Properties

Label 390.2.bb.c.361.1
Level $390$
Weight $2$
Character 390.361
Analytic conductor $3.114$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(3.17270 - 3.17270i\) of defining polynomial
Character \(\chi\) \(=\) 390.361
Dual form 390.2.bb.c.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(4.62926 - 2.67270i) q^{11} -1.00000 q^{12} +(-3.60194 - 0.161290i) q^{13} +2.32258 q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} -1.00000i q^{18} +(-3.48387 - 2.01141i) q^{19} +(0.866025 + 0.500000i) q^{20} +2.32258i q^{21} +(-2.67270 + 4.62926i) q^{22} +(-2.46797 - 4.27464i) q^{23} +(0.866025 - 0.500000i) q^{24} -1.00000 q^{25} +(3.20002 - 1.66129i) q^{26} +1.00000 q^{27} +(-2.01141 + 1.16129i) q^{28} +(-2.14539 - 3.71592i) q^{29} +(-0.500000 + 0.866025i) q^{30} -3.47183i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.62926 - 2.67270i) q^{33} +4.00000i q^{34} +(1.16129 - 2.01141i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.72733 + 1.57463i) q^{37} +4.02283 q^{38} +(1.66129 + 3.20002i) q^{39} -1.00000 q^{40} +(2.29078 - 1.32258i) q^{41} +(-1.16129 - 2.01141i) q^{42} +(6.12539 - 10.6095i) q^{43} -5.34541i q^{44} +(-0.866025 - 0.500000i) q^{45} +(4.27464 + 2.46797i) q^{46} +1.81894i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.802812 - 1.39051i) q^{49} +(0.866025 - 0.500000i) q^{50} -4.00000 q^{51} +(-1.94065 + 3.03873i) q^{52} -5.48693 q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.67270 + 4.62926i) q^{55} +(1.16129 - 2.01141i) q^{56} +4.02283i q^{57} +(3.71592 + 2.14539i) q^{58} +(5.87744 + 3.39334i) q^{59} -1.00000i q^{60} +(-0.267949 + 0.464102i) q^{61} +(1.73592 + 3.00670i) q^{62} +(2.01141 - 1.16129i) q^{63} -1.00000 q^{64} +(0.161290 - 3.60194i) q^{65} +5.34541 q^{66} +(3.55872 - 2.05463i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-2.46797 + 4.27464i) q^{69} +2.32258i q^{70} +(13.7454 + 7.93593i) q^{71} +(-0.866025 - 0.500000i) q^{72} +13.5734i q^{73} +(1.57463 - 2.72733i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-3.48387 + 2.01141i) q^{76} -12.4151 q^{77} +(-3.03873 - 1.94065i) q^{78} -7.96774 q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.32258 + 2.29078i) q^{82} +11.3360i q^{83} +(2.01141 + 1.16129i) q^{84} +(3.46410 + 2.00000i) q^{85} +12.2508i q^{86} +(-2.14539 + 3.71592i) q^{87} +(2.67270 + 4.62926i) q^{88} +(-1.50670 + 0.869891i) q^{89} +1.00000 q^{90} +(7.05769 + 4.50732i) q^{91} -4.93593 q^{92} +(-3.00670 + 1.73592i) q^{93} +(-0.909471 - 1.57525i) q^{94} +(2.01141 - 3.48387i) q^{95} -1.00000i q^{96} +(-13.9510 - 8.05463i) q^{97} +(1.39051 + 0.802812i) q^{98} +5.34541i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{3} + 4q^{4} - 4q^{9} - 4q^{10} + 6q^{11} - 8q^{12} - 12q^{13} + 4q^{14} - 4q^{16} + 16q^{17} - 6q^{19} + 2q^{22} + 4q^{23} - 8q^{25} - 12q^{26} + 8q^{27} - 8q^{29} - 4q^{30} - 6q^{33} + 2q^{35} + 4q^{36} + 30q^{37} + 6q^{39} - 8q^{40} - 2q^{42} + 14q^{43} - 6q^{46} - 4q^{48} + 14q^{49} - 32q^{51} - 6q^{52} + 16q^{53} - 2q^{55} + 2q^{56} - 6q^{58} + 24q^{59} - 16q^{61} + 4q^{62} - 8q^{64} - 6q^{65} - 4q^{66} + 24q^{67} - 16q^{68} + 4q^{69} - 12q^{71} + 10q^{74} + 4q^{75} - 6q^{76} + 16q^{77} + 6q^{78} - 20q^{79} - 4q^{81} + 4q^{82} - 8q^{87} - 2q^{88} + 42q^{89} + 8q^{90} - 10q^{91} + 8q^{92} + 30q^{93} - 8q^{94} - 24q^{97} + 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) −2.01141 1.16129i −0.760243 0.438926i 0.0691402 0.997607i \(-0.477974\pi\)
−0.829383 + 0.558681i \(0.811308\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 4.62926 2.67270i 1.39577 0.805850i 0.401827 0.915716i \(-0.368375\pi\)
0.993946 + 0.109865i \(0.0350420\pi\)
\(12\) −1.00000 −0.288675
\(13\) −3.60194 0.161290i −0.998999 0.0447338i
\(14\) 2.32258 0.620736
\(15\) 0.866025 0.500000i 0.223607 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.48387 2.01141i −0.799254 0.461450i 0.0439559 0.999033i \(-0.486004\pi\)
−0.843210 + 0.537584i \(0.819337\pi\)
\(20\) 0.866025 + 0.500000i 0.193649 + 0.111803i
\(21\) 2.32258i 0.506828i
\(22\) −2.67270 + 4.62926i −0.569822 + 0.986961i
\(23\) −2.46797 4.27464i −0.514607 0.891325i −0.999856 0.0169494i \(-0.994605\pi\)
0.485250 0.874376i \(-0.338729\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) −1.00000 −0.200000
\(26\) 3.20002 1.66129i 0.627575 0.325806i
\(27\) 1.00000 0.192450
\(28\) −2.01141 + 1.16129i −0.380121 + 0.219463i
\(29\) −2.14539 3.71592i −0.398388 0.690029i 0.595139 0.803623i \(-0.297097\pi\)
−0.993527 + 0.113594i \(0.963764\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 3.47183i 0.623560i −0.950154 0.311780i \(-0.899075\pi\)
0.950154 0.311780i \(-0.100925\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −4.62926 2.67270i −0.805850 0.465258i
\(34\) 4.00000i 0.685994i
\(35\) 1.16129 2.01141i 0.196294 0.339991i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −2.72733 + 1.57463i −0.448371 + 0.258867i −0.707142 0.707072i \(-0.750016\pi\)
0.258771 + 0.965939i \(0.416682\pi\)
\(38\) 4.02283 0.652589
\(39\) 1.66129 + 3.20002i 0.266019 + 0.512413i
\(40\) −1.00000 −0.158114
\(41\) 2.29078 1.32258i 0.357759 0.206552i −0.310338 0.950626i \(-0.600442\pi\)
0.668097 + 0.744074i \(0.267109\pi\)
\(42\) −1.16129 2.01141i −0.179191 0.310368i
\(43\) 6.12539 10.6095i 0.934113 1.61793i 0.157906 0.987454i \(-0.449526\pi\)
0.776207 0.630478i \(-0.217141\pi\)
\(44\) 5.34541i 0.805850i
\(45\) −0.866025 0.500000i −0.129099 0.0745356i
\(46\) 4.27464 + 2.46797i 0.630262 + 0.363882i
\(47\) 1.81894i 0.265320i 0.991162 + 0.132660i \(0.0423518\pi\)
−0.991162 + 0.132660i \(0.957648\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −0.802812 1.39051i −0.114687 0.198644i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) −4.00000 −0.560112
\(52\) −1.94065 + 3.03873i −0.269120 + 0.421396i
\(53\) −5.48693 −0.753687 −0.376844 0.926277i \(-0.622991\pi\)
−0.376844 + 0.926277i \(0.622991\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 2.67270 + 4.62926i 0.360387 + 0.624209i
\(56\) 1.16129 2.01141i 0.155184 0.268786i
\(57\) 4.02283i 0.532836i
\(58\) 3.71592 + 2.14539i 0.487924 + 0.281703i
\(59\) 5.87744 + 3.39334i 0.765177 + 0.441775i 0.831152 0.556046i \(-0.187682\pi\)
−0.0659742 + 0.997821i \(0.521016\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −0.267949 + 0.464102i −0.0343074 + 0.0594221i −0.882669 0.469995i \(-0.844256\pi\)
0.848362 + 0.529417i \(0.177589\pi\)
\(62\) 1.73592 + 3.00670i 0.220462 + 0.381851i
\(63\) 2.01141 1.16129i 0.253414 0.146309i
\(64\) −1.00000 −0.125000
\(65\) 0.161290 3.60194i 0.0200055 0.446766i
\(66\) 5.34541 0.657974
\(67\) 3.55872 2.05463i 0.434767 0.251013i −0.266608 0.963805i \(-0.585903\pi\)
0.701376 + 0.712792i \(0.252570\pi\)
\(68\) −2.00000 3.46410i −0.242536 0.420084i
\(69\) −2.46797 + 4.27464i −0.297108 + 0.514607i
\(70\) 2.32258i 0.277601i
\(71\) 13.7454 + 7.93593i 1.63128 + 0.941822i 0.983698 + 0.179830i \(0.0575547\pi\)
0.647586 + 0.761992i \(0.275779\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 13.5734i 1.58864i 0.607498 + 0.794321i \(0.292173\pi\)
−0.607498 + 0.794321i \(0.707827\pi\)
\(74\) 1.57463 2.72733i 0.183047 0.317046i
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) −3.48387 + 2.01141i −0.399627 + 0.230725i
\(77\) −12.4151 −1.41484
\(78\) −3.03873 1.94065i −0.344068 0.219736i
\(79\) −7.96774 −0.896441 −0.448220 0.893923i \(-0.647942\pi\)
−0.448220 + 0.893923i \(0.647942\pi\)
\(80\) 0.866025 0.500000i 0.0968246 0.0559017i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.32258 + 2.29078i −0.146054 + 0.252974i
\(83\) 11.3360i 1.24428i 0.782904 + 0.622142i \(0.213737\pi\)
−0.782904 + 0.622142i \(0.786263\pi\)
\(84\) 2.01141 + 1.16129i 0.219463 + 0.126707i
\(85\) 3.46410 + 2.00000i 0.375735 + 0.216930i
\(86\) 12.2508i 1.32104i
\(87\) −2.14539 + 3.71592i −0.230010 + 0.398388i
\(88\) 2.67270 + 4.62926i 0.284911 + 0.493480i
\(89\) −1.50670 + 0.869891i −0.159709 + 0.0922083i −0.577725 0.816232i \(-0.696059\pi\)
0.418015 + 0.908440i \(0.362726\pi\)
\(90\) 1.00000 0.105409
\(91\) 7.05769 + 4.50732i 0.739847 + 0.472495i
\(92\) −4.93593 −0.514607
\(93\) −3.00670 + 1.73592i −0.311780 + 0.180006i
\(94\) −0.909471 1.57525i −0.0938048 0.162475i
\(95\) 2.01141 3.48387i 0.206367 0.357437i
\(96\) 1.00000i 0.102062i
\(97\) −13.9510 8.05463i −1.41651 0.817824i −0.420522 0.907282i \(-0.638153\pi\)
−0.995991 + 0.0894586i \(0.971486\pi\)
\(98\) 1.39051 + 0.802812i 0.140463 + 0.0810962i
\(99\) 5.34541i 0.537233i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 6.34541 + 10.9906i 0.631391 + 1.09360i 0.987267 + 0.159069i \(0.0508492\pi\)
−0.355876 + 0.934533i \(0.615817\pi\)
\(102\) 3.46410 2.00000i 0.342997 0.198030i
\(103\) −4.79612 −0.472575 −0.236288 0.971683i \(-0.575931\pi\)
−0.236288 + 0.971683i \(0.575931\pi\)
\(104\) 0.161290 3.60194i 0.0158158 0.353199i
\(105\) −2.32258 −0.226661
\(106\) 4.75182 2.74346i 0.461537 0.266469i
\(107\) −1.53590 2.66025i −0.148481 0.257176i 0.782185 0.623046i \(-0.214105\pi\)
−0.930666 + 0.365869i \(0.880772\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 6.69081i 0.640864i 0.947272 + 0.320432i \(0.103828\pi\)
−0.947272 + 0.320432i \(0.896172\pi\)
\(110\) −4.62926 2.67270i −0.441382 0.254832i
\(111\) 2.72733 + 1.57463i 0.258867 + 0.149457i
\(112\) 2.32258i 0.219463i
\(113\) 3.55486 6.15720i 0.334413 0.579220i −0.648959 0.760823i \(-0.724795\pi\)
0.983372 + 0.181603i \(0.0581286\pi\)
\(114\) −2.01141 3.48387i −0.188386 0.326294i
\(115\) 4.27464 2.46797i 0.398613 0.230139i
\(116\) −4.29078 −0.398388
\(117\) 1.94065 3.03873i 0.179413 0.280931i
\(118\) −6.78668 −0.624765
\(119\) −8.04565 + 4.64516i −0.737544 + 0.425821i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 8.78668 15.2190i 0.798789 1.38354i
\(122\) 0.535898i 0.0485180i
\(123\) −2.29078 1.32258i −0.206552 0.119253i
\(124\) −3.00670 1.73592i −0.270009 0.155890i
\(125\) 1.00000i 0.0894427i
\(126\) −1.16129 + 2.01141i −0.103456 + 0.179191i
\(127\) −1.06604 1.84644i −0.0945961 0.163845i 0.814844 0.579680i \(-0.196823\pi\)
−0.909440 + 0.415835i \(0.863489\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −12.2508 −1.07862
\(130\) 1.66129 + 3.20002i 0.145705 + 0.280660i
\(131\) 1.25851 0.109957 0.0549785 0.998488i \(-0.482491\pi\)
0.0549785 + 0.998488i \(0.482491\pi\)
\(132\) −4.62926 + 2.67270i −0.402925 + 0.232629i
\(133\) 4.67167 + 8.09156i 0.405085 + 0.701628i
\(134\) −2.05463 + 3.55872i −0.177493 + 0.307427i
\(135\) 1.00000i 0.0860663i
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) 17.0736 + 9.85744i 1.45870 + 0.842178i 0.998947 0.0458713i \(-0.0146064\pi\)
0.459748 + 0.888049i \(0.347940\pi\)
\(138\) 4.93593i 0.420175i
\(139\) −2.83871 + 4.91679i −0.240776 + 0.417037i −0.960936 0.276772i \(-0.910735\pi\)
0.720159 + 0.693809i \(0.244069\pi\)
\(140\) −1.16129 2.01141i −0.0981469 0.169995i
\(141\) 1.57525 0.909471i 0.132660 0.0765913i
\(142\) −15.8719 −1.33194
\(143\) −17.1054 + 8.88027i −1.43043 + 0.742605i
\(144\) 1.00000 0.0833333
\(145\) 3.71592 2.14539i 0.308590 0.178165i
\(146\) −6.78668 11.7549i −0.561670 0.972841i
\(147\) −0.802812 + 1.39051i −0.0662148 + 0.114687i
\(148\) 3.14925i 0.258867i
\(149\) −16.8680 9.73875i −1.38188 0.797829i −0.389499 0.921027i \(-0.627352\pi\)
−0.992382 + 0.123198i \(0.960685\pi\)
\(150\) −0.866025 0.500000i −0.0707107 0.0408248i
\(151\) 14.5170i 1.18138i −0.806899 0.590690i \(-0.798856\pi\)
0.806899 0.590690i \(-0.201144\pi\)
\(152\) 2.01141 3.48387i 0.163147 0.282579i
\(153\) 2.00000 + 3.46410i 0.161690 + 0.280056i
\(154\) 10.7518 6.20757i 0.866406 0.500220i
\(155\) 3.47183 0.278864
\(156\) 3.60194 + 0.161290i 0.288386 + 0.0129135i
\(157\) 24.3829 1.94596 0.972982 0.230879i \(-0.0741602\pi\)
0.972982 + 0.230879i \(0.0741602\pi\)
\(158\) 6.90026 3.98387i 0.548956 0.316940i
\(159\) 2.74346 + 4.75182i 0.217571 + 0.376844i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 11.4641i 0.903498i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 20.4614 + 11.8134i 1.60266 + 0.925295i 0.990953 + 0.134208i \(0.0428492\pi\)
0.611704 + 0.791086i \(0.290484\pi\)
\(164\) 2.64516i 0.206552i
\(165\) 2.67270 4.62926i 0.208070 0.360387i
\(166\) −5.66799 9.81724i −0.439921 0.761966i
\(167\) 14.5035 8.37357i 1.12231 0.647967i 0.180321 0.983608i \(-0.442286\pi\)
0.941990 + 0.335641i \(0.108953\pi\)
\(168\) −2.32258 −0.179191
\(169\) 12.9480 + 1.16191i 0.995998 + 0.0893780i
\(170\) −4.00000 −0.306786
\(171\) 3.48387 2.01141i 0.266418 0.153817i
\(172\) −6.12539 10.6095i −0.467057 0.808966i
\(173\) 8.06604 13.9708i 0.613250 1.06218i −0.377439 0.926034i \(-0.623195\pi\)
0.990689 0.136146i \(-0.0434715\pi\)
\(174\) 4.29078i 0.325283i
\(175\) 2.01141 + 1.16129i 0.152049 + 0.0877853i
\(176\) −4.62926 2.67270i −0.348943 0.201463i
\(177\) 6.78668i 0.510118i
\(178\) 0.869891 1.50670i 0.0652011 0.112932i
\(179\) 3.66412 + 6.34644i 0.273869 + 0.474355i 0.969849 0.243706i \(-0.0783631\pi\)
−0.695980 + 0.718061i \(0.745030\pi\)
\(180\) −0.866025 + 0.500000i −0.0645497 + 0.0372678i
\(181\) −19.5734 −1.45488 −0.727438 0.686173i \(-0.759289\pi\)
−0.727438 + 0.686173i \(0.759289\pi\)
\(182\) −8.36580 0.374609i −0.620114 0.0277678i
\(183\) 0.535898 0.0396147
\(184\) 4.27464 2.46797i 0.315131 0.181941i
\(185\) −1.57463 2.72733i −0.115769 0.200518i
\(186\) 1.73592 3.00670i 0.127284 0.220462i
\(187\) 21.3816i 1.56358i
\(188\) 1.57525 + 0.909471i 0.114887 + 0.0663300i
\(189\) −2.01141 1.16129i −0.146309 0.0844714i
\(190\) 4.02283i 0.291846i
\(191\) 8.51873 14.7549i 0.616394 1.06763i −0.373744 0.927532i \(-0.621926\pi\)
0.990138 0.140094i \(-0.0447404\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 5.33031 3.07746i 0.383684 0.221520i −0.295736 0.955270i \(-0.595565\pi\)
0.679420 + 0.733750i \(0.262231\pi\)
\(194\) 16.1093 1.15658
\(195\) −3.20002 + 1.66129i −0.229158 + 0.118967i
\(196\) −1.60562 −0.114687
\(197\) −11.9396 + 6.89334i −0.850662 + 0.491130i −0.860874 0.508818i \(-0.830083\pi\)
0.0102119 + 0.999948i \(0.496749\pi\)
\(198\) −2.67270 4.62926i −0.189941 0.328987i
\(199\) 1.14152 1.97717i 0.0809203 0.140158i −0.822725 0.568439i \(-0.807547\pi\)
0.903646 + 0.428281i \(0.140881\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −3.55872 2.05463i −0.251013 0.144922i
\(202\) −10.9906 6.34541i −0.773293 0.446461i
\(203\) 9.96567i 0.699453i
\(204\) −2.00000 + 3.46410i −0.140028 + 0.242536i
\(205\) 1.32258 + 2.29078i 0.0923730 + 0.159995i
\(206\) 4.15356 2.39806i 0.289392 0.167081i
\(207\) 4.93593 0.343071
\(208\) 1.66129 + 3.20002i 0.115190 + 0.221881i
\(209\) −21.5036 −1.48744
\(210\) 2.01141 1.16129i 0.138801 0.0801366i
\(211\) −11.2387 19.4661i −0.773707 1.34010i −0.935518 0.353278i \(-0.885067\pi\)
0.161811 0.986822i \(-0.448267\pi\)
\(212\) −2.74346 + 4.75182i −0.188422 + 0.326356i
\(213\) 15.8719i 1.08752i
\(214\) 2.66025 + 1.53590i 0.181851 + 0.104992i
\(215\) 10.6095 + 6.12539i 0.723561 + 0.417748i
\(216\) 1.00000i 0.0680414i
\(217\) −4.03180 + 6.98329i −0.273697 + 0.474057i
\(218\) −3.34541 5.79441i −0.226579 0.392447i
\(219\) 11.7549 6.78668i 0.794321 0.458601i
\(220\) 5.34541 0.360387
\(221\) −7.76261 + 12.1549i −0.522170 + 0.817628i
\(222\) −3.14925 −0.211364
\(223\) 1.19417 0.689457i 0.0799678 0.0461694i −0.459483 0.888187i \(-0.651965\pi\)
0.539451 + 0.842017i \(0.318632\pi\)
\(224\) −1.16129 2.01141i −0.0775919 0.134393i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 7.10972i 0.472931i
\(227\) −16.7321 9.66025i −1.11055 0.641174i −0.171575 0.985171i \(-0.554885\pi\)
−0.938971 + 0.343998i \(0.888219\pi\)
\(228\) 3.48387 + 2.01141i 0.230725 + 0.133209i
\(229\) 15.7626i 1.04162i 0.853672 + 0.520811i \(0.174370\pi\)
−0.853672 + 0.520811i \(0.825630\pi\)
\(230\) −2.46797 + 4.27464i −0.162733 + 0.281862i
\(231\) 6.20757 + 10.7518i 0.408428 + 0.707418i
\(232\) 3.71592 2.14539i 0.243962 0.140852i
\(233\) −16.5549 −1.08455 −0.542275 0.840201i \(-0.682437\pi\)
−0.542275 + 0.840201i \(0.682437\pi\)
\(234\) −0.161290 + 3.60194i −0.0105438 + 0.235466i
\(235\) −1.81894 −0.118655
\(236\) 5.87744 3.39334i 0.382589 0.220888i
\(237\) 3.98387 + 6.90026i 0.258780 + 0.448220i
\(238\) 4.64516 8.04565i 0.301101 0.521522i
\(239\) 26.2006i 1.69477i −0.530976 0.847387i \(-0.678175\pi\)
0.530976 0.847387i \(-0.321825\pi\)
\(240\) −0.866025 0.500000i −0.0559017 0.0322749i
\(241\) −13.5529 7.82479i −0.873021 0.504039i −0.00466988 0.999989i \(-0.501486\pi\)
−0.868351 + 0.495950i \(0.834820\pi\)
\(242\) 17.5734i 1.12966i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0.267949 + 0.464102i 0.0171537 + 0.0297111i
\(245\) 1.39051 0.802812i 0.0888365 0.0512898i
\(246\) 2.64516 0.168649
\(247\) 12.2243 + 7.80691i 0.777812 + 0.496742i
\(248\) 3.47183 0.220462
\(249\) 9.81724 5.66799i 0.622142 0.359194i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −14.1708 + 24.5446i −0.894454 + 1.54924i −0.0599750 + 0.998200i \(0.519102\pi\)
−0.834479 + 0.551040i \(0.814231\pi\)
\(252\) 2.32258i 0.146309i
\(253\) −22.8497 13.1923i −1.43655 0.829392i
\(254\) 1.84644 + 1.06604i 0.115856 + 0.0668895i
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.25465 10.8334i −0.390154 0.675767i 0.602315 0.798258i \(-0.294245\pi\)
−0.992470 + 0.122491i \(0.960912\pi\)
\(258\) 10.6095 6.12539i 0.660518 0.381350i
\(259\) 7.31439 0.454494
\(260\) −3.03873 1.94065i −0.188454 0.120354i
\(261\) 4.29078 0.265592
\(262\) −1.08991 + 0.629257i −0.0673346 + 0.0388756i
\(263\) 5.35295 + 9.27159i 0.330077 + 0.571711i 0.982527 0.186122i \(-0.0595919\pi\)
−0.652449 + 0.757832i \(0.726259\pi\)
\(264\) 2.67270 4.62926i 0.164493 0.284911i
\(265\) 5.48693i 0.337059i
\(266\) −8.09156 4.67167i −0.496126 0.286438i
\(267\) 1.50670 + 0.869891i 0.0922083 + 0.0532365i
\(268\) 4.10926i 0.251013i
\(269\) −3.76261 + 6.51703i −0.229410 + 0.397350i −0.957633 0.287990i \(-0.907013\pi\)
0.728223 + 0.685340i \(0.240346\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 8.52920 4.92434i 0.518112 0.299132i −0.218050 0.975938i \(-0.569970\pi\)
0.736162 + 0.676805i \(0.236636\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0.374609 8.36580i 0.0226723 0.506321i
\(274\) −19.7149 −1.19102
\(275\) −4.62926 + 2.67270i −0.279155 + 0.161170i
\(276\) 2.46797 + 4.27464i 0.148554 + 0.257303i
\(277\) 0.476550 0.825410i 0.0286331 0.0495941i −0.851354 0.524592i \(-0.824218\pi\)
0.879987 + 0.474998i \(0.157551\pi\)
\(278\) 5.67742i 0.340509i
\(279\) 3.00670 + 1.73592i 0.180006 + 0.103927i
\(280\) 2.01141 + 1.16129i 0.120205 + 0.0694003i
\(281\) 5.57336i 0.332479i 0.986085 + 0.166239i \(0.0531625\pi\)
−0.986085 + 0.166239i \(0.946838\pi\)
\(282\) −0.909471 + 1.57525i −0.0541582 + 0.0938048i
\(283\) 11.0067 + 19.0642i 0.654280 + 1.13325i 0.982074 + 0.188497i \(0.0603616\pi\)
−0.327794 + 0.944749i \(0.606305\pi\)
\(284\) 13.7454 7.93593i 0.815642 0.470911i
\(285\) −4.02283 −0.238292
\(286\) 10.3736 16.2432i 0.613402 0.960483i
\(287\) −6.14359 −0.362645
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −2.14539 + 3.71592i −0.125981 + 0.218206i
\(291\) 16.1093i 0.944342i
\(292\) 11.7549 + 6.78668i 0.687902 + 0.397160i
\(293\) 5.92623 + 3.42151i 0.346214 + 0.199887i 0.663016 0.748605i \(-0.269276\pi\)
−0.316803 + 0.948491i \(0.602609\pi\)
\(294\) 1.60562i 0.0936419i
\(295\) −3.39334 + 5.87744i −0.197568 + 0.342198i
\(296\) −1.57463 2.72733i −0.0915233 0.158523i
\(297\) 4.62926 2.67270i 0.268617 0.155086i
\(298\) 19.4775 1.12830
\(299\) 8.20002 + 15.7951i 0.474219 + 0.913453i
\(300\) 1.00000 0.0577350
\(301\) −24.6414 + 14.2267i −1.42031 + 0.820014i
\(302\) 7.25851 + 12.5721i 0.417681 + 0.723444i
\(303\) 6.34541 10.9906i 0.364534 0.631391i
\(304\) 4.02283i 0.230725i
\(305\) −0.464102 0.267949i −0.0265744 0.0153427i
\(306\) −3.46410 2.00000i −0.198030 0.114332i
\(307\) 4.75442i 0.271349i 0.990753 + 0.135675i \(0.0433202\pi\)
−0.990753 + 0.135675i \(0.956680\pi\)
\(308\) −6.20757 + 10.7518i −0.353709 + 0.612642i
\(309\) 2.39806 + 4.15356i 0.136421 + 0.236288i
\(310\) −3.00670 + 1.73592i −0.170769 + 0.0985934i
\(311\) 1.93639 0.109803 0.0549013 0.998492i \(-0.482516\pi\)
0.0549013 + 0.998492i \(0.482516\pi\)
\(312\) −3.20002 + 1.66129i −0.181165 + 0.0940520i
\(313\) 25.5545 1.44443 0.722213 0.691671i \(-0.243125\pi\)
0.722213 + 0.691671i \(0.243125\pi\)
\(314\) −21.1162 + 12.1914i −1.19166 + 0.688002i
\(315\) 1.16129 + 2.01141i 0.0654313 + 0.113330i
\(316\) −3.98387 + 6.90026i −0.224110 + 0.388170i
\(317\) 12.6667i 0.711435i 0.934594 + 0.355717i \(0.115763\pi\)
−0.934594 + 0.355717i \(0.884237\pi\)
\(318\) −4.75182 2.74346i −0.266469 0.153846i
\(319\) −19.8631 11.4680i −1.11212 0.642083i
\(320\) 1.00000i 0.0559017i
\(321\) −1.53590 + 2.66025i −0.0857255 + 0.148481i
\(322\) −5.73205 9.92820i −0.319435 0.553277i
\(323\) −13.9355 + 8.04565i −0.775391 + 0.447672i
\(324\) −1.00000 −0.0555556
\(325\) 3.60194 + 0.161290i 0.199800 + 0.00894675i
\(326\) −23.6267 −1.30856
\(327\) 5.79441 3.34541i 0.320432 0.185001i
\(328\) 1.32258 + 2.29078i 0.0730272 + 0.126487i
\(329\) 2.11232 3.65864i 0.116456 0.201708i
\(330\) 5.34541i 0.294255i
\(331\) −20.5231 11.8490i −1.12805 0.651282i −0.184609 0.982812i \(-0.559102\pi\)
−0.943445 + 0.331530i \(0.892435\pi\)
\(332\) 9.81724 + 5.66799i 0.538791 + 0.311071i
\(333\) 3.14925i 0.172578i
\(334\) −8.37357 + 14.5035i −0.458182 + 0.793594i
\(335\) 2.05463 + 3.55872i 0.112256 + 0.194434i
\(336\) 2.01141 1.16129i 0.109732 0.0633536i
\(337\) 19.5554 1.06525 0.532625 0.846351i \(-0.321205\pi\)
0.532625 + 0.846351i \(0.321205\pi\)
\(338\) −11.7942 + 5.46774i −0.641521 + 0.297406i
\(339\) −7.10972 −0.386147
\(340\) 3.46410 2.00000i 0.187867 0.108465i
\(341\) −9.27918 16.0720i −0.502496 0.870348i
\(342\) −2.01141 + 3.48387i −0.108765 + 0.188386i
\(343\) 19.9872i 1.07921i
\(344\) 10.6095 + 6.12539i 0.572025 + 0.330259i
\(345\) −4.27464 2.46797i −0.230139 0.132871i
\(346\) 16.1321i 0.867266i
\(347\) 11.5187 19.9510i 0.618358 1.07103i −0.371427 0.928462i \(-0.621132\pi\)
0.989785 0.142565i \(-0.0455351\pi\)
\(348\) 2.14539 + 3.71592i 0.115005 + 0.199194i
\(349\) 13.2679 7.66025i 0.710217 0.410044i −0.100924 0.994894i \(-0.532180\pi\)
0.811141 + 0.584850i \(0.198847\pi\)
\(350\) −2.32258 −0.124147
\(351\) −3.60194 0.161290i −0.192257 0.00860902i
\(352\) 5.34541 0.284911
\(353\) 24.6018 14.2039i 1.30942 0.755996i 0.327424 0.944877i \(-0.393819\pi\)
0.982000 + 0.188881i \(0.0604860\pi\)
\(354\) 3.39334 + 5.87744i 0.180354 + 0.312382i
\(355\) −7.93593 + 13.7454i −0.421196 + 0.729532i
\(356\) 1.73978i 0.0922083i
\(357\) 8.04565 + 4.64516i 0.425821 + 0.245848i
\(358\) −6.34644 3.66412i −0.335420 0.193655i
\(359\) 23.5734i 1.24415i −0.782956 0.622077i \(-0.786289\pi\)
0.782956 0.622077i \(-0.213711\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) −1.40844 2.43948i −0.0741282 0.128394i
\(362\) 16.9510 9.78668i 0.890926 0.514377i
\(363\) −17.5734 −0.922362
\(364\) 7.43230 3.85848i 0.389558 0.202239i
\(365\) −13.5734 −0.710462
\(366\) −0.464102 + 0.267949i −0.0242590 + 0.0140059i
\(367\) −13.7454 23.8078i −0.717506 1.24276i −0.961985 0.273103i \(-0.911950\pi\)
0.244479 0.969655i \(-0.421383\pi\)
\(368\) −2.46797 + 4.27464i −0.128652 + 0.222831i
\(369\) 2.64516i 0.137701i
\(370\) 2.72733 + 1.57463i 0.141787 + 0.0818609i
\(371\) 11.0365 + 6.37191i 0.572985 + 0.330813i
\(372\) 3.47183i 0.180006i
\(373\) −13.1710 + 22.8129i −0.681971 + 1.18121i 0.292408 + 0.956294i \(0.405544\pi\)
−0.974379 + 0.224914i \(0.927790\pi\)
\(374\) 10.6908 + 18.5170i 0.552809 + 0.957493i
\(375\) −0.866025 + 0.500000i −0.0447214 + 0.0258199i
\(376\) −1.81894 −0.0938048
\(377\) 7.12822 + 13.7306i 0.367122 + 0.707160i
\(378\) 2.32258 0.119461
\(379\) 0.388456 0.224275i 0.0199537 0.0115202i −0.489990 0.871728i \(-0.663000\pi\)
0.509944 + 0.860208i \(0.329666\pi\)
\(380\) −2.01141 3.48387i −0.103183 0.178719i
\(381\) −1.06604 + 1.84644i −0.0546151 + 0.0945961i
\(382\) 17.0375i 0.871713i
\(383\) 10.4985 + 6.06133i 0.536450 + 0.309719i 0.743639 0.668582i \(-0.233098\pi\)
−0.207189 + 0.978301i \(0.566432\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 12.4151i 0.632734i
\(386\) −3.07746 + 5.33031i −0.156638 + 0.271306i
\(387\) 6.12539 + 10.6095i 0.311371 + 0.539311i
\(388\) −13.9510 + 8.05463i −0.708256 + 0.408912i
\(389\) 18.6195 0.944045 0.472022 0.881587i \(-0.343524\pi\)
0.472022 + 0.881587i \(0.343524\pi\)
\(390\) 1.94065 3.03873i 0.0982687 0.153872i
\(391\) −19.7437 −0.998484
\(392\) 1.39051 0.802812i 0.0702314 0.0405481i
\(393\) −0.629257 1.08991i −0.0317418 0.0549785i
\(394\) 6.89334 11.9396i 0.347281 0.601509i
\(395\) 7.96774i 0.400900i
\(396\) 4.62926 + 2.67270i 0.232629 + 0.134308i
\(397\) 9.78970 + 5.65208i 0.491331 + 0.283670i 0.725126 0.688616i \(-0.241781\pi\)
−0.233796 + 0.972286i \(0.575115\pi\)
\(398\) 2.28304i 0.114439i
\(399\) 4.67167 8.09156i 0.233876 0.405085i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −1.30406 + 0.752899i −0.0651216 + 0.0375980i −0.532207 0.846614i \(-0.678637\pi\)
0.467086 + 0.884212i \(0.345304\pi\)
\(402\) 4.10926 0.204951
\(403\) −0.559971 + 12.5053i −0.0278942 + 0.622935i
\(404\) 12.6908 0.631391
\(405\) 0.866025 0.500000i 0.0430331 0.0248452i
\(406\) −4.98283 8.63052i −0.247294 0.428326i
\(407\) −8.41702 + 14.5787i −0.417216 + 0.722640i
\(408\) 4.00000i 0.198030i
\(409\) 9.64697 + 5.56968i 0.477012 + 0.275403i 0.719170 0.694834i \(-0.244522\pi\)
−0.242158 + 0.970237i \(0.577855\pi\)
\(410\) −2.29078 1.32258i −0.113133 0.0653176i
\(411\) 19.7149i 0.972464i
\(412\) −2.39806 + 4.15356i −0.118144 + 0.204631i
\(413\) −7.88130 13.6508i −0.387814 0.671713i
\(414\) −4.27464 + 2.46797i −0.210087 + 0.121294i
\(415\) −11.3360 −0.556461
\(416\) −3.03873 1.94065i −0.148986 0.0951483i
\(417\) 5.67742 0.278024
\(418\) 18.6227 10.7518i 0.910866 0.525889i
\(419\) 7.75488 + 13.4318i 0.378851 + 0.656188i 0.990895 0.134635i \(-0.0429861\pi\)
−0.612045 + 0.790823i \(0.709653\pi\)
\(420\) −1.16129 + 2.01141i −0.0566651 + 0.0981469i
\(421\) 39.4452i 1.92244i 0.275778 + 0.961221i \(0.411065\pi\)
−0.275778 + 0.961221i \(0.588935\pi\)
\(422\) 19.4661 + 11.2387i 0.947594 + 0.547094i
\(423\) −1.57525 0.909471i −0.0765913 0.0442200i
\(424\) 5.48693i 0.266469i
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 7.93593 + 13.7454i 0.384497 + 0.665969i
\(427\) 1.07791 0.622333i 0.0521639 0.0301168i
\(428\) −3.07180 −0.148481
\(429\) 16.2432 + 10.3736i 0.784231 + 0.500841i
\(430\) −12.2508 −0.590785
\(431\) 1.86621 1.07746i 0.0898921 0.0518993i −0.454380 0.890808i \(-0.650139\pi\)
0.544272 + 0.838909i \(0.316806\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 0.669689 1.15994i 0.0321832 0.0557429i −0.849485 0.527612i \(-0.823087\pi\)
0.881668 + 0.471870i \(0.156421\pi\)
\(434\) 8.06361i 0.387066i
\(435\) −3.71592 2.14539i −0.178165 0.102863i
\(436\) 5.79441 + 3.34541i 0.277502 + 0.160216i
\(437\) 19.8564i 0.949861i
\(438\) −6.78668 + 11.7549i −0.324280 + 0.561670i
\(439\) −15.8490 27.4513i −0.756434 1.31018i −0.944658 0.328055i \(-0.893607\pi\)
0.188225 0.982126i \(-0.439727\pi\)
\(440\) −4.62926 + 2.67270i −0.220691 + 0.127416i
\(441\) 1.60562 0.0764583
\(442\) 0.645159 14.4078i 0.0306871 0.685308i
\(443\) −28.0904 −1.33461 −0.667307 0.744782i \(-0.732553\pi\)
−0.667307 + 0.744782i \(0.732553\pi\)
\(444\) 2.72733 1.57463i 0.129434 0.0747285i
\(445\) −0.869891 1.50670i −0.0412368 0.0714242i
\(446\) −0.689457 + 1.19417i −0.0326467 + 0.0565458i
\(447\) 19.4775i 0.921254i
\(448\) 2.01141 + 1.16129i 0.0950303 + 0.0548658i
\(449\) 25.0426 + 14.4583i 1.18183 + 0.682332i 0.956438 0.291936i \(-0.0942994\pi\)
0.225395 + 0.974267i \(0.427633\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 7.06973 12.2451i 0.332900 0.576600i
\(452\) −3.55486 6.15720i −0.167206 0.289610i
\(453\) −12.5721 + 7.25851i −0.590690 + 0.341035i
\(454\) 19.3205 0.906756
\(455\) −4.50732 + 7.05769i −0.211306 + 0.330870i
\(456\) −4.02283 −0.188386
\(457\) 8.39958 4.84950i 0.392916 0.226850i −0.290507 0.956873i \(-0.593824\pi\)
0.683423 + 0.730023i \(0.260491\pi\)
\(458\) −7.88130 13.6508i −0.368269 0.637861i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 4.93593i 0.230139i
\(461\) 10.3905 + 5.99896i 0.483934 + 0.279400i 0.722055 0.691836i \(-0.243198\pi\)
−0.238120 + 0.971236i \(0.576531\pi\)
\(462\) −10.7518 6.20757i −0.500220 0.288802i
\(463\) 6.42664i 0.298671i −0.988787 0.149336i \(-0.952287\pi\)
0.988787 0.149336i \(-0.0477135\pi\)
\(464\) −2.14539 + 3.71592i −0.0995971 + 0.172507i
\(465\) −1.73592 3.00670i −0.0805012 0.139432i
\(466\) 14.3370 8.27747i 0.664149 0.383447i
\(467\) 26.2642 1.21536 0.607681 0.794182i \(-0.292100\pi\)
0.607681 + 0.794182i \(0.292100\pi\)
\(468\) −1.66129 3.20002i −0.0767932 0.147921i
\(469\) −9.54409 −0.440705
\(470\) 1.57525 0.909471i 0.0726609 0.0419508i
\(471\) −12.1914 21.1162i −0.561752 0.972982i
\(472\) −3.39334 + 5.87744i −0.156191 + 0.270531i
\(473\) 65.4854i 3.01102i
\(474\) −6.90026 3.98387i −0.316940 0.182985i
\(475\) 3.48387 + 2.01141i 0.159851 + 0.0922900i
\(476\) 9.29032i 0.425821i
\(477\) 2.74346 4.75182i 0.125615 0.217571i
\(478\) 13.1003 + 22.6904i 0.599193 + 1.03783i
\(479\) −22.2418 + 12.8413i −1.01625 + 0.586735i −0.913017 0.407922i \(-0.866253\pi\)
−0.103237 + 0.994657i \(0.532920\pi\)
\(480\) 1.00000 0.0456435
\(481\) 10.0777 5.23182i 0.459502 0.238551i
\(482\) 15.6496 0.712818
\(483\) 9.92820 5.73205i 0.451749 0.260817i
\(484\) −8.78668 15.2190i −0.399395 0.691772i
\(485\) 8.05463 13.9510i 0.365742 0.633484i
\(486\) 1.00000i 0.0453609i
\(487\) −8.12238 4.68946i −0.368060 0.212500i 0.304551 0.952496i \(-0.401494\pi\)
−0.672611 + 0.739997i \(0.734827\pi\)
\(488\) −0.464102 0.267949i −0.0210089 0.0121295i
\(489\) 23.6267i 1.06844i
\(490\) −0.802812 + 1.39051i −0.0362673 + 0.0628169i
\(491\) −3.86927 6.70177i −0.174618 0.302447i 0.765411 0.643541i \(-0.222536\pi\)
−0.940029 + 0.341095i \(0.889202\pi\)
\(492\) −2.29078 + 1.32258i −0.103276 + 0.0596265i
\(493\) −17.1631 −0.772987
\(494\) −14.4900 0.648841i −0.651935 0.0291927i
\(495\) −5.34541 −0.240258
\(496\) −3.00670 + 1.73592i −0.135005 + 0.0779450i
\(497\) −18.4318 31.9249i −0.826781 1.43203i
\(498\) −5.66799 + 9.81724i −0.253989 + 0.439921i
\(499\) 3.18106i 0.142404i −0.997462 0.0712019i \(-0.977317\pi\)
0.997462 0.0712019i \(-0.0226834\pi\)
\(500\) −0.866025 0.500000i −0.0387298 0.0223607i
\(501\) −14.5035 8.37357i −0.647967 0.374104i
\(502\) 28.3416i 1.26495i
\(503\) 17.5379 30.3765i 0.781975 1.35442i −0.148814 0.988865i \(-0.547546\pi\)
0.930789 0.365556i \(-0.119121\pi\)
\(504\) 1.16129 + 2.01141i 0.0517280 + 0.0895955i
\(505\) −10.9906 + 6.34541i −0.489074 + 0.282367i
\(506\) 26.3846 1.17294
\(507\) −5.46774 11.7942i −0.242831 0.523800i
\(508\) −2.13209 −0.0945961
\(509\) −16.2697 + 9.39334i −0.721144 + 0.416353i −0.815173 0.579217i \(-0.803358\pi\)
0.0940298 + 0.995569i \(0.470025\pi\)
\(510\) 2.00000 + 3.46410i 0.0885615 + 0.153393i
\(511\) 15.7626 27.3016i 0.697297 1.20775i
\(512\) 1.00000i 0.0441942i
\(513\) −3.48387 2.01141i −0.153817 0.0888061i
\(514\) 10.8334 + 6.25465i 0.477839 + 0.275881i
\(515\) 4.79612i 0.211342i
\(516\) −6.12539 + 10.6095i −0.269655 + 0.467057i
\(517\) 4.86149 + 8.42035i 0.213808 + 0.370327i
\(518\) −6.33445 + 3.65720i −0.278320 + 0.160688i
\(519\) −16.1321 −0.708120
\(520\) 3.60194 + 0.161290i 0.157956 + 0.00707303i
\(521\) 5.28512 0.231545 0.115773 0.993276i \(-0.463066\pi\)
0.115773 + 0.993276i \(0.463066\pi\)
\(522\) −3.71592 + 2.14539i −0.162641 + 0.0939011i
\(523\) 10.3762 + 17.9721i 0.453718 + 0.785863i 0.998614 0.0526409i \(-0.0167639\pi\)
−0.544895 + 0.838504i \(0.683431\pi\)
\(524\) 0.629257 1.08991i 0.0274892 0.0476127i
\(525\) 2.32258i 0.101366i
\(526\) −9.27159 5.35295i −0.404260 0.233400i
\(527\) −12.0268 6.94367i −0.523895 0.302471i
\(528\) 5.34541i 0.232629i
\(529\) −0.681725 + 1.18078i −0.0296402 + 0.0513384i
\(530\) 2.74346 + 4.75182i 0.119168 + 0.206406i
\(531\) −5.87744 + 3.39334i −0.255059 + 0.147258i
\(532\) 9.34333 0.405085
\(533\) −8.46456 + 4.39438i −0.366641 + 0.190342i
\(534\) −1.73978 −0.0752877
\(535\) 2.66025 1.53590i 0.115013 0.0664027i
\(536\) 2.05463 + 3.55872i 0.0887465 + 0.153713i
\(537\) 3.66412 6.34644i 0.158118 0.273869i
\(538\) 7.52522i 0.324435i
\(539\) −7.43284 4.29135i −0.320155 0.184842i
\(540\) 0.866025 + 0.500000i 0.0372678 + 0.0215166i
\(541\) 28.7365i 1.23548i 0.786384 + 0.617739i \(0.211951\pi\)
−0.786384 + 0.617739i \(0.788049\pi\)
\(542\) −4.92434 + 8.52920i −0.211518 + 0.366361i
\(543\) 9.78668 + 16.9510i 0.419987 + 0.727438i
\(544\) 3.46410 2.00000i 0.148522 0.0857493i
\(545\) −6.69081 −0.286603
\(546\) 3.85848 + 7.43230i 0.165128 + 0.318073i
\(547\) 18.3768 0.785737 0.392869 0.919595i \(-0.371483\pi\)
0.392869 + 0.919595i \(0.371483\pi\)
\(548\) 17.0736 9.85744i 0.729348 0.421089i
\(549\) −0.267949 0.464102i −0.0114358 0.0198074i
\(550\) 2.67270 4.62926i 0.113964 0.197392i
\(551\) 17.2610i 0.735345i
\(552\) −4.27464 2.46797i −0.181941 0.105044i
\(553\) 16.0264 + 9.25285i 0.681512 + 0.393471i
\(554\) 0.953101i 0.0404934i
\(555\) −1.57463 + 2.72733i −0.0668392 + 0.115769i
\(556\) 2.83871 + 4.91679i 0.120388 + 0.208518i
\(557\) 22.9831 13.2693i 0.973826 0.562238i 0.0734252 0.997301i \(-0.476607\pi\)
0.900400 + 0.435062i \(0.143274\pi\)
\(558\) −3.47183 −0.146974
\(559\) −23.7745 + 37.2268i −1.00555 + 1.57453i
\(560\) −2.32258 −0.0981469
\(561\) −18.5170 + 10.6908i −0.781790 + 0.451366i
\(562\) −2.78668 4.82667i −0.117549 0.203601i
\(563\) −3.03056 + 5.24908i −0.127723 + 0.221222i −0.922794 0.385294i \(-0.874100\pi\)
0.795071 + 0.606516i \(0.207433\pi\)
\(564\) 1.81894i 0.0765913i
\(565\) 6.15720 + 3.55486i 0.259035 + 0.149554i
\(566\) −19.0642 11.0067i −0.801326 0.462646i
\(567\) 2.32258i 0.0975392i
\(568\) −7.93593 + 13.7454i −0.332984 + 0.576746i
\(569\) −7.24818 12.5542i −0.303860 0.526300i 0.673147 0.739509i \(-0.264942\pi\)
−0.977007 + 0.213208i \(0.931609\pi\)
\(570\) 3.48387 2.01141i 0.145923 0.0842488i
\(571\) −2.90413 −0.121534 −0.0607670 0.998152i \(-0.519355\pi\)
−0.0607670 + 0.998152i \(0.519355\pi\)
\(572\) −0.862160 + 19.2538i −0.0360487 + 0.805044i
\(573\) −17.0375 −0.711750
\(574\) 5.32051 3.07180i 0.222074 0.128214i
\(575\) 2.46797 + 4.27464i 0.102921 + 0.178265i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 18.8180i 0.783405i 0.920092 + 0.391702i \(0.128114\pi\)
−0.920092 + 0.391702i \(0.871886\pi\)
\(578\) −0.866025 0.500000i −0.0360219 0.0207973i
\(579\) −5.33031 3.07746i −0.221520 0.127895i
\(580\) 4.29078i 0.178165i
\(581\) 13.1643 22.8013i 0.546149 0.945958i
\(582\) −8.05463 13.9510i −0.333875 0.578289i
\(583\) −25.4004 + 14.6649i −1.05198 + 0.607359i
\(584\) −13.5734 −0.561670
\(585\) 3.03873 + 1.94065i 0.125636 + 0.0802361i
\(586\) −6.84302 −0.282682
\(587\) −3.40901 + 1.96820i −0.140705 + 0.0812361i −0.568700 0.822545i \(-0.692553\pi\)
0.427995 + 0.903781i \(0.359220\pi\)
\(588\) 0.802812 + 1.39051i 0.0331074 + 0.0573437i
\(589\) −6.98329 + 12.0954i −0.287741 + 0.498383i
\(590\) 6.78668i 0.279403i
\(591\) 11.9396 + 6.89334i 0.491130 + 0.283554i
\(592\) 2.72733 + 1.57463i 0.112093 + 0.0647168i
\(593\) 20.1227i 0.826338i −0.910654 0.413169i \(-0.864422\pi\)
0.910654 0.413169i \(-0.135578\pi\)
\(594\) −2.67270 + 4.62926i −0.109662 + 0.189941i
\(595\) −4.64516 8.04565i −0.190433 0.329840i
\(596\) −16.8680 + 9.73875i −0.690940 + 0.398915i
\(597\) −2.28304 −0.0934388
\(598\) −14.9990 9.57893i −0.613353 0.391712i
\(599\) 48.1172 1.96601 0.983007 0.183567i \(-0.0587644\pi\)
0.983007 + 0.183567i \(0.0587644\pi\)
\(600\) −0.866025 + 0.500000i −0.0353553 + 0.0204124i
\(601\) 2.12109 + 3.67383i 0.0865209 + 0.149859i 0.906038 0.423196i \(-0.139092\pi\)
−0.819517 + 0.573054i \(0.805758\pi\)
\(602\) 14.2267 24.6414i 0.579837 1.00431i
\(603\) 4.10926i 0.167342i
\(604\) −12.5721 7.25851i −0.511552 0.295345i
\(605\) 15.2190 + 8.78668i 0.618739 + 0.357229i
\(606\) 12.6908i 0.515529i
\(607\) −6.03424 + 10.4516i −0.244922 + 0.424218i −0.962110 0.272663i \(-0.912096\pi\)
0.717188 + 0.696880i \(0.245429\pi\)
\(608\) −2.01141 3.48387i −0.0815736 0.141290i
\(609\) 8.63052 4.98283i 0.349726 0.201915i
\(610\) 0.535898 0.0216979
\(611\) 0.293377 6.55172i 0.0118688 0.265054i
\(612\) 4.00000 0.161690
\(613\) 36.1497 20.8711i 1.46007 0.842974i 0.461060 0.887369i \(-0.347469\pi\)
0.999014 + 0.0443946i \(0.0141359\pi\)
\(614\) −2.37721 4.11745i −0.0959364 0.166167i
\(615\) 1.32258 2.29078i 0.0533316 0.0923730i
\(616\) 12.4151i 0.500220i
\(617\) −28.9760 16.7293i −1.16653 0.673497i −0.213670 0.976906i \(-0.568542\pi\)
−0.952860 + 0.303409i \(0.901875\pi\)
\(618\) −4.15356 2.39806i −0.167081 0.0964640i
\(619\) 38.0978i 1.53128i −0.643270 0.765639i \(-0.722423\pi\)
0.643270 0.765639i \(-0.277577\pi\)
\(620\) 1.73592 3.00670i 0.0697161 0.120752i
\(621\) −2.46797 4.27464i −0.0990361 0.171536i
\(622\) −1.67696 + 0.968196i −0.0672401 + 0.0388211i
\(623\) 4.04078 0.161891
\(624\) 1.94065 3.03873i 0.0776883 0.121646i
\(625\) 1.00000 0.0400000
\(626\) −22.1308 + 12.7772i −0.884526 + 0.510681i
\(627\) 10.7518 + 18.6227i 0.429386 + 0.743719i
\(628\) 12.1914 21.1162i 0.486491 0.842628i
\(629\) 12.5970i 0.502276i
\(630\) −2.01141 1.16129i −0.0801366 0.0462669i
\(631\) −21.4775 12.4000i −0.855005 0.493638i 0.00733109 0.999973i \(-0.497666\pi\)
−0.862337 + 0.506335i \(0.831000\pi\)
\(632\) 7.96774i 0.316940i
\(633\) −11.2387 + 19.4661i −0.446700 + 0.773707i
\(634\) −6.33337 10.9697i −0.251530 0.435663i
\(635\) 1.84644 1.06604i 0.0732738 0.0423046i
\(636\) 5.48693 0.217571
\(637\) 2.66741 + 5.13802i 0.105686 + 0.203576i
\(638\) 22.9359 0.908042
\(639\) −13.7454 + 7.93593i −0.543761 + 0.313941i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 2.04259 3.53788i 0.0806776 0.139738i −0.822864 0.568239i \(-0.807625\pi\)
0.903541 + 0.428501i \(0.140958\pi\)
\(642\) 3.07180i 0.121234i
\(643\) −31.6806 18.2908i −1.24936 0.721318i −0.278377 0.960472i \(-0.589797\pi\)
−0.970982 + 0.239154i \(0.923130\pi\)
\(644\) 9.92820 + 5.73205i 0.391226 + 0.225874i
\(645\) 12.2508i 0.482374i
\(646\) 8.04565 13.9355i 0.316552 0.548284i
\(647\) 8.61704 + 14.9251i 0.338771 + 0.586768i 0.984202 0.177050i \(-0.0566556\pi\)
−0.645431 + 0.763818i \(0.723322\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 36.2776 1.42402
\(650\) −3.20002 + 1.66129i −0.125515 + 0.0651611i
\(651\) 8.06361 0.316038
\(652\) 20.4614 11.8134i 0.801329 0.462647i
\(653\) 10.9637 + 18.9897i 0.429042 + 0.743123i 0.996788 0.0800806i \(-0.0255178\pi\)
−0.567746 + 0.823204i \(0.692184\pi\)
\(654\) −3.34541 + 5.79441i −0.130816 + 0.226579i
\(655\) 1.25851i 0.0491742i
\(656\) −2.29078 1.32258i −0.0894397 0.0516381i
\(657\) −11.7549 6.78668i −0.458601 0.264774i
\(658\) 4.22464i 0.164694i
\(659\) 24.2379 41.9813i 0.944176 1.63536i 0.186783 0.982401i \(-0.440194\pi\)
0.757393 0.652960i \(-0.226473\pi\)
\(660\) −2.67270 4.62926i −0.104035 0.180194i
\(661\) −25.8267 + 14.9110i −1.00454 + 0.579972i −0.909589 0.415510i \(-0.863603\pi\)
−0.0949524 + 0.995482i \(0.530270\pi\)
\(662\) 23.6981 0.921052
\(663\) 14.4078 + 0.645159i 0.559551 + 0.0250559i
\(664\) −11.3360 −0.439921
\(665\) −8.09156 + 4.67167i −0.313777 + 0.181159i
\(666\) 1.57463 + 2.72733i 0.0610155 + 0.105682i
\(667\) −10.5895 + 18.3415i −0.410027 + 0.710187i
\(668\) 16.7471i 0.647967i
\(669\) −1.19417 0.689457i −0.0461694 0.0266559i
\(670\) −3.55872 2.05463i −0.137486 0.0793773i
\(671\) 2.86459i 0.110586i
\(672\) −1.16129 + 2.01141i −0.0447977 + 0.0775919i
\(673\) −15.3360 26.5627i −0.591158 1.02392i −0.994077 0.108680i \(-0.965338\pi\)
0.402919 0.915236i \(-0.367996\pi\)
\(674\) −16.9355 + 9.77770i −0.652330 + 0.376623i
\(675\) −1.00000 −0.0384900
\(676\) 7.48023 10.6323i 0.287701 0.408935i
\(677\) 21.0831 0.810290 0.405145 0.914252i \(-0.367221\pi\)
0.405145 + 0.914252i \(0.367221\pi\)
\(678\) 6.15720 3.55486i 0.236466 0.136524i
\(679\) 18.7075 + 32.4024i 0.717929 + 1.24349i
\(680\) −2.00000 + 3.46410i −0.0766965 + 0.132842i
\(681\) 19.3205i 0.740363i
\(682\) 16.0720 + 9.27918i 0.615429 + 0.355318i
\(683\) −11.5493 6.66799i −0.441921 0.255143i 0.262491 0.964934i \(-0.415456\pi\)
−0.704412 + 0.709791i \(0.748789\pi\)
\(684\) 4.02283i 0.153817i
\(685\) −9.85744 + 17.0736i −0.376634 + 0.652348i
\(686\) −9.99362 17.3095i −0.381558 0.660878i
\(687\) 13.6508 7.88130i 0.520811 0.300691i
\(688\) −12.2508 −0.467057
\(689\) 19.7636 + 0.884986i 0.752933 + 0.0337153i
\(690\) 4.93593 0.187908
\(691\) −30.2289 + 17.4527i −1.14996 + 0.663932i −0.948878 0.315642i \(-0.897780\pi\)
−0.201085 + 0.979574i \(0.564447\pi\)
\(692\) −8.06604 13.9708i −0.306625 0.531090i
\(693\) 6.20757 10.7518i 0.235806 0.408428i
\(694\) 23.0375i 0.874490i
\(695\) −4.91679 2.83871i −0.186504 0.107678i
\(696\) −3.71592 2.14539i −0.140852 0.0813207i
\(697\) 10.5806i 0.400770i
\(698\) −7.66025 + 13.2679i −0.289945 + 0.502199i
\(699\) 8.27747 + 14.3370i 0.313083 + 0.542275i
\(700\) 2.01141 1.16129i 0.0760243 0.0438926i
\(701\) 39.6715 1.49837 0.749186 0.662360i \(-0.230445\pi\)
0.749186 + 0.662360i \(0.230445\pi\)
\(702\) 3.20002 1.66129i 0.120777 0.0627013i
\(703\) 12.6689 0.477817
\(704\) −4.62926 + 2.67270i −0.174472 + 0.100731i
\(705\) 0.909471 + 1.57525i 0.0342527 + 0.0593274i
\(706\) −14.2039 + 24.6018i −0.534570 + 0.925903i
\(707\) 29.4754i 1.10854i
\(708\) −5.87744 3.39334i −0.220888 0.127530i
\(709\) 2.45467 + 1.41720i 0.0921869 + 0.0532242i 0.545385 0.838186i \(-0.316384\pi\)
−0.453198 + 0.891410i \(0.649717\pi\)
\(710\) 15.8719i 0.595661i
\(711\) 3.98387 6.90026i 0.149407 0.258780i
\(712\) −0.869891 1.50670i −0.0326005 0.0564658i
\(713\) −14.8409 + 8.56837i −0.555794 + 0.320888i
\(714\) −9.29032 −0.347681
\(715\) −8.88027 17.1054i −0.332103 0.639706i
\(716\) 7.32824 0.273869
\(717\) −22.6904 + 13.1003i −0.847387 + 0.489239i
\(718\) 11.7867 + 20.4151i 0.439875 + 0.761886i
\(719\) −21.8564 + 37.8564i −0.815106 + 1.41181i 0.0941451 + 0.995558i \(0.469988\pi\)
−0.909251 + 0.416247i \(0.863345\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 9.64697 + 5.56968i 0.359272 + 0.207426i
\(722\) 2.43948 + 1.40844i 0.0907881 + 0.0524165i
\(723\) 15.6496i 0.582014i
\(724\) −9.78668 + 16.9510i −0.363719 + 0.629980i
\(725\) 2.14539 + 3.71592i 0.0796777 + 0.138006i
\(726\) 15.2190 8.78668i 0.564829 0.326104i
\(727\) −16.2568 −0.602932 −0.301466 0.953477i \(-0.597476\pi\)
−0.301466 + 0.953477i \(0.597476\pi\)
\(728\) −4.50732 + 7.05769i −0.167052 + 0.261575i
\(729\) 1.00000 0.0370370
\(730\) 11.7549 6.78668i 0.435068 0.251186i
\(731\) −24.5016 42.4380i −0.906223 1.56962i
\(732\) 0.267949 0.464102i 0.00990369 0.0171537i
\(733\) 4.96774i 0.183488i −0.995783 0.0917438i \(-0.970756\pi\)
0.995783 0.0917438i \(-0.0292441\pi\)
\(734\) 23.8078 + 13.7454i 0.878762 + 0.507354i
\(735\) −1.39051 0.802812i −0.0512898 0.0296122i
\(736\) 4.93593i 0.181941i
\(737\) 10.9828 19.0228i 0.404558 0.700715i
\(738\) −1.32258 2.29078i −0.0486848 0.0843246i
\(739\) 43.0306 24.8437i 1.58291 0.913892i 0.588475 0.808515i \(-0.299729\pi\)
0.994432 0.105377i \(-0.0336048\pi\)
\(740\) −3.14925 −0.115769
\(741\) 0.648841 14.4900i 0.0238358 0.532303i
\(742\) −12.7438 −0.467841
\(743\) 18.6559 10.7710i 0.684420 0.395150i −0.117098 0.993120i \(-0.537359\pi\)
0.801518 + 0.597970i \(0.204026\pi\)
\(744\) −1.73592 3.00670i −0.0636418 0.110231i
\(745\) 9.73875 16.8680i 0.356800 0.617996i
\(746\) 26.3421i 0.964452i
\(747\) −9.81724 5.66799i −0.359194 0.207381i
\(748\) −18.5170 10.6908i −0.677050 0.390895i
\(749\) 7.13449i 0.260689i
\(750\) 0.500000 0.866025i 0.0182574 0.0316228i
\(751\) −3.17436 5.49816i −0.115834 0.200631i 0.802279 0.596950i \(-0.203621\pi\)
−0.918113 + 0.396319i \(0.870287\pi\)
\(752\) 1.57525 0.909471i 0.0574435 0.0331650i
\(753\) 28.3416 1.03283
\(754\) −13.0385 8.32690i −0.474834 0.303248i
\(755\) 14.5170 0.528329
\(756\) −2.01141 + 1.16129i −0.0731544 + 0.0422357i
\(757\) 24.0554 + 41.6651i 0.874307 + 1.51434i 0.857499 + 0.514485i \(0.172017\pi\)
0.0168078 + 0.999859i \(0.494650\pi\)
\(758\) −0.224275 + 0.388456i −0.00814604 + 0.0141094i
\(759\) 26.3846i 0.957699i
\(760\) 3.48387 + 2.01141i 0.126373 + 0.0729616i
\(761\) 29.1734 + 16.8433i 1.05754 + 0.610569i 0.924750 0.380576i \(-0.124274\pi\)
0.132786 + 0.991145i \(0.457608\pi\)
\(762\) 2.13209i 0.0772374i
\(763\) 7.76997 13.4580i 0.281292 0.487212i
\(764\) −8.51873 14.7549i −0.308197 0.533813i
\(765\) −3.46410 + 2.00000i −0.125245 + 0.0723102i
\(766\) −12.1227 −0.438009
\(767\) −20.6229 13.1706i −0.744649 0.475562i
\(768\) 1.00000 0.0360844
\(769\) −5.18651 + 2.99443i −0.187030 + 0.107982i −0.590592 0.806971i \(-0.701106\pi\)
0.403561 + 0.914953i \(0.367772\pi\)
\(770\) 6.20757 + 10.7518i 0.223705 + 0.387469i
\(771\) −6.25465 + 10.8334i −0.225256 + 0.390154i
\(772\) 6.15491i 0.221520i
\(773\) 11.6811 + 6.74409i 0.420140 + 0.242568i 0.695137 0.718877i \(-0.255344\pi\)
−0.274997 + 0.961445i \(0.588677\pi\)
\(774\) −10.6095 6.12539i −0.381350 0.220173i
\(775\) 3.47183i 0.124712i