Properties

Label 845.2.e.m.146.3
Level $845$
Weight $2$
Character 845.146
Analytic conductor $6.747$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 146.3
Root \(-1.27597 + 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 845.146
Dual form 845.2.e.m.191.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.109843 + 0.190254i) q^{2} +(0.800098 + 1.38581i) q^{3} +(0.975869 - 1.69025i) q^{4} -1.00000 q^{5} +(-0.175771 + 0.304444i) q^{6} +(0.166123 - 0.287734i) q^{7} +0.868145 q^{8} +(0.219687 - 0.380509i) q^{9} +O(q^{10})\) \(q+(0.109843 + 0.190254i) q^{2} +(0.800098 + 1.38581i) q^{3} +(0.975869 - 1.69025i) q^{4} -1.00000 q^{5} +(-0.175771 + 0.304444i) q^{6} +(0.166123 - 0.287734i) q^{7} +0.868145 q^{8} +(0.219687 - 0.380509i) q^{9} +(-0.109843 - 0.190254i) q^{10} +(2.68591 + 4.65213i) q^{11} +3.12316 q^{12} +0.0729902 q^{14} +(-0.800098 - 1.38581i) q^{15} +(-1.85638 - 3.21534i) q^{16} +(2.53215 - 4.38581i) q^{17} +0.0965246 q^{18} +(-1.13397 + 1.96410i) q^{19} +(-0.975869 + 1.69025i) q^{20} +0.531659 q^{21} +(-0.590059 + 1.02201i) q^{22} +(1.41959 + 2.45880i) q^{23} +(0.694601 + 1.20308i) q^{24} +1.00000 q^{25} +5.50367 q^{27} +(-0.324229 - 0.561581i) q^{28} +(1.45174 + 2.51448i) q^{29} +(0.175771 - 0.304444i) q^{30} +5.46410 q^{31} +(1.27597 - 2.21004i) q^{32} +(-4.29798 + 7.44432i) q^{33} +1.11256 q^{34} +(-0.166123 + 0.287734i) q^{35} +(-0.428771 - 0.742653i) q^{36} +(-2.98601 - 5.17191i) q^{37} -0.498239 q^{38} -0.868145 q^{40} +(-1.86603 - 3.23205i) q^{41} +(0.0583993 + 0.101151i) q^{42} +(2.53215 - 4.38581i) q^{43} +10.4844 q^{44} +(-0.219687 + 0.380509i) q^{45} +(-0.311865 + 0.540166i) q^{46} +8.34285 q^{47} +(2.97057 - 5.14517i) q^{48} +(3.44481 + 5.96658i) q^{49} +(0.109843 + 0.190254i) q^{50} +8.10387 q^{51} -1.56063 q^{53} +(0.604542 + 1.04710i) q^{54} +(-2.68591 - 4.65213i) q^{55} +(0.144219 - 0.249795i) q^{56} -3.62916 q^{57} +(-0.318928 + 0.552399i) q^{58} +(-1.35366 + 2.34461i) q^{59} -3.12316 q^{60} +(-7.05193 + 12.2143i) q^{61} +(0.600196 + 1.03957i) q^{62} +(-0.0729902 - 0.126423i) q^{63} -6.86488 q^{64} -1.88842 q^{66} +(-5.16612 - 8.94799i) q^{67} +(-4.94209 - 8.55995i) q^{68} +(-2.27162 + 3.93456i) q^{69} -0.0729902 q^{70} +(-6.39866 + 11.0828i) q^{71} +(0.190720 - 0.330337i) q^{72} -9.68922 q^{73} +(0.655986 - 1.13620i) q^{74} +(0.800098 + 1.38581i) q^{75} +(2.21322 + 3.83341i) q^{76} +1.78477 q^{77} +4.51851 q^{79} +(1.85638 + 3.21534i) q^{80} +(3.74441 + 6.48552i) q^{81} +(0.409941 - 0.710039i) q^{82} -4.26371 q^{83} +(0.518830 - 0.898640i) q^{84} +(-2.53215 + 4.38581i) q^{85} +1.11256 q^{86} +(-2.32306 + 4.02367i) q^{87} +(2.33176 + 4.03872i) q^{88} +(-1.61292 - 2.79366i) q^{89} -0.0965246 q^{90} +5.54133 q^{92} +(4.37182 + 7.57221i) q^{93} +(0.916407 + 1.58726i) q^{94} +(1.13397 - 1.96410i) q^{95} +4.08359 q^{96} +(1.25396 - 2.17191i) q^{97} +(-0.756779 + 1.31078i) q^{98} +2.36023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} + 2q^{3} - 2q^{4} - 8q^{5} + 4q^{6} - 10q^{7} + 12q^{8} - 4q^{9} + O(q^{10}) \) \( 8q - 2q^{2} + 2q^{3} - 2q^{4} - 8q^{5} + 4q^{6} - 10q^{7} + 12q^{8} - 4q^{9} + 2q^{10} - 20q^{12} + 4q^{14} - 2q^{15} - 2q^{16} + 2q^{17} + 40q^{18} - 16q^{19} + 2q^{20} + 8q^{21} - 12q^{22} + 10q^{23} + 24q^{24} + 8q^{25} - 4q^{27} - 8q^{28} - 8q^{29} - 4q^{30} + 16q^{31} - 4q^{32} - 18q^{33} - 8q^{34} + 10q^{35} - 20q^{36} + 2q^{37} + 16q^{38} - 12q^{40} - 8q^{41} + 4q^{42} + 2q^{43} + 24q^{44} + 4q^{45} - 16q^{46} + 16q^{47} + 28q^{48} - 12q^{49} - 2q^{50} + 8q^{51} - 24q^{53} + 16q^{54} - 12q^{56} - 28q^{57} - 22q^{58} - 12q^{59} + 20q^{60} - 28q^{61} - 4q^{62} - 4q^{63} + 8q^{64} + 12q^{66} - 30q^{67} - 14q^{68} + 16q^{69} - 4q^{70} - 4q^{71} - 12q^{72} - 16q^{73} + 10q^{74} + 2q^{75} - 20q^{76} + 36q^{77} - 16q^{79} + 2q^{80} + 8q^{81} - 4q^{82} - 24q^{83} + 28q^{84} - 2q^{85} - 8q^{86} + 22q^{87} + 18q^{88} + 12q^{89} - 40q^{90} + 44q^{92} - 8q^{93} + 32q^{94} + 16q^{95} + 8q^{96} - 2q^{97} + 24q^{98} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.109843 + 0.190254i 0.0776710 + 0.134530i 0.902245 0.431224i \(-0.141918\pi\)
−0.824574 + 0.565755i \(0.808585\pi\)
\(3\) 0.800098 + 1.38581i 0.461937 + 0.800098i 0.999057 0.0434075i \(-0.0138214\pi\)
−0.537121 + 0.843505i \(0.680488\pi\)
\(4\) 0.975869 1.69025i 0.487934 0.845127i
\(5\) −1.00000 −0.447214
\(6\) −0.175771 + 0.304444i −0.0717582 + 0.124289i
\(7\) 0.166123 0.287734i 0.0627887 0.108753i −0.832922 0.553390i \(-0.813334\pi\)
0.895711 + 0.444637i \(0.146667\pi\)
\(8\) 0.868145 0.306936
\(9\) 0.219687 0.380509i 0.0732290 0.126836i
\(10\) −0.109843 0.190254i −0.0347355 0.0601637i
\(11\) 2.68591 + 4.65213i 0.809832 + 1.40267i 0.912980 + 0.408004i \(0.133775\pi\)
−0.103149 + 0.994666i \(0.532892\pi\)
\(12\) 3.12316 0.901579
\(13\) 0 0
\(14\) 0.0729902 0.0195074
\(15\) −0.800098 1.38581i −0.206584 0.357815i
\(16\) −1.85638 3.21534i −0.464094 0.803835i
\(17\) 2.53215 4.38581i 0.614136 1.06372i −0.376399 0.926458i \(-0.622838\pi\)
0.990535 0.137258i \(-0.0438288\pi\)
\(18\) 0.0965246 0.0227511
\(19\) −1.13397 + 1.96410i −0.260152 + 0.450596i −0.966282 0.257486i \(-0.917106\pi\)
0.706130 + 0.708082i \(0.250439\pi\)
\(20\) −0.975869 + 1.69025i −0.218211 + 0.377952i
\(21\) 0.531659 0.116018
\(22\) −0.590059 + 1.02201i −0.125801 + 0.217894i
\(23\) 1.41959 + 2.45880i 0.296005 + 0.512695i 0.975218 0.221246i \(-0.0710122\pi\)
−0.679213 + 0.733941i \(0.737679\pi\)
\(24\) 0.694601 + 1.20308i 0.141785 + 0.245578i
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.50367 1.05918
\(28\) −0.324229 0.561581i −0.0612735 0.106129i
\(29\) 1.45174 + 2.51448i 0.269581 + 0.466928i 0.968754 0.248025i \(-0.0797815\pi\)
−0.699173 + 0.714953i \(0.746448\pi\)
\(30\) 0.175771 0.304444i 0.0320912 0.0555837i
\(31\) 5.46410 0.981382 0.490691 0.871334i \(-0.336744\pi\)
0.490691 + 0.871334i \(0.336744\pi\)
\(32\) 1.27597 2.21004i 0.225561 0.390683i
\(33\) −4.29798 + 7.44432i −0.748182 + 1.29589i
\(34\) 1.11256 0.190802
\(35\) −0.166123 + 0.287734i −0.0280800 + 0.0486359i
\(36\) −0.428771 0.742653i −0.0714619 0.123776i
\(37\) −2.98601 5.17191i −0.490896 0.850257i 0.509049 0.860738i \(-0.329997\pi\)
−0.999945 + 0.0104803i \(0.996664\pi\)
\(38\) −0.498239 −0.0808250
\(39\) 0 0
\(40\) −0.868145 −0.137266
\(41\) −1.86603 3.23205i −0.291424 0.504762i 0.682723 0.730678i \(-0.260796\pi\)
−0.974147 + 0.225916i \(0.927462\pi\)
\(42\) 0.0583993 + 0.101151i 0.00901121 + 0.0156079i
\(43\) 2.53215 4.38581i 0.386149 0.668830i −0.605779 0.795633i \(-0.707138\pi\)
0.991928 + 0.126803i \(0.0404717\pi\)
\(44\) 10.4844 1.58058
\(45\) −0.219687 + 0.380509i −0.0327490 + 0.0567229i
\(46\) −0.311865 + 0.540166i −0.0459820 + 0.0796432i
\(47\) 8.34285 1.21693 0.608465 0.793581i \(-0.291786\pi\)
0.608465 + 0.793581i \(0.291786\pi\)
\(48\) 2.97057 5.14517i 0.428764 0.742642i
\(49\) 3.44481 + 5.96658i 0.492115 + 0.852368i
\(50\) 0.109843 + 0.190254i 0.0155342 + 0.0269060i
\(51\) 8.10387 1.13477
\(52\) 0 0
\(53\) −1.56063 −0.214369 −0.107184 0.994239i \(-0.534183\pi\)
−0.107184 + 0.994239i \(0.534183\pi\)
\(54\) 0.604542 + 1.04710i 0.0822678 + 0.142492i
\(55\) −2.68591 4.65213i −0.362168 0.627293i
\(56\) 0.144219 0.249795i 0.0192721 0.0333802i
\(57\) −3.62916 −0.480694
\(58\) −0.318928 + 0.552399i −0.0418773 + 0.0725335i
\(59\) −1.35366 + 2.34461i −0.176232 + 0.305242i −0.940587 0.339553i \(-0.889724\pi\)
0.764355 + 0.644795i \(0.223057\pi\)
\(60\) −3.12316 −0.403199
\(61\) −7.05193 + 12.2143i −0.902908 + 1.56388i −0.0792059 + 0.996858i \(0.525238\pi\)
−0.823702 + 0.567023i \(0.808095\pi\)
\(62\) 0.600196 + 1.03957i 0.0762249 + 0.132025i
\(63\) −0.0729902 0.126423i −0.00919590 0.0159278i
\(64\) −6.86488 −0.858111
\(65\) 0 0
\(66\) −1.88842 −0.232448
\(67\) −5.16612 8.94799i −0.631142 1.09317i −0.987319 0.158752i \(-0.949253\pi\)
0.356176 0.934419i \(-0.384080\pi\)
\(68\) −4.94209 8.55995i −0.599316 1.03805i
\(69\) −2.27162 + 3.93456i −0.273471 + 0.473666i
\(70\) −0.0729902 −0.00872400
\(71\) −6.39866 + 11.0828i −0.759382 + 1.31529i 0.183785 + 0.982967i \(0.441165\pi\)
−0.943166 + 0.332321i \(0.892168\pi\)
\(72\) 0.190720 0.330337i 0.0224766 0.0389306i
\(73\) −9.68922 −1.13404 −0.567019 0.823705i \(-0.691903\pi\)
−0.567019 + 0.823705i \(0.691903\pi\)
\(74\) 0.655986 1.13620i 0.0762569 0.132081i
\(75\) 0.800098 + 1.38581i 0.0923873 + 0.160020i
\(76\) 2.21322 + 3.83341i 0.253874 + 0.439722i
\(77\) 1.78477 0.203393
\(78\) 0 0
\(79\) 4.51851 0.508372 0.254186 0.967155i \(-0.418192\pi\)
0.254186 + 0.967155i \(0.418192\pi\)
\(80\) 1.85638 + 3.21534i 0.207549 + 0.359486i
\(81\) 3.74441 + 6.48552i 0.416046 + 0.720613i
\(82\) 0.409941 0.710039i 0.0452704 0.0784107i
\(83\) −4.26371 −0.468003 −0.234001 0.972236i \(-0.575182\pi\)
−0.234001 + 0.972236i \(0.575182\pi\)
\(84\) 0.518830 0.898640i 0.0566090 0.0980496i
\(85\) −2.53215 + 4.38581i −0.274650 + 0.475708i
\(86\) 1.11256 0.119970
\(87\) −2.32306 + 4.02367i −0.249059 + 0.431382i
\(88\) 2.33176 + 4.03872i 0.248566 + 0.430529i
\(89\) −1.61292 2.79366i −0.170969 0.296127i 0.767790 0.640702i \(-0.221356\pi\)
−0.938759 + 0.344575i \(0.888023\pi\)
\(90\) −0.0965246 −0.0101746
\(91\) 0 0
\(92\) 5.54133 0.577724
\(93\) 4.37182 + 7.57221i 0.453336 + 0.785201i
\(94\) 0.916407 + 1.58726i 0.0945202 + 0.163714i
\(95\) 1.13397 1.96410i 0.116343 0.201513i
\(96\) 4.08359 0.416780
\(97\) 1.25396 2.17191i 0.127320 0.220524i −0.795318 0.606193i \(-0.792696\pi\)
0.922637 + 0.385669i \(0.126029\pi\)
\(98\) −0.756779 + 1.31078i −0.0764462 + 0.132409i
\(99\) 2.36023 0.237213
\(100\) 0.975869 1.69025i 0.0975869 0.169025i
\(101\) −6.22336 10.7792i −0.619247 1.07257i −0.989623 0.143686i \(-0.954105\pi\)
0.370376 0.928882i \(-0.379229\pi\)
\(102\) 0.890157 + 1.54180i 0.0881386 + 0.152661i
\(103\) −15.0247 −1.48043 −0.740215 0.672370i \(-0.765276\pi\)
−0.740215 + 0.672370i \(0.765276\pi\)
\(104\) 0 0
\(105\) −0.531659 −0.0518846
\(106\) −0.171425 0.296916i −0.0166502 0.0288390i
\(107\) 6.53215 + 11.3140i 0.631487 + 1.09377i 0.987248 + 0.159190i \(0.0508883\pi\)
−0.355761 + 0.934577i \(0.615778\pi\)
\(108\) 5.37086 9.30260i 0.516811 0.895144i
\(109\) −11.2325 −1.07587 −0.537937 0.842985i \(-0.680796\pi\)
−0.537937 + 0.842985i \(0.680796\pi\)
\(110\) 0.590059 1.02201i 0.0562599 0.0974450i
\(111\) 4.77819 8.27607i 0.453526 0.785530i
\(112\) −1.23355 −0.116560
\(113\) 9.17191 15.8862i 0.862821 1.49445i −0.00637349 0.999980i \(-0.502029\pi\)
0.869195 0.494470i \(-0.164638\pi\)
\(114\) −0.398640 0.690464i −0.0373360 0.0646679i
\(115\) −1.41959 2.45880i −0.132377 0.229284i
\(116\) 5.66682 0.526151
\(117\) 0 0
\(118\) −0.594763 −0.0547524
\(119\) −0.841298 1.45717i −0.0771216 0.133579i
\(120\) −0.694601 1.20308i −0.0634081 0.109826i
\(121\) −8.92820 + 15.4641i −0.811655 + 1.40583i
\(122\) −3.09843 −0.280519
\(123\) 2.98601 5.17191i 0.269239 0.466336i
\(124\) 5.33225 9.23572i 0.478850 0.829392i
\(125\) −1.00000 −0.0894427
\(126\) 0.0160350 0.0277734i 0.00142851 0.00247425i
\(127\) −1.61998 2.80589i −0.143750 0.248982i 0.785156 0.619298i \(-0.212583\pi\)
−0.928906 + 0.370316i \(0.879249\pi\)
\(128\) −3.30600 5.72615i −0.292212 0.506125i
\(129\) 8.10387 0.713506
\(130\) 0 0
\(131\) 0.175664 0.0153478 0.00767390 0.999971i \(-0.497557\pi\)
0.00767390 + 0.999971i \(0.497557\pi\)
\(132\) 8.38853 + 14.5294i 0.730127 + 1.26462i
\(133\) 0.376759 + 0.652566i 0.0326692 + 0.0565846i
\(134\) 1.13493 1.96576i 0.0980430 0.169815i
\(135\) −5.50367 −0.473681
\(136\) 2.19827 3.80752i 0.188500 0.326492i
\(137\) 8.99144 15.5736i 0.768190 1.33054i −0.170353 0.985383i \(-0.554491\pi\)
0.938543 0.345162i \(-0.112176\pi\)
\(138\) −0.998090 −0.0849631
\(139\) −5.99307 + 10.3803i −0.508325 + 0.880445i 0.491628 + 0.870805i \(0.336402\pi\)
−0.999954 + 0.00964021i \(0.996931\pi\)
\(140\) 0.324229 + 0.561581i 0.0274024 + 0.0474623i
\(141\) 6.67510 + 11.5616i 0.562144 + 0.973663i
\(142\) −2.81140 −0.235928
\(143\) 0 0
\(144\) −1.63129 −0.135941
\(145\) −1.45174 2.51448i −0.120560 0.208816i
\(146\) −1.06430 1.84342i −0.0880819 0.152562i
\(147\) −5.51236 + 9.54769i −0.454652 + 0.787481i
\(148\) −11.6558 −0.958101
\(149\) 1.70520 2.95350i 0.139696 0.241960i −0.787686 0.616077i \(-0.788721\pi\)
0.927381 + 0.374117i \(0.122054\pi\)
\(150\) −0.175771 + 0.304444i −0.0143516 + 0.0248578i
\(151\) 7.96141 0.647890 0.323945 0.946076i \(-0.394991\pi\)
0.323945 + 0.946076i \(0.394991\pi\)
\(152\) −0.984454 + 1.70512i −0.0798498 + 0.138304i
\(153\) −1.11256 1.92701i −0.0899451 0.155790i
\(154\) 0.196045 + 0.339560i 0.0157978 + 0.0273625i
\(155\) −5.46410 −0.438887
\(156\) 0 0
\(157\) −16.4329 −1.31148 −0.655742 0.754985i \(-0.727644\pi\)
−0.655742 + 0.754985i \(0.727644\pi\)
\(158\) 0.496329 + 0.859667i 0.0394858 + 0.0683914i
\(159\) −1.24865 2.16273i −0.0990247 0.171516i
\(160\) −1.27597 + 2.21004i −0.100874 + 0.174719i
\(161\) 0.943307 0.0743430
\(162\) −0.822599 + 1.42478i −0.0646295 + 0.111942i
\(163\) −8.90361 + 15.4215i −0.697384 + 1.20791i 0.271986 + 0.962301i \(0.412320\pi\)
−0.969370 + 0.245604i \(0.921014\pi\)
\(164\) −7.28398 −0.568784
\(165\) 4.29798 7.44432i 0.334597 0.579539i
\(166\) −0.468341 0.811190i −0.0363503 0.0629605i
\(167\) 3.14683 + 5.45047i 0.243509 + 0.421770i 0.961711 0.274064i \(-0.0883682\pi\)
−0.718202 + 0.695834i \(0.755035\pi\)
\(168\) 0.461557 0.0356099
\(169\) 0 0
\(170\) −1.11256 −0.0853294
\(171\) 0.498239 + 0.862975i 0.0381013 + 0.0659933i
\(172\) −4.94209 8.55995i −0.376831 0.652690i
\(173\) −7.98756 + 13.8349i −0.607283 + 1.05184i 0.384404 + 0.923165i \(0.374407\pi\)
−0.991686 + 0.128679i \(0.958926\pi\)
\(174\) −1.02069 −0.0773786
\(175\) 0.166123 0.287734i 0.0125577 0.0217506i
\(176\) 9.97212 17.2722i 0.751677 1.30194i
\(177\) −4.33225 −0.325632
\(178\) 0.354337 0.613729i 0.0265587 0.0460010i
\(179\) −11.8087 20.4533i −0.882625 1.52875i −0.848412 0.529336i \(-0.822441\pi\)
−0.0342123 0.999415i \(-0.510892\pi\)
\(180\) 0.428771 + 0.742653i 0.0319587 + 0.0553541i
\(181\) −2.62590 −0.195182 −0.0975909 0.995227i \(-0.531114\pi\)
−0.0975909 + 0.995227i \(0.531114\pi\)
\(182\) 0 0
\(183\) −22.5689 −1.66834
\(184\) 1.23241 + 2.13459i 0.0908544 + 0.157364i
\(185\) 2.98601 + 5.17191i 0.219536 + 0.380247i
\(186\) −0.960431 + 1.66351i −0.0704222 + 0.121975i
\(187\) 27.2045 1.98939
\(188\) 8.14153 14.1015i 0.593782 1.02846i
\(189\) 0.914288 1.58359i 0.0665046 0.115189i
\(190\) 0.498239 0.0361460
\(191\) 1.00791 1.74575i 0.0729298 0.126318i −0.827254 0.561828i \(-0.810098\pi\)
0.900184 + 0.435509i \(0.143432\pi\)
\(192\) −5.49258 9.51343i −0.396393 0.686572i
\(193\) −11.4105 19.7636i −0.821348 1.42262i −0.904678 0.426095i \(-0.859889\pi\)
0.0833298 0.996522i \(-0.473445\pi\)
\(194\) 0.550955 0.0395563
\(195\) 0 0
\(196\) 13.4467 0.960480
\(197\) 0.321513 + 0.556877i 0.0229068 + 0.0396758i 0.877252 0.480031i \(-0.159375\pi\)
−0.854345 + 0.519707i \(0.826041\pi\)
\(198\) 0.259256 + 0.449045i 0.0184245 + 0.0319122i
\(199\) −1.53342 + 2.65596i −0.108701 + 0.188276i −0.915244 0.402899i \(-0.868003\pi\)
0.806543 + 0.591175i \(0.201336\pi\)
\(200\) 0.868145 0.0613871
\(201\) 8.26681 14.3185i 0.583096 1.00995i
\(202\) 1.36719 2.36804i 0.0961952 0.166615i
\(203\) 0.964670 0.0677065
\(204\) 7.90831 13.6976i 0.553693 0.959024i
\(205\) 1.86603 + 3.23205i 0.130329 + 0.225736i
\(206\) −1.65037 2.85852i −0.114987 0.199163i
\(207\) 1.24746 0.0867045
\(208\) 0 0
\(209\) −12.1830 −0.842716
\(210\) −0.0583993 0.101151i −0.00402993 0.00698005i
\(211\) 4.10020 + 7.10175i 0.282269 + 0.488904i 0.971943 0.235215i \(-0.0755796\pi\)
−0.689674 + 0.724120i \(0.742246\pi\)
\(212\) −1.52297 + 2.63786i −0.104598 + 0.181169i
\(213\) −20.4782 −1.40314
\(214\) −1.43503 + 2.48554i −0.0980964 + 0.169908i
\(215\) −2.53215 + 4.38581i −0.172691 + 0.299110i
\(216\) 4.77798 0.325101
\(217\) 0.907714 1.57221i 0.0616197 0.106728i
\(218\) −1.23381 2.13703i −0.0835643 0.144738i
\(219\) −7.75232 13.4274i −0.523854 0.907341i
\(220\) −10.4844 −0.706856
\(221\) 0 0
\(222\) 2.09941 0.140903
\(223\) −5.12210 8.87174i −0.343001 0.594095i 0.641987 0.766715i \(-0.278110\pi\)
−0.984989 + 0.172620i \(0.944777\pi\)
\(224\) −0.423935 0.734278i −0.0283254 0.0490610i
\(225\) 0.219687 0.380509i 0.0146458 0.0253673i
\(226\) 4.02990 0.268065
\(227\) −3.52190 + 6.10012i −0.233757 + 0.404879i −0.958911 0.283708i \(-0.908435\pi\)
0.725154 + 0.688587i \(0.241769\pi\)
\(228\) −3.54159 + 6.13421i −0.234547 + 0.406248i
\(229\) 1.32899 0.0878219 0.0439109 0.999035i \(-0.486018\pi\)
0.0439109 + 0.999035i \(0.486018\pi\)
\(230\) 0.311865 0.540166i 0.0205638 0.0356175i
\(231\) 1.42799 + 2.47335i 0.0939547 + 0.162734i
\(232\) 1.26032 + 2.18294i 0.0827440 + 0.143317i
\(233\) −1.24746 −0.0817238 −0.0408619 0.999165i \(-0.513010\pi\)
−0.0408619 + 0.999165i \(0.513010\pi\)
\(234\) 0 0
\(235\) −8.34285 −0.544227
\(236\) 2.64199 + 4.57606i 0.171979 + 0.297876i
\(237\) 3.61525 + 6.26180i 0.234836 + 0.406748i
\(238\) 0.184822 0.320121i 0.0119802 0.0207504i
\(239\) −9.94207 −0.643099 −0.321549 0.946893i \(-0.604204\pi\)
−0.321549 + 0.946893i \(0.604204\pi\)
\(240\) −2.97057 + 5.14517i −0.191749 + 0.332120i
\(241\) 11.2934 19.5608i 0.727475 1.26002i −0.230472 0.973079i \(-0.574027\pi\)
0.957947 0.286944i \(-0.0926395\pi\)
\(242\) −3.92282 −0.252168
\(243\) 2.26371 3.92086i 0.145217 0.251523i
\(244\) 13.7635 + 23.8391i 0.881119 + 1.52614i
\(245\) −3.44481 5.96658i −0.220081 0.381191i
\(246\) 1.31197 0.0836483
\(247\) 0 0
\(248\) 4.74363 0.301221
\(249\) −3.41139 5.90869i −0.216188 0.374448i
\(250\) −0.109843 0.190254i −0.00694711 0.0120327i
\(251\) 3.38418 5.86157i 0.213608 0.369979i −0.739233 0.673449i \(-0.764812\pi\)
0.952841 + 0.303470i \(0.0981453\pi\)
\(252\) −0.284915 −0.0179480
\(253\) −7.62577 + 13.2082i −0.479428 + 0.830394i
\(254\) 0.355888 0.616417i 0.0223304 0.0386774i
\(255\) −8.10387 −0.507484
\(256\) −6.13860 + 10.6324i −0.383663 + 0.664523i
\(257\) 5.12691 + 8.88007i 0.319808 + 0.553924i 0.980448 0.196779i \(-0.0630483\pi\)
−0.660640 + 0.750703i \(0.729715\pi\)
\(258\) 0.890157 + 1.54180i 0.0554187 + 0.0959881i
\(259\) −1.98418 −0.123291
\(260\) 0 0
\(261\) 1.27571 0.0789645
\(262\) 0.0192955 + 0.0334208i 0.00119208 + 0.00206474i
\(263\) −9.32850 16.1574i −0.575220 0.996310i −0.996018 0.0891555i \(-0.971583\pi\)
0.420798 0.907154i \(-0.361750\pi\)
\(264\) −3.73127 + 6.46275i −0.229644 + 0.397754i
\(265\) 1.56063 0.0958685
\(266\) −0.0827690 + 0.143360i −0.00507489 + 0.00878998i
\(267\) 2.58098 4.47040i 0.157954 0.273584i
\(268\) −20.1658 −1.23182
\(269\) −8.97894 + 15.5520i −0.547456 + 0.948221i 0.450992 + 0.892528i \(0.351070\pi\)
−0.998448 + 0.0556934i \(0.982263\pi\)
\(270\) −0.604542 1.04710i −0.0367913 0.0637243i
\(271\) −15.4488 26.7582i −0.938450 1.62544i −0.768363 0.640014i \(-0.778929\pi\)
−0.170086 0.985429i \(-0.554405\pi\)
\(272\) −18.8025 −1.14007
\(273\) 0 0
\(274\) 3.95060 0.238665
\(275\) 2.68591 + 4.65213i 0.161966 + 0.280534i
\(276\) 4.43361 + 7.67923i 0.266872 + 0.462235i
\(277\) −13.2522 + 22.9536i −0.796250 + 1.37915i 0.125792 + 0.992057i \(0.459853\pi\)
−0.922042 + 0.387089i \(0.873481\pi\)
\(278\) −2.63320 −0.157929
\(279\) 1.20039 2.07914i 0.0718656 0.124475i
\(280\) −0.144219 + 0.249795i −0.00861874 + 0.0149281i
\(281\) 4.97766 0.296942 0.148471 0.988917i \(-0.452565\pi\)
0.148471 + 0.988917i \(0.452565\pi\)
\(282\) −1.46643 + 2.53993i −0.0873247 + 0.151251i
\(283\) 6.29317 + 10.9001i 0.374090 + 0.647943i 0.990190 0.139725i \(-0.0446218\pi\)
−0.616100 + 0.787668i \(0.711288\pi\)
\(284\) 12.4885 + 21.6307i 0.741057 + 1.28355i
\(285\) 3.62916 0.214973
\(286\) 0 0
\(287\) −1.23996 −0.0731926
\(288\) −0.560626 0.971033i −0.0330352 0.0572187i
\(289\) −4.32355 7.48861i −0.254327 0.440507i
\(290\) 0.318928 0.552399i 0.0187281 0.0324380i
\(291\) 4.01315 0.235255
\(292\) −9.45541 + 16.3772i −0.553336 + 0.958406i
\(293\) −8.45880 + 14.6511i −0.494168 + 0.855925i −0.999977 0.00672072i \(-0.997861\pi\)
0.505809 + 0.862645i \(0.331194\pi\)
\(294\) −2.42199 −0.141253
\(295\) 1.35366 2.34461i 0.0788132 0.136508i
\(296\) −2.59229 4.48997i −0.150674 0.260974i
\(297\) 14.7824 + 25.6038i 0.857759 + 1.48568i
\(298\) 0.749222 0.0434012
\(299\) 0 0
\(300\) 3.12316 0.180316
\(301\) −0.841298 1.45717i −0.0484916 0.0839899i
\(302\) 0.874509 + 1.51469i 0.0503223 + 0.0871608i
\(303\) 9.95859 17.2488i 0.572106 0.990917i
\(304\) 8.42034 0.482940
\(305\) 7.05193 12.2143i 0.403793 0.699389i
\(306\) 0.244415 0.423339i 0.0139723 0.0242007i
\(307\) −4.30426 −0.245657 −0.122828 0.992428i \(-0.539197\pi\)
−0.122828 + 0.992428i \(0.539197\pi\)
\(308\) 1.74170 3.01671i 0.0992425 0.171893i
\(309\) −12.0213 20.8214i −0.683865 1.18449i
\(310\) −0.600196 1.03957i −0.0340888 0.0590436i
\(311\) −2.22512 −0.126175 −0.0630875 0.998008i \(-0.520095\pi\)
−0.0630875 + 0.998008i \(0.520095\pi\)
\(312\) 0 0
\(313\) 7.20887 0.407469 0.203735 0.979026i \(-0.434692\pi\)
0.203735 + 0.979026i \(0.434692\pi\)
\(314\) −1.80504 3.12642i −0.101864 0.176434i
\(315\) 0.0729902 + 0.126423i 0.00411253 + 0.00712311i
\(316\) 4.40948 7.63744i 0.248052 0.429639i
\(317\) −0.321644 −0.0180653 −0.00903266 0.999959i \(-0.502875\pi\)
−0.00903266 + 0.999959i \(0.502875\pi\)
\(318\) 0.274313 0.475124i 0.0153827 0.0266436i
\(319\) −7.79847 + 13.5073i −0.436630 + 0.756266i
\(320\) 6.86488 0.383759
\(321\) −10.4527 + 18.1046i −0.583414 + 1.01050i
\(322\) 0.103616 + 0.179468i 0.00577430 + 0.0100014i
\(323\) 5.74278 + 9.94679i 0.319537 + 0.553454i
\(324\) 14.6162 0.812013
\(325\) 0 0
\(326\) −3.91201 −0.216666
\(327\) −8.98707 15.5661i −0.496986 0.860805i
\(328\) −1.61998 2.80589i −0.0894485 0.154929i
\(329\) 1.38594 2.40052i 0.0764094 0.132345i
\(330\) 1.88842 0.103954
\(331\) −8.31600 + 14.4037i −0.457089 + 0.791701i −0.998806 0.0488600i \(-0.984441\pi\)
0.541717 + 0.840561i \(0.317775\pi\)
\(332\) −4.16082 + 7.20676i −0.228355 + 0.395522i
\(333\) −2.62395 −0.143791
\(334\) −0.691317 + 1.19740i −0.0378272 + 0.0655186i
\(335\) 5.16612 + 8.94799i 0.282255 + 0.488881i
\(336\) −0.986961 1.70947i −0.0538431 0.0932590i
\(337\) 24.2186 1.31927 0.659636 0.751586i \(-0.270711\pi\)
0.659636 + 0.751586i \(0.270711\pi\)
\(338\) 0 0
\(339\) 29.3537 1.59427
\(340\) 4.94209 + 8.55995i 0.268022 + 0.464229i
\(341\) 14.6761 + 25.4197i 0.794754 + 1.37655i
\(342\) −0.109456 + 0.189584i −0.00591873 + 0.0102515i
\(343\) 4.61478 0.249174
\(344\) 2.19827 3.80752i 0.118523 0.205288i
\(345\) 2.27162 3.93456i 0.122300 0.211830i
\(346\) −3.50952 −0.188673
\(347\) 3.13680 5.43309i 0.168392 0.291664i −0.769463 0.638692i \(-0.779476\pi\)
0.937855 + 0.347028i \(0.112809\pi\)
\(348\) 4.53401 + 7.85314i 0.243049 + 0.420972i
\(349\) −3.53497 6.12275i −0.189223 0.327743i 0.755769 0.654839i \(-0.227263\pi\)
−0.944991 + 0.327095i \(0.893930\pi\)
\(350\) 0.0729902 0.00390149
\(351\) 0 0
\(352\) 13.7085 0.730666
\(353\) 10.8949 + 18.8705i 0.579878 + 1.00438i 0.995493 + 0.0948371i \(0.0302330\pi\)
−0.415615 + 0.909541i \(0.636434\pi\)
\(354\) −0.475869 0.824229i −0.0252921 0.0438073i
\(355\) 6.39866 11.0828i 0.339606 0.588214i
\(356\) −6.29598 −0.333687
\(357\) 1.34624 2.33176i 0.0712506 0.123410i
\(358\) 2.59422 4.49332i 0.137109 0.237479i
\(359\) 23.9737 1.26528 0.632642 0.774444i \(-0.281971\pi\)
0.632642 + 0.774444i \(0.281971\pi\)
\(360\) −0.190720 + 0.330337i −0.0100518 + 0.0174103i
\(361\) 6.92820 + 12.0000i 0.364642 + 0.631579i
\(362\) −0.288438 0.499589i −0.0151600 0.0262578i
\(363\) −28.5737 −1.49973
\(364\) 0 0
\(365\) 9.68922 0.507157
\(366\) −2.47905 4.29384i −0.129582 0.224443i
\(367\) −3.19566 5.53505i −0.166812 0.288927i 0.770485 0.637458i \(-0.220014\pi\)
−0.937297 + 0.348531i \(0.886681\pi\)
\(368\) 5.27059 9.12892i 0.274748 0.475878i
\(369\) −1.63977 −0.0853628
\(370\) −0.655986 + 1.13620i −0.0341031 + 0.0590683i
\(371\) −0.259256 + 0.449045i −0.0134599 + 0.0233133i
\(372\) 17.0653 0.884793
\(373\) 10.0401 17.3899i 0.519855 0.900414i −0.479879 0.877335i \(-0.659319\pi\)
0.999734 0.0230798i \(-0.00734719\pi\)
\(374\) 2.98823 + 5.17577i 0.154518 + 0.267633i
\(375\) −0.800098 1.38581i −0.0413169 0.0715629i
\(376\) 7.24280 0.373519
\(377\) 0 0
\(378\) 0.401714 0.0206619
\(379\) 2.73091 + 4.73007i 0.140277 + 0.242968i 0.927601 0.373572i \(-0.121867\pi\)
−0.787324 + 0.616540i \(0.788534\pi\)
\(380\) −2.21322 3.83341i −0.113536 0.196650i
\(381\) 2.59229 4.48997i 0.132807 0.230028i
\(382\) 0.442849 0.0226581
\(383\) 2.83388 4.90842i 0.144804 0.250808i −0.784496 0.620134i \(-0.787078\pi\)
0.929300 + 0.369326i \(0.120411\pi\)
\(384\) 5.29024 9.16297i 0.269966 0.467596i
\(385\) −1.78477 −0.0909602
\(386\) 2.50675 4.34181i 0.127590 0.220992i
\(387\) −1.11256 1.92701i −0.0565546 0.0979554i
\(388\) −2.44739 4.23901i −0.124247 0.215203i
\(389\) 10.6174 0.538325 0.269162 0.963095i \(-0.413253\pi\)
0.269162 + 0.963095i \(0.413253\pi\)
\(390\) 0 0
\(391\) 14.3784 0.727149
\(392\) 2.99059 + 5.17986i 0.151048 + 0.261622i
\(393\) 0.140548 + 0.243436i 0.00708971 + 0.0122797i
\(394\) −0.0706321 + 0.122338i −0.00355840 + 0.00616332i
\(395\) −4.51851 −0.227351
\(396\) 2.30328 3.98940i 0.115744 0.200475i
\(397\) −14.0169 + 24.2780i −0.703487 + 1.21848i 0.263748 + 0.964592i \(0.415041\pi\)
−0.967235 + 0.253884i \(0.918292\pi\)
\(398\) −0.673745 −0.0337718
\(399\) −0.602888 + 1.04423i −0.0301822 + 0.0522770i
\(400\) −1.85638 3.21534i −0.0928189 0.160767i
\(401\) 11.2571 + 19.4979i 0.562155 + 0.973680i 0.997308 + 0.0733241i \(0.0233607\pi\)
−0.435154 + 0.900356i \(0.643306\pi\)
\(402\) 3.63222 0.181159
\(403\) 0 0
\(404\) −24.2927 −1.20861
\(405\) −3.74441 6.48552i −0.186061 0.322268i
\(406\) 0.105963 + 0.183533i 0.00525884 + 0.00910857i
\(407\) 16.0403 27.7826i 0.795087 1.37713i
\(408\) 7.03533 0.348301
\(409\) −2.14386 + 3.71328i −0.106007 + 0.183610i −0.914149 0.405378i \(-0.867140\pi\)
0.808142 + 0.588988i \(0.200473\pi\)
\(410\) −0.409941 + 0.710039i −0.0202456 + 0.0350663i
\(411\) 28.7761 1.41942
\(412\) −14.6622 + 25.3956i −0.722353 + 1.25115i
\(413\) 0.449749 + 0.778989i 0.0221307 + 0.0383315i
\(414\) 0.137025 + 0.237335i 0.00673443 + 0.0116644i
\(415\) 4.26371 0.209297
\(416\) 0 0
\(417\) −19.1802 −0.939257
\(418\) −1.33822 2.31787i −0.0654546 0.113371i
\(419\) −8.85578 15.3387i −0.432633 0.749343i 0.564466 0.825456i \(-0.309082\pi\)
−0.997099 + 0.0761137i \(0.975749\pi\)
\(420\) −0.518830 + 0.898640i −0.0253163 + 0.0438491i
\(421\) 12.8787 0.627672 0.313836 0.949477i \(-0.398386\pi\)
0.313836 + 0.949477i \(0.398386\pi\)
\(422\) −0.900759 + 1.56016i −0.0438483 + 0.0759474i
\(423\) 1.83281 3.17453i 0.0891145 0.154351i
\(424\) −1.35485 −0.0657973
\(425\) 2.53215 4.38581i 0.122827 0.212743i
\(426\) −2.24940 3.89607i −0.108984 0.188765i
\(427\) 2.34298 + 4.05816i 0.113385 + 0.196388i
\(428\) 25.4981 1.23250
\(429\) 0 0
\(430\) −1.11256 −0.0536524
\(431\) −4.74923 8.22590i −0.228762 0.396228i 0.728679 0.684855i \(-0.240134\pi\)
−0.957442 + 0.288627i \(0.906801\pi\)
\(432\) −10.2169 17.6962i −0.491560 0.851408i
\(433\) 0.698141 1.20922i 0.0335505 0.0581112i −0.848763 0.528774i \(-0.822652\pi\)
0.882313 + 0.470663i \(0.155985\pi\)
\(434\) 0.398826 0.0191443
\(435\) 2.32306 4.02367i 0.111382 0.192920i
\(436\) −10.9614 + 18.9857i −0.524956 + 0.909251i
\(437\) −6.43911 −0.308024
\(438\) 1.70308 2.94983i 0.0813765 0.140948i
\(439\) −2.08090 3.60422i −0.0993159 0.172020i 0.812086 0.583538i \(-0.198332\pi\)
−0.911402 + 0.411518i \(0.864999\pi\)
\(440\) −2.33176 4.03872i −0.111162 0.192539i
\(441\) 3.02711 0.144148
\(442\) 0 0
\(443\) 9.54563 0.453526 0.226763 0.973950i \(-0.427186\pi\)
0.226763 + 0.973950i \(0.427186\pi\)
\(444\) −9.32578 16.1527i −0.442582 0.766574i
\(445\) 1.61292 + 2.79366i 0.0764596 + 0.132432i
\(446\) 1.12526 1.94900i 0.0532825 0.0922880i
\(447\) 5.45732 0.258122
\(448\) −1.14042 + 1.97526i −0.0538796 + 0.0933223i
\(449\) −10.8585 + 18.8075i −0.512446 + 0.887582i 0.487450 + 0.873151i \(0.337927\pi\)
−0.999896 + 0.0144310i \(0.995406\pi\)
\(450\) 0.0965246 0.00455022
\(451\) 10.0239 17.3620i 0.472009 0.817544i
\(452\) −17.9012 31.0057i −0.842000 1.45839i
\(453\) 6.36991 + 11.0330i 0.299284 + 0.518376i
\(454\) −1.54743 −0.0726246
\(455\) 0 0
\(456\) −3.15064 −0.147542
\(457\) −2.36130 4.08989i −0.110457 0.191317i 0.805498 0.592599i \(-0.201898\pi\)
−0.915955 + 0.401282i \(0.868565\pi\)
\(458\) 0.145980 + 0.252845i 0.00682122 + 0.0118147i
\(459\) 13.9361 24.1381i 0.650482 1.12667i
\(460\) −5.54133 −0.258366
\(461\) 0.890753 1.54283i 0.0414865 0.0718568i −0.844537 0.535498i \(-0.820124\pi\)
0.886023 + 0.463641i \(0.153457\pi\)
\(462\) −0.313710 + 0.543362i −0.0145951 + 0.0252795i
\(463\) 6.80200 0.316116 0.158058 0.987430i \(-0.449477\pi\)
0.158058 + 0.987430i \(0.449477\pi\)
\(464\) 5.38995 9.33566i 0.250222 0.433397i
\(465\) −4.37182 7.57221i −0.202738 0.351153i
\(466\) −0.137025 0.237335i −0.00634758 0.0109943i
\(467\) 18.2374 0.843927 0.421963 0.906613i \(-0.361341\pi\)
0.421963 + 0.906613i \(0.361341\pi\)
\(468\) 0 0
\(469\) −3.43285 −0.158514
\(470\) −0.916407 1.58726i −0.0422707 0.0732150i
\(471\) −13.1479 22.7728i −0.605823 1.04932i
\(472\) −1.17517 + 2.03546i −0.0540918 + 0.0936897i
\(473\) 27.2045 1.25086
\(474\) −0.794223 + 1.37564i −0.0364799 + 0.0631850i
\(475\) −1.13397 + 1.96410i −0.0520303 + 0.0901192i
\(476\) −3.28398 −0.150521
\(477\) −0.342849 + 0.593832i −0.0156980 + 0.0271897i
\(478\) −1.09207 1.89152i −0.0499502 0.0865162i
\(479\) 17.5904 + 30.4674i 0.803724 + 1.39209i 0.917149 + 0.398544i \(0.130485\pi\)
−0.113425 + 0.993547i \(0.536182\pi\)
\(480\) −4.08359 −0.186390
\(481\) 0 0
\(482\) 4.96204 0.226015
\(483\) 0.754738 + 1.30724i 0.0343418 + 0.0594817i
\(484\) 17.4255 + 30.1819i 0.792069 + 1.37190i
\(485\) −1.25396 + 2.17191i −0.0569392 + 0.0986215i
\(486\) 0.994615 0.0451166
\(487\) 5.15200 8.92352i 0.233459 0.404363i −0.725364 0.688365i \(-0.758329\pi\)
0.958824 + 0.284002i \(0.0916621\pi\)
\(488\) −6.12210 + 10.6038i −0.277134 + 0.480011i
\(489\) −28.4950 −1.28859
\(490\) 0.756779 1.31078i 0.0341878 0.0592150i
\(491\) −4.66599 8.08174i −0.210573 0.364724i 0.741321 0.671151i \(-0.234200\pi\)
−0.951894 + 0.306427i \(0.900866\pi\)
\(492\) −5.82790 10.0942i −0.262742 0.455083i
\(493\) 14.7041 0.662238
\(494\) 0 0
\(495\) −2.36023 −0.106085
\(496\) −10.1434 17.5689i −0.455454 0.788869i
\(497\) 2.12593 + 3.68222i 0.0953611 + 0.165170i
\(498\) 0.749437 1.29806i 0.0335831 0.0581676i
\(499\) 23.9421 1.07179 0.535897 0.844283i \(-0.319974\pi\)
0.535897 + 0.844283i \(0.319974\pi\)
\(500\) −0.975869 + 1.69025i −0.0436422 + 0.0755905i
\(501\) −5.03554 + 8.72181i −0.224971 + 0.389662i
\(502\) 1.48692 0.0663645
\(503\) −21.0721 + 36.4980i −0.939560 + 1.62737i −0.173266 + 0.984875i \(0.555432\pi\)
−0.766294 + 0.642490i \(0.777901\pi\)
\(504\) −0.0633661 0.109753i −0.00282255 0.00488880i
\(505\) 6.22336 + 10.7792i 0.276936 + 0.479667i
\(506\) −3.35056 −0.148951
\(507\) 0 0
\(508\) −6.32355 −0.280562
\(509\) 16.7801 + 29.0640i 0.743765 + 1.28824i 0.950770 + 0.309899i \(0.100295\pi\)
−0.207005 + 0.978340i \(0.566371\pi\)
\(510\) −0.890157 1.54180i −0.0394168 0.0682719i
\(511\) −1.60960 + 2.78792i −0.0712047 + 0.123330i
\(512\) −15.9211 −0.703621
\(513\) −6.24102 + 10.8098i −0.275548 + 0.477263i
\(514\) −1.12632 + 1.95084i −0.0496796 + 0.0860477i
\(515\) 15.0247 0.662069
\(516\) 7.90831 13.6976i 0.348144 0.603003i
\(517\) 22.4081 + 38.8120i 0.985508 + 1.70695i
\(518\) −0.217949 0.377499i −0.00957614 0.0165864i
\(519\) −25.5633 −1.12210
\(520\) 0 0
\(521\) 12.4649 0.546098 0.273049 0.962000i \(-0.411968\pi\)
0.273049 + 0.962000i \(0.411968\pi\)
\(522\) 0.140128 + 0.242710i 0.00613326 + 0.0106231i
\(523\) 2.82978 + 4.90132i 0.123738 + 0.214320i 0.921239 0.388998i \(-0.127179\pi\)
−0.797501 + 0.603317i \(0.793845\pi\)
\(524\) 0.171425 0.296916i 0.00748872 0.0129708i
\(525\) 0.531659 0.0232035
\(526\) 2.04935 3.54958i 0.0893558 0.154769i
\(527\) 13.8359 23.9645i 0.602702 1.04391i
\(528\) 31.9147 1.38891
\(529\) 7.46953 12.9376i 0.324762 0.562505i
\(530\) 0.171425 + 0.296916i 0.00744621 + 0.0128972i
\(531\) 0.594763 + 1.03016i 0.0258105 + 0.0447051i
\(532\) 1.47067 0.0637616
\(533\) 0 0
\(534\) 1.13402 0.0490737
\(535\) −6.53215 11.3140i −0.282409 0.489147i
\(536\) −4.48494 7.76815i −0.193720 0.335533i
\(537\) 18.8963 32.7293i 0.815433 1.41237i
\(538\) −3.94511 −0.170086
\(539\) −18.5049 + 32.0514i −0.797061 + 1.38055i
\(540\) −5.37086 + 9.30260i −0.231125 + 0.400320i
\(541\) −15.4750 −0.665321 −0.332660 0.943047i \(-0.607946\pi\)
−0.332660 + 0.943047i \(0.607946\pi\)
\(542\) 3.39391 5.87842i 0.145781 0.252500i
\(543\) −2.10098 3.63900i −0.0901616 0.156165i
\(544\) −6.46187 11.1923i −0.277051 0.479866i
\(545\) 11.2325 0.481146
\(546\) 0 0
\(547\) 25.1765 1.07647 0.538234 0.842795i \(-0.319092\pi\)
0.538234 + 0.842795i \(0.319092\pi\)
\(548\) −17.5489 30.3956i −0.749653 1.29844i
\(549\) 3.09843 + 5.36665i 0.132238 + 0.229043i
\(550\) −0.590059 + 1.02201i −0.0251602 + 0.0435787i
\(551\) −6.58493 −0.280528
\(552\) −1.97210 + 3.41577i −0.0839380 + 0.145385i
\(553\) 0.750630 1.30013i 0.0319200 0.0552871i
\(554\) −5.82269 −0.247382
\(555\) −4.77819 + 8.27607i −0.202823 + 0.351300i
\(556\) 11.6969 + 20.2596i 0.496059 + 0.859199i
\(557\) −21.1744 36.6752i −0.897190 1.55398i −0.831071 0.556167i \(-0.812272\pi\)
−0.0661194 0.997812i \(-0.521062\pi\)
\(558\) 0.527420 0.0223275
\(559\) 0 0
\(560\) 1.23355 0.0521270
\(561\) 21.7662 + 37.7002i 0.918971 + 1.59171i
\(562\) 0.546763 + 0.947022i 0.0230638 + 0.0399477i
\(563\) −11.8953 + 20.6032i −0.501326 + 0.868322i 0.498673 + 0.866790i \(0.333821\pi\)
−0.999999 + 0.00153173i \(0.999512\pi\)
\(564\) 26.0561 1.09716
\(565\) −9.17191 + 15.8862i −0.385865 + 0.668338i
\(566\) −1.38253 + 2.39461i −0.0581119 + 0.100653i
\(567\) 2.48814 0.104492
\(568\) −5.55497 + 9.62148i −0.233081 + 0.403709i
\(569\) 13.3710 + 23.1593i 0.560543 + 0.970889i 0.997449 + 0.0713817i \(0.0227408\pi\)
−0.436906 + 0.899507i \(0.643926\pi\)
\(570\) 0.398640 + 0.690464i 0.0166972 + 0.0289204i
\(571\) −16.7159 −0.699539 −0.349769 0.936836i \(-0.613740\pi\)
−0.349769 + 0.936836i \(0.613740\pi\)
\(572\) 0 0
\(573\) 3.22571 0.134756
\(574\) −0.136202 0.235908i −0.00568494 0.00984661i
\(575\) 1.41959 + 2.45880i 0.0592010 + 0.102539i
\(576\) −1.50812 + 2.61215i −0.0628385 + 0.108840i
\(577\) −20.6768 −0.860786 −0.430393 0.902642i \(-0.641625\pi\)
−0.430393 + 0.902642i \(0.641625\pi\)
\(578\) 0.949828 1.64515i 0.0395076 0.0684292i
\(579\) 18.2591 31.6257i 0.758822 1.31432i
\(580\) −5.66682 −0.235302
\(581\) −0.708301 + 1.22681i −0.0293853 + 0.0508968i
\(582\) 0.440818 + 0.763519i 0.0182725 + 0.0316489i
\(583\) −4.19170 7.26023i −0.173602 0.300688i
\(584\) −8.41165 −0.348076
\(585\) 0 0
\(586\) −3.71657 −0.153530
\(587\) −10.3986 18.0109i −0.429196 0.743388i 0.567606 0.823300i \(-0.307870\pi\)
−0.996802 + 0.0799116i \(0.974536\pi\)
\(588\) 10.7587 + 18.6346i 0.443681 + 0.768478i
\(589\) −6.19615 + 10.7321i −0.255308 + 0.442206i
\(590\) 0.594763 0.0244860
\(591\) −0.514483 + 0.891111i −0.0211630 + 0.0366554i
\(592\) −11.0863 + 19.2021i −0.455644 + 0.789199i
\(593\) −21.8475 −0.897169 −0.448585 0.893740i \(-0.648072\pi\)
−0.448585 + 0.893740i \(0.648072\pi\)
\(594\) −3.24749 + 5.62482i −0.133246 + 0.230789i
\(595\) 0.841298 + 1.45717i 0.0344898 + 0.0597381i
\(596\) −3.32811 5.76446i −0.136325 0.236121i
\(597\) −4.90755 −0.200853
\(598\) 0 0
\(599\) −3.58040 −0.146291 −0.0731456 0.997321i \(-0.523304\pi\)
−0.0731456 + 0.997321i \(0.523304\pi\)
\(600\) 0.694601 + 1.20308i 0.0283570 + 0.0491157i
\(601\) −10.6743 18.4885i −0.435414 0.754160i 0.561915 0.827195i \(-0.310065\pi\)
−0.997329 + 0.0730352i \(0.976731\pi\)
\(602\) 0.184822 0.320121i 0.00753278 0.0130472i
\(603\) −4.53972 −0.184872
\(604\) 7.76929 13.4568i 0.316128 0.547550i
\(605\) 8.92820 15.4641i 0.362983 0.628705i
\(606\) 4.37554 0.177744
\(607\) 1.64988 2.85767i 0.0669665 0.115989i −0.830598 0.556872i \(-0.812001\pi\)
0.897565 + 0.440883i \(0.145335\pi\)
\(608\) 2.89383 + 5.01226i 0.117360 + 0.203274i
\(609\) 0.771830 + 1.33685i 0.0312761 + 0.0541718i
\(610\) 3.09843 0.125452
\(611\) 0 0
\(612\) −4.34285 −0.175549
\(613\) −4.94318 8.56183i −0.199653 0.345809i 0.748763 0.662838i \(-0.230648\pi\)
−0.948416 + 0.317029i \(0.897315\pi\)
\(614\) −0.472795 0.818904i −0.0190804 0.0330483i
\(615\) −2.98601 + 5.17191i −0.120407 + 0.208552i
\(616\) 1.54944 0.0624286
\(617\) 22.8584 39.5920i 0.920246 1.59391i 0.121213 0.992626i \(-0.461321\pi\)
0.799033 0.601287i \(-0.205345\pi\)
\(618\) 2.64091 4.57419i 0.106233 0.184001i
\(619\) 19.9143 0.800425 0.400212 0.916422i \(-0.368936\pi\)
0.400212 + 0.916422i \(0.368936\pi\)
\(620\) −5.33225 + 9.23572i −0.214148 + 0.370916i
\(621\) 7.81295 + 13.5324i 0.313523 + 0.543038i
\(622\) −0.244415 0.423339i −0.00980014 0.0169743i
\(623\) −1.07177 −0.0429397
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0.791847 + 1.37152i 0.0316486 + 0.0548169i
\(627\) −9.74760 16.8833i −0.389282 0.674255i
\(628\) −16.0363 + 27.7757i −0.639918 + 1.10837i
\(629\) −30.2440 −1.20591
\(630\) −0.0160350 + 0.0277734i −0.000638849 + 0.00110652i
\(631\) −7.29790 + 12.6403i −0.290525 + 0.503204i −0.973934 0.226832i \(-0.927163\pi\)
0.683409 + 0.730036i \(0.260497\pi\)
\(632\) 3.92272 0.156038
\(633\) −6.56112 + 11.3642i −0.260781 + 0.451686i
\(634\) −0.0353305 0.0611942i −0.00140315 0.00243033i
\(635\) 1.61998 + 2.80589i 0.0642870 + 0.111348i
\(636\) −4.87409 −0.193270
\(637\) 0 0
\(638\) −3.42644 −0.135654
\(639\) 2.81140 + 4.86950i 0.111217 + 0.192634i
\(640\) 3.30600 + 5.72615i 0.130681 + 0.226346i
\(641\) 7.08183 12.2661i 0.279716 0.484482i −0.691598 0.722282i \(-0.743093\pi\)
0.971314 + 0.237801i \(0.0764265\pi\)
\(642\) −4.59265 −0.181257
\(643\) −8.38581 + 14.5246i −0.330704 + 0.572796i −0.982650 0.185469i \(-0.940620\pi\)
0.651946 + 0.758265i \(0.273953\pi\)
\(644\) 0.920544 1.59443i 0.0362745 0.0628293i
\(645\) −8.10387 −0.319089
\(646\) −1.26161 + 2.18518i −0.0496376 + 0.0859748i
\(647\) 1.49584 + 2.59087i 0.0588075 + 0.101858i 0.893930 0.448206i \(-0.147937\pi\)
−0.835123 + 0.550063i \(0.814604\pi\)
\(648\) 3.25069 + 5.63037i 0.127699 + 0.221182i
\(649\) −14.5432 −0.570872
\(650\) 0 0
\(651\) 2.90504 0.113858
\(652\) 17.3775 + 30.0987i 0.680556 + 1.17876i
\(653\) 5.83217 + 10.1016i 0.228230 + 0.395307i 0.957284 0.289150i \(-0.0933727\pi\)
−0.729053 + 0.684457i \(0.760039\pi\)
\(654\) 1.97434 3.41966i 0.0772028 0.133719i
\(655\) −0.175664 −0.00686374
\(656\) −6.92810 + 11.9998i −0.270497 + 0.468514i
\(657\) −2.12859 + 3.68683i −0.0830444 + 0.143837i
\(658\) 0.608946 0.0237392
\(659\) 0.905237 1.56792i 0.0352630 0.0610773i −0.847855 0.530228i \(-0.822106\pi\)
0.883118 + 0.469150i \(0.155440\pi\)
\(660\) −8.38853 14.5294i −0.326523 0.565554i
\(661\) 6.17028 + 10.6872i 0.239996 + 0.415686i 0.960713 0.277544i \(-0.0895205\pi\)
−0.720717 + 0.693230i \(0.756187\pi\)
\(662\) −3.65383 −0.142010
\(663\) 0 0
\(664\) −3.70152 −0.143647
\(665\) −0.376759 0.652566i −0.0146101 0.0253054i
\(666\) −0.288223 0.499217i −0.0111684 0.0193443i
\(667\) −4.12174 + 7.13907i −0.159594 + 0.276426i
\(668\) 12.2836 0.475265
\(669\) 8.19636 14.1965i 0.316890 0.548869i
\(670\) −1.13493 + 1.96576i −0.0438461 + 0.0759438i
\(671\) −75.7634 −2.92481
\(672\) 0.678380 1.17499i 0.0261691 0.0453262i
\(673\) −4.63313 8.02481i −0.178594 0.309334i 0.762805 0.646628i \(-0.223822\pi\)
−0.941399 + 0.337295i \(0.890488\pi\)
\(674\) 2.66025 + 4.60770i 0.102469 + 0.177482i
\(675\) 5.50367 0.211836
\(676\) 0 0
\(677\) 13.8984 0.534158 0.267079 0.963675i \(-0.413941\pi\)
0.267079 + 0.963675i \(0.413941\pi\)
\(678\) 3.22431 + 5.58467i 0.123829 + 0.214478i
\(679\) −0.416622 0.721611i −0.0159885 0.0276929i
\(680\) −2.19827 + 3.80752i −0.0842999 + 0.146012i
\(681\) −11.2715 −0.431924
\(682\) −3.22414 + 5.58438i −0.123459 + 0.213837i
\(683\) 18.8756 32.6935i 0.722255 1.25098i −0.237838 0.971305i \(-0.576439\pi\)
0.960094 0.279678i \(-0.0902278\pi\)
\(684\) 1.94486 0.0743637
\(685\) −8.99144 + 15.5736i −0.343545 + 0.595038i
\(686\) 0.506903 + 0.877981i 0.0193536 + 0.0335215i
\(687\) 1.06332 + 1.84172i 0.0405681 + 0.0702661i
\(688\) −18.8025 −0.716838
\(689\) 0 0
\(690\) 0.998090 0.0379966
\(691\) 0.826456 + 1.43146i 0.0314399 + 0.0544554i 0.881317 0.472525i \(-0.156657\pi\)
−0.849877 + 0.526981i \(0.823324\pi\)
\(692\) 15.5896 + 27.0020i 0.592628 + 1.02646i
\(693\) 0.392090 0.679120i 0.0148943 0.0257976i
\(694\) 1.37823 0.0523168
\(695\) 5.99307 10.3803i 0.227330 0.393747i
\(696\) −2.01676 + 3.49312i −0.0764450 + 0.132407i
\(697\) −18.9002 −0.715897
\(698\) 0.776587 1.34509i 0.0293943 0.0509123i
\(699\) −0.998090 1.72874i −0.0377512 0.0653871i
\(700\) −0.324229 0.561581i −0.0122547 0.0212258i
\(701\) 20.4819 0.773590 0.386795 0.922166i \(-0.373582\pi\)
0.386795 + 0.922166i \(0.373582\pi\)
\(702\) 0 0
\(703\) 13.5442 0.510830
\(704\) −18.4384 31.9363i −0.694925 1.20365i
\(705\) −6.67510 11.5616i −0.251399 0.435435i
\(706\) −2.39347 + 4.14561i −0.0900794 + 0.156022i
\(707\) −4.13538 −0.155527
\(708\) −4.22770 + 7.32260i −0.158887 + 0.275200i
\(709\) −10.9709 + 19.0021i −0.412020 + 0.713639i −0.995110 0.0987679i \(-0.968510\pi\)
0.583091 + 0.812407i \(0.301843\pi\)
\(710\) 2.81140 0.105510
\(711\) 0.992658 1.71933i 0.0372276 0.0644801i
\(712\) −1.40025 2.42530i −0.0524764 0.0908919i
\(713\) 7.75678 + 13.4351i 0.290494 + 0.503150i
\(714\) 0.591503 0.0221364
\(715\) 0 0
\(716\) −46.0950 −1.72265
\(717\) −7.95463 13.7778i −0.297071 0.514542i
\(718\) 2.63335 + 4.56110i 0.0982759 + 0.170219i
\(719\) −19.4237 + 33.6429i −0.724384 + 1.25467i 0.234844 + 0.972033i \(0.424542\pi\)
−0.959227 + 0.282636i \(0.908791\pi\)
\(720\) 1.63129 0.0607945
\(721\) −2.49596 + 4.32312i −0.0929543 + 0.161002i
\(722\) −1.52204 + 2.63624i −0.0566443 + 0.0981108i
\(723\) 36.1434 1.34419
\(724\) −2.56254 + 4.43844i −0.0952359 + 0.164953i
\(725\) 1.45174 + 2.51448i 0.0539162 + 0.0933856i
\(726\) −3.13864 5.43628i −0.116486 0.201759i
\(727\) −30.6598 −1.13711 −0.568555 0.822645i \(-0.692497\pi\)
−0.568555 + 0.822645i \(0.692497\pi\)
\(728\) 0 0
\(729\) 29.7112 1.10042
\(730\) 1.06430 + 1.84342i 0.0393914 + 0.0682279i
\(731\) −12.8236 22.2110i −0.474296 0.821505i
\(732\) −22.0243 + 38.1473i −0.814043 + 1.40996i
\(733\) 24.3858 0.900709 0.450355 0.892850i \(-0.351298\pi\)
0.450355 + 0.892850i \(0.351298\pi\)
\(734\) 0.702045 1.21598i 0.0259130 0.0448826i
\(735\) 5.51236 9.54769i 0.203327 0.352172i
\(736\) 7.24539 0.267069
\(737\) 27.7515 48.0669i 1.02224 1.77057i
\(738\) −0.180117 0.311973i −0.00663021 0.0114839i
\(739\) −19.1394 33.1504i −0.704054 1.21946i −0.967032 0.254656i \(-0.918038\pi\)
0.262977 0.964802i \(-0.415296\pi\)
\(740\) 11.6558 0.428476
\(741\) 0 0
\(742\) −0.113910 −0.00418178
\(743\) 20.0040 + 34.6479i 0.733874 + 1.27111i 0.955216 + 0.295910i \(0.0956230\pi\)
−0.221342 + 0.975196i \(0.571044\pi\)
\(744\) 3.79537 + 6.57377i 0.139145 + 0.241006i
\(745\) −1.70520 + 2.95350i −0.0624738 + 0.108208i
\(746\) 4.41134 0.161511
\(747\) −0.936681 + 1.62238i −0.0342714 + 0.0593598i
\(748\) 26.5480 45.9825i 0.970691 1.68129i
\(749\) 4.34057 0.158601
\(750\) 0.175771 0.304444i 0.00641825 0.0111167i
\(751\) −12.8010 22.1720i −0.467115 0.809067i 0.532179 0.846632i \(-0.321373\pi\)
−0.999294 + 0.0375648i \(0.988040\pi\)
\(752\) −15.4875 26.8251i −0.564770 0.978211i
\(753\) 10.8307 0.394693
\(754\) 0 0
\(755\) −7.96141 −0.289745
\(756\) −1.78445 3.09076i −0.0648998 0.112410i
\(757\) 0.924239 + 1.60083i 0.0335920 + 0.0581831i 0.882333 0.470626i \(-0.155972\pi\)
−0.848741 + 0.528809i \(0.822639\pi\)
\(758\) −0.599945 + 1.03914i −0.0217910 + 0.0377431i
\(759\) −24.4055 −0.885862
\(760\) 0.984454 1.70512i 0.0357099 0.0618514i
\(761\) −13.1062 + 22.7006i −0.475099 + 0.822896i −0.999593 0.0285179i \(-0.990921\pi\)
0.524494 + 0.851414i \(0.324255\pi\)
\(762\) 1.13898 0.0412610
\(763\) −1.86597 + 3.23196i −0.0675528 + 0.117005i
\(764\) −1.96718 3.40725i −0.0711699 0.123270i
\(765\) 1.11256 + 1.92701i 0.0402247 + 0.0696712i
\(766\) 1.24513 0.0449884
\(767\) 0 0
\(768\) −19.6459 −0.708911
\(769\) 22.1747 + 38.4078i 0.799641 + 1.38502i 0.919850 + 0.392271i \(0.128310\pi\)
−0.120208 + 0.992749i \(0.538356\pi\)
\(770\) −0.196045 0.339560i −0.00706497 0.0122369i
\(771\) −8.20406 + 14.2099i −0.295462 + 0.511755i
\(772\) −44.5408 −1.60306
\(773\) 11.6319 20.1471i 0.418371 0.724640i −0.577405 0.816458i \(-0.695935\pi\)
0.995776 + 0.0918181i \(0.0292678\pi\)
\(774\) 0.244415 0.423339i 0.00878531 0.0152166i
\(775\) 5.46410 0.196276
\(776\) 1.08861 1.88554i 0.0390790 0.0676868i
\(777\) −1.58754 2.74970i −0.0569526 0.0986448i
\(778\) 1.16625 + 2.02001i 0.0418122 + 0.0724209i
\(779\) 8.46410 0.303258
\(780\) 0 0