Properties

Label 546.2.l.b.211.1
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.b.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-2.00000 - 3.46410i) q^{11} -1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +1.00000 q^{18} +(-2.00000 + 3.46410i) q^{19} +(-1.50000 + 2.59808i) q^{20} +1.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +4.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +(1.50000 - 2.59808i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} -5.00000 q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +4.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +3.00000 q^{40} +(-3.50000 - 6.06218i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +4.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(2.00000 - 3.46410i) q^{46} +12.0000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +5.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} +7.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-6.00000 - 10.3923i) q^{55} +(0.500000 - 0.866025i) q^{56} -4.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(4.00000 - 6.92820i) q^{59} -3.00000 q^{60} +(-3.50000 + 6.06218i) q^{61} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(10.5000 - 2.59808i) q^{65} -4.00000 q^{66} +(-6.00000 - 10.3923i) q^{67} +(2.50000 + 4.33013i) q^{68} +(-2.00000 + 3.46410i) q^{69} -3.00000 q^{70} +(-6.00000 + 10.3923i) q^{71} +(-0.500000 + 0.866025i) q^{72} -1.00000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(2.00000 + 3.46410i) q^{75} +(-2.00000 - 3.46410i) q^{76} -4.00000 q^{77} +(1.00000 - 3.46410i) q^{78} -16.0000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.50000 + 6.06218i) q^{82} -8.00000 q^{83} +(-0.500000 + 0.866025i) q^{84} +(7.50000 - 12.9904i) q^{85} +8.00000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(1.00000 - 3.46410i) q^{91} -4.00000 q^{92} +(-6.00000 - 10.3923i) q^{94} +(-6.00000 + 10.3923i) q^{95} -1.00000 q^{96} +(-9.00000 + 15.5885i) q^{97} +(-0.500000 + 0.866025i) q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + 6q^{5} + q^{6} + q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + 6q^{5} + q^{6} + q^{7} + 2q^{8} - q^{9} - 3q^{10} - 4q^{11} - 2q^{12} + 7q^{13} - 2q^{14} + 3q^{15} - q^{16} + 5q^{17} + 2q^{18} - 4q^{19} - 3q^{20} + 2q^{21} - 4q^{22} + 4q^{23} + q^{24} + 8q^{25} - 5q^{26} - 2q^{27} + q^{28} + 9q^{29} + 3q^{30} - q^{32} + 4q^{33} - 10q^{34} + 3q^{35} - q^{36} - 7q^{37} + 8q^{38} + 5q^{39} + 6q^{40} - 7q^{41} - q^{42} - 8q^{43} + 8q^{44} - 3q^{45} + 4q^{46} + 24q^{47} + q^{48} - q^{49} - 4q^{50} + 10q^{51} - 2q^{52} + 14q^{53} + q^{54} - 12q^{55} + q^{56} - 8q^{57} + 9q^{58} + 8q^{59} - 6q^{60} - 7q^{61} + q^{63} + 2q^{64} + 21q^{65} - 8q^{66} - 12q^{67} + 5q^{68} - 4q^{69} - 6q^{70} - 12q^{71} - q^{72} - 2q^{73} - 7q^{74} + 4q^{75} - 4q^{76} - 8q^{77} + 2q^{78} - 32q^{79} - 3q^{80} - q^{81} - 7q^{82} - 16q^{83} - q^{84} + 15q^{85} + 16q^{86} - 9q^{87} - 4q^{88} + 6q^{89} + 6q^{90} + 2q^{91} - 8q^{92} - 12q^{94} - 12q^{95} - 2q^{96} - 18q^{97} - q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.50000 0.866025i 0.970725 0.240192i
\(14\) −1.00000 −0.267261
\(15\) 1.50000 + 2.59808i 0.387298 + 0.670820i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.50000 4.33013i 0.606339 1.05021i −0.385499 0.922708i \(-0.625971\pi\)
0.991838 0.127502i \(-0.0406959\pi\)
\(18\) 1.00000 0.235702
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 1.00000 0.218218
\(22\) −2.00000 + 3.46410i −0.426401 + 0.738549i
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 4.00000 0.800000
\(26\) −2.50000 2.59808i −0.490290 0.509525i
\(27\) −1.00000 −0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.00000 3.46410i 0.348155 0.603023i
\(34\) −5.00000 −0.857493
\(35\) 1.50000 2.59808i 0.253546 0.439155i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i \(-0.971514\pi\)
0.420602 0.907245i \(-0.361819\pi\)
\(38\) 4.00000 0.648886
\(39\) 2.50000 + 2.59808i 0.400320 + 0.416025i
\(40\) 3.00000 0.474342
\(41\) −3.50000 6.06218i −0.546608 0.946753i −0.998504 0.0546823i \(-0.982585\pi\)
0.451896 0.892071i \(-0.350748\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 4.00000 0.603023
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) 2.00000 3.46410i 0.294884 0.510754i
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 5.00000 0.700140
\(52\) −1.00000 + 3.46410i −0.138675 + 0.480384i
\(53\) 7.00000 0.961524 0.480762 0.876851i \(-0.340360\pi\)
0.480762 + 0.876851i \(0.340360\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −6.00000 10.3923i −0.809040 1.40130i
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) −4.00000 −0.529813
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) −3.00000 −0.387298
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) 0 0
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 10.5000 2.59808i 1.30236 0.322252i
\(66\) −4.00000 −0.492366
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) 2.50000 + 4.33013i 0.303170 + 0.525105i
\(69\) −2.00000 + 3.46410i −0.240772 + 0.417029i
\(70\) −3.00000 −0.358569
\(71\) −6.00000 + 10.3923i −0.712069 + 1.23334i 0.252010 + 0.967725i \(0.418908\pi\)
−0.964079 + 0.265615i \(0.914425\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −1.00000 −0.117041 −0.0585206 0.998286i \(-0.518638\pi\)
−0.0585206 + 0.998286i \(0.518638\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) 2.00000 + 3.46410i 0.230940 + 0.400000i
\(76\) −2.00000 3.46410i −0.229416 0.397360i
\(77\) −4.00000 −0.455842
\(78\) 1.00000 3.46410i 0.113228 0.392232i
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.50000 + 6.06218i −0.386510 + 0.669456i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) −0.500000 + 0.866025i −0.0545545 + 0.0944911i
\(85\) 7.50000 12.9904i 0.813489 1.40900i
\(86\) 8.00000 0.862662
\(87\) −4.50000 + 7.79423i −0.482451 + 0.835629i
\(88\) −2.00000 3.46410i −0.213201 0.369274i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 3.00000 0.316228
\(91\) 1.00000 3.46410i 0.104828 0.363137i
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) −6.00000 10.3923i −0.618853 1.07188i
\(95\) −6.00000 + 10.3923i −0.615587 + 1.06623i
\(96\) −1.00000 −0.102062
\(97\) −9.00000 + 15.5885i −0.913812 + 1.58277i −0.105180 + 0.994453i \(0.533542\pi\)
−0.808632 + 0.588315i \(0.799792\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) 4.00000 0.402015
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) −2.50000 4.33013i −0.247537 0.428746i
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 3.50000 0.866025i 0.343203 0.0849208i
\(105\) 3.00000 0.292770
\(106\) −3.50000 6.06218i −0.339950 0.588811i
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −6.00000 + 10.3923i −0.572078 + 0.990867i
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) −1.00000 −0.0944911
\(113\) 2.50000 4.33013i 0.235180 0.407344i −0.724145 0.689648i \(-0.757765\pi\)
0.959325 + 0.282304i \(0.0910986\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) 6.00000 + 10.3923i 0.559503 + 0.969087i
\(116\) −9.00000 −0.835629
\(117\) −1.00000 + 3.46410i −0.0924500 + 0.320256i
\(118\) −8.00000 −0.736460
\(119\) −2.50000 4.33013i −0.229175 0.396942i
\(120\) 1.50000 + 2.59808i 0.136931 + 0.237171i
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 7.00000 0.633750
\(123\) 3.50000 6.06218i 0.315584 0.546608i
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0.500000 0.866025i 0.0445435 0.0771517i
\(127\) 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i \(-0.0511671\pi\)
−0.632166 + 0.774833i \(0.717834\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −8.00000 −0.704361
\(130\) −7.50000 7.79423i −0.657794 0.683599i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 2.00000 + 3.46410i 0.174078 + 0.301511i
\(133\) 2.00000 + 3.46410i 0.173422 + 0.300376i
\(134\) −6.00000 + 10.3923i −0.518321 + 0.897758i
\(135\) −3.00000 −0.258199
\(136\) 2.50000 4.33013i 0.214373 0.371305i
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 4.00000 0.340503
\(139\) −2.00000 + 3.46410i −0.169638 + 0.293821i −0.938293 0.345843i \(-0.887593\pi\)
0.768655 + 0.639664i \(0.220926\pi\)
\(140\) 1.50000 + 2.59808i 0.126773 + 0.219578i
\(141\) 6.00000 + 10.3923i 0.505291 + 0.875190i
\(142\) 12.0000 1.00702
\(143\) −10.0000 10.3923i −0.836242 0.869048i
\(144\) 1.00000 0.0833333
\(145\) 13.5000 + 23.3827i 1.12111 + 1.94183i
\(146\) 0.500000 + 0.866025i 0.0413803 + 0.0716728i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) 7.00000 0.575396
\(149\) −3.50000 + 6.06218i −0.286731 + 0.496633i −0.973028 0.230689i \(-0.925902\pi\)
0.686296 + 0.727322i \(0.259235\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −2.00000 + 3.46410i −0.162221 + 0.280976i
\(153\) 2.50000 + 4.33013i 0.202113 + 0.350070i
\(154\) 2.00000 + 3.46410i 0.161165 + 0.279145i
\(155\) 0 0
\(156\) −3.50000 + 0.866025i −0.280224 + 0.0693375i
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 8.00000 + 13.8564i 0.636446 + 1.10236i
\(159\) 3.50000 + 6.06218i 0.277568 + 0.480762i
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 4.00000 0.315244
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 7.00000 0.546608
\(165\) 6.00000 10.3923i 0.467099 0.809040i
\(166\) 4.00000 + 6.92820i 0.310460 + 0.537733i
\(167\) 4.00000 + 6.92820i 0.309529 + 0.536120i 0.978259 0.207385i \(-0.0664952\pi\)
−0.668730 + 0.743505i \(0.733162\pi\)
\(168\) 1.00000 0.0771517
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) −15.0000 −1.15045
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) −7.00000 + 12.1244i −0.532200 + 0.921798i 0.467093 + 0.884208i \(0.345301\pi\)
−0.999293 + 0.0375896i \(0.988032\pi\)
\(174\) 9.00000 0.682288
\(175\) 2.00000 3.46410i 0.151186 0.261861i
\(176\) −2.00000 + 3.46410i −0.150756 + 0.261116i
\(177\) 8.00000 0.601317
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −10.0000 17.3205i −0.747435 1.29460i −0.949048 0.315130i \(-0.897952\pi\)
0.201613 0.979465i \(-0.435382\pi\)
\(180\) −1.50000 2.59808i −0.111803 0.193649i
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) −3.50000 + 0.866025i −0.259437 + 0.0641941i
\(183\) −7.00000 −0.517455
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) −10.5000 18.1865i −0.771975 1.33710i
\(186\) 0 0
\(187\) −20.0000 −1.46254
\(188\) −6.00000 + 10.3923i −0.437595 + 0.757937i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) 12.0000 0.870572
\(191\) 12.0000 20.7846i 0.868290 1.50392i 0.00454614 0.999990i \(-0.498553\pi\)
0.863743 0.503932i \(-0.168114\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −9.50000 16.4545i −0.683825 1.18442i −0.973805 0.227387i \(-0.926982\pi\)
0.289980 0.957033i \(-0.406351\pi\)
\(194\) 18.0000 1.29232
\(195\) 7.50000 + 7.79423i 0.537086 + 0.558156i
\(196\) 1.00000 0.0714286
\(197\) −11.0000 19.0526i −0.783718 1.35744i −0.929762 0.368161i \(-0.879988\pi\)
0.146045 0.989278i \(-0.453346\pi\)
\(198\) −2.00000 3.46410i −0.142134 0.246183i
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 4.00000 0.282843
\(201\) 6.00000 10.3923i 0.423207 0.733017i
\(202\) −1.50000 + 2.59808i −0.105540 + 0.182800i
\(203\) 9.00000 0.631676
\(204\) −2.50000 + 4.33013i −0.175035 + 0.303170i
\(205\) −10.5000 18.1865i −0.733352 1.27020i
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) −4.00000 −0.278019
\(208\) −2.50000 2.59808i −0.173344 0.180144i
\(209\) 16.0000 1.10674
\(210\) −1.50000 2.59808i −0.103510 0.179284i
\(211\) 4.00000 + 6.92820i 0.275371 + 0.476957i 0.970229 0.242190i \(-0.0778659\pi\)
−0.694857 + 0.719148i \(0.744533\pi\)
\(212\) −3.50000 + 6.06218i −0.240381 + 0.416352i
\(213\) −12.0000 −0.822226
\(214\) 0 0
\(215\) −12.0000 + 20.7846i −0.818393 + 1.41750i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −7.00000 12.1244i −0.474100 0.821165i
\(219\) −0.500000 0.866025i −0.0337869 0.0585206i
\(220\) 12.0000 0.809040
\(221\) 5.00000 17.3205i 0.336336 1.16510i
\(222\) −7.00000 −0.469809
\(223\) 14.0000 + 24.2487i 0.937509 + 1.62381i 0.770097 + 0.637927i \(0.220208\pi\)
0.167412 + 0.985887i \(0.446459\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) −2.00000 + 3.46410i −0.133333 + 0.230940i
\(226\) −5.00000 −0.332595
\(227\) −12.0000 + 20.7846i −0.796468 + 1.37952i 0.125435 + 0.992102i \(0.459967\pi\)
−0.921903 + 0.387421i \(0.873366\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) 6.00000 10.3923i 0.395628 0.685248i
\(231\) −2.00000 3.46410i −0.131590 0.227921i
\(232\) 4.50000 + 7.79423i 0.295439 + 0.511716i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) 36.0000 2.34838
\(236\) 4.00000 + 6.92820i 0.260378 + 0.450988i
\(237\) −8.00000 13.8564i −0.519656 0.900070i
\(238\) −2.50000 + 4.33013i −0.162051 + 0.280680i
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 1.50000 2.59808i 0.0968246 0.167705i
\(241\) 4.50000 7.79423i 0.289870 0.502070i −0.683908 0.729568i \(-0.739721\pi\)
0.973779 + 0.227498i \(0.0730544\pi\)
\(242\) 5.00000 0.321412
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −3.50000 6.06218i −0.224065 0.388091i
\(245\) −1.50000 2.59808i −0.0958315 0.165985i
\(246\) −7.00000 −0.446304
\(247\) −4.00000 + 13.8564i −0.254514 + 0.881662i
\(248\) 0 0
\(249\) −4.00000 6.92820i −0.253490 0.439057i
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 8.00000 13.8564i 0.502956 0.871145i
\(254\) 4.00000 6.92820i 0.250982 0.434714i
\(255\) 15.0000 0.939336
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.50000 6.06218i −0.218324 0.378148i 0.735972 0.677012i \(-0.236726\pi\)
−0.954296 + 0.298864i \(0.903392\pi\)
\(258\) 4.00000 + 6.92820i 0.249029 + 0.431331i
\(259\) −7.00000 −0.434959
\(260\) −3.00000 + 10.3923i −0.186052 + 0.644503i
\(261\) −9.00000 −0.557086
\(262\) 6.00000 + 10.3923i 0.370681 + 0.642039i
\(263\) −4.00000 6.92820i −0.246651 0.427211i 0.715944 0.698158i \(-0.245997\pi\)
−0.962594 + 0.270947i \(0.912663\pi\)
\(264\) 2.00000 3.46410i 0.123091 0.213201i
\(265\) 21.0000 1.29002
\(266\) 2.00000 3.46410i 0.122628 0.212398i
\(267\) −3.00000 + 5.19615i −0.183597 + 0.317999i
\(268\) 12.0000 0.733017
\(269\) −7.00000 + 12.1244i −0.426798 + 0.739235i −0.996586 0.0825561i \(-0.973692\pi\)
0.569789 + 0.821791i \(0.307025\pi\)
\(270\) 1.50000 + 2.59808i 0.0912871 + 0.158114i
\(271\) −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i \(-0.906676\pi\)
0.228380 0.973572i \(-0.426657\pi\)
\(272\) −5.00000 −0.303170
\(273\) 3.50000 0.866025i 0.211830 0.0524142i
\(274\) 3.00000 0.181237
\(275\) −8.00000 13.8564i −0.482418 0.835573i
\(276\) −2.00000 3.46410i −0.120386 0.208514i
\(277\) −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i \(0.360033\pi\)
−0.996484 + 0.0837823i \(0.973300\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) 1.50000 2.59808i 0.0896421 0.155265i
\(281\) 15.0000 0.894825 0.447412 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(282\) 6.00000 10.3923i 0.357295 0.618853i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −6.00000 10.3923i −0.356034 0.616670i
\(285\) −12.0000 −0.710819
\(286\) −4.00000 + 13.8564i −0.236525 + 0.819346i
\(287\) −7.00000 −0.413197
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) 13.5000 23.3827i 0.792747 1.37308i
\(291\) −18.0000 −1.05518
\(292\) 0.500000 0.866025i 0.0292603 0.0506803i
\(293\) 16.5000 28.5788i 0.963940 1.66959i 0.251505 0.967856i \(-0.419075\pi\)
0.712436 0.701737i \(-0.247592\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 12.0000 20.7846i 0.698667 1.21013i
\(296\) −3.50000 6.06218i −0.203433 0.352357i
\(297\) 2.00000 + 3.46410i 0.116052 + 0.201008i
\(298\) 7.00000 0.405499
\(299\) 10.0000 + 10.3923i 0.578315 + 0.601003i
\(300\) −4.00000 −0.230940
\(301\) 4.00000 + 6.92820i 0.230556 + 0.399335i
\(302\) 4.00000 + 6.92820i 0.230174 + 0.398673i
\(303\) 1.50000 2.59808i 0.0861727 0.149256i
\(304\) 4.00000 0.229416
\(305\) −10.5000 + 18.1865i −0.601228 + 1.04136i
\(306\) 2.50000 4.33013i 0.142915 0.247537i
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 2.00000 3.46410i 0.113961 0.197386i
\(309\) −2.00000 3.46410i −0.113776 0.197066i
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 2.50000 + 2.59808i 0.141535 + 0.147087i
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 6.50000 + 11.2583i 0.366816 + 0.635344i
\(315\) 1.50000 + 2.59808i 0.0845154 + 0.146385i
\(316\) 8.00000 13.8564i 0.450035 0.779484i
\(317\) 35.0000 1.96580 0.982898 0.184151i \(-0.0589536\pi\)
0.982898 + 0.184151i \(0.0589536\pi\)
\(318\) 3.50000 6.06218i 0.196270 0.339950i
\(319\) 18.0000 31.1769i 1.00781 1.74557i
\(320\) 3.00000 0.167705
\(321\) 0 0
\(322\) −2.00000 3.46410i −0.111456 0.193047i
\(323\) 10.0000 + 17.3205i 0.556415 + 0.963739i
\(324\) 1.00000 0.0555556
\(325\) 14.0000 3.46410i 0.776580 0.192154i
\(326\) 4.00000 0.221540
\(327\) 7.00000 + 12.1244i 0.387101 + 0.670478i
\(328\) −3.50000 6.06218i −0.193255 0.334728i
\(329\) 6.00000 10.3923i 0.330791 0.572946i
\(330\) −12.0000 −0.660578
\(331\) 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) 4.00000 6.92820i 0.219529 0.380235i
\(333\) 7.00000 0.383598
\(334\) 4.00000 6.92820i 0.218870 0.379094i
\(335\) −18.0000 31.1769i −0.983445 1.70338i
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) −9.00000 −0.490261 −0.245131 0.969490i \(-0.578831\pi\)
−0.245131 + 0.969490i \(0.578831\pi\)
\(338\) −11.0000 6.92820i −0.598321 0.376845i
\(339\) 5.00000 0.271563
\(340\) 7.50000 + 12.9904i 0.406745 + 0.704502i
\(341\) 0 0
\(342\) −2.00000 + 3.46410i −0.108148 + 0.187317i
\(343\) −1.00000 −0.0539949
\(344\) −4.00000 + 6.92820i −0.215666 + 0.373544i
\(345\) −6.00000 + 10.3923i −0.323029 + 0.559503i
\(346\) 14.0000 0.752645
\(347\) −10.0000 + 17.3205i −0.536828 + 0.929814i 0.462244 + 0.886753i \(0.347044\pi\)
−0.999072 + 0.0430610i \(0.986289\pi\)
\(348\) −4.50000 7.79423i −0.241225 0.417815i
\(349\) −7.00000 12.1244i −0.374701 0.649002i 0.615581 0.788074i \(-0.288921\pi\)
−0.990282 + 0.139072i \(0.955588\pi\)
\(350\) −4.00000 −0.213809
\(351\) −3.50000 + 0.866025i −0.186816 + 0.0462250i
\(352\) 4.00000 0.213201
\(353\) 12.5000 + 21.6506i 0.665308 + 1.15235i 0.979202 + 0.202889i \(0.0650330\pi\)
−0.313894 + 0.949458i \(0.601634\pi\)
\(354\) −4.00000 6.92820i −0.212598 0.368230i
\(355\) −18.0000 + 31.1769i −0.955341 + 1.65470i
\(356\) −6.00000 −0.317999
\(357\) 2.50000 4.33013i 0.132314 0.229175i
\(358\) −10.0000 + 17.3205i −0.528516 + 0.915417i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) −1.50000 + 2.59808i −0.0790569 + 0.136931i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 2.50000 + 4.33013i 0.131397 + 0.227586i
\(363\) −5.00000 −0.262432
\(364\) 2.50000 + 2.59808i 0.131036 + 0.136176i
\(365\) −3.00000 −0.157027
\(366\) 3.50000 + 6.06218i 0.182948 + 0.316875i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 2.00000 3.46410i 0.104257 0.180579i
\(369\) 7.00000 0.364405
\(370\) −10.5000 + 18.1865i −0.545869 + 0.945473i
\(371\) 3.50000 6.06218i 0.181711 0.314733i
\(372\) 0 0
\(373\) −7.50000 + 12.9904i −0.388335 + 0.672616i −0.992226 0.124451i \(-0.960283\pi\)
0.603890 + 0.797067i \(0.293616\pi\)
\(374\) 10.0000 + 17.3205i 0.517088 + 0.895622i
\(375\) −1.50000 2.59808i −0.0774597 0.134164i
\(376\) 12.0000 0.618853
\(377\) 22.5000 + 23.3827i 1.15881 + 1.20427i
\(378\) 1.00000 0.0514344
\(379\) 14.0000 + 24.2487i 0.719132 + 1.24557i 0.961344 + 0.275349i \(0.0887935\pi\)
−0.242213 + 0.970223i \(0.577873\pi\)
\(380\) −6.00000 10.3923i −0.307794 0.533114i
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) −24.0000 −1.22795
\(383\) 14.0000 24.2487i 0.715367 1.23905i −0.247451 0.968900i \(-0.579593\pi\)
0.962818 0.270151i \(-0.0870736\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) −12.0000 −0.611577
\(386\) −9.50000 + 16.4545i −0.483537 + 0.837511i
\(387\) −4.00000 6.92820i −0.203331 0.352180i
\(388\) −9.00000 15.5885i −0.456906 0.791384i
\(389\) 7.00000 0.354914 0.177457 0.984129i \(-0.443213\pi\)
0.177457 + 0.984129i \(0.443213\pi\)
\(390\) 3.00000 10.3923i 0.151911 0.526235i
\(391\) 20.0000 1.01144
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) −6.00000 10.3923i −0.302660 0.524222i
\(394\) −11.0000 + 19.0526i −0.554172 + 0.959854i
\(395\) −48.0000 −2.41514
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) 1.00000 1.73205i 0.0501886 0.0869291i −0.839840 0.542834i \(-0.817351\pi\)
0.890028 + 0.455905i \(0.150684\pi\)
\(398\) 0 0
\(399\) −2.00000 + 3.46410i −0.100125 + 0.173422i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 8.50000 + 14.7224i 0.424470 + 0.735203i 0.996371 0.0851195i \(-0.0271272\pi\)
−0.571901 + 0.820323i \(0.693794\pi\)
\(402\) −12.0000 −0.598506
\(403\) 0 0
\(404\) 3.00000 0.149256
\(405\) −1.50000 2.59808i −0.0745356 0.129099i
\(406\) −4.50000 7.79423i −0.223331 0.386821i
\(407\) −14.0000 + 24.2487i −0.693954 + 1.20196i
\(408\) 5.00000 0.247537
\(409\) 6.50000 11.2583i 0.321404 0.556689i −0.659374 0.751815i \(-0.729178\pi\)
0.980778 + 0.195127i \(0.0625118\pi\)
\(410\) −10.5000 + 18.1865i −0.518558 + 0.898169i
\(411\) −3.00000 −0.147979
\(412\) 2.00000 3.46410i 0.0985329 0.170664i
\(413\) −4.00000 6.92820i −0.196827 0.340915i
\(414\) 2.00000 + 3.46410i 0.0982946 + 0.170251i
\(415\) −24.0000 −1.17811
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) −4.00000 −0.195881
\(418\) −8.00000 13.8564i −0.391293 0.677739i
\(419\) 8.00000 + 13.8564i 0.390826 + 0.676930i 0.992559 0.121768i \(-0.0388562\pi\)
−0.601733 + 0.798697i \(0.705523\pi\)
\(420\) −1.50000 + 2.59808i −0.0731925 + 0.126773i
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) 4.00000 6.92820i 0.194717 0.337260i
\(423\) −6.00000 + 10.3923i −0.291730 + 0.505291i
\(424\) 7.00000 0.339950
\(425\) 10.0000 17.3205i 0.485071 0.840168i
\(426\) 6.00000 + 10.3923i 0.290701 + 0.503509i
\(427\) 3.50000 + 6.06218i 0.169377 + 0.293369i
\(428\) 0 0
\(429\) 4.00000 13.8564i 0.193122 0.668994i
\(430\) 24.0000 1.15738
\(431\) 2.00000 + 3.46410i 0.0963366 + 0.166860i 0.910166 0.414244i \(-0.135954\pi\)
−0.813829 + 0.581104i \(0.802621\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −15.5000 + 26.8468i −0.744882 + 1.29017i 0.205367 + 0.978685i \(0.434161\pi\)
−0.950250 + 0.311489i \(0.899172\pi\)
\(434\) 0 0
\(435\) −13.5000 + 23.3827i −0.647275 + 1.12111i
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) −16.0000 −0.765384
\(438\) −0.500000 + 0.866025i −0.0238909 + 0.0413803i
\(439\) 8.00000 + 13.8564i 0.381819 + 0.661330i 0.991322 0.131453i \(-0.0419644\pi\)
−0.609503 + 0.792784i \(0.708631\pi\)
\(440\) −6.00000 10.3923i −0.286039 0.495434i
\(441\) 1.00000 0.0476190
\(442\) −17.5000 + 4.33013i −0.832390 + 0.205963i
\(443\) −16.0000 −0.760183 −0.380091 0.924949i \(-0.624107\pi\)
−0.380091 + 0.924949i \(0.624107\pi\)
\(444\) 3.50000 + 6.06218i 0.166103 + 0.287698i
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) 14.0000 24.2487i 0.662919 1.14821i
\(447\) −7.00000 −0.331089
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) 7.00000 12.1244i 0.330350 0.572184i −0.652230 0.758021i \(-0.726166\pi\)
0.982581 + 0.185837i \(0.0594997\pi\)
\(450\) 4.00000 0.188562
\(451\) −14.0000 + 24.2487i −0.659234 + 1.14183i
\(452\) 2.50000 + 4.33013i 0.117590 + 0.203672i
\(453\) −4.00000 6.92820i −0.187936 0.325515i
\(454\) 24.0000 1.12638
\(455\) 3.00000 10.3923i 0.140642 0.487199i
\(456\) −4.00000 −0.187317
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) −3.00000 5.19615i −0.140181 0.242800i
\(459\) −2.50000 + 4.33013i −0.116690 + 0.202113i
\(460\) −12.0000 −0.559503
\(461\) −9.50000 + 16.4545i −0.442459 + 0.766362i −0.997871 0.0652135i \(-0.979227\pi\)
0.555412 + 0.831575i \(0.312560\pi\)
\(462\) −2.00000 + 3.46410i −0.0930484 + 0.161165i
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −2.50000 2.59808i −0.115563 0.120096i
\(469\) −12.0000 −0.554109
\(470\) −18.0000 31.1769i −0.830278 1.43808i
\(471\) −6.50000 11.2583i −0.299504 0.518756i
\(472\) 4.00000 6.92820i 0.184115 0.318896i
\(473\) 32.0000 1.47136
\(474\) −8.00000 + 13.8564i −0.367452 + 0.636446i
\(475\) −8.00000 + 13.8564i −0.367065 + 0.635776i
\(476\) 5.00000 0.229175
\(477\) −3.50000 + 6.06218i −0.160254 + 0.277568i
\(478\) 2.00000 + 3.46410i 0.0914779 + 0.158444i
\(479\) −14.0000 24.2487i −0.639676 1.10795i −0.985504 0.169654i \(-0.945735\pi\)
0.345827 0.938298i \(-0.387598\pi\)
\(480\) −3.00000 −0.136931
\(481\) −17.5000 18.1865i −0.797931 0.829235i
\(482\) −9.00000 −0.409939
\(483\) 2.00000 + 3.46410i 0.0910032 + 0.157622i
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) −27.0000 + 46.7654i −1.22601 + 2.12351i
\(486\) −1.00000 −0.0453609
\(487\) −2.00000 + 3.46410i −0.0906287 + 0.156973i −0.907776 0.419456i \(-0.862221\pi\)
0.817147 + 0.576429i \(0.195554\pi\)
\(488\) −3.50000 + 6.06218i −0.158438 + 0.274422i
\(489\) −4.00000 −0.180886
\(490\) −1.50000 + 2.59808i −0.0677631 + 0.117369i
\(491\) −10.0000 17.3205i −0.451294 0.781664i 0.547173 0.837020i \(-0.315704\pi\)
−0.998467 + 0.0553560i \(0.982371\pi\)
\(492\) 3.50000 + 6.06218i 0.157792 + 0.273304i
\(493\) 45.0000 2.02670
\(494\) 14.0000 3.46410i 0.629890 0.155857i
\(495\) 12.0000 0.539360
\(496\) 0 0
\(497\) 6.00000 + 10.3923i 0.269137 + 0.466159i
\(498\) −4.00000 + 6.92820i −0.179244 + 0.310460i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) −4.00000 + 6.92820i −0.178707 + 0.309529i
\(502\) −12.0000 −0.535586
\(503\) 12.0000 20.7846i 0.535054 0.926740i −0.464107 0.885779i \(-0.653625\pi\)
0.999161 0.0409609i \(-0.0130419\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) −4.50000 7.79423i −0.200247 0.346839i
\(506\) −16.0000 −0.711287
\(507\) 11.0000 + 6.92820i 0.488527 + 0.307692i
\(508\) −8.00000 −0.354943
\(509\) −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i \(-0.274536\pi\)
−0.982988 + 0.183669i \(0.941202\pi\)
\(510\) −7.50000 12.9904i −0.332106 0.575224i
\(511\) −0.500000 + 0.866025i −0.0221187 + 0.0383107i
\(512\) 1.00000 0.0441942
\(513\) 2.00000 3.46410i 0.0883022 0.152944i
\(514\) −3.50000 + 6.06218i −0.154378 + 0.267391i
\(515\) −12.0000 −0.528783
\(516\) 4.00000 6.92820i 0.176090 0.304997i
\(517\) −24.0000 41.5692i −1.05552 1.82821i
\(518\) 3.50000 + 6.06218i 0.153781 + 0.266357i
\(519\) −14.0000 −0.614532
\(520\) 10.5000 2.59808i 0.460455 0.113933i
\(521\) −17.0000 −0.744784 −0.372392 0.928076i \(-0.621462\pi\)
−0.372392 + 0.928076i \(0.621462\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) 6.00000 10.3923i 0.262111 0.453990i
\(525\) 4.00000 0.174574
\(526\) −4.00000 + 6.92820i −0.174408 + 0.302084i
\(527\) 0 0
\(528\) −4.00000 −0.174078
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −10.5000 18.1865i −0.456091 0.789973i
\(531\) 4.00000 + 6.92820i 0.173585 + 0.300658i
\(532\) −4.00000 −0.173422
\(533\) −17.5000 18.1865i −0.758009 0.787746i
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 10.0000 17.3205i 0.431532 0.747435i
\(538\) 14.0000 0.603583
\(539\) −2.00000 + 3.46410i −0.0861461 + 0.149209i
\(540\) 1.50000 2.59808i 0.0645497 0.111803i
\(541\) 43.0000 1.84871 0.924357 0.381528i \(-0.124602\pi\)
0.924357 + 0.381528i \(0.124602\pi\)
\(542\) −12.0000 + 20.7846i −0.515444 + 0.892775i
\(543\) −2.50000 4.33013i −0.107285 0.185824i
\(544\) 2.50000 + 4.33013i 0.107187 + 0.185653i
\(545\) 42.0000 1.79908
\(546\) −2.50000 2.59808i −0.106990 0.111187i
\(547\) 16.0000 0.684111 0.342055 0.939680i \(-0.388877\pi\)
0.342055 + 0.939680i \(0.388877\pi\)
\(548\) −1.50000 2.59808i −0.0640768 0.110984i
\(549\) −3.50000 6.06218i −0.149376 0.258727i
\(550\) −8.00000 + 13.8564i −0.341121 + 0.590839i
\(551\) −36.0000 −1.53365
\(552\) −2.00000 + 3.46410i −0.0851257 + 0.147442i
\(553\) −8.00000 + 13.8564i −0.340195 + 0.589234i
\(554\) 19.0000 0.807233
\(555\) 10.5000 18.1865i 0.445700 0.771975i
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i \(0.0797613\pi\)
−0.269642 + 0.962961i \(0.586905\pi\)
\(558\) 0 0
\(559\) −8.00000 + 27.7128i −0.338364 + 1.17213i
\(560\) −3.00000 −0.126773
\(561\) −10.0000 17.3205i −0.422200 0.731272i
\(562\) −7.50000 12.9904i −0.316368 0.547966i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) −12.0000 −0.505291
\(565\) 7.50000 12.9904i 0.315527 0.546509i
\(566\) 2.00000 3.46410i 0.0840663 0.145607i
\(567\) −1.00000 −0.0419961
\(568\) −6.00000 + 10.3923i −0.251754 + 0.436051i
\(569\) 11.0000 + 19.0526i 0.461144 + 0.798725i 0.999018 0.0443003i \(-0.0141058\pi\)
−0.537874 + 0.843025i \(0.680772\pi\)
\(570\) 6.00000 + 10.3923i 0.251312 + 0.435286i
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 14.0000 3.46410i 0.585369 0.144841i
\(573\) 24.0000 1.00261
\(574\) 3.50000 + 6.06218i 0.146087 + 0.253030i
\(575\) 8.00000 + 13.8564i 0.333623 + 0.577852i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −5.00000 −0.208153 −0.104076 0.994569i \(-0.533189\pi\)
−0.104076 + 0.994569i \(0.533189\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 9.50000 16.4545i 0.394807 0.683825i
\(580\) −27.0000 −1.12111
\(581\) −4.00000 + 6.92820i −0.165948 + 0.287430i
\(582\) 9.00000 + 15.5885i 0.373062 + 0.646162i
\(583\) −14.0000 24.2487i −0.579821 1.00428i
\(584\) −1.00000 −0.0413803
\(585\) −3.00000 + 10.3923i −0.124035 + 0.429669i
\(586\) −33.0000 −1.36322
\(587\) 12.0000 + 20.7846i 0.495293 + 0.857873i 0.999985 0.00542667i \(-0.00172737\pi\)
−0.504692 + 0.863299i \(0.668394\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) 0 0
\(590\) −24.0000 −0.988064
\(591\) 11.0000 19.0526i 0.452480 0.783718i
\(592\) −3.50000 + 6.06218i −0.143849 + 0.249154i
\(593\) −33.0000 −1.35515 −0.677574 0.735455i \(-0.736969\pi\)
−0.677574 + 0.735455i \(0.736969\pi\)
\(594\) 2.00000 3.46410i 0.0820610 0.142134i
\(595\) −7.50000 12.9904i −0.307470 0.532554i
\(596\) −3.50000 6.06218i −0.143366 0.248316i
\(597\) 0 0
\(598\) 4.00000 13.8564i 0.163572 0.566631i
\(599\) −4.00000 −0.163436 −0.0817178 0.996656i \(-0.526041\pi\)
−0.0817178 + 0.996656i \(0.526041\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) 8.50000 + 14.7224i 0.346722 + 0.600541i 0.985665 0.168714i \(-0.0539613\pi\)
−0.638943 + 0.769254i \(0.720628\pi\)
\(602\) 4.00000 6.92820i 0.163028 0.282372i
\(603\) 12.0000 0.488678
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) −7.50000 + 12.9904i −0.304918 + 0.528134i
\(606\) −3.00000 −0.121867
\(607\) 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) −2.00000 3.46410i −0.0811107 0.140488i
\(609\) 4.50000 + 7.79423i 0.182349 + 0.315838i
\(610\) 21.0000 0.850265
\(611\) 42.0000 10.3923i 1.69914 0.420428i
\(612\) −5.00000 −0.202113
\(613\) 0.500000 + 0.866025i 0.0201948 + 0.0349784i 0.875946 0.482409i \(-0.160238\pi\)
−0.855751 + 0.517387i \(0.826905\pi\)
\(614\) −2.00000 3.46410i −0.0807134 0.139800i
\(615\) 10.5000 18.1865i 0.423401 0.733352i
\(616\) −4.00000 −0.161165
\(617\) 16.5000 28.5788i 0.664265 1.15054i −0.315219 0.949019i \(-0.602078\pi\)
0.979484 0.201522i \(-0.0645887\pi\)
\(618\) −2.00000 + 3.46410i −0.0804518 + 0.139347i
\(619\) −32.0000 −1.28619 −0.643094 0.765787i \(-0.722350\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 0 0
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) −4.00000 6.92820i −0.160385 0.277796i
\(623\) 6.00000 0.240385
\(624\) 1.00000 3.46410i 0.0400320 0.138675i
\(625\) −29.0000 −1.16000
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 8.00000 + 13.8564i 0.319489 + 0.553372i
\(628\) 6.50000 11.2583i 0.259378 0.449256i
\(629\) −35.0000 −1.39554
\(630\) 1.50000 2.59808i 0.0597614 0.103510i
\(631\) 20.0000 34.6410i 0.796187 1.37904i −0.125895 0.992044i \(-0.540180\pi\)
0.922082 0.386994i \(-0.126486\pi\)
\(632\) −16.0000 −0.636446
\(633\) −4.00000 + 6.92820i −0.158986 + 0.275371i
\(634\) −17.5000 30.3109i −0.695014 1.20380i
\(635\) 12.0000 + 20.7846i 0.476205 + 0.824812i
\(636\) −7.00000 −0.277568
\(637\) −2.50000 2.59808i −0.0990536 0.102940i
\(638\) −36.0000 −1.42525
\(639\) −6.00000 10.3923i −0.237356 0.411113i
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 0 0
\(643\) −6.00000 + 10.3923i −0.236617 + 0.409832i −0.959741 0.280885i \(-0.909372\pi\)
0.723124 + 0.690718i \(0.242705\pi\)
\(644\) −2.00000 + 3.46410i −0.0788110 + 0.136505i
\(645\) −24.0000 −0.944999
\(646\) 10.0000 17.3205i 0.393445 0.681466i
\(647\) −6.00000 10.3923i −0.235884 0.408564i 0.723645 0.690172i \(-0.242465\pi\)
−0.959529 + 0.281609i \(0.909132\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −32.0000 −1.25611
\(650\) −10.0000 10.3923i −0.392232 0.407620i
\(651\) 0 0
\(652\) −2.00000 3.46410i −0.0783260 0.135665i
\(653\) 17.0000 + 29.4449i 0.665261 + 1.15227i 0.979214 + 0.202828i \(0.0650132\pi\)
−0.313953 + 0.949439i \(0.601653\pi\)
\(654\) 7.00000 12.1244i 0.273722 0.474100i
\(655\) −36.0000 −1.40664
\(656\) −3.50000 + 6.06218i −0.136652 + 0.236688i
\(657\) 0.500000 0.866025i 0.0195069 0.0337869i
\(658\) −12.0000 −0.467809
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 6.00000 + 10.3923i 0.233550 + 0.404520i
\(661\) 0.500000 + 0.866025i 0.0194477 + 0.0336845i 0.875585 0.483063i \(-0.160476\pi\)
−0.856138 + 0.516748i \(0.827143\pi\)
\(662\) −20.0000 −0.777322
\(663\) 17.5000 4.33013i 0.679644 0.168168i
\(664\) −8.00000 −0.310460
\(665\) 6.00000 + 10.3923i 0.232670 + 0.402996i
\(666\) −3.50000 6.06218i −0.135622 0.234905i
\(667\) −18.0000 + 31.1769i −0.696963 + 1.20717i
\(668\) −8.00000 −0.309529
\(669\) −14.0000 + 24.2487i −0.541271 + 0.937509i
\(670\) −18.0000 + 31.1769i −0.695401 + 1.20447i
\(671\) 28.0000 1.08093
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) −9.50000 16.4545i −0.366198 0.634274i 0.622770 0.782405i \(-0.286007\pi\)
−0.988968 + 0.148132i \(0.952674\pi\)
\(674\) 4.50000 + 7.79423i 0.173334 + 0.300222i
\(675\) −4.00000 −0.153960
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) 22.0000 0.845529 0.422764 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) −2.50000 4.33013i −0.0960119 0.166298i
\(679\) 9.00000 + 15.5885i 0.345388 + 0.598230i
\(680\) 7.50000 12.9904i 0.287612 0.498158i
\(681\) −24.0000 −0.919682
\(682\) 0 0
\(683\) −10.0000 + 17.3205i −0.382639 + 0.662751i −0.991439 0.130573i \(-0.958318\pi\)
0.608799 + 0.793324i \(0.291651\pi\)
\(684\) 4.00000 0.152944
\(685\) −4.50000 + 7.79423i −0.171936 + 0.297802i
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 3.00000 + 5.19615i 0.114457 + 0.198246i
\(688\) 8.00000 0.304997
\(689\) 24.5000 6.06218i 0.933376 0.230951i
\(690\) 12.0000 0.456832
\(691\) 20.0000 + 34.6410i 0.760836 + 1.31781i 0.942420 + 0.334431i \(0.108544\pi\)
−0.181584 + 0.983375i \(0.558123\pi\)
\(692\) −7.00000 12.1244i −0.266100 0.460899i
\(693\) 2.00000 3.46410i 0.0759737 0.131590i
\(694\) 20.0000 0.759190
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) −4.50000 + 7.79423i −0.170572 + 0.295439i
\(697\) −35.0000 −1.32572
\(698\) −7.00000 + 12.1244i −0.264954 + 0.458914i
\(699\) −3.00000 5.19615i −0.113470 0.196537i
\(700\) 2.00000 + 3.46410i 0.0755929 + 0.130931i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 2.50000 + 2.59808i 0.0943564 + 0.0980581i
\(703\) 28.0000 1.05604
\(704\) −2.00000 3.46410i −0.0753778 0.130558i
\(705\) 18.0000 + 31.1769i 0.677919 + 1.17419i
\(706\) 12.5000 21.6506i 0.470444 0.814832i
\(707\) −3.00000 −0.112827
\(708\) −4.00000 + 6.92820i −0.150329 + 0.260378i
\(709\) 0.500000 0.866025i 0.0187779 0.0325243i −0.856484 0.516174i \(-0.827356\pi\)
0.875262 + 0.483650i \(0.160689\pi\)
\(710\) 36.0000 1.35106
\(711\) 8.00000 13.8564i 0.300023 0.519656i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 0 0
\(714\) −5.00000 −0.187120
\(715\) −30.0000 31.1769i −1.12194 1.16595i
\(716\) 20.0000 0.747435
\(717\) −2.00000 3.46410i −0.0746914 0.129369i
\(718\) 6.00000 + 10.3923i 0.223918 + 0.387837i
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 3.00000 0.111803
\(721\) −2.00000 + 3.46410i −0.0744839 + 0.129010i
\(722\) 1.50000 2.59808i 0.0558242 0.0966904i
\(723\) 9.00000 0.334714
\(724\) 2.50000 4.33013i 0.0929118 0.160928i
\(725\) 18.0000 + 31.1769i 0.668503 + 1.15788i
\(726\) 2.50000 + 4.33013i 0.0927837 + 0.160706i
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 1.00000 3.46410i 0.0370625 0.128388i
\(729\) 1.00000 0.0370370
\(730\) 1.50000 + 2.59808i 0.0555175 + 0.0961591i
\(731\) 20.0000 + 34.6410i 0.739727 + 1.28124i
\(732\) 3.50000 6.06218i 0.129364 0.224065i
\(733\) 23.0000 0.849524 0.424762 0.905305i \(-0.360358\pi\)
0.424762 + 0.905305i \(0.360358\pi\)
\(734\) 2.00000 3.46410i 0.0738213 0.127862i
\(735\) 1.50000 2.59808i 0.0553283 0.0958315i
\(736\) −4.00000 −0.147442
\(737\) −24.0000 + 41.5692i −0.884051 + 1.53122i
\(738\) −3.50000 6.06218i −0.128837 0.223152i
\(739\) −4.00000 6.92820i −0.147142 0.254858i 0.783028 0.621987i \(-0.213674\pi\)
−0.930170 + 0.367129i \(0.880341\pi\)
\(740\) 21.0000 0.771975
\(741\) −14.0000 + 3.46410i −0.514303 + 0.127257i
\(742\) −7.00000 −0.256978
\(743\) −8.00000 13.8564i −0.293492 0.508342i 0.681141 0.732152i \(-0.261484\pi\)
−0.974633 + 0.223810i \(0.928151\pi\)
\(744\) 0 0
\(745\) −10.5000 + 18.1865i −0.384690 + 0.666303i
\(746\) 15.0000 0.549189
\(747\) 4.00000 6.92820i 0.146352 0.253490i
\(748\) 10.0000 17.3205i 0.365636 0.633300i
\(749\) 0 0
\(750\) −1.50000 + 2.59808i −0.0547723 + 0.0948683i
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) −6.00000 10.3923i −0.218797 0.378968i
\(753\) 12.0000 0.437304
\(754\) 9.00000 31.1769i 0.327761 1.13540i
\(755\) −24.0000 −0.873449
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) −19.0000 32.9090i −0.690567 1.19610i −0.971652 0.236414i \(-0.924028\pi\)
0.281086 0.959683i \(-0.409305\pi\)
\(758\) 14.0000 24.2487i 0.508503 0.880753i
\(759\) 16.0000 0.580763
\(760\) −6.00000 + 10.3923i −0.217643 + 0.376969i
\(761\) −5.00000 + 8.66025i −0.181250 + 0.313934i −0.942306 0.334752i \(-0.891348\pi\)
0.761057 + 0.648686i \(0.224681\pi\)
\(762\) 8.00000 0.289809
\(763\) 7.00000 12.1244i 0.253417 0.438931i
\(764\) 12.0000 + 20.7846i 0.434145 + 0.751961i
\(765\) 7.50000 + 12.9904i 0.271163 + 0.469668i
\(766\) −28.0000 −1.01168
\(767\) 8.00000 27.7128i 0.288863 1.00065i
\(768\) −1.00000 −0.0360844
\(769\) −25.0000 43.3013i −0.901523 1.56148i −0.825518 0.564376i \(-0.809117\pi\)
−0.0760054 0.997107i \(-0.524217\pi\)
\(770\) 6.00000 + 10.3923i 0.216225 + 0.374513i
\(771\) 3.50000 6.06218i 0.126049 0.218324i
\(772\) 19.0000 0.683825
\(773\) −19.0000 + 32.9090i −0.683383 + 1.18365i 0.290560 + 0.956857i \(0.406159\pi\)
−0.973942 + 0.226796i \(0.927175\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) 0 0
\(776\) −9.00000 + 15.5885i −0.323081 + 0.559593i
\(777\) −3.50000 6.06218i −0.125562 0.217479i
\(778\) −3.50000 6.06218i −0.125481 0.217340i