Properties

Label 325.2.m.c.49.2
Level $325$
Weight $2$
Character 325.49
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 49.2
Root \(-1.27597 + 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 325.49
Dual form 325.2.m.c.199.2

$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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 \(-0.191415\pi\)
−0.902245 + 0.431224i \(0.858082\pi\)
\(3\) 1.38581 0.800098i 0.800098 0.461937i −0.0434075 0.999057i \(-0.513821\pi\)
0.843505 + 0.537121i \(0.180488\pi\)
\(4\) 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 \(-0.813334\pi\)
0.895711 + 0.444637i \(0.146667\pi\)
\(8\) −0.868145 −0.306936
\(9\) −0.219687 + 0.380509i −0.0732290 + 0.126836i
\(10\) 0 0
\(11\) 4.65213 2.68591i 1.40267 0.809832i 0.408004 0.912980i \(-0.366225\pi\)
0.994666 + 0.103149i \(0.0328917\pi\)
\(12\) 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 \(-0.543829\pi\)
−0.926458 + 0.376399i \(0.877162\pi\)
\(18\) 0.0965246 0.0227511
\(19\) 1.96410 + 1.13397i 0.450596 + 0.260152i 0.708082 0.706130i \(-0.249561\pi\)
−0.257486 + 0.966282i \(0.582894\pi\)
\(20\) 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 \(-0.762321\pi\)
0.221246 + 0.975218i \(0.428988\pi\)
\(24\) −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 0.699173 0.714953i \(-0.253552\pi\)
−0.968754 + 0.248025i \(0.920219\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i 0.871334 + 0.490691i \(0.163256\pi\)
−0.871334 + 0.490691i \(0.836744\pi\)
\(32\) −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 \(-0.329997\pi\)
−0.999945 + 0.0104803i \(0.996664\pi\)
\(38\) 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 −0.225916 0.974147i \(-0.572538\pi\)
0.730678 + 0.682723i \(0.239204\pi\)
\(42\) −0.101151 + 0.0583993i −0.0156079 + 0.00901121i
\(43\) 4.38581 + 2.53215i 0.668830 + 0.386149i 0.795633 0.605779i \(-0.207138\pi\)
−0.126803 + 0.991928i \(0.540472\pi\)
\(44\) 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 \(-0.291786\pi\)
0.608465 + 0.793581i \(0.291786\pi\)
\(48\) −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 0.339553 0.940587i \(-0.389724\pi\)
−0.644795 + 0.764355i \(0.723057\pi\)
\(60\) 0 0
\(61\) −7.05193 + 12.2143i −0.902908 + 1.56388i −0.0792059 + 0.996858i \(0.525238\pi\)
−0.823702 + 0.567023i \(0.808095\pi\)
\(62\) 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 0.987319 + 0.158752i \(0.0507470\pi\)
−0.356176 + 0.934419i \(0.615920\pi\)
\(68\) −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 −0.332321 0.943166i \(-0.607832\pi\)
−0.982967 + 0.183785i \(0.941165\pi\)
\(72\) 0.190720 0.330337i 0.0224766 0.0389306i
\(73\) 9.68922 1.13404 0.567019 0.823705i \(-0.308097\pi\)
0.567019 + 0.823705i \(0.308097\pi\)
\(74\) −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 \(-0.575182\pi\)
−0.234001 + 0.972236i \(0.575182\pi\)
\(84\) −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 −0.344575 0.938759i \(-0.611977\pi\)
0.640702 + 0.767790i \(0.278644\pi\)
\(90\) 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 \(-0.873971\pi\)
0.795318 + 0.606193i \(0.207304\pi\)
\(98\) 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 0.989623 + 0.143686i \(0.0458955\pi\)
−0.370376 + 0.928882i \(0.620771\pi\)
\(102\) 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 \(-0.884222\pi\)
−0.159190 + 0.987248i \(0.550888\pi\)
\(108\) 9.30260 + 5.37086i 0.895144 + 0.516811i
\(109\) 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
\(112\) −1.23355 −0.116560
\(113\) −15.8862 9.17191i −1.49445 0.862821i −0.494470 0.869195i \(-0.664638\pi\)
−0.999980 + 0.00637349i \(0.997971\pi\)
\(114\) −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 \(-0.712583\pi\)
0.370316 + 0.928906i \(0.379249\pi\)
\(128\) 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 −0.170353 0.985383i \(-0.554491\pi\)
0.938543 0.345162i \(-0.112176\pi\)
\(138\) 0.998090 0.0849631
\(139\) 5.99307 10.3803i 0.508325 0.880445i −0.491628 0.870805i \(-0.663598\pi\)
0.999954 0.00964021i \(-0.00306862\pi\)
\(140\) 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 0.374117 0.927381i \(-0.377946\pi\)
−0.616077 + 0.787686i \(0.711279\pi\)
\(150\) 0 0
\(151\) 7.96141i 0.647890i −0.946076 0.323945i \(-0.894991\pi\)
0.946076 0.323945i \(-0.105009\pi\)
\(152\) −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 −0.271986 0.962301i \(-0.587680\pi\)
0.969370 0.245604i \(-0.0789862\pi\)
\(164\) 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 \(-0.0883682\pi\)
−0.718202 + 0.695834i \(0.755035\pi\)
\(168\) 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 \(-0.541074\pi\)
−0.923165 + 0.384404i \(0.874407\pi\)
\(174\) 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 −0.848412 0.529336i \(-0.822441\pi\)
−0.0342123 0.999415i \(-0.510892\pi\)
\(180\) 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 −0.827254 0.561828i \(-0.810098\pi\)
0.900184 + 0.435509i \(0.143432\pi\)
\(192\) −9.51343 + 5.49258i −0.686572 + 0.396393i
\(193\) 11.4105 + 19.7636i 0.821348 + 1.42262i 0.904678 + 0.426095i \(0.140111\pi\)
−0.0833298 + 0.996522i \(0.526555\pi\)
\(194\) 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 \(-0.173959\pi\)
−0.877252 + 0.480031i \(0.840625\pi\)
\(198\) 0.449045 0.259256i 0.0319122 0.0184245i
\(199\) −1.53342 + 2.65596i −0.108701 + 0.188276i −0.915244 0.402899i \(-0.868003\pi\)
0.806543 + 0.591175i \(0.201336\pi\)
\(200\) 0 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 0.971943 0.235215i \(-0.0755796\pi\)
−0.689674 + 0.724120i \(0.742246\pi\)
\(212\) 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 \(-0.278110\pi\)
−0.984989 + 0.172620i \(0.944777\pi\)
\(224\) 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 \(-0.758231\pi\)
0.958911 + 0.283708i \(0.0915646\pi\)
\(228\) 3.54159 6.13421i 0.234547 0.406248i
\(229\) 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
\(232\) 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 \(0.104204\pi\)
−0.946893 + 0.321549i \(0.895796\pi\)
\(240\) 0 0
\(241\) −19.5608 11.2934i −1.26002 0.727475i −0.286944 0.957947i \(-0.592640\pi\)
−0.973079 + 0.230472i \(0.925973\pi\)
\(242\) −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 −0.952841 0.303470i \(-0.901855\pi\)
0.739233 + 0.673449i \(0.235188\pi\)
\(252\) 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 \(-0.563048\pi\)
0.750703 + 0.660640i \(0.229715\pi\)
\(258\) −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 \(-0.861750\pi\)
−0.0891555 + 0.996018i \(0.528417\pi\)
\(264\) −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 −0.450992 0.892528i \(-0.648930\pi\)
0.998448 0.0556934i \(-0.0177369\pi\)
\(270\) 0 0
\(271\) −26.7582 + 15.4488i −1.62544 + 0.938450i −0.640014 + 0.768363i \(0.721071\pi\)
−0.985429 + 0.170086i \(0.945595\pi\)
\(272\) 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 \(-0.0401472\pi\)
0.387089 + 0.922042i \(0.373481\pi\)
\(278\) −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 \(-0.952565\pi\)
0.988917 0.148471i \(-0.0474352\pi\)
\(282\) −2.53993 1.46643i −0.151251 0.0873247i
\(283\) −10.9001 + 6.29317i −0.647943 + 0.374090i −0.787668 0.616100i \(-0.788712\pi\)
0.139725 + 0.990190i \(0.455378\pi\)
\(284\) −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 \(-0.668806\pi\)
0.999977 + 0.00672072i \(0.00213929\pi\)
\(294\) 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 \(-0.539197\pi\)
−0.122828 + 0.992428i \(0.539197\pi\)
\(308\) −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 \(-0.497125\pi\)
0.00903266 + 0.999959i \(0.497125\pi\)
\(318\) 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 0.0488600 0.998806i \(-0.484441\pi\)
−0.840561 + 0.541717i \(0.817775\pi\)
\(332\) −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 \(-0.279476\pi\)
−0.347028 + 0.937855i \(0.612809\pi\)
\(348\) −7.85314 + 4.53401i −0.420972 + 0.243049i
\(349\) 6.12275 3.53497i 0.327743 0.189223i −0.327095 0.944991i \(-0.606070\pi\)
0.654839 + 0.755769i \(0.272737\pi\)
\(350\) 0 0
\(351\) −19.5487 3.40948i −1.04343 0.181984i
\(352\) 13.7085i 0.730666i
\(353\) 10.8949 + 18.8705i 0.579878 + 1.00438i 0.995493 + 0.0948371i \(0.0302330\pi\)
−0.415615 + 0.909541i \(0.636434\pi\)
\(354\) 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 \(0.218029\pi\)
−0.774444 + 0.632642i \(0.781971\pi\)
\(360\) 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 \(-0.613319\pi\)
0.637458 + 0.770485i \(0.279986\pi\)
\(368\) 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 \(-0.507347\pi\)
−0.877335 + 0.479879i \(0.840681\pi\)
\(374\) 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 −0.373572 0.927601i \(-0.621867\pi\)
0.616540 + 0.787324i \(0.288534\pi\)
\(380\) 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 \(-0.787078\pi\)
0.929300 + 0.369326i \(0.120411\pi\)
\(384\) 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 0.263748 + 0.964592i \(0.415041\pi\)
−0.967235 + 0.253884i \(0.918292\pi\)
\(398\) 0.673745 0.0337718
\(399\) 0.602888 1.04423i 0.0301822 0.0522770i
\(400\) 0 0
\(401\) 19.4979 11.2571i 0.973680 0.562155i 0.0733241 0.997308i \(-0.476639\pi\)
0.900356 + 0.435154i \(0.143306\pi\)
\(402\) 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 0.588988 0.808142i \(-0.299527\pi\)
−0.405378 + 0.914149i \(0.632860\pi\)
\(410\) 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 0.997099 0.0761137i \(-0.0242512\pi\)
−0.564466 + 0.825456i \(0.690918\pi\)
\(420\) 0 0
\(421\) 12.8787i 0.627672i 0.949477 + 0.313836i \(0.101614\pi\)
−0.949477 + 0.313836i \(0.898386\pi\)
\(422\) 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 −0.288627 0.957442i \(-0.593199\pi\)
0.684855 + 0.728679i \(0.259866\pi\)
\(432\) 17.6962 10.2169i 0.851408 0.491560i
\(433\) 1.20922 + 0.698141i 0.0581112 + 0.0335505i 0.528774 0.848763i \(-0.322652\pi\)
−0.470663 + 0.882313i \(0.655985\pi\)
\(434\) 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 0.812086 0.583538i \(-0.198332\pi\)
−0.911402 + 0.411518i \(0.864999\pi\)
\(440\) 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 −0.0144310 0.999896i \(-0.504594\pi\)
−0.873151 + 0.487450i \(0.837927\pi\)
\(450\) 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 \(-0.131435\pi\)
−0.805498 + 0.592599i \(0.798102\pi\)
\(458\) 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 0.535498 0.844537i \(-0.320124\pi\)
−0.463641 + 0.886023i \(0.653457\pi\)
\(462\) −0.313710 + 0.543362i −0.0145951 + 0.0252795i
\(463\) −6.80200 −0.316116 −0.158058 0.987430i \(-0.550523\pi\)
−0.158058 + 0.987430i \(0.550523\pi\)
\(464\) −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 −0.993547 0.113425i \(-0.963818\pi\)
−0.398544 + 0.917149i \(0.630485\pi\)
\(480\) 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 \(-0.908338\pi\)
0.725364 + 0.688365i \(0.241671\pi\)
\(488\) 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 0.951894 0.306427i \(-0.0991336\pi\)
−0.741321 + 0.671151i \(0.765800\pi\)
\(492\) −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 \(-0.819974\pi\)
0.844283 0.535897i \(-0.180026\pi\)
\(500\) 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 0.984875 + 0.173266i \(0.0554320\pi\)
0.642490 + 0.766294i \(0.277901\pi\)
\(504\) −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 0.309899 0.950770i \(-0.399705\pi\)
0.978340 + 0.207005i \(0.0663715\pi\)
\(510\) 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 \(-0.627179\pi\)
0.603317 + 0.797501i \(0.293845\pi\)
\(524\) 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 \(0.107946\pi\)
−0.943047 + 0.332660i \(0.892054\pi\)
\(542\) 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 −0.831071 0.556167i \(-0.812272\pi\)
−0.0661194 0.997812i \(-0.521062\pi\)
\(558\) 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 \(-0.500488\pi\)
−0.866790 + 0.498673i \(0.833821\pi\)
\(564\) 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 0.997449 + 0.0713817i \(0.0227408\pi\)
−0.436906 + 0.899507i \(0.643926\pi\)
\(570\) 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 \(-0.358375\pi\)
0.430393 + 0.902642i \(0.358375\pi\)
\(578\) 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 \(-0.0254638\pi\)
−0.567606 + 0.823300i \(0.692130\pi\)
\(588\) 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 \(-0.351928\pi\)
0.448585 + 0.893740i \(0.351928\pi\)
\(594\) 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 0.561915 0.827195i \(-0.310065\pi\)
−0.997329 + 0.0730352i \(0.976731\pi\)
\(602\) −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 \(-0.312001\pi\)
−0.440883 + 0.897565i \(0.645335\pi\)
\(608\) −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 \(-0.230648\pi\)
−0.948416 + 0.317029i \(0.897315\pi\)
\(614\) 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 −0.121213 + 0.992626i \(0.538679\pi\)
−0.799033 + 0.601287i \(0.794655\pi\)
\(618\) −2.64091 + 4.57419i −0.106233 + 0.184001i
\(619\) 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
\(622\) −0.244415 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 0.730036 0.683409i \(-0.239503\pi\)
−0.226832 + 0.973934i \(0.572837\pi\)
\(632\) 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 −0.971314 0.237801i \(-0.923573\pi\)
0.691598 + 0.722282i \(0.256907\pi\)
\(642\) 4.59265 0.181257
\(643\) −8.38581 + 14.5246i −0.330704 + 0.572796i −0.982650 0.185469i \(-0.940620\pi\)
0.651946 + 0.758265i \(0.273953\pi\)
\(644\) 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 \(-0.647937\pi\)
0.550063 + 0.835123i \(0.314604\pi\)
\(648\) −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 \(-0.593373\pi\)
0.684457 + 0.729053i \(0.260039\pi\)
\(654\) 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 −0.883118 0.469150i \(-0.844560\pi\)
0.847855 + 0.530228i \(0.177894\pi\)
\(660\) 0 0
\(661\) 10.6872 6.17028i 0.415686 0.239996i −0.277544 0.960713i \(-0.589520\pi\)
0.693230 + 0.720717i \(0.256187\pi\)
\(662\) 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 \(-0.609512\pi\)
0.646628 + 0.762805i \(0.276178\pi\)
\(674\) −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 0.237838 + 0.971305i \(0.423561\pi\)
−0.960094 + 0.279678i \(0.909772\pi\)
\(684\) 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 −0.526981 0.849877i \(-0.676676\pi\)
0.472525 + 0.881317i \(0.343343\pi\)
\(692\) −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 0.0987679 0.995110i \(-0.468510\pi\)
−0.812407 + 0.583091i \(0.801843\pi\)
\(710\) 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 0.234844 + 0.972033i \(0.424542\pi\)
−0.959227 + 0.282636i \(0.908791\pi\)
\(720\) 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 \(-0.351298\pi\)
0.450355 + 0.892850i \(0.351298\pi\)
\(734\) −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 0.254656 0.967032i \(-0.418038\pi\)
0.964802 + 0.262977i \(0.0847044\pi\)
\(740\) 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 0.955216 + 0.295910i \(0.0956230\pi\)
−0.221342 + 0.975196i \(0.571044\pi\)
\(744\) −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 0.999294 0.0375648i \(-0.0119601\pi\)
−0.532179 + 0.846632i \(0.678627\pi\)
\(752\) −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 \(-0.677361\pi\)
0.470626 + 0.882333i \(0.344028\pi\)
\(758\) −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 0.851414 0.524494i \(-0.175745\pi\)
−0.0285179 + 0.999593i \(0.509079\pi\)
\(762\) 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 0.392271 0.919850i \(-0.371690\pi\)
0.992749 + 0.120208i \(0.0383562\pi\)
\(770\) 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 \(-0.695935\pi\)
0.995776 + 0.0918181i \(0.0292678\pi\)
\(774\) 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