Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 631.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.631 |
Dual form | 770.2.n.d.421.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | 0.500000 | − | 1.53884i | 0.288675 | − | 0.888451i | −0.696598 | − | 0.717462i | \(-0.745304\pi\) |
0.985273 | − | 0.170989i | \(-0.0546962\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 0.809017 | − | 0.587785i | 0.361803 | − | 0.262866i | ||||
\(6\) | 1.30902 | − | 0.951057i | 0.534404 | − | 0.388267i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | 0.309017 | + | 0.224514i | 0.103006 | + | 0.0748380i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.309017 | + | 3.30220i | −0.0931721 | + | 0.995650i | ||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | 4.23607 | + | 3.07768i | 1.17487 | + | 0.853596i | 0.991584 | − | 0.129463i | \(-0.0413254\pi\) |
0.183290 | + | 0.983059i | \(0.441325\pi\) | |||||||
\(14\) | −0.309017 | + | 0.951057i | −0.0825883 | + | 0.254181i | ||||
\(15\) | −0.500000 | − | 1.53884i | −0.129099 | − | 0.397327i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −2.11803 | + | 1.53884i | −0.513699 | + | 0.373224i | −0.814225 | − | 0.580550i | \(-0.802838\pi\) |
0.300526 | + | 0.953774i | \(0.402838\pi\) | |||||||
\(18\) | 0.118034 | + | 0.363271i | 0.0278209 | + | 0.0856239i | ||||
\(19\) | 2.42705 | − | 7.46969i | 0.556804 | − | 1.71367i | −0.134328 | − | 0.990937i | \(-0.542888\pi\) |
0.691132 | − | 0.722729i | \(-0.257112\pi\) | |||||||
\(20\) | 0.809017 | + | 0.587785i | 0.180902 | + | 0.131433i | ||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | −2.19098 | + | 2.48990i | −0.467119 | + | 0.530848i | ||||
\(23\) | −0.472136 | −0.0984472 | −0.0492236 | − | 0.998788i | \(-0.515675\pi\) | ||||
−0.0492236 | + | 0.998788i | \(0.515675\pi\) | |||||||
\(24\) | 1.30902 | + | 0.951057i | 0.267202 | + | 0.194134i | ||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | 1.61803 | + | 4.97980i | 0.317323 | + | 0.976618i | ||||
\(27\) | 4.42705 | − | 3.21644i | 0.851986 | − | 0.619004i | ||||
\(28\) | −0.809017 | + | 0.587785i | −0.152890 | + | 0.111081i | ||||
\(29\) | 1.38197 | + | 4.25325i | 0.256625 | + | 0.789809i | 0.993505 | + | 0.113787i | \(0.0362980\pi\) |
−0.736881 | + | 0.676023i | \(0.763702\pi\) | |||||||
\(30\) | 0.500000 | − | 1.53884i | 0.0912871 | − | 0.280953i | ||||
\(31\) | −2.00000 | − | 1.45309i | −0.359211 | − | 0.260982i | 0.393512 | − | 0.919319i | \(-0.371260\pi\) |
−0.752723 | + | 0.658338i | \(0.771260\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.92705 | + | 2.12663i | 0.857689 | + | 0.370198i | ||||
\(34\) | −2.61803 | −0.448989 | ||||||||
\(35\) | 0.809017 | + | 0.587785i | 0.136749 | + | 0.0993538i | ||||
\(36\) | −0.118034 | + | 0.363271i | −0.0196723 | + | 0.0605452i | ||||
\(37\) | −3.47214 | − | 10.6861i | −0.570816 | − | 1.75679i | −0.650005 | − | 0.759930i | \(-0.725233\pi\) |
0.0791890 | − | 0.996860i | \(-0.474767\pi\) | |||||||
\(38\) | 6.35410 | − | 4.61653i | 1.03077 | − | 0.748899i | ||||
\(39\) | 6.85410 | − | 4.97980i | 1.09753 | − | 0.797406i | ||||
\(40\) | 0.309017 | + | 0.951057i | 0.0488599 | + | 0.150375i | ||||
\(41\) | 0.881966 | − | 2.71441i | 0.137740 | − | 0.423920i | −0.858266 | − | 0.513205i | \(-0.828458\pi\) |
0.996006 | + | 0.0892848i | \(0.0284581\pi\) | |||||||
\(42\) | 1.30902 | + | 0.951057i | 0.201986 | + | 0.146751i | ||||
\(43\) | −2.09017 | −0.318748 | −0.159374 | − | 0.987218i | \(-0.550948\pi\) | ||||
−0.159374 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(44\) | −3.23607 | + | 0.726543i | −0.487856 | + | 0.109530i | ||||
\(45\) | 0.381966 | 0.0569401 | ||||||||
\(46\) | −0.381966 | − | 0.277515i | −0.0563178 | − | 0.0409173i | ||||
\(47\) | 1.47214 | − | 4.53077i | 0.214733 | − | 0.660881i | −0.784439 | − | 0.620206i | \(-0.787049\pi\) |
0.999172 | − | 0.0406750i | \(-0.0129508\pi\) | |||||||
\(48\) | 0.500000 | + | 1.53884i | 0.0721688 | + | 0.222113i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0.809017 | − | 0.587785i | 0.114412 | − | 0.0831254i | ||||
\(51\) | 1.30902 | + | 4.02874i | 0.183299 | + | 0.564136i | ||||
\(52\) | −1.61803 | + | 4.97980i | −0.224381 | + | 0.690574i | ||||
\(53\) | 2.23607 | + | 1.62460i | 0.307148 | + | 0.223156i | 0.730672 | − | 0.682729i | \(-0.239207\pi\) |
−0.423524 | + | 0.905885i | \(0.639207\pi\) | |||||||
\(54\) | 5.47214 | 0.744663 | ||||||||
\(55\) | 1.69098 | + | 2.85317i | 0.228012 | + | 0.384721i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −10.2812 | − | 7.46969i | −1.36177 | − | 0.989385i | ||||
\(58\) | −1.38197 | + | 4.25325i | −0.181461 | + | 0.558480i | ||||
\(59\) | 1.28115 | + | 3.94298i | 0.166792 | + | 0.513333i | 0.999164 | − | 0.0408847i | \(-0.0130176\pi\) |
−0.832372 | + | 0.554217i | \(0.813018\pi\) | |||||||
\(60\) | 1.30902 | − | 0.951057i | 0.168993 | − | 0.122781i | ||||
\(61\) | −11.0902 | + | 8.05748i | −1.41995 | + | 1.03165i | −0.428171 | + | 0.903698i | \(0.640842\pi\) |
−0.991780 | + | 0.127957i | \(0.959158\pi\) | |||||||
\(62\) | −0.763932 | − | 2.35114i | −0.0970195 | − | 0.298595i | ||||
\(63\) | −0.118034 | + | 0.363271i | −0.0148709 | + | 0.0457679i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 5.23607 | 0.649454 | ||||||||
\(66\) | 2.73607 | + | 4.61653i | 0.336787 | + | 0.568255i | ||||
\(67\) | −3.38197 | −0.413173 | −0.206586 | − | 0.978428i | \(-0.566235\pi\) | ||||
−0.206586 | + | 0.978428i | \(0.566235\pi\) | |||||||
\(68\) | −2.11803 | − | 1.53884i | −0.256849 | − | 0.186612i | ||||
\(69\) | −0.236068 | + | 0.726543i | −0.0284192 | + | 0.0874654i | ||||
\(70\) | 0.309017 | + | 0.951057i | 0.0369346 | + | 0.113673i | ||||
\(71\) | −8.85410 | + | 6.43288i | −1.05079 | + | 0.763443i | −0.972362 | − | 0.233477i | \(-0.924990\pi\) |
−0.0784263 | + | 0.996920i | \(0.524990\pi\) | |||||||
\(72\) | −0.309017 | + | 0.224514i | −0.0364180 | + | 0.0264592i | ||||
\(73\) | 0.881966 | + | 2.71441i | 0.103226 | + | 0.317698i | 0.989310 | − | 0.145827i | \(-0.0465844\pi\) |
−0.886084 | + | 0.463525i | \(0.846584\pi\) | |||||||
\(74\) | 3.47214 | − | 10.6861i | 0.403628 | − | 1.24224i | ||||
\(75\) | −1.30902 | − | 0.951057i | −0.151152 | − | 0.109819i | ||||
\(76\) | 7.85410 | 0.900927 | ||||||||
\(77\) | −3.23607 | + | 0.726543i | −0.368784 | + | 0.0827972i | ||||
\(78\) | 8.47214 | 0.959280 | ||||||||
\(79\) | −3.23607 | − | 2.35114i | −0.364086 | − | 0.264524i | 0.390668 | − | 0.920532i | \(-0.372244\pi\) |
−0.754754 | + | 0.656007i | \(0.772244\pi\) | |||||||
\(80\) | −0.309017 | + | 0.951057i | −0.0345492 | + | 0.106331i | ||||
\(81\) | −2.38197 | − | 7.33094i | −0.264663 | − | 0.814549i | ||||
\(82\) | 2.30902 | − | 1.67760i | 0.254988 | − | 0.185260i | ||||
\(83\) | 7.16312 | − | 5.20431i | 0.786254 | − | 0.571247i | −0.120595 | − | 0.992702i | \(-0.538480\pi\) |
0.906850 | + | 0.421454i | \(0.138480\pi\) | |||||||
\(84\) | 0.500000 | + | 1.53884i | 0.0545545 | + | 0.167901i | ||||
\(85\) | −0.809017 | + | 2.48990i | −0.0877502 | + | 0.270067i | ||||
\(86\) | −1.69098 | − | 1.22857i | −0.182343 | − | 0.132480i | ||||
\(87\) | 7.23607 | 0.775788 | ||||||||
\(88\) | −3.04508 | − | 1.31433i | −0.324607 | − | 0.140108i | ||||
\(89\) | −14.8541 | −1.57453 | −0.787266 | − | 0.616614i | \(-0.788504\pi\) | ||||
−0.787266 | + | 0.616614i | \(0.788504\pi\) | |||||||
\(90\) | 0.309017 | + | 0.224514i | 0.0325733 | + | 0.0236659i | ||||
\(91\) | −1.61803 | + | 4.97980i | −0.169616 | + | 0.522025i | ||||
\(92\) | −0.145898 | − | 0.449028i | −0.0152109 | − | 0.0468144i | ||||
\(93\) | −3.23607 | + | 2.35114i | −0.335565 | + | 0.243802i | ||||
\(94\) | 3.85410 | − | 2.80017i | 0.397520 | − | 0.288815i | ||||
\(95\) | −2.42705 | − | 7.46969i | −0.249010 | − | 0.766375i | ||||
\(96\) | −0.500000 | + | 1.53884i | −0.0510310 | + | 0.157057i | ||||
\(97\) | 6.78115 | + | 4.92680i | 0.688522 | + | 0.500240i | 0.876174 | − | 0.481995i | \(-0.160088\pi\) |
−0.187652 | + | 0.982236i | \(0.560088\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −0.836881 | + | 0.951057i | −0.0841097 | + | 0.0955848i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.0902 | + | 8.78402i | 1.20302 | + | 0.874043i | 0.994578 | − | 0.103992i | \(-0.0331618\pi\) |
0.208439 | + | 0.978035i | \(0.433162\pi\) | |||||||
\(102\) | −1.30902 | + | 4.02874i | −0.129612 | + | 0.398905i | ||||
\(103\) | −1.85410 | − | 5.70634i | −0.182690 | − | 0.562262i | 0.817211 | − | 0.576339i | \(-0.195519\pi\) |
−0.999901 | + | 0.0140765i | \(0.995519\pi\) | |||||||
\(104\) | −4.23607 | + | 3.07768i | −0.415381 | + | 0.301792i | ||||
\(105\) | 1.30902 | − | 0.951057i | 0.127747 | − | 0.0928136i | ||||
\(106\) | 0.854102 | + | 2.62866i | 0.0829577 | + | 0.255318i | ||||
\(107\) | 0.881966 | − | 2.71441i | 0.0852629 | − | 0.262412i | −0.899331 | − | 0.437268i | \(-0.855946\pi\) |
0.984594 | + | 0.174856i | \(0.0559460\pi\) | |||||||
\(108\) | 4.42705 | + | 3.21644i | 0.425993 | + | 0.309502i | ||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | −0.309017 | + | 3.30220i | −0.0294636 | + | 0.314852i | ||||
\(111\) | −18.1803 | −1.72560 | ||||||||
\(112\) | −0.809017 | − | 0.587785i | −0.0764449 | − | 0.0555405i | ||||
\(113\) | 1.33688 | − | 4.11450i | 0.125763 | − | 0.387059i | −0.868276 | − | 0.496081i | \(-0.834772\pi\) |
0.994039 | + | 0.109022i | \(0.0347718\pi\) | |||||||
\(114\) | −3.92705 | − | 12.0862i | −0.367802 | − | 1.13198i | ||||
\(115\) | −0.381966 | + | 0.277515i | −0.0356185 | + | 0.0258784i | ||||
\(116\) | −3.61803 | + | 2.62866i | −0.335926 | + | 0.244065i | ||||
\(117\) | 0.618034 | + | 1.90211i | 0.0571373 | + | 0.175850i | ||||
\(118\) | −1.28115 | + | 3.94298i | −0.117940 | + | 0.362981i | ||||
\(119\) | −2.11803 | − | 1.53884i | −0.194160 | − | 0.141065i | ||||
\(120\) | 1.61803 | 0.147706 | ||||||||
\(121\) | −10.8090 | − | 2.04087i | −0.982638 | − | 0.185534i | ||||
\(122\) | −13.7082 | −1.24108 | ||||||||
\(123\) | −3.73607 | − | 2.71441i | −0.336870 | − | 0.244750i | ||||
\(124\) | 0.763932 | − | 2.35114i | 0.0686031 | − | 0.211139i | ||||
\(125\) | −0.309017 | − | 0.951057i | −0.0276393 | − | 0.0850651i | ||||
\(126\) | −0.309017 | + | 0.224514i | −0.0275294 | + | 0.0200013i | ||||
\(127\) | −10.0902 | + | 7.33094i | −0.895358 | + | 0.650516i | −0.937269 | − | 0.348606i | \(-0.886655\pi\) |
0.0419116 | + | 0.999121i | \(0.486655\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | −1.04508 | + | 3.21644i | −0.0920146 | + | 0.283192i | ||||
\(130\) | 4.23607 | + | 3.07768i | 0.371528 | + | 0.269931i | ||||
\(131\) | 5.09017 | 0.444730 | 0.222365 | − | 0.974963i | \(-0.428622\pi\) | ||||
0.222365 | + | 0.974963i | \(0.428622\pi\) | |||||||
\(132\) | −0.500000 | + | 5.34307i | −0.0435194 | + | 0.465054i | ||||
\(133\) | 7.85410 | 0.681037 | ||||||||
\(134\) | −2.73607 | − | 1.98787i | −0.236360 | − | 0.171726i | ||||
\(135\) | 1.69098 | − | 5.20431i | 0.145537 | − | 0.447916i | ||||
\(136\) | −0.809017 | − | 2.48990i | −0.0693726 | − | 0.213507i | ||||
\(137\) | −3.92705 | + | 2.85317i | −0.335511 | + | 0.243763i | −0.742765 | − | 0.669552i | \(-0.766486\pi\) |
0.407255 | + | 0.913315i | \(0.366486\pi\) | |||||||
\(138\) | −0.618034 | + | 0.449028i | −0.0526105 | + | 0.0382238i | ||||
\(139\) | −1.52786 | − | 4.70228i | −0.129592 | − | 0.398842i | 0.865118 | − | 0.501568i | \(-0.167243\pi\) |
−0.994710 | + | 0.102726i | \(0.967243\pi\) | |||||||
\(140\) | −0.309017 | + | 0.951057i | −0.0261167 | + | 0.0803789i | ||||
\(141\) | −6.23607 | − | 4.53077i | −0.525172 | − | 0.381560i | ||||
\(142\) | −10.9443 | −0.918423 | ||||||||
\(143\) | −11.4721 | + | 13.0373i | −0.959348 | + | 1.09023i | ||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | 3.61803 | + | 2.62866i | 0.300461 | + | 0.218298i | ||||
\(146\) | −0.881966 | + | 2.71441i | −0.0729920 | + | 0.224646i | ||||
\(147\) | 0.500000 | + | 1.53884i | 0.0412393 | + | 0.126922i | ||||
\(148\) | 9.09017 | − | 6.60440i | 0.747207 | − | 0.542878i | ||||
\(149\) | −9.47214 | + | 6.88191i | −0.775988 | + | 0.563788i | −0.903772 | − | 0.428014i | \(-0.859213\pi\) |
0.127785 | + | 0.991802i | \(0.459213\pi\) | |||||||
\(150\) | −0.500000 | − | 1.53884i | −0.0408248 | − | 0.125646i | ||||
\(151\) | 5.70820 | − | 17.5680i | 0.464527 | − | 1.42967i | −0.395049 | − | 0.918660i | \(-0.629272\pi\) |
0.859576 | − | 0.511007i | \(-0.170728\pi\) | |||||||
\(152\) | 6.35410 | + | 4.61653i | 0.515386 | + | 0.374450i | ||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −3.04508 | − | 1.31433i | −0.245380 | − | 0.105912i | ||||
\(155\) | −2.47214 | −0.198567 | ||||||||
\(156\) | 6.85410 | + | 4.97980i | 0.548767 | + | 0.398703i | ||||
\(157\) | −4.61803 | + | 14.2128i | −0.368559 | + | 1.13431i | 0.579163 | + | 0.815212i | \(0.303380\pi\) |
−0.947722 | + | 0.319097i | \(0.896620\pi\) | |||||||
\(158\) | −1.23607 | − | 3.80423i | −0.0983363 | − | 0.302648i | ||||
\(159\) | 3.61803 | − | 2.62866i | 0.286929 | − | 0.208466i | ||||
\(160\) | −0.809017 | + | 0.587785i | −0.0639584 | + | 0.0464685i | ||||
\(161\) | −0.145898 | − | 0.449028i | −0.0114984 | − | 0.0353884i | ||||
\(162\) | 2.38197 | − | 7.33094i | 0.187145 | − | 0.575973i | ||||
\(163\) | −18.4443 | − | 13.4005i | −1.44467 | − | 1.04961i | −0.987041 | − | 0.160467i | \(-0.948700\pi\) |
−0.457626 | − | 0.889145i | \(-0.651300\pi\) | |||||||
\(164\) | 2.85410 | 0.222868 | ||||||||
\(165\) | 5.23607 | − | 1.17557i | 0.407627 | − | 0.0915180i | ||||
\(166\) | 8.85410 | 0.687212 | ||||||||
\(167\) | −6.70820 | − | 4.87380i | −0.519096 | − | 0.377146i | 0.297167 | − | 0.954826i | \(-0.403958\pi\) |
−0.816263 | + | 0.577680i | \(0.803958\pi\) | |||||||
\(168\) | −0.500000 | + | 1.53884i | −0.0385758 | + | 0.118724i | ||||
\(169\) | 4.45492 | + | 13.7108i | 0.342686 | + | 1.05468i | ||||
\(170\) | −2.11803 | + | 1.53884i | −0.162446 | + | 0.118024i | ||||
\(171\) | 2.42705 | − | 1.76336i | 0.185601 | − | 0.134847i | ||||
\(172\) | −0.645898 | − | 1.98787i | −0.0492493 | − | 0.151574i | ||||
\(173\) | 6.14590 | − | 18.9151i | 0.467264 | − | 1.43809i | −0.388849 | − | 0.921302i | \(-0.627127\pi\) |
0.856113 | − | 0.516789i | \(-0.172873\pi\) | |||||||
\(174\) | 5.85410 | + | 4.25325i | 0.443798 | + | 0.322438i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −1.69098 | − | 2.85317i | −0.127463 | − | 0.215066i | ||||
\(177\) | 6.70820 | 0.504219 | ||||||||
\(178\) | −12.0172 | − | 8.73102i | −0.900729 | − | 0.654418i | ||||
\(179\) | 0.663119 | − | 2.04087i | 0.0495638 | − | 0.152542i | −0.923211 | − | 0.384293i | \(-0.874445\pi\) |
0.972775 | + | 0.231751i | \(0.0744454\pi\) | |||||||
\(180\) | 0.118034 | + | 0.363271i | 0.00879773 | + | 0.0270766i | ||||
\(181\) | −16.9443 | + | 12.3107i | −1.25946 | + | 0.915050i | −0.998731 | − | 0.0503630i | \(-0.983962\pi\) |
−0.260727 | + | 0.965413i | \(0.583962\pi\) | |||||||
\(182\) | −4.23607 | + | 3.07768i | −0.313998 | + | 0.228133i | ||||
\(183\) | 6.85410 | + | 21.0948i | 0.506670 | + | 1.55937i | ||||
\(184\) | 0.145898 | − | 0.449028i | 0.0107557 | − | 0.0331028i | ||||
\(185\) | −9.09017 | − | 6.60440i | −0.668323 | − | 0.485565i | ||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | −4.42705 | − | 7.46969i | −0.323738 | − | 0.546238i | ||||
\(188\) | 4.76393 | 0.347445 | ||||||||
\(189\) | 4.42705 | + | 3.21644i | 0.322021 | + | 0.233962i | ||||
\(190\) | 2.42705 | − | 7.46969i | 0.176077 | − | 0.541909i | ||||
\(191\) | −0.381966 | − | 1.17557i | −0.0276381 | − | 0.0850613i | 0.936286 | − | 0.351238i | \(-0.114239\pi\) |
−0.963924 | + | 0.266177i | \(0.914239\pi\) | |||||||
\(192\) | −1.30902 | + | 0.951057i | −0.0944702 | + | 0.0686366i | ||||
\(193\) | 17.3262 | − | 12.5882i | 1.24717 | − | 0.906122i | 0.249116 | − | 0.968474i | \(-0.419860\pi\) |
0.998054 | + | 0.0623518i | \(0.0198601\pi\) | |||||||
\(194\) | 2.59017 | + | 7.97172i | 0.185963 | + | 0.572336i | ||||
\(195\) | 2.61803 | − | 8.05748i | 0.187481 | − | 0.577008i | ||||
\(196\) | −0.809017 | − | 0.587785i | −0.0577869 | − | 0.0419847i | ||||
\(197\) | 11.5279 | 0.821326 | 0.410663 | − | 0.911787i | \(-0.365297\pi\) | ||||
0.410663 | + | 0.911787i | \(0.365297\pi\) | |||||||
\(198\) | −1.23607 | + | 0.277515i | −0.0878435 | + | 0.0197221i | ||||
\(199\) | 5.05573 | 0.358391 | 0.179196 | − | 0.983813i | \(-0.442651\pi\) | ||||
0.179196 | + | 0.983813i | \(0.442651\pi\) | |||||||
\(200\) | 0.809017 | + | 0.587785i | 0.0572061 | + | 0.0415627i | ||||
\(201\) | −1.69098 | + | 5.20431i | −0.119273 | + | 0.367084i | ||||
\(202\) | 4.61803 | + | 14.2128i | 0.324924 | + | 1.00001i | ||||
\(203\) | −3.61803 | + | 2.62866i | −0.253936 | + | 0.184495i | ||||
\(204\) | −3.42705 | + | 2.48990i | −0.239942 | + | 0.174328i | ||||
\(205\) | −0.881966 | − | 2.71441i | −0.0615992 | − | 0.189583i | ||||
\(206\) | 1.85410 | − | 5.70634i | 0.129181 | − | 0.397579i | ||||
\(207\) | −0.145898 | − | 0.106001i | −0.0101406 | − | 0.00736759i | ||||
\(208\) | −5.23607 | −0.363056 | ||||||||
\(209\) | 23.9164 | + | 10.3229i | 1.65433 | + | 0.714047i | ||||
\(210\) | 1.61803 | 0.111655 | ||||||||
\(211\) | −8.63525 | − | 6.27388i | −0.594475 | − | 0.431912i | 0.249438 | − | 0.968391i | \(-0.419754\pi\) |
−0.843914 | + | 0.536479i | \(0.819754\pi\) | |||||||
\(212\) | −0.854102 | + | 2.62866i | −0.0586600 | + | 0.180537i | ||||
\(213\) | 5.47214 | + | 16.8415i | 0.374945 | + | 1.15396i | ||||
\(214\) | 2.30902 | − | 1.67760i | 0.157841 | − | 0.114678i | ||||
\(215\) | −1.69098 | + | 1.22857i | −0.115324 | + | 0.0837879i | ||||
\(216\) | 1.69098 | + | 5.20431i | 0.115057 | + | 0.354108i | ||||
\(217\) | 0.763932 | − | 2.35114i | 0.0518591 | − | 0.159606i | ||||
\(218\) | 3.23607 | + | 2.35114i | 0.219174 | + | 0.159239i | ||||
\(219\) | 4.61803 | 0.312058 | ||||||||
\(220\) | −2.19098 | + | 2.48990i | −0.147716 | + | 0.167869i | ||||
\(221\) | −13.7082 | −0.922114 | ||||||||
\(222\) | −14.7082 | − | 10.6861i | −0.987150 | − | 0.717206i | ||||
\(223\) | 4.05573 | − | 12.4822i | 0.271592 | − | 0.835873i | −0.718509 | − | 0.695517i | \(-0.755175\pi\) |
0.990101 | − | 0.140356i | \(-0.0448247\pi\) | |||||||
\(224\) | −0.309017 | − | 0.951057i | −0.0206471 | − | 0.0635451i | ||||
\(225\) | 0.309017 | − | 0.224514i | 0.0206011 | − | 0.0149676i | ||||
\(226\) | 3.50000 | − | 2.54290i | 0.232817 | − | 0.169151i | ||||
\(227\) | 4.22542 | + | 13.0045i | 0.280451 | + | 0.863140i | 0.987725 | + | 0.156201i | \(0.0499247\pi\) |
−0.707274 | + | 0.706940i | \(0.750075\pi\) | |||||||
\(228\) | 3.92705 | − | 12.0862i | 0.260075 | − | 0.800429i | ||||
\(229\) | −18.0902 | − | 13.1433i | −1.19543 | − | 0.868532i | −0.201604 | − | 0.979467i | \(-0.564616\pi\) |
−0.993828 | + | 0.110935i | \(0.964616\pi\) | |||||||
\(230\) | −0.472136 | −0.0311317 | ||||||||
\(231\) | −0.500000 | + | 5.34307i | −0.0328976 | + | 0.351548i | ||||
\(232\) | −4.47214 | −0.293610 | ||||||||
\(233\) | −0.545085 | − | 0.396027i | −0.0357097 | − | 0.0259446i | 0.569787 | − | 0.821792i | \(-0.307026\pi\) |
−0.605497 | + | 0.795848i | \(0.707026\pi\) | |||||||
\(234\) | −0.618034 | + | 1.90211i | −0.0404021 | + | 0.124345i | ||||
\(235\) | −1.47214 | − | 4.53077i | −0.0960316 | − | 0.295555i | ||||
\(236\) | −3.35410 | + | 2.43690i | −0.218333 | + | 0.158629i | ||||
\(237\) | −5.23607 | + | 3.80423i | −0.340119 | + | 0.247111i | ||||
\(238\) | −0.809017 | − | 2.48990i | −0.0524408 | − | 0.161396i | ||||
\(239\) | 1.94427 | − | 5.98385i | 0.125764 | − | 0.387063i | −0.868275 | − | 0.496083i | \(-0.834771\pi\) |
0.994040 | + | 0.109020i | \(0.0347712\pi\) | |||||||
\(240\) | 1.30902 | + | 0.951057i | 0.0844967 | + | 0.0613904i | ||||
\(241\) | −30.9787 | −1.99551 | −0.997757 | − | 0.0669372i | \(-0.978677\pi\) | ||||
−0.997757 | + | 0.0669372i | \(0.978677\pi\) | |||||||
\(242\) | −7.54508 | − | 8.00448i | −0.485016 | − | 0.514547i | ||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | −11.0902 | − | 8.05748i | −0.709975 | − | 0.515827i | ||||
\(245\) | −0.309017 | + | 0.951057i | −0.0197424 | + | 0.0607608i | ||||
\(246\) | −1.42705 | − | 4.39201i | −0.0909854 | − | 0.280024i | ||||
\(247\) | 33.2705 | − | 24.1724i | 2.11695 | − | 1.53806i | ||||
\(248\) | 2.00000 | − | 1.45309i | 0.127000 | − | 0.0922710i | ||||
\(249\) | −4.42705 | − | 13.6251i | −0.280553 | − | 0.863453i | ||||
\(250\) | 0.309017 | − | 0.951057i | 0.0195440 | − | 0.0601501i | ||||
\(251\) | −16.1803 | − | 11.7557i | −1.02129 | − | 0.742014i | −0.0547463 | − | 0.998500i | \(-0.517435\pi\) |
−0.966548 | + | 0.256487i | \(0.917435\pi\) | |||||||
\(252\) | −0.381966 | −0.0240616 | ||||||||
\(253\) | 0.145898 | − | 1.55909i | 0.00917253 | − | 0.0980189i | ||||
\(254\) | −12.4721 | −0.782571 | ||||||||
\(255\) | 3.42705 | + | 2.48990i | 0.214610 | + | 0.155923i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 4.59017 | + | 14.1271i | 0.286327 | + | 0.881224i | 0.985998 | + | 0.166758i | \(0.0533300\pi\) |
−0.699671 | + | 0.714465i | \(0.746670\pi\) | |||||||
\(258\) | −2.73607 | + | 1.98787i | −0.170340 | + | 0.123759i | ||||
\(259\) | 9.09017 | − | 6.60440i | 0.564836 | − | 0.410377i | ||||
\(260\) | 1.61803 | + | 4.97980i | 0.100346 | + | 0.308834i | ||||
\(261\) | −0.527864 | + | 1.62460i | −0.0326740 | + | 0.100560i | ||||
\(262\) | 4.11803 | + | 2.99193i | 0.254413 | + | 0.184842i | ||||
\(263\) | 26.3607 | 1.62547 | 0.812735 | − | 0.582634i | \(-0.197978\pi\) | ||||
0.812735 | + | 0.582634i | \(0.197978\pi\) | |||||||
\(264\) | −3.54508 | + | 4.02874i | −0.218185 | + | 0.247952i | ||||
\(265\) | 2.76393 | 0.169787 | ||||||||
\(266\) | 6.35410 | + | 4.61653i | 0.389595 | + | 0.283057i | ||||
\(267\) | −7.42705 | + | 22.8581i | −0.454528 | + | 1.39889i | ||||
\(268\) | −1.04508 | − | 3.21644i | −0.0638387 | − | 0.196475i | ||||
\(269\) | 15.0902 | − | 10.9637i | 0.920064 | − | 0.668466i | −0.0234760 | − | 0.999724i | \(-0.507473\pi\) |
0.943540 | + | 0.331259i | \(0.107473\pi\) | |||||||
\(270\) | 4.42705 | − | 3.21644i | 0.269422 | − | 0.195746i | ||||
\(271\) | −1.90983 | − | 5.87785i | −0.116014 | − | 0.357054i | 0.876143 | − | 0.482051i | \(-0.160108\pi\) |
−0.992157 | + | 0.124997i | \(0.960108\pi\) | |||||||
\(272\) | 0.809017 | − | 2.48990i | 0.0490539 | − | 0.150972i | ||||
\(273\) | 6.85410 | + | 4.97980i | 0.414829 | + | 0.301391i | ||||
\(274\) | −4.85410 | −0.293247 | ||||||||
\(275\) | 3.04508 | + | 1.31433i | 0.183626 | + | 0.0792569i | ||||
\(276\) | −0.763932 | −0.0459833 | ||||||||
\(277\) | 9.70820 | + | 7.05342i | 0.583309 | + | 0.423799i | 0.839916 | − | 0.542717i | \(-0.182604\pi\) |
−0.256606 | + | 0.966516i | \(0.582604\pi\) | |||||||
\(278\) | 1.52786 | − | 4.70228i | 0.0916352 | − | 0.282024i | ||||
\(279\) | −0.291796 | − | 0.898056i | −0.0174694 | − | 0.0537652i | ||||
\(280\) | −0.809017 | + | 0.587785i | −0.0483480 | + | 0.0351269i | ||||
\(281\) | −9.16312 | + | 6.65740i | −0.546626 | + | 0.397147i | −0.826540 | − | 0.562878i | \(-0.809694\pi\) |
0.279914 | + | 0.960025i | \(0.409694\pi\) | |||||||
\(282\) | −2.38197 | − | 7.33094i | −0.141844 | − | 0.436551i | ||||
\(283\) | 5.05573 | − | 15.5599i | 0.300532 | − | 0.924942i | −0.680775 | − | 0.732493i | \(-0.738357\pi\) |
0.981307 | − | 0.192449i | \(-0.0616431\pi\) | |||||||
\(284\) | −8.85410 | − | 6.43288i | −0.525394 | − | 0.381721i | ||||
\(285\) | −12.7082 | −0.752769 | ||||||||
\(286\) | −16.9443 | + | 3.80423i | −1.00194 | + | 0.224949i | ||||
\(287\) | 2.85410 | 0.168472 | ||||||||
\(288\) | −0.309017 | − | 0.224514i | −0.0182090 | − | 0.0132296i | ||||
\(289\) | −3.13525 | + | 9.64932i | −0.184427 | + | 0.567607i | ||||
\(290\) | 1.38197 | + | 4.25325i | 0.0811518 | + | 0.249760i | ||||
\(291\) | 10.9721 | − | 7.97172i | 0.643198 | − | 0.467311i | ||||
\(292\) | −2.30902 | + | 1.67760i | −0.135125 | + | 0.0981741i | ||||
\(293\) | 5.70820 | + | 17.5680i | 0.333477 | + | 1.02634i | 0.967467 | + | 0.252995i | \(0.0814158\pi\) |
−0.633991 | + | 0.773341i | \(0.718584\pi\) | |||||||
\(294\) | −0.500000 | + | 1.53884i | −0.0291606 | + | 0.0897471i | ||||
\(295\) | 3.35410 | + | 2.43690i | 0.195283 | + | 0.141882i | ||||
\(296\) | 11.2361 | 0.653083 | ||||||||
\(297\) | 9.25329 | + | 15.6129i | 0.536930 | + | 0.905954i | ||||
\(298\) | −11.7082 | −0.678238 | ||||||||
\(299\) | −2.00000 | − | 1.45309i | −0.115663 | − | 0.0840341i | ||||
\(300\) | 0.500000 | − | 1.53884i | 0.0288675 | − | 0.0888451i | ||||
\(301\) | −0.645898 | − | 1.98787i | −0.0372289 | − | 0.114579i | ||||
\(302\) | 14.9443 | − | 10.8576i | 0.859946 | − | 0.624787i | ||||
\(303\) | 19.5623 | − | 14.2128i | 1.12383 | − | 0.816507i | ||||
\(304\) | 2.42705 | + | 7.46969i | 0.139201 | + | 0.428416i | ||||
\(305\) | −4.23607 | + | 13.0373i | −0.242557 | + | 0.746512i | ||||
\(306\) | −0.809017 | − | 0.587785i | −0.0462484 | − | 0.0336014i | ||||
\(307\) | 18.5623 | 1.05941 | 0.529703 | − | 0.848183i | \(-0.322303\pi\) | ||||
0.529703 | + | 0.848183i | \(0.322303\pi\) | |||||||
\(308\) | −1.69098 | − | 2.85317i | −0.0963527 | − | 0.162574i | ||||
\(309\) | −9.70820 | −0.552280 | ||||||||
\(310\) | −2.00000 | − | 1.45309i | −0.113592 | − | 0.0825297i | ||||
\(311\) | −0.673762 | + | 2.07363i | −0.0382055 | + | 0.117585i | −0.968340 | − | 0.249634i | \(-0.919690\pi\) |
0.930135 | + | 0.367218i | \(0.119690\pi\) | |||||||
\(312\) | 2.61803 | + | 8.05748i | 0.148217 | + | 0.456165i | ||||
\(313\) | 25.2984 | − | 18.3803i | 1.42995 | − | 1.03892i | 0.439922 | − | 0.898036i | \(-0.355006\pi\) |
0.990026 | − | 0.140883i | \(-0.0449940\pi\) | |||||||
\(314\) | −12.0902 | + | 8.78402i | −0.682288 | + | 0.495711i | ||||
\(315\) | 0.118034 | + | 0.363271i | 0.00665046 | + | 0.0204680i | ||||
\(316\) | 1.23607 | − | 3.80423i | 0.0695343 | − | 0.214004i | ||||
\(317\) | −24.5623 | − | 17.8456i | −1.37956 | − | 1.00231i | −0.996921 | − | 0.0784069i | \(-0.975017\pi\) |
−0.382635 | − | 0.923900i | \(-0.624983\pi\) | |||||||
\(318\) | 4.47214 | 0.250785 | ||||||||
\(319\) | −14.4721 | + | 3.24920i | −0.810284 | + | 0.181920i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.73607 | − | 2.71441i | −0.208527 | − | 0.151504i | ||||
\(322\) | 0.145898 | − | 0.449028i | 0.00813058 | − | 0.0250234i | ||||
\(323\) | 6.35410 | + | 19.5559i | 0.353552 | + | 1.08812i | ||||
\(324\) | 6.23607 | − | 4.53077i | 0.346448 | − | 0.251709i | ||||
\(325\) | 4.23607 | − | 3.07768i | 0.234975 | − | 0.170719i | ||||
\(326\) | −7.04508 | − | 21.6825i | −0.390191 | − | 1.20088i | ||||
\(327\) | 2.00000 | − | 6.15537i | 0.110600 | − | 0.340393i | ||||
\(328\) | 2.30902 | + | 1.67760i | 0.127494 | + | 0.0926299i | ||||
\(329\) | 4.76393 | 0.262644 | ||||||||
\(330\) | 4.92705 | + | 2.12663i | 0.271225 | + | 0.117067i | ||||
\(331\) | −0.965558 | −0.0530719 | −0.0265359 | − | 0.999648i | \(-0.508448\pi\) | ||||
−0.0265359 | + | 0.999648i | \(0.508448\pi\) | |||||||
\(332\) | 7.16312 | + | 5.20431i | 0.393127 | + | 0.285624i | ||||
\(333\) | 1.32624 | − | 4.08174i | 0.0726774 | − | 0.223678i | ||||
\(334\) | −2.56231 | − | 7.88597i | −0.140203 | − | 0.431501i | ||||
\(335\) | −2.73607 | + | 1.98787i | −0.149487 | + | 0.108609i | ||||
\(336\) | −1.30902 | + | 0.951057i | −0.0714127 | + | 0.0518844i | ||||
\(337\) | −0.371323 | − | 1.14281i | −0.0202272 | − | 0.0622531i | 0.940433 | − | 0.339978i | \(-0.110420\pi\) |
−0.960661 | + | 0.277725i | \(0.910420\pi\) | |||||||
\(338\) | −4.45492 | + | 13.7108i | −0.242315 | + | 0.745770i | ||||
\(339\) | −5.66312 | − | 4.11450i | −0.307578 | − | 0.223469i | ||||
\(340\) | −2.61803 | −0.141983 | ||||||||
\(341\) | 5.41641 | − | 6.15537i | 0.293315 | − | 0.333332i | ||||
\(342\) | 3.00000 | 0.162221 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | 0.645898 | − | 1.98787i | 0.0348245 | − | 0.107179i | ||||
\(345\) | 0.236068 | + | 0.726543i | 0.0127095 | + | 0.0391157i | ||||
\(346\) | 16.0902 | − | 11.6902i | 0.865013 | − | 0.628469i | ||||
\(347\) | −12.2082 | + | 8.86978i | −0.655371 | + | 0.476155i | −0.865096 | − | 0.501606i | \(-0.832743\pi\) |
0.209726 | + | 0.977760i | \(0.432743\pi\) | |||||||
\(348\) | 2.23607 | + | 6.88191i | 0.119866 | + | 0.368909i | ||||
\(349\) | −6.00000 | + | 18.4661i | −0.321173 | + | 0.988468i | 0.651966 | + | 0.758248i | \(0.273944\pi\) |
−0.973139 | + | 0.230220i | \(0.926056\pi\) | |||||||
\(350\) | 0.809017 | + | 0.587785i | 0.0432438 | + | 0.0314184i | ||||
\(351\) | 28.6525 | 1.52936 | ||||||||
\(352\) | 0.309017 | − | 3.30220i | 0.0164707 | − | 0.176008i | ||||
\(353\) | −11.5623 | −0.615399 | −0.307700 | − | 0.951484i | \(-0.599559\pi\) | ||||
−0.307700 | + | 0.951484i | \(0.599559\pi\) | |||||||
\(354\) | 5.42705 | + | 3.94298i | 0.288445 | + | 0.209567i | ||||
\(355\) | −3.38197 | + | 10.4086i | −0.179496 | + | 0.552432i | ||||
\(356\) | −4.59017 | − | 14.1271i | −0.243279 | − | 0.748734i | ||||
\(357\) | −3.42705 | + | 2.48990i | −0.181379 | + | 0.131779i | ||||
\(358\) | 1.73607 | − | 1.26133i | 0.0917540 | − | 0.0666632i | ||||
\(359\) | 9.14590 | + | 28.1482i | 0.482702 | + | 1.48560i | 0.835282 | + | 0.549822i | \(0.185305\pi\) |
−0.352580 | + | 0.935782i | \(0.614695\pi\) | |||||||
\(360\) | −0.118034 | + | 0.363271i | −0.00622094 | + | 0.0191461i | ||||
\(361\) | −34.5344 | − | 25.0907i | −1.81760 | − | 1.32057i | ||||
\(362\) | −20.9443 | −1.10081 | ||||||||
\(363\) | −8.54508 | + | 15.6129i | −0.448501 | + | 0.819466i | ||||
\(364\) | −5.23607 | −0.274445 | ||||||||
\(365\) | 2.30902 | + | 1.67760i | 0.120859 | + | 0.0878095i | ||||
\(366\) | −6.85410 | + | 21.0948i | −0.358270 | + | 1.10264i | ||||
\(367\) | 4.90983 | + | 15.1109i | 0.256291 | + | 0.788783i | 0.993573 | + | 0.113197i | \(0.0361091\pi\) |
−0.737282 | + | 0.675586i | \(0.763891\pi\) | |||||||
\(368\) | 0.381966 | − | 0.277515i | 0.0199114 | − | 0.0144664i | ||||
\(369\) | 0.881966 | − | 0.640786i | 0.0459133 | − | 0.0333580i | ||||
\(370\) | −3.47214 | − | 10.6861i | −0.180508 | − | 0.555546i | ||||
\(371\) | −0.854102 | + | 2.62866i | −0.0443428 | + | 0.136473i | ||||
\(372\) | −3.23607 | − | 2.35114i | −0.167782 | − | 0.121901i | ||||
\(373\) | 14.6525 | 0.758676 | 0.379338 | − | 0.925258i | \(-0.376152\pi\) | ||||
0.379338 | + | 0.925258i | \(0.376152\pi\) | |||||||
\(374\) | 0.809017 | − | 8.64527i | 0.0418333 | − | 0.447036i | ||||
\(375\) | −1.61803 | −0.0835549 | ||||||||
\(376\) | 3.85410 | + | 2.80017i | 0.198760 | + | 0.144408i | ||||
\(377\) | −7.23607 | + | 22.2703i | −0.372676 | + | 1.14698i | ||||
\(378\) | 1.69098 | + | 5.20431i | 0.0869748 | + | 0.267681i | ||||
\(379\) | −12.6353 | + | 9.18005i | −0.649029 | + | 0.471547i | −0.862940 | − | 0.505306i | \(-0.831380\pi\) |
0.213911 | + | 0.976853i | \(0.431380\pi\) | |||||||
\(380\) | 6.35410 | − | 4.61653i | 0.325959 | − | 0.236823i | ||||
\(381\) | 6.23607 | + | 19.1926i | 0.319483 | + | 0.983269i | ||||
\(382\) | 0.381966 | − | 1.17557i | 0.0195431 | − | 0.0601474i | ||||
\(383\) | 16.3262 | + | 11.8617i | 0.834232 | + | 0.606105i | 0.920753 | − | 0.390145i | \(-0.127575\pi\) |
−0.0865216 | + | 0.996250i | \(0.527575\pi\) | |||||||
\(384\) | −1.61803 | −0.0825700 | ||||||||
\(385\) | −2.19098 | + | 2.48990i | −0.111663 | + | 0.126897i | ||||
\(386\) | 21.4164 | 1.09007 | ||||||||
\(387\) | −0.645898 | − | 0.469272i | −0.0328328 | − | 0.0238545i | ||||
\(388\) | −2.59017 | + | 7.97172i | −0.131496 | + | 0.404703i | ||||
\(389\) | 7.94427 | + | 24.4500i | 0.402791 | + | 1.23966i | 0.922726 | + | 0.385456i | \(0.125956\pi\) |
−0.519935 | + | 0.854206i | \(0.674044\pi\) | |||||||
\(390\) | 6.85410 | − | 4.97980i | 0.347071 | − | 0.252162i | ||||
\(391\) | 1.00000 | − | 0.726543i | 0.0505722 | − | 0.0367428i | ||||
\(392\) | −0.309017 | − | 0.951057i | −0.0156077 | − | 0.0480356i | ||||
\(393\) | 2.54508 | − | 7.83297i | 0.128383 | − | 0.395121i | ||||
\(394\) | 9.32624 | + | 6.77591i | 0.469849 | + | 0.341365i | ||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | −1.16312 | − | 0.502029i | −0.0584489 | − | 0.0252279i | ||||
\(397\) | 0.111456 | 0.00559383 | 0.00279691 | − | 0.999996i | \(-0.499110\pi\) | ||||
0.00279691 | + | 0.999996i | \(0.499110\pi\) | |||||||
\(398\) | 4.09017 | + | 2.97168i | 0.205022 | + | 0.148957i | ||||
\(399\) | 3.92705 | − | 12.0862i | 0.196598 | − | 0.605068i | ||||
\(400\) | 0.309017 | + | 0.951057i | 0.0154508 | + | 0.0475528i | ||||
\(401\) | −2.07295 | + | 1.50609i | −0.103518 | + | 0.0752103i | −0.638340 | − | 0.769754i | \(-0.720379\pi\) |
0.534822 | + | 0.844965i | \(0.320379\pi\) | |||||||
\(402\) | −4.42705 | + | 3.21644i | −0.220801 | + | 0.160421i | ||||
\(403\) | −4.00000 | − | 12.3107i | −0.199254 | − | 0.613241i | ||||
\(404\) | −4.61803 | + | 14.2128i | −0.229756 | + | 0.707116i | ||||
\(405\) | −6.23607 | − | 4.53077i | −0.309873 | − | 0.225136i | ||||
\(406\) | −4.47214 | −0.221948 | ||||||||
\(407\) | 36.3607 | − | 8.16348i | 1.80233 | − | 0.404649i | ||||
\(408\) | −4.23607 | −0.209717 | ||||||||
\(409\) | 18.5623 | + | 13.4863i | 0.917847 | + | 0.666855i | 0.942987 | − | 0.332829i | \(-0.108003\pi\) |
−0.0251402 | + | 0.999684i | \(0.508003\pi\) | |||||||
\(410\) | 0.881966 | − | 2.71441i | 0.0435572 | − | 0.134055i | ||||
\(411\) | 2.42705 | + | 7.46969i | 0.119718 | + | 0.368453i | ||||
\(412\) | 4.85410 | − | 3.52671i | 0.239144 | − | 0.173749i | ||||
\(413\) | −3.35410 | + | 2.43690i | −0.165045 | + | 0.119912i | ||||
\(414\) | −0.0557281 | − | 0.171513i | −0.00273889 | − | 0.00842942i | ||||
\(415\) | 2.73607 | − | 8.42075i | 0.134308 | − | 0.413358i | ||||
\(416\) | −4.23607 | − | 3.07768i | −0.207690 | − | 0.150896i | ||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | 13.2812 | + | 22.4091i | 0.649602 | + | 1.09606i | ||||
\(419\) | 22.5623 | 1.10224 | 0.551120 | − | 0.834426i | \(-0.314200\pi\) | ||||
0.551120 | + | 0.834426i | \(0.314200\pi\) | |||||||
\(420\) | 1.30902 | + | 0.951057i | 0.0638735 | + | 0.0464068i | ||||
\(421\) | −11.3820 | + | 35.0301i | −0.554723 | + | 1.70726i | 0.141950 | + | 0.989874i | \(0.454663\pi\) |
−0.696674 | + | 0.717388i | \(0.745337\pi\) | |||||||
\(422\) | −3.29837 | − | 10.1514i | −0.160562 | − | 0.494160i | ||||
\(423\) | 1.47214 | − | 1.06957i | 0.0715777 | − | 0.0520042i | ||||
\(424\) | −2.23607 | + | 1.62460i | −0.108593 | + | 0.0788975i | ||||
\(425\) | 0.809017 | + | 2.48990i | 0.0392431 | + | 0.120778i | ||||
\(426\) | −5.47214 | + | 16.8415i | −0.265126 | + | 0.815973i | ||||
\(427\) | −11.0902 | − | 8.05748i | −0.536691 | − | 0.389929i | ||||
\(428\) | 2.85410 | 0.137958 | ||||||||
\(429\) | 14.3262 | + | 24.1724i | 0.691677 | + | 1.16706i | ||||
\(430\) | −2.09017 | −0.100797 | ||||||||
\(431\) | 0.527864 | + | 0.383516i | 0.0254263 | + | 0.0184733i | 0.600426 | − | 0.799680i | \(-0.294998\pi\) |
−0.575000 | + | 0.818154i | \(0.694998\pi\) | |||||||
\(432\) | −1.69098 | + | 5.20431i | −0.0813575 | + | 0.250393i | ||||
\(433\) | −2.71885 | − | 8.36775i | −0.130659 | − | 0.402128i | 0.864230 | − | 0.503097i | \(-0.167806\pi\) |
−0.994890 | + | 0.100968i | \(0.967806\pi\) | |||||||
\(434\) | 2.00000 | − | 1.45309i | 0.0960031 | − | 0.0697503i | ||||
\(435\) | 5.85410 | − | 4.25325i | 0.280683 | − | 0.203928i | ||||
\(436\) | 1.23607 | + | 3.80423i | 0.0591969 | + | 0.182189i | ||||
\(437\) | −1.14590 | + | 3.52671i | −0.0548157 | + | 0.168705i | ||||
\(438\) | 3.73607 | + | 2.71441i | 0.178516 | + | 0.129700i | ||||
\(439\) | 30.5410 | 1.45764 | 0.728822 | − | 0.684704i | \(-0.240068\pi\) | ||||
0.728822 | + | 0.684704i | \(0.240068\pi\) | |||||||
\(440\) | −3.23607 | + | 0.726543i | −0.154273 | + | 0.0346366i | ||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | −11.0902 | − | 8.05748i | −0.527506 | − | 0.383255i | ||||
\(443\) | −8.82624 | + | 27.1644i | −0.419347 | + | 1.29062i | 0.488957 | + | 0.872308i | \(0.337377\pi\) |
−0.908304 | + | 0.418310i | \(0.862623\pi\) | |||||||
\(444\) | −5.61803 | − | 17.2905i | −0.266620 | − | 0.820572i | ||||
\(445\) | −12.0172 | + | 8.73102i | −0.569671 | + | 0.413890i | ||||
\(446\) | 10.6180 | − | 7.71445i | 0.502778 | − | 0.365290i | ||||
\(447\) | 5.85410 | + | 18.0171i | 0.276890 | + | 0.852178i | ||||
\(448\) | 0.309017 | − | 0.951057i | 0.0145997 | − | 0.0449332i | ||||
\(449\) | 16.2082 | + | 11.7759i | 0.764912 | + | 0.555741i | 0.900413 | − | 0.435036i | \(-0.143264\pi\) |
−0.135501 | + | 0.990777i | \(0.543264\pi\) | |||||||
\(450\) | 0.381966 | 0.0180061 | ||||||||
\(451\) | 8.69098 | + | 3.75123i | 0.409242 | + | 0.176638i | ||||
\(452\) | 4.32624 | 0.203489 | ||||||||
\(453\) | −24.1803 | − | 17.5680i | −1.13609 | − | 0.825419i | ||||
\(454\) | −4.22542 | + | 13.0045i | −0.198309 | + | 0.610332i | ||||
\(455\) | 1.61803 | + | 4.97980i | 0.0758546 | + | 0.233456i | ||||
\(456\) | 10.2812 | − | 7.46969i | 0.481459 | − | 0.349801i | ||||
\(457\) | 21.0172 | − | 15.2699i | 0.983144 | − | 0.714296i | 0.0247350 | − | 0.999694i | \(-0.492126\pi\) |
0.958409 | + | 0.285398i | \(0.0921258\pi\) | |||||||
\(458\) | −6.90983 | − | 21.2663i | −0.322875 | − | 0.993708i | ||||
\(459\) | −4.42705 | + | 13.6251i | −0.206637 | + | 0.635963i | ||||
\(460\) | −0.381966 | − | 0.277515i | −0.0178093 | − | 0.0129392i | ||||
\(461\) | 23.0557 | 1.07381 | 0.536906 | − | 0.843642i | \(-0.319593\pi\) | ||||
0.536906 | + | 0.843642i | \(0.319593\pi\) | |||||||
\(462\) | −3.54508 | + | 4.02874i | −0.164932 | + | 0.187434i | ||||
\(463\) | −10.9443 | −0.508623 | −0.254312 | − | 0.967122i | \(-0.581849\pi\) | ||||
−0.254312 | + | 0.967122i | \(0.581849\pi\) | |||||||
\(464\) | −3.61803 | − | 2.62866i | −0.167963 | − | 0.122032i | ||||
\(465\) | −1.23607 | + | 3.80423i | −0.0573213 | + | 0.176417i | ||||
\(466\) | −0.208204 | − | 0.640786i | −0.00964486 | − | 0.0296838i | ||||
\(467\) | −10.4721 | + | 7.60845i | −0.484593 | + | 0.352077i | −0.803101 | − | 0.595843i | \(-0.796818\pi\) |
0.318508 | + | 0.947920i | \(0.396818\pi\) | |||||||
\(468\) | −1.61803 | + | 1.17557i | −0.0747936 | + | 0.0543408i | ||||
\(469\) | −1.04508 | − | 3.21644i | −0.0482575 | − | 0.148521i | ||||
\(470\) | 1.47214 | − | 4.53077i | 0.0679046 | − | 0.208989i | ||||
\(471\) | 19.5623 | + | 14.2128i | 0.901383 | + | 0.654893i | ||||
\(472\) | −4.14590 | −0.190830 | ||||||||
\(473\) | 0.645898 | − | 6.90215i | 0.0296984 | − | 0.317361i | ||||
\(474\) | −6.47214 | −0.297275 | ||||||||
\(475\) | −6.35410 | − | 4.61653i | −0.291546 | − | 0.211821i | ||||
\(476\) | 0.809017 | − | 2.48990i | 0.0370812 | − | 0.114124i | ||||
\(477\) | 0.326238 | + | 1.00406i | 0.0149374 | + | 0.0459726i | ||||
\(478\) | 5.09017 | − | 3.69822i | 0.232819 | − | 0.169153i | ||||
\(479\) | −18.0344 | + | 13.1028i | −0.824015 | + | 0.598682i | −0.917860 | − | 0.396905i | \(-0.870084\pi\) |
0.0938450 | + | 0.995587i | \(0.470084\pi\) | |||||||
\(480\) | 0.500000 | + | 1.53884i | 0.0228218 | + | 0.0702382i | ||||
\(481\) | 18.1803 | − | 55.9533i | 0.828952 | − | 2.55125i | ||||
\(482\) | −25.0623 | − | 18.2088i | −1.14156 | − | 0.829390i | ||||
\(483\) | −0.763932 | −0.0347601 | ||||||||
\(484\) | −1.39919 | − | 10.9106i | −0.0635994 | − | 0.495939i | ||||
\(485\) | 8.38197 | 0.380605 | ||||||||
\(486\) | 3.19098 | + | 2.31838i | 0.144746 | + | 0.105164i | ||||
\(487\) | 11.7984 | − | 36.3117i | 0.534635 | − | 1.64544i | −0.209800 | − | 0.977744i | \(-0.567281\pi\) |
0.744436 | − | 0.667694i | \(-0.232719\pi\) | |||||||
\(488\) | −4.23607 | − | 13.0373i | −0.191758 | − | 0.590170i | ||||
\(489\) | −29.8435 | + | 21.6825i | −1.34957 | + | 0.980518i | ||||
\(490\) | −0.809017 | + | 0.587785i | −0.0365477 | + | 0.0265534i | ||||
\(491\) | −5.93769 | − | 18.2743i | −0.267964 | − | 0.824710i | −0.990996 | − | 0.133894i | \(-0.957252\pi\) |
0.723031 | − | 0.690815i | \(-0.242748\pi\) | |||||||
\(492\) | 1.42705 | − | 4.39201i | 0.0643364 | − | 0.198007i | ||||
\(493\) | −9.47214 | − | 6.88191i | −0.426604 | − | 0.309946i | ||||
\(494\) | 41.1246 | 1.85028 | ||||||||
\(495\) | −0.118034 | + | 1.26133i | −0.00530523 | + | 0.0566924i | ||||
\(496\) | 2.47214 | 0.111002 | ||||||||
\(497\) | −8.85410 | − | 6.43288i | −0.397161 | − | 0.288554i | ||||
\(498\) | 4.42705 | − | 13.6251i | 0.198381 | − | 0.610554i | ||||
\(499\) | −6.17376 | − | 19.0009i | −0.276376 | − | 0.850596i | −0.988852 | − | 0.148901i | \(-0.952427\pi\) |
0.712477 | − | 0.701696i | \(-0.247573\pi\) | |||||||
\(500\) | 0.809017 | − | 0.587785i | 0.0361803 | − | 0.0262866i | ||||
\(501\) | −10.8541 | + | 7.88597i | −0.484926 | + | 0.352319i | ||||
\(502\) | −6.18034 | − | 19.0211i | −0.275842 | − | 0.848955i | ||||
\(503\) | −6.38197 | + | 19.6417i | −0.284558 | + | 0.875779i | 0.701973 | + | 0.712204i | \(0.252303\pi\) |
−0.986531 | + | 0.163575i | \(0.947697\pi\) | |||||||
\(504\) | −0.309017 | − | 0.224514i | −0.0137647 | − | 0.0100006i | ||||
\(505\) | 14.9443 | 0.665011 | ||||||||
\(506\) | 1.03444 | − | 1.17557i | 0.0459865 | − | 0.0522605i | ||||
\(507\) | 23.3262 | 1.03595 | ||||||||
\(508\) | −10.0902 | − | 7.33094i | −0.447679 | − | 0.325258i | ||||
\(509\) | 4.05573 | − | 12.4822i | 0.179767 | − | 0.553266i | −0.820052 | − | 0.572289i | \(-0.806056\pi\) |
0.999819 | + | 0.0190230i | \(0.00605559\pi\) | |||||||
\(510\) | 1.30902 | + | 4.02874i | 0.0579642 | + | 0.178396i | ||||
\(511\) | −2.30902 | + | 1.67760i | −0.102145 | + | 0.0742126i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | −13.2812 | − | 40.8752i | −0.586377 | − | 1.80468i | ||||
\(514\) | −4.59017 | + | 14.1271i | −0.202464 | + | 0.623119i | ||||
\(515\) | −4.85410 | − | 3.52671i | −0.213897 | − | 0.155405i | ||||
\(516\) | −3.38197 | −0.148883 | ||||||||
\(517\) | 14.5066 | + | 6.26137i | 0.637999 | + | 0.275375i | ||||
\(518\) | 11.2361 | 0.493684 | ||||||||
\(519\) | −26.0344 | − | 18.9151i | −1.14279 | − | 0.830282i | ||||
\(520\) | −1.61803 | + | 4.97980i | −0.0709555 | + | 0.218379i | ||||
\(521\) | −2.98936 | − | 9.20029i | −0.130966 | − | 0.403072i | 0.863975 | − | 0.503535i | \(-0.167968\pi\) |
−0.994941 | + | 0.100463i | \(0.967968\pi\) | |||||||
\(522\) | −1.38197 | + | 1.00406i | −0.0604870 | + | 0.0439464i | ||||
\(523\) | 16.8262 | − | 12.2250i | 0.735760 | − | 0.534561i | −0.155620 | − | 0.987817i | \(-0.549738\pi\) |
0.891380 | + | 0.453256i | \(0.149738\pi\) | |||||||
\(524\) | 1.57295 | + | 4.84104i | 0.0687146 | + | 0.211482i | ||||
\(525\) | 0.500000 | − | 1.53884i | 0.0218218 | − | 0.0671606i | ||||
\(526\) | 21.3262 | + | 15.4944i | 0.929868 | + | 0.675589i | ||||
\(527\) | 6.47214 | 0.281931 | ||||||||
\(528\) | −5.23607 | + | 1.17557i | −0.227871 | + | 0.0511601i | ||||
\(529\) | −22.7771 | −0.990308 | ||||||||
\(530\) | 2.23607 | + | 1.62460i | 0.0971286 | + | 0.0705680i | ||||
\(531\) | −0.489357 | + | 1.50609i | −0.0212363 | + | 0.0653585i | ||||
\(532\) | 2.42705 | + | 7.46969i | 0.105226 | + | 0.323852i | ||||
\(533\) | 12.0902 | − | 8.78402i | 0.523683 | − | 0.380478i | ||||
\(534\) | −19.4443 | + | 14.1271i | −0.841436 | + | 0.611339i | ||||
\(535\) | −0.881966 | − | 2.71441i | −0.0381307 | − | 0.117354i | ||||
\(536\) | 1.04508 | − | 3.21644i | 0.0451408 | − | 0.138929i | ||||
\(537\) | −2.80902 | − | 2.04087i | −0.121218 | − | 0.0880701i | ||||
\(538\) | 18.6525 | 0.804165 | ||||||||
\(539\) | −1.69098 | − | 2.85317i | −0.0728358 | − | 0.122895i | ||||
\(540\) | 5.47214 | 0.235483 | ||||||||
\(541\) | 34.7984 | + | 25.2825i | 1.49610 | + | 1.08698i | 0.971903 | + | 0.235382i | \(0.0756341\pi\) |
0.524196 | + | 0.851598i | \(0.324366\pi\) | |||||||
\(542\) | 1.90983 | − | 5.87785i | 0.0820342 | − | 0.252475i | ||||
\(543\) | 10.4721 | + | 32.2299i | 0.449402 | + | 1.38312i | ||||
\(544\) | 2.11803 | − | 1.53884i | 0.0908100 | − | 0.0659773i | ||||
\(545\) | 3.23607 | − | 2.35114i | 0.138618 | − | 0.100712i | ||||
\(546\) | 2.61803 | + | 8.05748i | 0.112042 | + | 0.344828i | ||||
\(547\) | −6.84346 | + | 21.0620i | −0.292605 | + | 0.900546i | 0.691410 | + | 0.722462i | \(0.256990\pi\) |
−0.984015 | + | 0.178084i | \(0.943010\pi\) | |||||||
\(548\) | −3.92705 | − | 2.85317i | −0.167755 | − | 0.121881i | ||||
\(549\) | −5.23607 | −0.223470 | ||||||||
\(550\) | 1.69098 | + | 2.85317i | 0.0721038 | + | 0.121660i | ||||
\(551\) | 35.1246 | 1.49636 | ||||||||
\(552\) | −0.618034 | − | 0.449028i | −0.0263053 | − | 0.0191119i | ||||
\(553\) | 1.23607 | − | 3.80423i | 0.0525630 | − | 0.161772i | ||||
\(554\) | 3.70820 | + | 11.4127i | 0.157546 | + | 0.484878i | ||||
\(555\) | −14.7082 | + | 10.6861i | −0.624328 | + | 0.453601i | ||||
\(556\) | 4.00000 | − | 2.90617i | 0.169638 | − | 0.123249i | ||||
\(557\) | 5.79837 | + | 17.8456i | 0.245685 | + | 0.756141i | 0.995523 | + | 0.0945192i | \(0.0301314\pi\) |
−0.749838 | + | 0.661621i | \(0.769869\pi\) | |||||||
\(558\) | 0.291796 | − | 0.898056i | 0.0123527 | − | 0.0380177i | ||||
\(559\) | −8.85410 | − | 6.43288i | −0.374489 | − | 0.272082i | ||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | −13.7082 | + | 3.07768i | −0.578761 | + | 0.129940i | ||||
\(562\) | −11.3262 | −0.477769 | ||||||||
\(563\) | −23.9615 | − | 17.4090i | −1.00986 | − | 0.733704i | −0.0456775 | − | 0.998956i | \(-0.514545\pi\) |
−0.964179 | + | 0.265253i | \(0.914545\pi\) | |||||||
\(564\) | 2.38197 | − | 7.33094i | 0.100299 | − | 0.308688i | ||||
\(565\) | −1.33688 | − | 4.11450i | −0.0562430 | − | 0.173098i | ||||
\(566\) | 13.2361 | − | 9.61657i | 0.556353 | − | 0.404214i | ||||
\(567\) | 6.23607 | − | 4.53077i | 0.261890 | − | 0.190274i | ||||
\(568\) | −3.38197 | − | 10.4086i | −0.141904 | − | 0.436736i | ||||
\(569\) | 13.6976 | − | 42.1568i | 0.574232 | − | 1.76730i | −0.0645493 | − | 0.997915i | \(-0.520561\pi\) |
0.638781 | − | 0.769389i | \(-0.279439\pi\) | |||||||
\(570\) | −10.2812 | − | 7.46969i | −0.430630 | − | 0.312871i | ||||
\(571\) | −34.8328 | −1.45771 | −0.728854 | − | 0.684669i | \(-0.759947\pi\) | ||||
−0.728854 | + | 0.684669i | \(0.759947\pi\) | |||||||
\(572\) | −15.9443 | − | 6.88191i | −0.666663 | − | 0.287747i | ||||
\(573\) | −2.00000 | −0.0835512 | ||||||||
\(574\) | 2.30902 | + | 1.67760i | 0.0963765 | + | 0.0700216i | ||||
\(575\) | −0.145898 | + | 0.449028i | −0.00608437 | + | 0.0187258i | ||||
\(576\) | −0.118034 | − | 0.363271i | −0.00491808 | − | 0.0151363i | ||||
\(577\) | 21.3541 | − | 15.5147i | 0.888983 | − | 0.645884i | −0.0466297 | − | 0.998912i | \(-0.514848\pi\) |
0.935613 | + | 0.353028i | \(0.114848\pi\) | |||||||
\(578\) | −8.20820 | + | 5.96361i | −0.341416 | + | 0.248053i | ||||
\(579\) | −10.7082 | − | 32.9565i | −0.445018 | − | 1.36962i | ||||
\(580\) | −1.38197 | + | 4.25325i | −0.0573830 | + | 0.176607i | ||||
\(581\) | 7.16312 | + | 5.20431i | 0.297176 | + | 0.215911i | ||||
\(582\) | 13.5623 | 0.562176 | ||||||||
\(583\) | −6.05573 | + | 6.88191i | −0.250803 | + | 0.285020i | ||||
\(584\) | −2.85410 | −0.118104 | ||||||||
\(585\) | 1.61803 | + | 1.17557i | 0.0668975 | + | 0.0486039i | ||||
\(586\) | −5.70820 | + | 17.5680i | −0.235804 | + | 0.725729i | ||||
\(587\) | −2.53851 | − | 7.81272i | −0.104775 | − | 0.322466i | 0.884902 | − | 0.465777i | \(-0.154225\pi\) |
−0.989678 | + | 0.143311i | \(0.954225\pi\) | |||||||
\(588\) | −1.30902 | + | 0.951057i | −0.0539830 | + | 0.0392209i | ||||
\(589\) | −15.7082 | + | 11.4127i | −0.647245 | + | 0.470251i | ||||
\(590\) | 1.28115 | + | 3.94298i | 0.0527442 | + | 0.162330i | ||||
\(591\) | 5.76393 | − | 17.7396i | 0.237096 | − | 0.729708i | ||||
\(592\) | 9.09017 | + | 6.60440i | 0.373604 | + | 0.271439i | ||||
\(593\) | −34.0344 | −1.39763 | −0.698814 | − | 0.715304i | \(-0.746288\pi\) | ||||
−0.698814 | + | 0.715304i | \(0.746288\pi\) | |||||||
\(594\) | −1.69098 | + | 18.0701i | −0.0693819 | + | 0.741424i | ||||
\(595\) | −2.61803 | −0.107329 | ||||||||
\(596\) | −9.47214 | − | 6.88191i | −0.387994 | − | 0.281894i | ||||
\(597\) | 2.52786 | − | 7.77997i | 0.103459 | − | 0.318413i | ||||
\(598\) | −0.763932 | − | 2.35114i | −0.0312395 | − | 0.0961453i | ||||
\(599\) | 29.1803 | − | 21.2008i | 1.19228 | − | 0.866239i | 0.198773 | − | 0.980045i | \(-0.436304\pi\) |
0.993503 | + | 0.113806i | \(0.0363042\pi\) | |||||||
\(600\) | 1.30902 | − | 0.951057i | 0.0534404 | − | 0.0388267i | ||||
\(601\) | −10.2984 | − | 31.6951i | −0.420079 | − | 1.29287i | −0.907628 | − | 0.419776i | \(-0.862109\pi\) |
0.487548 | − | 0.873096i | \(-0.337891\pi\) | |||||||
\(602\) | 0.645898 | − | 1.98787i | 0.0263248 | − | 0.0810195i | ||||
\(603\) | −1.04508 | − | 0.759299i | −0.0425592 | − | 0.0309210i | ||||
\(604\) | 18.4721 | 0.751621 | ||||||||
\(605\) | −9.94427 | + | 4.70228i | −0.404292 | + | 0.191175i | ||||
\(606\) | 24.1803 | 0.982259 | ||||||||
\(607\) | 5.52786 | + | 4.01623i | 0.224369 | + | 0.163014i | 0.694291 | − | 0.719694i | \(-0.255718\pi\) |
−0.469922 | + | 0.882708i | \(0.655718\pi\) | |||||||
\(608\) | −2.42705 | + | 7.46969i | −0.0984299 | + | 0.302936i | ||||
\(609\) | 2.23607 | + | 6.88191i | 0.0906100 | + | 0.278869i | ||||
\(610\) | −11.0902 | + | 8.05748i | −0.449028 | + | 0.326238i | ||||
\(611\) | 20.1803 | − | 14.6619i | 0.816409 | − | 0.593156i | ||||
\(612\) | −0.309017 | − | 0.951057i | −0.0124913 | − | 0.0384442i | ||||
\(613\) | −3.23607 | + | 9.95959i | −0.130704 | + | 0.402264i | −0.994897 | − | 0.100895i | \(-0.967829\pi\) |
0.864193 | + | 0.503160i | \(0.167829\pi\) | |||||||
\(614\) | 15.0172 | + | 10.9106i | 0.606046 | + | 0.440318i | ||||
\(615\) | −4.61803 | −0.186217 | ||||||||
\(616\) | 0.309017 | − | 3.30220i | 0.0124506 | − | 0.133049i | ||||
\(617\) | −5.56231 | −0.223930 | −0.111965 | − | 0.993712i | \(-0.535714\pi\) | ||||
−0.111965 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(618\) | −7.85410 | − | 5.70634i | −0.315938 | − | 0.229543i | ||||
\(619\) | 13.3713 | − | 41.1527i | 0.537439 | − | 1.65407i | −0.200881 | − | 0.979616i | \(-0.564380\pi\) |
0.738320 | − | 0.674451i | \(-0.235620\pi\) | |||||||
\(620\) | −0.763932 | − | 2.35114i | −0.0306802 | − | 0.0944241i | ||||
\(621\) | −2.09017 | + | 1.51860i | −0.0838756 | + | 0.0609392i | ||||
\(622\) | −1.76393 | + | 1.28157i | −0.0707272 | + | 0.0513863i | ||||
\(623\) | −4.59017 | − | 14.1271i | −0.183901 | − | 0.565990i | ||||
\(624\) | −2.61803 | + | 8.05748i | −0.104805 | + | 0.322557i | ||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | 31.2705 | 1.24982 | ||||||||
\(627\) | 27.8435 | − | 31.6421i | 1.11196 | − | 1.26367i | ||||
\(628\) | −14.9443 | −0.596341 | ||||||||
\(629\) | 23.7984 | + | 17.2905i | 0.948903 | + | 0.689419i | ||||
\(630\) | −0.118034 | + | 0.363271i | −0.00470259 | + | 0.0144731i | ||||
\(631\) | 7.76393 | + | 23.8949i | 0.309077 | + | 0.951242i | 0.978124 | + | 0.208022i | \(0.0667025\pi\) |
−0.669047 | + | 0.743220i | \(0.733297\pi\) | |||||||
\(632\) | 3.23607 | − | 2.35114i | 0.128724 | − | 0.0935234i | ||||
\(633\) | −13.9721 | + | 10.1514i | −0.555343 | + | 0.403480i | ||||
\(634\) | −9.38197 | − | 28.8747i | −0.372605 | − | 1.14676i | ||||
\(635\) | −3.85410 | + | 11.8617i | −0.152945 | + | 0.470717i | ||||
\(636\) | 3.61803 | + | 2.62866i | 0.143464 | + | 0.104233i | ||||
\(637\) | −5.23607 | −0.207461 | ||||||||
\(638\) | −13.6180 | − | 5.87785i | −0.539143 | − | 0.232706i | ||||
\(639\) | −4.18034 | −0.165372 | ||||||||
\(640\) | −0.809017 | − | 0.587785i | −0.0319792 | − | 0.0232343i | ||||
\(641\) | −12.6246 | + | 38.8546i | −0.498642 | + | 1.53466i | 0.312561 | + | 0.949898i | \(0.398813\pi\) |
−0.811203 | + | 0.584765i | \(0.801187\pi\) | |||||||
\(642\) | −1.42705 | − | 4.39201i | −0.0563212 | − | 0.173339i | ||||
\(643\) | 11.4894 | − | 8.34751i | 0.453096 | − | 0.329194i | −0.337721 | − | 0.941246i | \(-0.609656\pi\) |
0.790817 | + | 0.612053i | \(0.209656\pi\) | |||||||
\(644\) | 0.381966 | − | 0.277515i | 0.0150516 | − | 0.0109356i | ||||
\(645\) | 1.04508 | + | 3.21644i | 0.0411502 | + | 0.126647i | ||||
\(646\) | −6.35410 | + | 19.5559i | −0.249999 | + | 0.769417i | ||||
\(647\) | −30.5066 | − | 22.1643i | −1.19934 | − | 0.871370i | −0.205118 | − | 0.978737i | \(-0.565758\pi\) |
−0.994219 | + | 0.107368i | \(0.965758\pi\) | |||||||
\(648\) | 7.70820 | 0.302807 | ||||||||
\(649\) | −13.4164 | + | 3.01217i | −0.526640 | + | 0.118238i | ||||
\(650\) | 5.23607 | 0.205375 | ||||||||
\(651\) | −3.23607 | − | 2.35114i | −0.126832 | − | 0.0921485i | ||||
\(652\) | 7.04508 | − | 21.6825i | 0.275907 | − | 0.849154i | ||||
\(653\) | 13.7984 | + | 42.4670i | 0.539972 | + | 1.66186i | 0.732653 | + | 0.680602i | \(0.238282\pi\) |
−0.192681 | + | 0.981261i | \(0.561718\pi\) | |||||||
\(654\) | 5.23607 | − | 3.80423i | 0.204746 | − | 0.148757i | ||||
\(655\) | 4.11803 | − | 2.99193i | 0.160905 | − | 0.116904i | ||||
\(656\) | 0.881966 | + | 2.71441i | 0.0344350 | + | 0.105980i | ||||
\(657\) | −0.336881 | + | 1.03681i | −0.0131430 | + | 0.0404499i | ||||
\(658\) | 3.85410 | + | 2.80017i | 0.150249 | + | 0.109162i | ||||
\(659\) | −20.9787 | −0.817215 | −0.408607 | − | 0.912710i | \(-0.633985\pi\) | ||||
−0.408607 | + | 0.912710i | \(0.633985\pi\) | |||||||
\(660\) | 2.73607 | + | 4.61653i | 0.106501 | + | 0.179698i | ||||
\(661\) | 1.81966 | 0.0707766 | 0.0353883 | − | 0.999374i | \(-0.488733\pi\) | ||||
0.0353883 | + | 0.999374i | \(0.488733\pi\) | |||||||
\(662\) | −0.781153 | − | 0.567541i | −0.0303604 | − | 0.0220581i | ||||
\(663\) | −6.85410 | + | 21.0948i | −0.266191 | + | 0.819252i | ||||
\(664\) | 2.73607 | + | 8.42075i | 0.106180 | + | 0.326789i | ||||
\(665\) | 6.35410 | − | 4.61653i | 0.246402 | − | 0.179021i | ||||
\(666\) | 3.47214 | − | 2.52265i | 0.134543 | − | 0.0977509i | ||||
\(667\) | −0.652476 | − | 2.00811i | −0.0252640 | − | 0.0777545i | ||||
\(668\) | 2.56231 | − | 7.88597i | 0.0991386 | − | 0.305117i | ||||
\(669\) | −17.1803 | − | 12.4822i | −0.664230 | − | 0.482592i | ||||
\(670\) | −3.38197 | −0.130657 | ||||||||
\(671\) | −23.1803 | − | 39.1118i | −0.894867 | − | 1.50990i | ||||
\(672\) | −1.61803 | −0.0624170 | ||||||||
\(673\) | −12.5000 | − | 9.08178i | −0.481840 | − | 0.350077i | 0.320198 | − | 0.947351i | \(-0.396251\pi\) |
−0.802037 | + | 0.597274i | \(0.796251\pi\) | |||||||
\(674\) | 0.371323 | − | 1.14281i | 0.0143028 | − | 0.0440196i | ||||
\(675\) | −1.69098 | − | 5.20431i | −0.0650860 | − | 0.200314i | ||||
\(676\) | −11.6631 | + | 8.47375i | −0.448581 | + | 0.325914i | ||||
\(677\) | −9.23607 | + | 6.71040i | −0.354971 | + | 0.257901i | −0.750951 | − | 0.660357i | \(-0.770405\pi\) |
0.395980 | + | 0.918259i | \(0.370405\pi\) | |||||||
\(678\) | −2.16312 | − | 6.65740i | −0.0830741 | − | 0.255676i | ||||
\(679\) | −2.59017 | + | 7.97172i | −0.0994016 | + | 0.305927i | ||||
\(680\) | −2.11803 | − | 1.53884i | −0.0812229 | − | 0.0590119i | ||||
\(681\) | 22.1246 | 0.847817 | ||||||||
\(682\) | 8.00000 | − | 1.79611i | 0.306336 | − | 0.0687767i | ||||
\(683\) | 21.5279 | 0.823741 | 0.411870 | − | 0.911242i | \(-0.364876\pi\) | ||||
0.411870 | + | 0.911242i | \(0.364876\pi\) | |||||||
\(684\) | 2.42705 | + | 1.76336i | 0.0928006 | + | 0.0674236i | ||||
\(685\) | −1.50000 | + | 4.61653i | −0.0573121 | + | 0.176388i | ||||
\(686\) | −0.309017 | − | 0.951057i | −0.0117983 | − | 0.0363115i | ||||
\(687\) | −29.2705 | + | 21.2663i | −1.11674 | + | 0.811359i | ||||
\(688\) | 1.69098 | − | 1.22857i | 0.0644681 | − | 0.0468388i | ||||
\(689\) | 4.47214 | + | 13.7638i | 0.170375 | + | 0.524360i | ||||
\(690\) | −0.236068 | + | 0.726543i | −0.00898695 | + | 0.0276590i | ||||
\(691\) | 6.11803 | + | 4.44501i | 0.232741 | + | 0.169096i | 0.698043 | − | 0.716056i | \(-0.254054\pi\) |
−0.465302 | + | 0.885152i | \(0.654054\pi\) | |||||||
\(692\) | 19.8885 | 0.756049 | ||||||||
\(693\) | −1.16312 | − | 0.502029i | −0.0441832 | − | 0.0190705i | ||||
\(694\) | −15.0902 | −0.572815 | ||||||||
\(695\) | −4.00000 | − | 2.90617i | −0.151729 | − | 0.110237i | ||||
\(696\) | −2.23607 | + | 6.88191i | −0.0847579 | + | 0.260858i | ||||
\(697\) | 2.30902 | + | 7.10642i | 0.0874603 | + | 0.269175i | ||||
\(698\) | −15.7082 | + | 11.4127i | −0.594564 | + | 0.431976i | ||||
\(699\) | −0.881966 | + | 0.640786i | −0.0333590 | + | 0.0242367i | ||||
\(700\) | 0.309017 | + | 0.951057i | 0.0116797 | + | 0.0359466i | ||||
\(701\) | −10.7639 | + | 33.1280i | −0.406548 | + | 1.25123i | 0.513048 | + | 0.858360i | \(0.328516\pi\) |
−0.919596 | + | 0.392866i | \(0.871484\pi\) | |||||||
\(702\) | 23.1803 | + | 16.8415i | 0.874886 | + | 0.635642i | ||||
\(703\) | −88.2492 | −3.32838 | ||||||||
\(704\) | 2.19098 | − | 2.48990i | 0.0825758 | − | 0.0938416i | ||||
\(705\) | −7.70820 | −0.290308 | ||||||||
\(706\) | −9.35410 | − | 6.79615i | −0.352046 | − | 0.255777i | ||||
\(707\) | −4.61803 | + | 14.2128i | −0.173679 | + | 0.534529i | ||||
\(708\) | 2.07295 | + | 6.37988i | 0.0779062 | + | 0.239771i | ||||
\(709\) | −27.3262 | + | 19.8537i | −1.02626 | + | 0.745620i | −0.967556 | − | 0.252655i | \(-0.918696\pi\) |
−0.0587020 | + | 0.998276i | \(0.518696\pi\) | |||||||
\(710\) | −8.85410 | + | 6.43288i | −0.332289 | + | 0.241422i | ||||
\(711\) | −0.472136 | − | 1.45309i | −0.0177065 | − | 0.0544949i | ||||
\(712\) | 4.59017 | − | 14.1271i | 0.172024 | − | 0.529435i | ||||
\(713\) | 0.944272 | + | 0.686054i | 0.0353633 | + | 0.0256929i | ||||
\(714\) | −4.23607 | −0.158531 | ||||||||
\(715\) | −1.61803 | + | 17.2905i | −0.0605110 | + | 0.646629i | ||||
\(716\) | 2.14590 | 0.0801960 | ||||||||
\(717\) | −8.23607 | − | 5.98385i | −0.307582 | − | 0.223471i | ||||
\(718\) | −9.14590 | + | 28.1482i | −0.341322 | + | 1.05048i | ||||
\(719\) | 7.43769 | + | 22.8909i | 0.277379 | + | 0.853685i | 0.988580 | + | 0.150697i | \(0.0481516\pi\) |
−0.711201 | + | 0.702989i | \(0.751848\pi\) | |||||||
\(720\) | −0.309017 | + | 0.224514i | −0.0115164 | + | 0.00836714i | ||||
\(721\) | 4.85410 | − | 3.52671i | 0.180776 | − | 0.131342i | ||||
\(722\) | −13.1910 | − | 40.5977i | −0.490918 | − | 1.51089i | ||||
\(723\) | −15.4894 | + | 47.6713i | −0.576055 | + | 1.77292i | ||||
\(724\) | −16.9443 | − | 12.3107i | −0.629729 | − | 0.457525i | ||||
\(725\) | 4.47214 | 0.166091 | ||||||||
\(726\) | −16.0902 | + | 7.60845i | −0.597162 | + | 0.282376i | ||||
\(727\) | 50.2492 | 1.86364 | 0.931820 | − | 0.362920i | \(-0.118220\pi\) | ||||
0.931820 | + | 0.362920i | \(0.118220\pi\) | |||||||
\(728\) | −4.23607 | − | 3.07768i | −0.156999 | − | 0.114067i | ||||
\(729\) | 9.11803 | − | 28.0624i | 0.337705 | − | 1.03935i | ||||
\(730\) | 0.881966 | + | 2.71441i | 0.0326430 | + | 0.100465i | ||||
\(731\) | 4.42705 | − | 3.21644i | 0.163740 | − | 0.118964i | ||||
\(732\) | −17.9443 | + | 13.0373i | −0.663239 | + | 0.481872i | ||||
\(733\) | −11.0000 | − | 33.8545i | −0.406294 | − | 1.25045i | −0.919810 | − | 0.392365i | \(-0.871657\pi\) |
0.513515 | − | 0.858080i | \(-0.328343\pi\) | |||||||
\(734\) | −4.90983 | + | 15.1109i | −0.181225 | + | 0.557754i | ||||
\(735\) | 1.30902 | + | 0.951057i | 0.0482838 | + | 0.0350802i | ||||
\(736\) | 0.472136 | 0.0174032 | ||||||||
\(737\) | 1.04508 | − | 11.1679i | 0.0384962 | − | 0.411376i | ||||
\(738\) | 1.09017 | 0.0401297 | ||||||||
\(739\) | −8.20820 | − | 5.96361i | −0.301944 | − | 0.219375i | 0.426488 | − | 0.904493i | \(-0.359751\pi\) |
−0.728432 | + | 0.685118i | \(0.759751\pi\) | |||||||
\(740\) | 3.47214 | − | 10.6861i | 0.127638 | − | 0.392830i | ||||
\(741\) | −20.5623 | − | 63.2843i | −0.755375 | − | 2.32481i | ||||
\(742\) | −2.23607 | + | 1.62460i | −0.0820886 | + | 0.0596409i | ||||
\(743\) | 32.5623 | − | 23.6579i | 1.19460 | − | 0.867924i | 0.200853 | − | 0.979621i | \(-0.435629\pi\) |
0.993742 | + | 0.111697i | \(0.0356287\pi\) | |||||||
\(744\) | −1.23607 | − | 3.80423i | −0.0453165 | − | 0.139470i | ||||
\(745\) | −3.61803 | + | 11.1352i | −0.132555 | + | 0.407961i | ||||
\(746\) | 11.8541 | + | 8.61251i | 0.434010 | + | 0.315326i | ||||
\(747\) | 3.38197 | 0.123740 | ||||||||
\(748\) | 5.73607 | − | 6.51864i | 0.209731 | − | 0.238345i | ||||
\(749\) | 2.85410 | 0.104287 | ||||||||
\(750\) | −1.30902 | − | 0.951057i | −0.0477985 | − | 0.0347277i | ||||
\(751\) | −14.0000 | + | 43.0876i | −0.510867 | + | 1.57229i | 0.279811 | + | 0.960055i | \(0.409728\pi\) |
−0.790678 | + | 0.612233i | \(0.790272\pi\) | |||||||
\(752\) | 1.47214 | + | 4.53077i | 0.0536833 | + | 0.165220i | ||||
\(753\) | −26.1803 | + | 19.0211i | −0.954065 | + | 0.693169i | ||||
\(754\) | −18.9443 | + | 13.7638i | −0.689910 | + | 0.501249i | ||||
\(755\) | −5.70820 | − | 17.5680i | −0.207743 | − | 0.639367i | ||||
\(756\) | −1.69098 | + | 5.20431i | −0.0615005 | + | 0.189279i | ||||
\(757\) | −36.1246 | − | 26.2461i | −1.31297 | − | 0.953930i | −0.999991 | − | 0.00416982i | \(-0.998673\pi\) |
−0.312980 | − | 0.949760i | \(-0.601327\pi\) | |||||||
\(758\) | −15.6180 | −0.567273 | ||||||||
\(759\) | −2.32624 | − | 1.00406i | −0.0844371 | − | 0.0364450i | ||||
\(760\) | 7.85410 | 0.284898 | ||||||||
\(761\) | 40.2984 | + | 29.2785i | 1.46081 | + | 1.06134i | 0.983150 | + | 0.182802i | \(0.0585168\pi\) |
0.477665 | + | 0.878542i | \(0.341483\pi\) | |||||||
\(762\) | −6.23607 | + | 19.1926i | −0.225909 | + | 0.695276i | ||||
\(763\) | 1.23607 | + | 3.80423i | 0.0447487 | + | 0.137722i | ||||
\(764\) | 1.00000 | − | 0.726543i | 0.0361787 | − | 0.0262854i | ||||
\(765\) | −0.809017 | + | 0.587785i | −0.0292501 | + | 0.0212514i | ||||
\(766\) | 6.23607 | + | 19.1926i | 0.225318 | + | 0.693458i | ||||
\(767\) | −6.70820 | + | 20.6457i | −0.242219 | + | 0.745474i | ||||
\(768\) | −1.30902 | − | 0.951057i | −0.0472351 | − | 0.0343183i | ||||
\(769\) | 31.3050 | 1.12889 | 0.564443 | − | 0.825472i | \(-0.309091\pi\) | ||||
0.564443 | + | 0.825472i | \(0.309091\pi\) | |||||||
\(770\) | −3.23607 | + | 0.726543i | −0.116620 | + | 0.0261828i | ||||
\(771\) | 24.0344 | 0.865579 | ||||||||
\(772\) | 17.3262 | + | 12.5882i | 0.623585 | + | 0.453061i | ||||
\(773\) | 10.7426 | − | 33.0625i | 0.386386 | − | 1.18917i | −0.549084 | − | 0.835767i | \(-0.685023\pi\) |
0.935470 | − | 0.353407i | \(-0.114977\pi\) | |||||||
\(774\) | −0.246711 | − | 0.759299i | −0.00886785 | − | 0.0272924i | ||||
\(775\) | −2.00000 | + | 1.45309i | −0.0718421 | + | 0.0521964i | ||||
\(776\) | −6.78115 | + | 4.92680i | −0.243429 | + | 0.176862i | ||||
\(777\) | −5.61803 | − | 17.2905i | −0.201546 | − | 0.620294i | ||||
\(778\) | −7.94427 | + | 24.4500i | −0.284816 | + | 0.876573i | ||||
\(779\) | −18.1353 | − | 13.1760i | −0.649763 | − | 0.472080i | ||||
\(780\) | 8.47214 | 0.303351 | ||||||||
\(781\) | −18.5066 | − | 31.2259i | −0.662217 | − | 1.11735i | ||||
\(782\) | 1.23607 | 0.0442017 | ||||||||
\(783\) | 19.7984 | + | 14.3844i | 0.707536 | + | 0.514055i | ||||
\(784\) | 0.309017 | − | 0.951057i | 0.0110363 | − | 0.0339663i | ||||
\(785\) | 4.61803 | + | 14.2128i | 0.164825 | + | 0.507278i | ||||
\(786\) | 6.66312 | − | 4.84104i | 0.237666 | − | 0.172674i | ||||
\(787\) | −35.0066 | + | 25.4338i | −1.24785 | + | 0.906616i | −0.998095 | − | 0.0616933i | \(-0.980350\pi\) |
−0.249755 | + | 0.968309i | \(0.580350\pi\) | |||||||
\(788\) | 3.56231 | + | 10.9637i | 0.126902 | + | 0.390564i | ||||
\(789\) | 13.1803 | − | 40.5649i | 0.469233 | − | 1.44415i | ||||
\(790\) | −3.23607 | − | 2.35114i | −0.115134 | − | 0.0836498i | ||||
\(791\) | 4.32624 | 0.153823 | ||||||||
\(792\) | −0.645898 | − | 1.08981i | −0.0229510 | − | 0.0387248i | ||||
\(793\) | −71.7771 | −2.54888 | ||||||||
\(794\) | 0.0901699 | + | 0.0655123i | 0.00320001 | + | 0.00232494i | ||||
\(795\) | 1.38197 | − | 4.25325i | 0.0490133 | − | 0.150847i | ||||
\(796\) | 1.56231 | + | 4.80828i | 0.0553745 | + | 0.170425i | ||||
\(797\) | 6.61803 | − | 4.80828i | 0.234423 | − | 0.170318i | −0.464372 | − | 0.885640i | \(-0.653720\pi\) |
0.698795 | + | 0.715322i | \(0.253720\pi\) | |||||||
\(798\) | 10.2812 | − | 7.46969i | 0.363949 | − | 0.264424i | ||||
\(799\) | 3.85410 | + | 11.8617i | 0.136348 | + | 0.419637i | ||||
\(800\) | −0.309017 | + | 0.951057i | −0.0109254 | + | 0.0336249i | ||||
\(801\) | −4.59017 | − | 3.33495i | −0.162186 | − | 0.117835i | ||||
\(802\) | −2.56231 | −0.0904782 | ||||||||
\(803\) | −9.23607 | + | 2.07363i | −0.325934 | + | 0.0731767i | ||||
\(804\) | −5.47214 | −0.192987 | ||||||||
\(805\) | −0.381966 | − | 0.277515i | −0.0134625 | − | 0.00978110i | ||||
\(806\) | 4.00000 | − | 12.3107i | 0.140894 | − | 0.433627i | ||||
\(807\) | −9.32624 | − | 28.7032i | −0.328299 | − | 1.01040i | ||||
\(808\) | −12.0902 | + | 8.78402i | −0.425331 | + | 0.309021i | ||||
\(809\) | −21.9721 | + | 15.9637i | −0.772499 | + | 0.561253i | −0.902718 | − | 0.430232i | \(-0.858432\pi\) |
0.130219 | + | 0.991485i | \(0.458432\pi\) | |||||||
\(810\) | −2.38197 | − | 7.33094i | −0.0836938 | − | 0.257583i | ||||
\(811\) | 11.0279 | − | 33.9403i | 0.387241 | − | 1.19180i | −0.547601 | − | 0.836740i | \(-0.684459\pi\) |
0.934842 | − | 0.355065i | \(-0.115541\pi\) | |||||||
\(812\) | −3.61803 | − | 2.62866i | −0.126968 | − | 0.0922477i | ||||
\(813\) | −10.0000 | −0.350715 | ||||||||
\(814\) | 34.2148 | + | 14.7679i | 1.19923 | + | 0.517614i | ||||
\(815\) | −22.7984 | −0.798592 | ||||||||
\(816\) | −3.42705 | − | 2.48990i | −0.119971 | − | 0.0871639i | ||||
\(817\) | −5.07295 | + | 15.6129i | −0.177480 | + | 0.546227i | ||||
\(818\) | 7.09017 | + | 21.8213i | 0.247902 | + | 0.762964i | ||||
\(819\) | −1.61803 | + | 1.17557i | −0.0565387 | + | 0.0410778i | ||||
\(820\) | 2.30902 | − | 1.67760i | 0.0806344 | − | 0.0585843i | ||||
\(821\) | −0.0344419 | − | 0.106001i | −0.00120203 | − | 0.00369946i | 0.950454 | − | 0.310866i | \(-0.100619\pi\) |
−0.951656 | + | 0.307167i | \(0.900619\pi\) | |||||||
\(822\) | −2.42705 | + | 7.46969i | −0.0846531 | + | 0.260536i | ||||
\(823\) | 3.09017 | + | 2.24514i | 0.107717 | + | 0.0782607i | 0.640340 | − | 0.768092i | \(-0.278794\pi\) |
−0.532623 | + | 0.846353i | \(0.678794\pi\) | |||||||
\(824\) | 6.00000 | 0.209020 | ||||||||
\(825\) | 3.54508 | − | 4.02874i | 0.123424 | − | 0.140263i | ||||
\(826\) | −4.14590 | −0.144254 | ||||||||
\(827\) | −42.3328 | − | 30.7566i | −1.47206 | − | 1.06951i | −0.980011 | − | 0.198942i | \(-0.936250\pi\) |
−0.492045 | − | 0.870570i | \(-0.663750\pi\) | |||||||
\(828\) | 0.0557281 | − | 0.171513i | 0.00193669 | − | 0.00596050i | ||||
\(829\) | 10.3607 | + | 31.8869i | 0.359841 | + | 1.10748i | 0.953149 | + | 0.302502i | \(0.0978218\pi\) |
−0.593308 | + | 0.804976i | \(0.702178\pi\) | |||||||
\(830\) | 7.16312 | − | 5.20431i | 0.248635 | − | 0.180644i | ||||
\(831\) | 15.7082 | − | 11.4127i | 0.544912 | − | 0.395901i | ||||
\(832\) | −1.61803 | − | 4.97980i | −0.0560952 | − | 0.172643i | ||||
\(833\) | 0.809017 | − | 2.48990i | 0.0280308 | − | 0.0862699i | ||||
\(834\) | −6.47214 | − | 4.70228i | −0.224112 | − | 0.162827i | ||||
\(835\) | −8.29180 | −0.286949 | ||||||||
\(836\) | −2.42705 | + | 25.9358i | −0.0839413 | + | 0.897008i | ||||
\(837\) | −13.5279 | −0.467591 | ||||||||
\(838\) | 18.2533 | + | 13.2618i | 0.630549 | + | 0.458121i | ||||
\(839\) | 11.2148 | − | 34.5155i | 0.387177 | − | 1.19161i | −0.547711 | − | 0.836667i | \(-0.684501\pi\) |
0.934888 | − | 0.354942i | \(-0.115499\pi\) | |||||||
\(840\) | 0.500000 | + | 1.53884i | 0.0172516 | + | 0.0530951i | ||||
\(841\) | 7.28115 | − | 5.29007i | 0.251074 | − | 0.182416i | ||||
\(842\) | −29.7984 | + | 21.6498i | −1.02692 | + | 0.746101i | ||||
\(843\) | 5.66312 | + | 17.4293i | 0.195048 | + | 0.600297i | ||||
\(844\) | 3.29837 | − | 10.1514i | 0.113535 | − | 0.349424i | ||||
\(845\) | 11.6631 | + | 8.47375i | 0.401223 | + | 0.291506i | ||||
\(846\) | 1.81966 | 0.0625612 | ||||||||
\(847\) | −1.39919 | − | 10.9106i | −0.0480766 | − | 0.374894i | ||||
\(848\) | −2.76393 | −0.0949138 | ||||||||
\(849\) | −21.4164 | − | 15.5599i | −0.735009 | − | 0.534015i | ||||
\(850\) | −0.809017 | + | 2.48990i | −0.0277491 | + | 0.0854028i | ||||
\(851\) | 1.63932 | + | 5.04531i | 0.0561952 | + | 0.172951i | ||||
\(852\) | −14.3262 | + | 10.4086i | −0.490809 | + | 0.356593i | ||||
\(853\) | 10.8541 | − | 7.88597i | 0.371637 | − | 0.270010i | −0.386252 | − | 0.922393i | \(-0.626231\pi\) |
0.757890 | + | 0.652383i | \(0.226231\pi\) | |||||||
\(854\) | −4.23607 | − | 13.0373i | −0.144955 | − | 0.446126i | ||||
\(855\) | 0.927051 | − | 2.85317i | 0.0317045 | − | 0.0975763i | ||||
\(856\) | 2.30902 | + | 1.67760i | 0.0789206 | + | 0.0573392i | ||||
\(857\) | 24.5623 | 0.839032 | 0.419516 | − | 0.907748i | \(-0.362200\pi\) | ||||
0.419516 | + | 0.907748i | \(0.362200\pi\) | |||||||
\(858\) | −2.61803 | + | 27.9767i | −0.0893782 | + | 0.955108i | ||||
\(859\) | 14.3262 | 0.488805 | 0.244402 | − | 0.969674i | \(-0.421408\pi\) | ||||
0.244402 | + | 0.969674i | \(0.421408\pi\) | |||||||
\(860\) | −1.69098 | − | 1.22857i | −0.0576620 | − | 0.0418939i | ||||
\(861\) | 1.42705 | − | 4.39201i | 0.0486338 | − | 0.149679i | ||||
\(862\) | 0.201626 | + | 0.620541i | 0.00686741 | + | 0.0211357i | ||||
\(863\) | 11.4164 | − | 8.29451i | 0.388619 | − | 0.282348i | −0.376270 | − | 0.926510i | \(-0.622794\pi\) |
0.764889 | + | 0.644162i | \(0.222794\pi\) | |||||||
\(864\) | −4.42705 | + | 3.21644i | −0.150611 | + | 0.109426i | ||||
\(865\) | −6.14590 | − | 18.9151i | −0.208967 | − | 0.643134i | ||||
\(866\) | 2.71885 | − | 8.36775i | 0.0923902 | − | 0.284348i | ||||
\(867\) | 13.2812 | + | 9.64932i | 0.451052 | + | 0.327708i | ||||
\(868\) | 2.47214 | 0.0839098 | ||||||||
\(869\) | 8.76393 | − | 9.95959i | 0.297296 | − | 0.337856i | ||||
\(870\) | 7.23607 | 0.245326 | ||||||||
\(871\) | −14.3262 | − | 10.4086i | −0.485426 | − | 0.352683i | ||||
\(872\) | −1.23607 | + | 3.80423i | −0.0418585 | + | 0.128827i | ||||
\(873\) | 0.989357 | + | 3.04493i | 0.0334847 | + | 0.103055i | ||||
\(874\) | −3.00000 | + | 2.17963i | −0.101477 | + | 0.0737270i | ||||
\(875\) | 0.809017 | − | 0.587785i | 0.0273498 | − | 0.0198708i | ||||
\(876\) | 1.42705 | + | 4.39201i | 0.0482156 | + | 0.148392i | ||||
\(877\) | −0.854102 | + | 2.62866i | −0.0288410 | + | 0.0887634i | −0.964441 | − | 0.264299i | \(-0.914860\pi\) |
0.935600 | + | 0.353062i | \(0.114860\pi\) | |||||||
\(878\) | 24.7082 | + | 17.9516i | 0.833861 | + | 0.605836i | ||||
\(879\) | 29.8885 | 1.00812 | ||||||||
\(880\) | −3.04508 | − | 1.31433i | −0.102650 | − | 0.0443060i | ||||
\(881\) | 14.6738 | 0.494372 | 0.247186 | − | 0.968968i | \(-0.420494\pi\) | ||||
0.247186 | + | 0.968968i | \(0.420494\pi\) | |||||||
\(882\) | −0.309017 | − | 0.224514i | −0.0104051 | − | 0.00755978i | ||||
\(883\) | −13.3541 | + | 41.0997i | −0.449401 | + | 1.38312i | 0.428183 | + | 0.903692i | \(0.359154\pi\) |
−0.877584 | + | 0.479423i | \(0.840846\pi\) | |||||||
\(884\) | −4.23607 | − | 13.0373i | −0.142474 | − | 0.438491i | ||||
\(885\) | 5.42705 | − | 3.94298i | 0.182428 | − | 0.132542i | ||||
\(886\) | −23.1074 | + | 16.7885i | −0.776308 | + | 0.564021i | ||||
\(887\) | 8.20163 | + | 25.2420i | 0.275384 | + | 0.847544i | 0.989118 | + | 0.147127i | \(0.0470026\pi\) |
−0.713734 | + | 0.700417i | \(0.752997\pi\) | |||||||
\(888\) | 5.61803 | − | 17.2905i | 0.188529 | − | 0.580232i | ||||
\(889\) | −10.0902 | − | 7.33094i | −0.338413 | − | 0.245872i | ||||
\(890\) | −14.8541 | −0.497911 | ||||||||
\(891\) | 24.9443 | − | 5.60034i | 0.835665 | − | 0.187618i | ||||
\(892\) | 13.1246 | 0.439445 | ||||||||
\(893\) | −30.2705 | − | 21.9928i | −1.01296 | − | 0.735961i | ||||
\(894\) | −5.85410 | + | 18.0171i | −0.195790 | + | 0.602581i | ||||
\(895\) | −0.663119 | − | 2.04087i | −0.0221656 | − | 0.0682188i | ||||
\(896\) | 0.809017 | − | 0.587785i | 0.0270274 | − | 0.0196365i | ||||
\(897\) | −3.23607 | + | 2.35114i | −0.108049 | + | 0.0785023i | ||||
\(898\) | 6.19098 | + | 19.0539i | 0.206596 | + | 0.635836i | ||||
\(899\) | 3.41641 | − | 10.5146i | 0.113944 | − | 0.350682i | ||||
\(900\) | 0.309017 | + | 0.224514i | 0.0103006 | + | 0.00748380i | ||||
\(901\) | −7.23607 | −0.241068 | ||||||||
\(902\) | 4.82624 | + | 8.14324i | 0.160696 | + | 0.271140i | ||||
\(903\) | −3.38197 | −0.112545 | ||||||||
\(904\) | 3.50000 | + | 2.54290i | 0.116408 | + | 0.0845756i | ||||
\(905\) | −6.47214 | + | 19.9192i | −0.215141 | + | 0.662136i | ||||
\(906\) | −9.23607 | − | 28.4257i | −0.306848 | − | 0.944380i | ||||
\(907\) | −20.9164 | + | 15.1967i | −0.694518 | + | 0.504597i | −0.878142 | − | 0.478400i | \(-0.841217\pi\) |
0.183624 | + | 0.982997i | \(0.441217\pi\) | |||||||
\(908\) | −11.0623 | + | 8.03724i | −0.367116 | + | 0.266725i | ||||
\(909\) | 1.76393 | + | 5.42882i | 0.0585059 | + | 0.180063i | ||||
\(910\) | −1.61803 | + | 4.97980i | −0.0536373 | + | 0.165079i | ||||
\(911\) | −7.70820 | − | 5.60034i | −0.255384 | − | 0.185547i | 0.452725 | − | 0.891650i | \(-0.350452\pi\) |
−0.708110 | + | 0.706102i | \(0.750452\pi\) | |||||||
\(912\) | 12.7082 | 0.420811 | ||||||||
\(913\) | 14.9721 | + | 25.2623i | 0.495505 | + | 0.836059i | ||||
\(914\) | 25.9787 | 0.859299 | ||||||||
\(915\) | 17.9443 | + | 13.0373i | 0.593219 | + | 0.430999i | ||||
\(916\) | 6.90983 | − | 21.2663i | 0.228307 | − | 0.702657i | ||||
\(917\) | 1.57295 | + | 4.84104i | 0.0519434 | + | 0.159865i | ||||
\(918\) | −11.5902 | + | 8.42075i | −0.382533 | + | 0.277926i | ||||
\(919\) | −5.70820 | + | 4.14725i | −0.188296 | + | 0.136805i | −0.677940 | − | 0.735118i | \(-0.737127\pi\) |
0.489643 | + | 0.871923i | \(0.337127\pi\) | |||||||
\(920\) | −0.145898 | − | 0.449028i | −0.00481012 | − | 0.0148040i | ||||
\(921\) | 9.28115 | − | 28.5645i | 0.305824 | − | 0.941231i | ||||
\(922\) | 18.6525 | + | 13.5518i | 0.614287 | + | 0.446305i | ||||
\(923\) | −57.3050 | −1.88622 | ||||||||
\(924\) | −5.23607 | + | 1.17557i | −0.172254 | + | 0.0386734i | ||||
\(925\) | −11.2361 | −0.369440 | ||||||||
\(926\) | −8.85410 | − | 6.43288i | −0.290964 | − | 0.211398i | ||||
\(927\) | 0.708204 | − | 2.17963i | 0.0232605 | − | 0.0715884i | ||||
\(928\) | −1.38197 | − | 4.25325i | −0.0453653 | − | 0.139620i | ||||
\(929\) | −8.82624 | + | 6.41264i | −0.289579 | + | 0.210392i | −0.723085 | − | 0.690759i | \(-0.757276\pi\) |
0.433505 | + | 0.901151i | \(0.357276\pi\) | |||||||
\(930\) | −3.23607 | + | 2.35114i | −0.106115 | + | 0.0770970i | ||||
\(931\) | 2.42705 | + | 7.46969i | 0.0795434 | + | 0.244809i | ||||
\(932\) | 0.208204 | − | 0.640786i | 0.00681995 | − | 0.0209896i | ||||
\(933\) | 2.85410 | + | 2.07363i | 0.0934391 | + | 0.0678875i | ||||
\(934\) | −12.9443 | −0.423550 | ||||||||
\(935\) | −7.97214 | − | 3.44095i | −0.260717 | − | 0.112531i | ||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | 23.0623 | + | 16.7557i | 0.753413 | + | 0.547386i | 0.896883 | − | 0.442268i | \(-0.145826\pi\) |
−0.143470 | + | 0.989655i | \(0.545826\pi\) | |||||||
\(938\) | 1.04508 | − | 3.21644i | 0.0341232 | − | 0.105021i | ||||
\(939\) | −15.6353 | − | 48.1204i | −0.510237 | − | 1.57035i | ||||
\(940\) | 3.85410 | − | 2.80017i | 0.125707 | − | 0.0913314i | ||||
\(941\) | 19.7082 | − | 14.3188i | 0.642469 | − | 0.466781i | −0.218228 | − | 0.975898i | \(-0.570028\pi\) |
0.860698 | + | 0.509117i | \(0.170028\pi\) | |||||||
\(942\) | 7.47214 | + | 22.9969i | 0.243455 | + | 0.749279i | ||||
\(943\) | −0.416408 | + | 1.28157i | −0.0135601 | + | 0.0417337i | ||||
\(944\) | −3.35410 | − | 2.43690i | −0.109167 | − | 0.0793143i | ||||
\(945\) | 5.47214 | 0.178009 | ||||||||
\(946\) | 4.57953 | − | 5.20431i | 0.148893 | − | 0.169207i | ||||
\(947\) | −53.6312 | −1.74278 | −0.871390 | − | 0.490591i | \(-0.836781\pi\) | ||||
−0.871390 | + | 0.490591i | \(0.836781\pi\) | |||||||
\(948\) | −5.23607 | − | 3.80423i | −0.170060 | − | 0.123556i | ||||
\(949\) | −4.61803 | + | 14.2128i | −0.149908 | + | 0.461369i | ||||
\(950\) | −2.42705 | − | 7.46969i | −0.0787439 | − | 0.242349i | ||||
\(951\) | −39.7426 | + | 28.8747i | −1.28874 | + | 0.936327i | ||||
\(952\) | 2.11803 | − | 1.53884i | 0.0686459 | − | 0.0498741i | ||||
\(953\) | 0.263932 | + | 0.812299i | 0.00854960 | + | 0.0263130i | 0.955240 | − | 0.295831i | \(-0.0955965\pi\) |
−0.946691 | + | 0.322144i | \(0.895597\pi\) | |||||||
\(954\) | −0.326238 | + | 1.00406i | −0.0105623 | + | 0.0325075i | ||||
\(955\) | −1.00000 | − | 0.726543i | −0.0323592 | − | 0.0235104i | ||||
\(956\) | 6.29180 | 0.203491 | ||||||||
\(957\) | −2.23607 | + | 23.8949i | −0.0722818 | + | 0.772413i | ||||
\(958\) | −22.2918 | −0.720215 | ||||||||
\(959\) | −3.92705 | − | 2.85317i | −0.126811 | − | 0.0921337i | ||||
\(960\) | −0.500000 | + | 1.53884i | −0.0161374 | + | 0.0496659i | ||||
\(961\) | −7.69098 | − | 23.6704i | −0.248096 | − | 0.763562i | ||||
\(962\) | 47.5967 | − | 34.5811i | 1.53458 | − | 1.11494i | ||||
\(963\) | 0.881966 | − | 0.640786i | 0.0284210 | − | 0.0206490i | ||||
\(964\) | −9.57295 | − | 29.4625i | −0.308324 | − | 0.948923i | ||||
\(965\) | 6.61803 | − | 20.3682i | 0.213042 | − | 0.655676i | ||||
\(966\) | −0.618034 | − | 0.449028i | −0.0198849 | − | 0.0144472i | ||||
\(967\) | 17.3475 | 0.557859 | 0.278929 | − | 0.960312i | \(-0.410020\pi\) | ||||
0.278929 | + | 0.960312i | \(0.410020\pi\) | |||||||
\(968\) | 5.28115 | − | 9.64932i | 0.169743 | − | 0.310141i | ||||
\(969\) | 33.2705 | 1.06880 | ||||||||
\(970\) | 6.78115 | + | 4.92680i | 0.217730 | + | 0.158190i | ||||
\(971\) | −10.7639 | + | 33.1280i | −0.345431 | + | 1.06313i | 0.615922 | + | 0.787807i | \(0.288784\pi\) |
−0.961353 | + | 0.275320i | \(0.911216\pi\) | |||||||
\(972\) | 1.21885 | + | 3.75123i | 0.0390945 | + | 0.120321i | ||||
\(973\) | 4.00000 | − | 2.90617i | 0.128234 | − | 0.0931675i | ||||
\(974\) | 30.8885 | − | 22.4418i | 0.989733 | − | 0.719083i | ||||
\(975\) | −2.61803 | − | 8.05748i | −0.0838442 | − | 0.258046i | ||||
\(976\) | 4.23607 | − | 13.0373i | 0.135593 | − | 0.417313i | ||||
\(977\) | 30.0902 | + | 21.8618i | 0.962670 | + | 0.699421i | 0.953769 | − | 0.300540i | \(-0.0971668\pi\) |
0.00890056 | + | 0.999960i | \(0.497167\pi\) | |||||||
\(978\) | −36.8885 | −1.17957 | ||||||||
\(979\) | 4.59017 | − | 49.0512i | 0.146702 | − | 1.56768i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 1.23607 | + | 0.898056i | 0.0394646 | + | 0.0286727i | ||||
\(982\) | 5.93769 | − | 18.2743i | 0.189479 | − | 0.583158i | ||||
\(983\) | −2.76393 | − | 8.50651i | −0.0881557 | − | 0.271315i | 0.897254 | − | 0.441515i | \(-0.145559\pi\) |
−0.985410 | + | 0.170199i | \(0.945559\pi\) | |||||||
\(984\) | 3.73607 | − | 2.71441i | 0.119101 | − | 0.0865323i | ||||
\(985\) | 9.32624 | − | 6.77591i | 0.297159 | − | 0.215898i | ||||
\(986\) | −3.61803 | − | 11.1352i | −0.115222 | − | 0.354616i | ||||
\(987\) | 2.38197 | − | 7.33094i | 0.0758188 | − | 0.233346i | ||||
\(988\) | 33.2705 | + | 24.1724i | 1.05848 | + | 0.769028i | ||||
\(989\) | 0.986844 | 0.0313798 | ||||||||
\(990\) | −0.836881 | + | 0.951057i | −0.0265978 | + | 0.0302266i | ||||
\(991\) | 34.3607 | 1.09150 | 0.545751 | − | 0.837947i | \(-0.316244\pi\) | ||||
0.545751 | + | 0.837947i | \(0.316244\pi\) | |||||||
\(992\) | 2.00000 | + | 1.45309i | 0.0635001 | + | 0.0461355i | ||||
\(993\) | −0.482779 | + | 1.48584i | −0.0153205 | + | 0.0471517i | ||||
\(994\) | −3.38197 | − | 10.4086i | −0.107269 | − | 0.330141i | ||||
\(995\) | 4.09017 | − | 2.97168i | 0.129667 | − | 0.0942087i | ||||
\(996\) | 11.5902 | − | 8.42075i | 0.367249 | − | 0.266822i | ||||
\(997\) | −15.0902 | − | 46.4428i | −0.477910 | − | 1.47086i | −0.841992 | − | 0.539490i | \(-0.818617\pi\) |
0.364081 | − | 0.931367i | \(-0.381383\pi\) | |||||||
\(998\) | 6.17376 | − | 19.0009i | 0.195427 | − | 0.601463i | ||||
\(999\) | −49.7426 | − | 36.1401i | −1.57379 | − | 1.14342i |
(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 | 770.2.n.d.631.1 | yes | 4 | |
11.3 | even | 5 | inner | 770.2.n.d.421.1 | ✓ | 4 | |
11.5 | even | 5 | 8470.2.a.bp.1.2 | 2 | |||
11.6 | odd | 10 | 8470.2.a.cb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.d.421.1 | ✓ | 4 | 11.3 | even | 5 | inner | |
770.2.n.d.631.1 | yes | 4 | 1.1 | even | 1 | trivial | |
8470.2.a.bp.1.2 | 2 | 11.5 | even | 5 | |||
8470.2.a.cb.1.2 | 2 | 11.6 | odd | 10 |