Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (of order \(4\), degree \(2\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 497.3 | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.h.683.3 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −1.50338 | + | 0.860137i | −0.867979 | + | 0.496600i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.19538 | − | 0.424609i | 0.981805 | − | 0.189891i | ||||
\(6\) | 0.454844 | − | 1.67126i | 0.185689 | − | 0.682290i | ||||
\(7\) | −0.358790 | − | 0.358790i | −0.135610 | − | 0.135610i | 0.636043 | − | 0.771653i | \(-0.280570\pi\) |
−0.771653 | + | 0.636043i | \(0.780570\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.52033 | − | 2.58623i | 0.506776 | − | 0.862078i | ||||
\(10\) | −1.25213 | + | 1.85261i | −0.395957 | + | 0.585848i | ||||
\(11\) | − | 1.95505i | − | 0.589470i | −0.955579 | − | 0.294735i | \(-0.904769\pi\) | ||
0.955579 | − | 0.294735i | \(-0.0952313\pi\) | |||||||
\(12\) | 0.860137 | + | 1.50338i | 0.248300 | + | 0.433990i | ||||
\(13\) | 1.74122 | − | 1.74122i | 0.482927 | − | 0.482927i | −0.423138 | − | 0.906065i | \(-0.639071\pi\) |
0.906065 | + | 0.423138i | \(0.139071\pi\) | |||||||
\(14\) | 0.507406 | 0.135610 | ||||||||
\(15\) | −2.93528 | + | 2.52668i | −0.757886 | + | 0.652386i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.65749 | + | 3.65749i | −0.887071 | + | 0.887071i | −0.994241 | − | 0.107170i | \(-0.965821\pi\) |
0.107170 | + | 0.994241i | \(0.465821\pi\) | |||||||
\(18\) | 0.753709 | + | 2.90378i | 0.177651 | + | 0.684427i | ||||
\(19\) | − | 3.69824i | − | 0.848434i | −0.905561 | − | 0.424217i | \(-0.860549\pi\) | ||
0.905561 | − | 0.424217i | \(-0.139451\pi\) | |||||||
\(20\) | −0.424609 | − | 2.19538i | −0.0949456 | − | 0.490903i | ||||
\(21\) | 0.848008 | + | 0.230791i | 0.185051 | + | 0.0503626i | ||||
\(22\) | 1.38243 | + | 1.38243i | 0.294735 | + | 0.294735i | ||||
\(23\) | −6.27796 | − | 6.27796i | −1.30905 | − | 1.30905i | −0.922104 | − | 0.386942i | \(-0.873531\pi\) |
−0.386942 | − | 0.922104i | \(-0.626469\pi\) | |||||||
\(24\) | −1.67126 | − | 0.454844i | −0.341145 | − | 0.0928447i | ||||
\(25\) | 4.63941 | − | 1.86436i | 0.927883 | − | 0.372872i | ||||
\(26\) | 2.46246i | 0.482927i | ||||||||
\(27\) | −0.0611210 | + | 5.19579i | −0.0117627 | + | 0.999931i | ||||
\(28\) | −0.358790 | + | 0.358790i | −0.0678050 | + | 0.0678050i | ||||
\(29\) | −8.51841 | −1.58183 | −0.790914 | − | 0.611927i | \(-0.790395\pi\) | ||||
−0.790914 | + | 0.611927i | \(0.790395\pi\) | |||||||
\(30\) | 0.288924 | − | 3.86219i | 0.0527500 | − | 0.705136i | ||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 1.68161 | + | 2.93919i | 0.292731 | + | 0.511647i | ||||
\(34\) | − | 5.17247i | − | 0.887071i | ||||||
\(35\) | −0.940028 | − | 0.635336i | −0.158894 | − | 0.107391i | ||||
\(36\) | −2.58623 | − | 1.52033i | −0.431039 | − | 0.253388i | ||||
\(37\) | −1.92806 | − | 1.92806i | −0.316972 | − | 0.316972i | 0.530631 | − | 0.847603i | \(-0.321955\pi\) |
−0.847603 | + | 0.530631i | \(0.821955\pi\) | |||||||
\(38\) | 2.61505 | + | 2.61505i | 0.424217 | + | 0.424217i | ||||
\(39\) | −1.12003 | + | 4.11541i | −0.179349 | + | 0.658993i | ||||
\(40\) | 1.85261 | + | 1.25213i | 0.292924 | + | 0.197979i | ||||
\(41\) | − | 9.77147i | − | 1.52605i | −0.646371 | − | 0.763024i | \(-0.723714\pi\) | ||
0.646371 | − | 0.763024i | \(-0.276286\pi\) | |||||||
\(42\) | −0.762826 | + | 0.436439i | −0.117707 | + | 0.0673440i | ||||
\(43\) | −1.51772 | + | 1.51772i | −0.231451 | + | 0.231451i | −0.813298 | − | 0.581847i | \(-0.802330\pi\) |
0.581847 | + | 0.813298i | \(0.302330\pi\) | |||||||
\(44\) | −1.95505 | −0.294735 | ||||||||
\(45\) | 2.23956 | − | 6.32332i | 0.333854 | − | 0.942625i | ||||
\(46\) | 8.87838 | 1.30905 | ||||||||
\(47\) | −4.14558 | + | 4.14558i | −0.604695 | + | 0.604695i | −0.941555 | − | 0.336860i | \(-0.890635\pi\) |
0.336860 | + | 0.941555i | \(0.390635\pi\) | |||||||
\(48\) | 1.50338 | − | 0.860137i | 0.216995 | − | 0.124150i | ||||
\(49\) | − | 6.74254i | − | 0.963220i | ||||||
\(50\) | −1.96226 | + | 4.59886i | −0.277505 | + | 0.650377i | ||||
\(51\) | 2.35267 | − | 8.64455i | 0.329439 | − | 1.21048i | ||||
\(52\) | −1.74122 | − | 1.74122i | −0.241464 | − | 0.241464i | ||||
\(53\) | 9.34225 | + | 9.34225i | 1.28326 | + | 1.28326i | 0.938804 | + | 0.344452i | \(0.111935\pi\) |
0.344452 | + | 0.938804i | \(0.388065\pi\) | |||||||
\(54\) | −3.63076 | − | 3.71720i | −0.494084 | − | 0.505847i | ||||
\(55\) | −0.830133 | − | 4.29208i | −0.111935 | − | 0.578744i | ||||
\(56\) | − | 0.507406i | − | 0.0678050i | ||||||
\(57\) | 3.18099 | + | 5.55987i | 0.421333 | + | 0.736423i | ||||
\(58\) | 6.02342 | − | 6.02342i | 0.790914 | − | 0.790914i | ||||
\(59\) | −1.87779 | −0.244468 | −0.122234 | − | 0.992501i | \(-0.539006\pi\) | ||||
−0.122234 | + | 0.992501i | \(0.539006\pi\) | |||||||
\(60\) | 2.52668 | + | 2.93528i | 0.326193 | + | 0.378943i | ||||
\(61\) | 10.5206 | 1.34702 | 0.673510 | − | 0.739178i | \(-0.264786\pi\) | ||||
0.673510 | + | 0.739178i | \(0.264786\pi\) | |||||||
\(62\) | 0.707107 | − | 0.707107i | 0.0898027 | − | 0.0898027i | ||||
\(63\) | −1.47339 | + | 0.382436i | −0.185630 | + | 0.0481825i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 3.08330 | − | 4.56198i | 0.382437 | − | 0.565844i | ||||
\(66\) | −3.26740 | − | 0.889243i | −0.402189 | − | 0.109458i | ||||
\(67\) | −7.86226 | − | 7.86226i | −0.960528 | − | 0.960528i | 0.0387218 | − | 0.999250i | \(-0.487671\pi\) |
−0.999250 | + | 0.0387218i | \(0.987671\pi\) | |||||||
\(68\) | 3.65749 | + | 3.65749i | 0.443535 | + | 0.443535i | ||||
\(69\) | 14.8381 | + | 4.03828i | 1.78630 | + | 0.486152i | ||||
\(70\) | 1.11395 | − | 0.215449i | 0.133143 | − | 0.0257511i | ||||
\(71\) | − | 2.88620i | − | 0.342529i | −0.985225 | − | 0.171264i | \(-0.945215\pi\) | ||
0.985225 | − | 0.171264i | \(-0.0547852\pi\) | |||||||
\(72\) | 2.90378 | − | 0.753709i | 0.342213 | − | 0.0888255i | ||||
\(73\) | 9.70365 | − | 9.70365i | 1.13573 | − | 1.13573i | 0.146518 | − | 0.989208i | \(-0.453193\pi\) |
0.989208 | − | 0.146518i | \(-0.0468067\pi\) | |||||||
\(74\) | 2.72669 | 0.316972 | ||||||||
\(75\) | −5.37121 | + | 6.79338i | −0.620214 | + | 0.784432i | ||||
\(76\) | −3.69824 | −0.424217 | ||||||||
\(77\) | −0.701453 | + | 0.701453i | −0.0799379 | + | 0.0799379i | ||||
\(78\) | −2.11805 | − | 3.70202i | −0.239822 | − | 0.419171i | ||||
\(79\) | − | 1.35078i | − | 0.151974i | −0.997109 | − | 0.0759872i | \(-0.975789\pi\) | ||
0.997109 | − | 0.0759872i | \(-0.0242108\pi\) | |||||||
\(80\) | −2.19538 | + | 0.424609i | −0.245451 | + | 0.0474728i | ||||
\(81\) | −4.37721 | − | 7.86385i | −0.486356 | − | 0.873761i | ||||
\(82\) | 6.90947 | + | 6.90947i | 0.763024 | + | 0.763024i | ||||
\(83\) | −2.46289 | − | 2.46289i | −0.270337 | − | 0.270337i | 0.558899 | − | 0.829236i | \(-0.311224\pi\) |
−0.829236 | + | 0.558899i | \(0.811224\pi\) | |||||||
\(84\) | 0.230791 | − | 0.848008i | 0.0251813 | − | 0.0925253i | ||||
\(85\) | −6.47658 | + | 9.58259i | −0.702484 | + | 1.03938i | ||||
\(86\) | − | 2.14639i | − | 0.231451i | ||||||
\(87\) | 12.8064 | − | 7.32700i | 1.37299 | − | 0.785537i | ||||
\(88\) | 1.38243 | − | 1.38243i | 0.147367 | − | 0.147367i | ||||
\(89\) | 0.192825 | 0.0204395 | 0.0102197 | − | 0.999948i | \(-0.496747\pi\) | ||||
0.0102197 | + | 0.999948i | \(0.496747\pi\) | |||||||
\(90\) | 2.88765 | + | 6.05487i | 0.304385 | + | 0.638239i | ||||
\(91\) | −1.24946 | −0.130979 | ||||||||
\(92\) | −6.27796 | + | 6.27796i | −0.654523 | + | 0.654523i | ||||
\(93\) | 1.50338 | − | 0.860137i | 0.155894 | − | 0.0891921i | ||||
\(94\) | − | 5.86273i | − | 0.604695i | ||||||
\(95\) | −1.57031 | − | 8.11905i | −0.161110 | − | 0.832997i | ||||
\(96\) | −0.454844 | + | 1.67126i | −0.0464223 | + | 0.170572i | ||||
\(97\) | 1.01182 | + | 1.01182i | 0.102735 | + | 0.102735i | 0.756606 | − | 0.653871i | \(-0.226856\pi\) |
−0.653871 | + | 0.756606i | \(0.726856\pi\) | |||||||
\(98\) | 4.76770 | + | 4.76770i | 0.481610 | + | 0.481610i | ||||
\(99\) | −5.05622 | − | 2.97232i | −0.508169 | − | 0.298729i | ||||
\(100\) | −1.86436 | − | 4.63941i | −0.186436 | − | 0.463941i | ||||
\(101\) | 0.318549i | 0.0316969i | 0.999874 | + | 0.0158484i | \(0.00504492\pi\) | ||||
−0.999874 | + | 0.0158484i | \(0.994955\pi\) | |||||||
\(102\) | 4.44903 | + | 7.77620i | 0.440520 | + | 0.769959i | ||||
\(103\) | 11.0476 | − | 11.0476i | 1.08856 | − | 1.08856i | 0.0928796 | − | 0.995677i | \(-0.470393\pi\) |
0.995677 | − | 0.0928796i | \(-0.0296072\pi\) | |||||||
\(104\) | 2.46246 | 0.241464 | ||||||||
\(105\) | 1.95970 | + | 0.146602i | 0.191247 | + | 0.0143068i | ||||
\(106\) | −13.2119 | −1.28326 | ||||||||
\(107\) | 1.88705 | − | 1.88705i | 0.182428 | − | 0.182428i | −0.609985 | − | 0.792413i | \(-0.708824\pi\) |
0.792413 | + | 0.609985i | \(0.208824\pi\) | |||||||
\(108\) | 5.19579 | + | 0.0611210i | 0.499965 | + | 0.00588137i | ||||
\(109\) | − | 0.0819468i | − | 0.00784908i | −0.999992 | − | 0.00392454i | \(-0.998751\pi\) | ||
0.999992 | − | 0.00392454i | \(-0.00124922\pi\) | |||||||
\(110\) | 3.62195 | + | 2.44797i | 0.345340 | + | 0.233405i | ||||
\(111\) | 4.55702 | + | 1.24022i | 0.432533 | + | 0.117717i | ||||
\(112\) | 0.358790 | + | 0.358790i | 0.0339025 | + | 0.0339025i | ||||
\(113\) | 9.29128 | + | 9.29128i | 0.874050 | + | 0.874050i | 0.992911 | − | 0.118861i | \(-0.0379242\pi\) |
−0.118861 | + | 0.992911i | \(0.537924\pi\) | |||||||
\(114\) | −6.18072 | − | 1.68212i | −0.578878 | − | 0.157545i | ||||
\(115\) | −16.4482 | − | 11.1169i | −1.53380 | − | 1.03665i | ||||
\(116\) | 8.51841i | 0.790914i | ||||||||
\(117\) | −1.85598 | − | 7.15042i | −0.171585 | − | 0.661057i | ||||
\(118\) | 1.32780 | − | 1.32780i | 0.122234 | − | 0.122234i | ||||
\(119\) | 2.62454 | 0.240591 | ||||||||
\(120\) | −3.86219 | − | 0.288924i | −0.352568 | − | 0.0263750i | ||||
\(121\) | 7.17778 | 0.652525 | ||||||||
\(122\) | −7.43916 | + | 7.43916i | −0.673510 | + | 0.673510i | ||||
\(123\) | 8.40481 | + | 14.6903i | 0.757836 | + | 1.32458i | ||||
\(124\) | 1.00000i | 0.0898027i | ||||||||
\(125\) | 9.39366 | − | 6.06293i | 0.840195 | − | 0.542284i | ||||
\(126\) | 0.771423 | − | 1.31227i | 0.0687238 | − | 0.116906i | ||||
\(127\) | 5.42117 | + | 5.42117i | 0.481051 | + | 0.481051i | 0.905467 | − | 0.424416i | \(-0.139521\pi\) |
−0.424416 | + | 0.905467i | \(0.639521\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0.976271 | − | 3.58717i | 0.0859559 | − | 0.315833i | ||||
\(130\) | 1.04558 | + | 5.40603i | 0.0917036 | + | 0.474141i | ||||
\(131\) | − | 15.0074i | − | 1.31120i | −0.755107 | − | 0.655601i | \(-0.772415\pi\) | ||
0.755107 | − | 0.655601i | \(-0.227585\pi\) | |||||||
\(132\) | 2.93919 | − | 1.68161i | 0.255824 | − | 0.146365i | ||||
\(133\) | −1.32689 | + | 1.32689i | −0.115056 | + | 0.115056i | ||||
\(134\) | 11.1189 | 0.960528 | ||||||||
\(135\) | 2.07200 | + | 11.4327i | 0.178329 | + | 0.983971i | ||||
\(136\) | −5.17247 | −0.443535 | ||||||||
\(137\) | −2.32290 | + | 2.32290i | −0.198459 | + | 0.198459i | −0.799339 | − | 0.600880i | \(-0.794817\pi\) |
0.600880 | + | 0.799339i | \(0.294817\pi\) | |||||||
\(138\) | −13.3476 | + | 7.63663i | −1.13622 | + | 0.650073i | ||||
\(139\) | 9.23533i | 0.783331i | 0.920108 | + | 0.391665i | \(0.128101\pi\) | ||||
−0.920108 | + | 0.391665i | \(0.871899\pi\) | |||||||
\(140\) | −0.635336 | + | 0.940028i | −0.0536957 | + | 0.0794468i | ||||
\(141\) | 2.66663 | − | 9.79816i | 0.224571 | − | 0.825154i | ||||
\(142\) | 2.04085 | + | 2.04085i | 0.171264 | + | 0.171264i | ||||
\(143\) | −3.40417 | − | 3.40417i | −0.284671 | − | 0.284671i | ||||
\(144\) | −1.52033 | + | 2.58623i | −0.126694 | + | 0.215519i | ||||
\(145\) | −18.7012 | + | 3.61700i | −1.55305 | + | 0.300375i | ||||
\(146\) | 13.7230i | 1.13573i | ||||||||
\(147\) | 5.79951 | + | 10.1366i | 0.478335 | + | 0.836055i | ||||
\(148\) | −1.92806 | + | 1.92806i | −0.158486 | + | 0.158486i | ||||
\(149\) | 0.823443 | 0.0674591 | 0.0337295 | − | 0.999431i | \(-0.489262\pi\) | ||||
0.0337295 | + | 0.999431i | \(0.489262\pi\) | |||||||
\(150\) | −1.00562 | − | 8.60167i | −0.0821089 | − | 0.702323i | ||||
\(151\) | −11.6623 | −0.949068 | −0.474534 | − | 0.880237i | \(-0.657383\pi\) | ||||
−0.474534 | + | 0.880237i | \(0.657383\pi\) | |||||||
\(152\) | 2.61505 | − | 2.61505i | 0.212108 | − | 0.212108i | ||||
\(153\) | 3.89854 | + | 15.0197i | 0.315178 | + | 1.21427i | ||||
\(154\) | − | 0.992004i | − | 0.0799379i | ||||||
\(155\) | −2.19538 | + | 0.424609i | −0.176337 | + | 0.0341055i | ||||
\(156\) | 4.11541 | + | 1.12003i | 0.329496 | + | 0.0896745i | ||||
\(157\) | −14.8439 | − | 14.8439i | −1.18467 | − | 1.18467i | −0.978520 | − | 0.206152i | \(-0.933906\pi\) |
−0.206152 | − | 0.978520i | \(-0.566094\pi\) | |||||||
\(158\) | 0.955144 | + | 0.955144i | 0.0759872 | + | 0.0759872i | ||||
\(159\) | −22.0806 | − | 6.00937i | −1.75111 | − | 0.476574i | ||||
\(160\) | 1.25213 | − | 1.85261i | 0.0989893 | − | 0.146462i | ||||
\(161\) | 4.50494i | 0.355039i | ||||||||
\(162\) | 8.65573 | + | 2.46543i | 0.680058 | + | 0.193702i | ||||
\(163\) | −13.7523 | + | 13.7523i | −1.07716 | + | 1.07716i | −0.0803969 | + | 0.996763i | \(0.525619\pi\) |
−0.996763 | + | 0.0803969i | \(0.974381\pi\) | |||||||
\(164\) | −9.77147 | −0.763024 | ||||||||
\(165\) | 4.93979 | + | 5.73862i | 0.384562 | + | 0.446751i | ||||
\(166\) | 3.48305 | 0.270337 | ||||||||
\(167\) | −17.7715 | + | 17.7715i | −1.37520 | + | 1.37520i | −0.522652 | + | 0.852546i | \(0.675057\pi\) |
−0.852546 | + | 0.522652i | \(0.824943\pi\) | |||||||
\(168\) | 0.436439 | + | 0.762826i | 0.0336720 | + | 0.0588533i | ||||
\(169\) | 6.93631i | 0.533562i | ||||||||
\(170\) | −2.19628 | − | 11.3555i | −0.168447 | − | 0.870931i | ||||
\(171\) | −9.56450 | − | 5.62253i | −0.731416 | − | 0.429966i | ||||
\(172\) | 1.51772 | + | 1.51772i | 0.115725 | + | 0.115725i | ||||
\(173\) | −2.20529 | − | 2.20529i | −0.167665 | − | 0.167665i | 0.618287 | − | 0.785952i | \(-0.287827\pi\) |
−0.785952 | + | 0.618287i | \(0.787827\pi\) | |||||||
\(174\) | −3.87455 | + | 14.2365i | −0.293729 | + | 1.07927i | ||||
\(175\) | −2.33349 | − | 0.995662i | −0.176395 | − | 0.0752649i | ||||
\(176\) | 1.95505i | 0.147367i | ||||||||
\(177\) | 2.82304 | − | 1.61516i | 0.212193 | − | 0.121403i | ||||
\(178\) | −0.136348 | + | 0.136348i | −0.0102197 | + | 0.0102197i | ||||
\(179\) | −3.73765 | −0.279365 | −0.139682 | − | 0.990196i | \(-0.544608\pi\) | ||||
−0.139682 | + | 0.990196i | \(0.544608\pi\) | |||||||
\(180\) | −6.32332 | − | 2.23956i | −0.471312 | − | 0.166927i | ||||
\(181\) | −17.5399 | −1.30373 | −0.651863 | − | 0.758336i | \(-0.726012\pi\) | ||||
−0.651863 | + | 0.758336i | \(0.726012\pi\) | |||||||
\(182\) | 0.883505 | − | 0.883505i | 0.0654897 | − | 0.0654897i | ||||
\(183\) | −15.8164 | + | 9.04913i | −1.16919 | + | 0.668931i | ||||
\(184\) | − | 8.87838i | − | 0.654523i | ||||||
\(185\) | −5.05151 | − | 3.41416i | −0.371394 | − | 0.251014i | ||||
\(186\) | −0.454844 | + | 1.67126i | −0.0333508 | + | 0.122543i | ||||
\(187\) | 7.15057 | + | 7.15057i | 0.522901 | + | 0.522901i | ||||
\(188\) | 4.14558 | + | 4.14558i | 0.302347 | + | 0.302347i | ||||
\(189\) | 1.88613 | − | 1.84227i | 0.137196 | − | 0.134005i | ||||
\(190\) | 6.85141 | + | 4.63066i | 0.497053 | + | 0.335943i | ||||
\(191\) | 2.42501i | 0.175468i | 0.996144 | + | 0.0877339i | \(0.0279625\pi\) | ||||
−0.996144 | + | 0.0877339i | \(0.972037\pi\) | |||||||
\(192\) | −0.860137 | − | 1.50338i | −0.0620751 | − | 0.108497i | ||||
\(193\) | −8.58471 | + | 8.58471i | −0.617941 | + | 0.617941i | −0.945003 | − | 0.327062i | \(-0.893941\pi\) |
0.327062 | + | 0.945003i | \(0.393941\pi\) | |||||||
\(194\) | −1.43093 | −0.102735 | ||||||||
\(195\) | −0.711462 | + | 9.51048i | −0.0509488 | + | 0.681059i | ||||
\(196\) | −6.74254 | −0.481610 | ||||||||
\(197\) | 17.2273 | − | 17.2273i | 1.22740 | − | 1.22740i | 0.262452 | − | 0.964945i | \(-0.415469\pi\) |
0.964945 | − | 0.262452i | \(-0.0845311\pi\) | |||||||
\(198\) | 5.67703 | − | 1.47354i | 0.403449 | − | 0.104720i | ||||
\(199\) | 13.5961i | 0.963801i | 0.876226 | + | 0.481900i | \(0.160053\pi\) | ||||
−0.876226 | + | 0.481900i | \(0.839947\pi\) | |||||||
\(200\) | 4.59886 | + | 1.96226i | 0.325189 | + | 0.138753i | ||||
\(201\) | 18.5826 | + | 5.05738i | 1.31072 | + | 0.356720i | ||||
\(202\) | −0.225248 | − | 0.225248i | −0.0158484 | − | 0.0158484i | ||||
\(203\) | 3.05632 | + | 3.05632i | 0.214512 | + | 0.214512i | ||||
\(204\) | −8.64455 | − | 2.35267i | −0.605239 | − | 0.164720i | ||||
\(205\) | −4.14906 | − | 21.4521i | −0.289783 | − | 1.49828i | ||||
\(206\) | 15.6237i | 1.08856i | ||||||||
\(207\) | −25.7808 | + | 6.69172i | −1.79189 | + | 0.465107i | ||||
\(208\) | −1.74122 | + | 1.74122i | −0.120732 | + | 0.120732i | ||||
\(209\) | −7.23024 | −0.500126 | ||||||||
\(210\) | −1.48938 | + | 1.28205i | −0.102777 | + | 0.0884701i | ||||
\(211\) | 26.5004 | 1.82436 | 0.912182 | − | 0.409785i | \(-0.134396\pi\) | ||||
0.912182 | + | 0.409785i | \(0.134396\pi\) | |||||||
\(212\) | 9.34225 | − | 9.34225i | 0.641628 | − | 0.641628i | ||||
\(213\) | 2.48253 | + | 4.33906i | 0.170100 | + | 0.297308i | ||||
\(214\) | 2.66870i | 0.182428i | ||||||||
\(215\) | −2.68755 | + | 3.97643i | −0.183289 | + | 0.271190i | ||||
\(216\) | −3.71720 | + | 3.63076i | −0.252923 | + | 0.247042i | ||||
\(217\) | 0.358790 | + | 0.358790i | 0.0243563 | + | 0.0243563i | ||||
\(218\) | 0.0579452 | + | 0.0579452i | 0.00392454 | + | 0.00392454i | ||||
\(219\) | −6.24184 | + | 22.9348i | −0.421785 | + | 1.54979i | ||||
\(220\) | −4.29208 | + | 0.830133i | −0.289372 | + | 0.0559675i | ||||
\(221\) | 12.7370i | 0.856781i | ||||||||
\(222\) | −4.09927 | + | 2.34533i | −0.275125 | + | 0.157408i | ||||
\(223\) | 19.1668 | − | 19.1668i | 1.28350 | − | 1.28350i | 0.344842 | − | 0.938661i | \(-0.387933\pi\) |
0.938661 | − | 0.344842i | \(-0.112067\pi\) | |||||||
\(224\) | −0.507406 | −0.0339025 | ||||||||
\(225\) | 2.23176 | − | 14.8330i | 0.148784 | − | 0.988870i | ||||
\(226\) | −13.1399 | −0.874050 | ||||||||
\(227\) | −1.96350 | + | 1.96350i | −0.130322 | + | 0.130322i | −0.769259 | − | 0.638937i | \(-0.779374\pi\) |
0.638937 | + | 0.769259i | \(0.279374\pi\) | |||||||
\(228\) | 5.55987 | − | 3.18099i | 0.368211 | − | 0.210666i | ||||
\(229\) | 1.32660i | 0.0876644i | 0.999039 | + | 0.0438322i | \(0.0139567\pi\) | ||||
−0.999039 | + | 0.0438322i | \(0.986043\pi\) | |||||||
\(230\) | 19.4914 | − | 3.76984i | 1.28523 | − | 0.248576i | ||||
\(231\) | 0.451207 | − | 1.65790i | 0.0296873 | − | 0.109082i | ||||
\(232\) | −6.02342 | − | 6.02342i | −0.395457 | − | 0.395457i | ||||
\(233\) | −7.07940 | − | 7.07940i | −0.463787 | − | 0.463787i | 0.436108 | − | 0.899894i | \(-0.356357\pi\) |
−0.899894 | + | 0.436108i | \(0.856357\pi\) | |||||||
\(234\) | 6.36849 | + | 3.74374i | 0.416321 | + | 0.244736i | ||||
\(235\) | −7.34088 | + | 10.8614i | −0.478866 | + | 0.708519i | ||||
\(236\) | 1.87779i | 0.122234i | ||||||||
\(237\) | 1.16185 | + | 2.03074i | 0.0754705 | + | 0.131911i | ||||
\(238\) | −1.85583 | + | 1.85583i | −0.120296 | + | 0.120296i | ||||
\(239\) | 9.69880 | 0.627363 | 0.313682 | − | 0.949528i | \(-0.398438\pi\) | ||||
0.313682 | + | 0.949528i | \(0.398438\pi\) | |||||||
\(240\) | 2.93528 | − | 2.52668i | 0.189472 | − | 0.163097i | ||||
\(241\) | 1.35150 | 0.0870581 | 0.0435290 | − | 0.999052i | \(-0.486140\pi\) | ||||
0.0435290 | + | 0.999052i | \(0.486140\pi\) | |||||||
\(242\) | −5.07546 | + | 5.07546i | −0.326263 | + | 0.326263i | ||||
\(243\) | 13.3446 | + | 8.05738i | 0.856057 | + | 0.516881i | ||||
\(244\) | − | 10.5206i | − | 0.673510i | ||||||
\(245\) | −2.86295 | − | 14.8025i | −0.182907 | − | 0.945694i | ||||
\(246\) | −16.3307 | − | 4.44450i | −1.04121 | − | 0.283371i | ||||
\(247\) | −6.43944 | − | 6.43944i | −0.409732 | − | 0.409732i | ||||
\(248\) | −0.707107 | − | 0.707107i | −0.0449013 | − | 0.0449013i | ||||
\(249\) | 5.82109 | + | 1.58425i | 0.368897 | + | 0.100398i | ||||
\(250\) | −2.35519 | + | 10.9295i | −0.148955 | + | 0.691240i | ||||
\(251\) | − | 20.3533i | − | 1.28469i | −0.766417 | − | 0.642343i | \(-0.777962\pi\) | ||
0.766417 | − | 0.642343i | \(-0.222038\pi\) | |||||||
\(252\) | 0.382436 | + | 1.47339i | 0.0240912 | + | 0.0928151i | ||||
\(253\) | −12.2737 | + | 12.2737i | −0.771643 | + | 0.771643i | ||||
\(254\) | −7.66669 | −0.481051 | ||||||||
\(255\) | 1.49445 | − | 19.9771i | 0.0935860 | − | 1.25101i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.9170 | + | 17.9170i | −1.11763 | + | 1.11763i | −0.125546 | + | 0.992088i | \(0.540068\pi\) |
−0.992088 | + | 0.125546i | \(0.959932\pi\) | |||||||
\(258\) | 1.84619 | + | 3.22684i | 0.114939 | + | 0.200894i | ||||
\(259\) | 1.38354i | 0.0859690i | ||||||||
\(260\) | −4.56198 | − | 3.08330i | −0.282922 | − | 0.191218i | ||||
\(261\) | −12.9508 | + | 22.0306i | −0.801633 | + | 1.36366i | ||||
\(262\) | 10.6118 | + | 10.6118i | 0.655601 | + | 0.655601i | ||||
\(263\) | −14.2853 | − | 14.2853i | −0.880869 | − | 0.880869i | 0.112754 | − | 0.993623i | \(-0.464033\pi\) |
−0.993623 | + | 0.112754i | \(0.964033\pi\) | |||||||
\(264\) | −0.889243 | + | 3.26740i | −0.0547291 | + | 0.201095i | ||||
\(265\) | 24.4766 | + | 16.5430i | 1.50359 | + | 1.01623i | ||||
\(266\) | − | 1.87651i | − | 0.115056i | ||||||
\(267\) | −0.289891 | + | 0.165856i | −0.0177410 | + | 0.0101502i | ||||
\(268\) | −7.86226 | + | 7.86226i | −0.480264 | + | 0.480264i | ||||
\(269\) | 2.28146 | 0.139103 | 0.0695514 | − | 0.997578i | \(-0.477843\pi\) | ||||
0.0695514 | + | 0.997578i | \(0.477843\pi\) | |||||||
\(270\) | −9.54927 | − | 6.61902i | −0.581150 | − | 0.402821i | ||||
\(271\) | 16.6154 | 1.00931 | 0.504657 | − | 0.863320i | \(-0.331619\pi\) | ||||
0.504657 | + | 0.863320i | \(0.331619\pi\) | |||||||
\(272\) | 3.65749 | − | 3.65749i | 0.221768 | − | 0.221768i | ||||
\(273\) | 1.87843 | − | 1.07471i | 0.113687 | − | 0.0650445i | ||||
\(274\) | − | 3.28508i | − | 0.198459i | ||||||
\(275\) | −3.64492 | − | 9.07028i | −0.219797 | − | 0.546959i | ||||
\(276\) | 4.03828 | − | 14.8381i | 0.243076 | − | 0.893149i | ||||
\(277\) | −8.63825 | − | 8.63825i | −0.519022 | − | 0.519022i | 0.398253 | − | 0.917275i | \(-0.369616\pi\) |
−0.917275 | + | 0.398253i | \(0.869616\pi\) | |||||||
\(278\) | −6.53037 | − | 6.53037i | −0.391665 | − | 0.391665i | ||||
\(279\) | −1.52033 | + | 2.58623i | −0.0910196 | + | 0.154834i | ||||
\(280\) | −0.215449 | − | 1.11395i | −0.0128756 | − | 0.0665713i | ||||
\(281\) | 1.91141i | 0.114025i | 0.998373 | + | 0.0570126i | \(0.0181575\pi\) | ||||
−0.998373 | + | 0.0570126i | \(0.981842\pi\) | |||||||
\(282\) | 5.04276 | + | 8.81394i | 0.300292 | + | 0.524862i | ||||
\(283\) | 18.8289 | − | 18.8289i | 1.11926 | − | 1.11926i | 0.127413 | − | 0.991850i | \(-0.459333\pi\) |
0.991850 | − | 0.127413i | \(-0.0406672\pi\) | |||||||
\(284\) | −2.88620 | −0.171264 | ||||||||
\(285\) | 9.34427 | + | 10.8554i | 0.553507 | + | 0.643016i | ||||
\(286\) | 4.81422 | 0.284671 | ||||||||
\(287\) | −3.50591 | + | 3.50591i | −0.206947 | + | 0.206947i | ||||
\(288\) | −0.753709 | − | 2.90378i | −0.0444127 | − | 0.171107i | ||||
\(289\) | − | 9.75441i | − | 0.573789i | ||||||
\(290\) | 10.6661 | − | 15.7813i | 0.626336 | − | 0.926711i | ||||
\(291\) | −2.39146 | − | 0.650852i | −0.140190 | − | 0.0381536i | ||||
\(292\) | −9.70365 | − | 9.70365i | −0.567863 | − | 0.567863i | ||||
\(293\) | 13.7308 | + | 13.7308i | 0.802162 | + | 0.802162i | 0.983433 | − | 0.181271i | \(-0.0580211\pi\) |
−0.181271 | + | 0.983433i | \(0.558021\pi\) | |||||||
\(294\) | −11.2685 | − | 3.06681i | −0.657195 | − | 0.178860i | ||||
\(295\) | −4.12247 | + | 0.797328i | −0.240019 | + | 0.0464222i | ||||
\(296\) | − | 2.72669i | − | 0.158486i | ||||||
\(297\) | 10.1580 | + | 0.119495i | 0.589429 | + | 0.00693377i | ||||
\(298\) | −0.582262 | + | 0.582262i | −0.0337295 | + | 0.0337295i | ||||
\(299\) | −21.8626 | −1.26435 | ||||||||
\(300\) | 6.79338 | + | 5.37121i | 0.392216 | + | 0.310107i | ||||
\(301\) | 1.08909 | 0.0627741 | ||||||||
\(302\) | 8.24652 | − | 8.24652i | 0.474534 | − | 0.474534i | ||||
\(303\) | −0.273996 | − | 0.478902i | −0.0157407 | − | 0.0275122i | ||||
\(304\) | 3.69824i | 0.212108i | ||||||||
\(305\) | 23.0967 | − | 4.46713i | 1.32251 | − | 0.255787i | ||||
\(306\) | −13.3772 | − | 7.86385i | −0.764724 | − | 0.449546i | ||||
\(307\) | 19.1173 | + | 19.1173i | 1.09108 | + | 1.09108i | 0.995413 | + | 0.0956661i | \(0.0304981\pi\) |
0.0956661 | + | 0.995413i | \(0.469502\pi\) | |||||||
\(308\) | 0.701453 | + | 0.701453i | 0.0399690 | + | 0.0399690i | ||||
\(309\) | −7.10636 | + | 26.1113i | −0.404267 | + | 1.48542i | ||||
\(310\) | 1.25213 | − | 1.85261i | 0.0711160 | − | 0.105221i | ||||
\(311\) | 6.25550i | 0.354717i | 0.984146 | + | 0.177359i | \(0.0567552\pi\) | ||||
−0.984146 | + | 0.177359i | \(0.943245\pi\) | |||||||
\(312\) | −3.70202 | + | 2.11805i | −0.209585 | + | 0.119911i | ||||
\(313\) | −18.9730 | + | 18.9730i | −1.07242 | + | 1.07242i | −0.0752511 | + | 0.997165i | \(0.523976\pi\) |
−0.997165 | + | 0.0752511i | \(0.976024\pi\) | |||||||
\(314\) | 20.9924 | 1.18467 | ||||||||
\(315\) | −3.07228 | + | 1.46521i | −0.173103 | + | 0.0825553i | ||||
\(316\) | −1.35078 | −0.0759872 | ||||||||
\(317\) | 10.3258 | − | 10.3258i | 0.579954 | − | 0.579954i | −0.354937 | − | 0.934890i | \(-0.615498\pi\) |
0.934890 | + | 0.354937i | \(0.115498\pi\) | |||||||
\(318\) | 19.8626 | − | 11.3641i | 1.11384 | − | 0.637266i | ||||
\(319\) | 16.6539i | 0.932440i | ||||||||
\(320\) | 0.424609 | + | 2.19538i | 0.0237364 | + | 0.122726i | ||||
\(321\) | −1.21384 | + | 4.46009i | −0.0677501 | + | 0.248938i | ||||
\(322\) | −3.18548 | − | 3.18548i | −0.177520 | − | 0.177520i | ||||
\(323\) | 13.5263 | + | 13.5263i | 0.752621 | + | 0.752621i | ||||
\(324\) | −7.86385 | + | 4.37721i | −0.436880 | + | 0.243178i | ||||
\(325\) | 4.83197 | − | 11.3245i | 0.268030 | − | 0.628170i | ||||
\(326\) | − | 19.4486i | − | 1.07716i | ||||||
\(327\) | 0.0704855 | + | 0.123198i | 0.00389786 | + | 0.00681284i | ||||
\(328\) | 6.90947 | − | 6.90947i | 0.381512 | − | 0.381512i | ||||
\(329\) | 2.97479 | 0.164005 | ||||||||
\(330\) | −7.55078 | − | 0.564860i | −0.415657 | − | 0.0310945i | ||||
\(331\) | 2.07714 | 0.114170 | 0.0570850 | − | 0.998369i | \(-0.481819\pi\) | ||||
0.0570850 | + | 0.998369i | \(0.481819\pi\) | |||||||
\(332\) | −2.46289 | + | 2.46289i | −0.135169 | + | 0.135169i | ||||
\(333\) | −7.91771 | + | 2.05513i | −0.433888 | + | 0.112621i | ||||
\(334\) | − | 25.1327i | − | 1.37520i | ||||||
\(335\) | −20.5991 | − | 13.9223i | −1.12545 | − | 0.760656i | ||||
\(336\) | −0.848008 | − | 0.230791i | −0.0462626 | − | 0.0125907i | ||||
\(337\) | 7.26005 | + | 7.26005i | 0.395480 | + | 0.395480i | 0.876635 | − | 0.481155i | \(-0.159783\pi\) |
−0.481155 | + | 0.876635i | \(0.659783\pi\) | |||||||
\(338\) | −4.90471 | − | 4.90471i | −0.266781 | − | 0.266781i | ||||
\(339\) | −21.9601 | − | 5.97659i | −1.19271 | − | 0.324604i | ||||
\(340\) | 9.58259 | + | 6.47658i | 0.519689 | + | 0.351242i | ||||
\(341\) | 1.95505i | 0.105872i | ||||||||
\(342\) | 10.7389 | − | 2.78739i | 0.580691 | − | 0.150725i | ||||
\(343\) | −4.93069 | + | 4.93069i | −0.266232 | + | 0.266232i | ||||
\(344\) | −2.14639 | −0.115725 | ||||||||
\(345\) | 34.2900 | + | 2.56517i | 1.84611 | + | 0.138104i | ||||
\(346\) | 3.11875 | 0.167665 | ||||||||
\(347\) | 9.72013 | − | 9.72013i | 0.521804 | − | 0.521804i | −0.396312 | − | 0.918116i | \(-0.629710\pi\) |
0.918116 | + | 0.396312i | \(0.129710\pi\) | |||||||
\(348\) | −7.32700 | − | 12.8064i | −0.392768 | − | 0.686497i | ||||
\(349\) | − | 5.23665i | − | 0.280311i | −0.990129 | − | 0.140156i | \(-0.955240\pi\) | ||
0.990129 | − | 0.140156i | \(-0.0447603\pi\) | |||||||
\(350\) | 2.35407 | − | 0.945988i | 0.125830 | − | 0.0505652i | ||||
\(351\) | 8.94059 | + | 9.15344i | 0.477213 | + | 0.488574i | ||||
\(352\) | −1.38243 | − | 1.38243i | −0.0736837 | − | 0.0736837i | ||||
\(353\) | −9.32810 | − | 9.32810i | −0.496485 | − | 0.496485i | 0.413857 | − | 0.910342i | \(-0.364181\pi\) |
−0.910342 | + | 0.413857i | \(0.864181\pi\) | |||||||
\(354\) | −0.854102 | + | 3.13828i | −0.0453950 | + | 0.166798i | ||||
\(355\) | −1.22551 | − | 6.33631i | −0.0650431 | − | 0.336296i | ||||
\(356\) | − | 0.192825i | − | 0.0102197i | ||||||
\(357\) | −3.94569 | + | 2.25746i | −0.208828 | + | 0.119478i | ||||
\(358\) | 2.64291 | − | 2.64291i | 0.139682 | − | 0.139682i | ||||
\(359\) | 15.9315 | 0.840833 | 0.420417 | − | 0.907331i | \(-0.361884\pi\) | ||||
0.420417 | + | 0.907331i | \(0.361884\pi\) | |||||||
\(360\) | 6.05487 | − | 2.88765i | 0.319120 | − | 0.152193i | ||||
\(361\) | 5.32305 | 0.280160 | ||||||||
\(362\) | 12.4025 | − | 12.4025i | 0.651863 | − | 0.651863i | ||||
\(363\) | −10.7910 | + | 6.17388i | −0.566379 | + | 0.324044i | ||||
\(364\) | 1.24946i | 0.0654897i | ||||||||
\(365\) | 17.1830 | − | 25.4235i | 0.899398 | − | 1.33073i | ||||
\(366\) | 4.78522 | − | 17.5826i | 0.250127 | − | 0.919058i | ||||
\(367\) | 2.44539 | + | 2.44539i | 0.127648 | + | 0.127648i | 0.768045 | − | 0.640396i | \(-0.221230\pi\) |
−0.640396 | + | 0.768045i | \(0.721230\pi\) | |||||||
\(368\) | 6.27796 | + | 6.27796i | 0.327262 | + | 0.327262i | ||||
\(369\) | −25.2713 | − | 14.8558i | −1.31557 | − | 0.773364i | ||||
\(370\) | 5.98614 | − | 1.15778i | 0.311204 | − | 0.0601901i | ||||
\(371\) | − | 6.70381i | − | 0.348045i | ||||||
\(372\) | −0.860137 | − | 1.50338i | −0.0445960 | − | 0.0779468i | ||||
\(373\) | 14.3557 | − | 14.3557i | 0.743308 | − | 0.743308i | −0.229905 | − | 0.973213i | \(-0.573841\pi\) |
0.973213 | + | 0.229905i | \(0.0738415\pi\) | |||||||
\(374\) | −10.1124 | −0.522901 | ||||||||
\(375\) | −8.90734 | + | 17.1947i | −0.459973 | + | 0.887933i | ||||
\(376\) | −5.86273 | −0.302347 | ||||||||
\(377\) | −14.8324 | + | 14.8324i | −0.763908 | + | 0.763908i | ||||
\(378\) | −0.0310131 | + | 2.63638i | −0.00159514 | + | 0.135601i | ||||
\(379\) | 13.9990i | 0.719082i | 0.933129 | + | 0.359541i | \(0.117067\pi\) | ||||
−0.933129 | + | 0.359541i | \(0.882933\pi\) | |||||||
\(380\) | −8.11905 | + | 1.57031i | −0.416498 | + | 0.0805550i | ||||
\(381\) | −12.8130 | − | 3.48715i | −0.656432 | − | 0.178652i | ||||
\(382\) | −1.71474 | − | 1.71474i | −0.0877339 | − | 0.0877339i | ||||
\(383\) | 13.5580 | + | 13.5580i | 0.692781 | + | 0.692781i | 0.962843 | − | 0.270062i | \(-0.0870443\pi\) |
−0.270062 | + | 0.962843i | \(0.587044\pi\) | |||||||
\(384\) | 1.67126 | + | 0.454844i | 0.0852862 | + | 0.0232112i | ||||
\(385\) | −1.24211 | + | 1.83780i | −0.0633040 | + | 0.0936630i | ||||
\(386\) | − | 12.1406i | − | 0.617941i | ||||||
\(387\) | 1.61775 | + | 6.23263i | 0.0822349 | + | 0.316822i | ||||
\(388\) | 1.01182 | − | 1.01182i | 0.0513675 | − | 0.0513675i | ||||
\(389\) | 7.92369 | 0.401747 | 0.200874 | − | 0.979617i | \(-0.435622\pi\) | ||||
0.200874 | + | 0.979617i | \(0.435622\pi\) | |||||||
\(390\) | −6.22184 | − | 7.22800i | −0.315055 | − | 0.366004i | ||||
\(391\) | 45.9231 | 2.32243 | ||||||||
\(392\) | 4.76770 | − | 4.76770i | 0.240805 | − | 0.240805i | ||||
\(393\) | 12.9084 | + | 22.5619i | 0.651144 | + | 1.13810i | ||||
\(394\) | 24.3631i | 1.22740i | ||||||||
\(395\) | −0.573553 | − | 2.96547i | −0.0288586 | − | 0.149209i | ||||
\(396\) | −2.97232 | + | 5.05622i | −0.149365 | + | 0.254084i | ||||
\(397\) | −24.9906 | − | 24.9906i | −1.25424 | − | 1.25424i | −0.953801 | − | 0.300440i | \(-0.902866\pi\) |
−0.300440 | − | 0.953801i | \(-0.597134\pi\) | |||||||
\(398\) | −9.61388 | − | 9.61388i | −0.481900 | − | 0.481900i | ||||
\(399\) | 0.853518 | − | 3.13614i | 0.0427294 | − | 0.157003i | ||||
\(400\) | −4.63941 | + | 1.86436i | −0.231971 | + | 0.0932180i | ||||
\(401\) | 22.0069i | 1.09897i | 0.835502 | + | 0.549487i | \(0.185177\pi\) | ||||
−0.835502 | + | 0.549487i | \(0.814823\pi\) | |||||||
\(402\) | −16.7160 | + | 9.56380i | −0.833719 | + | 0.476999i | ||||
\(403\) | −1.74122 | + | 1.74122i | −0.0867363 | + | 0.0867363i | ||||
\(404\) | 0.318549 | 0.0158484 | ||||||||
\(405\) | −12.9487 | − | 15.4055i | −0.643427 | − | 0.765508i | ||||
\(406\) | −4.32229 | −0.214512 | ||||||||
\(407\) | −3.76946 | + | 3.76946i | −0.186845 | + | 0.186845i | ||||
\(408\) | 7.77620 | − | 4.44903i | 0.384979 | − | 0.220260i | ||||
\(409\) | 10.8865i | 0.538304i | 0.963098 | + | 0.269152i | \(0.0867434\pi\) | ||||
−0.963098 | + | 0.269152i | \(0.913257\pi\) | |||||||
\(410\) | 18.1028 | + | 12.2351i | 0.894032 | + | 0.604249i | ||||
\(411\) | 1.49420 | − | 5.49023i | 0.0737034 | − | 0.270813i | ||||
\(412\) | −11.0476 | − | 11.0476i | −0.544278 | − | 0.544278i | ||||
\(413\) | 0.673733 | + | 0.673733i | 0.0331522 | + | 0.0331522i | ||||
\(414\) | 13.4981 | − | 22.9616i | 0.663393 | − | 1.12850i | ||||
\(415\) | −6.45275 | − | 4.36122i | −0.316753 | − | 0.214084i | ||||
\(416\) | − | 2.46246i | − | 0.120732i | ||||||
\(417\) | −7.94365 | − | 13.8843i | −0.389002 | − | 0.679915i | ||||
\(418\) | 5.11255 | − | 5.11255i | 0.250063 | − | 0.250063i | ||||
\(419\) | −2.09340 | −0.102269 | −0.0511346 | − | 0.998692i | \(-0.516284\pi\) | ||||
−0.0511346 | + | 0.998692i | \(0.516284\pi\) | |||||||
\(420\) | 0.146602 | − | 1.95970i | 0.00715342 | − | 0.0956235i | ||||
\(421\) | 34.4422 | 1.67861 | 0.839306 | − | 0.543659i | \(-0.182962\pi\) | ||||
0.839306 | + | 0.543659i | \(0.182962\pi\) | |||||||
\(422\) | −18.7386 | + | 18.7386i | −0.912182 | + | 0.912182i | ||||
\(423\) | 4.41880 | + | 17.0241i | 0.214849 | + | 0.827739i | ||||
\(424\) | 13.2119i | 0.641628i | ||||||||
\(425\) | −10.1497 | + | 23.7875i | −0.492334 | + | 1.15386i | ||||
\(426\) | −4.82359 | − | 1.31277i | −0.233704 | − | 0.0636039i | ||||
\(427\) | −3.77467 | − | 3.77467i | −0.182669 | − | 0.182669i | ||||
\(428\) | −1.88705 | − | 1.88705i | −0.0912142 | − | 0.0912142i | ||||
\(429\) | 8.04583 | + | 2.18972i | 0.388456 | + | 0.105721i | ||||
\(430\) | −0.911376 | − | 4.71214i | −0.0439504 | − | 0.227240i | ||||
\(431\) | 24.8456i | 1.19677i | 0.801208 | + | 0.598386i | \(0.204191\pi\) | ||||
−0.801208 | + | 0.598386i | \(0.795809\pi\) | |||||||
\(432\) | 0.0611210 | − | 5.19579i | 0.00294068 | − | 0.249983i | ||||
\(433\) | −3.57481 | + | 3.57481i | −0.171794 | + | 0.171794i | −0.787767 | − | 0.615973i | \(-0.788763\pi\) |
0.615973 | + | 0.787767i | \(0.288763\pi\) | |||||||
\(434\) | −0.507406 | −0.0243563 | ||||||||
\(435\) | 25.0039 | − | 21.5233i | 1.19885 | − | 1.03196i | ||||
\(436\) | −0.0819468 | −0.00392454 | ||||||||
\(437\) | −23.2174 | + | 23.2174i | −1.11064 | + | 1.11064i | ||||
\(438\) | −11.8037 | − | 20.6310i | −0.564002 | − | 0.985787i | ||||
\(439\) | 11.5796i | 0.552664i | 0.961062 | + | 0.276332i | \(0.0891190\pi\) | ||||
−0.961062 | + | 0.276332i | \(0.910881\pi\) | |||||||
\(440\) | 2.44797 | − | 3.62195i | 0.116702 | − | 0.172670i | ||||
\(441\) | −17.4378 | − | 10.2509i | −0.830370 | − | 0.488137i | ||||
\(442\) | −9.00640 | − | 9.00640i | −0.428391 | − | 0.428391i | ||||
\(443\) | −8.88709 | − | 8.88709i | −0.422238 | − | 0.422238i | 0.463735 | − | 0.885974i | \(-0.346509\pi\) |
−0.885974 | + | 0.463735i | \(0.846509\pi\) | |||||||
\(444\) | 1.24022 | − | 4.55702i | 0.0588583 | − | 0.216267i | ||||
\(445\) | 0.423326 | − | 0.0818755i | 0.0200676 | − | 0.00388127i | ||||
\(446\) | 27.1059i | 1.28350i | ||||||||
\(447\) | −1.23795 | + | 0.708274i | −0.0585531 | + | 0.0335002i | ||||
\(448\) | 0.358790 | − | 0.358790i | 0.0169512 | − | 0.0169512i | ||||
\(449\) | 9.67396 | 0.456543 | 0.228271 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228271 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(450\) | 8.91046 | + | 12.0666i | 0.420043 | + | 0.568827i | ||||
\(451\) | −19.1037 | −0.899559 | ||||||||
\(452\) | 9.29128 | − | 9.29128i | 0.437025 | − | 0.437025i | ||||
\(453\) | 17.5330 | − | 10.0312i | 0.823772 | − | 0.471308i | ||||
\(454\) | − | 2.77681i | − | 0.130322i | ||||||
\(455\) | −2.74305 | + | 0.530534i | −0.128596 | + | 0.0248718i | ||||
\(456\) | −1.68212 | + | 6.18072i | −0.0787726 | + | 0.289439i | ||||
\(457\) | −4.89450 | − | 4.89450i | −0.228955 | − | 0.228955i | 0.583301 | − | 0.812256i | \(-0.301761\pi\) |
−0.812256 | + | 0.583301i | \(0.801761\pi\) | |||||||
\(458\) | −0.938050 | − | 0.938050i | −0.0438322 | − | 0.0438322i | ||||
\(459\) | −18.7800 | − | 19.2271i | −0.876575 | − | 0.897444i | ||||
\(460\) | −11.1169 | + | 16.4482i | −0.518326 | + | 0.766902i | ||||
\(461\) | 26.4567i | 1.23221i | 0.787663 | + | 0.616107i | \(0.211291\pi\) | ||||
−0.787663 | + | 0.616107i | \(0.788709\pi\) | |||||||
\(462\) | 0.853259 | + | 1.49136i | 0.0396972 | + | 0.0693845i | ||||
\(463\) | −22.0172 | + | 22.0172i | −1.02323 | + | 1.02323i | −0.0235013 | + | 0.999724i | \(0.507481\pi\) |
−0.999724 | + | 0.0235013i | \(0.992519\pi\) | |||||||
\(464\) | 8.51841 | 0.395457 | ||||||||
\(465\) | 2.93528 | − | 2.52668i | 0.136120 | − | 0.117172i | ||||
\(466\) | 10.0118 | 0.463787 | ||||||||
\(467\) | 12.2168 | − | 12.2168i | 0.565327 | − | 0.565327i | −0.365489 | − | 0.930816i | \(-0.619098\pi\) |
0.930816 | + | 0.365489i | \(0.119098\pi\) | |||||||
\(468\) | −7.15042 | + | 1.85598i | −0.330528 | + | 0.0857925i | ||||
\(469\) | 5.64180i | 0.260514i | ||||||||
\(470\) | −2.48937 | − | 12.8709i | −0.114826 | − | 0.593692i | ||||
\(471\) | 35.0839 | + | 9.54829i | 1.61658 | + | 0.439962i | ||||
\(472\) | −1.32780 | − | 1.32780i | −0.0611169 | − | 0.0611169i | ||||
\(473\) | 2.96723 | + | 2.96723i | 0.136433 | + | 0.136433i | ||||
\(474\) | −2.25750 | − | 0.614393i | −0.103691 | − | 0.0282200i | ||||
\(475\) | −6.89485 | − | 17.1576i | −0.316357 | − | 0.787247i | ||||
\(476\) | − | 2.62454i | − | 0.120296i | ||||||
\(477\) | 38.3645 | − | 9.95795i | 1.75659 | − | 0.455943i | ||||
\(478\) | −6.85809 | + | 6.85809i | −0.313682 | + | 0.313682i | ||||
\(479\) | 1.13514 | 0.0518660 | 0.0259330 | − | 0.999664i | \(-0.491744\pi\) | ||||
0.0259330 | + | 0.999664i | \(0.491744\pi\) | |||||||
\(480\) | −0.288924 | + | 3.86219i | −0.0131875 | + | 0.176284i | ||||
\(481\) | −6.71436 | −0.306149 | ||||||||
\(482\) | −0.955658 | + | 0.955658i | −0.0435290 | + | 0.0435290i | ||||
\(483\) | −3.87487 | − | 6.77266i | −0.176313 | − | 0.308167i | ||||
\(484\) | − | 7.17778i | − | 0.326263i | ||||||
\(485\) | 2.65097 | + | 1.79171i | 0.120374 | + | 0.0813573i | ||||
\(486\) | −15.1335 | + | 3.73863i | −0.686469 | + | 0.169588i | ||||
\(487\) | −25.5727 | − | 25.5727i | −1.15881 | − | 1.15881i | −0.984732 | − | 0.174080i | \(-0.944305\pi\) |
−0.174080 | − | 0.984732i | \(-0.555695\pi\) | |||||||
\(488\) | 7.43916 | + | 7.43916i | 0.336755 | + | 0.336755i | ||||
\(489\) | 8.84610 | − | 32.5038i | 0.400034 | − | 1.46987i | ||||
\(490\) | 12.4913 | + | 8.44251i | 0.564301 | + | 0.381394i | ||||
\(491\) | 6.43538i | 0.290425i | 0.989401 | + | 0.145212i | \(0.0463865\pi\) | ||||
−0.989401 | + | 0.145212i | \(0.953613\pi\) | |||||||
\(492\) | 14.6903 | − | 8.40481i | 0.662289 | − | 0.378918i | ||||
\(493\) | 31.1560 | − | 31.1560i | 1.40319 | − | 1.40319i | ||||
\(494\) | 9.10674 | 0.409732 | ||||||||
\(495\) | −12.3624 | − | 4.37846i | −0.555649 | − | 0.196797i | ||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −1.03554 | + | 1.03554i | −0.0464503 | + | 0.0464503i | ||||
\(498\) | −5.23637 | + | 2.99590i | −0.234647 | + | 0.134250i | ||||
\(499\) | 2.13426i | 0.0955426i | 0.998858 | + | 0.0477713i | \(0.0152119\pi\) | ||||
−0.998858 | + | 0.0477713i | \(0.984788\pi\) | |||||||
\(500\) | −6.06293 | − | 9.39366i | −0.271142 | − | 0.420097i | ||||
\(501\) | 11.4314 | − | 42.0033i | 0.510719 | − | 1.87657i | ||||
\(502\) | 14.3919 | + | 14.3919i | 0.642343 | + | 0.642343i | ||||
\(503\) | 16.0055 | + | 16.0055i | 0.713652 | + | 0.713652i | 0.967297 | − | 0.253645i | \(-0.0816296\pi\) |
−0.253645 | + | 0.967297i | \(0.581630\pi\) | |||||||
\(504\) | −1.31227 | − | 0.771423i | −0.0584532 | − | 0.0343619i | ||||
\(505\) | 0.135259 | + | 0.699338i | 0.00601895 | + | 0.0311201i | ||||
\(506\) | − | 17.3577i | − | 0.771643i | ||||||
\(507\) | −5.96618 | − | 10.4279i | −0.264967 | − | 0.463121i | ||||
\(508\) | 5.42117 | − | 5.42117i | 0.240525 | − | 0.240525i | ||||
\(509\) | −0.206280 | −0.00914319 | −0.00457160 | − | 0.999990i | \(-0.501455\pi\) | ||||
−0.00457160 | + | 0.999990i | \(0.501455\pi\) | |||||||
\(510\) | 13.0692 | + | 15.1826i | 0.578713 | + | 0.672299i | ||||
\(511\) | −6.96315 | −0.308032 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 19.2153 | + | 0.226040i | 0.848375 | + | 0.00997990i | ||||
\(514\) | − | 25.3385i | − | 1.11763i | ||||||
\(515\) | 19.5629 | − | 28.9448i | 0.862044 | − | 1.27546i | ||||
\(516\) | −3.58717 | − | 0.976271i | −0.157917 | − | 0.0429780i | ||||
\(517\) | 8.10481 | + | 8.10481i | 0.356449 | + | 0.356449i | ||||
\(518\) | −0.978311 | − | 0.978311i | −0.0429845 | − | 0.0429845i | ||||
\(519\) | 5.21225 | + | 1.41854i | 0.228792 | + | 0.0622672i | ||||
\(520\) | 5.40603 | − | 1.04558i | 0.237070 | − | 0.0458518i | ||||
\(521\) | − | 16.7588i | − | 0.734215i | −0.930178 | − | 0.367108i | \(-0.880348\pi\) | ||
0.930178 | − | 0.367108i | \(-0.119652\pi\) | |||||||
\(522\) | −6.42040 | − | 24.7356i | −0.281013 | − | 1.08265i | ||||
\(523\) | 17.4085 | − | 17.4085i | 0.761219 | − | 0.761219i | −0.215324 | − | 0.976543i | \(-0.569081\pi\) |
0.976543 | + | 0.215324i | \(0.0690807\pi\) | |||||||
\(524\) | −15.0074 | −0.655601 | ||||||||
\(525\) | 4.36454 | − | 0.510260i | 0.190484 | − | 0.0222696i | ||||
\(526\) | 20.2025 | 0.880869 | ||||||||
\(527\) | 3.65749 | − | 3.65749i | 0.159323 | − | 0.159323i | ||||
\(528\) | −1.68161 | − | 2.93919i | −0.0731827 | − | 0.127912i | ||||
\(529\) | 55.8257i | 2.42720i | ||||||||
\(530\) | −29.0052 | + | 5.60991i | −1.25991 | + | 0.243679i | ||||
\(531\) | −2.85486 | + | 4.85641i | −0.123890 | + | 0.210750i | ||||
\(532\) | 1.32689 | + | 1.32689i | 0.0575280 | + | 0.0575280i | ||||
\(533\) | −17.0143 | − | 17.0143i | −0.736970 | − | 0.736970i | ||||
\(534\) | 0.0877056 | − | 0.322262i | 0.00379539 | − | 0.0139456i | ||||
\(535\) | 3.34155 | − | 4.94407i | 0.144468 | − | 0.213751i | ||||
\(536\) | − | 11.1189i | − | 0.480264i | ||||||
\(537\) | 5.61912 | − | 3.21489i | 0.242483 | − | 0.138733i | ||||
\(538\) | −1.61323 | + | 1.61323i | −0.0695514 | + | 0.0695514i | ||||
\(539\) | −13.1820 | −0.567789 | ||||||||
\(540\) | 11.4327 | − | 2.07200i | 0.491985 | − | 0.0891646i | ||||
\(541\) | −29.6653 | −1.27541 | −0.637705 | − | 0.770281i | \(-0.720116\pi\) | ||||
−0.637705 | + | 0.770281i | \(0.720116\pi\) | |||||||
\(542\) | −11.7489 | + | 11.7489i | −0.504657 | + | 0.504657i | ||||
\(543\) | 26.3691 | − | 15.0867i | 1.13161 | − | 0.647431i | ||||
\(544\) | 5.17247i | 0.221768i | ||||||||
\(545\) | −0.0347954 | − | 0.179905i | −0.00149047 | − | 0.00770627i | ||||
\(546\) | −0.568312 | + | 2.08818i | −0.0243215 | + | 0.0893660i | ||||
\(547\) | −2.72287 | − | 2.72287i | −0.116421 | − | 0.116421i | 0.646496 | − | 0.762917i | \(-0.276234\pi\) |
−0.762917 | + | 0.646496i | \(0.776234\pi\) | |||||||
\(548\) | 2.32290 | + | 2.32290i | 0.0992295 | + | 0.0992295i | ||||
\(549\) | 15.9947 | − | 27.2086i | 0.682637 | − | 1.16124i | ||||
\(550\) | 8.99101 | + | 3.83631i | 0.383378 | + | 0.163581i | ||||
\(551\) | 31.5031i | 1.34208i | ||||||||
\(552\) | 7.63663 | + | 13.3476i | 0.325036 | + | 0.568112i | ||||
\(553\) | −0.484646 | + | 0.484646i | −0.0206092 | + | 0.0206092i | ||||
\(554\) | 12.2163 | 0.519022 | ||||||||
\(555\) | 10.5310 | + | 0.787806i | 0.447017 | + | 0.0334405i | ||||
\(556\) | 9.23533 | 0.391665 | ||||||||
\(557\) | 10.5384 | − | 10.5384i | 0.446526 | − | 0.446526i | −0.447672 | − | 0.894198i | \(-0.647747\pi\) |
0.894198 | + | 0.447672i | \(0.147747\pi\) | |||||||
\(558\) | −0.753709 | − | 2.90378i | −0.0319071 | − | 0.122927i | ||||
\(559\) | 5.28538i | 0.223548i | ||||||||
\(560\) | 0.940028 | + | 0.635336i | 0.0397234 | + | 0.0268479i | ||||
\(561\) | −16.9005 | − | 4.59958i | −0.713541 | − | 0.194194i | ||||
\(562\) | −1.35157 | − | 1.35157i | −0.0570126 | − | 0.0570126i | ||||
\(563\) | −23.4280 | − | 23.4280i | −0.987372 | − | 0.987372i | 0.0125491 | − | 0.999921i | \(-0.496005\pi\) |
−0.999921 | + | 0.0125491i | \(0.996005\pi\) | |||||||
\(564\) | −9.79816 | − | 2.66663i | −0.412577 | − | 0.112285i | ||||
\(565\) | 24.3431 | + | 16.4528i | 1.02412 | + | 0.692173i | ||||
\(566\) | 26.6281i | 1.11926i | ||||||||
\(567\) | −1.25097 | + | 4.39197i | −0.0525359 | + | 0.184445i | ||||
\(568\) | 2.04085 | − | 2.04085i | 0.0856321 | − | 0.0856321i | ||||
\(569\) | −7.44387 | −0.312063 | −0.156032 | − | 0.987752i | \(-0.549870\pi\) | ||||
−0.156032 | + | 0.987752i | \(0.549870\pi\) | |||||||
\(570\) | −14.2833 | − | 1.06851i | −0.598262 | − | 0.0447549i | ||||
\(571\) | −11.8316 | −0.495136 | −0.247568 | − | 0.968870i | \(-0.579631\pi\) | ||||
−0.247568 | + | 0.968870i | \(0.579631\pi\) | |||||||
\(572\) | −3.40417 | + | 3.40417i | −0.142335 | + | 0.142335i | ||||
\(573\) | −2.08584 | − | 3.64573i | −0.0871374 | − | 0.152302i | ||||
\(574\) | − | 4.95810i | − | 0.206947i | ||||||
\(575\) | −40.8305 | − | 17.4217i | −1.70275 | − | 0.726534i | ||||
\(576\) | 2.58623 | + | 1.52033i | 0.107760 | + | 0.0633470i | ||||
\(577\) | −14.3674 | − | 14.3674i | −0.598122 | − | 0.598122i | 0.341691 | − | 0.939812i | \(-0.389000\pi\) |
−0.939812 | + | 0.341691i | \(0.889000\pi\) | |||||||
\(578\) | 6.89741 | + | 6.89741i | 0.286895 | + | 0.286895i | ||||
\(579\) | 5.52209 | − | 20.2901i | 0.229490 | − | 0.843230i | ||||
\(580\) | 3.61700 | + | 18.7012i | 0.150188 | + | 0.776524i | ||||
\(581\) | 1.76732i | 0.0733209i | ||||||||
\(582\) | 2.15124 | − | 1.23080i | 0.0891719 | − | 0.0510183i | ||||
\(583\) | 18.2646 | − | 18.2646i | 0.756441 | − | 0.756441i | ||||
\(584\) | 13.7230 | 0.567863 | ||||||||
\(585\) | −7.11071 | − | 14.9099i | −0.293992 | − | 0.616447i | ||||
\(586\) | −19.4183 | −0.802162 | ||||||||
\(587\) | −4.80609 | + | 4.80609i | −0.198368 | + | 0.198368i | −0.799300 | − | 0.600932i | \(-0.794796\pi\) |
0.600932 | + | 0.799300i | \(0.294796\pi\) | |||||||
\(588\) | 10.1366 | − | 5.79951i | 0.418027 | − | 0.239168i | ||||
\(589\) | 3.69824i | 0.152383i | ||||||||
\(590\) | 2.35123 | − | 3.47882i | 0.0967986 | − | 0.143221i | ||||
\(591\) | −11.0814 | + | 40.7172i | −0.455829 | + | 1.67488i | ||||
\(592\) | 1.92806 | + | 1.92806i | 0.0792429 | + | 0.0792429i | ||||
\(593\) | −14.6591 | − | 14.6591i | −0.601979 | − | 0.601979i | 0.338859 | − | 0.940837i | \(-0.389959\pi\) |
−0.940837 | + | 0.338859i | \(0.889959\pi\) | |||||||
\(594\) | −7.26731 | + | 7.09832i | −0.298181 | + | 0.291248i | ||||
\(595\) | 5.76187 | − | 1.11440i | 0.236214 | − | 0.0456861i | ||||
\(596\) | − | 0.823443i | − | 0.0337295i | ||||||
\(597\) | −11.6945 | − | 20.4401i | −0.478624 | − | 0.836559i | ||||
\(598\) | 15.4592 | − | 15.4592i | 0.632174 | − | 0.632174i | ||||
\(599\) | 39.4780 | 1.61303 | 0.806514 | − | 0.591215i | \(-0.201352\pi\) | ||||
0.806514 | + | 0.591215i | \(0.201352\pi\) | |||||||
\(600\) | −8.60167 | + | 1.00562i | −0.351162 | + | 0.0410545i | ||||
\(601\) | −15.1492 | −0.617950 | −0.308975 | − | 0.951070i | \(-0.599986\pi\) | ||||
−0.308975 | + | 0.951070i | \(0.599986\pi\) | |||||||
\(602\) | −0.770102 | + | 0.770102i | −0.0313870 | + | 0.0313870i | ||||
\(603\) | −32.2869 | + | 8.38043i | −1.31482 | + | 0.341277i | ||||
\(604\) | 11.6623i | 0.474534i | ||||||||
\(605\) | 15.7580 | − | 3.04775i | 0.640653 | − | 0.123909i | ||||
\(606\) | 0.532380 | + | 0.144890i | 0.0216264 | + | 0.00588577i | ||||
\(607\) | 14.2742 | + | 14.2742i | 0.579373 | + | 0.579373i | 0.934730 | − | 0.355357i | \(-0.115641\pi\) |
−0.355357 | + | 0.934730i | \(0.615641\pi\) | |||||||
\(608\) | −2.61505 | − | 2.61505i | −0.106054 | − | 0.106054i | ||||
\(609\) | −7.22368 | − | 1.96597i | −0.292718 | − | 0.0796651i | ||||
\(610\) | −13.1731 | + | 19.4905i | −0.533362 | + | 0.789149i | ||||
\(611\) | 14.4367i | 0.584047i | ||||||||
\(612\) | 15.0197 | − | 3.89854i | 0.607135 | − | 0.157589i | ||||
\(613\) | 9.44047 | − | 9.44047i | 0.381297 | − | 0.381297i | −0.490272 | − | 0.871569i | \(-0.663103\pi\) |
0.871569 | + | 0.490272i | \(0.163103\pi\) | |||||||
\(614\) | −27.0359 | −1.09108 | ||||||||
\(615\) | 24.6894 | + | 28.6820i | 0.995573 | + | 1.15657i | ||||
\(616\) | −0.992004 | −0.0399690 | ||||||||
\(617\) | −33.3329 | + | 33.3329i | −1.34193 | + | 1.34193i | −0.447800 | + | 0.894134i | \(0.647792\pi\) |
−0.894134 | + | 0.447800i | \(0.852208\pi\) | |||||||
\(618\) | −13.4386 | − | 23.4885i | −0.540578 | − | 0.944845i | ||||
\(619\) | − | 33.8700i | − | 1.36135i | −0.732584 | − | 0.680676i | \(-0.761686\pi\) | ||
0.732584 | − | 0.680676i | \(-0.238314\pi\) | |||||||
\(620\) | 0.424609 | + | 2.19538i | 0.0170527 | + | 0.0881687i | ||||
\(621\) | 33.0027 | − | 32.2353i | 1.32435 | − | 1.29356i | ||||
\(622\) | −4.42331 | − | 4.42331i | −0.177359 | − | 0.177359i | ||||
\(623\) | −0.0691839 | − | 0.0691839i | −0.00277179 | − | 0.00277179i | ||||
\(624\) | 1.12003 | − | 4.11541i | 0.0448372 | − | 0.164748i | ||||
\(625\) | 18.0483 | − | 17.2991i | 0.721933 | − | 0.691963i | ||||
\(626\) | − | 26.8318i | − | 1.07242i | ||||||
\(627\) | 10.8698 | − | 6.21900i | 0.434099 | − | 0.248363i | ||||
\(628\) | −14.8439 | + | 14.8439i | −0.592336 | + | 0.592336i | ||||
\(629\) | 14.1037 | 0.562353 | ||||||||
\(630\) | 1.13637 | − | 3.20849i | 0.0452740 | − | 0.127829i | ||||
\(631\) | 2.45690 | 0.0978076 | 0.0489038 | − | 0.998803i | \(-0.484427\pi\) | ||||
0.0489038 | + | 0.998803i | \(0.484427\pi\) | |||||||
\(632\) | 0.955144 | − | 0.955144i | 0.0379936 | − | 0.0379936i | ||||
\(633\) | −39.8403 | + | 22.7940i | −1.58351 | + | 0.905980i | ||||
\(634\) | 14.6029i | 0.579954i | ||||||||
\(635\) | 14.2034 | + | 9.59966i | 0.563645 | + | 0.380951i | ||||
\(636\) | −6.00937 | + | 22.0806i | −0.238287 | + | 0.875553i | ||||
\(637\) | −11.7402 | − | 11.7402i | −0.465165 | − | 0.465165i | ||||
\(638\) | −11.7761 | − | 11.7761i | −0.466220 | − | 0.466220i | ||||
\(639\) | −7.46438 | − | 4.38796i | −0.295286 | − | 0.173585i | ||||
\(640\) | −1.85261 | − | 1.25213i | −0.0732310 | − | 0.0494946i | ||||
\(641\) | − | 25.5355i | − | 1.00859i | −0.863531 | − | 0.504297i | \(-0.831752\pi\) | ||
0.863531 | − | 0.504297i | \(-0.168248\pi\) | |||||||
\(642\) | −2.29545 | − | 4.01208i | −0.0905941 | − | 0.158344i | ||||
\(643\) | −14.0125 | + | 14.0125i | −0.552597 | + | 0.552597i | −0.927190 | − | 0.374592i | \(-0.877783\pi\) |
0.374592 | + | 0.927190i | \(0.377783\pi\) | |||||||
\(644\) | 4.50494 | 0.177520 | ||||||||
\(645\) | 0.620142 | − | 8.28976i | 0.0244181 | − | 0.326409i | ||||
\(646\) | −19.1290 | −0.752621 | ||||||||
\(647\) | −19.0335 | + | 19.0335i | −0.748283 | + | 0.748283i | −0.974157 | − | 0.225874i | \(-0.927476\pi\) |
0.225874 | + | 0.974157i | \(0.427476\pi\) | |||||||
\(648\) | 2.46543 | − | 8.65573i | 0.0968511 | − | 0.340029i | ||||
\(649\) | 3.67117i | 0.144106i | ||||||||
\(650\) | 4.59091 | + | 11.4244i | 0.180070 | + | 0.448100i | ||||
\(651\) | −0.848008 | − | 0.230791i | −0.0332361 | − | 0.00904540i | ||||
\(652\) | 13.7523 | + | 13.7523i | 0.538580 | + | 0.538580i | ||||
\(653\) | −12.3516 | − | 12.3516i | −0.483355 | − | 0.483355i | 0.422846 | − | 0.906201i | \(-0.361031\pi\) |
−0.906201 | + | 0.422846i | \(0.861031\pi\) | |||||||
\(654\) | −0.136955 | − | 0.0372730i | −0.00535535 | − | 0.00145749i | ||||
\(655\) | −6.37228 | − | 32.9470i | −0.248986 | − | 1.28735i | ||||
\(656\) | 9.77147i | 0.381512i | ||||||||
\(657\) | −10.3432 | − | 39.8486i | −0.403526 | − | 1.55464i | ||||
\(658\) | −2.10349 | + | 2.10349i | −0.0820026 | + | 0.0820026i | ||||
\(659\) | 35.0699 | 1.36613 | 0.683065 | − | 0.730358i | \(-0.260647\pi\) | ||||
0.683065 | + | 0.730358i | \(0.260647\pi\) | |||||||
\(660\) | 5.73862 | − | 4.93979i | 0.223376 | − | 0.192281i | ||||
\(661\) | 1.85106 | 0.0719978 | 0.0359989 | − | 0.999352i | \(-0.488539\pi\) | ||||
0.0359989 | + | 0.999352i | \(0.488539\pi\) | |||||||
\(662\) | −1.46876 | + | 1.46876i | −0.0570850 | + | 0.0570850i | ||||
\(663\) | −10.9555 | − | 19.1486i | −0.425478 | − | 0.743668i | ||||
\(664\) | − | 3.48305i | − | 0.135169i | ||||||
\(665\) | −2.34962 | + | 3.47644i | −0.0911145 | + | 0.134811i | ||||
\(666\) | 4.14547 | − | 7.05186i | 0.160634 | − | 0.273254i | ||||
\(667\) | 53.4782 | + | 53.4782i | 2.07069 | + | 2.07069i | ||||
\(668\) | 17.7715 | + | 17.7715i | 0.687599 | + | 0.687599i | ||||
\(669\) | −12.3290 | + | 45.3011i | −0.476666 | + | 1.75144i | ||||
\(670\) | 24.4103 | − | 4.72120i | 0.943052 | − | 0.182396i | ||||
\(671\) | − | 20.5682i | − | 0.794027i | ||||||
\(672\) | 0.762826 | − | 0.436439i | 0.0294267 | − | 0.0168360i | ||||
\(673\) | −8.95618 | + | 8.95618i | −0.345236 | + | 0.345236i | −0.858331 | − | 0.513096i | \(-0.828499\pi\) |
0.513096 | + | 0.858331i | \(0.328499\pi\) | |||||||
\(674\) | −10.2673 | −0.395480 | ||||||||
\(675\) | 9.40327 | + | 24.2194i | 0.361932 | + | 0.932205i | ||||
\(676\) | 6.93631 | 0.266781 | ||||||||
\(677\) | −18.2690 | + | 18.2690i | −0.702136 | + | 0.702136i | −0.964869 | − | 0.262733i | \(-0.915376\pi\) |
0.262733 | + | 0.964869i | \(0.415376\pi\) | |||||||
\(678\) | 19.7543 | − | 11.3021i | 0.758658 | − | 0.434054i | ||||
\(679\) | − | 0.726064i | − | 0.0278638i | ||||||
\(680\) | −11.3555 | + | 2.19628i | −0.435465 | + | 0.0842234i | ||||
\(681\) | 1.26302 | − | 4.64078i | 0.0483989 | − | 0.177835i | ||||
\(682\) | −1.38243 | − | 1.38243i | −0.0529359 | − | 0.0529359i | ||||
\(683\) | −10.9514 | − | 10.9514i | −0.419044 | − | 0.419044i | 0.465830 | − | 0.884874i | \(-0.345756\pi\) |
−0.884874 | + | 0.465830i | \(0.845756\pi\) | |||||||
\(684\) | −5.62253 | + | 9.56450i | −0.214983 | + | 0.365708i | ||||
\(685\) | −4.11333 | + | 6.08599i | −0.157162 | + | 0.232534i | ||||
\(686\) | − | 6.97305i | − | 0.266232i | ||||||
\(687\) | −1.14106 | − | 1.99439i | −0.0435342 | − | 0.0760909i | ||||
\(688\) | 1.51772 | − | 1.51772i | 0.0578627 | − | 0.0578627i | ||||
\(689\) | 32.5338 | 1.23944 | ||||||||
\(690\) | −26.0606 | + | 22.4328i | −0.992108 | + | 0.854004i | ||||
\(691\) | −27.1310 | −1.03211 | −0.516056 | − | 0.856555i | \(-0.672600\pi\) | ||||
−0.516056 | + | 0.856555i | \(0.672600\pi\) | |||||||
\(692\) | −2.20529 | + | 2.20529i | −0.0838325 | + | 0.0838325i | ||||
\(693\) | 0.747682 | + | 2.88056i | 0.0284021 | + | 0.109423i | ||||
\(694\) | 13.7463i | 0.521804i | ||||||||
\(695\) | 3.92141 | + | 20.2751i | 0.148748 | + | 0.769078i | ||||
\(696\) | 14.2365 | + | 3.87455i | 0.539633 | + | 0.146864i | ||||
\(697\) | 35.7390 | + | 35.7390i | 1.35371 | + | 1.35371i | ||||
\(698\) | 3.70287 | + | 3.70287i | 0.140156 | + | 0.140156i | ||||
\(699\) | 16.7323 | + | 4.55380i | 0.632874 | + | 0.172241i | ||||
\(700\) | −0.995662 | + | 2.33349i | −0.0376325 | + | 0.0881976i | ||||
\(701\) | − | 31.7577i | − | 1.19947i | −0.800198 | − | 0.599736i | \(-0.795272\pi\) | ||
0.800198 | − | 0.599736i | \(-0.204728\pi\) | |||||||
\(702\) | −12.7944 | − | 0.150508i | −0.482894 | − | 0.00568054i | ||||
\(703\) | −7.13043 | + | 7.13043i | −0.268929 | + | 0.268929i | ||||
\(704\) | 1.95505 | 0.0736837 | ||||||||
\(705\) | 1.69388 | − | 22.6430i | 0.0637953 | − | 0.852785i | ||||
\(706\) | 13.1919 | 0.496485 | ||||||||
\(707\) | 0.114292 | − | 0.114292i | 0.00429841 | − | 0.00429841i | ||||
\(708\) | −1.61516 | − | 2.82304i | −0.0607013 | − | 0.106096i | ||||
\(709\) | 5.36101i | 0.201337i | 0.994920 | + | 0.100668i | \(0.0320981\pi\) | ||||
−0.994920 | + | 0.100668i | \(0.967902\pi\) | |||||||
\(710\) | 5.34701 | + | 3.61388i | 0.200670 | + | 0.135627i | ||||
\(711\) | −3.49343 | − | 2.05362i | −0.131014 | − | 0.0770169i | ||||
\(712\) | 0.136348 | + | 0.136348i | 0.00510986 | + | 0.00510986i | ||||
\(713\) | 6.27796 | + | 6.27796i | 0.235112 | + | 0.235112i | ||||
\(714\) | 1.19376 | − | 4.38629i | 0.0446752 | − | 0.164153i | ||||
\(715\) | −8.91890 | − | 6.02801i | −0.333548 | − | 0.225435i | ||||
\(716\) | 3.73765i | 0.139682i | ||||||||
\(717\) | −14.5810 | + | 8.34230i | −0.544538 | + | 0.311549i | ||||
\(718\) | −11.2653 | + | 11.2653i | −0.420417 | + | 0.420417i | ||||
\(719\) | 15.2611 | 0.569144 | 0.284572 | − | 0.958655i | \(-0.408148\pi\) | ||||
0.284572 | + | 0.958655i | \(0.408148\pi\) | |||||||
\(720\) | −2.23956 | + | 6.32332i | −0.0834636 | + | 0.235656i | ||||
\(721\) | −7.92757 | −0.295238 | ||||||||
\(722\) | −3.76396 | + | 3.76396i | −0.140080 | + | 0.140080i | ||||
\(723\) | −2.03183 | + | 1.16248i | −0.0755646 | + | 0.0432331i | ||||
\(724\) | 17.5399i | 0.651863i | ||||||||
\(725\) | −39.5204 | + | 15.8814i | −1.46775 | + | 0.589820i | ||||
\(726\) | 3.26477 | − | 11.9960i | 0.121167 | − | 0.445212i | ||||
\(727\) | 14.7117 | + | 14.7117i | 0.545625 | + | 0.545625i | 0.925172 | − | 0.379547i | \(-0.123920\pi\) |
−0.379547 | + | 0.925172i | \(0.623920\pi\) | |||||||
\(728\) | −0.883505 | − | 0.883505i | −0.0327449 | − | 0.0327449i | ||||
\(729\) | −26.9925 | − | 0.635144i | −0.999723 | − | 0.0235238i | ||||
\(730\) | 5.82693 | + | 30.1273i | 0.215664 | + | 1.11506i | ||||
\(731\) | − | 11.1021i | − | 0.410626i | ||||||
\(732\) | 9.04913 | + | 15.8164i | 0.334465 | + | 0.584593i | ||||
\(733\) | −21.1638 | + | 21.1638i | −0.781704 | + | 0.781704i | −0.980118 | − | 0.198414i | \(-0.936421\pi\) |
0.198414 | + | 0.980118i | \(0.436421\pi\) | |||||||
\(734\) | −3.45830 | −0.127648 | ||||||||
\(735\) | 17.0363 | + | 19.7913i | 0.628392 | + | 0.730011i | ||||
\(736\) | −8.87838 | −0.327262 | ||||||||
\(737\) | −15.3711 | + | 15.3711i | −0.566202 | + | 0.566202i | ||||
\(738\) | 28.3742 | − | 7.36485i | 1.04447 | − | 0.271104i | ||||
\(739\) | 25.5918i | 0.941410i | 0.882291 | + | 0.470705i | \(0.156000\pi\) | ||||
−0.882291 | + | 0.470705i | \(0.844000\pi\) | |||||||
\(740\) | −3.41416 | + | 5.05151i | −0.125507 | + | 0.185697i | ||||
\(741\) | 15.2198 | + | 4.14215i | 0.559112 | + | 0.152166i | ||||
\(742\) | 4.74031 | + | 4.74031i | 0.174022 | + | 0.174022i | ||||
\(743\) | 13.6274 | + | 13.6274i | 0.499939 | + | 0.499939i | 0.911419 | − | 0.411480i | \(-0.134988\pi\) |
−0.411480 | + | 0.911419i | \(0.634988\pi\) | |||||||
\(744\) | 1.67126 | + | 0.454844i | 0.0612714 | + | 0.0166754i | ||||
\(745\) | 1.80777 | − | 0.349642i | 0.0662317 | − | 0.0128099i | ||||
\(746\) | 20.3020i | 0.743308i | ||||||||
\(747\) | −10.1140 | + | 2.62521i | −0.370052 | + | 0.0960514i | ||||
\(748\) | 7.15057 | − | 7.15057i | 0.261451 | − | 0.261451i | ||||
\(749\) | −1.35411 | −0.0494782 | ||||||||
\(750\) | −5.86008 | − | 18.4570i | −0.213980 | − | 0.673953i | ||||
\(751\) | 3.34996 | 0.122242 | 0.0611209 | − | 0.998130i | \(-0.480532\pi\) | ||||
0.0611209 | + | 0.998130i | \(0.480532\pi\) | |||||||
\(752\) | 4.14558 | − | 4.14558i | 0.151174 | − | 0.151174i | ||||
\(753\) | 17.5066 | + | 30.5988i | 0.637976 | + | 1.11508i | ||||
\(754\) | − | 20.9762i | − | 0.763908i | ||||||
\(755\) | −25.6033 | + | 4.95194i | −0.931800 | + | 0.180220i | ||||
\(756\) | −1.84227 | − | 1.88613i | −0.0670027 | − | 0.0685978i | ||||
\(757\) | −11.0695 | − | 11.0695i | −0.402329 | − | 0.402329i | 0.476724 | − | 0.879053i | \(-0.341824\pi\) |
−0.879053 | + | 0.476724i | \(0.841824\pi\) | |||||||
\(758\) | −9.89882 | − | 9.89882i | −0.359541 | − | 0.359541i | ||||
\(759\) | 7.89504 | − | 29.0092i | 0.286572 | − | 1.05297i | ||||
\(760\) | 4.63066 | − | 6.85141i | 0.167972 | − | 0.248527i | ||||
\(761\) | − | 13.9912i | − | 0.507180i | −0.967312 | − | 0.253590i | \(-0.918389\pi\) | ||
0.967312 | − | 0.253590i | \(-0.0816114\pi\) | |||||||
\(762\) | 11.5260 | − | 6.59440i | 0.417542 | − | 0.238890i | ||||
\(763\) | −0.0294017 | + | 0.0294017i | −0.00106441 | + | 0.00106441i | ||||
\(764\) | 2.42501 | 0.0877339 | ||||||||
\(765\) | 14.9363 | + | 31.3186i | 0.540022 | + | 1.13233i | ||||
\(766\) | −19.1739 | −0.692781 | ||||||||
\(767\) | −3.26965 | + | 3.26965i | −0.118060 | + | 0.118060i | ||||
\(768\) | −1.50338 | + | 0.860137i | −0.0542487 | + | 0.0310375i | ||||
\(769\) | 1.44997i | 0.0522874i | 0.999658 | + | 0.0261437i | \(0.00832275\pi\) | ||||
−0.999658 | + | 0.0261437i | \(0.991677\pi\) | |||||||
\(770\) | −0.421214 | − | 2.17783i | −0.0151795 | − | 0.0784835i | ||||
\(771\) | 11.5251 | − | 42.3473i | 0.415065 | − | 1.52510i | ||||
\(772\) | 8.58471 | + | 8.58471i | 0.308970 | + | 0.308970i | ||||
\(773\) | −6.72297 | − | 6.72297i | −0.241808 | − | 0.241808i | 0.575790 | − | 0.817598i | \(-0.304695\pi\) |
−0.817598 | + | 0.575790i | \(0.804695\pi\) | |||||||
\(774\) | −5.55106 | − | 3.26321i | −0.199529 | − | 0.117294i | ||||
\(775\) | −4.63941 | + | 1.86436i | −0.166653 | + | 0.0669698i | ||||
\(776\) | 1.43093i | 0.0513675i | ||||||||
\(777\) | −1.19003 | − | 2.07999i | −0.0426922 | − | 0.0746193i | ||||
\(778\) | −5.60289 | + | 5.60289i | −0.200874 | + | 0.200874i | ||||
\(779\) | −36.1372 | −1.29475 | ||||||||
\(780\) | 9.51048 | + | 0.711462i | 0.340530 | + | 0.0254744i | ||||
\(781\) | −5.64266 | −0.201910 | ||||||||
\(782\) | −32.4726 | + | 32.4726i | −1.16122 | + | 1.16122i | ||||
\(783\) | 0.520653 | − | 44.2599i | 0.0186066 | − | 1.58172i | ||||
\(784\) | 6.74254i | 0.240805i | ||||||||
\(785\) | −38.8909 | − | 26.2852i | −1.38808 | − | 0.938159i | ||||
\(786\) | −25.0813 | − | 6.82603i | −0.894620 | − | 0.243476i | ||||
\(787\) | −7.53390 | − | 7.53390i | −0.268555 | − | 0.268555i | 0.559963 | − | 0.828518i | \(-0.310815\pi\) |
−0.828518 | + | 0.559963i | \(0.810815\pi\) | |||||||
\(788\) | −17.2273 | − | 17.2273i | −0.613698 | − | 0.613698i | ||||
\(789\) | 33.7636 | + | 9.18897i | 1.20202 | + | 0.327136i | ||||
\(790\) | 2.50247 | + | 1.69134i | 0.0890339 | + | 0.0601753i | ||||
\(791\) | − | 6.66724i | − | 0.237060i | ||||||
\(792\) | −1.47354 | − | 5.67703i | −0.0523599 | − | 0.201724i | ||||
\(793\) | 18.3186 | − | 18.3186i | 0.650513 | − | 0.650513i | ||||
\(794\) | 35.3420 | 1.25424 | ||||||||
\(795\) | −51.0270 | − | 3.81724i | −1.80974 | − | 0.135384i | ||||
\(796\) | 13.5961 | 0.481900 | ||||||||
\(797\) | 36.9287 | − | 36.9287i | 1.30808 | − | 1.30808i | 0.385282 | − | 0.922799i | \(-0.374104\pi\) |
0.922799 | − | 0.385282i | \(-0.125896\pi\) | |||||||
\(798\) | 1.61405 | + | 2.82111i | 0.0571369 | + | 0.0998662i | ||||
\(799\) | − | 30.3248i | − | 1.07281i | ||||||
\(800\) | 1.96226 | − | 4.59886i | 0.0693763 | − | 0.162594i | ||||
\(801\) | 0.293158 | − | 0.498692i | 0.0103582 | − | 0.0176204i | ||||
\(802\) | −15.5613 | − | 15.5613i | −0.549487 | − | 0.549487i | ||||
\(803\) | −18.9711 | − | 18.9711i | −0.669476 | − | 0.669476i | ||||
\(804\) | 5.05738 | − | 18.5826i | 0.178360 | − | 0.655359i | ||||
\(805\) | 1.91284 | + | 9.89008i | 0.0674188 | + | 0.348579i | ||||
\(806\) | − | 2.46246i | − | 0.0867363i | ||||||
\(807\) | −3.42990 | + | 1.96237i | −0.120738 | + | 0.0690785i | ||||
\(808\) | −0.225248 | + | 0.225248i | −0.00792421 | + | 0.00792421i | ||||
\(809\) | 46.4784 | 1.63409 | 0.817046 | − | 0.576573i | \(-0.195610\pi\) | ||||
0.817046 | + | 0.576573i | \(0.195610\pi\) | |||||||
\(810\) | 20.0495 | + | 1.73725i | 0.704467 | + | 0.0610407i | ||||
\(811\) | −3.32637 | −0.116805 | −0.0584023 | − | 0.998293i | \(-0.518601\pi\) | ||||
−0.0584023 | + | 0.998293i | \(0.518601\pi\) | |||||||
\(812\) | 3.05632 | − | 3.05632i | 0.107256 | − | 0.107256i | ||||
\(813\) | −24.9793 | + | 14.2915i | −0.876064 | + | 0.501226i | ||||
\(814\) | − | 5.33082i | − | 0.186845i | ||||||
\(815\) | −24.3521 | + | 36.0308i | −0.853018 | + | 1.26210i | ||||
\(816\) | −2.35267 | + | 8.64455i | −0.0823598 | + | 0.302620i | ||||
\(817\) | 5.61290 | + | 5.61290i | 0.196371 | + | 0.196371i | ||||
\(818\) | −7.69794 | − | 7.69794i | −0.269152 | − | 0.269152i | ||||
\(819\) | −1.89960 | + | 3.23141i | −0.0663772 | + | 0.112914i | ||||
\(820\) | −21.4521 | + | 4.14906i | −0.749140 | + | 0.144891i | ||||
\(821\) | 6.46893i | 0.225767i | 0.993608 | + | 0.112884i | \(0.0360087\pi\) | ||||
−0.993608 | + | 0.112884i | \(0.963991\pi\) | |||||||
\(822\) | 2.82562 | + | 4.93874i | 0.0985548 | + | 0.172258i | ||||
\(823\) | −25.1379 | + | 25.1379i | −0.876252 | + | 0.876252i | −0.993145 | − | 0.116892i | \(-0.962707\pi\) |
0.116892 | + | 0.993145i | \(0.462707\pi\) | |||||||
\(824\) | 15.6237 | 0.544278 | ||||||||
\(825\) | 13.2814 | + | 10.5010i | 0.462399 | + | 0.365598i | ||||
\(826\) | −0.952802 | −0.0331522 | ||||||||
\(827\) | 25.7731 | − | 25.7731i | 0.896220 | − | 0.896220i | −0.0988794 | − | 0.995099i | \(-0.531526\pi\) |
0.995099 | + | 0.0988794i | \(0.0315258\pi\) | |||||||
\(828\) | 6.69172 | + | 25.7808i | 0.232553 | + | 0.895946i | ||||
\(829\) | 42.8699i | 1.48893i | 0.667659 | + | 0.744467i | \(0.267296\pi\) | ||||
−0.667659 | + | 0.744467i | \(0.732704\pi\) | |||||||
\(830\) | 7.64664 | − | 1.47894i | 0.265419 | − | 0.0513347i | ||||
\(831\) | 20.4167 | + | 5.55653i | 0.708247 | + | 0.192754i | ||||
\(832\) | 1.74122 | + | 1.74122i | 0.0603659 | + | 0.0603659i | ||||
\(833\) | 24.6607 | + | 24.6607i | 0.854444 | + | 0.854444i | ||||
\(834\) | 15.4347 | + | 4.20064i | 0.534459 | + | 0.145456i | ||||
\(835\) | −31.4693 | + | 46.5611i | −1.08904 | + | 1.61131i | ||||
\(836\) | 7.23024i | 0.250063i | ||||||||
\(837\) | 0.0611210 | − | 5.19579i | 0.00211265 | − | 0.179593i | ||||
\(838\) | 1.48026 | − | 1.48026i | 0.0511346 | − | 0.0511346i | ||||
\(839\) | 15.0781 | 0.520553 | 0.260276 | − | 0.965534i | \(-0.416186\pi\) | ||||
0.260276 | + | 0.965534i | \(0.416186\pi\) | |||||||
\(840\) | 1.28205 | + | 1.48938i | 0.0442350 | + | 0.0513885i | ||||
\(841\) | 43.5632 | 1.50218 | ||||||||
\(842\) | −24.3543 | + | 24.3543i | −0.839306 | + | 0.839306i | ||||
\(843\) | −1.64408 | − | 2.87359i | −0.0566250 | − | 0.0989716i | ||||
\(844\) | − | 26.5004i | − | 0.912182i | ||||||
\(845\) | 2.94522 | + | 15.2279i | 0.101319 | + | 0.523854i | ||||
\(846\) | −15.1624 | − | 8.91328i | −0.521294 | − | 0.306445i | ||||
\(847\) | −2.57532 | − | 2.57532i | −0.0884889 | − | 0.0884889i | ||||
\(848\) | −9.34225 | − | 9.34225i | −0.320814 | − | 0.320814i | ||||
\(849\) | −12.1116 | + | 44.5025i | −0.415670 | + | 1.52732i | ||||
\(850\) | −9.64334 | − | 23.9972i | −0.330764 | − | 0.823098i | ||||
\(851\) | 24.2086i | 0.829861i | ||||||||
\(852\) | 4.33906 | − | 2.48253i | 0.148654 | − | 0.0850499i | ||||
\(853\) | −32.7061 | + | 32.7061i | −1.11984 | + | 1.11984i | −0.128070 | + | 0.991765i | \(0.540878\pi\) |
−0.991765 | + | 0.128070i | \(0.959122\pi\) | |||||||
\(854\) | 5.33820 | 0.182669 | ||||||||
\(855\) | −23.3851 | − | 8.28243i | −0.799755 | − | 0.283253i | ||||
\(856\) | 2.66870 | 0.0912142 | ||||||||
\(857\) | −7.36603 | + | 7.36603i | −0.251619 | + | 0.251619i | −0.821634 | − | 0.570015i | \(-0.806937\pi\) |
0.570015 | + | 0.821634i | \(0.306937\pi\) | |||||||
\(858\) | −7.23763 | + | 4.14089i | −0.247089 | + | 0.141368i | ||||
\(859\) | 4.64716i | 0.158559i | 0.996852 | + | 0.0792796i | \(0.0252620\pi\) | ||||
−0.996852 | + | 0.0792796i | \(0.974738\pi\) | |||||||
\(860\) | 3.97643 | + | 2.68755i | 0.135595 | + | 0.0916446i | ||||
\(861\) | 2.25516 | − | 8.28629i | 0.0768558 | − | 0.282396i | ||||
\(862\) | −17.5685 | − | 17.5685i | −0.598386 | − | 0.598386i | ||||
\(863\) | 23.5547 | + | 23.5547i | 0.801810 | + | 0.801810i | 0.983378 | − | 0.181568i | \(-0.0581173\pi\) |
−0.181568 | + | 0.983378i | \(0.558117\pi\) | |||||||
\(864\) | 3.63076 | + | 3.71720i | 0.123521 | + | 0.126462i | ||||
\(865\) | −5.77784 | − | 3.90507i | −0.196452 | − | 0.132776i | ||||
\(866\) | − | 5.05554i | − | 0.171794i | ||||||
\(867\) | 8.39013 | + | 14.6646i | 0.284944 | + | 0.498037i | ||||
\(868\) | 0.358790 | − | 0.358790i | 0.0121781 | − | 0.0121781i | ||||
\(869\) | −2.64084 | −0.0895842 | ||||||||
\(870\) | −2.46117 | + | 32.8997i | −0.0834415 | + | 1.11540i | ||||
\(871\) | −27.3798 | −0.927731 | ||||||||
\(872\) | 0.0579452 | − | 0.0579452i | 0.00196227 | − | 0.00196227i | ||||
\(873\) | 4.15511 | − | 1.07851i | 0.140629 | − | 0.0365019i | ||||
\(874\) | − | 32.8344i | − | 1.11064i | ||||||
\(875\) | −5.54567 | − | 1.19504i | −0.187478 | − | 0.0403996i | ||||
\(876\) | 22.9348 | + | 6.24184i | 0.774894 | + | 0.210892i | ||||
\(877\) | 25.9850 | + | 25.9850i | 0.877452 | + | 0.877452i | 0.993270 | − | 0.115818i | \(-0.0369490\pi\) |
−0.115818 | + | 0.993270i | \(0.536949\pi\) | |||||||
\(878\) | −8.18801 | − | 8.18801i | −0.276332 | − | 0.276332i | ||||
\(879\) | −32.4531 | − | 8.83230i | −1.09461 | − | 0.297906i | ||||
\(880\) | 0.830133 | + | 4.29208i | 0.0279838 | + | 0.144686i | ||||
\(881\) | 57.2613i | 1.92918i | 0.263747 | + | 0.964592i | \(0.415042\pi\) | ||||
−0.263747 | + | 0.964592i | \(0.584958\pi\) | |||||||
\(882\) | 19.5788 | − | 5.08191i | 0.659254 | − | 0.171117i | ||||
\(883\) | −6.65521 | + | 6.65521i | −0.223966 | + | 0.223966i | −0.810166 | − | 0.586200i | \(-0.800623\pi\) |
0.586200 | + | 0.810166i | \(0.300623\pi\) | |||||||
\(884\) | 12.7370 | 0.428391 | ||||||||
\(885\) | 5.51184 | − | 4.74458i | 0.185279 | − | 0.159487i | ||||
\(886\) | 12.5682 | 0.422238 | ||||||||
\(887\) | 40.0415 | − | 40.0415i | 1.34446 | − | 1.34446i | 0.452901 | − | 0.891561i | \(-0.350389\pi\) |
0.891561 | − | 0.452901i | \(-0.149611\pi\) | |||||||
\(888\) | 2.34533 | + | 4.09927i | 0.0787041 | + | 0.137562i | ||||
\(889\) | − | 3.89012i | − | 0.130470i | ||||||
\(890\) | −0.241442 | + | 0.357231i | −0.00809315 | + | 0.0119744i | ||||
\(891\) | −15.3742 | + | 8.55766i | −0.515055 | + | 0.286692i | ||||
\(892\) | −19.1668 | − | 19.1668i | −0.641751 | − | 0.641751i | ||||
\(893\) | 15.3313 | + | 15.3313i | 0.513043 | + | 0.513043i | ||||
\(894\) | 0.374538 | − | 1.37619i | 0.0125264 | − | 0.0460266i | ||||
\(895\) | −8.20557 | + | 1.58704i | −0.274282 | + | 0.0530489i | ||||
\(896\) | 0.507406i | 0.0169512i | ||||||||
\(897\) | 32.8679 | − | 18.8049i | 1.09743 | − | 0.627876i | ||||
\(898\) | −6.84052 | + | 6.84052i | −0.228271 | + | 0.228271i | ||||
\(899\) | 8.51841 | 0.284105 | ||||||||
\(900\) | −14.8330 | − | 2.23176i | −0.494435 | − | 0.0743919i | ||||
\(901\) | −68.3383 | −2.27668 | ||||||||
\(902\) | 13.5084 | − | 13.5084i | 0.449779 | − | 0.449779i | ||||
\(903\) | −1.63732 | + | 0.936766i | −0.0544866 | + | 0.0311736i | ||||
\(904\) | 13.1399i | 0.437025i | ||||||||
\(905\) | −38.5067 | + | 7.44759i | −1.28001 | + | 0.247566i | ||||
\(906\) | −5.30455 | + | 19.4908i | −0.176232 | + | 0.647540i | ||||
\(907\) | −1.45442 | − | 1.45442i | −0.0482933 | − | 0.0482933i | 0.682548 | − | 0.730841i | \(-0.260872\pi\) |
−0.730841 | + | 0.682548i | \(0.760872\pi\) | |||||||
\(908\) | 1.96350 | + | 1.96350i | 0.0651611 | + | 0.0651611i | ||||
\(909\) | 0.823843 | + | 0.484300i | 0.0273252 | + | 0.0160632i | ||||
\(910\) | 1.56449 | − | 2.31478i | 0.0518622 | − | 0.0767341i | ||||
\(911\) | 4.45072i | 0.147459i | 0.997278 | + | 0.0737294i | \(0.0234901\pi\) | ||||
−0.997278 | + | 0.0737294i | \(0.976510\pi\) | |||||||
\(912\) | −3.18099 | − | 5.55987i | −0.105333 | − | 0.184106i | ||||
\(913\) | −4.81507 | + | 4.81507i | −0.159356 | + | 0.159356i | ||||
\(914\) | 6.92187 | 0.228955 | ||||||||
\(915\) | −30.8808 | + | 26.5821i | −1.02089 | + | 0.878778i | ||||
\(916\) | 1.32660 | 0.0438322 | ||||||||
\(917\) | −5.38451 | + | 5.38451i | −0.177812 | + | 0.177812i | ||||
\(918\) | 26.8751 | + | 0.316146i | 0.887009 | + | 0.0104344i | ||||
\(919\) | 2.60868i | 0.0860525i | 0.999074 | + | 0.0430263i | \(0.0136999\pi\) | ||||
−0.999074 | + | 0.0430263i | \(0.986300\pi\) | |||||||
\(920\) | −3.76984 | − | 19.4914i | −0.124288 | − | 0.642614i | ||||
\(921\) | −45.1841 | − | 12.2971i | −1.48887 | − | 0.405204i | ||||
\(922\) | −18.7077 | − | 18.7077i | −0.616107 | − | 0.616107i | ||||
\(923\) | −5.02550 | − | 5.02550i | −0.165416 | − | 0.165416i | ||||
\(924\) | −1.65790 | − | 0.451207i | −0.0545408 | − | 0.0148436i | ||||
\(925\) | −12.5397 | − | 5.35048i | −0.412302 | − | 0.175923i | ||||
\(926\) | − | 31.1370i | − | 1.02323i | ||||||
\(927\) | −11.7757 | − | 45.3678i | −0.386766 | − | 1.49008i | ||||
\(928\) | −6.02342 | + | 6.02342i | −0.197729 | + | 0.197729i | ||||
\(929\) | 23.7156 | 0.778084 | 0.389042 | − | 0.921220i | \(-0.372806\pi\) | ||||
0.389042 | + | 0.921220i | \(0.372806\pi\) | |||||||
\(930\) | −0.288924 | + | 3.86219i | −0.00947418 | + | 0.126646i | ||||
\(931\) | −24.9355 | −0.817228 | ||||||||
\(932\) | −7.07940 | + | 7.07940i | −0.231893 | + | 0.231893i | ||||
\(933\) | −5.38059 | − | 9.40443i | −0.176153 | − | 0.307887i | ||||
\(934\) | 17.2772i | 0.565327i | ||||||||
\(935\) | 18.7344 | + | 12.6620i | 0.612682 | + | 0.414093i | ||||
\(936\) | 3.74374 | − | 6.36849i | 0.122368 | − | 0.208160i | ||||
\(937\) | −12.5016 | − | 12.5016i | −0.408408 | − | 0.408408i | 0.472775 | − | 0.881183i | \(-0.343252\pi\) |
−0.881183 | + | 0.472775i | \(0.843252\pi\) | |||||||
\(938\) | −3.98936 | − | 3.98936i | −0.130257 | − | 0.130257i | ||||
\(939\) | 12.2043 | − | 44.8430i | 0.398272 | − | 1.46340i | ||||
\(940\) | 10.8614 | + | 7.34088i | 0.354259 | + | 0.239433i | ||||
\(941\) | − | 16.3893i | − | 0.534277i | −0.963658 | − | 0.267139i | \(-0.913922\pi\) | ||
0.963658 | − | 0.267139i | \(-0.0860782\pi\) | |||||||
\(942\) | −31.5597 | + | 18.0564i | −1.02827 | + | 0.588309i | ||||
\(943\) | −61.3449 | + | 61.3449i | −1.99767 | + | 1.99767i | ||||
\(944\) | 1.87779 | 0.0611169 | ||||||||
\(945\) | 3.35853 | − | 4.84536i | 0.109253 | − | 0.157619i | ||||
\(946\) | −4.19629 | −0.136433 | ||||||||
\(947\) | 34.5084 | − | 34.5084i | 1.12137 | − | 1.12137i | 0.129837 | − | 0.991535i | \(-0.458555\pi\) |
0.991535 | − | 0.129837i | \(-0.0414454\pi\) | |||||||
\(948\) | 2.03074 | − | 1.16185i | 0.0659553 | − | 0.0377353i | ||||
\(949\) | − | 33.7924i | − | 1.09695i | ||||||
\(950\) | 17.0077 | + | 7.25690i | 0.551802 | + | 0.235445i | ||||
\(951\) | −6.64202 | + | 24.4052i | −0.215382 | + | 0.791393i | ||||
\(952\) | 1.85583 | + | 1.85583i | 0.0601478 | + | 0.0601478i | ||||
\(953\) | −35.3174 | − | 35.3174i | −1.14404 | − | 1.14404i | −0.987703 | − | 0.156339i | \(-0.950031\pi\) |
−0.156339 | − | 0.987703i | \(-0.549969\pi\) | |||||||
\(954\) | −20.0865 | + | 34.1691i | −0.650323 | + | 1.10627i | ||||
\(955\) | 1.02968 | + | 5.32383i | 0.0333198 | + | 0.172275i | ||||
\(956\) | − | 9.69880i | − | 0.313682i | ||||||
\(957\) | −14.3246 | − | 25.0372i | −0.463050 | − | 0.809338i | ||||
\(958\) | −0.802667 | + | 0.802667i | −0.0259330 | + | 0.0259330i | ||||
\(959\) | 1.66687 | 0.0538260 | ||||||||
\(960\) | −2.52668 | − | 2.93528i | −0.0815483 | − | 0.0947358i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 4.74777 | − | 4.74777i | 0.153074 | − | 0.153074i | ||||
\(963\) | −2.01142 | − | 7.74930i | −0.0648172 | − | 0.249718i | ||||
\(964\) | − | 1.35150i | − | 0.0435290i | ||||||
\(965\) | −15.2016 | + | 22.4919i | −0.489356 | + | 0.724039i | ||||
\(966\) | 7.52894 | + | 2.04905i | 0.242240 | + | 0.0659270i | ||||
\(967\) | 19.7749 | + | 19.7749i | 0.635918 | + | 0.635918i | 0.949546 | − | 0.313628i | \(-0.101544\pi\) |
−0.313628 | + | 0.949546i | \(0.601544\pi\) | |||||||
\(968\) | 5.07546 | + | 5.07546i | 0.163131 | + | 0.163131i | ||||
\(969\) | −31.9696 | − | 8.70072i | −1.02701 | − | 0.279507i | ||||
\(970\) | −3.14145 | + | 0.607588i | −0.100866 | + | 0.0195085i | ||||
\(971\) | − | 16.1832i | − | 0.519344i | −0.965697 | − | 0.259672i | \(-0.916386\pi\) | ||
0.965697 | − | 0.259672i | \(-0.0836144\pi\) | |||||||
\(972\) | 8.05738 | − | 13.3446i | 0.258441 | − | 0.428029i | ||||
\(973\) | 3.31355 | − | 3.31355i | 0.106227 | − | 0.106227i | ||||
\(974\) | 36.1653 | 1.15881 | ||||||||
\(975\) | 2.47631 | + | 21.1812i | 0.0793053 | + | 0.678342i | ||||
\(976\) | −10.5206 | −0.336755 | ||||||||
\(977\) | 3.95607 | − | 3.95607i | 0.126566 | − | 0.126566i | −0.640986 | − | 0.767552i | \(-0.721474\pi\) |
0.767552 | + | 0.640986i | \(0.221474\pi\) | |||||||
\(978\) | 16.7285 | + | 29.2388i | 0.534918 | + | 0.934952i | ||||
\(979\) | − | 0.376983i | − | 0.0120484i | ||||||
\(980\) | −14.8025 | + | 2.86295i | −0.472847 | + | 0.0914535i | ||||
\(981\) | −0.211934 | − | 0.124586i | −0.00676652 | − | 0.00397773i | ||||
\(982\) | −4.55050 | − | 4.55050i | −0.145212 | − | 0.145212i | ||||
\(983\) | −25.3353 | − | 25.3353i | −0.808072 | − | 0.808072i | 0.176270 | − | 0.984342i | \(-0.443597\pi\) |
−0.984342 | + | 0.176270i | \(0.943597\pi\) | |||||||
\(984\) | −4.44450 | + | 16.3307i | −0.141685 | + | 0.520603i | ||||
\(985\) | 30.5057 | − | 45.1355i | 0.971993 | − | 1.43814i | ||||
\(986\) | 44.0612i | 1.40319i | ||||||||
\(987\) | −4.47225 | + | 2.55872i | −0.142353 | + | 0.0814451i | ||||
\(988\) | −6.43944 | + | 6.43944i | −0.204866 | + | 0.204866i | ||||
\(989\) | 19.0564 | 0.605959 | ||||||||
\(990\) | 11.8376 | − | 5.64550i | 0.376223 | − | 0.179426i | ||||
\(991\) | −55.7498 | −1.77095 | −0.885475 | − | 0.464687i | \(-0.846167\pi\) | ||||
−0.885475 | + | 0.464687i | \(0.846167\pi\) | |||||||
\(992\) | −0.707107 | + | 0.707107i | −0.0224507 | + | 0.0224507i | ||||
\(993\) | −3.12274 | + | 1.78663i | −0.0990972 | + | 0.0566969i | ||||
\(994\) | − | 1.46447i | − | 0.0464503i | ||||||
\(995\) | 5.77302 | + | 29.8486i | 0.183017 | + | 0.946264i | ||||
\(996\) | 1.58425 | − | 5.82109i | 0.0501988 | − | 0.184448i | ||||
\(997\) | −9.22969 | − | 9.22969i | −0.292307 | − | 0.292307i | 0.545684 | − | 0.837991i | \(-0.316270\pi\) |
−0.837991 | + | 0.545684i | \(0.816270\pi\) | |||||||
\(998\) | −1.50915 | − | 1.50915i | −0.0477713 | − | 0.0477713i | ||||
\(999\) | 10.1357 | − | 9.89997i | 0.320678 | − | 0.313221i |
(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 | 930.2.j.h.497.3 | ✓ | 40 | |
3.2 | odd | 2 | inner | 930.2.j.h.497.13 | yes | 40 | |
5.3 | odd | 4 | inner | 930.2.j.h.683.13 | yes | 40 | |
15.8 | even | 4 | inner | 930.2.j.h.683.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.h.497.3 | ✓ | 40 | 1.1 | even | 1 | trivial | |
930.2.j.h.497.13 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.j.h.683.3 | yes | 40 | 15.8 | even | 4 | inner | |
930.2.j.h.683.13 | yes | 40 | 5.3 | odd | 4 | inner |