Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\), degree \(4\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + 115 x^{11} + 1963 x^{10} + 323 x^{9} + 3007 x^{8} + 1828 x^{7} + 6736 x^{6} + \cdots + 121 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 196.4 | ||
Root | \(0.566002 + 1.74197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.196 |
Dual form | 429.2.n.b.313.4 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.566002 | − | 1.74197i | 0.400224 | − | 1.23176i | −0.524594 | − | 0.851352i | \(-0.675783\pi\) |
0.924818 | − | 0.380410i | \(-0.124217\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | −1.09608 | − | 0.796352i | −0.548042 | − | 0.398176i | ||||
\(5\) | 0.725100 | + | 2.23163i | 0.324274 | + | 0.998014i | 0.971767 | + | 0.235942i | \(0.0758177\pi\) |
−0.647493 | + | 0.762072i | \(0.724182\pi\) | |||||||
\(6\) | −0.566002 | − | 1.74197i | −0.231069 | − | 0.711158i | ||||
\(7\) | −1.01039 | − | 0.734092i | −0.381892 | − | 0.277461i | 0.380233 | − | 0.924891i | \(-0.375844\pi\) |
−0.762125 | + | 0.647430i | \(0.775844\pi\) | |||||||
\(8\) | 0.956015 | − | 0.694585i | 0.338002 | − | 0.245573i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 4.29785 | 1.35910 | ||||||||
\(11\) | 1.67300 | − | 2.86375i | 0.504429 | − | 0.863453i | ||||
\(12\) | −1.35483 | −0.391107 | ||||||||
\(13\) | −0.309017 | + | 0.951057i | −0.0857059 | + | 0.263776i | ||||
\(14\) | −1.85065 | + | 1.34458i | −0.494608 | + | 0.359354i | ||||
\(15\) | 1.89834 | + | 1.37922i | 0.490148 | + | 0.356113i | ||||
\(16\) | −1.50618 | − | 4.63554i | −0.376544 | − | 1.15888i | ||||
\(17\) | −0.204024 | − | 0.627921i | −0.0494830 | − | 0.152293i | 0.923262 | − | 0.384172i | \(-0.125513\pi\) |
−0.972745 | + | 0.231878i | \(0.925513\pi\) | |||||||
\(18\) | −1.48181 | − | 1.07660i | −0.349266 | − | 0.253757i | ||||
\(19\) | 4.72903 | − | 3.43584i | 1.08491 | − | 0.788235i | 0.106380 | − | 0.994326i | \(-0.466074\pi\) |
0.978533 | + | 0.206090i | \(0.0660740\pi\) | |||||||
\(20\) | 0.982390 | − | 3.02349i | 0.219669 | − | 0.676072i | ||||
\(21\) | −1.24891 | −0.272535 | ||||||||
\(22\) | −4.04166 | − | 4.53522i | −0.861684 | − | 0.966911i | ||||
\(23\) | −6.58972 | −1.37405 | −0.687026 | − | 0.726633i | \(-0.741084\pi\) | ||||
−0.687026 | + | 0.726633i | \(0.741084\pi\) | |||||||
\(24\) | 0.365165 | − | 1.12386i | 0.0745390 | − | 0.229408i | ||||
\(25\) | −0.409307 | + | 0.297379i | −0.0818613 | + | 0.0594757i | ||||
\(26\) | 1.48181 | + | 1.07660i | 0.290607 | + | 0.211139i | ||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | 0.522878 | + | 1.60925i | 0.0988146 | + | 0.304120i | ||||
\(29\) | 8.07280 | + | 5.86523i | 1.49908 | + | 1.08915i | 0.970746 | + | 0.240110i | \(0.0771834\pi\) |
0.528335 | + | 0.849036i | \(0.322817\pi\) | |||||||
\(30\) | 3.47703 | − | 2.52621i | 0.634816 | − | 0.461221i | ||||
\(31\) | −2.24966 | + | 6.92373i | −0.404050 | + | 1.24354i | 0.517635 | + | 0.855601i | \(0.326812\pi\) |
−0.921686 | + | 0.387938i | \(0.873188\pi\) | |||||||
\(32\) | −6.56409 | −1.16038 | ||||||||
\(33\) | −0.329783 | − | 3.30019i | −0.0574079 | − | 0.574489i | ||||
\(34\) | −1.20930 | −0.207393 | ||||||||
\(35\) | 0.905586 | − | 2.78711i | 0.153072 | − | 0.471107i | ||||
\(36\) | −1.09608 | + | 0.796352i | −0.182681 | + | 0.132725i | ||||
\(37\) | 5.94939 | + | 4.32248i | 0.978073 | + | 0.710612i | 0.957277 | − | 0.289172i | \(-0.0933799\pi\) |
0.0207961 | + | 0.999784i | \(0.493380\pi\) | |||||||
\(38\) | −3.30851 | − | 10.1825i | −0.536711 | − | 1.65183i | ||||
\(39\) | 0.309017 | + | 0.951057i | 0.0494823 | + | 0.152291i | ||||
\(40\) | 2.24326 | + | 1.62982i | 0.354691 | + | 0.257698i | ||||
\(41\) | −9.00644 | + | 6.54356i | −1.40657 | + | 1.02193i | −0.412760 | + | 0.910840i | \(0.635435\pi\) |
−0.993810 | + | 0.111093i | \(0.964565\pi\) | |||||||
\(42\) | −0.706887 | + | 2.17557i | −0.109075 | + | 0.335698i | ||||
\(43\) | −3.18815 | −0.486188 | −0.243094 | − | 0.970003i | \(-0.578162\pi\) | ||||
−0.243094 | + | 0.970003i | \(0.578162\pi\) | |||||||
\(44\) | −4.11430 | + | 1.80661i | −0.620254 | + | 0.272357i | ||||
\(45\) | 2.34647 | 0.349791 | ||||||||
\(46\) | −3.72980 | + | 11.4791i | −0.549928 | + | 1.69251i | ||||
\(47\) | −10.6940 | + | 7.76963i | −1.55988 | + | 1.13332i | −0.623766 | + | 0.781611i | \(0.714398\pi\) |
−0.936111 | + | 0.351706i | \(0.885602\pi\) | |||||||
\(48\) | −3.94322 | − | 2.86492i | −0.569155 | − | 0.413516i | ||||
\(49\) | −1.68112 | − | 5.17396i | −0.240160 | − | 0.739137i | ||||
\(50\) | 0.286358 | + | 0.881319i | 0.0404971 | + | 0.124637i | ||||
\(51\) | −0.534141 | − | 0.388076i | −0.0747947 | − | 0.0543416i | ||||
\(52\) | 1.09608 | − | 0.796352i | 0.151999 | − | 0.110434i | ||||
\(53\) | −3.01253 | + | 9.27163i | −0.413803 | + | 1.27356i | 0.499513 | + | 0.866306i | \(0.333512\pi\) |
−0.913317 | + | 0.407250i | \(0.866488\pi\) | |||||||
\(54\) | −1.83162 | −0.249252 | ||||||||
\(55\) | 7.60392 | + | 1.65701i | 1.02531 | + | 0.223432i | ||||
\(56\) | −1.47584 | −0.197217 | ||||||||
\(57\) | 1.80633 | − | 5.55930i | 0.239254 | − | 0.736348i | ||||
\(58\) | 14.7863 | − | 10.7429i | 1.94154 | − | 1.41061i | ||||
\(59\) | −7.02390 | − | 5.10316i | −0.914433 | − | 0.664375i | 0.0276989 | − | 0.999616i | \(-0.491182\pi\) |
−0.942132 | + | 0.335242i | \(0.891182\pi\) | |||||||
\(60\) | −0.982390 | − | 3.02349i | −0.126826 | − | 0.390330i | ||||
\(61\) | 3.00154 | + | 9.23780i | 0.384308 | + | 1.18278i | 0.936981 | + | 0.349380i | \(0.113608\pi\) |
−0.552673 | + | 0.833398i | \(0.686392\pi\) | |||||||
\(62\) | 10.7877 | + | 7.83769i | 1.37003 | + | 0.995388i | ||||
\(63\) | −1.01039 | + | 0.734092i | −0.127297 | + | 0.0924869i | ||||
\(64\) | −0.702933 | + | 2.16340i | −0.0878666 | + | 0.270426i | ||||
\(65\) | −2.34647 | −0.291044 | ||||||||
\(66\) | −5.93550 | − | 1.29344i | −0.730610 | − | 0.159211i | ||||
\(67\) | 8.16010 | 0.996914 | 0.498457 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498457 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(68\) | −0.276418 | + | 0.850729i | −0.0335207 | + | 0.103166i | ||||
\(69\) | −5.33120 | + | 3.87334i | −0.641801 | + | 0.466295i | ||||
\(70\) | −4.34251 | − | 3.15501i | −0.519029 | − | 0.377096i | ||||
\(71\) | −3.52354 | − | 10.8443i | −0.418167 | − | 1.28698i | −0.909388 | − | 0.415950i | \(-0.863449\pi\) |
0.491221 | − | 0.871035i | \(-0.336551\pi\) | |||||||
\(72\) | −0.365165 | − | 1.12386i | −0.0430351 | − | 0.132448i | ||||
\(73\) | 2.85886 | + | 2.07709i | 0.334605 | + | 0.243104i | 0.742382 | − | 0.669977i | \(-0.233696\pi\) |
−0.407777 | + | 0.913081i | \(0.633696\pi\) | |||||||
\(74\) | 10.8970 | − | 7.91715i | 1.26675 | − | 0.920350i | ||||
\(75\) | −0.156341 | + | 0.481169i | −0.0180527 | + | 0.0555606i | ||||
\(76\) | −7.91954 | −0.908434 | ||||||||
\(77\) | −3.79264 | + | 1.66537i | −0.432212 | + | 0.189787i | ||||
\(78\) | 1.83162 | 0.207390 | ||||||||
\(79\) | 2.78885 | − | 8.58321i | 0.313770 | − | 0.965686i | −0.662487 | − | 0.749073i | \(-0.730499\pi\) |
0.976258 | − | 0.216613i | \(-0.0695009\pi\) | |||||||
\(80\) | 9.25266 | − | 6.72245i | 1.03448 | − | 0.751593i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 6.30106 | + | 19.3927i | 0.695835 | + | 2.14156i | ||||
\(83\) | 2.87005 | + | 8.83309i | 0.315028 | + | 0.969558i | 0.975743 | + | 0.218920i | \(0.0702535\pi\) |
−0.660714 | + | 0.750637i | \(0.729747\pi\) | |||||||
\(84\) | 1.36891 | + | 0.994573i | 0.149361 | + | 0.108517i | ||||
\(85\) | 1.25335 | − | 0.910610i | 0.135945 | − | 0.0987696i | ||||
\(86\) | −1.80450 | + | 5.55367i | −0.194584 | + | 0.598868i | ||||
\(87\) | 9.97852 | 1.06981 | ||||||||
\(88\) | −0.389704 | − | 3.89983i | −0.0415426 | − | 0.415723i | ||||
\(89\) | −13.6611 | −1.44807 | −0.724036 | − | 0.689762i | \(-0.757715\pi\) | ||||
−0.724036 | + | 0.689762i | \(0.757715\pi\) | |||||||
\(90\) | 1.32811 | − | 4.08749i | 0.139995 | − | 0.430860i | ||||
\(91\) | 1.01039 | − | 0.734092i | 0.105918 | − | 0.0769538i | ||||
\(92\) | 7.22289 | + | 5.24773i | 0.753038 | + | 0.547114i | ||||
\(93\) | 2.24966 | + | 6.92373i | 0.233279 | + | 0.717958i | ||||
\(94\) | 7.48169 | + | 23.0263i | 0.771677 | + | 2.37498i | ||||
\(95\) | 11.0965 | + | 8.06210i | 1.13848 | + | 0.827154i | ||||
\(96\) | −5.31046 | + | 3.85828i | −0.541997 | + | 0.393784i | ||||
\(97\) | −0.821393 | + | 2.52799i | −0.0833998 | + | 0.256678i | −0.984057 | − | 0.177851i | \(-0.943085\pi\) |
0.900658 | + | 0.434530i | \(0.143085\pi\) | |||||||
\(98\) | −9.96442 | −1.00656 | ||||||||
\(99\) | −2.20660 | − | 2.47607i | −0.221772 | − | 0.248854i | ||||
\(100\) | 0.685452 | 0.0685452 | ||||||||
\(101\) | 4.25727 | − | 13.1025i | 0.423615 | − | 1.30375i | −0.480700 | − | 0.876885i | \(-0.659617\pi\) |
0.904315 | − | 0.426867i | \(-0.140383\pi\) | |||||||
\(102\) | −0.978344 | + | 0.710809i | −0.0968705 | + | 0.0703806i | ||||
\(103\) | −5.23467 | − | 3.80321i | −0.515787 | − | 0.374742i | 0.299227 | − | 0.954182i | \(-0.403271\pi\) |
−0.815015 | + | 0.579440i | \(0.803271\pi\) | |||||||
\(104\) | 0.365165 | + | 1.12386i | 0.0358074 | + | 0.110204i | ||||
\(105\) | −0.905586 | − | 2.78711i | −0.0883761 | − | 0.271994i | ||||
\(106\) | 14.4458 | + | 10.4955i | 1.40310 | + | 1.01941i | ||||
\(107\) | 4.07286 | − | 2.95911i | 0.393738 | − | 0.286068i | −0.373247 | − | 0.927732i | \(-0.621756\pi\) |
0.766986 | + | 0.641664i | \(0.221756\pi\) | |||||||
\(108\) | −0.418667 | + | 1.28852i | −0.0402862 | + | 0.123988i | ||||
\(109\) | −4.51232 | −0.432202 | −0.216101 | − | 0.976371i | \(-0.569334\pi\) | ||||
−0.216101 | + | 0.976371i | \(0.569334\pi\) | |||||||
\(110\) | 7.19031 | − | 12.3080i | 0.685569 | − | 1.17352i | ||||
\(111\) | 7.35385 | 0.697996 | ||||||||
\(112\) | −1.88108 | + | 5.78938i | −0.177746 | + | 0.547045i | ||||
\(113\) | 3.46703 | − | 2.51894i | 0.326151 | − | 0.236962i | −0.412645 | − | 0.910892i | \(-0.635395\pi\) |
0.738795 | + | 0.673930i | \(0.235395\pi\) | |||||||
\(114\) | −8.66178 | − | 6.29315i | −0.811250 | − | 0.589408i | ||||
\(115\) | −4.77821 | − | 14.7058i | −0.445570 | − | 1.37132i | ||||
\(116\) | −4.17768 | − | 12.8576i | −0.387888 | − | 1.19380i | ||||
\(117\) | 0.809017 | + | 0.587785i | 0.0747936 | + | 0.0543408i | ||||
\(118\) | −12.8651 | + | 9.34705i | −1.18433 | + | 0.860466i | ||||
\(119\) | −0.254808 | + | 0.784218i | −0.0233582 | + | 0.0718891i | ||||
\(120\) | 2.77282 | 0.253123 | ||||||||
\(121\) | −5.40213 | − | 9.58212i | −0.491103 | − | 0.871102i | ||||
\(122\) | 17.7909 | 1.61071 | ||||||||
\(123\) | −3.44015 | + | 10.5877i | −0.310188 | + | 0.954661i | ||||
\(124\) | 7.97954 | − | 5.79747i | 0.716584 | − | 0.520629i | ||||
\(125\) | 8.53125 | + | 6.19832i | 0.763058 | + | 0.554394i | ||||
\(126\) | 0.706887 | + | 2.17557i | 0.0629745 | + | 0.193815i | ||||
\(127\) | −1.83647 | − | 5.65208i | −0.162961 | − | 0.501541i | 0.835920 | − | 0.548852i | \(-0.184935\pi\) |
−0.998880 | + | 0.0473109i | \(0.984935\pi\) | |||||||
\(128\) | −7.25019 | − | 5.26757i | −0.640832 | − | 0.465592i | ||||
\(129\) | −2.57927 | + | 1.87395i | −0.227092 | + | 0.164992i | ||||
\(130\) | −1.32811 | + | 4.08749i | −0.116483 | + | 0.358497i | ||||
\(131\) | 12.1877 | 1.06485 | 0.532424 | − | 0.846478i | \(-0.321281\pi\) | ||||
0.532424 | + | 0.846478i | \(0.321281\pi\) | |||||||
\(132\) | −2.26664 | + | 3.87991i | −0.197286 | + | 0.337703i | ||||
\(133\) | −7.30039 | −0.633024 | ||||||||
\(134\) | 4.61863 | − | 14.2147i | 0.398989 | − | 1.22796i | ||||
\(135\) | 1.89834 | − | 1.37922i | 0.163383 | − | 0.118704i | ||||
\(136\) | −0.631194 | − | 0.458590i | −0.0541245 | − | 0.0393237i | ||||
\(137\) | 4.64698 | + | 14.3019i | 0.397019 | + | 1.22190i | 0.927378 | + | 0.374125i | \(0.122057\pi\) |
−0.530360 | + | 0.847773i | \(0.677943\pi\) | |||||||
\(138\) | 3.72980 | + | 11.4791i | 0.317501 | + | 0.977168i | ||||
\(139\) | 1.03867 | + | 0.754639i | 0.0880989 | + | 0.0640076i | 0.630963 | − | 0.775813i | \(-0.282660\pi\) |
−0.542864 | + | 0.839821i | \(0.682660\pi\) | |||||||
\(140\) | −3.21211 | + | 2.33374i | −0.271473 | + | 0.197237i | ||||
\(141\) | −4.08474 | + | 12.5715i | −0.343997 | + | 1.05871i | ||||
\(142\) | −20.8849 | −1.75262 | ||||||||
\(143\) | 2.20660 | + | 2.47607i | 0.184525 | + | 0.207059i | ||||
\(144\) | −4.87409 | −0.406174 | ||||||||
\(145\) | −7.23543 | + | 22.2684i | −0.600869 | + | 1.84929i | ||||
\(146\) | 5.23635 | − | 3.80443i | 0.433364 | − | 0.314857i | ||||
\(147\) | −4.40123 | − | 3.19768i | −0.363007 | − | 0.263740i | ||||
\(148\) | −3.07881 | − | 9.47561i | −0.253077 | − | 0.778890i | ||||
\(149\) | −3.94032 | − | 12.1271i | −0.322804 | − | 0.993487i | −0.972422 | − | 0.233227i | \(-0.925071\pi\) |
0.649619 | − | 0.760260i | \(-0.274929\pi\) | |||||||
\(150\) | 0.749694 | + | 0.544685i | 0.0612123 | + | 0.0444733i | ||||
\(151\) | 6.58135 | − | 4.78163i | 0.535582 | − | 0.389123i | −0.286859 | − | 0.957973i | \(-0.592611\pi\) |
0.822442 | + | 0.568849i | \(0.192611\pi\) | |||||||
\(152\) | 2.13453 | − | 6.56942i | 0.173134 | − | 0.532851i | ||||
\(153\) | −0.660235 | −0.0533768 | ||||||||
\(154\) | 0.754390 | + | 7.54929i | 0.0607905 | + | 0.608339i | ||||
\(155\) | −17.0824 | −1.37209 | ||||||||
\(156\) | 0.418667 | − | 1.28852i | 0.0335202 | − | 0.103164i | ||||
\(157\) | 2.58343 | − | 1.87697i | 0.206180 | − | 0.149799i | −0.479904 | − | 0.877321i | \(-0.659328\pi\) |
0.686084 | + | 0.727523i | \(0.259328\pi\) | |||||||
\(158\) | −13.3732 | − | 9.71622i | −1.06392 | − | 0.772981i | ||||
\(159\) | 3.01253 | + | 9.27163i | 0.238909 | + | 0.735288i | ||||
\(160\) | −4.75962 | − | 14.6486i | −0.376281 | − | 1.15807i | ||||
\(161\) | 6.65820 | + | 4.83746i | 0.524739 | + | 0.381245i | ||||
\(162\) | −1.48181 | + | 1.07660i | −0.116422 | + | 0.0845857i | ||||
\(163\) | −1.62343 | + | 4.99641i | −0.127157 | + | 0.391349i | −0.994288 | − | 0.106731i | \(-0.965962\pi\) |
0.867131 | + | 0.498080i | \(0.165962\pi\) | |||||||
\(164\) | 15.0828 | 1.17777 | ||||||||
\(165\) | 7.12567 | − | 3.12892i | 0.554732 | − | 0.243586i | ||||
\(166\) | 17.0115 | 1.32035 | ||||||||
\(167\) | −4.03467 | + | 12.4175i | −0.312213 | + | 0.960891i | 0.664674 | + | 0.747133i | \(0.268570\pi\) |
−0.976887 | + | 0.213758i | \(0.931430\pi\) | |||||||
\(168\) | −1.19398 | + | 0.867476i | −0.0921174 | + | 0.0669272i | ||||
\(169\) | −0.809017 | − | 0.587785i | −0.0622321 | − | 0.0452143i | ||||
\(170\) | −0.876863 | − | 2.69871i | −0.0672523 | − | 0.206981i | ||||
\(171\) | −1.80633 | − | 5.55930i | −0.138133 | − | 0.425131i | ||||
\(172\) | 3.49448 | + | 2.53889i | 0.266451 | + | 0.193588i | ||||
\(173\) | −1.98841 | + | 1.44467i | −0.151176 | + | 0.109836i | −0.660802 | − | 0.750560i | \(-0.729784\pi\) |
0.509626 | + | 0.860396i | \(0.329784\pi\) | |||||||
\(174\) | 5.64786 | − | 17.3823i | 0.428163 | − | 1.31775i | ||||
\(175\) | 0.631863 | 0.0477643 | ||||||||
\(176\) | −15.7949 | − | 3.44195i | −1.19058 | − | 0.259447i | ||||
\(177\) | −8.68201 | −0.652580 | ||||||||
\(178\) | −7.73220 | + | 23.7973i | −0.579553 | + | 1.78368i | ||||
\(179\) | −2.77090 | + | 2.01317i | −0.207107 | + | 0.150472i | −0.686504 | − | 0.727126i | \(-0.740855\pi\) |
0.479397 | + | 0.877598i | \(0.340855\pi\) | |||||||
\(180\) | −2.57193 | − | 1.86862i | −0.191700 | − | 0.139278i | ||||
\(181\) | −0.888085 | − | 2.73324i | −0.0660108 | − | 0.203160i | 0.912611 | − | 0.408830i | \(-0.134063\pi\) |
−0.978622 | + | 0.205669i | \(0.934063\pi\) | |||||||
\(182\) | −0.706887 | − | 2.17557i | −0.0523979 | − | 0.161264i | ||||
\(183\) | 7.85814 | + | 5.70927i | 0.580890 | + | 0.422041i | ||||
\(184\) | −6.29987 | + | 4.57712i | −0.464433 | + | 0.337430i | ||||
\(185\) | −5.33227 | + | 16.4110i | −0.392036 | + | 1.20656i | ||||
\(186\) | 13.3343 | 0.977717 | ||||||||
\(187\) | −2.13954 | − | 0.466239i | −0.156459 | − | 0.0340948i | ||||
\(188\) | 17.9089 | 1.30614 | ||||||||
\(189\) | −0.385935 | + | 1.18779i | −0.0280726 | + | 0.0863987i | ||||
\(190\) | 20.3246 | − | 14.7667i | 1.47450 | − | 1.07129i | ||||
\(191\) | 0.770354 | + | 0.559695i | 0.0557409 | + | 0.0404981i | 0.615307 | − | 0.788288i | \(-0.289032\pi\) |
−0.559566 | + | 0.828786i | \(0.689032\pi\) | |||||||
\(192\) | 0.702933 | + | 2.16340i | 0.0507298 | + | 0.156130i | ||||
\(193\) | −3.03999 | − | 9.35613i | −0.218823 | − | 0.673469i | −0.998860 | − | 0.0477351i | \(-0.984800\pi\) |
0.780037 | − | 0.625734i | \(-0.215200\pi\) | |||||||
\(194\) | 3.93878 | + | 2.86169i | 0.282788 | + | 0.205457i | ||||
\(195\) | −1.89834 | + | 1.37922i | −0.135943 | + | 0.0987681i | ||||
\(196\) | −2.27764 | + | 7.00985i | −0.162688 | + | 0.500704i | ||||
\(197\) | 6.22868 | 0.443775 | 0.221888 | − | 0.975072i | \(-0.428778\pi\) | ||||
0.221888 | + | 0.975072i | \(0.428778\pi\) | |||||||
\(198\) | −5.56219 | + | 2.44239i | −0.395287 | + | 0.173573i | ||||
\(199\) | 19.6648 | 1.39400 | 0.697001 | − | 0.717070i | \(-0.254517\pi\) | ||||
0.697001 | + | 0.717070i | \(0.254517\pi\) | |||||||
\(200\) | −0.184748 | + | 0.568597i | −0.0130637 | + | 0.0402059i | ||||
\(201\) | 6.60166 | − | 4.79638i | 0.465645 | − | 0.338311i | ||||
\(202\) | −20.4147 | − | 14.8321i | −1.43637 | − | 1.04358i | ||||
\(203\) | −3.85106 | − | 11.8524i | −0.270292 | − | 0.831872i | ||||
\(204\) | 0.276418 | + | 0.850729i | 0.0193532 | + | 0.0595629i | ||||
\(205\) | −21.1334 | − | 15.3543i | −1.47602 | − | 1.07239i | ||||
\(206\) | −9.58793 | + | 6.96604i | −0.668023 | + | 0.485347i | ||||
\(207\) | −2.03634 | + | 6.26720i | −0.141535 | + | 0.435600i | ||||
\(208\) | 4.87409 | 0.337958 | ||||||||
\(209\) | −1.92771 | − | 19.2909i | −0.133343 | − | 1.33438i | ||||
\(210\) | −5.36763 | −0.370402 | ||||||||
\(211\) | 0.991032 | − | 3.05008i | 0.0682254 | − | 0.209976i | −0.911131 | − | 0.412117i | \(-0.864790\pi\) |
0.979357 | + | 0.202140i | \(0.0647897\pi\) | |||||||
\(212\) | 10.6855 | − | 7.76344i | 0.733881 | − | 0.533196i | ||||
\(213\) | −9.22474 | − | 6.70216i | −0.632068 | − | 0.459225i | ||||
\(214\) | −2.84944 | − | 8.76968i | −0.194784 | − | 0.599483i | ||||
\(215\) | −2.31173 | − | 7.11476i | −0.157658 | − | 0.485222i | ||||
\(216\) | −0.956015 | − | 0.694585i | −0.0650486 | − | 0.0472605i | ||||
\(217\) | 7.35569 | − | 5.34422i | 0.499337 | − | 0.362789i | ||||
\(218\) | −2.55398 | + | 7.86035i | −0.172977 | + | 0.532370i | ||||
\(219\) | 3.53375 | 0.238789 | ||||||||
\(220\) | −7.01497 | − | 7.87162i | −0.472949 | − | 0.530704i | ||||
\(221\) | 0.660235 | 0.0444122 | ||||||||
\(222\) | 4.16229 | − | 12.8102i | 0.279355 | − | 0.859765i | ||||
\(223\) | −14.1619 | + | 10.2892i | −0.948351 | + | 0.689017i | −0.950416 | − | 0.310980i | \(-0.899343\pi\) |
0.00206512 | + | 0.999998i | \(0.499343\pi\) | |||||||
\(224\) | 6.63230 | + | 4.81865i | 0.443139 | + | 0.321959i | ||||
\(225\) | 0.156341 | + | 0.481169i | 0.0104227 | + | 0.0320779i | ||||
\(226\) | −2.42559 | − | 7.46520i | −0.161348 | − | 0.496578i | ||||
\(227\) | −1.07516 | − | 0.781147i | −0.0713606 | − | 0.0518465i | 0.551533 | − | 0.834153i | \(-0.314043\pi\) |
−0.622894 | + | 0.782307i | \(0.714043\pi\) | |||||||
\(228\) | −6.40705 | + | 4.65499i | −0.424317 | + | 0.308284i | ||||
\(229\) | −1.24789 | + | 3.84062i | −0.0824632 | + | 0.253795i | −0.983784 | − | 0.179356i | \(-0.942599\pi\) |
0.901321 | + | 0.433152i | \(0.142599\pi\) | |||||||
\(230\) | −28.3216 | −1.86747 | ||||||||
\(231\) | −2.08943 | + | 3.57657i | −0.137475 | + | 0.235321i | ||||
\(232\) | 11.7916 | 0.774157 | ||||||||
\(233\) | 4.50383 | − | 13.8614i | 0.295056 | − | 0.908088i | −0.688147 | − | 0.725571i | \(-0.741576\pi\) |
0.983203 | − | 0.182517i | \(-0.0584244\pi\) | |||||||
\(234\) | 1.48181 | − | 1.07660i | 0.0968691 | − | 0.0703795i | ||||
\(235\) | −25.0931 | − | 18.2312i | −1.63689 | − | 1.18927i | ||||
\(236\) | 3.63487 | + | 11.1870i | 0.236610 | + | 0.728210i | ||||
\(237\) | −2.78885 | − | 8.58321i | −0.181155 | − | 0.557539i | ||||
\(238\) | 1.22187 | + | 0.887738i | 0.0792018 | + | 0.0575435i | ||||
\(239\) | −2.08395 | + | 1.51408i | −0.134799 | + | 0.0979375i | −0.653142 | − | 0.757236i | \(-0.726549\pi\) |
0.518342 | + | 0.855173i | \(0.326549\pi\) | |||||||
\(240\) | 3.53420 | − | 10.8772i | 0.228132 | − | 0.702118i | ||||
\(241\) | −14.1580 | −0.911994 | −0.455997 | − | 0.889981i | \(-0.650717\pi\) | ||||
−0.455997 | + | 0.889981i | \(0.650717\pi\) | |||||||
\(242\) | −19.7494 | + | 3.98688i | −1.26954 | + | 0.256286i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.06659 | − | 12.5157i | 0.260337 | − | 0.801234i | ||||
\(245\) | 10.3274 | − | 7.50327i | 0.659791 | − | 0.479366i | ||||
\(246\) | 16.4964 | + | 11.9853i | 1.05177 | + | 0.764156i | ||||
\(247\) | 1.80633 | + | 5.55930i | 0.114934 | + | 0.353730i | ||||
\(248\) | 2.65842 | + | 8.18177i | 0.168810 | + | 0.519543i | ||||
\(249\) | 7.51388 | + | 5.45915i | 0.476173 | + | 0.345960i | ||||
\(250\) | 15.6260 | − | 11.3530i | 0.988276 | − | 0.718025i | ||||
\(251\) | −2.32634 | + | 7.15973i | −0.146837 | + | 0.451918i | −0.997243 | − | 0.0742097i | \(-0.976357\pi\) |
0.850406 | + | 0.526128i | \(0.176357\pi\) | |||||||
\(252\) | 1.69207 | 0.106590 | ||||||||
\(253\) | −11.0246 | + | 18.8713i | −0.693112 | + | 1.18643i | ||||
\(254\) | −10.8852 | −0.683000 | ||||||||
\(255\) | 0.478736 | − | 1.47340i | 0.0299796 | − | 0.0922678i | ||||
\(256\) | −16.9602 | + | 12.3223i | −1.06001 | + | 0.770144i | ||||
\(257\) | 9.40071 | + | 6.83001i | 0.586400 | + | 0.426045i | 0.841026 | − | 0.540995i | \(-0.181952\pi\) |
−0.254626 | + | 0.967040i | \(0.581952\pi\) | |||||||
\(258\) | 1.80450 | + | 5.55367i | 0.112343 | + | 0.345757i | ||||
\(259\) | −2.83811 | − | 8.73480i | −0.176351 | − | 0.542754i | ||||
\(260\) | 2.57193 | + | 1.86862i | 0.159504 | + | 0.115887i | ||||
\(261\) | 8.07280 | − | 5.86523i | 0.499694 | − | 0.363049i | ||||
\(262\) | 6.89829 | − | 21.2307i | 0.426178 | − | 1.31164i | ||||
\(263\) | −12.1716 | −0.750536 | −0.375268 | − | 0.926916i | \(-0.622449\pi\) | ||||
−0.375268 | + | 0.926916i | \(0.622449\pi\) | |||||||
\(264\) | −2.60754 | − | 2.92597i | −0.160483 | − | 0.180081i | ||||
\(265\) | −22.8752 | −1.40521 | ||||||||
\(266\) | −4.13203 | + | 12.7171i | −0.253351 | + | 0.779735i | ||||
\(267\) | −11.0521 | + | 8.02979i | −0.676375 | + | 0.491415i | ||||
\(268\) | −8.94415 | − | 6.49830i | −0.546351 | − | 0.396947i | ||||
\(269\) | −9.68752 | − | 29.8151i | −0.590659 | − | 1.81786i | −0.575247 | − | 0.817980i | \(-0.695094\pi\) |
−0.0154115 | − | 0.999881i | \(-0.504906\pi\) | |||||||
\(270\) | −1.32811 | − | 4.08749i | −0.0808261 | − | 0.248757i | ||||
\(271\) | −5.25083 | − | 3.81495i | −0.318965 | − | 0.231742i | 0.416769 | − | 0.909013i | \(-0.363163\pi\) |
−0.735734 | + | 0.677271i | \(0.763163\pi\) | |||||||
\(272\) | −2.60345 | + | 1.89152i | −0.157858 | + | 0.114690i | ||||
\(273\) | 0.385935 | − | 1.18779i | 0.0233579 | − | 0.0718881i | ||||
\(274\) | 27.5438 | 1.66398 | ||||||||
\(275\) | 0.166847 | + | 1.66967i | 0.0100613 | + | 0.100685i | ||||
\(276\) | 8.92798 | 0.537401 | ||||||||
\(277\) | −1.71510 | + | 5.27852i | −0.103050 | + | 0.317156i | −0.989268 | − | 0.146113i | \(-0.953324\pi\) |
0.886218 | + | 0.463269i | \(0.153324\pi\) | |||||||
\(278\) | 1.90245 | − | 1.38221i | 0.114101 | − | 0.0828996i | ||||
\(279\) | 5.88968 | + | 4.27910i | 0.352606 | + | 0.256183i | ||||
\(280\) | −1.07013 | − | 3.29352i | −0.0639525 | − | 0.196826i | ||||
\(281\) | 4.08252 | + | 12.5647i | 0.243543 | + | 0.749547i | 0.995873 | + | 0.0907610i | \(0.0289299\pi\) |
−0.752330 | + | 0.658786i | \(0.771070\pi\) | |||||||
\(282\) | 19.5873 | + | 14.2310i | 1.16641 | + | 0.847444i | ||||
\(283\) | 18.7307 | − | 13.6087i | 1.11343 | − | 0.808951i | 0.130226 | − | 0.991484i | \(-0.458430\pi\) |
0.983200 | + | 0.182533i | \(0.0584296\pi\) | |||||||
\(284\) | −4.77381 | + | 14.6923i | −0.283273 | + | 0.871826i | ||||
\(285\) | 13.7161 | 0.812469 | ||||||||
\(286\) | 5.56219 | − | 2.44239i | 0.328899 | − | 0.144421i | ||||
\(287\) | 13.9036 | 0.820704 | ||||||||
\(288\) | −2.02842 | + | 6.24282i | −0.119526 | + | 0.367862i | ||||
\(289\) | 13.4006 | − | 9.73613i | 0.788272 | − | 0.572713i | ||||
\(290\) | 34.6956 | + | 25.2079i | 2.03740 | + | 1.48026i | ||||
\(291\) | 0.821393 | + | 2.52799i | 0.0481509 | + | 0.148193i | ||||
\(292\) | −1.47946 | − | 4.55332i | −0.0865790 | − | 0.266463i | ||||
\(293\) | −7.59960 | − | 5.52143i | −0.443973 | − | 0.322565i | 0.343238 | − | 0.939248i | \(-0.388476\pi\) |
−0.787212 | + | 0.616683i | \(0.788476\pi\) | |||||||
\(294\) | −8.06138 | + | 5.85694i | −0.470149 | + | 0.341584i | ||||
\(295\) | 6.29532 | − | 19.3750i | 0.366528 | − | 1.12806i | ||||
\(296\) | 8.69004 | 0.505098 | ||||||||
\(297\) | −3.24057 | − | 0.706172i | −0.188037 | − | 0.0409762i | ||||
\(298\) | −23.3553 | −1.35293 | ||||||||
\(299\) | 2.03634 | − | 6.26720i | 0.117764 | − | 0.362441i | ||||
\(300\) | 0.554542 | − | 0.402899i | 0.0320165 | − | 0.0232614i | ||||
\(301\) | 3.22128 | + | 2.34039i | 0.185671 | + | 0.134898i | ||||
\(302\) | −4.60442 | − | 14.1709i | −0.264955 | − | 0.815446i | ||||
\(303\) | −4.25727 | − | 13.1025i | −0.244574 | − | 0.752721i | ||||
\(304\) | −23.0497 | − | 16.7466i | −1.32199 | − | 0.960483i | ||||
\(305\) | −18.4389 | + | 13.3966i | −1.05581 | + | 0.767090i | ||||
\(306\) | −0.373694 | + | 1.15011i | −0.0213627 | + | 0.0657476i | ||||
\(307\) | 25.1837 | 1.43731 | 0.718656 | − | 0.695366i | \(-0.244758\pi\) | ||||
0.718656 | + | 0.695366i | \(0.244758\pi\) | |||||||
\(308\) | 5.48327 | + | 1.19489i | 0.312439 | + | 0.0680852i | ||||
\(309\) | −6.47041 | −0.368089 | ||||||||
\(310\) | −9.66868 | + | 29.7571i | −0.549144 | + | 1.69009i | ||||
\(311\) | −2.92371 | + | 2.12420i | −0.165788 | + | 0.120452i | −0.667586 | − | 0.744533i | \(-0.732672\pi\) |
0.501797 | + | 0.864985i | \(0.332672\pi\) | |||||||
\(312\) | 0.956015 | + | 0.694585i | 0.0541237 | + | 0.0393231i | ||||
\(313\) | −7.19236 | − | 22.1358i | −0.406536 | − | 1.25119i | −0.919606 | − | 0.392843i | \(-0.871492\pi\) |
0.513070 | − | 0.858347i | \(-0.328508\pi\) | |||||||
\(314\) | −1.80741 | − | 5.56264i | −0.101998 | − | 0.313918i | ||||
\(315\) | −2.37085 | − | 1.72253i | −0.133583 | − | 0.0970534i | ||||
\(316\) | −9.89206 | + | 7.18701i | −0.556472 | + | 0.404301i | ||||
\(317\) | −5.50231 | + | 16.9344i | −0.309041 | + | 0.951129i | 0.669098 | + | 0.743174i | \(0.266681\pi\) |
−0.978138 | + | 0.207955i | \(0.933319\pi\) | |||||||
\(318\) | 17.8560 | 1.00132 | ||||||||
\(319\) | 30.3024 | − | 13.3059i | 1.69661 | − | 0.744989i | ||||
\(320\) | −5.33761 | −0.298381 | ||||||||
\(321\) | 1.55570 | − | 4.78794i | 0.0868304 | − | 0.267237i | ||||
\(322\) | 12.1953 | − | 8.86040i | 0.679617 | − | 0.493771i | ||||
\(323\) | −3.12227 | − | 2.26846i | −0.173728 | − | 0.126221i | ||||
\(324\) | 0.418667 | + | 1.28852i | 0.0232593 | + | 0.0715847i | ||||
\(325\) | −0.156341 | − | 0.481169i | −0.00867225 | − | 0.0266904i | ||||
\(326\) | 7.78476 | + | 5.65596i | 0.431158 | + | 0.313255i | ||||
\(327\) | −3.65054 | + | 2.65227i | −0.201876 | + | 0.146671i | ||||
\(328\) | −4.06523 | + | 12.5115i | −0.224465 | + | 0.690831i | ||||
\(329\) | 16.5087 | 0.910155 | ||||||||
\(330\) | −1.41736 | − | 14.1837i | −0.0780230 | − | 0.780787i | ||||
\(331\) | 24.0291 | 1.32076 | 0.660378 | − | 0.750933i | \(-0.270396\pi\) | ||||
0.660378 | + | 0.750933i | \(0.270396\pi\) | |||||||
\(332\) | 3.88844 | − | 11.9674i | 0.213406 | − | 0.656795i | ||||
\(333\) | 5.94939 | − | 4.32248i | 0.326024 | − | 0.236871i | ||||
\(334\) | 19.3473 | + | 14.0566i | 1.05863 | + | 0.769143i | ||||
\(335\) | 5.91688 | + | 18.2103i | 0.323274 | + | 0.994935i | ||||
\(336\) | 1.88108 | + | 5.78938i | 0.102621 | + | 0.315836i | ||||
\(337\) | 7.32066 | + | 5.31877i | 0.398782 | + | 0.289732i | 0.769045 | − | 0.639195i | \(-0.220732\pi\) |
−0.370263 | + | 0.928927i | \(0.620732\pi\) | |||||||
\(338\) | −1.48181 | + | 1.07660i | −0.0806000 | + | 0.0585593i | ||||
\(339\) | 1.32429 | − | 4.07574i | 0.0719254 | − | 0.221364i | ||||
\(340\) | −2.09894 | −0.113831 | ||||||||
\(341\) | 16.0642 | + | 18.0259i | 0.869923 | + | 0.976156i | ||||
\(342\) | −10.7065 | −0.578944 | ||||||||
\(343\) | −4.80112 | + | 14.7763i | −0.259236 | + | 0.797846i | ||||
\(344\) | −3.04792 | + | 2.21444i | −0.164333 | + | 0.119395i | ||||
\(345\) | −12.5095 | − | 9.08869i | −0.673489 | − | 0.489318i | ||||
\(346\) | 1.39113 | + | 4.28145i | 0.0747875 | + | 0.230172i | ||||
\(347\) | 9.35859 | + | 28.8028i | 0.502396 | + | 1.54621i | 0.805105 | + | 0.593132i | \(0.202109\pi\) |
−0.302710 | + | 0.953083i | \(0.597891\pi\) | |||||||
\(348\) | −10.9373 | − | 7.94641i | −0.586301 | − | 0.425972i | ||||
\(349\) | −14.5595 | + | 10.5781i | −0.779351 | + | 0.566232i | −0.904784 | − | 0.425870i | \(-0.859968\pi\) |
0.125433 | + | 0.992102i | \(0.459968\pi\) | |||||||
\(350\) | 0.357636 | − | 1.10069i | 0.0191164 | − | 0.0588343i | ||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −10.9817 | + | 18.7979i | −0.585328 | + | 1.00193i | ||||
\(353\) | 0.659345 | 0.0350934 | 0.0175467 | − | 0.999846i | \(-0.494414\pi\) | ||||
0.0175467 | + | 0.999846i | \(0.494414\pi\) | |||||||
\(354\) | −4.91404 | + | 15.1238i | −0.261178 | + | 0.803823i | ||||
\(355\) | 21.6456 | − | 15.7264i | 1.14883 | − | 0.834673i | ||||
\(356\) | 14.9737 | + | 10.8790i | 0.793605 | + | 0.576588i | ||||
\(357\) | 0.254808 | + | 0.784218i | 0.0134859 | + | 0.0415052i | ||||
\(358\) | 1.93857 | + | 5.96629i | 0.102456 | + | 0.315328i | ||||
\(359\) | 7.89566 | + | 5.73653i | 0.416717 | + | 0.302763i | 0.776315 | − | 0.630345i | \(-0.217086\pi\) |
−0.359599 | + | 0.933107i | \(0.617086\pi\) | |||||||
\(360\) | 2.24326 | − | 1.62982i | 0.118230 | − | 0.0858993i | ||||
\(361\) | 4.68738 | − | 14.4263i | 0.246704 | − | 0.759277i | ||||
\(362\) | −5.26390 | −0.276664 | ||||||||
\(363\) | −10.0026 | − | 4.57680i | −0.525003 | − | 0.240220i | ||||
\(364\) | −1.69207 | −0.0886885 | ||||||||
\(365\) | −2.56232 | + | 7.88601i | −0.134118 | + | 0.412773i | ||||
\(366\) | 14.3931 | − | 10.4572i | 0.752341 | − | 0.546608i | ||||
\(367\) | −7.05518 | − | 5.12589i | −0.368277 | − | 0.267569i | 0.388219 | − | 0.921567i | \(-0.373090\pi\) |
−0.756496 | + | 0.653998i | \(0.773090\pi\) | |||||||
\(368\) | 9.92529 | + | 30.5469i | 0.517392 | + | 1.59237i | ||||
\(369\) | 3.44015 | + | 10.5877i | 0.179087 | + | 0.551174i | ||||
\(370\) | 25.5696 | + | 18.5774i | 1.32930 | + | 0.965791i | ||||
\(371\) | 9.85006 | − | 7.15649i | 0.511390 | − | 0.371546i | ||||
\(372\) | 3.04791 | − | 9.38051i | 0.158027 | − | 0.486357i | ||||
\(373\) | 10.9749 | 0.568261 | 0.284130 | − | 0.958786i | \(-0.408295\pi\) | ||||
0.284130 | + | 0.958786i | \(0.408295\pi\) | |||||||
\(374\) | −2.02316 | + | 3.46313i | −0.104615 | + | 0.179074i | ||||
\(375\) | 10.5452 | 0.544552 | ||||||||
\(376\) | −4.82693 | + | 14.8558i | −0.248930 | + | 0.766127i | ||||
\(377\) | −8.07280 | + | 5.86523i | −0.415770 | + | 0.302075i | ||||
\(378\) | 1.85065 | + | 1.34458i | 0.0951873 | + | 0.0691576i | ||||
\(379\) | −8.99087 | − | 27.6710i | −0.461830 | − | 1.42137i | −0.862926 | − | 0.505330i | \(-0.831371\pi\) |
0.401096 | − | 0.916036i | \(-0.368629\pi\) | |||||||
\(380\) | −5.74246 | − | 17.6735i | −0.294582 | − | 0.906630i | ||||
\(381\) | −4.80795 | − | 3.49318i | −0.246319 | − | 0.178961i | ||||
\(382\) | 1.41100 | − | 1.02515i | 0.0721929 | − | 0.0524512i | ||||
\(383\) | −1.20672 | + | 3.71392i | −0.0616607 | + | 0.189772i | −0.977142 | − | 0.212589i | \(-0.931810\pi\) |
0.915481 | + | 0.402361i | \(0.131810\pi\) | |||||||
\(384\) | −8.96172 | −0.457326 | ||||||||
\(385\) | −6.46653 | − | 7.25621i | −0.329565 | − | 0.369810i | ||||
\(386\) | −18.0188 | −0.917132 | ||||||||
\(387\) | −0.985192 | + | 3.03211i | −0.0500801 | + | 0.154131i | ||||
\(388\) | 2.91348 | − | 2.11677i | 0.147910 | − | 0.107463i | ||||
\(389\) | −17.7746 | − | 12.9140i | −0.901208 | − | 0.654766i | 0.0375677 | − | 0.999294i | \(-0.488039\pi\) |
−0.938776 | + | 0.344528i | \(0.888039\pi\) | |||||||
\(390\) | 1.32811 | + | 4.08749i | 0.0672513 | + | 0.206978i | ||||
\(391\) | 1.34446 | + | 4.13782i | 0.0679923 | + | 0.209259i | ||||
\(392\) | −5.20093 | − | 3.77870i | −0.262687 | − | 0.190853i | ||||
\(393\) | 9.86009 | − | 7.16378i | 0.497376 | − | 0.361365i | ||||
\(394\) | 3.52545 | − | 10.8502i | 0.177609 | − | 0.546626i | ||||
\(395\) | 21.1767 | 1.06552 | ||||||||
\(396\) | 0.446801 | + | 4.47121i | 0.0224526 | + | 0.224687i | ||||
\(397\) | 6.96474 | 0.349550 | 0.174775 | − | 0.984608i | \(-0.444080\pi\) | ||||
0.174775 | + | 0.984608i | \(0.444080\pi\) | |||||||
\(398\) | 11.1303 | − | 34.2556i | 0.557913 | − | 1.71708i | ||||
\(399\) | −5.90614 | + | 4.29106i | −0.295677 | + | 0.214822i | ||||
\(400\) | 1.99500 | + | 1.44945i | 0.0997499 | + | 0.0724725i | ||||
\(401\) | −10.8370 | − | 33.3530i | −0.541176 | − | 1.66557i | −0.729912 | − | 0.683542i | \(-0.760439\pi\) |
0.188735 | − | 0.982028i | \(-0.439561\pi\) | |||||||
\(402\) | −4.61863 | − | 14.2147i | −0.230356 | − | 0.708964i | ||||
\(403\) | −5.88968 | − | 4.27910i | −0.293386 | − | 0.213157i | ||||
\(404\) | −15.1006 | + | 10.9712i | −0.751281 | + | 0.545838i | ||||
\(405\) | 0.725100 | − | 2.23163i | 0.0360305 | − | 0.110890i | ||||
\(406\) | −22.8262 | −1.13285 | ||||||||
\(407\) | 22.3318 | − | 9.80604i | 1.10695 | − | 0.486067i | ||||
\(408\) | −0.780199 | −0.0386256 | ||||||||
\(409\) | −9.22887 | + | 28.4036i | −0.456338 | + | 1.40447i | 0.413218 | + | 0.910632i | \(0.364405\pi\) |
−0.869557 | + | 0.493833i | \(0.835595\pi\) | |||||||
\(410\) | −38.7083 | + | 28.1232i | −1.91167 | + | 1.38891i | ||||
\(411\) | 12.1660 | + | 8.83909i | 0.600103 | + | 0.436000i | ||||
\(412\) | 2.70895 | + | 8.33728i | 0.133460 | + | 0.410748i | ||||
\(413\) | 3.35069 | + | 10.3124i | 0.164877 | + | 0.507439i | ||||
\(414\) | 9.76473 | + | 7.09449i | 0.479910 | + | 0.348675i | ||||
\(415\) | −17.6311 | + | 12.8097i | −0.865477 | + | 0.628806i | ||||
\(416\) | 2.02842 | − | 6.24282i | 0.0994513 | − | 0.306079i | ||||
\(417\) | 1.28387 | 0.0628713 | ||||||||
\(418\) | −34.6954 | − | 7.56066i | −1.69701 | − | 0.369804i | ||||
\(419\) | −4.38709 | −0.214324 | −0.107162 | − | 0.994242i | \(-0.534176\pi\) | ||||
−0.107162 | + | 0.994242i | \(0.534176\pi\) | |||||||
\(420\) | −1.22692 | + | 3.77607i | −0.0598675 | + | 0.184253i | ||||
\(421\) | −18.1662 | + | 13.1985i | −0.885366 | + | 0.643256i | −0.934666 | − | 0.355528i | \(-0.884301\pi\) |
0.0492998 | + | 0.998784i | \(0.484301\pi\) | |||||||
\(422\) | −4.75224 | − | 3.45271i | −0.231335 | − | 0.168075i | ||||
\(423\) | 4.08474 | + | 12.5715i | 0.198607 | + | 0.611248i | ||||
\(424\) | 3.55991 | + | 10.9563i | 0.172884 | + | 0.532084i | ||||
\(425\) | 0.270239 | + | 0.196340i | 0.0131085 | + | 0.00952388i | ||||
\(426\) | −16.8962 | + | 12.2758i | −0.818624 | + | 0.594765i | ||||
\(427\) | 3.74866 | − | 11.5372i | 0.181410 | − | 0.558324i | ||||
\(428\) | −6.82069 | −0.329690 | ||||||||
\(429\) | 3.24057 | + | 0.706172i | 0.156456 | + | 0.0340943i | ||||
\(430\) | −13.7022 | −0.660777 | ||||||||
\(431\) | 9.23981 | − | 28.4372i | 0.445066 | − | 1.36977i | −0.437345 | − | 0.899294i | \(-0.644081\pi\) |
0.882411 | − | 0.470479i | \(-0.155919\pi\) | |||||||
\(432\) | −3.94322 | + | 2.86492i | −0.189718 | + | 0.137839i | ||||
\(433\) | −2.85047 | − | 2.07098i | −0.136985 | − | 0.0995252i | 0.517183 | − | 0.855875i | \(-0.326981\pi\) |
−0.654167 | + | 0.756350i | \(0.726981\pi\) | |||||||
\(434\) | −5.14617 | − | 15.8383i | −0.247024 | − | 0.760261i | ||||
\(435\) | 7.23543 | + | 22.2684i | 0.346912 | + | 1.06769i | ||||
\(436\) | 4.94588 | + | 3.59339i | 0.236865 | + | 0.172092i | ||||
\(437\) | −31.1630 | + | 22.6412i | −1.49073 | + | 1.08308i | ||||
\(438\) | 2.00011 | − | 6.15570i | 0.0955689 | − | 0.294131i | ||||
\(439\) | 19.7905 | 0.944550 | 0.472275 | − | 0.881451i | \(-0.343433\pi\) | ||||
0.472275 | + | 0.881451i | \(0.343433\pi\) | |||||||
\(440\) | 8.42039 | − | 3.69744i | 0.401426 | − | 0.176269i | ||||
\(441\) | −5.44022 | −0.259058 | ||||||||
\(442\) | 0.373694 | − | 1.15011i | 0.0177748 | − | 0.0547053i | ||||
\(443\) | 21.2362 | − | 15.4290i | 1.00896 | − | 0.733056i | 0.0449728 | − | 0.998988i | \(-0.485680\pi\) |
0.963992 | + | 0.265933i | \(0.0856799\pi\) | |||||||
\(444\) | −8.06043 | − | 5.85625i | −0.382531 | − | 0.277925i | ||||
\(445\) | −9.90565 | − | 30.4865i | −0.469573 | − | 1.44520i | ||||
\(446\) | 9.90791 | + | 30.4934i | 0.469153 | + | 1.44390i | ||||
\(447\) | −10.3159 | − | 7.49493i | −0.487925 | − | 0.354498i | ||||
\(448\) | 2.29838 | − | 1.66987i | 0.108588 | − | 0.0788938i | ||||
\(449\) | −9.62804 | + | 29.6321i | −0.454375 | + | 1.39842i | 0.417491 | + | 0.908681i | \(0.362909\pi\) |
−0.871867 | + | 0.489743i | \(0.837091\pi\) | |||||||
\(450\) | 0.926673 | 0.0436838 | ||||||||
\(451\) | 3.67134 | + | 36.7396i | 0.172876 | + | 1.73000i | ||||
\(452\) | −5.80612 | −0.273097 | ||||||||
\(453\) | 2.51385 | − | 7.73684i | 0.118111 | − | 0.363508i | ||||
\(454\) | −1.96928 | + | 1.43076i | −0.0924228 | + | 0.0671491i | ||||
\(455\) | 2.37085 | + | 1.72253i | 0.111147 | + | 0.0807533i | ||||
\(456\) | −2.13453 | − | 6.56942i | −0.0999588 | − | 0.307641i | ||||
\(457\) | −2.21580 | − | 6.81953i | −0.103651 | − | 0.319004i | 0.885761 | − | 0.464142i | \(-0.153637\pi\) |
−0.989411 | + | 0.145138i | \(0.953637\pi\) | |||||||
\(458\) | 5.98396 | + | 4.34760i | 0.279612 | + | 0.203150i | ||||
\(459\) | −0.534141 | + | 0.388076i | −0.0249316 | + | 0.0181139i | ||||
\(460\) | −6.47368 | + | 19.9239i | −0.301837 | + | 0.928958i | ||||
\(461\) | 35.4005 | 1.64876 | 0.824382 | − | 0.566034i | \(-0.191523\pi\) | ||||
0.824382 | + | 0.566034i | \(0.191523\pi\) | |||||||
\(462\) | 5.04768 | + | 5.66408i | 0.234839 | + | 0.263517i | ||||
\(463\) | −17.3932 | −0.808332 | −0.404166 | − | 0.914686i | \(-0.632438\pi\) | ||||
−0.404166 | + | 0.914686i | \(0.632438\pi\) | |||||||
\(464\) | 15.0294 | − | 46.2558i | 0.697724 | − | 2.14737i | ||||
\(465\) | −13.8200 | + | 10.0408i | −0.640886 | + | 0.465631i | ||||
\(466\) | −21.5970 | − | 15.6911i | −1.00046 | − | 0.726877i | ||||
\(467\) | 6.53856 | + | 20.1236i | 0.302568 | + | 0.931210i | 0.980573 | + | 0.196152i | \(0.0628447\pi\) |
−0.678005 | + | 0.735057i | \(0.737155\pi\) | |||||||
\(468\) | −0.418667 | − | 1.28852i | −0.0193529 | − | 0.0595620i | ||||
\(469\) | −8.24489 | − | 5.99026i | −0.380714 | − | 0.276605i | ||||
\(470\) | −45.9611 | + | 33.3927i | −2.12003 | + | 1.54029i | ||||
\(471\) | 0.986782 | − | 3.03700i | 0.0454685 | − | 0.139938i | ||||
\(472\) | −10.2595 | −0.472233 | ||||||||
\(473\) | −5.33378 | + | 9.13006i | −0.245247 | + | 0.419801i | ||||
\(474\) | −16.5302 | −0.759258 | ||||||||
\(475\) | −0.913876 | + | 2.81262i | −0.0419315 | + | 0.129052i | ||||
\(476\) | 0.903804 | − | 0.656652i | 0.0414258 | − | 0.0300976i | ||||
\(477\) | 7.88692 | + | 5.73018i | 0.361117 | + | 0.262367i | ||||
\(478\) | 1.45797 | + | 4.48716i | 0.0666858 | + | 0.205238i | ||||
\(479\) | −8.80709 | − | 27.1054i | −0.402406 | − | 1.23848i | −0.923042 | − | 0.384700i | \(-0.874305\pi\) |
0.520635 | − | 0.853779i | \(-0.325695\pi\) | |||||||
\(480\) | −12.4608 | − | 9.05334i | −0.568757 | − | 0.413226i | ||||
\(481\) | −5.94939 | + | 4.32248i | −0.271269 | + | 0.197088i | ||||
\(482\) | −8.01343 | + | 24.6628i | −0.365002 | + | 1.12336i | ||||
\(483\) | 8.22998 | 0.374477 | ||||||||
\(484\) | −1.70955 | + | 14.8048i | −0.0777067 | + | 0.672945i | ||||
\(485\) | −6.23712 | −0.283213 | ||||||||
\(486\) | −0.566002 | + | 1.74197i | −0.0256744 | + | 0.0790176i | ||||
\(487\) | 2.99794 | − | 2.17813i | 0.135850 | − | 0.0987005i | −0.517785 | − | 0.855511i | \(-0.673243\pi\) |
0.653635 | + | 0.756810i | \(0.273243\pi\) | |||||||
\(488\) | 9.28595 | + | 6.74664i | 0.420355 | + | 0.305406i | ||||
\(489\) | 1.62343 | + | 4.99641i | 0.0734142 | + | 0.225946i | ||||
\(490\) | −7.22520 | − | 22.2369i | −0.326401 | − | 1.00456i | ||||
\(491\) | −29.1694 | − | 21.1928i | −1.31640 | − | 0.956417i | −0.999970 | − | 0.00779960i | \(-0.997517\pi\) |
−0.316425 | − | 0.948617i | \(-0.602483\pi\) | |||||||
\(492\) | 12.2022 | − | 8.86544i | 0.550119 | − | 0.399685i | ||||
\(493\) | 2.03586 | − | 6.26572i | 0.0916904 | − | 0.282194i | ||||
\(494\) | 10.7065 | 0.481710 | ||||||||
\(495\) | 3.92565 | − | 6.71971i | 0.176445 | − | 0.302028i | ||||
\(496\) | 35.4836 | 1.59326 | ||||||||
\(497\) | −4.40059 | + | 13.5436i | −0.197393 | + | 0.607514i | ||||
\(498\) | 13.7626 | − | 9.99909i | 0.616715 | − | 0.448070i | ||||
\(499\) | 21.4965 | + | 15.6182i | 0.962317 | + | 0.699165i | 0.953688 | − | 0.300798i | \(-0.0972531\pi\) |
0.00862966 | + | 0.999963i | \(0.497253\pi\) | |||||||
\(500\) | −4.41493 | − | 13.5878i | −0.197442 | − | 0.607663i | ||||
\(501\) | 4.03467 | + | 12.4175i | 0.180256 | + | 0.554771i | ||||
\(502\) | 11.1554 | + | 8.10484i | 0.497888 | + | 0.361737i | ||||
\(503\) | 6.19728 | − | 4.50259i | 0.276323 | − | 0.200761i | −0.440989 | − | 0.897513i | \(-0.645372\pi\) |
0.717312 | + | 0.696752i | \(0.245372\pi\) | |||||||
\(504\) | −0.456059 | + | 1.40361i | −0.0203145 | + | 0.0625216i | ||||
\(505\) | 32.3269 | 1.43853 | ||||||||
\(506\) | 26.6334 | + | 29.8858i | 1.18400 | + | 1.32859i | ||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −2.48811 | + | 7.65763i | −0.110392 | + | 0.339752i | ||||
\(509\) | 27.4173 | − | 19.9198i | 1.21525 | − | 0.882930i | 0.219553 | − | 0.975601i | \(-0.429540\pi\) |
0.995697 | + | 0.0926703i | \(0.0295403\pi\) | |||||||
\(510\) | −2.29566 | − | 1.66789i | −0.101653 | − | 0.0738555i | ||||
\(511\) | −1.36380 | − | 4.19734i | −0.0603308 | − | 0.185679i | ||||
\(512\) | 6.32699 | + | 19.4725i | 0.279616 | + | 0.860570i | ||||
\(513\) | −4.72903 | − | 3.43584i | −0.208792 | − | 0.151696i | ||||
\(514\) | 17.2185 | − | 12.5100i | 0.759477 | − | 0.551792i | ||||
\(515\) | 4.69169 | − | 14.4395i | 0.206741 | − | 0.636282i | ||||
\(516\) | 4.31941 | 0.190151 | ||||||||
\(517\) | 4.35923 | + | 43.6235i | 0.191719 | + | 1.91856i | ||||
\(518\) | −16.8222 | −0.739124 | ||||||||
\(519\) | −0.759506 | + | 2.33752i | −0.0333386 | + | 0.102606i | ||||
\(520\) | −2.24326 | + | 1.62982i | −0.0983735 | + | 0.0714726i | ||||
\(521\) | 19.0034 | + | 13.8067i | 0.832552 | + | 0.604884i | 0.920280 | − | 0.391260i | \(-0.127961\pi\) |
−0.0877282 | + | 0.996144i | \(0.527961\pi\) | |||||||
\(522\) | −5.64786 | − | 17.3823i | −0.247200 | − | 0.760804i | ||||
\(523\) | −7.66110 | − | 23.5784i | −0.334996 | − | 1.03101i | −0.966724 | − | 0.255822i | \(-0.917654\pi\) |
0.631728 | − | 0.775191i | \(-0.282346\pi\) | |||||||
\(524\) | −13.3588 | − | 9.70573i | −0.583581 | − | 0.423997i | ||||
\(525\) | 0.511188 | − | 0.371400i | 0.0223101 | − | 0.0162092i | ||||
\(526\) | −6.88918 | + | 21.2027i | −0.300382 | + | 0.924482i | ||||
\(527\) | 4.80654 | 0.209376 | ||||||||
\(528\) | −14.8014 | + | 6.49939i | −0.644150 | + | 0.282850i | ||||
\(529\) | 20.4244 | 0.888019 | ||||||||
\(530\) | −12.9474 | + | 39.8480i | −0.562400 | + | 1.73089i | ||||
\(531\) | −7.02390 | + | 5.10316i | −0.304811 | + | 0.221458i | ||||
\(532\) | 8.00184 | + | 5.81367i | 0.346924 | + | 0.252055i | ||||
\(533\) | −3.44015 | − | 10.5877i | −0.149010 | − | 0.458604i | ||||
\(534\) | 7.73220 | + | 23.7973i | 0.334605 | + | 1.02981i | ||||
\(535\) | 9.55686 | + | 6.94346i | 0.413179 | + | 0.300192i | ||||
\(536\) | 7.80117 | − | 5.66788i | 0.336959 | − | 0.244815i | ||||
\(537\) | −1.05839 | + | 3.25738i | −0.0456728 | + | 0.140567i | ||||
\(538\) | −57.4204 | −2.47557 | ||||||||
\(539\) | −17.6294 | − | 3.84173i | −0.759353 | − | 0.165475i | ||||
\(540\) | −3.17908 | −0.136806 | ||||||||
\(541\) | 4.99251 | − | 15.3654i | 0.214645 | − | 0.660608i | −0.784534 | − | 0.620086i | \(-0.787098\pi\) |
0.999179 | − | 0.0405224i | \(-0.0129022\pi\) | |||||||
\(542\) | −9.61753 | + | 6.98754i | −0.413108 | + | 0.300141i | ||||
\(543\) | −2.32504 | − | 1.68924i | −0.0997769 | − | 0.0724921i | ||||
\(544\) | 1.33923 | + | 4.12173i | 0.0574191 | + | 0.176718i | ||||
\(545\) | −3.27188 | − | 10.0698i | −0.140152 | − | 0.431344i | ||||
\(546\) | −1.85065 | − | 1.34458i | −0.0792006 | − | 0.0575426i | ||||
\(547\) | −17.8444 | + | 12.9647i | −0.762971 | + | 0.554331i | −0.899820 | − | 0.436261i | \(-0.856302\pi\) |
0.136849 | + | 0.990592i | \(0.456302\pi\) | |||||||
\(548\) | 6.29589 | − | 19.3768i | 0.268947 | − | 0.827734i | ||||
\(549\) | 9.71319 | 0.414549 | ||||||||
\(550\) | 3.00295 | + | 0.654391i | 0.128046 | + | 0.0279033i | ||||
\(551\) | 58.3284 | 2.48488 | ||||||||
\(552\) | −2.40634 | + | 7.40594i | −0.102420 | + | 0.315218i | ||||
\(553\) | −9.11869 | + | 6.62512i | −0.387766 | + | 0.281729i | ||||
\(554\) | 8.22430 | + | 5.97531i | 0.349417 | + | 0.253866i | ||||
\(555\) | 5.33227 | + | 16.4110i | 0.226342 | + | 0.696610i | ||||
\(556\) | −0.537513 | − | 1.65429i | −0.0227956 | − | 0.0701577i | ||||
\(557\) | −27.8190 | − | 20.2117i | −1.17873 | − | 0.856398i | −0.186702 | − | 0.982417i | \(-0.559780\pi\) |
−0.992028 | + | 0.126019i | \(0.959780\pi\) | |||||||
\(558\) | 10.7877 | − | 7.83769i | 0.456678 | − | 0.331796i | ||||
\(559\) | 0.985192 | − | 3.03211i | 0.0416692 | − | 0.128245i | ||||
\(560\) | −14.2837 | −0.603597 | ||||||||
\(561\) | −2.00497 | + | 0.880395i | −0.0846500 | + | 0.0371703i | ||||
\(562\) | 24.1981 | 1.02074 | ||||||||
\(563\) | 3.28457 | − | 10.1089i | 0.138428 | − | 0.426038i | −0.857679 | − | 0.514185i | \(-0.828094\pi\) |
0.996107 | + | 0.0881468i | \(0.0280945\pi\) | |||||||
\(564\) | 14.4886 | − | 10.5266i | 0.610079 | − | 0.443248i | ||||
\(565\) | 8.13529 | + | 5.91063i | 0.342254 | + | 0.248662i | ||||
\(566\) | −13.1043 | − | 40.3310i | −0.550816 | − | 1.69524i | ||||
\(567\) | 0.385935 | + | 1.18779i | 0.0162077 | + | 0.0498823i | ||||
\(568\) | −10.9009 | − | 7.91994i | −0.457390 | − | 0.332313i | ||||
\(569\) | 11.1839 | − | 8.12556i | 0.468852 | − | 0.340641i | −0.328141 | − | 0.944629i | \(-0.606422\pi\) |
0.796994 | + | 0.603987i | \(0.206422\pi\) | |||||||
\(570\) | 7.76332 | − | 23.8930i | 0.325170 | − | 1.00077i | ||||
\(571\) | −17.1095 | −0.716010 | −0.358005 | − | 0.933720i | \(-0.616543\pi\) | ||||
−0.358005 | + | 0.933720i | \(0.616543\pi\) | |||||||
\(572\) | −0.446801 | − | 4.47121i | −0.0186817 | − | 0.186951i | ||||
\(573\) | 0.952210 | 0.0397791 | ||||||||
\(574\) | 7.86947 | − | 24.2197i | 0.328465 | − | 1.01091i | ||||
\(575\) | 2.69722 | − | 1.95964i | 0.112482 | − | 0.0817227i | ||||
\(576\) | 1.84030 | + | 1.33706i | 0.0766792 | + | 0.0557107i | ||||
\(577\) | −10.1830 | − | 31.3402i | −0.423925 | − | 1.30471i | −0.904020 | − | 0.427491i | \(-0.859398\pi\) |
0.480094 | − | 0.877217i | \(-0.340602\pi\) | |||||||
\(578\) | −9.37531 | − | 28.8542i | −0.389961 | − | 1.20018i | ||||
\(579\) | −7.95880 | − | 5.78241i | −0.330756 | − | 0.240309i | ||||
\(580\) | 25.6641 | − | 18.6460i | 1.06564 | − | 0.774235i | ||||
\(581\) | 3.58443 | − | 11.0318i | 0.148707 | − | 0.457674i | ||||
\(582\) | 4.86860 | 0.201810 | ||||||||
\(583\) | 21.5116 | + | 24.1386i | 0.890921 | + | 0.999718i | ||||
\(584\) | 4.17583 | 0.172797 | ||||||||
\(585\) | −0.725100 | + | 2.23163i | −0.0299792 | + | 0.0922664i | ||||
\(586\) | −13.9196 | + | 10.1132i | −0.575012 | + | 0.417771i | ||||
\(587\) | 22.9206 | + | 16.6528i | 0.946035 | + | 0.687334i | 0.949866 | − | 0.312658i | \(-0.101219\pi\) |
−0.00383099 | + | 0.999993i | \(0.501219\pi\) | |||||||
\(588\) | 2.27764 | + | 7.00985i | 0.0939282 | + | 0.289081i | ||||
\(589\) | 13.1501 | + | 40.4720i | 0.541842 | + | 1.66762i | ||||
\(590\) | −30.1876 | − | 21.9326i | −1.24280 | − | 0.902951i | ||||
\(591\) | 5.03911 | − | 3.66113i | 0.207281 | − | 0.150599i | ||||
\(592\) | 11.0762 | − | 34.0890i | 0.455229 | − | 1.40105i | ||||
\(593\) | −30.5267 | −1.25358 | −0.626790 | − | 0.779188i | \(-0.715632\pi\) | ||||
−0.626790 | + | 0.779188i | \(0.715632\pi\) | |||||||
\(594\) | −3.06430 | + | 5.24530i | −0.125730 | + | 0.215217i | ||||
\(595\) | −1.93484 | −0.0793208 | ||||||||
\(596\) | −5.33848 | + | 16.4302i | −0.218673 | + | 0.673005i | ||||
\(597\) | 15.9092 | − | 11.5587i | 0.651119 | − | 0.473066i | ||||
\(598\) | −9.76473 | − | 7.09449i | −0.399310 | − | 0.290115i | ||||
\(599\) | 1.44269 | + | 4.44016i | 0.0589469 | + | 0.181420i | 0.976194 | − | 0.216898i | \(-0.0695940\pi\) |
−0.917247 | + | 0.398318i | \(0.869594\pi\) | |||||||
\(600\) | 0.184748 | + | 0.568597i | 0.00754232 | + | 0.0232129i | ||||
\(601\) | 0.307025 | + | 0.223067i | 0.0125238 | + | 0.00909909i | 0.594030 | − | 0.804443i | \(-0.297536\pi\) |
−0.581506 | + | 0.813542i | \(0.697536\pi\) | |||||||
\(602\) | 5.90016 | − | 4.28671i | 0.240472 | − | 0.174713i | ||||
\(603\) | 2.52161 | − | 7.76071i | 0.102688 | − | 0.316041i | ||||
\(604\) | −11.0216 | −0.448461 | ||||||||
\(605\) | 17.4666 | − | 19.0035i | 0.710120 | − | 0.772603i | ||||
\(606\) | −25.2339 | −1.02506 | ||||||||
\(607\) | 8.48174 | − | 26.1041i | 0.344263 | − | 1.05953i | −0.617714 | − | 0.786403i | \(-0.711941\pi\) |
0.961977 | − | 0.273130i | \(-0.0880589\pi\) | |||||||
\(608\) | −31.0418 | + | 22.5532i | −1.25891 | + | 0.914651i | ||||
\(609\) | −10.0822 | − | 7.32516i | −0.408552 | − | 0.296830i | ||||
\(610\) | 12.9002 | + | 39.7026i | 0.522312 | + | 1.60751i | ||||
\(611\) | −4.08474 | − | 12.5715i | −0.165251 | − | 0.508589i | ||||
\(612\) | 0.723673 | + | 0.525779i | 0.0292527 | + | 0.0212534i | ||||
\(613\) | 24.9296 | − | 18.1124i | 1.00690 | − | 0.731555i | 0.0433422 | − | 0.999060i | \(-0.486199\pi\) |
0.963556 | + | 0.267506i | \(0.0861994\pi\) | |||||||
\(614\) | 14.2540 | − | 43.8694i | 0.575246 | − | 1.77043i | ||||
\(615\) | −26.1223 | −1.05335 | ||||||||
\(616\) | −2.46908 | + | 4.22643i | −0.0994821 | + | 0.170288i | ||||
\(617\) | 2.05318 | 0.0826581 | 0.0413290 | − | 0.999146i | \(-0.486841\pi\) | ||||
0.0413290 | + | 0.999146i | \(0.486841\pi\) | |||||||
\(618\) | −3.66226 | + | 11.2713i | −0.147318 | + | 0.453398i | ||||
\(619\) | −9.22767 | + | 6.70430i | −0.370891 | + | 0.269468i | −0.757581 | − | 0.652742i | \(-0.773619\pi\) |
0.386689 | + | 0.922210i | \(0.373619\pi\) | |||||||
\(620\) | 18.7238 | + | 13.6036i | 0.751964 | + | 0.546334i | ||||
\(621\) | 2.03634 | + | 6.26720i | 0.0817153 | + | 0.251494i | ||||
\(622\) | 2.04548 | + | 6.29533i | 0.0820162 | + | 0.252420i | ||||
\(623\) | 13.8030 | + | 10.0285i | 0.553007 | + | 0.401783i | ||||
\(624\) | 3.94322 | − | 2.86492i | 0.157855 | − | 0.114689i | ||||
\(625\) | −8.42803 | + | 25.9388i | −0.337121 | + | 1.03755i | ||||
\(626\) | −42.6309 | −1.70387 | ||||||||
\(627\) | −12.8985 | − | 14.4736i | −0.515115 | − | 0.578020i | ||||
\(628\) | −4.32638 | −0.172641 | ||||||||
\(629\) | 1.50036 | − | 4.61763i | 0.0598233 | − | 0.184117i | ||||
\(630\) | −4.34251 | + | 3.15501i | −0.173010 | + | 0.125699i | ||||
\(631\) | 8.80933 | + | 6.40035i | 0.350694 | + | 0.254794i | 0.749160 | − | 0.662389i | \(-0.230457\pi\) |
−0.398466 | + | 0.917183i | \(0.630457\pi\) | |||||||
\(632\) | −3.29558 | − | 10.1428i | −0.131091 | − | 0.403458i | ||||
\(633\) | −0.991032 | − | 3.05008i | −0.0393900 | − | 0.121230i | ||||
\(634\) | 26.3849 | + | 19.1698i | 1.04788 | + | 0.761329i | ||||
\(635\) | 11.2817 | − | 8.19664i | 0.447701 | − | 0.325274i | ||||
\(636\) | 4.08148 | − | 12.5615i | 0.161841 | − | 0.498097i | ||||
\(637\) | 5.44022 | 0.215549 | ||||||||
\(638\) | −6.02740 | − | 60.3171i | −0.238627 | − | 2.38798i | ||||
\(639\) | −11.4024 | −0.451072 | ||||||||
\(640\) | 6.49814 | − | 19.9992i | 0.256862 | − | 0.790539i | ||||
\(641\) | −13.6541 | + | 9.92026i | −0.539303 | + | 0.391827i | −0.823826 | − | 0.566842i | \(-0.808165\pi\) |
0.284523 | + | 0.958669i | \(0.408165\pi\) | |||||||
\(642\) | −7.45994 | − | 5.41996i | −0.294420 | − | 0.213909i | ||||
\(643\) | −6.51399 | − | 20.0480i | −0.256887 | − | 0.790616i | −0.993452 | − | 0.114250i | \(-0.963554\pi\) |
0.736565 | − | 0.676366i | \(-0.236446\pi\) | |||||||
\(644\) | −3.44562 | − | 10.6045i | −0.135776 | − | 0.417877i | ||||
\(645\) | −6.05217 | − | 4.39716i | −0.238304 | − | 0.173138i | ||||
\(646\) | −5.71881 | + | 4.15496i | −0.225004 | + | 0.163475i | ||||
\(647\) | −1.22818 | + | 3.77995i | −0.0482848 | + | 0.148605i | −0.972292 | − | 0.233770i | \(-0.924894\pi\) |
0.924007 | + | 0.382375i | \(0.124894\pi\) | |||||||
\(648\) | −1.18170 | −0.0464215 | ||||||||
\(649\) | −26.3652 | + | 11.5771i | −1.03492 | + | 0.454440i | ||||
\(650\) | −0.926673 | −0.0363471 | ||||||||
\(651\) | 2.80962 | − | 8.64713i | 0.110118 | − | 0.338908i | ||||
\(652\) | 5.75832 | − | 4.18366i | 0.225513 | − | 0.163845i | ||||
\(653\) | −17.9600 | − | 13.0487i | −0.702830 | − | 0.510636i | 0.178023 | − | 0.984026i | \(-0.443030\pi\) |
−0.880853 | + | 0.473391i | \(0.843030\pi\) | |||||||
\(654\) | 2.55398 | + | 7.86035i | 0.0998686 | + | 0.307364i | ||||
\(655\) | 8.83733 | + | 27.1985i | 0.345303 | + | 1.06273i | ||||
\(656\) | 43.8982 | + | 31.8939i | 1.71394 | + | 1.24525i | ||||
\(657\) | 2.85886 | − | 2.07709i | 0.111535 | − | 0.0810348i | ||||
\(658\) | 9.34397 | − | 28.7578i | 0.364266 | − | 1.12109i | ||||
\(659\) | −14.4189 | −0.561682 | −0.280841 | − | 0.959754i | \(-0.590613\pi\) | ||||
−0.280841 | + | 0.959754i | \(0.590613\pi\) | |||||||
\(660\) | −10.3020 | − | 2.24498i | −0.401007 | − | 0.0873856i | ||||
\(661\) | −10.6304 | −0.413474 | −0.206737 | − | 0.978397i | \(-0.566284\pi\) | ||||
−0.206737 | + | 0.978397i | \(0.566284\pi\) | |||||||
\(662\) | 13.6005 | − | 41.8580i | 0.528598 | − | 1.62686i | ||||
\(663\) | 0.534141 | − | 0.388076i | 0.0207443 | − | 0.0150716i | ||||
\(664\) | 8.87914 | + | 6.45107i | 0.344577 | + | 0.250350i | ||||
\(665\) | −5.29351 | − | 16.2917i | −0.205273 | − | 0.631767i | ||||
\(666\) | −4.16229 | − | 12.8102i | −0.161286 | − | 0.496386i | ||||
\(667\) | −53.1975 | − | 38.6502i | −2.05981 | − | 1.49654i | ||||
\(668\) | 14.3110 | − | 10.3975i | 0.553709 | − | 0.402293i | ||||
\(669\) | −5.40937 | + | 16.6483i | −0.209138 | + | 0.643661i | ||||
\(670\) | 35.0708 | 1.35490 | ||||||||
\(671\) | 31.4763 | + | 6.85918i | 1.21513 | + | 0.264796i | ||||
\(672\) | 8.19797 | 0.316244 | ||||||||
\(673\) | −5.02735 | + | 15.4726i | −0.193790 | + | 0.596424i | 0.806199 | + | 0.591645i | \(0.201521\pi\) |
−0.999989 | + | 0.00477910i | \(0.998479\pi\) | |||||||
\(674\) | 13.4087 | − | 9.74197i | 0.516483 | − | 0.375247i | ||||
\(675\) | 0.409307 | + | 0.297379i | 0.0157542 | + | 0.0114461i | ||||
\(676\) | 0.418667 | + | 1.28852i | 0.0161026 | + | 0.0495586i | ||||
\(677\) | −14.6867 | − | 45.2010i | −0.564455 | − | 1.73721i | −0.669565 | − | 0.742753i | \(-0.733519\pi\) |
0.105110 | − | 0.994461i | \(-0.466481\pi\) | |||||||
\(678\) | −6.35028 | − | 4.61375i | −0.243881 | − | 0.177190i | ||||
\(679\) | 2.68570 | − | 1.95128i | 0.103068 | − | 0.0748832i | ||||
\(680\) | 0.565722 | − | 1.74111i | 0.0216945 | − | 0.0667687i | ||||
\(681\) | −1.32897 | −0.0509261 | ||||||||
\(682\) | 40.4930 | − | 17.7807i | 1.55056 | − | 0.680858i | ||||
\(683\) | −33.3076 | −1.27448 | −0.637239 | − | 0.770666i | \(-0.719924\pi\) | ||||
−0.637239 | + | 0.770666i | \(0.719924\pi\) | |||||||
\(684\) | −2.44727 | + | 7.53193i | −0.0935738 | + | 0.287991i | ||||
\(685\) | −28.5471 | + | 20.7407i | −1.09073 | + | 0.792460i | ||||
\(686\) | 23.0225 | + | 16.7268i | 0.879004 | + | 0.638634i | ||||
\(687\) | 1.24789 | + | 3.84062i | 0.0476101 | + | 0.146529i | ||||
\(688\) | 4.80192 | + | 14.7788i | 0.183071 | + | 0.563436i | ||||
\(689\) | −7.88692 | − | 5.73018i | −0.300468 | − | 0.218302i | ||||
\(690\) | −22.9127 | + | 16.6470i | −0.872270 | + | 0.633741i | ||||
\(691\) | −1.52007 | + | 4.67830i | −0.0578263 | + | 0.177971i | −0.975798 | − | 0.218676i | \(-0.929826\pi\) |
0.917971 | + | 0.396647i | \(0.129826\pi\) | |||||||
\(692\) | 3.32993 | 0.126585 | ||||||||
\(693\) | 0.411870 | + | 4.12164i | 0.0156457 | + | 0.156568i | ||||
\(694\) | 55.4707 | 2.10564 | ||||||||
\(695\) | −0.930933 | + | 2.86512i | −0.0353123 | + | 0.108680i | ||||
\(696\) | 9.53962 | − | 6.93094i | 0.361598 | − | 0.262716i | ||||
\(697\) | 5.94637 | + | 4.32029i | 0.225235 | + | 0.163643i | ||||
\(698\) | 10.1861 | + | 31.3495i | 0.385548 | + | 1.18659i | ||||
\(699\) | −4.50383 | − | 13.8614i | −0.170350 | − | 0.524285i | ||||
\(700\) | −0.692575 | − | 0.503185i | −0.0261769 | − | 0.0190186i | ||||
\(701\) | −3.74878 | + | 2.72365i | −0.141590 | + | 0.102871i | −0.656325 | − | 0.754478i | \(-0.727890\pi\) |
0.514736 | + | 0.857349i | \(0.327890\pi\) | |||||||
\(702\) | 0.566002 | − | 1.74197i | 0.0213624 | − | 0.0657466i | ||||
\(703\) | 42.9862 | 1.62125 | ||||||||
\(704\) | 5.01944 | + | 5.63240i | 0.189177 | + | 0.212279i | ||||
\(705\) | −31.0168 | −1.16816 | ||||||||
\(706\) | 0.373191 | − | 1.14856i | 0.0140452 | − | 0.0432267i | ||||
\(707\) | −13.9200 | + | 10.1135i | −0.523515 | + | 0.380356i | ||||
\(708\) | 9.51621 | + | 6.91393i | 0.357641 | + | 0.259842i | ||||
\(709\) | 14.4720 | + | 44.5402i | 0.543507 | + | 1.67274i | 0.724514 | + | 0.689260i | \(0.242064\pi\) |
−0.181008 | + | 0.983482i | \(0.557936\pi\) | |||||||
\(710\) | −15.1436 | − | 46.6073i | −0.568330 | − | 1.74914i | ||||
\(711\) | −7.30131 | − | 5.30471i | −0.273821 | − | 0.198942i | ||||
\(712\) | −13.0602 | + | 9.48879i | −0.489452 | + | 0.355608i | ||||
\(713\) | 14.8246 | − | 45.6255i | 0.555186 | − | 1.70869i | ||||
\(714\) | 1.51031 | 0.0565219 | ||||||||
\(715\) | −3.92565 | + | 6.71971i | −0.146811 | + | 0.251303i | ||||
\(716\) | 4.64033 | 0.173417 | ||||||||
\(717\) | −0.795998 | + | 2.44983i | −0.0297271 | + | 0.0914905i | ||||
\(718\) | 14.4619 | − | 10.5071i | 0.539711 | − | 0.392123i | ||||
\(719\) | −9.14050 | − | 6.64096i | −0.340883 | − | 0.247666i | 0.404151 | − | 0.914692i | \(-0.367567\pi\) |
−0.745034 | + | 0.667026i | \(0.767567\pi\) | |||||||
\(720\) | −3.53420 | − | 10.8772i | −0.131712 | − | 0.405368i | ||||
\(721\) | 2.49716 | + | 7.68546i | 0.0929990 | + | 0.286222i | ||||
\(722\) | −22.4771 | − | 16.3306i | −0.836512 | − | 0.607761i | ||||
\(723\) | −11.4540 | + | 8.32184i | −0.425980 | + | 0.309493i | ||||
\(724\) | −1.20321 | + | 3.70309i | −0.0447169 | + | 0.137624i | ||||
\(725\) | −5.04844 | −0.187494 | ||||||||
\(726\) | −13.6342 | + | 14.8339i | −0.506012 | + | 0.550537i | ||||
\(727\) | −15.0362 | −0.557660 | −0.278830 | − | 0.960340i | \(-0.589947\pi\) | ||||
−0.278830 | + | 0.960340i | \(0.589947\pi\) | |||||||
\(728\) | 0.456059 | − | 1.40361i | 0.0169027 | − | 0.0520211i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 12.2870 | + | 8.92699i | 0.454760 | + | 0.330403i | ||||
\(731\) | 0.650458 | + | 2.00190i | 0.0240581 | + | 0.0740431i | ||||
\(732\) | −4.06659 | − | 12.5157i | −0.150306 | − | 0.462593i | ||||
\(733\) | −10.1338 | − | 7.36265i | −0.374301 | − | 0.271946i | 0.384691 | − | 0.923045i | \(-0.374308\pi\) |
−0.758992 | + | 0.651100i | \(0.774308\pi\) | |||||||
\(734\) | −12.9224 | + | 9.38868i | −0.476975 | + | 0.346542i | ||||
\(735\) | 3.94470 | − | 12.1405i | 0.145502 | − | 0.447811i | ||||
\(736\) | 43.2555 | 1.59442 | ||||||||
\(737\) | 13.6519 | − | 23.3685i | 0.502873 | − | 0.860789i | ||||
\(738\) | 20.3907 | 0.750590 | ||||||||
\(739\) | 14.2955 | − | 43.9970i | 0.525868 | − | 1.61846i | −0.236725 | − | 0.971577i | \(-0.576074\pi\) |
0.762593 | − | 0.646878i | \(-0.223926\pi\) | |||||||
\(740\) | 18.9136 | − | 13.7415i | 0.695277 | − | 0.505148i | ||||
\(741\) | 4.72903 | + | 3.43584i | 0.173725 | + | 0.126219i | ||||
\(742\) | −6.89127 | − | 21.2092i | −0.252987 | − | 0.778612i | ||||
\(743\) | −6.07429 | − | 18.6947i | −0.222844 | − | 0.685844i | −0.998503 | − | 0.0546917i | \(-0.982582\pi\) |
0.775659 | − | 0.631152i | \(-0.217418\pi\) | |||||||
\(744\) | 6.95983 | + | 5.05661i | 0.255160 | + | 0.185384i | ||||
\(745\) | 24.2059 | − | 17.5867i | 0.886837 | − | 0.644325i | ||||
\(746\) | 6.21183 | − | 19.1181i | 0.227431 | − | 0.699962i | ||||
\(747\) | 9.28766 | 0.339818 | ||||||||
\(748\) | 1.97383 | + | 2.21486i | 0.0721702 | + | 0.0809834i | ||||
\(749\) | −6.28744 | −0.229738 | ||||||||
\(750\) | 5.96861 | − | 18.3695i | 0.217943 | − | 0.670759i | ||||
\(751\) | 18.1738 | − | 13.2040i | 0.663171 | − | 0.481822i | −0.204561 | − | 0.978854i | \(-0.565577\pi\) |
0.867732 | + | 0.497032i | \(0.165577\pi\) | |||||||
\(752\) | 52.1234 | + | 37.8699i | 1.90075 | + | 1.38097i | ||||
\(753\) | 2.32634 | + | 7.15973i | 0.0847764 | + | 0.260915i | ||||
\(754\) | 5.64786 | + | 17.3823i | 0.205683 | + | 0.633027i | ||||
\(755\) | 15.4429 | + | 11.2200i | 0.562026 | + | 0.408336i | ||||
\(756\) | 1.36891 | − | 0.994573i | 0.0497869 | − | 0.0361723i | ||||
\(757\) | −5.34460 | + | 16.4490i | −0.194253 | + | 0.597848i | 0.805732 | + | 0.592281i | \(0.201772\pi\) |
−0.999985 | + | 0.00556772i | \(0.998228\pi\) | |||||||
\(758\) | −53.2911 | −1.93562 | ||||||||
\(759\) | 2.17318 | + | 21.7473i | 0.0788814 | + | 0.789378i | ||||
\(760\) | 16.2083 | 0.587935 | ||||||||
\(761\) | 5.86939 | − | 18.0641i | 0.212765 | − | 0.654824i | −0.786540 | − | 0.617540i | \(-0.788129\pi\) |
0.999305 | − | 0.0372839i | \(-0.0118706\pi\) | |||||||
\(762\) | −8.80633 | + | 6.39817i | −0.319020 | + | 0.231781i | ||||
\(763\) | 4.55921 | + | 3.31246i | 0.165054 | + | 0.119919i | ||||
\(764\) | −0.398659 | − | 1.22695i | −0.0144230 | − | 0.0443893i | ||||
\(765\) | −0.478736 | − | 1.47340i | −0.0173087 | − | 0.0532708i | ||||
\(766\) | 5.78654 | + | 4.20417i | 0.209076 | + | 0.151903i | ||||
\(767\) | 7.02390 | − | 5.10316i | 0.253618 | − | 0.184264i | ||||
\(768\) | −6.47822 | + | 19.9379i | −0.233763 | + | 0.719447i | ||||
\(769\) | −6.72145 | −0.242382 | −0.121191 | − | 0.992629i | \(-0.538671\pi\) | ||||
−0.121191 | + | 0.992629i | \(0.538671\pi\) | |||||||
\(770\) | −16.3002 | + | 7.15750i | −0.587418 | + | 0.257939i | ||||
\(771\) | 11.6199 | 0.418481 | ||||||||
\(772\) | −4.11868 | + | 12.6760i | −0.148235 | + | 0.456219i | ||||
\(773\) | −0.529226 | + | 0.384505i | −0.0190349 | + | 0.0138297i | −0.597262 | − | 0.802046i | \(-0.703745\pi\) |
0.578227 | + | 0.815876i | \(0.303745\pi\) | |||||||
\(774\) | 4.72424 | + | 3.43236i | 0.169809 | + | 0.123374i | ||||
\(775\) | −1.13817 | − | 3.50293i | −0.0408843 | − | 0.125829i | ||||
\(776\) | 0.970639 | + | 2.98732i | 0.0348439 | + | 0.107239i | ||||
\(777\) | −7.43026 | − | 5.39840i | −0.266559 | − | 0.193667i | ||||
\(778\) | −32.5563 | + | 23.6536i | −1.16720 | + | 0.848021i | ||||
\(779\) | −20.1091 | + | 61.8893i | −0.720482 | + | 2.21742i | ||||
\(780\) | 3.17908 | 0.113829 | ||||||||
\(781\) | −36.9503 | − | 8.05205i | −1.32219 | − | 0.288125i | ||||
\(782\) | 7.96895 | 0.284969 | ||||||||
\(783\) | 3.08353 | − | 9.49014i | 0.110197 | − | 0.339150i | ||||
\(784\) | −21.4520 | + | 15.5858i | −0.766143 | + | 0.556635i | ||||
\(785\) | 6.06194 | + | 4.40426i | 0.216360 | + | 0.157195i | ||||
\(786\) | −6.89829 | − | 21.2307i | −0.246054 | − | 0.757275i | ||||
\(787\) | −3.15914 | − | 9.72284i | −0.112611 | − | 0.346582i | 0.878830 | − | 0.477135i | \(-0.158325\pi\) |
−0.991441 | + | 0.130553i | \(0.958325\pi\) | |||||||
\(788\) | −6.82716 | − | 4.96022i | −0.243207 | − | 0.176701i | ||||
\(789\) | −9.84707 | + | 7.15432i | −0.350565 | + | 0.254700i | ||||
\(790\) | 11.9861 | − | 36.8893i | 0.426445 | − | 1.31246i | ||||
\(791\) | −5.35219 | −0.190302 | ||||||||
\(792\) | −3.82938 | − | 0.834483i | −0.136071 | − | 0.0296521i | ||||
\(793\) | −9.71319 | −0.344926 | ||||||||
\(794\) | 3.94206 | − | 12.1324i | 0.139898 | − | 0.430563i | ||||
\(795\) | −18.5064 | + | 13.4457i | −0.656355 | + | 0.476870i | ||||
\(796\) | −21.5543 | − | 15.6601i | −0.763972 | − | 0.555058i | ||||
\(797\) | 15.4278 | + | 47.4819i | 0.546481 | + | 1.68189i | 0.717443 | + | 0.696617i | \(0.245312\pi\) |
−0.170962 | + | 0.985278i | \(0.554688\pi\) | |||||||
\(798\) | 4.13203 | + | 12.7171i | 0.146272 | + | 0.450180i | ||||
\(799\) | 7.06054 | + | 5.12978i | 0.249784 | + | 0.181479i | ||||
\(800\) | 2.68673 | − | 1.95202i | 0.0949901 | − | 0.0690143i | ||||
\(801\) | −4.22151 | + | 12.9925i | −0.149160 | + | 0.459066i | ||||
\(802\) | −64.2339 | −2.26818 | ||||||||
\(803\) | 10.7311 | − | 4.71210i | 0.378694 | − | 0.166286i | ||||
\(804\) | −11.0556 | −0.389900 | ||||||||
\(805\) | −5.96756 | + | 18.3663i | −0.210329 | + | 0.647325i | ||||
\(806\) | −10.7877 | + | 7.83769i | −0.379979 | + | 0.276071i | ||||
\(807\) | −25.3623 | − | 18.4268i | −0.892794 | − | 0.648653i | ||||
\(808\) | −5.03082 | − | 15.4833i | −0.176984 | − | 0.544699i | ||||
\(809\) | 3.64815 | + | 11.2279i | 0.128262 | + | 0.394751i | 0.994481 | − | 0.104914i | \(-0.0334567\pi\) |
−0.866219 | + | 0.499664i | \(0.833457\pi\) | |||||||
\(810\) | −3.47703 | − | 2.52621i | −0.122170 | − | 0.0887620i | ||||
\(811\) | −8.82279 | + | 6.41014i | −0.309810 | + | 0.225090i | −0.731815 | − | 0.681503i | \(-0.761327\pi\) |
0.422005 | + | 0.906594i | \(0.361327\pi\) | |||||||
\(812\) | −5.21755 | + | 16.0580i | −0.183100 | + | 0.563524i | ||||
\(813\) | −6.49038 | −0.227628 | ||||||||
\(814\) | −4.44200 | − | 44.4518i | −0.155692 | − | 1.55803i | ||||
\(815\) | −12.3273 | −0.431806 | ||||||||
\(816\) | −0.994431 | + | 3.06054i | −0.0348121 | + | 0.107140i | ||||
\(817\) | −15.0768 | + | 10.9540i | −0.527472 | + | 0.383231i | ||||
\(818\) | 44.2547 | + | 32.1529i | 1.54733 | + | 1.12420i | ||||
\(819\) | −0.385935 | − | 1.18779i | −0.0134857 | − | 0.0415046i | ||||
\(820\) | 10.9365 | + | 33.6592i | 0.381920 | + | 1.17543i | ||||
\(821\) | 34.9585 | + | 25.3988i | 1.22006 | + | 0.886425i | 0.996105 | − | 0.0881751i | \(-0.0281035\pi\) |
0.223954 | + | 0.974600i | \(0.428104\pi\) | |||||||
\(822\) | 22.2834 | − | 16.1899i | 0.777224 | − | 0.564686i | ||||
\(823\) | −1.89544 | + | 5.83357i | −0.0660709 | + | 0.203345i | −0.978642 | − | 0.205573i | \(-0.934094\pi\) |
0.912571 | + | 0.408919i | \(0.134094\pi\) | |||||||
\(824\) | −7.64608 | −0.266364 | ||||||||
\(825\) | 1.11639 | + | 1.25272i | 0.0388676 | + | 0.0436141i | ||||
\(826\) | 19.8604 | 0.691031 | ||||||||
\(827\) | −15.0660 | + | 46.3683i | −0.523896 | + | 1.61238i | 0.242594 | + | 0.970128i | \(0.422002\pi\) |
−0.766489 | + | 0.642257i | \(0.777998\pi\) | |||||||
\(828\) | 7.22289 | − | 5.24773i | 0.251013 | − | 0.182371i | ||||
\(829\) | 2.86395 | + | 2.08078i | 0.0994689 | + | 0.0722684i | 0.636408 | − | 0.771353i | \(-0.280419\pi\) |
−0.536939 | + | 0.843621i | \(0.680419\pi\) | |||||||
\(830\) | 12.3350 | + | 37.9633i | 0.428155 | + | 1.31772i | ||||
\(831\) | 1.71510 | + | 5.27852i | 0.0594960 | + | 0.183110i | ||||
\(832\) | −1.84030 | − | 1.33706i | −0.0638010 | − | 0.0463541i | ||||
\(833\) | −2.90585 | + | 2.11122i | −0.100682 | + | 0.0731495i | ||||
\(834\) | 0.726672 | − | 2.23647i | 0.0251626 | − | 0.0774425i | ||||
\(835\) | −30.6367 | −1.06023 | ||||||||
\(836\) | −13.2494 | + | 22.6796i | −0.458240 | + | 0.784390i | ||||
\(837\) | 7.28004 | 0.251635 | ||||||||
\(838\) | −2.48310 | + | 7.64221i | −0.0857774 | + | 0.263996i | ||||
\(839\) | −21.4859 | + | 15.6104i | −0.741776 | + | 0.538931i | −0.893267 | − | 0.449527i | \(-0.851592\pi\) |
0.151491 | + | 0.988459i | \(0.451592\pi\) | |||||||
\(840\) | −2.80164 | − | 2.03551i | −0.0966656 | − | 0.0702317i | ||||
\(841\) | 21.8076 | + | 67.1170i | 0.751987 | + | 2.31438i | ||||
\(842\) | 12.7094 | + | 39.1154i | 0.437994 | + | 1.34801i | ||||
\(843\) | 10.6882 | + | 7.76542i | 0.368120 | + | 0.267455i | ||||
\(844\) | −3.51519 | + | 2.55394i | −0.120998 | + | 0.0879101i | ||||
\(845\) | 0.725100 | − | 2.23163i | 0.0249442 | − | 0.0767703i | ||||
\(846\) | 24.2112 | 0.832400 | ||||||||
\(847\) | −1.57589 | + | 13.6473i | −0.0541484 | + | 0.468928i | ||||
\(848\) | 47.5164 | 1.63172 | ||||||||
\(849\) | 7.15450 | − | 22.0193i | 0.245542 | − | 0.755700i | ||||
\(850\) | 0.494974 | − | 0.359620i | 0.0169775 | − | 0.0123349i | ||||
\(851\) | −39.2048 | − | 28.4840i | −1.34392 | − | 0.976418i | ||||
\(852\) | 4.77381 | + | 14.6923i | 0.163548 | + | 0.503349i | ||||
\(853\) | 9.80387 | + | 30.1732i | 0.335678 | + | 1.03311i | 0.966387 | + | 0.257091i | \(0.0827641\pi\) |
−0.630709 | + | 0.776019i | \(0.717236\pi\) | |||||||
\(854\) | −17.9757 | − | 13.0601i | −0.615117 | − | 0.446909i | ||||
\(855\) | 11.0965 | − | 8.06210i | 0.379493 | − | 0.275718i | ||||
\(856\) | 1.83836 | − | 5.65790i | 0.0628340 | − | 0.193383i | ||||
\(857\) | 13.2476 | 0.452528 | 0.226264 | − | 0.974066i | \(-0.427349\pi\) | ||||
0.226264 | + | 0.974066i | \(0.427349\pi\) | |||||||
\(858\) | 3.06430 | − | 5.24530i | 0.104614 | − | 0.179072i | ||||
\(859\) | −29.2959 | −0.999562 | −0.499781 | − | 0.866152i | \(-0.666586\pi\) | ||||
−0.499781 | + | 0.866152i | \(0.666586\pi\) | |||||||
\(860\) | −3.13200 | + | 9.63932i | −0.106800 | + | 0.328698i | ||||
\(861\) | 11.2483 | − | 8.17233i | 0.383339 | − | 0.278512i | ||||
\(862\) | −44.3072 | − | 32.1910i | −1.50911 | − | 1.09643i | ||||
\(863\) | −6.71103 | − | 20.6544i | −0.228446 | − | 0.703085i | −0.997923 | − | 0.0644108i | \(-0.979483\pi\) |
0.769477 | − | 0.638674i | \(-0.220517\pi\) | |||||||
\(864\) | 2.02842 | + | 6.24282i | 0.0690081 | + | 0.212385i | ||||
\(865\) | −4.66575 | − | 3.38987i | −0.158640 | − | 0.115259i | ||||
\(866\) | −5.22097 | + | 3.79326i | −0.177416 | + | 0.128900i | ||||
\(867\) | 5.11859 | − | 15.7534i | 0.173836 | − | 0.535013i | ||||
\(868\) | −12.3183 | −0.418112 | ||||||||
\(869\) | −19.9144 | − | 22.3463i | −0.675550 | − | 0.758046i | ||||
\(870\) | 42.8862 | 1.45398 | ||||||||
\(871\) | −2.52161 | + | 7.76071i | −0.0854414 | + | 0.262962i | ||||
\(872\) | −4.31384 | + | 3.13419i | −0.146085 | + | 0.106137i | ||||
\(873\) | 2.15043 | + | 1.56238i | 0.0727812 | + | 0.0528786i | ||||
\(874\) | 21.8021 | + | 67.1001i | 0.737468 | + | 2.26969i | ||||
\(875\) | −4.06977 | − | 12.5254i | −0.137583 | − | 0.423437i | ||||
\(876\) | −3.87328 | − | 2.81411i | −0.130866 | − | 0.0950798i | ||||
\(877\) | −36.0322 | + | 26.1790i | −1.21672 | + | 0.884001i | −0.995824 | − | 0.0912961i | \(-0.970899\pi\) |
−0.220899 | + | 0.975297i | \(0.570899\pi\) | |||||||
\(878\) | 11.2015 | − | 34.4746i | 0.378031 | − | 1.16346i | ||||
\(879\) | −9.39362 | −0.316839 | ||||||||
\(880\) | −3.77170 | − | 37.7440i | −0.127144 | − | 1.27235i | ||||
\(881\) | 12.1937 | 0.410817 | 0.205409 | − | 0.978676i | \(-0.434148\pi\) | ||||
0.205409 | + | 0.978676i | \(0.434148\pi\) | |||||||
\(882\) | −3.07917 | + | 9.47672i | −0.103681 | + | 0.319098i | ||||
\(883\) | −5.10126 | + | 3.70628i | −0.171671 | + | 0.124726i | −0.670303 | − | 0.742087i | \(-0.733836\pi\) |
0.498632 | + | 0.866814i | \(0.333836\pi\) | |||||||
\(884\) | −0.723673 | − | 0.525779i | −0.0243398 | − | 0.0176839i | ||||
\(885\) | −6.29532 | − | 19.3750i | −0.211615 | − | 0.651284i | ||||
\(886\) | −14.8572 | − | 45.7259i | −0.499138 | − | 1.53619i | ||||
\(887\) | −18.9371 | − | 13.7586i | −0.635846 | − | 0.461969i | 0.222574 | − | 0.974916i | \(-0.428554\pi\) |
−0.858421 | + | 0.512946i | \(0.828554\pi\) | |||||||
\(888\) | 7.03039 | − | 5.10787i | 0.235924 | − | 0.171409i | ||||
\(889\) | −2.29359 | + | 7.05895i | −0.0769246 | + | 0.236750i | ||||
\(890\) | −58.7133 | −1.96807 | ||||||||
\(891\) | −3.03676 | + | 1.33346i | −0.101735 | + | 0.0446725i | ||||
\(892\) | 23.7165 | 0.794086 | ||||||||
\(893\) | −23.8769 | + | 73.4855i | −0.799010 | + | 2.45910i | ||||
\(894\) | −18.8948 | + | 13.7279i | −0.631937 | + | 0.459129i | ||||
\(895\) | −6.50183 | − | 4.72386i | −0.217332 | − | 0.157901i | ||||
\(896\) | 3.45864 | + | 10.6446i | 0.115545 | + | 0.355611i | ||||
\(897\) | −2.03634 | − | 6.26720i | −0.0679913 | − | 0.209256i | ||||
\(898\) | 46.1688 | + | 33.5436i | 1.54067 | + | 1.11937i | ||||
\(899\) | −58.7703 | + | 42.6991i | −1.96010 | + | 1.42410i | ||||
\(900\) | 0.211816 | − | 0.651904i | 0.00706055 | − | 0.0217301i | ||||
\(901\) | 6.43648 | 0.214430 | ||||||||
\(902\) | 66.0774 | + | 14.3993i | 2.20014 | + | 0.479444i | ||||
\(903\) | 3.98172 | 0.132503 | ||||||||
\(904\) | 1.56491 | − | 4.81629i | 0.0520481 | − | 0.160188i | ||||
\(905\) | 5.45563 | − | 3.96375i | 0.181351 | − | 0.131760i | ||||
\(906\) | −12.0545 | − | 8.75813i | −0.400485 | − | 0.290969i | ||||
\(907\) | 10.7831 | + | 33.1868i | 0.358045 | + | 1.10195i | 0.954223 | + | 0.299098i | \(0.0966856\pi\) |
−0.596177 | + | 0.802853i | \(0.703314\pi\) | |||||||
\(908\) | 0.556394 | + | 1.71240i | 0.0184646 | + | 0.0568281i | ||||
\(909\) | −11.1457 | − | 8.09782i | −0.369679 | − | 0.268588i | ||||
\(910\) | 4.34251 | − | 3.15501i | 0.143953 | − | 0.104588i | ||||
\(911\) | −16.3189 | + | 50.2245i | −0.540670 | + | 1.66401i | 0.190397 | + | 0.981707i | \(0.439022\pi\) |
−0.731068 | + | 0.682305i | \(0.760978\pi\) | |||||||
\(912\) | −28.4910 | −0.943432 | ||||||||
\(913\) | 30.0974 | + | 6.55869i | 0.996077 | + | 0.217061i | ||||
\(914\) | −13.1336 | −0.434420 | ||||||||
\(915\) | −7.04303 | + | 21.6762i | −0.232835 | + | 0.716594i | ||||
\(916\) | 4.42628 | − | 3.21588i | 0.146248 | − | 0.106256i | ||||
\(917\) | −12.3144 | − | 8.94693i | −0.406657 | − | 0.295454i | ||||
\(918\) | 0.373694 | + | 1.15011i | 0.0123337 | + | 0.0379594i | ||||
\(919\) | −13.8045 | − | 42.4857i | −0.455367 | − | 1.40148i | −0.870704 | − | 0.491808i | \(-0.836336\pi\) |
0.415337 | − | 0.909668i | \(-0.363664\pi\) | |||||||
\(920\) | −14.7825 | − | 10.7401i | −0.487364 | − | 0.354090i | ||||
\(921\) | 20.3741 | − | 14.8026i | 0.671348 | − | 0.487763i | ||||
\(922\) | 20.0367 | − | 61.6667i | 0.659875 | − | 2.03088i | ||||
\(923\) | 11.4024 | 0.375315 | ||||||||
\(924\) | 5.13840 | − | 2.25630i | 0.169041 | − | 0.0742268i | ||||
\(925\) | −3.72054 | −0.122331 | ||||||||
\(926\) | −9.84461 | + | 30.2986i | −0.323514 | + | 0.995673i | ||||
\(927\) | −5.23467 | + | 3.80321i | −0.171929 | + | 0.124914i | ||||
\(928\) | −52.9906 | − | 38.4999i | −1.73950 | − | 1.26382i | ||||
\(929\) | −2.71131 | − | 8.34457i | −0.0889553 | − | 0.273776i | 0.896676 | − | 0.442688i | \(-0.145975\pi\) |
−0.985631 | + | 0.168911i | \(0.945975\pi\) | |||||||
\(930\) | 9.66868 | + | 29.7571i | 0.317049 | + | 0.975775i | ||||
\(931\) | −25.7269 | − | 18.6917i | −0.843166 | − | 0.612596i | ||||
\(932\) | −15.9751 | + | 11.6066i | −0.523282 | + | 0.380186i | ||||
\(933\) | −1.11676 | + | 3.43703i | −0.0365610 | + | 0.112523i | ||||
\(934\) | 38.7557 | 1.26812 | ||||||||
\(935\) | −0.510908 | − | 5.11273i | −0.0167085 | − | 0.167204i | ||||
\(936\) | 1.18170 | 0.0386250 | ||||||||
\(937\) | −1.96982 | + | 6.06250i | −0.0643514 | + | 0.198053i | −0.978063 | − | 0.208311i | \(-0.933203\pi\) |
0.913711 | + | 0.406364i | \(0.133203\pi\) | |||||||
\(938\) | −15.1015 | + | 10.9719i | −0.493082 | + | 0.358245i | ||||
\(939\) | −18.8298 | − | 13.6807i | −0.614489 | − | 0.446452i | ||||
\(940\) | 12.9857 | + | 39.9659i | 0.423547 | + | 1.30354i | ||||
\(941\) | −10.4244 | − | 32.0831i | −0.339826 | − | 1.04588i | −0.964296 | − | 0.264829i | \(-0.914685\pi\) |
0.624469 | − | 0.781049i | \(-0.285315\pi\) | |||||||
\(942\) | −4.73186 | − | 3.43790i | −0.154172 | − | 0.112013i | ||||
\(943\) | 59.3499 | − | 43.1203i | 1.93270 | − | 1.40419i | ||||
\(944\) | −13.0767 | + | 40.2458i | −0.425609 | + | 1.30989i | ||||
\(945\) | −2.93054 | −0.0953304 | ||||||||
\(946\) | 12.8854 | + | 14.4589i | 0.418941 | + | 0.470101i | ||||
\(947\) | −3.21082 | −0.104338 | −0.0521688 | − | 0.998638i | \(-0.516613\pi\) | ||||
−0.0521688 | + | 0.998638i | \(0.516613\pi\) | |||||||
\(948\) | −3.77843 | + | 11.6288i | −0.122718 | + | 0.377686i | ||||
\(949\) | −2.85886 | + | 2.07709i | −0.0928026 | + | 0.0674250i | ||||
\(950\) | 4.38226 | + | 3.18390i | 0.142179 | + | 0.103299i | ||||
\(951\) | 5.50231 | + | 16.9344i | 0.178425 | + | 0.549135i | ||||
\(952\) | 0.301106 | + | 0.926710i | 0.00975891 | + | 0.0300348i | ||||
\(953\) | 1.57601 | + | 1.14504i | 0.0510518 | + | 0.0370913i | 0.613019 | − | 0.790069i | \(-0.289955\pi\) |
−0.561967 | + | 0.827160i | \(0.689955\pi\) | |||||||
\(954\) | 14.4458 | − | 10.4955i | 0.467701 | − | 0.339805i | ||||
\(955\) | −0.690447 | + | 2.12498i | −0.0223423 | + | 0.0687627i | ||||
\(956\) | 3.48992 | 0.112872 | ||||||||
\(957\) | 16.6941 | − | 28.5760i | 0.539643 | − | 0.923731i | ||||
\(958\) | −52.2018 | −1.68656 | ||||||||
\(959\) | 5.80367 | − | 17.8619i | 0.187410 | − | 0.576790i | ||||
\(960\) | −4.31822 | + | 3.13737i | −0.139370 | + | 0.101258i | ||||
\(961\) | −17.7976 | − | 12.9307i | −0.574116 | − | 0.417120i | ||||
\(962\) | 4.16229 | + | 12.8102i | 0.134198 | + | 0.413018i | ||||
\(963\) | −1.55570 | − | 4.78794i | −0.0501316 | − | 0.154289i | ||||
\(964\) | 15.5183 | + | 11.2747i | 0.499811 | + | 0.363134i | ||||
\(965\) | 18.6751 | − | 13.5683i | 0.601173 | − | 0.436777i | ||||
\(966\) | 4.65819 | − | 14.3364i | 0.149875 | − | 0.461267i | ||||
\(967\) | 33.4224 | 1.07479 | 0.537396 | − | 0.843330i | \(-0.319408\pi\) | ||||
0.537396 | + | 0.843330i | \(0.319408\pi\) | |||||||
\(968\) | −11.8201 | − | 5.40841i | −0.379913 | − | 0.173833i | ||||
\(969\) | −3.85934 | −0.123980 | ||||||||
\(970\) | −3.53022 | + | 10.8649i | −0.113349 | + | 0.348851i | ||||
\(971\) | −2.61592 | + | 1.90058i | −0.0839488 | + | 0.0609924i | −0.628968 | − | 0.777431i | \(-0.716522\pi\) |
0.545019 | + | 0.838424i | \(0.316522\pi\) | |||||||
\(972\) | 1.09608 | + | 0.796352i | 0.0351569 | + | 0.0255430i | ||||
\(973\) | −0.495490 | − | 1.52496i | −0.0158847 | − | 0.0488880i | ||||
\(974\) | −2.09741 | − | 6.45516i | −0.0672053 | − | 0.206837i | ||||
\(975\) | −0.409307 | − | 0.297379i | −0.0131083 | − | 0.00952374i | ||||
\(976\) | 38.3013 | − | 27.8275i | 1.22599 | − | 0.890737i | ||||
\(977\) | −10.8607 | + | 33.4258i | −0.347464 | + | 1.06939i | 0.612787 | + | 0.790248i | \(0.290048\pi\) |
−0.960251 | + | 0.279137i | \(0.909952\pi\) | |||||||
\(978\) | 9.62249 | 0.307693 | ||||||||
\(979\) | −22.8550 | + | 39.1220i | −0.730450 | + | 1.25034i | ||||
\(980\) | −17.2949 | −0.552465 | ||||||||
\(981\) | −1.39438 | + | 4.29147i | −0.0445192 | + | 0.137016i | ||||
\(982\) | −53.4272 | + | 38.8171i | −1.70493 | + | 1.23870i | ||||
\(983\) | −31.1949 | − | 22.6644i | −0.994963 | − | 0.722883i | −0.0339608 | − | 0.999423i | \(-0.510812\pi\) |
−0.961002 | + | 0.276540i | \(0.910812\pi\) | |||||||
\(984\) | 4.06523 | + | 12.5115i | 0.129595 | + | 0.398852i | ||||
\(985\) | 4.51642 | + | 13.9001i | 0.143905 | + | 0.442894i | ||||
\(986\) | −9.76243 | − | 7.09282i | −0.310899 | − | 0.225881i | ||||
\(987\) | 13.3558 | − | 9.70358i | 0.425121 | − | 0.308868i | ||||
\(988\) | 2.44727 | − | 7.53193i | 0.0778581 | − | 0.239623i | ||||
\(989\) | 21.0090 | 0.668048 | ||||||||
\(990\) | −9.48364 | − | 10.6418i | −0.301410 | − | 0.338217i | ||||
\(991\) | −23.7277 | −0.753737 | −0.376868 | − | 0.926267i | \(-0.622999\pi\) | ||||
−0.376868 | + | 0.926267i | \(0.622999\pi\) | |||||||
\(992\) | 14.7670 | − | 45.4480i | 0.468851 | − | 1.44298i | ||||
\(993\) | 19.4399 | − | 14.1239i | 0.616907 | − | 0.448209i | ||||
\(994\) | 21.1019 | + | 15.3314i | 0.669311 | + | 0.486283i | ||||
\(995\) | 14.2590 | + | 43.8845i | 0.452039 | + | 1.39123i | ||||
\(996\) | −3.88844 | − | 11.9674i | −0.123210 | − | 0.379201i | ||||
\(997\) | 12.0832 | + | 8.77898i | 0.382680 | + | 0.278033i | 0.762449 | − | 0.647048i | \(-0.223997\pi\) |
−0.379770 | + | 0.925081i | \(0.623997\pi\) | |||||||
\(998\) | 39.3735 | − | 28.6065i | 1.24635 | − | 0.905524i | ||||
\(999\) | 2.27246 | − | 6.99392i | 0.0718976 | − | 0.221278i |
(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 | 429.2.n.b.196.4 | ✓ | 20 | |
11.4 | even | 5 | 4719.2.a.bn.1.8 | 10 | |||
11.5 | even | 5 | inner | 429.2.n.b.313.4 | yes | 20 | |
11.7 | odd | 10 | 4719.2.a.bi.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.b.196.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
429.2.n.b.313.4 | yes | 20 | 11.5 | even | 5 | inner | |
4719.2.a.bi.1.3 | 10 | 11.7 | odd | 10 | |||
4719.2.a.bn.1.8 | 10 | 11.4 | even | 5 |