Properties

Label 1110.2.x.d.841.7
Level $1110$
Weight $2$
Character 1110.841
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 841.7
Root \(2.16125i\) of defining polynomial
Character \(\chi\) \(=\) 1110.841
Dual form 1110.2.x.d.751.7

$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

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 0.994715 0.102675i \(-0.0327402\pi\)
−0.586277 + 0.810111i \(0.699407\pi\)
\(8\) 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 −0.971795 0.235828i \(-0.924220\pi\)
−0.281664 + 0.959513i \(0.590886\pi\)
\(14\) 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 0.793798 0.608182i \(-0.208101\pi\)
−0.129802 + 0.991540i \(0.541434\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) 0.178213 0.102891i 0.0408848 0.0236048i −0.479418 0.877587i \(-0.659152\pi\)
0.520303 + 0.853982i \(0.325819\pi\)
\(20\) 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 \(-0.881584\pi\)
0.931596 0.363494i \(-0.118416\pi\)
\(24\) 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 \(0.204087\pi\)
−0.801404 + 0.598123i \(0.795913\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 6.19187i 1.11209i 0.831151 + 0.556046i \(0.187682\pi\)
−0.831151 + 0.556046i \(0.812318\pi\)
\(32\) −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 0.964221 0.265100i \(-0.0854050\pi\)
−0.711694 + 0.702490i \(0.752072\pi\)
\(42\) 1.87170 1.08063i 0.288809 0.166744i
\(43\) 2.70535i 0.412563i −0.978493 0.206281i \(-0.933864\pi\)
0.978493 0.206281i \(-0.0661362\pi\)
\(44\) 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 −0.823523 0.567284i \(-0.807994\pi\)
0.903043 + 0.429550i \(0.141328\pi\)
\(54\) 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 0.734330 0.678793i \(-0.237496\pi\)
−0.220687 + 0.975345i \(0.570830\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 9.21562 5.32064i 1.17994 0.681238i 0.223939 0.974603i \(-0.428108\pi\)
0.956001 + 0.293365i \(0.0947751\pi\)
\(62\) −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 0.876827 0.480805i \(-0.159656\pi\)
−0.854803 + 0.518952i \(0.826322\pi\)
\(68\) 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 0.968470 0.249129i \(-0.0801443\pi\)
−0.699987 + 0.714155i \(0.746811\pi\)
\(72\) −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 −0.379400 0.925233i \(-0.623870\pi\)
0.611575 + 0.791187i \(0.290536\pi\)
\(80\) 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 0.173347 + 0.984861i \(0.444542\pi\)
−0.939588 + 0.342308i \(0.888791\pi\)
\(84\) 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 −0.428466 0.903558i \(-0.640946\pi\)
−0.996737 + 0.0807166i \(0.974279\pi\)
\(90\) −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 \(-0.997527\pi\)
0.999970 0.00776981i \(-0.00247323\pi\)
\(98\) 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 \(0.0655834\pi\)
−0.978849 + 0.204582i \(0.934417\pi\)
\(104\) −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 −0.905589 0.424155i \(-0.860571\pi\)
0.0854653 0.996341i \(-0.472762\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −1.32344 0.764087i −0.126762 0.0731863i 0.435278 0.900296i \(-0.356650\pi\)
−0.562040 + 0.827110i \(0.689983\pi\)
\(110\) 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 −0.988756 0.149539i \(-0.952221\pi\)
−0.623883 0.781518i \(-0.714446\pi\)
\(114\) −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 −0.895948 0.444159i \(-0.853503\pi\)
0.832627 + 0.553834i \(0.186836\pi\)
\(128\) −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 −0.243045 0.970015i \(-0.578146\pi\)
−0.961580 + 0.274524i \(0.911480\pi\)
\(132\) 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 −0.801377 0.598159i \(-0.795899\pi\)
0.918710 + 0.394934i \(0.129232\pi\)
\(140\) 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 0.812178 0.583409i \(-0.198282\pi\)
−0.911336 + 0.411663i \(0.864948\pi\)
\(152\) 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 −0.892801 0.450451i \(-0.851263\pi\)
0.836503 + 0.547963i \(0.184596\pi\)
\(158\) 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 0.129000 0.991645i \(-0.458823\pi\)
−0.794289 + 0.607539i \(0.792157\pi\)
\(164\) −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 −0.915134 0.403151i \(-0.867915\pi\)
−0.108428 + 0.994104i \(0.534582\pi\)
\(168\) 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 −0.808666 0.588268i \(-0.799810\pi\)
0.913788 + 0.406191i \(0.133143\pi\)
\(174\) 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 \(0.0139691\pi\)
−0.999037 + 0.0438712i \(0.986031\pi\)
\(180\) −0.866025 + 0.500000i −0.0645497 + 0.0372678i
\(181\) −10.5795 18.3242i −0.786366 1.36203i −0.928179 0.372133i \(-0.878626\pi\)
0.141813 0.989893i \(-0.454707\pi\)
\(182\) −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 \(0.128437\pi\)
−0.919694 + 0.392637i \(0.871563\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 22.9744i 1.65373i −0.562399 0.826866i \(-0.690122\pi\)
0.562399 0.826866i \(-0.309878\pi\)
\(194\) 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 −0.326433 0.945221i \(-0.605847\pi\)
0.981801 0.189911i \(-0.0608201\pi\)
\(198\) −4.02112 + 2.32159i −0.285768 + 0.164988i
\(199\) 10.9340i 0.775090i −0.921851 0.387545i \(-0.873323\pi\)
0.921851 0.387545i \(-0.126677\pi\)
\(200\) 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 −0.990458 0.137814i \(-0.955992\pi\)
−0.375879 + 0.926669i \(0.622659\pi\)
\(228\) 0.205782i 0.0136283i
\(229\) −2.27891 3.94718i −0.150594 0.260837i 0.780852 0.624716i \(-0.214785\pi\)
−0.931446 + 0.363879i \(0.881452\pi\)
\(230\) 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 0.946557 0.322537i \(-0.104536\pi\)
0.193953 + 0.981011i \(0.437869\pi\)
\(240\) 0.866025 0.500000i 0.0559017 0.0322749i
\(241\) 13.3225 7.69174i 0.858176 0.495468i −0.00522493 0.999986i \(-0.501663\pi\)
0.863401 + 0.504518i \(0.168330\pi\)
\(242\) 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 \(0.137658\pi\)
−0.907936 + 0.419110i \(0.862342\pi\)
\(252\) −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 0.419059 0.907959i \(-0.362360\pi\)
−0.576786 + 0.816895i \(0.695693\pi\)
\(258\) −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 0.660767 0.750591i \(-0.270231\pi\)
−0.980414 + 0.196946i \(0.936898\pi\)
\(264\) 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 −0.999993 0.00377716i \(-0.998798\pi\)
0.503268 + 0.864131i \(0.332131\pi\)
\(272\) −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 −0.410233 0.911981i \(-0.634553\pi\)
0.584682 + 0.811263i \(0.301219\pi\)
\(278\) 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 0.410287 0.911956i \(-0.365428\pi\)
−0.584634 + 0.811297i \(0.698762\pi\)
\(282\) 0.834167i 0.0496740i
\(283\) 18.0520 10.4223i 1.07308 0.619543i 0.144059 0.989569i \(-0.453984\pi\)
0.929022 + 0.370026i \(0.120651\pi\)
\(284\) −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 0.897096 0.441835i \(-0.145672\pi\)
−0.831189 + 0.555991i \(0.812339\pi\)
\(294\) −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 0.901158 0.433490i \(-0.142718\pi\)
0.0751653 + 0.997171i \(0.476052\pi\)
\(312\) −2.60928 + 4.51941i −0.147722 + 0.255861i
\(313\) −21.0731 12.1665i −1.19112 0.687694i −0.232560 0.972582i \(-0.574710\pi\)
−0.958561 + 0.284888i \(0.908043\pi\)
\(314\) −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 −0.794124 0.607756i \(-0.792070\pi\)
0.923394 + 0.383853i \(0.125403\pi\)
\(318\) −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 −0.278082 0.960557i \(-0.589699\pi\)
−0.970908 + 0.239453i \(0.923032\pi\)
\(332\) −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 0.967129 0.254288i \(-0.0818412\pi\)
−0.703784 + 0.710414i \(0.748508\pi\)
\(338\) 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 \(-0.575266\pi\)
0.234259 0.972174i \(-0.424734\pi\)
\(348\) 5.57892 + 3.22099i 0.299062 + 0.172663i
\(349\) 4.27797 7.40967i 0.228995 0.396630i −0.728516 0.685029i \(-0.759789\pi\)
0.957510 + 0.288399i \(0.0931228\pi\)
\(350\) 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 0.994710 + 0.102719i \(0.0327542\pi\)
0.586312 + 0.810085i \(0.300579\pi\)
\(354\) 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 0.997755 + 0.0669678i \(0.0213325\pi\)
−0.440882 + 0.897565i \(0.645334\pi\)
\(368\) 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 −0.988284 0.152626i \(-0.951227\pi\)
0.361964 0.932192i \(-0.382106\pi\)
\(374\) 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 −0.365488 0.930816i \(-0.619098\pi\)
0.988854 0.148886i \(-0.0475689\pi\)
\(380\) 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 −0.758030 0.652220i \(-0.773838\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(384\) 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 −0.750788 0.660543i \(-0.770326\pi\)
0.196653 + 0.980473i \(0.436993\pi\)
\(390\) 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 \(0.162018\pi\)
−0.873235 + 0.487299i \(0.837982\pi\)
\(402\) 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 0.263061 0.964779i \(-0.415268\pi\)
−0.703993 + 0.710207i \(0.748601\pi\)
\(410\) 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 −0.930954 0.365136i \(-0.881022\pi\)
0.781694 + 0.623662i \(0.214356\pi\)
\(420\) 1.87170 1.08063i 0.0913296 0.0527291i
\(421\) 28.0074i 1.36500i −0.730888 0.682498i \(-0.760894\pi\)
0.730888 0.682498i \(-0.239106\pi\)
\(422\) −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 −0.786348 0.617783i \(-0.788031\pi\)
0.141842 + 0.989889i \(0.454698\pi\)
\(432\) −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 −0.575750 0.817626i \(-0.695290\pi\)
0.420210 + 0.907427i \(0.361957\pi\)
\(440\) 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 −0.578005 0.816033i \(-0.696169\pi\)
0.417703 + 0.908584i \(0.362835\pi\)
\(450\) 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 −0.604272 0.796778i \(-0.706536\pi\)
0.387894 + 0.921704i \(0.373203\pi\)
\(458\) 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 0.927767 0.373161i \(-0.121726\pi\)
0.140716 + 0.990050i \(0.455059\pi\)
\(462\) 8.69065 5.01755i 0.404326 0.233437i
\(463\) −29.0544 + 16.7746i −1.35027 + 0.779580i −0.988287 0.152604i \(-0.951234\pi\)
−0.361984 + 0.932184i \(0.617901\pi\)
\(464\) −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 \(0.148802\pi\)
−0.892709 + 0.450633i \(0.851198\pi\)
\(468\) 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 0.730083 0.683359i \(-0.239482\pi\)
−0.226765 + 0.973950i \(0.572815\pi\)
\(480\) 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 \(0.269523\pi\)
−0.662435 + 0.749119i \(0.730477\pi\)
\(488\) 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 0.523826 0.851825i \(-0.324504\pi\)
0.999615 0.0277344i \(-0.00882925\pi\)
\(500\) 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 −0.197211 0.980361i \(-0.563188\pi\)
−0.947623 + 0.319391i \(0.896522\pi\)
\(504\) 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 0.174836 + 0.984598i \(0.444060\pi\)
−0.940105 + 0.340886i \(0.889273\pi\)
\(510\) 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 0.719983 + 0.693992i \(0.244150\pi\)
0.241023 + 0.970519i \(0.422517\pi\)
\(522\) −3.22099 5.57892i −0.140979 0.244183i
\(523\) 24.1241 13.9281i 1.05487 0.609031i 0.130864 0.991400i \(-0.458225\pi\)
0.924010 + 0.382369i \(0.124892\pi\)
\(524\) 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 \(0.0678866\pi\)
−0.977344 + 0.211659i \(0.932113\pi\)
\(542\) −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 \(0.158339\pi\)
−0.878809 + 0.477174i \(0.841661\pi\)
\(548\) 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 0.344441 0.938808i \(-0.388068\pi\)
−0.640811 + 0.767699i \(0.721402\pi\)
\(558\) −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 \(0.101010\pi\)
−0.950071 + 0.312034i \(0.898990\pi\)
\(564\) 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 \(-0.818982\pi\)
0.842611 0.538523i \(-0.181018\pi\)
\(570\) −0.178213 0.102891i −0.00746450 0.00430963i
\(571\) −2.31582 + 4.01112i −0.0969142 + 0.167860i −0.910406 0.413716i \(-0.864231\pi\)
0.813492 + 0.581576i \(0.197564\pi\)
\(572\) −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 −0.176101 0.984372i \(-0.556349\pi\)
−0.940542 + 0.339678i \(0.889682\pi\)
\(578\) 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 −0.986375 0.164512i \(-0.947395\pi\)
−0.350716 + 0.936482i \(0.614062\pi\)
\(588\) −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 −0.790037 0.613059i \(-0.789939\pi\)
−0.135906 0.990722i \(-0.543394\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) 19.7964 34.2884i 0.807514 1.39865i −0.107067 0.994252i \(-0.534146\pi\)
0.914581 0.404403i \(-0.132521\pi\)
\(602\) 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 0.996960 0.0779145i \(-0.0248261\pi\)
0.431004 + 0.902350i \(0.358159\pi\)
\(608\) −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 −0.979324 0.202298i \(-0.935159\pi\)
0.664857 + 0.746970i \(0.268492\pi\)
\(614\) 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 −0.573373 0.819295i \(-0.694365\pi\)
0.996216 + 0.0869081i \(0.0276987\pi\)
\(618\) 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 0.0679026 0.997692i \(-0.478369\pi\)
−0.830075 + 0.557651i \(0.811703\pi\)
\(632\) 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 −0.906471 0.422268i \(-0.861234\pi\)
0.818930 + 0.573893i \(0.194568\pi\)
\(642\) −14.6937 + 8.48343i −0.579915 + 0.334814i
\(643\) 44.3817i 1.75024i −0.483902 0.875122i \(-0.660781\pi\)
0.483902 0.875122i \(-0.339219\pi\)
\(644\) 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 −0.996424 0.0844957i \(-0.973072\pi\)
−0.425037 + 0.905176i \(0.639739\pi\)
\(648\) 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 −0.153236 0.988190i \(-0.548969\pi\)
0.779179 + 0.626801i \(0.215636\pi\)
\(654\) −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 0.931803 0.362965i \(-0.118236\pi\)
−0.780238 + 0.625482i \(0.784902\pi\)
\(660\) 4.64319i 0.180736i
\(661\) 24.6064 14.2065i 0.957077 0.552569i 0.0618049 0.998088i \(-0.480314\pi\)
0.895272 + 0.445520i \(0.146981\pi\)
\(662\) −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 0.554640 0.832090i \(-0.312856\pi\)
−0.997931 + 0.0642874i \(0.979523\pi\)
\(674\) 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 0.332583 0.943074i \(-0.392080\pi\)
−0.650434 + 0.759563i \(0.725413\pi\)
\(684\) −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 0.463420 + 0.886139i \(0.346622\pi\)
−0.999129 + 0.0417362i \(0.986711\pi\)
\(692\) 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 0.875353 0.483485i \(-0.160629\pi\)
0.0189664 + 0.999820i \(0.493962\pi\)
\(702\) −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 \(-0.988504\pi\)
0.999348 0.0361087i \(-0.0114963\pi\)
\(710\) 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 −0.611869 0.790959i \(-0.709582\pi\)
0.990925 + 0.134415i \(0.0429155\pi\)
\(720\) −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 −0.984135 0.177420i \(-0.943225\pi\)
−0.338418 + 0.940996i \(0.609892\pi\)
\(728\) 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 0.986349 + 0.164669i \(0.0526556\pi\)
−0.350567 + 0.936538i \(0.614011\pi\)
\(734\) 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 0.997971 0.0636630i \(-0.0202783\pi\)
−0.554119 + 0.832437i \(0.686945\pi\)
\(744\) 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 0.996700 + 0.0811706i \(0.0258659\pi\)
0.568646 + 0.822582i \(0.307467\pi\)
\(758\) 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 −0.905825 0.423652i \(-0.860748\pi\)
0.819806 + 0.572642i \(0.194081\pi\)
\(762\) 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 \(0.218788\pi\)
−0.772934 + 0.634486i \(0.781212\pi\)
\(770\) 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 0.847251 0.531192i \(-0.178256\pi\)
−0.883652 + 0.468145i \(0.844922\pi\)
\(774\) 1.35268 + 2.34291i 0.0486210 + 0.0842140i
\(775\) 5.36232 + 3.09594i 0.192620 + 0.111209i
\(776\) 0.153047 0.00549408
\(777\) −7.00249 11.1262i