.31446i | −0.0933282 | + | 0.161649i | ||||
\(206\) | −1.12335 | − | 5.73051i | −0.0782676 | − | 0.399264i | ||||
\(207\) | 5.83564 | − | 3.36921i | 0.405605 | − | 0.234176i | ||||
\(208\) | 3.23151 | − | 11.5461i | 0.224065 | − | 0.800577i | ||||
\(209\) | 5.26385i | 0.364108i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1798i | 1.25155i | 0.780004 | + | 0.625774i | \(0.215217\pi\) | ||||
−0.780004 | + | 0.625774i | \(0.784783\pi\) | |||||||
\(212\) | 0.132699 | − | 0.0541049i | 0.00911378 | − | 0.00371594i | ||||
\(213\) | 2.53126 | − | 1.46142i | 0.173439 | − | 0.100135i | ||||
\(214\) | −19.2104 | + | 3.76582i | −1.31320 | + | 0.257426i | ||||
\(215\) | −7.69111 | + | 13.3214i | −0.524530 | + | 0.908512i | ||||
\(216\) | −1.55176 | − | 2.36475i | −0.105584 | − | 0.160901i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.31739 | − | 0.451274i | −0.0892251 | − | 0.0305642i | ||||
\(219\) | −7.01910 | − | 4.05248i | −0.474307 | − | 0.273841i | ||||
\(220\) | 0.844315 | − | 6.14936i | 0.0569237 | − | 0.414590i | ||||
\(221\) | −2.74744 | − | 4.75871i | −0.184813 | − | 0.320106i | ||||
\(222\) | 8.00602 | − | 6.98190i | 0.537329 | − | 0.468594i | ||||
\(223\) | −11.5996 | −0.776769 | −0.388385 | − | 0.921497i | \(-0.626967\pi\) | ||||
−0.388385 | + | 0.921497i | \(0.626967\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.01532 | −0.0676883 | ||||||||
\(226\) | −5.36320 | + | 4.67714i | −0.356754 | + | 0.311119i | ||||
\(227\) | 5.08054 | + | 8.79975i | 0.337207 | + | 0.584060i | 0.983906 | − | 0.178685i | \(-0.0571844\pi\) |
−0.646699 | + | 0.762745i | \(0.723851\pi\) | |||||||
\(228\) | 1.13169 | − | 8.24238i | 0.0749480 | − | 0.545865i | ||||
\(229\) | −20.0025 | − | 11.5485i | −1.32181 | − | 0.763145i | −0.337789 | − | 0.941222i | \(-0.609679\pi\) |
−0.984017 | + | 0.178077i | \(0.943012\pi\) | |||||||
\(230\) | −22.1111 | − | 7.57417i | −1.45796 | − | 0.499426i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.6226 | − | 22.2836i | −0.960022 | − | 1.46299i | ||||
\(233\) | 3.42774 | − | 5.93701i | 0.224558 | − | 0.388947i | −0.731628 | − | 0.681704i | \(-0.761239\pi\) |
0.956187 | + | 0.292757i | \(0.0945727\pi\) | |||||||
\(234\) | 4.15985 | − | 0.815456i | 0.271938 | − | 0.0533080i | ||||
\(235\) | 15.6150 | − | 9.01530i | 1.01861 | − | 0.588093i | ||||
\(236\) | −6.23543 | + | 2.54236i | −0.405892 | + | 0.165494i | ||||
\(237\) | − | 1.78368i | − | 0.115863i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.2257i | − | 1.43766i | −0.695184 | − | 0.718832i | \(-0.744677\pi\) | ||
0.695184 | − | 0.718832i | \(-0.255323\pi\) | |||||||
\(240\) | −2.64413 | + | 9.44742i | −0.170678 | + | 0.609828i | ||||
\(241\) | −13.3605 | + | 7.71367i | −0.860623 | + | 0.496881i | −0.864221 | − | 0.503112i | \(-0.832188\pi\) |
0.00359762 | + | 0.999994i | \(0.498855\pi\) | |||||||
\(242\) | −2.55694 | − | 13.0436i | −0.164366 | − | 0.838476i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 13.6150 | − | 17.5410i | 0.871608 | − | 1.12295i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.499388 | + | 1.45785i | −0.0318398 | + | 0.0929490i | ||||
\(247\) | 10.7984 | + | 6.23447i | 0.687087 | + | 0.396690i | ||||
\(248\) | 12.0079 | − | 23.8472i | 0.762501 | − | 1.51430i | ||||
\(249\) | 2.66813 | + | 4.62133i | 0.169086 | + | 0.292865i | ||||
\(250\) | −9.08392 | − | 10.4164i | −0.574517 | − | 0.658789i | ||||
\(251\) | −22.2954 | −1.40727 | −0.703636 | − | 0.710561i | \(-0.748441\pi\) | ||||
−0.703636 | + | 0.710561i | \(0.748441\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.52676 | 0.536073 | ||||||||
\(254\) | 5.93336 | + | 6.80369i | 0.372292 | + | 0.426901i | ||||
\(255\) | 2.24806 | + | 3.89375i | 0.140779 | + | 0.243836i | ||||
\(256\) | 13.6755 | + | 8.30553i | 0.854716 | + | 0.519096i | ||||
\(257\) | −2.48529 | − | 1.43488i | −0.155028 | − | 0.0895055i | 0.420479 | − | 0.907302i | \(-0.361862\pi\) |
−0.575507 | + | 0.817797i | \(0.695195\pi\) | |||||||
\(258\) | −2.87433 | + | 8.39096i | −0.178948 | + | 0.522399i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −11.6150 | − | 9.01530i | −0.720329 | − | 0.559105i | ||||
\(261\) | 4.71162 | − | 8.16076i | 0.291642 | − | 0.505138i | ||||
\(262\) | 1.05338 | + | 5.37359i | 0.0650783 | + | 0.331981i | ||||
\(263\) | 8.98186 | − | 5.18568i | 0.553845 | − | 0.319763i | −0.196826 | − | 0.980438i | \(-0.563063\pi\) |
0.750672 | + | 0.660676i | \(0.229730\pi\) | |||||||
\(264\) | −0.204351 | − | 3.57324i | −0.0125769 | − | 0.219917i | ||||
\(265\) | − | 0.175736i | − | 0.0107954i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.57161i | − | 0.524574i | ||||||
\(268\) | 2.12007 | + | 5.19973i | 0.129504 | + | 0.317624i | ||||
\(269\) | −4.48011 | + | 2.58659i | −0.273157 | + | 0.157707i | −0.630322 | − | 0.776334i | \(-0.717077\pi\) |
0.357164 | + | 0.934042i | \(0.383744\pi\) | |||||||
\(270\) | −3.40374 | + | 0.667235i | −0.207145 | + | 0.0406066i | ||||
\(271\) | 12.1195 | − | 20.9916i | 0.736209 | − | 1.27515i | −0.217982 | − | 0.975953i | \(-0.569947\pi\) |
0.954191 | − | 0.299198i | \(-0.0967192\pi\) | |||||||
\(272\) | 7.10353 | − | 1.81914i | 0.430714 | − | 0.110302i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.6713 | − | 6.73842i | −1.18839 | − | 0.407083i | ||||
\(275\) | −1.11266 | − | 0.642393i | −0.0670957 | − | 0.0387377i | ||||
\(276\) | −13.3516 | − | 1.83319i | −0.803671 | − | 0.110345i | ||||
\(277\) | 1.50766 | + | 2.61135i | 0.0905866 | + | 0.156901i | 0.907758 | − | 0.419494i | \(-0.137792\pi\) |
−0.817171 | + | 0.576395i | \(0.804459\pi\) | |||||||
\(278\) | 2.14933 | − | 1.87439i | 0.128908 | − | 0.112418i | ||||
\(279\) | 9.43978 | 0.565145 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.91922 | −0.412766 | −0.206383 | − | 0.978471i | \(-0.566169\pi\) | ||||
−0.206383 | + | 0.978471i | \(0.566169\pi\) | |||||||
\(282\) | 7.83564 | − | 6.83331i | 0.466606 | − | 0.406918i | ||||
\(283\) | 10.2870 | + | 17.8176i | 0.611497 | + | 1.05914i | 0.990988 | + | 0.133949i | \(0.0427658\pi\) |
−0.379491 | + | 0.925195i | \(0.623901\pi\) | |||||||
\(284\) | −5.79136 | − | 0.795162i | −0.343654 | − | 0.0471842i | ||||
\(285\) | −8.83564 | − | 5.10126i | −0.523378 | − | 0.302173i | ||||
\(286\) | 5.07457 | + | 1.73830i | 0.300066 | + | 0.102788i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.448237 | + | 5.63907i | −0.0264126 | + | 0.332285i | ||||
\(289\) | −6.81971 | + | 11.8121i | −0.401159 | + | 0.694828i | ||||
\(290\) | −32.0742 | + | 6.28751i | −1.88346 | + | 0.369215i | ||||
\(291\) | 6.15219 | − | 3.55197i | 0.360648 | − | 0.208220i | ||||
\(292\) | 6.12007 | + | 15.0102i | 0.358150 | + | 0.878405i | ||||
\(293\) | − | 28.3113i | − | 1.65396i | −0.562229 | − | 0.826982i | \(-0.690056\pi\) | ||
0.562229 | − | 0.826982i | \(-0.309944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.25772i | 0.480783i | ||||||||
\(296\) | −21.2109 | + | 1.21304i | −1.23286 | + | 0.0705063i | ||||
\(297\) | 1.09586 | − | 0.632697i | 0.0635884 | − | 0.0367128i | ||||
\(298\) | 0.134967 | + | 0.688502i | 0.00781843 | + | 0.0398838i | ||||
\(299\) | 10.0990 | − | 17.4920i | 0.584042 | − | 1.01159i | ||||
\(300\) | 1.60414 | + | 1.24510i | 0.0926149 | + | 0.0718859i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.06647 | − | 17.7097i | 0.349086 | − | 1.01908i | ||||
\(303\) | −0.808273 | − | 0.466657i | −0.0464341 | − | 0.0268087i | ||||
\(304\) | −11.8957 | + | 11.6346i | −0.682264 | + | 0.667288i | ||||
\(305\) | −13.6150 | − | 23.5818i | −0.779590 | − | 1.35029i | ||||
\(306\) | 1.70395 | + | 1.95390i | 0.0974086 | + | 0.111697i | ||||
\(307\) | 8.65596 | 0.494022 | 0.247011 | − | 0.969013i | \(-0.420552\pi\) | ||||
0.247011 | + | 0.969013i | \(0.420552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.12921 | −0.234902 | ||||||||
\(310\) | −21.5200 | − | 24.6766i | −1.22225 | − | 1.40154i | ||||
\(311\) | 4.67129 | + | 8.09091i | 0.264884 | + | 0.458793i | 0.967533 | − | 0.252743i | \(-0.0813329\pi\) |
−0.702649 | + | 0.711537i | \(0.748000\pi\) | |||||||
\(312\) | −7.57226 | − | 3.81290i | −0.428695 | − | 0.215863i | ||||
\(313\) | 6.38734 | + | 3.68773i | 0.361034 | + | 0.208443i | 0.669534 | − | 0.742781i | \(-0.266494\pi\) |
−0.308500 | + | 0.951224i | \(0.599827\pi\) | |||||||
\(314\) | 2.31971 | − | 6.77186i | 0.130909 | − | 0.382158i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.18734 | + | 2.81809i | −0.123048 | + | 0.158530i | ||||
\(317\) | 1.81514 | − | 3.14392i | 0.101949 | − | 0.176580i | −0.810539 | − | 0.585685i | \(-0.800826\pi\) |
0.912487 | + | 0.409105i | \(0.134159\pi\) | |||||||
\(318\) | −0.0194931 | − | 0.0994392i | −0.00109312 | − | 0.00557627i | ||||
\(319\) | 10.3266 | − | 5.96205i | 0.578177 | − | 0.333811i | ||||
\(320\) | 15.7630 | − | 11.6837i | 0.881178 | − | 0.653139i | ||||
\(321\) | 13.8424i | 0.772605i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.62580i | 0.424311i | ||||||||
\(324\) | −1.85198 | + | 0.755103i | −0.102888 | + | 0.0419502i | ||||
\(325\) | −2.63564 | + | 1.52169i | −0.146199 | + | 0.0844081i | ||||
\(326\) | −16.7032 | + | 3.27432i | −0.925103 | + | 0.181348i | ||||
\(327\) | −0.492338 | + | 0.852754i | −0.0272264 | + | 0.0471574i | ||||
\(328\) | 2.57677 | − | 1.69089i | 0.142278 | − | 0.0933638i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.15219 | − | 1.42234i | −0.228571 | − | 0.0782971i | ||||
\(331\) | −0.544164 | − | 0.314173i | −0.0299100 | − | 0.0172685i | 0.484970 | − | 0.874531i | \(-0.338830\pi\) |
−0.514880 | + | 0.857262i | \(0.672164\pi\) | |||||||
\(332\) | 1.45173 | − | 10.5733i | 0.0796741 | − | 0.580286i | ||||
\(333\) | −3.75572 | − | 6.50509i | −0.205812 | − | 0.356477i | ||||
\(334\) | −7.95572 | + | 6.93803i | −0.435318 | + | 0.379632i | ||||
\(335\) | 6.88612 | 0.376229 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.3119 | −1.21541 | −0.607704 | − | 0.794164i | \(-0.707909\pi\) | ||||
−0.607704 | + | 0.794164i | \(0.707909\pi\) | |||||||
\(338\) | −4.27971 | + | 3.73225i | −0.232786 | + | 0.203008i | ||||
\(339\) | 2.51594 | + | 4.35773i | 0.136647 | + | 0.236679i | ||||
\(340\) | 1.22317 | − | 8.90864i | 0.0663356 | − | 0.483139i | ||||
\(341\) | 10.3447 | + | 5.97252i | 0.560198 | + | 0.323430i | ||||
\(342\) | −5.56545 | − | 1.90645i | −0.300945 | − | 0.103089i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.8311 | − | 9.73229i | 0.799642 | − | 0.524730i | ||||
\(345\) | −8.26338 | + | 14.3126i | −0.444885 | + | 0.770564i | ||||
\(346\) | 6.05633 | − | 1.18722i | 0.325590 | − | 0.0638254i | ||||
\(347\) | −5.97104 | + | 3.44738i | −0.320542 | + | 0.185065i | −0.651634 | − | 0.758533i | \(-0.725916\pi\) |
0.331092 | + | 0.943598i | \(0.392583\pi\) | |||||||
\(348\) | −17.4516 | + | 7.11551i | −0.935505 | + | 0.381431i | ||||
\(349\) | 13.4768i | 0.721399i | 0.932682 | + | 0.360699i | \(0.117462\pi\) | ||||
−0.932682 | + | 0.360699i | \(0.882538\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.99744i | − | 0.159992i | ||||||
\(352\) | −4.05903 | + | 5.89605i | −0.216347 | + | 0.314260i | ||||
\(353\) | 24.7550 | − | 14.2923i | 1.31758 | − | 0.760702i | 0.334237 | − | 0.942489i | \(-0.391521\pi\) |
0.983338 | + | 0.181787i | \(0.0581881\pi\) | |||||||
\(354\) | 0.915968 | + | 4.67259i | 0.0486831 | + | 0.248345i | ||||
\(355\) | −3.58431 | + | 6.20821i | −0.190236 | + | 0.329498i | ||||
\(356\) | −10.5114 | + | 13.5425i | −0.557105 | + | 0.717752i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.2589 | + | 32.8677i | −0.595050 | + | 1.73711i | ||||
\(359\) | 6.00000 | + | 3.46410i | 0.316668 | + | 0.182828i | 0.649906 | − | 0.760014i | \(-0.274808\pi\) |
−0.333238 | + | 0.942843i | \(0.608141\pi\) | |||||||
\(360\) | 6.19590 | + | 3.11985i | 0.326552 | + | 0.164431i | ||||
\(361\) | 0.847808 | + | 1.46845i | 0.0446215 | + | 0.0772867i | ||||
\(362\) | −10.8921 | − | 12.4898i | −0.572478 | − | 0.656451i | ||||
\(363\) | −9.39878 | −0.493308 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.8783 | 1.04048 | ||||||||
\(366\) | −10.3197 | − | 11.8334i | −0.539420 | − | 0.618544i | ||||
\(367\) | −6.47184 | − | 11.2095i | −0.337827 | − | 0.585134i | 0.646197 | − | 0.763171i | \(-0.276359\pi\) |
−0.984024 | + | 0.178037i | \(0.943025\pi\) | |||||||
\(368\) | 18.8465 | + | 19.2695i | 0.982440 | + | 1.00449i | ||||
\(369\) | 0.943672 | + | 0.544829i | 0.0491256 | + | 0.0283627i | ||||
\(370\) | −8.44306 | + | 24.6476i | −0.438934 | + | 1.28137i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −14.9142 | − | 11.5761i | −0.773263 | − | 0.600192i | ||||
\(373\) | −1.53954 | + | 2.66655i | −0.0797141 | + | 0.138069i | −0.903127 | − | 0.429374i | \(-0.858734\pi\) |
0.823412 | + | 0.567443i | \(0.192067\pi\) | |||||||
\(374\) | 0.631077 | + | 3.21929i | 0.0326322 | + | 0.166466i | ||||
\(375\) | −8.46356 | + | 4.88644i | −0.437056 | + | 0.252335i | ||||
\(376\) | −20.7595 | + | 1.18722i | −1.07059 | + | 0.0612263i | ||||
\(377\) | − | 28.2456i | − | 1.45472i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.21020i | 0.267630i | 0.991006 | + | 0.133815i | \(0.0427228\pi\) | ||||
−0.991006 | + | 0.133815i | \(0.957277\pi\) | |||||||
\(380\) | 7.70395 | + | 18.8948i | 0.395205 | + | 0.969285i | ||||
\(381\) | 5.52816 | − | 3.19169i | 0.283216 | − | 0.163515i | ||||
\(382\) | 22.0547 | − | 4.32339i | 1.12842 | − | 0.221204i | ||||
\(383\) | 19.4353 | − | 33.6629i | 0.993096 | − | 1.72009i | 0.394963 | − | 0.918697i | \(-0.370758\pi\) |
0.598134 | − | 0.801396i | \(-0.295909\pi\) | |||||||
\(384\) | 7.62342 | − | 8.35964i | 0.389031 | − | 0.426601i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.4018 | + | 9.04395i | 1.34381 | + | 0.460325i | ||||
\(387\) | 5.43151 | + | 3.13588i | 0.276099 | + | 0.159406i | ||||
\(388\) | −14.0758 | − | 1.93263i | −0.714592 | − | 0.0981144i | ||||
\(389\) | 1.86752 | + | 3.23463i | 0.0946869 | + | 0.164002i | 0.909478 | − | 0.415752i | \(-0.136482\pi\) |
−0.814791 | + | 0.579755i | \(0.803148\pi\) | |||||||
\(390\) | −7.83564 | + | 6.83331i | −0.396773 | + | 0.346018i | ||||
\(391\) | 12.3528 | 0.624708 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.87202 | 0.195318 | ||||||||
\(394\) | −1.06454 | + | 0.928364i | −0.0536307 | + | 0.0467703i | ||||
\(395\) | 2.18734 | + | 3.78859i | 0.110057 | + | 0.190625i | ||||
\(396\) | −2.50727 | − | 0.344251i | −0.125995 | − | 0.0172993i | ||||
\(397\) | 5.81082 | + | 3.35488i | 0.291637 | + | 0.168377i | 0.638680 | − | 0.769473i | \(-0.279481\pi\) |
−0.347043 | + | 0.937849i | \(0.612814\pi\) | |||||||
\(398\) | −3.61655 | − | 1.23885i | −0.181281 | − | 0.0620980i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00754 | − | 3.93433i | −0.0503772 | − | 0.196717i | ||||
\(401\) | −2.92385 | + | 5.06425i | −0.146010 | + | 0.252897i | −0.929749 | − | 0.368193i | \(-0.879976\pi\) |
0.783739 | + | 0.621090i | \(0.213310\pi\) | |||||||
\(402\) | 3.89647 | − | 0.763826i | 0.194338 | − | 0.0380962i | ||||
\(403\) | 24.5044 | − | 14.1476i | 1.22065 | − | 0.704743i | ||||
\(404\) | 0.704748 | + | 1.72848i | 0.0350625 | + | 0.0859949i | ||||
\(405\) | 2.45262i | 0.121871i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.50492i | − | 0.471142i | ||||||
\(408\) | −0.296046 | − | 5.17659i | −0.0146564 | − | 0.256279i | ||||
\(409\) | 26.7299 | − | 15.4325i | 1.32171 | − | 0.763089i | 0.337708 | − | 0.941251i | \(-0.390348\pi\) |
0.984001 | + | 0.178162i | \(0.0570150\pi\) | |||||||
\(410\) | −0.727058 | − | 3.70891i | −0.0359068 | − | 0.183170i | ||||
\(411\) | −7.35158 | + | 12.7333i | −0.362627 | + | 0.628088i | ||||
\(412\) | 6.52384 | + | 5.06368i | 0.321407 | + | 0.249469i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.08820 | + | 9.01530i | −0.151777 | + | 0.443078i | ||||
\(415\) | −11.3344 | − | 6.54389i | −0.556382 | − | 0.321227i | ||||
\(416\) | 7.28783 | + | 15.3100i | 0.357315 | + | 0.750636i | ||||
\(417\) | −1.00827 | − | 1.74638i | −0.0493754 | − | 0.0855207i | ||||
\(418\) | −4.89277 | − | 5.61045i | −0.239313 | − | 0.274416i | ||||
\(419\) | −29.0866 | −1.42097 | −0.710487 | − | 0.703710i | \(-0.751525\pi\) | ||||
−0.710487 | + | 0.703710i | \(0.751525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8642 | 0.675702 | 0.337851 | − | 0.941200i | \(-0.390300\pi\) | ||||
0.337851 | + | 0.941200i | \(0.390300\pi\) | |||||||
\(422\) | −16.8982 | − | 19.3768i | −0.822590 | − | 0.943250i | ||||
\(423\) | −3.67579 | − | 6.36666i | −0.178723 | − | 0.309557i | ||||
\(424\) | −0.0911455 | + | 0.181011i | −0.00442642 | + | 0.00879068i | ||||
\(425\) | −1.61192 | − | 0.930641i | −0.0781895 | − | 0.0451427i | ||||
\(426\) | −1.33953 | + | 3.91046i | −0.0649006 | + | 0.189463i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.9750 | − | 21.8699i | 0.820517 | − | 1.05712i | ||||
\(429\) | 1.89647 | − | 3.28479i | 0.0915627 | − | 0.158591i | ||||
\(430\) | −4.18474 | − | 21.3475i | −0.201806 | − | 1.02947i | ||||
\(431\) | −27.6258 | + | 15.9498i | −1.33069 | + | 0.768273i | −0.985405 | − | 0.170226i | \(-0.945550\pi\) |
−0.345282 | + | 0.938499i | \(0.612217\pi\) | |||||||
\(432\) | 3.85198 | + | 1.07809i | 0.185328 | + | 0.0518695i | ||||
\(433\) | 9.82239i | 0.472034i | 0.971749 | + | 0.236017i | \(0.0758421\pi\) | ||||
−0.971749 | + | 0.236017i | \(0.924158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.1116i | 1.10811i | ||||||||
\(436\) | 1.82360 | − | 0.743532i | 0.0873345 | − | 0.0356087i | ||||
\(437\) | −24.2754 | + | 14.0154i | −1.16125 | + | 0.670449i | ||||
\(438\) | 11.2481 | − | 2.20496i | 0.537453 | − | 0.105357i | ||||
\(439\) | −8.51989 | + | 14.7569i | −0.406632 | + | 0.704308i | −0.994510 | − | 0.104642i | \(-0.966630\pi\) |
0.587878 | + | 0.808950i | \(0.299964\pi\) | |||||||
\(440\) | 4.81594 | + | 7.33906i | 0.229591 | + | 0.349876i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.35158 | + | 2.51829i | 0.349679 | + | 0.119783i | ||||
\(443\) | 7.30000 | + | 4.21466i | 0.346833 | + | 0.200244i | 0.663290 | − | 0.748363i | \(-0.269160\pi\) |
−0.316456 | + | 0.948607i | \(0.602493\pi\) | |||||||
\(444\) | −2.04349 | + | 14.8832i | −0.0969797 | + | 0.706327i | ||||
\(445\) | 10.5114 | + | 18.2063i | 0.498290 | + | 0.863063i | ||||
\(446\) | 12.3634 | − | 10.7819i | 0.585425 | − | 0.510537i | ||||
\(447\) | 0.496110 | 0.0234652 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.64064 | 0.454970 | 0.227485 | − | 0.973782i | \(-0.426950\pi\) | ||||
0.227485 | + | 0.973782i | \(0.426950\pi\) | |||||||
\(450\) | 1.08218 | − | 0.943746i | 0.0510144 | − | 0.0444886i | ||||
\(451\) | 0.689424 | + | 1.19412i | 0.0324637 | + | 0.0562288i | ||||
\(452\) | 1.36892 | − | 9.97021i | 0.0643887 | − | 0.468959i | ||||
\(453\) | −11.4636 | − | 6.61849i | −0.538605 | − | 0.310964i | ||||
\(454\) | −13.5945 | − | 4.65680i | −0.638020 | − | 0.218554i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.45511 | + | 9.83701i | 0.302288 | + | 0.460660i | ||||
\(457\) | 14.5229 | − | 25.1543i | 0.679351 | − | 1.17667i | −0.295825 | − | 0.955242i | \(-0.595595\pi\) |
0.975177 | − | 0.221429i | \(-0.0710720\pi\) | |||||||
\(458\) | 32.0539 | − | 6.28353i | 1.49778 | − | 0.293610i | ||||
\(459\) | 1.58759 | − | 0.916595i | 0.0741023 | − | 0.0427830i | ||||
\(460\) | 30.6072 | − | 12.4794i | 1.42707 | − | 0.581855i | ||||
\(461\) | 23.9796i | 1.11684i | 0.829559 | + | 0.558420i | \(0.188592\pi\) | ||||
−0.829559 | + | 0.558420i | \(0.811408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.4975i | − | 1.32439i | −0.749331 | − | 0.662196i | \(-0.769625\pi\) | ||
0.749331 | − | 0.662196i | \(-0.230375\pi\) | |||||||
\(464\) | 36.2981 | + | 10.1591i | 1.68510 | + | 0.471623i | ||||
\(465\) | −20.0504 | + | 11.5761i | −0.929813 | + | 0.536828i | ||||
\(466\) | 1.86503 | + | 9.51402i | 0.0863960 | + | 0.440729i | ||||
\(467\) | −9.29075 | + | 16.0921i | −0.429925 | + | 0.744651i | −0.996866 | − | 0.0791067i | \(-0.974793\pi\) |
0.566942 | + | 0.823758i | \(0.308127\pi\) | |||||||
\(468\) | −3.67579 | + | 4.73574i | −0.169913 | + | 0.218910i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.26338 | + | 24.1231i | −0.381161 | + | 1.11271i | ||||
\(471\) | −4.38345 | − | 2.53079i | −0.201979 | − | 0.116613i | ||||
\(472\) | 4.28287 | − | 8.50561i | 0.197135 | − | 0.391502i | ||||
\(473\) | 3.96813 | + | 6.87300i | 0.182455 | + | 0.316021i | ||||
\(474\) | 1.65794 | + | 1.90113i | 0.0761515 | + | 0.0873217i | ||||
\(475\) | 4.22360 | 0.193792 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0716524 | −0.00328074 | ||||||||
\(478\) | 20.6589 | + | 23.6892i | 0.944915 | + | 1.08352i | ||||
\(479\) | −14.1707 | − | 24.5443i | −0.647475 | − | 1.12146i | −0.983724 | − | 0.179686i | \(-0.942492\pi\) |
0.336249 | − | 0.941773i | \(-0.390842\pi\) | |||||||
\(480\) | −5.96316 | − | 12.5272i | −0.272180 | − | 0.571786i | ||||
\(481\) | −19.4987 | − | 11.2576i | −0.889062 | − | 0.513300i | ||||
\(482\) | 7.07031 | − | 20.6402i | 0.322044 | − | 0.940134i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.8494 | + | 11.5258i | 0.674972 | + | 0.523900i | ||||
\(485\) | −8.71162 | + | 15.0890i | −0.395574 | + | 0.685154i | ||||
\(486\) | 0.272050 | + | 1.38780i | 0.0123405 | + | 0.0629519i | ||||
\(487\) | −35.9498 | + | 20.7556i | −1.62904 | + | 0.940528i | −0.644662 | + | 0.764468i | \(0.723002\pi\) |
−0.984379 | + | 0.176060i | \(0.943665\pi\) | |||||||
\(488\) | 1.79295 | + | 31.3511i | 0.0811630 | + | 1.41920i | ||||
\(489\) | 12.0357i | 0.544274i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.72728i | − | 0.0779509i | −0.999240 | − | 0.0389755i | \(-0.987591\pi\) | ||
0.999240 | − | 0.0389755i | \(-0.0124094\pi\) | |||||||
\(492\) | −0.822804 | − | 2.01802i | −0.0370949 | − | 0.0909795i | ||||
\(493\) | 14.9602 | − | 8.63729i | 0.673774 | − | 0.389004i | ||||
\(494\) | −17.3044 | + | 3.39218i | −0.778561 | + | 0.152621i | ||||
\(495\) | −1.55176 | + | 2.68773i | −0.0697465 | + | 0.120805i | ||||
\(496\) | 9.36745 | + | 36.5787i | 0.420611 | + | 1.64243i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.13935 | − | 2.44559i | −0.319922 | − | 0.109590i | ||||
\(499\) | −36.6216 | − | 21.1435i | −1.63941 | − | 0.946514i | −0.981037 | − | 0.193822i | \(-0.937911\pi\) |
−0.658373 | − | 0.752691i | \(-0.728755\pi\) | |||||||
\(500\) | 19.3641 | + | 2.65872i | 0.865988 | + | 0.118901i | ||||
\(501\) | 3.73212 | + | 6.46422i | 0.166739 | + | 0.288800i | ||||
\(502\) | 23.7634 | − | 20.7236i | 1.06061 | − | 0.924940i | ||||
\(503\) | −4.23770 | −0.188950 | −0.0944748 | − | 0.995527i | \(-0.530117\pi\) | ||||
−0.0944748 | + | 0.995527i | \(0.530117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.28906 | 0.101862 | ||||||||
\(506\) | −9.08820 | + | 7.92564i | −0.404020 | + | 0.352338i | ||||
\(507\) | 2.00766 | + | 3.47737i | 0.0891634 | + | 0.154436i | ||||
\(508\) | −12.6481 | − | 1.73660i | −0.561168 | − | 0.0770491i | ||||
\(509\) | 36.1788 | + | 20.8878i | 1.60360 | + | 0.925836i | 0.990760 | + | 0.135626i | \(0.0433046\pi\) |
0.612836 | + | 0.790210i | \(0.290029\pi\) | |||||||
\(510\) | −6.01532 | − | 2.06056i | −0.266363 | − | 0.0912429i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.2959 | + | 3.85896i | −0.985350 | + | 0.170544i | ||||
\(513\) | −2.07993 | + | 3.60254i | −0.0918310 | + | 0.159056i | ||||
\(514\) | 3.98266 | − | 0.780720i | 0.175668 | − | 0.0344361i | ||||
\(515\) | 8.77055 | − | 5.06368i | 0.386476 | − | 0.223132i | ||||
\(516\) | −4.73583 | − | 11.6152i | −0.208483 | − | 0.511329i | ||||
\(517\) | − | 9.30265i | − | 0.409130i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.36398i | − | 0.191557i | ||||||
\(520\) | 20.7595 | − | 1.18722i | 0.910364 | − | 0.0520631i | ||||
\(521\) | −30.2681 | + | 17.4753i | −1.32607 | + | 0.765607i | −0.984689 | − | 0.174318i | \(-0.944228\pi\) |
−0.341381 | + | 0.939925i | \(0.610895\pi\) | |||||||
\(522\) | 2.56359 | + | 13.0776i | 0.112205 | + | 0.572389i | ||||
\(523\) | −6.13503 | + | 10.6262i | −0.268266 | + | 0.464651i | −0.968414 | − | 0.249347i | \(-0.919784\pi\) |
0.700148 | + | 0.713998i | \(0.253117\pi\) | |||||||
\(524\) | −6.11751 | − | 4.74829i | −0.267245 | − | 0.207430i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.75317 | + | 13.8758i | −0.207248 | + | 0.605014i | ||||
\(527\) | 14.9865 | + | 8.65246i | 0.652822 | + | 0.376907i | ||||
\(528\) | 3.53914 | + | 3.61857i | 0.154021 | + | 0.157478i | ||||
\(529\) | 11.2032 | + | 19.4044i | 0.487094 | + | 0.843671i | ||||
\(530\) | 0.163347 | + | 0.187307i | 0.00709534 | + | 0.00813610i | ||||
\(531\) | 3.36690 | 0.146111 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.26619 | 0.141474 | ||||||||
\(534\) | 7.96733 | + | 9.13601i | 0.344780 | + | 0.395354i | ||||
\(535\) | −16.9750 | − | 29.4016i | −0.733893 | − | 1.27114i | ||||
\(536\) | −7.09283 | − | 3.57149i | −0.306364 | − | 0.154265i | ||||
\(537\) | 21.2754 | + | 12.2834i | 0.918102 | + | 0.530067i | ||||
\(538\) | 2.37086 | − | 6.92118i | 0.102215 | − | 0.298393i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.00766 | − | 3.87495i | 0.129429 | − | 0.166751i | ||||
\(541\) | 0.467883 | − | 0.810397i | 0.0201158 | − | 0.0348417i | −0.855792 | − | 0.517320i | \(-0.826930\pi\) |
0.875908 | + | 0.482478i | \(0.160263\pi\) | |||||||
\(542\) | 6.59424 | + | 33.6390i | 0.283247 | + | 1.44492i | ||||
\(543\) | −10.1483 | + | 5.85912i | −0.435505 | + | 0.251439i | ||||
\(544\) | −5.88036 | + | 8.54167i | −0.252118 | + | 0.366221i | ||||
\(545\) | − | 2.41503i | − | 0.103449i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.13048i | 0.304877i | 0.988313 | + | 0.152439i | \(0.0487127\pi\) | ||||
−0.988313 | + | 0.152439i | \(0.951287\pi\) | |||||||
\(548\) | 27.2299 | − | 11.1024i | 1.16320 | − | 0.474271i | ||||
\(549\) | −9.61496 | + | 5.55120i | −0.410356 | + | 0.236919i | ||||
\(550\) | 1.78302 | − | 0.349526i | 0.0760284 | − | 0.0149038i | ||||
\(551\) | −19.5996 | + | 33.9476i | −0.834973 | + | 1.44621i | ||||
\(552\) | 15.9347 | − | 10.4564i | 0.678224 | − | 0.445055i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.03419 | − | 1.38192i | −0.171396 | − | 0.0587120i | ||||
\(555\) | 15.9545 | + | 9.21133i | 0.677231 | + | 0.390999i | ||||
\(556\) | −0.548603 | + | 3.99561i | −0.0232659 | + | 0.169452i | ||||
\(557\) | −4.97622 | − | 8.61907i | −0.210849 | − | 0.365202i | 0.741131 | − | 0.671360i | \(-0.234290\pi\) |
−0.951981 | + | 0.306159i | \(0.900956\pi\) | |||||||
\(558\) | −10.0613 | + | 8.77430i | −0.425931 | + | 0.371446i | ||||
\(559\) | 18.7993 | 0.795124 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.31971 | 0.0979381 | ||||||||
\(562\) | 7.37481 | − | 6.43143i | 0.311088 | − | 0.271293i | ||||
\(563\) | −0.844531 | − | 1.46277i | −0.0355927 | − | 0.0616484i | 0.847680 | − | 0.530507i | \(-0.177999\pi\) |
−0.883273 | + | 0.468859i | \(0.844665\pi\) | |||||||
\(564\) | −2.00000 | + | 14.5665i | −0.0842152 | + | 0.613360i | ||||
\(565\) | −10.6878 | − | 6.17063i | −0.449641 | − | 0.259600i | ||||
\(566\) | −27.5258 | − | 9.42899i | −1.15700 | − | 0.396330i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.91180 | − | 4.53557i | 0.290013 | − | 0.190308i | ||||
\(569\) | 6.96935 | − | 12.0713i | 0.292170 | − | 0.506054i | −0.682152 | − | 0.731210i | \(-0.738956\pi\) |
0.974323 | + | 0.225156i | \(0.0722892\pi\) | |||||||
\(570\) | 14.1591 | − | 2.77560i | 0.593058 | − | 0.116257i | ||||
\(571\) | −16.1591 | + | 9.32947i | −0.676238 | + | 0.390426i | −0.798436 | − | 0.602079i | \(-0.794339\pi\) |
0.122198 | + | 0.992506i | \(0.461006\pi\) | |||||||
\(572\) | −7.02446 | + | 2.86407i | −0.293707 | + | 0.119753i | ||||
\(573\) | − | 15.8919i | − | 0.663893i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.84168i | − | 0.285318i | ||||||
\(576\) | −4.76378 | − | 6.42701i | −0.198491 | − | 0.267792i | ||||
\(577\) | −29.4591 | + | 17.0082i | −1.22640 | + | 0.708062i | −0.966275 | − | 0.257513i | \(-0.917097\pi\) |
−0.260125 | + | 0.965575i | \(0.583764\pi\) | |||||||
\(578\) | −3.71061 | − | 18.9288i | −0.154341 | − | 0.787333i | ||||
\(579\) | 9.86690 | − | 17.0900i | 0.410055 | − | 0.710235i | ||||
\(580\) | 28.3419 | − | 36.5146i | 1.17683 | − | 1.51619i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.25572 | + | 9.50433i | −0.134954 | + | 0.393967i | ||||
\(583\) | −0.0785213 | − | 0.0453343i | −0.00325202 | − | 0.00187755i | ||||
\(584\) | −20.4751 | − | 10.3099i | −0.847264 | − | 0.426627i | ||||
\(585\) | 3.67579 | + | 6.36666i | 0.151975 | + | 0.263229i | ||||
\(586\) | 26.3154 | + | 30.1755i | 1.08708 | + | 1.24654i | ||||
\(587\) | 41.9153 | 1.73003 | 0.865015 | − | 0.501746i | \(-0.167309\pi\) | ||||
0.865015 | + | 0.501746i | \(0.167309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.2681 | −1.61801 | ||||||||
\(590\) | −7.67557 | − | 8.80145i | −0.315998 | − | 0.362350i | ||||
\(591\) | 0.499388 | + | 0.864965i | 0.0205421 | + | 0.0355799i | ||||
\(592\) | 21.4800 | − | 21.0085i | 0.882822 | − | 0.863443i | ||||
\(593\) | −21.1354 | − | 12.2025i | −0.867927 | − | 0.501098i | −0.00126806 | − | 0.999999i | \(-0.500404\pi\) |
−0.866659 | + | 0.498901i | \(0.833737\pi\) | |||||||
\(594\) | −0.579927 | + | 1.69296i | −0.0237947 | + | 0.0694632i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.783818 | − | 0.608384i | −0.0321064 | − | 0.0249204i | ||||
\(597\) | −1.35158 | + | 2.34101i | −0.0553165 | + | 0.0958110i | ||||
\(598\) | 5.49489 | + | 28.0308i | 0.224703 | + | 1.14627i | ||||
\(599\) | −18.0000 | + | 10.3923i | −0.735460 | + | 0.424618i | −0.820416 | − | 0.571767i | \(-0.806258\pi\) |
0.0849563 | + | 0.996385i | \(0.472925\pi\) | |||||||
\(600\) | −2.86709 | + | 0.163967i | −0.117048 | + | 0.00669391i | ||||
\(601\) | − | 10.6623i | − | 0.434924i | −0.976069 | − | 0.217462i | \(-0.930222\pi\) | ||
0.976069 | − | 0.217462i | \(-0.0697778\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.80766i | − | 0.114337i | ||||||
\(604\) | 9.99528 | + | 24.5146i | 0.406702 | + | 0.997484i | ||||
\(605\) | 19.9633 | − | 11.5258i | 0.811622 | − | 0.468590i | ||||
\(606\) | 1.29525 | − | 0.253908i | 0.0526160 | − | 0.0103143i | ||||
\(607\) | −20.0215 | + | 34.6782i | −0.812646 | + | 1.40754i | 0.0983597 | + | 0.995151i | \(0.468640\pi\) |
−0.911006 | + | 0.412393i | \(0.864693\pi\) | |||||||
\(608\) | 1.86460 | − | 23.4577i | 0.0756196 | − | 0.951335i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.4308 | + | 12.4794i | 1.47504 | + | 0.505276i | ||||
\(611\) | −19.0837 | − | 11.0180i | −0.772044 | − | 0.445740i | ||||
\(612\) | −3.63230 | − | 0.498720i | −0.146827 | − | 0.0201596i | ||||
\(613\) | −11.2481 | − | 19.4822i | −0.454305 | − | 0.786879i | 0.544343 | − | 0.838863i | \(-0.316779\pi\) |
−0.998648 | + | 0.0519838i | \(0.983446\pi\) | |||||||
\(614\) | −9.22591 | + | 8.04574i | −0.372328 | + | 0.324700i | ||||
\(615\) | −2.67251 | −0.107766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0820 | −0.727954 | −0.363977 | − | 0.931408i | \(-0.618581\pi\) | ||||
−0.363977 | + | 0.931408i | \(0.618581\pi\) | |||||||
\(618\) | 4.40109 | − | 3.83811i | 0.177038 | − | 0.154391i | ||||
\(619\) | −16.0465 | − | 27.7933i | −0.644962 | − | 1.11711i | −0.984310 | − | 0.176446i | \(-0.943540\pi\) |
0.339348 | − | 0.940661i | \(-0.389793\pi\) | |||||||
\(620\) | 45.8739 | + | 6.29855i | 1.84234 | + | 0.252956i | ||||
\(621\) | 5.83564 | + | 3.36921i | 0.234176 | + | 0.135202i | ||||
\(622\) | −12.4994 | − | 4.28168i | −0.501180 | − | 0.171680i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.6150 | − | 2.97448i | 0.464971 | − | 0.119074i | ||||
\(625\) | 14.5229 | − | 25.1543i | 0.580915 | − | 1.00617i | ||||
\(626\) | −10.2357 | + | 2.00650i | −0.409100 | + | 0.0801958i | ||||
\(627\) | −4.55863 | + | 2.63193i | −0.182054 | + | 0.105109i | ||||
\(628\) | 3.82201 | + | 9.37392i | 0.152515 | + | 0.374060i | ||||
\(629\) | − | 13.7699i | − | 0.549041i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.95509i | − | 0.117640i | −0.998269 | − | 0.0588201i | \(-0.981266\pi\) | ||
0.998269 | − | 0.0588201i | \(-0.0187338\pi\) | |||||||
\(632\) | −0.288050 | − | 5.03678i | −0.0114580 | − | 0.200352i | ||||
\(633\) | −15.7442 | + | 9.08990i | −0.625774 | + | 0.361291i | ||||
\(634\) | 0.987620 | + | 5.03811i | 0.0392234 | + | 0.200089i | ||||
\(635\) | −7.82798 | + | 13.5585i | −0.310644 | + | 0.538051i | ||||
\(636\) | 0.113206 | + | 0.0878679i | 0.00448889 | + | 0.00348419i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.46479 | + | 15.9532i | −0.216353 | + | 0.631593i | ||||
\(639\) | 2.53126 | + | 1.46142i | 0.100135 | + | 0.0578130i | ||||
\(640\) | −5.94085 | + | 27.1048i | −0.234833 | + | 1.07141i | ||||
\(641\) | 20.7459 | + | 35.9329i | 0.819412 | + | 1.41926i | 0.906116 | + | 0.423029i | \(0.139033\pi\) |
−0.0867040 | + | 0.996234i | \(0.527633\pi\) | |||||||
\(642\) | −12.8665 | − | 14.7538i | −0.507801 | − | 0.582286i | ||||
\(643\) | −16.7686 | −0.661290 | −0.330645 | − | 0.943755i | \(-0.607266\pi\) | ||||
−0.330645 | + | 0.943755i | \(0.607266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.3822 | −0.605675 | ||||||||
\(646\) | −7.08820 | − | 8.12792i | −0.278882 | − | 0.319789i | ||||
\(647\) | −9.31180 | − | 16.1285i | −0.366085 | − | 0.634077i | 0.622865 | − | 0.782329i | \(-0.285969\pi\) |
−0.988950 | + | 0.148252i | \(0.952635\pi\) | |||||||
\(648\) | 1.27205 | − | 2.52624i | 0.0499709 | − | 0.0992401i | ||||
\(649\) | 3.68967 | + | 2.13023i | 0.144832 | + | 0.0836189i | ||||
\(650\) | 1.39477 | − | 4.07172i | 0.0547075 | − | 0.159706i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.7595 | − | 19.0155i | 0.578026 | − | 0.744706i | ||||
\(653\) | −12.8305 | + | 22.2230i | −0.502095 | + | 0.869654i | 0.497902 | + | 0.867233i | \(0.334104\pi\) |
−0.999997 | + | 0.00242072i | \(0.999229\pi\) | |||||||
\(654\) | −0.267881 | − | 1.36653i | −0.0104750 | − | 0.0534357i | ||||
\(655\) | −8.22428 | + | 4.74829i | −0.321349 | + | 0.185531i | ||||
\(656\) | −1.17475 | + | 4.19734i | −0.0458661 | + | 0.163879i | ||||
\(657\) | − | 8.10495i | − | 0.316204i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27.7044i | − | 1.07921i | −0.841919 | − | 0.539604i | \(-0.818574\pi\) | ||
0.841919 | − | 0.539604i | \(-0.181426\pi\) | |||||||
\(660\) | 5.74766 | − | 2.34348i | 0.223727 | − | 0.0912199i | ||||
\(661\) | 29.5472 | − | 17.0591i | 1.14925 | − | 0.663522i | 0.200548 | − | 0.979684i | \(-0.435728\pi\) |
0.948705 | + | 0.316162i | \(0.102394\pi\) | |||||||
\(662\) | 0.872019 | − | 0.170942i | 0.0338920 | − | 0.00664385i | ||||
\(663\) | 2.74744 | − | 4.75871i | 0.106702 | − | 0.184813i | ||||
\(664\) | 8.28060 | + | 12.6189i | 0.321350 | + | 0.489708i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0495 | + | 3.44247i | 0.389411 | + | 0.133393i | ||||
\(667\) | 54.9906 | + | 31.7489i | 2.12925 | + | 1.22932i | ||||
\(668\) | 2.03065 | − | 14.7897i | 0.0785681 | − | 0.572231i | ||||
\(669\) | −5.79982 | − | 10.0456i | −0.224234 | − | 0.388385i | ||||
\(670\) | −7.33953 | + | 6.40066i | −0.283551 | + | 0.247279i | ||||
\(671\) | −14.0489 | −0.542352 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.7032 | −0.682407 | −0.341203 | − | 0.939990i | \(-0.610834\pi\) | ||||
−0.341203 | + | 0.939990i | \(0.610834\pi\) | |||||||
\(674\) | 23.7811 | − | 20.7390i | 0.916012 | − | 0.798836i | ||||
\(675\) | −0.507662 | − | 0.879296i | −0.0195399 | − | 0.0338441i | ||||
\(676\) | 1.09237 | − | 7.95601i | 0.0420142 | − | 0.306000i | ||||
\(677\) | 35.5808 | + | 20.5426i | 1.36748 | + | 0.789516i | 0.990606 | − | 0.136747i | \(-0.0436649\pi\) |
0.376876 | + | 0.926264i | \(0.376998\pi\) | |||||||
\(678\) | −6.73212 | − | 2.30609i | −0.258545 | − | 0.0885650i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.97690 | + | 10.6322i | 0.267552 | + | 0.407725i | ||||
\(681\) | −5.08054 | + | 8.79975i | −0.194687 | + | 0.337207i | ||||
\(682\) | −16.5773 | + | 3.24965i | −0.634779 | + | 0.124436i | ||||
\(683\) | −18.3842 | + | 10.6141i | −0.703450 | + | 0.406137i | −0.808631 | − | 0.588316i | \(-0.799791\pi\) |
0.105181 | + | 0.994453i | \(0.466458\pi\) | |||||||
\(684\) | 7.70395 | − | 3.14112i | 0.294568 | − | 0.120104i | ||||
\(685\) | − | 36.0612i | − | 1.37783i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 23.0970i | − | 0.881204i | ||||||
\(688\) | −6.76151 | + | 24.1587i | −0.257780 | + | 0.921042i | ||||
\(689\) | −0.186000 | + | 0.107387i | −0.00708603 | + | 0.00409112i | ||||
\(690\) | −4.49611 | − | 22.9358i | −0.171164 | − | 0.873152i | ||||
\(691\) | 19.4878 | − | 33.7539i | 0.741352 | − | 1.28406i | −0.210528 | − | 0.977588i | \(-0.567518\pi\) |
0.951880 | − | 0.306472i | \(-0.0991485\pi\) | |||||||
\(692\) | −5.35158 | + | 6.89477i | −0.203437 | + | 0.262100i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.15985 | − | 9.22447i | 0.119946 | − | 0.350156i | ||||
\(695\) | 4.28321 | + | 2.47291i | 0.162471 | + | 0.0938028i | ||||
\(696\) | 11.9868 | − | 23.8053i | 0.454359 | − | 0.902339i | ||||
\(697\) | 0.998775 | + | 1.72993i | 0.0378313 | + | 0.0655257i | ||||
\(698\) | −12.5268 | − | 14.3642i | −0.474145 | − | 0.543694i | ||||
\(699\) | 6.85547 | 0.259298 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.28115 | 0.161697 | 0.0808485 | − | 0.996726i | \(-0.474237\pi\) | ||||
0.0808485 | + | 0.996726i | \(0.474237\pi\) | |||||||
\(702\) | 2.78613 | + | 3.19481i | 0.105156 | + | 0.120580i | ||||
\(703\) | 15.6232 | + | 27.0602i | 0.589241 | + | 1.02060i | ||||
\(704\) | −1.15410 | − | 10.0572i | −0.0434967 | − | 0.379043i | ||||
\(705\) | 15.6150 | + | 9.01530i | 0.588093 | + | 0.339536i | ||||
\(706\) | −13.1002 | + | 38.2432i | −0.493034 | + | 1.43930i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5.31946 | − | 4.12886i | −0.199918 | − | 0.155172i | ||||
\(709\) | 21.8796 | − | 37.8965i | 0.821704 | − | 1.42323i | −0.0827080 | − | 0.996574i | \(-0.526357\pi\) |
0.904412 | − | 0.426660i | \(-0.140310\pi\) | |||||||
\(710\) | −1.95023 | − | 9.94861i | −0.0731907 | − | 0.373365i | ||||
\(711\) | 1.54471 | − | 0.891841i | 0.0579313 | − | 0.0334466i | ||||
\(712\) | −1.38425 | − | 24.2046i | −0.0518768 | − | 0.907107i | ||||
\(713\) | 63.6092i | 2.38218i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.30265i | 0.347899i | ||||||||
\(716\) | −18.5504 | − | 45.4971i | −0.693262 | − | 1.70030i | ||||
\(717\) | 19.2481 | − | 11.1129i | 0.718832 | − | 0.415018i | ||||
\(718\) | −9.61496 | + | 1.88482i | −0.358827 | + | 0.0703409i | ||||
\(719\) | 20.7657 | − | 35.9672i | 0.774429 | − | 1.34135i | −0.160685 | − | 0.987006i | \(-0.551370\pi\) |
0.935115 | − | 0.354345i | \(-0.115296\pi\) | |||||||
\(720\) | −9.50377 | + | 2.43382i | −0.354185 | + | 0.0907033i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.26856 | − | 0.777097i | −0.0844270 | − | 0.0289205i | ||||
\(723\) | −13.3605 | − | 7.71367i | −0.496881 | − | 0.286874i | ||||
\(724\) | 23.2187 | + | 3.18795i | 0.862915 | + | 0.118479i | ||||
\(725\) | −4.78382 | − | 8.28582i | −0.177667 | − | 0.307727i | ||||
\(726\) | 10.0176 | − | 8.73619i | 0.371789 | − | 0.324230i | ||||
\(727\) | 7.19963 | 0.267020 | 0.133510 | − | 0.991047i | \(-0.457375\pi\) | ||||
0.133510 | + | 0.991047i | \(0.457375\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −21.1872 | + | 18.4770i | −0.784174 | + | 0.683863i | ||||
\(731\) | 5.74867 | + | 9.95698i | 0.212622 | + | 0.368272i | ||||
\(732\) | 21.9984 | + | 3.02041i | 0.813085 | + | 0.111638i | ||||
\(733\) | −20.9219 | − | 12.0793i | −0.772768 | − | 0.446158i | 0.0610934 | − | 0.998132i | \(-0.480541\pi\) |
−0.833861 | + | 0.551974i | \(0.813875\pi\) | |||||||
\(734\) | 17.3173 | + | 5.93205i | 0.639192 | + | 0.218956i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.9984 | − | 3.02041i | −1.40064 | − | 0.111334i | ||||
\(737\) | 1.77640 | − | 3.07682i | 0.0654345 | − | 0.113336i | ||||
\(738\) | −1.51223 | + | 0.296442i | −0.0556659 | + | 0.0109122i | ||||
\(739\) | 8.16690 | − | 4.71516i | 0.300424 | − | 0.173450i | −0.342209 | − | 0.939624i | \(-0.611175\pi\) |
0.642634 | + | 0.766174i | \(0.277842\pi\) | |||||||
\(740\) | −13.9110 | − | 34.1184i | −0.511379 | − | 1.25422i | ||||
\(741\) | 12.4689i | 0.458058i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.32851i | 0.0854248i | 0.999087 | + | 0.0427124i | \(0.0135999\pi\) | ||||
−0.999087 | + | 0.0427124i | \(0.986400\pi\) | |||||||
\(744\) | 26.6562 | − | 1.52445i | 0.977263 | − | 0.0558890i | ||||
\(745\) | −1.05375 | + | 0.608384i | −0.0386065 | + | 0.0222895i | ||||
\(746\) | −0.837662 | − | 4.27313i | −0.0306690 | − | 0.156451i | ||||
\(747\) | −2.66813 | + | 4.62133i | −0.0976217 | + | 0.169086i | ||||
\(748\) | −3.66497 | − | 2.84468i | −0.134005 | − | 0.104012i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.47889 | − | 13.0751i | 0.163546 | − | 0.477435i | ||||
\(751\) | −26.9834 | − | 15.5789i | −0.984638 | − | 0.568481i | −0.0809709 | − | 0.996716i | \(-0.525802\pi\) |
−0.903667 | + | 0.428235i | \(0.859135\pi\) | |||||||
\(752\) | 21.0229 | − | 20.5614i | 0.766625 | − | 0.749797i | ||||
\(753\) | −11.1477 | − | 19.3084i | −0.406244 | − | 0.703636i | ||||
\(754\) | 26.2544 | + | 30.1054i | 0.956128 | + | 1.09638i | ||||
\(755\) | 32.4652 | 1.18153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.559856 | −0.0203483 | −0.0101742 | − | 0.999948i | \(-0.503239\pi\) | ||||
−0.0101742 | + | 0.999948i | \(0.503239\pi\) | |||||||
\(758\) | −4.84289 | − | 5.55326i | −0.175902 | − | 0.201704i | ||||
\(759\) | 4.26338 | + | 7.38439i | 0.154751 | + | 0.268036i | ||||
\(760\) | −25.7740 | − | 12.9781i | −0.934922 | − | 0.470766i | ||||
\(761\) | −39.6196 | − | 22.8744i | −1.43621 | − | 0.829196i | −0.438625 | − | 0.898670i | \(-0.644534\pi\) |
−0.997584 | + | 0.0694744i | \(0.977868\pi\) | |||||||
\(762\) | −2.92548 | + | 8.54029i | −0.105979 | + | 0.309382i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19.4883 | + | 25.1080i | −0.705063 | + | 0.908376i | ||||
\(765\) | −2.24806 | + | 3.89375i | −0.0812786 | + | 0.140779i | ||||
\(766\) | 10.5747 | + | 53.9446i | 0.382081 | + | 1.94910i | ||||
\(767\) | 8.74002 | − | 5.04606i | 0.315584 | − | 0.182203i | ||||
\(768\) | −0.355074 | + | 15.9961i | −0.0128126 | + | 0.577208i | ||||
\(769\) | − | 8.33377i | − | 0.300524i | −0.988646 | − | 0.150262i | \(-0.951988\pi\) | ||
0.988646 | − | 0.150262i | \(-0.0480117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 2.86976i | − | 0.103352i | ||||||
\(772\) | −36.5466 | + | 14.9011i | −1.31534 | + | 0.536301i | ||||
\(773\) | −26.5674 | + | 15.3387i | −0.955563 | + | 0.551695i | −0.894805 | − | 0.446458i | \(-0.852685\pi\) |
−0.0607584 | + | 0.998153i | \(0.519352\pi\) | |||||||
\(774\) | −8.70395 | + | 1.70624i | −0.312857 | + | 0.0613294i | ||||
\(775\) | 4.79222 | − | 8.30037i | 0.172142 | − | 0.298158i | ||||
\(776\) | 16.7990 | − | 11.0236i | 0.603050 | − | 0.395725i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.99708 | − | 1.71176i | −0.179154 | − | 0.0613695i | ||||
\(779\) | −3.92554 | − | 2.26641i | −0.140647 | − | 0.0812025i | ||||
\(780\) | 2.00000 | − | 14.5665i | 0.0716115 | − | 0.521564i | ||||
\(781\) | 1.84928 | + | 3.20304i | 0.0661723 | + | 0.114614i | ||||
\(782\) | −13.1662 | + | 11.4820i | −0.470821 | + | 0.410594i | ||||
\(783\) | 9.42323 | 0.336759 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.4141 | 0.443078 | ||||||||
\(786\) | −4.12697 | + | 3.59905i | −0.147204 | + | 0.128374i | ||||
\(787\) | −11.0792 | − | 19.1897i | −0.394931 | − | 0.684040i | 0.598162 | − | 0.801375i | \(-0.295898\pi\) |
−0.993092 | + | 0.117335i | \(0.962565\pi\) | |||||||
\(788\) | 0.271717 | − | 1.97898i | 0.00967952 | − | 0.0704984i | ||||
\(789\) | 8.98186 | + | 5.18568i | 0.319763 | + | 0.184615i | ||||
\(790\) | −5.85287 | − | 2.00491i | −0.208236 | − | 0.0713314i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.99234 | − | 1.96359i | 0.106328 | − | 0.0697732i | ||||
\(793\) | −16.6394 | + | 28.8203i | −0.590883 | + | 1.02344i | ||||
\(794\) | −9.31180 | + | 1.82539i | −0.330463 | + | 0.0647807i | ||||
\(795\) | 0.152192 | − | 0.0878679i | 0.00539768 | − | 0.00311635i | ||||
\(796\) | 5.00619 | − | 2.04116i | 0.177440 | − | 0.0723472i | ||||
\(797\) | 24.1705i | 0.856164i | 0.903740 | + | 0.428082i | \(0.140811\pi\) | ||||
−0.903740 | + | 0.428082i | \(0.859189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 13.4768i | − | 0.476776i | ||||||
\(800\) | 4.73086 | + | 3.25687i | 0.167261 | + | 0.115148i | ||||
\(801\) | 7.42323 | − | 4.28581i | 0.262287 | − | 0.151431i | ||||
\(802\) | −1.59087 | − | 8.11542i | −0.0561754 | − | 0.286566i | ||||
\(803\) | 5.12798 | − | 8.88192i | 0.180963 | − | 0.313436i | ||||
\(804\) | −3.44306 | + | 4.43590i | −0.121427 | + | 0.156442i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.9676 | + | 37.8560i | −0.456765 | + | 1.33342i | ||||
\(807\) | −4.48011 | − | 2.58659i | −0.157707 | − | 0.0910524i | ||||
\(808\) | −2.35777 | − | 1.18722i | −0.0829462 | − | 0.0417663i | ||||
\(809\) | −7.61046 | − | 13.1817i | −0.267569 | − | 0.463444i | 0.700664 | − | 0.713491i | \(-0.252887\pi\) |
−0.968234 | + | 0.250047i | \(0.919554\pi\) | |||||||
\(810\) | −2.27971 | − | 2.61411i | −0.0801009 | − | 0.0918504i | ||||
\(811\) | −48.4574 | −1.70157 | −0.850785 | − | 0.525515i | \(-0.823873\pi\) | ||||
−0.850785 | + | 0.525515i | \(0.823873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.2391 | 0.850101 | ||||||||
\(814\) | 8.83485 | + | 10.1308i | 0.309661 | + | 0.355083i | ||||
\(815\) | −14.7595 | − | 25.5642i | −0.517002 | − | 0.895474i | ||||
\(816\) | 5.12719 | + | 5.24226i | 0.179487 | + | 0.183516i | ||||
\(817\) | −22.5943 | − | 13.0448i | −0.790474 | − | 0.456380i | ||||
\(818\) | −14.1454 | + | 41.2942i | −0.494581 | + | 1.44382i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.22238 | + | 3.27732i | 0.147452 | + | 0.114449i | ||||
\(821\) | −25.7647 | + | 44.6257i | −0.899193 | + | 1.55745i | −0.0706654 | + | 0.997500i | \(0.522512\pi\) |
−0.828528 | + | 0.559948i | \(0.810821\pi\) | |||||||
\(822\) | −4.00000 | − | 20.4050i | −0.139516 | − | 0.711708i | ||||
\(823\) | 1.90279 | − | 1.09858i | 0.0663272 | − | 0.0382941i | −0.466470 | − | 0.884537i | \(-0.654474\pi\) |
0.532797 | + | 0.846243i | \(0.321141\pi\) | |||||||
\(824\) | −11.6601 | + | 0.666834i | −0.406199 | + | 0.0232303i | ||||
\(825\) | − | 1.28479i | − | 0.0447305i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.2864i | 0.357693i | 0.983877 | + | 0.178846i | \(0.0572365\pi\) | ||||
−0.983877 | + | 0.178846i | \(0.942763\pi\) | |||||||
\(828\) | −5.08820 | − | 12.4794i | −0.176827 | − | 0.433689i | ||||
\(829\) | −0.662548 | + | 0.382522i | −0.0230112 | + | 0.0132855i | −0.511461 | − | 0.859306i | \(-0.670896\pi\) |
0.488450 | + | 0.872592i | \(0.337562\pi\) | |||||||
\(830\) | 18.1632 | − | 3.56054i | 0.630455 | − | 0.123588i | ||||
\(831\) | −1.50766 | + | 2.61135i | −0.0523002 | + | 0.0905866i | ||||
\(832\) | −21.9984 | − | 9.54406i | −0.762658 | − | 0.330881i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.69793 | + | 0.924179i | 0.0934217 | + | 0.0320017i | ||||
\(835\) | −15.8542 | − | 9.15345i | −0.548659 | − | 0.316768i | ||||
\(836\) | 10.4299 | + | 1.43203i | 0.360724 | + | 0.0495279i | ||||
\(837\) | 4.71989 | + | 8.17509i | 0.163143 | + | 0.282572i | ||||
\(838\) | 31.0018 | − | 27.0361i | 1.07094 | − | 0.933946i | ||||
\(839\) | 3.50389 | 0.120968 | 0.0604839 | − | 0.998169i | \(-0.480736\pi\) | ||||
0.0604839 | + | 0.998169i | \(0.480736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.7973 | 2.06198 | ||||||||
\(842\) | −14.7771 | + | 12.8868i | −0.509253 | + | 0.444110i | ||||
\(843\) | −3.45961 | − | 5.99222i | −0.119155 | − | 0.206383i | ||||
\(844\) | 36.0216 | + | 4.94582i | 1.23992 | + | 0.170242i | ||||
\(845\) | −8.52866 | − | 4.92402i | −0.293395 | − | 0.169392i | ||||
\(846\) | 9.83564 | + | 3.36921i | 0.338156 | + | 0.115836i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.0711034 | − | 0.277650i | −0.00244170 | − | 0.00953453i | ||||
\(849\) | −10.2870 | + | 17.8176i | −0.353048 | + | 0.611497i | ||||
\(850\) | 2.58309 | − | 0.506362i | 0.0885991 | − | 0.0173681i | ||||
\(851\) | 43.8341 | − | 25.3076i | 1.50261 | − | 0.867534i | ||||
\(852\) | −2.20705 | − | 5.41305i | −0.0756123 | − | 0.185448i | ||||
\(853\) | − | 25.3974i | − | 0.869589i | −0.900530 | − | 0.434795i | \(-0.856821\pi\) | ||
0.900530 | − | 0.434795i | \(-0.143179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 10.2025i | − | 0.348919i | ||||||
\(856\) | 2.23543 | + | 39.0882i | 0.0764055 | + | 1.33601i | ||||
\(857\) | 25.0609 | − | 14.4689i | 0.856065 | − | 0.494249i | −0.00662744 | − | 0.999978i | \(-0.502110\pi\) |
0.862693 | + | 0.505729i | \(0.168776\pi\) | |||||||
\(858\) | 1.03187 | + | 5.26385i | 0.0352276 | + | 0.179705i | ||||
\(859\) | −2.34404 | + | 4.05999i | −0.0799775 | + | 0.138525i | −0.903240 | − | 0.429136i | \(-0.858818\pi\) |
0.823263 | + | 0.567661i | \(0.192152\pi\) | |||||||
\(860\) | 24.3028 | + | 18.8633i | 0.828718 | + | 0.643235i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.6195 | − | 42.6782i | 0.497941 | − | 1.45363i | ||||
\(863\) | −37.6419 | − | 21.7325i | −1.28134 | − | 0.739784i | −0.304250 | − | 0.952592i | \(-0.598406\pi\) |
−0.977094 | + | 0.212808i | \(0.931739\pi\) | |||||||
\(864\) | −5.10769 | + | 2.43135i | −0.173767 | + | 0.0827162i | ||||
\(865\) | 5.35158 | + | 9.26921i | 0.181959 | + | 0.315163i | ||||
\(866\) | −9.12993 | − | 10.4691i | −0.310248 | − | 0.355756i | ||||
\(867\) | −13.6394 | −0.463219 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.25706 | 0.0765655 | ||||||||
\(870\) | −21.4823 | − | 24.6333i | −0.728317 | − | 0.835149i | ||||
\(871\) | −4.20791 | − | 7.28831i | −0.142580 | − | 0.246955i | ||||
\(872\) | −1.25256 | + | 2.48753i | −0.0424169 | + | 0.0842383i | ||||
\(873\) | 6.15219 | + | 3.55197i | 0.208220 | + | 0.120216i | ||||
\(874\) | 12.8465 | − | 37.5023i | 0.434538 | − | 1.26854i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.93917 | + | 12.8052i | −0.335813 | + | 0.432649i | ||||
\(877\) | 23.0063 | − | 39.8481i | 0.776868 | − | 1.34558i | −0.156870 | − | 0.987619i | \(-0.550140\pi\) |
0.933738 | − | 0.357956i | \(-0.116526\pi\) | |||||||
\(878\) | −4.63568 | − | 23.6478i | −0.156447 | − | 0.798075i | ||||
\(879\) | 24.5183 | − | 14.1556i | 0.826982 | − | 0.477458i | ||||
\(880\) | −11.9547 | − | 3.34587i | −0.402993 | − | 0.112789i | ||||
\(881\) | − | 40.8047i | − | 1.37475i | −0.726304 | − | 0.687373i | \(-0.758764\pi\) | ||
0.726304 | − | 0.687373i | \(-0.241236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.06234i | − | 0.204014i | −0.994784 | − | 0.102007i | \(-0.967474\pi\) | ||
0.994784 | − | 0.102007i | \(-0.0325264\pi\) | |||||||
\(884\) | −10.1764 | + | 4.14920i | −0.342269 | + | 0.139553i | ||||
\(885\) | −7.15140 | + | 4.12886i | −0.240392 | + | 0.138790i | ||||
\(886\) | −11.6982 | + | 2.29320i | −0.393009 | + | 0.0770415i | ||||
\(887\) | −22.1276 | + | 38.3262i | −0.742973 | + | 1.28687i | 0.208163 | + | 0.978094i | \(0.433251\pi\) |
−0.951136 | + | 0.308772i | \(0.900082\pi\) | |||||||
\(888\) | −11.6560 | − | 17.7626i | −0.391149 | − | 0.596075i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −28.1264 | − | 9.63473i | −0.942799 | − | 0.322957i | ||||
\(891\) | 1.09586 | + | 0.632697i | 0.0367128 | + | 0.0211961i | ||||
\(892\) | −3.15568 | + | 22.9836i | −0.105660 | + | 0.769549i | ||||
\(893\) | 15.2908 | + | 26.4844i | 0.511685 | + | 0.886265i | ||||
\(894\) | −0.528777 | + | 0.461136i | −0.0176849 | + | 0.0154227i | ||||
\(895\) | −60.2528 | −2.01403 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.1980 | 0.674393 | ||||||||
\(898\) | −10.2754 | + | 8.96100i | −0.342895 | + | 0.299032i | ||||
\(899\) | 44.4766 | + | 77.0358i | 1.48338 | + | 2.56929i | ||||
\(900\) | −0.276219 | + | 2.01177i | −0.00920731 | + | 0.0670591i | ||||
\(901\) | −0.113755 | − | 0.0656762i | −0.00378971 | − | 0.00218799i | ||||
\(902\) | −1.84475 | − | 0.631922i | −0.0614236 | − | 0.0210407i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.80827 | + | 11.8991i | 0.259699 | + | 0.395759i | ||||
\(905\) | 14.3702 | − | 24.8899i | 0.477681 | − | 0.827368i | ||||
\(906\) | 18.3703 | − | 3.60113i | 0.610312 | − | 0.119639i | ||||
\(907\) | −5.54526 | + | 3.20156i | −0.184127 | + | 0.106306i | −0.589230 | − | 0.807965i | \(-0.700569\pi\) |
0.405103 | + | 0.914271i | \(0.367236\pi\) | |||||||
\(908\) | 18.8181 | − | 7.67266i | 0.624500 | − | 0.254626i | ||||
\(909\) | − | 0.933313i | − | 0.0309561i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.9687i | 1.62241i | 0.584765 | + | 0.811203i | \(0.301187\pi\) | ||||
−0.584765 | + | 0.811203i | \(0.698813\pi\) | |||||||
\(912\) | −16.0237 | − | 4.48468i | −0.530596 | − | 0.148503i | ||||
\(913\) | −5.84781 | + | 3.37623i | −0.193534 | + | 0.111737i | ||||
\(914\) | 7.90190 | + | 40.3097i | 0.261372 | + | 1.33333i | ||||
\(915\) | 13.6150 | − | 23.5818i | 0.450097 | − | 0.779590i | ||||
\(916\) | −28.3240 | + | 36.4915i | −0.935850 | + | 1.20571i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.840146 | + | 2.45262i | −0.0277290 | + | 0.0809484i | ||||
\(919\) | −21.2676 | − | 12.2789i | −0.701554 | − | 0.405042i | 0.106372 | − | 0.994326i | \(-0.466077\pi\) |
−0.807926 | + | 0.589284i | \(0.799410\pi\) | |||||||
\(920\) | −21.0229 | + | 41.7506i | −0.693103 | + | 1.37648i | ||||
\(921\) | 4.32798 | + | 7.49628i | 0.142612 | + | 0.247011i | ||||
\(922\) | −22.2891 | − | 25.5585i | −0.734051 | − | 0.841724i | ||||
\(923\) | 8.76108 | 0.288374 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.62654 | −0.250759 | ||||||||
\(926\) | 26.4885 | + | 30.3739i | 0.870466 | + | 0.998149i | ||||
\(927\) | −2.06460 | − | 3.57600i | −0.0678105 | − | 0.117451i | ||||
\(928\) | −48.1310 | + | 22.9112i | −1.57998 | + | 0.752096i | ||||
\(929\) | 8.51680 | + | 4.91718i | 0.279427 | + | 0.161327i | 0.633164 | − | 0.774018i | \(-0.281756\pi\) |
−0.353737 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(930\) | 10.6106 | − | 30.9752i | 0.347934 | − | 1.01572i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.8311 | − | 8.40692i | −0.354786 | − | 0.275378i | ||||
\(933\) | −4.67129 | + | 8.09091i | −0.152931 | + | 0.264884i | ||||
\(934\) | −5.05510 | − | 25.7874i | −0.165408 | − | 0.843790i | ||||
\(935\) | −4.92712 | + | 2.84468i | −0.161134 | + | 0.0930308i | ||||
\(936\) | −0.484063 | − | 8.46422i | −0.0158221 | − | 0.276662i | ||||
\(937\) | 38.1447i | 1.24613i | 0.782168 | + | 0.623067i | \(0.214114\pi\) | ||||
−0.782168 | + | 0.623067i | \(0.785886\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.37547i | 0.240689i | ||||||||
\(940\) | −13.6150 | − | 33.3923i | −0.444071 | − | 1.08914i | ||||
\(941\) | −29.7788 | + | 17.1928i | −0.970760 | + | 0.560469i | −0.899468 | − | 0.436987i | \(-0.856046\pi\) |
−0.0712922 | + | 0.997455i | \(0.522712\pi\) | |||||||
\(942\) | 7.02446 | − | 1.37700i | 0.228869 | − | 0.0448652i | ||||
\(943\) | −3.67129 | + | 6.35886i | −0.119554 | + | 0.207073i | ||||
\(944\) | 3.34111 | + | 13.0466i | 0.108744 | + | 0.424631i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.6179 | − | 3.63716i | −0.345217 | − | 0.118254i | ||||
\(947\) | 14.2630 | + | 8.23476i | 0.463486 | + | 0.267594i | 0.713509 | − | 0.700646i | \(-0.247105\pi\) |
−0.250023 | + | 0.968240i | \(0.580438\pi\) | |||||||
\(948\) | −3.53420 | − | 0.485251i | −0.114786 | − | 0.0157602i | ||||
\(949\) | −12.1471 | − | 21.0394i | −0.394311 | − | 0.682966i | ||||
\(950\) | −4.50170 | + | 3.92585i | −0.146055 | + | 0.127371i | ||||
\(951\) | 3.63028 | 0.117720 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.4540 | −1.69915 | −0.849576 | − | 0.527466i | \(-0.823142\pi\) | ||||
−0.849576 | + | 0.527466i | \(0.823142\pi\) | |||||||
\(954\) | 0.0763704 | − | 0.0666011i | 0.00247258 | − | 0.00215629i | ||||
\(955\) | 19.4883 | + | 33.7548i | 0.630628 | + | 1.09228i | ||||
\(956\) | −44.0383 | − | 6.04652i | −1.42430 | − | 0.195558i | ||||
\(957\) | 10.3266 | + | 5.96205i | 0.333811 | + | 0.192726i | ||||
\(958\) | 37.9178 | + | 12.9888i | 1.22507 | + | 0.419648i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 17.9999 | + | 7.80929i | 0.580944 | + | 0.252044i | ||||
\(961\) | −29.0547 | + | 50.3243i | −0.937250 | + | 1.62336i | ||||
\(962\) | 31.2465 | − | 6.12524i | 1.00743 | − | 0.197486i | ||||
\(963\) | −11.9878 | + | 6.92118i | −0.386303 | + | 0.223032i | ||||
\(964\) | 11.6492 | + | 28.5711i | 0.375196 | + | 0.920213i | ||||
\(965\) | 48.3995i | 1.55803i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.3573i | 0.526016i | 0.964794 | + | 0.263008i | \(0.0847146\pi\) | ||||
−0.964794 | + | 0.263008i | \(0.915285\pi\) | |||||||
\(968\) | −26.5404 | + | 1.51783i | −0.853040 | + | 0.0487848i | ||||
\(969\) | −6.60414 | + | 3.81290i | −0.212155 | + | 0.122488i | ||||
\(970\) | −4.74000 | − | 24.1800i | −0.152192 | − | 0.776372i | ||||
\(971\) | 11.6591 | − | 20.1942i | 0.374159 | − | 0.648063i | −0.616042 | − | 0.787714i | \(-0.711265\pi\) |
0.990201 | + | 0.139651i | \(0.0445981\pi\) | |||||||
\(972\) | −1.57993 | − | 1.22631i | −0.0506762 | − | 0.0393338i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.0245 | − | 55.5377i | 0.609585 | − | 1.77954i | ||||
\(975\) | −2.63564 | − | 1.52169i | −0.0844081 | − | 0.0487331i | ||||
\(976\) | −31.0519 | − | 31.7489i | −0.993948 | − | 1.01626i | ||||
\(977\) | −19.9922 | − | 34.6275i | −0.639608 | − | 1.10783i | −0.985519 | − | 0.169566i | \(-0.945763\pi\) |
0.345911 | − | 0.938267i | \(-0.387570\pi\) | |||||||
\(978\) | −11.1872 | − | 12.8282i | −0.357728 | − | 0.410201i | ||||
\(979\) | 10.8465 | 0.346655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.984676 | −0.0314383 | ||||||||
\(982\) | 1.60551 | + | 1.84101i | 0.0512338 | + | 0.0587490i | ||||
\(983\) | −10.7628 | − | 18.6417i | −0.343279 | − | 0.594577i | 0.641761 | − | 0.766905i | \(-0.278204\pi\) |
−0.985040 | + | 0.172328i | \(0.944871\pi\) | |||||||
\(984\) | 2.75274 | + | 1.38610i | 0.0877541 | + | 0.0441873i | ||||
\(985\) | −2.12143 | − | 1.22481i | −0.0675943 | − | 0.0390256i | ||||
\(986\) | −7.91689 | + | 23.1116i | −0.252125 | + | 0.736022i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.2908 | − | 19.7000i | 0.486464 | − | 0.626741i | ||||
\(989\) | −21.1309 | + | 36.5998i | −0.671923 | + | 1.16381i | ||||
\(990\) | −0.844315 | − | 4.30707i | −0.0268341 | − | 0.136888i | ||||
\(991\) | 9.69666 | − | 5.59837i | 0.308025 | − | 0.177838i | −0.338018 | − | 0.941140i | \(-0.609756\pi\) |
0.646042 | + | 0.763302i | \(0.276423\pi\) | |||||||
\(992\) | −43.9843 | − | 30.2802i | −1.39650 | − | 0.961396i | ||||
\(993\) | − | 0.628347i | − | 0.0199400i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 6.62982i | − | 0.210179i | ||||||
\(996\) | 9.88263 | − | 4.02942i | 0.313143 | − | 0.127677i | ||||
\(997\) | 49.1699 | − | 28.3883i | 1.55723 | − | 0.899066i | 0.559707 | − | 0.828690i | \(-0.310914\pi\) |
0.997521 | − | 0.0703755i | \(-0.0224197\pi\) | |||||||
\(998\) | 58.6859 | − | 11.5042i | 1.85767 | − | 0.364159i | ||||
\(999\) | 3.75572 | − | 6.50509i | 0.118826 | − | 0.205812i |
(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 | 588.2.o.d.19.1 | 8 | ||
4.3 | odd | 2 | 588.2.o.b.19.2 | 8 | |||
7.2 | even | 3 | 588.2.b.a.391.8 | 8 | |||
7.3 | odd | 6 | 588.2.o.b.31.2 | 8 | |||
7.4 | even | 3 | 84.2.o.b.31.2 | yes | 8 | ||
7.5 | odd | 6 | 588.2.b.b.391.8 | 8 | |||
7.6 | odd | 2 | 84.2.o.a.19.1 | ✓ | 8 | ||
21.2 | odd | 6 | 1764.2.b.j.1567.1 | 8 | |||
21.5 | even | 6 | 1764.2.b.i.1567.1 | 8 | |||
21.11 | odd | 6 | 252.2.bf.f.199.3 | 8 | |||
21.20 | even | 2 | 252.2.bf.g.19.4 | 8 | |||
28.3 | even | 6 | inner | 588.2.o.d.31.1 | 8 | ||
28.11 | odd | 6 | 84.2.o.a.31.1 | yes | 8 | ||
28.19 | even | 6 | 588.2.b.a.391.7 | 8 | |||
28.23 | odd | 6 | 588.2.b.b.391.7 | 8 | |||
28.27 | even | 2 | 84.2.o.b.19.2 | yes | 8 | ||
56.11 | odd | 6 | 1344.2.bl.j.703.1 | 8 | |||
56.13 | odd | 2 | 1344.2.bl.j.1279.1 | 8 | |||
56.27 | even | 2 | 1344.2.bl.i.1279.1 | 8 | |||
56.53 | even | 6 | 1344.2.bl.i.703.1 | 8 | |||
84.11 | even | 6 | 252.2.bf.g.199.4 | 8 | |||
84.23 | even | 6 | 1764.2.b.i.1567.2 | 8 | |||
84.47 | odd | 6 | 1764.2.b.j.1567.2 | 8 | |||
84.83 | odd | 2 | 252.2.bf.f.19.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.o.a.19.1 | ✓ | 8 | 7.6 | odd | 2 | ||
84.2.o.a.31.1 | yes | 8 | 28.11 | odd | 6 | ||
84.2.o.b.19.2 | yes | 8 | 28.27 | even | 2 | ||
84.2.o.b.31.2 | yes | 8 | 7.4 | even | 3 | ||
252.2.bf.f.19.3 | 8 | 84.83 | odd | 2 | |||
252.2.bf.f.199.3 | 8 | 21.11 | odd | 6 | |||
252.2.bf.g.19.4 | 8 | 21.20 | even | 2 | |||
252.2.bf.g.199.4 | 8 | 84.11 | even | 6 | |||
588.2.b.a.391.7 | 8 | 28.19 | even | 6 | |||
588.2.b.a.391.8 | 8 | 7.2 | even | 3 | |||
588.2.b.b.391.7 | 8 | 28.23 | odd | 6 | |||
588.2.b.b.391.8 | 8 | 7.5 | odd | 6 | |||
588.2.o.b.19.2 | 8 | 4.3 | odd | 2 | |||
588.2.o.b.31.2 | 8 | 7.3 | odd | 6 | |||
588.2.o.d.19.1 | 8 | 1.1 | even | 1 | trivial | ||
588.2.o.d.31.1 | 8 | 28.3 | even | 6 | inner | ||
1344.2.bl.i.703.1 | 8 | 56.53 | even | 6 | |||
1344.2.bl.i.1279.1 | 8 | 56.27 | even | 2 | |||
1344.2.bl.j.703.1 | 8 | 56.11 | odd | 6 | |||
1344.2.bl.j.1279.1 | 8 | 56.13 | odd | 2 | |||
1764.2.b.i.1567.1 | 8 | 21.5 | even | 6 | |||
1764.2.b.i.1567.2 | 8 | 84.23 | even | 6 | |||
1764.2.b.j.1567.1 | 8 | 21.2 | odd | 6 | |||
1764.2.b.j.1567.2 | 8 | 84.47 | odd | 6 |