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 | 95.14 | ||
Character | \(\chi\) | \(=\) | 768.95 |
Dual form | 768.2.o.b.671.14 |
$q$-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 | ||||||||
\(3\) | 1.70463 | − | 0.306981i | 0.984168 | − | 0.177236i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.70066 | − | 1.11865i | 1.20777 | − | 0.500275i | 0.314269 | − | 0.949334i | \(-0.398241\pi\) |
0.893502 | + | 0.449059i | \(0.148241\pi\) | |||||||
\(6\) | 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 | ||||||||
\(9\) | 2.81152 | − | 1.04658i | 0.937175 | − | 0.348860i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.276697 | + | 0.114612i | −0.0834272 | + | 0.0345567i | −0.424007 | − | 0.905659i | \(-0.639377\pi\) |
0.340580 | + | 0.940216i | \(0.389377\pi\) | |||||||
\(12\) | 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 | \(-0.554979\pi\) | ||||
−0.171864 | + | 0.985121i | \(0.554979\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | −6.60218 | − | 4.58713i | −1.44071 | − | 1.00099i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.30034 | − | 3.30034i | −0.688169 | − | 0.688169i | 0.273658 | − | 0.961827i | \(-0.411766\pi\) |
−0.961827 | + | 0.273658i | \(0.911766\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50664 | − | 2.50664i | 0.501328 | − | 0.501328i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.47133 | − | 2.64711i | 0.860508 | − | 0.509438i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.650676 | − | 1.57087i | 0.120827 | − | 0.291703i | −0.851880 | − | 0.523736i | \(-0.824538\pi\) |
0.972708 | + | 0.232033i | \(0.0745377\pi\) | |||||||
\(30\) | 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 | ||||||||
\(39\) | 0.149615 | − | 0.686701i | 0.0239575 | − | 0.109960i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.81949 | − | 3.81949i | 0.596504 | − | 0.596504i | −0.342877 | − | 0.939380i | \(-0.611401\pi\) |
0.939380 | + | 0.342877i | \(0.111401\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 6.42221 | − | 5.97156i | 0.957367 | − | 0.890188i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.44085i | 0.793629i | 0.917899 | + | 0.396815i | \(0.129884\pi\) | ||||
−0.917899 | + | 0.396815i | \(0.870116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.5435i | 2.07765i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41585 | + | 0.435062i | −0.338286 | + | 0.0609209i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.85159 | + | 4.47012i | 0.254335 | + | 0.614019i | 0.998545 | − | 0.0539269i | \(-0.0171738\pi\) |
−0.744210 | + | 0.667946i | \(0.767174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.619053 | + | 0.619053i | −0.0834731 | + | 0.0834731i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.61558 | + | 1.00562i | 0.611348 | + | 0.133197i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.37699 | + | 3.32434i | 0.179268 | + | 0.432792i | 0.987814 | − | 0.155642i | \(-0.0497447\pi\) |
−0.808545 | + | 0.588434i | \(0.799745\pi\) | |||||||
\(60\) | 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 | ||||||||
\(69\) | −6.63900 | − | 4.61272i | −0.799242 | − | 0.555306i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.77857 | − | 3.77857i | 0.448434 | − | 0.448434i | −0.446400 | − | 0.894834i | \(-0.647294\pi\) |
0.894834 | + | 0.446400i | \(0.147294\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 3.50340 | − | 5.04239i | 0.404538 | − | 0.582245i | ||||
\(76\) | 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 | \(-0.702100\pi\) |
0.988699 | − | 0.149916i | \(-0.0479003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.82744 | + | 1.58538i | −0.415145 | + | 0.171959i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.626933 | − | 2.87750i | 0.0672143 | − | 0.308500i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.69926 | − | 3.69926i | −0.392121 | − | 0.392121i | 0.483322 | − | 0.875443i | \(-0.339430\pi\) |
−0.875443 | + | 0.483322i | \(0.839430\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.74001 | + | 0.720735i | −0.182402 | + | 0.0755536i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.27920 | + | 7.10323i | 0.132647 | + | 0.736570i | ||||
\(94\) | 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 | ||||||||
\(99\) | −0.657990 | + | 0.611818i | −0.0661305 | + | 0.0614900i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.51499 | − | 1.04174i | 0.250251 | − | 0.103657i | −0.254032 | − | 0.967196i | \(-0.581757\pi\) |
0.504283 | + | 0.863538i | \(0.331757\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | −22.9616 | − | 5.00275i | −2.24082 | − | 0.488219i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.394269 | + | 0.163312i | −0.0381154 | + | 0.0157879i | −0.401660 | − | 0.915789i | \(-0.631567\pi\) |
0.363544 | + | 0.931577i | \(0.381567\pi\) | |||||||
\(108\) | 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 | \(-0.836974\pi\) | ||||
−0.871687 | + | 0.490063i | \(0.836974\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6050 | − | 5.22117i | −1.17542 | − | 0.486876i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0442333 | − | 1.21650i | 0.00408937 | − | 0.112465i | ||||
\(118\) | 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 | ||||||||
\(123\) | 5.33830 | − | 7.68333i | 0.481339 | − | 0.692782i | ||||
\(124\) | 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 | \(0.0299073\pi\) |
0.770328 | + | 0.637648i | \(0.220093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.84434 | − | 11.6953i | −0.420057 | − | 1.01411i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.11434 | − | 12.1508i | 0.784437 | − | 1.04577i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.7302 | − | 12.7302i | 1.08762 | − | 1.08762i | 0.0918436 | − | 0.995773i | \(-0.470724\pi\) |
0.995773 | − | 0.0918436i | \(-0.0292760\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 1.67024 | + | 9.27463i | 0.140660 | + | 0.781065i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.121525i | 0.0101624i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.97026i | − | 0.412758i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.46459 | + | 24.7913i | 0.368233 | + | 2.04475i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.31949 | − | 10.4282i | −0.353866 | − | 0.854308i | −0.996136 | − | 0.0878294i | \(-0.972007\pi\) |
0.642269 | − | 0.766479i | \(-0.277993\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | −3.98457 | + | 1.48324i | −0.322133 | + | 0.119913i | ||||
\(154\) | 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 | ||||||||
\(165\) | −0.865219 | + | 1.24529i | −0.0673572 | + | 0.0969460i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.7585 | + | 14.7585i | −1.14205 | + | 1.14205i | −0.153970 | + | 0.988076i | \(0.549206\pi\) |
−0.988076 | + | 0.153970i | \(0.950794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.07596 | + | 9.07596i | 0.698151 | + | 0.698151i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.17656 | + | 0.297309i | 0.625277 | + | 0.0227358i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.60827 | − | 3.15145i | −0.578446 | − | 0.239600i | 0.0742253 | − | 0.997241i | \(-0.476352\pi\) |
−0.652671 | + | 0.757641i | \(0.726352\pi\) | |||||||
\(174\) | 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 | −0.863515 | − | 0.504323i | \(-0.831742\pi\) |
0.967208 | + | 0.253987i | \(0.0817422\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 20.0817 | + | 4.37529i | 1.48448 | + | 0.323431i | ||||
\(184\) | 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 | ||||||||
\(189\) | −23.3630 | − | 5.98714i | −1.69941 | − | 0.435500i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8097 | 1.36102 | 0.680511 | − | 0.732737i | \(-0.261758\pi\) | ||||
0.680511 | + | 0.732737i | \(0.261758\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1498 | −0.802582 | −0.401291 | − | 0.915951i | \(-0.631438\pi\) | ||||
−0.401291 | + | 0.915951i | \(0.631438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.364119 | − | 2.02191i | −0.0260751 | − | 0.144792i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.7643 | + | 6.11558i | −1.05191 | + | 0.435717i | −0.840575 | − | 0.541696i | \(-0.817783\pi\) |
−0.211340 | + | 0.977413i | \(0.567783\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | −4.04566 | + | 18.5688i | −0.285359 | + | 1.30974i | ||||
\(202\) | 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 | ||||||||
\(213\) | 5.28111 | − | 7.60101i | 0.361856 | − | 0.520813i | ||||
\(214\) | 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 | ||||||||
\(219\) | −7.82792 | − | 5.43876i | −0.528962 | − | 0.367518i | ||||
\(220\) | 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 | 0.00672494 | − | 0.999977i | \(-0.497859\pi\) |
−0.702336 | + | 0.711846i | \(0.747859\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | 2.35254 | + | 0.512559i | 0.154786 | + | 0.0337239i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.9703 | + | 15.9703i | −1.04625 | + | 1.04625i | −0.0473714 | + | 0.998877i | \(0.515084\pi\) |
−0.998877 | + | 0.0473714i | \(0.984916\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.08640 | + | 14.6939i | 0.397033 | + | 0.958522i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.21623 | − | 1.47963i | 0.533702 | − | 0.0961126i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.5155i | − | 1.45641i | −0.685361 | − | 0.728204i | \(-0.740355\pi\) | ||
0.685361 | − | 0.728204i | \(-0.259645\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 21.7886i | − | 1.40353i | −0.712409 | − | 0.701765i | \(-0.752396\pi\) | ||
0.712409 | − | 0.701765i | \(-0.247604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.80084 | − | 12.1220i | 0.628724 | − | 0.777628i | ||||
\(244\) | 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 | ||||||||
\(249\) | 3.47249 | − | 15.9380i | 0.220060 | − | 1.01003i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.96821 | + | 14.4085i | 0.376710 | + | 0.909458i | 0.992578 | + | 0.121609i | \(0.0388054\pi\) |
−0.615868 | + | 0.787849i | \(0.711195\pi\) | |||||||
\(252\) | 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 | \(0.120802\pi\) | ||||
−0.928846 | + | 0.370467i | \(0.879198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.1242 | − | 31.6845i | 0.815495 | − | 1.96878i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.185352 | − | 5.09752i | 0.0114730 | − | 0.315529i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.29543 | + | 3.29543i | −0.203205 | + | 0.203205i | −0.801372 | − | 0.598167i | \(-0.795896\pi\) |
0.598167 | + | 0.801372i | \(0.295896\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0010 | + | 10.0010i | 0.614357 | + | 0.614357i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.44148 | − | 5.17027i | −0.455411 | − | 0.316415i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.9975 | − | 11.1827i | −1.64607 | − | 0.681824i | −0.649180 | − | 0.760635i | \(-0.724888\pi\) |
−0.996890 | + | 0.0788107i | \(0.974888\pi\) | |||||||
\(270\) | 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 | ||||||||
\(279\) | 4.36112 | + | 11.7157i | 0.261093 | + | 0.701399i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1081 | − | 14.1081i | −0.841616 | − | 0.841616i | 0.147453 | − | 0.989069i | \(-0.452893\pi\) |
−0.989069 | + | 0.147453i | \(0.952893\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 13.5900 | − | 2.44738i | 0.805004 | − | 0.144971i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.0714 | −1.47992 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9915 | −0.881851 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.7438 | − | 3.37552i | 1.09878 | − | 0.197876i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6538 | − | 8.96928i | 1.26503 | − | 0.523991i | 0.353577 | − | 0.935405i | \(-0.384965\pi\) |
0.911448 | + | 0.411414i | \(0.134965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.43753 | + | 7.43753i | 0.433030 | + | 0.433030i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.933812 | + | 1.24491i | −0.0541853 | + | 0.0722372i | ||||
\(298\) | 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 | ||||||||
\(309\) | −0.669635 | − | 0.465256i | −0.0380942 | − | 0.0264675i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5699 | − | 10.5699i | −0.599365 | − | 0.599365i | 0.340779 | − | 0.940144i | \(-0.389309\pi\) |
−0.940144 | + | 0.340779i | \(0.889309\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | −40.6768 | − | 1.47905i | −2.29188 | − | 0.0833352i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.93517 | − | 21.5714i | 0.501849 | − | 1.21157i | −0.446626 | − | 0.894721i | \(-0.647375\pi\) |
0.948475 | − | 0.316851i | \(-0.102625\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −1.75149 | + | 8.03897i | −0.0968575 | + | 0.444556i | ||||
\(328\) | 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 | ||||||||
\(333\) | 15.0941 | + | 16.2332i | 0.827151 | + | 0.889573i | ||||
\(334\) | 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 | ||||||||
\(339\) | −31.5907 | + | 5.68907i | −1.71577 | + | 0.308988i | ||||
\(340\) | 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 | ||||||||
\(345\) | −23.0897 | − | 5.03065i | −1.24311 | − | 0.270841i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.88801 | − | 6.97227i | −0.155037 | − | 0.374291i | 0.827208 | − | 0.561896i | \(-0.189928\pi\) |
−0.982245 | + | 0.187604i | \(0.939928\pi\) | |||||||
\(348\) | 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 | \(-0.657982\pi\) | ||
0.476189 | − | 0.879343i | \(-0.342018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.97773 | − | 14.4315i | 0.317265 | − | 0.765945i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.35679 | + | 6.50101i | 0.495214 | + | 0.344070i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.02805 | + | 1.02805i | −0.0542584 | + | 0.0542584i | −0.733715 | − | 0.679457i | \(-0.762215\pi\) |
0.679457 | + | 0.733715i | \(0.262215\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.17537 | − | 8.17537i | −0.430283 | − | 0.430283i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.7825 | + | 15.5191i | −0.565935 | + | 0.814540i | ||||
\(364\) | 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 | ||||||||
\(375\) | −1.56832 | + | 7.19829i | −0.0809879 | + | 0.371718i | ||||
\(376\) | 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 | ||||||||
\(381\) | 1.47355 | + | 8.18244i | 0.0754923 | + | 0.419199i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.9536 | 1.47946 | 0.739729 | − | 0.672905i | \(-0.234954\pi\) | ||||
0.739729 | + | 0.672905i | \(0.234954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.06351 | 0.207096 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.0573 | − | 11.8918i | −0.562076 | − | 0.604493i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.31149 | + | 2.61431i | −0.320005 | + | 0.132551i | −0.536903 | − | 0.843644i | \(-0.680406\pi\) |
0.216898 | + | 0.976194i | \(0.430406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.67733 | + | 4.67733i | 0.236543 | + | 0.236543i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.0238 | + | 8.06654i | 1.86760 | + | 0.406903i | ||||
\(394\) | 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 | \(-0.531352\pi\) | ||||
−0.0983371 | + | 0.995153i | \(0.531352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.56214 | + | 0.647058i | 0.0778155 | + | 0.0322322i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.8065 | − | 23.5105i | 0.586670 | − | 1.16825i | ||||
\(406\) | 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 | ||||||||
\(411\) | 17.7924 | − | 25.6083i | 0.877634 | − | 1.26316i | ||||
\(412\) | 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 | 0.520113 | − | 0.854097i | \(-0.325890\pi\) |
−0.236163 | + | 0.971714i | \(0.575890\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 5.69428 | + | 15.2971i | 0.276865 | + | 0.743770i | ||||
\(424\) | 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 | ||||||||
\(429\) | 0.0373060 | + | 0.207155i | 0.00180115 | + | 0.0100016i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 33.6809i | − | 1.62235i | −0.584801 | − | 0.811177i | \(-0.698827\pi\) | ||
0.584801 | − | 0.811177i | \(-0.301173\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.3471i | − | 0.977819i | −0.872335 | − | 0.488909i | \(-0.837395\pi\) | ||
0.872335 | − | 0.488909i | \(-0.162605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.52578 | − | 8.47245i | −0.0731554 | − | 0.406223i | ||||
\(436\) | 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 | ||||||||
\(441\) | 15.2209 | + | 40.8895i | 0.724807 | + | 1.94712i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.7190 | − | 25.8778i | −0.509273 | − | 1.22949i | −0.944303 | − | 0.329077i | \(-0.893262\pi\) |
0.435030 | − | 0.900416i | \(-0.356738\pi\) | |||||||
\(444\) | 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 | \(-0.874788\pi\) | ||
0.923625 | − | 0.383298i | \(-0.125212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.619083 | + | 1.49460i | −0.0291515 | + | 0.0703779i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.2438 | + | 27.6973i | −0.904154 | + | 1.30133i | ||||
\(454\) | 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 | ||||||||
\(459\) | −6.33689 | + | 3.75156i | −0.295781 | + | 0.175108i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.8642 | + | 8.64224i | 0.971743 | + | 0.402509i | 0.811361 | − | 0.584546i | \(-0.198727\pi\) |
0.160382 | + | 0.987055i | \(0.448727\pi\) | |||||||
\(462\) | 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 | −0.984847 | − | 0.173428i | \(-0.944516\pi\) |
0.819024 | + | 0.573760i | \(0.194516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 47.0508 | − | 19.4891i | 2.17260 | − | 0.899922i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.5565 | − | 3.17148i | −0.670726 | − | 0.146134i | ||||
\(472\) | 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 | ||||||||
\(477\) | 9.88412 | + | 10.6300i | 0.452563 | + | 0.486716i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.51545 | −0.0692426 | −0.0346213 | − | 0.999401i | \(-0.511023\pi\) | ||||
−0.0346213 | + | 0.999401i | \(0.511023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.99813 | 0.136703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.65035 | + | 36.9286i | 0.302601 | + | 1.68031i | ||||
\(484\) | 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 | ||||||||
\(489\) | −4.60203 | + | 21.1224i | −0.208111 | + | 0.955188i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.2550 | + | 8.38989i | −0.914095 | + | 0.378630i | −0.789623 | − | 0.613593i | \(-0.789724\pi\) |
−0.124472 | + | 0.992223i | \(0.539724\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | −20.6272 | + | 29.6883i | −0.921554 | + | 1.32638i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.9291 | + | 14.9291i | 0.665655 | + | 0.665655i | 0.956707 | − | 0.291052i | \(-0.0940054\pi\) |
−0.291052 | + | 0.956707i | \(0.594005\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.62678 | − | 5.62678i | 0.250389 | − | 0.250389i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.2573 | + | 12.6850i | 0.810836 | + | 0.563361i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.540947 | + | 1.30596i | −0.0239770 | + | 0.0578857i | −0.935415 | − | 0.353553i | \(-0.884973\pi\) |
0.911438 | + | 0.411438i | \(0.134973\pi\) | |||||||
\(510\) | 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 | ||||||||
\(519\) | −13.9367 | − | 3.03645i | −0.611754 | − | 0.133286i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.02013 | + | 4.02013i | −0.176125 | + | 0.176125i | −0.789664 | − | 0.613539i | \(-0.789745\pi\) |
0.613539 | + | 0.789664i | \(0.289745\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −28.0476 | + | 5.05100i | −1.22410 | + | 0.220444i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5.90561i | − | 0.257253i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.21549i | − | 0.0528475i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.35061 | + | 7.90533i | 0.318989 | + | 0.343062i | ||||
\(532\) | 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 | ||||||||
\(537\) | 1.33669 | − | 6.13513i | 0.0576823 | − | 0.264750i | ||||
\(538\) | 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 | ||||||||
\(549\) | 35.5750 | + | 1.29354i | 1.51830 | + | 0.0552071i | ||||
\(550\) | 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 | ||||||||
\(555\) | 30.7225 | + | 21.3457i | 1.30410 | + | 0.906074i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.6235 | + | 13.9273i | 1.42467 | + | 0.590119i | 0.956030 | − | 0.293268i | \(-0.0947428\pi\) |
0.468644 | + | 0.883387i | \(0.344743\pi\) | |||||||
\(558\) | 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 | \(0.316897\pi\) |
−0.977997 | + | 0.208620i | \(0.933103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50.0494 | + | 20.7312i | −2.10560 | + | 0.872166i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −41.6632 | − | 3.03385i | −1.74969 | − | 0.127410i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.01618 | + | 5.01618i | 0.210289 | + | 0.210289i | 0.804390 | − | 0.594101i | \(-0.202492\pi\) |
−0.594101 | + | 0.804390i | \(0.702492\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 32.0636 | − | 5.77423i | 1.33948 | − | 0.241222i | ||||
\(574\) | 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 | ||||||||
\(579\) | −19.0063 | + | 3.42279i | −0.789875 | + | 0.142246i | ||||
\(580\) | 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 | ||||||||
\(585\) | −1.24138 | − | 3.33483i | −0.0513246 | − | 0.137878i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.3129 | + | 9.24233i | −0.920954 | + | 0.381472i | −0.792240 | − | 0.610210i | \(-0.791085\pi\) |
−0.128714 | + | 0.991682i | \(0.541085\pi\) | |||||||
\(588\) | 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 | \(-0.514102\pi\) | ||||
−0.0442868 | + | 0.999019i | \(0.514102\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.7651 | + | 7.35854i | 0.728297 | + | 0.301671i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.38035 | + | 0.959057i | 0.0564942 | + | 0.0392516i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.80949 | + | 4.80949i | 0.196511 | + | 0.196511i | 0.798502 | − | 0.601992i | \(-0.205626\pi\) |
−0.601992 | + | 0.798502i | \(0.705626\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | −1.19609 | + | 32.8948i | −0.0487086 | + | 1.33958i | ||||
\(604\) | 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 | ||||||||
\(615\) | 5.82198 | − | 26.7217i | 0.234765 | − | 1.07752i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.7968 | + | 10.7968i | −0.434663 | + | 0.434663i | −0.890211 | − | 0.455548i | \(-0.849443\pi\) |
0.455548 | + | 0.890211i | \(0.349443\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | −23.4933 | − | 6.02053i | −0.942753 | − | 0.241595i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.2822i | 0.972848i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.1581i | 1.20633i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.39237 | + | 0.250748i | −0.0556059 | + | 0.0100139i | ||||
\(628\) | 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 | ||||||||
\(633\) | −4.13741 | − | 0.901437i | −0.164447 | − | 0.0358289i | ||||
\(634\) | 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 | \(0.247563\pi\) | ||||
−0.712500 | + | 0.701672i | \(0.752437\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | −22.5061 | − | 15.6370i | −0.886176 | − | 0.615707i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.34579 | − | 9.34579i | 0.367421 | − | 0.367421i | −0.499115 | − | 0.866536i | \(-0.666341\pi\) |
0.866536 | + | 0.499115i | \(0.166341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.762015 | − | 0.762015i | −0.0299117 | − | 0.0299117i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.1147 | − | 27.5114i | 0.749163 | − | 1.07826i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.13779 | + | 1.29972i | 0.122791 | + | 0.0508618i | 0.443233 | − | 0.896406i | \(-0.353831\pi\) |
−0.320442 | + | 0.947268i | \(0.603831\pi\) | |||||||
\(654\) | 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 | \(-0.664335\pi\) |
0.964004 | − | 0.265889i | \(-0.0856653\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −0.212038 | + | 0.973211i | −0.00823487 | + | 0.0377964i | ||||
\(664\) | 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 | ||||||||
\(669\) | −3.17640 | − | 17.6382i | −0.122807 | − | 0.681931i | ||||
\(670\) | 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 | ||||||||
\(675\) | 4.57265 | − | 17.8434i | 0.176001 | − | 0.686792i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.25960 | + | 2.59281i | −0.240576 | + | 0.0996498i | −0.499714 | − | 0.866191i | \(-0.666562\pi\) |
0.259138 | + | 0.965840i | \(0.416562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.0887 | − | 36.0887i | −1.38496 | − | 1.38496i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.1979 | − | 4.18273i | −0.735665 | − | 0.160283i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.2767 | − | 10.8842i | 1.00545 | − | 0.416471i | 0.181657 | − | 0.983362i | \(-0.441854\pi\) |
0.823793 | + | 0.566891i | \(0.191854\pi\) | |||||||
\(684\) | 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 | ||||||||
\(693\) | 4.16756 | + | 0.151537i | 0.158312 | + | 0.00575641i | ||||
\(694\) | 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 | ||||||||
\(699\) | −22.3209 | + | 32.1260i | −0.844252 | + | 1.21512i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.7331 | + | 37.9830i | −0.594230 | + | 1.43460i | 0.285153 | + | 0.958482i | \(0.407956\pi\) |
−0.879383 | + | 0.476116i | \(0.842044\pi\) | |||||||
\(702\) | 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 | ||||||||
\(711\) | 13.5514 | − | 5.04446i | 0.508218 | − | 0.189182i | ||||
\(712\) | 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 | ||||||||
\(717\) | −6.91184 | − | 38.3806i | −0.258127 | − | 1.43335i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.72495i | 0.250798i | 0.992106 | + | 0.125399i | \(0.0400211\pi\) | ||||
−0.992106 | + | 0.125399i | \(0.959979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.18508i | 0.0813766i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.68870 | − | 37.1415i | −0.248756 | − | 1.38131i | ||||
\(724\) | 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 | ||||||||
\(729\) | 12.9856 | − | 23.6722i | 0.480947 | − | 0.876750i | ||||
\(730\) | 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 | ||||||||
\(741\) | 1.09370 | − | 1.57414i | 0.0401779 | − | 0.0578274i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.0574 | − | 34.0574i | 1.24944 | − | 1.24944i | 0.293479 | − | 0.955966i | \(-0.405187\pi\) |
0.955966 | − | 0.293479i | \(-0.0948130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.3309 | − | 23.3309i | −0.854778 | − | 0.854778i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.02663 | − | 28.2344i | 0.0375626 | − | 1.03304i | ||||
\(748\) | 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 | ||||||||
\(759\) | 2.36566 | + | 0.515417i | 0.0858681 | + | 0.0187085i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.3477 | + | 29.3477i | 1.06385 | + | 1.06385i | 0.997817 | + | 0.0660371i | \(0.0210356\pi\) |
0.0660371 | + | 0.997817i | \(0.478964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.3697 | − | 8.43740i | 0.737432 | − | 0.305454i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.10173 | + | 8.46306i | −0.329074 | + | 0.305982i | ||||
\(766\) | 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 | ||||||||
\(771\) | 3.64635 | + | 20.2477i | 0.131320 | + | 0.729204i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.3588 | − | 5.11920i | 0.444517 | − | 0.184125i | −0.149186 | − | 0.988809i | \(-0.547665\pi\) |
0.593703 | + | 0.804684i | \(0.297665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.4452 | + | 10.4452i | 0.375203 | + | 0.375203i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.6453 | − | 58.0392i | 0.453647 | − | 2.08215i | ||||
\(778\) | 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 | ||||||||
\(789\) | −4.60585 | + | 6.62911i | −0.163972 | + | 0.236003i | ||||
\(790\) | 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 | ||||||||
\(795\) | 20.1181 | + | 13.9779i | 0.713516 | + | 0.495744i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.35573 | − | 12.9299i | 0.189710 | − | 0.458000i | −0.800194 | − | 0.599741i | \(-0.795270\pi\) |
0.989904 | + | 0.141742i | \(0.0452702\pi\) | |||||||
\(798\) | 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 | ||||||||
\(807\) | −49.4537 | − | 10.7747i | −1.74085 | − | 0.379288i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.7156 | + | 20.7156i | −0.728323 | + | 0.728323i | −0.970286 | − | 0.241963i | \(-0.922209\pi\) |
0.241963 | + | 0.970286i | \(0.422209\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 5.96326 | − | 1.07390i | 0.209141 | − | 0.0376635i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.4844i | 1.27799i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.7623i | − | 0.516466i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.13777 | + | 3.84742i | −0.144585 | + | 0.134440i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.72933 | + | 18.6602i | 0.269755 | + | 0.651247i | 0.999472 | − | 0.0325031i | \(-0.0103479\pi\) |
−0.729716 | + | 0.683750i | \(0.760348\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | −0.391464 | + | 1.79674i | −0.0136290 | + | 0.0625545i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.63867 | − | 6.37031i | −0.0917555 | − | 0.221517i | 0.871339 | − | 0.490682i | \(-0.163252\pi\) |
−0.963094 | + | 0.269165i | \(0.913252\pi\) | |||||||
\(828\) | 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 | ||||||||
\(837\) | 11.0306 | + | 18.6321i | 0.381273 | + | 0.644020i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.1199 | + | 26.1199i | −0.901760 | + | 0.901760i | −0.995588 | − | 0.0938284i | \(-0.970089\pi\) |
0.0938284 | + | 0.995588i | \(0.470089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.4618 | + | 18.4618i | 0.636615 | + | 0.636615i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.3799 | − | 19.7181i | −0.977457 | − | 0.679128i | ||||
\(844\) | 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 | ||||||||
\(855\) | 22.4147 | − | 8.34377i | 0.766565 | − | 0.285351i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.0113831 | − | 0.0113831i | −0.000388840 | − | 0.000388840i | 0.706912 | − | 0.707301i | \(-0.250088\pi\) |
−0.707301 | + | 0.706912i | \(0.750088\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −42.7375 | + | 7.69645i | −1.45649 | + | 0.262294i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.4680 | 0.560576 | 0.280288 | − | 0.959916i | \(-0.409570\pi\) | ||||
0.280288 | + | 0.959916i | \(0.409570\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.0727 | −0.818496 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.5549 | + | 4.60210i | −0.867890 | + | 0.156296i | ||||
\(868\) | 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 | ||||||||
\(873\) | 30.9151 | − | 11.5080i | 1.04632 | − | 0.389487i | ||||
\(874\) | 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 | \(-0.410988\pi\) | ||||
0.276008 | + | 0.961155i | \(0.410988\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | 14.9614 | + | 10.3951i | 0.502923 | + | 0.349426i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.9346 | − | 30.9346i | −1.03868 | − | 1.03868i | −0.999221 | − | 0.0394616i | \(-0.987436\pi\) |
−0.0394616 | − | 0.999221i | \(-0.512564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.7542 | − | 15.7542i | 0.528379 | − | 0.528379i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.20964 | + | 2.40878i | −0.0405244 | + | 0.0806972i | ||||
\(892\) | 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 | ||||||||
\(903\) | −9.26342 | + | 42.5172i | −0.308267 | + | 1.41488i | ||||
\(904\) | 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 | ||||||||
\(909\) | 5.98069 | − | 5.56102i | 0.198367 | − | 0.184447i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.5810i | − | 1.07946i | −0.841840 | − | 0.539728i | \(-0.818527\pi\) | ||
0.841840 | − | 0.539728i | \(-0.181473\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.82055i | 0.0933464i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 59.1282 | − | 10.6482i | 1.95472 | − | 0.352019i | ||||
\(916\) | 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 | ||||||||
\(921\) | 36.1144 | + | 7.86841i | 1.19001 | + | 0.259273i | ||||
\(922\) | 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 | \(-0.848019\pi\) | ||
0.888165 | − | 0.459525i | \(-0.151981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.1791 | + | 36.6456i | −0.497474 | + | 1.20101i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.2626 | − | 14.7730i | −0.696105 | − | 0.483647i | ||||
\(934\) | 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 | ||||||||
\(939\) | −33.6259 | + | 48.3972i | −1.09734 | + | 1.57938i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.7582 | − | 4.45619i | −0.350707 | − | 0.145268i | 0.200374 | − | 0.979720i | \(-0.435784\pi\) |
−0.551081 | + | 0.834452i | \(0.685784\pi\) | |||||||
\(942\) | 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 | \(0.258153\pi\) |
−0.999672 | + | 0.0256122i | \(0.991847\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.06305 | + | 0.854544i | −0.0669695 | + | 0.0277397i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.60914 | − | 39.5142i | 0.279170 | − | 1.28134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.73365 | − | 3.73365i | −0.120945 | − | 0.120945i | 0.644044 | − | 0.764989i | \(-0.277255\pi\) |
−0.764989 | + | 0.644044i | \(0.777255\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.7986 | − | 21.0415i | 1.64380 | − | 0.680886i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.156324 | + | 0.868048i | 0.00505324 | + | 0.0280600i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −83.5622 | −2.69836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6359 | 0.439869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.937579 | + | 0.871788i | −0.0302130 | + | 0.0280930i | ||||
\(964\) | 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 | ||||||||
\(969\) | −6.54132 | − | 1.42519i | −0.210138 | − | 0.0457836i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.2848 | − | 21.2429i | 1.64581 | − | 0.681716i | 0.648942 | − | 0.760838i | \(-0.275212\pi\) |
0.996865 | + | 0.0791224i | \(0.0252118\pi\) | |||||||
\(972\) | 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 | \(-0.365167\pi\) | ||||
0.411036 | + | 0.911619i | \(0.365167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.44755 | + | 0.599596i | 0.0462640 | + | 0.0191632i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.517824 | + | 14.2411i | −0.0165328 | + | 0.454685i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.5980 | − | 40.5980i | −1.29487 | − | 1.29487i | −0.931735 | − | 0.363140i | \(-0.881705\pi\) |
−0.363140 | − | 0.931735i | \(-0.618295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.0322 | + | 33.0322i | −1.05249 | + | 1.05249i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.9579 | − | 35.9215i | 0.794419 | − | 1.14339i | ||||
\(988\) | 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 | ||||||||
\(999\) | 30.7131 | + | 23.0380i | 0.971720 | + | 0.728889i |
(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.95.14 | 56 | ||
3.2 | odd | 2 | inner | 768.2.o.b.95.5 | 56 | ||
4.3 | odd | 2 | 768.2.o.a.95.1 | 56 | |||
8.3 | odd | 2 | 384.2.o.a.47.14 | 56 | |||
8.5 | even | 2 | 96.2.o.a.35.7 | yes | 56 | ||
12.11 | even | 2 | 768.2.o.a.95.10 | 56 | |||
24.5 | odd | 2 | 96.2.o.a.35.8 | yes | 56 | ||
24.11 | even | 2 | 384.2.o.a.47.5 | 56 | |||
32.5 | even | 8 | 384.2.o.a.335.5 | 56 | |||
32.11 | odd | 8 | inner | 768.2.o.b.671.5 | 56 | ||
32.21 | even | 8 | 768.2.o.a.671.10 | 56 | |||
32.27 | odd | 8 | 96.2.o.a.11.8 | yes | 56 | ||
96.5 | odd | 8 | 384.2.o.a.335.14 | 56 | |||
96.11 | even | 8 | inner | 768.2.o.b.671.14 | 56 | ||
96.53 | odd | 8 | 768.2.o.a.671.1 | 56 | |||
96.59 | even | 8 | 96.2.o.a.11.7 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.11.7 | ✓ | 56 | 96.59 | even | 8 | ||
96.2.o.a.11.8 | yes | 56 | 32.27 | odd | 8 | ||
96.2.o.a.35.7 | yes | 56 | 8.5 | even | 2 | ||
96.2.o.a.35.8 | yes | 56 | 24.5 | odd | 2 | ||
384.2.o.a.47.5 | 56 | 24.11 | even | 2 | |||
384.2.o.a.47.14 | 56 | 8.3 | odd | 2 | |||
384.2.o.a.335.5 | 56 | 32.5 | even | 8 | |||
384.2.o.a.335.14 | 56 | 96.5 | odd | 8 | |||
768.2.o.a.95.1 | 56 | 4.3 | odd | 2 | |||
768.2.o.a.95.10 | 56 | 12.11 | even | 2 | |||
768.2.o.a.671.1 | 56 | 96.53 | odd | 8 | |||
768.2.o.a.671.10 | 56 | 32.21 | even | 8 | |||
768.2.o.b.95.5 | 56 | 3.2 | odd | 2 | inner | ||
768.2.o.b.95.14 | 56 | 1.1 | even | 1 | trivial | ||
768.2.o.b.671.5 | 56 | 32.11 | odd | 8 | inner | ||
768.2.o.b.671.14 | 56 | 96.11 | even | 8 | inner |