Properties

Label 171.2.g.a.106.1
Level $171$
Weight $2$
Character 171.106
Analytic conductor $1.365$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.36544187456\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
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 106.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 171.106
Dual form 171.2.g.a.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-2.50000 + 4.33013i) q^{11} +1.73205i q^{12} +(-1.00000 + 1.73205i) q^{13} -1.00000 q^{14} +(-4.50000 + 2.59808i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +3.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} +(1.50000 - 2.59808i) q^{20} -1.73205i q^{21} -5.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(-4.50000 + 2.59808i) q^{24} +4.00000 q^{25} -2.00000 q^{26} +5.19615i q^{27} +(0.500000 + 0.866025i) q^{28} -1.00000 q^{29} +(-4.50000 - 2.59808i) q^{30} +(-1.50000 - 2.59808i) q^{31} +(2.50000 - 4.33013i) q^{32} -8.66025i q^{33} +5.00000 q^{34} +(-1.50000 + 2.59808i) q^{35} +(-1.50000 - 2.59808i) q^{36} -6.00000 q^{37} +(-3.50000 - 2.59808i) q^{38} -3.46410i q^{39} +9.00000 q^{40} -9.00000 q^{41} +(1.50000 - 0.866025i) q^{42} +(-4.00000 - 6.92820i) q^{43} +(2.50000 + 4.33013i) q^{44} +(4.50000 - 7.79423i) q^{45} +8.00000 q^{46} +3.00000 q^{47} +(-1.50000 - 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(2.00000 + 3.46410i) q^{50} +8.66025i q^{51} +(1.00000 + 1.73205i) q^{52} +(0.500000 + 0.866025i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(-7.50000 + 12.9904i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(4.50000 - 6.06218i) q^{57} +(-0.500000 - 0.866025i) q^{58} +5.00000 q^{59} +5.19615i q^{60} -13.0000 q^{61} +(1.50000 - 2.59808i) q^{62} +(1.50000 + 2.59808i) q^{63} +7.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(7.50000 - 4.33013i) q^{66} +(2.00000 - 3.46410i) q^{67} +(-2.50000 - 4.33013i) q^{68} +13.8564i q^{69} -3.00000 q^{70} +(-1.50000 + 2.59808i) q^{71} +(4.50000 - 7.79423i) q^{72} +(2.50000 - 4.33013i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(-6.00000 + 3.46410i) q^{75} +(-0.500000 + 4.33013i) q^{76} +(-2.50000 - 4.33013i) q^{77} +(3.00000 - 1.73205i) q^{78} +(-2.00000 - 3.46410i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(-1.50000 - 0.866025i) q^{84} +(7.50000 - 12.9904i) q^{85} +(4.00000 - 6.92820i) q^{86} +(1.50000 - 0.866025i) q^{87} +(-7.50000 + 12.9904i) q^{88} +(4.50000 + 7.79423i) q^{89} +9.00000 q^{90} +(-1.00000 - 1.73205i) q^{91} +(-4.00000 - 6.92820i) q^{92} +(4.50000 + 2.59808i) q^{93} +(1.50000 + 2.59808i) q^{94} +(-12.0000 + 5.19615i) q^{95} +8.66025i q^{96} +(5.00000 + 8.66025i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - 3 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - 3 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 5 q^{11} - 2 q^{13} - 2 q^{14} - 9 q^{15} + q^{16} + 5 q^{17} + 6 q^{18} - 8 q^{19} + 3 q^{20} - 10 q^{22} + 8 q^{23} - 9 q^{24} + 8 q^{25} - 4 q^{26} + q^{28} - 2 q^{29} - 9 q^{30} - 3 q^{31} + 5 q^{32} + 10 q^{34} - 3 q^{35} - 3 q^{36} - 12 q^{37} - 7 q^{38} + 18 q^{40} - 18 q^{41} + 3 q^{42} - 8 q^{43} + 5 q^{44} + 9 q^{45} + 16 q^{46} + 6 q^{47} - 3 q^{48} + 6 q^{49} + 4 q^{50} + 2 q^{52} + q^{53} - 9 q^{54} - 15 q^{55} - 3 q^{56} + 9 q^{57} - q^{58} + 10 q^{59} - 26 q^{61} + 3 q^{62} + 3 q^{63} + 14 q^{64} - 6 q^{65} + 15 q^{66} + 4 q^{67} - 5 q^{68} - 6 q^{70} - 3 q^{71} + 9 q^{72} + 5 q^{73} - 6 q^{74} - 12 q^{75} - q^{76} - 5 q^{77} + 6 q^{78} - 4 q^{79} + 3 q^{80} - 9 q^{81} - 9 q^{82} - 9 q^{83} - 3 q^{84} + 15 q^{85} + 8 q^{86} + 3 q^{87} - 15 q^{88} + 9 q^{89} + 18 q^{90} - 2 q^{91} - 8 q^{92} + 9 q^{93} + 3 q^{94} - 24 q^{95} + 10 q^{97} - 6 q^{98} + 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) −1.50000 + 0.866025i −0.866025 + 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 \(0.265942\pi\)
\(6\) −1.50000 0.866025i −0.612372 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i −0.944911 0.327327i \(-0.893852\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 1.73205i 0.500000i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −1.00000 −0.267261
\(15\) −4.50000 + 2.59808i −1.16190 + 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 \(-0.0406959\pi\)
\(18\) 3.00000 0.707107
\(19\) −4.00000 + 1.73205i −0.917663 + 0.397360i
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 1.73205i 0.377964i
\(22\) −5.00000 −1.06600
\(23\) 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i \(-0.519345\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(24\) −4.50000 + 2.59808i −0.918559 + 0.530330i
\(25\) 4.00000 0.800000
\(26\) −2.00000 −0.392232
\(27\) 5.19615i 1.00000i
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) −4.50000 2.59808i −0.821584 0.474342i
\(31\) −1.50000 2.59808i −0.269408 0.466628i 0.699301 0.714827i \(-0.253495\pi\)
−0.968709 + 0.248199i \(0.920161\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 8.66025i 1.50756i
\(34\) 5.00000 0.857493
\(35\) −1.50000 + 2.59808i −0.253546 + 0.439155i
\(36\) −1.50000 2.59808i −0.250000 0.433013i
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) −3.50000 2.59808i −0.567775 0.421464i
\(39\) 3.46410i 0.554700i
\(40\) 9.00000 1.42302
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 1.50000 0.866025i 0.231455 0.133631i
\(43\) −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i \(-0.957838\pi\)
0.381246 0.924473i \(-0.375495\pi\)
\(44\) 2.50000 + 4.33013i 0.376889 + 0.652791i
\(45\) 4.50000 7.79423i 0.670820 1.16190i
\(46\) 8.00000 1.17954
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −1.50000 0.866025i −0.216506 0.125000i
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 8.66025i 1.21268i
\(52\) 1.00000 + 1.73205i 0.138675 + 0.240192i
\(53\) 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) −7.50000 + 12.9904i −1.01130 + 1.75162i
\(56\) −1.50000 + 2.59808i −0.200446 + 0.347183i
\(57\) 4.50000 6.06218i 0.596040 0.802955i
\(58\) −0.500000 0.866025i −0.0656532 0.113715i
\(59\) 5.00000 0.650945 0.325472 0.945552i \(-0.394477\pi\)
0.325472 + 0.945552i \(0.394477\pi\)
\(60\) 5.19615i 0.670820i
\(61\) −13.0000 −1.66448 −0.832240 0.554416i \(-0.812942\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 1.50000 2.59808i 0.190500 0.329956i
\(63\) 1.50000 + 2.59808i 0.188982 + 0.327327i
\(64\) 7.00000 0.875000
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 7.50000 4.33013i 0.923186 0.533002i
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) −2.50000 4.33013i −0.303170 0.525105i
\(69\) 13.8564i 1.66812i
\(70\) −3.00000 −0.358569
\(71\) −1.50000 + 2.59808i −0.178017 + 0.308335i −0.941201 0.337846i \(-0.890302\pi\)
0.763184 + 0.646181i \(0.223635\pi\)
\(72\) 4.50000 7.79423i 0.530330 0.918559i
\(73\) 2.50000 4.33013i 0.292603 0.506803i −0.681822 0.731519i \(-0.738812\pi\)
0.974424 + 0.224716i \(0.0721453\pi\)
\(74\) −3.00000 5.19615i −0.348743 0.604040i
\(75\) −6.00000 + 3.46410i −0.692820 + 0.400000i
\(76\) −0.500000 + 4.33013i −0.0573539 + 0.496700i
\(77\) −2.50000 4.33013i −0.284901 0.493464i
\(78\) 3.00000 1.73205i 0.339683 0.196116i
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −4.50000 7.79423i −0.496942 0.860729i
\(83\) −4.50000 + 7.79423i −0.493939 + 0.855528i −0.999976 0.00698436i \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) −1.50000 0.866025i −0.163663 0.0944911i
\(85\) 7.50000 12.9904i 0.813489 1.40900i
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 1.50000 0.866025i 0.160817 0.0928477i
\(88\) −7.50000 + 12.9904i −0.799503 + 1.38478i
\(89\) 4.50000 + 7.79423i 0.476999 + 0.826187i 0.999653 0.0263586i \(-0.00839118\pi\)
−0.522654 + 0.852545i \(0.675058\pi\)
\(90\) 9.00000 0.948683
\(91\) −1.00000 1.73205i −0.104828 0.181568i
\(92\) −4.00000 6.92820i −0.417029 0.722315i
\(93\) 4.50000 + 2.59808i 0.466628 + 0.269408i
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) −12.0000 + 5.19615i −1.23117 + 0.533114i
\(96\) 8.66025i 0.883883i
\(97\) 5.00000 + 8.66025i 0.507673 + 0.879316i 0.999961 + 0.00888289i \(0.00282755\pi\)
−0.492287 + 0.870433i \(0.663839\pi\)
\(98\) −3.00000 + 5.19615i −0.303046 + 0.524891i
\(99\) 7.50000 + 12.9904i 0.753778 + 1.30558i
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) 7.00000 0.696526 0.348263 0.937397i \(-0.386772\pi\)
0.348263 + 0.937397i \(0.386772\pi\)
\(102\) −7.50000 + 4.33013i −0.742611 + 0.428746i
\(103\) 2.50000 + 4.33013i 0.246332 + 0.426660i 0.962505 0.271263i \(-0.0874412\pi\)
−0.716173 + 0.697923i \(0.754108\pi\)
\(104\) −3.00000 + 5.19615i −0.294174 + 0.509525i
\(105\) 5.19615i 0.507093i
\(106\) −0.500000 + 0.866025i −0.0485643 + 0.0841158i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) 2.50000 4.33013i 0.239457 0.414751i −0.721102 0.692829i \(-0.756364\pi\)
0.960558 + 0.278078i \(0.0896974\pi\)
\(110\) −15.0000 −1.43019
\(111\) 9.00000 5.19615i 0.854242 0.493197i
\(112\) −1.00000 −0.0944911
\(113\) 8.50000 + 14.7224i 0.799613 + 1.38497i 0.919868 + 0.392227i \(0.128295\pi\)
−0.120256 + 0.992743i \(0.538371\pi\)
\(114\) 7.50000 + 0.866025i 0.702439 + 0.0811107i
\(115\) 12.0000 20.7846i 1.11901 1.93817i
\(116\) −0.500000 + 0.866025i −0.0464238 + 0.0804084i
\(117\) 3.00000 + 5.19615i 0.277350 + 0.480384i
\(118\) 2.50000 + 4.33013i 0.230144 + 0.398621i
\(119\) 2.50000 + 4.33013i 0.229175 + 0.396942i
\(120\) −13.5000 + 7.79423i −1.23238 + 0.711512i
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) −6.50000 11.2583i −0.588482 1.01928i
\(123\) 13.5000 7.79423i 1.21725 0.702782i
\(124\) −3.00000 −0.269408
\(125\) −3.00000 −0.268328
\(126\) −1.50000 + 2.59808i −0.133631 + 0.231455i
\(127\) −6.50000 11.2583i −0.576782 0.999015i −0.995846 0.0910585i \(-0.970975\pi\)
0.419064 0.907957i \(-0.362358\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 12.0000 + 6.92820i 1.05654 + 0.609994i
\(130\) −6.00000 −0.526235
\(131\) −7.00000 −0.611593 −0.305796 0.952097i \(-0.598923\pi\)
−0.305796 + 0.952097i \(0.598923\pi\)
\(132\) −7.50000 4.33013i −0.652791 0.376889i
\(133\) 0.500000 4.33013i 0.0433555 0.375470i
\(134\) 4.00000 0.345547
\(135\) 15.5885i 1.34164i
\(136\) 7.50000 12.9904i 0.643120 1.11392i
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) −12.0000 + 6.92820i −1.02151 + 0.589768i
\(139\) −10.0000 + 17.3205i −0.848189 + 1.46911i 0.0346338 + 0.999400i \(0.488974\pi\)
−0.882823 + 0.469706i \(0.844360\pi\)
\(140\) 1.50000 + 2.59808i 0.126773 + 0.219578i
\(141\) −4.50000 + 2.59808i −0.378968 + 0.218797i
\(142\) −3.00000 −0.251754
\(143\) −5.00000 8.66025i −0.418121 0.724207i
\(144\) 3.00000 0.250000
\(145\) −3.00000 −0.249136
\(146\) 5.00000 0.413803
\(147\) −9.00000 5.19615i −0.742307 0.428571i
\(148\) −3.00000 + 5.19615i −0.246598 + 0.427121i
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) −6.00000 3.46410i −0.489898 0.282843i
\(151\) 7.50000 12.9904i 0.610341 1.05714i −0.380841 0.924640i \(-0.624366\pi\)
0.991183 0.132502i \(-0.0423010\pi\)
\(152\) −12.0000 + 5.19615i −0.973329 + 0.421464i
\(153\) −7.50000 12.9904i −0.606339 1.05021i
\(154\) 2.50000 4.33013i 0.201456 0.348932i
\(155\) −4.50000 7.79423i −0.361449 0.626048i
\(156\) −3.00000 1.73205i −0.240192 0.138675i
\(157\) 3.00000 0.239426 0.119713 0.992809i \(-0.461803\pi\)
0.119713 + 0.992809i \(0.461803\pi\)
\(158\) 2.00000 3.46410i 0.159111 0.275589i
\(159\) −1.50000 0.866025i −0.118958 0.0686803i
\(160\) 7.50000 12.9904i 0.592927 1.02698i
\(161\) 4.00000 + 6.92820i 0.315244 + 0.546019i
\(162\) 4.50000 7.79423i 0.353553 0.612372i
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) −4.50000 + 7.79423i −0.351391 + 0.608627i
\(165\) 25.9808i 2.02260i
\(166\) −9.00000 −0.698535
\(167\) 2.00000 3.46410i 0.154765 0.268060i −0.778209 0.628006i \(-0.783871\pi\)
0.932973 + 0.359946i \(0.117205\pi\)
\(168\) 5.19615i 0.400892i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 15.0000 1.15045
\(171\) −1.50000 + 12.9904i −0.114708 + 0.993399i
\(172\) −8.00000 −0.609994
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 1.50000 + 0.866025i 0.113715 + 0.0656532i
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) −5.00000 −0.376889
\(177\) −7.50000 + 4.33013i −0.563735 + 0.325472i
\(178\) −4.50000 + 7.79423i −0.337289 + 0.584202i
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) −4.50000 7.79423i −0.335410 0.580948i
\(181\) −3.50000 6.06218i −0.260153 0.450598i 0.706129 0.708083i \(-0.250440\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 1.00000 1.73205i 0.0741249 0.128388i
\(183\) 19.5000 11.2583i 1.44148 0.832240i
\(184\) 12.0000 20.7846i 0.884652 1.53226i
\(185\) −18.0000 −1.32339
\(186\) 5.19615i 0.381000i
\(187\) 12.5000 + 21.6506i 0.914091 + 1.58325i
\(188\) 1.50000 2.59808i 0.109399 0.189484i
\(189\) −4.50000 2.59808i −0.327327 0.188982i
\(190\) −10.5000 7.79423i −0.761750 0.565453i
\(191\) 1.50000 2.59808i 0.108536 0.187990i −0.806641 0.591041i \(-0.798717\pi\)
0.915177 + 0.403051i \(0.132050\pi\)
\(192\) −10.5000 + 6.06218i −0.757772 + 0.437500i
\(193\) −17.0000 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(194\) −5.00000 + 8.66025i −0.358979 + 0.621770i
\(195\) 10.3923i 0.744208i
\(196\) 6.00000 0.428571
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −7.50000 + 12.9904i −0.533002 + 0.923186i
\(199\) 1.50000 + 2.59808i 0.106332 + 0.184173i 0.914282 0.405079i \(-0.132756\pi\)
−0.807950 + 0.589252i \(0.799423\pi\)
\(200\) 12.0000 0.848528
\(201\) 6.92820i 0.488678i
\(202\) 3.50000 + 6.06218i 0.246259 + 0.426533i
\(203\) 0.500000 0.866025i 0.0350931 0.0607831i
\(204\) 7.50000 + 4.33013i 0.525105 + 0.303170i
\(205\) −27.0000 −1.88576
\(206\) −2.50000 + 4.33013i −0.174183 + 0.301694i
\(207\) −12.0000 20.7846i −0.834058 1.44463i
\(208\) −2.00000 −0.138675
\(209\) 2.50000 21.6506i 0.172929 1.49761i
\(210\) 4.50000 2.59808i 0.310530 0.179284i
\(211\) −15.0000 −1.03264 −0.516321 0.856395i \(-0.672699\pi\)
−0.516321 + 0.856395i \(0.672699\pi\)
\(212\) 1.00000 0.0686803
\(213\) 5.19615i 0.356034i
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) −12.0000 20.7846i −0.818393 1.41750i
\(216\) 15.5885i 1.06066i
\(217\) 3.00000 0.203653
\(218\) 5.00000 0.338643
\(219\) 8.66025i 0.585206i
\(220\) 7.50000 + 12.9904i 0.505650 + 0.875811i
\(221\) 5.00000 + 8.66025i 0.336336 + 0.582552i
\(222\) 9.00000 + 5.19615i 0.604040 + 0.348743i
\(223\) 12.0000 + 20.7846i 0.803579 + 1.39184i 0.917246 + 0.398321i \(0.130407\pi\)
−0.113666 + 0.993519i \(0.536260\pi\)
\(224\) 2.50000 + 4.33013i 0.167038 + 0.289319i
\(225\) 6.00000 10.3923i 0.400000 0.692820i
\(226\) −8.50000 + 14.7224i −0.565412 + 0.979322i
\(227\) −10.5000 + 18.1865i −0.696909 + 1.20708i 0.272623 + 0.962121i \(0.412109\pi\)
−0.969533 + 0.244962i \(0.921225\pi\)
\(228\) −3.00000 6.92820i −0.198680 0.458831i
\(229\) 8.50000 + 14.7224i 0.561696 + 0.972886i 0.997349 + 0.0727709i \(0.0231842\pi\)
−0.435653 + 0.900115i \(0.643482\pi\)
\(230\) 24.0000 1.58251
\(231\) 7.50000 + 4.33013i 0.493464 + 0.284901i
\(232\) −3.00000 −0.196960
\(233\) 4.50000 7.79423i 0.294805 0.510617i −0.680135 0.733087i \(-0.738079\pi\)
0.974939 + 0.222470i \(0.0714120\pi\)
\(234\) −3.00000 + 5.19615i −0.196116 + 0.339683i
\(235\) 9.00000 0.587095
\(236\) 2.50000 4.33013i 0.162736 0.281867i
\(237\) 6.00000 + 3.46410i 0.389742 + 0.225018i
\(238\) −2.50000 + 4.33013i −0.162051 + 0.280680i
\(239\) −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i \(-0.327896\pi\)
−0.999854 + 0.0170808i \(0.994563\pi\)
\(240\) −4.50000 2.59808i −0.290474 0.167705i
\(241\) −1.00000 −0.0644157 −0.0322078 0.999481i \(-0.510254\pi\)
−0.0322078 + 0.999481i \(0.510254\pi\)
\(242\) 7.00000 12.1244i 0.449977 0.779383i
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) −6.50000 + 11.2583i −0.416120 + 0.720741i
\(245\) 9.00000 + 15.5885i 0.574989 + 0.995910i
\(246\) 13.5000 + 7.79423i 0.860729 + 0.496942i
\(247\) 1.00000 8.66025i 0.0636285 0.551039i
\(248\) −4.50000 7.79423i −0.285750 0.494934i
\(249\) 15.5885i 0.987878i
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) −2.50000 4.33013i −0.157799 0.273315i 0.776276 0.630393i \(-0.217106\pi\)
−0.934075 + 0.357078i \(0.883773\pi\)
\(252\) 3.00000 0.188982
\(253\) 20.0000 + 34.6410i 1.25739 + 2.17786i
\(254\) 6.50000 11.2583i 0.407846 0.706410i
\(255\) 25.9808i 1.62698i
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 5.00000 8.66025i 0.311891 0.540212i −0.666880 0.745165i \(-0.732371\pi\)
0.978772 + 0.204953i \(0.0657041\pi\)
\(258\) 13.8564i 0.862662i
\(259\) 3.00000 5.19615i 0.186411 0.322873i
\(260\) 3.00000 + 5.19615i 0.186052 + 0.322252i
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) −3.50000 6.06218i −0.216231 0.374523i
\(263\) 4.00000 + 6.92820i 0.246651 + 0.427211i 0.962594 0.270947i \(-0.0873367\pi\)
−0.715944 + 0.698158i \(0.754003\pi\)
\(264\) 25.9808i 1.59901i
\(265\) 1.50000 + 2.59808i 0.0921443 + 0.159599i
\(266\) 4.00000 1.73205i 0.245256 0.106199i
\(267\) −13.5000 7.79423i −0.826187 0.476999i
\(268\) −2.00000 3.46410i −0.122169 0.211604i
\(269\) 12.5000 21.6506i 0.762138 1.32006i −0.179608 0.983738i \(-0.557483\pi\)
0.941746 0.336324i \(-0.109184\pi\)
\(270\) −13.5000 + 7.79423i −0.821584 + 0.474342i
\(271\) −13.5000 + 23.3827i −0.820067 + 1.42040i 0.0855654 + 0.996333i \(0.472730\pi\)
−0.905632 + 0.424064i \(0.860603\pi\)
\(272\) 5.00000 0.303170
\(273\) 3.00000 + 1.73205i 0.181568 + 0.104828i
\(274\) 1.50000 + 2.59808i 0.0906183 + 0.156956i
\(275\) −10.0000 + 17.3205i −0.603023 + 1.04447i
\(276\) 12.0000 + 6.92820i 0.722315 + 0.417029i
\(277\) −3.50000 + 6.06218i −0.210295 + 0.364241i −0.951807 0.306699i \(-0.900776\pi\)
0.741512 + 0.670940i \(0.234109\pi\)
\(278\) −20.0000 −1.19952
\(279\) −9.00000 −0.538816
\(280\) −4.50000 + 7.79423i −0.268926 + 0.465794i
\(281\) 11.0000 0.656205 0.328102 0.944642i \(-0.393591\pi\)
0.328102 + 0.944642i \(0.393591\pi\)
\(282\) −4.50000 2.59808i −0.267971 0.154713i
\(283\) 29.0000 1.72387 0.861936 0.507018i \(-0.169252\pi\)
0.861936 + 0.507018i \(0.169252\pi\)
\(284\) 1.50000 + 2.59808i 0.0890086 + 0.154167i
\(285\) 13.5000 18.1865i 0.799671 1.07728i
\(286\) 5.00000 8.66025i 0.295656 0.512092i
\(287\) 4.50000 7.79423i 0.265627 0.460079i
\(288\) −7.50000 12.9904i −0.441942 0.765466i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) −1.50000 2.59808i −0.0880830 0.152564i
\(291\) −15.0000 8.66025i −0.879316 0.507673i
\(292\) −2.50000 4.33013i −0.146301 0.253402i
\(293\) 2.50000 + 4.33013i 0.146052 + 0.252969i 0.929765 0.368154i \(-0.120010\pi\)
−0.783713 + 0.621123i \(0.786677\pi\)
\(294\) 10.3923i 0.606092i
\(295\) 15.0000 0.873334
\(296\) −18.0000 −1.04623
\(297\) −22.5000 12.9904i −1.30558 0.753778i
\(298\) 7.50000 + 12.9904i 0.434463 + 0.752513i
\(299\) 8.00000 + 13.8564i 0.462652 + 0.801337i
\(300\) 6.92820i 0.400000i
\(301\) 8.00000 0.461112
\(302\) 15.0000 0.863153
\(303\) −10.5000 + 6.06218i −0.603209 + 0.348263i
\(304\) −3.50000 2.59808i −0.200739 0.149010i
\(305\) −39.0000 −2.23313
\(306\) 7.50000 12.9904i 0.428746 0.742611i
\(307\) 16.5000 28.5788i 0.941705 1.63108i 0.179486 0.983760i \(-0.442556\pi\)
0.762218 0.647320i \(-0.224110\pi\)
\(308\) −5.00000 −0.284901
\(309\) −7.50000 4.33013i −0.426660 0.246332i
\(310\) 4.50000 7.79423i 0.255583 0.442682i
\(311\) 10.5000 + 18.1865i 0.595400 + 1.03126i 0.993490 + 0.113917i \(0.0363399\pi\)
−0.398090 + 0.917346i \(0.630327\pi\)
\(312\) 10.3923i 0.588348i
\(313\) −17.0000 −0.960897 −0.480448 0.877023i \(-0.659526\pi\)
−0.480448 + 0.877023i \(0.659526\pi\)
\(314\) 1.50000 + 2.59808i 0.0846499 + 0.146618i
\(315\) 4.50000 + 7.79423i 0.253546 + 0.439155i
\(316\) −4.00000 −0.225018
\(317\) −17.0000 −0.954815 −0.477408 0.878682i \(-0.658423\pi\)
−0.477408 + 0.878682i \(0.658423\pi\)
\(318\) 1.73205i 0.0971286i
\(319\) 2.50000 4.33013i 0.139973 0.242441i
\(320\) 21.0000 1.17394
\(321\) −18.0000 + 10.3923i −1.00466 + 0.580042i
\(322\) −4.00000 + 6.92820i −0.222911 + 0.386094i
\(323\) −2.50000 + 21.6506i −0.139104 + 1.20467i
\(324\) −9.00000 −0.500000
\(325\) −4.00000 + 6.92820i −0.221880 + 0.384308i
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) 8.66025i 0.478913i
\(328\) −27.0000 −1.49083
\(329\) −1.50000 + 2.59808i −0.0826977 + 0.143237i
\(330\) 22.5000 12.9904i 1.23858 0.715097i
\(331\) 9.50000 16.4545i 0.522167 0.904420i −0.477500 0.878632i \(-0.658457\pi\)
0.999667 0.0257885i \(-0.00820965\pi\)
\(332\) 4.50000 + 7.79423i 0.246970 + 0.427764i
\(333\) −9.00000 + 15.5885i −0.493197 + 0.854242i
\(334\) 4.00000 0.218870
\(335\) 6.00000 10.3923i 0.327815 0.567792i
\(336\) 1.50000 0.866025i 0.0818317 0.0472456i
\(337\) −5.00000 −0.272367 −0.136184 0.990684i \(-0.543484\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) −25.5000 14.7224i −1.38497 0.799613i
\(340\) −7.50000 12.9904i −0.406745 0.704502i
\(341\) 15.0000 0.812296
\(342\) −12.0000 + 5.19615i −0.648886 + 0.280976i
\(343\) −13.0000 −0.701934
\(344\) −12.0000 20.7846i −0.646997 1.12063i
\(345\) 41.5692i 2.23801i
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) 1.00000 0.0536828 0.0268414 0.999640i \(-0.491455\pi\)
0.0268414 + 0.999640i \(0.491455\pi\)
\(348\) 1.73205i 0.0928477i
\(349\) −7.50000 + 12.9904i −0.401466 + 0.695359i −0.993903 0.110257i \(-0.964832\pi\)
0.592437 + 0.805617i \(0.298166\pi\)
\(350\) −4.00000 −0.213809
\(351\) −9.00000 5.19615i −0.480384 0.277350i
\(352\) 12.5000 + 21.6506i 0.666252 + 1.15398i
\(353\) 18.5000 32.0429i 0.984656 1.70547i 0.341199 0.939991i \(-0.389167\pi\)
0.643457 0.765482i \(-0.277500\pi\)
\(354\) −7.50000 4.33013i −0.398621 0.230144i
\(355\) −4.50000 + 7.79423i −0.238835 + 0.413675i
\(356\) 9.00000 0.476999
\(357\) −7.50000 4.33013i −0.396942 0.229175i
\(358\) −6.00000 10.3923i −0.317110 0.549250i
\(359\) 6.50000 11.2583i 0.343057 0.594192i −0.641942 0.766753i \(-0.721871\pi\)
0.984999 + 0.172561i \(0.0552043\pi\)
\(360\) 13.5000 23.3827i 0.711512 1.23238i
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 3.50000 6.06218i 0.183956 0.318621i
\(363\) 21.0000 + 12.1244i 1.10221 + 0.636364i
\(364\) −2.00000 −0.104828
\(365\) 7.50000 12.9904i 0.392568 0.679948i
\(366\) 19.5000 + 11.2583i 1.01928 + 0.588482i
\(367\) −5.00000 −0.260998 −0.130499 0.991448i \(-0.541658\pi\)
−0.130499 + 0.991448i \(0.541658\pi\)
\(368\) 8.00000 0.417029
\(369\) −13.5000 + 23.3827i −0.702782 + 1.21725i
\(370\) −9.00000 15.5885i −0.467888 0.810405i
\(371\) −1.00000 −0.0519174
\(372\) 4.50000 2.59808i 0.233314 0.134704i
\(373\) 2.50000 + 4.33013i 0.129445 + 0.224205i 0.923462 0.383691i \(-0.125347\pi\)
−0.794017 + 0.607896i \(0.792014\pi\)
\(374\) −12.5000 + 21.6506i −0.646360 + 1.11953i
\(375\) 4.50000 2.59808i 0.232379 0.134164i
\(376\) 9.00000 0.464140
\(377\) 1.00000 1.73205i 0.0515026 0.0892052i
\(378\) 5.19615i 0.267261i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −1.50000 + 12.9904i −0.0769484 + 0.666392i
\(381\) 19.5000 + 11.2583i 0.999015 + 0.576782i
\(382\) 3.00000 0.153493
\(383\) −23.0000 −1.17525 −0.587623 0.809135i \(-0.699936\pi\)
−0.587623 + 0.809135i \(0.699936\pi\)
\(384\) 4.50000 + 2.59808i 0.229640 + 0.132583i
\(385\) −7.50000 12.9904i −0.382235 0.662051i
\(386\) −8.50000 14.7224i −0.432639 0.749352i
\(387\) −24.0000 −1.21999
\(388\) 10.0000 0.507673
\(389\) 3.00000 0.152106 0.0760530 0.997104i \(-0.475768\pi\)
0.0760530 + 0.997104i \(0.475768\pi\)
\(390\) 9.00000 5.19615i 0.455733 0.263117i
\(391\) −20.0000 34.6410i −1.01144 1.75187i
\(392\) 9.00000 + 15.5885i 0.454569 + 0.787336i
\(393\) 10.5000 6.06218i 0.529655 0.305796i
\(394\) 1.00000 + 1.73205i 0.0503793 + 0.0872595i
\(395\) −6.00000 10.3923i −0.301893 0.522894i
\(396\) 15.0000 0.753778
\(397\) −3.50000 + 6.06218i −0.175660 + 0.304252i −0.940389 0.340099i \(-0.889539\pi\)
0.764730 + 0.644351i \(0.222873\pi\)
\(398\) −1.50000 + 2.59808i −0.0751882 + 0.130230i
\(399\) 3.00000 + 6.92820i 0.150188 + 0.346844i
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) −33.0000 −1.64794 −0.823971 0.566632i \(-0.808246\pi\)
−0.823971 + 0.566632i \(0.808246\pi\)
\(402\) −6.00000 + 3.46410i −0.299253 + 0.172774i
\(403\) 6.00000 0.298881
\(404\) 3.50000 6.06218i 0.174132 0.301605i
\(405\) −13.5000 23.3827i −0.670820 1.16190i
\(406\) 1.00000 0.0496292
\(407\) 15.0000 25.9808i 0.743522 1.28782i
\(408\) 25.9808i 1.28624i
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) −13.5000 23.3827i −0.666717 1.15479i
\(411\) −4.50000 + 2.59808i −0.221969 + 0.128154i
\(412\) 5.00000 0.246332
\(413\) −2.50000 + 4.33013i −0.123017 + 0.213072i
\(414\) 12.0000 20.7846i 0.589768 1.02151i
\(415\) −13.5000 + 23.3827i −0.662689 + 1.14781i
\(416\) 5.00000 + 8.66025i 0.245145 + 0.424604i
\(417\) 34.6410i 1.69638i
\(418\) 20.0000 8.66025i 0.978232 0.423587i
\(419\) 0.500000 + 0.866025i 0.0244266 + 0.0423081i 0.877980 0.478697i \(-0.158891\pi\)
−0.853554 + 0.521005i \(0.825557\pi\)
\(420\) −4.50000 2.59808i −0.219578 0.126773i
\(421\) −13.0000 22.5167i −0.633581 1.09739i −0.986814 0.161859i \(-0.948251\pi\)
0.353233 0.935536i \(-0.385082\pi\)
\(422\) −7.50000 12.9904i −0.365094 0.632362i
\(423\) 4.50000 7.79423i 0.218797 0.378968i
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) 10.0000 17.3205i 0.485071 0.840168i
\(426\) 4.50000 2.59808i 0.218026 0.125877i
\(427\) 6.50000 11.2583i 0.314557 0.544829i
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 15.0000 + 8.66025i 0.724207 + 0.418121i
\(430\) 12.0000 20.7846i 0.578691 1.00232i
\(431\) −0.500000 0.866025i −0.0240842 0.0417150i 0.853732 0.520712i \(-0.174334\pi\)
−0.877816 + 0.478997i \(0.841000\pi\)
\(432\) −4.50000 + 2.59808i −0.216506 + 0.125000i
\(433\) −13.5000 23.3827i −0.648769 1.12370i −0.983417 0.181357i \(-0.941951\pi\)
0.334649 0.942343i \(-0.391382\pi\)
\(434\) 1.50000 + 2.59808i 0.0720023 + 0.124712i
\(435\) 4.50000 2.59808i 0.215758 0.124568i
\(436\) −2.50000 4.33013i −0.119728 0.207375i
\(437\) −4.00000 + 34.6410i −0.191346 + 1.65710i
\(438\) −7.50000 + 4.33013i −0.358364 + 0.206901i
\(439\) 8.00000 + 13.8564i 0.381819 + 0.661330i 0.991322 0.131453i \(-0.0419644\pi\)
−0.609503 + 0.792784i \(0.708631\pi\)
\(440\) −22.5000 + 38.9711i −1.07265 + 1.85788i
\(441\) 18.0000 0.857143
\(442\) −5.00000 + 8.66025i −0.237826 + 0.411926i
\(443\) −25.0000 −1.18779 −0.593893 0.804544i \(-0.702410\pi\)
−0.593893 + 0.804544i \(0.702410\pi\)
\(444\) 10.3923i 0.493197i
\(445\) 13.5000 + 23.3827i 0.639961 + 1.10845i
\(446\) −12.0000 + 20.7846i −0.568216 + 0.984180i
\(447\) −22.5000 + 12.9904i −1.06421 + 0.614424i
\(448\) −3.50000 + 6.06218i −0.165359 + 0.286411i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 12.0000 0.565685
\(451\) 22.5000 38.9711i 1.05948 1.83508i
\(452\) 17.0000 0.799613
\(453\) 25.9808i 1.22068i
\(454\) −21.0000 −0.985579
\(455\) −3.00000 5.19615i −0.140642 0.243599i
\(456\) 13.5000 18.1865i 0.632195 0.851662i
\(457\) −9.50000 + 16.4545i −0.444391 + 0.769708i −0.998010 0.0630623i \(-0.979913\pi\)
0.553618 + 0.832771i \(0.313247\pi\)
\(458\) −8.50000 + 14.7224i −0.397179 + 0.687934i
\(459\) 22.5000 + 12.9904i 1.05021 + 0.606339i
\(460\) −12.0000 20.7846i −0.559503 0.969087i
\(461\) 15.0000 + 25.9808i 0.698620 + 1.21004i 0.968945 + 0.247276i \(0.0795353\pi\)
−0.270326 + 0.962769i \(0.587131\pi\)
\(462\) 8.66025i 0.402911i
\(463\) 0.500000 + 0.866025i 0.0232370 + 0.0402476i 0.877410 0.479741i \(-0.159269\pi\)
−0.854173 + 0.519989i \(0.825936\pi\)
\(464\) −0.500000 0.866025i −0.0232119 0.0402042i
\(465\) 13.5000 + 7.79423i 0.626048 + 0.361449i
\(466\) 9.00000 0.416917
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 6.00000 0.277350
\(469\) 2.00000 + 3.46410i 0.0923514 + 0.159957i
\(470\) 4.50000 + 7.79423i 0.207570 + 0.359521i
\(471\) −4.50000 + 2.59808i −0.207349 + 0.119713i
\(472\) 15.0000 0.690431
\(473\) 40.0000 1.83920
\(474\) 6.92820i 0.318223i
\(475\) −16.0000 + 6.92820i −0.734130 + 0.317888i
\(476\) 5.00000 0.229175
\(477\) 3.00000 0.137361
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) −5.00000 −0.228456 −0.114228 0.993455i \(-0.536439\pi\)
−0.114228 + 0.993455i \(0.536439\pi\)
\(480\) 25.9808i 1.18585i
\(481\) 6.00000 10.3923i 0.273576 0.473848i
\(482\) −0.500000 0.866025i −0.0227744 0.0394464i
\(483\) −12.0000 6.92820i −0.546019 0.315244i
\(484\) −14.0000 −0.636364
\(485\) 15.0000 + 25.9808i 0.681115 + 1.17973i
\(486\) 15.5885i 0.707107i
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) −39.0000 −1.76545
\(489\) −18.0000 + 10.3923i −0.813988 + 0.469956i
\(490\) −9.00000 + 15.5885i −0.406579 + 0.704215i
\(491\) −27.0000 −1.21849 −0.609246 0.792981i \(-0.708528\pi\)
−0.609246 + 0.792981i \(0.708528\pi\)
\(492\) 15.5885i 0.702782i
\(493\) −2.50000 + 4.33013i −0.112594 + 0.195019i
\(494\) 8.00000 3.46410i 0.359937 0.155857i
\(495\) 22.5000 + 38.9711i 1.01130 + 1.75162i
\(496\) 1.50000 2.59808i 0.0673520 0.116657i
\(497\) −1.50000 2.59808i −0.0672842 0.116540i
\(498\) 13.5000 7.79423i 0.604949 0.349268i
\(499\) 29.0000 1.29822 0.649109 0.760695i \(-0.275142\pi\)
0.649109 + 0.760695i \(0.275142\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 6.92820i 0.309529i
\(502\) 2.50000 4.33013i 0.111580 0.193263i
\(503\) −14.5000 25.1147i −0.646523 1.11981i −0.983948 0.178458i \(-0.942889\pi\)
0.337424 0.941353i \(-0.390444\pi\)
\(504\) 4.50000 + 7.79423i 0.200446 + 0.347183i
\(505\) 21.0000 0.934488
\(506\) −20.0000 + 34.6410i −0.889108 + 1.53998i
\(507\) −13.5000 7.79423i −0.599556 0.346154i
\(508\) −13.0000 −0.576782
\(509\) −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) −22.5000 + 12.9904i −0.996317 + 0.575224i
\(511\) 2.50000 + 4.33013i 0.110593 + 0.191554i
\(512\) 11.0000 0.486136
\(513\) −9.00000 20.7846i −0.397360 0.917663i
\(514\) 10.0000 0.441081
\(515\) 7.50000 + 12.9904i 0.330489 + 0.572425i
\(516\) 12.0000 6.92820i 0.528271 0.304997i
\(517\) −7.50000 + 12.9904i −0.329850 + 0.571316i
\(518\) 6.00000 0.263625
\(519\) −9.00000 5.19615i −0.395056 0.228086i
\(520\) −9.00000 + 15.5885i −0.394676 + 0.683599i
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) −3.00000 −0.131306
\(523\) −14.5000 25.1147i −0.634041 1.09819i −0.986718 0.162446i \(-0.948062\pi\)
0.352677 0.935745i \(-0.385272\pi\)
\(524\) −3.50000 + 6.06218i −0.152898 + 0.264827i
\(525\) 6.92820i 0.302372i
\(526\) −4.00000 + 6.92820i −0.174408 + 0.302084i
\(527\) −15.0000 −0.653410
\(528\) 7.50000 4.33013i 0.326396 0.188445i
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) −1.50000 + 2.59808i −0.0651558 + 0.112853i
\(531\) 7.50000 12.9904i 0.325472 0.563735i
\(532\) −3.50000 2.59808i −0.151744 0.112641i
\(533\) 9.00000 15.5885i 0.389833 0.675211i
\(534\) 15.5885i 0.674579i
\(535\) 36.0000 1.55642
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 18.0000 10.3923i 0.776757 0.448461i
\(538\) 25.0000 1.07783
\(539\) −30.0000 −1.29219
\(540\) 13.5000 + 7.79423i 0.580948 + 0.335410i
\(541\) −1.50000 2.59808i −0.0644900 0.111700i 0.831978 0.554809i \(-0.187209\pi\)
−0.896468 + 0.443109i \(0.853875\pi\)
\(542\) −27.0000 −1.15975
\(543\) 10.5000 + 6.06218i 0.450598 + 0.260153i
\(544\) −12.5000 21.6506i −0.535933 0.928263i
\(545\) 7.50000 12.9904i 0.321265 0.556447i
\(546\) 3.46410i 0.148250i
\(547\) −5.00000 −0.213785 −0.106892 0.994271i \(-0.534090\pi\)
−0.106892 + 0.994271i \(0.534090\pi\)
\(548\) 1.50000 2.59808i 0.0640768 0.110984i
\(549\) −19.5000 + 33.7750i −0.832240 + 1.44148i
\(550\) −20.0000 −0.852803
\(551\) 4.00000 1.73205i 0.170406 0.0737878i
\(552\) 41.5692i 1.76930i
\(553\) 4.00000 0.170097
\(554\) −7.00000 −0.297402
\(555\) 27.0000 15.5885i 1.14609 0.661693i
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) 6.50000 + 11.2583i 0.275414 + 0.477031i 0.970239 0.242147i \(-0.0778518\pi\)
−0.694826 + 0.719178i \(0.744518\pi\)
\(558\) −4.50000 7.79423i −0.190500 0.329956i
\(559\) 16.0000 0.676728
\(560\) −3.00000 −0.126773
\(561\) −37.5000 21.6506i −1.58325 0.914091i
\(562\) 5.50000 + 9.52628i 0.232003 + 0.401842i
\(563\) −13.5000 23.3827i −0.568957 0.985463i −0.996669 0.0815478i \(-0.974014\pi\)
0.427712 0.903915i \(-0.359320\pi\)
\(564\) 5.19615i 0.218797i
\(565\) 25.5000 + 44.1673i 1.07279 + 1.85813i
\(566\) 14.5000 + 25.1147i 0.609480 + 1.05565i
\(567\) 9.00000 0.377964
\(568\) −4.50000 + 7.79423i −0.188816 + 0.327039i
\(569\) 4.50000 7.79423i 0.188650 0.326751i −0.756151 0.654398i \(-0.772922\pi\)
0.944800 + 0.327647i \(0.106256\pi\)
\(570\) 22.5000 + 2.59808i 0.942421 + 0.108821i
\(571\) 10.5000 + 18.1865i 0.439411 + 0.761083i 0.997644 0.0686016i \(-0.0218537\pi\)
−0.558233 + 0.829684i \(0.688520\pi\)
\(572\) −10.0000 −0.418121
\(573\) 5.19615i 0.217072i
\(574\) 9.00000 0.375653
\(575\) 16.0000 27.7128i 0.667246 1.15570i
\(576\) 10.5000 18.1865i 0.437500 0.757772i
\(577\) −42.0000 −1.74848 −0.874241 0.485491i \(-0.838641\pi\)
−0.874241 + 0.485491i \(0.838641\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 25.5000 14.7224i 1.05974 0.611843i
\(580\) −1.50000 + 2.59808i −0.0622841 + 0.107879i
\(581\) −4.50000 7.79423i −0.186691 0.323359i
\(582\) 17.3205i 0.717958i
\(583\) −5.00000 −0.207079
\(584\) 7.50000 12.9904i 0.310352 0.537546i
\(585\) 9.00000 + 15.5885i 0.372104 + 0.644503i
\(586\) −2.50000 + 4.33013i −0.103274 + 0.178876i
\(587\) 2.00000 + 3.46410i 0.0825488 + 0.142979i 0.904344 0.426804i \(-0.140361\pi\)
−0.821795 + 0.569783i \(0.807027\pi\)
\(588\) −9.00000 + 5.19615i −0.371154 + 0.214286i
\(589\) 10.5000 + 7.79423i 0.432645 + 0.321156i
\(590\) 7.50000 + 12.9904i 0.308770 + 0.534806i
\(591\) −3.00000 + 1.73205i −0.123404 + 0.0712470i
\(592\) −3.00000 5.19615i −0.123299 0.213561i
\(593\) 4.50000 + 7.79423i 0.184793 + 0.320071i 0.943507 0.331353i \(-0.107505\pi\)
−0.758714 + 0.651424i \(0.774172\pi\)
\(594\) 25.9808i 1.06600i
\(595\) 7.50000 + 12.9904i 0.307470 + 0.532554i
\(596\) 7.50000 12.9904i 0.307212 0.532107i
\(597\) −4.50000 2.59808i −0.184173 0.106332i
\(598\) −8.00000 + 13.8564i −0.327144 + 0.566631i
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) −18.0000 + 10.3923i −0.734847 + 0.424264i
\(601\) −1.50000 + 2.59808i −0.0611863 + 0.105978i −0.894996 0.446074i \(-0.852822\pi\)
0.833810 + 0.552052i \(0.186155\pi\)
\(602\) 4.00000 + 6.92820i 0.163028 + 0.282372i
\(603\) −6.00000 10.3923i −0.244339 0.423207i
\(604\) −7.50000 12.9904i −0.305171 0.528571i
\(605\) −21.0000 36.3731i −0.853771 1.47878i
\(606\) −10.5000 6.06218i −0.426533 0.246259i
\(607\) −11.5000 19.9186i −0.466771 0.808470i 0.532509 0.846424i \(-0.321249\pi\)
−0.999279 + 0.0379540i \(0.987916\pi\)
\(608\) −2.50000 + 21.6506i −0.101388 + 0.878049i
\(609\) 1.73205i 0.0701862i
\(610\) −19.5000 33.7750i −0.789532 1.36751i
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) −15.0000 −0.606339
\(613\) 4.50000 7.79423i 0.181753 0.314806i −0.760724 0.649075i \(-0.775156\pi\)
0.942478 + 0.334269i \(0.108489\pi\)
\(614\) 33.0000 1.33177
\(615\) 40.5000 23.3827i 1.63312 0.942881i
\(616\) −7.50000 12.9904i −0.302184 0.523397i
\(617\) −15.0000 + 25.9808i −0.603877 + 1.04595i 0.388351 + 0.921512i \(0.373045\pi\)
−0.992228 + 0.124434i \(0.960288\pi\)
\(618\) 8.66025i 0.348367i
\(619\) 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i \(-0.762380\pi\)
0.955131 + 0.296183i \(0.0957138\pi\)
\(620\) −9.00000 −0.361449
\(621\) 36.0000 + 20.7846i 1.44463 + 0.834058i
\(622\) −10.5000 + 18.1865i −0.421012 + 0.729214i
\(623\) −9.00000 −0.360577
\(624\) 3.00000 1.73205i 0.120096 0.0693375i
\(625\) −29.0000 −1.16000
\(626\) −8.50000 14.7224i −0.339728 0.588427i
\(627\) 15.0000 + 34.6410i 0.599042 + 1.38343i
\(628\) 1.50000 2.59808i 0.0598565 0.103675i
\(629\) −15.0000 + 25.9808i −0.598089 + 1.03592i
\(630\) −4.50000 + 7.79423i −0.179284 + 0.310530i
\(631\) 19.5000 + 33.7750i 0.776283 + 1.34456i 0.934071 + 0.357088i \(0.116230\pi\)
−0.157788 + 0.987473i \(0.550436\pi\)
\(632\) −6.00000 10.3923i −0.238667 0.413384i
\(633\) 22.5000 12.9904i 0.894295 0.516321i
\(634\) −8.50000 14.7224i −0.337578 0.584702i
\(635\) −19.5000 33.7750i −0.773834 1.34032i
\(636\) −1.50000 + 0.866025i −0.0594789 + 0.0343401i
\(637\) −12.0000 −0.475457
\(638\) 5.00000 0.197952
\(639\) 4.50000 + 7.79423i 0.178017 + 0.308335i
\(640\) −4.50000 7.79423i −0.177878 0.308094i
\(641\) 15.0000 + 25.9808i 0.592464 + 1.02618i 0.993899 + 0.110291i \(0.0351782\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(642\) −18.0000 10.3923i −0.710403 0.410152i
\(643\) −7.00000 −0.276053 −0.138027 0.990429i \(-0.544076\pi\)
−0.138027 + 0.990429i \(0.544076\pi\)
\(644\) 8.00000 0.315244
\(645\) 36.0000 + 20.7846i 1.41750 + 0.818393i
\(646\) −20.0000 + 8.66025i −0.786889 + 0.340733i
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) −13.5000 23.3827i −0.530330 0.918559i
\(649\) −12.5000 + 21.6506i −0.490668 + 0.849862i
\(650\) −8.00000 −0.313786
\(651\) −4.50000 + 2.59808i −0.176369 + 0.101827i
\(652\) 6.00000 10.3923i 0.234978 0.406994i
\(653\) 4.50000 + 7.79423i 0.176099 + 0.305012i 0.940541 0.339680i \(-0.110319\pi\)
−0.764442 + 0.644692i \(0.776986\pi\)
\(654\) −7.50000 + 4.33013i −0.293273 + 0.169321i
\(655\) −21.0000 −0.820538
\(656\) −4.50000 7.79423i −0.175695 0.304314i
\(657\) −7.50000 12.9904i −0.292603 0.506803i
\(658\) −3.00000 −0.116952
\(659\) 23.0000 0.895953 0.447976 0.894045i \(-0.352145\pi\)
0.447976 + 0.894045i \(0.352145\pi\)
\(660\) −22.5000 12.9904i −0.875811 0.505650i
\(661\) 15.0000 25.9808i 0.583432 1.01053i −0.411636 0.911348i \(-0.635043\pi\)
0.995069 0.0991864i \(-0.0316240\pi\)
\(662\) 19.0000 0.738456
\(663\) −15.0000 8.66025i −0.582552 0.336336i
\(664\) −13.5000 + 23.3827i −0.523902 + 0.907424i
\(665\) 1.50000 12.9904i 0.0581675 0.503745i
\(666\) −18.0000 −0.697486
\(667\) −4.00000 + 6.92820i −0.154881 + 0.268261i
\(668\) −2.00000 3.46410i −0.0773823 0.134030i
\(669\) −36.0000 20.7846i −1.39184 0.803579i
\(670\) 12.0000 0.463600
\(671\) 32.5000 56.2917i 1.25465 2.17312i
\(672\) −7.50000 4.33013i −0.289319 0.167038i
\(673\) 4.50000 7.79423i 0.173462 0.300445i −0.766166 0.642643i \(-0.777838\pi\)
0.939628 + 0.342198i \(0.111171\pi\)
\(674\) −2.50000 4.33013i −0.0962964 0.166790i
\(675\) 20.7846i 0.800000i
\(676\) 9.00000 0.346154
\(677\) 18.5000 32.0429i 0.711013 1.23151i −0.253465 0.967345i \(-0.581570\pi\)
0.964477 0.264166i \(-0.0850965\pi\)
\(678\) 29.4449i 1.13082i
\(679\) −10.0000 −0.383765
\(680\) 22.5000 38.9711i 0.862836 1.49448i
\(681\) 36.3731i 1.39382i
\(682\) 7.50000 + 12.9904i 0.287190 + 0.497427i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 10.5000 + 7.79423i 0.401478 + 0.298020i
\(685\) 9.00000 0.343872
\(686\) −6.50000 11.2583i −0.248171 0.429845i
\(687\) −25.5000 14.7224i −0.972886 0.561696i
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) −2.00000 −0.0761939
\(690\) −36.0000 + 20.7846i −1.37050 + 0.791257i
\(691\) 9.50000 16.4545i 0.361397 0.625958i −0.626794 0.779185i \(-0.715633\pi\)
0.988191 + 0.153227i \(0.0489666\pi\)
\(692\) 6.00000 0.228086
\(693\) −15.0000 −0.569803
\(694\) 0.500000 + 0.866025i 0.0189797 + 0.0328739i
\(695\) −30.0000 + 51.9615i −1.13796 + 1.97101i
\(696\) 4.50000 2.59808i 0.170572 0.0984798i
\(697\) −22.5000 + 38.9711i −0.852248 + 1.47614i
\(698\) −15.0000 −0.567758
\(699\) 15.5885i 0.589610i
\(700\) 2.00000 + 3.46410i 0.0755929 + 0.130931i
\(701\) −9.50000 + 16.4545i −0.358810 + 0.621477i −0.987762 0.155967i \(-0.950151\pi\)
0.628952 + 0.777444i \(0.283484\pi\)
\(702\) 10.3923i 0.392232i
\(703\) 24.0000 10.3923i 0.905177 0.391953i
\(704\) −17.5000 + 30.3109i −0.659556 + 1.14238i
\(705\) −13.5000 + 7.79423i −0.508439 + 0.293548i
\(706\) 37.0000 1.39251
\(707\) −3.50000 + 6.06218i −0.131631 + 0.227992i
\(708\) 8.66025i 0.325472i
\(709\) 39.0000 1.46468 0.732338 0.680941i \(-0.238429\pi\)
0.732338 + 0.680941i \(0.238429\pi\)
\(710\) −9.00000 −0.337764
\(711\) −12.0000 −0.450035
\(712\) 13.5000 + 23.3827i 0.505934 + 0.876303i
\(713\) −24.0000 −0.898807
\(714\) 8.66025i 0.324102i
\(715\) −15.0000 25.9808i −0.560968 0.971625i
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 22.5000 + 12.9904i 0.840278 + 0.485135i
\(718\) 13.0000 0.485156
\(719\) −1.50000 + 2.59808i −0.0559406 + 0.0968919i −0.892640 0.450771i \(-0.851149\pi\)
0.836699 + 0.547663i \(0.184482\pi\)
\(720\) 9.00000 0.335410
\(721\) −5.00000 −0.186210
\(722\) 18.5000 + 4.33013i 0.688499 + 0.161151i
\(723\) 1.50000 0.866025i 0.0557856 0.0322078i
\(724\) −7.00000 −0.260153
\(725\) −4.00000 −0.148556
\(726\) 24.2487i 0.899954i
\(727\) 4.00000 + 6.92820i 0.148352 + 0.256953i 0.930618 0.365991i \(-0.119270\pi\)
−0.782267 + 0.622944i \(0.785937\pi\)
\(728\) −3.00000 5.19615i −0.111187 0.192582i
\(729\) −27.0000 −1.00000
\(730\) 15.0000 0.555175
\(731\) −40.0000 −1.47945
\(732\) 22.5167i 0.832240i
\(733\) −9.50000 16.4545i −0.350891 0.607760i 0.635515 0.772088i \(-0.280788\pi\)
−0.986406 + 0.164328i \(0.947454\pi\)
\(734\) −2.50000 4.33013i −0.0922767 0.159828i
\(735\) −27.0000 15.5885i −0.995910 0.574989i
\(736\) −20.0000 34.6410i −0.737210 1.27688i
\(737\) 10.0000 + 17.3205i 0.368355 + 0.638009i
\(738\) −27.0000 −0.993884
\(739\) −9.50000 + 16.4545i −0.349463 + 0.605288i −0.986154 0.165831i \(-0.946969\pi\)
0.636691 + 0.771119i \(0.280303\pi\)
\(740\) −9.00000 + 15.5885i −0.330847 + 0.573043i
\(741\) 6.00000 + 13.8564i 0.220416 + 0.509028i
\(742\) −0.500000 0.866025i −0.0183556 0.0317928i
\(743\) 41.0000 1.50414 0.752072 0.659081i \(-0.229055\pi\)
0.752072 + 0.659081i \(0.229055\pi\)
\(744\) 13.5000 + 7.79423i 0.494934 + 0.285750i
\(745\) 45.0000 1.64867
\(746\) −2.50000 + 4.33013i −0.0915315 + 0.158537i
\(747\) 13.5000 + 23.3827i 0.493939 + 0.855528i
\(748\) 25.0000 0.914091
\(749\) −6.00000 + 10.3923i −0.219235 + 0.379727i
\(750\) 4.50000 + 2.59808i 0.164317 + 0.0948683i
\(751\) −12.0000 + 20.7846i −0.437886 + 0.758441i −0.997526 0.0702946i \(-0.977606\pi\)
0.559640 + 0.828736i \(0.310939\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) 7.50000 + 4.33013i 0.273315 + 0.157799i
\(754\) 2.00000 0.0728357
\(755\) 22.5000 38.9711i 0.818859 1.41831i
\(756\) −4.50000 + 2.59808i −0.163663 + 0.0944911i
\(757\) −15.5000 + 26.8468i −0.563357 + 0.975763i 0.433843 + 0.900988i \(0.357157\pi\)
−0.997200 + 0.0747748i \(0.976176\pi\)
\(758\) −10.0000 17.3205i −0.363216 0.629109i
\(759\) −60.0000 34.6410i −2.17786 1.25739i
\(760\) −36.0000 + 15.5885i −1.30586 + 0.565453i
\(761\) 4.50000 + 7.79423i 0.163125 + 0.282541i 0.935988 0.352032i \(-0.114509\pi\)
−0.772863 + 0.634573i \(0.781176\pi\)
\(762\) 22.5167i 0.815693i
\(763\) 2.50000 + 4.33013i 0.0905061 + 0.156761i
\(764\) −1.50000 2.59808i −0.0542681 0.0939951i
\(765\) −22.5000 38.9711i −0.813489 1.40900i
\(766\) −11.5000 19.9186i −0.415512 0.719688i
\(767\) −5.00000 + 8.66025i −0.180540 + 0.312704i
\(768\) 29.4449i 1.06250i
\(769\) −7.00000 + 12.1244i −0.252426 + 0.437215i −0.964193 0.265200i \(-0.914562\pi\)
0.711767 + 0.702416i \(0.247895\pi\)
\(770\) 7.50000 12.9904i 0.270281 0.468141i
\(771\) 17.3205i 0.623783i
\(772\) −8.50000 + 14.7224i −0.305922 + 0.529872i
\(773\) 8.50000 + 14.7224i 0.305724 +