Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.39");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.10 | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.7.b.a.39.9 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.15940 | + | 3.56973i | −0.894925 | + | 0.446216i | ||||
\(3\) | 19.3279i | 0.715848i | 0.933751 | + | 0.357924i | \(0.116515\pi\) | ||||
−0.933751 | + | 0.357924i | \(0.883485\pi\) | |||||||
\(4\) | 38.5141 | − | 51.1142i | 0.601783 | − | 0.798660i | ||||
\(5\) | −43.0893 | −0.344714 | −0.172357 | − | 0.985035i | \(-0.555138\pi\) | ||||
−0.172357 | + | 0.985035i | \(0.555138\pi\) | |||||||
\(6\) | −68.9953 | − | 138.376i | −0.319422 | − | 0.640630i | ||||
\(7\) | − | 282.338i | − | 0.823143i | −0.911377 | − | 0.411571i | \(-0.864980\pi\) | ||
0.911377 | − | 0.411571i | \(-0.135020\pi\) | |||||||
\(8\) | −93.2744 | + | 503.432i | −0.182177 | + | 0.983266i | ||||
\(9\) | 355.433 | 0.487562 | ||||||||
\(10\) | 308.494 | − | 153.817i | 0.308494 | − | 0.153817i | ||||
\(11\) | 1423.66i | 1.06962i | 0.844972 | + | 0.534810i | \(0.179617\pi\) | ||||
−0.844972 | + | 0.534810i | \(0.820383\pi\) | |||||||
\(12\) | 987.930 | + | 744.397i | 0.571719 | + | 0.430785i | ||||
\(13\) | −64.5564 | −0.0293839 | −0.0146919 | − | 0.999892i | \(-0.504677\pi\) | ||||
−0.0146919 | + | 0.999892i | \(0.504677\pi\) | |||||||
\(14\) | 1007.87 | + | 2021.37i | 0.367299 | + | 0.736652i | ||||
\(15\) | − | 832.825i | − | 0.246763i | ||||||
\(16\) | −1129.32 | − | 3937.24i | −0.275714 | − | 0.961240i | ||||
\(17\) | 6845.77 | 1.39340 | 0.696700 | − | 0.717363i | \(-0.254651\pi\) | ||||
0.696700 | + | 0.717363i | \(0.254651\pi\) | |||||||
\(18\) | −2544.69 | + | 1268.80i | −0.436332 | + | 0.217558i | ||||
\(19\) | 1573.56i | 0.229416i | ||||||||
\(20\) | −1659.55 | + | 2202.48i | −0.207443 | + | 0.275309i | ||||
\(21\) | 5457.00 | 0.589245 | ||||||||
\(22\) | −5082.09 | − | 10192.6i | −0.477281 | − | 0.957230i | ||||
\(23\) | 8610.09i | 0.707659i | 0.935310 | + | 0.353829i | \(0.115121\pi\) | ||||
−0.935310 | + | 0.353829i | \(0.884879\pi\) | |||||||
\(24\) | −9730.28 | − | 1802.80i | −0.703869 | − | 0.130411i | ||||
\(25\) | −13768.3 | −0.881172 | ||||||||
\(26\) | 462.185 | − | 230.449i | 0.0262964 | − | 0.0131115i | ||||
\(27\) | 20959.8i | 1.06487i | ||||||||
\(28\) | −14431.5 | − | 10874.0i | −0.657411 | − | 0.495354i | ||||
\(29\) | −37754.8 | −1.54803 | −0.774013 | − | 0.633170i | \(-0.781754\pi\) | ||||
−0.774013 | + | 0.633170i | \(0.781754\pi\) | |||||||
\(30\) | 2972.96 | + | 5962.53i | 0.110110 | + | 0.220835i | ||||
\(31\) | 16053.5i | 0.538871i | 0.963018 | + | 0.269435i | \(0.0868370\pi\) | ||||
−0.963018 | + | 0.269435i | \(0.913163\pi\) | |||||||
\(32\) | 22140.2 | + | 24156.9i | 0.675664 | + | 0.737210i | ||||
\(33\) | −27516.4 | −0.765685 | ||||||||
\(34\) | −49011.6 | + | 24437.5i | −1.24699 | + | 0.621757i | ||||
\(35\) | 12165.7i | 0.283749i | ||||||||
\(36\) | 13689.2 | − | 18167.7i | 0.293407 | − | 0.389396i | ||||
\(37\) | −89414.3 | −1.76523 | −0.882616 | − | 0.470095i | \(-0.844220\pi\) | ||||
−0.882616 | + | 0.470095i | \(0.844220\pi\) | |||||||
\(38\) | −5617.19 | − | 11265.8i | −0.102369 | − | 0.205310i | ||||
\(39\) | − | 1247.74i | − | 0.0210344i | ||||||
\(40\) | 4019.13 | − | 21692.5i | 0.0627989 | − | 0.338946i | ||||
\(41\) | 53959.7 | 0.782921 | 0.391460 | − | 0.920195i | \(-0.371970\pi\) | ||||
0.391460 | + | 0.920195i | \(0.371970\pi\) | |||||||
\(42\) | −39068.8 | + | 19480.0i | −0.527330 | + | 0.262930i | ||||
\(43\) | 97929.6i | 1.23171i | 0.787859 | + | 0.615855i | \(0.211189\pi\) | ||||
−0.787859 | + | 0.615855i | \(0.788811\pi\) | |||||||
\(44\) | 72769.5 | + | 54831.2i | 0.854262 | + | 0.643679i | ||||
\(45\) | −15315.3 | −0.168070 | ||||||||
\(46\) | −30735.6 | − | 61643.1i | −0.315769 | − | 0.633302i | ||||
\(47\) | 23989.0i | 0.231057i | 0.993304 | + | 0.115528i | \(0.0368561\pi\) | ||||
−0.993304 | + | 0.115528i | \(0.963144\pi\) | |||||||
\(48\) | 76098.5 | − | 21827.5i | 0.688101 | − | 0.197369i | ||||
\(49\) | 37934.2 | 0.322436 | ||||||||
\(50\) | 98572.9 | − | 49149.1i | 0.788583 | − | 0.393193i | ||||
\(51\) | 132314.i | 0.997462i | ||||||||
\(52\) | −2486.33 | + | 3299.75i | −0.0176827 | + | 0.0234677i | ||||
\(53\) | −80853.1 | −0.543087 | −0.271543 | − | 0.962426i | \(-0.587534\pi\) | ||||
−0.271543 | + | 0.962426i | \(0.587534\pi\) | |||||||
\(54\) | −74820.7 | − | 150060.i | −0.475161 | − | 0.952977i | ||||
\(55\) | − | 61344.7i | − | 0.368713i | ||||||
\(56\) | 142138. | + | 26334.9i | 0.809368 | + | 0.149957i | ||||
\(57\) | −30413.6 | −0.164227 | ||||||||
\(58\) | 270302. | − | 134774.i | 1.38537 | − | 0.690753i | ||||
\(59\) | − | 102427.i | − | 0.498720i | −0.968411 | − | 0.249360i | \(-0.919780\pi\) | ||
0.968411 | − | 0.249360i | \(-0.0802203\pi\) | |||||||
\(60\) | −42569.2 | − | 32075.5i | −0.197080 | − | 0.148498i | ||||
\(61\) | −66372.6 | −0.292415 | −0.146207 | − | 0.989254i | \(-0.546707\pi\) | ||||
−0.146207 | + | 0.989254i | \(0.546707\pi\) | |||||||
\(62\) | −57306.6 | − | 114933.i | −0.240453 | − | 0.482249i | ||||
\(63\) | − | 100352.i | − | 0.401333i | ||||||
\(64\) | −244744. | − | 93914.7i | −0.933623 | − | 0.358256i | ||||
\(65\) | 2781.69 | 0.0101290 | ||||||||
\(66\) | 197001. | − | 98226.1i | 0.685231 | − | 0.341661i | ||||
\(67\) | 178825.i | 0.594571i | 0.954789 | + | 0.297286i | \(0.0960814\pi\) | ||||
−0.954789 | + | 0.297286i | \(0.903919\pi\) | |||||||
\(68\) | 263659. | − | 349916.i | 0.838524 | − | 1.11285i | ||||
\(69\) | −166415. | −0.506576 | ||||||||
\(70\) | −43428.4 | − | 87099.5i | −0.126613 | − | 0.253934i | ||||
\(71\) | 536228.i | 1.49822i | 0.662447 | + | 0.749108i | \(0.269518\pi\) | ||||
−0.662447 | + | 0.749108i | \(0.730482\pi\) | |||||||
\(72\) | −33152.8 | + | 178936.i | −0.0888224 | + | 0.479403i | ||||
\(73\) | 727200. | 1.86933 | 0.934663 | − | 0.355535i | \(-0.115701\pi\) | ||||
0.934663 | + | 0.355535i | \(0.115701\pi\) | |||||||
\(74\) | 640153. | − | 319184.i | 1.57975 | − | 0.787674i | ||||
\(75\) | − | 266112.i | − | 0.630785i | ||||||
\(76\) | 80431.4 | + | 60604.4i | 0.183225 | + | 0.138059i | ||||
\(77\) | 401955. | 0.880450 | ||||||||
\(78\) | 4454.08 | + | 8933.06i | 0.00938587 | + | 0.0188242i | ||||
\(79\) | 514579.i | 1.04369i | 0.853041 | + | 0.521844i | \(0.174756\pi\) | ||||
−0.853041 | + | 0.521844i | \(0.825244\pi\) | |||||||
\(80\) | 48661.8 | + | 169653.i | 0.0950426 | + | 0.331353i | ||||
\(81\) | −145998. | −0.274721 | ||||||||
\(82\) | −386319. | + | 192621.i | −0.700656 | + | 0.349351i | ||||
\(83\) | 560472.i | 0.980210i | 0.871663 | + | 0.490105i | \(0.163042\pi\) | ||||
−0.871663 | + | 0.490105i | \(0.836958\pi\) | |||||||
\(84\) | 210171. | − | 278930.i | 0.354598 | − | 0.470606i | ||||
\(85\) | −294980. | −0.480325 | ||||||||
\(86\) | −349582. | − | 701117.i | −0.549608 | − | 1.10229i | ||||
\(87\) | − | 729721.i | − | 1.10815i | ||||||
\(88\) | −716718. | − | 132791.i | −1.05172 | − | 0.194860i | ||||
\(89\) | −310222. | −0.440051 | −0.220025 | − | 0.975494i | \(-0.570614\pi\) | ||||
−0.220025 | + | 0.975494i | \(0.570614\pi\) | |||||||
\(90\) | 109649. | − | 54671.6i | 0.150410 | − | 0.0749953i | ||||
\(91\) | 18226.7i | 0.0241871i | ||||||||
\(92\) | 440098. | + | 331610.i | 0.565179 | + | 0.425857i | ||||
\(93\) | −310280. | −0.385749 | ||||||||
\(94\) | −85634.1 | − | 171747.i | −0.103101 | − | 0.206778i | ||||
\(95\) | − | 67803.7i | − | 0.0790829i | ||||||
\(96\) | −466902. | + | 427922.i | −0.527730 | + | 0.483672i | ||||
\(97\) | −475542. | −0.521043 | −0.260521 | − | 0.965468i | \(-0.583894\pi\) | ||||
−0.260521 | + | 0.965468i | \(0.583894\pi\) | |||||||
\(98\) | −271587. | + | 135415.i | −0.288556 | + | 0.143876i | ||||
\(99\) | 506017.i | 0.521506i | ||||||||
\(100\) | −530274. | + | 703756.i | −0.530274 | + | 0.703756i | ||||
\(101\) | 366846. | 0.356057 | 0.178028 | − | 0.984025i | \(-0.443028\pi\) | ||||
0.178028 | + | 0.984025i | \(0.443028\pi\) | |||||||
\(102\) | −472326. | − | 947292.i | −0.445083 | − | 0.892654i | ||||
\(103\) | 662397.i | 0.606187i | 0.952961 | + | 0.303094i | \(0.0980195\pi\) | ||||
−0.952961 | + | 0.303094i | \(0.901981\pi\) | |||||||
\(104\) | 6021.46 | − | 32499.8i | 0.00535306 | − | 0.0288922i | ||||
\(105\) | −235138. | −0.203121 | ||||||||
\(106\) | 578860. | − | 288623.i | 0.486022 | − | 0.242334i | ||||
\(107\) | − | 638219.i | − | 0.520977i | −0.965477 | − | 0.260489i | \(-0.916116\pi\) | ||
0.965477 | − | 0.260489i | \(-0.0838836\pi\) | |||||||
\(108\) | 1.07134e6 | + | 807248.i | 0.850467 | + | 0.640820i | ||||
\(109\) | −1.54663e6 | −1.19428 | −0.597139 | − | 0.802138i | \(-0.703696\pi\) | ||||
−0.597139 | + | 0.802138i | \(0.703696\pi\) | |||||||
\(110\) | 218984. | + | 439191.i | 0.164526 | + | 0.329971i | ||||
\(111\) | − | 1.72819e6i | − | 1.26364i | ||||||
\(112\) | −1.11163e6 | + | 318851.i | −0.791238 | + | 0.226952i | ||||
\(113\) | 985871. | 0.683258 | 0.341629 | − | 0.939835i | \(-0.389021\pi\) | ||||
0.341629 | + | 0.939835i | \(0.389021\pi\) | |||||||
\(114\) | 217744. | − | 108568.i | 0.146971 | − | 0.0732805i | ||||
\(115\) | − | 371003.i | − | 0.243940i | ||||||
\(116\) | −1.45409e6 | + | 1.92981e6i | −0.931576 | + | 1.23635i | ||||
\(117\) | −22945.4 | −0.0143265 | ||||||||
\(118\) | 365635. | + | 733314.i | 0.222537 | + | 0.446317i | ||||
\(119\) | − | 1.93282e6i | − | 1.14697i | ||||||
\(120\) | 419271. | + | 77681.3i | 0.242634 | + | 0.0449545i | ||||
\(121\) | −255259. | −0.144087 | ||||||||
\(122\) | 475188. | − | 236932.i | 0.261689 | − | 0.130480i | ||||
\(123\) | 1.04293e6i | 0.560452i | ||||||||
\(124\) | 820562. | + | 618286.i | 0.430374 | + | 0.324283i | ||||
\(125\) | 1.26654e6 | 0.648467 | ||||||||
\(126\) | 358230. | + | 718462.i | 0.179081 | + | 0.359163i | ||||
\(127\) | 1.79774e6i | 0.877640i | 0.898575 | + | 0.438820i | \(0.144603\pi\) | ||||
−0.898575 | + | 0.438820i | \(0.855397\pi\) | |||||||
\(128\) | 2.08747e6 | − | 201295.i | 0.995383 | − | 0.0959848i | ||||
\(129\) | −1.89277e6 | −0.881717 | ||||||||
\(130\) | −19915.2 | + | 9929.87i | −0.00906474 | + | 0.00451974i | ||||
\(131\) | 2.43254e6i | 1.08205i | 0.841007 | + | 0.541024i | \(0.181963\pi\) | ||||
−0.841007 | + | 0.541024i | \(0.818037\pi\) | |||||||
\(132\) | −1.05977e6 | + | 1.40648e6i | −0.460776 | + | 0.611522i | ||||
\(133\) | 444277. | 0.188842 | ||||||||
\(134\) | −638357. | − | 1.28028e6i | −0.265307 | − | 0.532097i | ||||
\(135\) | − | 903143.i | − | 0.367075i | ||||||
\(136\) | −638536. | + | 3.44638e6i | −0.253845 | + | 1.37008i | ||||
\(137\) | 3.44256e6 | 1.33881 | 0.669406 | − | 0.742897i | \(-0.266549\pi\) | ||||
0.669406 | + | 0.742897i | \(0.266549\pi\) | |||||||
\(138\) | 1.19143e6 | − | 594055.i | 0.453348 | − | 0.226042i | ||||
\(139\) | − | 5.01559e6i | − | 1.86757i | −0.357831 | − | 0.933787i | \(-0.616483\pi\) | ||
0.357831 | − | 0.933787i | \(-0.383517\pi\) | |||||||
\(140\) | 621843. | + | 468553.i | 0.226619 | + | 0.170755i | ||||
\(141\) | −463657. | −0.165401 | ||||||||
\(142\) | −1.91419e6 | − | 3.83907e6i | −0.668528 | − | 1.34079i | ||||
\(143\) | − | 91906.6i | − | 0.0314296i | ||||||
\(144\) | −401399. | − | 1.39942e6i | −0.134428 | − | 0.468664i | ||||
\(145\) | 1.62683e6 | 0.533627 | ||||||||
\(146\) | −5.20632e6 | + | 2.59590e6i | −1.67291 | + | 0.834123i | ||||
\(147\) | 733189.i | 0.230815i | ||||||||
\(148\) | −3.44371e6 | + | 4.57034e6i | −1.06229 | + | 1.40982i | ||||
\(149\) | −2.90677e6 | −0.878723 | −0.439362 | − | 0.898310i | \(-0.644795\pi\) | ||||
−0.439362 | + | 0.898310i | \(0.644795\pi\) | |||||||
\(150\) | 949948. | + | 1.90521e6i | 0.281466 | + | 0.564506i | ||||
\(151\) | − | 1.83580e6i | − | 0.533206i | −0.963806 | − | 0.266603i | \(-0.914099\pi\) | ||
0.963806 | − | 0.266603i | \(-0.0859013\pi\) | |||||||
\(152\) | −792182. | − | 146773.i | −0.225577 | − | 0.0417942i | ||||
\(153\) | 2.43321e6 | 0.679369 | ||||||||
\(154\) | −2.87775e6 | + | 1.43487e6i | −0.787937 | + | 0.392871i | ||||
\(155\) | − | 691734.i | − | 0.185756i | ||||||
\(156\) | −63777.2 | − | 48055.5i | −0.0167993 | − | 0.0126581i | ||||
\(157\) | 351824. | 0.0909131 | 0.0454566 | − | 0.998966i | \(-0.485526\pi\) | ||||
0.0454566 | + | 0.998966i | \(0.485526\pi\) | |||||||
\(158\) | −1.83691e6 | − | 3.68408e6i | −0.465710 | − | 0.934024i | ||||
\(159\) | − | 1.56272e6i | − | 0.388767i | ||||||
\(160\) | −954004. | − | 1.04090e6i | −0.232911 | − | 0.254127i | ||||
\(161\) | 2.43095e6 | 0.582504 | ||||||||
\(162\) | 1.04526e6 | − | 521173.i | 0.245855 | − | 0.122585i | ||||
\(163\) | − | 5.22903e6i | − | 1.20742i | −0.797204 | − | 0.603710i | \(-0.793688\pi\) | ||
0.797204 | − | 0.603710i | \(-0.206312\pi\) | |||||||
\(164\) | 2.07821e6 | − | 2.75811e6i | 0.471148 | − | 0.625287i | ||||
\(165\) | 1.18566e6 | 0.263943 | ||||||||
\(166\) | −2.00073e6 | − | 4.01264e6i | −0.437385 | − | 0.877215i | ||||
\(167\) | − | 611903.i | − | 0.131381i | −0.997840 | − | 0.0656906i | \(-0.979075\pi\) | ||
0.997840 | − | 0.0656906i | \(-0.0209250\pi\) | |||||||
\(168\) | −508998. | + | 2.74723e6i | −0.107347 | + | 0.579384i | ||||
\(169\) | −4.82264e6 | −0.999137 | ||||||||
\(170\) | 2.11188e6 | − | 1.05300e6i | 0.429855 | − | 0.214329i | ||||
\(171\) | 559296.i | 0.111854i | ||||||||
\(172\) | 5.00559e6 | + | 3.77167e6i | 0.983717 | + | 0.741223i | ||||
\(173\) | 4.58401e6 | 0.885335 | 0.442667 | − | 0.896686i | \(-0.354032\pi\) | ||||
0.442667 | + | 0.896686i | \(0.354032\pi\) | |||||||
\(174\) | 2.60490e6 | + | 5.22437e6i | 0.494474 | + | 0.991712i | ||||
\(175\) | 3.88732e6i | 0.725330i | ||||||||
\(176\) | 5.60530e6 | − | 1.60778e6i | 1.02816 | − | 0.294909i | ||||
\(177\) | 1.97969e6 | 0.357008 | ||||||||
\(178\) | 2.22101e6 | − | 1.10741e6i | 0.393813 | − | 0.196358i | ||||
\(179\) | − | 8.95423e6i | − | 1.56124i | −0.625008 | − | 0.780619i | \(-0.714904\pi\) | ||
0.625008 | − | 0.780619i | \(-0.285096\pi\) | |||||||
\(180\) | −589857. | + | 782832.i | −0.101141 | + | 0.134230i | ||||
\(181\) | −1.98646e6 | −0.334999 | −0.167499 | − | 0.985872i | \(-0.553569\pi\) | ||||
−0.167499 | + | 0.985872i | \(0.553569\pi\) | |||||||
\(182\) | −65064.4 | − | 130492.i | −0.0107927 | − | 0.0216457i | ||||
\(183\) | − | 1.28284e6i | − | 0.209325i | ||||||
\(184\) | −4.33459e6 | − | 803101.i | −0.695817 | − | 0.128919i | ||||
\(185\) | 3.85280e6 | 0.608501 | ||||||||
\(186\) | 2.22142e6 | − | 1.10761e6i | 0.345217 | − | 0.172127i | ||||
\(187\) | 9.74608e6i | 1.49041i | ||||||||
\(188\) | 1.22618e6 | + | 923915.i | 0.184536 | + | 0.139046i | ||||
\(189\) | 5.91775e6 | 0.876538 | ||||||||
\(190\) | 242041. | + | 485434.i | 0.0352880 | + | 0.0707733i | ||||
\(191\) | − | 6.05943e6i | − | 0.869625i | −0.900521 | − | 0.434812i | \(-0.856815\pi\) | ||
0.900521 | − | 0.434812i | \(-0.143185\pi\) | |||||||
\(192\) | 1.81517e6 | − | 4.73038e6i | 0.256457 | − | 0.668332i | ||||
\(193\) | 5.78772e6 | 0.805073 | 0.402537 | − | 0.915404i | \(-0.368129\pi\) | ||||
0.402537 | + | 0.915404i | \(0.368129\pi\) | |||||||
\(194\) | 3.40460e6 | − | 1.69755e6i | 0.466294 | − | 0.232497i | ||||
\(195\) | 53764.2i | 0.00725085i | ||||||||
\(196\) | 1.46100e6 | − | 1.93898e6i | 0.194036 | − | 0.257516i | ||||
\(197\) | −4.55224e6 | −0.595424 | −0.297712 | − | 0.954656i | \(-0.596224\pi\) | ||||
−0.297712 | + | 0.954656i | \(0.596224\pi\) | |||||||
\(198\) | −1.80634e6 | − | 3.62278e6i | −0.232704 | − | 0.466709i | ||||
\(199\) | 5.21399e6i | 0.661624i | 0.943697 | + | 0.330812i | \(0.107323\pi\) | ||||
−0.943697 | + | 0.330812i | \(0.892677\pi\) | |||||||
\(200\) | 1.28423e6 | − | 6.93141e6i | 0.160529 | − | 0.866426i | ||||
\(201\) | −3.45631e6 | −0.425623 | ||||||||
\(202\) | −2.62640e6 | + | 1.30954e6i | −0.318644 | + | 0.158878i | ||||
\(203\) | 1.06596e7i | 1.27425i | ||||||||
\(204\) | 6.76314e6 | + | 5.09597e6i | 0.796632 | + | 0.600256i | ||||
\(205\) | −2.32508e6 | −0.269884 | ||||||||
\(206\) | −2.36458e6 | − | 4.74237e6i | −0.270490 | − | 0.542492i | ||||
\(207\) | 3.06031e6i | 0.345028i | ||||||||
\(208\) | 72905.1 | + | 254174.i | 0.00810155 | + | 0.0282449i | ||||
\(209\) | −2.24022e6 | −0.245388 | ||||||||
\(210\) | 1.68345e6 | − | 839379.i | 0.181778 | − | 0.0906359i | ||||
\(211\) | − | 6.10836e6i | − | 0.650245i | −0.945672 | − | 0.325123i | \(-0.894594\pi\) | ||
0.945672 | − | 0.325123i | \(-0.105406\pi\) | |||||||
\(212\) | −3.11399e6 | + | 4.13274e6i | −0.326820 | + | 0.433741i | ||||
\(213\) | −1.03642e7 | −1.07250 | ||||||||
\(214\) | 2.27827e6 | + | 4.56927e6i | 0.232468 | + | 0.466236i | ||||
\(215\) | − | 4.21972e6i | − | 0.424588i | ||||||
\(216\) | −1.05518e7 | − | 1.95501e6i | −1.04705 | − | 0.193994i | ||||
\(217\) | 4.53251e6 | 0.443568 | ||||||||
\(218\) | 1.10729e7 | − | 5.52103e6i | 1.06879 | − | 0.532906i | ||||
\(219\) | 1.40552e7i | 1.33815i | ||||||||
\(220\) | −3.13559e6 | − | 2.36264e6i | −0.294476 | − | 0.221886i | ||||
\(221\) | −441938. | −0.0409435 | ||||||||
\(222\) | 6.16916e6 | + | 1.23728e7i | 0.563855 | + | 1.13086i | ||||
\(223\) | − | 3.06268e6i | − | 0.276177i | −0.990420 | − | 0.138088i | \(-0.955904\pi\) | ||
0.990420 | − | 0.138088i | \(-0.0440958\pi\) | |||||||
\(224\) | 6.82041e6 | − | 6.25101e6i | 0.606829 | − | 0.556168i | ||||
\(225\) | −4.89371e6 | −0.429626 | ||||||||
\(226\) | −7.05825e6 | + | 3.51929e6i | −0.611465 | + | 0.304880i | ||||
\(227\) | 6.97393e6i | 0.596211i | 0.954533 | + | 0.298106i | \(0.0963548\pi\) | ||||
−0.954533 | + | 0.298106i | \(0.903645\pi\) | |||||||
\(228\) | −1.17135e6 | + | 1.55457e6i | −0.0988289 | + | 0.131161i | ||||
\(229\) | −8.36599e6 | −0.696644 | −0.348322 | − | 0.937375i | \(-0.613248\pi\) | ||||
−0.348322 | + | 0.937375i | \(0.613248\pi\) | |||||||
\(230\) | 1.32438e6 | + | 2.65616e6i | 0.108850 | + | 0.218308i | ||||
\(231\) | 7.76893e6i | 0.630268i | ||||||||
\(232\) | 3.52156e6 | − | 1.90070e7i | 0.282014 | − | 1.52212i | ||||
\(233\) | −778446. | −0.0615404 | −0.0307702 | − | 0.999526i | \(-0.509796\pi\) | ||||
−0.0307702 | + | 0.999526i | \(0.509796\pi\) | |||||||
\(234\) | 164276. | − | 81908.9i | 0.0128211 | − | 0.00639269i | ||||
\(235\) | − | 1.03367e6i | − | 0.0796486i | ||||||
\(236\) | −5.23546e6 | − | 3.94487e6i | −0.398308 | − | 0.300121i | ||||
\(237\) | −9.94573e6 | −0.747122 | ||||||||
\(238\) | 6.89964e6 | + | 1.38379e7i | 0.511795 | + | 1.02645i | ||||
\(239\) | − | 1.27720e7i | − | 0.935546i | −0.883849 | − | 0.467773i | \(-0.845056\pi\) | ||
0.883849 | − | 0.467773i | \(-0.154944\pi\) | |||||||
\(240\) | −3.27903e6 | + | 940530.i | −0.237198 | + | 0.0680360i | ||||
\(241\) | −2.50051e7 | −1.78639 | −0.893197 | − | 0.449666i | \(-0.851543\pi\) | ||||
−0.893197 | + | 0.449666i | \(0.851543\pi\) | |||||||
\(242\) | 1.82750e6 | − | 911203.i | 0.128947 | − | 0.0642938i | ||||
\(243\) | 1.24579e7i | 0.868209i | ||||||||
\(244\) | −2.55628e6 | + | 3.39258e6i | −0.175970 | + | 0.233540i | ||||
\(245\) | −1.63456e6 | −0.111148 | ||||||||
\(246\) | −3.72296e6 | − | 7.46673e6i | −0.250082 | − | 0.501563i | ||||
\(247\) | − | 101583.i | − | 0.00674112i | ||||||
\(248\) | −8.08184e6 | − | 1.49738e6i | −0.529853 | − | 0.0981696i | ||||
\(249\) | −1.08327e7 | −0.701681 | ||||||||
\(250\) | −9.06765e6 | + | 4.52119e6i | −0.580330 | + | 0.289356i | ||||
\(251\) | 1.95555e7i | 1.23665i | 0.785921 | + | 0.618327i | \(0.212189\pi\) | ||||
−0.785921 | + | 0.618327i | \(0.787811\pi\) | |||||||
\(252\) | −5.12942e6 | − | 3.86498e6i | −0.320529 | − | 0.241516i | ||||
\(253\) | −1.22579e7 | −0.756926 | ||||||||
\(254\) | −6.41745e6 | − | 1.28708e7i | −0.391617 | − | 0.785422i | ||||
\(255\) | − | 5.70133e6i | − | 0.343839i | ||||||
\(256\) | −1.42265e7 | + | 8.89284e6i | −0.847963 | + | 0.530055i | ||||
\(257\) | 2.98305e7 | 1.75736 | 0.878682 | − | 0.477408i | \(-0.158423\pi\) | ||||
0.878682 | + | 0.477408i | \(0.158423\pi\) | |||||||
\(258\) | 1.35511e7 | − | 6.75668e6i | 0.789071 | − | 0.393436i | ||||
\(259\) | 2.52451e7i | 1.45304i | ||||||||
\(260\) | 107134. | − | 142184.i | 0.00609549 | − | 0.00808966i | ||||
\(261\) | −1.34193e7 | −0.754759 | ||||||||
\(262\) | −8.68351e6 | − | 1.74156e7i | −0.482827 | − | 0.968352i | ||||
\(263\) | 2.07385e7i | 1.14002i | 0.821639 | + | 0.570008i | \(0.193060\pi\) | ||||
−0.821639 | + | 0.570008i | \(0.806940\pi\) | |||||||
\(264\) | 2.56658e6 | − | 1.38527e7i | 0.139490 | − | 0.752872i | ||||
\(265\) | 3.48390e6 | 0.187210 | ||||||||
\(266\) | −3.18075e6 | + | 1.58595e6i | −0.168999 | + | 0.0842642i | ||||
\(267\) | − | 5.99594e6i | − | 0.315009i | ||||||
\(268\) | 9.14050e6 | + | 6.88729e6i | 0.474860 | + | 0.357803i | ||||
\(269\) | 2.53362e7 | 1.30162 | 0.650811 | − | 0.759240i | \(-0.274429\pi\) | ||||
0.650811 | + | 0.759240i | \(0.274429\pi\) | |||||||
\(270\) | 3.22397e6 | + | 6.46596e6i | 0.163795 | + | 0.328505i | ||||
\(271\) | 2.55619e7i | 1.28435i | 0.766556 | + | 0.642177i | \(0.221969\pi\) | ||||
−0.766556 | + | 0.642177i | \(0.778031\pi\) | |||||||
\(272\) | −7.73110e6 | − | 2.69534e7i | −0.384180 | − | 1.33939i | ||||
\(273\) | −352284. | −0.0173143 | ||||||||
\(274\) | −2.46467e7 | + | 1.22890e7i | −1.19814 | + | 0.597399i | ||||
\(275\) | − | 1.96015e7i | − | 0.942519i | ||||||
\(276\) | −6.40932e6 | + | 8.50616e6i | −0.304849 | + | 0.404582i | ||||
\(277\) | 2.15062e7 | 1.01187 | 0.505935 | − | 0.862572i | \(-0.331148\pi\) | ||||
0.505935 | + | 0.862572i | \(0.331148\pi\) | |||||||
\(278\) | 1.79043e7 | + | 3.59086e7i | 0.833340 | + | 1.67134i | ||||
\(279\) | 5.70594e6i | 0.262733i | ||||||||
\(280\) | −6.12463e6 | − | 1.13475e6i | −0.279001 | − | 0.0516925i | ||||
\(281\) | −1.14760e7 | −0.517216 | −0.258608 | − | 0.965982i | \(-0.583264\pi\) | ||||
−0.258608 | + | 0.965982i | \(0.583264\pi\) | |||||||
\(282\) | 3.31951e6 | − | 1.65513e6i | 0.148022 | − | 0.0738047i | ||||
\(283\) | − | 2.77075e7i | − | 1.22247i | −0.791450 | − | 0.611234i | \(-0.790674\pi\) | ||
0.791450 | − | 0.611234i | \(-0.209326\pi\) | |||||||
\(284\) | 2.74089e7 | + | 2.06524e7i | 1.19657 | + | 0.901602i | ||||
\(285\) | 1.31050e6 | 0.0566113 | ||||||||
\(286\) | 328081. | + | 657996.i | 0.0140244 | + | 0.0281271i | ||||
\(287\) | − | 1.52349e7i | − | 0.644456i | ||||||
\(288\) | 7.86933e6 | + | 8.58615e6i | 0.329428 | + | 0.359436i | ||||
\(289\) | 2.27270e7 | 0.941562 | ||||||||
\(290\) | −1.16471e7 | + | 5.80733e6i | −0.477556 | + | 0.238113i | ||||
\(291\) | − | 9.19122e6i | − | 0.372987i | ||||||
\(292\) | 2.80075e7 | − | 3.71702e7i | 1.12493 | − | 1.49296i | ||||
\(293\) | −951701. | −0.0378353 | −0.0189177 | − | 0.999821i | \(-0.506022\pi\) | ||||
−0.0189177 | + | 0.999821i | \(0.506022\pi\) | |||||||
\(294\) | −2.61728e6 | − | 5.24920e6i | −0.102993 | − | 0.206562i | ||||
\(295\) | 4.41349e6i | 0.171916i | ||||||||
\(296\) | 8.34007e6 | − | 4.50140e7i | 0.321584 | − | 1.73569i | ||||
\(297\) | −2.98397e7 | −1.13900 | ||||||||
\(298\) | 2.08108e7 | − | 1.03764e7i | 0.786392 | − | 0.392100i | ||||
\(299\) | − | 555836.i | − | 0.0207938i | ||||||
\(300\) | −1.36021e7 | − | 1.02491e7i | −0.503782 | − | 0.379596i | ||||
\(301\) | 2.76492e7 | 1.01387 | ||||||||
\(302\) | 6.55331e6 | + | 1.31433e7i | 0.237925 | + | 0.477180i | ||||
\(303\) | 7.09035e6i | 0.254882i | ||||||||
\(304\) | 6.19549e6 | − | 1.77706e6i | 0.220524 | − | 0.0632532i | ||||
\(305\) | 2.85995e6 | 0.100800 | ||||||||
\(306\) | −1.74203e7 | + | 8.68590e6i | −0.607984 | + | 0.303145i | ||||
\(307\) | − | 5.68676e6i | − | 0.196539i | −0.995160 | − | 0.0982697i | \(-0.968669\pi\) | ||
0.995160 | − | 0.0982697i | \(-0.0313308\pi\) | |||||||
\(308\) | 1.54809e7 | − | 2.05456e7i | 0.529840 | − | 0.703180i | ||||
\(309\) | −1.28027e7 | −0.433938 | ||||||||
\(310\) | 2.46930e6 | + | 4.95240e6i | 0.0828874 | + | 0.166238i | ||||
\(311\) | − | 3.40240e7i | − | 1.13111i | −0.824711 | − | 0.565554i | \(-0.808662\pi\) | ||
0.824711 | − | 0.565554i | \(-0.191338\pi\) | |||||||
\(312\) | 628152. | + | 116382.i | 0.0206824 | + | 0.00383197i | ||||
\(313\) | 1.98948e7 | 0.648795 | 0.324398 | − | 0.945921i | \(-0.394838\pi\) | ||||
0.324398 | + | 0.945921i | \(0.394838\pi\) | |||||||
\(314\) | −2.51885e6 | + | 1.25592e6i | −0.0813605 | + | 0.0405669i | ||||
\(315\) | 4.32410e6i | 0.138345i | ||||||||
\(316\) | 2.63023e7 | + | 1.98186e7i | 0.833552 | + | 0.628074i | ||||
\(317\) | 4.51404e7 | 1.41706 | 0.708530 | − | 0.705681i | \(-0.249359\pi\) | ||||
0.708530 | + | 0.705681i | \(0.249359\pi\) | |||||||
\(318\) | 5.57848e6 | + | 1.11881e7i | 0.173474 | + | 0.347918i | ||||
\(319\) | − | 5.37502e7i | − | 1.65580i | ||||||
\(320\) | 1.05458e7 | + | 4.04672e6i | 0.321833 | + | 0.123496i | ||||
\(321\) | 1.23354e7 | 0.372940 | ||||||||
\(322\) | −1.74042e7 | + | 8.67784e6i | −0.521298 | + | 0.259923i | ||||
\(323\) | 1.07723e7i | 0.319668i | ||||||||
\(324\) | −5.62299e6 | + | 7.46258e6i | −0.165323 | + | 0.219409i | ||||
\(325\) | 888832. | 0.0258922 | ||||||||
\(326\) | 1.86662e7 | + | 3.74367e7i | 0.538770 | + | 1.08055i | ||||
\(327\) | − | 2.98930e7i | − | 0.854922i | ||||||
\(328\) | −5.03306e6 | + | 2.71650e7i | −0.142630 | + | 0.769819i | ||||
\(329\) | 6.77301e6 | 0.190193 | ||||||||
\(330\) | −8.48864e6 | + | 4.23249e6i | −0.236209 | + | 0.117775i | ||||
\(331\) | − | 2.76425e7i | − | 0.762243i | −0.924525 | − | 0.381121i | \(-0.875538\pi\) | ||
0.924525 | − | 0.381121i | \(-0.124462\pi\) | |||||||
\(332\) | 2.86481e7 | + | 2.15861e7i | 0.782854 | + | 0.589874i | ||||
\(333\) | −3.17808e7 | −0.860660 | ||||||||
\(334\) | 2.18432e6 | + | 4.38086e6i | 0.0586243 | + | 0.117576i | ||||
\(335\) | − | 7.70545e6i | − | 0.204957i | ||||||
\(336\) | −6.16272e6 | − | 2.14855e7i | −0.162463 | − | 0.566406i | ||||
\(337\) | 3.15251e7 | 0.823696 | 0.411848 | − | 0.911253i | \(-0.364883\pi\) | ||||
0.411848 | + | 0.911253i | \(0.364883\pi\) | |||||||
\(338\) | 3.45272e7 | − | 1.72155e7i | 0.894153 | − | 0.445830i | ||||
\(339\) | 1.90548e7i | 0.489109i | ||||||||
\(340\) | −1.13609e7 | + | 1.50776e7i | −0.289051 | + | 0.383616i | ||||
\(341\) | −2.28548e7 | −0.576387 | ||||||||
\(342\) | −1.99653e6 | − | 4.00422e6i | −0.0499112 | − | 0.100101i | ||||
\(343\) | − | 4.39271e7i | − | 1.08855i | ||||||
\(344\) | −4.93009e7 | − | 9.13433e6i | −1.21110 | − | 0.224389i | ||||
\(345\) | 7.17070e6 | 0.174624 | ||||||||
\(346\) | −3.28188e7 | + | 1.63637e7i | −0.792309 | + | 0.395050i | ||||
\(347\) | 4.77274e7i | 1.14230i | 0.820846 | + | 0.571149i | \(0.193502\pi\) | ||||
−0.820846 | + | 0.571149i | \(0.806498\pi\) | |||||||
\(348\) | −3.72991e7 | − | 2.81046e7i | −0.885035 | − | 0.666867i | ||||
\(349\) | −4.37619e7 | −1.02949 | −0.514743 | − | 0.857345i | \(-0.672112\pi\) | ||||
−0.514743 | + | 0.857345i | \(0.672112\pi\) | |||||||
\(350\) | −1.38767e7 | − | 2.78309e7i | −0.323654 | − | 0.649117i | ||||
\(351\) | − | 1.35309e6i | − | 0.0312899i | ||||||
\(352\) | −3.43913e7 | + | 3.15201e7i | −0.788534 | + | 0.722703i | ||||
\(353\) | −6.05613e7 | −1.37680 | −0.688401 | − | 0.725331i | \(-0.741687\pi\) | ||||
−0.688401 | + | 0.725331i | \(0.741687\pi\) | |||||||
\(354\) | −1.41734e7 | + | 7.06695e6i | −0.319495 | + | 0.159302i | ||||
\(355\) | − | 2.31057e7i | − | 0.516457i | ||||||
\(356\) | −1.19479e7 | + | 1.58568e7i | −0.264815 | + | 0.351451i | ||||
\(357\) | 3.73574e7 | 0.821054 | ||||||||
\(358\) | 3.19641e7 | + | 6.41069e7i | 0.696649 | + | 1.39719i | ||||
\(359\) | − | 6.33798e7i | − | 1.36983i | −0.728622 | − | 0.684916i | \(-0.759839\pi\) | ||
0.728622 | − | 0.684916i | \(-0.240161\pi\) | |||||||
\(360\) | 1.42853e6 | − | 7.71024e6i | 0.0306184 | − | 0.165257i | ||||
\(361\) | −2.47610e6 | −0.0526316 | ||||||||
\(362\) | 1.42218e7 | − | 7.09110e6i | 0.299799 | − | 0.149482i | ||||
\(363\) | − | 4.93361e6i | − | 0.103144i | ||||||
\(364\) | 931644. | + | 701986.i | 0.0193173 | + | 0.0145554i | ||||
\(365\) | −3.13345e7 | −0.644384 | ||||||||
\(366\) | 4.57940e6 | + | 9.18439e6i | 0.0934039 | + | 0.187330i | ||||
\(367\) | − | 7.53606e7i | − | 1.52457i | −0.647244 | − | 0.762283i | \(-0.724079\pi\) | ||
0.647244 | − | 0.762283i | \(-0.275921\pi\) | |||||||
\(368\) | 3.39000e7 | − | 9.72359e6i | 0.680230 | − | 0.195112i | ||||
\(369\) | 1.91790e7 | 0.381722 | ||||||||
\(370\) | −2.75837e7 | + | 1.37534e7i | −0.544563 | + | 0.271523i | ||||
\(371\) | 2.28279e7i | 0.447038i | ||||||||
\(372\) | −1.19502e7 | + | 1.58597e7i | −0.232137 | + | 0.308082i | ||||
\(373\) | 9.87750e7 | 1.90336 | 0.951679 | − | 0.307096i | \(-0.0993571\pi\) | ||||
0.951679 | + | 0.307096i | \(0.0993571\pi\) | |||||||
\(374\) | −3.47908e7 | − | 6.97761e7i | −0.665043 | − | 1.33380i | ||||
\(375\) | 2.44795e7i | 0.464204i | ||||||||
\(376\) | −1.20768e7 | − | 2.23756e6i | −0.227190 | − | 0.0420931i | ||||
\(377\) | 2.43731e6 | 0.0454870 | ||||||||
\(378\) | −4.23675e7 | + | 2.11247e7i | −0.784437 | + | 0.391125i | ||||
\(379\) | 9.59013e7i | 1.76160i | 0.473491 | + | 0.880799i | \(0.342994\pi\) | ||||
−0.473491 | + | 0.880799i | \(0.657006\pi\) | |||||||
\(380\) | −3.46573e6 | − | 2.61140e6i | −0.0631603 | − | 0.0475908i | ||||
\(381\) | −3.47466e7 | −0.628256 | ||||||||
\(382\) | 2.16305e7 | + | 4.33819e7i | 0.388040 | + | 0.778249i | ||||
\(383\) | 4.83660e7i | 0.860882i | 0.902619 | + | 0.430441i | \(0.141642\pi\) | ||||
−0.902619 | + | 0.430441i | \(0.858358\pi\) | |||||||
\(384\) | 3.89060e6 | + | 4.03464e7i | 0.0687105 | + | 0.712543i | ||||
\(385\) | −1.73199e7 | −0.303504 | ||||||||
\(386\) | −4.14366e7 | + | 2.06606e7i | −0.720481 | + | 0.359236i | ||||
\(387\) | 3.48074e7i | 0.600535i | ||||||||
\(388\) | −1.83151e7 | + | 2.43069e7i | −0.313555 | + | 0.416136i | ||||
\(389\) | 2.77967e7 | 0.472220 | 0.236110 | − | 0.971726i | \(-0.424127\pi\) | ||||
0.236110 | + | 0.971726i | \(0.424127\pi\) | |||||||
\(390\) | −191923. | − | 384919.i | −0.00323544 | − | 0.00648897i | ||||
\(391\) | 5.89427e7i | 0.986052i | ||||||||
\(392\) | −3.53830e6 | + | 1.90973e7i | −0.0587403 | + | 0.317040i | ||||
\(393\) | −4.70159e7 | −0.774582 | ||||||||
\(394\) | 3.25913e7 | − | 1.62502e7i | 0.532860 | − | 0.265688i | ||||
\(395\) | − | 2.21729e7i | − | 0.359775i | ||||||
\(396\) | 2.58646e7 | + | 1.94888e7i | 0.416506 | + | 0.313834i | ||||
\(397\) | 8.91953e7 | 1.42551 | 0.712756 | − | 0.701412i | \(-0.247447\pi\) | ||||
0.712756 | + | 0.701412i | \(0.247447\pi\) | |||||||
\(398\) | −1.86125e7 | − | 3.73291e7i | −0.295227 | − | 0.592104i | ||||
\(399\) | 8.58693e6i | 0.135182i | ||||||||
\(400\) | 1.55489e7 | + | 5.42091e7i | 0.242952 | + | 0.847017i | ||||
\(401\) | −2.66394e6 | −0.0413134 | −0.0206567 | − | 0.999787i | \(-0.506576\pi\) | ||||
−0.0206567 | + | 0.999787i | \(0.506576\pi\) | |||||||
\(402\) | 2.47451e7 | − | 1.23381e7i | 0.380901 | − | 0.189920i | ||||
\(403\) | − | 1.03636e6i | − | 0.0158341i | ||||||
\(404\) | 1.41287e7 | − | 1.87510e7i | 0.214269 | − | 0.284368i | ||||
\(405\) | 6.29096e6 | 0.0947004 | ||||||||
\(406\) | −3.80519e7 | − | 7.63165e7i | −0.568589 | − | 1.14036i | ||||
\(407\) | − | 1.27296e8i | − | 1.88813i | ||||||
\(408\) | −6.66113e7 | − | 1.23415e7i | −0.980770 | − | 0.181714i | ||||
\(409\) | −8.84457e7 | −1.29273 | −0.646364 | − | 0.763030i | \(-0.723711\pi\) | ||||
−0.646364 | + | 0.763030i | \(0.723711\pi\) | |||||||
\(410\) | 1.66462e7 | − | 8.29991e6i | 0.241526 | − | 0.120426i | ||||
\(411\) | 6.65374e7i | 0.958385i | ||||||||
\(412\) | 3.38579e7 | + | 2.55116e7i | 0.484137 | + | 0.364793i | ||||
\(413\) | −2.89189e7 | −0.410518 | ||||||||
\(414\) | −1.09245e7 | − | 2.19100e7i | −0.153957 | − | 0.308774i | ||||
\(415\) | − | 2.41503e7i | − | 0.337893i | ||||||
\(416\) | −1.42929e6 | − | 1.55948e6i | −0.0198536 | − | 0.0216621i | ||||
\(417\) | 9.69408e7 | 1.33690 | ||||||||
\(418\) | 1.60387e7 | − | 7.99699e6i | 0.219604 | − | 0.109496i | ||||
\(419\) | − | 2.40174e7i | − | 0.326500i | −0.986585 | − | 0.163250i | \(-0.947802\pi\) | ||
0.986585 | − | 0.163250i | \(-0.0521978\pi\) | |||||||
\(420\) | −9.05614e6 | + | 1.20189e7i | −0.122235 | + | 0.162225i | ||||
\(421\) | 1.78676e7 | 0.239453 | 0.119726 | − | 0.992807i | \(-0.461798\pi\) | ||||
0.119726 | + | 0.992807i | \(0.461798\pi\) | |||||||
\(422\) | 2.18052e7 | + | 4.37322e7i | 0.290150 | + | 0.581921i | ||||
\(423\) | 8.52647e6i | 0.112654i | ||||||||
\(424\) | 7.54153e6 | − | 4.07040e7i | 0.0989377 | − | 0.533998i | ||||
\(425\) | −9.42547e7 | −1.22782 | ||||||||
\(426\) | 7.42012e7 | − | 3.69972e7i | 0.959803 | − | 0.478564i | ||||
\(427\) | 1.87395e7i | 0.240699i | ||||||||
\(428\) | −3.26221e7 | − | 2.45805e7i | −0.416083 | − | 0.313515i | ||||
\(429\) | 1.77636e6 | 0.0224988 | ||||||||
\(430\) | 1.50632e7 | + | 3.02107e7i | 0.189458 | + | 0.379975i | ||||
\(431\) | 1.36332e8i | 1.70281i | 0.524506 | + | 0.851407i | \(0.324250\pi\) | ||||
−0.524506 | + | 0.851407i | \(0.675750\pi\) | |||||||
\(432\) | 8.25237e7 | − | 2.36704e7i | 1.02359 | − | 0.293599i | ||||
\(433\) | −6.16047e7 | −0.758840 | −0.379420 | − | 0.925225i | \(-0.623876\pi\) | ||||
−0.379420 | + | 0.925225i | \(0.623876\pi\) | |||||||
\(434\) | −3.24501e7 | + | 1.61798e7i | −0.396960 | + | 0.197927i | ||||
\(435\) | 3.14432e7i | 0.381996i | ||||||||
\(436\) | −5.95669e7 | + | 7.90545e7i | −0.718697 | + | 0.953822i | ||||
\(437\) | −1.35485e7 | −0.162348 | ||||||||
\(438\) | −5.01733e7 | − | 1.00627e8i | −0.597105 | − | 1.19755i | ||||
\(439\) | − | 1.61483e8i | − | 1.90869i | −0.298713 | − | 0.954343i | \(-0.596557\pi\) | ||
0.298713 | − | 0.954343i | \(-0.403443\pi\) | |||||||
\(440\) | 3.08829e7 | + | 5.72189e6i | 0.362543 | + | 0.0671710i | ||||
\(441\) | 1.34831e7 | 0.157207 | ||||||||
\(442\) | 3.16401e6 | − | 1.57760e6i | 0.0366414 | − | 0.0182696i | ||||
\(443\) | − | 5.94878e7i | − | 0.684252i | −0.939654 | − | 0.342126i | \(-0.888853\pi\) | ||
0.939654 | − | 0.342126i | \(-0.111147\pi\) | |||||||
\(444\) | −8.83350e7 | − | 6.65597e7i | −1.00922 | − | 0.760436i | ||||
\(445\) | 1.33673e7 | 0.151692 | ||||||||
\(446\) | 1.09329e7 | + | 2.19270e7i | 0.123234 | + | 0.247157i | ||||
\(447\) | − | 5.61818e7i | − | 0.629032i | ||||||
\(448\) | −2.65157e7 | + | 6.91005e7i | −0.294896 | + | 0.768505i | ||||
\(449\) | 5.06345e7 | 0.559381 | 0.279690 | − | 0.960090i | \(-0.409768\pi\) | ||||
0.279690 | + | 0.960090i | \(0.409768\pi\) | |||||||
\(450\) | 3.50360e7 | − | 1.74692e7i | 0.384483 | − | 0.191706i | ||||
\(451\) | 7.68204e7i | 0.837427i | ||||||||
\(452\) | 3.79700e7 | − | 5.03920e7i | 0.411173 | − | 0.545690i | ||||
\(453\) | 3.54822e7 | 0.381695 | ||||||||
\(454\) | −2.48950e7 | − | 4.99292e7i | −0.266039 | − | 0.533565i | ||||
\(455\) | − | 785377.i | − | 0.00833765i | ||||||
\(456\) | 2.83682e6 | − | 1.53112e7i | 0.0299183 | − | 0.161479i | ||||
\(457\) | −1.24003e8 | −1.29922 | −0.649610 | − | 0.760267i | \(-0.725068\pi\) | ||||
−0.649610 | + | 0.760267i | \(0.725068\pi\) | |||||||
\(458\) | 5.98955e7 | − | 2.98643e7i | 0.623445 | − | 0.310854i | ||||
\(459\) | 1.43486e8i | 1.48379i | ||||||||
\(460\) | −1.89635e7 | − | 1.42888e7i | −0.194825 | − | 0.146799i | ||||
\(461\) | 4.15495e7 | 0.424095 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(462\) | −2.77330e7 | − | 5.56209e7i | −0.281236 | − | 0.564043i | ||||
\(463\) | − | 3.90890e7i | − | 0.393832i | −0.980420 | − | 0.196916i | \(-0.936907\pi\) | ||
0.980420 | − | 0.196916i | \(-0.0630927\pi\) | |||||||
\(464\) | 4.26374e7 | + | 1.48650e8i | 0.426813 | + | 1.48802i | ||||
\(465\) | 1.33698e7 | 0.132973 | ||||||||
\(466\) | 5.57321e6 | − | 2.77884e6i | 0.0550741 | − | 0.0274603i | ||||
\(467\) | 1.69657e8i | 1.66580i | 0.553425 | + | 0.832899i | \(0.313320\pi\) | ||||
−0.553425 | + | 0.832899i | \(0.686680\pi\) | |||||||
\(468\) | −883724. | + | 1.17284e6i | −0.00862142 | + | 0.0114420i | ||||
\(469\) | 5.04891e7 | 0.489417 | ||||||||
\(470\) | 3.68991e6 | + | 7.40045e6i | 0.0355404 | + | 0.0712795i | ||||
\(471\) | 6.80002e6i | 0.0650799i | ||||||||
\(472\) | 5.15649e7 | + | 9.55379e6i | 0.490374 | + | 0.0908551i | ||||
\(473\) | −1.39419e8 | −1.31746 | ||||||||
\(474\) | 7.12055e7 | − | 3.55035e7i | 0.668619 | − | 0.333378i | ||||
\(475\) | − | 2.16653e7i | − | 0.202155i | ||||||
\(476\) | −9.87947e7 | − | 7.44409e7i | −0.916036 | − | 0.690225i | ||||
\(477\) | −2.87378e7 | −0.264788 | ||||||||
\(478\) | 4.55925e7 | + | 9.14399e7i | 0.417455 | + | 0.837244i | ||||
\(479\) | 1.19896e8i | 1.09093i | 0.838134 | + | 0.545465i | \(0.183647\pi\) | ||||
−0.838134 | + | 0.545465i | \(0.816353\pi\) | |||||||
\(480\) | 2.01185e7 | − | 1.84389e7i | 0.181916 | − | 0.166729i | ||||
\(481\) | 5.77226e6 | 0.0518694 | ||||||||
\(482\) | 1.79021e8 | − | 8.92613e7i | 1.59869 | − | 0.797117i | ||||
\(483\) | 4.69852e7i | 0.416985i | ||||||||
\(484\) | −9.83106e6 | + | 1.30473e7i | −0.0867090 | + | 0.115076i | ||||
\(485\) | 2.04908e7 | 0.179611 | ||||||||
\(486\) | −4.44711e7 | − | 8.91908e7i | −0.387409 | − | 0.776983i | ||||
\(487\) | − | 9.71669e7i | − | 0.841262i | −0.907232 | − | 0.420631i | \(-0.861809\pi\) | ||
0.907232 | − | 0.420631i | \(-0.138191\pi\) | |||||||
\(488\) | 6.19087e6 | − | 3.34141e7i | 0.0532712 | − | 0.287522i | ||||
\(489\) | 1.01066e8 | 0.864329 | ||||||||
\(490\) | 1.17025e7 | − | 5.83493e6i | 0.0994694 | − | 0.0495961i | ||||
\(491\) | 1.28590e8i | 1.08634i | 0.839624 | + | 0.543168i | \(0.182775\pi\) | ||||
−0.839624 | + | 0.543168i | \(0.817225\pi\) | |||||||
\(492\) | 5.33084e7 | + | 4.01674e7i | 0.447610 | + | 0.337271i | ||||
\(493\) | −2.58461e8 | −2.15702 | ||||||||
\(494\) | 362625. | + | 727277.i | 0.00300799 | + | 0.00603280i | ||||
\(495\) | − | 2.18039e7i | − | 0.179771i | ||||||
\(496\) | 6.32064e7 | − | 1.81296e7i | 0.517984 | − | 0.148574i | ||||
\(497\) | 1.51398e8 | 1.23325 | ||||||||
\(498\) | 7.75559e7 | − | 3.86699e7i | 0.627953 | − | 0.313101i | ||||
\(499\) | − | 5.54855e7i | − | 0.446558i | −0.974755 | − | 0.223279i | \(-0.928324\pi\) | ||
0.974755 | − | 0.223279i | \(-0.0716761\pi\) | |||||||
\(500\) | 4.87796e7 | − | 6.47381e7i | 0.390237 | − | 0.517904i | ||||
\(501\) | 1.18268e7 | 0.0940489 | ||||||||
\(502\) | −6.98078e7 | − | 1.40006e8i | −0.551814 | − | 1.10671i | ||||
\(503\) | 4.66881e7i | 0.366861i | 0.983033 | + | 0.183431i | \(0.0587203\pi\) | ||||
−0.983033 | + | 0.183431i | \(0.941280\pi\) | |||||||
\(504\) | 5.05205e7 | + | 9.36029e6i | 0.394617 | + | 0.0731135i | ||||
\(505\) | −1.58071e7 | −0.122738 | ||||||||
\(506\) | 8.77591e7 | − | 4.37572e7i | 0.677392 | − | 0.337752i | ||||
\(507\) | − | 9.32115e7i | − | 0.715230i | ||||||
\(508\) | 9.18902e7 | + | 6.92384e7i | 0.700935 | + | 0.528149i | ||||
\(509\) | −6.56054e7 | −0.497492 | −0.248746 | − | 0.968569i | \(-0.580019\pi\) | ||||
−0.248746 | + | 0.968569i | \(0.580019\pi\) | |||||||
\(510\) | 2.03522e7 | + | 4.08181e7i | 0.153427 | + | 0.307711i | ||||
\(511\) | − | 2.05316e8i | − | 1.53872i | ||||||
\(512\) | 7.01080e7 | − | 1.14452e8i | 0.522345 | − | 0.852734i | ||||
\(513\) | −3.29815e7 | −0.244297 | ||||||||
\(514\) | −2.13569e8 | + | 1.06487e8i | −1.57271 | + | 0.784163i | ||||
\(515\) | − | 2.85422e7i | − | 0.208961i | ||||||
\(516\) | −7.28985e7 | + | 9.67476e7i | −0.530602 | + | 0.704192i | ||||
\(517\) | −3.41523e7 | −0.247143 | ||||||||
\(518\) | −9.01179e7 | − | 1.80740e8i | −0.648368 | − | 1.30036i | ||||
\(519\) | 8.85993e7i | 0.633765i | ||||||||
\(520\) | −259460. | + | 1.40039e6i | −0.00184528 | + | 0.00995954i | ||||
\(521\) | −3.52168e7 | −0.249021 | −0.124511 | − | 0.992218i | \(-0.539736\pi\) | ||||
−0.124511 | + | 0.992218i | \(0.539736\pi\) | |||||||
\(522\) | 9.60741e7 | − | 4.79032e7i | 0.675453 | − | 0.336785i | ||||
\(523\) | − | 1.22732e8i | − | 0.857933i | −0.903320 | − | 0.428967i | \(-0.858878\pi\) | ||
0.903320 | − | 0.428967i | \(-0.141122\pi\) | |||||||
\(524\) | 1.24337e8 | + | 9.36872e7i | 0.864188 | + | 0.651158i | ||||
\(525\) | −7.51336e7 | −0.519226 | ||||||||
\(526\) | −7.40309e7 | − | 1.48476e8i | −0.508693 | − | 1.02023i | ||||
\(527\) | 1.09899e8i | 0.750862i | ||||||||
\(528\) | 3.10750e7 | + | 1.08339e8i | 0.211110 | + | 0.736007i | ||||
\(529\) | 7.39023e7 | 0.499219 | ||||||||
\(530\) | −2.49427e7 | + | 1.24366e7i | −0.167539 | + | 0.0835359i | ||||
\(531\) | − | 3.64058e7i | − | 0.243157i | ||||||
\(532\) | 1.71109e7 | − | 2.27088e7i | 0.113642 | − | 0.150820i | ||||
\(533\) | −3.48344e6 | −0.0230052 | ||||||||
\(534\) | 2.14039e7 | + | 4.29273e7i | 0.140562 | + | 0.281910i | ||||
\(535\) | 2.75004e7i | 0.179588i | ||||||||
\(536\) | −9.00263e7 | − | 1.66798e7i | −0.584622 | − | 0.108317i | ||||
\(537\) | 1.73066e8 | 1.11761 | ||||||||
\(538\) | −1.81392e8 | + | 9.04434e7i | −1.16486 | + | 0.580804i | ||||
\(539\) | 5.40056e7i | 0.344884i | ||||||||
\(540\) | −4.61634e7 | − | 3.47838e7i | −0.293168 | − | 0.220900i | ||||
\(541\) | 1.84803e8 | 1.16712 | 0.583562 | − | 0.812068i | \(-0.301658\pi\) | ||||
0.583562 | + | 0.812068i | \(0.301658\pi\) | |||||||
\(542\) | −9.12489e7 | − | 1.83008e8i | −0.573099 | − | 1.14940i | ||||
\(543\) | − | 3.83940e7i | − | 0.239808i | ||||||
\(544\) | 1.51566e8 | + | 1.65373e8i | 0.941470 | + | 1.02723i | ||||
\(545\) | 6.66430e7 | 0.411685 | ||||||||
\(546\) | 2.52214e6 | − | 1.25756e6i | 0.0154950 | − | 0.00772591i | ||||
\(547\) | 1.70180e8i | 1.03979i | 0.854230 | + | 0.519895i | \(0.174029\pi\) | ||||
−0.854230 | + | 0.519895i | \(0.825971\pi\) | |||||||
\(548\) | 1.32587e8 | − | 1.75964e8i | 0.805674 | − | 1.06925i | ||||
\(549\) | −2.35910e7 | −0.142570 | ||||||||
\(550\) | 6.99718e7 | + | 1.40335e8i | 0.420567 | + | 0.843484i | ||||
\(551\) | − | 5.94095e7i | − | 0.355142i | ||||||
\(552\) | 1.55222e7 | − | 8.37786e7i | 0.0922863 | − | 0.498099i | ||||
\(553\) | 1.45285e8 | 0.859105 | ||||||||
\(554\) | −1.53972e8 | + | 7.67712e7i | −0.905547 | + | 0.451512i | ||||
\(555\) | 7.44665e7i | 0.435594i | ||||||||
\(556\) | −2.56368e8 | − | 1.93171e8i | −1.49156 | − | 1.12387i | ||||
\(557\) | −1.27648e8 | −0.738664 | −0.369332 | − | 0.929298i | \(-0.620413\pi\) | ||||
−0.369332 | + | 0.929298i | \(0.620413\pi\) | |||||||
\(558\) | −2.03686e7 | − | 4.08511e7i | −0.117236 | − | 0.235126i | ||||
\(559\) | − | 6.32198e6i | − | 0.0361924i | ||||||
\(560\) | 4.78994e7 | − | 1.37391e7i | 0.272751 | − | 0.0782337i | ||||
\(561\) | −1.88371e8 | −1.06691 | ||||||||
\(562\) | 8.21614e7 | − | 4.09662e7i | 0.462870 | − | 0.230790i | ||||
\(563\) | 1.68278e8i | 0.942978i | 0.881872 | + | 0.471489i | \(0.156283\pi\) | ||||
−0.881872 | + | 0.471489i | \(0.843717\pi\) | |||||||
\(564\) | −1.78573e7 | + | 2.36994e7i | −0.0995358 | + | 0.132099i | ||||
\(565\) | −4.24805e7 | −0.235529 | ||||||||
\(566\) | 9.89080e7 | + | 1.98369e8i | 0.545484 | + | 1.09402i | ||||
\(567\) | 4.12208e7i | 0.226135i | ||||||||
\(568\) | −2.69955e8 | − | 5.00164e7i | −1.47315 | − | 0.272940i | ||||
\(569\) | 2.36146e8 | 1.28187 | 0.640933 | − | 0.767597i | \(-0.278547\pi\) | ||||
0.640933 | + | 0.767597i | \(0.278547\pi\) | |||||||
\(570\) | −9.38242e6 | + | 4.67813e6i | −0.0506629 | + | 0.0252609i | ||||
\(571\) | − | 1.96411e8i | − | 1.05501i | −0.849551 | − | 0.527506i | \(-0.823127\pi\) | ||
0.849551 | − | 0.527506i | \(-0.176873\pi\) | |||||||
\(572\) | −4.69773e6 | − | 3.53970e6i | −0.0251015 | − | 0.0189138i | ||||
\(573\) | 1.17116e8 | 0.622519 | ||||||||
\(574\) | 5.43843e7 | + | 1.09073e8i | 0.287566 | + | 0.576740i | ||||
\(575\) | − | 1.18546e8i | − | 0.623569i | ||||||
\(576\) | −8.69899e7 | − | 3.33804e7i | −0.455199 | − | 0.174672i | ||||
\(577\) | 1.75233e8 | 0.912198 | 0.456099 | − | 0.889929i | \(-0.349246\pi\) | ||||
0.456099 | + | 0.889929i | \(0.349246\pi\) | |||||||
\(578\) | −1.62712e8 | + | 8.11292e7i | −0.842628 | + | 0.420140i | ||||
\(579\) | 1.11864e8i | 0.576310i | ||||||||
\(580\) | 6.26559e7 | − | 8.31540e7i | 0.321128 | − | 0.426186i | ||||
\(581\) | 1.58242e8 | 0.806853 | ||||||||
\(582\) | 3.28101e7 | + | 6.58036e7i | 0.166433 | + | 0.333796i | ||||
\(583\) | − | 1.15108e8i | − | 0.580896i | ||||||
\(584\) | −6.78291e7 | + | 3.66096e8i | −0.340548 | + | 1.83804i | ||||
\(585\) | 988703. | 0.00493854 | ||||||||
\(586\) | 6.81361e6 | − | 3.39731e6i | 0.0338598 | − | 0.0168827i | ||||
\(587\) | 2.00189e8i | 0.989751i | 0.868964 | + | 0.494875i | \(0.164786\pi\) | ||||
−0.868964 | + | 0.494875i | \(0.835214\pi\) | |||||||
\(588\) | 3.74764e7 | + | 2.82381e7i | 0.184343 | + | 0.138901i | ||||
\(589\) | −2.52612e7 | −0.123625 | ||||||||
\(590\) | −1.57550e7 | − | 3.15980e7i | −0.0767116 | − | 0.153852i | ||||
\(591\) | − | 8.79852e7i | − | 0.426233i | ||||||
\(592\) | 1.00978e8 | + | 3.52045e8i | 0.486699 | + | 1.69681i | ||||
\(593\) | −3.18572e8 | −1.52772 | −0.763860 | − | 0.645382i | \(-0.776698\pi\) | ||||
−0.763860 | + | 0.645382i | \(0.776698\pi\) | |||||||
\(594\) | 2.13635e8 | − | 1.06520e8i | 1.01932 | − | 0.508241i | ||||
\(595\) | 8.32839e7i | 0.395376i | ||||||||
\(596\) | −1.11952e8 | + | 1.48577e8i | −0.528801 | + | 0.701801i | ||||
\(597\) | −1.00776e8 | −0.473622 | ||||||||
\(598\) | 1.98418e6 | + | 3.97945e6i | 0.00927850 | + | 0.0186089i | ||||
\(599\) | − | 2.78200e8i | − | 1.29442i | −0.762311 | − | 0.647211i | \(-0.775935\pi\) | ||
0.762311 | − | 0.647211i | \(-0.224065\pi\) | |||||||
\(600\) | 1.33970e8 | + | 2.48215e7i | 0.620229 | + | 0.114914i | ||||
\(601\) | 3.80068e6 | 0.0175080 | 0.00875402 | − | 0.999962i | \(-0.497213\pi\) | ||||
0.00875402 | + | 0.999962i | \(0.497213\pi\) | |||||||
\(602\) | −1.97952e8 | + | 9.87002e7i | −0.907341 | + | 0.452406i | ||||
\(603\) | 6.35603e7i | 0.289890i | ||||||||
\(604\) | −9.38356e7 | − | 7.07043e7i | −0.425850 | − | 0.320875i | ||||
\(605\) | 1.09989e7 | 0.0496688 | ||||||||
\(606\) | −2.53106e7 | − | 5.07627e7i | −0.113733 | − | 0.228101i | ||||
\(607\) | − | 1.91879e8i | − | 0.857950i | −0.903316 | − | 0.428975i | \(-0.858875\pi\) | ||
0.903316 | − | 0.428975i | \(-0.141125\pi\) | |||||||
\(608\) | −3.80124e7 | + | 3.48389e7i | −0.169128 | + | 0.155008i | ||||
\(609\) | −2.06028e8 | −0.912167 | ||||||||
\(610\) | −2.04755e7 | + | 1.02092e7i | −0.0902081 | + | 0.0449784i | ||||
\(611\) | − | 1.54864e6i | − | 0.00678934i | ||||||
\(612\) | 9.37130e7 | − | 1.24372e8i | 0.408833 | − | 0.542584i | ||||
\(613\) | 1.79924e7 | 0.0781104 | 0.0390552 | − | 0.999237i | \(-0.487565\pi\) | ||||
0.0390552 | + | 0.999237i | \(0.487565\pi\) | |||||||
\(614\) | 2.03002e7 | + | 4.07138e7i | 0.0876989 | + | 0.175888i | ||||
\(615\) | − | 4.49390e7i | − | 0.193196i | ||||||
\(616\) | −3.74921e7 | + | 2.02357e8i | −0.160397 | + | 0.865716i | ||||
\(617\) | 873438. | 0.00371858 | 0.00185929 | − | 0.999998i | \(-0.499408\pi\) | ||||
0.00185929 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(618\) | 9.16600e7 | − | 4.57023e7i | 0.388342 | − | 0.193630i | ||||
\(619\) | − | 6.52368e7i | − | 0.275056i | −0.990498 | − | 0.137528i | \(-0.956084\pi\) | ||
0.990498 | − | 0.137528i | \(-0.0439157\pi\) | |||||||
\(620\) | −3.53574e7 | − | 2.66415e7i | −0.148356 | − | 0.111785i | ||||
\(621\) | −1.80466e8 | −0.753563 | ||||||||
\(622\) | 1.21456e8 | + | 2.43592e8i | 0.504718 | + | 1.01226i | ||||
\(623\) | 8.75875e7i | 0.362225i | ||||||||
\(624\) | −4.91264e6 | + | 1.40910e6i | −0.0202191 | + | 0.00579948i | ||||
\(625\) | 1.60556e8 | 0.657636 | ||||||||
\(626\) | −1.42435e8 | + | 7.10191e7i | −0.580623 | + | 0.289503i | ||||
\(627\) | − | 4.32988e7i | − | 0.175660i | ||||||
\(628\) | 1.35502e7 | − | 1.79832e7i | 0.0547100 | − | 0.0726086i | ||||
\(629\) | −6.12110e8 | −2.45967 | ||||||||
\(630\) | −1.54359e7 | − | 3.09580e7i | −0.0617319 | − | 0.123809i | ||||
\(631\) | 9.10812e7i | 0.362527i | 0.983435 | + | 0.181264i | \(0.0580187\pi\) | ||||
−0.983435 | + | 0.181264i | \(0.941981\pi\) | |||||||
\(632\) | −2.59056e8 | − | 4.79971e7i | −1.02622 | − | 0.190136i | ||||
\(633\) | 1.18062e8 | 0.465476 | ||||||||
\(634\) | −3.23179e8 | + | 1.61139e8i | −1.26816 | + | 0.632314i | ||||
\(635\) | − | 7.74634e7i | − | 0.302535i | ||||||
\(636\) | −7.98772e7 | − | 6.01868e7i | −0.310493 | − | 0.233954i | ||||
\(637\) | −2.44890e6 | −0.00947441 | ||||||||
\(638\) | 1.91873e8 | + | 3.84819e8i | 0.738844 | + | 1.48182i | ||||
\(639\) | 1.90593e8i | 0.730474i | ||||||||
\(640\) | −8.99476e7 | + | 8.67365e6i | −0.343123 | + | 0.0330874i | ||||
\(641\) | −5.68906e7 | −0.216006 | −0.108003 | − | 0.994151i | \(-0.534446\pi\) | ||||
−0.108003 | + | 0.994151i | \(0.534446\pi\) | |||||||
\(642\) | −8.83144e7 | + | 4.40341e7i | −0.333754 | + | 0.166412i | ||||
\(643\) | − | 1.16275e8i | − | 0.437374i | −0.975795 | − | 0.218687i | \(-0.929823\pi\) | ||
0.975795 | − | 0.218687i | \(-0.0701773\pi\) | |||||||
\(644\) | 9.36261e7 | − | 1.24256e8i | 0.350541 | − | 0.465223i | ||||
\(645\) | 8.15582e7 | 0.303941 | ||||||||
\(646\) | −3.84540e7 | − | 7.71229e7i | −0.142641 | − | 0.286079i | ||||
\(647\) | − | 4.90342e8i | − | 1.81045i | −0.424932 | − | 0.905225i | \(-0.639702\pi\) | ||
0.424932 | − | 0.905225i | \(-0.360298\pi\) | |||||||
\(648\) | 1.36179e7 | − | 7.35002e7i | 0.0500478 | − | 0.270124i | ||||
\(649\) | 1.45821e8 | 0.533441 | ||||||||
\(650\) | −6.36351e6 | + | 3.17289e6i | −0.0231716 | + | 0.0115535i | ||||
\(651\) | 8.76039e7i | 0.317527i | ||||||||
\(652\) | −2.67278e8 | − | 2.01392e8i | −0.964317 | − | 0.726605i | ||||
\(653\) | −4.41624e8 | −1.58604 | −0.793018 | − | 0.609199i | \(-0.791491\pi\) | ||||
−0.793018 | + | 0.609199i | \(0.791491\pi\) | |||||||
\(654\) | 1.06710e8 | + | 2.14016e8i | 0.381479 | + | 0.765091i | ||||
\(655\) | − | 1.04817e8i | − | 0.372998i | ||||||
\(656\) | −6.09380e7 | − | 2.12452e8i | −0.215862 | − | 0.752574i | ||||
\(657\) | 2.58471e8 | 0.911412 | ||||||||
\(658\) | −4.84907e7 | + | 2.41778e7i | −0.170208 | + | 0.0848669i | ||||
\(659\) | 3.14533e7i | 0.109903i | 0.998489 | + | 0.0549516i | \(0.0175004\pi\) | ||||
−0.998489 | + | 0.0549516i | \(0.982500\pi\) | |||||||
\(660\) | 4.56648e7 | − | 6.06042e7i | 0.158836 | − | 0.210800i | ||||
\(661\) | 1.10180e8 | 0.381504 | 0.190752 | − | 0.981638i | \(-0.438907\pi\) | ||||
0.190752 | + | 0.981638i | \(0.438907\pi\) | |||||||
\(662\) | 9.86761e7 | + | 1.97904e8i | 0.340125 | + | 0.682150i | ||||
\(663\) | − | 8.54173e6i | − | 0.0293093i | ||||||
\(664\) | −2.82159e8 | − | 5.22777e7i | −0.963807 | − | 0.178571i | ||||
\(665\) | −1.91436e7 | −0.0650965 | ||||||||
\(666\) | 2.27531e8 | − | 1.13449e8i | 0.770227 | − | 0.384040i | ||||
\(667\) | − | 3.25072e8i | − | 1.09547i | ||||||
\(668\) | −3.12769e7 | − | 2.35669e7i | −0.104929 | − | 0.0790629i | ||||
\(669\) | 5.91951e7 | 0.197700 | ||||||||
\(670\) | 2.75063e7 | + | 5.51664e7i | 0.0914552 | + | 0.183422i | ||||
\(671\) | − | 9.44923e7i | − | 0.312773i | ||||||
\(672\) | 1.20819e8 | + | 1.31824e8i | 0.398131 | + | 0.434397i | ||||
\(673\) | 1.37869e8 | 0.452296 | 0.226148 | − | 0.974093i | \(-0.427387\pi\) | ||||
0.226148 | + | 0.974093i | \(0.427387\pi\) | |||||||
\(674\) | −2.25701e8 | + | 1.12536e8i | −0.737147 | + | 0.367546i | ||||
\(675\) | − | 2.88581e8i | − | 0.938332i | ||||||
\(676\) | −1.85740e8 | + | 2.46506e8i | −0.601264 | + | 0.797970i | ||||
\(677\) | 4.07109e8 | 1.31203 | 0.656017 | − | 0.754746i | \(-0.272240\pi\) | ||||
0.656017 | + | 0.754746i | \(0.272240\pi\) | |||||||
\(678\) | −6.80204e7 | − | 1.36421e8i | −0.218248 | − | 0.437716i | ||||
\(679\) | 1.34264e8i | 0.428893i | ||||||||
\(680\) | 2.75141e7 | − | 1.48502e8i | 0.0875040 | − | 0.472287i | ||||
\(681\) | −1.34791e8 | −0.426796 | ||||||||
\(682\) | 1.63627e8 | − | 8.15853e7i | 0.515823 | − | 0.257193i | ||||
\(683\) | 3.44159e8i | 1.08018i | 0.841606 | + | 0.540091i | \(0.181610\pi\) | ||||
−0.841606 | + | 0.540091i | \(0.818390\pi\) | |||||||
\(684\) | 2.85880e7 | + | 2.15408e7i | 0.0893336 | + | 0.0673121i | ||||
\(685\) | −1.48337e8 | −0.461508 | ||||||||
\(686\) | 1.56808e8 | + | 3.14492e8i | 0.485730 | + | 0.974174i | ||||
\(687\) | − | 1.61697e8i | − | 0.498691i | ||||||
\(688\) | 3.85572e8 | − | 1.10594e8i | 1.18397 | − | 0.339600i | ||||
\(689\) | 5.21958e6 | 0.0159580 | ||||||||
\(690\) | −5.13379e7 | + | 2.55974e7i | −0.156276 | + | 0.0779200i | ||||
\(691\) | − | 1.55237e8i | − | 0.470502i | −0.971935 | − | 0.235251i | \(-0.924409\pi\) | ||
0.971935 | − | 0.235251i | \(-0.0755912\pi\) | |||||||
\(692\) | 1.76549e8 | − | 2.34308e8i | 0.532780 | − | 0.707081i | ||||
\(693\) | 1.42868e8 | 0.429274 | ||||||||
\(694\) | −1.70374e8 | − | 3.41700e8i | −0.509711 | − | 1.02227i | ||||
\(695\) | 2.16118e8i | 0.643779i | ||||||||
\(696\) | 3.67365e8 | + | 6.80643e7i | 1.08961 | + | 0.201879i | ||||
\(697\) | 3.69396e8 | 1.09092 | ||||||||
\(698\) | 3.13309e8 | − | 1.56218e8i | 0.921312 | − | 0.459372i | ||||
\(699\) | − | 1.50457e7i | − | 0.0440536i | ||||||
\(700\) | 1.98697e8 | + | 1.49717e8i | 0.579292 | + | 0.436492i | ||||
\(701\) | 7.17366e7 | 0.208251 | 0.104125 | − | 0.994564i | \(-0.466796\pi\) | ||||
0.104125 | + | 0.994564i | \(0.466796\pi\) | |||||||
\(702\) | 4.83015e6 | + | 9.68731e6i | 0.0139621 | + | 0.0280022i | ||||
\(703\) | − | 1.40699e8i | − | 0.404972i | ||||||
\(704\) | 1.33703e8 | − | 3.48433e8i | 0.383198 | − | 0.998622i | ||||
\(705\) | 1.99786e7 | 0.0570162 | ||||||||
\(706\) | 4.33583e8 | − | 2.16187e8i | 1.23213 | − | 0.614350i | ||||
\(707\) | − | 1.03574e8i | − | 0.293086i | ||||||
\(708\) | 7.62460e7 | − | 1.01190e8i | 0.214841 | − | 0.285128i | ||||
\(709\) | 6.55343e8 | 1.83878 | 0.919390 | − | 0.393347i | \(-0.128683\pi\) | ||||
0.919390 | + | 0.393347i | \(0.128683\pi\) | |||||||
\(710\) | 8.24810e7 | + | 1.65423e8i | 0.230451 | + | 0.462190i | ||||
\(711\) | 1.82898e8i | 0.508863i | ||||||||
\(712\) | 2.89358e7 | − | 1.56176e8i | 0.0801670 | − | 0.432687i | ||||
\(713\) | −1.38222e8 | −0.381337 | ||||||||
\(714\) | −2.67456e8 | + | 1.33356e8i | −0.734782 | + | 0.366367i | ||||
\(715\) | 3.96019e6i | 0.0108342i | ||||||||
\(716\) | −4.57688e8 | − | 3.44864e8i | −1.24690 | − | 0.939526i | ||||
\(717\) | 2.46856e8 | 0.669709 | ||||||||
\(718\) | 2.26248e8 | + | 4.53761e8i | 0.611240 | + | 1.22590i | ||||
\(719\) | 3.54721e8i | 0.954334i | 0.878813 | + | 0.477167i | \(0.158336\pi\) | ||||
−0.878813 | + | 0.477167i | \(0.841664\pi\) | |||||||
\(720\) | 1.72960e7 | + | 6.03002e7i | 0.0463392 | + | 0.161555i | ||||
\(721\) | 1.87020e8 | 0.498979 | ||||||||
\(722\) | 1.77274e7 | − | 8.83899e6i | 0.0471013 | − | 0.0234850i | ||||
\(723\) | − | 4.83295e8i | − | 1.27879i | ||||||
\(724\) | −7.65066e7 | + | 1.01536e8i | −0.201597 | + | 0.267550i | ||||
\(725\) | 5.19820e8 | 1.36408 | ||||||||
\(726\) | 1.76116e7 | + | 3.53217e7i | 0.0460246 | + | 0.0923064i | ||||
\(727\) | − | 6.62723e8i | − | 1.72476i | −0.506260 | − | 0.862381i | \(-0.668973\pi\) | ||
0.506260 | − | 0.862381i | \(-0.331027\pi\) | |||||||
\(728\) | −9.17592e6 | − | 1.70009e6i | −0.0237824 | − | 0.00440633i | ||||
\(729\) | −3.47217e8 | −0.896227 | ||||||||
\(730\) | 2.24337e8 | − | 1.11856e8i | 0.576675 | − | 0.287534i | ||||
\(731\) | 6.70404e8i | 1.71626i | ||||||||
\(732\) | −6.55715e7 | − | 4.94076e7i | −0.167179 | − | 0.125968i | ||||
\(733\) | 4.71983e8 | 1.19844 | 0.599218 | − | 0.800586i | \(-0.295478\pi\) | ||||
0.599218 | + | 0.800586i | \(0.295478\pi\) | |||||||
\(734\) | 2.69017e8 | + | 5.39537e8i | 0.680285 | + | 1.36437i | ||||
\(735\) | − | 3.15926e7i | − | 0.0795652i | ||||||
\(736\) | −2.07993e8 | + | 1.90629e8i | −0.521693 | + | 0.478140i | ||||
\(737\) | −2.54587e8 | −0.635966 | ||||||||
\(738\) | −1.37310e8 | + | 6.84639e7i | −0.341613 | + | 0.170330i | ||||
\(739\) | 1.09317e8i | 0.270866i | 0.990786 | + | 0.135433i | \(0.0432426\pi\) | ||||
−0.990786 | + | 0.135433i | \(0.956757\pi\) | |||||||
\(740\) | 1.48387e8 | − | 1.96933e8i | 0.366186 | − | 0.485985i | ||||
\(741\) | 1.96339e6 | 0.00482562 | ||||||||
\(742\) | −8.14893e7 | − | 1.63434e8i | −0.199475 | − | 0.400066i | ||||
\(743\) | 3.61211e8i | 0.880632i | 0.897843 | + | 0.440316i | \(0.145134\pi\) | ||||
−0.897843 | + | 0.440316i | \(0.854866\pi\) | |||||||
\(744\) | 2.89412e7 | − | 1.56205e8i | 0.0702745 | − | 0.379294i | ||||
\(745\) | 1.25251e8 | 0.302909 | ||||||||
\(746\) | −7.07170e8 | + | 3.52599e8i | −1.70336 | + | 0.849308i | ||||
\(747\) | 1.99210e8i | 0.477913i | ||||||||
\(748\) | 4.98163e8 | + | 3.75362e8i | 1.19033 | + | 0.896902i | ||||
\(749\) | −1.80194e8 | −0.428839 | ||||||||
\(750\) | −8.73851e7 | − | 1.75259e8i | −0.207135 | − | 0.415428i | ||||
\(751\) | − | 3.77340e7i | − | 0.0890867i | −0.999007 | − | 0.0445434i | \(-0.985817\pi\) | ||
0.999007 | − | 0.0445434i | \(-0.0141833\pi\) | |||||||
\(752\) | 9.44504e7 | − | 2.70914e7i | 0.222101 | − | 0.0637056i | ||||
\(753\) | −3.77967e8 | −0.885256 | ||||||||
\(754\) | −1.74497e7 | + | 8.70054e6i | −0.0407075 | + | 0.0202970i | ||||
\(755\) | 7.91035e7i | 0.183804i | ||||||||
\(756\) | 2.27917e8 | − | 3.02481e8i | 0.527486 | − | 0.700056i | ||||
\(757\) | −5.14247e7 | −0.118545 | −0.0592726 | − | 0.998242i | \(-0.518878\pi\) | ||||
−0.0592726 | + | 0.998242i | \(0.518878\pi\) | |||||||
\(758\) | −3.42341e8 | − | 6.86596e8i | −0.786053 | − | 1.57650i | ||||
\(759\) | − | 2.36919e8i | − | 0.541844i | ||||||
\(760\) | 3.41346e7 | + | 6.32435e6i | 0.0777595 | + | 0.0144071i | ||||
\(761\) | −3.37064e8 | −0.764818 | −0.382409 | − | 0.923993i | \(-0.624905\pi\) | ||||
−0.382409 | + | 0.923993i | \(0.624905\pi\) | |||||||
\(762\) | 2.48765e8 | − | 1.24036e8i | 0.562243 | − | 0.280338i | ||||
\(763\) | 4.36671e8i | 0.983062i | ||||||||
\(764\) | −3.09723e8 | − | 2.33374e8i | −0.694534 | − | 0.523326i | ||||
\(765\) | −1.04845e8 | −0.234188 | ||||||||
\(766\) | −1.72653e8 | − | 3.46272e8i | −0.384139 | − | 0.770425i | ||||
\(767\) | 6.61229e6i | 0.0146543i | ||||||||
\(768\) | −1.71880e8 | − | 2.74968e8i | −0.379438 | − | 0.607013i | ||||
\(769\) | 1.89775e8 | 0.417312 | 0.208656 | − | 0.977989i | \(-0.433091\pi\) | ||||
0.208656 | + | 0.977989i | \(0.433091\pi\) | |||||||
\(770\) | 1.24000e8 | − | 6.18274e7i | 0.271613 | − | 0.135428i | ||||
\(771\) | 5.76561e8i | 1.25801i | ||||||||
\(772\) | 2.22909e8 | − | 2.95835e8i | 0.484480 | − | 0.642980i | ||||
\(773\) | −3.47147e8 | −0.751580 | −0.375790 | − | 0.926705i | \(-0.622629\pi\) | ||||
−0.375790 | + | 0.926705i | \(0.622629\pi\) | |||||||
\(774\) | −1.24253e8 | − | 2.49200e8i | −0.267968 | − | 0.537434i | ||||
\(775\) | − | 2.21030e8i | − | 0.474838i | ||||||
\(776\) | 4.43559e7 | − | 2.39403e8i | 0.0949218 | − | 0.512324i | ||||
\(777\) | −4.87934e8 | −1.04015 | ||||||||
\(778\) | −1.99008e8 | + | 9.92265e7i | −0.422601 | + | 0.210712i | ||||
\(779\) | 8.49089e7i | 0.179614i | ||||||||
\(780\) | 2.74811e6 | + | 2.07068e6i | 0.00579096 | + | 0.00436344i | ||||
\(781\) | −7.63409e8 | −1.60252 | ||||||||
\(782\) | −2.10409e8 | − | 4.21995e8i | −0.439992 | − | 0.882443i | ||||
\(783\) | − | 7.91333e8i | − | 1.64844i | ||||||
\(784\) | −4.28401e7 | − | 1.49356e8i | −0.0889001 | − | 0.309938i | ||||
\(785\) | −1.51599e7 | −0.0313391 | ||||||||
\(786\) | 3.36606e8 | − | 1.67834e8i | 0.693193 | − | 0.345630i | ||||
\(787\) | 7.77357e8i | 1.59476i | 0.603476 | + | 0.797381i | \(0.293782\pi\) | ||||
−0.603476 | + | 0.797381i | \(0.706218\pi\) | |||||||
\(788\) | −1.75325e8 | + | 2.32684e8i | −0.358316 | + | 0.475541i | ||||
\(789\) | −4.00832e8 | −0.816078 | ||||||||
\(790\) | 7.91510e7 | + | 1.58744e8i | 0.160537 | + | 0.321971i | ||||
\(791\) | − | 2.78349e8i | − | 0.562419i | ||||||
\(792\) | −2.54745e8 | − | 4.71984e7i | −0.512779 | − | 0.0950062i | ||||
\(793\) | 4.28478e6 | 0.00859228 | ||||||||
\(794\) | −6.38585e8 | + | 3.18403e8i | −1.27573 | + | 0.636085i | ||||
\(795\) | 6.73365e7i | 0.134014i | ||||||||
\(796\) | 2.66509e8 | + | 2.00812e8i | 0.528412 | + | 0.398154i | ||||
\(797\) | 5.55254e8 | 1.09677 | 0.548387 | − | 0.836225i | \(-0.315242\pi\) | ||||
0.548387 | + | 0.836225i | \(0.315242\pi\) | |||||||
\(798\) | −3.06530e7 | − | 6.14773e7i | −0.0603204 | − | 0.120978i | ||||
\(799\) | 1.64223e8i | 0.321954i | ||||||||
\(800\) | −3.04833e8 | − | 3.32600e8i | −0.595376 | − | 0.649609i | ||||
\(801\) | −1.10263e8 | −0.214552 | ||||||||
\(802\) | 1.90722e7 | − | 9.50954e6i | 0.0369725 | − | 0.0184347i | ||||
\(803\) | 1.03529e9i | 1.99947i | ||||||||
\(804\) | −1.33117e8 | + | 1.76667e8i | −0.256133 | + | 0.339928i | ||||
\(805\) | −1.04748e8 | −0.200798 | ||||||||
\(806\) | 3.69950e6 | + | 7.41969e6i | 0.00706543 | + | 0.0141703i | ||||
\(807\) | 4.89696e8i | 0.931763i | ||||||||
\(808\) | −3.42173e7 | + | 1.84682e8i | −0.0648652 | + | 0.350098i | ||||
\(809\) | −8.19417e8 | −1.54760 | −0.773801 | − | 0.633429i | \(-0.781647\pi\) | ||||
−0.773801 | + | 0.633429i | \(0.781647\pi\) | |||||||
\(810\) | −4.50395e7 | + | 2.24570e7i | −0.0847498 | + | 0.0422568i | ||||
\(811\) | − | 6.14350e8i | − | 1.15174i | −0.817542 | − | 0.575868i | \(-0.804664\pi\) | ||
0.817542 | − | 0.575868i | \(-0.195336\pi\) | |||||||
\(812\) | 5.44858e8 | + | 4.10546e8i | 1.01769 | + | 0.766820i | ||||
\(813\) | −4.94057e8 | −0.919402 | ||||||||
\(814\) | 4.54411e8 | + | 9.11363e8i | 0.842512 | + | 1.68973i | ||||
\(815\) | 2.25315e8i | 0.416215i | ||||||||
\(816\) | 5.20953e8 | − | 1.49426e8i | 0.958800 | − | 0.275014i | ||||
\(817\) | −1.54098e8 | −0.282574 | ||||||||
\(818\) | 6.33219e8 | − | 3.15727e8i | 1.15689 | − | 0.576835i | ||||
\(819\) | 6.47837e6i | 0.0117927i | ||||||||
\(820\) | −8.95486e7 | + | 1.18845e8i | −0.162412 | + | 0.215545i | ||||
\(821\) | 8.00270e8 | 1.44613 | 0.723065 | − | 0.690780i | \(-0.242733\pi\) | ||||
0.723065 | + | 0.690780i | \(0.242733\pi\) | |||||||
\(822\) | −2.37520e8 | − | 4.76368e8i | −0.427646 | − | 0.857683i | ||||
\(823\) | 8.94897e8i | 1.60536i | 0.596408 | + | 0.802682i | \(0.296594\pi\) | ||||
−0.596408 | + | 0.802682i | \(0.703406\pi\) | |||||||
\(824\) | −3.33472e8 | − | 6.17847e7i | −0.596043 | − | 0.110433i | ||||
\(825\) | 3.78855e8 | 0.674700 | ||||||||
\(826\) | 2.07042e8 | − | 1.03233e8i | 0.367383 | − | 0.183180i | ||||
\(827\) | − | 3.99694e8i | − | 0.706661i | −0.935499 | − | 0.353330i | \(-0.885049\pi\) | ||
0.935499 | − | 0.353330i | \(-0.114951\pi\) | |||||||
\(828\) | 1.56425e8 | + | 1.17865e8i | 0.275560 | + | 0.207632i | ||||
\(829\) | −1.02755e9 | −1.80360 | −0.901798 | − | 0.432158i | \(-0.857752\pi\) | ||||
−0.901798 | + | 0.432158i | \(0.857752\pi\) | |||||||
\(830\) | 8.62100e7 | + | 1.72902e8i | 0.150773 | + | 0.302389i | ||||
\(831\) | 4.15669e8i | 0.724344i | ||||||||
\(832\) | 1.57998e7 | + | 6.06279e6i | 0.0274335 | + | 0.0105270i | ||||
\(833\) | 2.59689e8 | 0.449282 | ||||||||
\(834\) | −6.94038e8 | + | 3.46052e8i | −1.19642 | + | 0.596545i | ||||
\(835\) | 2.63665e7i | 0.0452890i | ||||||||
\(836\) | −8.62803e7 | + | 1.14507e8i | −0.147670 | + | 0.195981i | ||||
\(837\) | −3.36478e8 | −0.573826 | ||||||||
\(838\) | 8.57354e7 | + | 1.71950e8i | 0.145690 | + | 0.292193i | ||||
\(839\) | 6.44404e8i | 1.09112i | 0.838072 | + | 0.545560i | \(0.183683\pi\) | ||||
−0.838072 | + | 0.545560i | \(0.816317\pi\) | |||||||
\(840\) | 2.19324e7 | − | 1.18376e8i | 0.0370039 | − | 0.199722i | ||||
\(841\) | 8.30602e8 | 1.39638 | ||||||||
\(842\) | −1.27921e8 | + | 6.37824e7i | −0.214292 | + | 0.106848i | ||||
\(843\) | − | 2.21807e8i | − | 0.370248i | ||||||
\(844\) | −3.12224e8 | − | 2.35258e8i | −0.519324 | − | 0.391306i | ||||
\(845\) | 2.07804e8 | 0.344417 | ||||||||
\(846\) | −3.04372e7 | − | 6.10445e7i | −0.0502682 | − | 0.100817i | ||||
\(847\) | 7.20692e7i | 0.118604i | ||||||||
\(848\) | 9.13094e7 | + | 3.18338e8i | 0.149737 | + | 0.522036i | ||||
\(849\) | 5.35527e8 | 0.875101 | ||||||||
\(850\) | 6.74808e8 | − | 3.36463e8i | 1.09881 | − | 0.547875i | ||||
\(851\) | − | 7.69865e8i | − | 1.24918i | ||||||
\(852\) | −3.99167e8 | + | 5.29756e8i | −0.645410 | + | 0.856559i | ||||
\(853\) | −3.67847e8 | −0.592680 | −0.296340 | − | 0.955083i | \(-0.595766\pi\) | ||||
−0.296340 | + | 0.955083i | \(0.595766\pi\) | |||||||
\(854\) | −6.68949e7 | − | 1.34164e8i | −0.107404 | − | 0.215408i | ||||
\(855\) | − | 2.40997e7i | − | 0.0385578i | ||||||
\(856\) | 3.21300e8 | + | 5.95296e7i | 0.512259 | + | 0.0949099i | ||||
\(857\) | −1.15746e9 | −1.83892 | −0.919461 | − | 0.393182i | \(-0.871374\pi\) | ||||
−0.919461 | + | 0.393182i | \(0.871374\pi\) | |||||||
\(858\) | −1.27177e7 | + | 6.34112e6i | −0.0201347 | + | 0.0100393i | ||||
\(859\) | − | 6.82772e8i | − | 1.07720i | −0.842561 | − | 0.538600i | \(-0.818953\pi\) | ||
0.842561 | − | 0.538600i | \(-0.181047\pi\) | |||||||
\(860\) | −2.15688e8 | − | 1.62519e8i | −0.339101 | − | 0.255510i | ||||
\(861\) | 2.94458e8 | 0.461332 | ||||||||
\(862\) | −4.86669e8 | − | 9.76059e8i | −0.759822 | − | 1.52389i | ||||
\(863\) | 2.21195e8i | 0.344146i | 0.985084 | + | 0.172073i | \(0.0550465\pi\) | ||||
−0.985084 | + | 0.172073i | \(0.944953\pi\) | |||||||
\(864\) | −5.06324e8 | + | 4.64053e8i | −0.785031 | + | 0.719493i | ||||
\(865\) | −1.97522e8 | −0.305188 | ||||||||
\(866\) | 4.41053e8 | − | 2.19912e8i | 0.679105 | − | 0.338606i | ||||
\(867\) | 4.39265e8i | 0.674015i | ||||||||
\(868\) | 1.74566e8 | − | 2.31676e8i | 0.266931 | − | 0.354259i | ||||
\(869\) | −7.32588e8 | −1.11635 | ||||||||
\(870\) | −1.12243e8 | − | 2.25114e8i | −0.170452 | − | 0.341858i | ||||
\(871\) | − | 1.15443e7i | − | 0.0174708i | ||||||
\(872\) | 1.44261e8 | − | 7.78621e8i | 0.217570 | − | 1.17429i | ||||
\(873\) | −1.69023e8 | −0.254041 | ||||||||
\(874\) | 9.69993e7 | − | 4.83645e7i | 0.145289 | − | 0.0724423i | ||||
\(875\) | − | 3.57592e8i | − | 0.533781i | ||||||
\(876\) | 7.18422e8 | + | 5.41325e8i | 1.06873 | + | 0.805278i | ||||
\(877\) | 1.91647e8 | 0.284121 | 0.142061 | − | 0.989858i | \(-0.454627\pi\) | ||||
0.142061 | + | 0.989858i | \(0.454627\pi\) | |||||||
\(878\) | 5.76452e8 | + | 1.15613e9i | 0.851686 | + | 1.70813i | ||||
\(879\) | − | 1.83944e7i | − | 0.0270843i | ||||||
\(880\) | −2.41529e8 | + | 6.92781e7i | −0.354422 | + | 0.101659i | ||||
\(881\) | 5.07899e8 | 0.742763 | 0.371381 | − | 0.928480i | \(-0.378884\pi\) | ||||
0.371381 | + | 0.928480i | \(0.378884\pi\) | |||||||
\(882\) | −9.65308e7 | + | 4.81309e7i | −0.140689 | + | 0.0701484i | ||||
\(883\) | 1.96495e8i | 0.285410i | 0.989765 | + | 0.142705i | \(0.0455800\pi\) | ||||
−0.989765 | + | 0.142705i | \(0.954420\pi\) | |||||||
\(884\) | −1.70209e7 | + | 2.25893e7i | −0.0246391 | + | 0.0326999i | ||||
\(885\) | −8.53035e7 | −0.123066 | ||||||||
\(886\) | 2.12355e8 | + | 4.25897e8i | 0.305324 | + | 0.612355i | ||||
\(887\) | 6.08868e8i | 0.872473i | 0.899832 | + | 0.436237i | \(0.143689\pi\) | ||||
−0.899832 | + | 0.436237i | \(0.856311\pi\) | |||||||
\(888\) | 8.70026e8 | + | 1.61196e8i | 1.24249 | + | 0.230205i | ||||
\(889\) | 5.07571e8 | 0.722423 | ||||||||
\(890\) | −9.57016e7 | + | 4.77174e7i | −0.135753 | + | 0.0676873i | ||||
\(891\) | − | 2.07852e8i | − | 0.293847i | ||||||
\(892\) | −1.56546e8 | − | 1.17956e8i | −0.220571 | − | 0.166198i | ||||
\(893\) | −3.77482e7 | −0.0530080 | ||||||||
\(894\) | 2.00553e8 | + | 4.02228e8i | 0.280684 | + | 0.562937i | ||||
\(895\) | 3.85831e8i | 0.538181i | ||||||||
\(896\) | −5.68332e7 | − | 5.89372e8i | −0.0790092 | − | 0.819342i | ||||
\(897\) | 1.07431e7 | 0.0148852 | ||||||||
\(898\) | −3.62513e8 | + | 1.80751e8i | −0.500604 | + | 0.249605i | ||||
\(899\) | − | 6.06097e8i | − | 0.834186i | ||||||
\(900\) | −1.88477e8 | + | 2.50138e8i | −0.258542 | + | 0.343125i | ||||
\(901\) | −5.53502e8 | −0.756737 | ||||||||
\(902\) | −2.74228e8 | − | 5.49989e8i | −0.373673 | − | 0.749435i | ||||
\(903\) | 5.34402e8i | 0.725779i | ||||||||
\(904\) | −9.19566e7 | + | 4.96319e8i | −0.124474 | + | 0.671824i | ||||
\(905\) | 8.55950e7 | 0.115479 | ||||||||
\(906\) | −2.54031e8 | + | 1.26662e8i | −0.341588 | + | 0.170318i | ||||
\(907\) | − | 1.36257e9i | − | 1.82615i | −0.407786 | − | 0.913077i | \(-0.633699\pi\) | ||
0.407786 | − | 0.913077i | \(-0.366301\pi\) | |||||||
\(908\) | 3.56467e8 | + | 2.68595e8i | 0.476170 | + | 0.358790i | ||||
\(909\) | 1.30389e8 | 0.173600 | ||||||||
\(910\) | 2.80358e6 | + | 5.62283e6i | 0.00372039 | + | 0.00746158i | ||||
\(911\) | − | 2.01475e8i | − | 0.266481i | −0.991084 | − | 0.133241i | \(-0.957462\pi\) | ||
0.991084 | − | 0.133241i | \(-0.0425383\pi\) | |||||||
\(912\) | 3.43469e7 | + | 1.19746e8i | 0.0452796 | + | 0.157861i | ||||
\(913\) | −7.97923e8 | −1.04845 | ||||||||
\(914\) | 8.87786e8 | − | 4.42656e8i | 1.16271 | − | 0.579733i | ||||
\(915\) | 5.52768e7i | 0.0721572i | ||||||||
\(916\) | −3.22209e8 | + | 4.27621e8i | −0.419229 | + | 0.556381i | ||||
\(917\) | 6.86799e8 | 0.890680 | ||||||||
\(918\) | −5.12206e8 | − | 1.02727e9i | −0.662089 | − | 1.32788i | ||||
\(919\) | − | 9.53855e8i | − | 1.22895i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) | ||
0.788935 | − | 0.614477i | \(-0.210633\pi\) | |||||||
\(920\) | 1.86775e8 | + | 3.46051e7i | 0.239858 | + | 0.0444402i | ||||
\(921\) | 1.09913e8 | 0.140692 | ||||||||
\(922\) | −2.97470e8 | + | 1.48320e8i | −0.379533 | + | 0.189238i | ||||
\(923\) | − | 3.46170e7i | − | 0.0440234i | ||||||
\(924\) | 3.97103e8 | + | 2.99214e8i | 0.503370 | + | 0.379285i | ||||
\(925\) | 1.23108e9 | 1.55547 | ||||||||
\(926\) | 1.39537e8 | + | 2.79854e8i | 0.175734 | + | 0.352451i | ||||
\(927\) | 2.35438e8i | 0.295554i | ||||||||
\(928\) | −8.35897e8 | − | 9.12039e8i | −1.04595 | − | 1.14122i | ||||
\(929\) | 1.08935e9 | 1.35869 | 0.679345 | − | 0.733819i | \(-0.262264\pi\) | ||||
0.679345 | + | 0.733819i | \(0.262264\pi\) | |||||||
\(930\) | −9.57195e7 | + | 4.77264e7i | −0.119001 | + | 0.0593348i | ||||
\(931\) | 5.96919e7i | 0.0739718i | ||||||||
\(932\) | −2.99811e7 | + | 3.97896e7i | −0.0370340 | + | 0.0491498i | ||||
\(933\) | 6.57612e8 | 0.809701 | ||||||||
\(934\) | −6.05630e8 | − | 1.21465e9i | −0.743305 | − | 1.49076i | ||||
\(935\) | − | 4.19952e8i | − | 0.513765i | ||||||
\(936\) | 2.14022e6 | − | 1.15515e7i | 0.00260995 | − | 0.0140867i | ||||
\(937\) | 1.91934e8 | 0.233310 | 0.116655 | − | 0.993173i | \(-0.462783\pi\) | ||||
0.116655 | + | 0.993173i | \(0.462783\pi\) | |||||||
\(938\) | −3.61472e8 | + | 1.80232e8i | −0.437992 | + | 0.218386i | ||||
\(939\) | 3.84525e8i | 0.464439i | ||||||||
\(940\) | −5.28352e7 | − | 3.98109e7i | −0.0636121 | − | 0.0479312i | ||||
\(941\) | 8.75876e8 | 1.05117 | 0.525586 | − | 0.850740i | \(-0.323846\pi\) | ||||
0.525586 | + | 0.850740i | \(0.323846\pi\) | |||||||
\(942\) | −2.42742e7 | − | 4.86841e7i | −0.0290397 | − | 0.0582417i | ||||
\(943\) | 4.64597e8i | 0.554041i | ||||||||
\(944\) | −4.03278e8 | + | 1.15673e8i | −0.479390 | + | 0.137504i | ||||
\(945\) | −2.54992e8 | −0.302155 | ||||||||
\(946\) | 9.98156e8 | − | 4.97687e8i | 1.17903 | − | 0.587872i | ||||
\(947\) | − | 5.39757e8i | − | 0.635548i | −0.948166 | − | 0.317774i | \(-0.897065\pi\) | ||
0.948166 | − | 0.317774i | \(-0.102935\pi\) | |||||||
\(948\) | −3.83051e8 | + | 5.08368e8i | −0.449606 | + | 0.596696i | ||||
\(949\) | −4.69454e7 | −0.0549281 | ||||||||
\(950\) | 7.73392e7 | + | 1.55111e8i | 0.0902046 | + | 0.180913i | ||||
\(951\) | 8.72469e8i | 1.01440i | ||||||||
\(952\) | 9.73044e8 | + | 1.80283e8i | 1.12777 | + | 0.208951i | ||||
\(953\) | 1.58037e7 | 0.0182592 | 0.00912958 | − | 0.999958i | \(-0.497094\pi\) | ||||
0.00912958 | + | 0.999958i | \(0.497094\pi\) | |||||||
\(954\) | 2.05746e8 | − | 1.02586e8i | 0.236966 | − | 0.118153i | ||||
\(955\) | 2.61097e8i | 0.299772i | ||||||||
\(956\) | −6.52831e8 | − | 4.91902e8i | −0.747183 | − | 0.562996i | ||||
\(957\) | 1.03888e9 | 1.18530 | ||||||||
\(958\) | −4.27994e8 | − | 8.58381e8i | −0.486790 | − | 0.976301i | ||||
\(959\) | − | 9.71965e8i | − | 1.10203i | ||||||
\(960\) | −7.82145e7 | + | 2.03829e8i | −0.0884044 | + | 0.230384i | ||||
\(961\) | 6.29789e8 | 0.709618 | ||||||||
\(962\) | −4.13260e7 | + | 2.06054e7i | −0.0464192 | + | 0.0231449i | ||||
\(963\) | − | 2.26844e8i | − | 0.254009i | ||||||
\(964\) | −9.63049e8 | + | 1.27811e9i | −1.07502 | + | 1.42672i | ||||
\(965\) | −2.49389e8 | −0.277520 | ||||||||
\(966\) | −1.67724e8 | − | 3.36386e8i | −0.186065 | − | 0.373170i | ||||
\(967\) | − | 9.26100e8i | − | 1.02419i | −0.858930 | − | 0.512093i | \(-0.828870\pi\) | ||
0.858930 | − | 0.512093i | \(-0.171130\pi\) | |||||||
\(968\) | 2.38091e7 | − | 1.28505e8i | 0.0262492 | − | 0.141676i | ||||
\(969\) | −2.08205e8 | −0.228833 | ||||||||
\(970\) | −1.46702e8 | + | 7.31464e7i | −0.160738 | + | 0.0801452i | ||||
\(971\) | − | 7.96889e8i | − | 0.870443i | −0.900323 | − | 0.435221i | \(-0.856670\pi\) | ||
0.900323 | − | 0.435221i | \(-0.143330\pi\) | |||||||
\(972\) | 6.36773e8 | + | 4.79803e8i | 0.693404 | + | 0.522474i | ||||
\(973\) | −1.41609e9 | −1.53728 | ||||||||
\(974\) | 3.46859e8 | + | 6.95657e8i | 0.375384 | + | 0.752867i | ||||
\(975\) | 1.71793e7i | 0.0185349i | ||||||||
\(976\) | 7.49563e7 | + | 2.61325e8i | 0.0806229 | + | 0.281081i | ||||
\(977\) | 4.11830e8 | 0.441605 | 0.220803 | − | 0.975319i | \(-0.429132\pi\) | ||||
0.220803 | + | 0.975319i | \(0.429132\pi\) | |||||||
\(978\) | −7.23573e8 | + | 3.60778e8i | −0.773510 | + | 0.385677i | ||||
\(979\) | − | 4.41652e8i | − | 0.470687i | ||||||
\(980\) | −6.29536e7 | + | 8.35492e7i | −0.0668871 | + | 0.0887696i | ||||
\(981\) | −5.49721e8 | −0.582285 | ||||||||
\(982\) | −4.59032e8 | − | 9.20630e8i | −0.484740 | − | 0.972189i | ||||
\(983\) | − | 4.34128e8i | − | 0.457043i | −0.973539 | − | 0.228522i | \(-0.926611\pi\) | ||
0.973539 | − | 0.228522i | \(-0.0733892\pi\) | |||||||
\(984\) | −5.25043e8 | − | 9.72784e7i | −0.551073 | − | 0.102101i | ||||
\(985\) | 1.96153e8 | 0.205251 | ||||||||
\(986\) | 1.85043e9 | − | 9.22634e8i | 1.93037 | − | 0.962496i | ||||
\(987\) | 1.30908e8i | 0.136149i | ||||||||
\(988\) | −5.19236e6 | − | 3.91240e6i | −0.00538386 | − | 0.00405669i | ||||
\(989\) | −8.43182e8 | −0.871631 | ||||||||
\(990\) | 7.78340e7 | + | 1.56103e8i | 0.0802165 | + | 0.160881i | ||||
\(991\) | 1.87758e9i | 1.92920i | 0.263725 | + | 0.964598i | \(0.415049\pi\) | ||||
−0.263725 | + | 0.964598i | \(0.584951\pi\) | |||||||
\(992\) | −3.87803e8 | + | 3.55427e8i | −0.397261 | + | 0.364095i | ||||
\(993\) | 5.34271e8 | 0.545650 | ||||||||
\(994\) | −1.08392e9 | + | 5.40448e8i | −1.10366 | + | 0.550294i | ||||
\(995\) | − | 2.24667e8i | − | 0.228071i | ||||||
\(996\) | −4.17213e8 | + | 5.53707e8i | −0.422260 | + | 0.560405i | ||||
\(997\) | 1.35522e9 | 1.36749 | 0.683744 | − | 0.729722i | \(-0.260350\pi\) | ||||
0.683744 | + | 0.729722i | \(0.260350\pi\) | |||||||
\(998\) | 1.98068e8 | + | 3.97243e8i | 0.199261 | + | 0.399636i | ||||
\(999\) | − | 1.87411e9i | − | 1.87974i |
(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 | 76.7.b.a.39.10 | yes | 54 | |
4.3 | odd | 2 | inner | 76.7.b.a.39.9 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.b.a.39.9 | ✓ | 54 | 4.3 | odd | 2 | inner | |
76.7.b.a.39.10 | yes | 54 | 1.1 | even | 1 | trivial |