Properties

Label 363.2.e.n.124.3
Level $363$
Weight $2$
Character 363.124
Analytic conductor $2.899$
Analytic rank $0$
Dimension $16$
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,2,Mod(124,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.124");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.e (of order \(5\), degree \(4\), not 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: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: 16.0.22502537891856000000000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 7x^{14} + 45x^{12} + 287x^{10} + 1829x^{8} + 1148x^{6} + 720x^{4} + 448x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 124.3
Root \(0.640974 + 0.465695i\) of defining polynomial
Character \(\chi\) \(=\) 363.124
Dual form 363.2.e.n.202.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.640974 - 0.465695i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.424058 + 1.30512i) q^{4} +(-2.72823 - 1.98218i) q^{5} +(0.640974 + 0.465695i) q^{6} +(-0.780063 + 2.40079i) q^{7} +(0.825636 + 2.54105i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.640974 - 0.465695i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.424058 + 1.30512i) q^{4} +(-2.72823 - 1.98218i) q^{5} +(0.640974 + 0.465695i) q^{6} +(-0.780063 + 2.40079i) q^{7} +(0.825636 + 2.54105i) q^{8} +(-0.809017 + 0.587785i) q^{9} -2.67181 q^{10} -1.37228 q^{12} +(-4.72544 + 3.43323i) q^{13} +(0.618034 + 1.90211i) q^{14} +(1.04209 - 3.20723i) q^{15} +(-0.507835 - 0.368964i) q^{16} +(2.16154 + 1.57045i) q^{17} +(-0.244830 + 0.753510i) q^{18} +(0.290403 + 0.893769i) q^{19} +(3.74390 - 2.72010i) q^{20} -2.52434 q^{21} +2.00000 q^{23} +(-2.16154 + 1.57045i) q^{24} +(1.96914 + 6.06040i) q^{25} +(-1.43004 + 4.40122i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.80252 - 2.03615i) q^{28} +(0.244830 - 0.753510i) q^{29} +(-0.825636 - 2.54105i) q^{30} +(-1.31685 + 0.956749i) q^{31} -5.84096 q^{32} +2.11684 q^{34} +(6.88698 - 5.00368i) q^{35} +(-0.424058 - 1.30512i) q^{36} +(1.54508 - 4.75528i) q^{37} +(0.602364 + 0.437643i) q^{38} +(-4.72544 - 3.43323i) q^{39} +(2.78428 - 8.56912i) q^{40} +(3.36508 + 10.3567i) q^{41} +(-1.61803 + 1.17557i) q^{42} +6.63325 q^{43} +3.37228 q^{45} +(1.28195 - 0.931389i) q^{46} +(-3.93829 - 12.1208i) q^{47} +(0.193976 - 0.596996i) q^{48} +(0.507835 + 0.368964i) q^{49} +(4.08446 + 2.96754i) q^{50} +(-0.825636 + 2.54105i) q^{51} +(-2.47691 - 7.62314i) q^{52} +(3.33060 - 2.41982i) q^{53} -0.792287 q^{54} -6.74456 q^{56} +(-0.760285 + 0.552379i) q^{57} +(-0.193976 - 0.596996i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(3.74390 + 2.72010i) q^{60} +(4.84475 + 3.51992i) q^{61} +(-0.398515 + 1.22650i) q^{62} +(-0.780063 - 2.40079i) q^{63} +(-2.72823 + 1.98218i) q^{64} +19.6974 q^{65} -1.11684 q^{67} +(-2.96625 + 2.15510i) q^{68} +(0.618034 + 1.90211i) q^{69} +(2.08418 - 6.41446i) q^{70} +(8.69253 + 6.31550i) q^{71} +(-2.16154 - 1.57045i) q^{72} +(-2.82985 + 8.70938i) q^{73} +(-1.22415 - 3.76755i) q^{74} +(-5.15528 + 3.74553i) q^{75} -1.28962 q^{76} -4.62772 q^{78} +(3.32418 - 2.41516i) q^{79} +(0.654141 + 2.01324i) q^{80} +(0.309017 - 0.951057i) q^{81} +(6.97997 + 5.07125i) q^{82} +(-1.52057 - 1.10476i) q^{83} +(1.07047 - 3.29456i) q^{84} +(-2.78428 - 8.56912i) q^{85} +(4.25174 - 3.08907i) q^{86} +0.792287 q^{87} -0.627719 q^{89} +(2.16154 - 1.57045i) q^{90} +(-4.55632 - 14.0229i) q^{91} +(-0.848116 + 2.61023i) q^{92} +(-1.31685 - 0.956749i) q^{93} +(-8.16893 - 5.93507i) q^{94} +(0.979321 - 3.01404i) q^{95} +(-1.80496 - 5.55509i) q^{96} +(-8.48588 + 6.16535i) q^{97} +0.497333 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9} + 24 q^{12} - 8 q^{14} - 2 q^{15} - 14 q^{16} + 30 q^{20} + 32 q^{23} - 14 q^{25} + 30 q^{26} - 4 q^{27} - 18 q^{31} - 104 q^{34} - 6 q^{36} - 20 q^{37} - 20 q^{38} - 8 q^{42} + 8 q^{45} + 28 q^{47} - 14 q^{48} + 14 q^{49} - 18 q^{53} - 16 q^{56} + 14 q^{58} + 24 q^{59} + 30 q^{60} - 2 q^{64} + 120 q^{67} - 8 q^{69} - 4 q^{70} + 20 q^{71} - 14 q^{75} - 120 q^{78} + 26 q^{80} - 4 q^{81} + 46 q^{82} + 44 q^{86} - 56 q^{89} + 36 q^{91} - 12 q^{92} - 18 q^{93} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.640974 0.465695i 0.453237 0.329296i −0.337636 0.941277i \(-0.609627\pi\)
0.790872 + 0.611981i \(0.209627\pi\)
\(3\) 0.309017 + 0.951057i 0.178411 + 0.549093i
\(4\) −0.424058 + 1.30512i −0.212029 + 0.652559i
\(5\) −2.72823 1.98218i −1.22010 0.886457i −0.223994 0.974590i \(-0.571910\pi\)
−0.996109 + 0.0881339i \(0.971910\pi\)
\(6\) 0.640974 + 0.465695i 0.261676 + 0.190119i
\(7\) −0.780063 + 2.40079i −0.294836 + 0.907413i 0.688440 + 0.725293i \(0.258296\pi\)
−0.983276 + 0.182119i \(0.941704\pi\)
\(8\) 0.825636 + 2.54105i 0.291906 + 0.898396i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) −2.67181 −0.844902
\(11\) 0 0
\(12\) −1.37228 −0.396143
\(13\) −4.72544 + 3.43323i −1.31060 + 0.952207i −0.310602 + 0.950540i \(0.600531\pi\)
−0.999999 + 0.00166711i \(0.999469\pi\)
\(14\) 0.618034 + 1.90211i 0.165177 + 0.508361i
\(15\) 1.04209 3.20723i 0.269067 0.828103i
\(16\) −0.507835 0.368964i −0.126959 0.0922409i
\(17\) 2.16154 + 1.57045i 0.524251 + 0.380891i 0.818203 0.574929i \(-0.194970\pi\)
−0.293952 + 0.955820i \(0.594970\pi\)
\(18\) −0.244830 + 0.753510i −0.0577070 + 0.177604i
\(19\) 0.290403 + 0.893769i 0.0666230 + 0.205045i 0.978826 0.204694i \(-0.0656199\pi\)
−0.912203 + 0.409739i \(0.865620\pi\)
\(20\) 3.74390 2.72010i 0.837162 0.608234i
\(21\) −2.52434 −0.550856
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) −2.16154 + 1.57045i −0.441223 + 0.320567i
\(25\) 1.96914 + 6.06040i 0.393829 + 1.21208i
\(26\) −1.43004 + 4.40122i −0.280455 + 0.863151i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) −2.80252 2.03615i −0.529626 0.384796i
\(29\) 0.244830 0.753510i 0.0454638 0.139923i −0.925748 0.378141i \(-0.876563\pi\)
0.971212 + 0.238218i \(0.0765633\pi\)
\(30\) −0.825636 2.54105i −0.150740 0.463930i
\(31\) −1.31685 + 0.956749i −0.236514 + 0.171837i −0.699729 0.714409i \(-0.746696\pi\)
0.463215 + 0.886246i \(0.346696\pi\)
\(32\) −5.84096 −1.03255
\(33\) 0 0
\(34\) 2.11684 0.363036
\(35\) 6.88698 5.00368i 1.16411 0.845777i
\(36\) −0.424058 1.30512i −0.0706764 0.217520i
\(37\) 1.54508 4.75528i 0.254010 0.781764i −0.740013 0.672593i \(-0.765181\pi\)
0.994023 0.109171i \(-0.0348195\pi\)
\(38\) 0.602364 + 0.437643i 0.0977163 + 0.0709951i
\(39\) −4.72544 3.43323i −0.756676 0.549757i
\(40\) 2.78428 8.56912i 0.440233 1.35490i
\(41\) 3.36508 + 10.3567i 0.525538 + 1.61744i 0.763250 + 0.646103i \(0.223602\pi\)
−0.237712 + 0.971336i \(0.576398\pi\)
\(42\) −1.61803 + 1.17557i −0.249668 + 0.181394i
\(43\) 6.63325 1.01156 0.505781 0.862662i \(-0.331205\pi\)
0.505781 + 0.862662i \(0.331205\pi\)
\(44\) 0 0
\(45\) 3.37228 0.502710
\(46\) 1.28195 0.931389i 0.189013 0.137326i
\(47\) −3.93829 12.1208i −0.574458 1.76800i −0.638017 0.770022i \(-0.720245\pi\)
0.0635590 0.997978i \(-0.479755\pi\)
\(48\) 0.193976 0.596996i 0.0279980 0.0861689i
\(49\) 0.507835 + 0.368964i 0.0725479 + 0.0527091i
\(50\) 4.08446 + 2.96754i 0.577630 + 0.419673i
\(51\) −0.825636 + 2.54105i −0.115612 + 0.355818i
\(52\) −2.47691 7.62314i −0.343485 1.05714i
\(53\) 3.33060 2.41982i 0.457493 0.332388i −0.335054 0.942199i \(-0.608755\pi\)
0.792547 + 0.609811i \(0.208755\pi\)
\(54\) −0.792287 −0.107817
\(55\) 0 0
\(56\) −6.74456 −0.901280
\(57\) −0.760285 + 0.552379i −0.100702 + 0.0731644i
\(58\) −0.193976 0.596996i −0.0254703 0.0783894i
\(59\) −1.85410 + 5.70634i −0.241384 + 0.742902i 0.754827 + 0.655924i \(0.227721\pi\)
−0.996210 + 0.0869778i \(0.972279\pi\)
\(60\) 3.74390 + 2.72010i 0.483336 + 0.351164i
\(61\) 4.84475 + 3.51992i 0.620307 + 0.450679i 0.853029 0.521864i \(-0.174763\pi\)
−0.232722 + 0.972543i \(0.574763\pi\)
\(62\) −0.398515 + 1.22650i −0.0506114 + 0.155766i
\(63\) −0.780063 2.40079i −0.0982787 0.302471i
\(64\) −2.72823 + 1.98218i −0.341029 + 0.247772i
\(65\) 19.6974 2.44316
\(66\) 0 0
\(67\) −1.11684 −0.136444 −0.0682221 0.997670i \(-0.521733\pi\)
−0.0682221 + 0.997670i \(0.521733\pi\)
\(68\) −2.96625 + 2.15510i −0.359710 + 0.261345i
\(69\) 0.618034 + 1.90211i 0.0744025 + 0.228988i
\(70\) 2.08418 6.41446i 0.249108 0.766675i
\(71\) 8.69253 + 6.31550i 1.03161 + 0.749511i 0.968631 0.248503i \(-0.0799386\pi\)
0.0629829 + 0.998015i \(0.479939\pi\)
\(72\) −2.16154 1.57045i −0.254740 0.185080i
\(73\) −2.82985 + 8.70938i −0.331209 + 1.01936i 0.637351 + 0.770574i \(0.280030\pi\)
−0.968559 + 0.248782i \(0.919970\pi\)
\(74\) −1.22415 3.76755i −0.142305 0.437969i
\(75\) −5.15528 + 3.74553i −0.595281 + 0.432497i
\(76\) −1.28962 −0.147930
\(77\) 0 0
\(78\) −4.62772 −0.523986
\(79\) 3.32418 2.41516i 0.373999 0.271726i −0.384868 0.922972i \(-0.625753\pi\)
0.758867 + 0.651245i \(0.225753\pi\)
\(80\) 0.654141 + 2.01324i 0.0731352 + 0.225087i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 6.97997 + 5.07125i 0.770809 + 0.560025i
\(83\) −1.52057 1.10476i −0.166904 0.121263i 0.501198 0.865333i \(-0.332893\pi\)
−0.668102 + 0.744070i \(0.732893\pi\)
\(84\) 1.07047 3.29456i 0.116797 0.359466i
\(85\) −2.78428 8.56912i −0.301997 0.929452i
\(86\) 4.25174 3.08907i 0.458477 0.333103i
\(87\) 0.792287 0.0849421
\(88\) 0 0
\(89\) −0.627719 −0.0665380 −0.0332690 0.999446i \(-0.510592\pi\)
−0.0332690 + 0.999446i \(0.510592\pi\)
\(90\) 2.16154 1.57045i 0.227847 0.165540i
\(91\) −4.55632 14.0229i −0.477632 1.47000i
\(92\) −0.848116 + 2.61023i −0.0884223 + 0.272136i
\(93\) −1.31685 0.956749i −0.136551 0.0992103i
\(94\) −8.16893 5.93507i −0.842561 0.612156i
\(95\) 0.979321 3.01404i 0.100476 0.309234i
\(96\) −1.80496 5.55509i −0.184218 0.566964i
\(97\) −8.48588 + 6.16535i −0.861611 + 0.625997i −0.928323 0.371776i \(-0.878749\pi\)
0.0667120 + 0.997772i \(0.478749\pi\)
\(98\) 0.497333 0.0502383
\(99\) 0 0
\(100\) −8.74456 −0.874456
\(101\) 9.68950 7.03983i 0.964141 0.700490i 0.0100323 0.999950i \(-0.496807\pi\)
0.954109 + 0.299460i \(0.0968066\pi\)
\(102\) 0.654141 + 2.01324i 0.0647696 + 0.199340i
\(103\) −2.81726 + 8.67063i −0.277593 + 0.854343i 0.710929 + 0.703264i \(0.248275\pi\)
−0.988522 + 0.151079i \(0.951725\pi\)
\(104\) −12.6255 9.17296i −1.23803 0.899483i
\(105\) 6.88698 + 5.00368i 0.672101 + 0.488310i
\(106\) 1.00793 3.10208i 0.0978986 0.301301i
\(107\) −4.19072 12.8977i −0.405132 1.24687i −0.920785 0.390071i \(-0.872451\pi\)
0.515653 0.856798i \(-0.327549\pi\)
\(108\) 1.11020 0.806607i 0.106829 0.0776158i
\(109\) −9.94987 −0.953025 −0.476513 0.879168i \(-0.658099\pi\)
−0.476513 + 0.879168i \(0.658099\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) 1.28195 0.931389i 0.121133 0.0880080i
\(113\) 0.424058 + 1.30512i 0.0398920 + 0.122775i 0.969019 0.246985i \(-0.0794399\pi\)
−0.929127 + 0.369760i \(0.879440\pi\)
\(114\) −0.230083 + 0.708121i −0.0215492 + 0.0663216i
\(115\) −5.45647 3.96435i −0.508818 0.369678i
\(116\) 0.879596 + 0.639064i 0.0816685 + 0.0593356i
\(117\) 1.80496 5.55509i 0.166868 0.513568i
\(118\) 1.46898 + 4.52106i 0.135231 + 0.416197i
\(119\) −5.45647 + 3.96435i −0.500193 + 0.363412i
\(120\) 9.01011 0.822507
\(121\) 0 0
\(122\) 4.74456 0.429553
\(123\) −8.80990 + 6.40077i −0.794362 + 0.577138i
\(124\) −0.690248 2.12436i −0.0619861 0.190773i
\(125\) 1.43004 4.40122i 0.127907 0.393657i
\(126\) −1.61803 1.17557i −0.144146 0.104728i
\(127\) −7.88589 5.72943i −0.699759 0.508405i 0.180094 0.983649i \(-0.442360\pi\)
−0.879854 + 0.475244i \(0.842360\pi\)
\(128\) 2.78428 8.56912i 0.246098 0.757411i
\(129\) 2.04979 + 6.30860i 0.180474 + 0.555441i
\(130\) 12.6255 9.17296i 1.10733 0.804522i
\(131\) −6.63325 −0.579550 −0.289775 0.957095i \(-0.593580\pi\)
−0.289775 + 0.957095i \(0.593580\pi\)
\(132\) 0 0
\(133\) −2.37228 −0.205703
\(134\) −0.715868 + 0.520108i −0.0618415 + 0.0449305i
\(135\) 1.04209 + 3.20723i 0.0896890 + 0.276034i
\(136\) −2.20595 + 6.78921i −0.189158 + 0.582170i
\(137\) 8.69253 + 6.31550i 0.742653 + 0.539569i 0.893541 0.448982i \(-0.148213\pi\)
−0.150888 + 0.988551i \(0.548213\pi\)
\(138\) 1.28195 + 0.931389i 0.109127 + 0.0792851i
\(139\) −3.21140 + 9.88367i −0.272387 + 0.838322i 0.717512 + 0.696547i \(0.245281\pi\)
−0.989899 + 0.141775i \(0.954719\pi\)
\(140\) 3.60991 + 11.1102i 0.305093 + 0.938981i
\(141\) 10.3106 7.49107i 0.868306 0.630862i
\(142\) 8.51278 0.714376
\(143\) 0 0
\(144\) 0.627719 0.0523099
\(145\) −2.16154 + 1.57045i −0.179506 + 0.130419i
\(146\) 2.24205 + 6.90033i 0.185554 + 0.571075i
\(147\) −0.193976 + 0.596996i −0.0159988 + 0.0492394i
\(148\) 5.55099 + 4.03303i 0.456289 + 0.331513i
\(149\) 2.16154 + 1.57045i 0.177081 + 0.128657i 0.672795 0.739829i \(-0.265094\pi\)
−0.495714 + 0.868486i \(0.665094\pi\)
\(150\) −1.56013 + 4.80158i −0.127384 + 0.392047i
\(151\) 6.82131 + 20.9938i 0.555111 + 1.70845i 0.695651 + 0.718380i \(0.255116\pi\)
−0.140541 + 0.990075i \(0.544884\pi\)
\(152\) −2.03134 + 1.47586i −0.164763 + 0.119708i
\(153\) −2.67181 −0.216003
\(154\) 0 0
\(155\) 5.48913 0.440897
\(156\) 6.48463 4.71136i 0.519186 0.377211i
\(157\) 3.82325 + 11.7667i 0.305128 + 0.939088i 0.979629 + 0.200814i \(0.0643588\pi\)
−0.674501 + 0.738274i \(0.735641\pi\)
\(158\) 1.00599 3.09610i 0.0800319 0.246313i
\(159\) 3.33060 + 2.41982i 0.264134 + 0.191904i
\(160\) 15.9355 + 11.5778i 1.25981 + 0.915307i
\(161\) −1.56013 + 4.80158i −0.122955 + 0.378417i
\(162\) −0.244830 0.753510i −0.0192357 0.0592013i
\(163\) 2.93489 2.13232i 0.229878 0.167016i −0.466884 0.884319i \(-0.654623\pi\)
0.696762 + 0.717302i \(0.254623\pi\)
\(164\) −14.9436 −1.16690
\(165\) 0 0
\(166\) −1.48913 −0.115579
\(167\) −19.1404 + 13.9063i −1.48113 + 1.07610i −0.503935 + 0.863741i \(0.668115\pi\)
−0.977192 + 0.212360i \(0.931885\pi\)
\(168\) −2.08418 6.41446i −0.160798 0.494886i
\(169\) 6.52546 20.0833i 0.501959 1.54487i
\(170\) −5.77524 4.19596i −0.442941 0.321815i
\(171\) −0.760285 0.552379i −0.0581404 0.0422415i
\(172\) −2.81288 + 8.65717i −0.214480 + 0.660103i
\(173\) −2.14093 6.58911i −0.162772 0.500961i 0.836093 0.548588i \(-0.184834\pi\)
−0.998865 + 0.0476266i \(0.984834\pi\)
\(174\) 0.507835 0.368964i 0.0384989 0.0279711i
\(175\) −16.0858 −1.21597
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) −0.402351 + 0.292325i −0.0301575 + 0.0219107i
\(179\) 3.16238 + 9.73282i 0.236368 + 0.727465i 0.996937 + 0.0782082i \(0.0249199\pi\)
−0.760569 + 0.649257i \(0.775080\pi\)
\(180\) −1.43004 + 4.40122i −0.106589 + 0.328048i
\(181\) −13.7533 9.99235i −1.02227 0.742725i −0.0555261 0.998457i \(-0.517684\pi\)
−0.966748 + 0.255732i \(0.917684\pi\)
\(182\) −9.45088 6.86646i −0.700546 0.508976i
\(183\) −1.85053 + 5.69534i −0.136795 + 0.421012i
\(184\) 1.65127 + 5.08209i 0.121733 + 0.374657i
\(185\) −13.6412 + 9.91089i −1.00292 + 0.728663i
\(186\) −1.28962 −0.0945596
\(187\) 0 0
\(188\) 17.4891 1.27553
\(189\) 2.04223 1.48377i 0.148551 0.107928i
\(190\) −0.775903 2.38798i −0.0562899 0.173243i
\(191\) 1.69623 5.22047i 0.122735 0.377740i −0.870747 0.491732i \(-0.836364\pi\)
0.993482 + 0.113992i \(0.0363639\pi\)
\(192\) −2.72823 1.98218i −0.196893 0.143051i
\(193\) 8.52686 + 6.19513i 0.613777 + 0.445935i 0.850742 0.525583i \(-0.176153\pi\)
−0.236965 + 0.971518i \(0.576153\pi\)
\(194\) −2.56805 + 7.90366i −0.184376 + 0.567450i
\(195\) 6.08682 + 18.7333i 0.435886 + 1.34152i
\(196\) −0.696893 + 0.506322i −0.0497780 + 0.0361659i
\(197\) −2.08191 −0.148330 −0.0741649 0.997246i \(-0.523629\pi\)
−0.0741649 + 0.997246i \(0.523629\pi\)
\(198\) 0 0
\(199\) 21.8614 1.54971 0.774857 0.632137i \(-0.217822\pi\)
0.774857 + 0.632137i \(0.217822\pi\)
\(200\) −13.7740 + 10.0074i −0.973966 + 0.707628i
\(201\) −0.345124 1.06218i −0.0243432 0.0749205i
\(202\) 2.93230 9.02469i 0.206316 0.634975i
\(203\) 1.61803 + 1.17557i 0.113564 + 0.0825089i
\(204\) −2.96625 2.15510i −0.207679 0.150887i
\(205\) 11.3480 34.9256i 0.792579 2.43931i
\(206\) 2.23208 + 6.86963i 0.155516 + 0.478630i
\(207\) −1.61803 + 1.17557i −0.112461 + 0.0817078i
\(208\) 3.66648 0.254225
\(209\) 0 0
\(210\) 6.74456 0.465419
\(211\) 8.69059 6.31408i 0.598285 0.434679i −0.246985 0.969019i \(-0.579440\pi\)
0.845270 + 0.534340i \(0.179440\pi\)
\(212\) 1.74578 + 5.37296i 0.119901 + 0.369017i
\(213\) −3.32025 + 10.2187i −0.227500 + 0.700173i
\(214\) −8.69253 6.31550i −0.594209 0.431718i
\(215\) −18.0970 13.1483i −1.23421 0.896705i
\(216\) 0.825636 2.54105i 0.0561774 0.172896i
\(217\) −1.26972 3.90781i −0.0861945 0.265279i
\(218\) −6.37761 + 4.63360i −0.431946 + 0.313827i
\(219\) −9.15759 −0.618812
\(220\) 0 0
\(221\) −15.6060 −1.04977
\(222\) 3.20487 2.32847i 0.215097 0.156277i
\(223\) 7.37358 + 22.6935i 0.493771 + 1.51967i 0.818863 + 0.573990i \(0.194605\pi\)
−0.325091 + 0.945683i \(0.605395\pi\)
\(224\) 4.55632 14.0229i 0.304432 0.936945i
\(225\) −5.15528 3.74553i −0.343686 0.249702i
\(226\) 0.879596 + 0.639064i 0.0585099 + 0.0425099i
\(227\) −2.44830 + 7.53510i −0.162499 + 0.500122i −0.998843 0.0480833i \(-0.984689\pi\)
0.836344 + 0.548205i \(0.184689\pi\)
\(228\) −0.398515 1.22650i −0.0263923 0.0812271i
\(229\) 7.58233 5.50889i 0.501055 0.364038i −0.308365 0.951268i \(-0.599782\pi\)
0.809420 + 0.587231i \(0.199782\pi\)
\(230\) −5.34363 −0.352348
\(231\) 0 0
\(232\) 2.11684 0.138978
\(233\) 0.640974 0.465695i 0.0419916 0.0305087i −0.566591 0.823999i \(-0.691738\pi\)
0.608583 + 0.793490i \(0.291738\pi\)
\(234\) −1.43004 4.40122i −0.0934849 0.287717i
\(235\) −13.2810 + 40.8747i −0.866358 + 2.66637i
\(236\) −6.66119 4.83964i −0.433607 0.315034i
\(237\) 3.32418 + 2.41516i 0.215929 + 0.156881i
\(238\) −1.65127 + 5.08209i −0.107036 + 0.329423i
\(239\) −7.00360 21.5549i −0.453025 1.39427i −0.873438 0.486936i \(-0.838115\pi\)
0.420412 0.907333i \(-0.361885\pi\)
\(240\) −1.71256 + 1.24425i −0.110545 + 0.0803160i
\(241\) 13.2665 0.854570 0.427285 0.904117i \(-0.359470\pi\)
0.427285 + 0.904117i \(0.359470\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −6.64836 + 4.83032i −0.425618 + 0.309229i
\(245\) −0.654141 2.01324i −0.0417915 0.128621i
\(246\) −2.66611 + 8.20545i −0.169985 + 0.523160i
\(247\) −4.44080 3.22643i −0.282561 0.205293i
\(248\) −3.51838 2.55626i −0.223418 0.162322i
\(249\) 0.580806 1.78754i 0.0368071 0.113281i
\(250\) −1.13301 3.48703i −0.0716575 0.220539i
\(251\) 19.0031 13.8066i 1.19947 0.871462i 0.205233 0.978713i \(-0.434205\pi\)
0.994232 + 0.107251i \(0.0342047\pi\)
\(252\) 3.46410 0.218218
\(253\) 0 0
\(254\) −7.72281 −0.484572
\(255\) 7.28933 5.29601i 0.456476 0.331649i
\(256\) −4.29013 13.2037i −0.268133 0.825229i
\(257\) 5.75628 17.7160i 0.359067 1.10509i −0.594547 0.804061i \(-0.702668\pi\)
0.953614 0.301033i \(-0.0973316\pi\)
\(258\) 4.25174 + 3.08907i 0.264702 + 0.192317i
\(259\) 10.2112 + 7.41884i 0.634491 + 0.460984i
\(260\) −8.35283 + 25.7074i −0.518021 + 1.59430i
\(261\) 0.244830 + 0.753510i 0.0151546 + 0.0466411i
\(262\) −4.25174 + 3.08907i −0.262673 + 0.190843i
\(263\) −15.7359 −0.970319 −0.485160 0.874426i \(-0.661239\pi\)
−0.485160 + 0.874426i \(0.661239\pi\)
\(264\) 0 0
\(265\) −13.8832 −0.852835
\(266\) −1.52057 + 1.10476i −0.0932321 + 0.0677371i
\(267\) −0.193976 0.596996i −0.0118711 0.0365356i
\(268\) 0.473607 1.45761i 0.0289301 0.0890378i
\(269\) 6.56666 + 4.77096i 0.400377 + 0.290891i 0.769694 0.638413i \(-0.220409\pi\)
−0.369318 + 0.929303i \(0.620409\pi\)
\(270\) 2.16154 + 1.57045i 0.131547 + 0.0955747i
\(271\) −3.21140 + 9.88367i −0.195079 + 0.600390i 0.804897 + 0.593414i \(0.202220\pi\)
−0.999976 + 0.00697572i \(0.997780\pi\)
\(272\) −0.518267 1.59506i −0.0314246 0.0967149i
\(273\) 11.9286 8.66664i 0.721952 0.524529i
\(274\) 8.51278 0.514276
\(275\) 0 0
\(276\) −2.74456 −0.165203
\(277\) 7.00629 5.09037i 0.420967 0.305851i −0.357060 0.934082i \(-0.616221\pi\)
0.778027 + 0.628231i \(0.216221\pi\)
\(278\) 2.54435 + 7.83070i 0.152600 + 0.469654i
\(279\) 0.502993 1.54805i 0.0301134 0.0926795i
\(280\) 18.4007 + 13.3689i 1.09965 + 0.798946i
\(281\) 21.9429 + 15.9424i 1.30900 + 0.951046i 1.00000 1.45384e-5i \(-4.62772e-6\pi\)
0.309003 + 0.951061i \(0.400005\pi\)
\(282\) 3.12025 9.60315i 0.185808 0.571859i
\(283\) 2.34019 + 7.20236i 0.139110 + 0.428136i 0.996207 0.0870193i \(-0.0277342\pi\)
−0.857097 + 0.515155i \(0.827734\pi\)
\(284\) −11.9286 + 8.66664i −0.707832 + 0.514270i
\(285\) 3.16915 0.187724
\(286\) 0 0
\(287\) −27.4891 −1.62263
\(288\) 4.72544 3.43323i 0.278449 0.202305i
\(289\) −3.04734 9.37876i −0.179255 0.551691i
\(290\) −0.654141 + 2.01324i −0.0384125 + 0.118221i
\(291\) −8.48588 6.16535i −0.497451 0.361419i
\(292\) −10.1667 7.38657i −0.594964 0.432266i
\(293\) 9.20707 28.3365i 0.537883 1.65543i −0.199453 0.979907i \(-0.563916\pi\)
0.737336 0.675526i \(-0.236084\pi\)
\(294\) 0.153684 + 0.472992i 0.00896306 + 0.0275855i
\(295\) 16.3694 11.8931i 0.953063 0.692441i
\(296\) 13.3591 0.776480
\(297\) 0 0
\(298\) 2.11684 0.122625
\(299\) −9.45088 + 6.86646i −0.546558 + 0.397098i
\(300\) −2.70222 8.31657i −0.156013 0.480158i
\(301\) −5.17435 + 15.9250i −0.298245 + 0.917903i
\(302\) 14.1490 + 10.2798i 0.814183 + 0.591539i
\(303\) 9.68950 + 7.03983i 0.556647 + 0.404428i
\(304\) 0.182291 0.561035i 0.0104551 0.0321776i
\(305\) −6.24051 19.2063i −0.357330 1.09975i
\(306\) −1.71256 + 1.24425i −0.0979007 + 0.0711290i
\(307\) −1.23472 −0.0704690 −0.0352345 0.999379i \(-0.511218\pi\)
−0.0352345 + 0.999379i \(0.511218\pi\)
\(308\) 0 0
\(309\) −9.11684 −0.518639
\(310\) 3.51838 2.55626i 0.199831 0.145186i
\(311\) −9.11264 28.0458i −0.516730 1.59033i −0.780111 0.625641i \(-0.784838\pi\)
0.263381 0.964692i \(-0.415162\pi\)
\(312\) 4.82251 14.8422i 0.273021 0.840272i
\(313\) 6.56666 + 4.77096i 0.371170 + 0.269671i 0.757696 0.652608i \(-0.226325\pi\)
−0.386526 + 0.922278i \(0.626325\pi\)
\(314\) 7.93031 + 5.76170i 0.447533 + 0.325152i
\(315\) −2.63059 + 8.09613i −0.148217 + 0.456165i
\(316\) 1.74242 + 5.36261i 0.0980187 + 0.301670i
\(317\) −21.6368 + 15.7201i −1.21524 + 0.882927i −0.995696 0.0926753i \(-0.970458\pi\)
−0.219548 + 0.975602i \(0.570458\pi\)
\(318\) 3.26172 0.182908
\(319\) 0 0
\(320\) 11.3723 0.635730
\(321\) 10.9714 7.97122i 0.612366 0.444910i
\(322\) 1.23607 + 3.80423i 0.0688834 + 0.212001i
\(323\) −0.775903 + 2.38798i −0.0431724 + 0.132871i
\(324\) 1.11020 + 0.806607i 0.0616777 + 0.0448115i
\(325\) −30.1118 21.8775i −1.67030 1.21355i
\(326\) 0.888175 2.73352i 0.0491915 0.151396i
\(327\) −3.07468 9.46289i −0.170030 0.523299i
\(328\) −23.5384 + 17.1017i −1.29969 + 0.944282i
\(329\) 32.1716 1.77368
\(330\) 0 0
\(331\) −6.37228 −0.350252 −0.175126 0.984546i \(-0.556033\pi\)
−0.175126 + 0.984546i \(0.556033\pi\)
\(332\) 2.08665 1.51604i 0.114520 0.0832035i
\(333\) 1.54508 + 4.75528i 0.0846701 + 0.260588i
\(334\) −5.79239 + 17.8271i −0.316945 + 0.975458i
\(335\) 3.04701 + 2.21378i 0.166476 + 0.120952i
\(336\) 1.28195 + 0.931389i 0.0699360 + 0.0508114i
\(337\) 0.626379 1.92780i 0.0341210 0.105014i −0.932545 0.361053i \(-0.882417\pi\)
0.966666 + 0.256039i \(0.0824175\pi\)
\(338\) −5.17004 15.9117i −0.281213 0.865485i
\(339\) −1.11020 + 0.806607i −0.0602977 + 0.0438089i
\(340\) 12.3644 0.670554
\(341\) 0 0
\(342\) −0.744563 −0.0402613
\(343\) −15.5776 + 11.3178i −0.841110 + 0.611102i
\(344\) 5.47665 + 16.8554i 0.295281 + 0.908782i
\(345\) 2.08418 6.41446i 0.112209 0.345343i
\(346\) −4.44080 3.22643i −0.238739 0.173454i
\(347\) −22.9862 16.7005i −1.23396 0.896528i −0.236784 0.971562i \(-0.576093\pi\)
−0.997181 + 0.0750345i \(0.976093\pi\)
\(348\) −0.335976 + 1.03403i −0.0180102 + 0.0554297i
\(349\) −8.02850 24.7092i −0.429756 1.32265i −0.898366 0.439247i \(-0.855245\pi\)
0.468611 0.883405i \(-0.344755\pi\)
\(350\) −10.3106 + 7.49107i −0.551123 + 0.400414i
\(351\) 5.84096 0.311768
\(352\) 0 0
\(353\) 22.3505 1.18960 0.594799 0.803874i \(-0.297231\pi\)
0.594799 + 0.803874i \(0.297231\pi\)
\(354\) −3.84584 + 2.79417i −0.204404 + 0.148508i
\(355\) −11.1968 34.4603i −0.594266 1.82896i
\(356\) 0.266189 0.819246i 0.0141080 0.0434200i
\(357\) −5.45647 3.96435i −0.288787 0.209816i
\(358\) 6.55952 + 4.76577i 0.346682 + 0.251879i
\(359\) 5.75085 17.6993i 0.303518 0.934132i −0.676708 0.736251i \(-0.736594\pi\)
0.980226 0.197881i \(-0.0634060\pi\)
\(360\) 2.78428 + 8.56912i 0.146744 + 0.451633i
\(361\) 14.6568 10.6488i 0.771412 0.560464i
\(362\) −13.4689 −0.707909
\(363\) 0 0
\(364\) 20.2337 1.06053
\(365\) 24.9840 18.1520i 1.30772 0.950117i
\(366\) 1.46615 + 4.51235i 0.0766369 + 0.235864i
\(367\) 10.4209 32.0723i 0.543968 1.67416i −0.179464 0.983765i \(-0.557436\pi\)
0.723432 0.690396i \(-0.242564\pi\)
\(368\) −1.01567 0.737928i −0.0529455 0.0384671i
\(369\) −8.80990 6.40077i −0.458625 0.333211i
\(370\) −4.12818 + 12.7052i −0.214614 + 0.660514i
\(371\) 3.21140 + 9.88367i 0.166728 + 0.513135i
\(372\) 1.80709 1.31293i 0.0936933 0.0680722i
\(373\) 5.39853 0.279525 0.139763 0.990185i \(-0.455366\pi\)
0.139763 + 0.990185i \(0.455366\pi\)
\(374\) 0 0
\(375\) 4.62772 0.238974
\(376\) 27.5479 20.0147i 1.42068 1.03218i
\(377\) 1.43004 + 4.40122i 0.0736510 + 0.226674i
\(378\) 0.618034 1.90211i 0.0317882 0.0978341i
\(379\) 27.2823 + 19.8218i 1.40140 + 1.01818i 0.994504 + 0.104701i \(0.0333886\pi\)
0.406895 + 0.913475i \(0.366611\pi\)
\(380\) 3.51838 + 2.55626i 0.180489 + 0.131133i
\(381\) 3.01214 9.27042i 0.154317 0.474938i
\(382\) −1.34390 4.13611i −0.0687601 0.211622i
\(383\) 0.413306 0.300285i 0.0211190 0.0153438i −0.577176 0.816620i \(-0.695845\pi\)
0.598295 + 0.801276i \(0.295845\pi\)
\(384\) 9.01011 0.459795
\(385\) 0 0
\(386\) 8.35053 0.425031
\(387\) −5.36641 + 3.89893i −0.272790 + 0.198194i
\(388\) −4.44800 13.6895i −0.225813 0.694981i
\(389\) 2.50824 7.71958i 0.127173 0.391398i −0.867118 0.498103i \(-0.834030\pi\)
0.994291 + 0.106705i \(0.0340301\pi\)
\(390\) 12.6255 + 9.17296i 0.639317 + 0.464491i
\(391\) 4.32309 + 3.14091i 0.218628 + 0.158842i
\(392\) −0.518267 + 1.59506i −0.0261764 + 0.0805628i
\(393\) −2.04979 6.30860i −0.103398 0.318227i
\(394\) −1.33445 + 0.969533i −0.0672285 + 0.0488444i
\(395\) −13.8564 −0.697191
\(396\) 0 0
\(397\) 1.51087 0.0758286 0.0379143 0.999281i \(-0.487929\pi\)
0.0379143 + 0.999281i \(0.487929\pi\)
\(398\) 14.0126 10.1807i 0.702387 0.510314i
\(399\) −0.733075 2.25617i −0.0366997 0.112950i
\(400\) 1.23607 3.80423i 0.0618034 0.190211i
\(401\) 1.52351 + 1.10689i 0.0760802 + 0.0552755i 0.625175 0.780484i \(-0.285027\pi\)
−0.549095 + 0.835760i \(0.685027\pi\)
\(402\) −0.715868 0.520108i −0.0357042 0.0259406i
\(403\) 2.93796 9.04212i 0.146350 0.450420i
\(404\) 5.07889 + 15.6312i 0.252684 + 0.777683i
\(405\) −2.72823 + 1.98218i −0.135567 + 0.0984952i
\(406\) 1.58457 0.0786411
\(407\) 0 0
\(408\) −7.13859 −0.353413
\(409\) −16.4572 + 11.9568i −0.813755 + 0.591227i −0.914917 0.403643i \(-0.867744\pi\)
0.101162 + 0.994870i \(0.467744\pi\)
\(410\) −8.99088 27.6711i −0.444028 1.36658i
\(411\) −3.32025 + 10.2187i −0.163776 + 0.504051i
\(412\) −10.1215 7.35371i −0.498651 0.362291i
\(413\) −12.2534 8.90261i −0.602950 0.438069i
\(414\) −0.489660 + 1.50702i −0.0240655 + 0.0740660i
\(415\) 1.95864 + 6.02808i 0.0961459 + 0.295907i
\(416\) 27.6011 20.0534i 1.35326 0.983198i
\(417\) −10.3923 −0.508913
\(418\) 0 0
\(419\) −31.4891 −1.53834 −0.769172 0.639042i \(-0.779331\pi\)
−0.769172 + 0.639042i \(0.779331\pi\)
\(420\) −9.45088 + 6.86646i −0.461156 + 0.335049i
\(421\) 10.7728 + 33.1552i 0.525033 + 1.61588i 0.764251 + 0.644918i \(0.223109\pi\)
−0.239219 + 0.970966i \(0.576891\pi\)
\(422\) 2.63000 8.09432i 0.128027 0.394025i
\(423\) 10.3106 + 7.49107i 0.501317 + 0.364228i
\(424\) 8.89874 + 6.46531i 0.432161 + 0.313983i
\(425\) −5.26119 + 16.1923i −0.255205 + 0.785440i
\(426\) 2.63059 + 8.09613i 0.127453 + 0.392259i
\(427\) −12.2298 + 8.88546i −0.591841 + 0.429997i
\(428\) 18.6101 0.899555
\(429\) 0 0
\(430\) −17.7228 −0.854670
\(431\) 2.32527 1.68941i 0.112004 0.0813760i −0.530373 0.847764i \(-0.677948\pi\)
0.642378 + 0.766388i \(0.277948\pi\)
\(432\) 0.193976 + 0.596996i 0.00933266 + 0.0287230i
\(433\) 3.47140 10.6839i 0.166825 0.513434i −0.832341 0.554263i \(-0.813000\pi\)
0.999166 + 0.0408294i \(0.0130000\pi\)
\(434\) −2.63370 1.91350i −0.126422 0.0918508i
\(435\) −2.16154 1.57045i −0.103638 0.0752975i
\(436\) 4.21933 12.9858i 0.202069 0.621905i
\(437\) 0.580806 + 1.78754i 0.0277837 + 0.0855095i
\(438\) −5.86977 + 4.26464i −0.280469 + 0.203772i
\(439\) −5.39853 −0.257658 −0.128829 0.991667i \(-0.541122\pi\)
−0.128829 + 0.991667i \(0.541122\pi\)
\(440\) 0 0
\(441\) −0.627719 −0.0298914
\(442\) −10.0030 + 7.26762i −0.475795 + 0.345685i
\(443\) 2.86009 + 8.80244i 0.135887 + 0.418217i 0.995727 0.0923468i \(-0.0294368\pi\)
−0.859840 + 0.510563i \(0.829437\pi\)
\(444\) −2.12029 + 6.52559i −0.100625 + 0.309691i
\(445\) 1.71256 + 1.24425i 0.0811833 + 0.0589831i
\(446\) 15.2945 + 11.1121i 0.724217 + 0.526175i
\(447\) −0.825636 + 2.54105i −0.0390512 + 0.120187i
\(448\) −2.63059 8.09613i −0.124284 0.382506i
\(449\) 12.6255 9.17296i 0.595834 0.432899i −0.248564 0.968616i \(-0.579959\pi\)
0.844398 + 0.535717i \(0.179959\pi\)
\(450\) −5.04868 −0.237997
\(451\) 0 0
\(452\) −1.88316 −0.0885762
\(453\) −17.8584 + 12.9749i −0.839062 + 0.609614i
\(454\) 1.93976 + 5.96996i 0.0910373 + 0.280184i
\(455\) −15.3652 + 47.2892i −0.720331 + 2.21695i
\(456\) −2.03134 1.47586i −0.0951262 0.0691132i
\(457\) 30.9914 + 22.5166i 1.44972 + 1.05328i 0.985897 + 0.167352i \(0.0535216\pi\)
0.463820 + 0.885929i \(0.346478\pi\)
\(458\) 2.29462 7.06210i 0.107220 0.329990i
\(459\) −0.825636 2.54105i −0.0385374 0.118606i
\(460\) 7.48781 5.44021i 0.349121 0.253651i
\(461\) 4.55134 0.211977 0.105989 0.994367i \(-0.466199\pi\)
0.105989 + 0.994367i \(0.466199\pi\)
\(462\) 0 0
\(463\) −14.7446 −0.685238 −0.342619 0.939474i \(-0.611314\pi\)
−0.342619 + 0.939474i \(0.611314\pi\)
\(464\) −0.402351 + 0.292325i −0.0186787 + 0.0135709i
\(465\) 1.69623 + 5.22047i 0.0786609 + 0.242093i
\(466\) 0.193976 0.596996i 0.00898575 0.0276553i
\(467\) −9.89726 7.19078i −0.457991 0.332750i 0.334752 0.942306i \(-0.391347\pi\)
−0.792743 + 0.609557i \(0.791347\pi\)
\(468\) 6.48463 + 4.71136i 0.299752 + 0.217783i
\(469\) 0.871209 2.68131i 0.0402287 0.123811i
\(470\) 10.5224 + 32.3845i 0.485361 + 1.49379i
\(471\) −10.0094 + 7.27224i −0.461208 + 0.335087i
\(472\) −16.0309 −0.737881
\(473\) 0 0
\(474\) 3.25544 0.149527
\(475\) −4.84475 + 3.51992i −0.222292 + 0.161505i
\(476\) −2.86009 8.80244i −0.131092 0.403459i
\(477\) −1.27217 + 3.91535i −0.0582489 + 0.179272i
\(478\) −14.5271 10.5546i −0.664455 0.482755i
\(479\) −8.88480 6.45518i −0.405957 0.294945i 0.366006 0.930612i \(-0.380725\pi\)
−0.771963 + 0.635668i \(0.780725\pi\)
\(480\) −6.08682 + 18.7333i −0.277824 + 0.855055i
\(481\) 9.02478 + 27.7754i 0.411495 + 1.26645i
\(482\) 8.50348 6.17814i 0.387323 0.281406i
\(483\) −5.04868 −0.229723
\(484\) 0 0
\(485\) 35.3723 1.60617
\(486\) 0.640974 0.465695i 0.0290752 0.0211243i
\(487\) −0.387951 1.19399i −0.0175798 0.0541049i 0.941882 0.335944i \(-0.109055\pi\)
−0.959462 + 0.281839i \(0.909055\pi\)
\(488\) −4.94427 + 15.2169i −0.223817 + 0.688837i
\(489\) 2.93489 + 2.13232i 0.132720 + 0.0964268i
\(490\) −1.35684 0.985803i −0.0612958 0.0445340i
\(491\) −0.398515 + 1.22650i −0.0179847 + 0.0553513i −0.959646 0.281211i \(-0.909264\pi\)
0.941661 + 0.336562i \(0.109264\pi\)
\(492\) −4.61784 14.2123i −0.208188 0.640738i
\(493\) 1.71256 1.24425i 0.0771299 0.0560382i
\(494\) −4.34896 −0.195669
\(495\) 0 0
\(496\) 1.02175 0.0458779
\(497\) −21.9429 + 15.9424i −0.984273 + 0.715116i
\(498\) −0.460165 1.41624i −0.0206205 0.0634633i
\(499\) 11.3841 35.0366i 0.509621 1.56845i −0.283238 0.959050i \(-0.591409\pi\)
0.792860 0.609404i \(-0.208591\pi\)
\(500\) 5.13769 + 3.73275i 0.229764 + 0.166934i
\(501\) −19.1404 13.9063i −0.855129 0.621287i
\(502\) 5.75085 17.6993i 0.256673 0.789958i
\(503\) 0.671952 + 2.06805i 0.0299608 + 0.0922100i 0.964919 0.262549i \(-0.0845630\pi\)
−0.934958 + 0.354759i \(0.884563\pi\)
\(504\) 5.45647 3.96435i 0.243050 0.176586i
\(505\) −40.3894 −1.79730
\(506\) 0 0
\(507\) 21.1168 0.937832
\(508\) 10.8217 7.86239i 0.480133 0.348837i
\(509\) 1.53836 + 4.73460i 0.0681868 + 0.209857i 0.979344 0.202202i \(-0.0648097\pi\)
−0.911157 + 0.412059i \(0.864810\pi\)
\(510\) 2.20595 6.78921i 0.0976810 0.300631i
\(511\) −18.7019 13.5877i −0.827324 0.601086i
\(512\) 5.67993 + 4.12671i 0.251020 + 0.182377i
\(513\) 0.290403 0.893769i 0.0128216 0.0394608i
\(514\) −4.56063 14.0362i −0.201161 0.619109i
\(515\) 24.8729 18.0712i 1.09603 0.796312i
\(516\) −9.10268 −0.400723
\(517\) 0 0
\(518\) 10.0000 0.439375
\(519\) 5.60503 4.07230i 0.246034 0.178754i
\(520\) 16.2629 + 50.0519i 0.713174 + 2.19492i
\(521\) −8.95477 + 27.5600i −0.392316 + 1.20742i 0.538717 + 0.842487i \(0.318909\pi\)
−0.931032 + 0.364937i \(0.881091\pi\)
\(522\) 0.507835 + 0.368964i 0.0222273 + 0.0161491i
\(523\) −29.3515 21.3251i −1.28345 0.932483i −0.283802 0.958883i \(-0.591596\pi\)
−0.999651 + 0.0263998i \(0.991596\pi\)
\(524\) 2.81288 8.65717i 0.122881 0.378190i
\(525\) −4.97078 15.2985i −0.216943 0.667681i
\(526\) −10.0863 + 7.32814i −0.439784 + 0.319522i
\(527\) −4.34896 −0.189444
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) −8.89874 + 6.46531i −0.386536 + 0.280835i
\(531\) −1.85410 5.70634i −0.0804612 0.247634i
\(532\) 1.00599 3.09610i 0.0436150 0.134233i
\(533\) −51.4583 37.3867i −2.22891 1.61940i
\(534\) −0.402351 0.292325i −0.0174114 0.0126501i
\(535\) −14.1323 + 43.4947i −0.610992 + 1.88044i
\(536\) −0.922107 2.83795i −0.0398289 0.122581i
\(537\) −8.27923 + 6.01521i −0.357275 + 0.259576i
\(538\) 6.43087 0.277254
\(539\) 0 0
\(540\) −4.62772 −0.199145
\(541\) 22.4201 16.2892i 0.963917 0.700327i 0.00985982 0.999951i \(-0.496861\pi\)
0.954057 + 0.299625i \(0.0968615\pi\)
\(542\) 2.54435 + 7.83070i 0.109289 + 0.336357i
\(543\) 5.25329 16.1680i 0.225440 0.693834i
\(544\) −12.6255 9.17296i −0.541314 0.393287i
\(545\) 27.1456 + 19.7224i 1.16279 + 0.844815i
\(546\) 3.60991 11.1102i 0.154490 0.475471i
\(547\) −5.47741 16.8577i −0.234197 0.720785i −0.997227 0.0744212i \(-0.976289\pi\)
0.763030 0.646363i \(-0.223711\pi\)
\(548\) −11.9286 + 8.66664i −0.509565 + 0.370220i
\(549\) −5.98844 −0.255580
\(550\) 0 0
\(551\) 0.744563 0.0317194
\(552\) −4.32309 + 3.14091i −0.184003 + 0.133686i
\(553\) 3.20521 + 9.86463i 0.136299 + 0.419487i
\(554\) 2.12029 6.52559i 0.0900825 0.277246i
\(555\) −13.6412 9.91089i −0.579035 0.420694i
\(556\) −11.5375 8.38250i −0.489300 0.355497i
\(557\) −9.36076 + 28.8095i −0.396628 + 1.22070i 0.531058 + 0.847335i \(0.321795\pi\)
−0.927686 + 0.373360i \(0.878205\pi\)
\(558\) −0.398515 1.22650i −0.0168705 0.0519220i
\(559\) −31.3450 + 22.7735i −1.32575 + 0.963216i
\(560\) −5.34363 −0.225810
\(561\) 0 0
\(562\) 21.4891 0.906464
\(563\) 25.7887 18.7366i 1.08687 0.789654i 0.107998 0.994151i \(-0.465556\pi\)
0.978867 + 0.204497i \(0.0655559\pi\)
\(564\) 5.40444 + 16.6331i 0.227568 + 0.700382i
\(565\) 1.43004 4.40122i 0.0601624 0.185161i
\(566\) 4.85410 + 3.52671i 0.204033 + 0.148239i
\(567\) 2.04223 + 1.48377i 0.0857657 + 0.0623124i
\(568\) −8.87110 + 27.3024i −0.372223 + 1.14558i
\(569\) 11.6840 + 35.9596i 0.489818 + 1.50750i 0.824879 + 0.565309i \(0.191243\pi\)
−0.335061 + 0.942196i \(0.608757\pi\)
\(570\) 2.03134 1.47586i 0.0850835 0.0618168i
\(571\) 14.5012 0.606857 0.303429 0.952854i \(-0.401869\pi\)
0.303429 + 0.952854i \(0.401869\pi\)
\(572\) 0 0
\(573\) 5.48913 0.229311
\(574\) −17.6198 + 12.8015i −0.735436 + 0.534326i
\(575\) 3.93829 + 12.1208i 0.164238 + 0.505472i
\(576\) 1.04209 3.20723i 0.0434205 0.133635i
\(577\) −5.24981 3.81421i −0.218553 0.158788i 0.473122 0.880997i \(-0.343127\pi\)
−0.691675 + 0.722209i \(0.743127\pi\)
\(578\) −6.32090 4.59240i −0.262915 0.191019i
\(579\) −3.25697 + 10.0239i −0.135355 + 0.416580i
\(580\) −1.13301 3.48703i −0.0470455 0.144791i
\(581\) 3.83843 2.78878i 0.159245 0.115698i
\(582\) −8.31040 −0.344477
\(583\) 0 0
\(584\) −24.4674 −1.01247
\(585\) −15.9355 + 11.5778i −0.658852 + 0.478684i
\(586\) −7.29465 22.4506i −0.301339 0.927426i
\(587\) −2.15640 + 6.63671i −0.0890041 + 0.273926i −0.985645 0.168833i \(-0.946000\pi\)
0.896641 + 0.442759i \(0.146000\pi\)
\(588\) −0.696893 0.506322i −0.0287394 0.0208804i
\(589\) −1.23753 0.899118i −0.0509915 0.0370475i
\(590\) 4.95382 15.2463i 0.203945 0.627679i
\(591\) −0.643345 1.98001i −0.0264637 0.0814468i
\(592\) −2.53918 + 1.84482i −0.104359 + 0.0758216i
\(593\) −8.71516 −0.357889 −0.178944 0.983859i \(-0.557268\pi\)
−0.178944 + 0.983859i \(0.557268\pi\)
\(594\) 0 0
\(595\) 22.7446 0.932436
\(596\) −2.96625 + 2.15510i −0.121502 + 0.0882765i
\(597\) 6.75555 + 20.7914i 0.276486 + 0.850937i
\(598\) −2.86009 + 8.80244i −0.116958 + 0.359959i
\(599\) 23.0306 + 16.7327i 0.941004 + 0.683680i 0.948662 0.316291i \(-0.102438\pi\)
−0.00765781 + 0.999971i \(0.502438\pi\)
\(600\) −13.7740 10.0074i −0.562320 0.408549i
\(601\) 6.01264 18.5050i 0.245261 0.754835i −0.750333 0.661060i \(-0.770107\pi\)
0.995593 0.0937746i \(-0.0298933\pi\)
\(602\) 4.09957 + 12.6172i 0.167086 + 0.514238i
\(603\) 0.903546 0.656464i 0.0367952 0.0267333i
\(604\) −30.2921 −1.23257
\(605\) 0 0
\(606\) 9.48913 0.385469
\(607\) −26.5046 + 19.2567i −1.07579 + 0.781606i −0.976944 0.213497i \(-0.931515\pi\)
−0.0988448 + 0.995103i \(0.531515\pi\)
\(608\) −1.69623 5.22047i −0.0687913 0.211718i
\(609\) −0.618034 + 1.90211i −0.0250440 + 0.0770775i
\(610\) −12.9443 9.40456i −0.524098 0.380780i
\(611\) 60.2236 + 43.7550i 2.43639 + 1.77014i
\(612\) 1.13301 3.48703i 0.0457990 0.140955i
\(613\) 9.13290 + 28.1082i 0.368874 + 1.13528i 0.947519 + 0.319699i \(0.103582\pi\)
−0.578645 + 0.815579i \(0.696418\pi\)
\(614\) −0.791421 + 0.575001i −0.0319392 + 0.0232052i
\(615\) 36.7229 1.48081
\(616\) 0 0
\(617\) 15.1386 0.609457 0.304728 0.952439i \(-0.401434\pi\)
0.304728 + 0.952439i \(0.401434\pi\)
\(618\) −5.84366 + 4.24567i −0.235066 + 0.170786i
\(619\) −7.48862 23.0476i −0.300993 0.926362i −0.981142 0.193288i \(-0.938085\pi\)
0.680149 0.733074i \(-0.261915\pi\)
\(620\) −2.32771 + 7.16395i −0.0934830 + 0.287711i
\(621\) −1.61803 1.17557i −0.0649295 0.0471740i
\(622\) −18.9018 13.7329i −0.757891 0.550640i
\(623\) 0.489660 1.50702i 0.0196178 0.0603775i
\(624\) 1.13301 + 3.48703i 0.0453565 + 0.139593i
\(625\) 13.1509 9.55471i 0.526037 0.382188i
\(626\) 6.43087 0.257029
\(627\) 0 0
\(628\) −16.9783 −0.677506
\(629\) 10.8077 7.85227i 0.430932 0.313090i
\(630\) 2.08418 + 6.41446i 0.0830359 + 0.255558i
\(631\) −3.78042 + 11.6349i −0.150496 + 0.463179i −0.997677 0.0681257i \(-0.978298\pi\)
0.847181 + 0.531305i \(0.178298\pi\)
\(632\) 8.88159 + 6.45285i 0.353291 + 0.256681i
\(633\) 8.69059 + 6.31408i 0.345420 + 0.250962i
\(634\) −6.54788 + 20.1523i −0.260049 + 0.800350i
\(635\) 10.1578 + 31.2625i 0.403100 + 1.24061i
\(636\) −4.57052 + 3.32067i −0.181233 + 0.131673i
\(637\) −3.66648 −0.145271
\(638\) 0 0
\(639\) −10.7446 −0.425048
\(640\) −24.5817 + 17.8596i −0.971676 + 0.705964i
\(641\) −3.12628 9.62169i −0.123481 0.380034i 0.870141 0.492803i \(-0.164028\pi\)
−0.993621 + 0.112770i \(0.964028\pi\)
\(642\) 3.32025 10.2187i 0.131040 0.403299i
\(643\) 34.0556 + 24.7429i 1.34302 + 0.975764i 0.999327 + 0.0366830i \(0.0116792\pi\)
0.343697 + 0.939081i \(0.388321\pi\)
\(644\) −5.60503 4.07230i −0.220869 0.160471i
\(645\) 6.91246 21.2744i 0.272178 0.837677i
\(646\) 0.614738 + 1.89197i 0.0241865 + 0.0744385i
\(647\) 9.70820 7.05342i 0.381669 0.277299i −0.380364 0.924837i \(-0.624201\pi\)
0.762033 + 0.647538i \(0.224201\pi\)
\(648\) 2.67181 0.104959
\(649\) 0 0
\(650\) −29.4891 −1.15666
\(651\) 3.32418 2.41516i 0.130285 0.0946575i
\(652\) 1.53836 + 4.73460i 0.0602470 + 0.185421i
\(653\) 8.49461 26.1437i 0.332420 1.02308i −0.635559 0.772052i \(-0.719231\pi\)
0.967979 0.251031i \(-0.0807695\pi\)
\(654\) −6.37761 4.63360i −0.249384 0.181188i
\(655\) 18.0970 + 13.1483i 0.707110 + 0.513746i
\(656\) 2.11233 6.50107i 0.0824725 0.253824i
\(657\) −2.82985 8.70938i −0.110403 0.339785i
\(658\) 20.6211 14.9821i 0.803896 0.584064i
\(659\) 15.7359 0.612985 0.306492 0.951873i \(-0.400845\pi\)
0.306492 + 0.951873i \(0.400845\pi\)
\(660\) 0 0
\(661\) 30.7228 1.19498 0.597489 0.801877i \(-0.296165\pi\)
0.597489 + 0.801877i \(0.296165\pi\)
\(662\) −4.08446 + 2.96754i −0.158747 + 0.115337i
\(663\) −4.82251 14.8422i −0.187291 0.576422i
\(664\) 1.55181 4.77597i 0.0602217 0.185343i
\(665\) 6.47214 + 4.70228i 0.250979 + 0.182347i
\(666\) 3.20487 + 2.32847i 0.124186 + 0.0902265i
\(667\) 0.489660 1.50702i 0.0189597 0.0583520i
\(668\) −10.0327 30.8775i −0.388177 1.19469i
\(669\) −19.3043 + 14.0254i −0.746347 + 0.542253i
\(670\) 2.98400 0.115282
\(671\) 0 0
\(672\) 14.7446 0.568784
\(673\) 1.32636 0.963660i 0.0511276 0.0371464i −0.561928 0.827186i \(-0.689940\pi\)
0.613056 + 0.790040i \(0.289940\pi\)
\(674\) −0.496272 1.52737i −0.0191157 0.0588320i
\(675\) 1.96914 6.06040i 0.0757924 0.233265i
\(676\) 23.4439 + 17.0330i 0.901688 + 0.655115i
\(677\) 5.53014 + 4.01788i 0.212541 + 0.154420i 0.688962 0.724797i \(-0.258066\pi\)
−0.476422 + 0.879217i \(0.658066\pi\)
\(678\) −0.335976 + 1.03403i −0.0129031 + 0.0397116i
\(679\) −8.18218 25.1822i −0.314003 0.966403i
\(680\) 19.4757 14.1500i 0.746861 0.542626i
\(681\) −7.92287 −0.303605
\(682\) 0 0
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) 1.04332 0.758020i 0.0398925 0.0289836i
\(685\) −11.1968 34.4603i −0.427809 1.31666i
\(686\) −4.71419 + 14.5088i −0.179989 + 0.553948i
\(687\) 7.58233 + 5.50889i 0.289284 + 0.210177i
\(688\) −3.36860 2.44743i −0.128427 0.0933073i
\(689\) −7.43073 + 22.8694i −0.283088 + 0.871256i
\(690\) −1.65127 5.08209i −0.0628629 0.193472i
\(691\) −10.6117 + 7.70989i −0.403690 + 0.293298i −0.771042 0.636784i \(-0.780264\pi\)
0.367352 + 0.930082i \(0.380264\pi\)
\(692\) 9.50744 0.361419
\(693\) 0 0
\(694\) −22.5109 −0.854501
\(695\) 28.3526 20.5994i 1.07548 0.781379i
\(696\) 0.654141 + 2.01324i 0.0247951 + 0.0763116i
\(697\) −8.99088 + 27.6711i −0.340554 + 1.04812i
\(698\) −16.6530 12.0991i −0.630325 0.457958i
\(699\) 0.640974 + 0.465695i 0.0242438 + 0.0176142i
\(700\) 6.82131 20.9938i 0.257821 0.793493i
\(701\) 10.2775 + 31.6310i 0.388177 + 1.19469i 0.934149 + 0.356883i \(0.116161\pi\)
−0.545972 + 0.837804i \(0.683839\pi\)
\(702\) 3.74390 2.72010i 0.141305 0.102664i
\(703\) 4.69882 0.177219
\(704\) 0 0
\(705\) −42.9783 −1.61865
\(706\) 14.3261 10.4085i 0.539170 0.391730i
\(707\) 9.34272 + 28.7539i 0.351369 + 1.08140i
\(708\) 2.54435 7.83070i 0.0956225 0.294296i
\(709\) −4.85410 3.52671i −0.182300 0.132448i 0.492893 0.870090i \(-0.335939\pi\)
−0.675192 + 0.737642i \(0.735939\pi\)
\(710\) −23.2248 16.8738i −0.871613 0.633264i
\(711\) −1.26972 + 3.90781i −0.0476184 + 0.146554i
\(712\) −0.518267 1.59506i −0.0194229 0.0597775i
\(713\) −2.63370 + 1.91350i −0.0986330 + 0.0716611i
\(714\) −5.34363 −0.199980
\(715\) 0 0
\(716\) −14.0435 −0.524830
\(717\) 18.3357 13.3216i 0.684758 0.497506i
\(718\) −4.55632 14.0229i −0.170040 0.523330i
\(719\) −1.85410 + 5.70634i −0.0691463 + 0.212811i −0.979659 0.200672i \(-0.935688\pi\)
0.910512 + 0.413482i \(0.135688\pi\)
\(720\) −1.71256 1.24425i −0.0638234 0.0463704i
\(721\) −18.6187 13.5273i −0.693397 0.503782i
\(722\) 4.43555 13.6512i 0.165074 0.508046i
\(723\) 4.09957 + 12.6172i 0.152465 + 0.469238i
\(724\) 18.8734 13.7123i 0.701424 0.509614i
\(725\) 5.04868 0.187503
\(726\) 0 0
\(727\) 18.7446 0.695197 0.347599 0.937643i \(-0.386997\pi\)
0.347599 + 0.937643i \(0.386997\pi\)
\(728\) 31.8710 23.1556i 1.18122 0.858205i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 7.56083 23.2699i 0.279839 0.861256i
\(731\) 14.3381 + 10.4172i 0.530312 + 0.385294i
\(732\) −6.64836 4.83032i −0.245730 0.178534i
\(733\) 2.29462 7.06210i 0.0847536 0.260845i −0.899695 0.436520i \(-0.856211\pi\)
0.984448 + 0.175675i \(0.0562108\pi\)
\(734\) −8.25636 25.4105i −0.304748 0.937917i
\(735\) 1.71256 1.24425i 0.0631688 0.0458948i
\(736\) −11.6819 −0.430601
\(737\) 0 0
\(738\) −8.62772 −0.317591
\(739\) 28.7855 20.9139i 1.05889 0.769329i 0.0850074 0.996380i \(-0.472909\pi\)
0.973883 + 0.227052i \(0.0729086\pi\)
\(740\) −7.15022 22.0061i −0.262847 0.808961i
\(741\) 1.69623 5.22047i 0.0623127 0.191779i
\(742\) 6.66119 + 4.83964i 0.244540 + 0.177669i
\(743\) −28.3526 20.5994i −1.04016 0.755718i −0.0698409 0.997558i \(-0.522249\pi\)
−0.970316 + 0.241840i \(0.922249\pi\)
\(744\) 1.34390 4.13611i 0.0492699 0.151637i
\(745\) −2.78428 8.56912i −0.102008 0.313948i
\(746\) 3.46032 2.51407i 0.126691 0.0920465i
\(747\) 1.87953 0.0687683
\(748\) 0 0
\(749\) 34.2337 1.25087
\(750\) 2.96625 2.15510i 0.108312 0.0786933i
\(751\) 10.9239 + 33.6204i 0.398619 + 1.22682i 0.926107 + 0.377261i \(0.123134\pi\)
−0.527488 + 0.849563i \(0.676866\pi\)
\(752\) −2.47214 + 7.60845i −0.0901495 + 0.277452i
\(753\) 19.0031 + 13.8066i 0.692512 + 0.503139i
\(754\) 2.96625 + 2.15510i 0.108024 + 0.0784842i
\(755\) 23.0034 70.7971i 0.837179 2.57657i
\(756\) 1.07047 + 3.29456i 0.0389325 + 0.119822i
\(757\) −26.2843 + 19.0966i −0.955317 + 0.694079i −0.952059 0.305916i \(-0.901037\pi\)
−0.00325894 + 0.999995i \(0.501037\pi\)
\(758\) 26.7181 0.970447
\(759\) 0 0
\(760\) 8.46738 0.307144
\(761\) −30.1867 + 21.9319i −1.09427 + 0.795032i −0.980115 0.198431i \(-0.936415\pi\)
−0.114153 + 0.993463i \(0.536415\pi\)
\(762\) −2.38648 7.34483i −0.0864531 0.266075i
\(763\) 7.76153 23.8875i 0.280986 0.864787i
\(764\) 6.09402 + 4.42757i 0.220474 + 0.160184i
\(765\) 7.28933 + 5.29601i 0.263546 + 0.191478i
\(766\) 0.125078 0.384949i 0.00451923 0.0139088i
\(767\) −10.8297 33.3305i −0.391039 1.20350i
\(768\) 11.2317 8.16031i 0.405289 0.294460i
\(769\) 41.4217 1.49371 0.746853 0.664989i \(-0.231564\pi\)
0.746853 + 0.664989i \(0.231564\pi\)
\(770\) 0 0
\(771\) 18.6277 0.670861
\(772\) −11.7013 + 8.50146i −0.421137 + 0.305974i