Properties

Label 325.2.n.d.251.3
Level $325$
Weight $2$
Character 325.251
Analytic conductor $2.595$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.59513806569\)
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 251.3
Root \(-1.27597 + 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 325.251
Dual form 325.2.n.d.101.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.190254 + 0.109843i) q^{2} +(-0.800098 + 1.38581i) q^{3} +(-0.975869 - 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(0.287734 - 0.166123i) q^{7} -0.868145i q^{8} +(0.219687 + 0.380509i) q^{9} +O(q^{10})\) \(q+(0.190254 + 0.109843i) q^{2} +(-0.800098 + 1.38581i) q^{3} +(-0.975869 - 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(0.287734 - 0.166123i) q^{7} -0.868145i q^{8} +(0.219687 + 0.380509i) q^{9} +(4.65213 + 2.68591i) q^{11} +3.12316 q^{12} +(3.55193 - 0.619491i) q^{13} +0.0729902 q^{14} +(-1.85638 + 3.21534i) q^{16} +(2.53215 + 4.38581i) q^{17} +0.0965246i q^{18} +(-1.96410 + 1.13397i) q^{19} +0.531659i q^{21} +(0.590059 + 1.02201i) q^{22} +(1.41959 - 2.45880i) q^{23} +(1.20308 + 0.694601i) q^{24} +(0.743818 + 0.272296i) q^{26} -5.50367 q^{27} +(-0.561581 - 0.324229i) q^{28} +(1.45174 - 2.51448i) q^{29} -5.46410i q^{31} +(-2.21004 + 1.27597i) q^{32} +(-7.44432 + 4.29798i) q^{33} +1.11256i q^{34} +(0.428771 - 0.742653i) q^{36} +(5.17191 + 2.98601i) q^{37} -0.498239 q^{38} +(-1.98340 + 5.41796i) q^{39} +(3.23205 + 1.86603i) q^{41} +(-0.0583993 + 0.101151i) q^{42} +(2.53215 + 4.38581i) q^{43} -10.4844i q^{44} +(0.540166 - 0.311865i) q^{46} -8.34285i q^{47} +(-2.97057 - 5.14517i) q^{48} +(-3.44481 + 5.96658i) q^{49} -8.10387 q^{51} +(-4.51332 - 5.39913i) q^{52} +1.56063 q^{53} +(-1.04710 - 0.604542i) q^{54} +(-0.144219 - 0.249795i) q^{56} -3.62916i q^{57} +(0.552399 - 0.318928i) q^{58} +(2.34461 - 1.35366i) q^{59} +(-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} +(-11.0828 + 6.39866i) q^{71} +(0.330337 - 0.190720i) q^{72} +9.68922i q^{73} +(0.655986 + 1.13620i) q^{74} +(3.83341 + 2.21322i) q^{76} +1.78477 q^{77} +(-0.972477 + 0.812927i) q^{78} +4.51851 q^{79} +(3.74441 - 6.48552i) q^{81} +(0.409941 + 0.710039i) q^{82} -4.26371i q^{83} +(0.898640 - 0.518830i) q^{84} +1.11256i q^{86} +(2.32306 + 4.02367i) q^{87} +(2.33176 - 4.03872i) q^{88} +(-2.79366 - 1.61292i) q^{89} +(0.919100 - 0.768307i) q^{91} -5.54133 q^{92} +(7.57221 + 4.37182i) q^{93} +(0.916407 - 1.58726i) q^{94} -4.08359i q^{96} +(-2.17191 + 1.25396i) q^{97} +(-1.31078 + 0.756779i) q^{98} +2.36023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} + 2q^{4} - 18q^{6} + 6q^{7} - 4q^{9} + O(q^{10}) \) \( 8q - 2q^{3} + 2q^{4} - 18q^{6} + 6q^{7} - 4q^{9} - 20q^{12} + 4q^{14} - 2q^{16} + 2q^{17} + 12q^{19} + 12q^{22} + 10q^{23} - 12q^{24} + 10q^{26} + 4q^{27} + 18q^{28} - 8q^{29} - 6q^{32} - 42q^{33} + 20q^{36} - 6q^{37} + 16q^{38} + 12q^{41} - 4q^{42} + 2q^{43} - 42q^{46} - 28q^{48} + 12q^{49} - 8q^{51} + 6q^{52} + 24q^{53} + 18q^{54} + 12q^{56} - 36q^{58} - 12q^{59} - 28q^{61} - 4q^{62} + 24q^{63} - 8q^{64} + 12q^{66} - 6q^{67} + 14q^{68} - 16q^{69} + 48q^{72} + 10q^{74} + 54q^{76} + 36q^{77} + 56q^{78} - 16q^{79} + 8q^{81} - 4q^{82} - 30q^{84} - 22q^{87} + 18q^{88} + 24q^{89} + 28q^{91} - 44q^{92} + 32q^{94} + 30q^{97} - 72q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.190254 + 0.109843i 0.134530 + 0.0776710i 0.565755 0.824574i \(-0.308585\pi\)
−0.431224 + 0.902245i \(0.641918\pi\)
\(3\) −0.800098 + 1.38581i −0.461937 + 0.800098i −0.999057 0.0434075i \(-0.986179\pi\)
0.537121 + 0.843505i \(0.319512\pi\)
\(4\) −0.975869 1.69025i −0.487934 0.845127i
\(5\) 0 0
\(6\) −0.304444 + 0.175771i −0.124289 + 0.0717582i
\(7\) 0.287734 0.166123i 0.108753 0.0627887i −0.444637 0.895711i \(-0.646667\pi\)
0.553390 + 0.832922i \(0.313334\pi\)
\(8\) 0.868145i 0.306936i
\(9\) 0.219687 + 0.380509i 0.0732290 + 0.126836i
\(10\) 0 0
\(11\) 4.65213 + 2.68591i 1.40267 + 0.809832i 0.994666 0.103149i \(-0.0328917\pi\)
0.408004 + 0.912980i \(0.366225\pi\)
\(12\) 3.12316 0.901579
\(13\) 3.55193 0.619491i 0.985129 0.171816i
\(14\) 0.0729902 0.0195074
\(15\) 0 0
\(16\) −1.85638 + 3.21534i −0.464094 + 0.803835i
\(17\) 2.53215 + 4.38581i 0.614136 + 1.06372i 0.990535 + 0.137258i \(0.0438288\pi\)
−0.376399 + 0.926458i \(0.622838\pi\)
\(18\) 0.0965246i 0.0227511i
\(19\) −1.96410 + 1.13397i −0.450596 + 0.260152i −0.708082 0.706130i \(-0.750439\pi\)
0.257486 + 0.966282i \(0.417106\pi\)
\(20\) 0 0
\(21\) 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 \(-0.737679\pi\)
0.975218 + 0.221246i \(0.0710122\pi\)
\(24\) 1.20308 + 0.694601i 0.245578 + 0.141785i
\(25\) 0 0
\(26\) 0.743818 + 0.272296i 0.145875 + 0.0534016i
\(27\) −5.50367 −1.05918
\(28\) −0.561581 0.324229i −0.106129 0.0612735i
\(29\) 1.45174 2.51448i 0.269581 0.466928i −0.699173 0.714953i \(-0.746448\pi\)
0.968754 + 0.248025i \(0.0797815\pi\)
\(30\) 0 0
\(31\) 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 0
\(36\) 0.428771 0.742653i 0.0714619 0.123776i
\(37\) 5.17191 + 2.98601i 0.850257 + 0.490896i 0.860738 0.509049i \(-0.170003\pi\)
−0.0104803 + 0.999945i \(0.503336\pi\)
\(38\) −0.498239 −0.0808250
\(39\) −1.98340 + 5.41796i −0.317598 + 0.867568i
\(40\) 0 0
\(41\) 3.23205 + 1.86603i 0.504762 + 0.291424i 0.730678 0.682723i \(-0.239204\pi\)
−0.225916 + 0.974147i \(0.572538\pi\)
\(42\) −0.0583993 + 0.101151i −0.00901121 + 0.0156079i
\(43\) 2.53215 + 4.38581i 0.386149 + 0.668830i 0.991928 0.126803i \(-0.0404717\pi\)
−0.605779 + 0.795633i \(0.707138\pi\)
\(44\) 10.4844i 1.58058i
\(45\) 0 0
\(46\) 0.540166 0.311865i 0.0796432 0.0459820i
\(47\) 8.34285i 1.21693i −0.793581 0.608465i \(-0.791786\pi\)
0.793581 0.608465i \(-0.208214\pi\)
\(48\) −2.97057 5.14517i −0.428764 0.742642i
\(49\) −3.44481 + 5.96658i −0.492115 + 0.852368i
\(50\) 0 0
\(51\) −8.10387 −1.13477
\(52\) −4.51332 5.39913i −0.625885 0.748724i
\(53\) 1.56063 0.214369 0.107184 0.994239i \(-0.465817\pi\)
0.107184 + 0.994239i \(0.465817\pi\)
\(54\) −1.04710 0.604542i −0.142492 0.0822678i
\(55\) 0 0
\(56\) −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 \(-0.610276\pi\)
0.644795 + 0.764355i \(0.276943\pi\)
\(60\) 0 0
\(61\) −7.05193 12.2143i −0.902908 1.56388i −0.823702 0.567023i \(-0.808095\pi\)
−0.0792059 0.996858i \(-0.525238\pi\)
\(62\) 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 −0.158752 0.987319i \(-0.550747\pi\)
−0.934419 + 0.356176i \(0.884080\pi\)
\(68\) 4.94209 8.55995i 0.599316 1.03805i
\(69\) 2.27162 + 3.93456i 0.273471 + 0.473666i
\(70\) 0 0
\(71\) −11.0828 + 6.39866i −1.31529 + 0.759382i −0.982967 0.183785i \(-0.941165\pi\)
−0.332321 + 0.943166i \(0.607832\pi\)
\(72\) 0.330337 0.190720i 0.0389306 0.0224766i
\(73\) 9.68922i 1.13404i 0.823705 + 0.567019i \(0.191903\pi\)
−0.823705 + 0.567019i \(0.808097\pi\)
\(74\) 0.655986 + 1.13620i 0.0762569 + 0.132081i
\(75\) 0 0
\(76\) 3.83341 + 2.21322i 0.439722 + 0.253874i
\(77\) 1.78477 0.203393
\(78\) −0.972477 + 0.812927i −0.110111 + 0.0920459i
\(79\) 4.51851 0.508372 0.254186 0.967155i \(-0.418192\pi\)
0.254186 + 0.967155i \(0.418192\pi\)
\(80\) 0 0
\(81\) 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 \(-0.924818\pi\)
0.972236 0.234001i \(-0.0751821\pi\)
\(84\) 0.898640 0.518830i 0.0980496 0.0566090i
\(85\) 0 0
\(86\) 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 \(-0.388023\pi\)
−0.640702 + 0.767790i \(0.721356\pi\)
\(90\) 0 0
\(91\) 0.919100 0.768307i 0.0963478 0.0805405i
\(92\) −5.54133 −0.577724
\(93\) 7.57221 + 4.37182i 0.785201 + 0.453336i
\(94\) 0.916407 1.58726i 0.0945202 0.163714i
\(95\) 0 0
\(96\) 4.08359i 0.416780i
\(97\) −2.17191 + 1.25396i −0.220524 + 0.127320i −0.606193 0.795318i \(-0.707304\pi\)
0.385669 + 0.922637i \(0.373971\pi\)
\(98\) −1.31078 + 0.756779i −0.132409 + 0.0764462i
\(99\) 2.36023i 0.237213i
\(100\) 0 0
\(101\) 6.22336 10.7792i 0.619247 1.07257i −0.370376 0.928882i \(-0.620771\pi\)
0.989623 0.143686i \(-0.0458955\pi\)
\(102\) −1.54180 0.890157i −0.152661 0.0881386i
\(103\) −15.0247 −1.48043 −0.740215 0.672370i \(-0.765276\pi\)
−0.740215 + 0.672370i \(0.765276\pi\)
\(104\) −0.537808 3.08359i −0.0527364 0.302371i
\(105\) 0 0
\(106\) 0.296916 + 0.171425i 0.0288390 + 0.0166502i
\(107\) −6.53215 + 11.3140i −0.631487 + 1.09377i 0.355761 + 0.934577i \(0.384222\pi\)
−0.987248 + 0.159190i \(0.949112\pi\)
\(108\) 5.37086 + 9.30260i 0.516811 + 0.895144i
\(109\) 11.2325i 1.07587i 0.842985 + 0.537937i \(0.180796\pi\)
−0.842985 + 0.537937i \(0.819204\pi\)
\(110\) 0 0
\(111\) −8.27607 + 4.77819i −0.785530 + 0.453526i
\(112\) 1.23355i 0.116560i
\(113\) −9.17191 15.8862i −0.862821 1.49445i −0.869195 0.494470i \(-0.835362\pi\)
0.00637349 0.999980i \(-0.497971\pi\)
\(114\) 0.398640 0.690464i 0.0373360 0.0646679i
\(115\) 0 0
\(116\) −5.66682 −0.526151
\(117\) 1.01603 + 1.21545i 0.0939325 + 0.112368i
\(118\) 0.594763 0.0547524
\(119\) 1.45717 + 0.841298i 0.133579 + 0.0771216i
\(120\) 0 0
\(121\) 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
\(125\) 0 0
\(126\) 0.0160350 + 0.0277734i 0.00142851 + 0.00247425i
\(127\) −1.61998 + 2.80589i −0.143750 + 0.248982i −0.928906 0.370316i \(-0.879249\pi\)
0.785156 + 0.619298i \(0.212583\pi\)
\(128\) 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
\(135\) 0 0
\(136\) 3.80752 2.19827i 0.326492 0.188500i
\(137\) 15.5736 8.99144i 1.33054 0.768190i 0.345162 0.938543i \(-0.387824\pi\)
0.985383 + 0.170353i \(0.0544907\pi\)
\(138\) 0.998090i 0.0849631i
\(139\) −5.99307 10.3803i −0.508325 0.880445i −0.999954 0.00964021i \(-0.996931\pi\)
0.491628 0.870805i \(-0.336402\pi\)
\(140\) 0 0
\(141\) 11.5616 + 6.67510i 0.973663 + 0.562144i
\(142\) −2.81140 −0.235928
\(143\) 18.1879 + 6.65821i 1.52095 + 0.556788i
\(144\) −1.63129 −0.135941
\(145\) 0 0
\(146\) −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 \(-0.622054\pi\)
0.616077 + 0.787686i \(0.288721\pi\)
\(150\) 0 0
\(151\) 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
\(155\) 0 0
\(156\) 11.0933 1.93477i 0.888172 0.154906i
\(157\) 16.4329 1.31148 0.655742 0.754985i \(-0.272356\pi\)
0.655742 + 0.754985i \(0.272356\pi\)
\(158\) 0.859667 + 0.496329i 0.0683914 + 0.0394858i
\(159\) −1.24865 + 2.16273i −0.0990247 + 0.171516i
\(160\) 0 0
\(161\) 0.943307i 0.0743430i
\(162\) 1.42478 0.822599i 0.111942 0.0646295i
\(163\) −15.4215 + 8.90361i −1.20791 + 0.697384i −0.962301 0.271986i \(-0.912320\pi\)
−0.245604 + 0.969370i \(0.578986\pi\)
\(164\) 7.28398i 0.568784i
\(165\) 0 0
\(166\) 0.468341 0.811190i 0.0363503 0.0629605i
\(167\) −5.45047 3.14683i −0.421770 0.243509i 0.274064 0.961711i \(-0.411632\pi\)
−0.695834 + 0.718202i \(0.744965\pi\)
\(168\) 0.461557 0.0356099
\(169\) 12.2325 4.40078i 0.940959 0.338522i
\(170\) 0 0
\(171\) −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 −0.991686 0.128679i \(-0.958926\pi\)
0.384404 0.923165i \(-0.374407\pi\)
\(174\) 1.02069i 0.0773786i
\(175\) 0 0
\(176\) −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 0.0342123 0.999415i \(-0.489108\pi\)
0.848412 0.529336i \(-0.177559\pi\)
\(180\) 0 0
\(181\) 2.62590 0.195182 0.0975909 0.995227i \(-0.468886\pi\)
0.0975909 + 0.995227i \(0.468886\pi\)
\(182\) 0.259256 0.0452168i 0.0192174 0.00335169i
\(183\) 22.5689 1.66834
\(184\) −2.13459 1.23241i −0.157364 0.0908544i
\(185\) 0 0
\(186\) 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 0
\(191\) 1.00791 + 1.74575i 0.0729298 + 0.126318i 0.900184 0.435509i \(-0.143432\pi\)
−0.827254 + 0.561828i \(0.810098\pi\)
\(192\) −5.49258 + 9.51343i −0.396393 + 0.686572i
\(193\) 19.7636 + 11.4105i 1.42262 + 0.821348i 0.996522 0.0833298i \(-0.0265555\pi\)
0.426095 + 0.904678i \(0.359889\pi\)
\(194\) −0.550955 −0.0395563
\(195\) 0 0
\(196\) 13.4467 0.960480
\(197\) 0.556877 + 0.321513i 0.0396758 + 0.0229068i 0.519707 0.854345i \(-0.326041\pi\)
−0.480031 + 0.877252i \(0.659375\pi\)
\(198\) −0.259256 + 0.449045i −0.0184245 + 0.0319122i
\(199\) 1.53342 + 2.65596i 0.108701 + 0.188276i 0.915244 0.402899i \(-0.131997\pi\)
−0.806543 + 0.591175i \(0.798664\pi\)
\(200\) 0 0
\(201\) 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
\(205\) 0 0
\(206\) −2.85852 1.65037i −0.199163 0.114987i
\(207\) 1.24746 0.0867045
\(208\) −4.60185 + 12.5707i −0.319081 + 0.871620i
\(209\) −12.1830 −0.842716
\(210\) 0 0
\(211\) 4.10020 7.10175i 0.282269 0.488904i −0.689674 0.724120i \(-0.742246\pi\)
0.971943 + 0.235215i \(0.0755796\pi\)
\(212\) −1.52297 2.63786i −0.104598 0.181169i
\(213\) 20.4782i 1.40314i
\(214\) −2.48554 + 1.43503i −0.169908 + 0.0980964i
\(215\) 0 0
\(216\) 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
\(220\) 0 0
\(221\) 11.7110 + 14.0095i 0.787767 + 0.942378i
\(222\) −2.09941 −0.140903
\(223\) −8.87174 5.12210i −0.594095 0.343001i 0.172620 0.984989i \(-0.444777\pi\)
−0.766715 + 0.641987i \(0.778110\pi\)
\(224\) −0.423935 + 0.734278i −0.0283254 + 0.0490610i
\(225\) 0 0
\(226\) 4.02990i 0.268065i
\(227\) 6.10012 3.52190i 0.404879 0.233757i −0.283708 0.958911i \(-0.591565\pi\)
0.688587 + 0.725154i \(0.258231\pi\)
\(228\) −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 0
\(231\) −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 \(-0.513010\pi\)
−0.0408619 + 0.999165i \(0.513010\pi\)
\(234\) 0.0597962 + 0.342849i 0.00390900 + 0.0224127i
\(235\) 0 0
\(236\) −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 \(0.895796\pi\)
\(240\) 0 0
\(241\) −19.5608 + 11.2934i −1.26002 + 0.727475i −0.973079 0.230472i \(-0.925973\pi\)
−0.286944 + 0.957947i \(0.592640\pi\)
\(242\) 3.92282i 0.252168i
\(243\) −2.26371 3.92086i −0.145217 0.251523i
\(244\) −13.7635 + 23.8391i −0.881119 + 1.52614i
\(245\) 0 0
\(246\) −1.31197 −0.0836483
\(247\) −6.27387 + 5.24455i −0.399197 + 0.333702i
\(248\) −4.74363 −0.301221
\(249\) 5.90869 + 3.41139i 0.374448 + 0.216188i
\(250\) 0 0
\(251\) −3.38418 5.86157i −0.213608 0.369979i 0.739233 0.673449i \(-0.235188\pi\)
−0.952841 + 0.303470i \(0.901855\pi\)
\(252\) 0.284915i 0.0179480i
\(253\) 13.2082 7.62577i 0.830394 0.479428i
\(254\) −0.616417 + 0.355888i −0.0386774 + 0.0223304i
\(255\) 0 0
\(256\) −6.13860 10.6324i −0.383663 0.664523i
\(257\) 5.12691 8.88007i 0.319808 0.553924i −0.660640 0.750703i \(-0.729715\pi\)
0.980448 + 0.196779i \(0.0630483\pi\)
\(258\) −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 −0.420798 0.907154i \(-0.638250\pi\)
0.996018 0.0891555i \(-0.0284168\pi\)
\(264\) 3.73127 + 6.46275i 0.229644 + 0.397754i
\(265\) 0 0
\(266\) −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 −0.998448 0.0556934i \(-0.982263\pi\)
0.450992 0.892528i \(-0.351070\pi\)
\(270\) 0 0
\(271\) −26.7582 15.4488i −1.62544 0.938450i −0.985429 0.170086i \(-0.945595\pi\)
−0.640014 0.768363i \(-0.721071\pi\)
\(272\) −18.8025 −1.14007
\(273\) 0.329358 + 1.88842i 0.0199337 + 0.114292i
\(274\) 3.95060 0.238665
\(275\) 0 0
\(276\) 4.43361 7.67923i 0.266872 0.462235i
\(277\) −13.2522 22.9536i −0.796250 1.37915i −0.922042 0.387089i \(-0.873481\pi\)
0.125792 0.992057i \(-0.459853\pi\)
\(278\) 2.63320i 0.157929i
\(279\) 2.07914 1.20039i 0.124475 0.0718656i
\(280\) 0 0
\(281\) 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 \(-0.711288\pi\)
0.990190 + 0.139725i \(0.0446218\pi\)
\(284\) 21.6307 + 12.4885i 1.28355 + 0.741057i
\(285\) 0 0
\(286\) 2.72898 + 3.26458i 0.161368 + 0.193039i
\(287\) 1.23996 0.0731926
\(288\) −0.971033 0.560626i −0.0572187 0.0330352i
\(289\) −4.32355 + 7.48861i −0.254327 + 0.440507i
\(290\) 0 0
\(291\) 4.01315i 0.235255i
\(292\) 16.3772 9.45541i 0.958406 0.553336i
\(293\) −14.6511 + 8.45880i −0.855925 + 0.494168i −0.862645 0.505809i \(-0.831194\pi\)
0.00672072 + 0.999977i \(0.497861\pi\)
\(294\) 2.42199i 0.141253i
\(295\) 0 0
\(296\) 2.59229 4.48997i 0.150674 0.260974i
\(297\) −25.6038 14.7824i −1.48568 0.857759i
\(298\) 0.749222 0.0434012
\(299\) 3.51908 9.61292i 0.203514 0.555929i
\(300\) 0 0
\(301\) 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
\(305\) 0 0
\(306\) −0.423339 + 0.244415i −0.0242007 + 0.0139723i
\(307\) 4.30426i 0.245657i 0.992428 + 0.122828i \(0.0391965\pi\)
−0.992428 + 0.122828i \(0.960803\pi\)
\(308\) −1.74170 3.01671i −0.0992425 0.171893i
\(309\) 12.0213 20.8214i 0.683865 1.18449i
\(310\) 0 0
\(311\) 2.22512 0.126175 0.0630875 0.998008i \(-0.479905\pi\)
0.0630875 + 0.998008i \(0.479905\pi\)
\(312\) 4.70357 + 1.72188i 0.266287 + 0.0974820i
\(313\) −7.20887 −0.407469 −0.203735 0.979026i \(-0.565308\pi\)
−0.203735 + 0.979026i \(0.565308\pi\)
\(314\) 3.12642 + 1.80504i 0.176434 + 0.101864i
\(315\) 0 0
\(316\) −4.40948 7.63744i −0.248052 0.429639i
\(317\) 0.321644i 0.0180653i −0.999959 0.00903266i \(-0.997125\pi\)
0.999959 0.00903266i \(-0.00287522\pi\)
\(318\) −0.475124 + 0.274313i −0.0266436 + 0.0153827i
\(319\) 13.5073 7.79847i 0.756266 0.436630i
\(320\) 0 0
\(321\) −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
\(330\) 0 0
\(331\) −14.4037 + 8.31600i −0.791701 + 0.457089i −0.840561 0.541717i \(-0.817775\pi\)
0.0488600 + 0.998806i \(0.484441\pi\)
\(332\) −7.20676 + 4.16082i −0.395522 + 0.228355i
\(333\) 2.62395i 0.143791i
\(334\) −0.691317 1.19740i −0.0378272 0.0655186i
\(335\) 0 0
\(336\) −1.70947 0.986961i −0.0932590 0.0538431i
\(337\) 24.2186 1.31927 0.659636 0.751586i \(-0.270711\pi\)
0.659636 + 0.751586i \(0.270711\pi\)
\(338\) 2.81068 + 0.506387i 0.152881 + 0.0275438i
\(339\) 29.3537 1.59427
\(340\) 0 0
\(341\) 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
\(345\) 0 0
\(346\) 3.50952i 0.188673i
\(347\) −3.13680 5.43309i −0.168392 0.291664i 0.769463 0.638692i \(-0.220524\pi\)
−0.937855 + 0.347028i \(0.887191\pi\)
\(348\) 4.53401 7.85314i 0.243049 0.420972i
\(349\) −6.12275 3.53497i −0.327743 0.189223i 0.327095 0.944991i \(-0.393930\pi\)
−0.654839 + 0.755769i \(0.727263\pi\)
\(350\) 0 0
\(351\) −19.5487 + 3.40948i −1.04343 + 0.181984i
\(352\) −13.7085 −0.730666
\(353\) 18.8705 + 10.8949i 1.00438 + 0.579878i 0.909541 0.415615i \(-0.136434\pi\)
0.0948371 + 0.995493i \(0.469767\pi\)
\(354\) −0.475869 + 0.824229i −0.0252921 + 0.0438073i
\(355\) 0 0
\(356\) 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 0
\(361\) −6.92820 + 12.0000i −0.364642 + 0.631579i
\(362\) 0.499589 + 0.288438i 0.0262578 + 0.0151600i
\(363\) −28.5737 −1.49973
\(364\) −2.19556 0.803745i −0.115078 0.0421277i
\(365\) 0 0
\(366\) 4.29384 + 2.47905i 0.224443 + 0.129582i
\(367\) 3.19566 5.53505i 0.166812 0.288927i −0.770485 0.637458i \(-0.779986\pi\)
0.937297 + 0.348531i \(0.113319\pi\)
\(368\) 5.27059 + 9.12892i 0.274748 + 0.475878i
\(369\) 1.63977i 0.0853628i
\(370\) 0 0
\(371\) 0.449045 0.259256i 0.0233133 0.0134599i
\(372\) 17.0653i 0.884793i
\(373\) −10.0401 17.3899i −0.519855 0.900414i −0.999734 0.0230798i \(-0.992653\pi\)
0.479879 0.877335i \(-0.340681\pi\)
\(374\) −2.98823 + 5.17577i −0.154518 + 0.267633i
\(375\) 0 0
\(376\) −7.24280 −0.373519
\(377\) 3.59878 9.83062i 0.185346 0.506302i
\(378\) −0.401714 −0.0206619
\(379\) −4.73007 2.73091i −0.242968 0.140277i 0.373572 0.927601i \(-0.378133\pi\)
−0.616540 + 0.787324i \(0.711466\pi\)
\(380\) 0 0
\(381\) −2.59229 4.48997i −0.132807 0.230028i
\(382\) 0.442849i 0.0226581i
\(383\) −4.90842 + 2.83388i −0.250808 + 0.144804i −0.620134 0.784496i \(-0.712922\pi\)
0.369326 + 0.929300i \(0.379589\pi\)
\(384\) −9.16297 + 5.29024i −0.467596 + 0.269966i
\(385\) 0 0
\(386\) 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
\(395\) 0 0
\(396\) 3.98940 2.30328i 0.200475 0.115744i
\(397\) −24.2780 + 14.0169i −1.21848 + 0.703487i −0.964592 0.263748i \(-0.915041\pi\)
−0.253884 + 0.967235i \(0.581708\pi\)
\(398\) 0.673745i 0.0337718i
\(399\) −0.602888 1.04423i −0.0301822 0.0522770i
\(400\) 0 0
\(401\) 19.4979 + 11.2571i 0.973680 + 0.562155i 0.900356 0.435154i \(-0.143306\pi\)
0.0733241 + 0.997308i \(0.476639\pi\)
\(402\) 3.63222 0.181159
\(403\) −3.38496 19.4081i −0.168617 0.966788i
\(404\) −24.2927 −1.20861
\(405\) 0 0
\(406\) 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 \(-0.700473\pi\)
0.405378 + 0.914149i \(0.367140\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) −7.05946 + 5.90125i −0.346119 + 0.289333i
\(417\) 19.1802 0.939257
\(418\) −2.31787 1.33822i −0.113371 0.0654546i
\(419\) −8.85578 + 15.3387i −0.432633 + 0.749343i −0.997099 0.0761137i \(-0.975749\pi\)
0.564466 + 0.825456i \(0.309082\pi\)
\(420\) 0 0
\(421\) 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
\(425\) 0 0
\(426\) 2.24940 3.89607i 0.108984 0.188765i
\(427\) −4.05816 2.34298i −0.196388 0.113385i
\(428\) 25.4981 1.23250
\(429\) −23.7792 + 19.8778i −1.14807 + 0.959710i
\(430\) 0 0
\(431\) 8.22590 + 4.74923i 0.396228 + 0.228762i 0.684855 0.728679i \(-0.259866\pi\)
−0.288627 + 0.957442i \(0.593199\pi\)
\(432\) 10.2169 17.6962i 0.491560 0.851408i
\(433\) 0.698141 + 1.20922i 0.0335505 + 0.0581112i 0.882313 0.470663i \(-0.155985\pi\)
−0.848763 + 0.528774i \(0.822652\pi\)
\(434\) 0.398826i 0.0191443i
\(435\) 0 0
\(436\) 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 −0.812086 0.583538i \(-0.801668\pi\)
0.911402 + 0.411518i \(0.135001\pi\)
\(440\) 0 0
\(441\) −3.02711 −0.144148
\(442\) 0.689221 + 3.95174i 0.0327829 + 0.187965i
\(443\) −9.54563 −0.453526 −0.226763 0.973950i \(-0.572814\pi\)
−0.226763 + 0.973950i \(0.572814\pi\)
\(444\) 16.1527 + 9.32578i 0.766574 + 0.442582i
\(445\) 0 0
\(446\) −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 \(-0.495406\pi\)
0.873151 + 0.487450i \(0.162073\pi\)
\(450\) 0 0
\(451\) 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 0.401282 0.915955i \(-0.368565\pi\)
−0.592599 + 0.805498i \(0.701898\pi\)
\(458\) −0.145980 + 0.252845i −0.00682122 + 0.0118147i
\(459\) −13.9361 24.1381i −0.650482 1.12667i
\(460\) 0 0
\(461\) 1.54283 0.890753i 0.0718568 0.0414865i −0.463641 0.886023i \(-0.653457\pi\)
0.535498 + 0.844537i \(0.320124\pi\)
\(462\) −0.543362 + 0.313710i −0.0252795 + 0.0145951i
\(463\) 6.80200i 0.316116i −0.987430 0.158058i \(-0.949477\pi\)
0.987430 0.158058i \(-0.0505232\pi\)
\(464\) 5.38995 + 9.33566i 0.250222 + 0.433397i
\(465\) 0 0
\(466\) −0.237335 0.137025i −0.0109943 0.00634758i
\(467\) 18.2374 0.843927 0.421963 0.906613i \(-0.361341\pi\)
0.421963 + 0.906613i \(0.361341\pi\)
\(468\) 1.06290 2.90348i 0.0491325 0.134213i
\(469\) −3.43285 −0.158514
\(470\) 0 0
\(471\) −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
\(475\) 0 0
\(476\) 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 \(-0.0361821\pi\)
0.398544 + 0.917149i \(0.369515\pi\)
\(480\) 0 0
\(481\) 20.2201 + 7.40214i 0.921957 + 0.337508i
\(482\) −4.96204 −0.226015
\(483\) 1.30724 + 0.754738i 0.0594817 + 0.0343418i
\(484\) 17.4255 30.1819i 0.792069 1.37190i
\(485\) 0 0
\(486\) 0.994615i 0.0451166i
\(487\) −8.92352 + 5.15200i −0.404363 + 0.233459i −0.688365 0.725364i \(-0.741671\pi\)
0.284002 + 0.958824i \(0.408338\pi\)
\(488\) −10.6038 + 6.12210i −0.480011 + 0.277134i
\(489\) 28.4950i 1.28859i
\(490\) 0 0
\(491\) 4.66599 8.08174i 0.210573 0.364724i −0.741321 0.671151i \(-0.765800\pi\)
0.951894 + 0.306427i \(0.0991336\pi\)
\(492\) 10.0942 + 5.82790i 0.455083 + 0.262742i
\(493\) 14.7041 0.662238
\(494\) −1.76971 + 0.308654i −0.0796230 + 0.0138870i
\(495\) 0 0
\(496\) 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 \(-0.180026\pi\)
\(500\) 0 0
\(501\) 8.72181 5.03554i 0.389662 0.224971i
\(502\) 1.48692i 0.0663645i
\(503\) 21.0721 + 36.4980i 0.939560 + 1.62737i 0.766294 + 0.642490i \(0.222099\pi\)
0.173266 + 0.984875i \(0.444568\pi\)
\(504\) 0.0633661 0.109753i 0.00282255 0.00488880i
\(505\) 0 0
\(506\) 3.35056 0.148951
\(507\) −3.68852 + 20.4729i −0.163813 + 0.909235i
\(508\) 6.32355 0.280562
\(509\) −29.0640 16.7801i −1.28824 0.743765i −0.309899 0.950770i \(-0.600295\pi\)
−0.978340 + 0.207005i \(0.933629\pi\)
\(510\) 0 0
\(511\) 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
\(515\) 0 0
\(516\) 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 \(-0.872821\pi\)
0.797501 + 0.603317i \(0.206155\pi\)
\(524\) −0.171425 0.296916i −0.00748872 0.0129708i
\(525\) 0 0
\(526\) 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 0
\(531\) 1.03016 + 0.594763i 0.0447051 + 0.0258105i
\(532\) 1.47067 0.0637616
\(533\) 12.6360 + 4.62577i 0.547327 + 0.200364i
\(534\) 1.13402 0.0490737
\(535\) 0 0
\(536\) −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
\(540\) 0 0
\(541\) 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
\(545\) 0 0
\(546\) −0.144769 + 0.395458i −0.00619552 + 0.0169240i
\(547\) −25.1765 −1.07647 −0.538234 0.842795i \(-0.680908\pi\)
−0.538234 + 0.842795i \(0.680908\pi\)
\(548\) −30.3956 17.5489i −1.29844 0.749653i
\(549\) 3.09843 5.36665i 0.132238 0.229043i
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) −11.6969 + 20.2596i −0.496059 + 0.859199i
\(557\) 36.6752 + 21.1744i 1.55398 + 0.897190i 0.997812 + 0.0661194i \(0.0210618\pi\)
0.556167 + 0.831071i \(0.312272\pi\)
\(558\) 0.527420 0.0223275
\(559\) 11.7110 + 14.0095i 0.495322 + 0.592537i
\(560\) 0 0
\(561\) −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 −0.999999 0.00153173i \(-0.999512\pi\)
0.498673 0.866790i \(-0.333821\pi\)
\(564\) 26.0561i 1.09716i
\(565\) 0 0
\(566\) 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 0.436906 + 0.899507i \(0.356074\pi\)
−0.997449 + 0.0713817i \(0.977259\pi\)
\(570\) 0 0
\(571\) 16.7159 0.699539 0.349769 0.936836i \(-0.386260\pi\)
0.349769 + 0.936836i \(0.386260\pi\)
\(572\) −6.49498 37.2398i −0.271569 1.55707i
\(573\) −3.22571 −0.134756
\(574\) 0.235908 + 0.136202i 0.00984661 + 0.00568494i
\(575\) 0 0
\(576\) 1.50812 + 2.61215i 0.0628385 + 0.108840i
\(577\) 20.6768i 0.860786i −0.902642 0.430393i \(-0.858375\pi\)
0.902642 0.430393i \(-0.141625\pi\)
\(578\) −1.64515 + 0.949828i −0.0684292 + 0.0395076i
\(579\) −31.6257 + 18.2591i −1.31432 + 0.758822i
\(580\) 0 0
\(581\) −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 0.0799116 0.996802i \(-0.474536\pi\)
−0.823300 + 0.567606i \(0.807870\pi\)
\(588\) −10.7587 + 18.6346i −0.443681 + 0.768478i
\(589\) 6.19615 + 10.7321i 0.255308 + 0.442206i
\(590\) 0 0
\(591\) −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 \(0.148072\pi\)
−0.893740 + 0.448585i \(0.851928\pi\)
\(594\) −3.24749 5.62482i −0.133246 0.230789i
\(595\) 0 0
\(596\) −5.76446 3.32811i −0.236121 0.136325i
\(597\) −4.90755 −0.200853
\(598\) 1.72544 1.44235i 0.0705583 0.0589822i
\(599\) −3.58040 −0.146291 −0.0731456 0.997321i \(-0.523304\pi\)
−0.0731456 + 0.997321i \(0.523304\pi\)
\(600\) 0 0
\(601\) −10.6743 + 18.4885i −0.435414 + 0.754160i −0.997329 0.0730352i \(-0.976731\pi\)
0.561915 + 0.827195i \(0.310065\pi\)
\(602\) 0.184822 + 0.320121i 0.00753278 + 0.0130472i
\(603\) 4.53972i 0.184872i
\(604\) 13.4568 7.76929i 0.547550 0.316128i
\(605\) 0 0
\(606\) 4.37554i 0.177744i
\(607\) −1.64988 2.85767i −0.0669665 0.115989i 0.830598 0.556872i \(-0.187999\pi\)
−0.897565 + 0.440883i \(0.854665\pi\)
\(608\) 2.89383 5.01226i 0.117360 0.203274i
\(609\) 1.33685 + 0.771830i 0.0541718 + 0.0312761i
\(610\) 0 0
\(611\) −5.16832 29.6332i −0.209088 1.19883i
\(612\) 4.34285 0.175549
\(613\) −8.56183 4.94318i −0.345809 0.199653i 0.317029 0.948416i \(-0.397315\pi\)
−0.662838 + 0.748763i \(0.730648\pi\)
\(614\) −0.472795 + 0.818904i −0.0190804 + 0.0330483i
\(615\) 0 0
\(616\) 1.54944i 0.0624286i
\(617\) −39.5920 + 22.8584i −1.59391 + 0.920246i −0.601287 + 0.799033i \(0.705345\pi\)
−0.992626 + 0.121213i \(0.961321\pi\)
\(618\) 4.57419 2.64091i 0.184001 0.106233i
\(619\) 19.9143i 0.800425i 0.916422 + 0.400212i \(0.131064\pi\)
−0.916422 + 0.400212i \(0.868936\pi\)
\(620\) 0 0
\(621\) −7.81295 + 13.5324i −0.313523 + 0.543038i
\(622\) 0.423339 + 0.244415i 0.0169743 + 0.00980014i
\(623\) −1.07177 −0.0429397
\(624\) −13.7386 16.4351i −0.549986 0.657930i
\(625\) 0 0
\(626\) −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 0
\(631\) 12.6403 7.29790i 0.503204 0.290525i −0.226832 0.973934i \(-0.572837\pi\)
0.730036 + 0.683409i \(0.239503\pi\)
\(632\) 3.92272i 0.156038i
\(633\) 6.56112 + 11.3642i 0.260781 + 0.451686i
\(634\) 0.0353305 0.0611942i 0.00140315 0.00243033i
\(635\) 0 0
\(636\) 4.87409 0.193270
\(637\) −8.53948 + 23.3269i −0.338346 + 0.924246i
\(638\) 3.42644 0.135654
\(639\) −4.86950 2.81140i −0.192634 0.111217i
\(640\) 0 0
\(641\) −7.08183 12.2661i −0.279716 0.484482i 0.691598 0.722282i \(-0.256907\pi\)
−0.971314 + 0.237801i \(0.923573\pi\)
\(642\) 4.59265i 0.181257i
\(643\) 14.5246 8.38581i 0.572796 0.330704i −0.185469 0.982650i \(-0.559380\pi\)
0.758265 + 0.651946i \(0.226047\pi\)
\(644\) −1.59443 + 0.920544i −0.0628293 + 0.0362745i
\(645\) 0 0
\(646\) −1.26161 2.18518i −0.0496376 0.0859748i
\(647\) 1.49584 2.59087i 0.0588075 0.101858i −0.835123 0.550063i \(-0.814604\pi\)
0.893930 + 0.448206i \(0.147937\pi\)
\(648\) −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 \(-0.906627\pi\)
0.729053 + 0.684457i \(0.239961\pi\)
\(654\) −1.97434 3.41966i −0.0772028 0.133719i
\(655\) 0 0
\(656\) −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 0.883118 0.469150i \(-0.155440\pi\)
−0.847855 + 0.530228i \(0.822106\pi\)
\(660\) 0 0
\(661\) 10.6872 + 6.17028i 0.415686 + 0.239996i 0.693230 0.720717i \(-0.256187\pi\)
−0.277544 + 0.960713i \(0.589520\pi\)
\(662\) −3.65383 −0.142010
\(663\) −28.7844 + 5.02027i −1.11789 + 0.194971i
\(664\) −3.70152 −0.143647
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) 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 \(-0.890488\pi\)
0.762805 + 0.646628i \(0.223822\pi\)
\(674\) 4.60770 + 2.66025i 0.177482 + 0.102469i
\(675\) 0 0
\(676\) −19.3757 16.3814i −0.745220 0.630053i
\(677\) −13.8984 −0.534158 −0.267079 0.963675i \(-0.586059\pi\)
−0.267079 + 0.963675i \(0.586059\pi\)
\(678\) 5.58467 + 3.22431i 0.214478 + 0.123829i
\(679\) −0.416622 + 0.721611i −0.0159885 + 0.0276929i
\(680\) 0 0
\(681\) 11.2715i 0.431924i
\(682\) 5.58438 3.22414i 0.213837 0.123459i
\(683\) 32.6935 18.8756i 1.25098 0.722255i 0.279678 0.960094i \(-0.409772\pi\)
0.971305 + 0.237838i \(0.0764388\pi\)
\(684\) 1.94486i 0.0743637i
\(685\) 0 0
\(686\) −0.506903 + 0.877981i −0.0193536 + 0.0335215i
\(687\) −1.84172 1.06332i −0.0702661 0.0405681i
\(688\) −18.8025 −0.716838
\(689\) 5.54324 0.966794i 0.211181 0.0368319i
\(690\) 0 0
\(691\) −1.43146 0.826456i −0.0544554 0.0314399i 0.472525 0.881317i \(-0.343343\pi\)
−0.526981 + 0.849877i \(0.676676\pi\)
\(692\) −15.5896 + 27.0020i −0.592628 + 1.02646i
\(693\) 0.392090 + 0.679120i 0.0148943 + 0.0257976i
\(694\) 1.37823i 0.0523168i
\(695\) 0 0
\(696\) 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 0
\(701\) −20.4819 −0.773590 −0.386795 0.922166i \(-0.626418\pi\)
−0.386795 + 0.922166i \(0.626418\pi\)
\(702\) −4.09373 1.49863i −0.154508 0.0565620i
\(703\) −13.5442 −0.510830
\(704\) 31.9363 + 18.4384i 1.20365 + 0.694925i
\(705\) 0 0
\(706\) 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 \(-0.531490\pi\)
0.812407 + 0.583091i \(0.198157\pi\)
\(710\) 0 0
\(711\) 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 0.959227 + 0.282636i \(0.0912089\pi\)
−0.234844 + 0.972033i \(0.575458\pi\)
\(720\) 0 0
\(721\) −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
\(725\) 0 0
\(726\) −5.43628 3.13864i −0.201759 0.116486i
\(727\) −30.6598 −1.13711 −0.568555 0.822645i \(-0.692497\pi\)
−0.568555 + 0.822645i \(0.692497\pi\)
\(728\) −0.667002 0.797912i −0.0247207 0.0295726i
\(729\) 29.7112 1.10042
\(730\) 0 0
\(731\) −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 \(0.148702\pi\)
−0.892850 + 0.450355i \(0.851298\pi\)
\(734\) 1.21598 0.702045i 0.0448826 0.0259130i
\(735\) 0 0
\(736\) 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 \(-0.581962\pi\)
−0.964802 + 0.262977i \(0.915296\pi\)
\(740\) 0 0
\(741\) −2.24823 12.8905i −0.0825909 0.473546i
\(742\) 0.113910 0.00418178
\(743\) 34.6479 + 20.0040i 1.27111 + 0.733874i 0.975196 0.221342i \(-0.0710437\pi\)
0.295910 + 0.955216i \(0.404377\pi\)
\(744\) 3.79537 6.57377i 0.139145 0.241006i
\(745\) 0 0
\(746\) 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 0
\(751\) 12.8010 22.1720i 0.467115 0.809067i −0.532179 0.846632i \(-0.678627\pi\)
0.999294 + 0.0375648i \(0.0119601\pi\)
\(752\) 26.8251 + 15.4875i 0.978211 + 0.564770i
\(753\) 10.8307 0.394693
\(754\) 1.76451 1.47502i 0.0642597 0.0537169i
\(755\) 0 0
\(756\) 3.09076 + 1.78445i 0.112410 + 0.0648998i
\(757\) −0.924239 + 1.60083i −0.0335920 + 0.0581831i −0.882333 0.470626i \(-0.844028\pi\)
0.848741 + 0.528809i \(0.177361\pi\)
\(758\) −0.599945 1.03914i −0.0217910 0.0377431i
\(759\) 24.4055i 0.885862i
\(760\) 0 0
\(761\) 22.7006 13.1062i 0.822896 0.475099i −0.0285179 0.999593i \(-0.509079\pi\)
0.851414 + 0.524494i \(0.175745\pi\)
\(762\) 1.13898i 0.0412610i
\(763\) 1.86597 + 3.23196i 0.0675528 + 0.117005i
\(764\) 1.96718 3.40725i 0.0711699 0.123270i
\(765\) 0 0
\(766\) −1.24513 −0.0449884
\(767\) 7.48932 6.26058i 0.270424 0.226056i
\(768\) 19.6459 0.708911
\(769\) −38.4078 22.1747i −1.38502 0.799641i −0.392271 0.919850i \(-0.628310\pi\)
−0.992749 + 0.120208i \(0.961644\pi\)
\(770\) 0 0
\(771\) 8.20406 + 14.2099i 0.295462 + 0.511755i
\(772\) 44.5408i 1.60306i
\(773\) −20.1471 + 11.6319i −0.724640 + 0.418371i −0.816458 0.577405i \(-0.804065\pi\)
0.0918181 + 0.995776i \(0.470732\pi\)
\(774\) −0.423339 + 0.244415i −0.0152166 + 0.00878531i
\(775\) 0 0
\(776\) 1.08861 + 1.88554i 0.0390790 + 0.0676868i
\(777\) −1.58754 + 2.74970i −0.0569526 + 0.0986448i
\(778\) −2.02001 1.16625i −0.0724209 0.0418122i
\(779\) −8.46410 −0.303258
\(780\) 0 0
\(781\) −68.7449 −2.45989
\(782\) 2.73556 + 1.57938i 0.0978235 + 0.0564784i
\(783\)