Properties

Label 91.2.h.a.74.1
Level $91$
Weight $2$
Character 91.74
Analytic conductor $0.727$
Analytic rank $0$
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.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 74.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 91.74
Dual form 91.2.h.a.16.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.50000 + 2.59808i) q^{3} -1.00000 q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.50000 + 2.59808i) q^{3} -1.00000 q^{4} +(-1.50000 - 2.59808i) q^{5} +(1.50000 + 2.59808i) q^{6} +(2.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) 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} -1.00000 q^{16} -2.00000 q^{17} +(-3.00000 + 5.19615i) q^{18} +(0.500000 - 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{20} +(7.50000 + 2.59808i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-4.50000 - 7.79423i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(-1.00000 - 3.46410i) q^{26} -9.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} +(-3.50000 + 6.06218i) q^{29} +(4.50000 - 7.79423i) q^{30} +(-1.50000 + 2.59808i) q^{31} +5.00000 q^{32} +(-4.50000 + 7.79423i) q^{33} -2.00000 q^{34} +(-7.50000 - 2.59808i) q^{35} +(3.00000 - 5.19615i) q^{36} +2.00000 q^{37} +(0.500000 - 0.866025i) q^{38} +(7.50000 - 7.79423i) q^{39} +(4.50000 + 7.79423i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(7.50000 + 2.59808i) q^{42} +(3.50000 + 6.06218i) q^{43} +(-1.50000 - 2.59808i) q^{44} +18.0000 q^{45} +(-0.500000 - 0.866025i) q^{47} +(-1.50000 - 2.59808i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-3.00000 - 5.19615i) q^{51} +(1.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{54} +(4.50000 - 7.79423i) q^{55} +(-6.00000 + 5.19615i) q^{56} +3.00000 q^{57} +(-3.50000 + 6.06218i) q^{58} -4.00000 q^{59} +(-4.50000 + 7.79423i) q^{60} +(6.50000 - 11.2583i) q^{61} +(-1.50000 + 2.59808i) q^{62} +(3.00000 + 15.5885i) q^{63} +7.00000 q^{64} +(-7.50000 + 7.79423i) q^{65} +(-4.50000 + 7.79423i) q^{66} +(1.50000 + 2.59808i) q^{67} +2.00000 q^{68} +(-7.50000 - 2.59808i) q^{70} +(-6.50000 - 11.2583i) q^{71} +(9.00000 - 15.5885i) q^{72} +(6.50000 - 11.2583i) q^{73} +2.00000 q^{74} -12.0000 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} +(1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-7.50000 - 2.59808i) q^{84} +(3.00000 + 5.19615i) q^{85} +(3.50000 + 6.06218i) q^{86} -21.0000 q^{87} +(-4.50000 - 7.79423i) q^{88} +6.00000 q^{89} +18.0000 q^{90} +(-8.00000 - 5.19615i) q^{91} -9.00000 q^{93} +(-0.500000 - 0.866025i) q^{94} -3.00000 q^{95} +(7.50000 + 12.9904i) q^{96} +(2.50000 + 4.33013i) q^{97} +(1.00000 - 6.92820i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 3q^{3} - 2q^{4} - 3q^{5} + 3q^{6} + 4q^{7} - 6q^{8} - 6q^{9} + O(q^{10}) \) \( 2q + 2q^{2} + 3q^{3} - 2q^{4} - 3q^{5} + 3q^{6} + 4q^{7} - 6q^{8} - 6q^{9} - 3q^{10} + 3q^{11} - 3q^{12} - 2q^{13} + 4q^{14} + 9q^{15} - 2q^{16} - 4q^{17} - 6q^{18} + q^{19} + 3q^{20} + 15q^{21} + 3q^{22} - 9q^{24} - 4q^{25} - 2q^{26} - 18q^{27} - 4q^{28} - 7q^{29} + 9q^{30} - 3q^{31} + 10q^{32} - 9q^{33} - 4q^{34} - 15q^{35} + 6q^{36} + 4q^{37} + q^{38} + 15q^{39} + 9q^{40} - 3q^{41} + 15q^{42} + 7q^{43} - 3q^{44} + 36q^{45} - q^{47} - 3q^{48} + 2q^{49} - 4q^{50} - 6q^{51} + 2q^{52} - 3q^{53} - 18q^{54} + 9q^{55} - 12q^{56} + 6q^{57} - 7q^{58} - 8q^{59} - 9q^{60} + 13q^{61} - 3q^{62} + 6q^{63} + 14q^{64} - 15q^{65} - 9q^{66} + 3q^{67} + 4q^{68} - 15q^{70} - 13q^{71} + 18q^{72} + 13q^{73} + 4q^{74} - 24q^{75} - q^{76} + 15q^{77} + 15q^{78} + 3q^{79} + 3q^{80} - 9q^{81} - 3q^{82} - 15q^{84} + 6q^{85} + 7q^{86} - 42q^{87} - 9q^{88} + 12q^{89} + 36q^{90} - 16q^{91} - 18q^{93} - q^{94} - 6q^{95} + 15q^{96} + 5q^{97} + 2q^{98} - 36q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 1.50000 + 2.59808i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 1.50000 + 2.59808i 0.612372 + 1.06066i
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) −3.00000 −1.06066
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) −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
\(16\) −1.00000 −0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −3.00000 + 5.19615i −0.707107 + 1.22474i
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −4.50000 7.79423i −0.918559 1.59099i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −1.00000 3.46410i −0.196116 0.679366i
\(27\) −9.00000 −1.73205
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) −3.50000 + 6.06218i −0.649934 + 1.12572i 0.333205 + 0.942855i \(0.391870\pi\)
−0.983138 + 0.182864i \(0.941463\pi\)
\(30\) 4.50000 7.79423i 0.821584 1.42302i
\(31\) −1.50000 + 2.59808i −0.269408 + 0.466628i −0.968709 0.248199i \(-0.920161\pi\)
0.699301 + 0.714827i \(0.253495\pi\)
\(32\) 5.00000 0.883883
\(33\) −4.50000 + 7.79423i −0.783349 + 1.35680i
\(34\) −2.00000 −0.342997
\(35\) −7.50000 2.59808i −1.26773 0.439155i
\(36\) 3.00000 5.19615i 0.500000 0.866025i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0.500000 0.866025i 0.0811107 0.140488i
\(39\) 7.50000 7.79423i 1.20096 1.24808i
\(40\) 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 \(0.241934\pi\)
\(42\) 7.50000 + 2.59808i 1.15728 + 0.400892i
\(43\) 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
\(45\) 18.0000 2.68328
\(46\) 0 0
\(47\) −0.500000 0.866025i −0.0729325 0.126323i 0.827253 0.561830i \(-0.189902\pi\)
−0.900185 + 0.435507i \(0.856569\pi\)
\(48\) −1.50000 2.59808i −0.216506 0.375000i
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) −3.00000 5.19615i −0.420084 0.727607i
\(52\) 1.00000 + 3.46410i 0.138675 + 0.480384i
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) −9.00000 −1.22474
\(55\) 4.50000 7.79423i 0.606780 1.05097i
\(56\) −6.00000 + 5.19615i −0.801784 + 0.694365i
\(57\) 3.00000 0.397360
\(58\) −3.50000 + 6.06218i −0.459573 + 0.796003i
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) −4.50000 + 7.79423i −0.580948 + 1.00623i
\(61\) 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i \(-0.520392\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) −1.50000 + 2.59808i −0.190500 + 0.329956i
\(63\) 3.00000 + 15.5885i 0.377964 + 1.96396i
\(64\) 7.00000 0.875000
\(65\) −7.50000 + 7.79423i −0.930261 + 0.966755i
\(66\) −4.50000 + 7.79423i −0.553912 + 0.959403i
\(67\) 1.50000 + 2.59808i 0.183254 + 0.317406i 0.942987 0.332830i \(-0.108004\pi\)
−0.759733 + 0.650236i \(0.774670\pi\)
\(68\) 2.00000 0.242536
\(69\) 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 \(-0.447114\pi\)
\(72\) 9.00000 15.5885i 1.06066 1.83712i
\(73\) 6.50000 11.2583i 0.760767 1.31769i −0.181688 0.983356i \(-0.558156\pi\)
0.942455 0.334332i \(-0.108511\pi\)
\(74\) 2.00000 0.232495
\(75\) −12.0000 −1.38564
\(76\) −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 0.937985 0.346675i \(-0.112689\pi\)
−0.769222 + 0.638982i \(0.779356\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −7.50000 2.59808i −0.818317 0.283473i
\(85\) 3.00000 + 5.19615i 0.325396 + 0.563602i
\(86\) 3.50000 + 6.06218i 0.377415 + 0.653701i
\(87\) −21.0000 −2.25144
\(88\) −4.50000 7.79423i −0.479702 0.830868i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 18.0000 1.89737
\(91\) −8.00000 5.19615i −0.838628 0.544705i
\(92\) 0 0
\(93\) −9.00000 −0.933257
\(94\) −0.500000 0.866025i −0.0515711 0.0893237i
\(95\) −3.00000 −0.307794
\(96\) 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 \(0.751641\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) −18.0000 −1.80907
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) 2.50000 + 4.33013i 0.248759 + 0.430864i 0.963182 0.268851i \(-0.0866439\pi\)
−0.714423 + 0.699715i \(0.753311\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) −2.50000 4.33013i −0.246332 0.426660i 0.716173 0.697923i \(-0.245892\pi\)
−0.962505 + 0.271263i \(0.912559\pi\)
\(104\) 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
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 9.00000 0.866025
\(109\) −3.50000 + 6.06218i −0.335239 + 0.580651i −0.983531 0.180741i \(-0.942150\pi\)
0.648292 + 0.761392i \(0.275484\pi\)
\(110\) 4.50000 7.79423i 0.429058 0.743151i
\(111\) 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 \(-0.415962\pi\)
\(114\) 3.00000 0.280976
\(115\) 0 0
\(116\) 3.50000 6.06218i 0.324967 0.562859i
\(117\) 21.0000 + 5.19615i 1.94145 + 0.480384i
\(118\) −4.00000 −0.368230
\(119\) −4.00000 + 3.46410i −0.366679 + 0.317554i
\(120\) −13.5000 + 23.3827i −1.23238 + 2.13454i
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 6.50000 11.2583i 0.588482 1.01928i
\(123\) −9.00000 −0.811503
\(124\) 1.50000 2.59808i 0.134704 0.233314i
\(125\) −3.00000 −0.268328
\(126\) 3.00000 + 15.5885i 0.267261 + 1.38873i
\(127\) −5.50000 + 9.52628i −0.488046 + 0.845321i −0.999905 0.0137486i \(-0.995624\pi\)
0.511859 + 0.859069i \(0.328957\pi\)
\(128\) −3.00000 −0.265165
\(129\) −10.5000 + 18.1865i −0.924473 + 1.60123i
\(130\) −7.50000 + 7.79423i −0.657794 + 0.683599i
\(131\) −2.50000 4.33013i −0.218426 0.378325i 0.735901 0.677089i \(-0.236759\pi\)
−0.954327 + 0.298764i \(0.903426\pi\)
\(132\) 4.50000 7.79423i 0.391675 0.678401i
\(133\) −0.500000 2.59808i −0.0433555 0.225282i
\(134\) 1.50000 + 2.59808i 0.129580 + 0.224440i
\(135\) 13.5000 + 23.3827i 1.16190 + 2.01246i
\(136\) 6.00000 0.514496
\(137\) 10.0000 0.854358 0.427179 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) 7.50000 + 12.9904i 0.636142 + 1.10183i 0.986272 + 0.165129i \(0.0528040\pi\)
−0.350130 + 0.936701i \(0.613863\pi\)
\(140\) 7.50000 + 2.59808i 0.633866 + 0.219578i
\(141\) 1.50000 2.59808i 0.126323 0.218797i
\(142\) −6.50000 11.2583i −0.545468 0.944778i
\(143\) 7.50000 7.79423i 0.627182 0.651786i
\(144\) 3.00000 5.19615i 0.250000 0.433013i
\(145\) 21.0000 1.74396
\(146\) 6.50000 11.2583i 0.537944 0.931746i
\(147\) 19.5000 7.79423i 1.60833 0.642857i
\(148\) −2.00000 −0.164399
\(149\) −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i \(0.377278\pi\)
−0.990485 + 0.137619i \(0.956055\pi\)
\(150\) −12.0000 −0.979796
\(151\) 10.5000 18.1865i 0.854478 1.48000i −0.0226507 0.999743i \(-0.507211\pi\)
0.877129 0.480256i \(-0.159456\pi\)
\(152\) −1.50000 + 2.59808i −0.121666 + 0.210732i
\(153\) 6.00000 10.3923i 0.485071 0.840168i
\(154\) 7.50000 + 2.59808i 0.604367 + 0.209359i
\(155\) 9.00000 0.722897
\(156\) −7.50000 + 7.79423i −0.600481 + 0.624038i
\(157\) −9.50000 + 16.4545i −0.758183 + 1.31321i 0.185594 + 0.982627i \(0.440579\pi\)
−0.943777 + 0.330584i \(0.892754\pi\)
\(158\) 1.50000 + 2.59808i 0.119334 + 0.206692i
\(159\) −9.00000 −0.713746
\(160\) −7.50000 12.9904i −0.592927 1.02698i
\(161\) 0 0
\(162\) −4.50000 7.79423i −0.353553 0.612372i
\(163\) 0.500000 0.866025i 0.0391630 0.0678323i −0.845780 0.533533i \(-0.820864\pi\)
0.884943 + 0.465700i \(0.154198\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) 27.0000 2.10195
\(166\) 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
\(171\) 3.00000 + 5.19615i 0.229416 + 0.397360i
\(172\) −3.50000 6.06218i −0.266872 0.462237i
\(173\) −9.50000 + 16.4545i −0.722272 + 1.25101i 0.237816 + 0.971310i \(0.423569\pi\)
−0.960087 + 0.279701i \(0.909765\pi\)
\(174\) −21.0000 −1.59201
\(175\) 2.00000 + 10.3923i 0.151186 + 0.785584i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) −6.00000 10.3923i −0.450988 0.781133i
\(178\) 6.00000 0.449719
\(179\) −8.50000 14.7224i −0.635320 1.10041i −0.986447 0.164079i \(-0.947535\pi\)
0.351127 0.936328i \(-0.385798\pi\)
\(180\) −18.0000 −1.34164
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −8.00000 5.19615i −0.592999 0.385164i
\(183\) 39.0000 2.88296
\(184\) 0 0
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) −9.00000 −0.659912
\(187\) −3.00000 5.19615i −0.219382 0.379980i
\(188\) 0.500000 + 0.866025i 0.0364662 + 0.0631614i
\(189\) −18.0000 + 15.5885i −1.30931 + 1.13389i
\(190\) −3.00000 −0.217643
\(191\) 8.50000 14.7224i 0.615038 1.06528i −0.375339 0.926887i \(-0.622474\pi\)
0.990378 0.138390i \(-0.0441928\pi\)
\(192\) 10.5000 + 18.1865i 0.757772 + 1.31250i
\(193\) −3.50000 6.06218i −0.251936 0.436365i 0.712123 0.702055i \(-0.247734\pi\)
−0.964059 + 0.265689i \(0.914400\pi\)
\(194\) 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 \(0.155325\pi\)
\(198\) −18.0000 −1.27920
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 6.00000 10.3923i 0.424264 0.734847i
\(201\) −4.50000 + 7.79423i −0.317406 + 0.549762i
\(202\) 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
\(205\) 9.00000 0.628587
\(206\) −2.50000 4.33013i −0.174183 0.301694i
\(207\) 0 0
\(208\) 1.00000 + 3.46410i 0.0693375 + 0.240192i
\(209\) 3.00000 0.207514
\(210\) −4.50000 23.3827i −0.310530 1.61356i
\(211\) −3.50000 + 6.06218i −0.240950 + 0.417338i −0.960985 0.276600i \(-0.910792\pi\)
0.720035 + 0.693938i \(0.244126\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) 19.5000 33.7750i 1.33612 2.31422i
\(214\) 8.00000 0.546869
\(215\) 10.5000 18.1865i 0.716094 1.24031i
\(216\) 27.0000 1.83712
\(217\) 1.50000 + 7.79423i 0.101827 + 0.529107i
\(218\) −3.50000 + 6.06218i −0.237050 + 0.410582i
\(219\) 39.0000 2.63538
\(220\) −4.50000 + 7.79423i −0.303390 + 0.525487i
\(221\) 2.00000 + 6.92820i 0.134535 + 0.466041i
\(222\) 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 \(0.0692320\pi\)
\(224\) 10.0000 8.66025i 0.668153 0.578638i
\(225\) −12.0000 20.7846i −0.800000 1.38564i
\(226\) −7.50000 12.9904i −0.498893 0.864107i
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) −3.00000 −0.198680
\(229\) 6.50000 + 11.2583i 0.429532 + 0.743971i 0.996832 0.0795401i \(-0.0253452\pi\)
−0.567300 + 0.823511i \(0.692012\pi\)
\(230\) 0 0
\(231\) 4.50000 + 23.3827i 0.296078 + 1.53847i
\(232\) 10.5000 18.1865i 0.689359 1.19400i
\(233\) 10.5000 + 18.1865i 0.687878 + 1.19144i 0.972523 + 0.232806i \(0.0747909\pi\)
−0.284645 + 0.958633i \(0.591876\pi\)
\(234\) 21.0000 + 5.19615i 1.37281 + 0.339683i
\(235\) −1.50000 + 2.59808i −0.0978492 + 0.169480i
\(236\) 4.00000 0.260378
\(237\) −4.50000 + 7.79423i −0.292306 + 0.506290i
\(238\) −4.00000 + 3.46410i −0.259281 + 0.224544i
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) −4.50000 + 7.79423i −0.290474 + 0.503115i
\(241\) −26.0000 −1.67481 −0.837404 0.546585i \(-0.815928\pi\)
−0.837404 + 0.546585i \(0.815928\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) 0 0
\(244\) −6.50000 + 11.2583i −0.416120 + 0.720741i
\(245\) −19.5000 + 7.79423i −1.24581 + 0.497955i
\(246\) −9.00000 −0.573819
\(247\) −3.50000 0.866025i −0.222700 0.0551039i
\(248\) 4.50000 7.79423i 0.285750 0.494934i
\(249\) 0 0
\(250\) −3.00000 −0.189737
\(251\) 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
\(254\) −5.50000 + 9.52628i −0.345101 + 0.597732i
\(255\) −9.00000 + 15.5885i −0.563602 + 0.976187i
\(256\) −17.0000 −1.06250
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) −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
\(262\) −2.50000 4.33013i −0.154451 0.267516i
\(263\) 13.5000 + 23.3827i 0.832446 + 1.44184i 0.896093 + 0.443866i \(0.146393\pi\)
−0.0636476 + 0.997972i \(0.520273\pi\)
\(264\) 13.5000 23.3827i 0.830868 1.43910i
\(265\) 9.00000 0.552866
\(266\) −0.500000 2.59808i −0.0306570 0.159298i
\(267\) 9.00000 + 15.5885i 0.550791 + 0.953998i
\(268\) −1.50000 2.59808i −0.0916271 0.158703i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 13.5000 + 23.3827i 0.821584 + 1.42302i
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 2.00000 0.121268
\(273\) 1.50000 28.5788i 0.0907841 1.72967i
\(274\) 10.0000 0.604122
\(275\) −12.0000 −0.723627
\(276\) 0 0
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) 7.50000 + 12.9904i 0.449820 + 0.779111i
\(279\) −9.00000 15.5885i −0.538816 0.933257i
\(280\) 22.5000 + 7.79423i 1.34463 + 0.465794i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 1.50000 2.59808i 0.0893237 0.154713i
\(283\) −0.500000 0.866025i −0.0297219 0.0514799i 0.850782 0.525519i \(-0.176129\pi\)
−0.880504 + 0.474039i \(0.842796\pi\)
\(284\) 6.50000 + 11.2583i 0.385704 + 0.668059i
\(285\) −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
\(289\) −13.0000 −0.764706
\(290\) 21.0000 1.23316
\(291\) −7.50000 + 12.9904i −0.439658 + 0.761510i
\(292\) −6.50000 + 11.2583i −0.380384 + 0.658844i
\(293\) −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
\(296\) −6.00000 −0.348743
\(297\) −13.5000 23.3827i −0.783349 1.35680i
\(298\) −7.50000 + 12.9904i −0.434463 + 0.752513i
\(299\) 0 0
\(300\) 12.0000 0.692820
\(301\) 17.5000 + 6.06218i 1.00868 + 0.349418i
\(302\) 10.5000 18.1865i 0.604207 1.04652i
\(303\) −7.50000 + 12.9904i −0.430864 + 0.746278i
\(304\) −0.500000 + 0.866025i −0.0286770 + 0.0496700i
\(305\) −39.0000 −2.23313
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) −7.50000 2.59808i −0.427352 0.148039i
\(309\) 7.50000 12.9904i 0.426660 0.738997i
\(310\) 9.00000 0.511166
\(311\) 4.50000 7.79423i 0.255172 0.441970i −0.709771 0.704433i \(-0.751201\pi\)
0.964942 + 0.262463i \(0.0845347\pi\)
\(312\) −22.5000 + 23.3827i −1.27381 + 1.32378i
\(313\) −9.50000 16.4545i −0.536972 0.930062i −0.999065 0.0432311i \(-0.986235\pi\)
0.462093 0.886831i \(-0.347098\pi\)
\(314\) −9.50000 + 16.4545i −0.536116 + 0.928580i
\(315\) 36.0000 31.1769i 2.02837 1.75662i
\(316\) −1.50000 2.59808i −0.0843816 0.146153i
\(317\) 4.50000 + 7.79423i 0.252745 + 0.437767i 0.964281 0.264883i \(-0.0853332\pi\)
−0.711535 + 0.702650i \(0.752000\pi\)
\(318\) −9.00000 −0.504695
\(319\) −21.0000 −1.17577
\(320\) −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
\(325\) 14.0000 + 3.46410i 0.776580 + 0.192154i
\(326\) 0.500000 0.866025i 0.0276924 0.0479647i
\(327\) −21.0000 −1.16130
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) −2.50000 0.866025i −0.137829 0.0477455i
\(330\) 27.0000 1.48630
\(331\) 14.5000 25.1147i 0.796992 1.38043i −0.124574 0.992210i \(-0.539757\pi\)
0.921567 0.388221i \(-0.126910\pi\)
\(332\) 0 0
\(333\) −6.00000 + 10.3923i −0.328798 + 0.569495i
\(334\) 6.50000 11.2583i 0.355664 0.616028i
\(335\) 4.50000 7.79423i 0.245861 0.425844i
\(336\) −7.50000 2.59808i −0.409159 0.141737i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −11.0000 + 6.92820i −0.598321 + 0.376845i
\(339\) 22.5000 38.9711i 1.22203 2.11662i
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) −9.00000 −0.487377
\(342\) 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
\(347\) −8.00000 −0.429463 −0.214731 0.976673i \(-0.568888\pi\)
−0.214731 + 0.976673i \(0.568888\pi\)
\(348\) 21.0000 1.12572
\(349\) −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
\(353\) 12.5000 + 21.6506i 0.665308 + 1.15235i 0.979202 + 0.202889i \(0.0650330\pi\)
−0.313894 + 0.949458i \(0.601634\pi\)
\(354\) −6.00000 10.3923i −0.318896 0.552345i
\(355\) −19.5000 + 33.7750i −1.03495 + 1.79259i
\(356\) −6.00000 −0.317999
\(357\) −15.0000 5.19615i −0.793884 0.275010i
\(358\) −8.50000 14.7224i −0.449239 0.778105i
\(359\) −8.50000 14.7224i −0.448613 0.777020i 0.549683 0.835373i \(-0.314748\pi\)
−0.998296 + 0.0583530i \(0.981415\pi\)
\(360\) −54.0000 −2.84605
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −22.0000 −1.15629
\(363\) 6.00000 0.314918
\(364\) 8.00000 + 5.19615i 0.419314 + 0.272352i
\(365\) −39.0000 −2.04135
\(366\) 39.0000 2.03856
\(367\) 15.5000 + 26.8468i 0.809093 + 1.40139i 0.913493 + 0.406855i \(0.133375\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) 0 0
\(369\) −9.00000 15.5885i −0.468521 0.811503i
\(370\) −3.00000 5.19615i −0.155963 0.270135i
\(371\) 1.50000 + 7.79423i 0.0778761 + 0.404656i
\(372\) 9.00000 0.466628
\(373\) 4.50000 7.79423i 0.233001 0.403570i −0.725689 0.688023i \(-0.758479\pi\)
0.958690 + 0.284453i \(0.0918121\pi\)
\(374\) −3.00000 5.19615i −0.155126 0.268687i
\(375\) −4.50000 7.79423i −0.232379 0.402492i
\(376\) 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 \(-0.155255\pi\)
\(380\) 3.00000 0.153897
\(381\) −33.0000 −1.69064
\(382\) 8.50000 14.7224i 0.434898 0.753265i
\(383\) 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) −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
\(387\) −42.0000 −2.13498
\(388\) −2.50000 4.33013i −0.126918 0.219829i
\(389\) 16.5000 28.5788i 0.836583 1.44900i −0.0561516 0.998422i \(-0.517883\pi\)
0.892735 0.450582i \(-0.148784\pi\)
\(390\) −31.5000 7.79423i −1.59506 0.394676i
\(391\) 0 0
\(392\) −3.00000 + 20.7846i −0.151523 + 1.04978i
\(393\) 7.50000 12.9904i 0.378325 0.655278i
\(394\) 0.500000 0.866025i 0.0251896 0.0436297i
\(395\) 4.50000 7.79423i 0.226420 0.392170i
\(396\) 18.0000 0.904534
\(397\) 0.500000 0.866025i 0.0250943 0.0434646i −0.853206 0.521575i \(-0.825345\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) −20.0000 −1.00251
\(399\) 6.00000 5.19615i 0.300376 0.260133i
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) −4.50000 + 7.79423i −0.224440 + 0.388741i
\(403\) 10.5000 + 2.59808i 0.523042 + 0.129419i
\(404\) −2.50000 4.33013i −0.124380 0.215432i
\(405\) −13.5000 + 23.3827i −0.670820 + 1.16190i
\(406\) 3.50000 + 18.1865i 0.173702 + 0.902583i
\(407\) 3.00000 + 5.19615i 0.148704 + 0.257564i
\(408\) 9.00000 + 15.5885i 0.445566 + 0.771744i
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 9.00000 0.444478
\(411\) 15.0000 + 25.9808i 0.739895 + 1.28154i
\(412\) 2.50000 + 4.33013i 0.123166 + 0.213330i
\(413\) −8.00000 + 6.92820i −0.393654 + 0.340915i
\(414\) 0 0
\(415\) 0 0
\(416\) −5.00000 17.3205i −0.245145 0.849208i
\(417\) −22.5000 + 38.9711i −1.10183 + 1.90843i
\(418\) 3.00000 0.146735
\(419\) 12.5000 21.6506i 0.610665 1.05770i −0.380464 0.924796i \(-0.624236\pi\)
0.991129 0.132907i \(-0.0424311\pi\)
\(420\) 4.50000 + 23.3827i 0.219578 + 1.14096i
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) −3.50000 + 6.06218i −0.170377 + 0.295102i
\(423\) 6.00000 0.291730
\(424\) 4.50000 7.79423i 0.218539 0.378521i
\(425\) 4.00000 6.92820i 0.194029 0.336067i
\(426\) 19.5000 33.7750i 0.944778 1.63640i
\(427\) −6.50000 33.7750i −0.314557 1.63449i
\(428\) −8.00000 −0.386695
\(429\) 31.5000 + 7.79423i 1.52083 + 0.376309i
\(430\) 10.5000 18.1865i 0.506355 0.877033i
\(431\) −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i \(-0.236215\pi\)
−0.953815 + 0.300395i \(0.902881\pi\)
\(432\) 9.00000 0.433013
\(433\) −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
\(436\) 3.50000 6.06218i 0.167620 0.290326i
\(437\) 0 0
\(438\) 39.0000 1.86349
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) −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 0.966591 0.256323i \(-0.0825112\pi\)
−0.705278 + 0.708931i \(0.749178\pi\)
\(444\) −3.00000 5.19615i −0.142374 0.246598i
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) 4.50000 7.79423i 0.213081 0.369067i
\(447\) −45.0000 −2.12843
\(448\) 14.0000 12.1244i 0.661438 0.572822i
\(449\) −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
\(451\) −9.00000 −0.423793
\(452\) 7.50000 + 12.9904i 0.352770 + 0.611016i
\(453\) 63.0000 2.96000
\(454\) −4.00000 −0.187729
\(455\) −1.50000 + 28.5788i −0.0703211 + 1.33980i
\(456\) −9.00000 −0.421464
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) 6.50000 + 11.2583i 0.303725 + 0.526067i
\(459\) 18.0000 0.840168
\(460\) 0 0
\(461\) −17.5000 30.3109i −0.815056 1.41172i −0.909288 0.416169i \(-0.863373\pi\)
0.0942312 0.995550i \(-0.469961\pi\)
\(462\) 4.50000 + 23.3827i 0.209359 + 1.08786i
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 3.50000 6.06218i 0.162483 0.281430i
\(465\) 13.5000 + 23.3827i 0.626048 + 1.08435i
\(466\) 10.5000 + 18.1865i 0.486403 + 0.842475i
\(467\) 3.50000 + 6.06218i 0.161961 + 0.280524i 0.935572 0.353137i \(-0.114885\pi\)
−0.773611 + 0.633661i \(0.781552\pi\)
\(468\) −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
\(471\) −57.0000 −2.62642
\(472\) 12.0000 0.552345
\(473\) −10.5000 + 18.1865i −0.482791 + 0.836218i
\(474\) −4.50000 + 7.79423i −0.206692 + 0.358001i
\(475\) 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
\(478\) −4.00000 −0.182956
\(479\) 17.5000 + 30.3109i 0.799595 + 1.38494i 0.919880 + 0.392200i \(0.128286\pi\)
−0.120284 + 0.992739i \(0.538381\pi\)
\(480\) 22.5000 38.9711i 1.02698 1.77878i
\(481\) −2.00000 6.92820i −0.0911922 0.315899i
\(482\) −26.0000 −1.18427
\(483\) 0 0
\(484\) −1.00000 + 1.73205i −0.0454545 + 0.0787296i
\(485\) 7.50000 12.9904i 0.340557 0.589863i
\(486\) 0 0
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) −19.5000 + 33.7750i −0.882724 + 1.52892i
\(489\) 3.00000 0.135665
\(490\) −19.5000 + 7.79423i −0.880920 + 0.352107i
\(491\) −7.50000 + 12.9904i −0.338470 + 0.586248i −0.984145 0.177365i \(-0.943243\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(492\) 9.00000 0.405751
\(493\) 7.00000 12.1244i 0.315264 0.546054i
\(494\) −3.50000 0.866025i −0.157472 0.0389643i
\(495\) 27.0000 + 46.7654i 1.21356 + 2.10195i
\(496\) 1.50000 2.59808i 0.0673520 0.116657i
\(497\) −32.5000 11.2583i −1.45782 0.505005i
\(498\) 0 0
\(499\) 15.5000 + 26.8468i 0.693875 + 1.20183i 0.970558 + 0.240866i \(0.0774314\pi\)
−0.276683 + 0.960961i \(0.589235\pi\)
\(500\) 3.00000 0.134164
\(501\) 39.0000 1.74239
\(502\) 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 \(0.590455\pi\)
\(504\) −9.00000 46.7654i −0.400892 2.08310i
\(505\) 7.50000 12.9904i 0.333746 0.578064i
\(506\) 0 0
\(507\) −34.5000 18.1865i −1.53220 0.807692i
\(508\) 5.50000 9.52628i 0.244023 0.422660i
\(509\) −34.0000 −1.50702 −0.753512 0.657434i \(-0.771642\pi\)
−0.753512 + 0.657434i \(0.771642\pi\)
\(510\) −9.00000 + 15.5885i −0.398527 + 0.690268i
\(511\) −6.50000 33.7750i −0.287543 1.49412i
\(512\) −11.0000 −0.486136
\(513\) −4.50000 + 7.79423i −0.198680 + 0.344124i
\(514\) −2.00000 −0.0882162
\(515\) −7.50000 + 12.9904i −0.330489 + 0.572425i
\(516\) 10.5000 18.1865i 0.462237 0.800617i
\(517\) 1.50000 2.59808i 0.0659699 0.114263i
\(518\) 4.00000 3.46410i 0.175750 0.152204i
\(519\) −57.0000 −2.50202
\(520\) 22.5000 23.3827i 0.986690 1.02540i
\(521\) 8.50000 14.7224i 0.372392 0.645001i −0.617541 0.786539i \(-0.711871\pi\)
0.989933 + 0.141537i \(0.0452044\pi\)
\(522\) −21.0000 36.3731i −0.919145 1.59201i
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 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
\(527\) 3.00000 5.19615i 0.130682 0.226348i
\(528\) 4.50000 7.79423i 0.195837 0.339200i
\(529\) −23.0000 −1.00000
\(530\) 9.00000 0.390935
\(531\) 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
\(535\) −12.0000 20.7846i −0.518805 0.898597i
\(536\) −4.50000 7.79423i −0.194370 0.336659i
\(537\) 25.5000 44.1673i 1.10041 1.90596i
\(538\) 18.0000 0.776035
\(539\) 19.5000 7.79423i 0.839924 0.335721i
\(540\) −13.5000 23.3827i −0.580948 1.00623i
\(541\) 18.5000 + 32.0429i 0.795377 + 1.37763i 0.922599 + 0.385759i \(0.126061\pi\)
−0.127222 + 0.991874i \(0.540606\pi\)
\(542\) −16.0000 −0.687259
\(543\) −33.0000 57.1577i −1.41617 2.45287i
\(544\) −10.0000 −0.428746
\(545\) 21.0000 0.899541
\(546\) 1.50000 28.5788i 0.0641941 1.22306i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −10.0000 −0.427179
\(549\) 39.0000 + 67.5500i 1.66448 + 2.88296i
\(550\) −12.0000 −0.511682
\(551\) 3.50000 + 6.06218i 0.149105 + 0.258257i
\(552\) 0 0
\(553\) 7.50000 + 2.59808i 0.318932 + 0.110481i
\(554\) 22.0000 0.934690
\(555\) 9.00000 15.5885i 0.382029 0.661693i
\(556\) −7.50000 12.9904i −0.318071 0.550915i
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) −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
\(562\) −18.0000 −0.759284
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) −1.50000 + 2.59808i −0.0631614 + 0.109399i
\(565\) −22.5000 + 38.9711i −0.946582 + 1.63953i
\(566\) −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
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) −4.50000 7.79423i −0.188484 0.326464i
\(571\) −21.5000 + 37.2391i −0.899747 + 1.55841i −0.0719297 + 0.997410i \(0.522916\pi\)
−0.827817 + 0.560998i \(0.810418\pi\)
\(572\) −7.50000 + 7.79423i −0.313591 + 0.325893i
\(573\) 51.0000 2.13056
\(574\) 1.50000 + 7.79423i 0.0626088 + 0.325325i
\(575\) 0 0
\(576\) −21.0000 + 36.3731i −0.875000 + 1.51554i
\(577\) 0.500000 0.866025i 0.0208153 0.0360531i −0.855430 0.517918i \(-0.826707\pi\)
0.876245 + 0.481865i \(0.160040\pi\)
\(578\) −13.0000 −0.540729
\(579\) 10.5000 18.1865i 0.436365 0.755807i
\(580\) −21.0000 −0.871978
\(581\) 0 0
\(582\) −7.50000 + 12.9904i −0.310885 + 0.538469i
\(583\) −9.00000 −0.372742
\(584\) −19.5000 + 33.7750i −0.806916 + 1.39762i
\(585\) −18.0000 62.3538i −0.744208 2.57801i
\(586\) −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 \(-0.0718001\pi\)
\(588\) −19.5000 + 7.79423i −0.804166 + 0.321429i
\(589\) 1.50000 + 2.59808i 0.0618064 + 0.107052i
\(590\) 6.00000 + 10.3923i 0.247016 + 0.427844i
\(591\) 3.00000 0.123404
\(592\) −2.00000 −0.0821995
\(593\) −13.5000 23.3827i −0.554379 0.960212i −0.997952 0.0639736i \(-0.979623\pi\)
0.443573 0.896238i \(-0.353711\pi\)
\(594\) −13.5000 23.3827i −0.553912 0.959403i
\(595\) 15.0000 + 5.19615i 0.614940 + 0.213021i
\(596\) 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 −0.489186 0.872179i \(-0.662706\pi\)
0.999923 0.0124417i \(-0.00396043\pi\)
\(600\) 36.0000 1.46969
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 17.5000 + 6.06218i 0.713247 + 0.247076i
\(603\) −18.0000 −0.733017
\(604\) −10.5000 + 18.1865i −0.427239 + 0.740000i
\(605\) −6.00000 −0.243935
\(606\) −7.50000 + 12.9904i −0.304667 + 0.527698i
\(607\) −5.50000 + 9.52628i −0.223238 + 0.386660i −0.955789 0.294052i \(-0.904996\pi\)
0.732551 + 0.680712i \(0.238329\pi\)
\(608\) 2.50000 4.33013i 0.101388 0.175610i
\(609\) −42.0000 + 36.3731i −1.70193 + 1.47391i
\(610\) −39.0000 −1.57906
\(611\) −2.50000 + 2.59808i −0.101139 + 0.105107i
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i \(0.00179300\pi\)
−0.495114 + 0.868828i \(0.664874\pi\)
\(614\) 12.0000 0.484281
\(615\) 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 \(0.602078\pi\)
\(618\) 7.50000 12.9904i 0.301694 0.522550i
\(619\) −5.50000 + 9.52628i −0.221064 + 0.382893i −0.955131 0.296183i \(-0.904286\pi\)
0.734068 + 0.679076i \(0.237620\pi\)
\(620\) −9.00000 −0.361449
\(621\) 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
\(626\) −9.50000 16.4545i −0.379696 0.657653i
\(627\) 4.50000 + 7.79423i 0.179713 + 0.311272i
\(628\) 9.50000 16.4545i 0.379091 0.656605i
\(629\) −4.00000 −0.159490
\(630\) 36.0000 31.1769i 1.43427 1.24212i
\(631\) −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
\(633\) −21.0000 −0.834675
\(634\) 4.50000 + 7.79423i 0.178718 + 0.309548i
\(635\) 33.0000 1.30957
\(636\) 9.00000 0.356873
\(637\) −25.0000 + 3.46410i −0.990536 + 0.137253i
\(638\) −21.0000 −0.831398
\(639\) 78.0000 3.08563
\(640\) 4.50000 + 7.79423i 0.177878 + 0.308094i
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 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
\(646\) −1.00000 + 1.73205i −0.0393445 + 0.0681466i
\(647\) −4.50000 7.79423i −0.176913 0.306423i 0.763908 0.645325i \(-0.223278\pi\)
−0.940822 + 0.338902i \(0.889945\pi\)
\(648\) 13.5000 + 23.3827i 0.530330 + 0.918559i
\(649\) −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
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) −21.0000 −0.821165
\(655\) −7.50000 + 12.9904i −0.293049 + 0.507576i
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) 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 \(-0.357729\pi\)
\(660\) −27.0000 −1.05097
\(661\) 4.50000 + 7.79423i 0.175030 + 0.303160i 0.940172 0.340701i \(-0.110665\pi\)
−0.765142 + 0.643862i \(0.777331\pi\)
\(662\) 14.5000 25.1147i 0.563559 0.976112i
\(663\) −15.0000 + 15.5885i −0.582552 + 0.605406i
\(664\) 0 0
\(665\) −6.00000 + 5.19615i −0.232670 + 0.201498i
\(666\) −6.00000 + 10.3923i −0.232495 + 0.402694i
\(667\) 0 0
\(668\) −6.50000 + 11.2583i −0.251493 + 0.435598i
\(669\) 27.0000 1.04388
\(670\) 4.50000 7.79423i 0.173850 0.301117i
\(671\) 39.0000 1.50558
\(672\) 37.5000 + 12.9904i 1.44659 + 0.501115i
\(673\) 20.5000 35.5070i 0.790217 1.36870i −0.135615 0.990762i \(-0.543301\pi\)
0.925832 0.377934i \(-0.123365\pi\)
\(674\) 14.0000 0.539260
\(675\) 18.0000 31.1769i 0.692820 1.20000i
\(676\) 11.0000 6.92820i 0.423077 0.266469i
\(677\) −3.50000 6.06218i −0.134516 0.232988i 0.790897 0.611950i \(-0.209615\pi\)
−0.925412 + 0.378962i \(0.876281\pi\)
\(678\) 22.5000 38.9711i 0.864107 1.49668i
\(679\) 12.5000 + 4.33013i 0.479706 + 0.166175i
\(680\) −9.00000 15.5885i −0.345134 0.597790i
\(681\) −6.00000 10.3923i −0.229920 0.398234i
\(682\) −9.00000 −0.344628
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −3.00000 5.19615i −0.114708 0.198680i
\(685\) −15.0000 25.9808i −0.573121 0.992674i
\(686\) −10.0000 15.5885i −0.381802 0.595170i
\(687\) −19.5000 + 33.7750i −0.743971 + 1.28860i
\(688\) −3.50000 6.06218i −0.133436 0.231118i
\(689\) 10.5000 + 2.59808i 0.400018 + 0.0989788i
\(690\) 0 0
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) 9.50000 16.4545i 0.361136 0.625506i
\(693\) −36.0000 + 31.1769i −1.36753 + 1.18431i
\(694\) −8.00000 −0.303676
\(695\) 22.5000 38.9711i 0.853474 1.47826i
\(696\) 63.0000 2.38801
\(697\) 3.00000 5.19615i 0.113633 0.196818i
\(698\) −11.5000 + 19.9186i −0.435281 + 0.753930i
\(699\) −31.5000 + 54.5596i −1.19144 + 2.06363i
\(700\) −2.00000 10.3923i −0.0755929 0.392792i
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 9.00000 + 31.1769i 0.339683 + 1.17670i
\(703\) 1.00000 1.73205i 0.0377157 0.0653255i
\(704\) 10.5000 + 18.1865i 0.395734 + 0.685431i
\(705\) −9.00000 −0.338960
\(706\) 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
\(709\) −5.50000 + 9.52628i −0.206557 + 0.357767i −0.950628 0.310334i \(-0.899559\pi\)
0.744071 + 0.668101i \(0.232892\pi\)
\(710\) −19.5000 + 33.7750i −0.731822 + 1.26755i
\(711\) −18.0000 −0.675053
\(712\) −18.0000 −0.674579
\(713\) 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
\(717\) −6.00000 10.3923i −0.224074 0.388108i
\(718\) −8.50000 14.7224i −0.317217 0.549436i
\(719\) 4.50000 7.79423i 0.167822 0.290676i −0.769832 0.638247i \(-0.779660\pi\)
0.937654 + 0.347571i \(0.112993\pi\)
\(720\) −18.0000 −0.670820
\(721\) −12.5000 4.33013i −0.465524 0.161262i
\(722\) 9.00000 + 15.5885i 0.334945 + 0.580142i
\(723\) −39.0000 67.5500i −1.45043 2.51221i
\(724\) 22.0000 0.817624
\(725\) −14.0000 24.2487i −0.519947 0.900575i
\(726\) 6.00000 0.222681
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 24.0000 + 15.5885i 0.889499 + 0.577747i
\(729\) −27.0000 −1.00000
\(730\) −39.0000 −1.44345
\(731\) −7.00000 12.1244i −0.258904 0.448435i
\(732\) −39.0000 −1.44148
\(733\) 4.50000 + 7.79423i 0.166211 + 0.287886i 0.937085 0.349102i \(-0.113513\pi\)
−0.770873 + 0.636988i \(0.780180\pi\)
\(734\) 15.5000 + 26.8468i 0.572115 + 0.990933i
\(735\) −49.5000 38.9711i −1.82584 1.43747i
\(736\) 0 0
\(737\) −4.50000 + 7.79423i −0.165760 + 0.287104i
\(738\) −9.00000 15.5885i −0.331295 0.573819i
\(739\) −0.500000 0.866025i −0.0183928 0.0318573i 0.856683 0.515844i \(-0.172522\pi\)
−0.875075 + 0.483987i \(0.839188\pi\)
\(740\) 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 \(0.781612\pi\)
\(744\) 27.0000 0.989868
\(745\) 45.0000 1.64867
\(746\) 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
\(751\) 28.0000 1.02173 0.510867 0.859660i \(-0.329324\pi\)
0.510867 + 0.859660i \(0.329324\pi\)
\(752\) 0.500000 + 0.866025i 0.0182331 + 0.0315807i
\(753\) −34.5000 + 59.7558i −1.25725 + 2.17762i
\(754\) 24.5000 + 6.06218i 0.892237 + 0.220771i
\(755\) −63.0000 −2.29280
\(756\) 18.0000 15.5885i 0.654654 0.566947i
\(757\) −1.50000 + 2.59808i −0.0545184 + 0.0944287i −0.891997 0.452042i \(-0.850696\pi\)
0.837478 + 0.546471i \(0.184029\pi\)
\(758\) 16.5000 28.5788i 0.599307 1.03803i
\(759\) 0 0
\(760\) 9.00000 0.326464
\(761\) 4.50000 7.79423i 0.163125 0.282541i −0.772863 0.634573i \(-0.781176\pi\)
0.935988 + 0.352032i \(0.114509\pi\)
\(762\) −33.0000 −1.19546
\(763\) 3.50000 + 18.1865i 0.126709 + 0.658397i
\(764\) −8.50000 + 14.7224i −0.307519 + 0.532639i
\(765\) −36.0000 −1.30158
\(766\) 10.5000 18.1865i 0.379380 0.657106i
\(767\) 4.00000 + 13.8564i 0.144432 + 0.500326i
\(768\) −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 \(0.277967\pi\)
\(770\) −4.50000 23.3827i −0.162169 0.842654i
\(771\) −3.00000 5.19615i −0.108042 0.187135i
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) −42.0000 −1.50966
\(775\) −6.00000 10.3923i −0.215526 0.373303i
\(776\) −7.50000 12.9904i −0.269234 0.466328i
\(777\) 15.0000 + 5.19615i 0.538122 + 0.186411i
\(778\) 16.5000 28.5788i 0.591554