Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(95,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.o (of order \(8\), 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: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 95.5 | ||
Character | \(\chi\) | \(=\) | 768.95 |
Dual form | 768.2.o.b.671.5 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.988287 | − | 1.42242i | −0.570588 | − | 0.821237i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.70066 | + | 1.11865i | −1.20777 | + | 0.500275i | −0.893502 | − | 0.449059i | \(-0.851759\pi\) |
−0.314269 | + | 0.949334i | \(0.601759\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.28204 | − | 3.28204i | −1.24049 | − | 1.24049i | −0.959797 | − | 0.280697i | \(-0.909435\pi\) |
−0.280697 | − | 0.959797i | \(-0.590565\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.04658 | + | 2.81152i | −0.348860 | + | 0.937175i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.276697 | − | 0.114612i | 0.0834272 | − | 0.0345567i | −0.340580 | − | 0.940216i | \(-0.610623\pi\) |
0.424007 | + | 0.905659i | \(0.360623\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.155281 | − | 0.374881i | 0.0430671 | − | 0.103973i | −0.900882 | − | 0.434064i | \(-0.857079\pi\) |
0.943949 | + | 0.330091i | \(0.107079\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.26022 | + | 2.73593i | 1.09998 | + | 0.706415i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41723 | 0.343728 | 0.171864 | − | 0.985121i | \(-0.445021\pi\) | ||||
0.171864 | + | 0.985121i | \(0.445021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.51972 | + | 1.04370i | 0.578062 | + | 0.239441i | 0.652506 | − | 0.757784i | \(-0.273718\pi\) |
−0.0744431 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.42485 | + | 7.91204i | −0.310929 | + | 1.72655i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.30034 | + | 3.30034i | 0.688169 | + | 0.688169i | 0.961827 | − | 0.273658i | \(-0.0882337\pi\) |
−0.273658 | + | 0.961827i | \(0.588234\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50664 | − | 2.50664i | 0.501328 | − | 0.501328i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.03350 | − | 1.28991i | 0.968698 | − | 0.248244i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.650676 | + | 1.57087i | −0.120827 | + | 0.291703i | −0.972708 | − | 0.232033i | \(-0.925462\pi\) |
0.851880 | + | 0.523736i | \(0.175462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.16702i | 0.748419i | 0.927344 | + | 0.374209i | \(0.122086\pi\) | ||||
−0.927344 | + | 0.374209i | \(0.877914\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.436482 | − | 0.280311i | −0.0759817 | − | 0.0487959i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.5351 | + | 5.19221i | 2.11882 | + | 0.877644i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82757 | + | 6.82635i | 0.464849 | + | 1.12225i | 0.966383 | + | 0.257107i | \(0.0827693\pi\) |
−0.501534 | + | 0.865138i | \(0.667231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.686701 | + | 0.149615i | −0.109960 | + | 0.0239575i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.81949 | + | 3.81949i | −0.596504 | + | 0.596504i | −0.939380 | − | 0.342877i | \(-0.888599\pi\) |
0.342877 | + | 0.939380i | \(0.388599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.07136 | − | 5.00071i | −0.315880 | − | 0.762602i | −0.999464 | − | 0.0327301i | \(-0.989580\pi\) |
0.683584 | − | 0.729872i | \(-0.260420\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.318658 | − | 8.76372i | −0.0475028 | − | 1.30642i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.44085i | − | 0.793629i | −0.917899 | − | 0.396815i | \(-0.870116\pi\) | ||
0.917899 | − | 0.396815i | \(-0.129884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.5435i | 2.07765i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.40063 | − | 2.01590i | −0.196127 | − | 0.282282i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.85159 | − | 4.47012i | −0.254335 | − | 0.614019i | 0.744210 | − | 0.667946i | \(-0.232826\pi\) |
−0.998545 | + | 0.0539269i | \(0.982826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.619053 | + | 0.619053i | −0.0834731 | + | 0.0834731i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00562 | − | 4.61558i | −0.133197 | − | 0.611348i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.37699 | − | 3.32434i | −0.179268 | − | 0.432792i | 0.808545 | − | 0.588434i | \(-0.200255\pi\) |
−0.987814 | + | 0.155642i | \(0.950255\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9629 | + | 4.54098i | 1.40366 | + | 0.581413i | 0.950698 | − | 0.310119i | \(-0.100369\pi\) |
0.452958 | + | 0.891532i | \(0.350369\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.6624 | − | 5.79262i | 1.59532 | − | 0.729801i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.18613i | 0.147121i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.19888 | + | 10.1370i | −0.512974 | + | 1.23843i | 0.429170 | + | 0.903224i | \(0.358806\pi\) |
−0.942145 | + | 0.335206i | \(0.891194\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.43280 | − | 7.95617i | 0.172489 | − | 0.957810i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.77857 | + | 3.77857i | −0.448434 | + | 0.448434i | −0.894834 | − | 0.446400i | \(-0.852706\pi\) |
0.446400 | + | 0.894834i | \(0.352706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.89137 | − | 3.89137i | −0.455450 | − | 0.455450i | 0.441708 | − | 0.897159i | \(-0.354373\pi\) |
−0.897159 | + | 0.441708i | \(0.854373\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.04279 | − | 1.08823i | −0.697761 | − | 0.125657i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.28429 | − | 0.531970i | −0.146358 | − | 0.0606236i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.81995 | 0.542287 | 0.271143 | − | 0.962539i | \(-0.412598\pi\) | ||||
0.271143 | + | 0.962539i | \(0.412598\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.80935 | − | 5.88497i | −0.756594 | − | 0.653885i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.60399 | + | 8.70081i | −0.395590 | + | 0.955038i | 0.593109 | + | 0.805122i | \(0.297900\pi\) |
−0.988699 | + | 0.149916i | \(0.952100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.82744 | + | 1.58538i | −0.415145 | + | 0.171959i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.87750 | − | 0.626933i | 0.308500 | − | 0.0672143i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.69926 | + | 3.69926i | 0.392121 | + | 0.392121i | 0.875443 | − | 0.483322i | \(-0.160570\pi\) |
−0.483322 | + | 0.875443i | \(0.660570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.74001 | + | 0.720735i | −0.182402 | + | 0.0755536i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.92727 | − | 4.11821i | 0.614629 | − | 0.427039i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.97242 | −0.817953 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9958 | 1.11646 | 0.558229 | − | 0.829687i | \(-0.311481\pi\) | ||||
0.558229 | + | 0.829687i | \(0.311481\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0326483 | + | 0.897890i | 0.00328127 | + | 0.0902413i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.51499 | + | 1.04174i | −0.250251 | + | 0.103657i | −0.504283 | − | 0.863538i | \(-0.668243\pi\) |
0.254032 | + | 0.967196i | \(0.418243\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.332885 | − | 0.332885i | −0.0328001 | − | 0.0328001i | 0.690517 | − | 0.723317i | \(-0.257383\pi\) |
−0.723317 | + | 0.690517i | \(0.757383\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.00275 | − | 22.9616i | −0.488219 | − | 2.24082i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.394269 | − | 0.163312i | 0.0381154 | − | 0.0157879i | −0.363544 | − | 0.931577i | \(-0.618433\pi\) |
0.401660 | + | 0.915789i | \(0.368433\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.81782 | + | 4.38860i | −0.174115 | + | 0.420352i | −0.986713 | − | 0.162474i | \(-0.948053\pi\) |
0.812598 | + | 0.582825i | \(0.198053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.91552 | − | 10.7684i | 0.656392 | − | 1.02209i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.5323 | 1.74337 | 0.871687 | − | 0.490063i | \(-0.163026\pi\) | ||||
0.871687 | + | 0.490063i | \(0.163026\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6050 | − | 5.22117i | −1.17542 | − | 0.486876i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.891473 | + | 0.828917i | 0.0824167 | + | 0.0766334i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.65139 | − | 4.65139i | −0.426392 | − | 0.426392i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.71475 | + | 7.71475i | −0.701341 | + | 0.701341i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.20768 | + | 1.65818i | 0.830229 | + | 0.149513i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.62772 | − | 3.92966i | 0.145587 | − | 0.351479i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.80013i | 0.425943i | 0.977058 | + | 0.212971i | \(0.0683141\pi\) | ||||
−0.977058 | + | 0.212971i | \(0.931686\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.06603 | + | 7.88850i | −0.446039 | + | 0.694543i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.2118 | − | 8.37202i | −1.76592 | − | 0.731467i | −0.995589 | − | 0.0938185i | \(-0.970093\pi\) |
−0.770328 | − | 0.637648i | \(-0.779907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.84434 | − | 11.6953i | −0.420057 | − | 1.01411i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.1508 | + | 9.11434i | −1.04577 | + | 0.784437i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.7302 | + | 12.7302i | −1.08762 | + | 1.08762i | −0.0918436 | + | 0.995773i | \(0.529276\pi\) |
−0.995773 | + | 0.0918436i | \(0.970724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.193431 | − | 0.466984i | −0.0164066 | − | 0.0396091i | 0.915464 | − | 0.402400i | \(-0.131824\pi\) |
−0.931871 | + | 0.362791i | \(0.881824\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.73919 | + | 5.37712i | −0.651758 | + | 0.452835i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.121525i | − | 0.0101624i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.97026i | − | 0.412758i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.6871 | − | 14.3732i | 1.70624 | − | 1.18548i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.31949 | + | 10.4282i | 0.353866 | + | 0.854308i | 0.996136 | + | 0.0878294i | \(0.0279930\pi\) |
−0.642269 | + | 0.766479i | \(0.722007\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.7687 | + | 13.7687i | −1.12048 | + | 1.12048i | −0.128814 | + | 0.991669i | \(0.541117\pi\) |
−0.991669 | + | 0.128814i | \(0.958883\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.48324 | + | 3.98457i | −0.119913 | + | 0.322133i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.66143 | − | 11.2537i | −0.374415 | − | 0.903918i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.94660 | − | 3.29159i | −0.634208 | − | 0.262697i | 0.0423321 | − | 0.999104i | \(-0.486521\pi\) |
−0.676540 | + | 0.736406i | \(0.736521\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.52851 | + | 7.05151i | −0.359135 | + | 0.559221i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 21.6637i | − | 1.70734i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.77631 | + | 11.5310i | −0.374110 | + | 0.903181i | 0.618935 | + | 0.785442i | \(0.287565\pi\) |
−0.993045 | + | 0.117739i | \(0.962435\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.49236 | + | 0.268754i | 0.116180 | + | 0.0209225i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.7585 | − | 14.7585i | 1.14205 | − | 1.14205i | 0.153970 | − | 0.988076i | \(-0.450794\pi\) |
0.988076 | − | 0.153970i | \(-0.0492059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.07596 | + | 9.07596i | 0.698151 | + | 0.698151i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.57147 | + | 5.99193i | −0.426061 | + | 0.458214i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.60827 | + | 3.15145i | 0.578446 | + | 0.239600i | 0.652671 | − | 0.757641i | \(-0.273648\pi\) |
−0.0742253 | + | 0.997241i | \(0.523648\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.4538 | −1.24379 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.36776 | + | 5.24406i | −0.253136 | + | 0.394167i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.38731 | + | 3.34926i | −0.103692 | + | 0.250335i | −0.967208 | − | 0.253987i | \(-0.918258\pi\) |
0.863515 | + | 0.504323i | \(0.168258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.51464 | + | 2.69845i | −0.484229 | + | 0.200574i | −0.611424 | − | 0.791303i | \(-0.709403\pi\) |
0.127194 | + | 0.991878i | \(0.459403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.37529 | − | 20.0817i | −0.323431 | − | 1.48448i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.2726 | − | 15.2726i | −1.12286 | − | 1.12286i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.392142 | − | 0.162431i | 0.0286763 | − | 0.0118781i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −20.7537 | − | 12.2866i | −1.50961 | − | 0.893718i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8097 | −1.36102 | −0.680511 | − | 0.732737i | \(-0.738242\pi\) | ||||
−0.680511 | + | 0.732737i | \(0.738242\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1498 | −0.802582 | −0.401291 | − | 0.915951i | \(-0.631438\pi\) | ||||
−0.401291 | + | 0.915951i | \(0.631438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.68718 | − | 1.17224i | 0.120821 | − | 0.0839455i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7643 | − | 6.11558i | 1.05191 | − | 0.435717i | 0.211340 | − | 0.977413i | \(-0.432217\pi\) |
0.840575 | + | 0.541696i | \(0.182217\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.686194 | + | 0.686194i | 0.0486430 | + | 0.0486430i | 0.731010 | − | 0.682367i | \(-0.239049\pi\) |
−0.682367 | + | 0.731010i | \(0.739049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.5688 | − | 4.04566i | 1.30974 | − | 0.285359i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.29119 | − | 3.02011i | 0.511742 | − | 0.211970i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.04246 | − | 14.5878i | 0.422024 | − | 1.01886i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.7331 | + | 5.82492i | −0.885009 | + | 0.404860i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.816817 | 0.0565004 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.25868 | − | 0.935575i | −0.155494 | − | 0.0644076i | 0.303579 | − | 0.952806i | \(-0.401818\pi\) |
−0.459073 | + | 0.888399i | \(0.651818\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.10904 | + | 1.64042i | 0.624141 | + | 0.112400i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.1881 | + | 11.1881i | 0.763021 | + | 0.763021i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.6763 | − | 13.6763i | 0.928409 | − | 0.928409i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.68939 | + | 9.38096i | −0.114158 | + | 0.633907i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.220068 | − | 0.531291i | 0.0148034 | − | 0.0357385i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.3472i | − | 0.692900i | −0.938068 | − | 0.346450i | \(-0.887387\pi\) | ||
0.938068 | − | 0.346450i | \(-0.112613\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.42409 | + | 9.67088i | 0.294939 | + | 0.644725i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.4804 | + | 4.34114i | 0.695611 | + | 0.288131i | 0.702336 | − | 0.711846i | \(-0.252141\pi\) |
−0.00672494 | + | 0.999977i | \(0.502141\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.39471 | + | 17.8524i | 0.488656 | + | 1.17972i | 0.955396 | + | 0.295326i | \(0.0954284\pi\) |
−0.466740 | + | 0.884395i | \(0.654572\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.512559 | + | 2.35254i | 0.0337239 | + | 0.154786i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9703 | − | 15.9703i | 1.04625 | − | 1.04625i | 0.0473714 | − | 0.998877i | \(-0.484916\pi\) |
0.998877 | − | 0.0473714i | \(-0.0150844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.08640 | + | 14.6939i | 0.397033 | + | 0.958522i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.76349 | − | 6.85601i | −0.309422 | − | 0.445346i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.5155i | 1.45641i | 0.685361 | + | 0.728204i | \(0.259645\pi\) | ||||
−0.685361 | + | 0.728204i | \(0.740355\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 21.7886i | − | 1.40353i | −0.712409 | − | 0.701765i | \(-0.752396\pi\) | ||
0.712409 | − | 0.701765i | \(-0.247604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.64133 | + | 15.5018i | −0.105291 | + | 0.994441i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.2691 | − | 39.2771i | −1.03939 | − | 2.50932i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.782526 | − | 0.782526i | 0.0497909 | − | 0.0497909i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.9380 | − | 3.47249i | 1.01003 | − | 0.220060i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.96821 | − | 14.4085i | −0.376710 | − | 0.909458i | −0.992578 | − | 0.121609i | \(-0.961195\pi\) |
0.615868 | − | 0.787849i | \(-0.288805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.29145 | + | 0.534937i | 0.0811928 | + | 0.0336312i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.03769 | + | 3.87744i | 0.378095 | + | 0.242815i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.8781i | − | 0.740934i | −0.928846 | − | 0.370467i | \(-0.879198\pi\) | ||
0.928846 | − | 0.370467i | \(-0.120802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.1242 | − | 31.6845i | 0.815495 | − | 1.96878i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.73556 | − | 3.47343i | −0.231225 | − | 0.215000i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.29543 | − | 3.29543i | 0.203205 | − | 0.203205i | −0.598167 | − | 0.801372i | \(-0.704104\pi\) |
0.801372 | + | 0.598167i | \(0.204104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0010 | + | 10.0010i | 0.614357 | + | 0.614357i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.60599 | − | 8.91786i | 0.0982849 | − | 0.545764i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.9975 | + | 11.1827i | 1.64607 | + | 0.681824i | 0.996890 | − | 0.0788107i | \(-0.0251123\pi\) |
0.649180 | + | 0.760635i | \(0.275112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.49827 | 0.212505 | 0.106252 | − | 0.994339i | \(-0.466115\pi\) | ||||
0.106252 | + | 0.994339i | \(0.466115\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.74482 | + | 1.76274i | 0.166124 | + | 0.106686i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.406289 | − | 0.980869i | 0.0245002 | − | 0.0591486i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1905 | − | 4.22105i | 0.612289 | − | 0.253619i | −0.0549177 | − | 0.998491i | \(-0.517490\pi\) |
0.667207 | + | 0.744872i | \(0.267490\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.7157 | − | 4.36112i | −0.701399 | − | 0.261093i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1081 | + | 14.1081i | 0.841616 | + | 0.841616i | 0.989069 | − | 0.147453i | \(-0.0471074\pi\) |
−0.147453 | + | 0.989069i | \(0.547107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.2200 | + | 7.13275i | −1.02362 | + | 0.423998i | −0.830406 | − | 0.557159i | \(-0.811892\pi\) |
−0.193215 | + | 0.981156i | \(0.561892\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.87904 | + | 11.3402i | 0.466714 | + | 0.671733i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.0714 | 1.47992 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9915 | −0.881851 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.8670 | − | 15.6407i | −0.637037 | − | 0.916877i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.6538 | + | 8.96928i | −1.26503 | + | 0.523991i | −0.911448 | − | 0.411414i | \(-0.865035\pi\) |
−0.353577 | + | 0.935405i | \(0.615035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.43753 | + | 7.43753i | 0.433030 | + | 0.433030i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.24491 | − | 0.933812i | 0.0722372 | − | 0.0541853i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.74971 | − | 0.724755i | 0.101189 | − | 0.0419137i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.61423 | + | 23.2108i | −0.554155 | + | 1.33785i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.96733 | + | 2.54784i | 0.227917 | + | 0.146370i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −34.6868 | −1.98616 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.7154 | + | 8.16639i | 1.12522 | + | 0.466081i | 0.866153 | − | 0.499779i | \(-0.166585\pi\) |
0.259065 | + | 0.965860i | \(0.416585\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.144518 | + | 0.802489i | −0.00822132 | + | 0.0456520i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5699 | + | 10.5699i | 0.599365 | + | 0.599365i | 0.940144 | − | 0.340779i | \(-0.110691\pi\) |
−0.340779 | + | 0.940144i | \(0.610691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.0589 | + | 24.0589i | −1.35989 | + | 1.35989i | −0.485846 | + | 0.874044i | \(0.661489\pi\) |
−0.874044 | + | 0.485846i | \(0.838511\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −27.7170 | + | 29.8087i | −1.56168 | + | 1.67953i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.93517 | + | 21.5714i | −0.501849 | + | 1.21157i | 0.446626 | + | 0.894721i | \(0.352625\pi\) |
−0.948475 | + | 0.316851i | \(0.897375\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.509230i | 0.0285114i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.621949 | − | 0.399419i | −0.0347138 | − | 0.0222934i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.57101 | + | 1.47916i | 0.198696 | + | 0.0823027i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.550458 | − | 1.32892i | −0.0305339 | − | 0.0737154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.03897 | − | 1.75149i | 0.444556 | − | 0.0968575i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.8571 | + | 17.8571i | −0.984492 | + | 0.984492i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6785 | + | 25.7802i | 0.586943 | + | 1.41701i | 0.886411 | + | 0.462900i | \(0.153191\pi\) |
−0.299467 | + | 0.954107i | \(0.596809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.1517 | + | 0.805461i | −1.21391 | + | 0.0441390i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 32.0736i | − | 1.75237i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.72298i | 0.420698i | 0.977626 | + | 0.210349i | \(0.0674600\pi\) | ||||
−0.977626 | + | 0.210349i | \(0.932540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.3152 | − | 26.3608i | −0.994747 | − | 1.43172i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.477589 | + | 1.15300i | 0.0258629 | + | 0.0624385i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.7581 | − | 24.7581i | 1.33681 | − | 1.33681i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.03065 | + | 23.0897i | 0.270841 | + | 1.24311i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.88801 | + | 6.97227i | 0.155037 | + | 0.374291i | 0.982245 | − | 0.187604i | \(-0.0600723\pi\) |
−0.827208 | + | 0.561896i | \(0.810072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.70439 | − | 1.53441i | −0.198292 | − | 0.0821351i | 0.281328 | − | 0.959612i | \(-0.409225\pi\) |
−0.479619 | + | 0.877477i | \(0.659225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.298041 | − | 2.08726i | 0.0159083 | − | 0.111410i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.0427i | 1.75869i | 0.476189 | + | 0.879343i | \(0.342018\pi\) | ||||
−0.476189 | + | 0.879343i | \(0.657982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.97773 | − | 14.4315i | 0.317265 | − | 0.765945i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.01934 | + | 11.2132i | −0.106875 | + | 0.593463i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.02805 | − | 1.02805i | 0.0542584 | − | 0.0542584i | −0.679457 | − | 0.733715i | \(-0.737785\pi\) |
0.733715 | + | 0.679457i | \(0.237785\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.17537 | − | 8.17537i | −0.430283 | − | 0.430283i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.5980 | + | 3.34926i | 0.976143 | + | 0.175791i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.8623 | + | 6.15618i | 0.777930 | + | 0.322229i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6801 | 0.609694 | 0.304847 | − | 0.952401i | \(-0.401395\pi\) | ||||
0.304847 | + | 0.952401i | \(0.401395\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.74119 | − | 14.7360i | −0.350932 | − | 0.767125i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.59414 | + | 20.7481i | −0.446185 | + | 1.07719i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.6155 | − | 4.81129i | 0.601427 | − | 0.249119i | −0.0611312 | − | 0.998130i | \(-0.519471\pi\) |
0.662558 | + | 0.749011i | \(0.269471\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.19829 | + | 1.56832i | −0.371718 | + | 0.0809879i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.487851 | + | 0.487851i | 0.0251256 | + | 0.0251256i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.2623 | − | 6.32186i | 0.783972 | − | 0.324732i | 0.0454550 | − | 0.998966i | \(-0.485526\pi\) |
0.738517 | + | 0.674234i | \(0.235526\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.82782 | − | 4.74390i | 0.349800 | − | 0.243038i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.9536 | −1.47946 | −0.739729 | − | 0.672905i | \(-0.765046\pi\) | ||||
−0.739729 | + | 0.672905i | \(0.765046\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.06351 | 0.207096 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.2275 | − | 0.590049i | 0.824889 | − | 0.0299939i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.31149 | − | 2.61431i | 0.320005 | − | 0.132551i | −0.216898 | − | 0.976194i | \(-0.569594\pi\) |
0.536903 | + | 0.843644i | \(0.319594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.67733 | + | 4.67733i | 0.236543 | + | 0.236543i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.06654 | + | 37.0238i | 0.406903 | + | 1.86760i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0170 | + | 5.39183i | −0.654958 | + | 0.271293i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.66407 | − | 4.01741i | 0.0835171 | − | 0.201628i | −0.876604 | − | 0.481212i | \(-0.840197\pi\) |
0.960121 | + | 0.279584i | \(0.0901966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.8480 | + | 18.4490i | −0.593143 | + | 0.923604i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.93840 | 0.196674 | 0.0983371 | − | 0.995153i | \(-0.468648\pi\) | ||||
0.0983371 | + | 0.995153i | \(0.468648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.56214 | + | 0.647058i | 0.0778155 | + | 0.0322322i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.9729 | + | 8.27601i | 1.24091 | + | 0.411238i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.56476 | + | 1.56476i | 0.0775621 | + | 0.0775621i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.8960 | − | 12.8960i | 0.637664 | − | 0.637664i | −0.312314 | − | 0.949979i | \(-0.601104\pi\) |
0.949979 | + | 0.312314i | \(0.101104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.6889 | + | 5.52667i | 1.51377 | + | 0.272610i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.39128 | + | 15.4299i | −0.314494 | + | 0.759256i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 27.5295i | − | 1.35137i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.473084 | + | 0.736656i | −0.0231670 | + | 0.0360742i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.81232 | − | 2.40754i | −0.283951 | − | 0.117616i | 0.236163 | − | 0.971714i | \(-0.424110\pi\) |
−0.520113 | + | 0.854097i | \(0.674110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.88620 | − | 19.0390i | −0.384350 | − | 0.927903i | −0.991113 | − | 0.133020i | \(-0.957532\pi\) |
0.606763 | − | 0.794883i | \(-0.292468\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.2971 | + | 5.69428i | 0.743770 | + | 0.276865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.55248 | − | 3.55248i | 0.172321 | − | 0.172321i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.0770 | − | 50.8843i | −1.01999 | − | 2.46246i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.172860 | + | 0.120102i | −0.00834578 | + | 0.00579857i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.6809i | 1.62235i | 0.584801 | + | 0.811177i | \(0.301173\pi\) | ||||
−0.584801 | + | 0.811177i | \(0.698827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.3471i | − | 0.977819i | −0.872335 | − | 0.488909i | \(-0.837395\pi\) | ||
0.872335 | − | 0.488909i | \(-0.162605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.06982 | + | 4.91204i | −0.338972 | + | 0.235514i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.87135 | + | 11.7605i | 0.233028 | + | 0.562580i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.4753 | − | 12.4753i | 0.595414 | − | 0.595414i | −0.343675 | − | 0.939089i | \(-0.611672\pi\) |
0.939089 | + | 0.343675i | \(0.111672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −40.8895 | − | 15.2209i | −1.94712 | − | 0.724807i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7190 | + | 25.8778i | 0.509273 | + | 1.22949i | 0.944303 | + | 0.329077i | \(0.106738\pi\) |
−0.435030 | + | 0.900416i | \(0.643262\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1286 | − | 5.85227i | −0.669761 | − | 0.277424i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5644 | − | 16.4502i | 0.499678 | − | 0.778066i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.2439i | 0.766596i | 0.923625 | + | 0.383298i | \(0.125212\pi\) | ||||
−0.923625 | + | 0.383298i | \(0.874788\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.619083 | + | 1.49460i | −0.0291515 | + | 0.0703779i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.1924 | + | 5.97751i | 1.55952 | + | 0.280848i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.89292 | − | 3.89292i | 0.182503 | − | 0.182503i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.84177 | − | 2.84177i | −0.132932 | − | 0.132932i | 0.637510 | − | 0.770442i | \(-0.279965\pi\) |
−0.770442 | + | 0.637510i | \(0.779965\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.13361 | − | 1.82810i | 0.332968 | − | 0.0853284i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.8642 | − | 8.64224i | −0.971743 | − | 0.402509i | −0.160382 | − | 0.987055i | \(-0.551273\pi\) |
−0.811361 | + | 0.584546i | \(0.801273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.3599 | −1.03915 | −0.519576 | − | 0.854424i | \(-0.673910\pi\) | ||||
−0.519576 | + | 0.854424i | \(0.673910\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.4007 | + | 17.7524i | −0.528694 | + | 0.823248i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.58346 | − | 8.65124i | 0.165823 | − | 0.400332i | −0.819024 | − | 0.573760i | \(-0.805484\pi\) |
0.984847 | + | 0.173428i | \(0.0554844\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 47.0508 | − | 19.4891i | 2.17260 | − | 0.899922i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.17148 | + | 14.5565i | 0.146134 | + | 0.670726i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.14628 | − | 1.14628i | −0.0527060 | − | 0.0527060i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.93220 | − | 3.69984i | 0.409838 | − | 0.169760i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.5057 | − | 0.527443i | 0.664170 | − | 0.0241500i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.51545 | 0.0692426 | 0.0346213 | − | 0.999401i | \(-0.488977\pi\) | ||||
0.0346213 | + | 0.999401i | \(0.488977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.99813 | 0.136703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.8149 | + | 21.4099i | −1.40213 | + | 0.974185i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.6960 | + | 12.3005i | −1.34843 | + | 0.558536i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.7114 | + | 10.7114i | 0.485378 | + | 0.485378i | 0.906844 | − | 0.421466i | \(-0.138484\pi\) |
−0.421466 | + | 0.906844i | \(0.638484\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.1224 | − | 4.60203i | 0.955188 | − | 0.208111i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2550 | − | 8.38989i | 0.914095 | − | 0.378630i | 0.124472 | − | 0.992223i | \(-0.460276\pi\) |
0.789623 | + | 0.613593i | \(0.210276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.922155 | + | 2.22628i | −0.0415318 | + | 0.100267i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.09260 | − | 2.38837i | −0.0491085 | − | 0.107349i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.8028 | 1.11256 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.2527 | − | 4.24681i | −0.458974 | − | 0.190113i | 0.141203 | − | 0.989981i | \(-0.454903\pi\) |
−0.600177 | + | 0.799867i | \(0.704903\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.5784 | − | 6.40720i | −1.58953 | − | 0.286253i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.9291 | − | 14.9291i | −0.665655 | − | 0.665655i | 0.291052 | − | 0.956707i | \(-0.405995\pi\) |
−0.956707 | + | 0.291052i | \(0.905995\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.62678 | − | 5.62678i | 0.250389 | − | 0.250389i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.94021 | − | 21.8795i | 0.174991 | − | 0.971704i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.540947 | − | 1.30596i | 0.0239770 | − | 0.0578857i | −0.911438 | − | 0.411438i | \(-0.865027\pi\) |
0.935415 | + | 0.353553i | \(0.115027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.5432i | 1.12997i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.0293 | + | 2.00325i | 0.619407 | + | 0.0884456i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.27139 | + | 0.526627i | 0.0560241 | + | 0.0232059i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.623584 | − | 1.50547i | −0.0274252 | − | 0.0662103i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.03645 | − | 13.9367i | −0.133286 | − | 0.611754i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.02013 | − | 4.02013i | 0.176125 | − | 0.176125i | −0.613539 | − | 0.789664i | \(-0.710255\pi\) |
0.789664 | + | 0.613539i | \(0.210255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.35502 | − | 5.68552i | −0.102978 | − | 0.248610i | 0.863990 | − | 0.503509i | \(-0.167958\pi\) |
−0.966968 | + | 0.254899i | \(0.917958\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.2610 | + | 23.4042i | 0.709690 | + | 1.02144i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.90561i | 0.257253i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.21549i | − | 0.0528475i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.7876 | − | 0.392248i | 0.468141 | − | 0.0170221i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.838760 | + | 2.02495i | 0.0363307 | + | 0.0877101i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.882097 | + | 0.882097i | −0.0381364 | + | 0.0381364i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.13513 | − | 1.33669i | 0.264750 | − | 0.0576823i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.66686 | + | 4.02415i | 0.0717966 | + | 0.173332i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.0891 | − | 11.2207i | −1.16465 | − | 0.482414i | −0.285230 | − | 0.958459i | \(-0.592070\pi\) |
−0.879421 | + | 0.476045i | \(0.842070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.2767 | + | 6.59973i | 0.441014 | + | 0.283222i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 13.8856i | − | 0.594794i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.18960 | + | 5.28616i | −0.0936205 | + | 0.226020i | −0.963752 | − | 0.266800i | \(-0.914034\pi\) |
0.870132 | + | 0.492820i | \(0.164034\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.2406 | + | 26.0700i | −1.03456 | + | 1.11264i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.27904 | + | 3.27904i | −0.139692 | + | 0.139692i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.8193 | − | 15.8193i | −0.672703 | − | 0.672703i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.63039 | + | 36.8178i | −0.281445 | + | 1.56283i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.6235 | − | 13.9273i | −1.42467 | − | 0.590119i | −0.468644 | − | 0.883387i | \(-0.655257\pi\) |
−0.956030 | + | 0.293268i | \(0.905257\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.19631 | −0.0928941 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.618594 | − | 0.397264i | −0.0261171 | − | 0.0167725i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.2970 | − | 24.8591i | 0.433965 | − | 1.04768i | −0.544031 | − | 0.839065i | \(-0.683103\pi\) |
0.977997 | − | 0.208620i | \(-0.0668972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50.0494 | + | 20.7312i | −2.10560 | + | 0.872166i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.03385 | + | 41.6632i | 0.127410 | + | 1.74969i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.01618 | − | 5.01618i | −0.210289 | − | 0.210289i | 0.594101 | − | 0.804390i | \(-0.297508\pi\) |
−0.804390 | + | 0.594101i | \(0.797508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.20928 | − | 3.40040i | 0.343548 | − | 0.142302i | −0.204237 | − | 0.978921i | \(-0.565471\pi\) |
0.547785 | + | 0.836619i | \(0.315471\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.5894 | + | 26.7554i | 0.776583 | + | 1.11772i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.5455 | 0.689997 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.7704 | 1.53077 | 0.765386 | − | 0.643571i | \(-0.222548\pi\) | ||||
0.765386 | + | 0.643571i | \(0.222548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.0192 | + | 15.8598i | 0.457943 | + | 0.659109i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.3848 | − | 16.7279i | 1.67544 | − | 0.693992i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.02466 | − | 1.02466i | −0.0424369 | − | 0.0424369i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.33483 | − | 1.24138i | −0.137878 | − | 0.0513246i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.3129 | − | 9.24233i | 0.920954 | − | 0.381472i | 0.128714 | − | 0.991682i | \(-0.458915\pi\) |
0.792240 | + | 0.610210i | \(0.208915\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.34912 | + | 10.4997i | −0.179202 | + | 0.432633i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.2903 | − | 14.9572i | −0.958036 | − | 0.615256i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.15691 | 0.0885737 | 0.0442868 | − | 0.999019i | \(-0.485898\pi\) | ||||
0.0442868 | + | 0.999019i | \(0.485898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.7651 | + | 7.35854i | 0.728297 | + | 0.301671i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.297902 | − | 1.65421i | 0.0121923 | − | 0.0677025i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.80949 | − | 4.80949i | −0.196511 | − | 0.196511i | 0.601992 | − | 0.798502i | \(-0.294374\pi\) |
−0.798502 | + | 0.601992i | \(0.794374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.18282 | − | 5.18282i | 0.211411 | − | 0.211411i | −0.593455 | − | 0.804867i | \(-0.702237\pi\) |
0.804867 | + | 0.593455i | \(0.202237\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.1059 | − | 22.4144i | −0.981669 | − | 0.912785i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.2048 | − | 29.4650i | 0.496196 | − | 1.19792i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.19779i | − | 0.210972i | −0.994421 | − | 0.105486i | \(-0.966360\pi\) | ||
0.994421 | − | 0.105486i | \(-0.0336398\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.5017 | − | 7.38643i | −0.466071 | − | 0.299313i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.03967 | − | 0.844859i | −0.0825162 | − | 0.0341793i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.1586 | − | 29.3536i | −0.491083 | − | 1.18558i | −0.954170 | − | 0.299266i | \(-0.903258\pi\) |
0.463087 | − | 0.886313i | \(-0.346742\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −26.7217 | + | 5.82198i | −1.07752 | + | 0.234765i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.7968 | − | 10.7968i | 0.434663 | − | 0.434663i | −0.455548 | − | 0.890211i | \(-0.650557\pi\) |
0.890211 | + | 0.455548i | \(0.150557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7667 | + | 28.4074i | 0.472944 | + | 1.14179i | 0.962856 | + | 0.270016i | \(0.0870290\pi\) |
−0.489912 | + | 0.871772i | \(0.662971\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.8694 | + | 12.3551i | 0.837461 | + | 0.495794i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 24.2822i | − | 0.972848i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.1581i | 1.20633i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.807250 | − | 1.16186i | −0.0322384 | − | 0.0464002i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.00730 | + | 9.67449i | 0.159782 | + | 0.385747i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.17311 | + | 5.17311i | −0.205938 | + | 0.205938i | −0.802539 | − | 0.596600i | \(-0.796518\pi\) |
0.596600 | + | 0.802539i | \(0.296518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.901437 | + | 4.13741i | 0.0358289 | + | 0.164447i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.36966 | − | 12.9635i | −0.213088 | − | 0.514441i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.45209 | + | 2.25833i | 0.216020 | + | 0.0894782i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.66897 | − | 14.5781i | −0.263820 | − | 0.576701i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 35.5298i | − | 1.40334i | −0.712500 | − | 0.701672i | \(-0.752437\pi\) | ||
0.712500 | − | 0.701672i | \(-0.247563\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.04889 | + | 7.36067i | −0.120237 | + | 0.290277i | −0.972526 | − | 0.232793i | \(-0.925213\pi\) |
0.852290 | + | 0.523070i | \(0.175213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.85716 | − | 26.9712i | 0.191251 | − | 1.06199i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.34579 | + | 9.34579i | −0.367421 | + | 0.367421i | −0.866536 | − | 0.499115i | \(-0.833659\pi\) |
0.499115 | + | 0.866536i | \(0.333659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.762015 | − | 0.762015i | −0.0299117 | − | 0.0299117i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.9696 | − | 5.93739i | −1.29218 | − | 0.232705i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.13779 | − | 1.29972i | −0.122791 | − | 0.0508618i | 0.320442 | − | 0.947268i | \(-0.396169\pi\) |
−0.443233 | + | 0.896406i | \(0.646169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 63.9506 | 2.49876 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.0133 | − | 6.86805i | 0.585725 | − | 0.267948i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0747 | + | 29.1508i | −0.470362 | + | 1.13555i | 0.493642 | + | 0.869665i | \(0.335665\pi\) |
−0.964004 | + | 0.265889i | \(0.914335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.5134 | + | 8.91114i | −0.836774 | + | 0.346603i | −0.759581 | − | 0.650413i | \(-0.774596\pi\) |
−0.0771932 | + | 0.997016i | \(0.524596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.973211 | + | 0.212038i | −0.0377964 | + | 0.00823487i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.1658 | + | 26.1658i | 1.01467 | + | 1.01467i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.33186 | + | 3.03696i | −0.283891 | + | 0.117591i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.7181 | + | 10.2260i | −0.569035 | + | 0.395360i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.55385 | 0.137195 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.9251 | −1.07643 | −0.538216 | − | 0.842807i | \(-0.680902\pi\) | ||||
−0.538216 | + | 0.842807i | \(0.680902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.38383 | − | 15.8505i | 0.361184 | − | 0.610087i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.25960 | − | 2.59281i | 0.240576 | − | 0.0996498i | −0.259138 | − | 0.965840i | \(-0.583438\pi\) |
0.499714 | + | 0.866191i | \(0.333438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.0887 | − | 36.0887i | −1.38496 | − | 1.38496i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.18273 | − | 19.1979i | −0.160283 | − | 0.735665i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2767 | + | 10.8842i | −1.00545 | + | 0.416471i | −0.823793 | − | 0.566891i | \(-0.808146\pi\) |
−0.181657 | + | 0.983362i | \(0.558146\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.1393 | − | 48.6207i | 0.769484 | − | 1.85770i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.0856 | − | 28.1617i | 0.690009 | − | 1.07444i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.96328 | −0.0747950 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.2910 | + | 10.8901i | 1.00016 | + | 0.414279i | 0.821855 | − | 0.569697i | \(-0.192939\pi\) |
0.178303 | + | 0.983976i | \(0.442939\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.83975 | − | 3.05406i | 0.107873 | − | 0.116014i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.04478 | + | 1.04478i | 0.0396309 | + | 0.0396309i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.41308 | + | 5.41308i | −0.205035 | + | 0.205035i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −38.4998 | − | 6.93330i | −1.45619 | − | 0.262241i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.7331 | − | 37.9830i | 0.594230 | − | 1.43460i | −0.285153 | − | 0.958482i | \(-0.592044\pi\) |
0.879383 | − | 0.476116i | \(-0.157956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.1516i | 0.760032i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.8858 | − | 23.1792i | 0.560632 | − | 0.872979i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.6733 | + | 4.83525i | 0.439021 | + | 0.181848i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.26185 | − | 7.87481i | −0.122501 | − | 0.295745i | 0.850718 | − | 0.525622i | \(-0.176167\pi\) |
−0.973220 | + | 0.229877i | \(0.926167\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.04446 | + | 13.5514i | −0.189182 | + | 0.508218i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.7526 | + | 13.7526i | −0.515039 | + | 0.515039i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.135944 | + | 0.328198i | 0.00508402 | + | 0.0122739i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.0266 | − | 22.2518i | 1.19606 | − | 0.831008i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 6.72495i | − | 0.250798i | −0.992106 | − | 0.125399i | \(-0.959979\pi\) | ||
0.992106 | − | 0.125399i | \(-0.0400211\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.18508i | 0.0813766i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.9927 | + | 21.5334i | −1.15263 | + | 0.800836i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.30660 | + | 5.56862i | 0.0856649 | + | 0.206813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.8994 | + | 11.8994i | −0.441326 | + | 0.441326i | −0.892457 | − | 0.451132i | \(-0.851021\pi\) |
0.451132 | + | 0.892457i | \(0.351021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.6722 | − | 12.9856i | 0.876750 | − | 0.480947i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.93559 | − | 7.08715i | −0.108577 | − | 0.262128i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.8224 | + | 11.5244i | 1.02764 | + | 0.425664i | 0.831861 | − | 0.554984i | \(-0.187276\pi\) |
0.195782 | + | 0.980647i | \(0.437276\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −39.7901 | + | 61.9586i | −1.46768 | + | 2.28538i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.28611i | 0.121045i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.46555 | − | 22.8519i | 0.348196 | − | 0.840619i | −0.648637 | − | 0.761098i | \(-0.724661\pi\) |
0.996833 | − | 0.0795214i | \(-0.0253392\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.88644 | − | 0.339724i | −0.0693002 | − | 0.0124801i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.0574 | + | 34.0574i | −1.24944 | + | 1.24944i | −0.293479 | + | 0.955966i | \(0.594813\pi\) |
−0.955966 | + | 0.293479i | \(0.905187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.3309 | − | 23.3309i | −0.854778 | − | 0.854778i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.6907 | − | 19.2388i | −0.757033 | − | 0.703911i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.83000 | − | 0.758011i | −0.0668667 | − | 0.0276971i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.4849 | −1.03943 | −0.519714 | − | 0.854341i | \(-0.673961\pi\) | ||||
−0.519714 | + | 0.854341i | \(0.673961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.5967 | + | 22.7291i | −0.531935 | + | 0.828294i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.7822 | − | 52.5870i | 0.792737 | − | 1.91384i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.6728 | + | 10.6340i | −0.933093 | + | 0.386500i | −0.796851 | − | 0.604176i | \(-0.793502\pi\) |
−0.136242 | + | 0.990676i | \(0.543502\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.515417 | − | 2.36566i | −0.0187085 | − | 0.0858681i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.3477 | − | 29.3477i | −1.06385 | − | 1.06385i | −0.997817 | − | 0.0660371i | \(-0.978964\pi\) |
−0.0660371 | − | 0.997817i | \(-0.521036\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.3697 | − | 8.43740i | 0.737432 | − | 0.305454i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.451611 | − | 12.4202i | −0.0163280 | − | 0.449053i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.46005 | −0.0527193 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.2426 | −1.16270 | −0.581349 | − | 0.813654i | \(-0.697475\pi\) | ||||
−0.581349 | + | 0.813654i | \(0.697475\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.8957 | + | 11.7389i | −0.608482 | + | 0.422768i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.3588 | + | 5.11920i | −0.444517 | + | 0.184125i | −0.593703 | − | 0.804684i | \(-0.702335\pi\) |
0.149186 | + | 0.988809i | \(0.452335\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.4452 | + | 10.4452i | 0.375203 | + | 0.375203i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −58.0392 | + | 12.6453i | −2.08215 | + | 0.453647i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.6104 | + | 5.63762i | −0.487644 | + | 0.201989i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.612450 | + | 1.47859i | −0.0219152 | + | 0.0529079i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.24889 | + | 8.74629i | −0.0446316 | + | 0.312567i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.1432 | 0.897398 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.0948 | − | 15.7794i | −1.35793 | − | 0.562475i | −0.419444 | − | 0.907781i | \(-0.637775\pi\) |
−0.938490 | + | 0.345307i | \(0.887775\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.94432 | − | 1.43067i | −0.282825 | − | 0.0509331i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −60.8237 | − | 60.8237i | −2.16264 | − | 2.16264i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.40465 | − | 3.40465i | 0.120903 | − | 0.120903i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.34181 | − | 24.1095i | 0.153988 | − | 0.855076i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.35573 | + | 12.9299i | −0.189710 | + | 0.458000i | −0.989904 | − | 0.141742i | \(-0.954730\pi\) |
0.800194 | + | 0.599741i | \(0.204730\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.71092i | − | 0.272793i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.2721 | + | 6.52900i | −0.504282 | + | 0.230691i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.52272 | − | 0.630733i | −0.0537358 | − | 0.0222581i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.2341 | + | 58.5062i | 0.854138 | + | 2.06207i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.7747 | − | 49.4537i | −0.379288 | − | 1.74085i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.7156 | − | 20.7156i | 0.728323 | − | 0.728323i | −0.241963 | − | 0.970286i | \(-0.577791\pi\) |
0.970286 | + | 0.241963i | \(0.0777911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.3246 | − | 27.3401i | −0.397662 | − | 0.960040i | −0.988219 | − | 0.153045i | \(-0.951092\pi\) |
0.590557 | − | 0.806996i | \(-0.298908\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.45730 | − | 4.97603i | −0.121253 | − | 0.174517i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 36.4844i | − | 1.27799i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.7623i | − | 0.516466i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.205309 | − | 5.64638i | −0.00717407 | − | 0.197301i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.72933 | − | 18.6602i | −0.269755 | − | 0.651247i | 0.729716 | − | 0.683750i | \(-0.239652\pi\) |
−0.999472 | + | 0.0325031i | \(0.989652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.01439 | + | 9.01439i | −0.314222 | + | 0.314222i | −0.846543 | − | 0.532321i | \(-0.821320\pi\) |
0.532321 | + | 0.846543i | \(0.321320\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.79674 | + | 0.391464i | −0.0625545 | + | 0.0136290i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.63867 | + | 6.37031i | 0.0917555 | + | 0.221517i | 0.963094 | − | 0.269165i | \(-0.0867476\pi\) |
−0.871339 | + | 0.490682i | \(0.836748\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.8454 | + | 5.73494i | 0.480870 | + | 0.199183i | 0.609932 | − | 0.792454i | \(-0.291197\pi\) |
−0.129062 | + | 0.991636i | \(0.541197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0753 | − | 10.3236i | −0.557645 | − | 0.358123i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.6115i | 0.714145i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.3480 | + | 56.3672i | −0.807992 | + | 1.95067i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.37510 | + | 20.9747i | 0.185791 | + | 0.724992i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.1199 | − | 26.1199i | 0.901760 | − | 0.901760i | −0.0938284 | − | 0.995588i | \(-0.529911\pi\) |
0.995588 | + | 0.0938284i | \(0.0299105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.4618 | + | 18.4618i | 0.636615 | + | 0.636615i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.12483 | − | 34.0105i | 0.210950 | − | 1.17138i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.6639 | − | 14.3583i | −1.19247 | − | 0.493939i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.6402 | 1.74002 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.1641 | + | 17.4449i | 0.932268 | + | 0.598708i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.1974 | + | 31.8612i | −0.452399 | + | 1.09219i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.69735 | − | 0.703064i | 0.0581161 | − | 0.0240725i | −0.353436 | − | 0.935459i | \(-0.614987\pi\) |
0.411552 | + | 0.911386i | \(0.364987\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.34377 | − | 22.4147i | 0.285351 | − | 0.766565i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.0113831 | + | 0.0113831i | 0.000388840 | + | 0.000388840i | 0.707301 | − | 0.706912i | \(-0.249912\pi\) |
−0.706912 | + | 0.707301i | \(0.749912\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.9835 | + | 10.3485i | −0.852428 | + | 0.353087i | −0.765741 | − | 0.643149i | \(-0.777628\pi\) |
−0.0866863 | + | 0.996236i | \(0.527628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.7777 | − | 35.6622i | −0.844423 | − | 1.21536i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.4680 | −0.560576 | −0.280288 | − | 0.959916i | \(-0.590430\pi\) | ||||
−0.280288 | + | 0.959916i | \(0.590430\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.0727 | −0.818496 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.8159 | + | 21.3242i | 0.503173 | + | 0.724209i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.33366 | − | 0.552422i | 0.0452415 | − | 0.0187396i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.14815 | + | 3.14815i | 0.106671 | + | 0.106671i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.5080 | + | 30.9151i | −0.389487 | + | 1.04632i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.2395 | + | 7.55505i | −0.616608 | + | 0.255407i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7332 | − | 28.3264i | 0.396202 | − | 0.956515i | −0.592357 | − | 0.805676i | \(-0.701802\pi\) |
0.988558 | − | 0.150840i | \(-0.0481977\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34.1582 | + | 21.9366i | 1.15213 | + | 0.739903i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.3847 | −0.552015 | −0.276008 | − | 0.961155i | \(-0.589012\pi\) | ||||
−0.276008 | + | 0.961155i | \(0.589012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.3631 | − | 9.26309i | −0.752577 | − | 0.311728i | −0.0267846 | − | 0.999641i | \(-0.508527\pi\) |
−0.725793 | + | 0.687914i | \(0.758527\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.22891 | − | 17.9297i | 0.108539 | − | 0.602702i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.9346 | + | 30.9346i | 1.03868 | + | 1.03868i | 0.999221 | + | 0.0394616i | \(0.0125643\pi\) |
0.0394616 | + | 0.999221i | \(0.487436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.7542 | − | 15.7542i | 0.528379 | − | 0.528379i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.55861 | − | 0.847921i | −0.0857166 | − | 0.0284064i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.67862 | − | 13.7094i | 0.190028 | − | 0.458767i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10.5971i | − | 0.354222i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.76013 | − | 1.77257i | −0.0921579 | − | 0.0591843i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.54585 | − | 2.71138i | −0.218316 | − | 0.0904295i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.62412 | − | 6.33518i | −0.0874220 | − | 0.211055i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42.5172 | − | 9.26342i | 1.41488 | − | 0.308267i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.5752 | − | 14.5752i | 0.484496 | − | 0.484496i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.03654 | + | 12.1593i | 0.167235 | + | 0.403742i | 0.985173 | − | 0.171565i | \(-0.0548825\pi\) |
−0.817937 | + | 0.575307i | \(0.804882\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.296751 | − | 8.16122i | −0.00984261 | − | 0.270691i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.5810i | 1.07946i | 0.841840 | + | 0.539728i | \(0.181473\pi\) | ||||
−0.841840 | + | 0.539728i | \(0.818527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.82055i | 0.0933464i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34.2805 | + | 49.3393i | 1.13328 | + | 1.63111i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.8587 | + | 93.8133i | 1.28323 | + | 3.09799i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.42914 | + | 8.42914i | −0.278052 | + | 0.278052i | −0.832331 | − | 0.554279i | \(-0.812994\pi\) |
0.554279 | + | 0.832331i | \(0.312994\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.86841 | − | 36.1144i | −0.259273 | − | 1.19001i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.829774 | + | 2.00325i | 0.0273123 | + | 0.0659378i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.1989 | + | 10.0235i | 0.795655 | + | 0.329571i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.28430 | − | 0.587524i | 0.0421821 | − | 0.0192968i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.0122i | 0.919051i | 0.888165 | + | 0.459525i | \(0.151981\pi\) | ||||
−0.888165 | + | 0.459525i | \(0.848019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.1791 | + | 36.6456i | −0.497474 | + | 1.20101i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.58879 | − | 25.4810i | 0.150230 | − | 0.834211i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.877339 | + | 0.877339i | −0.0286920 | + | 0.0286920i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.3178 | − | 16.3178i | −0.533079 | − | 0.533079i | 0.388408 | − | 0.921487i | \(-0.373025\pi\) |
−0.921487 | + | 0.388408i | \(0.873025\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 57.9991 | + | 10.4449i | 1.89273 | + | 0.340855i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.7582 | + | 4.45619i | 0.350707 | + | 0.145268i | 0.551081 | − | 0.834452i | \(-0.314216\pi\) |
−0.200374 | + | 0.979720i | \(0.564216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.2112 | −0.820991 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 69.7929 | + | 9.96578i | 2.27036 | + | 0.324187i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.56768 | − | 23.0984i | 0.310908 | − | 0.750598i | −0.688764 | − | 0.724985i | \(-0.741847\pi\) |
0.999672 | − | 0.0256122i | \(-0.00815350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.06305 | + | 0.854544i | −0.0669695 | + | 0.0277397i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.5142 | − | 8.60914i | 1.28134 | − | 0.279170i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.73365 | + | 3.73365i | 0.120945 | + | 0.120945i | 0.764989 | − | 0.644044i | \(-0.222745\pi\) |
−0.644044 | + | 0.764989i | \(0.722745\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.7986 | − | 21.0415i | 1.64380 | − | 0.680886i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.724340 | − | 0.503265i | 0.0234146 | − | 0.0162682i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 83.5622 | 2.69836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6359 | 0.439869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0465209 | + | 1.27942i | 0.00149912 | + | 0.0412286i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.1118 | − | 12.4727i | 0.969334 | − | 0.401511i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.6431 | − | 32.6431i | −1.04973 | − | 1.04973i | −0.998697 | − | 0.0510357i | \(-0.983748\pi\) |
−0.0510357 | − | 0.998697i | \(-0.516252\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.42519 | − | 6.54132i | −0.0457836 | − | 0.210138i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.2848 | + | 21.2429i | −1.64581 | + | 0.681716i | −0.996865 | − | 0.0791224i | \(-0.974788\pi\) |
−0.648942 | + | 0.760838i | \(0.724788\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.897811 | + | 2.16751i | −0.0287825 | + | 0.0694871i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.34628 | + | 2.09634i | −0.0431155 | + | 0.0671367i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.6955 | −0.822072 | −0.411036 | − | 0.911619i | \(-0.634833\pi\) | ||||
−0.411036 | + | 0.911619i | \(0.634833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.44755 | + | 0.599596i | 0.0462640 | + | 0.0191632i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.4362 | − | 9.70386i | −0.333201 | − | 0.309820i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.5980 | + | 40.5980i | 1.29487 | + | 1.29487i | 0.931735 | + | 0.363140i | \(0.118295\pi\) |
0.363140 | + | 0.931735i | \(0.381705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.0322 | + | 33.0322i | −1.05249 | + | 1.05249i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 43.0482 | + | 7.75242i | 1.37024 | + | 0.246762i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.66786 | − | 23.3403i | 0.307420 | − | 0.742177i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.4960i | 1.00050i | 0.865880 | + | 0.500251i | \(0.166759\pi\) | ||||
−0.865880 | + | 0.500251i | \(0.833241\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.1169 | − | 40.6676i | 0.828795 | − | 1.29055i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.62078 | − | 1.08556i | −0.0830844 | − | 0.0344147i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.47755 | + | 18.0524i | 0.236816 | + | 0.571726i | 0.996950 | − | 0.0780412i | \(-0.0248666\pi\) |
−0.760134 | + | 0.649767i | \(0.774867\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.0380 | + | 30.7131i | 0.728889 | + | 0.971720i |
(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 | 768.2.o.b.95.5 | 56 | ||
3.2 | odd | 2 | inner | 768.2.o.b.95.14 | 56 | ||
4.3 | odd | 2 | 768.2.o.a.95.10 | 56 | |||
8.3 | odd | 2 | 384.2.o.a.47.5 | 56 | |||
8.5 | even | 2 | 96.2.o.a.35.8 | yes | 56 | ||
12.11 | even | 2 | 768.2.o.a.95.1 | 56 | |||
24.5 | odd | 2 | 96.2.o.a.35.7 | yes | 56 | ||
24.11 | even | 2 | 384.2.o.a.47.14 | 56 | |||
32.5 | even | 8 | 384.2.o.a.335.14 | 56 | |||
32.11 | odd | 8 | inner | 768.2.o.b.671.14 | 56 | ||
32.21 | even | 8 | 768.2.o.a.671.1 | 56 | |||
32.27 | odd | 8 | 96.2.o.a.11.7 | ✓ | 56 | ||
96.5 | odd | 8 | 384.2.o.a.335.5 | 56 | |||
96.11 | even | 8 | inner | 768.2.o.b.671.5 | 56 | ||
96.53 | odd | 8 | 768.2.o.a.671.10 | 56 | |||
96.59 | even | 8 | 96.2.o.a.11.8 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.11.7 | ✓ | 56 | 32.27 | odd | 8 | ||
96.2.o.a.11.8 | yes | 56 | 96.59 | even | 8 | ||
96.2.o.a.35.7 | yes | 56 | 24.5 | odd | 2 | ||
96.2.o.a.35.8 | yes | 56 | 8.5 | even | 2 | ||
384.2.o.a.47.5 | 56 | 8.3 | odd | 2 | |||
384.2.o.a.47.14 | 56 | 24.11 | even | 2 | |||
384.2.o.a.335.5 | 56 | 96.5 | odd | 8 | |||
384.2.o.a.335.14 | 56 | 32.5 | even | 8 | |||
768.2.o.a.95.1 | 56 | 12.11 | even | 2 | |||
768.2.o.a.95.10 | 56 | 4.3 | odd | 2 | |||
768.2.o.a.671.1 | 56 | 32.21 | even | 8 | |||
768.2.o.a.671.10 | 56 | 96.53 | odd | 8 | |||
768.2.o.b.95.5 | 56 | 1.1 | even | 1 | trivial | ||
768.2.o.b.95.14 | 56 | 3.2 | odd | 2 | inner | ||
768.2.o.b.671.5 | 56 | 96.11 | even | 8 | inner | ||
768.2.o.b.671.14 | 56 | 32.11 | odd | 8 | inner |