Properties

Label 1110.2.x.d.751.7
Level $1110$
Weight $2$
Character 1110.751
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.7
Root \(-2.16125i\) of defining polynomial
Character \(\chi\) \(=\) 1110.751
Dual form 1110.2.x.d.841.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.08063 - 1.87170i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.08063 - 1.87170i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +4.64319 q^{11} +(0.500000 + 0.866025i) q^{12} +(-4.51941 - 2.60928i) q^{13} -2.16125i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.73772 - 1.58063i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.178213 + 0.102891i) q^{19} +(0.866025 - 0.500000i) q^{20} +(1.08063 + 1.87170i) q^{21} +(4.02112 - 2.32159i) q^{22} +3.48652i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.21857 q^{26} +1.00000 q^{27} +(-1.08063 - 1.87170i) q^{28} -6.44199i q^{29} +(-0.500000 + 0.866025i) q^{30} -6.19187i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.32159 + 4.02112i) q^{33} +(1.58063 - 2.73772i) q^{34} +(1.87170 - 1.08063i) q^{35} -1.00000 q^{36} +(2.83833 + 5.37995i) q^{37} +0.205782 q^{38} +(4.51941 - 2.60928i) q^{39} +(0.500000 - 0.866025i) q^{40} +(1.61696 - 2.80066i) q^{41} +(1.87170 + 1.08063i) q^{42} +2.70535i q^{43} +(2.32159 - 4.02112i) q^{44} -1.00000i q^{45} +(1.74326 + 3.01941i) q^{46} +0.834167 q^{47} +1.00000 q^{48} +(1.16450 + 2.01696i) q^{49} +(0.866025 + 0.500000i) q^{50} +3.16125i q^{51} +(-4.51941 + 2.60928i) q^{52} +(0.578919 + 1.00272i) q^{53} +(0.866025 - 0.500000i) q^{54} +(4.02112 + 2.32159i) q^{55} +(-1.87170 - 1.08063i) q^{56} +(-0.178213 + 0.102891i) q^{57} +(-3.22099 - 5.57892i) q^{58} +(3.94537 - 2.27786i) q^{59} +1.00000i q^{60} +(9.21562 + 5.32064i) q^{61} +(-3.09594 - 5.36232i) q^{62} -2.16125 q^{63} -1.00000 q^{64} +(-2.60928 - 4.51941i) q^{65} +4.64319i q^{66} +(0.180274 - 0.312243i) q^{67} -3.16125i q^{68} +(-3.01941 - 1.74326i) q^{69} +(1.08063 - 1.87170i) q^{70} +(2.26228 - 3.91838i) q^{71} +(-0.866025 + 0.500000i) q^{72} +4.91562 q^{73} +(5.14804 + 3.24001i) q^{74} -1.00000 q^{75} +(0.178213 - 0.102891i) q^{76} +(5.01755 - 8.69065i) q^{77} +(2.60928 - 4.51941i) q^{78} +(2.06361 + 1.19143i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -3.23393i q^{82} +(-6.98079 - 12.0911i) q^{83} +2.16125 q^{84} +3.16125 q^{85} +(1.35268 + 2.34291i) q^{86} +(5.57892 + 3.22099i) q^{87} -4.64319i q^{88} +(-13.4453 + 7.76267i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-9.76759 + 5.63932i) q^{91} +(3.01941 + 1.74326i) q^{92} +(5.36232 + 3.09594i) q^{93} +(0.722410 - 0.417084i) q^{94} +(0.102891 + 0.178213i) q^{95} +(0.866025 - 0.500000i) q^{96} +0.153047i q^{97} +(2.01696 + 1.16450i) q^{98} +(-2.32159 - 4.02112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 1.00000i 0.408248i
\(7\) 1.08063 1.87170i 0.408438 0.707436i −0.586277 0.810111i \(-0.699407\pi\)
0.994715 + 0.102675i \(0.0327402\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 0.316228
\(11\) 4.64319 1.39997 0.699987 0.714156i \(-0.253189\pi\)
0.699987 + 0.714156i \(0.253189\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −4.51941 2.60928i −1.25346 0.723685i −0.281664 0.959513i \(-0.590886\pi\)
−0.971795 + 0.235828i \(0.924220\pi\)
\(14\) 2.16125i 0.577619i
\(15\) −0.866025 + 0.500000i −0.223607 + 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.73772 1.58063i 0.663996 0.383358i −0.129802 0.991540i \(-0.541434\pi\)
0.793798 + 0.608182i \(0.208101\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 0.178213 + 0.102891i 0.0408848 + 0.0236048i 0.520303 0.853982i \(-0.325819\pi\)
−0.479418 + 0.877587i \(0.659152\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 1.08063 + 1.87170i 0.235812 + 0.408438i
\(22\) 4.02112 2.32159i 0.857305 0.494965i
\(23\) 3.48652i 0.726989i 0.931596 + 0.363494i \(0.118416\pi\)
−0.931596 + 0.363494i \(0.881584\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −5.21857 −1.02345
\(27\) 1.00000 0.192450
\(28\) −1.08063 1.87170i −0.204219 0.353718i
\(29\) 6.44199i 1.19625i −0.801404 0.598123i \(-0.795913\pi\)
0.801404 0.598123i \(-0.204087\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 6.19187i 1.11209i −0.831151 0.556046i \(-0.812318\pi\)
0.831151 0.556046i \(-0.187682\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −2.32159 + 4.02112i −0.404138 + 0.699987i
\(34\) 1.58063 2.73772i 0.271075 0.469516i
\(35\) 1.87170 1.08063i 0.316375 0.182659i
\(36\) −1.00000 −0.166667
\(37\) 2.83833 + 5.37995i 0.466618 + 0.884459i
\(38\) 0.205782 0.0333823
\(39\) 4.51941 2.60928i 0.723685 0.417820i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 1.61696 2.80066i 0.252527 0.437390i −0.711694 0.702490i \(-0.752072\pi\)
0.964221 + 0.265100i \(0.0854050\pi\)
\(42\) 1.87170 + 1.08063i 0.288809 + 0.166744i
\(43\) 2.70535i 0.412563i 0.978493 + 0.206281i \(0.0661362\pi\)
−0.978493 + 0.206281i \(0.933864\pi\)
\(44\) 2.32159 4.02112i 0.349993 0.606206i
\(45\) 1.00000i 0.149071i
\(46\) 1.74326 + 3.01941i 0.257029 + 0.445188i
\(47\) 0.834167 0.121676 0.0608379 0.998148i \(-0.480623\pi\)
0.0608379 + 0.998148i \(0.480623\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.16450 + 2.01696i 0.166356 + 0.288138i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 3.16125i 0.442664i
\(52\) −4.51941 + 2.60928i −0.626730 + 0.361843i
\(53\) 0.578919 + 1.00272i 0.0795207 + 0.137734i 0.903043 0.429550i \(-0.141328\pi\)
−0.823523 + 0.567284i \(0.807994\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 4.02112 + 2.32159i 0.542207 + 0.313044i
\(56\) −1.87170 1.08063i −0.250116 0.144405i
\(57\) −0.178213 + 0.102891i −0.0236048 + 0.0136283i
\(58\) −3.22099 5.57892i −0.422937 0.732549i
\(59\) 3.94537 2.27786i 0.513643 0.296552i −0.220687 0.975345i \(-0.570830\pi\)
0.734330 + 0.678793i \(0.237496\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 9.21562 + 5.32064i 1.17994 + 0.681238i 0.956001 0.293365i \(-0.0947751\pi\)
0.223939 + 0.974603i \(0.428108\pi\)
\(62\) −3.09594 5.36232i −0.393184 0.681015i
\(63\) −2.16125 −0.272292
\(64\) −1.00000 −0.125000
\(65\) −2.60928 4.51941i −0.323642 0.560564i
\(66\) 4.64319i 0.571537i
\(67\) 0.180274 0.312243i 0.0220239 0.0381465i −0.854803 0.518952i \(-0.826322\pi\)
0.876827 + 0.480805i \(0.159656\pi\)
\(68\) 3.16125i 0.383358i
\(69\) −3.01941 1.74326i −0.363494 0.209864i
\(70\) 1.08063 1.87170i 0.129160 0.223711i
\(71\) 2.26228 3.91838i 0.268483 0.465027i −0.699987 0.714155i \(-0.746811\pi\)
0.968470 + 0.249129i \(0.0801443\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 4.91562 0.575329 0.287665 0.957731i \(-0.407121\pi\)
0.287665 + 0.957731i \(0.407121\pi\)
\(74\) 5.14804 + 3.24001i 0.598447 + 0.376644i
\(75\) −1.00000 −0.115470
\(76\) 0.178213 0.102891i 0.0204424 0.0118024i
\(77\) 5.01755 8.69065i 0.571803 0.990391i
\(78\) 2.60928 4.51941i 0.295443 0.511723i
\(79\) 2.06361 + 1.19143i 0.232174 + 0.134046i 0.611575 0.791187i \(-0.290536\pi\)
−0.379400 + 0.925233i \(0.623870\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.23393i 0.357127i
\(83\) −6.98079 12.0911i −0.766241 1.32717i −0.939588 0.342308i \(-0.888791\pi\)
0.173347 0.984861i \(-0.444542\pi\)
\(84\) 2.16125 0.235812
\(85\) 3.16125 0.342886
\(86\) 1.35268 + 2.34291i 0.145863 + 0.252642i
\(87\) 5.57892 + 3.22099i 0.598123 + 0.345327i
\(88\) 4.64319i 0.494965i
\(89\) −13.4453 + 7.76267i −1.42520 + 0.822841i −0.996737 0.0807166i \(-0.974279\pi\)
−0.428466 + 0.903558i \(0.640946\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) −9.76759 + 5.63932i −1.02392 + 0.591161i
\(92\) 3.01941 + 1.74326i 0.314795 + 0.181747i
\(93\) 5.36232 + 3.09594i 0.556046 + 0.321034i
\(94\) 0.722410 0.417084i 0.0745109 0.0430189i
\(95\) 0.102891 + 0.178213i 0.0105564 + 0.0182842i
\(96\) 0.866025 0.500000i 0.0883883 0.0510310i
\(97\) 0.153047i 0.0155396i 0.999970 + 0.00776981i \(0.00247323\pi\)
−0.999970 + 0.00776981i \(0.997527\pi\)
\(98\) 2.01696 + 1.16450i 0.203744 + 0.117632i
\(99\) −2.32159 4.02112i −0.233329 0.404138i
\(100\) 1.00000 0.100000
\(101\) 8.43932 0.839744 0.419872 0.907583i \(-0.362075\pi\)
0.419872 + 0.907583i \(0.362075\pi\)
\(102\) 1.58063 + 2.73772i 0.156505 + 0.271075i
\(103\) 4.15256i 0.409164i −0.978849 0.204582i \(-0.934417\pi\)
0.978849 0.204582i \(-0.0655834\pi\)
\(104\) −2.60928 + 4.51941i −0.255861 + 0.443165i
\(105\) 2.16125i 0.210917i
\(106\) 1.00272 + 0.578919i 0.0973926 + 0.0562296i
\(107\) −8.48343 + 14.6937i −0.820124 + 1.42050i 0.0854653 + 0.996341i \(0.472762\pi\)
−0.905589 + 0.424155i \(0.860571\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −1.32344 + 0.764087i −0.126762 + 0.0731863i −0.562040 0.827110i \(-0.689983\pi\)
0.435278 + 0.900296i \(0.356650\pi\)
\(110\) 4.64319 0.442711
\(111\) −6.07834 0.231916i −0.576930 0.0220125i
\(112\) −2.16125 −0.204219
\(113\) −17.1426 + 9.89727i −1.61264 + 0.931057i −0.623883 + 0.781518i \(0.714446\pi\)
−0.988756 + 0.149539i \(0.952221\pi\)
\(114\) −0.102891 + 0.178213i −0.00963663 + 0.0166911i
\(115\) −1.74326 + 3.01941i −0.162560 + 0.281562i
\(116\) −5.57892 3.22099i −0.517990 0.299062i
\(117\) 5.21857i 0.482457i
\(118\) 2.27786 3.94537i 0.209694 0.363201i
\(119\) 6.83226i 0.626312i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 10.5592 0.959926
\(122\) 10.6413 0.963416
\(123\) 1.61696 + 2.80066i 0.145797 + 0.252527i
\(124\) −5.36232 3.09594i −0.481550 0.278023i
\(125\) 1.00000i 0.0894427i
\(126\) −1.87170 + 1.08063i −0.166744 + 0.0962698i
\(127\) −0.713592 1.23598i −0.0633210 0.109675i 0.832627 0.553834i \(-0.186836\pi\)
−0.895948 + 0.444159i \(0.853503\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −2.34291 1.35268i −0.206281 0.119097i
\(130\) −4.51941 2.60928i −0.396379 0.228849i
\(131\) −13.7876 + 7.96026i −1.20463 + 0.695491i −0.961580 0.274524i \(-0.911480\pi\)
−0.243045 + 0.970015i \(0.578146\pi\)
\(132\) 2.32159 + 4.02112i 0.202069 + 0.349993i
\(133\) 0.385162 0.222373i 0.0333978 0.0192822i
\(134\) 0.360547i 0.0311465i
\(135\) 0.866025 + 0.500000i 0.0745356 + 0.0430331i
\(136\) −1.58063 2.73772i −0.135538 0.234758i
\(137\) 1.14116 0.0974958 0.0487479 0.998811i \(-0.484477\pi\)
0.0487479 + 0.998811i \(0.484477\pi\)
\(138\) −3.48652 −0.296792
\(139\) 1.38333 + 2.39599i 0.117332 + 0.203225i 0.918710 0.394934i \(-0.129232\pi\)
−0.801377 + 0.598159i \(0.795899\pi\)
\(140\) 2.16125i 0.182659i
\(141\) −0.417084 + 0.722410i −0.0351248 + 0.0608379i
\(142\) 4.52456i 0.379693i
\(143\) −20.9845 12.1154i −1.75481 1.01314i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 3.22099 5.57892i 0.267489 0.463304i
\(146\) 4.25705 2.45781i 0.352316 0.203410i
\(147\) −2.32899 −0.192092
\(148\) 6.07834 + 0.231916i 0.499636 + 0.0190633i
\(149\) 10.1666 0.832881 0.416441 0.909163i \(-0.363277\pi\)
0.416441 + 0.909163i \(0.363277\pi\)
\(150\) −0.866025 + 0.500000i −0.0707107 + 0.0408248i
\(151\) −1.21847 + 2.11046i −0.0991580 + 0.171747i −0.911336 0.411663i \(-0.864948\pi\)
0.812178 + 0.583409i \(0.198282\pi\)
\(152\) 0.102891 0.178213i 0.00834557 0.0144549i
\(153\) −2.73772 1.58063i −0.221332 0.127786i
\(154\) 10.0351i 0.808651i
\(155\) 3.09594 5.36232i 0.248672 0.430712i
\(156\) 5.21857i 0.417820i
\(157\) −0.705413 1.22181i −0.0562981 0.0975111i 0.836503 0.547963i \(-0.184596\pi\)
−0.892801 + 0.450451i \(0.851263\pi\)
\(158\) 2.38285 0.189569
\(159\) −1.15784 −0.0918226
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 6.52571 + 3.76762i 0.514298 + 0.296930i
\(162\) 1.00000i 0.0785674i
\(163\) −8.49385 + 4.90393i −0.665290 + 0.384105i −0.794289 0.607539i \(-0.792157\pi\)
0.129000 + 0.991645i \(0.458823\pi\)
\(164\) −1.61696 2.80066i −0.126264 0.218695i
\(165\) −4.02112 + 2.32159i −0.313044 + 0.180736i
\(166\) −12.0911 6.98079i −0.938450 0.541814i
\(167\) −13.2273 7.63680i −1.02356 0.590953i −0.108428 0.994104i \(-0.534582\pi\)
−0.915134 + 0.403151i \(0.867915\pi\)
\(168\) 1.87170 1.08063i 0.144405 0.0833721i
\(169\) 7.11672 + 12.3265i 0.547440 + 0.948194i
\(170\) 2.73772 1.58063i 0.209974 0.121228i
\(171\) 0.205782i 0.0157366i
\(172\) 2.34291 + 1.35268i 0.178645 + 0.103141i
\(173\) 1.38267 + 2.39485i 0.105122 + 0.182077i 0.913788 0.406191i \(-0.133143\pi\)
−0.808666 + 0.588268i \(0.799810\pi\)
\(174\) 6.44199 0.488366
\(175\) 2.16125 0.163375
\(176\) −2.32159 4.02112i −0.174997 0.303103i
\(177\) 4.55572i 0.342429i
\(178\) −7.76267 + 13.4453i −0.581837 + 1.00777i
\(179\) 1.17391i 0.0877424i −0.999037 0.0438712i \(-0.986031\pi\)
0.999037 0.0438712i \(-0.0139691\pi\)
\(180\) −0.866025 0.500000i −0.0645497 0.0372678i
\(181\) −10.5795 + 18.3242i −0.786366 + 1.36203i 0.141813 + 0.989893i \(0.454707\pi\)
−0.928179 + 0.372133i \(0.878626\pi\)
\(182\) −5.63932 + 9.76759i −0.418014 + 0.724022i
\(183\) −9.21562 + 5.32064i −0.681238 + 0.393313i
\(184\) 3.48652 0.257029
\(185\) −0.231916 + 6.07834i −0.0170508 + 0.446888i
\(186\) 6.19187 0.454010
\(187\) 12.7118 7.33914i 0.929577 0.536691i
\(188\) 0.417084 0.722410i 0.0304190 0.0526872i
\(189\) 1.08063 1.87170i 0.0786040 0.136146i
\(190\) 0.178213 + 0.102891i 0.0129289 + 0.00746450i
\(191\) 10.8527i 0.785274i −0.919694 0.392637i \(-0.871563\pi\)
0.919694 0.392637i \(-0.128437\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 22.9744i 1.65373i 0.562399 + 0.826866i \(0.309878\pi\)
−0.562399 + 0.826866i \(0.690122\pi\)
\(194\) 0.0765237 + 0.132543i 0.00549408 + 0.00951603i
\(195\) 5.21857 0.373709
\(196\) 2.32899 0.166356
\(197\) 9.19854 + 15.9323i 0.655369 + 1.13513i 0.981801 + 0.189911i \(0.0608201\pi\)
−0.326433 + 0.945221i \(0.605847\pi\)
\(198\) −4.02112 2.32159i −0.285768 0.164988i
\(199\) 10.9340i 0.775090i 0.921851 + 0.387545i \(0.126677\pi\)
−0.921851 + 0.387545i \(0.873323\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) 0.180274 + 0.312243i 0.0127155 + 0.0220239i
\(202\) 7.30867 4.21966i 0.514236 0.296894i
\(203\) −12.0575 6.96138i −0.846268 0.488593i
\(204\) 2.73772 + 1.58063i 0.191679 + 0.110666i
\(205\) 2.80066 1.61696i 0.195607 0.112934i
\(206\) −2.07628 3.59622i −0.144661 0.250561i
\(207\) 3.01941 1.74326i 0.209864 0.121165i
\(208\) 5.21857i 0.361843i
\(209\) 0.827474 + 0.477742i 0.0572376 + 0.0330461i
\(210\) 1.08063 + 1.87170i 0.0745703 + 0.129160i
\(211\) −5.36913 −0.369626 −0.184813 0.982774i \(-0.559168\pi\)
−0.184813 + 0.982774i \(0.559168\pi\)
\(212\) 1.15784 0.0795207
\(213\) 2.26228 + 3.91838i 0.155009 + 0.268483i
\(214\) 16.9669i 1.15983i
\(215\) −1.35268 + 2.34291i −0.0922518 + 0.159785i
\(216\) 1.00000i 0.0680414i
\(217\) −11.5893 6.69110i −0.786734 0.454221i
\(218\) −0.764087 + 1.32344i −0.0517505 + 0.0896345i
\(219\) −2.45781 + 4.25705i −0.166083 + 0.287665i
\(220\) 4.02112 2.32159i 0.271104 0.156522i
\(221\) −16.4972 −1.10972
\(222\) −5.37995 + 2.83833i −0.361079 + 0.190496i
\(223\) −23.1628 −1.55109 −0.775547 0.631289i \(-0.782526\pi\)
−0.775547 + 0.631289i \(0.782526\pi\)
\(224\) −1.87170 + 1.08063i −0.125058 + 0.0722024i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) −9.89727 + 17.1426i −0.658357 + 1.14031i
\(227\) −20.5859 11.8853i −1.36634 0.788855i −0.375879 0.926669i \(-0.622659\pi\)
−0.990458 + 0.137814i \(0.955992\pi\)
\(228\) 0.205782i 0.0136283i
\(229\) −2.27891 + 3.94718i −0.150594 + 0.260837i −0.931446 0.363879i \(-0.881452\pi\)
0.780852 + 0.624716i \(0.214785\pi\)
\(230\) 3.48652i 0.229894i
\(231\) 5.01755 + 8.69065i 0.330130 + 0.571803i
\(232\) −6.44199 −0.422937
\(233\) −18.2804 −1.19759 −0.598793 0.800904i \(-0.704353\pi\)
−0.598793 + 0.800904i \(0.704353\pi\)
\(234\) 2.60928 + 4.51941i 0.170574 + 0.295443i
\(235\) 0.722410 + 0.417084i 0.0471248 + 0.0272075i
\(236\) 4.55572i 0.296552i
\(237\) −2.06361 + 1.19143i −0.134046 + 0.0773914i
\(238\) −3.41613 5.91691i −0.221435 0.383536i
\(239\) 17.6319 10.1798i 1.14051 0.658474i 0.193953 0.981011i \(-0.437869\pi\)
0.946557 + 0.322537i \(0.104536\pi\)
\(240\) 0.866025 + 0.500000i 0.0559017 + 0.0322749i
\(241\) 13.3225 + 7.69174i 0.858176 + 0.495468i 0.863401 0.504518i \(-0.168330\pi\)
−0.00522493 + 0.999986i \(0.501663\pi\)
\(242\) 9.14453 5.27959i 0.587832 0.339385i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 9.21562 5.32064i 0.589970 0.340619i
\(245\) 2.32899i 0.148794i
\(246\) 2.80066 + 1.61696i 0.178564 + 0.103094i
\(247\) −0.536944 0.930014i −0.0341649 0.0591754i
\(248\) −6.19187 −0.393184
\(249\) 13.9616 0.884779
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 13.2799i 0.838219i −0.907936 0.419110i \(-0.862342\pi\)
0.907936 0.419110i \(-0.137658\pi\)
\(252\) −1.08063 + 1.87170i −0.0680730 + 0.117906i
\(253\) 16.1885i 1.01777i
\(254\) −1.23598 0.713592i −0.0775521 0.0447747i
\(255\) −1.58063 + 2.73772i −0.0989826 + 0.171443i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −2.52855 + 1.45986i −0.157727 + 0.0910636i −0.576786 0.816895i \(-0.695693\pi\)
0.419059 + 0.907959i \(0.362360\pi\)
\(258\) −2.70535 −0.168428
\(259\) 13.1368 + 0.501228i 0.816282 + 0.0311448i
\(260\) −5.21857 −0.323642
\(261\) −5.57892 + 3.22099i −0.345327 + 0.199374i
\(262\) −7.96026 + 13.7876i −0.491786 + 0.851799i
\(263\) −5.18381 + 8.97862i −0.319647 + 0.553645i −0.980414 0.196946i \(-0.936898\pi\)
0.660767 + 0.750591i \(0.270231\pi\)
\(264\) 4.02112 + 2.32159i 0.247483 + 0.142884i
\(265\) 1.15784i 0.0711255i
\(266\) 0.222373 0.385162i 0.0136346 0.0236158i
\(267\) 15.5253i 0.950135i
\(268\) −0.180274 0.312243i −0.0110120 0.0190733i
\(269\) 25.2440 1.53915 0.769577 0.638554i \(-0.220467\pi\)
0.769577 + 0.638554i \(0.220467\pi\)
\(270\) 1.00000 0.0608581
\(271\) −8.17713 14.1632i −0.496725 0.860353i 0.503268 0.864131i \(-0.332131\pi\)
−0.999993 + 0.00377716i \(0.998798\pi\)
\(272\) −2.73772 1.58063i −0.165999 0.0958395i
\(273\) 11.2786i 0.682614i
\(274\) 0.988273 0.570579i 0.0597037 0.0344700i
\(275\) 2.32159 + 4.02112i 0.139997 + 0.242483i
\(276\) −3.01941 + 1.74326i −0.181747 + 0.104932i
\(277\) 2.90340 + 1.67628i 0.174448 + 0.100718i 0.584682 0.811263i \(-0.301219\pi\)
−0.410233 + 0.911981i \(0.634553\pi\)
\(278\) 2.39599 + 1.38333i 0.143702 + 0.0829664i
\(279\) −5.36232 + 3.09594i −0.321034 + 0.185349i
\(280\) −1.08063 1.87170i −0.0645798 0.111855i
\(281\) −2.92257 + 1.68735i −0.174346 + 0.100659i −0.584634 0.811297i \(-0.698762\pi\)
0.410287 + 0.911956i \(0.365428\pi\)
\(282\) 0.834167i 0.0496740i
\(283\) 18.0520 + 10.4223i 1.07308 + 0.619543i 0.929022 0.370026i \(-0.120651\pi\)
0.144059 + 0.989569i \(0.453984\pi\)
\(284\) −2.26228 3.91838i −0.134242 0.232513i
\(285\) −0.205782 −0.0121895
\(286\) −24.2308 −1.43280
\(287\) −3.49466 6.05294i −0.206283 0.357293i
\(288\) 1.00000i 0.0589256i
\(289\) −3.50324 + 6.06780i −0.206073 + 0.356929i
\(290\) 6.44199i 0.378286i
\(291\) −0.132543 0.0765237i −0.00776981 0.00448590i
\(292\) 2.45781 4.25705i 0.143832 0.249125i
\(293\) 1.12816 1.95403i 0.0659077 0.114156i −0.831189 0.555991i \(-0.812339\pi\)
0.897096 + 0.441835i \(0.145672\pi\)
\(294\) −2.01696 + 1.16450i −0.117632 + 0.0679147i
\(295\) 4.55572 0.265244
\(296\) 5.37995 2.83833i 0.312704 0.164974i
\(297\) 4.64319 0.269425
\(298\) 8.80454 5.08331i 0.510034 0.294468i
\(299\) 9.09731 15.7570i 0.526111 0.911251i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) 5.06361 + 2.92348i 0.291862 + 0.168506i
\(302\) 2.43695i 0.140231i
\(303\) −4.21966 + 7.30867i −0.242413 + 0.419872i
\(304\) 0.205782i 0.0118024i
\(305\) 5.32064 + 9.21562i 0.304659 + 0.527685i
\(306\) −3.16125 −0.180717
\(307\) 14.0079 0.799474 0.399737 0.916630i \(-0.369101\pi\)
0.399737 + 0.916630i \(0.369101\pi\)
\(308\) −5.01755 8.69065i −0.285901 0.495196i
\(309\) 3.59622 + 2.07628i 0.204582 + 0.118115i
\(310\) 6.19187i 0.351675i
\(311\) 17.2177 9.94062i 0.976323 0.563681i 0.0751653 0.997171i \(-0.476052\pi\)
0.901158 + 0.433490i \(0.142718\pi\)
\(312\) −2.60928 4.51941i −0.147722 0.255861i
\(313\) −21.0731 + 12.1665i −1.19112 + 0.687694i −0.958561 0.284888i \(-0.908043\pi\)
−0.232560 + 0.972582i \(0.574710\pi\)
\(314\) −1.22181 0.705413i −0.0689508 0.0398087i
\(315\) −1.87170 1.08063i −0.105458 0.0608864i
\(316\) 2.06361 1.19143i 0.116087 0.0670229i
\(317\) 2.30160 + 3.98649i 0.129271 + 0.223903i 0.923394 0.383853i \(-0.125403\pi\)
−0.794124 + 0.607756i \(0.792070\pi\)
\(318\) −1.00272 + 0.578919i −0.0562296 + 0.0324642i
\(319\) 29.9113i 1.67471i
\(320\) −0.866025 0.500000i −0.0484123 0.0279508i
\(321\) −8.48343 14.6937i −0.473499 0.820124i
\(322\) 7.53524 0.419922
\(323\) 0.650529 0.0361964
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 5.21857i 0.289474i
\(326\) −4.90393 + 8.49385i −0.271603 + 0.470431i
\(327\) 1.52817i 0.0845083i
\(328\) −2.80066 1.61696i −0.154641 0.0892818i
\(329\) 0.901423 1.56131i 0.0496971 0.0860778i
\(330\) −2.32159 + 4.02112i −0.127800 + 0.221355i
\(331\) −22.7234 + 13.1193i −1.24899 + 0.721105i −0.970908 0.239453i \(-0.923032\pi\)
−0.278082 + 0.960557i \(0.589699\pi\)
\(332\) −13.9616 −0.766241
\(333\) 3.24001 5.14804i 0.177552 0.282111i
\(334\) −15.2736 −0.835734
\(335\) 0.312243 0.180274i 0.0170597 0.00984940i
\(336\) 1.08063 1.87170i 0.0589530 0.102110i
\(337\) 4.83436 8.37335i 0.263344 0.456126i −0.703784 0.710414i \(-0.748508\pi\)
0.967129 + 0.254288i \(0.0818412\pi\)
\(338\) 12.3265 + 7.11672i 0.670474 + 0.387099i
\(339\) 19.7945i 1.07509i
\(340\) 1.58063 2.73772i 0.0857215 0.148474i
\(341\) 28.7500i 1.55690i
\(342\) −0.102891 0.178213i −0.00556371 0.00963663i
\(343\) 20.1623 1.08866
\(344\) 2.70535 0.145863
\(345\) −1.74326 3.01941i −0.0938539 0.162560i
\(346\) 2.39485 + 1.38267i 0.128748 + 0.0743327i
\(347\) 36.2192i 1.94435i 0.234259 + 0.972174i \(0.424734\pi\)
−0.234259 + 0.972174i \(0.575266\pi\)
\(348\) 5.57892 3.22099i 0.299062 0.172663i
\(349\) 4.27797 + 7.40967i 0.228995 + 0.396630i 0.957510 0.288399i \(-0.0931228\pi\)
−0.728516 + 0.685029i \(0.759789\pi\)
\(350\) 1.87170 1.08063i 0.100047 0.0577619i
\(351\) −4.51941 2.60928i −0.241228 0.139273i
\(352\) −4.02112 2.32159i −0.214326 0.123741i
\(353\) 29.7047 17.1500i 1.58102 0.912804i 0.586312 0.810085i \(-0.300579\pi\)
0.994710 0.102719i \(-0.0327542\pi\)
\(354\) 2.27786 + 3.94537i 0.121067 + 0.209694i
\(355\) 3.91838 2.26228i 0.207966 0.120069i
\(356\) 15.5253i 0.822841i
\(357\) 5.91691 + 3.41613i 0.313156 + 0.180801i
\(358\) −0.586956 1.01664i −0.0310216 0.0537310i
\(359\) −0.531359 −0.0280441 −0.0140220 0.999902i \(-0.504464\pi\)
−0.0140220 + 0.999902i \(0.504464\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −9.47883 16.4178i −0.498886 0.864095i
\(362\) 21.1590i 1.11209i
\(363\) −5.27959 + 9.14453i −0.277107 + 0.479963i
\(364\) 11.2786i 0.591161i
\(365\) 4.25705 + 2.45781i 0.222824 + 0.128648i
\(366\) −5.32064 + 9.21562i −0.278114 + 0.481708i
\(367\) 10.6682 18.4778i 0.556873 0.964533i −0.440882 0.897565i \(-0.645334\pi\)
0.997755 0.0669678i \(-0.0213325\pi\)
\(368\) 3.01941 1.74326i 0.157398 0.0908736i
\(369\) −3.23393 −0.168351
\(370\) 2.83833 + 5.37995i 0.147557 + 0.279691i
\(371\) 2.50238 0.129917
\(372\) 5.36232 3.09594i 0.278023 0.160517i
\(373\) −12.0963 + 20.9513i −0.626320 + 1.08482i 0.361964 + 0.932192i \(0.382106\pi\)
−0.988284 + 0.152626i \(0.951227\pi\)
\(374\) 7.33914 12.7118i 0.379498 0.657310i
\(375\) −0.866025 0.500000i −0.0447214 0.0258199i
\(376\) 0.834167i 0.0430189i
\(377\) −16.8090 + 29.1140i −0.865706 + 1.49945i
\(378\) 2.16125i 0.111163i
\(379\) 12.1357 + 21.0196i 0.623367 + 1.07970i 0.988854 + 0.148886i \(0.0475689\pi\)
−0.365488 + 0.930816i \(0.619098\pi\)
\(380\) 0.205782 0.0105564
\(381\) 1.42718 0.0731169
\(382\) −5.42635 9.39872i −0.277636 0.480880i
\(383\) −11.1983 6.46534i −0.572206 0.330363i 0.185824 0.982583i \(-0.440505\pi\)
−0.758030 + 0.652220i \(0.773838\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 8.69065 5.01755i 0.442917 0.255718i
\(386\) 11.4872 + 19.8964i 0.584682 + 1.01270i
\(387\) 2.34291 1.35268i 0.119097 0.0687605i
\(388\) 0.132543 + 0.0765237i 0.00672885 + 0.00388490i
\(389\) −10.9293 6.31001i −0.554136 0.319930i 0.196653 0.980473i \(-0.436993\pi\)
−0.750788 + 0.660543i \(0.770326\pi\)
\(390\) 4.51941 2.60928i 0.228849 0.132126i
\(391\) 5.51088 + 9.54512i 0.278697 + 0.482718i
\(392\) 2.01696 1.16450i 0.101872 0.0588159i
\(393\) 15.9205i 0.803084i
\(394\) 15.9323 + 9.19854i 0.802659 + 0.463416i
\(395\) 1.19143 + 2.06361i 0.0599471 + 0.103831i
\(396\) −4.64319 −0.233329
\(397\) 1.44241 0.0723926 0.0361963 0.999345i \(-0.488476\pi\)
0.0361963 + 0.999345i \(0.488476\pi\)
\(398\) 5.46700 + 9.46911i 0.274036 + 0.474644i
\(399\) 0.444747i 0.0222652i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 19.5163i 0.974597i −0.873235 0.487299i \(-0.837982\pi\)
0.873235 0.487299i \(-0.162018\pi\)
\(402\) 0.312243 + 0.180274i 0.0155733 + 0.00899123i
\(403\) −16.1563 + 27.9836i −0.804805 + 1.39396i
\(404\) 4.21966 7.30867i 0.209936 0.363620i
\(405\) −0.866025 + 0.500000i −0.0430331 + 0.0248452i
\(406\) −13.9228 −0.690975
\(407\) 13.1789 + 24.9801i 0.653253 + 1.23822i
\(408\) 3.16125 0.156505
\(409\) −8.91730 + 5.14840i −0.440932 + 0.254572i −0.703993 0.710207i \(-0.748601\pi\)
0.263061 + 0.964779i \(0.415268\pi\)
\(410\) 1.61696 2.80066i 0.0798561 0.138315i
\(411\) −0.570579 + 0.988273i −0.0281446 + 0.0487479i
\(412\) −3.59622 2.07628i −0.177173 0.102291i
\(413\) 9.84606i 0.484493i
\(414\) 1.74326 3.01941i 0.0856765 0.148396i
\(415\) 13.9616i 0.685347i
\(416\) 2.60928 + 4.51941i 0.127931 + 0.221582i
\(417\) −2.76665 −0.135484
\(418\) 0.955485 0.0467343
\(419\) −3.05527 5.29188i −0.149260 0.258525i 0.781694 0.623662i \(-0.214356\pi\)
−0.930954 + 0.365136i \(0.881022\pi\)
\(420\) 1.87170 + 1.08063i 0.0913296 + 0.0527291i
\(421\) 28.0074i 1.36500i 0.730888 + 0.682498i \(0.239106\pi\)
−0.730888 + 0.682498i \(0.760894\pi\)
\(422\) −4.64980 + 2.68456i −0.226349 + 0.130683i
\(423\) −0.417084 0.722410i −0.0202793 0.0351248i
\(424\) 1.00272 0.578919i 0.0486963 0.0281148i
\(425\) 2.73772 + 1.58063i 0.132799 + 0.0766716i
\(426\) 3.91838 + 2.26228i 0.189846 + 0.109608i
\(427\) 19.9173 11.4992i 0.963865 0.556487i
\(428\) 8.48343 + 14.6937i 0.410062 + 0.710248i
\(429\) 20.9845 12.1154i 1.01314 0.584937i
\(430\) 2.70535i 0.130464i
\(431\) −13.3803 7.72513i −0.644507 0.372106i 0.141842 0.989889i \(-0.454698\pi\)
−0.786348 + 0.617783i \(0.788031\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 17.9207 0.861215 0.430607 0.902539i \(-0.358299\pi\)
0.430607 + 0.902539i \(0.358299\pi\)
\(434\) −13.3822 −0.642366
\(435\) 3.22099 + 5.57892i 0.154435 + 0.267489i
\(436\) 1.52817i 0.0731863i
\(437\) −0.358731 + 0.621341i −0.0171604 + 0.0297228i
\(438\) 4.91562i 0.234877i
\(439\) −3.25893 1.88155i −0.155540 0.0898013i 0.420210 0.907427i \(-0.361957\pi\)
−0.575750 + 0.817626i \(0.695290\pi\)
\(440\) 2.32159 4.02112i 0.110678 0.191699i
\(441\) 1.16450 2.01696i 0.0554522 0.0960460i
\(442\) −14.2870 + 8.24860i −0.679563 + 0.392346i
\(443\) 39.4966 1.87654 0.938271 0.345902i \(-0.112427\pi\)
0.938271 + 0.345902i \(0.112427\pi\)
\(444\) −3.24001 + 5.14804i −0.153764 + 0.244315i
\(445\) −15.5253 −0.735972
\(446\) −20.0596 + 11.5814i −0.949848 + 0.548395i
\(447\) −5.08331 + 8.80454i −0.240432 + 0.416441i
\(448\) −1.08063 + 1.87170i −0.0510548 + 0.0884295i
\(449\) −3.39675 1.96112i −0.160303 0.0925508i 0.417703 0.908584i \(-0.362835\pi\)
−0.578005 + 0.816033i \(0.696169\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 7.50786 13.0040i 0.353531 0.612334i
\(452\) 19.7945i 0.931057i
\(453\) −1.21847 2.11046i −0.0572489 0.0991580i
\(454\) −23.7706 −1.11561
\(455\) −11.2786 −0.528751
\(456\) 0.102891 + 0.178213i 0.00481831 + 0.00834557i
\(457\) −4.62565 2.67062i −0.216379 0.124926i 0.387894 0.921704i \(-0.373203\pi\)
−0.604272 + 0.796778i \(0.706536\pi\)
\(458\) 4.55782i 0.212973i
\(459\) 2.73772 1.58063i 0.127786 0.0737773i
\(460\) 1.74326 + 3.01941i 0.0812798 + 0.140781i
\(461\) 22.9413 13.2452i 1.06848 0.616889i 0.140716 0.990050i \(-0.455059\pi\)
0.927767 + 0.373161i \(0.121726\pi\)
\(462\) 8.69065 + 5.01755i 0.404326 + 0.233437i
\(463\) −29.0544 16.7746i −1.35027 0.779580i −0.361984 0.932184i \(-0.617901\pi\)
−0.988287 + 0.152604i \(0.951234\pi\)
\(464\) −5.57892 + 3.22099i −0.258995 + 0.149531i
\(465\) 3.09594 + 5.36232i 0.143571 + 0.248672i
\(466\) −15.8313 + 9.14018i −0.733369 + 0.423411i
\(467\) 19.4765i 0.901265i −0.892709 0.450633i \(-0.851198\pi\)
0.892709 0.450633i \(-0.148802\pi\)
\(468\) 4.51941 + 2.60928i 0.208910 + 0.120614i
\(469\) −0.389617 0.674836i −0.0179908 0.0311610i
\(470\) 0.834167 0.0384773
\(471\) 1.41083 0.0650074
\(472\) −2.27786 3.94537i −0.104847 0.181600i
\(473\) 12.5615i 0.577577i
\(474\) −1.19143 + 2.06361i −0.0547240 + 0.0947847i
\(475\) 0.205782i 0.00944193i
\(476\) −5.91691 3.41613i −0.271201 0.156578i
\(477\) 0.578919 1.00272i 0.0265069 0.0459113i
\(478\) 10.1798 17.6319i 0.465611 0.806462i
\(479\) 11.0157 6.35989i 0.503318 0.290591i −0.226765 0.973950i \(-0.572815\pi\)
0.730083 + 0.683359i \(0.239482\pi\)
\(480\) 1.00000 0.0456435
\(481\) 1.21027 31.7202i 0.0551834 1.44632i
\(482\) 15.3835 0.700698
\(483\) −6.52571 + 3.76762i −0.296930 + 0.171433i
\(484\) 5.27959 9.14453i 0.239982 0.415660i
\(485\) −0.0765237 + 0.132543i −0.00347476 + 0.00601847i
\(486\) −0.866025 0.500000i −0.0392837 0.0226805i
\(487\) 33.0632i 1.49824i −0.662435 0.749119i \(-0.730477\pi\)
0.662435 0.749119i \(-0.269523\pi\)
\(488\) 5.32064 9.21562i 0.240854 0.417172i
\(489\) 9.80785i 0.443526i
\(490\) 1.16450 + 2.01696i 0.0526065 + 0.0911172i
\(491\) 18.4326 0.831853 0.415927 0.909398i \(-0.363457\pi\)
0.415927 + 0.909398i \(0.363457\pi\)
\(492\) 3.23393 0.145797
\(493\) −10.1824 17.6364i −0.458591 0.794303i
\(494\) −0.930014 0.536944i −0.0418433 0.0241582i
\(495\) 4.64319i 0.208696i
\(496\) −5.36232 + 3.09594i −0.240775 + 0.139012i
\(497\) −4.88936 8.46861i −0.219318 0.379869i
\(498\) 12.0911 6.98079i 0.541814 0.312817i
\(499\) 34.0311 + 19.6479i 1.52344 + 0.879559i 0.999615 + 0.0277344i \(0.00882925\pi\)
0.523826 + 0.851825i \(0.324504\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 13.2273 7.63680i 0.590953 0.341187i
\(502\) −6.63994 11.5007i −0.296355 0.513302i
\(503\) −25.6760 + 14.8240i −1.14483 + 0.660970i −0.947623 0.319391i \(-0.896522\pi\)
−0.197211 + 0.980361i \(0.563188\pi\)
\(504\) 2.16125i 0.0962698i
\(505\) 7.30867 + 4.21966i 0.325231 + 0.187772i
\(506\) 8.09427 + 14.0197i 0.359834 + 0.623251i
\(507\) −14.2334 −0.632129
\(508\) −1.42718 −0.0633210
\(509\) −17.2652 29.9043i −0.765268 1.32548i −0.940105 0.340886i \(-0.889273\pi\)
0.174836 0.984598i \(-0.444060\pi\)
\(510\) 3.16125i 0.139983i
\(511\) 5.31194 9.20055i 0.234986 0.407008i
\(512\) 1.00000i 0.0441942i
\(513\) 0.178213 + 0.102891i 0.00786828 + 0.00454275i
\(514\) −1.45986 + 2.52855i −0.0643917 + 0.111530i
\(515\) 2.07628 3.59622i 0.0914918 0.158468i
\(516\) −2.34291 + 1.35268i −0.103141 + 0.0595483i
\(517\) 3.87320 0.170343
\(518\) 11.6274 6.13434i 0.510880 0.269527i
\(519\) −2.76534 −0.121385
\(520\) −4.51941 + 2.60928i −0.198189 + 0.114425i
\(521\) 21.9354 37.9932i 0.961006 1.66451i 0.241023 0.970519i \(-0.422517\pi\)
0.719983 0.693992i \(-0.244150\pi\)
\(522\) −3.22099 + 5.57892i −0.140979 + 0.244183i
\(523\) 24.1241 + 13.9281i 1.05487 + 0.609031i 0.924010 0.382369i \(-0.124892\pi\)
0.130864 + 0.991400i \(0.458225\pi\)
\(524\) 15.9205i 0.695491i
\(525\) −1.08063 + 1.87170i −0.0471624 + 0.0816876i
\(526\) 10.3676i 0.452049i
\(527\) −9.78703 16.9516i −0.426330 0.738425i
\(528\) 4.64319 0.202069
\(529\) 10.8442 0.471487
\(530\) 0.578919 + 1.00272i 0.0251466 + 0.0435553i
\(531\) −3.94537 2.27786i −0.171214 0.0988507i
\(532\) 0.444747i 0.0192822i
\(533\) −14.6154 + 8.43823i −0.633065 + 0.365500i
\(534\) −7.76267 13.4453i −0.335924 0.581837i
\(535\) −14.6937 + 8.48343i −0.635265 + 0.366771i
\(536\) −0.312243 0.180274i −0.0134868 0.00778663i
\(537\) 1.01664 + 0.586956i 0.0438712 + 0.0253290i
\(538\) 21.8620 12.6220i 0.942536 0.544173i
\(539\) 5.40697 + 9.36515i 0.232895 + 0.403385i
\(540\) 0.866025 0.500000i 0.0372678 0.0215166i
\(541\) 9.84613i 0.423318i −0.977344 0.211659i \(-0.932113\pi\)
0.977344 0.211659i \(-0.0678866\pi\)
\(542\) −14.1632 8.17713i −0.608362 0.351238i
\(543\) −10.5795 18.3242i −0.454009 0.786366i
\(544\) −3.16125 −0.135538
\(545\) −1.52817 −0.0654598
\(546\) −5.63932 9.76759i −0.241341 0.418014i
\(547\) 22.3203i 0.954348i −0.878809 0.477174i \(-0.841661\pi\)
0.878809 0.477174i \(-0.158339\pi\)
\(548\) 0.570579 0.988273i 0.0243739 0.0422169i
\(549\) 10.6413i 0.454159i
\(550\) 4.02112 + 2.32159i 0.171461 + 0.0989931i
\(551\) 0.662823 1.14804i 0.0282372 0.0489083i
\(552\) −1.74326 + 3.01941i −0.0741980 + 0.128515i
\(553\) 4.45998 2.57497i 0.189658 0.109499i
\(554\) 3.35255 0.142436
\(555\) −5.14804 3.24001i −0.218522 0.137531i
\(556\) 2.76665 0.117332
\(557\) −6.99456 + 4.03831i −0.296369 + 0.171109i −0.640811 0.767699i \(-0.721402\pi\)
0.344441 + 0.938808i \(0.388068\pi\)
\(558\) −3.09594 + 5.36232i −0.131061 + 0.227005i
\(559\) 7.05904 12.2266i 0.298565 0.517131i
\(560\) −1.87170 1.08063i −0.0790937 0.0456648i
\(561\) 14.6783i 0.619718i
\(562\) −1.68735 + 2.92257i −0.0711765 + 0.123281i
\(563\) 14.8077i 0.624069i −0.950071 0.312034i \(-0.898990\pi\)
0.950071 0.312034i \(-0.101010\pi\)
\(564\) 0.417084 + 0.722410i 0.0175624 + 0.0304190i
\(565\) −19.7945 −0.832763
\(566\) 20.8447 0.876167
\(567\) 1.08063 + 1.87170i 0.0453820 + 0.0786040i
\(568\) −3.91838 2.26228i −0.164412 0.0949232i
\(569\) 25.6916i 1.07705i 0.842611 + 0.538523i \(0.181018\pi\)
−0.842611 + 0.538523i \(0.818982\pi\)
\(570\) −0.178213 + 0.102891i −0.00746450 + 0.00430963i
\(571\) −2.31582 4.01112i −0.0969142 0.167860i 0.813492 0.581576i \(-0.197564\pi\)
−0.910406 + 0.413716i \(0.864231\pi\)
\(572\) −20.9845 + 12.1154i −0.877405 + 0.506570i
\(573\) 9.39872 + 5.42635i 0.392637 + 0.226689i
\(574\) −6.05294 3.49466i −0.252645 0.145864i
\(575\) −3.01941 + 1.74326i −0.125918 + 0.0726989i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) −26.8227 + 15.4861i −1.11664 + 0.644694i −0.940542 0.339678i \(-0.889682\pi\)
−0.176101 + 0.984372i \(0.556349\pi\)
\(578\) 7.00649i 0.291431i
\(579\) −19.8964 11.4872i −0.826866 0.477391i
\(580\) −3.22099 5.57892i −0.133744 0.231652i
\(581\) −30.1745 −1.25185
\(582\) −0.153047 −0.00634402
\(583\) 2.68803 + 4.65581i 0.111327 + 0.192824i
\(584\) 4.91562i 0.203410i
\(585\) −2.60928 + 4.51941i −0.107881 + 0.186855i
\(586\) 2.25632i 0.0932076i
\(587\) −32.3952 18.7033i −1.33709 0.771970i −0.350716 0.936482i \(-0.614062\pi\)
−0.986375 + 0.164512i \(0.947395\pi\)
\(588\) −1.16450 + 2.01696i −0.0480230 + 0.0831782i
\(589\) 0.637088 1.10347i 0.0262508 0.0454676i
\(590\) 3.94537 2.27786i 0.162428 0.0937780i
\(591\) −18.3971 −0.756755
\(592\) 3.24001 5.14804i 0.133164 0.211583i
\(593\) −10.9308 −0.448876 −0.224438 0.974488i \(-0.572055\pi\)
−0.224438 + 0.974488i \(0.572055\pi\)
\(594\) 4.02112 2.32159i 0.164988 0.0952561i
\(595\) 3.41613 5.91691i 0.140048 0.242570i
\(596\) 5.08331 8.80454i 0.208220 0.360648i
\(597\) −9.46911 5.46700i −0.387545 0.223749i
\(598\) 18.1946i 0.744033i
\(599\) −22.6620 + 39.2517i −0.925943 + 1.60378i −0.135906 + 0.990722i \(0.543394\pi\)
−0.790037 + 0.613059i \(0.789939\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) 19.7964 + 34.2884i 0.807514 + 1.39865i 0.914581 + 0.404403i \(0.132521\pi\)
−0.107067 + 0.994252i \(0.534146\pi\)
\(602\) 5.84695 0.238304
\(603\) −0.360547 −0.0146826
\(604\) 1.21847 + 2.11046i 0.0495790 + 0.0858733i
\(605\) 9.14453 + 5.27959i 0.371778 + 0.214646i
\(606\) 8.43932i 0.342824i
\(607\) 35.1813 20.3119i 1.42796 0.824435i 0.431004 0.902350i \(-0.358159\pi\)
0.996960 + 0.0779145i \(0.0248261\pi\)
\(608\) −0.102891 0.178213i −0.00417278 0.00722747i
\(609\) 12.0575 6.96138i 0.488593 0.282089i
\(610\) 9.21562 + 5.32064i 0.373130 + 0.215426i
\(611\) −3.76995 2.17658i −0.152516 0.0880550i
\(612\) −2.73772 + 1.58063i −0.110666 + 0.0638930i
\(613\) −7.78583 13.4855i −0.314467 0.544672i 0.664857 0.746970i \(-0.268492\pi\)
−0.979324 + 0.202298i \(0.935159\pi\)
\(614\) 12.1312 7.00396i 0.489576 0.282657i
\(615\) 3.23393i 0.130404i
\(616\) −8.69065 5.01755i −0.350156 0.202163i
\(617\) 10.5032 + 18.1921i 0.422843 + 0.732386i 0.996216 0.0869081i \(-0.0276987\pi\)
−0.573373 + 0.819295i \(0.694365\pi\)
\(618\) 4.15256 0.167040
\(619\) −29.8151 −1.19837 −0.599186 0.800610i \(-0.704509\pi\)
−0.599186 + 0.800610i \(0.704509\pi\)
\(620\) −3.09594 5.36232i −0.124336 0.215356i
\(621\) 3.48652i 0.139909i
\(622\) 9.94062 17.2177i 0.398582 0.690365i
\(623\) 33.5542i 1.34432i
\(624\) −4.51941 2.60928i −0.180921 0.104455i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −12.1665 + 21.0731i −0.486273 + 0.842249i
\(627\) −0.827474 + 0.477742i −0.0330461 + 0.0190792i
\(628\) −1.41083 −0.0562981
\(629\) 16.2742 + 10.2425i 0.648897 + 0.408395i
\(630\) −2.16125 −0.0861063
\(631\) −19.1456 + 11.0537i −0.762173 + 0.440041i −0.830075 0.557651i \(-0.811703\pi\)
0.0679026 + 0.997692i \(0.478369\pi\)
\(632\) 1.19143 2.06361i 0.0473924 0.0820860i
\(633\) 2.68456 4.64980i 0.106702 0.184813i
\(634\) 3.98649 + 2.30160i 0.158324 + 0.0914081i
\(635\) 1.42718i 0.0566361i
\(636\) −0.578919 + 1.00272i −0.0229556 + 0.0397603i
\(637\) 12.1540i 0.481559i
\(638\) −14.9557 25.9040i −0.592101 1.02555i
\(639\) −4.52456 −0.178989
\(640\) −1.00000 −0.0395285
\(641\) −2.21636 3.83886i −0.0875411 0.151626i 0.818930 0.573893i \(-0.194568\pi\)
−0.906471 + 0.422268i \(0.861234\pi\)
\(642\) −14.6937 8.48343i −0.579915 0.334814i
\(643\) 44.3817i 1.75024i 0.483902 + 0.875122i \(0.339219\pi\)
−0.483902 + 0.875122i \(0.660781\pi\)
\(644\) 6.52571 3.76762i 0.257149 0.148465i
\(645\) −1.35268 2.34291i −0.0532616 0.0922518i
\(646\) 0.563375 0.325265i 0.0221657 0.0127974i
\(647\) −36.1565 20.8750i −1.42146 0.820681i −0.425037 0.905176i \(-0.639739\pi\)
−0.996424 + 0.0844957i \(0.973072\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 18.3191 10.5765i 0.719087 0.415165i
\(650\) −2.60928 4.51941i −0.102345 0.177266i
\(651\) 11.5893 6.69110i 0.454221 0.262245i
\(652\) 9.80785i 0.384105i
\(653\) 15.9953 + 9.23488i 0.625944 + 0.361389i 0.779179 0.626801i \(-0.215636\pi\)
−0.153236 + 0.988190i \(0.548969\pi\)
\(654\) −0.764087 1.32344i −0.0298782 0.0517505i
\(655\) −15.9205 −0.622066
\(656\) −3.23393 −0.126264
\(657\) −2.45781 4.25705i −0.0958882 0.166083i
\(658\) 1.80285i 0.0702823i
\(659\) 3.89081 6.73909i 0.151565 0.262518i −0.780238 0.625482i \(-0.784902\pi\)
0.931803 + 0.362965i \(0.118236\pi\)
\(660\) 4.64319i 0.180736i
\(661\) 24.6064 + 14.2065i 0.957077 + 0.552569i 0.895272 0.445520i \(-0.146981\pi\)
0.0618049 + 0.998088i \(0.480314\pi\)
\(662\) −13.1193 + 22.7234i −0.509898 + 0.883169i
\(663\) 8.24860 14.2870i 0.320349 0.554861i
\(664\) −12.0911 + 6.98079i −0.469225 + 0.270907i
\(665\) 0.444747 0.0172465
\(666\) 0.231916 6.07834i 0.00898655 0.235531i
\(667\) 22.4601 0.869658
\(668\) −13.2273 + 7.63680i −0.511781 + 0.295477i
\(669\) 11.5814 20.0596i 0.447763 0.775547i
\(670\) 0.180274 0.312243i 0.00696457 0.0120630i
\(671\) 42.7899 + 24.7047i 1.65188 + 0.953716i
\(672\) 2.16125i 0.0833721i
\(673\) −11.5000 + 19.9185i −0.443291 + 0.767803i −0.997931 0.0642874i \(-0.979523\pi\)
0.554640 + 0.832090i \(0.312856\pi\)
\(674\) 9.66872i 0.372425i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 14.2334 0.547440
\(677\) 41.5752 1.59786 0.798932 0.601422i \(-0.205399\pi\)
0.798932 + 0.601422i \(0.205399\pi\)
\(678\) −9.89727 17.1426i −0.380103 0.658357i
\(679\) 0.286459 + 0.165387i 0.0109933 + 0.00634697i
\(680\) 3.16125i 0.121228i
\(681\) 20.5859 11.8853i 0.788855 0.455446i
\(682\) −14.3750 24.8982i −0.550448 0.953403i
\(683\) −8.30680 + 4.79594i −0.317851 + 0.183511i −0.650434 0.759563i \(-0.725413\pi\)
0.332583 + 0.943074i \(0.392080\pi\)
\(684\) −0.178213 0.102891i −0.00681413 0.00393414i
\(685\) 0.988273 + 0.570579i 0.0377600 + 0.0218007i
\(686\) 17.4611 10.0811i 0.666666 0.384900i
\(687\) −2.27891 3.94718i −0.0869458 0.150594i
\(688\) 2.34291 1.35268i 0.0893224 0.0515703i
\(689\) 6.04226i 0.230192i
\(690\) −3.01941 1.74326i −0.114947 0.0663647i
\(691\) −14.0821 24.3909i −0.535709 0.927875i −0.999129 0.0417362i \(-0.986711\pi\)
0.463420 0.886139i \(-0.346622\pi\)
\(692\) 2.76534 0.105122
\(693\) −10.0351 −0.381202
\(694\) 18.1096 + 31.3667i 0.687431 + 1.19067i
\(695\) 2.76665i 0.104945i
\(696\) 3.22099 5.57892i 0.122091 0.211469i
\(697\) 10.2233i 0.387233i
\(698\) 7.40967 + 4.27797i 0.280460 + 0.161924i
\(699\) 9.14018 15.8313i 0.345713 0.598793i
\(700\) 1.08063 1.87170i 0.0408438 0.0707436i
\(701\) 23.6784 13.6707i 0.894319 0.516335i 0.0189664 0.999820i \(-0.493962\pi\)
0.875353 + 0.483485i \(0.160629\pi\)
\(702\) −5.21857 −0.196962
\(703\) −0.0477241 + 1.25081i −0.00179995 + 0.0471753i
\(704\) −4.64319 −0.174997
\(705\) −0.722410 + 0.417084i −0.0272075 + 0.0157083i
\(706\) 17.1500 29.7047i 0.645450 1.11795i
\(707\) 9.11975 15.7959i 0.342983 0.594065i
\(708\) 3.94537 + 2.27786i 0.148276 + 0.0856072i
\(709\) 1.92294i 0.0722174i 0.999348 + 0.0361087i \(0.0114963\pi\)
−0.999348 + 0.0361087i \(0.988504\pi\)
\(710\) 2.26228 3.91838i 0.0849019 0.147054i
\(711\) 2.38285i 0.0893639i
\(712\) 7.76267 + 13.4453i 0.290918 + 0.503885i
\(713\) 21.5881 0.808479
\(714\) 6.83226 0.255691
\(715\) −12.1154 20.9845i −0.453090 0.784775i
\(716\) −1.01664 0.586956i −0.0379936 0.0219356i
\(717\) 20.3595i 0.760340i
\(718\) −0.460171 + 0.265680i −0.0171734 + 0.00991508i
\(719\) 10.1641 + 17.6047i 0.379056 + 0.656544i 0.990925 0.134415i \(-0.0429155\pi\)
−0.611869 + 0.790959i \(0.709582\pi\)
\(720\) −0.866025 + 0.500000i −0.0322749 + 0.0186339i
\(721\) −7.77234 4.48736i −0.289457 0.167118i
\(722\) −16.4178 9.47883i −0.611008 0.352765i
\(723\) −13.3225 + 7.69174i −0.495468 + 0.286059i
\(724\) 10.5795 + 18.3242i 0.393183 + 0.681013i
\(725\) 5.57892 3.22099i 0.207196 0.119625i
\(726\) 10.5592i 0.391888i
\(727\) −35.6599 20.5883i −1.32255 0.763576i −0.338418 0.940996i \(-0.609892\pi\)
−0.984135 + 0.177420i \(0.943225\pi\)
\(728\) 5.63932 + 9.76759i 0.209007 + 0.362011i
\(729\) 1.00000 0.0370370
\(730\) 4.91562 0.181935
\(731\) 4.27615 + 7.40652i 0.158159 + 0.273940i
\(732\) 10.6413i 0.393313i
\(733\) 17.2131 29.8140i 0.635782 1.10121i −0.350567 0.936538i \(-0.614011\pi\)
0.986349 0.164669i \(-0.0526556\pi\)
\(734\) 21.3363i 0.787538i
\(735\) −2.01696 1.16450i −0.0743969 0.0429531i
\(736\) 1.74326 3.01941i 0.0642573 0.111297i
\(737\) 0.837044 1.44980i 0.0308329 0.0534042i
\(738\) −2.80066 + 1.61696i −0.103094 + 0.0595212i
\(739\) 29.2229 1.07498 0.537490 0.843270i \(-0.319372\pi\)
0.537490 + 0.843270i \(0.319372\pi\)
\(740\) 5.14804 + 3.24001i 0.189246 + 0.119105i
\(741\) 1.07389 0.0394503
\(742\) 2.16713 1.25119i 0.0795577 0.0459326i
\(743\) 12.0985 20.9553i 0.443852 0.768774i −0.554119 0.832437i \(-0.686945\pi\)
0.997971 + 0.0636630i \(0.0202783\pi\)
\(744\) 3.09594 5.36232i 0.113503 0.196592i
\(745\) 8.80454 + 5.08331i 0.322574 + 0.186238i
\(746\) 24.1925i 0.885750i
\(747\) −6.98079 + 12.0911i −0.255414 + 0.442390i
\(748\) 14.6783i 0.536691i
\(749\) 18.3348 + 31.7569i 0.669940 + 1.16037i
\(750\) −1.00000 −0.0365148
\(751\) 17.0205 0.621085 0.310543 0.950559i \(-0.399489\pi\)
0.310543 + 0.950559i \(0.399489\pi\)
\(752\) −0.417084 0.722410i −0.0152095 0.0263436i
\(753\) 11.5007 + 6.63994i 0.419110 + 0.241973i
\(754\) 33.6179i 1.22429i
\(755\) −2.11046 + 1.21847i −0.0768074 + 0.0443448i
\(756\) −1.08063 1.87170i −0.0393020 0.0680730i
\(757\) 43.0684 24.8655i 1.56535 0.903753i 0.568646 0.822582i \(-0.307467\pi\)
0.996700 0.0811706i \(-0.0258659\pi\)
\(758\) 21.0196 + 12.1357i 0.763465 + 0.440787i
\(759\) −14.0197 8.09427i −0.508883 0.293804i
\(760\) 0.178213 0.102891i 0.00646445 0.00373225i
\(761\) −2.37295 4.11007i −0.0860193 0.148990i 0.819806 0.572642i \(-0.194081\pi\)
−0.905825 + 0.423652i \(0.860748\pi\)
\(762\) 1.23598 0.713592i 0.0447747 0.0258507i
\(763\) 3.30277i 0.119568i
\(764\) −9.39872 5.42635i −0.340034 0.196319i
\(765\) −1.58063 2.73772i −0.0571477 0.0989826i
\(766\) −12.9307 −0.467204
\(767\) −23.7743 −0.858441
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 35.1897i 1.26897i −0.772934 0.634486i \(-0.781212\pi\)
0.772934 0.634486i \(-0.218788\pi\)
\(770\) 5.01755 8.69065i 0.180820 0.313189i
\(771\) 2.91972i 0.105151i
\(772\) 19.8964 + 11.4872i 0.716087 + 0.413433i
\(773\) −1.01203 + 1.75289i −0.0364003 + 0.0630471i −0.883652 0.468145i \(-0.844922\pi\)
0.847251 + 0.531192i \(0.178256\pi\)
\(774\) 1.35268 2.34291i 0.0486210 0.0842140i
\(775\) 5.36232 3.09594i 0.192620 0.111209i
\(776\) 0.153047 0.00549408
\(777\) −7.00