Properties

Label 325.2.m.b.199.3
Level $325$
Weight $2$
Character 325.199
Analytic conductor $2.595$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.m (of order \(6\), degree \(2\), not 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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.3
Root \(-1.27597 - 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 325.199
Dual form 325.2.m.b.49.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.109843 - 0.190254i) q^{2} +(-1.38581 - 0.800098i) q^{3} +(0.975869 + 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(-0.166123 - 0.287734i) q^{7} +0.868145 q^{8} +(-0.219687 - 0.380509i) q^{9} +O(q^{10})\) \(q+(0.109843 - 0.190254i) q^{2} +(-1.38581 - 0.800098i) q^{3} +(0.975869 + 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(-0.166123 - 0.287734i) q^{7} +0.868145 q^{8} +(-0.219687 - 0.380509i) q^{9} +(4.65213 + 2.68591i) q^{11} -3.12316i q^{12} +(0.619491 + 3.55193i) q^{13} -0.0729902 q^{14} +(-1.85638 + 3.21534i) q^{16} +(4.38581 - 2.53215i) q^{17} -0.0965246 q^{18} +(1.96410 - 1.13397i) q^{19} +0.531659i q^{21} +(1.02201 - 0.590059i) q^{22} +(2.45880 + 1.41959i) q^{23} +(-1.20308 - 0.694601i) q^{24} +(0.743818 + 0.272296i) q^{26} +5.50367i q^{27} +(0.324229 - 0.561581i) q^{28} +(-1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(1.27597 + 2.21004i) q^{32} +(-4.29798 - 7.44432i) q^{33} -1.11256i q^{34} +(0.428771 - 0.742653i) q^{36} +(2.98601 - 5.17191i) q^{37} -0.498239i q^{38} +(1.98340 - 5.41796i) q^{39} +(3.23205 + 1.86603i) q^{41} +(0.101151 + 0.0583993i) q^{42} +(-4.38581 + 2.53215i) q^{43} +10.4844i q^{44} +(0.540166 - 0.311865i) q^{46} -8.34285 q^{47} +(5.14517 - 2.97057i) q^{48} +(3.44481 - 5.96658i) q^{49} -8.10387 q^{51} +(-5.39913 + 4.51332i) q^{52} +1.56063i q^{53} +(1.04710 + 0.604542i) q^{54} +(-0.144219 - 0.249795i) q^{56} -3.62916 q^{57} +(0.318928 + 0.552399i) q^{58} +(-2.34461 + 1.35366i) q^{59} +(-7.05193 - 12.2143i) q^{61} +(-1.03957 - 0.600196i) q^{62} +(-0.0729902 + 0.126423i) q^{63} -6.86488 q^{64} -1.88842 q^{66} +(-5.16612 + 8.94799i) q^{67} +(8.55995 + 4.94209i) q^{68} +(-2.27162 - 3.93456i) q^{69} +(-11.0828 + 6.39866i) q^{71} +(-0.190720 - 0.330337i) q^{72} -9.68922 q^{73} +(-0.655986 - 1.13620i) q^{74} +(3.83341 + 2.21322i) q^{76} -1.78477i q^{77} +(-0.812927 - 0.972477i) q^{78} -4.51851 q^{79} +(3.74441 - 6.48552i) q^{81} +(0.710039 - 0.409941i) q^{82} +4.26371 q^{83} +(-0.898640 + 0.518830i) q^{84} +1.11256i q^{86} +(4.02367 - 2.32306i) q^{87} +(4.03872 + 2.33176i) q^{88} +(2.79366 + 1.61292i) q^{89} +(0.919100 - 0.768307i) q^{91} +5.54133i q^{92} +(-4.37182 + 7.57221i) q^{93} +(-0.916407 + 1.58726i) q^{94} -4.08359i q^{96} +(1.25396 + 2.17191i) q^{97} +(-0.756779 - 1.31078i) q^{98} -2.36023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} + 6q^{3} - 2q^{4} - 18q^{6} + 10q^{7} + 12q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 2q^{2} + 6q^{3} - 2q^{4} - 18q^{6} + 10q^{7} + 12q^{8} + 4q^{9} + 8q^{13} - 4q^{14} - 2q^{16} + 18q^{17} - 40q^{18} - 12q^{19} + 6q^{22} + 6q^{23} + 12q^{24} + 10q^{26} + 8q^{28} + 8q^{29} - 4q^{32} - 18q^{33} + 20q^{36} - 2q^{37} + 12q^{41} - 42q^{42} - 18q^{43} - 42q^{46} - 16q^{47} - 6q^{48} - 12q^{49} - 8q^{51} + 16q^{52} - 18q^{54} + 12q^{56} - 28q^{57} + 22q^{58} + 12q^{59} - 28q^{61} + 12q^{62} - 4q^{63} + 8q^{64} + 12q^{66} - 30q^{67} + 12q^{68} + 16q^{69} + 12q^{72} - 16q^{73} - 10q^{74} + 54q^{76} + 18q^{78} + 16q^{79} + 8q^{81} - 6q^{82} + 24q^{83} + 30q^{84} + 54q^{87} + 42q^{88} - 24q^{89} + 28q^{91} + 8q^{93} - 32q^{94} - 2q^{97} + 24q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.109843 0.190254i 0.0776710 0.134530i −0.824574 0.565755i \(-0.808585\pi\)
0.902245 + 0.431224i \(0.141918\pi\)
\(3\) −1.38581 0.800098i −0.800098 0.461937i 0.0434075 0.999057i \(-0.486179\pi\)
−0.843505 + 0.537121i \(0.819512\pi\)
\(4\) 0.975869 + 1.69025i 0.487934 + 0.845127i
\(5\) 0 0
\(6\) −0.304444 + 0.175771i −0.124289 + 0.0717582i
\(7\) −0.166123 0.287734i −0.0627887 0.108753i 0.832922 0.553390i \(-0.186666\pi\)
−0.895711 + 0.444637i \(0.853333\pi\)
\(8\) 0.868145 0.306936
\(9\) −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 \(0.366225\pi\)
\(12\) 3.12316i 0.901579i
\(13\) 0.619491 + 3.55193i 0.171816 + 0.985129i
\(14\) −0.0729902 −0.0195074
\(15\) 0 0
\(16\) −1.85638 + 3.21534i −0.464094 + 0.803835i
\(17\) 4.38581 2.53215i 1.06372 0.614136i 0.137258 0.990535i \(-0.456171\pi\)
0.926458 + 0.376399i \(0.122838\pi\)
\(18\) −0.0965246 −0.0227511
\(19\) 1.96410 1.13397i 0.450596 0.260152i −0.257486 0.966282i \(-0.582894\pi\)
0.708082 + 0.706130i \(0.249561\pi\)
\(20\) 0 0
\(21\) 0.531659i 0.116018i
\(22\) 1.02201 0.590059i 0.217894 0.125801i
\(23\) 2.45880 + 1.41959i 0.512695 + 0.296005i 0.733941 0.679213i \(-0.237679\pi\)
−0.221246 + 0.975218i \(0.571012\pi\)
\(24\) −1.20308 0.694601i −0.245578 0.141785i
\(25\) 0 0
\(26\) 0.743818 + 0.272296i 0.145875 + 0.0534016i
\(27\) 5.50367i 1.05918i
\(28\) 0.324229 0.561581i 0.0612735 0.106129i
\(29\) −1.45174 + 2.51448i −0.269581 + 0.466928i −0.968754 0.248025i \(-0.920219\pi\)
0.699173 + 0.714953i \(0.253552\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i −0.871334 0.490691i \(-0.836744\pi\)
0.871334 0.490691i \(-0.163256\pi\)
\(32\) 1.27597 + 2.21004i 0.225561 + 0.390683i
\(33\) −4.29798 7.44432i −0.748182 1.29589i
\(34\) 1.11256i 0.190802i
\(35\) 0 0
\(36\) 0.428771 0.742653i 0.0714619 0.123776i
\(37\) 2.98601 5.17191i 0.490896 0.850257i −0.509049 0.860738i \(-0.670003\pi\)
0.999945 + 0.0104803i \(0.00333604\pi\)
\(38\) 0.498239i 0.0808250i
\(39\) 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 \(0.572538\pi\)
\(42\) 0.101151 + 0.0583993i 0.0156079 + 0.00901121i
\(43\) −4.38581 + 2.53215i −0.668830 + 0.386149i −0.795633 0.605779i \(-0.792862\pi\)
0.126803 + 0.991928i \(0.459528\pi\)
\(44\) 10.4844i 1.58058i
\(45\) 0 0
\(46\) 0.540166 0.311865i 0.0796432 0.0459820i
\(47\) −8.34285 −1.21693 −0.608465 0.793581i \(-0.708214\pi\)
−0.608465 + 0.793581i \(0.708214\pi\)
\(48\) 5.14517 2.97057i 0.742642 0.428764i
\(49\) 3.44481 5.96658i 0.492115 0.852368i
\(50\) 0 0
\(51\) −8.10387 −1.13477
\(52\) −5.39913 + 4.51332i −0.748724 + 0.625885i
\(53\) 1.56063i 0.214369i 0.994239 + 0.107184i \(0.0341835\pi\)
−0.994239 + 0.107184i \(0.965817\pi\)
\(54\) 1.04710 + 0.604542i 0.142492 + 0.0822678i
\(55\) 0 0
\(56\) −0.144219 0.249795i −0.0192721 0.0333802i
\(57\) −3.62916 −0.480694
\(58\) 0.318928 + 0.552399i 0.0418773 + 0.0725335i
\(59\) −2.34461 + 1.35366i −0.305242 + 0.176232i −0.644795 0.764355i \(-0.723057\pi\)
0.339553 + 0.940587i \(0.389724\pi\)
\(60\) 0 0
\(61\) −7.05193 12.2143i −0.902908 1.56388i −0.823702 0.567023i \(-0.808095\pi\)
−0.0792059 0.996858i \(-0.525238\pi\)
\(62\) −1.03957 0.600196i −0.132025 0.0762249i
\(63\) −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 0.356176 + 0.934419i \(0.384080\pi\)
−0.987319 + 0.158752i \(0.949253\pi\)
\(68\) 8.55995 + 4.94209i 1.03805 + 0.599316i
\(69\) −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 \(0.607832\pi\)
\(72\) −0.190720 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 0
\(76\) 3.83341 + 2.21322i 0.439722 + 0.253874i
\(77\) 1.78477i 0.203393i
\(78\) −0.812927 0.972477i −0.0920459 0.110111i
\(79\) −4.51851 −0.508372 −0.254186 0.967155i \(-0.581808\pi\)
−0.254186 + 0.967155i \(0.581808\pi\)
\(80\) 0 0
\(81\) 3.74441 6.48552i 0.416046 0.720613i
\(82\) 0.710039 0.409941i 0.0784107 0.0452704i
\(83\) 4.26371 0.468003 0.234001 0.972236i \(-0.424818\pi\)
0.234001 + 0.972236i \(0.424818\pi\)
\(84\) −0.898640 + 0.518830i −0.0980496 + 0.0566090i
\(85\) 0 0
\(86\) 1.11256i 0.119970i
\(87\) 4.02367 2.32306i 0.431382 0.249059i
\(88\) 4.03872 + 2.33176i 0.430529 + 0.248566i
\(89\) 2.79366 + 1.61292i 0.296127 + 0.170969i 0.640702 0.767790i \(-0.278644\pi\)
−0.344575 + 0.938759i \(0.611977\pi\)
\(90\) 0 0
\(91\) 0.919100 0.768307i 0.0963478 0.0805405i
\(92\) 5.54133i 0.577724i
\(93\) −4.37182 + 7.57221i −0.453336 + 0.785201i
\(94\) −0.916407 + 1.58726i −0.0945202 + 0.163714i
\(95\) 0 0
\(96\) 4.08359i 0.416780i
\(97\) 1.25396 + 2.17191i 0.127320 + 0.220524i 0.922637 0.385669i \(-0.126029\pi\)
−0.795318 + 0.606193i \(0.792696\pi\)
\(98\) −0.756779 1.31078i −0.0764462 0.132409i
\(99\) 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 \(-0.0458955\pi\)
\(102\) −0.890157 + 1.54180i −0.0881386 + 0.152661i
\(103\) 15.0247i 1.48043i −0.672370 0.740215i \(-0.734724\pi\)
0.672370 0.740215i \(-0.265276\pi\)
\(104\) 0.537808 + 3.08359i 0.0527364 + 0.302371i
\(105\) 0 0
\(106\) 0.296916 + 0.171425i 0.0288390 + 0.0166502i
\(107\) 11.3140 + 6.53215i 1.09377 + 0.631487i 0.934577 0.355761i \(-0.115778\pi\)
0.159190 + 0.987248i \(0.449112\pi\)
\(108\) −9.30260 + 5.37086i −0.895144 + 0.516811i
\(109\) 11.2325i 1.07587i −0.842985 0.537937i \(-0.819204\pi\)
0.842985 0.537937i \(-0.180796\pi\)
\(110\) 0 0
\(111\) −8.27607 + 4.77819i −0.785530 + 0.453526i
\(112\) 1.23355 0.116560
\(113\) 15.8862 9.17191i 1.49445 0.862821i 0.494470 0.869195i \(-0.335362\pi\)
0.999980 + 0.00637349i \(0.00202876\pi\)
\(114\) −0.398640 + 0.690464i −0.0373360 + 0.0646679i
\(115\) 0 0
\(116\) −5.66682 −0.526151
\(117\) 1.21545 1.01603i 0.112368 0.0939325i
\(118\) 0.594763i 0.0547524i
\(119\) −1.45717 0.841298i −0.133579 0.0771216i
\(120\) 0 0
\(121\) 8.92820 + 15.4641i 0.811655 + 1.40583i
\(122\) −3.09843 −0.280519
\(123\) −2.98601 5.17191i −0.269239 0.466336i
\(124\) 9.23572 5.33225i 0.829392 0.478850i
\(125\) 0 0
\(126\) 0.0160350 + 0.0277734i 0.00142851 + 0.00247425i
\(127\) 2.80589 + 1.61998i 0.248982 + 0.143750i 0.619298 0.785156i \(-0.287417\pi\)
−0.370316 + 0.928906i \(0.620751\pi\)
\(128\) −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
\(133\) −0.652566 0.376759i −0.0565846 0.0326692i
\(134\) 1.13493 + 1.96576i 0.0980430 + 0.169815i
\(135\) 0 0
\(136\) 3.80752 2.19827i 0.326492 0.188500i
\(137\) −8.99144 15.5736i −0.768190 1.33054i −0.938543 0.345162i \(-0.887824\pi\)
0.170353 0.985383i \(-0.445509\pi\)
\(138\) −0.998090 −0.0849631
\(139\) 5.99307 + 10.3803i 0.508325 + 0.880445i 0.999954 + 0.00964021i \(0.00306862\pi\)
−0.491628 + 0.870805i \(0.663598\pi\)
\(140\) 0 0
\(141\) 11.5616 + 6.67510i 0.973663 + 0.562144i
\(142\) 2.81140i 0.235928i
\(143\) −6.65821 + 18.1879i −0.556788 + 1.52095i
\(144\) 1.63129 0.135941
\(145\) 0 0
\(146\) −1.06430 + 1.84342i −0.0880819 + 0.152562i
\(147\) −9.54769 + 5.51236i −0.787481 + 0.454652i
\(148\) 11.6558 0.958101
\(149\) −2.95350 + 1.70520i −0.241960 + 0.139696i −0.616077 0.787686i \(-0.711279\pi\)
0.374117 + 0.927381i \(0.377946\pi\)
\(150\) 0 0
\(151\) 7.96141i 0.647890i 0.946076 + 0.323945i \(0.105009\pi\)
−0.946076 + 0.323945i \(0.894991\pi\)
\(152\) 1.70512 0.984454i 0.138304 0.0798498i
\(153\) −1.92701 1.11256i −0.155790 0.0899451i
\(154\) −0.339560 0.196045i −0.0273625 0.0157978i
\(155\) 0 0
\(156\) 11.0933 1.93477i 0.888172 0.154906i
\(157\) 16.4329i 1.31148i −0.754985 0.655742i \(-0.772356\pi\)
0.754985 0.655742i \(-0.227644\pi\)
\(158\) −0.496329 + 0.859667i −0.0394858 + 0.0683914i
\(159\) 1.24865 2.16273i 0.0990247 0.171516i
\(160\) 0 0
\(161\) 0.943307i 0.0743430i
\(162\) −0.822599 1.42478i −0.0646295 0.111942i
\(163\) −8.90361 15.4215i −0.697384 1.20791i −0.969370 0.245604i \(-0.921014\pi\)
0.271986 0.962301i \(-0.412320\pi\)
\(164\) 7.28398i 0.568784i
\(165\) 0 0
\(166\) 0.468341 0.811190i 0.0363503 0.0629605i
\(167\) −3.14683 + 5.45047i −0.243509 + 0.421770i −0.961711 0.274064i \(-0.911632\pi\)
0.718202 + 0.695834i \(0.244965\pi\)
\(168\) 0.461557i 0.0356099i
\(169\) −12.2325 + 4.40078i −0.940959 + 0.338522i
\(170\) 0 0
\(171\) −0.862975 0.498239i −0.0659933 0.0381013i
\(172\) −8.55995 4.94209i −0.652690 0.376831i
\(173\) 13.8349 7.98756i 1.05184 0.607283i 0.128679 0.991686i \(-0.458926\pi\)
0.923165 + 0.384404i \(0.125593\pi\)
\(174\) 1.02069i 0.0773786i
\(175\) 0 0
\(176\) −17.2722 + 9.97212i −1.30194 + 0.751677i
\(177\) 4.33225 0.325632
\(178\) 0.613729 0.354337i 0.0460010 0.0265587i
\(179\) −11.8087 + 20.4533i −0.882625 + 1.52875i −0.0342123 + 0.999415i \(0.510892\pi\)
−0.848412 + 0.529336i \(0.822441\pi\)
\(180\) 0 0
\(181\) 2.62590 0.195182 0.0975909 0.995227i \(-0.468886\pi\)
0.0975909 + 0.995227i \(0.468886\pi\)
\(182\) −0.0452168 0.259256i −0.00335169 0.0192174i
\(183\) 22.5689i 1.66834i
\(184\) 2.13459 + 1.23241i 0.157364 + 0.0908544i
\(185\) 0 0
\(186\) 0.960431 + 1.66351i 0.0704222 + 0.121975i
\(187\) 27.2045 1.98939
\(188\) −8.14153 14.1015i −0.593782 1.02846i
\(189\) 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 \(0.810098\pi\)
\(192\) 9.51343 + 5.49258i 0.686572 + 0.396393i
\(193\) −11.4105 + 19.7636i −0.821348 + 1.42262i 0.0833298 + 0.996522i \(0.473445\pi\)
−0.904678 + 0.426095i \(0.859889\pi\)
\(194\) 0.550955 0.0395563
\(195\) 0 0
\(196\) 13.4467 0.960480
\(197\) 0.321513 0.556877i 0.0229068 0.0396758i −0.854345 0.519707i \(-0.826041\pi\)
0.877252 + 0.480031i \(0.159375\pi\)
\(198\) −0.449045 0.259256i −0.0319122 0.0184245i
\(199\) −1.53342 2.65596i −0.108701 0.188276i 0.806543 0.591175i \(-0.201336\pi\)
−0.915244 + 0.402899i \(0.868003\pi\)
\(200\) 0 0
\(201\) 14.3185 8.26681i 1.00995 0.583096i
\(202\) −1.36719 2.36804i −0.0961952 0.166615i
\(203\) 0.964670 0.0677065
\(204\) −7.90831 13.6976i −0.553693 0.959024i
\(205\) 0 0
\(206\) −2.85852 1.65037i −0.199163 0.114987i
\(207\) 1.24746i 0.0867045i
\(208\) −12.5707 4.60185i −0.871620 0.319081i
\(209\) 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 \(0.0755796\pi\)
\(212\) −2.63786 + 1.52297i −0.181169 + 0.104598i
\(213\) 20.4782 1.40314
\(214\) 2.48554 1.43503i 0.169908 0.0980964i
\(215\) 0 0
\(216\) 4.77798i 0.325101i
\(217\) −1.57221 + 0.907714i −0.106728 + 0.0616197i
\(218\) −2.13703 1.23381i −0.144738 0.0835643i
\(219\) 13.4274 + 7.75232i 0.907341 + 0.523854i
\(220\) 0 0
\(221\) 11.7110 + 14.0095i 0.787767 + 0.942378i
\(222\) 2.09941i 0.140903i
\(223\) 5.12210 8.87174i 0.343001 0.594095i −0.641987 0.766715i \(-0.721890\pi\)
0.984989 + 0.172620i \(0.0552232\pi\)
\(224\) 0.423935 0.734278i 0.0283254 0.0490610i
\(225\) 0 0
\(226\) 4.02990i 0.268065i
\(227\) −3.52190 6.10012i −0.233757 0.404879i 0.725154 0.688587i \(-0.241769\pi\)
−0.958911 + 0.283708i \(0.908435\pi\)
\(228\) −3.54159 6.13421i −0.234547 0.406248i
\(229\) 1.32899i 0.0878219i −0.999035 0.0439109i \(-0.986018\pi\)
0.999035 0.0439109i \(-0.0139818\pi\)
\(230\) 0 0
\(231\) −1.42799 + 2.47335i −0.0939547 + 0.162734i
\(232\) −1.26032 + 2.18294i −0.0827440 + 0.143317i
\(233\) 1.24746i 0.0817238i −0.999165 0.0408619i \(-0.986990\pi\)
0.999165 0.0408619i \(-0.0130104\pi\)
\(234\) −0.0597962 0.342849i −0.00390900 0.0224127i
\(235\) 0 0
\(236\) −4.57606 2.64199i −0.297876 0.171979i
\(237\) 6.26180 + 3.61525i 0.406748 + 0.234836i
\(238\) −0.320121 + 0.184822i −0.0207504 + 0.0119802i
\(239\) 9.94207i 0.643099i −0.946893 0.321549i \(-0.895796\pi\)
0.946893 0.321549i \(-0.104204\pi\)
\(240\) 0 0
\(241\) −19.5608 + 11.2934i −1.26002 + 0.727475i −0.973079 0.230472i \(-0.925973\pi\)
−0.286944 + 0.957947i \(0.592640\pi\)
\(242\) 3.92282 0.252168
\(243\) 3.92086 2.26371i 0.251523 0.145217i
\(244\) 13.7635 23.8391i 0.881119 1.52614i
\(245\) 0 0
\(246\) −1.31197 −0.0836483
\(247\) 5.24455 + 6.27387i 0.333702 + 0.399197i
\(248\) 4.74363i 0.301221i
\(249\) −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 \(0.901855\pi\)
\(252\) −0.284915 −0.0179480
\(253\) 7.62577 + 13.2082i 0.479428 + 0.830394i
\(254\) 0.616417 0.355888i 0.0386774 0.0223304i
\(255\) 0 0
\(256\) −6.13860 10.6324i −0.383663 0.664523i
\(257\) −8.88007 5.12691i −0.553924 0.319808i 0.196779 0.980448i \(-0.436952\pi\)
−0.750703 + 0.660640i \(0.770285\pi\)
\(258\) 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
\(263\) 16.1574 + 9.32850i 0.996310 + 0.575220i 0.907154 0.420798i \(-0.138250\pi\)
0.0891555 + 0.996018i \(0.471583\pi\)
\(264\) −3.73127 6.46275i −0.229644 0.397754i
\(265\) 0 0
\(266\) −0.143360 + 0.0827690i −0.00878998 + 0.00507489i
\(267\) −2.58098 4.47040i −0.157954 0.273584i
\(268\) −20.1658 −1.23182
\(269\) 8.97894 + 15.5520i 0.547456 + 0.948221i 0.998448 + 0.0556934i \(0.0177369\pi\)
−0.450992 + 0.892528i \(0.648930\pi\)
\(270\) 0 0
\(271\) −26.7582 15.4488i −1.62544 0.938450i −0.985429 0.170086i \(-0.945595\pi\)
−0.640014 0.768363i \(-0.721071\pi\)
\(272\) 18.8025i 1.14007i
\(273\) −1.88842 + 0.329358i −0.114292 + 0.0199337i
\(274\) −3.95060 −0.238665
\(275\) 0 0
\(276\) 4.43361 7.67923i 0.266872 0.462235i
\(277\) −22.9536 + 13.2522i −1.37915 + 0.796250i −0.992057 0.125792i \(-0.959853\pi\)
−0.387089 + 0.922042i \(0.626519\pi\)
\(278\) 2.63320 0.157929
\(279\) −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 \(0.952565\pi\)
\(282\) 2.53993 1.46643i 0.151251 0.0873247i
\(283\) 10.9001 + 6.29317i 0.647943 + 0.374090i 0.787668 0.616100i \(-0.211288\pi\)
−0.139725 + 0.990190i \(0.544622\pi\)
\(284\) −21.6307 12.4885i −1.28355 0.741057i
\(285\) 0 0
\(286\) 2.72898 + 3.26458i 0.161368 + 0.193039i
\(287\) 1.23996i 0.0731926i
\(288\) 0.560626 0.971033i 0.0330352 0.0572187i
\(289\) 4.32355 7.48861i 0.254327 0.440507i
\(290\) 0 0
\(291\) 4.01315i 0.235255i
\(292\) −9.45541 16.3772i −0.553336 0.958406i
\(293\) −8.45880 14.6511i −0.494168 0.855925i 0.505809 0.862645i \(-0.331194\pi\)
−0.999977 + 0.00672072i \(0.997861\pi\)
\(294\) 2.42199i 0.141253i
\(295\) 0 0
\(296\) 2.59229 4.48997i 0.150674 0.260974i
\(297\) −14.7824 + 25.6038i −0.857759 + 1.48568i
\(298\) 0.749222i 0.0434012i
\(299\) −3.51908 + 9.61292i −0.203514 + 0.555929i
\(300\) 0 0
\(301\) 1.45717 + 0.841298i 0.0839899 + 0.0484916i
\(302\) 1.51469 + 0.874509i 0.0871608 + 0.0503223i
\(303\) −17.2488 + 9.95859i −0.990917 + 0.572106i
\(304\) 8.42034i 0.482940i
\(305\) 0 0
\(306\) −0.423339 + 0.244415i −0.0242007 + 0.0139723i
\(307\) 4.30426 0.245657 0.122828 0.992428i \(-0.460803\pi\)
0.122828 + 0.992428i \(0.460803\pi\)
\(308\) 3.01671 1.74170i 0.171893 0.0992425i
\(309\) −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 \(0.479905\pi\)
\(312\) 1.72188 4.70357i 0.0974820 0.266287i
\(313\) 7.20887i 0.407469i −0.979026 0.203735i \(-0.934692\pi\)
0.979026 0.203735i \(-0.0653080\pi\)
\(314\) −3.12642 1.80504i −0.176434 0.101864i
\(315\) 0 0
\(316\) −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
\(319\) −13.5073 + 7.79847i −0.756266 + 0.436630i
\(320\) 0 0
\(321\) −10.4527 18.1046i −0.583414 1.01050i
\(322\) −0.179468 0.103616i −0.0100014 0.00577430i
\(323\) 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
\(328\) 2.80589 + 1.61998i 0.154929 + 0.0894485i
\(329\) 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 \(0.484441\pi\)
\(332\) 4.16082 + 7.20676i 0.228355 + 0.395522i
\(333\) −2.62395 −0.143791
\(334\) 0.691317 + 1.19740i 0.0378272 + 0.0655186i
\(335\) 0 0
\(336\) −1.70947 0.986961i −0.0932590 0.0538431i
\(337\) 24.2186i 1.31927i −0.751586 0.659636i \(-0.770711\pi\)
0.751586 0.659636i \(-0.229289\pi\)
\(338\) −0.506387 + 2.81068i −0.0275438 + 0.152881i
\(339\) −29.3537 −1.59427
\(340\) 0 0
\(341\) 14.6761 25.4197i 0.794754 1.37655i
\(342\) −0.189584 + 0.109456i −0.0102515 + 0.00591873i
\(343\) −4.61478 −0.249174
\(344\) −3.80752 + 2.19827i −0.205288 + 0.118523i
\(345\) 0 0
\(346\) 3.50952i 0.188673i
\(347\) −5.43309 + 3.13680i −0.291664 + 0.168392i −0.638692 0.769463i \(-0.720524\pi\)
0.347028 + 0.937855i \(0.387191\pi\)
\(348\) 7.85314 + 4.53401i 0.420972 + 0.243049i
\(349\) 6.12275 + 3.53497i 0.327743 + 0.189223i 0.654839 0.755769i \(-0.272737\pi\)
−0.327095 + 0.944991i \(0.606070\pi\)
\(350\) 0 0
\(351\) −19.5487 + 3.40948i −1.04343 + 0.181984i
\(352\) 13.7085i 0.730666i
\(353\) −10.8949 + 18.8705i −0.579878 + 1.00438i 0.415615 + 0.909541i \(0.363566\pi\)
−0.995493 + 0.0948371i \(0.969767\pi\)
\(354\) 0.475869 0.824229i 0.0252921 0.0438073i
\(355\) 0 0
\(356\) 6.29598i 0.333687i
\(357\) 1.34624 + 2.33176i 0.0712506 + 0.123410i
\(358\) 2.59422 + 4.49332i 0.137109 + 0.237479i
\(359\) 23.9737i 1.26528i −0.774444 0.632642i \(-0.781971\pi\)
0.774444 0.632642i \(-0.218029\pi\)
\(360\) 0 0
\(361\) −6.92820 + 12.0000i −0.364642 + 0.631579i
\(362\) 0.288438 0.499589i 0.0151600 0.0262578i
\(363\) 28.5737i 1.49973i
\(364\) 2.19556 + 0.803745i 0.115078 + 0.0421277i
\(365\) 0 0
\(366\) 4.29384 + 2.47905i 0.224443 + 0.129582i
\(367\) −5.53505 3.19566i −0.288927 0.166812i 0.348531 0.937297i \(-0.386681\pi\)
−0.637458 + 0.770485i \(0.720014\pi\)
\(368\) −9.12892 + 5.27059i −0.475878 + 0.274748i
\(369\) 1.63977i 0.0853628i
\(370\) 0 0
\(371\) 0.449045 0.259256i 0.0233133 0.0134599i
\(372\) −17.0653 −0.884793
\(373\) 17.3899 10.0401i 0.900414 0.519855i 0.0230798 0.999734i \(-0.492653\pi\)
0.877335 + 0.479879i \(0.159319\pi\)
\(374\) 2.98823 5.17577i 0.154518 0.267633i
\(375\) 0 0
\(376\) −7.24280 −0.373519
\(377\) −9.83062 3.59878i −0.506302 0.185346i
\(378\) 0.401714i 0.0206619i
\(379\) 4.73007 + 2.73091i 0.242968 + 0.140277i 0.616540 0.787324i \(-0.288534\pi\)
−0.373572 + 0.927601i \(0.621867\pi\)
\(380\) 0 0
\(381\) −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 \(-0.212922\pi\)
−0.929300 + 0.369326i \(0.879589\pi\)
\(384\) 9.16297 5.29024i 0.467596 0.269966i
\(385\) 0 0
\(386\) 2.50675 + 4.34181i 0.127590 + 0.220992i
\(387\) 1.92701 + 1.11256i 0.0979554 + 0.0565546i
\(388\) −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
\(393\) −0.243436 0.140548i −0.0122797 0.00708971i
\(394\) −0.0706321 0.122338i −0.00355840 0.00616332i
\(395\) 0 0
\(396\) 3.98940 2.30328i 0.200475 0.115744i
\(397\) 14.0169 + 24.2780i 0.703487 + 1.21848i 0.967235 + 0.253884i \(0.0817081\pi\)
−0.263748 + 0.964592i \(0.584959\pi\)
\(398\) −0.673745 −0.0337718
\(399\) 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 \(0.476639\pi\)
\(402\) 3.63222i 0.181159i
\(403\) 19.4081 3.38496i 0.966788 0.168617i
\(404\) 24.2927 1.20861
\(405\) 0 0
\(406\) 0.105963 0.183533i 0.00525884 0.00910857i
\(407\) 27.7826 16.0403i 1.37713 0.795087i
\(408\) −7.03533 −0.348301
\(409\) 3.71328 2.14386i 0.183610 0.106007i −0.405378 0.914149i \(-0.632860\pi\)
0.588988 + 0.808142i \(0.299527\pi\)
\(410\) 0 0
\(411\) 28.7761i 1.41942i
\(412\) 25.3956 14.6622i 1.25115 0.722353i
\(413\) 0.778989 + 0.449749i 0.0383315 + 0.0221307i
\(414\) −0.237335 0.137025i −0.0116644 0.00673443i
\(415\) 0 0
\(416\) −7.05946 + 5.90125i −0.346119 + 0.289333i
\(417\) 19.1802i 0.939257i
\(418\) 1.33822 2.31787i 0.0654546 0.113371i
\(419\) 8.85578 15.3387i 0.432633 0.749343i −0.564466 0.825456i \(-0.690918\pi\)
0.997099 + 0.0761137i \(0.0242512\pi\)
\(420\) 0 0
\(421\) 12.8787i 0.627672i −0.949477 0.313836i \(-0.898386\pi\)
0.949477 0.313836i \(-0.101614\pi\)
\(422\) −0.900759 1.56016i −0.0438483 0.0759474i
\(423\) 1.83281 + 3.17453i 0.0891145 + 0.154351i
\(424\) 1.35485i 0.0657973i
\(425\) 0 0
\(426\) 2.24940 3.89607i 0.108984 0.188765i
\(427\) −2.34298 + 4.05816i −0.113385 + 0.196388i
\(428\) 25.4981i 1.23250i
\(429\) 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 \(0.593199\pi\)
\(432\) −17.6962 10.2169i −0.851408 0.491560i
\(433\) −1.20922 + 0.698141i −0.0581112 + 0.0335505i −0.528774 0.848763i \(-0.677348\pi\)
0.470663 + 0.882313i \(0.344015\pi\)
\(434\) 0.398826i 0.0191443i
\(435\) 0 0
\(436\) 18.9857 10.9614i 0.909251 0.524956i
\(437\) 6.43911 0.308024
\(438\) 2.94983 1.70308i 0.140948 0.0813765i
\(439\) −2.08090 + 3.60422i −0.0993159 + 0.172020i −0.911402 0.411518i \(-0.864999\pi\)
0.812086 + 0.583538i \(0.198332\pi\)
\(440\) 0 0
\(441\) −3.02711 −0.144148
\(442\) 3.95174 0.689221i 0.187965 0.0327829i
\(443\) 9.54563i 0.453526i −0.973950 0.226763i \(-0.927186\pi\)
0.973950 0.226763i \(-0.0728144\pi\)
\(444\) −16.1527 9.32578i −0.766574 0.442582i
\(445\) 0 0
\(446\) −1.12526 1.94900i −0.0532825 0.0922880i
\(447\) 5.45732 0.258122
\(448\) 1.14042 + 1.97526i 0.0538796 + 0.0933223i
\(449\) −18.8075 + 10.8585i −0.887582 + 0.512446i −0.873151 0.487450i \(-0.837927\pi\)
−0.0144310 + 0.999896i \(0.504594\pi\)
\(450\) 0 0
\(451\) 10.0239 + 17.3620i 0.472009 + 0.817544i
\(452\) 31.0057 + 17.9012i 1.45839 + 0.842000i
\(453\) 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 −0.915955 0.401282i \(-0.868565\pi\)
0.805498 + 0.592599i \(0.201898\pi\)
\(458\) −0.252845 0.145980i −0.0118147 0.00682122i
\(459\) 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 \(0.320124\pi\)
\(462\) 0.313710 + 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
\(465\) 0 0
\(466\) −0.237335 0.137025i −0.0109943 0.00634758i
\(467\) 18.2374i 0.843927i −0.906613 0.421963i \(-0.861341\pi\)
0.906613 0.421963i \(-0.138659\pi\)
\(468\) 2.90348 + 1.06290i 0.134213 + 0.0491325i
\(469\) 3.43285 0.158514
\(470\) 0 0
\(471\) −13.1479 + 22.7728i −0.605823 + 1.04932i
\(472\) −2.03546 + 1.17517i −0.0936897 + 0.0540918i
\(473\) −27.2045 −1.25086
\(474\) 1.37564 0.794223i 0.0631850 0.0364799i
\(475\) 0 0
\(476\) 3.28398i 0.150521i
\(477\) 0.593832 0.342849i 0.0271897 0.0156980i
\(478\) −1.89152 1.09207i −0.0865162 0.0499502i
\(479\) −30.4674 17.5904i −1.39209 0.803724i −0.398544 0.917149i \(-0.630485\pi\)
−0.993547 + 0.113425i \(0.963818\pi\)
\(480\) 0 0
\(481\) 20.2201 + 7.40214i 0.921957 + 0.337508i
\(482\) 4.96204i 0.226015i
\(483\) −0.754738 + 1.30724i −0.0343418 + 0.0594817i
\(484\) −17.4255 + 30.1819i −0.792069 + 1.37190i
\(485\) 0 0
\(486\) 0.994615i 0.0451166i
\(487\) 5.15200 + 8.92352i 0.233459 + 0.404363i 0.958824 0.284002i \(-0.0916621\pi\)
−0.725364 + 0.688365i \(0.758329\pi\)
\(488\) −6.12210 10.6038i −0.277134 0.480011i
\(489\) 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 \(0.0991336\pi\)
\(492\) 5.82790 10.0942i 0.262742 0.455083i
\(493\) 14.7041i 0.662238i
\(494\) 1.76971 0.308654i 0.0796230 0.0138870i
\(495\) 0 0
\(496\) 17.5689 + 10.1434i 0.788869 + 0.455454i
\(497\) 3.68222 + 2.12593i 0.165170 + 0.0953611i
\(498\) −1.29806 + 0.749437i −0.0581676 + 0.0335831i
\(499\) 23.9421i 1.07179i 0.844283 + 0.535897i \(0.180026\pi\)
−0.844283 + 0.535897i \(0.819974\pi\)
\(500\) 0 0
\(501\) 8.72181 5.03554i 0.389662 0.224971i
\(502\) −1.48692 −0.0663645
\(503\) −36.4980 + 21.0721i −1.62737 + 0.939560i −0.642490 + 0.766294i \(0.722099\pi\)
−0.984875 + 0.173266i \(0.944568\pi\)
\(504\) −0.0633661 + 0.109753i −0.00282255 + 0.00488880i
\(505\) 0 0
\(506\) 3.35056 0.148951
\(507\) 20.4729 + 3.68852i 0.909235 + 0.163813i
\(508\) 6.32355i 0.280562i
\(509\) 29.0640 + 16.7801i 1.28824 + 0.743765i 0.978340 0.207005i \(-0.0663715\pi\)
0.309899 + 0.950770i \(0.399705\pi\)
\(510\) 0 0
\(511\) 1.60960 + 2.78792i 0.0712047 + 0.123330i
\(512\) −15.9211 −0.703621
\(513\) 6.24102 + 10.8098i 0.275548 + 0.477263i
\(514\) −1.95084 + 1.12632i −0.0860477 + 0.0496796i
\(515\) 0 0
\(516\) 7.90831 + 13.6976i 0.348144 + 0.603003i
\(517\) −38.8120 22.4081i −1.70695 0.985508i
\(518\) −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
\(523\) −4.90132 2.82978i −0.214320 0.123738i 0.388998 0.921239i \(-0.372821\pi\)
−0.603317 + 0.797501i \(0.706155\pi\)
\(524\) 0.171425 + 0.296916i 0.00748872 + 0.0129708i
\(525\) 0 0
\(526\) 3.54958 2.04935i 0.154769 0.0893558i
\(527\) −13.8359 23.9645i −0.602702 1.04391i
\(528\) 31.9147 1.38891
\(529\) −7.46953 12.9376i −0.324762 0.562505i
\(530\) 0 0
\(531\) 1.03016 + 0.594763i 0.0447051 + 0.0258105i
\(532\) 1.47067i 0.0637616i
\(533\) −4.62577 + 12.6360i −0.200364 + 0.547327i
\(534\) −1.13402 −0.0490737
\(535\) 0 0
\(536\) −4.48494 + 7.76815i −0.193720 + 0.335533i
\(537\) 32.7293 18.8963i 1.41237 0.815433i
\(538\) 3.94511 0.170086
\(539\) 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 \(-0.107946\pi\)
\(542\) −5.87842 + 3.39391i −0.252500 + 0.145781i
\(543\) −3.63900 2.10098i −0.156165 0.0901616i
\(544\) 11.1923 + 6.46187i 0.479866 + 0.277051i
\(545\) 0 0
\(546\) −0.144769 + 0.395458i −0.00619552 + 0.0169240i
\(547\) 25.1765i 1.07647i 0.842795 + 0.538234i \(0.180908\pi\)
−0.842795 + 0.538234i \(0.819092\pi\)
\(548\) 17.5489 30.3956i 0.749653 1.29844i
\(549\) −3.09843 + 5.36665i −0.132238 + 0.229043i
\(550\) 0 0
\(551\) 6.58493i 0.280528i
\(552\) −1.97210 3.41577i −0.0839380 0.145385i
\(553\) 0.750630 + 1.30013i 0.0319200 + 0.0552871i
\(554\) 5.82269i 0.247382i
\(555\) 0 0
\(556\) −11.6969 + 20.2596i −0.496059 + 0.859199i
\(557\) 21.1744 36.6752i 0.897190 1.55398i 0.0661194 0.997812i \(-0.478938\pi\)
0.831071 0.556167i \(-0.187728\pi\)
\(558\) 0.527420i 0.0223275i
\(559\) −11.7110 14.0095i −0.495322 0.592537i
\(560\) 0 0
\(561\) −37.7002 21.7662i −1.59171 0.918971i
\(562\) 0.947022 + 0.546763i 0.0399477 + 0.0230638i
\(563\) 20.6032 11.8953i 0.868322 0.501326i 0.00153173 0.999999i \(-0.499512\pi\)
0.866790 + 0.498673i \(0.166179\pi\)
\(564\) 26.0561i 1.09716i
\(565\) 0 0
\(566\) 2.39461 1.38253i 0.100653 0.0581119i
\(567\) −2.48814 −0.104492
\(568\) −9.62148 + 5.55497i −0.403709 + 0.233081i
\(569\) 13.3710 23.1593i 0.560543 0.970889i −0.436906 0.899507i \(-0.643926\pi\)
0.997449 0.0713817i \(-0.0227408\pi\)
\(570\) 0 0
\(571\) 16.7159 0.699539 0.349769 0.936836i \(-0.386260\pi\)
0.349769 + 0.936836i \(0.386260\pi\)
\(572\) −37.2398 + 6.49498i −1.55707 + 0.271569i
\(573\) 3.22571i 0.134756i
\(574\) −0.235908 0.136202i −0.00984661 0.00568494i
\(575\) 0 0
\(576\) 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
\(579\) 31.6257 18.2591i 1.31432 0.758822i
\(580\) 0 0
\(581\) −0.708301 1.22681i −0.0293853 0.0508968i
\(582\) −0.763519 0.440818i −0.0316489 0.0182725i
\(583\) −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 −0.996802 0.0799116i \(-0.974536\pi\)
0.567606 + 0.823300i \(0.307870\pi\)
\(588\) −18.6346 10.7587i −0.768478 0.443681i
\(589\) −6.19615 10.7321i −0.255308 0.442206i
\(590\) 0 0
\(591\) −0.891111 + 0.514483i −0.0366554 + 0.0211630i
\(592\) 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 0
\(596\) −5.76446 3.32811i −0.236121 0.136325i
\(597\) 4.90755i 0.200853i
\(598\) 1.44235 + 1.72544i 0.0589822 + 0.0705583i
\(599\) 3.58040 0.146291 0.0731456 0.997321i \(-0.476696\pi\)
0.0731456 + 0.997321i \(0.476696\pi\)
\(600\) 0 0
\(601\) −10.6743 + 18.4885i −0.435414 + 0.754160i −0.997329 0.0730352i \(-0.976731\pi\)
0.561915 + 0.827195i \(0.310065\pi\)
\(602\) 0.320121 0.184822i 0.0130472 0.00753278i
\(603\) 4.53972 0.184872
\(604\) −13.4568 + 7.76929i −0.547550 + 0.316128i
\(605\) 0 0
\(606\) 4.37554i 0.177744i
\(607\) −2.85767 + 1.64988i −0.115989 + 0.0669665i −0.556872 0.830598i \(-0.687999\pi\)
0.440883 + 0.897565i \(0.354665\pi\)
\(608\) 5.01226 + 2.89383i 0.203274 + 0.117360i
\(609\) −1.33685 0.771830i −0.0541718 0.0312761i
\(610\) 0 0
\(611\) −5.16832 29.6332i −0.209088 1.19883i
\(612\) 4.34285i 0.175549i
\(613\) 4.94318 8.56183i 0.199653 0.345809i −0.748763 0.662838i \(-0.769352\pi\)
0.948416 + 0.317029i \(0.102685\pi\)
\(614\) 0.472795 0.818904i 0.0190804 0.0330483i
\(615\) 0 0
\(616\) 1.54944i 0.0624286i
\(617\) 22.8584 + 39.5920i 0.920246 + 1.59391i 0.799033 + 0.601287i \(0.205345\pi\)
0.121213 + 0.992626i \(0.461321\pi\)
\(618\) 2.64091 + 4.57419i 0.106233 + 0.184001i
\(619\) 19.9143i 0.800425i −0.916422 0.400212i \(-0.868936\pi\)
0.916422 0.400212i \(-0.131064\pi\)
\(620\) 0 0
\(621\) −7.81295 + 13.5324i −0.313523 + 0.543038i
\(622\) 0.244415 0.423339i 0.00980014 0.0169743i
\(623\) 1.07177i 0.0429397i
\(624\) 13.7386 + 16.4351i 0.549986 + 0.657930i
\(625\) 0 0
\(626\) −1.37152 0.791847i −0.0548169 0.0316486i
\(627\) −16.8833 9.74760i −0.674255 0.389282i
\(628\) 27.7757 16.0363i 1.10837 0.639918i
\(629\) 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 \(0.239503\pi\)
\(632\) −3.92272 −0.156038
\(633\) −11.3642 + 6.56112i −0.451686 + 0.260781i
\(634\) −0.0353305 + 0.0611942i −0.00140315 + 0.00243033i
\(635\) 0 0
\(636\) 4.87409 0.193270
\(637\) 23.3269 + 8.53948i 0.924246 + 0.338346i
\(638\) 3.42644i 0.135654i
\(639\) 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 \(0.923573\pi\)
\(642\) −4.59265 −0.181257
\(643\) 8.38581 + 14.5246i 0.330704 + 0.572796i 0.982650 0.185469i \(-0.0593805\pi\)
−0.651946 + 0.758265i \(0.726047\pi\)
\(644\) 1.59443 0.920544i 0.0628293 0.0362745i
\(645\) 0 0
\(646\) −1.26161 2.18518i −0.0496376 0.0859748i
\(647\) −2.59087 1.49584i −0.101858 0.0588075i 0.448206 0.893930i \(-0.352063\pi\)
−0.550063 + 0.835123i \(0.685396\pi\)
\(648\) 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
\(653\) −10.1016 5.83217i −0.395307 0.228230i 0.289150 0.957284i \(-0.406627\pi\)
−0.684457 + 0.729053i \(0.739961\pi\)
\(654\) 1.97434 + 3.41966i 0.0772028 + 0.133719i
\(655\) 0 0
\(656\) −11.9998 + 6.92810i −0.468514 + 0.270497i
\(657\) 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 \(-0.177894\pi\)
−0.883118 + 0.469150i \(0.844560\pi\)
\(660\) 0 0
\(661\) 10.6872 + 6.17028i 0.415686 + 0.239996i 0.693230 0.720717i \(-0.256187\pi\)
−0.277544 + 0.960713i \(0.589520\pi\)
\(662\) 3.65383i 0.142010i
\(663\) −5.02027 28.7844i −0.194971 1.11789i
\(664\) 3.70152 0.143647
\(665\) 0 0
\(666\) −0.288223 + 0.499217i −0.0111684 + 0.0193443i
\(667\) −7.13907 + 4.12174i −0.276426 + 0.159594i
\(668\) −12.2836 −0.475265
\(669\) −14.1965 + 8.19636i −0.548869 + 0.316890i
\(670\) 0 0
\(671\) 75.7634i 2.92481i
\(672\) −1.17499 + 0.678380i −0.0453262 + 0.0261691i
\(673\) −8.02481 4.63313i −0.309334 0.178594i 0.337295 0.941399i \(-0.390488\pi\)
−0.646628 + 0.762805i \(0.723822\pi\)
\(674\) −4.60770 2.66025i −0.177482 0.102469i
\(675\) 0 0
\(676\) −19.3757 16.3814i −0.745220 0.630053i
\(677\) 13.8984i 0.534158i 0.963675 + 0.267079i \(0.0860585\pi\)
−0.963675 + 0.267079i \(0.913941\pi\)
\(678\) −3.22431 + 5.58467i −0.123829 + 0.214478i
\(679\) 0.416622 0.721611i 0.0159885 0.0276929i
\(680\) 0 0
\(681\) 11.2715i 0.431924i
\(682\) −3.22414 5.58438i −0.123459 0.213837i
\(683\) 18.8756 + 32.6935i 0.722255 + 1.25098i 0.960094 + 0.279678i \(0.0902278\pi\)
−0.237838 + 0.971305i \(0.576439\pi\)
\(684\) 1.94486i 0.0743637i
\(685\) 0 0
\(686\) −0.506903 + 0.877981i −0.0193536 + 0.0335215i
\(687\) −1.06332 + 1.84172i −0.0405681 + 0.0702661i
\(688\) 18.8025i 0.716838i
\(689\) −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 \(0.676676\pi\)
\(692\) 27.0020 + 15.5896i 1.02646 + 0.592628i
\(693\) −0.679120 + 0.392090i −0.0257976 + 0.0148943i
\(694\) 1.37823i 0.0523168i
\(695\) 0 0
\(696\) 3.49312 2.01676i 0.132407 0.0764450i
\(697\) 18.9002 0.715897
\(698\) 1.34509 0.776587i 0.0509123 0.0293943i
\(699\) −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 \(0.626418\pi\)
\(702\) −1.49863 + 4.09373i −0.0565620 + 0.154508i
\(703\) 13.5442i 0.510830i
\(704\) −31.9363 18.4384i −1.20365 0.694925i
\(705\) 0 0
\(706\) 2.39347 + 4.14561i 0.0900794 + 0.156022i
\(707\) −4.13538 −0.155527
\(708\) 4.22770 + 7.32260i 0.158887 + 0.275200i
\(709\) −19.0021 + 10.9709i −0.713639 + 0.412020i −0.812407 0.583091i \(-0.801843\pi\)
0.0987679 + 0.995110i \(0.468510\pi\)
\(710\) 0 0
\(711\) 0.992658 + 1.71933i 0.0372276 + 0.0644801i
\(712\) 2.42530 + 1.40025i 0.0908919 + 0.0524764i
\(713\) 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
\(718\) −4.56110 2.63335i −0.170219 0.0982759i
\(719\) −19.4237 33.6429i −0.724384 1.25467i −0.959227 0.282636i \(-0.908791\pi\)
0.234844 0.972033i \(-0.424542\pi\)
\(720\) 0 0
\(721\) −4.32312 + 2.49596i −0.161002 + 0.0929543i
\(722\) 1.52204 + 2.63624i 0.0566443 + 0.0981108i
\(723\) 36.1434 1.34419
\(724\) 2.56254 + 4.43844i 0.0952359 + 0.164953i
\(725\) 0 0
\(726\) −5.43628 3.13864i −0.201759 0.116486i
\(727\) 30.6598i 1.13711i 0.822645 + 0.568555i \(0.192497\pi\)
−0.822645 + 0.568555i \(0.807503\pi\)
\(728\) 0.797912 0.667002i 0.0295726 0.0247207i
\(729\) −29.7112 −1.10042
\(730\) 0 0
\(731\) −12.8236 + 22.2110i −0.474296 + 0.821505i
\(732\) −38.1473 + 22.0243i −1.40996 + 0.814043i
\(733\) −24.3858 −0.900709 −0.450355 0.892850i \(-0.648702\pi\)
−0.450355 + 0.892850i \(0.648702\pi\)
\(734\) −1.21598 + 0.702045i −0.0448826 + 0.0259130i
\(735\) 0 0
\(736\) 7.24539i 0.267069i
\(737\) −48.0669 + 27.7515i −1.77057 + 1.02224i
\(738\) −0.311973 0.180117i −0.0114839 0.00663021i
\(739\) 33.1504 + 19.1394i 1.21946 + 0.704054i 0.964802 0.262977i \(-0.0847044\pi\)
0.254656 + 0.967032i \(0.418038\pi\)
\(740\) 0 0
\(741\) −2.24823 12.8905i −0.0825909 0.473546i
\(742\) 0.113910i 0.00418178i
\(743\) −20.0040 + 34.6479i −0.733874 + 1.27111i 0.221342 + 0.975196i \(0.428956\pi\)
−0.955216 + 0.295910i \(0.904377\pi\)
\(744\) −3.79537 + 6.57377i −0.139145 + 0.241006i
\(745\) 0 0
\(746\) 4.41134i 0.161511i
\(747\) −0.936681 1.62238i −0.0342714 0.0593598i
\(748\) 26.5480 + 45.9825i 0.970691 + 1.68129i
\(749\) 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 \(0.0119601\pi\)
\(752\) 15.4875 26.8251i 0.564770 0.978211i
\(753\) 10.8307i 0.394693i
\(754\) −1.76451 + 1.47502i −0.0642597 + 0.0537169i
\(755\) 0 0
\(756\) 3.09076 + 1.78445i 0.112410 + 0.0648998i
\(757\) 1.60083 + 0.924239i 0.0581831 + 0.0335920i 0.528809 0.848741i \(-0.322639\pi\)
−0.470626 + 0.882333i \(0.655972\pi\)
\(758\) 1.03914 0.599945i 0.0377431 0.0217910i
\(759\) 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 \(0.175745\pi\)
\(762\) −1.13898 −0.0412610
\(763\) −3.23196 + 1.86597i −0.117005 + 0.0675528i
\(764\) −1.96718 + 3.40725i −0.0711699 + 0.123270i
\(765\) 0 0
\(766\) −1.24513 −0.0449884
\(767\) −6.26058 7.48932i −0.226056 0.270424i
\(768\) 19.6459i 0.708911i
\(769\) 38.4078 + 22.1747i 1.38502 + 0.799641i 0.992749 0.120208i \(-0.0383562\pi\)
0.392271 + 0.919850i \(0.371690\pi\)
\(770\) 0 0
\(771\) 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 \(-0.304065\pi\)
−0.995776 + 0.0918181i \(0.970732\pi\)
\(774\) 0.423339 0.244415i 0.0152166 0.00878531i
\(775\) 0 0
\(776\) 1.08861 + 1.88554i 0.0390790 + 0.0676868i
\(777\) 2.74970 + 1.58754i 0.0986448 + 0.0569526i
\(778\) 1.16625 2.02001i 0.0418122 0.0724209i
\(779\) 8.46410 0.303258
\(780\) 0 0
\(781\) −68.7449 −2.45989
\(782\) 1.57938 2.73556i 0.0564784 0.0978235i
\(783\)