Properties

Label 91.2.i.a.34.5
Level $91$
Weight $2$
Character 91.34
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 35 x^{8} + 295 x^{4} + 169\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 34.5
Root \(1.33026 - 1.33026i\) of defining polynomial
Character \(\chi\) \(=\) 91.34
Dual form 91.2.i.a.83.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.854638 + 0.854638i) q^{2} -2.27378i q^{3} -0.539189i q^{4} +(-0.612999 + 0.612999i) q^{5} +(1.94326 - 1.94326i) q^{6} +(0.0148122 + 2.64571i) q^{7} +(2.17009 - 2.17009i) q^{8} -2.17009 q^{9} +O(q^{10})\) \(q+(0.854638 + 0.854638i) q^{2} -2.27378i q^{3} -0.539189i q^{4} +(-0.612999 + 0.612999i) q^{5} +(1.94326 - 1.94326i) q^{6} +(0.0148122 + 2.64571i) q^{7} +(2.17009 - 2.17009i) q^{8} -2.17009 q^{9} -1.04778 q^{10} +(-1.85464 + 1.85464i) q^{11} -1.22600 q^{12} +(-0.104263 + 3.60404i) q^{13} +(-2.24846 + 2.27378i) q^{14} +(1.39383 + 1.39383i) q^{15} +2.63090 q^{16} -3.04726 q^{17} +(-1.85464 - 1.85464i) q^{18} +(0.104263 - 0.104263i) q^{19} +(0.330522 + 0.330522i) q^{20} +(6.01577 - 0.0336798i) q^{21} -3.17009 q^{22} -6.51026i q^{23} +(-4.93430 - 4.93430i) q^{24} +4.24846i q^{25} +(-3.16926 + 2.99104i) q^{26} -1.88704i q^{27} +(1.42654 - 0.00798659i) q^{28} -3.78765 q^{29} +2.38243i q^{30} +(6.77330 - 6.77330i) q^{31} +(-2.09171 - 2.09171i) q^{32} +(4.21704 + 4.21704i) q^{33} +(-2.60430 - 2.60430i) q^{34} +(-1.63090 - 1.61274i) q^{35} +1.17009i q^{36} +(-2.02472 + 2.02472i) q^{37} +0.178214 q^{38} +(8.19481 + 0.237071i) q^{39} +2.66052i q^{40} +(-2.27378 + 2.27378i) q^{41} +(5.17009 + 5.11252i) q^{42} +3.18342i q^{43} +(1.00000 + 1.00000i) q^{44} +(1.33026 - 1.33026i) q^{45} +(5.56391 - 5.56391i) q^{46} +(5.21678 + 5.21678i) q^{47} -5.98209i q^{48} +(-6.99956 + 0.0783777i) q^{49} +(-3.63090 + 3.63090i) q^{50} +6.92881i q^{51} +(1.94326 + 0.0562174i) q^{52} +3.43188 q^{53} +(1.61274 - 1.61274i) q^{54} -2.27378i q^{55} +(5.77356 + 5.70928i) q^{56} +(-0.237071 - 0.237071i) q^{57} +(-3.23707 - 3.23707i) q^{58} +(-9.15135 - 9.15135i) q^{59} +(0.751536 - 0.751536i) q^{60} -9.20756i q^{61} +11.5774 q^{62} +(-0.0321438 - 5.74142i) q^{63} -8.83710i q^{64} +(-2.14536 - 2.27319i) q^{65} +7.20809i q^{66} +(-1.04945 - 1.04945i) q^{67} +1.64305i q^{68} -14.8029 q^{69} +(-0.0155200 - 2.77213i) q^{70} +(-4.10310 - 4.10310i) q^{71} +(-4.70928 + 4.70928i) q^{72} +(6.92561 + 6.92561i) q^{73} -3.46081 q^{74} +9.66008 q^{75} +(-0.0562174 - 0.0562174i) q^{76} +(-4.93430 - 4.87936i) q^{77} +(6.80098 + 7.20620i) q^{78} +17.5958 q^{79} +(-1.61274 + 1.61274i) q^{80} -10.8010 q^{81} -3.88652 q^{82} +(-10.5474 + 10.5474i) q^{83} +(-0.0181598 - 3.24364i) q^{84} +(1.86797 - 1.86797i) q^{85} +(-2.72067 + 2.72067i) q^{86} +8.61230i q^{87} +8.04945i q^{88} +(3.39552 + 3.39552i) q^{89} +2.27378 q^{90} +(-9.53680 - 0.222465i) q^{91} -3.51026 q^{92} +(-15.4010 - 15.4010i) q^{93} +8.91692i q^{94} +0.127826i q^{95} +(-4.75609 + 4.75609i) q^{96} +(4.44330 - 4.44330i) q^{97} +(-6.04907 - 5.91510i) q^{98} +(4.02472 - 4.02472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - 8q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - 8q^{7} + 4q^{8} - 4q^{9} - 8q^{11} + 8q^{14} - 4q^{15} + 16q^{16} - 8q^{18} - 16q^{22} - 20q^{28} - 4q^{29} - 16q^{32} - 4q^{35} + 12q^{37} + 40q^{39} + 40q^{42} + 12q^{44} + 24q^{46} - 28q^{50} - 12q^{53} - 8q^{57} - 44q^{58} + 44q^{60} + 20q^{63} - 40q^{65} + 60q^{67} + 4q^{70} - 28q^{72} - 48q^{74} + 44q^{78} - 4q^{79} - 92q^{81} - 4q^{84} + 12q^{85} + 36q^{86} - 32q^{91} + 24q^{92} - 28q^{93} - 28q^{98} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.854638 + 0.854638i 0.604320 + 0.604320i 0.941456 0.337136i \(-0.109458\pi\)
−0.337136 + 0.941456i \(0.609458\pi\)
\(3\) 2.27378i 1.31277i −0.754427 0.656384i \(-0.772085\pi\)
0.754427 0.656384i \(-0.227915\pi\)
\(4\) 0.539189i 0.269594i
\(5\) −0.612999 + 0.612999i −0.274142 + 0.274142i −0.830765 0.556623i \(-0.812097\pi\)
0.556623 + 0.830765i \(0.312097\pi\)
\(6\) 1.94326 1.94326i 0.793333 0.793333i
\(7\) 0.0148122 + 2.64571i 0.00559850 + 0.999984i
\(8\) 2.17009 2.17009i 0.767241 0.767241i
\(9\) −2.17009 −0.723362
\(10\) −1.04778 −0.331338
\(11\) −1.85464 + 1.85464i −0.559194 + 0.559194i −0.929078 0.369884i \(-0.879398\pi\)
0.369884 + 0.929078i \(0.379398\pi\)
\(12\) −1.22600 −0.353915
\(13\) −0.104263 + 3.60404i −0.0289173 + 0.999582i
\(14\) −2.24846 + 2.27378i −0.600927 + 0.607694i
\(15\) 1.39383 + 1.39383i 0.359884 + 0.359884i
\(16\) 2.63090 0.657724
\(17\) −3.04726 −0.739070 −0.369535 0.929217i \(-0.620483\pi\)
−0.369535 + 0.929217i \(0.620483\pi\)
\(18\) −1.85464 1.85464i −0.437142 0.437142i
\(19\) 0.104263 0.104263i 0.0239195 0.0239195i −0.695046 0.718965i \(-0.744616\pi\)
0.718965 + 0.695046i \(0.244616\pi\)
\(20\) 0.330522 + 0.330522i 0.0739070 + 0.0739070i
\(21\) 6.01577 0.0336798i 1.31275 0.00734953i
\(22\) −3.17009 −0.675865
\(23\) 6.51026i 1.35748i −0.734377 0.678741i \(-0.762526\pi\)
0.734377 0.678741i \(-0.237474\pi\)
\(24\) −4.93430 4.93430i −1.00721 1.00721i
\(25\) 4.24846i 0.849693i
\(26\) −3.16926 + 2.99104i −0.621543 + 0.586592i
\(27\) 1.88704i 0.363162i
\(28\) 1.42654 0.00798659i 0.269590 0.00150932i
\(29\) −3.78765 −0.703350 −0.351675 0.936122i \(-0.614388\pi\)
−0.351675 + 0.936122i \(0.614388\pi\)
\(30\) 2.38243i 0.434971i
\(31\) 6.77330 6.77330i 1.21652 1.21652i 0.247679 0.968842i \(-0.420332\pi\)
0.968842 0.247679i \(-0.0796677\pi\)
\(32\) −2.09171 2.09171i −0.369765 0.369765i
\(33\) 4.21704 + 4.21704i 0.734093 + 0.734093i
\(34\) −2.60430 2.60430i −0.446635 0.446635i
\(35\) −1.63090 1.61274i −0.275672 0.272602i
\(36\) 1.17009i 0.195014i
\(37\) −2.02472 + 2.02472i −0.332863 + 0.332863i −0.853673 0.520810i \(-0.825630\pi\)
0.520810 + 0.853673i \(0.325630\pi\)
\(38\) 0.178214 0.0289101
\(39\) 8.19481 + 0.237071i 1.31222 + 0.0379618i
\(40\) 2.66052i 0.420665i
\(41\) −2.27378 + 2.27378i −0.355105 + 0.355105i −0.862005 0.506900i \(-0.830791\pi\)
0.506900 + 0.862005i \(0.330791\pi\)
\(42\) 5.17009 + 5.11252i 0.797762 + 0.788879i
\(43\) 3.18342i 0.485467i 0.970093 + 0.242733i \(0.0780440\pi\)
−0.970093 + 0.242733i \(0.921956\pi\)
\(44\) 1.00000 + 1.00000i 0.150756 + 0.150756i
\(45\) 1.33026 1.33026i 0.198304 0.198304i
\(46\) 5.56391 5.56391i 0.820354 0.820354i
\(47\) 5.21678 + 5.21678i 0.760946 + 0.760946i 0.976493 0.215548i \(-0.0691536\pi\)
−0.215548 + 0.976493i \(0.569154\pi\)
\(48\) 5.98209i 0.863440i
\(49\) −6.99956 + 0.0783777i −0.999937 + 0.0111968i
\(50\) −3.63090 + 3.63090i −0.513486 + 0.513486i
\(51\) 6.92881i 0.970227i
\(52\) 1.94326 + 0.0562174i 0.269482 + 0.00779595i
\(53\) 3.43188 0.471405 0.235703 0.971825i \(-0.424261\pi\)
0.235703 + 0.971825i \(0.424261\pi\)
\(54\) 1.61274 1.61274i 0.219466 0.219466i
\(55\) 2.27378i 0.306597i
\(56\) 5.77356 + 5.70928i 0.771525 + 0.762934i
\(57\) −0.237071 0.237071i −0.0314008 0.0314008i
\(58\) −3.23707 3.23707i −0.425048 0.425048i
\(59\) −9.15135 9.15135i −1.19140 1.19140i −0.976673 0.214731i \(-0.931113\pi\)
−0.214731 0.976673i \(-0.568887\pi\)
\(60\) 0.751536 0.751536i 0.0970229 0.0970229i
\(61\) 9.20756i 1.17891i −0.807802 0.589454i \(-0.799343\pi\)
0.807802 0.589454i \(-0.200657\pi\)
\(62\) 11.5774 1.47034
\(63\) −0.0321438 5.74142i −0.00404974 0.723351i
\(64\) 8.83710i 1.10464i
\(65\) −2.14536 2.27319i −0.266099 0.281954i
\(66\) 7.20809i 0.887254i
\(67\) −1.04945 1.04945i −0.128211 0.128211i 0.640090 0.768300i \(-0.278897\pi\)
−0.768300 + 0.640090i \(0.778897\pi\)
\(68\) 1.64305i 0.199249i
\(69\) −14.8029 −1.78206
\(70\) −0.0155200 2.77213i −0.00185500 0.331333i
\(71\) −4.10310 4.10310i −0.486949 0.486949i 0.420393 0.907342i \(-0.361892\pi\)
−0.907342 + 0.420393i \(0.861892\pi\)
\(72\) −4.70928 + 4.70928i −0.554993 + 0.554993i
\(73\) 6.92561 + 6.92561i 0.810581 + 0.810581i 0.984721 0.174140i \(-0.0557144\pi\)
−0.174140 + 0.984721i \(0.555714\pi\)
\(74\) −3.46081 −0.402311
\(75\) 9.66008 1.11545
\(76\) −0.0562174 0.0562174i −0.00644858 0.00644858i
\(77\) −4.93430 4.87936i −0.562316 0.556055i
\(78\) 6.80098 + 7.20620i 0.770060 + 0.815942i
\(79\) 17.5958 1.97968 0.989842 0.142168i \(-0.0454074\pi\)
0.989842 + 0.142168i \(0.0454074\pi\)
\(80\) −1.61274 + 1.61274i −0.180310 + 0.180310i
\(81\) −10.8010 −1.20011
\(82\) −3.88652 −0.429194
\(83\) −10.5474 + 10.5474i −1.15773 + 1.15773i −0.172763 + 0.984963i \(0.555269\pi\)
−0.984963 + 0.172763i \(0.944731\pi\)
\(84\) −0.0181598 3.24364i −0.00198139 0.353910i
\(85\) 1.86797 1.86797i 0.202610 0.202610i
\(86\) −2.72067 + 2.72067i −0.293377 + 0.293377i
\(87\) 8.61230i 0.923335i
\(88\) 8.04945i 0.858074i
\(89\) 3.39552 + 3.39552i 0.359924 + 0.359924i 0.863785 0.503861i \(-0.168088\pi\)
−0.503861 + 0.863785i \(0.668088\pi\)
\(90\) 2.27378 0.239678
\(91\) −9.53680 0.222465i −0.999728 0.0233207i
\(92\) −3.51026 −0.365970
\(93\) −15.4010 15.4010i −1.59701 1.59701i
\(94\) 8.91692i 0.919710i
\(95\) 0.127826i 0.0131147i
\(96\) −4.75609 + 4.75609i −0.485416 + 0.485416i
\(97\) 4.44330 4.44330i 0.451149 0.451149i −0.444587 0.895736i \(-0.646649\pi\)
0.895736 + 0.444587i \(0.146649\pi\)
\(98\) −6.04907 5.91510i −0.611049 0.597516i
\(99\) 4.02472 4.02472i 0.404500 0.404500i
\(100\) 2.29072 0.229072
\(101\) 1.16022 0.115446 0.0577231 0.998333i \(-0.481616\pi\)
0.0577231 + 0.998333i \(0.481616\pi\)
\(102\) −5.92162 + 5.92162i −0.586328 + 0.586328i
\(103\) −5.32104 −0.524298 −0.262149 0.965027i \(-0.584431\pi\)
−0.262149 + 0.965027i \(0.584431\pi\)
\(104\) 7.59483 + 8.04735i 0.744734 + 0.789107i
\(105\) −3.66701 + 3.70831i −0.357864 + 0.361894i
\(106\) 2.93302 + 2.93302i 0.284880 + 0.284880i
\(107\) 10.2485 0.990756 0.495378 0.868677i \(-0.335029\pi\)
0.495378 + 0.868677i \(0.335029\pi\)
\(108\) −1.01747 −0.0979063
\(109\) −5.85464 5.85464i −0.560773 0.560773i 0.368754 0.929527i \(-0.379784\pi\)
−0.929527 + 0.368754i \(0.879784\pi\)
\(110\) 1.94326 1.94326i 0.185283 0.185283i
\(111\) 4.60378 + 4.60378i 0.436972 + 0.436972i
\(112\) 0.0389695 + 6.96059i 0.00368227 + 0.657714i
\(113\) 5.74539 0.540481 0.270241 0.962793i \(-0.412897\pi\)
0.270241 + 0.962793i \(0.412897\pi\)
\(114\) 0.405220i 0.0379523i
\(115\) 3.99078 + 3.99078i 0.372142 + 0.372142i
\(116\) 2.04226i 0.189619i
\(117\) 0.226259 7.82109i 0.0209177 0.723060i
\(118\) 15.6422i 1.43998i
\(119\) −0.0451368 8.06217i −0.00413768 0.739058i
\(120\) 6.04945 0.552237
\(121\) 4.12064i 0.374603i
\(122\) 7.86913 7.86913i 0.712438 0.712438i
\(123\) 5.17009 + 5.17009i 0.466171 + 0.466171i
\(124\) −3.65209 3.65209i −0.327967 0.327967i
\(125\) −5.66930 5.66930i −0.507078 0.507078i
\(126\) 4.87936 4.93430i 0.434688 0.439583i
\(127\) 7.37629i 0.654540i 0.944931 + 0.327270i \(0.106129\pi\)
−0.944931 + 0.327270i \(0.893871\pi\)
\(128\) 3.36910 3.36910i 0.297789 0.297789i
\(129\) 7.23840 0.637305
\(130\) 0.109245 3.77626i 0.00958142 0.331200i
\(131\) 11.9642i 1.04532i −0.852543 0.522658i \(-0.824941\pi\)
0.852543 0.522658i \(-0.175059\pi\)
\(132\) 2.27378 2.27378i 0.197907 0.197907i
\(133\) 0.277394 + 0.274305i 0.0240531 + 0.0237853i
\(134\) 1.79380i 0.154960i
\(135\) 1.15676 + 1.15676i 0.0995577 + 0.0995577i
\(136\) −6.61282 + 6.61282i −0.567045 + 0.567045i
\(137\) 1.88357 1.88357i 0.160924 0.160924i −0.622052 0.782976i \(-0.713701\pi\)
0.782976 + 0.622052i \(0.213701\pi\)
\(138\) −12.6511 12.6511i −1.07694 1.07694i
\(139\) 6.36883i 0.540197i 0.962833 + 0.270098i \(0.0870563\pi\)
−0.962833 + 0.270098i \(0.912944\pi\)
\(140\) −0.869570 + 0.879362i −0.0734921 + 0.0743196i
\(141\) 11.8618 11.8618i 0.998946 0.998946i
\(142\) 7.01333i 0.588546i
\(143\) −6.49082 6.87756i −0.542790 0.575131i
\(144\) −5.70928 −0.475773
\(145\) 2.32183 2.32183i 0.192817 0.192817i
\(146\) 11.8378i 0.979701i
\(147\) 0.178214 + 15.9155i 0.0146988 + 1.31269i
\(148\) 1.09171 + 1.09171i 0.0897379 + 0.0897379i
\(149\) 13.3360 + 13.3360i 1.09253 + 1.09253i 0.995258 + 0.0972667i \(0.0310100\pi\)
0.0972667 + 0.995258i \(0.468990\pi\)
\(150\) 8.25587 + 8.25587i 0.674089 + 0.674089i
\(151\) 7.64229 7.64229i 0.621921 0.621921i −0.324102 0.946022i \(-0.605062\pi\)
0.946022 + 0.324102i \(0.105062\pi\)
\(152\) 0.452519i 0.0367041i
\(153\) 6.61282 0.534615
\(154\) −0.0469561 8.38713i −0.00378383 0.675854i
\(155\) 8.30406i 0.666998i
\(156\) 0.127826 4.41855i 0.0102343 0.353767i
\(157\) 21.0290i 1.67830i 0.543903 + 0.839148i \(0.316946\pi\)
−0.543903 + 0.839148i \(0.683054\pi\)
\(158\) 15.0381 + 15.0381i 1.19636 + 1.19636i
\(159\) 7.80335i 0.618846i
\(160\) 2.56443 0.202736
\(161\) 17.2243 0.0964315i 1.35746 0.00759987i
\(162\) −9.23093 9.23093i −0.725250 0.725250i
\(163\) −7.03612 + 7.03612i −0.551111 + 0.551111i −0.926762 0.375650i \(-0.877419\pi\)
0.375650 + 0.926762i \(0.377419\pi\)
\(164\) 1.22600 + 1.22600i 0.0957344 + 0.0957344i
\(165\) −5.17009 −0.402491
\(166\) −18.0284 −1.39927
\(167\) 12.0684 + 12.0684i 0.933884 + 0.933884i 0.997946 0.0640620i \(-0.0204055\pi\)
−0.0640620 + 0.997946i \(0.520406\pi\)
\(168\) 12.9816 13.1278i 1.00156 1.01283i
\(169\) −12.9783 0.751536i −0.998328 0.0578104i
\(170\) 3.19287 0.244882
\(171\) −0.226259 + 0.226259i −0.0173025 + 0.0173025i
\(172\) 1.71646 0.130879
\(173\) −7.48239 −0.568876 −0.284438 0.958694i \(-0.591807\pi\)
−0.284438 + 0.958694i \(0.591807\pi\)
\(174\) −7.36040 + 7.36040i −0.557990 + 0.557990i
\(175\) −11.2402 + 0.0629292i −0.849680 + 0.00475700i
\(176\) −4.87936 + 4.87936i −0.367796 + 0.367796i
\(177\) −20.8082 + 20.8082i −1.56404 + 1.56404i
\(178\) 5.80387i 0.435019i
\(179\) 22.7009i 1.69674i −0.529402 0.848371i \(-0.677584\pi\)
0.529402 0.848371i \(-0.322416\pi\)
\(180\) −0.717262 0.717262i −0.0534615 0.0534615i
\(181\) −1.91735 −0.142516 −0.0712579 0.997458i \(-0.522701\pi\)
−0.0712579 + 0.997458i \(0.522701\pi\)
\(182\) −7.96038 8.34063i −0.590063 0.618249i
\(183\) −20.9360 −1.54763
\(184\) −14.1278 14.1278i −1.04152 1.04152i
\(185\) 2.48231i 0.182503i
\(186\) 26.3246i 1.93021i
\(187\) 5.65157 5.65157i 0.413283 0.413283i
\(188\) 2.81283 2.81283i 0.205147 0.205147i
\(189\) 4.99257 0.0279513i 0.363156 0.00203316i
\(190\) −0.109245 + 0.109245i −0.00792546 + 0.00792546i
\(191\) −10.0072 −0.724095 −0.362047 0.932160i \(-0.617922\pi\)
−0.362047 + 0.932160i \(0.617922\pi\)
\(192\) −20.0936 −1.45013
\(193\) −10.2351 + 10.2351i −0.736741 + 0.736741i −0.971946 0.235205i \(-0.924424\pi\)
0.235205 + 0.971946i \(0.424424\pi\)
\(194\) 7.59483 0.545277
\(195\) −5.16874 + 4.87809i −0.370141 + 0.349327i
\(196\) 0.0422604 + 3.77409i 0.00301860 + 0.269578i
\(197\) 15.2690 + 15.2690i 1.08787 + 1.08787i 0.995748 + 0.0921223i \(0.0293651\pi\)
0.0921223 + 0.995748i \(0.470635\pi\)
\(198\) 6.87936 0.488895
\(199\) 22.4635 1.59240 0.796198 0.605036i \(-0.206841\pi\)
0.796198 + 0.605036i \(0.206841\pi\)
\(200\) 9.21953 + 9.21953i 0.651920 + 0.651920i
\(201\) −2.38622 + 2.38622i −0.168311 + 0.168311i
\(202\) 0.991567 + 0.991567i 0.0697664 + 0.0697664i
\(203\) −0.0561036 10.0210i −0.00393770 0.703339i
\(204\) 3.73594 0.261568
\(205\) 2.78765i 0.194698i
\(206\) −4.54756 4.54756i −0.316844 0.316844i
\(207\) 14.1278i 0.981952i
\(208\) −0.274305 + 9.48187i −0.0190196 + 0.657449i
\(209\) 0.386740i 0.0267513i
\(210\) −6.30323 + 0.0352892i −0.434964 + 0.00243518i
\(211\) −18.8504 −1.29772 −0.648859 0.760909i \(-0.724753\pi\)
−0.648859 + 0.760909i \(0.724753\pi\)
\(212\) 1.85043i 0.127088i
\(213\) −9.32956 + 9.32956i −0.639251 + 0.639251i
\(214\) 8.75872 + 8.75872i 0.598734 + 0.598734i
\(215\) −1.95143 1.95143i −0.133087 0.133087i
\(216\) −4.09505 4.09505i −0.278633 0.278633i
\(217\) 18.0205 + 17.8199i 1.22331 + 1.20969i
\(218\) 10.0072i 0.677772i
\(219\) 15.7473 15.7473i 1.06411 1.06411i
\(220\) −1.22600 −0.0826568
\(221\) 0.317716 10.9825i 0.0213719 0.738760i
\(222\) 7.86913i 0.528142i
\(223\) 4.32131 4.32131i 0.289376 0.289376i −0.547457 0.836833i \(-0.684404\pi\)
0.836833 + 0.547457i \(0.184404\pi\)
\(224\) 5.50307 5.56504i 0.367689 0.371830i
\(225\) 9.21953i 0.614636i
\(226\) 4.91023 + 4.91023i 0.326624 + 0.326624i
\(227\) −4.69031 + 4.69031i −0.311307 + 0.311307i −0.845416 0.534109i \(-0.820647\pi\)
0.534109 + 0.845416i \(0.320647\pi\)
\(228\) −0.127826 + 0.127826i −0.00846549 + 0.00846549i
\(229\) −0.264743 0.264743i −0.0174947 0.0174947i 0.698305 0.715800i \(-0.253938\pi\)
−0.715800 + 0.698305i \(0.753938\pi\)
\(230\) 6.82135i 0.449786i
\(231\) −11.0946 + 11.2195i −0.729972 + 0.738191i
\(232\) −8.21953 + 8.21953i −0.539639 + 0.539639i
\(233\) 6.16290i 0.403745i −0.979412 0.201872i \(-0.935297\pi\)
0.979412 0.201872i \(-0.0647026\pi\)
\(234\) 6.87756 6.49082i 0.449600 0.424319i
\(235\) −6.39576 −0.417214
\(236\) −4.93430 + 4.93430i −0.321196 + 0.321196i
\(237\) 40.0091i 2.59887i
\(238\) 6.85166 6.92881i 0.444127 0.449128i
\(239\) −5.63090 5.63090i −0.364232 0.364232i 0.501136 0.865369i \(-0.332916\pi\)
−0.865369 + 0.501136i \(0.832916\pi\)
\(240\) 3.66701 + 3.66701i 0.236705 + 0.236705i
\(241\) 1.11217 + 1.11217i 0.0716414 + 0.0716414i 0.742020 0.670378i \(-0.233868\pi\)
−0.670378 + 0.742020i \(0.733868\pi\)
\(242\) −3.52165 + 3.52165i −0.226380 + 0.226380i
\(243\) 18.8980i 1.21230i
\(244\) −4.96462 −0.317827
\(245\) 4.24268 4.33877i 0.271055 0.277194i
\(246\) 8.83710i 0.563433i
\(247\) 0.364897 + 0.386639i 0.0232178 + 0.0246012i
\(248\) 29.3973i 1.86673i
\(249\) 23.9825 + 23.9825i 1.51983 + 1.51983i
\(250\) 9.69040i 0.612874i
\(251\) 12.1069 0.764182 0.382091 0.924125i \(-0.375204\pi\)
0.382091 + 0.924125i \(0.375204\pi\)
\(252\) −3.09571 + 0.0173316i −0.195011 + 0.00109179i
\(253\) 12.0742 + 12.0742i 0.759097 + 0.759097i
\(254\) −6.30406 + 6.30406i −0.395552 + 0.395552i
\(255\) −4.24735 4.24735i −0.265980 0.265980i
\(256\) −11.9155 −0.744717
\(257\) 17.5759 1.09635 0.548176 0.836363i \(-0.315322\pi\)
0.548176 + 0.836363i \(0.315322\pi\)
\(258\) 6.18621 + 6.18621i 0.385137 + 0.385137i
\(259\) −5.38682 5.32684i −0.334721 0.330994i
\(260\) −1.22568 + 1.15676i −0.0760133 + 0.0717389i
\(261\) 8.21953 0.508776
\(262\) 10.2250 10.2250i 0.631705 0.631705i
\(263\) −14.5259 −0.895703 −0.447851 0.894108i \(-0.647811\pi\)
−0.447851 + 0.894108i \(0.647811\pi\)
\(264\) 18.3027 1.12645
\(265\) −2.10374 + 2.10374i −0.129232 + 0.129232i
\(266\) 0.00263975 + 0.471502i 0.000161853 + 0.0289097i
\(267\) 7.72067 7.72067i 0.472497 0.472497i
\(268\) −0.565851 + 0.565851i −0.0345648 + 0.0345648i
\(269\) 23.4152i 1.42765i −0.700324 0.713825i \(-0.746961\pi\)
0.700324 0.713825i \(-0.253039\pi\)
\(270\) 1.97721i 0.120329i
\(271\) 2.41653 + 2.41653i 0.146794 + 0.146794i 0.776684 0.629890i \(-0.216900\pi\)
−0.629890 + 0.776684i \(0.716900\pi\)
\(272\) −8.01703 −0.486104
\(273\) −0.505838 + 21.6846i −0.0306147 + 1.31241i
\(274\) 3.21953 0.194499
\(275\) −7.87936 7.87936i −0.475143 0.475143i
\(276\) 7.98157i 0.480434i
\(277\) 29.0722i 1.74678i −0.487020 0.873391i \(-0.661916\pi\)
0.487020 0.873391i \(-0.338084\pi\)
\(278\) −5.44304 + 5.44304i −0.326452 + 0.326452i
\(279\) −14.6987 + 14.6987i −0.879985 + 0.879985i
\(280\) −7.03897 + 0.0394083i −0.420659 + 0.00235509i
\(281\) 9.68455 9.68455i 0.577732 0.577732i −0.356546 0.934278i \(-0.616046\pi\)
0.934278 + 0.356546i \(0.116046\pi\)
\(282\) 20.2751 1.20737
\(283\) −4.30357 −0.255821 −0.127910 0.991786i \(-0.540827\pi\)
−0.127910 + 0.991786i \(0.540827\pi\)
\(284\) −2.21235 + 2.21235i −0.131279 + 0.131279i
\(285\) 0.290649 0.0172165
\(286\) 0.330522 11.4251i 0.0195442 0.675582i
\(287\) −6.04945 5.98209i −0.357088 0.353112i
\(288\) 4.53919 + 4.53919i 0.267474 + 0.267474i
\(289\) −7.71420 −0.453776
\(290\) 3.96864 0.233047
\(291\) −10.1031 10.1031i −0.592254 0.592254i
\(292\) 3.73421 3.73421i 0.218528 0.218528i
\(293\) 3.57373 + 3.57373i 0.208780 + 0.208780i 0.803749 0.594969i \(-0.202836\pi\)
−0.594969 + 0.803749i \(0.702836\pi\)
\(294\) −13.4497 + 13.7543i −0.784400 + 0.802166i
\(295\) 11.2195 0.653227
\(296\) 8.78765i 0.510772i
\(297\) 3.49978 + 3.49978i 0.203078 + 0.203078i
\(298\) 22.7948i 1.32047i
\(299\) 23.4633 + 0.678778i 1.35692 + 0.0392548i
\(300\) 5.20861i 0.300719i
\(301\) −8.42240 + 0.0471535i −0.485459 + 0.00271788i
\(302\) 13.0628 0.751678
\(303\) 2.63809i 0.151554i
\(304\) 0.274305 0.274305i 0.0157325 0.0157325i
\(305\) 5.64423 + 5.64423i 0.323188 + 0.323188i
\(306\) 5.65157 + 5.65157i 0.323079 + 0.323079i
\(307\) −8.59457 8.59457i −0.490518 0.490518i 0.417952 0.908469i \(-0.362748\pi\)
−0.908469 + 0.417952i \(0.862748\pi\)
\(308\) −2.63090 + 2.66052i −0.149909 + 0.151597i
\(309\) 12.0989i 0.688282i
\(310\) −7.09696 + 7.09696i −0.403080 + 0.403080i
\(311\) −22.5405 −1.27815 −0.639077 0.769143i \(-0.720683\pi\)
−0.639077 + 0.769143i \(0.720683\pi\)
\(312\) 18.2979 17.2690i 1.03592 0.977664i
\(313\) 4.30873i 0.243544i −0.992558 0.121772i \(-0.961142\pi\)
0.992558 0.121772i \(-0.0388576\pi\)
\(314\) −17.9722 + 17.9722i −1.01423 + 1.01423i
\(315\) 3.53919 + 3.49978i 0.199411 + 0.197190i
\(316\) 9.48747i 0.533712i
\(317\) 3.97107 + 3.97107i 0.223038 + 0.223038i 0.809776 0.586739i \(-0.199588\pi\)
−0.586739 + 0.809776i \(0.699588\pi\)
\(318\) 6.66904 6.66904i 0.373981 0.373981i
\(319\) 7.02472 7.02472i 0.393309 0.393309i
\(320\) 5.41714 + 5.41714i 0.302827 + 0.302827i
\(321\) 23.3028i 1.30063i
\(322\) 14.8029 + 14.6381i 0.824934 + 0.815749i
\(323\) −0.317716 + 0.317716i −0.0176782 + 0.0176782i
\(324\) 5.82377i 0.323543i
\(325\) −15.3116 0.442957i −0.849338 0.0245708i
\(326\) −12.0267 −0.666095
\(327\) −13.3122 + 13.3122i −0.736165 + 0.736165i
\(328\) 9.86861i 0.544903i
\(329\) −13.7248 + 13.8794i −0.756674 + 0.765194i
\(330\) −4.41855 4.41855i −0.243233 0.243233i
\(331\) 1.70928 + 1.70928i 0.0939503 + 0.0939503i 0.752520 0.658570i \(-0.228838\pi\)
−0.658570 + 0.752520i \(0.728838\pi\)
\(332\) 5.68703 + 5.68703i 0.312117 + 0.312117i
\(333\) 4.39383 4.39383i 0.240780 0.240780i
\(334\) 20.6283i 1.12873i
\(335\) 1.28662 0.0702957
\(336\) 15.8269 0.0886081i 0.863427 0.00483397i
\(337\) 23.1327i 1.26012i −0.776546 0.630061i \(-0.783030\pi\)
0.776546 0.630061i \(-0.216970\pi\)
\(338\) −10.4494 11.7340i −0.568373 0.638245i
\(339\) 13.0638i 0.709527i
\(340\) −1.00719 1.00719i −0.0546224 0.0546224i
\(341\) 25.1240i 1.36054i
\(342\) −0.386740 −0.0209125
\(343\) −0.311044 18.5176i −0.0167948 0.999859i
\(344\) 6.90829 + 6.90829i 0.372470 + 0.372470i
\(345\) 9.07417 9.07417i 0.488537 0.488537i
\(346\) −6.39473 6.39473i −0.343783 0.343783i
\(347\) −8.60424 −0.461900 −0.230950 0.972966i \(-0.574183\pi\)
−0.230950 + 0.972966i \(0.574183\pi\)
\(348\) 4.64366 0.248926
\(349\) −19.0680 19.0680i −1.02069 1.02069i −0.999781 0.0209053i \(-0.993345\pi\)
−0.0209053 0.999781i \(-0.506655\pi\)
\(350\) −9.66008 9.55252i −0.516353 0.510604i
\(351\) 6.80098 + 0.196748i 0.363010 + 0.0105017i
\(352\) 7.75872 0.413541
\(353\) −4.81231 + 4.81231i −0.256133 + 0.256133i −0.823479 0.567346i \(-0.807970\pi\)
0.567346 + 0.823479i \(0.307970\pi\)
\(354\) −35.5669 −1.89036
\(355\) 5.03040 0.266986
\(356\) 1.83083 1.83083i 0.0970336 0.0970336i
\(357\) −18.3316 + 0.102631i −0.970212 + 0.00543182i
\(358\) 19.4010 19.4010i 1.02538 1.02538i
\(359\) −12.5506 + 12.5506i −0.662394 + 0.662394i −0.955944 0.293549i \(-0.905163\pi\)
0.293549 + 0.955944i \(0.405163\pi\)
\(360\) 5.77356i 0.304293i
\(361\) 18.9783i 0.998856i
\(362\) −1.63864 1.63864i −0.0861252 0.0861252i
\(363\) 9.36943 0.491768
\(364\) −0.119951 + 5.14214i −0.00628713 + 0.269521i
\(365\) −8.49079 −0.444428
\(366\) −17.8927 17.8927i −0.935266 0.935266i
\(367\) 22.8806i 1.19436i −0.802109 0.597178i \(-0.796289\pi\)
0.802109 0.597178i \(-0.203711\pi\)
\(368\) 17.1278i 0.892850i
\(369\) 4.93430 4.93430i 0.256870 0.256870i
\(370\) 2.12147 2.12147i 0.110290 0.110290i
\(371\) 0.0508338 + 9.07976i 0.00263916 + 0.471398i
\(372\) −8.30406 + 8.30406i −0.430545 + 0.430545i
\(373\) 10.5041 0.543883 0.271941 0.962314i \(-0.412334\pi\)
0.271941 + 0.962314i \(0.412334\pi\)
\(374\) 9.66008 0.499511
\(375\) −12.8908 + 12.8908i −0.665676 + 0.665676i
\(376\) 22.6417 1.16766
\(377\) 0.394912 13.6509i 0.0203390 0.703055i
\(378\) 4.29072 + 4.24295i 0.220691 + 0.218234i
\(379\) 3.64229 + 3.64229i 0.187092 + 0.187092i 0.794438 0.607346i \(-0.207766\pi\)
−0.607346 + 0.794438i \(0.707766\pi\)
\(380\) 0.0689224 0.00353564
\(381\) 16.7721 0.859260
\(382\) −8.55252 8.55252i −0.437585 0.437585i
\(383\) −24.5591 + 24.5591i −1.25491 + 1.25491i −0.301419 + 0.953492i \(0.597460\pi\)
−0.953492 + 0.301419i \(0.902540\pi\)
\(384\) −7.66061 7.66061i −0.390929 0.390929i
\(385\) 6.01577 0.0336798i 0.306592 0.00171648i
\(386\) −17.4947 −0.890455
\(387\) 6.90829i 0.351168i
\(388\) −2.39578 2.39578i −0.121627 0.121627i
\(389\) 6.48974i 0.329043i 0.986374 + 0.164521i \(0.0526080\pi\)
−0.986374 + 0.164521i \(0.947392\pi\)
\(390\) −8.58639 0.248399i −0.434789 0.0125782i
\(391\) 19.8385i 1.00327i
\(392\) −15.0196 + 15.3597i −0.758603 + 0.775784i
\(393\) −27.2039 −1.37226
\(394\) 26.0989i 1.31484i
\(395\) −10.7862 + 10.7862i −0.542714 + 0.542714i
\(396\) −2.17009 2.17009i −0.109051 0.109051i
\(397\) −6.89530 6.89530i −0.346065 0.346065i 0.512576 0.858642i \(-0.328691\pi\)
−0.858642 + 0.512576i \(0.828691\pi\)
\(398\) 19.1982 + 19.1982i 0.962317 + 0.962317i
\(399\) 0.623710 0.630733i 0.0312245 0.0315761i
\(400\) 11.1773i 0.558864i
\(401\) 9.02279 9.02279i 0.450576 0.450576i −0.444969 0.895546i \(-0.646785\pi\)
0.895546 + 0.444969i \(0.146785\pi\)
\(402\) −4.07870 −0.203427
\(403\) 23.7051 + 25.1175i 1.18083 + 1.25119i
\(404\) 0.625577i 0.0311236i
\(405\) 6.62099 6.62099i 0.329000 0.329000i
\(406\) 8.51640 8.61230i 0.422662 0.427421i
\(407\) 7.51026i 0.372270i
\(408\) 15.0361 + 15.0361i 0.744399 + 0.744399i
\(409\) 2.86088 2.86088i 0.141461 0.141461i −0.632830 0.774291i \(-0.718107\pi\)
0.774291 + 0.632830i \(0.218107\pi\)
\(410\) 2.38243 2.38243i 0.117660 0.117660i
\(411\) −4.28282 4.28282i −0.211256 0.211256i
\(412\) 2.86905i 0.141348i
\(413\) 24.0763 24.3474i 1.18472 1.19806i
\(414\) −12.0742 + 12.0742i −0.593413 + 0.593413i
\(415\) 12.9311i 0.634762i
\(416\) 7.75670 7.32052i 0.380303 0.358918i
\(417\) 14.4813 0.709154
\(418\) −0.330522 + 0.330522i −0.0161664 + 0.0161664i
\(419\) 35.4097i 1.72988i 0.501878 + 0.864939i \(0.332643\pi\)
−0.501878 + 0.864939i \(0.667357\pi\)
\(420\) 1.99948 + 1.97721i 0.0975645 + 0.0964781i
\(421\) 18.9307 + 18.9307i 0.922628 + 0.922628i 0.997215 0.0745864i \(-0.0237636\pi\)
−0.0745864 + 0.997215i \(0.523764\pi\)
\(422\) −16.1103 16.1103i −0.784237 0.784237i
\(423\) −11.3209 11.3209i −0.550439 0.550439i
\(424\) 7.44748 7.44748i 0.361682 0.361682i
\(425\) 12.9462i 0.627982i
\(426\) −15.9468 −0.772624
\(427\) 24.3605 0.136385i 1.17889 0.00660011i
\(428\) 5.52586i 0.267102i
\(429\) −15.6381 + 14.7587i −0.755014 + 0.712558i
\(430\) 3.33553i 0.160854i
\(431\) 12.6042 + 12.6042i 0.607125 + 0.607125i 0.942194 0.335069i \(-0.108760\pi\)
−0.335069 + 0.942194i \(0.608760\pi\)
\(432\) 4.96462i 0.238860i
\(433\) 14.3392 0.689098 0.344549 0.938768i \(-0.388032\pi\)
0.344549 + 0.938768i \(0.388032\pi\)
\(434\) 0.171488 + 30.6305i 0.00823167 + 1.47031i
\(435\) −5.27933 5.27933i −0.253125 0.253125i
\(436\) −3.15676 + 3.15676i −0.151181 + 0.151181i
\(437\) −0.678778 0.678778i −0.0324704 0.0324704i
\(438\) 26.9165 1.28612
\(439\) −19.9812 −0.953651 −0.476826 0.878998i \(-0.658213\pi\)
−0.476826 + 0.878998i \(0.658213\pi\)
\(440\) −4.93430 4.93430i −0.235234 0.235234i
\(441\) 15.1897 0.170086i 0.723317 0.00809936i
\(442\) 9.65756 9.11450i 0.459363 0.433532i
\(443\) −5.63809 −0.267874 −0.133937 0.990990i \(-0.542762\pi\)
−0.133937 + 0.990990i \(0.542762\pi\)
\(444\) 2.48231 2.48231i 0.117805 0.117805i
\(445\) −4.16290 −0.197340
\(446\) 7.38630 0.349751
\(447\) 30.3231 30.3231i 1.43423 1.43423i
\(448\) 23.3804 0.130897i 1.10462 0.00618431i
\(449\) −12.9060 + 12.9060i −0.609073 + 0.609073i −0.942704 0.333631i \(-0.891726\pi\)
0.333631 + 0.942704i \(0.391726\pi\)
\(450\) 7.87936 7.87936i 0.371437 0.371437i
\(451\) 8.43409i 0.397146i
\(452\) 3.09785i 0.145711i
\(453\) −17.3769 17.3769i −0.816438 0.816438i
\(454\) −8.01703 −0.376258
\(455\) 5.98242 5.70968i 0.280460 0.267674i
\(456\) −1.02893 −0.0481840
\(457\) 6.96687 + 6.96687i 0.325896 + 0.325896i 0.851024 0.525127i \(-0.175982\pi\)
−0.525127 + 0.851024i \(0.675982\pi\)
\(458\) 0.452519i 0.0211448i
\(459\) 5.75031i 0.268402i
\(460\) 2.15179 2.15179i 0.100328 0.100328i
\(461\) 7.20809 7.20809i 0.335714 0.335714i −0.519037 0.854752i \(-0.673709\pi\)
0.854752 + 0.519037i \(0.173709\pi\)
\(462\) −19.0705 + 0.106768i −0.887240 + 0.00496729i
\(463\) −4.06084 + 4.06084i −0.188723 + 0.188723i −0.795144 0.606421i \(-0.792605\pi\)
0.606421 + 0.795144i \(0.292605\pi\)
\(464\) −9.96493 −0.462610
\(465\) 18.8816 0.875614
\(466\) 5.26705 5.26705i 0.243991 0.243991i
\(467\) −17.3673 −0.803665 −0.401832 0.915713i \(-0.631627\pi\)
−0.401832 + 0.915713i \(0.631627\pi\)
\(468\) −4.21704 0.121997i −0.194933 0.00563929i
\(469\) 2.76099 2.79208i 0.127491 0.128926i
\(470\) −5.46606 5.46606i −0.252131 0.252131i
\(471\) 47.8154 2.20322
\(472\) −39.7184 −1.82819
\(473\) −5.90409 5.90409i −0.271470 0.271470i
\(474\) 34.1933 34.1933i 1.57055 1.57055i
\(475\) 0.442957 + 0.442957i 0.0203243 + 0.0203243i
\(476\) −4.34703 + 0.0243372i −0.199246 + 0.00111550i
\(477\) −7.44748 −0.340997
\(478\) 9.62475i 0.440226i
\(479\) 9.88634 + 9.88634i 0.451719 + 0.451719i 0.895925 0.444206i \(-0.146514\pi\)
−0.444206 + 0.895925i \(0.646514\pi\)
\(480\) 5.83096i 0.266146i
\(481\) −7.08609 7.50830i −0.323098 0.342349i
\(482\) 1.90101i 0.0865887i
\(483\) −0.219264 39.1642i −0.00997687 1.78203i
\(484\) 2.22180 0.100991
\(485\) 5.44748i 0.247357i
\(486\) −16.1509 + 16.1509i −0.732620 + 0.732620i
\(487\) −12.6092 12.6092i −0.571375 0.571375i 0.361137 0.932513i \(-0.382389\pi\)
−0.932513 + 0.361137i \(0.882389\pi\)
\(488\) −19.9812 19.9812i −0.904507 0.904507i
\(489\) 15.9986 + 15.9986i 0.723482 + 0.723482i
\(490\) 7.33403 0.0821230i 0.331318 0.00370994i
\(491\) 1.72487i 0.0778425i 0.999242 + 0.0389212i \(0.0123921\pi\)
−0.999242 + 0.0389212i \(0.987608\pi\)
\(492\) 2.78765 2.78765i 0.125677 0.125677i
\(493\) 11.5420 0.519824
\(494\) −0.0185811 + 0.642291i −0.000836003 + 0.0288980i
\(495\) 4.93430i 0.221780i
\(496\) 17.8199 17.8199i 0.800135 0.800135i
\(497\) 10.7948 10.9164i 0.484215 0.489667i
\(498\) 40.9926i 1.83692i
\(499\) −27.5555 27.5555i −1.23355 1.23355i −0.962589 0.270964i \(-0.912657\pi\)
−0.270964 0.962589i \(-0.587343\pi\)
\(500\) −3.05682 + 3.05682i −0.136705 + 0.136705i
\(501\) 27.4410 27.4410i 1.22597 1.22597i
\(502\) 10.3470 + 10.3470i 0.461811 + 0.461811i
\(503\) 20.8862i 0.931272i 0.884976 + 0.465636i \(0.154174\pi\)
−0.884976 + 0.465636i \(0.845826\pi\)
\(504\) −12.5291 12.3896i −0.558092 0.551878i
\(505\) −0.711213 + 0.711213i −0.0316486 + 0.0316486i
\(506\) 20.6381i 0.917475i
\(507\) −1.70883 + 29.5097i −0.0758918 + 1.31057i
\(508\) 3.97721 0.176460
\(509\) 15.2473 15.2473i 0.675823 0.675823i −0.283229 0.959052i \(-0.591406\pi\)
0.959052 + 0.283229i \(0.0914057\pi\)
\(510\) 7.25990i 0.321474i
\(511\) −18.2206 + 18.4257i −0.806031 + 0.815107i
\(512\) −16.9216 16.9216i −0.747837 0.747837i
\(513\) −0.196748 0.196748i −0.00868666 0.00868666i
\(514\) 15.0210 + 15.0210i 0.662548 + 0.662548i
\(515\) 3.26180 3.26180i 0.143732 0.143732i
\(516\) 3.90286i 0.171814i
\(517\) −19.3505 −0.851033
\(518\) −0.0512623 9.15630i −0.00225234 0.402305i
\(519\) 17.0133i 0.746802i
\(520\) −9.58864 0.277394i −0.420490 0.0121645i
\(521\) 20.1543i 0.882975i 0.897268 + 0.441487i \(0.145549\pi\)
−0.897268 + 0.441487i \(0.854451\pi\)
\(522\) 7.02472 + 7.02472i 0.307464 + 0.307464i
\(523\) 11.3031i 0.494251i 0.968983 + 0.247126i \(0.0794861\pi\)
−0.968983 + 0.247126i \(0.920514\pi\)
\(524\) −6.45095 −0.281811
\(525\) 0.143087 + 25.5578i 0.00624485 + 1.11543i
\(526\) −12.4143 12.4143i −0.541291 0.541291i
\(527\) −20.6400 + 20.6400i −0.899094 + 0.899094i
\(528\) 11.0946 + 11.0946i 0.482831 + 0.482831i
\(529\) −19.3835 −0.842760
\(530\) −3.59587 −0.156195
\(531\) 19.8592 + 19.8592i 0.861817 + 0.861817i
\(532\) 0.147902 0.149568i 0.00641237 0.00648458i
\(533\) −7.95774 8.43188i −0.344688 0.365225i
\(534\) 13.1967 0.571079
\(535\) −6.28230 + 6.28230i −0.271607 + 0.271607i
\(536\) −4.55479 −0.196737
\(537\) −51.6168 −2.22743
\(538\) 20.0115 20.0115i 0.862758 0.862758i
\(539\) 12.8363 13.1270i 0.552898 0.565420i
\(540\) 0.623710 0.623710i 0.0268402 0.0268402i
\(541\) −9.28879 + 9.28879i −0.399356 + 0.399356i −0.878006 0.478650i \(-0.841126\pi\)
0.478650 + 0.878006i \(0.341126\pi\)
\(542\) 4.13051i 0.177421i
\(543\) 4.35965i 0.187090i
\(544\) 6.37398 + 6.37398i 0.273282 + 0.273282i
\(545\) 7.17778 0.307462
\(546\) −18.9648 + 18.1002i −0.811618 + 0.774616i
\(547\) 12.8999 0.551559 0.275780 0.961221i \(-0.411064\pi\)
0.275780 + 0.961221i \(0.411064\pi\)
\(548\) −1.01560 1.01560i −0.0433842 0.0433842i
\(549\) 19.9812i 0.852777i
\(550\) 13.4680i 0.574277i
\(551\) −0.394912 + 0.394912i −0.0168238 + 0.0168238i
\(552\) −32.1236 + 32.1236i −1.36727 + 1.36727i
\(553\) 0.260633 + 46.5534i 0.0110833 + 1.97965i
\(554\) 24.8462 24.8462i 1.05562 1.05562i
\(555\) −5.64423 −0.239584
\(556\) 3.43400 0.145634
\(557\) −16.6153 + 16.6153i −0.704013 + 0.704013i −0.965269 0.261257i \(-0.915863\pi\)
0.261257 + 0.965269i \(0.415863\pi\)
\(558\) −25.1240 −1.06359
\(559\) −11.4732 0.331912i −0.485264 0.0140384i
\(560\) −4.29072 4.24295i −0.181316 0.179297i
\(561\) −12.8504 12.8504i −0.542546 0.542546i
\(562\) 16.5536 0.698270
\(563\) −21.6761 −0.913538 −0.456769 0.889585i \(-0.650993\pi\)
−0.456769 + 0.889585i \(0.650993\pi\)
\(564\) −6.39576 6.39576i −0.269310 0.269310i
\(565\) −3.52192 + 3.52192i −0.148168 + 0.148168i
\(566\) −3.67799 3.67799i −0.154598 0.154598i
\(567\) −0.159987 28.5763i −0.00671881 1.20009i
\(568\) −17.8082 −0.747214
\(569\) 18.0738i 0.757695i −0.925459 0.378847i \(-0.876321\pi\)
0.925459 0.378847i \(-0.123679\pi\)
\(570\) 0.248399 + 0.248399i 0.0104043 + 0.0104043i
\(571\) 8.53692i 0.357259i 0.983916 + 0.178630i \(0.0571664\pi\)
−0.983916 + 0.178630i \(0.942834\pi\)
\(572\) −3.70831 + 3.49978i −0.155052 + 0.146333i
\(573\) 22.7542i 0.950569i
\(574\) −0.0575680 10.2826i −0.00240284 0.429188i
\(575\) 27.6586 1.15344
\(576\) 19.1773i 0.799053i
\(577\) −8.56564 + 8.56564i −0.356592 + 0.356592i −0.862555 0.505963i \(-0.831137\pi\)
0.505963 + 0.862555i \(0.331137\pi\)
\(578\) −6.59284 6.59284i −0.274226 0.274226i
\(579\) 23.2725 + 23.2725i 0.967171 + 0.967171i
\(580\) −1.25190 1.25190i −0.0519825 0.0519825i
\(581\) −28.0616 27.7491i −1.16419 1.15123i
\(582\) 17.2690i 0.715822i
\(583\) −6.36490 + 6.36490i −0.263607 + 0.263607i
\(584\) 30.0583 1.24382
\(585\) 4.65562 + 4.93302i 0.192486 + 0.203955i
\(586\) 6.10849i 0.252339i
\(587\) −0.308382 + 0.308382i −0.0127283 + 0.0127283i −0.713442 0.700714i \(-0.752865\pi\)
0.700714 + 0.713442i \(0.252865\pi\)
\(588\) 8.58145 0.0960910i 0.353893 0.00396272i
\(589\) 1.41241i 0.0581972i
\(590\) 9.58864 + 9.58864i 0.394758 + 0.394758i
\(591\) 34.7183 34.7183i 1.42812 1.42812i
\(592\) −5.32684 + 5.32684i −0.218932 + 0.218932i
\(593\) −4.95204 4.95204i −0.203356 0.203356i 0.598080 0.801436i \(-0.295930\pi\)
−0.801436 + 0.598080i \(0.795930\pi\)
\(594\) 5.98209i 0.245448i
\(595\) 4.96977 + 4.91443i 0.203741 + 0.201472i
\(596\) 7.19061 7.19061i 0.294539 0.294539i
\(597\) 51.0772i 2.09045i
\(598\) 19.4725 + 20.6327i 0.796289 + 0.843734i
\(599\) −17.6309 −0.720379 −0.360189 0.932879i \(-0.617288\pi\)
−0.360189 + 0.932879i \(0.617288\pi\)
\(600\) 20.9632 20.9632i 0.855820 0.855820i
\(601\) 7.14746i 0.291551i 0.989318 + 0.145776i \(0.0465677\pi\)
−0.989318 + 0.145776i \(0.953432\pi\)
\(602\) −7.23840 7.15780i −0.295015 0.291730i
\(603\) 2.27739 + 2.27739i 0.0927426 + 0.0927426i
\(604\) −4.12064 4.12064i −0.167666 0.167666i
\(605\) −2.52595 2.52595i −0.102694 0.102694i
\(606\) 2.25461 2.25461i 0.0915872 0.0915872i
\(607\) 29.8550i 1.21178i −0.795550 0.605888i \(-0.792818\pi\)
0.795550 0.605888i \(-0.207182\pi\)
\(608\) −0.436175 −0.0176892
\(609\) −22.7856 + 0.127567i −0.923321 + 0.00516929i
\(610\) 9.64754i 0.390618i
\(611\) −19.3454 + 18.2576i −0.782632 + 0.738623i
\(612\) 3.56556i 0.144129i
\(613\) −6.43907 6.43907i −0.260072 0.260072i 0.565011 0.825083i \(-0.308872\pi\)
−0.825083 + 0.565011i \(0.808872\pi\)
\(614\) 14.6905i 0.592859i
\(615\) −6.33852 −0.255594
\(616\) −21.2965 + 0.119230i −0.858061 + 0.00480393i
\(617\) 16.4908 + 16.4908i 0.663894 + 0.663894i 0.956296 0.292402i \(-0.0944544\pi\)
−0.292402 + 0.956296i \(0.594454\pi\)
\(618\) −10.3402 + 10.3402i −0.415943 + 0.415943i
\(619\) −22.3208 22.3208i −0.897148 0.897148i 0.0980353 0.995183i \(-0.468744\pi\)
−0.995183 + 0.0980353i \(0.968744\pi\)
\(620\) 4.47745 0.179819
\(621\) −12.2851 −0.492986
\(622\) −19.2639 19.2639i −0.772414 0.772414i
\(623\) −8.93326 + 9.03385i −0.357903 + 0.361934i
\(624\) 21.5597 + 0.623710i 0.863079 + 0.0249684i
\(625\) −14.2918 −0.571671
\(626\) 3.68240 3.68240i 0.147178 0.147178i
\(627\) 0.879362 0.0351183
\(628\) 11.3386 0.452459
\(629\) 6.16986 6.16986i 0.246009 0.246009i
\(630\) 0.0336798 + 6.01577i 0.00134184 + 0.239674i
\(631\) 3.75154 3.75154i 0.149346 0.149346i −0.628480 0.777826i \(-0.716322\pi\)
0.777826 + 0.628480i \(0.216322\pi\)
\(632\) 38.1845 38.1845i 1.51890 1.51890i
\(633\) 42.8618i 1.70360i
\(634\) 6.78765i 0.269572i
\(635\) −4.52166 4.52166i −0.179437 0.179437i
\(636\) −4.20748 −0.166837
\(637\) 0.447317 25.2349i 0.0177234 0.999843i
\(638\) 12.0072 0.475369
\(639\) 8.90409 + 8.90409i 0.352240 + 0.352240i
\(640\) 4.13051i 0.163273i
\(641\) 25.6947i 1.01488i 0.861687 + 0.507440i \(0.169408\pi\)
−0.861687 + 0.507440i \(0.830592\pi\)
\(642\) 19.9154 19.9154i 0.785999 0.785999i
\(643\) 22.1537 22.1537i 0.873658 0.873658i −0.119211 0.992869i \(-0.538036\pi\)
0.992869 + 0.119211i \(0.0380363\pi\)
\(644\) −0.0519948 9.28713i −0.00204888 0.365964i
\(645\) −4.43713 + 4.43713i −0.174712 + 0.174712i
\(646\) −0.543065 −0.0213666
\(647\) 32.4446 1.27553 0.637764 0.770232i \(-0.279860\pi\)
0.637764 + 0.770232i \(0.279860\pi\)
\(648\) −23.4391 + 23.4391i −0.920774 + 0.920774i
\(649\) 33.9449 1.33245
\(650\) −12.7073 13.4645i −0.498423 0.528120i
\(651\) 40.5185 40.9747i 1.58804 1.60593i
\(652\) 3.79380 + 3.79380i 0.148577 + 0.148577i
\(653\) 31.6514 1.23862 0.619308 0.785148i \(-0.287413\pi\)
0.619308 + 0.785148i \(0.287413\pi\)
\(654\) −22.7542 −0.889758
\(655\) 7.33403 + 7.33403i 0.286564 + 0.286564i
\(656\) −5.98209 + 5.98209i −0.233561 + 0.233561i
\(657\) −15.0292 15.0292i −0.586344 0.586344i
\(658\) −23.5916 + 0.132079i −0.919695 + 0.00514899i
\(659\) 30.5330 1.18940 0.594699 0.803948i \(-0.297271\pi\)
0.594699 + 0.803948i \(0.297271\pi\)
\(660\) 2.78765i 0.108509i
\(661\) 9.20895 + 9.20895i 0.358187 + 0.358187i 0.863144 0.504957i \(-0.168492\pi\)
−0.504957 + 0.863144i \(0.668492\pi\)
\(662\) 2.92162i 0.113552i
\(663\) −24.9717 0.722418i −0.969822 0.0280564i
\(664\) 45.7775i 1.77651i
\(665\) −0.338191 + 0.00189339i −0.0131145 + 7.34225e-5i
\(666\) 7.51026 0.291017
\(667\) 24.6586i 0.954785i
\(668\) 6.50717 6.50717i 0.251770 0.251770i
\(669\) −9.82571 9.82571i −0.379884 0.379884i
\(670\) 1.09960 + 1.09960i 0.0424811 + 0.0424811i
\(671\) 17.0767 + 17.0767i 0.659239 + 0.659239i
\(672\) −12.6537 12.5128i −0.488126 0.482691i
\(673\) 22.6319i 0.872397i −0.899850 0.436199i \(-0.856325\pi\)
0.899850 0.436199i \(-0.143675\pi\)
\(674\) 19.7701 19.7701i 0.761516 0.761516i
\(675\) 8.01703 0.308576
\(676\) −0.405220 + 6.99773i −0.0155854 + 0.269144i
\(677\) 10.7242i 0.412165i 0.978535 + 0.206082i \(0.0660715\pi\)
−0.978535 + 0.206082i \(0.933928\pi\)
\(678\) 11.1648 11.1648i 0.428781 0.428781i
\(679\) 11.8215 + 11.6899i 0.453668 + 0.448616i
\(680\) 8.10731i 0.310901i
\(681\) 10.6647 + 10.6647i 0.408674 + 0.408674i
\(682\) −21.4720 + 21.4720i −0.822204 + 0.822204i
\(683\) −3.70701 + 3.70701i −0.141845 + 0.141845i −0.774463 0.632619i \(-0.781980\pi\)
0.632619 + 0.774463i \(0.281980\pi\)
\(684\) 0.121997 + 0.121997i 0.00466466 + 0.00466466i
\(685\) 2.30925i 0.0882319i
\(686\) 15.5600 16.0917i 0.594085 0.614384i
\(687\) −0.601968 + 0.601968i −0.0229665 + 0.0229665i
\(688\) 8.37525i 0.319303i
\(689\) −0.357818 + 12.3687i −0.0136318 + 0.471208i
\(690\) 15.5103 0.590465
\(691\) −0.266133 + 0.266133i −0.0101242 + 0.0101242i −0.712151 0.702027i \(-0.752279\pi\)
0.702027 + 0.712151i \(0.252279\pi\)
\(692\) 4.03442i 0.153366i
\(693\) 10.7079 + 10.5886i 0.406758 + 0.402229i
\(694\) −7.35350 7.35350i −0.279135 0.279135i
\(695\) −3.90409 3.90409i −0.148090 0.148090i
\(696\) 18.6894 + 18.6894i 0.708421 + 0.708421i
\(697\) 6.92881 6.92881i 0.262447 0.262447i
\(698\) 32.5925i 1.23364i
\(699\) −14.0131 −0.530024
\(700\) 0.0339307 + 6.06059i 0.00128246 + 0.229069i
\(701\) 34.0349i 1.28548i 0.766084 + 0.642740i \(0.222202\pi\)
−0.766084 + 0.642740i \(0.777798\pi\)
\(702\) 5.64423 + 5.98053i 0.213028 + 0.225720i
\(703\) 0.422207i 0.0159238i
\(704\) 16.3896 + 16.3896i 0.617707 + 0.617707i
\(705\) 14.5426i 0.547705i
\(706\) −8.22556 −0.309573
\(707\) 0.0171854 + 3.06960i 0.000646325 + 0.115444i
\(708\) 11.2195 + 11.2195i 0.421656 + 0.421656i
\(709\) 11.4989 11.4989i 0.431849 0.431849i −0.457408 0.889257i \(-0.651222\pi\)
0.889257 + 0.457408i \(0.151222\pi\)
\(710\) 4.29917 + 4.29917i 0.161345 + 0.161345i
\(711\) −38.1845 −1.43203
\(712\) 14.7371 0.552297
\(713\) −44.0960 44.0960i −1.65141 1.65141i
\(714\) −15.7546 15.5792i −0.589601 0.583036i
\(715\) 8.19481 + 0.237071i 0.306469 + 0.00886596i
\(716\) −12.2401 −0.457432
\(717\) −12.8034 + 12.8034i −0.478153 + 0.478153i
\(718\) −21.4524 −0.800596
\(719\) 35.0445 1.30694 0.653469 0.756953i \(-0.273313\pi\)
0.653469 + 0.756953i \(0.273313\pi\)
\(720\) 3.49978 3.49978i 0.130429 0.130429i
\(721\) −0.0788166 14.0779i −0.00293528 0.524290i
\(722\) −16.2195 + 16.2195i −0.603629 + 0.603629i
\(723\) 2.52884 2.52884i 0.0940486 0.0940486i
\(724\) 1.03382i 0.0384215i
\(725\) 16.0917i 0.597631i
\(726\) 8.00747 + 8.00747i 0.297185 + 0.297185i
\(727\) 15.0936 0.559789 0.279895 0.960031i \(-0.409700\pi\)
0.279895 + 0.960031i \(0.409700\pi\)
\(728\) −21.1784 + 20.2129i −0.784925 + 0.749140i
\(729\) 10.5669 0.391367
\(730\) −7.25655 7.25655i −0.268577 0.268577i
\(731\) 9.70071i 0.358794i
\(732\) 11.2885i 0.417233i
\(733\) −14.8155 + 14.8155i −0.547223 + 0.547223i −0.925637 0.378414i \(-0.876470\pi\)
0.378414 + 0.925637i \(0.376470\pi\)
\(734\) 19.5546 19.5546i 0.721773 0.721773i
\(735\) −9.86542 9.64693i −0.363891 0.355832i
\(736\) −13.6176 + 13.6176i −0.501950 + 0.501950i
\(737\) 3.89269 0.143389
\(738\) 8.43409 0.310463
\(739\) 16.1370 16.1370i 0.593607 0.593607i −0.344997 0.938604i \(-0.612120\pi\)
0.938604 + 0.344997i \(0.112120\pi\)
\(740\) −1.33843 −0.0492018
\(741\) 0.879132 0.829697i 0.0322957 0.0304797i
\(742\) −7.71646 + 7.80335i −0.283280 + 0.286470i
\(743\) −24.1350 24.1350i −0.885428 0.885428i 0.108652 0.994080i \(-0.465347\pi\)
−0.994080 + 0.108652i \(0.965347\pi\)
\(744\) −66.8431 −2.45059
\(745\) −16.3499 −0.599013
\(746\) 8.97721 + 8.97721i 0.328679 + 0.328679i
\(747\) 22.8887 22.8887i 0.837455 0.837455i
\(748\) −3.04726 3.04726i −0.111419 0.111419i
\(749\) 0.151803 + 27.1145i 0.00554675 + 0.990741i
\(750\) −22.0338 −0.804562
\(751\) 16.7770i 0.612201i 0.951999 + 0.306100i \(0.0990243\pi\)
−0.951999 + 0.306100i \(0.900976\pi\)
\(752\) 13.7248 + 13.7248i 0.500493 + 0.500493i
\(753\) 27.5285i 1.00319i
\(754\) 12.0041 11.3290i 0.437162 0.412579i
\(755\) 9.36943i 0.340989i
\(756\) −0.0150710 2.69194i −0.000548128 0.0979048i
\(757\) −20.7321 −0.753520 −0.376760 0.926311i \(-0.622962\pi\)
−0.376760 + 0.926311i \(0.622962\pi\)
\(758\) 6.22568i 0.226127i
\(759\) 27.4540 27.4540i 0.996519 0.996519i
\(760\) 0.277394 + 0.277394i 0.0100621 + 0.0100621i
\(761\) −2.11330 2.11330i −0.0766071 0.0766071i 0.667765 0.744372i \(-0.267251\pi\)
−0.744372 + 0.667765i \(0.767251\pi\)
\(762\) 14.3341 + 14.3341i 0.519268 + 0.519268i
\(763\) 15.4030 15.5764i 0.557624 0.563903i
\(764\) 5.39576i 0.195212i
\(765\) −4.05365 + 4.05365i −0.146560 + 0.146560i
\(766\) −41.9782 −1.51674
\(767\) 33.9360 32.0277i 1.22536 1.15645i
\(768\) 27.0932i 0.977642i
\(769\) −25.9456 + 25.9456i −0.935621 + 0.935621i −0.998049 0.0624284i \(-0.980115\pi\)
0.0624284 + 0.998049i \(0.480115\pi\)
\(770\) 5.17009 + 5.11252i 0.186317 + 0.184242i
\(771\) 39.9637i 1.43926i
\(772\) 5.51867 + 5.51867i 0.198621 + 0.198621i
\(773\) −0.951693 + 0.951693i −0.0342300 + 0.0342300i −0.724015 0.689785i \(-0.757705\pi\)
0.689785 + 0.724015i \(0.257705\pi\)
\(774\) 5.90409 5.90409i 0.212218 0.212218i
\(775\) 28.7761 + 28.7761i 1.03367 + 1.03367i
\(776\) 19.2847i 0.692280i
\(777\) −12.1121 + 12.2485i −0.434518 + 0.439411i
\(778\) −5.54638 + 5.54638i −0.198847 + 0.198847i
\(779\) 0.474142i