Properties

Label 845.2.m.g.361.3
Level $845$
Weight $2$
Character 845.361
Analytic conductor $6.747$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.3
Root \(-1.27597 - 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 845.361
Dual form 845.2.m.g.316.3

$q$-expansion

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

Character values

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

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.190254 0.109843i 0.134530 0.0776710i −0.431224 0.902245i \(-0.641918\pi\)
0.565755 + 0.824574i \(0.308585\pi\)
\(3\) 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
\(5\) 1.00000i 0.447214i
\(6\) 0.304444 + 0.175771i 0.124289 + 0.0717582i
\(7\) 0.287734 + 0.166123i 0.108753 + 0.0627887i 0.553390 0.832922i \(-0.313334\pi\)
−0.444637 + 0.895711i \(0.646667\pi\)
\(8\) 0.868145i 0.306936i
\(9\) 0.219687 0.380509i 0.0732290 0.126836i
\(10\) 0.109843 + 0.190254i 0.0347355 + 0.0601637i
\(11\) −4.65213 + 2.68591i −1.40267 + 0.809832i −0.994666 0.103149i \(-0.967108\pi\)
−0.408004 + 0.912980i \(0.633775\pi\)
\(12\) −3.12316 −0.901579
\(13\) 0 0
\(14\) 0.0729902 0.0195074
\(15\) −1.38581 + 0.800098i −0.357815 + 0.206584i
\(16\) −1.85638 3.21534i −0.464094 0.803835i
\(17\) −2.53215 + 4.38581i −0.614136 + 1.06372i 0.376399 + 0.926458i \(0.377162\pi\)
−0.990535 + 0.137258i \(0.956171\pi\)
\(18\) 0.0965246i 0.0227511i
\(19\) 1.96410 + 1.13397i 0.450596 + 0.260152i 0.708082 0.706130i \(-0.249561\pi\)
−0.257486 + 0.966282i \(0.582894\pi\)
\(20\) −1.69025 0.975869i −0.377952 0.218211i
\(21\) 0.531659i 0.116018i
\(22\) −0.590059 + 1.02201i −0.125801 + 0.217894i
\(23\) −1.41959 2.45880i −0.296005 0.512695i 0.679213 0.733941i \(-0.262321\pi\)
−0.975218 + 0.221246i \(0.928988\pi\)
\(24\) −1.20308 + 0.694601i −0.245578 + 0.141785i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 5.50367 1.05918
\(28\) −0.561581 + 0.324229i −0.106129 + 0.0612735i
\(29\) 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
\(31\) 5.46410i 0.981382i −0.871334 0.490691i \(-0.836744\pi\)
0.871334 0.490691i \(-0.163256\pi\)
\(32\) −2.21004 1.27597i −0.390683 0.225561i
\(33\) −7.44432 4.29798i −1.29589 0.748182i
\(34\) 1.11256i 0.190802i
\(35\) −0.166123 + 0.287734i −0.0280800 + 0.0486359i
\(36\) 0.428771 + 0.742653i 0.0714619 + 0.123776i
\(37\) 5.17191 2.98601i 0.850257 0.490896i −0.0104803 0.999945i \(-0.503336\pi\)
0.860738 + 0.509049i \(0.170003\pi\)
\(38\) 0.498239 0.0808250
\(39\) 0 0
\(40\) −0.868145 −0.137266
\(41\) −3.23205 + 1.86603i −0.504762 + 0.291424i −0.730678 0.682723i \(-0.760796\pi\)
0.225916 + 0.974147i \(0.427462\pi\)
\(42\) 0.0583993 + 0.101151i 0.00901121 + 0.0156079i
\(43\) −2.53215 + 4.38581i −0.386149 + 0.668830i −0.991928 0.126803i \(-0.959528\pi\)
0.605779 + 0.795633i \(0.292862\pi\)
\(44\) 10.4844i 1.58058i
\(45\) 0.380509 + 0.219687i 0.0567229 + 0.0327490i
\(46\) −0.540166 0.311865i −0.0796432 0.0459820i
\(47\) 8.34285i 1.21693i 0.793581 + 0.608465i \(0.208214\pi\)
−0.793581 + 0.608465i \(0.791786\pi\)
\(48\) 2.97057 5.14517i 0.428764 0.742642i
\(49\) −3.44481 5.96658i −0.492115 0.852368i
\(50\) −0.190254 + 0.109843i −0.0269060 + 0.0155342i
\(51\) −8.10387 −1.13477
\(52\) 0 0
\(53\) −1.56063 −0.214369 −0.107184 0.994239i \(-0.534183\pi\)
−0.107184 + 0.994239i \(0.534183\pi\)
\(54\) 1.04710 0.604542i 0.142492 0.0822678i
\(55\) −2.68591 4.65213i −0.362168 0.627293i
\(56\) −0.144219 + 0.249795i −0.0192721 + 0.0333802i
\(57\) 3.62916i 0.480694i
\(58\) 0.552399 + 0.318928i 0.0725335 + 0.0418773i
\(59\) −2.34461 1.35366i −0.305242 0.176232i 0.339553 0.940587i \(-0.389724\pi\)
−0.644795 + 0.764355i \(0.723057\pi\)
\(60\) 3.12316i 0.403199i
\(61\) −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
\(63\) 0.126423 0.0729902i 0.0159278 0.00919590i
\(64\) 6.86488 0.858111
\(65\) 0 0
\(66\) −1.88842 −0.232448
\(67\) −8.94799 + 5.16612i −1.09317 + 0.631142i −0.934419 0.356176i \(-0.884080\pi\)
−0.158752 + 0.987319i \(0.550747\pi\)
\(68\) −4.94209 8.55995i −0.599316 1.03805i
\(69\) 2.27162 3.93456i 0.273471 0.473666i
\(70\) 0.0729902i 0.00872400i
\(71\) 11.0828 + 6.39866i 1.31529 + 0.759382i 0.982967 0.183785i \(-0.0588349\pi\)
0.332321 + 0.943166i \(0.392168\pi\)
\(72\) 0.330337 + 0.190720i 0.0389306 + 0.0224766i
\(73\) 9.68922i 1.13404i −0.823705 0.567019i \(-0.808097\pi\)
0.823705 0.567019i \(-0.191903\pi\)
\(74\) 0.655986 1.13620i 0.0762569 0.132081i
\(75\) −0.800098 1.38581i −0.0923873 0.160020i
\(76\) −3.83341 + 2.21322i −0.439722 + 0.253874i
\(77\) −1.78477 −0.203393
\(78\) 0 0
\(79\) 4.51851 0.508372 0.254186 0.967155i \(-0.418192\pi\)
0.254186 + 0.967155i \(0.418192\pi\)
\(80\) 3.21534 1.85638i 0.359486 0.207549i
\(81\) 3.74441 + 6.48552i 0.416046 + 0.720613i
\(82\) −0.409941 + 0.710039i −0.0452704 + 0.0784107i
\(83\) 4.26371i 0.468003i 0.972236 + 0.234001i \(0.0751821\pi\)
−0.972236 + 0.234001i \(0.924818\pi\)
\(84\) −0.898640 0.518830i −0.0980496 0.0566090i
\(85\) −4.38581 2.53215i −0.475708 0.274650i
\(86\) 1.11256i 0.119970i
\(87\) −2.32306 + 4.02367i −0.249059 + 0.431382i
\(88\) −2.33176 4.03872i −0.248566 0.430529i
\(89\) 2.79366 1.61292i 0.296127 0.170969i −0.344575 0.938759i \(-0.611977\pi\)
0.640702 + 0.767790i \(0.278644\pi\)
\(90\) 0.0965246 0.0101746
\(91\) 0 0
\(92\) 5.54133 0.577724
\(93\) 7.57221 4.37182i 0.785201 0.453336i
\(94\) 0.916407 + 1.58726i 0.0945202 + 0.163714i
\(95\) −1.13397 + 1.96410i −0.116343 + 0.201513i
\(96\) 4.08359i 0.416780i
\(97\) −2.17191 1.25396i −0.220524 0.127320i 0.385669 0.922637i \(-0.373971\pi\)
−0.606193 + 0.795318i \(0.707304\pi\)
\(98\) −1.31078 0.756779i −0.132409 0.0764462i
\(99\) 2.36023i 0.237213i
\(100\) 0.975869 1.69025i 0.0975869 0.169025i
\(101\) 6.22336 + 10.7792i 0.619247 + 1.07257i 0.989623 + 0.143686i \(0.0458955\pi\)
−0.370376 + 0.928882i \(0.620771\pi\)
\(102\) −1.54180 + 0.890157i −0.152661 + 0.0881386i
\(103\) 15.0247 1.48043 0.740215 0.672370i \(-0.234724\pi\)
0.740215 + 0.672370i \(0.234724\pi\)
\(104\) 0 0
\(105\) −0.531659 −0.0518846
\(106\) −0.296916 + 0.171425i −0.0288390 + 0.0166502i
\(107\) 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
\(109\) 11.2325i 1.07587i 0.842985 + 0.537937i \(0.180796\pi\)
−0.842985 + 0.537937i \(0.819204\pi\)
\(110\) −1.02201 0.590059i −0.0974450 0.0562599i
\(111\) 8.27607 + 4.77819i 0.785530 + 0.453526i
\(112\) 1.23355i 0.116560i
\(113\) 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
\(115\) 2.45880 1.41959i 0.229284 0.132377i
\(116\) −5.66682 −0.526151
\(117\) 0 0
\(118\) −0.594763 −0.0547524
\(119\) −1.45717 + 0.841298i −0.133579 + 0.0771216i
\(120\) −0.694601 1.20308i −0.0634081 0.109826i
\(121\) 8.92820 15.4641i 0.811655 1.40583i
\(122\) 3.09843i 0.280519i
\(123\) −5.17191 2.98601i −0.466336 0.269239i
\(124\) 9.23572 + 5.33225i 0.829392 + 0.478850i
\(125\) 1.00000i 0.0894427i
\(126\) 0.0160350 0.0277734i 0.00142851 0.00247425i
\(127\) 1.61998 + 2.80589i 0.143750 + 0.248982i 0.928906 0.370316i \(-0.120751\pi\)
−0.785156 + 0.619298i \(0.787417\pi\)
\(128\) 5.72615 3.30600i 0.506125 0.292212i
\(129\) −8.10387 −0.713506
\(130\) 0 0
\(131\) 0.175664 0.0153478 0.00767390 0.999971i \(-0.497557\pi\)
0.00767390 + 0.999971i \(0.497557\pi\)
\(132\) 14.5294 8.38853i 1.26462 0.730127i
\(133\) 0.376759 + 0.652566i 0.0326692 + 0.0565846i
\(134\) −1.13493 + 1.96576i −0.0980430 + 0.169815i
\(135\) 5.50367i 0.473681i
\(136\) −3.80752 2.19827i −0.326492 0.188500i
\(137\) 15.5736 + 8.99144i 1.33054 + 0.768190i 0.985383 0.170353i \(-0.0544907\pi\)
0.345162 + 0.938543i \(0.387824\pi\)
\(138\) 0.998090i 0.0849631i
\(139\) −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
\(141\) −11.5616 + 6.67510i −0.973663 + 0.562144i
\(142\) 2.81140 0.235928
\(143\) 0 0
\(144\) −1.63129 −0.135941
\(145\) −2.51448 + 1.45174i −0.208816 + 0.120560i
\(146\) −1.06430 1.84342i −0.0880819 0.152562i
\(147\) 5.51236 9.54769i 0.454652 0.787481i
\(148\) 11.6558i 0.958101i
\(149\) −2.95350 1.70520i −0.241960 0.139696i 0.374117 0.927381i \(-0.377946\pi\)
−0.616077 + 0.787686i \(0.711279\pi\)
\(150\) −0.304444 0.175771i −0.0248578 0.0143516i
\(151\) 7.96141i 0.647890i 0.946076 + 0.323945i \(0.105009\pi\)
−0.946076 + 0.323945i \(0.894991\pi\)
\(152\) −0.984454 + 1.70512i −0.0798498 + 0.138304i
\(153\) 1.11256 + 1.92701i 0.0899451 + 0.155790i
\(154\) −0.339560 + 0.196045i −0.0273625 + 0.0157978i
\(155\) 5.46410 0.438887
\(156\) 0 0
\(157\) −16.4329 −1.31148 −0.655742 0.754985i \(-0.727644\pi\)
−0.655742 + 0.754985i \(0.727644\pi\)
\(158\) 0.859667 0.496329i 0.0683914 0.0394858i
\(159\) −1.24865 2.16273i −0.0990247 0.171516i
\(160\) 1.27597 2.21004i 0.100874 0.174719i
\(161\) 0.943307i 0.0743430i
\(162\) 1.42478 + 0.822599i 0.111942 + 0.0646295i
\(163\) −15.4215 8.90361i −1.20791 0.697384i −0.245604 0.969370i \(-0.578986\pi\)
−0.962301 + 0.271986i \(0.912320\pi\)
\(164\) 7.28398i 0.568784i
\(165\) 4.29798 7.44432i 0.334597 0.579539i
\(166\) 0.468341 + 0.811190i 0.0363503 + 0.0629605i
\(167\) −5.45047 + 3.14683i −0.421770 + 0.243509i −0.695834 0.718202i \(-0.744965\pi\)
0.274064 + 0.961711i \(0.411632\pi\)
\(168\) −0.461557 −0.0356099
\(169\) 0 0
\(170\) −1.11256 −0.0853294
\(171\) 0.862975 0.498239i 0.0659933 0.0381013i
\(172\) −4.94209 8.55995i −0.376831 0.652690i
\(173\) 7.98756 13.8349i 0.607283 1.05184i −0.384404 0.923165i \(-0.625593\pi\)
0.991686 0.128679i \(-0.0410738\pi\)
\(174\) 1.02069i 0.0773786i
\(175\) −0.287734 0.166123i −0.0217506 0.0125577i
\(176\) 17.2722 + 9.97212i 1.30194 + 0.751677i
\(177\) 4.33225i 0.325632i
\(178\) 0.354337 0.613729i 0.0265587 0.0460010i
\(179\) 11.8087 + 20.4533i 0.882625 + 1.52875i 0.848412 + 0.529336i \(0.177559\pi\)
0.0342123 + 0.999415i \(0.489108\pi\)
\(180\) −0.742653 + 0.428771i −0.0553541 + 0.0319587i
\(181\) 2.62590 0.195182 0.0975909 0.995227i \(-0.468886\pi\)
0.0975909 + 0.995227i \(0.468886\pi\)
\(182\) 0 0
\(183\) −22.5689 −1.66834
\(184\) 2.13459 1.23241i 0.157364 0.0908544i
\(185\) 2.98601 + 5.17191i 0.219536 + 0.380247i
\(186\) 0.960431 1.66351i 0.0704222 0.121975i
\(187\) 27.2045i 1.98939i
\(188\) −14.1015 8.14153i −1.02846 0.593782i
\(189\) 1.58359 + 0.914288i 0.115189 + 0.0665046i
\(190\) 0.498239i 0.0361460i
\(191\) 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
\(193\) 19.7636 11.4105i 1.42262 0.821348i 0.426095 0.904678i \(-0.359889\pi\)
0.996522 + 0.0833298i \(0.0265555\pi\)
\(194\) −0.550955 −0.0395563
\(195\) 0 0
\(196\) 13.4467 0.960480
\(197\) 0.556877 0.321513i 0.0396758 0.0229068i −0.480031 0.877252i \(-0.659375\pi\)
0.519707 + 0.854345i \(0.326041\pi\)
\(198\) 0.259256 + 0.449045i 0.0184245 + 0.0319122i
\(199\) 1.53342 2.65596i 0.108701 0.188276i −0.806543 0.591175i \(-0.798664\pi\)
0.915244 + 0.402899i \(0.131997\pi\)
\(200\) 0.868145i 0.0613871i
\(201\) −14.3185 8.26681i −1.00995 0.583096i
\(202\) 2.36804 + 1.36719i 0.166615 + 0.0961952i
\(203\) 0.964670i 0.0677065i
\(204\) 7.90831 13.6976i 0.553693 0.959024i
\(205\) −1.86603 3.23205i −0.130329 0.225736i
\(206\) 2.85852 1.65037i 0.199163 0.114987i
\(207\) −1.24746 −0.0867045
\(208\) 0 0
\(209\) −12.1830 −0.842716
\(210\) −0.101151 + 0.0583993i −0.00698005 + 0.00402993i
\(211\) 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
\(213\) 20.4782i 1.40314i
\(214\) 2.48554 + 1.43503i 0.169908 + 0.0980964i
\(215\) −4.38581 2.53215i −0.299110 0.172691i
\(216\) 4.77798i 0.325101i
\(217\) 0.907714 1.57221i 0.0616197 0.106728i
\(218\) 1.23381 + 2.13703i 0.0835643 + 0.144738i
\(219\) 13.4274 7.75232i 0.907341 0.523854i
\(220\) 10.4844 0.706856
\(221\) 0 0
\(222\) 2.09941 0.140903
\(223\) −8.87174 + 5.12210i −0.594095 + 0.343001i −0.766715 0.641987i \(-0.778110\pi\)
0.172620 + 0.984989i \(0.444777\pi\)
\(224\) −0.423935 0.734278i −0.0283254 0.0490610i
\(225\) −0.219687 + 0.380509i −0.0146458 + 0.0253673i
\(226\) 4.02990i 0.268065i
\(227\) 6.10012 + 3.52190i 0.404879 + 0.233757i 0.688587 0.725154i \(-0.258231\pi\)
−0.283708 + 0.958911i \(0.591565\pi\)
\(228\) −6.13421 3.54159i −0.406248 0.234547i
\(229\) 1.32899i 0.0878219i 0.999035 + 0.0439109i \(0.0139818\pi\)
−0.999035 + 0.0439109i \(0.986018\pi\)
\(230\) 0.311865 0.540166i 0.0205638 0.0356175i
\(231\) −1.42799 2.47335i −0.0939547 0.162734i
\(232\) −2.18294 + 1.26032i −0.143317 + 0.0827440i
\(233\) 1.24746 0.0817238 0.0408619 0.999165i \(-0.486990\pi\)
0.0408619 + 0.999165i \(0.486990\pi\)
\(234\) 0 0
\(235\) −8.34285 −0.544227
\(236\) 4.57606 2.64199i 0.297876 0.171979i
\(237\) 3.61525 + 6.26180i 0.234836 + 0.406748i
\(238\) −0.184822 + 0.320121i −0.0119802 + 0.0207504i
\(239\) 9.94207i 0.643099i 0.946893 + 0.321549i \(0.104204\pi\)
−0.946893 + 0.321549i \(0.895796\pi\)
\(240\) 5.14517 + 2.97057i 0.332120 + 0.191749i
\(241\) 19.5608 + 11.2934i 1.26002 + 0.727475i 0.973079 0.230472i \(-0.0740272\pi\)
0.286944 + 0.957947i \(0.407360\pi\)
\(242\) 3.92282i 0.252168i
\(243\) 2.26371 3.92086i 0.145217 0.251523i
\(244\) −13.7635 23.8391i −0.881119 1.52614i
\(245\) 5.96658 3.44481i 0.381191 0.220081i
\(246\) −1.31197 −0.0836483
\(247\) 0 0
\(248\) 4.74363 0.301221
\(249\) −5.90869 + 3.41139i −0.374448 + 0.216188i
\(250\) −0.109843 0.190254i −0.00694711 0.0120327i
\(251\) −3.38418 + 5.86157i −0.213608 + 0.369979i −0.952841 0.303470i \(-0.901855\pi\)
0.739233 + 0.673449i \(0.235188\pi\)
\(252\) 0.284915i 0.0179480i
\(253\) 13.2082 + 7.62577i 0.830394 + 0.479428i
\(254\) 0.616417 + 0.355888i 0.0386774 + 0.0223304i
\(255\) 8.10387i 0.507484i
\(256\) −6.13860 + 10.6324i −0.383663 + 0.664523i
\(257\) −5.12691 8.88007i −0.319808 0.553924i 0.660640 0.750703i \(-0.270285\pi\)
−0.980448 + 0.196779i \(0.936952\pi\)
\(258\) −1.54180 + 0.890157i −0.0959881 + 0.0554187i
\(259\) 1.98418 0.123291
\(260\) 0 0
\(261\) 1.27571 0.0789645
\(262\) 0.0334208 0.0192955i 0.00206474 0.00119208i
\(263\) −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
\(265\) 1.56063i 0.0958685i
\(266\) 0.143360 + 0.0827690i 0.00878998 + 0.00507489i
\(267\) 4.47040 + 2.58098i 0.273584 + 0.157954i
\(268\) 20.1658i 1.23182i
\(269\) −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
\(271\) 26.7582 15.4488i 1.62544 0.938450i 0.640014 0.768363i \(-0.278929\pi\)
0.985429 0.170086i \(-0.0544047\pi\)
\(272\) 18.8025 1.14007
\(273\) 0 0
\(274\) 3.95060 0.238665
\(275\) 4.65213 2.68591i 0.280534 0.161966i
\(276\) 4.43361 + 7.67923i 0.266872 + 0.462235i
\(277\) 13.2522 22.9536i 0.796250 1.37915i −0.125792 0.992057i \(-0.540147\pi\)
0.922042 0.387089i \(-0.126519\pi\)
\(278\) 2.63320i 0.157929i
\(279\) −2.07914 1.20039i −0.124475 0.0718656i
\(280\) −0.249795 0.144219i −0.0149281 0.00861874i
\(281\) 4.97766i 0.296942i 0.988917 + 0.148471i \(0.0474352\pi\)
−0.988917 + 0.148471i \(0.952565\pi\)
\(282\) −1.46643 + 2.53993i −0.0873247 + 0.151251i
\(283\) −6.29317 10.9001i −0.374090 0.647943i 0.616100 0.787668i \(-0.288712\pi\)
−0.990190 + 0.139725i \(0.955378\pi\)
\(284\) −21.6307 + 12.4885i −1.28355 + 0.741057i
\(285\) −3.62916 −0.214973
\(286\) 0 0
\(287\) −1.23996 −0.0731926
\(288\) −0.971033 + 0.560626i −0.0572187 + 0.0330352i
\(289\) −4.32355 7.48861i −0.254327 0.440507i
\(290\) −0.318928 + 0.552399i −0.0187281 + 0.0324380i
\(291\) 4.01315i 0.235255i
\(292\) 16.3772 + 9.45541i 0.958406 + 0.553336i
\(293\) −14.6511 8.45880i −0.855925 0.494168i 0.00672072 0.999977i \(-0.497861\pi\)
−0.862645 + 0.505809i \(0.831194\pi\)
\(294\) 2.42199i 0.141253i
\(295\) 1.35366 2.34461i 0.0788132 0.136508i
\(296\) 2.59229 + 4.48997i 0.150674 + 0.260974i
\(297\) −25.6038 + 14.7824i −1.48568 + 0.857759i
\(298\) −0.749222 −0.0434012
\(299\) 0 0
\(300\) 3.12316 0.180316
\(301\) −1.45717 + 0.841298i −0.0839899 + 0.0484916i
\(302\) 0.874509 + 1.51469i 0.0503223 + 0.0871608i
\(303\) −9.95859 + 17.2488i −0.572106 + 0.990917i
\(304\) 8.42034i 0.482940i
\(305\) −12.2143 7.05193i −0.699389 0.403793i
\(306\) 0.423339 + 0.244415i 0.0242007 + 0.0139723i
\(307\) 4.30426i 0.245657i −0.992428 0.122828i \(-0.960803\pi\)
0.992428 0.122828i \(-0.0391965\pi\)
\(308\) 1.74170 3.01671i 0.0992425 0.171893i
\(309\) 12.0213 + 20.8214i 0.683865 + 1.18449i
\(310\) 1.03957 0.600196i 0.0590436 0.0340888i
\(311\) 2.22512 0.126175 0.0630875 0.998008i \(-0.479905\pi\)
0.0630875 + 0.998008i \(0.479905\pi\)
\(312\) 0 0
\(313\) 7.20887 0.407469 0.203735 0.979026i \(-0.434692\pi\)
0.203735 + 0.979026i \(0.434692\pi\)
\(314\) −3.12642 + 1.80504i −0.176434 + 0.101864i
\(315\) 0.0729902 + 0.126423i 0.00411253 + 0.00712311i
\(316\) −4.40948 + 7.63744i −0.248052 + 0.429639i
\(317\) 0.321644i 0.0180653i 0.999959 + 0.00903266i \(0.00287522\pi\)
−0.999959 + 0.00903266i \(0.997125\pi\)
\(318\) −0.475124 0.274313i −0.0266436 0.0153827i
\(319\) −13.5073 7.79847i −0.756266 0.436630i
\(320\) 6.86488i 0.383759i
\(321\) −10.4527 + 18.1046i −0.583414 + 1.01050i
\(322\) −0.103616 0.179468i −0.00577430 0.0100014i
\(323\) −9.94679 + 5.74278i −0.553454 + 0.319537i
\(324\) −14.6162 −0.812013
\(325\) 0 0
\(326\) −3.91201 −0.216666
\(327\) −15.5661 + 8.98707i −0.860805 + 0.496986i
\(328\) −1.61998 2.80589i −0.0894485 0.154929i
\(329\) −1.38594 + 2.40052i −0.0764094 + 0.132345i
\(330\) 1.88842i 0.103954i
\(331\) 14.4037 + 8.31600i 0.791701 + 0.457089i 0.840561 0.541717i \(-0.182225\pi\)
−0.0488600 + 0.998806i \(0.515559\pi\)
\(332\) −7.20676 4.16082i −0.395522 0.228355i
\(333\) 2.62395i 0.143791i
\(334\) −0.691317 + 1.19740i −0.0378272 + 0.0655186i
\(335\) −5.16612 8.94799i −0.282255 0.488881i
\(336\) 1.70947 0.986961i 0.0932590 0.0538431i
\(337\) −24.2186 −1.31927 −0.659636 0.751586i \(-0.729289\pi\)
−0.659636 + 0.751586i \(0.729289\pi\)
\(338\) 0 0
\(339\) 29.3537 1.59427
\(340\) 8.55995 4.94209i 0.464229 0.268022i
\(341\) 14.6761 + 25.4197i 0.794754 + 1.37655i
\(342\) 0.109456 0.189584i 0.00591873 0.0102515i
\(343\) 4.61478i 0.249174i
\(344\) −3.80752 2.19827i −0.205288 0.118523i
\(345\) 3.93456 + 2.27162i 0.211830 + 0.122300i
\(346\) 3.50952i 0.188673i
\(347\) 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
\(349\) 6.12275 3.53497i 0.327743 0.189223i −0.327095 0.944991i \(-0.606070\pi\)
0.654839 + 0.755769i \(0.272737\pi\)
\(350\) −0.0729902 −0.00390149
\(351\) 0 0
\(352\) 13.7085 0.730666
\(353\) 18.8705 10.8949i 1.00438 0.579878i 0.0948371 0.995493i \(-0.469767\pi\)
0.909541 + 0.415615i \(0.136434\pi\)
\(354\) −0.475869 0.824229i −0.0252921 0.0438073i
\(355\) −6.39866 + 11.0828i −0.339606 + 0.588214i
\(356\) 6.29598i 0.333687i
\(357\) −2.33176 1.34624i −0.123410 0.0712506i
\(358\) 4.49332 + 2.59422i 0.237479 + 0.137109i
\(359\) 23.9737i 1.26528i 0.774444 + 0.632642i \(0.218029\pi\)
−0.774444 + 0.632642i \(0.781971\pi\)
\(360\) −0.190720 + 0.330337i −0.0100518 + 0.0174103i
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 0.499589 0.288438i 0.0262578 0.0151600i
\(363\) 28.5737 1.49973
\(364\) 0 0
\(365\) 9.68922 0.507157
\(366\) −4.29384 + 2.47905i −0.224443 + 0.129582i
\(367\) −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
\(369\) 1.63977i 0.0853628i
\(370\) 1.13620 + 0.655986i 0.0590683 + 0.0341031i
\(371\) −0.449045 0.259256i −0.0233133 0.0134599i
\(372\) 17.0653i 0.884793i
\(373\) 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
\(375\) 1.38581 0.800098i 0.0715629 0.0413169i
\(376\) −7.24280 −0.373519
\(377\) 0 0
\(378\) 0.401714 0.0206619
\(379\) 4.73007 2.73091i 0.242968 0.140277i −0.373572 0.927601i \(-0.621867\pi\)
0.616540 + 0.787324i \(0.288534\pi\)
\(380\) −2.21322 3.83341i −0.113536 0.196650i
\(381\) −2.59229 + 4.48997i −0.132807 + 0.230028i
\(382\) 0.442849i 0.0226581i
\(383\) −4.90842 2.83388i −0.250808 0.144804i 0.369326 0.929300i \(-0.379589\pi\)
−0.620134 + 0.784496i \(0.712922\pi\)
\(384\) 9.16297 + 5.29024i 0.467596 + 0.269966i
\(385\) 1.78477i 0.0909602i
\(386\) 2.50675 4.34181i 0.127590 0.220992i
\(387\) 1.11256 + 1.92701i 0.0565546 + 0.0979554i
\(388\) 4.23901 2.44739i 0.215203 0.124247i
\(389\) −10.6174 −0.538325 −0.269162 0.963095i \(-0.586747\pi\)
−0.269162 + 0.963095i \(0.586747\pi\)
\(390\) 0 0
\(391\) 14.3784 0.727149
\(392\) 5.17986 2.99059i 0.261622 0.151048i
\(393\) 0.140548 + 0.243436i 0.00708971 + 0.0122797i
\(394\) 0.0706321 0.122338i 0.00355840 0.00616332i
\(395\) 4.51851i 0.227351i
\(396\) −3.98940 2.30328i −0.200475 0.115744i
\(397\) −24.2780 14.0169i −1.21848 0.703487i −0.253884 0.967235i \(-0.581708\pi\)
−0.964592 + 0.263748i \(0.915041\pi\)
\(398\) 0.673745i 0.0337718i
\(399\) −0.602888 + 1.04423i −0.0301822 + 0.0522770i
\(400\) 1.85638 + 3.21534i 0.0928189 + 0.160767i
\(401\) −19.4979 + 11.2571i −0.973680 + 0.562155i −0.900356 0.435154i \(-0.856694\pi\)
−0.0733241 + 0.997308i \(0.523361\pi\)
\(402\) −3.63222 −0.181159
\(403\) 0 0
\(404\) −24.2927 −1.20861
\(405\) −6.48552 + 3.74441i −0.322268 + 0.186061i
\(406\) 0.105963 + 0.183533i 0.00525884 + 0.00910857i
\(407\) −16.0403 + 27.7826i −0.795087 + 1.37713i
\(408\) 7.03533i 0.348301i
\(409\) 3.71328 + 2.14386i 0.183610 + 0.106007i 0.588988 0.808142i \(-0.299527\pi\)
−0.405378 + 0.914149i \(0.632860\pi\)
\(410\) −0.710039 0.409941i −0.0350663 0.0202456i
\(411\) 28.7761i 1.41942i
\(412\) −14.6622 + 25.3956i −0.722353 + 1.25115i
\(413\) −0.449749 0.778989i −0.0221307 0.0383315i
\(414\) −0.237335 + 0.137025i −0.0116644 + 0.00673443i
\(415\) −4.26371 −0.209297
\(416\) 0 0
\(417\) −19.1802 −0.939257
\(418\) −2.31787 + 1.33822i −0.113371 + 0.0654546i
\(419\) −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
\(421\) 12.8787i 0.627672i −0.949477 0.313836i \(-0.898386\pi\)
0.949477 0.313836i \(-0.101614\pi\)
\(422\) 1.56016 + 0.900759i 0.0759474 + 0.0438483i
\(423\) 3.17453 + 1.83281i 0.154351 + 0.0891145i
\(424\) 1.35485i 0.0657973i
\(425\) 2.53215 4.38581i 0.122827 0.212743i
\(426\) 2.24940 + 3.89607i 0.108984 + 0.188765i
\(427\) −4.05816 + 2.34298i −0.196388 + 0.113385i
\(428\) −25.4981 −1.23250
\(429\) 0 0
\(430\) −1.11256 −0.0536524
\(431\) −8.22590 + 4.74923i −0.396228 + 0.228762i −0.684855 0.728679i \(-0.740134\pi\)
0.288627 + 0.957442i \(0.406801\pi\)
\(432\) −10.2169 17.6962i −0.491560 0.851408i
\(433\) −0.698141 + 1.20922i −0.0335505 + 0.0581112i −0.882313 0.470663i \(-0.844015\pi\)
0.848763 + 0.528774i \(0.177348\pi\)
\(434\) 0.398826i 0.0191443i
\(435\) −4.02367 2.32306i −0.192920 0.111382i
\(436\) −18.9857 10.9614i −0.909251 0.524956i
\(437\) 6.43911i 0.308024i
\(438\) 1.70308 2.94983i 0.0813765 0.140948i
\(439\) 2.08090 + 3.60422i 0.0993159 + 0.172020i 0.911402 0.411518i \(-0.135001\pi\)
−0.812086 + 0.583538i \(0.801668\pi\)
\(440\) 4.03872 2.33176i 0.192539 0.111162i
\(441\) −3.02711 −0.144148
\(442\) 0 0
\(443\) 9.54563 0.453526 0.226763 0.973950i \(-0.427186\pi\)
0.226763 + 0.973950i \(0.427186\pi\)
\(444\) −16.1527 + 9.32578i −0.766574 + 0.442582i
\(445\) 1.61292 + 2.79366i 0.0764596 + 0.132432i
\(446\) −1.12526 + 1.94900i −0.0532825 + 0.0922880i
\(447\) 5.45732i 0.258122i
\(448\) 1.97526 + 1.14042i 0.0933223 + 0.0538796i
\(449\) −18.8075 10.8585i −0.887582 0.512446i −0.0144310 0.999896i \(-0.504594\pi\)
−0.873151 + 0.487450i \(0.837927\pi\)
\(450\) 0.0965246i 0.00455022i
\(451\) 10.0239 17.3620i 0.472009 0.817544i
\(452\) 17.9012 + 31.0057i 0.842000 + 1.45839i
\(453\) −11.0330 + 6.36991i −0.518376 + 0.299284i
\(454\) 1.54743 0.0726246
\(455\) 0 0
\(456\) −3.15064 −0.147542
\(457\) −4.08989 + 2.36130i −0.191317 + 0.110457i −0.592599 0.805498i \(-0.701898\pi\)
0.401282 + 0.915955i \(0.368565\pi\)
\(458\) 0.145980 + 0.252845i 0.00682122 + 0.0118147i
\(459\) −13.9361 + 24.1381i −0.650482 + 1.12667i
\(460\) 5.54133i 0.258366i
\(461\) −1.54283 0.890753i −0.0718568 0.0414865i 0.463641 0.886023i \(-0.346543\pi\)
−0.535498 + 0.844537i \(0.679876\pi\)
\(462\) −0.543362 0.313710i −0.0252795 0.0145951i
\(463\) 6.80200i 0.316116i 0.987430 + 0.158058i \(0.0505232\pi\)
−0.987430 + 0.158058i \(0.949477\pi\)
\(464\) 5.38995 9.33566i 0.250222 0.433397i
\(465\) 4.37182 + 7.57221i 0.202738 + 0.351153i
\(466\) 0.237335 0.137025i 0.0109943 0.00634758i
\(467\) −18.2374 −0.843927 −0.421963 0.906613i \(-0.638659\pi\)
−0.421963 + 0.906613i \(0.638659\pi\)
\(468\) 0 0
\(469\) −3.43285 −0.158514
\(470\) −1.58726 + 0.916407i −0.0732150 + 0.0422707i
\(471\) −13.1479 22.7728i −0.605823 1.04932i
\(472\) 1.17517 2.03546i 0.0540918 0.0936897i
\(473\) 27.2045i 1.25086i
\(474\) 1.37564 + 0.794223i 0.0631850 + 0.0364799i
\(475\) −1.96410 1.13397i −0.0901192 0.0520303i
\(476\) 3.28398i 0.150521i
\(477\) −0.342849 + 0.593832i −0.0156980 + 0.0271897i
\(478\) 1.09207 + 1.89152i 0.0499502 + 0.0865162i
\(479\) −30.4674 + 17.5904i −1.39209 + 0.803724i −0.993547 0.113425i \(-0.963818\pi\)
−0.398544 + 0.917149i \(0.630485\pi\)
\(480\) 4.08359 0.186390
\(481\) 0 0
\(482\) 4.96204 0.226015
\(483\) 1.30724 0.754738i 0.0594817 0.0343418i
\(484\) 17.4255 + 30.1819i 0.792069 + 1.37190i
\(485\) 1.25396 2.17191i 0.0569392 0.0986215i
\(486\) 0.994615i 0.0451166i
\(487\) −8.92352 5.15200i −0.404363 0.233459i 0.284002 0.958824i \(-0.408338\pi\)
−0.688365 + 0.725364i \(0.741671\pi\)
\(488\) −10.6038 6.12210i −0.480011 0.277134i
\(489\) 28.4950i 1.28859i
\(490\) 0.756779 1.31078i 0.0341878 0.0592150i
\(491\) 4.66599 + 8.08174i 0.210573 + 0.364724i 0.951894 0.306427i \(-0.0991336\pi\)
−0.741321 + 0.671151i \(0.765800\pi\)
\(492\) 10.0942 5.82790i 0.455083 0.262742i
\(493\) −14.7041 −0.662238
\(494\) 0 0
\(495\) −2.36023 −0.106085
\(496\) −17.5689 + 10.1434i −0.788869 + 0.455454i
\(497\) 2.12593 + 3.68222i 0.0953611 + 0.165170i
\(498\) −0.749437 + 1.29806i −0.0335831 + 0.0581676i
\(499\) 23.9421i 1.07179i −0.844283 0.535897i \(-0.819974\pi\)
0.844283 0.535897i \(-0.180026\pi\)
\(500\) 1.69025 + 0.975869i 0.0755905 + 0.0436422i
\(501\) −8.72181 5.03554i −0.389662 0.224971i
\(502\) 1.48692i 0.0663645i
\(503\) −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
\(505\) −10.7792 + 6.22336i −0.479667 + 0.276936i
\(506\) 3.35056 0.148951
\(507\) 0 0
\(508\) −6.32355 −0.280562
\(509\) 29.0640 16.7801i 1.28824 0.743765i 0.309899 0.950770i \(-0.399705\pi\)
0.978340 + 0.207005i \(0.0663715\pi\)
\(510\) −0.890157 1.54180i −0.0394168 0.0682719i
\(511\) 1.60960 2.78792i 0.0712047 0.123330i
\(512\) 15.9211i 0.703621i
\(513\) 10.8098 + 6.24102i 0.477263 + 0.275548i
\(514\) −1.95084 1.12632i −0.0860477 0.0496796i
\(515\) 15.0247i 0.662069i
\(516\) 7.90831 13.6976i 0.348144 0.603003i
\(517\) −22.4081 38.8120i −0.985508 1.70695i
\(518\) 0.377499 0.217949i 0.0165864 0.00957614i
\(519\) 25.5633 1.12210
\(520\) 0 0
\(521\) 12.4649 0.546098 0.273049 0.962000i \(-0.411968\pi\)
0.273049 + 0.962000i \(0.411968\pi\)
\(522\) 0.242710 0.140128i 0.0106231 0.00613326i
\(523\) 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
\(525\) 0.531659i 0.0232035i
\(526\) −3.54958 2.04935i −0.154769 0.0893558i
\(527\) 23.9645 + 13.8359i 1.04391 + 0.602702i
\(528\) 31.9147i 1.38891i
\(529\) 7.46953 12.9376i 0.324762 0.562505i
\(530\) −0.171425 0.296916i −0.00744621 0.0128972i
\(531\) −1.03016 + 0.594763i −0.0447051 + 0.0258105i
\(532\) −1.47067 −0.0637616
\(533\) 0 0
\(534\) 1.13402 0.0490737
\(535\) −11.3140 + 6.53215i −0.489147 + 0.282409i
\(536\) −4.48494 7.76815i −0.193720 0.335533i
\(537\) −18.8963 + 32.7293i −0.815433 + 1.41237i
\(538\) 3.94511i 0.170086i
\(539\) 32.0514 + 18.5049i 1.38055 + 0.797061i
\(540\) −9.30260 5.37086i −0.400320 0.231125i
\(541\) 15.4750i 0.665321i −0.943047 0.332660i \(-0.892054\pi\)
0.943047 0.332660i \(-0.107946\pi\)
\(542\) 3.39391 5.87842i 0.145781 0.252500i
\(543\) 2.10098 + 3.63900i 0.0901616 + 0.156165i
\(544\) 11.1923 6.46187i 0.479866 0.277051i
\(545\) −11.2325 −0.481146
\(546\) 0 0
\(547\) 25.1765 1.07647 0.538234 0.842795i \(-0.319092\pi\)
0.538234 + 0.842795i \(0.319092\pi\)
\(548\) −30.3956 + 17.5489i −1.29844 + 0.749653i
\(549\) 3.09843 + 5.36665i 0.132238 + 0.229043i
\(550\) 0.590059 1.02201i 0.0251602 0.0435787i
\(551\) 6.58493i 0.280528i
\(552\) 3.41577 + 1.97210i 0.145385 + 0.0839380i
\(553\) 1.30013 + 0.750630i 0.0552871 + 0.0319200i
\(554\) 5.82269i 0.247382i
\(555\) −4.77819 + 8.27607i −0.202823 + 0.351300i
\(556\) −11.6969 20.2596i −0.496059 0.859199i
\(557\) 36.6752 21.1744i 1.55398 0.897190i 0.556167 0.831071i \(-0.312272\pi\)
0.997812 0.0661194i \(-0.0210618\pi\)
\(558\) −0.527420 −0.0223275
\(559\) 0 0
\(560\) 1.23355 0.0521270
\(561\) 37.7002 21.7662i 1.59171 0.918971i
\(562\) 0.546763 + 0.947022i 0.0230638 + 0.0399477i
\(563\) 11.8953 20.6032i 0.501326 0.868322i −0.498673 0.866790i \(-0.666179\pi\)
0.999999 0.00153173i \(-0.000487565\pi\)
\(564\) 26.0561i 1.09716i
\(565\) 15.8862 + 9.17191i 0.668338 + 0.385865i
\(566\) −2.39461 1.38253i −0.100653 0.0581119i
\(567\) 2.48814i 0.104492i
\(568\) −5.55497 + 9.62148i −0.233081 + 0.403709i
\(569\) −13.3710 23.1593i −0.560543 0.970889i −0.997449 0.0713817i \(-0.977259\pi\)
0.436906 0.899507i \(-0.356074\pi\)
\(570\) −0.690464 + 0.398640i −0.0289204 + 0.0166972i
\(571\) 16.7159 0.699539 0.349769 0.936836i \(-0.386260\pi\)
0.349769 + 0.936836i \(0.386260\pi\)
\(572\) 0 0
\(573\) 3.22571 0.134756
\(574\) −0.235908 + 0.136202i −0.00984661 + 0.00568494i
\(575\) 1.41959 + 2.45880i 0.0592010 + 0.102539i
\(576\) 1.50812 2.61215i 0.0628385 0.108840i
\(577\) 20.6768i 0.860786i 0.902642 + 0.430393i \(0.141625\pi\)
−0.902642 + 0.430393i \(0.858375\pi\)
\(578\) −1.64515 0.949828i −0.0684292 0.0395076i
\(579\) 31.6257 + 18.2591i 1.31432 + 0.758822i
\(580\) 5.66682i 0.235302i
\(581\) −0.708301 + 1.22681i −0.0293853 + 0.0508968i
\(582\) −0.440818 0.763519i −0.0182725 0.0316489i
\(583\) 7.26023 4.19170i 0.300688 0.173602i
\(584\) 8.41165 0.348076
\(585\) 0 0
\(586\) −3.71657 −0.153530
\(587\) −18.0109 + 10.3986i −0.743388 + 0.429196i −0.823300 0.567606i \(-0.807870\pi\)
0.0799116 + 0.996802i \(0.474536\pi\)
\(588\) 10.7587 + 18.6346i 0.443681 + 0.768478i
\(589\) 6.19615 10.7321i 0.255308 0.442206i
\(590\) 0.594763i 0.0244860i
\(591\) 0.891111 + 0.514483i 0.0366554 + 0.0211630i
\(592\) −19.2021 11.0863i −0.789199 0.455644i
\(593\) 21.8475i 0.897169i −0.893740 0.448585i \(-0.851928\pi\)
0.893740 0.448585i \(-0.148072\pi\)
\(594\) −3.24749 + 5.62482i −0.133246 + 0.230789i
\(595\) −0.841298 1.45717i −0.0344898 0.0597381i
\(596\) 5.76446 3.32811i 0.236121 0.136325i
\(597\) 4.90755 0.200853
\(598\) 0 0
\(599\) −3.58040 −0.146291 −0.0731456 0.997321i \(-0.523304\pi\)
−0.0731456 + 0.997321i \(0.523304\pi\)
\(600\) 1.20308 0.694601i 0.0491157 0.0283570i
\(601\) −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
\(603\) 4.53972i 0.184872i
\(604\) −13.4568 7.76929i −0.547550 0.316128i
\(605\) 15.4641 + 8.92820i 0.628705 + 0.362983i
\(606\) 4.37554i 0.177744i
\(607\) 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
\(609\) −1.33685 + 0.771830i −0.0541718 + 0.0312761i
\(610\) −3.09843 −0.125452
\(611\) 0 0
\(612\) −4.34285 −0.175549
\(613\) −8.56183 + 4.94318i −0.345809 + 0.199653i −0.662838 0.748763i \(-0.730648\pi\)
0.317029 + 0.948416i \(0.397315\pi\)
\(614\) −0.472795 0.818904i −0.0190804 0.0330483i
\(615\) 2.98601 5.17191i 0.120407 0.208552i
\(616\) 1.54944i 0.0624286i
\(617\) −39.5920 22.8584i −1.59391 0.920246i −0.992626 0.121213i \(-0.961321\pi\)
−0.601287 0.799033i \(-0.705345\pi\)
\(618\) 4.57419 + 2.64091i 0.184001 + 0.106233i
\(619\) 19.9143i 0.800425i 0.916422 + 0.400212i \(0.131064\pi\)
−0.916422 + 0.400212i \(0.868936\pi\)
\(620\) −5.33225 + 9.23572i −0.214148 + 0.370916i
\(621\) −7.81295 13.5324i −0.313523 0.543038i
\(622\) 0.423339 0.244415i 0.0169743 0.00980014i
\(623\) 1.07177 0.0429397
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 1.37152 0.791847i 0.0548169 0.0316486i
\(627\) −9.74760 16.8833i −0.389282 0.674255i
\(628\) 16.0363 27.7757i 0.639918 1.10837i
\(629\) 30.2440i 1.20591i
\(630\) 0.0277734 + 0.0160350i 0.00110652 + 0.000638849i
\(631\) −12.6403 7.29790i −0.503204 0.290525i 0.226832 0.973934i \(-0.427163\pi\)
−0.730036 + 0.683409i \(0.760497\pi\)
\(632\) 3.92272i 0.156038i
\(633\) −6.56112 + 11.3642i −0.260781 + 0.451686i
\(634\) 0.0353305 + 0.0611942i 0.00140315 + 0.00243033i
\(635\) −2.80589 + 1.61998i −0.111348 + 0.0642870i
\(636\) 4.87409 0.193270
\(637\) 0 0
\(638\) −3.42644 −0.135654
\(639\) 4.86950 2.81140i 0.192634 0.111217i
\(640\) 3.30600 + 5.72615i 0.130681 + 0.226346i
\(641\) −7.08183 + 12.2661i −0.279716 + 0.484482i −0.971314 0.237801i \(-0.923573\pi\)
0.691598 + 0.722282i \(0.256907\pi\)
\(642\) 4.59265i 0.181257i
\(643\) 14.5246 + 8.38581i 0.572796 + 0.330704i 0.758265 0.651946i \(-0.226047\pi\)
−0.185469 + 0.982650i \(0.559380\pi\)
\(644\) 1.59443 + 0.920544i 0.0628293 + 0.0362745i
\(645\) 8.10387i 0.319089i
\(646\) −1.26161 + 2.18518i −0.0496376 + 0.0859748i
\(647\) −1.49584 2.59087i −0.0588075 0.101858i 0.835123 0.550063i \(-0.185396\pi\)
−0.893930 + 0.448206i \(0.852063\pi\)
\(648\) −5.63037 + 3.25069i −0.221182 + 0.127699i
\(649\) 14.5432 0.570872
\(650\) 0 0
\(651\) 2.90504 0.113858
\(652\) 30.0987 17.3775i 1.17876 0.680556i
\(653\) 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
\(655\) 0.175664i 0.00686374i
\(656\) 11.9998 + 6.92810i 0.468514 + 0.270497i
\(657\) −3.68683 2.12859i −0.143837 0.0830444i
\(658\) 0.608946i 0.0237392i
\(659\) 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
\(661\) −10.6872 + 6.17028i −0.415686 + 0.239996i −0.693230 0.720717i \(-0.743813\pi\)
0.277544 + 0.960713i \(0.410480\pi\)
\(662\) 3.65383 0.142010
\(663\) 0 0
\(664\) −3.70152 −0.143647
\(665\) −0.652566 + 0.376759i −0.0253054 + 0.0146101i
\(666\) −0.288223 0.499217i −0.0111684 0.0193443i
\(667\) 4.12174 7.13907i 0.159594 0.276426i
\(668\) 12.2836i 0.475265i
\(669\) −14.1965 8.19636i −0.548869 0.316890i
\(670\) −1.96576 1.13493i −0.0759438 0.0438461i
\(671\) 75.7634i 2.92481i
\(672\) 0.678380 1.17499i 0.0261691 0.0453262i
\(673\) 4.63313 + 8.02481i 0.178594 + 0.309334i 0.941399 0.337295i \(-0.109512\pi\)
−0.762805 + 0.646628i \(0.776178\pi\)
\(674\) −4.60770 + 2.66025i −0.177482 + 0.102469i
\(675\) −5.50367 −0.211836
\(676\) 0 0
\(677\) 13.8984 0.534158 0.267079 0.963675i \(-0.413941\pi\)
0.267079 + 0.963675i \(0.413941\pi\)
\(678\) 5.58467 3.22431i 0.214478 0.123829i
\(679\) −0.416622 0.721611i −0.0159885 0.0276929i
\(680\) 2.19827 3.80752i 0.0842999 0.146012i
\(681\) 11.2715i 0.431924i
\(682\) 5.58438 + 3.22414i 0.213837 + 0.123459i
\(683\) 32.6935 + 18.8756i 1.25098 + 0.722255i 0.971305 0.237838i \(-0.0764388\pi\)
0.279678 + 0.960094i \(0.409772\pi\)
\(684\) 1.94486i 0.0743637i
\(685\) −8.99144 + 15.5736i −0.343545 + 0.595038i
\(686\) −0.506903 0.877981i −0.0193536 0.0335215i
\(687\) −1.84172 + 1.06332i −0.0702661 + 0.0405681i
\(688\) 18.8025 0.716838
\(689\) 0 0
\(690\) 0.998090 0.0379966
\(691\) 1.43146 0.826456i 0.0544554 0.0314399i −0.472525 0.881317i \(-0.656657\pi\)
0.526981 + 0.849877i \(0.323324\pi\)
\(692\) 15.5896 + 27.0020i 0.592628 + 1.02646i
\(693\) −0.392090 + 0.679120i −0.0148943 + 0.0257976i
\(694\) 1.37823i 0.0523168i
\(695\) −10.3803 5.99307i −0.393747 0.227330i
\(696\) −3.49312 2.01676i −0.132407 0.0764450i
\(697\) 18.9002i 0.715897i
\(698\) 0.776587 1.34509i 0.0293943 0.0509123i
\(699\) 0.998090 + 1.72874i 0.0377512 + 0.0653871i
\(700\) 0.561581 0.324229i 0.0212258 0.0122547i
\(701\) −20.4819 −0.773590 −0.386795 0.922166i \(-0.626418\pi\)
−0.386795 + 0.922166i \(0.626418\pi\)
\(702\) 0 0
\(703\) 13.5442 0.510830
\(704\) −31.9363 + 18.4384i −1.20365 + 0.694925i
\(705\) −6.67510 11.5616i −0.251399 0.435435i
\(706\) 2.39347 4.14561i 0.0900794 0.156022i
\(707\) 4.13538i 0.155527i
\(708\) 7.32260 + 4.22770i 0.275200 + 0.158887i
\(709\) −19.0021 10.9709i −0.713639 0.412020i 0.0987679 0.995110i \(-0.468510\pi\)
−0.812407 + 0.583091i \(0.801843\pi\)
\(710\) 2.81140i 0.105510i
\(711\) 0.992658 1.71933i 0.0372276 0.0644801i
\(712\) 1.40025 + 2.42530i 0.0524764 + 0.0908919i
\(713\) −13.4351 + 7.75678i −0.503150 + 0.290494i
\(714\) −0.591503 −0.0221364
\(715\) 0 0
\(716\) −46.0950 −1.72265
\(717\) −13.7778 + 7.95463i −0.514542 + 0.297071i
\(718\) 2.63335 + 4.56110i 0.0982759 + 0.170219i
\(719\) 19.4237 33.6429i 0.724384 1.25467i −0.234844 0.972033i \(-0.575458\pi\)
0.959227 0.282636i \(-0.0912089\pi\)
\(720\) 1.63129i 0.0607945i
\(721\) 4.32312 + 2.49596i 0.161002 + 0.0929543i
\(722\) −2.63624 1.52204i −0.0981108 0.0566443i
\(723\) 36.1434i 1.34419i
\(724\) −2.56254 + 4.43844i −0.0952359 + 0.164953i
\(725\) −1.45174 2.51448i −0.0539162 0.0933856i
\(726\) 5.43628 3.13864i 0.201759 0.116486i
\(727\) 30.6598 1.13711 0.568555 0.822645i \(-0.307503\pi\)
0.568555 + 0.822645i \(0.307503\pi\)
\(728\) 0 0
\(729\) 29.7112 1.10042
\(730\) 1.84342 1.06430i 0.0682279 0.0393914i
\(731\) −12.8236 22.2110i −0.474296 0.821505i
\(732\) 22.0243 38.1473i 0.814043 1.40996i
\(733\) 24.3858i 0.900709i −0.892850 0.450355i \(-0.851298\pi\)
0.892850 0.450355i \(-0.148702\pi\)
\(734\) −1.21598 0.702045i −0.0448826 0.0259130i
\(735\) 9.54769 + 5.51236i 0.352172 + 0.203327i
\(736\) 7.24539i 0.267069i
\(737\) 27.7515 48.0669i 1.02224 1.77057i
\(738\) 0.180117 + 0.311973i 0.00663021 + 0.0114839i
\(739\) 33.1504 19.1394i 1.21946 0.704054i 0.254656 0.967032i \(-0.418038\pi\)
0.964802 + 0.262977i \(0.0847044\pi\)
\(740\) −11.6558 −0.428476
\(741\) 0 0
\(742\) −0.113910 −0.00418178
\(743\) 34.6479 20.0040i 1.27111 0.733874i 0.295910 0.955216i \(-0.404377\pi\)
0.975196 + 0.221342i \(0.0710437\pi\)
\(744\) 3.79537 + 6.57377i 0.139145 + 0.241006i
\(745\) 1.70520 2.95350i 0.0624738 0.108208i
\(746\) 4.41134i 0.161511i
\(747\) 1.62238 + 0.936681i 0.0593598 + 0.0342714i
\(748\) 45.9825 + 26.5480i 1.68129 + 0.970691i
\(749\) 4.34057i 0.158601i
\(750\) 0.175771 0.304444i 0.00641825 0.0111167i
\(751\) 12.8010 + 22.1720i 0.467115 + 0.809067i 0.999294 0.0375648i \(-0.0119601\pi\)
−0.532179 + 0.846632i \(0.678627\pi\)
\(752\) 26.8251 15.4875i 0.978211 0.564770i
\(753\) −10.8307 −0.394693
\(754\) 0 0
\(755\) −7.96141 −0.289745
\(756\) −3.09076 + 1.78445i −0.112410 + 0.0648998i
\(757\) 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
\(759\) 24.4055i 0.885862i
\(760\) −1.70512 0.984454i −0.0618514 0.0357099i
\(761\) −22.7006 13.1062i −0.822896 0.475099i 0.0285179 0.999593i \(-0.490921\pi\)
−0.851414 + 0.524494i \(0.824255\pi\)
\(762\) 1.13898i 0.0412610i
\(763\) −1.86597 + 3.23196i −0.0675528 + 0.117005i
\(764\) 1.96718 + 3.40725i 0.0711699 + 0.123270i
\(765\) −1.92701 + 1.11256i −0.0696712 + 0.0402247i
\(766\) −1.24513 −0.0449884
\(767\) 0 0
\(768\) −19.6459 −0.708911
\(769\) 38.4078 22.1747i 1.38502 0.799641i 0.392271 0.919850i \(-0.371690\pi\)
0.992749 + 0.120208i \(0.0383562\pi\)
\(770\) −0.196045 0.339560i −0.00706497 0.0122369i
\(771\) 8.20406 14.2099i 0.295462 0.511755i
\(772\) 44.5408i 1.60306i
\(773\) −20.1471 11.6319i −0.724640 0.418371i 0.0918181 0.995776i \(-0.470732\pi\)
−0.816458 + 0.577405i \(0.804065\pi\)
\(774\) 0.423339 + 0.244415i 0.0152166 + 0.00878531i
\(775\) 5.46410i 0.196276i
\(776\) 1.08861 1.88554i 0.0390790 0.0676868i
\(777\) 1.58754 + 2.74970i 0.0569526 + 0.0986448i
\(778\) −2.02001 + 1.16625i