Properties

Label 91.2.g.a.9.1
Level $91$
Weight $2$
Character 91.9
Analytic conductor $0.727$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(1\)
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 9.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 91.9
Dual form 91.2.g.a.81.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(-2.50000 + 0.866025i) q^{7} -3.00000 q^{8} +6.00000 q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(-2.50000 + 0.866025i) q^{7} -3.00000 q^{8} +6.00000 q^{9} +3.00000 q^{10} -3.00000 q^{11} +(-1.50000 + 2.59808i) q^{12} +(-1.00000 - 3.46410i) q^{13} +(2.00000 + 1.73205i) q^{14} +(4.50000 - 7.79423i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-3.00000 - 5.19615i) q^{18} -1.00000 q^{19} +(1.50000 + 2.59808i) q^{20} +(7.50000 - 2.59808i) q^{21} +(1.50000 + 2.59808i) q^{22} +9.00000 q^{24} +(-2.00000 - 3.46410i) q^{25} +(-2.50000 + 2.59808i) q^{26} -9.00000 q^{27} +(-0.500000 + 2.59808i) q^{28} +(-3.50000 + 6.06218i) q^{29} -9.00000 q^{30} +(-1.50000 - 2.59808i) q^{31} +(-2.50000 + 4.33013i) q^{32} +9.00000 q^{33} -2.00000 q^{34} +(1.50000 - 7.79423i) q^{35} +(3.00000 - 5.19615i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.500000 + 0.866025i) q^{38} +(3.00000 + 10.3923i) q^{39} +(4.50000 - 7.79423i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(-6.00000 - 5.19615i) q^{42} +(3.50000 + 6.06218i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(-9.00000 + 15.5885i) q^{45} +(-0.500000 + 0.866025i) q^{47} +(-1.50000 - 2.59808i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(-3.50000 - 0.866025i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(4.50000 + 7.79423i) q^{54} +(4.50000 - 7.79423i) q^{55} +(7.50000 - 2.59808i) q^{56} +3.00000 q^{57} +7.00000 q^{58} +(2.00000 - 3.46410i) q^{59} +(-4.50000 - 7.79423i) q^{60} -13.0000 q^{61} +(-1.50000 + 2.59808i) q^{62} +(-15.0000 + 5.19615i) q^{63} +7.00000 q^{64} +(10.5000 + 2.59808i) q^{65} +(-4.50000 - 7.79423i) q^{66} -3.00000 q^{67} +(-1.00000 - 1.73205i) q^{68} +(-7.50000 + 2.59808i) q^{70} +(-6.50000 - 11.2583i) q^{71} -18.0000 q^{72} +(6.50000 + 11.2583i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(6.00000 + 10.3923i) q^{75} +(-0.500000 + 0.866025i) q^{76} +(7.50000 - 2.59808i) q^{77} +(7.50000 - 7.79423i) q^{78} +(1.50000 - 2.59808i) q^{79} -3.00000 q^{80} +9.00000 q^{81} +3.00000 q^{82} +(1.50000 - 7.79423i) q^{84} +(3.00000 + 5.19615i) q^{85} +(3.50000 - 6.06218i) q^{86} +(10.5000 - 18.1865i) q^{87} +9.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +18.0000 q^{90} +(5.50000 + 7.79423i) q^{91} +(4.50000 + 7.79423i) q^{93} +1.00000 q^{94} +(1.50000 - 2.59808i) q^{95} +(7.50000 - 12.9904i) q^{96} +(2.50000 + 4.33013i) q^{97} +(-6.50000 - 2.59808i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - 6 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 12 q^{9} + O(q^{10}) \) \( 2 q - q^{2} - 6 q^{3} + q^{4} - 3 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 12 q^{9} + 6 q^{10} - 6 q^{11} - 3 q^{12} - 2 q^{13} + 4 q^{14} + 9 q^{15} + q^{16} + 2 q^{17} - 6 q^{18} - 2 q^{19} + 3 q^{20} + 15 q^{21} + 3 q^{22} + 18 q^{24} - 4 q^{25} - 5 q^{26} - 18 q^{27} - q^{28} - 7 q^{29} - 18 q^{30} - 3 q^{31} - 5 q^{32} + 18 q^{33} - 4 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} + q^{38} + 6 q^{39} + 9 q^{40} - 3 q^{41} - 12 q^{42} + 7 q^{43} - 3 q^{44} - 18 q^{45} - q^{47} - 3 q^{48} + 11 q^{49} - 4 q^{50} - 6 q^{51} - 7 q^{52} - 3 q^{53} + 9 q^{54} + 9 q^{55} + 15 q^{56} + 6 q^{57} + 14 q^{58} + 4 q^{59} - 9 q^{60} - 26 q^{61} - 3 q^{62} - 30 q^{63} + 14 q^{64} + 21 q^{65} - 9 q^{66} - 6 q^{67} - 2 q^{68} - 15 q^{70} - 13 q^{71} - 36 q^{72} + 13 q^{73} - 2 q^{74} + 12 q^{75} - q^{76} + 15 q^{77} + 15 q^{78} + 3 q^{79} - 6 q^{80} + 18 q^{81} + 6 q^{82} + 3 q^{84} + 6 q^{85} + 7 q^{86} + 21 q^{87} + 18 q^{88} - 6 q^{89} + 36 q^{90} + 11 q^{91} + 9 q^{93} + 2 q^{94} + 3 q^{95} + 15 q^{96} + 5 q^{97} - 13 q^{98} - 36 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) −3.00000 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 1.50000 + 2.59808i 0.612372 + 1.06066i
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) −3.00000 −1.06066
\(9\) 6.00000 2.00000
\(10\) 3.00000 0.948683
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) −1.50000 + 2.59808i −0.433013 + 0.750000i
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) 4.50000 7.79423i 1.16190 2.01246i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) −3.00000 5.19615i −0.707107 1.22474i
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 1.50000 + 2.59808i 0.335410 + 0.580948i
\(21\) 7.50000 2.59808i 1.63663 0.566947i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 9.00000 1.83712
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −2.50000 + 2.59808i −0.490290 + 0.509525i
\(27\) −9.00000 −1.73205
\(28\) −0.500000 + 2.59808i −0.0944911 + 0.490990i
\(29\) −3.50000 + 6.06218i −0.649934 + 1.12572i 0.333205 + 0.942855i \(0.391870\pi\)
−0.983138 + 0.182864i \(0.941463\pi\)
\(30\) −9.00000 −1.64317
\(31\) −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
\(33\) 9.00000 1.56670
\(34\) −2.00000 −0.342997
\(35\) 1.50000 7.79423i 0.253546 1.31747i
\(36\) 3.00000 5.19615i 0.500000 0.866025i
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) 3.00000 + 10.3923i 0.480384 + 1.66410i
\(40\) 4.50000 7.79423i 0.711512 1.23238i
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) −6.00000 5.19615i −0.925820 0.801784i
\(43\) 3.50000 + 6.06218i 0.533745 + 0.924473i 0.999223 + 0.0394140i \(0.0125491\pi\)
−0.465478 + 0.885059i \(0.654118\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) −9.00000 + 15.5885i −1.34164 + 2.32379i
\(46\) 0 0
\(47\) −0.500000 + 0.866025i −0.0729325 + 0.126323i −0.900185 0.435507i \(-0.856569\pi\)
0.827253 + 0.561830i \(0.189902\pi\)
\(48\) −1.50000 2.59808i −0.216506 0.375000i
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) −3.50000 0.866025i −0.485363 0.120096i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 4.50000 + 7.79423i 0.612372 + 1.06066i
\(55\) 4.50000 7.79423i 0.606780 1.05097i
\(56\) 7.50000 2.59808i 1.00223 0.347183i
\(57\) 3.00000 0.397360
\(58\) 7.00000 0.919145
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) −4.50000 7.79423i −0.580948 1.00623i
\(61\) −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
\(63\) −15.0000 + 5.19615i −1.88982 + 0.654654i
\(64\) 7.00000 0.875000
\(65\) 10.5000 + 2.59808i 1.30236 + 0.322252i
\(66\) −4.50000 7.79423i −0.553912 0.959403i
\(67\) −3.00000 −0.366508 −0.183254 0.983066i \(-0.558663\pi\)
−0.183254 + 0.983066i \(0.558663\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) 0 0
\(70\) −7.50000 + 2.59808i −0.896421 + 0.310530i
\(71\) −6.50000 11.2583i −0.771408 1.33612i −0.936791 0.349889i \(-0.886219\pi\)
0.165383 0.986229i \(-0.447114\pi\)
\(72\) −18.0000 −2.12132
\(73\) 6.50000 + 11.2583i 0.760767 + 1.31769i 0.942455 + 0.334332i \(0.108511\pi\)
−0.181688 + 0.983356i \(0.558156\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 6.00000 + 10.3923i 0.692820 + 1.20000i
\(76\) −0.500000 + 0.866025i −0.0573539 + 0.0993399i
\(77\) 7.50000 2.59808i 0.854704 0.296078i
\(78\) 7.50000 7.79423i 0.849208 0.882523i
\(79\) 1.50000 2.59808i 0.168763 0.292306i −0.769222 0.638982i \(-0.779356\pi\)
0.937985 + 0.346675i \(0.112689\pi\)
\(80\) −3.00000 −0.335410
\(81\) 9.00000 1.00000
\(82\) 3.00000 0.331295
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 1.50000 7.79423i 0.163663 0.850420i
\(85\) 3.00000 + 5.19615i 0.325396 + 0.563602i
\(86\) 3.50000 6.06218i 0.377415 0.653701i
\(87\) 10.5000 18.1865i 1.12572 1.94980i
\(88\) 9.00000 0.959403
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 18.0000 1.89737
\(91\) 5.50000 + 7.79423i 0.576557 + 0.817057i
\(92\) 0 0
\(93\) 4.50000 + 7.79423i 0.466628 + 0.808224i
\(94\) 1.00000 0.103142
\(95\) 1.50000 2.59808i 0.153897 0.266557i
\(96\) 7.50000 12.9904i 0.765466 1.32583i
\(97\) 2.50000 + 4.33013i 0.253837 + 0.439658i 0.964579 0.263795i \(-0.0849741\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) −6.50000 2.59808i −0.656599 0.262445i
\(99\) −18.0000 −1.80907
\(100\) −4.00000 −0.400000
\(101\) −5.00000 −0.497519 −0.248759 0.968565i \(-0.580023\pi\)
−0.248759 + 0.968565i \(0.580023\pi\)
\(102\) 6.00000 0.594089
\(103\) −2.50000 + 4.33013i −0.246332 + 0.426660i −0.962505 0.271263i \(-0.912559\pi\)
0.716173 + 0.697923i \(0.245892\pi\)
\(104\) 3.00000 + 10.3923i 0.294174 + 1.01905i
\(105\) −4.50000 + 23.3827i −0.439155 + 2.28192i
\(106\) −1.50000 + 2.59808i −0.145693 + 0.252347i
\(107\) −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) −4.50000 + 7.79423i −0.433013 + 0.750000i
\(109\) −3.50000 6.06218i −0.335239 0.580651i 0.648292 0.761392i \(-0.275484\pi\)
−0.983531 + 0.180741i \(0.942150\pi\)
\(110\) −9.00000 −0.858116
\(111\) 3.00000 + 5.19615i 0.284747 + 0.493197i
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) −7.50000 12.9904i −0.705541 1.22203i −0.966496 0.256681i \(-0.917371\pi\)
0.260955 0.965351i \(-0.415962\pi\)
\(114\) −1.50000 2.59808i −0.140488 0.243332i
\(115\) 0 0
\(116\) 3.50000 + 6.06218i 0.324967 + 0.562859i
\(117\) −6.00000 20.7846i −0.554700 1.92154i
\(118\) −4.00000 −0.368230
\(119\) −1.00000 + 5.19615i −0.0916698 + 0.476331i
\(120\) −13.5000 + 23.3827i −1.23238 + 2.13454i
\(121\) −2.00000 −0.181818
\(122\) 6.50000 + 11.2583i 0.588482 + 1.01928i
\(123\) 4.50000 7.79423i 0.405751 0.702782i
\(124\) −3.00000 −0.269408
\(125\) −3.00000 −0.268328
\(126\) 12.0000 + 10.3923i 1.06904 + 0.925820i
\(127\) −5.50000 + 9.52628i −0.488046 + 0.845321i −0.999905 0.0137486i \(-0.995624\pi\)
0.511859 + 0.859069i \(0.328957\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) −10.5000 18.1865i −0.924473 1.60123i
\(130\) −3.00000 10.3923i −0.263117 0.911465i
\(131\) −2.50000 + 4.33013i −0.218426 + 0.378325i −0.954327 0.298764i \(-0.903426\pi\)
0.735901 + 0.677089i \(0.236759\pi\)
\(132\) 4.50000 7.79423i 0.391675 0.678401i
\(133\) 2.50000 0.866025i 0.216777 0.0750939i
\(134\) 1.50000 + 2.59808i 0.129580 + 0.224440i
\(135\) 13.5000 23.3827i 1.16190 2.01246i
\(136\) −3.00000 + 5.19615i −0.257248 + 0.445566i
\(137\) −5.00000 + 8.66025i −0.427179 + 0.739895i −0.996621 0.0821359i \(-0.973826\pi\)
0.569442 + 0.822031i \(0.307159\pi\)
\(138\) 0 0
\(139\) 7.50000 + 12.9904i 0.636142 + 1.10183i 0.986272 + 0.165129i \(0.0528040\pi\)
−0.350130 + 0.936701i \(0.613863\pi\)
\(140\) −6.00000 5.19615i −0.507093 0.439155i
\(141\) 1.50000 2.59808i 0.126323 0.218797i
\(142\) −6.50000 + 11.2583i −0.545468 + 0.944778i
\(143\) 3.00000 + 10.3923i 0.250873 + 0.869048i
\(144\) 3.00000 + 5.19615i 0.250000 + 0.433013i
\(145\) −10.5000 18.1865i −0.871978 1.51031i
\(146\) 6.50000 11.2583i 0.537944 0.931746i
\(147\) −16.5000 + 12.9904i −1.36090 + 1.07143i
\(148\) −2.00000 −0.164399
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 6.00000 10.3923i 0.489898 0.848528i
\(151\) 10.5000 + 18.1865i 0.854478 + 1.48000i 0.877129 + 0.480256i \(0.159456\pi\)
−0.0226507 + 0.999743i \(0.507211\pi\)
\(152\) 3.00000 0.243332
\(153\) 6.00000 10.3923i 0.485071 0.840168i
\(154\) −6.00000 5.19615i −0.483494 0.418718i
\(155\) 9.00000 0.722897
\(156\) 10.5000 + 2.59808i 0.840673 + 0.208013i
\(157\) −9.50000 16.4545i −0.758183 1.31321i −0.943777 0.330584i \(-0.892754\pi\)
0.185594 0.982627i \(-0.440579\pi\)
\(158\) −3.00000 −0.238667
\(159\) 4.50000 + 7.79423i 0.356873 + 0.618123i
\(160\) −7.50000 12.9904i −0.592927 1.02698i
\(161\) 0 0
\(162\) −4.50000 7.79423i −0.353553 0.612372i
\(163\) −1.00000 −0.0783260 −0.0391630 0.999233i \(-0.512469\pi\)
−0.0391630 + 0.999233i \(0.512469\pi\)
\(164\) 1.50000 + 2.59808i 0.117130 + 0.202876i
\(165\) −13.5000 + 23.3827i −1.05097 + 1.82034i
\(166\) 0 0
\(167\) 6.50000 11.2583i 0.502985 0.871196i −0.497009 0.867745i \(-0.665568\pi\)
0.999994 0.00345033i \(-0.00109828\pi\)
\(168\) −22.5000 + 7.79423i −1.73591 + 0.601338i
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) −6.00000 −0.458831
\(172\) 7.00000 0.533745
\(173\) 19.0000 1.44454 0.722272 0.691609i \(-0.243098\pi\)
0.722272 + 0.691609i \(0.243098\pi\)
\(174\) −21.0000 −1.59201
\(175\) 8.00000 + 6.92820i 0.604743 + 0.523723i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 17.0000 1.27064 0.635320 0.772249i \(-0.280868\pi\)
0.635320 + 0.772249i \(0.280868\pi\)
\(180\) 9.00000 + 15.5885i 0.670820 + 1.16190i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 4.00000 8.66025i 0.296500 0.641941i
\(183\) 39.0000 2.88296
\(184\) 0 0
\(185\) 6.00000 0.441129
\(186\) 4.50000 7.79423i 0.329956 0.571501i
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) 0.500000 + 0.866025i 0.0364662 + 0.0631614i
\(189\) 22.5000 7.79423i 1.63663 0.566947i
\(190\) −3.00000 −0.217643
\(191\) −17.0000 −1.23008 −0.615038 0.788497i \(-0.710860\pi\)
−0.615038 + 0.788497i \(0.710860\pi\)
\(192\) −21.0000 −1.51554
\(193\) 7.00000 0.503871 0.251936 0.967744i \(-0.418933\pi\)
0.251936 + 0.967744i \(0.418933\pi\)
\(194\) 2.50000 4.33013i 0.179490 0.310885i
\(195\) −31.5000 7.79423i −2.25576 0.558156i
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) 0.500000 0.866025i 0.0356235 0.0617018i −0.847664 0.530534i \(-0.821992\pi\)
0.883287 + 0.468832i \(0.155325\pi\)
\(198\) 9.00000 + 15.5885i 0.639602 + 1.10782i
\(199\) 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i \(-0.582534\pi\)
0.965272 0.261245i \(-0.0841331\pi\)
\(200\) 6.00000 + 10.3923i 0.424264 + 0.734847i
\(201\) 9.00000 0.634811
\(202\) 2.50000 + 4.33013i 0.175899 + 0.304667i
\(203\) 3.50000 18.1865i 0.245652 1.27644i
\(204\) 3.00000 + 5.19615i 0.210042 + 0.363803i
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 5.00000 0.348367
\(207\) 0 0
\(208\) 2.50000 2.59808i 0.173344 0.180144i
\(209\) 3.00000 0.207514
\(210\) 22.5000 7.79423i 1.55265 0.537853i
\(211\) −3.50000 + 6.06218i −0.240950 + 0.417338i −0.960985 0.276600i \(-0.910792\pi\)
0.720035 + 0.693938i \(0.244126\pi\)
\(212\) −3.00000 −0.206041
\(213\) 19.5000 + 33.7750i 1.33612 + 2.31422i
\(214\) −4.00000 + 6.92820i −0.273434 + 0.473602i
\(215\) −21.0000 −1.43219
\(216\) 27.0000 1.83712
\(217\) 6.00000 + 5.19615i 0.407307 + 0.352738i
\(218\) −3.50000 + 6.06218i −0.237050 + 0.410582i
\(219\) −19.5000 33.7750i −1.31769 2.28230i
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) −7.00000 1.73205i −0.470871 0.116510i
\(222\) 3.00000 5.19615i 0.201347 0.348743i
\(223\) 4.50000 7.79423i 0.301342 0.521940i −0.675098 0.737728i \(-0.735899\pi\)
0.976440 + 0.215788i \(0.0692320\pi\)
\(224\) 2.50000 12.9904i 0.167038 0.867956i
\(225\) −12.0000 20.7846i −0.800000 1.38564i
\(226\) −7.50000 + 12.9904i −0.498893 + 0.864107i
\(227\) 2.00000 3.46410i 0.132745 0.229920i −0.791989 0.610535i \(-0.790954\pi\)
0.924734 + 0.380615i \(0.124288\pi\)
\(228\) 1.50000 2.59808i 0.0993399 0.172062i
\(229\) 6.50000 11.2583i 0.429532 0.743971i −0.567300 0.823511i \(-0.692012\pi\)
0.996832 + 0.0795401i \(0.0253452\pi\)
\(230\) 0 0
\(231\) −22.5000 + 7.79423i −1.48039 + 0.512823i
\(232\) 10.5000 18.1865i 0.689359 1.19400i
\(233\) 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i \(-0.591876\pi\)
0.972523 0.232806i \(-0.0747909\pi\)
\(234\) −15.0000 + 15.5885i −0.980581 + 1.01905i
\(235\) −1.50000 2.59808i −0.0978492 0.169480i
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) −4.50000 + 7.79423i −0.292306 + 0.506290i
\(238\) 5.00000 1.73205i 0.324102 0.112272i
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 9.00000 0.580948
\(241\) 13.0000 22.5167i 0.837404 1.45043i −0.0546547 0.998505i \(-0.517406\pi\)
0.892058 0.451920i \(-0.149261\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0 0
\(244\) −6.50000 + 11.2583i −0.416120 + 0.720741i
\(245\) 3.00000 + 20.7846i 0.191663 + 1.32788i
\(246\) −9.00000 −0.573819
\(247\) 1.00000 + 3.46410i 0.0636285 + 0.220416i
\(248\) 4.50000 + 7.79423i 0.285750 + 0.494934i
\(249\) 0 0
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) 11.5000 + 19.9186i 0.725874 + 1.25725i 0.958613 + 0.284711i \(0.0918976\pi\)
−0.232740 + 0.972539i \(0.574769\pi\)
\(252\) −3.00000 + 15.5885i −0.188982 + 0.981981i
\(253\) 0 0
\(254\) 11.0000 0.690201
\(255\) −9.00000 15.5885i −0.563602 0.976187i
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 1.00000 + 1.73205i 0.0623783 + 0.108042i 0.895528 0.445005i \(-0.146798\pi\)
−0.833150 + 0.553047i \(0.813465\pi\)
\(258\) −10.5000 + 18.1865i −0.653701 + 1.13224i
\(259\) 4.00000 + 3.46410i 0.248548 + 0.215249i
\(260\) 7.50000 7.79423i 0.465130 0.483378i
\(261\) −21.0000 + 36.3731i −1.29987 + 2.25144i
\(262\) 5.00000 0.308901
\(263\) −27.0000 −1.66489 −0.832446 0.554107i \(-0.813060\pi\)
−0.832446 + 0.554107i \(0.813060\pi\)
\(264\) −27.0000 −1.66174
\(265\) 9.00000 0.552866
\(266\) −2.00000 1.73205i −0.122628 0.106199i
\(267\) 9.00000 + 15.5885i 0.550791 + 0.953998i
\(268\) −1.50000 + 2.59808i −0.0916271 + 0.158703i
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) −27.0000 −1.64317
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 2.00000 0.121268
\(273\) −16.5000 23.3827i −0.998625 1.41518i
\(274\) 10.0000 0.604122
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 0 0
\(277\) −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i \(0.396503\pi\)
−0.980373 + 0.197153i \(0.936830\pi\)
\(278\) 7.50000 12.9904i 0.449820 0.779111i
\(279\) −9.00000 15.5885i −0.538816 0.933257i
\(280\) −4.50000 + 23.3827i −0.268926 + 1.39738i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −3.00000 −0.178647
\(283\) 1.00000 0.0594438 0.0297219 0.999558i \(-0.490538\pi\)
0.0297219 + 0.999558i \(0.490538\pi\)
\(284\) −13.0000 −0.771408
\(285\) −4.50000 + 7.79423i −0.266557 + 0.461690i
\(286\) 7.50000 7.79423i 0.443484 0.460882i
\(287\) 1.50000 7.79423i 0.0885422 0.460079i
\(288\) −15.0000 + 25.9808i −0.883883 + 1.53093i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −10.5000 + 18.1865i −0.616581 + 1.06795i
\(291\) −7.50000 12.9904i −0.439658 0.761510i
\(292\) 13.0000 0.760767
\(293\) −5.50000 9.52628i −0.321313 0.556531i 0.659446 0.751752i \(-0.270791\pi\)
−0.980759 + 0.195221i \(0.937458\pi\)
\(294\) 19.5000 + 7.79423i 1.13726 + 0.454569i
\(295\) 6.00000 + 10.3923i 0.349334 + 0.605063i
\(296\) 3.00000 + 5.19615i 0.174371 + 0.302020i
\(297\) 27.0000 1.56670
\(298\) −7.50000 12.9904i −0.434463 0.752513i
\(299\) 0 0
\(300\) 12.0000 0.692820
\(301\) −14.0000 12.1244i −0.806947 0.698836i
\(302\) 10.5000 18.1865i 0.604207 1.04652i
\(303\) 15.0000 0.861727
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) 19.5000 33.7750i 1.11657 1.93395i
\(306\) −12.0000 −0.685994
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 1.50000 7.79423i 0.0854704 0.444117i
\(309\) 7.50000 12.9904i 0.426660 0.738997i
\(310\) −4.50000 7.79423i −0.255583 0.442682i
\(311\) 4.50000 + 7.79423i 0.255172 + 0.441970i 0.964942 0.262463i \(-0.0845347\pi\)
−0.709771 + 0.704433i \(0.751201\pi\)
\(312\) −9.00000 31.1769i −0.509525 1.76505i
\(313\) −9.50000 + 16.4545i −0.536972 + 0.930062i 0.462093 + 0.886831i \(0.347098\pi\)
−0.999065 + 0.0432311i \(0.986235\pi\)
\(314\) −9.50000 + 16.4545i −0.536116 + 0.928580i
\(315\) 9.00000 46.7654i 0.507093 2.63493i
\(316\) −1.50000 2.59808i −0.0843816 0.146153i
\(317\) 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i \(-0.752000\pi\)
0.964281 + 0.264883i \(0.0853332\pi\)
\(318\) 4.50000 7.79423i 0.252347 0.437079i
\(319\) 10.5000 18.1865i 0.587887 1.01825i
\(320\) −10.5000 + 18.1865i −0.586968 + 1.01666i
\(321\) 12.0000 + 20.7846i 0.669775 + 1.16008i
\(322\) 0 0
\(323\) −1.00000 + 1.73205i −0.0556415 + 0.0963739i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) −10.0000 + 10.3923i −0.554700 + 0.576461i
\(326\) 0.500000 + 0.866025i 0.0276924 + 0.0479647i
\(327\) 10.5000 + 18.1865i 0.580651 + 1.00572i
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) 0.500000 2.59808i 0.0275659 0.143237i
\(330\) 27.0000 1.48630
\(331\) −29.0000 −1.59398 −0.796992 0.603990i \(-0.793577\pi\)
−0.796992 + 0.603990i \(0.793577\pi\)
\(332\) 0 0
\(333\) −6.00000 10.3923i −0.328798 0.569495i
\(334\) −13.0000 −0.711328
\(335\) 4.50000 7.79423i 0.245861 0.425844i
\(336\) 6.00000 + 5.19615i 0.327327 + 0.283473i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 11.5000 + 6.06218i 0.625518 + 0.329739i
\(339\) 22.5000 + 38.9711i 1.22203 + 2.11662i
\(340\) 6.00000 0.325396
\(341\) 4.50000 + 7.79423i 0.243689 + 0.422081i
\(342\) 3.00000 + 5.19615i 0.162221 + 0.280976i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −10.5000 18.1865i −0.566122 0.980552i
\(345\) 0 0
\(346\) −9.50000 16.4545i −0.510723 0.884598i
\(347\) 4.00000 6.92820i 0.214731 0.371925i −0.738458 0.674299i \(-0.764446\pi\)
0.953189 + 0.302374i \(0.0977791\pi\)
\(348\) −10.5000 18.1865i −0.562859 0.974901i
\(349\) −11.5000 + 19.9186i −0.615581 + 1.06622i 0.374701 + 0.927146i \(0.377745\pi\)
−0.990282 + 0.139072i \(0.955588\pi\)
\(350\) 2.00000 10.3923i 0.106904 0.555492i
\(351\) 9.00000 + 31.1769i 0.480384 + 1.66410i
\(352\) 7.50000 12.9904i 0.399751 0.692390i
\(353\) −25.0000 −1.33062 −0.665308 0.746569i \(-0.731700\pi\)
−0.665308 + 0.746569i \(0.731700\pi\)
\(354\) 12.0000 0.637793
\(355\) 39.0000 2.06991
\(356\) −6.00000 −0.317999
\(357\) 3.00000 15.5885i 0.158777 0.825029i
\(358\) −8.50000 14.7224i −0.449239 0.778105i
\(359\) −8.50000 + 14.7224i −0.448613 + 0.777020i −0.998296 0.0583530i \(-0.981415\pi\)
0.549683 + 0.835373i \(0.314748\pi\)
\(360\) 27.0000 46.7654i 1.42302 2.46475i
\(361\) −18.0000 −0.947368
\(362\) 11.0000 + 19.0526i 0.578147 + 1.00138i
\(363\) 6.00000 0.314918
\(364\) 9.50000 0.866025i 0.497935 0.0453921i
\(365\) −39.0000 −2.04135
\(366\) −19.5000 33.7750i −1.01928 1.76545i
\(367\) −31.0000 −1.61819 −0.809093 0.587680i \(-0.800041\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 0 0
\(369\) −9.00000 + 15.5885i −0.468521 + 0.811503i
\(370\) −3.00000 5.19615i −0.155963 0.270135i
\(371\) 6.00000 + 5.19615i 0.311504 + 0.269771i
\(372\) 9.00000 0.466628
\(373\) −9.00000 −0.466002 −0.233001 0.972476i \(-0.574855\pi\)
−0.233001 + 0.972476i \(0.574855\pi\)
\(374\) 6.00000 0.310253
\(375\) 9.00000 0.464758
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) 24.5000 + 6.06218i 1.26181 + 0.312218i
\(378\) −18.0000 15.5885i −0.925820 0.801784i
\(379\) 16.5000 28.5788i 0.847548 1.46800i −0.0358418 0.999357i \(-0.511411\pi\)
0.883390 0.468639i \(-0.155255\pi\)
\(380\) −1.50000 2.59808i −0.0769484 0.133278i
\(381\) 16.5000 28.5788i 0.845321 1.46414i
\(382\) 8.50000 + 14.7224i 0.434898 + 0.753265i
\(383\) −21.0000 −1.07305 −0.536525 0.843884i \(-0.680263\pi\)
−0.536525 + 0.843884i \(0.680263\pi\)
\(384\) −4.50000 7.79423i −0.229640 0.397748i
\(385\) −4.50000 + 23.3827i −0.229341 + 1.19169i
\(386\) −3.50000 6.06218i −0.178145 0.308557i
\(387\) 21.0000 + 36.3731i 1.06749 + 1.84895i
\(388\) 5.00000 0.253837
\(389\) 16.5000 + 28.5788i 0.836583 + 1.44900i 0.892735 + 0.450582i \(0.148784\pi\)
−0.0561516 + 0.998422i \(0.517883\pi\)
\(390\) 9.00000 + 31.1769i 0.455733 + 1.57870i
\(391\) 0 0
\(392\) −16.5000 + 12.9904i −0.833376 + 0.656113i
\(393\) 7.50000 12.9904i 0.378325 0.655278i
\(394\) −1.00000 −0.0503793
\(395\) 4.50000 + 7.79423i 0.226420 + 0.392170i
\(396\) −9.00000 + 15.5885i −0.452267 + 0.783349i
\(397\) −1.00000 −0.0501886 −0.0250943 0.999685i \(-0.507989\pi\)
−0.0250943 + 0.999685i \(0.507989\pi\)
\(398\) −20.0000 −1.00251
\(399\) −7.50000 + 2.59808i −0.375470 + 0.130066i
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) 1.00000 + 1.73205i 0.0499376 + 0.0864945i 0.889914 0.456129i \(-0.150764\pi\)
−0.839976 + 0.542623i \(0.817431\pi\)
\(402\) −4.50000 7.79423i −0.224440 0.388741i
\(403\) −7.50000 + 7.79423i −0.373602 + 0.388258i
\(404\) −2.50000 + 4.33013i −0.124380 + 0.215432i
\(405\) −13.5000 + 23.3827i −0.670820 + 1.16190i
\(406\) −17.5000 + 6.06218i −0.868510 + 0.300861i
\(407\) 3.00000 + 5.19615i 0.148704 + 0.257564i
\(408\) 9.00000 15.5885i 0.445566 0.771744i
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −4.50000 + 7.79423i −0.222239 + 0.384930i
\(411\) 15.0000 25.9808i 0.739895 1.28154i
\(412\) 2.50000 + 4.33013i 0.123166 + 0.213330i
\(413\) −2.00000 + 10.3923i −0.0984136 + 0.511372i
\(414\) 0 0
\(415\) 0 0
\(416\) 17.5000 + 4.33013i 0.858008 + 0.212302i
\(417\) −22.5000 38.9711i −1.10183 1.90843i
\(418\) −1.50000 2.59808i −0.0733674 0.127076i
\(419\) 12.5000 21.6506i 0.610665 1.05770i −0.380464 0.924796i \(-0.624236\pi\)
0.991129 0.132907i \(-0.0424311\pi\)
\(420\) 18.0000 + 15.5885i 0.878310 + 0.760639i
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) 7.00000 0.340755
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) −8.00000 −0.388057
\(426\) 19.5000 33.7750i 0.944778 1.63640i
\(427\) 32.5000 11.2583i 1.57279 0.544829i
\(428\) −8.00000 −0.386695
\(429\) −9.00000 31.1769i −0.434524 1.50524i
\(430\) 10.5000 + 18.1865i 0.506355 + 0.877033i
\(431\) 9.00000 0.433515 0.216757 0.976226i \(-0.430452\pi\)
0.216757 + 0.976226i \(0.430452\pi\)
\(432\) −4.50000 7.79423i −0.216506 0.375000i
\(433\) −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 7.79423i 0.0720023 0.374135i
\(435\) 31.5000 + 54.5596i 1.51031 + 2.61593i
\(436\) −7.00000 −0.335239
\(437\) 0 0
\(438\) −19.5000 + 33.7750i −0.931746 + 1.61383i
\(439\) 8.00000 + 13.8564i 0.381819 + 0.661330i 0.991322 0.131453i \(-0.0419644\pi\)
−0.609503 + 0.792784i \(0.708631\pi\)
\(440\) −13.5000 + 23.3827i −0.643587 + 1.11473i
\(441\) 33.0000 25.9808i 1.57143 1.23718i
\(442\) 2.00000 + 6.92820i 0.0951303 + 0.329541i
\(443\) 5.50000 9.52628i 0.261313 0.452607i −0.705278 0.708931i \(-0.749178\pi\)
0.966591 + 0.256323i \(0.0825112\pi\)
\(444\) 6.00000 0.284747
\(445\) 18.0000 0.853282
\(446\) −9.00000 −0.426162
\(447\) −45.0000 −2.12843
\(448\) −17.5000 + 6.06218i −0.826797 + 0.286411i
\(449\) −7.50000 12.9904i −0.353947 0.613054i 0.632990 0.774160i \(-0.281827\pi\)
−0.986937 + 0.161106i \(0.948494\pi\)
\(450\) −12.0000 + 20.7846i −0.565685 + 0.979796i
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) −15.0000 −0.705541
\(453\) −31.5000 54.5596i −1.48000 2.56343i
\(454\) −4.00000 −0.187729
\(455\) −28.5000 + 2.59808i −1.33610 + 0.121800i
\(456\) −9.00000 −0.421464
\(457\) 9.00000 + 15.5885i 0.421002 + 0.729197i 0.996038 0.0889312i \(-0.0283451\pi\)
−0.575036 + 0.818128i \(0.695012\pi\)
\(458\) −13.0000 −0.607450
\(459\) −9.00000 + 15.5885i −0.420084 + 0.727607i
\(460\) 0 0
\(461\) −17.5000 30.3109i −0.815056 1.41172i −0.909288 0.416169i \(-0.863373\pi\)
0.0942312 0.995550i \(-0.469961\pi\)
\(462\) 18.0000 + 15.5885i 0.837436 + 0.725241i
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) −7.00000 −0.324967
\(465\) −27.0000 −1.25210
\(466\) −21.0000 −0.972806
\(467\) 3.50000 6.06218i 0.161961 0.280524i −0.773611 0.633661i \(-0.781552\pi\)
0.935572 + 0.353137i \(0.114885\pi\)
\(468\) −21.0000 5.19615i −0.970725 0.240192i
\(469\) 7.50000 2.59808i 0.346318 0.119968i
\(470\) −1.50000 + 2.59808i −0.0691898 + 0.119840i
\(471\) 28.5000 + 49.3634i 1.31321 + 2.27455i
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) −10.5000 18.1865i −0.482791 0.836218i
\(474\) 9.00000 0.413384
\(475\) 2.00000 + 3.46410i 0.0917663 + 0.158944i
\(476\) 4.00000 + 3.46410i 0.183340 + 0.158777i
\(477\) −9.00000 15.5885i −0.412082 0.713746i
\(478\) 2.00000 + 3.46410i 0.0914779 + 0.158444i
\(479\) −35.0000 −1.59919 −0.799595 0.600539i \(-0.794953\pi\)
−0.799595 + 0.600539i \(0.794953\pi\)
\(480\) 22.5000 + 38.9711i 1.02698 + 1.77878i
\(481\) −5.00000 + 5.19615i −0.227980 + 0.236924i
\(482\) −26.0000 −1.18427
\(483\) 0 0
\(484\) −1.00000 + 1.73205i −0.0454545 + 0.0787296i
\(485\) −15.0000 −0.681115
\(486\) 0 0
\(487\) −8.00000 + 13.8564i −0.362515 + 0.627894i −0.988374 0.152042i \(-0.951415\pi\)
0.625859 + 0.779936i \(0.284748\pi\)
\(488\) 39.0000 1.76545
\(489\) 3.00000 0.135665
\(490\) 16.5000 12.9904i 0.745394 0.586846i
\(491\) −7.50000 + 12.9904i −0.338470 + 0.586248i −0.984145 0.177365i \(-0.943243\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(492\) −4.50000 7.79423i −0.202876 0.351391i
\(493\) 7.00000 + 12.1244i 0.315264 + 0.546054i
\(494\) 2.50000 2.59808i 0.112480 0.116893i
\(495\) 27.0000 46.7654i 1.21356 2.10195i
\(496\) 1.50000 2.59808i 0.0673520 0.116657i
\(497\) 26.0000 + 22.5167i 1.16626 + 1.01001i
\(498\) 0 0
\(499\) 15.5000 26.8468i 0.693875 1.20183i −0.276683 0.960961i \(-0.589235\pi\)
0.970558 0.240866i \(-0.0774314\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) −19.5000 + 33.7750i −0.871196 + 1.50896i
\(502\) 11.5000 19.9186i 0.513270 0.889010i
\(503\) 15.5000 + 26.8468i 0.691111 + 1.19704i 0.971474 + 0.237145i \(0.0762117\pi\)
−0.280363 + 0.959894i \(0.590455\pi\)
\(504\) 45.0000 15.5885i 2.00446 0.694365i
\(505\) 7.50000 12.9904i 0.333746 0.578064i
\(506\) 0 0
\(507\) 33.0000 20.7846i 1.46558 0.923077i
\(508\) 5.50000 + 9.52628i 0.244023 + 0.422660i
\(509\) 17.0000 + 29.4449i 0.753512 + 1.30512i 0.946111 + 0.323843i \(0.104975\pi\)
−0.192599 + 0.981278i \(0.561692\pi\)
\(510\) −9.00000 + 15.5885i −0.398527 + 0.690268i
\(511\) −26.0000 22.5167i −1.15017 0.996078i
\(512\) −11.0000 −0.486136
\(513\) 9.00000 0.397360
\(514\) 1.00000 1.73205i 0.0441081 0.0763975i
\(515\) −7.50000 12.9904i −0.330489 0.572425i
\(516\) −21.0000 −0.924473
\(517\) 1.50000 2.59808i 0.0659699 0.114263i
\(518\) 1.00000 5.19615i 0.0439375 0.228306i
\(519\) −57.0000 −2.50202
\(520\) −31.5000 7.79423i −1.38137 0.341800i
\(521\) 8.50000 + 14.7224i 0.372392 + 0.645001i 0.989933 0.141537i \(-0.0452044\pi\)
−0.617541 + 0.786539i \(0.711871\pi\)
\(522\) 42.0000 1.83829
\(523\) −2.00000 3.46410i −0.0874539 0.151475i 0.818980 0.573822i \(-0.194540\pi\)
−0.906434 + 0.422347i \(0.861206\pi\)
\(524\) 2.50000 + 4.33013i 0.109213 + 0.189162i
\(525\) −24.0000 20.7846i −1.04745 0.907115i
\(526\) 13.5000 + 23.3827i 0.588628 + 1.01953i
\(527\) −6.00000 −0.261364
\(528\) 4.50000 + 7.79423i 0.195837 + 0.339200i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −4.50000 7.79423i −0.195468 0.338560i
\(531\) 12.0000 20.7846i 0.520756 0.901975i
\(532\) 0.500000 2.59808i 0.0216777 0.112641i
\(533\) 10.5000 + 2.59808i 0.454805 + 0.112535i
\(534\) 9.00000 15.5885i 0.389468 0.674579i
\(535\) 24.0000 1.03761
\(536\) 9.00000 0.388741
\(537\) −51.0000 −2.20081
\(538\) 18.0000 0.776035
\(539\) −16.5000 + 12.9904i −0.710705 + 0.559535i
\(540\) −13.5000 23.3827i −0.580948 1.00623i
\(541\) 18.5000 32.0429i 0.795377 1.37763i −0.127222 0.991874i \(-0.540606\pi\)
0.922599 0.385759i \(-0.126061\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 66.0000 2.83233
\(544\) 5.00000 + 8.66025i 0.214373 + 0.371305i
\(545\) 21.0000 0.899541
\(546\) −12.0000 + 25.9808i −0.513553 + 1.11187i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 5.00000 + 8.66025i 0.213589 + 0.369948i
\(549\) −78.0000 −3.32896
\(550\) 6.00000 10.3923i 0.255841 0.443129i
\(551\) 3.50000 6.06218i 0.149105 0.258257i
\(552\) 0 0
\(553\) −1.50000 + 7.79423i −0.0637865 + 0.331444i
\(554\) 22.0000 0.934690
\(555\) −18.0000 −0.764057
\(556\) 15.0000 0.636142
\(557\) 3.00000 0.127114 0.0635570 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(558\) −9.00000 + 15.5885i −0.381000 + 0.659912i
\(559\) 17.5000 18.1865i 0.740171 0.769208i
\(560\) 7.50000 2.59808i 0.316933 0.109789i
\(561\) 9.00000 15.5885i 0.379980 0.658145i
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) −2.00000 + 3.46410i −0.0842900 + 0.145994i −0.905088 0.425223i \(-0.860196\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(564\) −1.50000 2.59808i −0.0631614 0.109399i
\(565\) 45.0000 1.89316
\(566\) −0.500000 0.866025i −0.0210166 0.0364018i
\(567\) −22.5000 + 7.79423i −0.944911 + 0.327327i
\(568\) 19.5000 + 33.7750i 0.818202 + 1.41717i
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 9.00000 0.376969
\(571\) −21.5000 37.2391i −0.899747 1.55841i −0.827817 0.560998i \(-0.810418\pi\)
−0.0719297 0.997410i \(-0.522916\pi\)
\(572\) 10.5000 + 2.59808i 0.439027 + 0.108631i
\(573\) 51.0000 2.13056
\(574\) −7.50000 + 2.59808i −0.313044 + 0.108442i
\(575\) 0 0
\(576\) 42.0000 1.75000
\(577\) 0.500000 + 0.866025i 0.0208153 + 0.0360531i 0.876245 0.481865i \(-0.160040\pi\)
−0.855430 + 0.517918i \(0.826707\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) −21.0000 −0.872730
\(580\) −21.0000 −0.871978
\(581\) 0 0
\(582\) −7.50000 + 12.9904i −0.310885 + 0.538469i
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) −19.5000 33.7750i −0.806916 1.39762i
\(585\) 63.0000 + 15.5885i 2.60473 + 0.644503i
\(586\) −5.50000 + 9.52628i −0.227203 + 0.393527i
\(587\) 16.5000 28.5788i 0.681028 1.17957i −0.293640 0.955916i \(-0.594867\pi\)
0.974668 0.223659i \(-0.0718001\pi\)
\(588\) 3.00000 + 20.7846i 0.123718 + 0.857143i
\(589\) 1.50000 + 2.59808i 0.0618064 + 0.107052i
\(590\) 6.00000 10.3923i 0.247016 0.427844i
\(591\) −1.50000 + 2.59808i −0.0617018 + 0.106871i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −13.5000 + 23.3827i −0.554379 + 0.960212i 0.443573 + 0.896238i \(0.353711\pi\)
−0.997952 + 0.0639736i \(0.979623\pi\)
\(594\) −13.5000 23.3827i −0.553912 0.959403i
\(595\) −12.0000 10.3923i −0.491952 0.426043i
\(596\) 7.50000 12.9904i 0.307212 0.532107i
\(597\) −30.0000 + 51.9615i −1.22782 + 2.12664i
\(598\) 0 0
\(599\) 12.5000 + 21.6506i 0.510736 + 0.884621i 0.999923 + 0.0124417i \(0.00396043\pi\)
−0.489186 + 0.872179i \(0.662706\pi\)
\(600\) −18.0000 31.1769i −0.734847 1.27279i
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) −3.50000 + 18.1865i −0.142649 + 0.741228i
\(603\) −18.0000 −0.733017
\(604\) 21.0000 0.854478
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) −7.50000 12.9904i −0.304667 0.527698i
\(607\) 11.0000 0.446476 0.223238 0.974764i \(-0.428337\pi\)
0.223238 + 0.974764i \(0.428337\pi\)
\(608\) 2.50000 4.33013i 0.101388 0.175610i
\(609\) −10.5000 + 54.5596i −0.425481 + 2.21087i
\(610\) −39.0000 −1.57906
\(611\) 3.50000 + 0.866025i 0.141595 + 0.0350356i
\(612\) −6.00000 10.3923i −0.242536 0.420084i
\(613\) −25.0000 −1.00974 −0.504870 0.863195i \(-0.668460\pi\)
−0.504870 + 0.863195i \(0.668460\pi\)
\(614\) −6.00000 10.3923i −0.242140 0.419399i
\(615\) 13.5000 + 23.3827i 0.544373 + 0.942881i
\(616\) −22.5000 + 7.79423i −0.906551 + 0.314038i
\(617\) 16.5000 + 28.5788i 0.664265 + 1.15054i 0.979484 + 0.201522i \(0.0645887\pi\)
−0.315219 + 0.949019i \(0.602078\pi\)
\(618\) −15.0000 −0.603388
\(619\) −5.50000 9.52628i −0.221064 0.382893i 0.734068 0.679076i \(-0.237620\pi\)
−0.955131 + 0.296183i \(0.904286\pi\)
\(620\) 4.50000 7.79423i 0.180724 0.313024i
\(621\) 0 0
\(622\) 4.50000 7.79423i 0.180434 0.312520i
\(623\) 12.0000 + 10.3923i 0.480770 + 0.416359i
\(624\) −7.50000 + 7.79423i −0.300240 + 0.312019i
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 19.0000 0.759393
\(627\) −9.00000 −0.359425
\(628\) −19.0000 −0.758183
\(629\) −4.00000 −0.159490
\(630\) −45.0000 + 15.5885i −1.79284 + 0.621059i
\(631\) −12.5000 21.6506i −0.497617 0.861898i 0.502379 0.864647i \(-0.332458\pi\)
−0.999996 + 0.00274930i \(0.999125\pi\)
\(632\) −4.50000 + 7.79423i −0.179000 + 0.310038i
\(633\) 10.5000 18.1865i 0.417338 0.722850i
\(634\) −9.00000 −0.357436
\(635\) −16.5000 28.5788i −0.654783 1.13412i
\(636\) 9.00000 0.356873
\(637\) −20.5000 14.7224i −0.812240 0.583324i
\(638\) −21.0000 −0.831398
\(639\) −39.0000 67.5500i −1.54282 2.67224i
\(640\) −9.00000 −0.355756
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 12.0000 20.7846i 0.473602 0.820303i
\(643\) 9.50000 + 16.4545i 0.374643 + 0.648901i 0.990274 0.139134i \(-0.0444318\pi\)
−0.615630 + 0.788035i \(0.711098\pi\)
\(644\) 0 0
\(645\) 63.0000 2.48062
\(646\) 2.00000 0.0786889
\(647\) 9.00000 0.353827 0.176913 0.984226i \(-0.443389\pi\)
0.176913 + 0.984226i \(0.443389\pi\)
\(648\) −27.0000 −1.06066
\(649\) −6.00000 + 10.3923i −0.235521 + 0.407934i
\(650\) 14.0000 + 3.46410i 0.549125 + 0.135873i
\(651\) −18.0000 15.5885i −0.705476 0.610960i
\(652\) −0.500000 + 0.866025i −0.0195815 + 0.0339162i
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 10.5000 18.1865i 0.410582 0.711150i
\(655\) −7.50000 12.9904i −0.293049 0.507576i
\(656\) −3.00000 −0.117130
\(657\) 39.0000 + 67.5500i 1.52153 + 2.63538i
\(658\) −2.50000 + 0.866025i −0.0974601 + 0.0337612i
\(659\) −14.5000 25.1147i −0.564840 0.978331i −0.997065 0.0765653i \(-0.975605\pi\)
0.432225 0.901766i \(-0.357729\pi\)
\(660\) 13.5000 + 23.3827i 0.525487 + 0.910170i
\(661\) −9.00000 −0.350059 −0.175030 0.984563i \(-0.556002\pi\)
−0.175030 + 0.984563i \(0.556002\pi\)
\(662\) 14.5000 + 25.1147i 0.563559 + 0.976112i
\(663\) 21.0000 + 5.19615i 0.815572 + 0.201802i
\(664\) 0 0
\(665\) −1.50000 + 7.79423i −0.0581675 + 0.302247i
\(666\) −6.00000 + 10.3923i −0.232495 + 0.402694i
\(667\) 0 0
\(668\) −6.50000 11.2583i −0.251493 0.435598i
\(669\) −13.5000 + 23.3827i −0.521940 + 0.904027i
\(670\) −9.00000 −0.347700
\(671\) 39.0000 1.50558
\(672\) −7.50000 + 38.9711i −0.289319 + 1.50334i
\(673\) 20.5000 35.5070i 0.790217 1.36870i −0.135615 0.990762i \(-0.543301\pi\)
0.925832 0.377934i \(-0.123365\pi\)
\(674\) −7.00000 12.1244i −0.269630 0.467013i
\(675\) 18.0000 + 31.1769i 0.692820 + 1.20000i
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) −3.50000 + 6.06218i −0.134516 + 0.232988i −0.925412 0.378962i \(-0.876281\pi\)
0.790897 + 0.611950i \(0.209615\pi\)
\(678\) 22.5000 38.9711i 0.864107 1.49668i
\(679\) −10.0000 8.66025i −0.383765 0.332350i
\(680\) −9.00000 15.5885i −0.345134 0.597790i
\(681\) −6.00000 + 10.3923i −0.229920 + 0.398234i
\(682\) 4.50000 7.79423i 0.172314 0.298456i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) −3.00000 + 5.19615i −0.114708 + 0.198680i
\(685\) −15.0000 25.9808i −0.573121 0.992674i
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) −19.5000 + 33.7750i −0.743971 + 1.28860i
\(688\) −3.50000 + 6.06218i −0.133436 + 0.231118i
\(689\) −7.50000 + 7.79423i −0.285727 + 0.296936i
\(690\) 0 0
\(691\) 2.00000 + 3.46410i 0.0760836 + 0.131781i 0.901557 0.432660i \(-0.142425\pi\)
−0.825473 + 0.564441i \(0.809092\pi\)
\(692\) 9.50000 16.4545i 0.361136 0.625506i
\(693\) 45.0000 15.5885i 1.70941 0.592157i
\(694\) −8.00000 −0.303676
\(695\) −45.0000 −1.70695
\(696\) −31.5000 + 54.5596i −1.19400 + 2.06808i
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) 23.0000 0.870563
\(699\) −31.5000 + 54.5596i −1.19144 + 2.06363i
\(700\) 10.0000 3.46410i 0.377964 0.130931i
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 22.5000 23.3827i 0.849208 0.882523i
\(703\) 1.00000 + 1.73205i 0.0377157 + 0.0653255i
\(704\) −21.0000 −0.791467
\(705\) 4.50000 + 7.79423i 0.169480 + 0.293548i
\(706\) 12.5000 + 21.6506i 0.470444 + 0.814832i
\(707\) 12.5000 4.33013i 0.470111 0.162851i
\(708\) 6.00000 + 10.3923i 0.225494 + 0.390567i
\(709\) 11.0000 0.413114 0.206557 0.978435i \(-0.433774\pi\)
0.206557 + 0.978435i \(0.433774\pi\)
\(710\) −19.5000 33.7750i −0.731822 1.26755i
\(711\) 9.00000 15.5885i 0.337526 0.584613i
\(712\) 9.00000 + 15.5885i 0.337289 + 0.584202i
\(713\) 0 0
\(714\) −15.0000 + 5.19615i −0.561361 + 0.194461i
\(715\) −31.5000 7.79423i −1.17803 0.291488i
\(716\) 8.50000 14.7224i 0.317660 0.550203i
\(717\) 12.0000 0.448148
\(718\) 17.0000 0.634434
\(719\) −9.00000 −0.335643 −0.167822 0.985817i \(-0.553673\pi\)
−0.167822 + 0.985817i \(0.553673\pi\)
\(720\) −18.0000 −0.670820
\(721\) 2.50000 12.9904i 0.0931049 0.483787i
\(722\) 9.00000 + 15.5885i 0.334945 + 0.580142i
\(723\) −39.0000 + 67.5500i −1.45043 + 2.51221i
\(724\) −11.0000 + 19.0526i −0.408812 + 0.708083i
\(725\) 28.0000 1.03989
\(726\) −3.00000 5.19615i −0.111340 0.192847i
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) −16.5000 23.3827i −0.611531 0.866620i
\(729\) −27.0000 −1.00000
\(730\) 19.5000 + 33.7750i 0.721727 + 1.25007i
\(731\) 14.0000 0.517809
\(732\) 19.5000 33.7750i 0.720741 1.24836i
\(733\) 4.50000 7.79423i 0.166211 0.287886i −0.770873 0.636988i \(-0.780180\pi\)
0.937085 + 0.349102i \(0.113513\pi\)
\(734\) 15.5000 + 26.8468i 0.572115 + 0.990933i
\(735\) −9.00000 62.3538i −0.331970 2.29996i
\(736\) 0 0
\(737\) 9.00000 0.331519
\(738\) 18.0000 0.662589
\(739\) 1.00000 0.0367856 0.0183928 0.999831i \(-0.494145\pi\)
0.0183928 + 0.999831i \(0.494145\pi\)
\(740\) 3.00000 5.19615i 0.110282 0.191014i
\(741\) −3.00000 10.3923i −0.110208 0.381771i
\(742\) 1.50000 7.79423i 0.0550667 0.286135i
\(743\) −25.5000 + 44.1673i −0.935504 + 1.62034i −0.161772 + 0.986828i \(0.551721\pi\)
−0.773732 + 0.633513i \(0.781612\pi\)
\(744\) −13.5000 23.3827i −0.494934 0.857251i
\(745\) −22.5000 + 38.9711i −0.824336 + 1.42779i
\(746\) 4.50000 + 7.79423i 0.164757 + 0.285367i
\(747\) 0 0
\(748\) 3.00000 + 5.19615i 0.109691 + 0.189990i
\(749\) 16.0000 + 13.8564i 0.584627 + 0.506302i
\(750\) −4.50000 7.79423i −0.164317 0.284605i
\(751\) −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i \(-0.995991\pi\)
0.489053 0.872254i \(-0.337342\pi\)
\(752\) −1.00000 −0.0364662
\(753\) −34.5000 59.7558i −1.25725 2.17762i
\(754\) −7.00000 24.2487i −0.254925 0.883086i
\(755\) −63.0000 −2.29280
\(756\) 4.50000 23.3827i 0.163663 0.850420i
\(757\) −1.50000 + 2.59808i −0.0545184 + 0.0944287i −0.891997 0.452042i \(-0.850696\pi\)
0.837478 + 0.546471i \(0.184029\pi\)
\(758\) −33.0000 −1.19861
\(759\) 0 0
\(760\) −4.50000 + 7.79423i −0.163232 + 0.282726i
\(761\) −9.00000 −0.326250 −0.163125 0.986605i \(-0.552157\pi\)
−0.163125 + 0.986605i \(0.552157\pi\)
\(762\) −33.0000 −1.19546
\(763\) 14.0000 + 12.1244i 0.506834 + 0.438931i
\(764\) −8.50000 + 14.7224i −0.307519 + 0.532639i
\(765\) 18.0000 + 31.1769i 0.650791 + 1.12720i
\(766\) 10.5000 + 18.1865i 0.379380 + 0.657106i
\(767\) −14.0000 3.46410i −0.505511 0.125081i
\(768\) −25.5000 + 44.1673i −0.920152 + 1.59375i
\(769\) −9.50000 + 16.4545i −0.342579 + 0.593364i −0.984911 0.173063i \(-0.944634\pi\)
0.642332 + 0.766426i \(0.277967\pi\)
\(770\) 22.5000 7.79423i 0.810844 0.280885i
\(771\) −3.00000 5.19615i −0.108042 0.187135i
\(772\) 3.50000 6.06218i 0.125968 0.218183i
\(773\) 3.00000 5.19615i 0.107903 0.186893i −0.807018 0.590527i \(-0.798920\pi\)
0.914920 + 0.403634i \(0.132253\pi\)
\(774\) 21.0000 36.3731i 0.754829 1.30740i
\(775\) −6.00000 + 10.3923i −0.215526 + 0.373303i