Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(109,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.z (of order \(10\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(0.951057 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.349 |
Dual form | 930.2.z.a.469.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.951057 | − | 0.309017i | −0.672499 | − | 0.218508i | ||||
\(3\) | 0.951057 | − | 0.309017i | 0.549093 | − | 0.178411i | ||||
\(4\) | 0.809017 | + | 0.587785i | 0.404508 | + | 0.293893i | ||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.726543 | + | 1.00000i | −0.274607 | + | 0.377964i | −0.923938 | − | 0.382541i | \(-0.875049\pi\) |
0.649331 | + | 0.760506i | \(0.275049\pi\) | |||||||
\(8\) | −0.587785 | − | 0.809017i | −0.207813 | − | 0.286031i | ||||
\(9\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | ||||
\(10\) | 2.12663 | + | 0.690983i | 0.672499 | + | 0.218508i | ||||
\(11\) | 1.92705 | + | 1.40008i | 0.581028 | + | 0.422141i | 0.839094 | − | 0.543986i | \(-0.183085\pi\) |
−0.258067 | + | 0.966127i | \(0.583085\pi\) | |||||||
\(12\) | 0.951057 | + | 0.309017i | 0.274546 | + | 0.0892055i | ||||
\(13\) | −0.138757 | + | 0.0450850i | −0.0384843 | + | 0.0125043i | −0.328196 | − | 0.944610i | \(-0.606441\pi\) |
0.289712 | + | 0.957114i | \(0.406441\pi\) | |||||||
\(14\) | 1.00000 | − | 0.726543i | 0.267261 | − | 0.194177i | ||||
\(15\) | −2.12663 | + | 0.690983i | −0.549093 | + | 0.178411i | ||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −1.08981 | − | 1.50000i | −0.264319 | − | 0.363803i | 0.656143 | − | 0.754637i | \(-0.272187\pi\) |
−0.920461 | + | 0.390833i | \(0.872187\pi\) | |||||||
\(18\) | −0.951057 | + | 0.309017i | −0.224166 | + | 0.0728360i | ||||
\(19\) | −1.38197 | + | 4.25325i | −0.317045 | + | 0.975763i | 0.657860 | + | 0.753140i | \(0.271462\pi\) |
−0.974905 | + | 0.222623i | \(0.928538\pi\) | |||||||
\(20\) | −1.80902 | − | 1.31433i | −0.404508 | − | 0.293893i | ||||
\(21\) | −0.381966 | + | 1.17557i | −0.0833518 | + | 0.256531i | ||||
\(22\) | −1.40008 | − | 1.92705i | −0.298499 | − | 0.410849i | ||||
\(23\) | −3.44095 | − | 4.73607i | −0.717489 | − | 0.987538i | −0.999603 | − | 0.0281578i | \(-0.991036\pi\) |
0.282115 | − | 0.959381i | \(-0.408964\pi\) | |||||||
\(24\) | −0.809017 | − | 0.587785i | −0.165140 | − | 0.119981i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0.145898 | 0.0286130 | ||||||||
\(27\) | 0.587785 | − | 0.809017i | 0.113119 | − | 0.155695i | ||||
\(28\) | −1.17557 | + | 0.381966i | −0.222162 | + | 0.0721848i | ||||
\(29\) | −2.11803 | + | 6.51864i | −0.393309 | + | 1.21048i | 0.536962 | + | 0.843607i | \(0.319572\pi\) |
−0.930271 | + | 0.366874i | \(0.880428\pi\) | |||||||
\(30\) | 2.23607 | 0.408248 | ||||||||
\(31\) | −2.19098 | + | 5.11855i | −0.393512 | + | 0.919319i | ||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 2.26538 | + | 0.736068i | 0.394353 | + | 0.128133i | ||||
\(34\) | 0.572949 | + | 1.76336i | 0.0982599 | + | 0.302413i | ||||
\(35\) | 1.62460 | − | 2.23607i | 0.274607 | − | 0.377964i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.8541i | 1.78440i | 0.451637 | + | 0.892202i | \(0.350840\pi\) | ||||
−0.451637 | + | 0.892202i | \(0.649160\pi\) | |||||||
\(38\) | 2.62866 | − | 3.61803i | 0.426424 | − | 0.586923i | ||||
\(39\) | −0.118034 | + | 0.0857567i | −0.0189006 | + | 0.0137321i | ||||
\(40\) | 1.31433 | + | 1.80902i | 0.207813 | + | 0.286031i | ||||
\(41\) | −2.38197 | + | 7.33094i | −0.372001 | + | 1.14490i | 0.573479 | + | 0.819220i | \(0.305593\pi\) |
−0.945480 | + | 0.325680i | \(0.894407\pi\) | |||||||
\(42\) | 0.726543 | − | 1.00000i | 0.112108 | − | 0.154303i | ||||
\(43\) | 3.80423 | + | 1.23607i | 0.580139 | + | 0.188499i | 0.584363 | − | 0.811492i | \(-0.301344\pi\) |
−0.00422383 | + | 0.999991i | \(0.501344\pi\) | |||||||
\(44\) | 0.736068 | + | 2.26538i | 0.110966 | + | 0.341520i | ||||
\(45\) | −1.80902 | + | 1.31433i | −0.269672 | + | 0.195928i | ||||
\(46\) | 1.80902 | + | 5.56758i | 0.266725 | + | 0.820895i | ||||
\(47\) | −2.93893 | + | 0.954915i | −0.428686 | + | 0.139289i | −0.515410 | − | 0.856944i | \(-0.672360\pi\) |
0.0867235 | + | 0.996232i | \(0.472360\pi\) | |||||||
\(48\) | 0.587785 | + | 0.809017i | 0.0848395 | + | 0.116772i | ||||
\(49\) | 1.69098 | + | 5.20431i | 0.241569 | + | 0.743473i | ||||
\(50\) | −4.75528 | − | 1.54508i | −0.672499 | − | 0.218508i | ||||
\(51\) | −1.50000 | − | 1.08981i | −0.210042 | − | 0.152604i | ||||
\(52\) | −0.138757 | − | 0.0450850i | −0.0192422 | − | 0.00625216i | ||||
\(53\) | −4.53077 | − | 6.23607i | −0.622349 | − | 0.856590i | 0.375172 | − | 0.926955i | \(-0.377584\pi\) |
−0.997521 | + | 0.0703653i | \(0.977584\pi\) | |||||||
\(54\) | −0.809017 | + | 0.587785i | −0.110093 | + | 0.0799874i | ||||
\(55\) | −4.30902 | − | 3.13068i | −0.581028 | − | 0.422141i | ||||
\(56\) | 1.23607 | 0.165177 | ||||||||
\(57\) | 4.47214i | 0.592349i | ||||||||
\(58\) | 4.02874 | − | 5.54508i | 0.528999 | − | 0.728105i | ||||
\(59\) | 0.972136 | + | 2.99193i | 0.126561 | + | 0.389516i | 0.994182 | − | 0.107710i | \(-0.0343519\pi\) |
−0.867621 | + | 0.497226i | \(0.834352\pi\) | |||||||
\(60\) | −2.12663 | − | 0.690983i | −0.274546 | − | 0.0892055i | ||||
\(61\) | 2.76393 | 0.353885 | 0.176943 | − | 0.984221i | \(-0.443379\pi\) | ||||
0.176943 | + | 0.984221i | \(0.443379\pi\) | |||||||
\(62\) | 3.66547 | − | 4.19098i | 0.465515 | − | 0.532255i | ||||
\(63\) | 1.23607i | 0.155730i | ||||||||
\(64\) | −0.309017 | + | 0.951057i | −0.0386271 | + | 0.118882i | ||||
\(65\) | 0.310271 | − | 0.100813i | 0.0384843 | − | 0.0125043i | ||||
\(66\) | −1.92705 | − | 1.40008i | −0.237204 | − | 0.172338i | ||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | − | 1.85410i | − | 0.224843i | ||||||
\(69\) | −4.73607 | − | 3.44095i | −0.570156 | − | 0.414242i | ||||
\(70\) | −2.23607 | + | 1.62460i | −0.267261 | + | 0.194177i | ||||
\(71\) | 3.23607 | − | 2.35114i | 0.384051 | − | 0.279029i | −0.378963 | − | 0.925412i | \(-0.623719\pi\) |
0.763013 | + | 0.646383i | \(0.223719\pi\) | |||||||
\(72\) | −0.951057 | − | 0.309017i | −0.112083 | − | 0.0364180i | ||||
\(73\) | 1.73060 | − | 2.38197i | 0.202551 | − | 0.278788i | −0.695642 | − | 0.718389i | \(-0.744880\pi\) |
0.898193 | + | 0.439601i | \(0.144880\pi\) | |||||||
\(74\) | 3.35410 | − | 10.3229i | 0.389906 | − | 1.20001i | ||||
\(75\) | 4.75528 | − | 1.54508i | 0.549093 | − | 0.178411i | ||||
\(76\) | −3.61803 | + | 2.62866i | −0.415017 | + | 0.301527i | ||||
\(77\) | −2.80017 | + | 0.909830i | −0.319109 | + | 0.103685i | ||||
\(78\) | 0.138757 | − | 0.0450850i | 0.0157112 | − | 0.00510487i | ||||
\(79\) | 4.92705 | − | 3.57971i | 0.554337 | − | 0.402749i | −0.275045 | − | 0.961431i | \(-0.588693\pi\) |
0.829382 | + | 0.558682i | \(0.188693\pi\) | |||||||
\(80\) | −0.690983 | − | 2.12663i | −0.0772542 | − | 0.237764i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 4.53077 | − | 6.23607i | 0.500340 | − | 0.688659i | ||||
\(83\) | −2.62866 | − | 0.854102i | −0.288532 | − | 0.0937499i | 0.161175 | − | 0.986926i | \(-0.448472\pi\) |
−0.449707 | + | 0.893176i | \(0.648472\pi\) | |||||||
\(84\) | −1.00000 | + | 0.726543i | −0.109109 | + | 0.0792723i | ||||
\(85\) | 2.43690 | + | 3.35410i | 0.264319 | + | 0.363803i | ||||
\(86\) | −3.23607 | − | 2.35114i | −0.348954 | − | 0.253530i | ||||
\(87\) | 6.85410i | 0.734837i | ||||||||
\(88\) | − | 2.38197i | − | 0.253918i | ||||||
\(89\) | 1.85410 | + | 1.34708i | 0.196534 | + | 0.142791i | 0.681700 | − | 0.731632i | \(-0.261241\pi\) |
−0.485166 | + | 0.874422i | \(0.661241\pi\) | |||||||
\(90\) | 2.12663 | − | 0.690983i | 0.224166 | − | 0.0728360i | ||||
\(91\) | 0.0557281 | − | 0.171513i | 0.00584189 | − | 0.0179795i | ||||
\(92\) | − | 5.85410i | − | 0.610332i | ||||||
\(93\) | −0.502029 | + | 5.54508i | −0.0520579 | + | 0.574999i | ||||
\(94\) | 3.09017 | 0.318727 | ||||||||
\(95\) | 3.09017 | − | 9.51057i | 0.317045 | − | 0.975763i | ||||
\(96\) | −0.309017 | − | 0.951057i | −0.0315389 | − | 0.0970668i | ||||
\(97\) | 0.555029 | − | 0.763932i | 0.0563547 | − | 0.0775655i | −0.779910 | − | 0.625892i | \(-0.784735\pi\) |
0.836264 | + | 0.548327i | \(0.184735\pi\) | |||||||
\(98\) | − | 5.47214i | − | 0.552769i | ||||||
\(99\) | 2.38197 | 0.239397 | ||||||||
\(100\) | 4.04508 | + | 2.93893i | 0.404508 | + | 0.293893i | ||||
\(101\) | −6.16312 | + | 4.47777i | −0.613253 | + | 0.445555i | −0.850558 | − | 0.525881i | \(-0.823736\pi\) |
0.237305 | + | 0.971435i | \(0.423736\pi\) | |||||||
\(102\) | 1.08981 | + | 1.50000i | 0.107908 | + | 0.148522i | ||||
\(103\) | −7.77997 | − | 2.52786i | −0.766583 | − | 0.249078i | −0.100481 | − | 0.994939i | \(-0.532038\pi\) |
−0.666102 | + | 0.745861i | \(0.732038\pi\) | |||||||
\(104\) | 0.118034 | + | 0.0857567i | 0.0115742 | + | 0.00840914i | ||||
\(105\) | 0.854102 | − | 2.62866i | 0.0833518 | − | 0.256531i | ||||
\(106\) | 2.38197 | + | 7.33094i | 0.231357 | + | 0.712044i | ||||
\(107\) | 9.23305 | + | 12.7082i | 0.892593 | + | 1.22855i | 0.972771 | + | 0.231768i | \(0.0744510\pi\) |
−0.0801784 | + | 0.996781i | \(0.525549\pi\) | |||||||
\(108\) | 0.951057 | − | 0.309017i | 0.0915155 | − | 0.0297352i | ||||
\(109\) | −3.85410 | − | 11.8617i | −0.369156 | − | 1.13615i | −0.947337 | − | 0.320237i | \(-0.896237\pi\) |
0.578181 | − | 0.815908i | \(-0.303763\pi\) | |||||||
\(110\) | 3.13068 | + | 4.30902i | 0.298499 | + | 0.410849i | ||||
\(111\) | 3.35410 | + | 10.3229i | 0.318357 | + | 0.979803i | ||||
\(112\) | −1.17557 | − | 0.381966i | −0.111081 | − | 0.0360924i | ||||
\(113\) | −4.97980 | + | 6.85410i | −0.468460 | + | 0.644780i | −0.976236 | − | 0.216709i | \(-0.930468\pi\) |
0.507776 | + | 0.861489i | \(0.330468\pi\) | |||||||
\(114\) | 1.38197 | − | 4.25325i | 0.129433 | − | 0.398354i | ||||
\(115\) | 7.69421 | + | 10.5902i | 0.717489 | + | 0.987538i | ||||
\(116\) | −5.54508 | + | 4.02874i | −0.514848 | + | 0.374059i | ||||
\(117\) | −0.0857567 | + | 0.118034i | −0.00792821 | + | 0.0109122i | ||||
\(118\) | − | 3.14590i | − | 0.289603i | ||||||
\(119\) | 2.29180 | 0.210089 | ||||||||
\(120\) | 1.80902 | + | 1.31433i | 0.165140 | + | 0.119981i | ||||
\(121\) | −1.64590 | − | 5.06555i | −0.149627 | − | 0.460505i | ||||
\(122\) | −2.62866 | − | 0.854102i | −0.237987 | − | 0.0773268i | ||||
\(123\) | 7.70820i | 0.695025i | ||||||||
\(124\) | −4.78115 | + | 2.85317i | −0.429360 | + | 0.256222i | ||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0.381966 | − | 1.17557i | 0.0340282 | − | 0.104728i | ||||
\(127\) | −15.9434 | + | 5.18034i | −1.41475 | + | 0.459681i | −0.913931 | − | 0.405870i | \(-0.866969\pi\) |
−0.500821 | + | 0.865551i | \(0.666969\pi\) | |||||||
\(128\) | 0.587785 | − | 0.809017i | 0.0519534 | − | 0.0715077i | ||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | −0.326238 | −0.0286130 | ||||||||
\(131\) | 4.69098 | + | 3.40820i | 0.409853 | + | 0.297776i | 0.773542 | − | 0.633745i | \(-0.218483\pi\) |
−0.363689 | + | 0.931520i | \(0.618483\pi\) | |||||||
\(132\) | 1.40008 | + | 1.92705i | 0.121862 | + | 0.167728i | ||||
\(133\) | −3.24920 | − | 4.47214i | −0.281741 | − | 0.387783i | ||||
\(134\) | 2.47214 | − | 7.60845i | 0.213560 | − | 0.657270i | ||||
\(135\) | −1.31433 | + | 1.80902i | −0.113119 | + | 0.155695i | ||||
\(136\) | −0.572949 | + | 1.76336i | −0.0491300 | + | 0.151207i | ||||
\(137\) | 8.95554 | − | 2.90983i | 0.765123 | − | 0.248604i | 0.0996471 | − | 0.995023i | \(-0.468229\pi\) |
0.665476 | + | 0.746419i | \(0.268229\pi\) | |||||||
\(138\) | 3.44095 | + | 4.73607i | 0.292914 | + | 0.403161i | ||||
\(139\) | −0.909830 | − | 2.80017i | −0.0771708 | − | 0.237507i | 0.905028 | − | 0.425352i | \(-0.139850\pi\) |
−0.982199 | + | 0.187845i | \(0.939850\pi\) | |||||||
\(140\) | 2.62866 | − | 0.854102i | 0.222162 | − | 0.0721848i | ||||
\(141\) | −2.50000 | + | 1.81636i | −0.210538 | + | 0.152965i | ||||
\(142\) | −3.80423 | + | 1.23607i | −0.319244 | + | 0.103729i | ||||
\(143\) | −0.330515 | − | 0.107391i | −0.0276391 | − | 0.00898048i | ||||
\(144\) | 0.809017 | + | 0.587785i | 0.0674181 | + | 0.0489821i | ||||
\(145\) | 4.73607 | − | 14.5761i | 0.393309 | − | 1.21048i | ||||
\(146\) | −2.38197 | + | 1.73060i | −0.197133 | + | 0.143225i | ||||
\(147\) | 3.21644 | + | 4.42705i | 0.265288 | + | 0.365137i | ||||
\(148\) | −6.37988 | + | 8.78115i | −0.524423 | + | 0.721806i | ||||
\(149\) | 14.6180 | 1.19756 | 0.598778 | − | 0.800915i | \(-0.295653\pi\) | ||||
0.598778 | + | 0.800915i | \(0.295653\pi\) | |||||||
\(150\) | −5.00000 | −0.408248 | ||||||||
\(151\) | 14.4721 | + | 10.5146i | 1.17773 | + | 0.855668i | 0.991913 | − | 0.126917i | \(-0.0405083\pi\) |
0.185812 | + | 0.982585i | \(0.440508\pi\) | |||||||
\(152\) | 4.25325 | − | 1.38197i | 0.344984 | − | 0.112092i | ||||
\(153\) | −1.76336 | − | 0.572949i | −0.142559 | − | 0.0463202i | ||||
\(154\) | 2.94427 | 0.237256 | ||||||||
\(155\) | 4.89919 | − | 11.4454i | 0.393512 | − | 0.919319i | ||||
\(156\) | −0.145898 | −0.0116812 | ||||||||
\(157\) | 16.2537 | + | 5.28115i | 1.29719 | + | 0.421482i | 0.874602 | − | 0.484841i | \(-0.161123\pi\) |
0.422586 | + | 0.906323i | \(0.361123\pi\) | |||||||
\(158\) | −5.79210 | + | 1.88197i | −0.460794 | + | 0.149721i | ||||
\(159\) | −6.23607 | − | 4.53077i | −0.494552 | − | 0.359313i | ||||
\(160\) | 2.23607i | 0.176777i | ||||||||
\(161\) | 7.23607 | 0.570282 | ||||||||
\(162\) | −0.587785 | + | 0.809017i | −0.0461808 | + | 0.0635624i | ||||
\(163\) | −7.66145 | − | 10.5451i | −0.600091 | − | 0.825955i | 0.395625 | − | 0.918412i | \(-0.370528\pi\) |
−0.995717 | + | 0.0924572i | \(0.970528\pi\) | |||||||
\(164\) | −6.23607 | + | 4.53077i | −0.486955 | + | 0.353794i | ||||
\(165\) | −5.06555 | − | 1.64590i | −0.394353 | − | 0.128133i | ||||
\(166\) | 2.23607 | + | 1.62460i | 0.173553 | + | 0.126093i | ||||
\(167\) | −13.4005 | − | 4.35410i | −1.03697 | − | 0.336931i | −0.259425 | − | 0.965763i | \(-0.583533\pi\) |
−0.777541 | + | 0.628833i | \(0.783533\pi\) | |||||||
\(168\) | 1.17557 | − | 0.381966i | 0.0906972 | − | 0.0294693i | ||||
\(169\) | −10.5000 | + | 7.62870i | −0.807692 | + | 0.586823i | ||||
\(170\) | −1.28115 | − | 3.94298i | −0.0982599 | − | 0.302413i | ||||
\(171\) | 1.38197 | + | 4.25325i | 0.105682 | + | 0.325254i | ||||
\(172\) | 2.35114 | + | 3.23607i | 0.179273 | + | 0.246748i | ||||
\(173\) | 11.5842 | − | 3.76393i | 0.880730 | − | 0.286166i | 0.166469 | − | 0.986047i | \(-0.446763\pi\) |
0.714260 | + | 0.699880i | \(0.246763\pi\) | |||||||
\(174\) | 2.11803 | − | 6.51864i | 0.160568 | − | 0.494177i | ||||
\(175\) | −3.63271 | + | 5.00000i | −0.274607 | + | 0.377964i | ||||
\(176\) | −0.736068 | + | 2.26538i | −0.0554832 | + | 0.170760i | ||||
\(177\) | 1.84911 | + | 2.54508i | 0.138988 | + | 0.191300i | ||||
\(178\) | −1.34708 | − | 1.85410i | −0.100968 | − | 0.138971i | ||||
\(179\) | −16.5902 | − | 12.0535i | −1.24001 | − | 0.900918i | −0.242409 | − | 0.970174i | \(-0.577937\pi\) |
−0.997599 | + | 0.0692560i | \(0.977937\pi\) | |||||||
\(180\) | −2.23607 | −0.166667 | ||||||||
\(181\) | −13.2361 | −0.983829 | −0.491915 | − | 0.870643i | \(-0.663703\pi\) | ||||
−0.491915 | + | 0.870643i | \(0.663703\pi\) | |||||||
\(182\) | −0.106001 | + | 0.145898i | −0.00785733 | + | 0.0108147i | ||||
\(183\) | 2.62866 | − | 0.854102i | 0.194316 | − | 0.0631370i | ||||
\(184\) | −1.80902 | + | 5.56758i | −0.133363 | + | 0.410448i | ||||
\(185\) | − | 24.2705i | − | 1.78440i | ||||||
\(186\) | 2.19098 | − | 5.11855i | 0.160651 | − | 0.375311i | ||||
\(187\) | − | 4.41641i | − | 0.322960i | ||||||
\(188\) | −2.93893 | − | 0.954915i | −0.214343 | − | 0.0696443i | ||||
\(189\) | 0.381966 | + | 1.17557i | 0.0277839 | + | 0.0855102i | ||||
\(190\) | −5.87785 | + | 8.09017i | −0.426424 | + | 0.586923i | ||||
\(191\) | −7.23607 | −0.523584 | −0.261792 | − | 0.965124i | \(-0.584313\pi\) | ||||
−0.261792 | + | 0.965124i | \(0.584313\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 10.4086 | − | 14.3262i | 0.749229 | − | 1.03123i | −0.248805 | − | 0.968554i | \(-0.580038\pi\) |
0.998034 | − | 0.0626716i | \(-0.0199621\pi\) | |||||||
\(194\) | −0.763932 | + | 0.555029i | −0.0548471 | + | 0.0398488i | ||||
\(195\) | 0.263932 | − | 0.191758i | 0.0189006 | − | 0.0137321i | ||||
\(196\) | −1.69098 | + | 5.20431i | −0.120785 | + | 0.371736i | ||||
\(197\) | −4.08174 | + | 5.61803i | −0.290812 | + | 0.400268i | −0.929278 | − | 0.369382i | \(-0.879569\pi\) |
0.638466 | + | 0.769650i | \(0.279569\pi\) | |||||||
\(198\) | −2.26538 | − | 0.736068i | −0.160994 | − | 0.0523101i | ||||
\(199\) | −7.29837 | − | 22.4621i | −0.517368 | − | 1.59229i | −0.778932 | − | 0.627109i | \(-0.784238\pi\) |
0.261564 | − | 0.965186i | \(-0.415762\pi\) | |||||||
\(200\) | −2.93893 | − | 4.04508i | −0.207813 | − | 0.286031i | ||||
\(201\) | 2.47214 | + | 7.60845i | 0.174371 | + | 0.536659i | ||||
\(202\) | 7.24518 | − | 2.35410i | 0.509769 | − | 0.165634i | ||||
\(203\) | −4.97980 | − | 6.85410i | −0.349513 | − | 0.481064i | ||||
\(204\) | −0.572949 | − | 1.76336i | −0.0401145 | − | 0.123460i | ||||
\(205\) | 5.32624 | − | 16.3925i | 0.372001 | − | 1.14490i | ||||
\(206\) | 6.61803 | + | 4.80828i | 0.461100 | + | 0.335009i | ||||
\(207\) | −5.56758 | − | 1.80902i | −0.386974 | − | 0.125735i | ||||
\(208\) | −0.0857567 | − | 0.118034i | −0.00594616 | − | 0.00818418i | ||||
\(209\) | −8.61803 | + | 6.26137i | −0.596122 | + | 0.433108i | ||||
\(210\) | −1.62460 | + | 2.23607i | −0.112108 | + | 0.154303i | ||||
\(211\) | 12.6525 | 0.871032 | 0.435516 | − | 0.900181i | \(-0.356566\pi\) | ||||
0.435516 | + | 0.900181i | \(0.356566\pi\) | |||||||
\(212\) | − | 7.70820i | − | 0.529402i | ||||||
\(213\) | 2.35114 | − | 3.23607i | 0.161098 | − | 0.221732i | ||||
\(214\) | −4.85410 | − | 14.9394i | −0.331820 | − | 1.02124i | ||||
\(215\) | −8.50651 | − | 2.76393i | −0.580139 | − | 0.188499i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.52671 | − | 5.90983i | −0.239409 | − | 0.401185i | ||||
\(218\) | 12.4721i | 0.844720i | ||||||||
\(219\) | 0.909830 | − | 2.80017i | 0.0614806 | − | 0.189218i | ||||
\(220\) | −1.64590 | − | 5.06555i | −0.110966 | − | 0.341520i | ||||
\(221\) | 0.218847 | + | 0.159002i | 0.0147212 | + | 0.0106956i | ||||
\(222\) | − | 10.8541i | − | 0.728480i | ||||||
\(223\) | 25.8885i | 1.73363i | 0.498634 | + | 0.866813i | \(0.333835\pi\) | ||||
−0.498634 | + | 0.866813i | \(0.666165\pi\) | |||||||
\(224\) | 1.00000 | + | 0.726543i | 0.0668153 | + | 0.0485442i | ||||
\(225\) | 4.04508 | − | 2.93893i | 0.269672 | − | 0.195928i | ||||
\(226\) | 6.85410 | − | 4.97980i | 0.455928 | − | 0.331251i | ||||
\(227\) | −5.42882 | − | 1.76393i | −0.360324 | − | 0.117076i | 0.123260 | − | 0.992374i | \(-0.460665\pi\) |
−0.483584 | + | 0.875298i | \(0.660665\pi\) | |||||||
\(228\) | −2.62866 | + | 3.61803i | −0.174087 | + | 0.239610i | ||||
\(229\) | 7.90983 | − | 24.3440i | 0.522696 | − | 1.60869i | −0.246131 | − | 0.969237i | \(-0.579159\pi\) |
0.768827 | − | 0.639457i | \(-0.220841\pi\) | |||||||
\(230\) | −4.04508 | − | 12.4495i | −0.266725 | − | 0.820895i | ||||
\(231\) | −2.38197 | + | 1.73060i | −0.156722 | + | 0.113865i | ||||
\(232\) | 6.51864 | − | 2.11803i | 0.427970 | − | 0.139056i | ||||
\(233\) | 12.0005 | − | 3.89919i | 0.786176 | − | 0.255444i | 0.111701 | − | 0.993742i | \(-0.464370\pi\) |
0.674475 | + | 0.738298i | \(0.264370\pi\) | |||||||
\(234\) | 0.118034 | − | 0.0857567i | 0.00771612 | − | 0.00560609i | ||||
\(235\) | 6.57164 | − | 2.13525i | 0.428686 | − | 0.139289i | ||||
\(236\) | −0.972136 | + | 2.99193i | −0.0632807 | + | 0.194758i | ||||
\(237\) | 3.57971 | − | 4.92705i | 0.232527 | − | 0.320046i | ||||
\(238\) | −2.17963 | − | 0.708204i | −0.141284 | − | 0.0459060i | ||||
\(239\) | 12.2361 | − | 8.89002i | 0.791485 | − | 0.575048i | −0.116918 | − | 0.993142i | \(-0.537302\pi\) |
0.908404 | + | 0.418094i | \(0.137302\pi\) | |||||||
\(240\) | −1.31433 | − | 1.80902i | −0.0848395 | − | 0.116772i | ||||
\(241\) | −5.97214 | − | 4.33901i | −0.384699 | − | 0.279500i | 0.378581 | − | 0.925568i | \(-0.376412\pi\) |
−0.763280 | + | 0.646068i | \(0.776412\pi\) | |||||||
\(242\) | 5.32624i | 0.342384i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 2.23607 | + | 1.62460i | 0.143150 | + | 0.104004i | ||||
\(245\) | −3.78115 | − | 11.6372i | −0.241569 | − | 0.743473i | ||||
\(246\) | 2.38197 | − | 7.33094i | 0.151869 | − | 0.467404i | ||||
\(247\) | − | 0.652476i | − | 0.0415160i | ||||||
\(248\) | 5.42882 | − | 1.23607i | 0.344731 | − | 0.0784904i | ||||
\(249\) | −2.76393 | −0.175157 | ||||||||
\(250\) | 10.6331 | + | 3.45492i | 0.672499 | + | 0.218508i | ||||
\(251\) | −4.04508 | − | 12.4495i | −0.255323 | − | 0.785805i | −0.993766 | − | 0.111488i | \(-0.964438\pi\) |
0.738442 | − | 0.674317i | \(-0.235562\pi\) | |||||||
\(252\) | −0.726543 | + | 1.00000i | −0.0457679 | + | 0.0629941i | ||||
\(253\) | − | 13.9443i | − | 0.876669i | ||||||
\(254\) | 16.7639 | 1.05186 | ||||||||
\(255\) | 3.35410 | + | 2.43690i | 0.210042 | + | 0.152604i | ||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | −8.00448 | − | 11.0172i | −0.499306 | − | 0.687235i | 0.482765 | − | 0.875750i | \(-0.339633\pi\) |
−0.982070 | + | 0.188515i | \(0.939633\pi\) | |||||||
\(258\) | −3.80423 | − | 1.23607i | −0.236841 | − | 0.0769542i | ||||
\(259\) | −10.8541 | − | 7.88597i | −0.674441 | − | 0.490010i | ||||
\(260\) | 0.310271 | + | 0.100813i | 0.0192422 | + | 0.00625216i | ||||
\(261\) | 2.11803 | + | 6.51864i | 0.131103 | + | 0.403494i | ||||
\(262\) | −3.40820 | − | 4.69098i | −0.210559 | − | 0.289810i | ||||
\(263\) | −6.34712 | + | 2.06231i | −0.391380 | + | 0.127167i | −0.498095 | − | 0.867122i | \(-0.665967\pi\) |
0.106714 | + | 0.994290i | \(0.465967\pi\) | |||||||
\(264\) | −0.736068 | − | 2.26538i | −0.0453019 | − | 0.139425i | ||||
\(265\) | 10.1311 | + | 13.9443i | 0.622349 | + | 0.856590i | ||||
\(266\) | 1.70820 | + | 5.25731i | 0.104737 | + | 0.322346i | ||||
\(267\) | 2.17963 | + | 0.708204i | 0.133391 | + | 0.0433414i | ||||
\(268\) | −4.70228 | + | 6.47214i | −0.287238 | + | 0.395349i | ||||
\(269\) | −3.10081 | + | 9.54332i | −0.189060 | + | 0.581867i | −0.999995 | − | 0.00327003i | \(-0.998959\pi\) |
0.810935 | + | 0.585137i | \(0.198959\pi\) | |||||||
\(270\) | 1.80902 | − | 1.31433i | 0.110093 | − | 0.0799874i | ||||
\(271\) | −16.2082 | + | 11.7759i | −0.984578 | + | 0.715338i | −0.958727 | − | 0.284328i | \(-0.908230\pi\) |
−0.0258512 | + | 0.999666i | \(0.508230\pi\) | |||||||
\(272\) | 1.08981 | − | 1.50000i | 0.0660797 | − | 0.0909509i | ||||
\(273\) | − | 0.180340i | − | 0.0109147i | ||||||
\(274\) | −9.41641 | −0.568866 | ||||||||
\(275\) | 9.63525 | + | 7.00042i | 0.581028 | + | 0.422141i | ||||
\(276\) | −1.80902 | − | 5.56758i | −0.108890 | − | 0.335129i | ||||
\(277\) | 3.38795 | + | 1.10081i | 0.203562 | + | 0.0661414i | 0.409024 | − | 0.912524i | \(-0.365869\pi\) |
−0.205461 | + | 0.978665i | \(0.565869\pi\) | |||||||
\(278\) | 2.94427i | 0.176586i | ||||||||
\(279\) | 1.23607 | + | 5.42882i | 0.0740015 | + | 0.325015i | ||||
\(280\) | −2.76393 | −0.165177 | ||||||||
\(281\) | −3.81966 | + | 11.7557i | −0.227862 | + | 0.701287i | 0.770127 | + | 0.637891i | \(0.220193\pi\) |
−0.997988 | + | 0.0633956i | \(0.979807\pi\) | |||||||
\(282\) | 2.93893 | − | 0.954915i | 0.175011 | − | 0.0568644i | ||||
\(283\) | 6.06961 | − | 8.35410i | 0.360801 | − | 0.496600i | −0.589571 | − | 0.807717i | \(-0.700703\pi\) |
0.950372 | + | 0.311117i | \(0.100703\pi\) | |||||||
\(284\) | 4.00000 | 0.237356 | ||||||||
\(285\) | − | 10.0000i | − | 0.592349i | ||||||
\(286\) | 0.281153 | + | 0.204270i | 0.0166249 | + | 0.0120787i | ||||
\(287\) | −5.60034 | − | 7.70820i | −0.330577 | − | 0.455001i | ||||
\(288\) | −0.587785 | − | 0.809017i | −0.0346356 | − | 0.0476718i | ||||
\(289\) | 4.19098 | − | 12.8985i | 0.246528 | − | 0.758736i | ||||
\(290\) | −9.00854 | + | 12.3992i | −0.528999 | + | 0.728105i | ||||
\(291\) | 0.291796 | − | 0.898056i | 0.0171054 | − | 0.0526450i | ||||
\(292\) | 2.80017 | − | 0.909830i | 0.163867 | − | 0.0532438i | ||||
\(293\) | −3.97574 | − | 5.47214i | −0.232265 | − | 0.319686i | 0.676937 | − | 0.736041i | \(-0.263307\pi\) |
−0.909202 | + | 0.416356i | \(0.863307\pi\) | |||||||
\(294\) | −1.69098 | − | 5.20431i | −0.0986201 | − | 0.303522i | ||||
\(295\) | −2.17376 | − | 6.69015i | −0.126561 | − | 0.389516i | ||||
\(296\) | 8.78115 | − | 6.37988i | 0.510394 | − | 0.370823i | ||||
\(297\) | 2.26538 | − | 0.736068i | 0.131451 | − | 0.0427110i | ||||
\(298\) | −13.9026 | − | 4.51722i | −0.805355 | − | 0.261676i | ||||
\(299\) | 0.690983 | + | 0.502029i | 0.0399606 | + | 0.0290331i | ||||
\(300\) | 4.75528 | + | 1.54508i | 0.274546 | + | 0.0892055i | ||||
\(301\) | −4.00000 | + | 2.90617i | −0.230556 | + | 0.167509i | ||||
\(302\) | −10.5146 | − | 14.4721i | −0.605049 | − | 0.832778i | ||||
\(303\) | −4.47777 | + | 6.16312i | −0.257241 | + | 0.354062i | ||||
\(304\) | −4.47214 | −0.256495 | ||||||||
\(305\) | −6.18034 | −0.353885 | ||||||||
\(306\) | 1.50000 | + | 1.08981i | 0.0857493 | + | 0.0623005i | ||||
\(307\) | −6.96767 | + | 2.26393i | −0.397666 | + | 0.129209i | −0.501021 | − | 0.865435i | \(-0.667042\pi\) |
0.103355 | + | 0.994644i | \(0.467042\pi\) | |||||||
\(308\) | −2.80017 | − | 0.909830i | −0.159554 | − | 0.0518424i | ||||
\(309\) | −8.18034 | −0.465363 | ||||||||
\(310\) | −8.19624 | + | 9.37132i | −0.465515 | + | 0.532255i | ||||
\(311\) | 13.4164 | 0.760775 | 0.380387 | − | 0.924827i | \(-0.375791\pi\) | ||||
0.380387 | + | 0.924827i | \(0.375791\pi\) | |||||||
\(312\) | 0.138757 | + | 0.0450850i | 0.00785558 | + | 0.00255243i | ||||
\(313\) | 4.97980 | − | 1.61803i | 0.281475 | − | 0.0914567i | −0.164877 | − | 0.986314i | \(-0.552723\pi\) |
0.446352 | + | 0.894857i | \(0.352723\pi\) | |||||||
\(314\) | −13.8262 | − | 10.0453i | −0.780260 | − | 0.566892i | ||||
\(315\) | − | 2.76393i | − | 0.155730i | ||||||
\(316\) | 6.09017 | 0.342599 | ||||||||
\(317\) | 10.4086 | − | 14.3262i | 0.584606 | − | 0.804642i | −0.409585 | − | 0.912272i | \(-0.634326\pi\) |
0.994191 | + | 0.107630i | \(0.0343263\pi\) | |||||||
\(318\) | 4.53077 | + | 6.23607i | 0.254073 | + | 0.349701i | ||||
\(319\) | −13.2082 | + | 9.59632i | −0.739517 | + | 0.537291i | ||||
\(320\) | 0.690983 | − | 2.12663i | 0.0386271 | − | 0.118882i | ||||
\(321\) | 12.7082 | + | 9.23305i | 0.709303 | + | 0.515339i | ||||
\(322\) | −6.88191 | − | 2.23607i | −0.383514 | − | 0.124611i | ||||
\(323\) | 7.88597 | − | 2.56231i | 0.438787 | − | 0.142571i | ||||
\(324\) | 0.809017 | − | 0.587785i | 0.0449454 | − | 0.0326547i | ||||
\(325\) | −0.693786 | + | 0.225425i | −0.0384843 | + | 0.0125043i | ||||
\(326\) | 4.02786 | + | 12.3965i | 0.223083 | + | 0.686578i | ||||
\(327\) | −7.33094 | − | 10.0902i | −0.405402 | − | 0.557988i | ||||
\(328\) | 7.33094 | − | 2.38197i | 0.404783 | − | 0.131522i | ||||
\(329\) | 1.18034 | − | 3.63271i | 0.0650742 | − | 0.200278i | ||||
\(330\) | 4.30902 | + | 3.13068i | 0.237204 | + | 0.172338i | ||||
\(331\) | 4.09017 | − | 12.5882i | 0.224816 | − | 0.691913i | −0.773494 | − | 0.633803i | \(-0.781493\pi\) |
0.998310 | − | 0.0581093i | \(-0.0185072\pi\) | |||||||
\(332\) | −1.62460 | − | 2.23607i | −0.0891614 | − | 0.122720i | ||||
\(333\) | 6.37988 | + | 8.78115i | 0.349615 | + | 0.481204i | ||||
\(334\) | 11.3992 | + | 8.28199i | 0.623736 | + | 0.453171i | ||||
\(335\) | − | 17.8885i | − | 0.977356i | ||||||
\(336\) | −1.23607 | −0.0674330 | ||||||||
\(337\) | −5.60034 | + | 7.70820i | −0.305070 | + | 0.419893i | −0.933836 | − | 0.357702i | \(-0.883560\pi\) |
0.628766 | + | 0.777595i | \(0.283560\pi\) | |||||||
\(338\) | 12.3435 | − | 4.01064i | 0.671397 | − | 0.218150i | ||||
\(339\) | −2.61803 | + | 8.05748i | −0.142192 | + | 0.437622i | ||||
\(340\) | 4.14590i | 0.224843i | ||||||||
\(341\) | −11.3885 | + | 6.79615i | −0.616724 | + | 0.368032i | ||||
\(342\) | − | 4.47214i | − | 0.241825i | ||||||
\(343\) | −14.6619 | − | 4.76393i | −0.791667 | − | 0.257228i | ||||
\(344\) | −1.23607 | − | 3.80423i | −0.0666443 | − | 0.205110i | ||||
\(345\) | 10.5902 | + | 7.69421i | 0.570156 | + | 0.414242i | ||||
\(346\) | −12.1803 | −0.654819 | ||||||||
\(347\) | 8.00000i | 0.429463i | 0.976673 | + | 0.214731i | \(0.0688876\pi\) | ||||
−0.976673 | + | 0.214731i | \(0.931112\pi\) | |||||||
\(348\) | −4.02874 | + | 5.54508i | −0.215963 | + | 0.297248i | ||||
\(349\) | 7.85410 | − | 5.70634i | 0.420420 | − | 0.305453i | −0.357387 | − | 0.933957i | \(-0.616332\pi\) |
0.777807 | + | 0.628503i | \(0.216332\pi\) | |||||||
\(350\) | 5.00000 | − | 3.63271i | 0.267261 | − | 0.194177i | ||||
\(351\) | −0.0450850 | + | 0.138757i | −0.00240646 | + | 0.00740632i | ||||
\(352\) | 1.40008 | − | 1.92705i | 0.0746248 | − | 0.102712i | ||||
\(353\) | 25.2623 | + | 8.20820i | 1.34457 | + | 0.436879i | 0.890864 | − | 0.454271i | \(-0.150100\pi\) |
0.453710 | + | 0.891149i | \(0.350100\pi\) | |||||||
\(354\) | −0.972136 | − | 2.99193i | −0.0516684 | − | 0.159019i | ||||
\(355\) | −7.23607 | + | 5.25731i | −0.384051 | + | 0.279029i | ||||
\(356\) | 0.708204 | + | 2.17963i | 0.0375347 | + | 0.115520i | ||||
\(357\) | 2.17963 | − | 0.708204i | 0.115358 | − | 0.0374821i | ||||
\(358\) | 12.0535 | + | 16.5902i | 0.637045 | + | 0.876818i | ||||
\(359\) | 9.32624 | + | 28.7032i | 0.492220 | + | 1.51490i | 0.821245 | + | 0.570576i | \(0.193280\pi\) |
−0.329025 | + | 0.944321i | \(0.606720\pi\) | |||||||
\(360\) | 2.12663 | + | 0.690983i | 0.112083 | + | 0.0364180i | ||||
\(361\) | −0.809017 | − | 0.587785i | −0.0425798 | − | 0.0309361i | ||||
\(362\) | 12.5882 | + | 4.09017i | 0.661624 | + | 0.214975i | ||||
\(363\) | −3.13068 | − | 4.30902i | −0.164318 | − | 0.226165i | ||||
\(364\) | 0.145898 | − | 0.106001i | 0.00764713 | − | 0.00555597i | ||||
\(365\) | −3.86974 | + | 5.32624i | −0.202551 | + | 0.278788i | ||||
\(366\) | −2.76393 | −0.144473 | ||||||||
\(367\) | 20.7639i | 1.08387i | 0.840421 | + | 0.541934i | \(0.182308\pi\) | ||||
−0.840421 | + | 0.541934i | \(0.817692\pi\) | |||||||
\(368\) | 3.44095 | − | 4.73607i | 0.179372 | − | 0.246885i | ||||
\(369\) | 2.38197 | + | 7.33094i | 0.124000 | + | 0.381633i | ||||
\(370\) | −7.50000 | + | 23.0826i | −0.389906 | + | 1.20001i | ||||
\(371\) | 9.52786 | 0.494662 | ||||||||
\(372\) | −3.66547 | + | 4.19098i | −0.190046 | + | 0.217292i | ||||
\(373\) | − | 38.0344i | − | 1.96935i | −0.174403 | − | 0.984674i | \(-0.555800\pi\) | ||
0.174403 | − | 0.984674i | \(-0.444200\pi\) | |||||||
\(374\) | −1.36475 | + | 4.20025i | −0.0705693 | + | 0.217190i | ||||
\(375\) | −10.6331 | + | 3.45492i | −0.549093 | + | 0.178411i | ||||
\(376\) | 2.50000 | + | 1.81636i | 0.128928 | + | 0.0936714i | ||||
\(377\) | − | 1.00000i | − | 0.0515026i | ||||||
\(378\) | − | 1.23607i | − | 0.0635765i | ||||||
\(379\) | 5.85410 | + | 4.25325i | 0.300705 | + | 0.218475i | 0.727898 | − | 0.685686i | \(-0.240497\pi\) |
−0.427193 | + | 0.904161i | \(0.640497\pi\) | |||||||
\(380\) | 8.09017 | − | 5.87785i | 0.415017 | − | 0.301527i | ||||
\(381\) | −13.5623 | + | 9.85359i | −0.694818 | + | 0.504815i | ||||
\(382\) | 6.88191 | + | 2.23607i | 0.352109 | + | 0.114407i | ||||
\(383\) | −19.8007 | + | 27.2533i | −1.01177 | + | 1.39258i | −0.0939490 | + | 0.995577i | \(0.529949\pi\) |
−0.917818 | + | 0.397001i | \(0.870051\pi\) | |||||||
\(384\) | 0.309017 | − | 0.951057i | 0.0157695 | − | 0.0485334i | ||||
\(385\) | 6.26137 | − | 2.03444i | 0.319109 | − | 0.103685i | ||||
\(386\) | −14.3262 | + | 10.4086i | −0.729186 | + | 0.529785i | ||||
\(387\) | 3.80423 | − | 1.23607i | 0.193380 | − | 0.0628329i | ||||
\(388\) | 0.898056 | − | 0.291796i | 0.0455919 | − | 0.0148137i | ||||
\(389\) | 11.3262 | − | 8.22899i | 0.574263 | − | 0.417227i | −0.262388 | − | 0.964962i | \(-0.584510\pi\) |
0.836651 | + | 0.547736i | \(0.184510\pi\) | |||||||
\(390\) | −0.310271 | + | 0.100813i | −0.0157112 | + | 0.00510487i | ||||
\(391\) | −3.35410 | + | 10.3229i | −0.169624 | + | 0.522050i | ||||
\(392\) | 3.21644 | − | 4.42705i | 0.162455 | − | 0.223600i | ||||
\(393\) | 5.51458 | + | 1.79180i | 0.278174 | + | 0.0903842i | ||||
\(394\) | 5.61803 | − | 4.08174i | 0.283032 | − | 0.205635i | ||||
\(395\) | −11.0172 | + | 8.00448i | −0.554337 | + | 0.402749i | ||||
\(396\) | 1.92705 | + | 1.40008i | 0.0968380 | + | 0.0703569i | ||||
\(397\) | − | 6.61803i | − | 0.332150i | −0.986113 | − | 0.166075i | \(-0.946891\pi\) | ||
0.986113 | − | 0.166075i | \(-0.0531093\pi\) | |||||||
\(398\) | 23.6180i | 1.18387i | ||||||||
\(399\) | −4.47214 | − | 3.24920i | −0.223887 | − | 0.162663i | ||||
\(400\) | 1.54508 | + | 4.75528i | 0.0772542 | + | 0.237764i | ||||
\(401\) | −3.32624 | + | 10.2371i | −0.166104 | + | 0.511217i | −0.999116 | − | 0.0420388i | \(-0.986615\pi\) |
0.833012 | + | 0.553256i | \(0.186615\pi\) | |||||||
\(402\) | − | 8.00000i | − | 0.399004i | ||||||
\(403\) | 0.0732450 | − | 0.809017i | 0.00364859 | − | 0.0403000i | ||||
\(404\) | −7.61803 | −0.379011 | ||||||||
\(405\) | −0.690983 | + | 2.12663i | −0.0343352 | + | 0.105673i | ||||
\(406\) | 2.61803 | + | 8.05748i | 0.129931 | + | 0.399886i | ||||
\(407\) | −15.1967 | + | 20.9164i | −0.753270 | + | 1.03679i | ||||
\(408\) | 1.85410i | 0.0917917i | ||||||||
\(409\) | 30.5623 | 1.51121 | 0.755604 | − | 0.655028i | \(-0.227343\pi\) | ||||
0.755604 | + | 0.655028i | \(0.227343\pi\) | |||||||
\(410\) | −10.1311 | + | 13.9443i | −0.500340 | + | 0.688659i | ||||
\(411\) | 7.61803 | − | 5.53483i | 0.375770 | − | 0.273013i | ||||
\(412\) | −4.80828 | − | 6.61803i | −0.236887 | − | 0.326047i | ||||
\(413\) | −3.69822 | − | 1.20163i | −0.181978 | − | 0.0591282i | ||||
\(414\) | 4.73607 | + | 3.44095i | 0.232765 | + | 0.169114i | ||||
\(415\) | 5.87785 | + | 1.90983i | 0.288532 | + | 0.0937499i | ||||
\(416\) | 0.0450850 | + | 0.138757i | 0.00221047 | + | 0.00680314i | ||||
\(417\) | −1.73060 | − | 2.38197i | −0.0847478 | − | 0.116645i | ||||
\(418\) | 10.1311 | − | 3.29180i | 0.495529 | − | 0.161007i | ||||
\(419\) | 11.9336 | + | 36.7279i | 0.582996 | + | 1.79428i | 0.607174 | + | 0.794569i | \(0.292303\pi\) |
−0.0241776 | + | 0.999708i | \(0.507697\pi\) | |||||||
\(420\) | 2.23607 | − | 1.62460i | 0.109109 | − | 0.0792723i | ||||
\(421\) | 7.14590 | + | 21.9928i | 0.348270 | + | 1.07186i | 0.959810 | + | 0.280651i | \(0.0905503\pi\) |
−0.611540 | + | 0.791213i | \(0.709450\pi\) | |||||||
\(422\) | −12.0332 | − | 3.90983i | −0.585768 | − | 0.190328i | ||||
\(423\) | −1.81636 | + | 2.50000i | −0.0883143 | + | 0.121554i | ||||
\(424\) | −2.38197 | + | 7.33094i | −0.115678 | + | 0.356022i | ||||
\(425\) | −5.44907 | − | 7.50000i | −0.264319 | − | 0.363803i | ||||
\(426\) | −3.23607 | + | 2.35114i | −0.156788 | + | 0.113913i | ||||
\(427\) | −2.00811 | + | 2.76393i | −0.0971795 | + | 0.133756i | ||||
\(428\) | 15.7082i | 0.759285i | ||||||||
\(429\) | −0.347524 | −0.0167786 | ||||||||
\(430\) | 7.23607 | + | 5.25731i | 0.348954 | + | 0.253530i | ||||
\(431\) | −7.18034 | − | 22.0988i | −0.345865 | − | 1.06446i | −0.961119 | − | 0.276134i | \(-0.910947\pi\) |
0.615254 | − | 0.788329i | \(-0.289053\pi\) | |||||||
\(432\) | 0.951057 | + | 0.309017i | 0.0457577 | + | 0.0148676i | ||||
\(433\) | − | 10.7639i | − | 0.517282i | −0.965974 | − | 0.258641i | \(-0.916725\pi\) | ||
0.965974 | − | 0.258641i | \(-0.0832746\pi\) | |||||||
\(434\) | 1.52786 | + | 6.71040i | 0.0733398 | + | 0.322109i | ||||
\(435\) | − | 15.3262i | − | 0.734837i | ||||||
\(436\) | 3.85410 | − | 11.8617i | 0.184578 | − | 0.568073i | ||||
\(437\) | 24.8990 | − | 8.09017i | 1.19108 | − | 0.387005i | ||||
\(438\) | −1.73060 | + | 2.38197i | −0.0826912 | + | 0.113815i | ||||
\(439\) | −27.0344 | −1.29028 | −0.645142 | − | 0.764063i | \(-0.723202\pi\) | ||||
−0.645142 | + | 0.764063i | \(0.723202\pi\) | |||||||
\(440\) | 5.32624i | 0.253918i | ||||||||
\(441\) | 4.42705 | + | 3.21644i | 0.210812 | + | 0.153164i | ||||
\(442\) | −0.159002 | − | 0.218847i | −0.00756294 | − | 0.0104095i | ||||
\(443\) | 20.5397 | + | 28.2705i | 0.975872 | + | 1.34317i | 0.939024 | + | 0.343852i | \(0.111732\pi\) |
0.0368479 | + | 0.999321i | \(0.488268\pi\) | |||||||
\(444\) | −3.35410 | + | 10.3229i | −0.159179 | + | 0.489901i | ||||
\(445\) | −4.14590 | − | 3.01217i | −0.196534 | − | 0.142791i | ||||
\(446\) | 8.00000 | − | 24.6215i | 0.378811 | − | 1.16586i | ||||
\(447\) | 13.9026 | − | 4.51722i | 0.657569 | − | 0.213657i | ||||
\(448\) | −0.726543 | − | 1.00000i | −0.0343259 | − | 0.0472456i | ||||
\(449\) | 2.47214 | + | 7.60845i | 0.116667 | + | 0.359065i | 0.992291 | − | 0.123929i | \(-0.0395494\pi\) |
−0.875624 | + | 0.482994i | \(0.839549\pi\) | |||||||
\(450\) | −4.75528 | + | 1.54508i | −0.224166 | + | 0.0728360i | ||||
\(451\) | −14.8541 | + | 10.7921i | −0.699452 | + | 0.508182i | ||||
\(452\) | −8.05748 | + | 2.61803i | −0.378992 | + | 0.123142i | ||||
\(453\) | 17.0130 | + | 5.52786i | 0.799341 | + | 0.259722i | ||||
\(454\) | 4.61803 | + | 3.35520i | 0.216735 | + | 0.157467i | ||||
\(455\) | −0.124612 | + | 0.383516i | −0.00584189 | + | 0.0179795i | ||||
\(456\) | 3.61803 | − | 2.62866i | 0.169430 | − | 0.123098i | ||||
\(457\) | 15.6659 | + | 21.5623i | 0.732821 | + | 1.00864i | 0.999000 | + | 0.0447183i | \(0.0142390\pi\) |
−0.266178 | + | 0.963924i | \(0.585761\pi\) | |||||||
\(458\) | −15.0454 | + | 20.7082i | −0.703025 | + | 0.967631i | ||||
\(459\) | −1.85410 | −0.0865421 | ||||||||
\(460\) | 13.0902i | 0.610332i | ||||||||
\(461\) | 10.5623 | + | 7.67396i | 0.491936 | + | 0.357412i | 0.805928 | − | 0.592013i | \(-0.201667\pi\) |
−0.313993 | + | 0.949425i | \(0.601667\pi\) | |||||||
\(462\) | 2.80017 | − | 0.909830i | 0.130276 | − | 0.0423291i | ||||
\(463\) | −24.0664 | − | 7.81966i | −1.11846 | − | 0.363410i | −0.309282 | − | 0.950970i | \(-0.600089\pi\) |
−0.809181 | + | 0.587560i | \(0.800089\pi\) | |||||||
\(464\) | −6.85410 | −0.318194 | ||||||||
\(465\) | 1.12257 | − | 12.3992i | 0.0520579 | − | 0.574999i | ||||
\(466\) | −12.6180 | −0.584519 | ||||||||
\(467\) | 25.1765 | + | 8.18034i | 1.16503 | + | 0.378541i | 0.826785 | − | 0.562517i | \(-0.190167\pi\) |
0.338244 | + | 0.941058i | \(0.390167\pi\) | |||||||
\(468\) | −0.138757 | + | 0.0450850i | −0.00641406 | + | 0.00208405i | ||||
\(469\) | −8.00000 | − | 5.81234i | −0.369406 | − | 0.268389i | ||||
\(470\) | −6.90983 | −0.318727 | ||||||||
\(471\) | 17.0902 | 0.787473 | ||||||||
\(472\) | 1.84911 | − | 2.54508i | 0.0851123 | − | 0.117147i | ||||
\(473\) | 5.60034 | + | 7.70820i | 0.257504 | + | 0.354424i | ||||
\(474\) | −4.92705 | + | 3.57971i | −0.226307 | + | 0.164422i | ||||
\(475\) | −6.90983 | + | 21.2663i | −0.317045 | + | 0.975763i | ||||
\(476\) | 1.85410 | + | 1.34708i | 0.0849826 | + | 0.0617435i | ||||
\(477\) | −7.33094 | − | 2.38197i | −0.335661 | − | 0.109063i | ||||
\(478\) | −14.3844 | + | 4.67376i | −0.657925 | + | 0.213773i | ||||
\(479\) | 14.4721 | − | 10.5146i | 0.661249 | − | 0.480425i | −0.205836 | − | 0.978587i | \(-0.565991\pi\) |
0.867084 | + | 0.498161i | \(0.165991\pi\) | |||||||
\(480\) | 0.690983 | + | 2.12663i | 0.0315389 | + | 0.0970668i | ||||
\(481\) | −0.489357 | − | 1.50609i | −0.0223128 | − | 0.0686716i | ||||
\(482\) | 4.33901 | + | 5.97214i | 0.197637 | + | 0.272023i | ||||
\(483\) | 6.88191 | − | 2.23607i | 0.313138 | − | 0.101745i | ||||
\(484\) | 1.64590 | − | 5.06555i | 0.0748135 | − | 0.230252i | ||||
\(485\) | −1.24108 | + | 1.70820i | −0.0563547 | + | 0.0775655i | ||||
\(486\) | −0.309017 | + | 0.951057i | −0.0140173 | + | 0.0431408i | ||||
\(487\) | −5.32282 | − | 7.32624i | −0.241200 | − | 0.331984i | 0.671205 | − | 0.741272i | \(-0.265777\pi\) |
−0.912405 | + | 0.409288i | \(0.865777\pi\) | |||||||
\(488\) | −1.62460 | − | 2.23607i | −0.0735421 | − | 0.101222i | ||||
\(489\) | −10.5451 | − | 7.66145i | −0.476865 | − | 0.346463i | ||||
\(490\) | 12.2361i | 0.552769i | ||||||||
\(491\) | −10.0344 | −0.452848 | −0.226424 | − | 0.974029i | \(-0.572703\pi\) | ||||
−0.226424 | + | 0.974029i | \(0.572703\pi\) | |||||||
\(492\) | −4.53077 | + | 6.23607i | −0.204263 | + | 0.281144i | ||||
\(493\) | 12.0862 | − | 3.92705i | 0.544336 | − | 0.176865i | ||||
\(494\) | −0.201626 | + | 0.620541i | −0.00907159 | + | 0.0279195i | ||||
\(495\) | −5.32624 | −0.239397 | ||||||||
\(496\) | −5.54508 | − | 0.502029i | −0.248982 | − | 0.0225417i | ||||
\(497\) | 4.94427i | 0.221781i | ||||||||
\(498\) | 2.62866 | + | 0.854102i | 0.117793 | + | 0.0382732i | ||||
\(499\) | −1.18034 | − | 3.63271i | −0.0528393 | − | 0.162623i | 0.921155 | − | 0.389197i | \(-0.127247\pi\) |
−0.973994 | + | 0.226574i | \(0.927247\pi\) | |||||||
\(500\) | −9.04508 | − | 6.57164i | −0.404508 | − | 0.293893i | ||||
\(501\) | −14.0902 | −0.629502 | ||||||||
\(502\) | 13.0902i | 0.584243i | ||||||||
\(503\) | −12.1190 | + | 16.6803i | −0.540358 | + | 0.743740i | −0.988665 | − | 0.150140i | \(-0.952027\pi\) |
0.448306 | + | 0.893880i | \(0.352027\pi\) | |||||||
\(504\) | 1.00000 | − | 0.726543i | 0.0445435 | − | 0.0323628i | ||||
\(505\) | 13.7812 | − | 10.0126i | 0.613253 | − | 0.445555i | ||||
\(506\) | −4.30902 | + | 13.2618i | −0.191559 | + | 0.589559i | ||||
\(507\) | −7.62870 | + | 10.5000i | −0.338802 | + | 0.466321i | ||||
\(508\) | −15.9434 | − | 5.18034i | −0.707376 | − | 0.229840i | ||||
\(509\) | 1.59017 | + | 4.89404i | 0.0704830 | + | 0.216925i | 0.980093 | − | 0.198539i | \(-0.0636195\pi\) |
−0.909610 | + | 0.415463i | \(0.863620\pi\) | |||||||
\(510\) | −2.43690 | − | 3.35410i | −0.107908 | − | 0.148522i | ||||
\(511\) | 1.12461 | + | 3.46120i | 0.0497499 | + | 0.153114i | ||||
\(512\) | 0.951057 | − | 0.309017i | 0.0420312 | − | 0.0136568i | ||||
\(513\) | 2.62866 | + | 3.61803i | 0.116058 | + | 0.159740i | ||||
\(514\) | 4.20820 | + | 12.9515i | 0.185616 | + | 0.571267i | ||||
\(515\) | 17.3965 | + | 5.65248i | 0.766583 | + | 0.249078i | ||||
\(516\) | 3.23607 | + | 2.35114i | 0.142460 | + | 0.103503i | ||||
\(517\) | −7.00042 | − | 2.27458i | −0.307878 | − | 0.100036i | ||||
\(518\) | 7.88597 | + | 10.8541i | 0.346489 | + | 0.476902i | ||||
\(519\) | 9.85410 | − | 7.15942i | 0.432547 | − | 0.314264i | ||||
\(520\) | −0.263932 | − | 0.191758i | −0.0115742 | − | 0.00840914i | ||||
\(521\) | −24.4721 | −1.07214 | −0.536072 | − | 0.844172i | \(-0.680092\pi\) | ||||
−0.536072 | + | 0.844172i | \(0.680092\pi\) | |||||||
\(522\) | − | 6.85410i | − | 0.299996i | ||||||
\(523\) | −4.44501 | + | 6.11803i | −0.194367 | + | 0.267523i | −0.895066 | − | 0.445934i | \(-0.852872\pi\) |
0.700699 | + | 0.713457i | \(0.252872\pi\) | |||||||
\(524\) | 1.79180 | + | 5.51458i | 0.0782750 | + | 0.240906i | ||||
\(525\) | −1.90983 | + | 5.87785i | −0.0833518 | + | 0.256531i | ||||
\(526\) | 6.67376 | 0.290990 | ||||||||
\(527\) | 10.0656 | − | 2.29180i | 0.438464 | − | 0.0998322i | ||||
\(528\) | 2.38197i | 0.103662i | ||||||||
\(529\) | −3.48278 | + | 10.7189i | −0.151425 | + | 0.466039i | ||||
\(530\) | −5.32624 | − | 16.3925i | −0.231357 | − | 0.712044i | ||||
\(531\) | 2.54508 | + | 1.84911i | 0.110447 | + | 0.0802446i | ||||
\(532\) | − | 5.52786i | − | 0.239663i | ||||||
\(533\) | − | 1.12461i | − | 0.0487123i | ||||||
\(534\) | −1.85410 | − | 1.34708i | −0.0802348 | − | 0.0582940i | ||||
\(535\) | −20.6457 | − | 28.4164i | −0.892593 | − | 1.22855i | ||||
\(536\) | 6.47214 | − | 4.70228i | 0.279554 | − | 0.203108i | ||||
\(537\) | −19.5029 | − | 6.33688i | −0.841613 | − | 0.273457i | ||||
\(538\) | 5.89810 | − | 8.11803i | 0.254285 | − | 0.349993i | ||||
\(539\) | −4.02786 | + | 12.3965i | −0.173492 | + | 0.533955i | ||||
\(540\) | −2.12663 | + | 0.690983i | −0.0915155 | + | 0.0297352i | ||||
\(541\) | 36.1803 | − | 26.2866i | 1.55551 | − | 1.13015i | 0.615945 | − | 0.787789i | \(-0.288774\pi\) |
0.939570 | − | 0.342358i | \(-0.111226\pi\) | |||||||
\(542\) | 19.0539 | − | 6.19098i | 0.818435 | − | 0.265925i | ||||
\(543\) | −12.5882 | + | 4.09017i | −0.540213 | + | 0.175526i | ||||
\(544\) | −1.50000 | + | 1.08981i | −0.0643120 | + | 0.0467254i | ||||
\(545\) | 8.61803 | + | 26.5236i | 0.369156 | + | 1.13615i | ||||
\(546\) | −0.0557281 | + | 0.171513i | −0.00238494 | + | 0.00734010i | ||||
\(547\) | 6.58415 | − | 9.06231i | 0.281518 | − | 0.387476i | −0.644718 | − | 0.764421i | \(-0.723025\pi\) |
0.926236 | + | 0.376944i | \(0.123025\pi\) | |||||||
\(548\) | 8.95554 | + | 2.90983i | 0.382562 | + | 0.124302i | ||||
\(549\) | 2.23607 | − | 1.62460i | 0.0954331 | − | 0.0693362i | ||||
\(550\) | −7.00042 | − | 9.63525i | −0.298499 | − | 0.410849i | ||||
\(551\) | −24.7984 | − | 18.0171i | −1.05645 | − | 0.767553i | ||||
\(552\) | 5.85410i | 0.249167i | ||||||||
\(553\) | 7.52786i | 0.320117i | ||||||||
\(554\) | −2.88197 | − | 2.09387i | −0.122443 | − | 0.0889600i | ||||
\(555\) | −7.50000 | − | 23.0826i | −0.318357 | − | 0.979803i | ||||
\(556\) | 0.909830 | − | 2.80017i | 0.0385854 | − | 0.118754i | ||||
\(557\) | 8.65248i | 0.366617i | 0.983055 | + | 0.183309i | \(0.0586808\pi\) | ||||
−0.983055 | + | 0.183309i | \(0.941319\pi\) | |||||||
\(558\) | 0.502029 | − | 5.54508i | 0.0212526 | − | 0.234742i | ||||
\(559\) | −0.583592 | −0.0246833 | ||||||||
\(560\) | 2.62866 | + | 0.854102i | 0.111081 | + | 0.0360924i | ||||
\(561\) | −1.36475 | − | 4.20025i | −0.0576196 | − | 0.177335i | ||||
\(562\) | 7.26543 | − | 10.0000i | 0.306473 | − | 0.421825i | ||||
\(563\) | 10.0000i | 0.421450i | 0.977545 | + | 0.210725i | \(0.0675824\pi\) | ||||
−0.977545 | + | 0.210725i | \(0.932418\pi\) | |||||||
\(564\) | −3.09017 | −0.130120 | ||||||||
\(565\) | 11.1352 | − | 15.3262i | 0.468460 | − | 0.644780i | ||||
\(566\) | −8.35410 | + | 6.06961i | −0.351149 | + | 0.255125i | ||||
\(567\) | 0.726543 | + | 1.00000i | 0.0305119 | + | 0.0419961i | ||||
\(568\) | −3.80423 | − | 1.23607i | −0.159622 | − | 0.0518643i | ||||
\(569\) | 0.618034 | + | 0.449028i | 0.0259093 | + | 0.0188242i | 0.600665 | − | 0.799501i | \(-0.294903\pi\) |
−0.574755 | + | 0.818325i | \(0.694903\pi\) | |||||||
\(570\) | −3.09017 | + | 9.51057i | −0.129433 | + | 0.398354i | ||||
\(571\) | 8.65248 | + | 26.6296i | 0.362095 | + | 1.11441i | 0.951780 | + | 0.306780i | \(0.0992517\pi\) |
−0.589685 | + | 0.807633i | \(0.700748\pi\) | |||||||
\(572\) | −0.204270 | − | 0.281153i | −0.00854094 | − | 0.0117556i | ||||
\(573\) | −6.88191 | + | 2.23607i | −0.287496 | + | 0.0934131i | ||||
\(574\) | 2.94427 | + | 9.06154i | 0.122892 | + | 0.378221i | ||||
\(575\) | −17.2048 | − | 23.6803i | −0.717489 | − | 0.987538i | ||||
\(576\) | 0.309017 | + | 0.951057i | 0.0128757 | + | 0.0396274i | ||||
\(577\) | −18.7436 | − | 6.09017i | −0.780307 | − | 0.253537i | −0.108336 | − | 0.994114i | \(-0.534552\pi\) |
−0.671971 | + | 0.740577i | \(0.734552\pi\) | |||||||
\(578\) | −7.97172 | + | 10.9721i | −0.331580 | + | 0.456381i | ||||
\(579\) | 5.47214 | − | 16.8415i | 0.227414 | − | 0.699909i | ||||
\(580\) | 12.3992 | − | 9.00854i | 0.514848 | − | 0.374059i | ||||
\(581\) | 2.76393 | − | 2.00811i | 0.114667 | − | 0.0833106i | ||||
\(582\) | −0.555029 | + | 0.763932i | −0.0230067 | + | 0.0316660i | ||||
\(583\) | − | 18.3607i | − | 0.760422i | ||||||
\(584\) | −2.94427 | −0.121835 | ||||||||
\(585\) | 0.191758 | − | 0.263932i | 0.00792821 | − | 0.0109122i | ||||
\(586\) | 2.09017 | + | 6.43288i | 0.0863441 | + | 0.265740i | ||||
\(587\) | −24.0009 | − | 7.79837i | −0.990624 | − | 0.321873i | −0.231511 | − | 0.972832i | \(-0.574367\pi\) |
−0.759113 | + | 0.650959i | \(0.774367\pi\) | |||||||
\(588\) | 5.47214i | 0.225667i | ||||||||
\(589\) | −18.7426 | − | 16.3925i | −0.772277 | − | 0.675440i | ||||
\(590\) | 7.03444i | 0.289603i | ||||||||
\(591\) | −2.14590 | + | 6.60440i | −0.0882705 | + | 0.271669i | ||||
\(592\) | −10.3229 | + | 3.35410i | −0.424267 | + | 0.137853i | ||||
\(593\) | −1.64484 | + | 2.26393i | −0.0675456 | + | 0.0929685i | −0.841453 | − | 0.540330i | \(-0.818299\pi\) |
0.773908 | + | 0.633298i | \(0.218299\pi\) | |||||||
\(594\) | −2.38197 | −0.0977332 | ||||||||
\(595\) | −5.12461 | −0.210089 | ||||||||
\(596\) | 11.8262 | + | 8.59226i | 0.484422 | + | 0.351953i | ||||
\(597\) | −13.8823 | − | 19.1074i | −0.568166 | − | 0.782013i | ||||
\(598\) | −0.502029 | − | 0.690983i | −0.0205295 | − | 0.0282564i | ||||
\(599\) | −10.7984 | + | 33.2340i | −0.441210 | + | 1.35790i | 0.445378 | + | 0.895343i | \(0.353069\pi\) |
−0.886588 | + | 0.462561i | \(0.846931\pi\) | |||||||
\(600\) | −4.04508 | − | 2.93893i | −0.165140 | − | 0.119981i | ||||
\(601\) | 7.91641 | − | 24.3642i | 0.322917 | − | 0.993836i | −0.649455 | − | 0.760400i | \(-0.725003\pi\) |
0.972372 | − | 0.233436i | \(-0.0749971\pi\) | |||||||
\(602\) | 4.70228 | − | 1.52786i | 0.191651 | − | 0.0622711i | ||||
\(603\) | 4.70228 | + | 6.47214i | 0.191492 | + | 0.263566i | ||||
\(604\) | 5.52786 | + | 17.0130i | 0.224926 | + | 0.692250i | ||||
\(605\) | 3.68034 | + | 11.3269i | 0.149627 | + | 0.460505i | ||||
\(606\) | 6.16312 | − | 4.47777i | 0.250360 | − | 0.181897i | ||||
\(607\) | 10.5801 | − | 3.43769i | 0.429434 | − | 0.139532i | −0.0863214 | − | 0.996267i | \(-0.527511\pi\) |
0.515756 | + | 0.856736i | \(0.327511\pi\) | |||||||
\(608\) | 4.25325 | + | 1.38197i | 0.172492 | + | 0.0560461i | ||||
\(609\) | −6.85410 | − | 4.97980i | −0.277742 | − | 0.201792i | ||||
\(610\) | 5.87785 | + | 1.90983i | 0.237987 | + | 0.0773268i | ||||
\(611\) | 0.364745 | − | 0.265003i | 0.0147560 | − | 0.0107209i | ||||
\(612\) | −1.08981 | − | 1.50000i | −0.0440531 | − | 0.0606339i | ||||
\(613\) | 22.3888 | − | 30.8156i | 0.904277 | − | 1.24463i | −0.0648069 | − | 0.997898i | \(-0.520643\pi\) |
0.969084 | − | 0.246732i | \(-0.0793568\pi\) | |||||||
\(614\) | 7.32624 | 0.295663 | ||||||||
\(615\) | − | 17.2361i | − | 0.695025i | ||||||
\(616\) | 2.38197 | + | 1.73060i | 0.0959721 | + | 0.0697278i | ||||
\(617\) | −9.09429 | + | 2.95492i | −0.366122 | + | 0.118960i | −0.486300 | − | 0.873792i | \(-0.661654\pi\) |
0.120177 | + | 0.992752i | \(0.461654\pi\) | |||||||
\(618\) | 7.77997 | + | 2.52786i | 0.312956 | + | 0.101686i | ||||
\(619\) | −6.65248 | −0.267386 | −0.133693 | − | 0.991023i | \(-0.542684\pi\) | ||||
−0.133693 | + | 0.991023i | \(0.542684\pi\) | |||||||
\(620\) | 10.6910 | − | 6.37988i | 0.429360 | − | 0.256222i | ||||
\(621\) | −5.85410 | −0.234917 | ||||||||
\(622\) | −12.7598 | − | 4.14590i | −0.511620 | − | 0.166235i | ||||
\(623\) | −2.69417 | + | 0.875388i | −0.107940 | + | 0.0350717i | ||||
\(624\) | −0.118034 | − | 0.0857567i | −0.00472514 | − | 0.00343302i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −5.23607 | −0.209275 | ||||||||
\(627\) | −6.26137 | + | 8.61803i | −0.250055 | + | 0.344171i | ||||
\(628\) | 10.0453 | + | 13.8262i | 0.400853 | + | 0.551727i | ||||
\(629\) | 16.2812 | − | 11.8290i | 0.649172 | − | 0.471651i | ||||
\(630\) | −0.854102 | + | 2.62866i | −0.0340282 | + | 0.104728i | ||||
\(631\) | 23.2082 | + | 16.8617i | 0.923904 | + | 0.671256i | 0.944493 | − | 0.328532i | \(-0.106554\pi\) |
−0.0205887 | + | 0.999788i | \(0.506554\pi\) | |||||||
\(632\) | −5.79210 | − | 1.88197i | −0.230397 | − | 0.0748606i | ||||
\(633\) | 12.0332 | − | 3.90983i | 0.478278 | − | 0.155402i | ||||
\(634\) | −14.3262 | + | 10.4086i | −0.568968 | + | 0.413379i | ||||
\(635\) | 35.6506 | − | 11.5836i | 1.41475 | − | 0.459681i | ||||
\(636\) | −2.38197 | − | 7.33094i | −0.0944511 | − | 0.290691i | ||||
\(637\) | −0.469272 | − | 0.645898i | −0.0185932 | − | 0.0255914i | ||||
\(638\) | 15.5272 | − | 5.04508i | 0.614727 | − | 0.199737i | ||||
\(639\) | 1.23607 | − | 3.80423i | 0.0488981 | − | 0.150493i | ||||
\(640\) | −1.31433 | + | 1.80902i | −0.0519534 | + | 0.0715077i | ||||
\(641\) | 3.88854 | − | 11.9677i | 0.153588 | − | 0.472696i | −0.844427 | − | 0.535671i | \(-0.820059\pi\) |
0.998015 | + | 0.0629748i | \(0.0200588\pi\) | |||||||
\(642\) | −9.23305 | − | 12.7082i | −0.364399 | − | 0.501553i | ||||
\(643\) | −6.65740 | − | 9.16312i | −0.262542 | − | 0.361358i | 0.657312 | − | 0.753618i | \(-0.271693\pi\) |
−0.919854 | + | 0.392260i | \(0.871693\pi\) | |||||||
\(644\) | 5.85410 | + | 4.25325i | 0.230684 | + | 0.167602i | ||||
\(645\) | −8.94427 | −0.352180 | ||||||||
\(646\) | −8.29180 | −0.326236 | ||||||||
\(647\) | −13.4005 | + | 18.4443i | −0.526830 | + | 0.725119i | −0.986643 | − | 0.162896i | \(-0.947916\pi\) |
0.459813 | + | 0.888016i | \(0.347916\pi\) | |||||||
\(648\) | −0.951057 | + | 0.309017i | −0.0373610 | + | 0.0121393i | ||||
\(649\) | −2.31559 | + | 7.12667i | −0.0908950 | + | 0.279746i | ||||
\(650\) | 0.729490 | 0.0286130 | ||||||||
\(651\) | −5.18034 | − | 4.53077i | −0.203034 | − | 0.177575i | ||||
\(652\) | − | 13.0344i | − | 0.510468i | ||||||
\(653\) | 43.3651 | + | 14.0902i | 1.69701 | + | 0.551391i | 0.988087 | − | 0.153898i | \(-0.0491827\pi\) |
0.708920 | + | 0.705289i | \(0.249183\pi\) | |||||||
\(654\) | 3.85410 | + | 11.8617i | 0.150707 | + | 0.463829i | ||||
\(655\) | −10.4894 | − | 7.62096i | −0.409853 | − | 0.297776i | ||||
\(656\) | −7.70820 | −0.300955 | ||||||||
\(657\) | − | 2.94427i | − | 0.114867i | ||||||
\(658\) | −2.24514 | + | 3.09017i | −0.0875247 | + | 0.120467i | ||||
\(659\) | 12.8262 | − | 9.31881i | 0.499639 | − | 0.363009i | −0.309240 | − | 0.950984i | \(-0.600075\pi\) |
0.808879 | + | 0.587975i | \(0.200075\pi\) | |||||||
\(660\) | −3.13068 | − | 4.30902i | −0.121862 | − | 0.167728i | ||||
\(661\) | −8.70820 | + | 26.8011i | −0.338710 | + | 1.04244i | 0.626156 | + | 0.779698i | \(0.284627\pi\) |
−0.964866 | + | 0.262744i | \(0.915373\pi\) | |||||||
\(662\) | −7.77997 | + | 10.7082i | −0.302377 | + | 0.416186i | ||||
\(663\) | 0.257270 | + | 0.0835921i | 0.00999154 | + | 0.00324645i | ||||
\(664\) | 0.854102 | + | 2.62866i | 0.0331456 | + | 0.102012i | ||||
\(665\) | 7.26543 | + | 10.0000i | 0.281741 | + | 0.387783i | ||||
\(666\) | −3.35410 | − | 10.3229i | −0.129969 | − | 0.400003i | ||||
\(667\) | 38.1608 | − | 12.3992i | 1.47759 | − | 0.480098i | ||||
\(668\) | −8.28199 | − | 11.3992i | −0.320440 | − | 0.441048i | ||||
\(669\) | 8.00000 | + | 24.6215i | 0.309298 | + | 0.951921i | ||||
\(670\) | −5.52786 | + | 17.0130i | −0.213560 | + | 0.657270i | ||||
\(671\) | 5.32624 | + | 3.86974i | 0.205617 | + | 0.149390i | ||||
\(672\) | 1.17557 | + | 0.381966i | 0.0453486 | + | 0.0147347i | ||||
\(673\) | −25.7970 | − | 35.5066i | −0.994403 | − | 1.36868i | −0.928697 | − | 0.370839i | \(-0.879070\pi\) |
−0.0657056 | − | 0.997839i | \(-0.520930\pi\) | |||||||
\(674\) | 7.70820 | − | 5.60034i | 0.296909 | − | 0.215717i | ||||
\(675\) | 2.93893 | − | 4.04508i | 0.113119 | − | 0.155695i | ||||
\(676\) | −12.9787 | −0.499181 | ||||||||
\(677\) | 20.9443i | 0.804954i | 0.915430 | + | 0.402477i | \(0.131851\pi\) | ||||
−0.915430 | + | 0.402477i | \(0.868149\pi\) | |||||||
\(678\) | 4.97980 | − | 6.85410i | 0.191248 | − | 0.263230i | ||||
\(679\) | 0.360680 | + | 1.11006i | 0.0138416 | + | 0.0426001i | ||||
\(680\) | 1.28115 | − | 3.94298i | 0.0491300 | − | 0.151207i | ||||
\(681\) | −5.70820 | −0.218739 | ||||||||
\(682\) | 12.9313 | − | 2.94427i | 0.495164 | − | 0.112742i | ||||
\(683\) | 8.58359i | 0.328442i | 0.986424 | + | 0.164221i | \(0.0525110\pi\) | ||||
−0.986424 | + | 0.164221i | \(0.947489\pi\) | |||||||
\(684\) | −1.38197 | + | 4.25325i | −0.0528408 | + | 0.162627i | ||||
\(685\) | −20.0252 | + | 6.50658i | −0.765123 | + | 0.248604i | ||||
\(686\) | 12.4721 | + | 9.06154i | 0.476188 | + | 0.345971i | ||||
\(687\) | − | 25.5967i | − | 0.976577i | ||||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | 0.909830 | + | 0.661030i | 0.0346618 | + | 0.0251832i | ||||
\(690\) | −7.69421 | − | 10.5902i | −0.292914 | − | 0.403161i | ||||
\(691\) | 7.76393 | − | 5.64083i | 0.295354 | − | 0.214587i | −0.430233 | − | 0.902718i | \(-0.641569\pi\) |
0.725587 | + | 0.688131i | \(0.241569\pi\) | |||||||
\(692\) | 11.5842 | + | 3.76393i | 0.440365 | + | 0.143083i | ||||
\(693\) | −1.73060 | + | 2.38197i | −0.0657400 | + | 0.0904834i | ||||
\(694\) | 2.47214 | − | 7.60845i | 0.0938410 | − | 0.288813i | ||||
\(695\) | 2.03444 | + | 6.26137i | 0.0771708 | + | 0.237507i | ||||
\(696\) | 5.54508 | − | 4.02874i | 0.210186 | − | 0.152709i | ||||
\(697\) | 13.5923 | − | 4.41641i | 0.514845 | − | 0.167283i | ||||
\(698\) | −9.23305 | + | 3.00000i | −0.349476 | + | 0.113552i | ||||
\(699\) | 10.2082 | − | 7.41669i | 0.386110 | − | 0.280525i | ||||
\(700\) | −5.87785 | + | 1.90983i | −0.222162 | + | 0.0721848i | ||||
\(701\) | 3.17376 | − | 9.76784i | 0.119871 | − | 0.368926i | −0.873061 | − | 0.487612i | \(-0.837868\pi\) |
0.992932 | + | 0.118686i | \(0.0378681\pi\) | |||||||
\(702\) | 0.0857567 | − | 0.118034i | 0.00323668 | − | 0.00445491i | ||||
\(703\) | −46.1653 | − | 15.0000i | −1.74116 | − | 0.565736i | ||||
\(704\) | −1.92705 | + | 1.40008i | −0.0726285 | + | 0.0527677i | ||||
\(705\) | 5.59017 | − | 4.06150i | 0.210538 | − | 0.152965i | ||||
\(706\) | −21.4894 | − | 15.6129i | −0.808763 | − | 0.587600i | ||||
\(707\) | − | 9.41641i | − | 0.354140i | ||||||
\(708\) | 3.14590i | 0.118230i | ||||||||
\(709\) | 31.2705 | + | 22.7194i | 1.17439 | + | 0.853243i | 0.991528 | − | 0.129895i | \(-0.0414642\pi\) |
0.182861 | + | 0.983139i | \(0.441464\pi\) | |||||||
\(710\) | 8.50651 | − | 2.76393i | 0.319244 | − | 0.103729i | ||||
\(711\) | 1.88197 | − | 5.79210i | 0.0705792 | − | 0.217221i | ||||
\(712\) | − | 2.29180i | − | 0.0858887i | ||||||
\(713\) | 31.7809 | − | 7.23607i | 1.19020 | − | 0.270993i | ||||
\(714\) | −2.29180 | −0.0857683 | ||||||||
\(715\) | 0.739054 | + | 0.240133i | 0.0276391 | + | 0.00898048i | ||||
\(716\) | −6.33688 | − | 19.5029i | −0.236820 | − | 0.728858i | ||||
\(717\) | 8.89002 | − | 12.2361i | 0.332004 | − | 0.456964i | ||||
\(718\) | − | 30.1803i | − | 1.12632i | ||||||
\(719\) | −3.88854 | −0.145018 | −0.0725091 | − | 0.997368i | \(-0.523101\pi\) | ||||
−0.0725091 | + | 0.997368i | \(0.523101\pi\) | |||||||
\(720\) | −1.80902 | − | 1.31433i | −0.0674181 | − | 0.0489821i | ||||
\(721\) | 8.18034 | − | 5.94336i | 0.304652 | − | 0.221342i | ||||
\(722\) | 0.587785 | + | 0.809017i | 0.0218751 | + | 0.0301085i | ||||
\(723\) | −7.02067 | − | 2.28115i | −0.261101 | − | 0.0848370i | ||||
\(724\) | −10.7082 | − | 7.77997i | −0.397967 | − | 0.289140i | ||||
\(725\) | −10.5902 | + | 32.5932i | −0.393309 | + | 1.21048i | ||||
\(726\) | 1.64590 | + | 5.06555i | 0.0610850 | + | 0.188000i | ||||
\(727\) | 21.3723 | + | 29.4164i | 0.792654 | + | 1.09099i | 0.993773 | + | 0.111427i | \(0.0355422\pi\) |
−0.201119 | + | 0.979567i | \(0.564458\pi\) | |||||||
\(728\) | −0.171513 | + | 0.0557281i | −0.00635671 | + | 0.00206542i | ||||
\(729\) | −0.309017 | − | 0.951057i | −0.0114451 | − | 0.0352243i | ||||
\(730\) | 5.32624 | − | 3.86974i | 0.197133 | − | 0.143225i | ||||
\(731\) | −2.29180 | − | 7.05342i | −0.0847651 | − | 0.260880i | ||||
\(732\) | 2.62866 | + | 0.854102i | 0.0971579 | + | 0.0315685i | ||||
\(733\) | −23.7109 | + | 32.6353i | −0.875782 | + | 1.20541i | 0.101789 | + | 0.994806i | \(0.467543\pi\) |
−0.977571 | + | 0.210605i | \(0.932457\pi\) | |||||||
\(734\) | 6.41641 | − | 19.7477i | 0.236834 | − | 0.728900i | ||||
\(735\) | −7.19218 | − | 9.89919i | −0.265288 | − | 0.365137i | ||||
\(736\) | −4.73607 | + | 3.44095i | −0.174574 | + | 0.126835i | ||||
\(737\) | −11.2007 | + | 15.4164i | −0.412582 | + | 0.567871i | ||||
\(738\) | − | 7.70820i | − | 0.283743i | ||||||
\(739\) | 18.4721 | 0.679509 | 0.339754 | − | 0.940514i | \(-0.389656\pi\) | ||||
0.339754 | + | 0.940514i | \(0.389656\pi\) | |||||||
\(740\) | 14.2658 | − | 19.6353i | 0.524423 | − | 0.721806i | ||||
\(741\) | −0.201626 | − | 0.620541i | −0.00740692 | − | 0.0227962i | ||||
\(742\) | −9.06154 | − | 2.94427i | −0.332659 | − | 0.108088i | ||||
\(743\) | 11.9787i | 0.439456i | 0.975561 | + | 0.219728i | \(0.0705170\pi\) | ||||
−0.975561 | + | 0.219728i | \(0.929483\pi\) | |||||||
\(744\) | 4.78115 | − | 2.85317i | 0.175286 | − | 0.104602i | ||||
\(745\) | −32.6869 | −1.19756 | ||||||||
\(746\) | −11.7533 | + | 36.1729i | −0.430318 | + | 1.32438i | ||||
\(747\) | −2.62866 | + | 0.854102i | −0.0961775 | + | 0.0312500i | ||||
\(748\) | 2.59590 | − | 3.57295i | 0.0949155 | − | 0.130640i | ||||
\(749\) | −19.4164 | −0.709460 | ||||||||
\(750\) | 11.1803 | 0.408248 | ||||||||
\(751\) | −14.3090 | − | 10.3961i | −0.522143 | − | 0.379359i | 0.295267 | − | 0.955415i | \(-0.404591\pi\) |
−0.817411 | + | 0.576055i | \(0.804591\pi\) | |||||||
\(752\) | −1.81636 | − | 2.50000i | −0.0662357 | − | 0.0911656i | ||||
\(753\) | −7.69421 | − | 10.5902i | −0.280393 | − | 0.385927i | ||||
\(754\) | −0.309017 | + | 0.951057i | −0.0112537 | + | 0.0346354i | ||||
\(755\) | −32.3607 | − | 23.5114i | −1.17773 | − | 0.855668i | ||||
\(756\) | −0.381966 | + | 1.17557i | −0.0138920 | + | 0.0427551i | ||||
\(757\) | −44.4347 | + | 14.4377i | −1.61500 | + | 0.524747i | −0.970756 | − | 0.240069i | \(-0.922830\pi\) |
−0.644249 | + | 0.764816i | \(0.722830\pi\) | |||||||
\(758\) | −4.25325 | − | 5.85410i | −0.154485 | − | 0.212631i | ||||
\(759\) | −4.30902 | − | 13.2618i | −0.156407 | − | 0.481373i | ||||
\(760\) | −9.51057 | + | 3.09017i | −0.344984 | + | 0.112092i | ||||
\(761\) | 31.7426 | − | 23.0624i | 1.15067 | − | 0.836011i | 0.162100 | − | 0.986774i | \(-0.448173\pi\) |
0.988570 | + | 0.150764i | \(0.0481732\pi\) | |||||||
\(762\) | 15.9434 | − | 5.18034i | 0.577570 | − | 0.187664i | ||||
\(763\) | 14.6619 | + | 4.76393i | 0.530796 | + | 0.172466i | ||||
\(764\) | −5.85410 | − | 4.25325i | −0.211794 | − | 0.153877i | ||||
\(765\) | 3.94298 | + | 1.28115i | 0.142559 | + | 0.0463202i | ||||
\(766\) | 27.2533 | − | 19.8007i | 0.984701 | − | 0.715427i | ||||
\(767\) | −0.269782 | − | 0.371323i | −0.00974126 | − | 0.0134077i | ||||
\(768\) | −0.587785 | + | 0.809017i | −0.0212099 | + | 0.0291929i | ||||
\(769\) | 36.0902 | 1.30144 | 0.650722 | − | 0.759316i | \(-0.274466\pi\) | ||||
0.650722 | + | 0.759316i | \(0.274466\pi\) | |||||||
\(770\) | −6.58359 | −0.237256 | ||||||||
\(771\) | −11.0172 | − | 8.00448i | −0.396776 | − | 0.288274i | ||||
\(772\) | 16.8415 | − | 5.47214i | 0.606139 | − | 0.196946i | ||||
\(773\) | −30.2218 | − | 9.81966i | −1.08700 | − | 0.353189i | −0.289915 | − | 0.957052i | \(-0.593627\pi\) |
−0.797088 | + | 0.603864i | \(0.793627\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | −10.9549 | + | 25.5928i | −0.393512 | + | 0.919319i | ||||
\(776\) | −0.944272 | −0.0338974 | ||||||||
\(777\) | −12.7598 | − | 4.14590i | −0.457754 | − | 0.148733i | ||||
\(778\) | −13.3148 | + | 4.32624i | −0.477358 | + | 0.155103i | ||||
\(779\) | −27.8885 | − | 20.2622i | −0.999211 | − | 0.725969i | ||||
\(780\) | 0.326238 | 0.0116812 | ||||||||
\(781\) | 9.52786 | 0.340934 | ||||||||
\(782\) | 6.37988 | − | 8.78115i | 0.228144 | − | 0.314013i | ||||
\(783\) | 4.02874 | + | 5.54508i | 0.143975 | + | 0.198165i | ||||
\(784\) | −4.42705 | + | 3.21644i | −0.158109 | + | 0.114873i | ||||
\(785\) | −36.3444 | − | 11.8090i | −1.29719 | − | 0.421482i | ||||
\(786\) | −4.69098 | − | 3.40820i | −0.167322 | − | 0.121566i | ||||
\(787\) | 14.4046 | + | 4.68034i | 0.513469 | + | 0.166836i | 0.554279 | − | 0.832331i | \(-0.312994\pi\) |
−0.0408105 | + | 0.999167i | \(0.512994\pi\) | |||||||
\(788\) | −6.60440 | + | 2.14590i | −0.235272 | + | 0.0764445i | ||||
\(789\) | −5.39919 | + | 3.92274i | −0.192216 | + | 0.139653i | ||||
\(790\) | 12.9515 | − | 4.20820i | 0.460794 | − | 0.149721i | ||||
\(791\) | −3.23607 | − | 9.95959i | −0.115061 | − | 0.354122i | ||||
\(792\) | −1.40008 | − | 1.92705i | −0.0497498 | − | 0.0684748i | ||||
\(793\) | −0.383516 | + | 0.124612i | −0.0136190 | + | 0.00442509i | ||||
\(794\) | −2.04508 | + | 6.29412i | −0.0725773 | + | 0.223370i | ||||
\(795\) | 13.9443 | + | 10.1311i | 0.494552 | + | 0.359313i | ||||
\(796\) | 7.29837 | − | 22.4621i | 0.258684 | − | 0.796147i | ||||
\(797\) | 14.9394 | + | 20.5623i | 0.529180 | + | 0.728354i | 0.987005 | − | 0.160688i | \(-0.0513713\pi\) |
−0.457825 | + | 0.889042i | \(0.651371\pi\) | |||||||
\(798\) | 3.24920 | + | 4.47214i | 0.115020 | + | 0.158312i | ||||
\(799\) | 4.63525 | + | 3.36771i | 0.163984 | + | 0.119141i | ||||
\(800\) | − | 5.00000i | − | 0.176777i | ||||||
\(801\) | 2.29180 | 0.0809766 | ||||||||
\(802\) | 6.32688 | − | 8.70820i | 0.223410 | − | 0.307497i | ||||
\(803\) | 6.66991 | − | 2.16718i | 0.235376 | − | 0.0764783i | ||||
\(804\) | −2.47214 | + | 7.60845i | −0.0871855 | + | 0.268329i | ||||
\(805\) | −16.1803 | −0.570282 | ||||||||
\(806\) | −0.319660 | + | 0.746787i | −0.0112595 | + | 0.0263044i | ||||
\(807\) | 10.0344i | 0.353229i | ||||||||
\(808\) | 7.24518 | + | 2.35410i | 0.254885 | + | 0.0828170i | ||||
\(809\) | −4.90983 | − | 15.1109i | −0.172620 | − | 0.531271i | 0.826896 | − | 0.562354i | \(-0.190104\pi\) |
−0.999517 | + | 0.0310833i | \(0.990104\pi\) | |||||||
\(810\) | 1.31433 | − | 1.80902i | 0.0461808 | − | 0.0635624i | ||||
\(811\) | −34.3607 | −1.20657 | −0.603283 | − | 0.797527i | \(-0.706141\pi\) | ||||
−0.603283 | + | 0.797527i | \(0.706141\pi\) | |||||||
\(812\) | − | 8.47214i | − | 0.297314i | ||||||
\(813\) | −11.7759 | + | 16.2082i | −0.413001 | + | 0.568447i | ||||
\(814\) | 20.9164 | − | 15.1967i | 0.733120 | − | 0.532643i | ||||
\(815\) | 17.1315 | + | 23.5795i | 0.600091 | + | 0.825955i | ||||
\(816\) | 0.572949 | − | 1.76336i | 0.0200572 | − | 0.0617298i | ||||
\(817\) | −10.5146 | + | 14.4721i | −0.367860 | + | 0.506316i | ||||
\(818\) | −29.0665 | − | 9.44427i | −1.01629 | − | 0.330211i | ||||
\(819\) | −0.0557281 | − | 0.171513i | −0.00194730 | − | 0.00599316i | ||||
\(820\) | 13.9443 | − | 10.1311i | 0.486955 | − | 0.353794i | ||||
\(821\) | −13.3926 | − | 41.2182i | −0.467405 | − | 1.43853i | −0.855932 | − | 0.517088i | \(-0.827016\pi\) |
0.388527 | − | 0.921437i | \(-0.372984\pi\) | |||||||
\(822\) | −8.95554 | + | 2.90983i | −0.312360 | + | 0.101492i | ||||
\(823\) | 11.2412 | + | 15.4721i | 0.391842 | + | 0.539325i | 0.958673 | − | 0.284509i | \(-0.0918307\pi\) |
−0.566831 | + | 0.823834i | \(0.691831\pi\) | |||||||
\(824\) | 2.52786 | + | 7.77997i | 0.0880623 | + | 0.271028i | ||||
\(825\) | 11.3269 | + | 3.68034i | 0.394353 | + | 0.128133i | ||||
\(826\) | 3.14590 | + | 2.28563i | 0.109460 | + | 0.0795272i | ||||
\(827\) | 15.2824 | + | 4.96556i | 0.531422 | + | 0.172669i | 0.562423 | − | 0.826850i | \(-0.309869\pi\) |
−0.0310008 | + | 0.999519i | \(0.509869\pi\) | |||||||
\(828\) | −3.44095 | − | 4.73607i | −0.119581 | − | 0.164590i | ||||
\(829\) | −11.0000 | + | 7.99197i | −0.382046 | + | 0.277573i | −0.762188 | − | 0.647355i | \(-0.775875\pi\) |
0.380142 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(830\) | −5.00000 | − | 3.63271i | −0.173553 | − | 0.126093i | ||||
\(831\) | 3.56231 | 0.123575 | ||||||||
\(832\) | − | 0.145898i | − | 0.00505810i | ||||||
\(833\) | 5.96361 | − | 8.20820i | 0.206627 | − | 0.284397i | ||||
\(834\) | 0.909830 | + | 2.80017i | 0.0315048 | + | 0.0969619i | ||||
\(835\) | 29.9645 | + | 9.73607i | 1.03697 | + | 0.336931i | ||||
\(836\) | −10.6525 | −0.368424 | ||||||||
\(837\) | 2.85317 | + | 4.78115i | 0.0986200 | + | 0.165261i | ||||
\(838\) | − | 38.6180i | − | 1.33404i | ||||||
\(839\) | −1.52786 | + | 4.70228i | −0.0527477 | + | 0.162341i | −0.973960 | − | 0.226719i | \(-0.927200\pi\) |
0.921212 | + | 0.389060i | \(0.127200\pi\) | |||||||
\(840\) | −2.62866 | + | 0.854102i | −0.0906972 | + | 0.0294693i | ||||
\(841\) | −14.5451 | − | 10.5676i | −0.501555 | − | 0.364401i | ||||
\(842\) | − | 23.1246i | − | 0.796927i | ||||||
\(843\) | 12.3607i | 0.425724i | ||||||||
\(844\) | 10.2361 | + | 7.43694i | 0.352340 | + | 0.255990i | ||||
\(845\) | 23.4787 | − | 17.0583i | 0.807692 | − | 0.586823i | ||||
\(846\) | 2.50000 | − | 1.81636i | 0.0859518 | − | 0.0624476i | ||||
\(847\) | 6.26137 | + | 2.03444i | 0.215143 | + | 0.0699042i | ||||
\(848\) | 4.53077 | − | 6.23607i | 0.155587 | − | 0.214147i | ||||
\(849\) | 3.19098 | − | 9.82084i | 0.109514 | − | 0.337050i | ||||
\(850\) | 2.86475 | + | 8.81678i | 0.0982599 | + | 0.302413i | ||||
\(851\) | 51.4058 | − | 37.3485i | 1.76217 | − | 1.28029i | ||||
\(852\) | 3.80423 | − | 1.23607i | 0.130331 | − | 0.0423470i | ||||
\(853\) | 28.4459 | − | 9.24265i | 0.973970 | − | 0.316462i | 0.221553 | − | 0.975148i | \(-0.428888\pi\) |
0.752418 | + | 0.658686i | \(0.228888\pi\) | |||||||
\(854\) | 2.76393 | − | 2.00811i | 0.0945798 | − | 0.0687163i | ||||
\(855\) | −3.09017 | − | 9.51057i | −0.105682 | − | 0.325254i | ||||
\(856\) | 4.85410 | − | 14.9394i | 0.165910 | − | 0.510618i | ||||
\(857\) | −32.0382 | + | 44.0967i | −1.09440 | + | 1.50632i | −0.251801 | + | 0.967779i | \(0.581023\pi\) |
−0.842602 | + | 0.538537i | \(0.818977\pi\) | |||||||
\(858\) | 0.330515 | + | 0.107391i | 0.0112836 | + | 0.00366626i | ||||
\(859\) | 7.32624 | − | 5.32282i | 0.249968 | − | 0.181612i | −0.455745 | − | 0.890111i | \(-0.650627\pi\) |
0.705713 | + | 0.708498i | \(0.250627\pi\) | |||||||
\(860\) | −5.25731 | − | 7.23607i | −0.179273 | − | 0.246748i | ||||
\(861\) | −7.70820 | − | 5.60034i | −0.262695 | − | 0.190859i | ||||
\(862\) | 23.2361i | 0.791424i | ||||||||
\(863\) | 6.83282i | 0.232592i | 0.993215 | + | 0.116296i | \(0.0371021\pi\) | ||||
−0.993215 | + | 0.116296i | \(0.962898\pi\) | |||||||
\(864\) | −0.809017 | − | 0.587785i | −0.0275233 | − | 0.0199969i | ||||
\(865\) | −25.9030 | + | 8.41641i | −0.880730 | + | 0.286166i | ||||
\(866\) | −3.32624 | + | 10.2371i | −0.113030 | + | 0.347871i | ||||
\(867\) | − | 13.5623i | − | 0.460600i | ||||||
\(868\) | 0.620541 | − | 6.85410i | 0.0210625 | − | 0.232643i | ||||
\(869\) | 14.5066 | 0.492102 | ||||||||
\(870\) | −4.73607 | + | 14.5761i | −0.160568 | + | 0.494177i | ||||
\(871\) | −0.360680 | − | 1.11006i | −0.0122212 | − | 0.0376129i | ||||
\(872\) | −7.33094 | + | 10.0902i | −0.248257 | + | 0.341696i | ||||
\(873\) | − | 0.944272i | − | 0.0319588i | ||||||
\(874\) | −26.1803 | −0.885563 | ||||||||
\(875\) | 8.12299 | − | 11.1803i | 0.274607 | − | 0.377964i | ||||
\(876\) | 2.38197 | − | 1.73060i | 0.0804792 | − | 0.0584715i | ||||
\(877\) | 3.52671 | + | 4.85410i | 0.119089 | + | 0.163911i | 0.864399 | − | 0.502806i | \(-0.167699\pi\) |
−0.745311 | + | 0.666717i | \(0.767699\pi\) | |||||||
\(878\) | 25.7113 | + | 8.35410i | 0.867714 | + | 0.281937i | ||||
\(879\) | −5.47214 | − | 3.97574i | −0.184571 | − | 0.134098i | ||||
\(880\) | 1.64590 | − | 5.06555i | 0.0554832 | − | 0.170760i | ||||
\(881\) | −7.18034 | − | 22.0988i | −0.241912 | − | 0.744528i | −0.996129 | − | 0.0879030i | \(-0.971983\pi\) |
0.754217 | − | 0.656625i | \(-0.228017\pi\) | |||||||
\(882\) | −3.21644 | − | 4.42705i | −0.108303 | − | 0.149067i | ||||
\(883\) | −35.5524 | + | 11.5517i | −1.19643 | + | 0.388744i | −0.838447 | − | 0.544983i | \(-0.816536\pi\) |
−0.357985 | + | 0.933727i | \(0.616536\pi\) | |||||||
\(884\) | 0.0835921 | + | 0.257270i | 0.00281151 | + | 0.00865293i | ||||
\(885\) | −4.13474 | − | 5.69098i | −0.138988 | − | 0.191300i | ||||
\(886\) | −10.7984 | − | 33.2340i | −0.362778 | − | 1.11652i | ||||
\(887\) | −34.2178 | − | 11.1180i | −1.14892 | − | 0.373307i | −0.328184 | − | 0.944614i | \(-0.606437\pi\) |
−0.820737 | + | 0.571307i | \(0.806437\pi\) | |||||||
\(888\) | 6.37988 | − | 8.78115i | 0.214095 | − | 0.294676i | ||||
\(889\) | 6.40325 | − | 19.7072i | 0.214758 | − | 0.660958i | ||||
\(890\) | 3.01217 | + | 4.14590i | 0.100968 | + | 0.138971i | ||||
\(891\) | 1.92705 | − | 1.40008i | 0.0645586 | − | 0.0469046i | ||||
\(892\) | −15.2169 | + | 20.9443i | −0.509500 | + | 0.701266i | ||||
\(893\) | − | 13.8197i | − | 0.462457i | ||||||
\(894\) | −14.6180 | −0.488900 | ||||||||
\(895\) | 37.0967 | + | 26.9524i | 1.24001 | + | 0.900918i | ||||
\(896\) | 0.381966 | + | 1.17557i | 0.0127606 | + | 0.0392731i | ||||
\(897\) | 0.812299 | + | 0.263932i | 0.0271219 | + | 0.00881243i | ||||
\(898\) | − | 8.00000i | − | 0.266963i | ||||||
\(899\) | −28.7254 | − | 25.1235i | −0.958047 | − | 0.837916i | ||||
\(900\) | 5.00000 | 0.166667 | ||||||||
\(901\) | −4.41641 | + | 13.5923i | −0.147132 | + | 0.452825i | ||||
\(902\) | 17.4620 | − | 5.67376i | 0.581422 | − | 0.188916i | ||||
\(903\) | −2.90617 | + | 4.00000i | −0.0967113 | + | 0.133112i | ||||
\(904\) | 8.47214 | 0.281779 | ||||||||
\(905\) | 29.5967 | 0.983829 | ||||||||
\(906\) | −14.4721 | − | 10.5146i | −0.480805 | − | 0.349325i | ||||
\(907\) | 2.26538 | + | 3.11803i | 0.0752209 | + | 0.103533i | 0.844970 | − | 0.534814i | \(-0.179618\pi\) |
−0.769749 | + | 0.638347i | \(0.779618\pi\) | |||||||
\(908\) | −3.35520 | − | 4.61803i | −0.111346 | − | 0.153255i | ||||
\(909\) | −2.35410 | + | 7.24518i | −0.0780806 | + | 0.240307i | ||||
\(910\) | 0.237026 | − | 0.326238i | 0.00785733 | − | 0.0108147i | ||||
\(911\) | 16.5623 | − | 50.9735i | 0.548734 | − | 1.68883i | −0.163209 | − | 0.986591i | \(-0.552185\pi\) |
0.711943 | − | 0.702237i | \(-0.247815\pi\) | |||||||
\(912\) | −4.25325 | + | 1.38197i | −0.140839 | + | 0.0457615i | ||||
\(913\) | −3.86974 | − | 5.32624i | −0.128070 | − | 0.176273i | ||||
\(914\) | −8.23607 | − | 25.3480i | −0.272425 | − | 0.838438i | ||||
\(915\) | −5.87785 | + | 1.90983i | −0.194316 | + | 0.0631370i | ||||
\(916\) | 20.7082 | − | 15.0454i | 0.684218 | − | 0.497114i | ||||
\(917\) | −6.81640 | + | 2.21478i | −0.225097 | + | 0.0731385i | ||||
\(918\) | 1.76336 | + | 0.572949i | 0.0581994 | + | 0.0189101i | ||||
\(919\) | 19.6803 | + | 14.2986i | 0.649195 | + | 0.471667i | 0.862997 | − | 0.505210i | \(-0.168585\pi\) |
−0.213802 | + | 0.976877i | \(0.568585\pi\) | |||||||
\(920\) | 4.04508 | − | 12.4495i | 0.133363 | − | 0.410448i | ||||
\(921\) | −5.92705 | + | 4.30625i | −0.195303 | + | 0.141896i | ||||
\(922\) | −7.67396 | − | 10.5623i | −0.252729 | − | 0.347851i | ||||
\(923\) | −0.343027 | + | 0.472136i | −0.0112909 | + | 0.0155405i | ||||
\(924\) | −2.94427 | −0.0968594 | ||||||||
\(925\) | 54.2705i | 1.78440i | ||||||||
\(926\) | 20.4721 | + | 14.8739i | 0.672756 | + | 0.488786i | ||||
\(927\) | −7.77997 | + | 2.52786i | −0.255528 | + | 0.0830259i | ||||
\(928\) | 6.51864 | + | 2.11803i | 0.213985 | + | 0.0695279i | ||||
\(929\) | −53.4164 | −1.75254 | −0.876268 | − | 0.481824i | \(-0.839974\pi\) | ||||
−0.876268 | + | 0.481824i | \(0.839974\pi\) | |||||||
\(930\) | −4.89919 | + | 11.4454i | −0.160651 | + | 0.375311i | ||||
\(931\) | −24.4721 | −0.802042 | ||||||||
\(932\) | 12.0005 | + | 3.89919i | 0.393088 | + | 0.127722i | ||||
\(933\) | 12.7598 | − | 4.14590i | 0.417736 | − | 0.135731i | ||||
\(934\) | −21.4164 | − | 15.5599i | −0.700766 | − | 0.509136i | ||||
\(935\) | 9.87539i | 0.322960i | ||||||||
\(936\) | 0.145898 | 0.00476883 | ||||||||
\(937\) | −3.11817 | + | 4.29180i | −0.101866 | + | 0.140207i | −0.856907 | − | 0.515471i | \(-0.827617\pi\) |
0.755041 | + | 0.655678i | \(0.227617\pi\) | |||||||
\(938\) | 5.81234 | + | 8.00000i | 0.189780 | + | 0.261209i | ||||
\(939\) | 4.23607 | − | 3.07768i | 0.138239 | − | 0.100436i | ||||
\(940\) | 6.57164 | + | 2.13525i | 0.214343 | + | 0.0696443i | ||||
\(941\) | −35.4336 | − | 25.7440i | −1.15510 | − | 0.839232i | −0.165952 | − | 0.986134i | \(-0.553070\pi\) |
−0.989151 | + | 0.146902i | \(0.953070\pi\) | |||||||
\(942\) | −16.2537 | − | 5.28115i | −0.529575 | − | 0.172069i | ||||
\(943\) | 42.9161 | − | 13.9443i | 1.39754 | − | 0.454088i | ||||
\(944\) | −2.54508 | + | 1.84911i | −0.0828355 | + | 0.0601835i | ||||
\(945\) | −0.854102 | − | 2.62866i | −0.0277839 | − | 0.0855102i | ||||
\(946\) | −2.94427 | − | 9.06154i | −0.0957265 | − | 0.294616i | ||||
\(947\) | −25.1765 | − | 34.6525i | −0.818126 | − | 1.12605i | −0.990018 | − | 0.140938i | \(-0.954988\pi\) |
0.171892 | − | 0.985116i | \(-0.445012\pi\) | |||||||
\(948\) | 5.79210 | − | 1.88197i | 0.188119 | − | 0.0611234i | ||||
\(949\) | −0.132742 | + | 0.408539i | −0.00430900 | + | 0.0132617i | ||||
\(950\) | 13.1433 | − | 18.0902i | 0.426424 | − | 0.586923i | ||||
\(951\) | 5.47214 | − | 16.8415i | 0.177446 | − | 0.546123i | ||||
\(952\) | −1.34708 | − | 1.85410i | −0.0436592 | − | 0.0600918i | ||||
\(953\) | 19.8662 | + | 27.3435i | 0.643529 | + | 0.885742i | 0.998798 | − | 0.0490227i | \(-0.0156107\pi\) |
−0.355269 | + | 0.934764i | \(0.615611\pi\) | |||||||
\(954\) | 6.23607 | + | 4.53077i | 0.201900 | + | 0.146689i | ||||
\(955\) | 16.1803 | 0.523584 | ||||||||
\(956\) | 15.1246 | 0.489165 | ||||||||
\(957\) | −9.59632 | + | 13.2082i | −0.310205 | + | 0.426961i | ||||
\(958\) | −17.0130 | + | 5.52786i | −0.549666 | + | 0.178597i | ||||
\(959\) | −3.59675 | + | 11.0697i | −0.116145 | + | 0.357458i | ||||
\(960\) | − | 2.23607i | − | 0.0721688i | ||||||
\(961\) | −21.3992 | − | 22.4293i | −0.690296 | − | 0.723527i | ||||
\(962\) | 1.58359i | 0.0510571i | ||||||||
\(963\) | 14.9394 | + | 4.85410i | 0.481415 | + | 0.156421i | ||||
\(964\) | −2.28115 | − | 7.02067i | −0.0734710 | − | 0.226120i | ||||
\(965\) | −23.2744 | + | 32.0344i | −0.749229 | + | 1.03123i | ||||
\(966\) | −7.23607 | −0.232817 | ||||||||
\(967\) | 53.5967i | 1.72356i | 0.507286 | + | 0.861778i | \(0.330649\pi\) | ||||
−0.507286 | + | 0.861778i | \(0.669351\pi\) | |||||||
\(968\) | −3.13068 | + | 4.30902i | −0.100624 | + | 0.138497i | ||||
\(969\) | 6.70820 | − | 4.87380i | 0.215499 | − | 0.156569i | ||||
\(970\) | 1.70820 | − | 1.24108i | 0.0548471 | − | 0.0398488i | ||||
\(971\) | −12.0836 | + | 37.1895i | −0.387781 | + | 1.19347i | 0.546662 | + | 0.837353i | \(0.315898\pi\) |
−0.934443 | + | 0.356113i | \(0.884102\pi\) | |||||||
\(972\) | 0.587785 | − | 0.809017i | 0.0188532 | − | 0.0259492i | ||||
\(973\) | 3.46120 | + | 1.12461i | 0.110961 | + | 0.0360534i | ||||
\(974\) | 2.79837 | + | 8.61251i | 0.0896657 | + | 0.275963i | ||||
\(975\) | −0.590170 | + | 0.428784i | −0.0189006 | + | 0.0137321i | ||||
\(976\) | 0.854102 | + | 2.62866i | 0.0273391 | + | 0.0841412i | ||||
\(977\) | −0.983813 | + | 0.319660i | −0.0314750 | + | 0.0102268i | −0.324712 | − | 0.945813i | \(-0.605267\pi\) |
0.293237 | + | 0.956040i | \(0.405267\pi\) | |||||||
\(978\) | 7.66145 | + | 10.5451i | 0.244986 | + | 0.337195i | ||||
\(979\) | 1.68692 | + | 5.19180i | 0.0539141 | + | 0.165931i | ||||
\(980\) | 3.78115 | − | 11.6372i | 0.120785 | − | 0.371736i | ||||
\(981\) | −10.0902 | − | 7.33094i | −0.322154 | − | 0.234059i | ||||
\(982\) | 9.54332 | + | 3.10081i | 0.304540 | + | 0.0989509i | ||||
\(983\) | 12.8533 | + | 17.6910i | 0.409955 | + | 0.564255i | 0.963207 | − | 0.268759i | \(-0.0866135\pi\) |
−0.553252 | + | 0.833014i | \(0.686613\pi\) | |||||||
\(984\) | 6.23607 | − | 4.53077i | 0.198799 | − | 0.144436i | ||||
\(985\) | 9.12705 | − | 12.5623i | 0.290812 | − | 0.400268i | ||||
\(986\) | −12.7082 | −0.404712 | ||||||||
\(987\) | − | 3.81966i | − | 0.121581i | ||||||
\(988\) | 0.383516 | − | 0.527864i | 0.0122013 | − | 0.0167936i | ||||
\(989\) | −7.23607 | − | 22.2703i | −0.230094 | − | 0.708155i | ||||
\(990\) | 5.06555 | + | 1.64590i | 0.160994 | + | 0.0523101i | ||||
\(991\) | −19.4164 | −0.616783 | −0.308391 | − | 0.951260i | \(-0.599791\pi\) | ||||
−0.308391 | + | 0.951260i | \(0.599791\pi\) | |||||||
\(992\) | 5.11855 | + | 2.19098i | 0.162514 | + | 0.0695638i | ||||
\(993\) | − | 13.2361i | − | 0.420034i | ||||||
\(994\) | 1.52786 | − | 4.70228i | 0.0484609 | − | 0.149147i | ||||
\(995\) | 16.3197 | + | 50.2267i | 0.517368 | + | 1.59229i | ||||
\(996\) | −2.23607 | − | 1.62460i | −0.0708525 | − | 0.0514774i | ||||
\(997\) | 36.1459i | 1.14475i | 0.819991 | + | 0.572376i | \(0.193978\pi\) | ||||
−0.819991 | + | 0.572376i | \(0.806022\pi\) | |||||||
\(998\) | 3.81966i | 0.120909i | ||||||||
\(999\) | 8.78115 | + | 6.37988i | 0.277823 | + | 0.201851i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 930.2.z.a.349.1 | ✓ | 8 | |
5.4 | even | 2 | inner | 930.2.z.a.349.2 | yes | 8 | |
31.4 | even | 5 | inner | 930.2.z.a.469.2 | yes | 8 | |
155.4 | even | 10 | inner | 930.2.z.a.469.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.z.a.349.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
930.2.z.a.349.2 | yes | 8 | 5.4 | even | 2 | inner | |
930.2.z.a.469.1 | yes | 8 | 155.4 | even | 10 | inner | |
930.2.z.a.469.2 | yes | 8 | 31.4 | even | 5 | inner |