Properties

Label 637.2.g.b.373.1
Level $637$
Weight $2$
Character 637.373
Analytic conductor $5.086$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(0.809017 + 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 637.373
Dual form 637.2.g.b.263.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30902 - 2.26728i) q^{2} -2.61803 q^{3} +(-2.42705 + 4.20378i) q^{4} +(-1.30902 + 2.26728i) q^{5} +(3.42705 + 5.93583i) q^{6} +7.47214 q^{8} +3.85410 q^{9} +O(q^{10})\) \(q+(-1.30902 - 2.26728i) q^{2} -2.61803 q^{3} +(-2.42705 + 4.20378i) q^{4} +(-1.30902 + 2.26728i) q^{5} +(3.42705 + 5.93583i) q^{6} +7.47214 q^{8} +3.85410 q^{9} +6.85410 q^{10} +1.85410 q^{11} +(6.35410 - 11.0056i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(3.42705 - 5.93583i) q^{15} +(-4.92705 - 8.53390i) q^{16} +(0.736068 - 1.27491i) q^{17} +(-5.04508 - 8.73834i) q^{18} -1.85410 q^{19} +(-6.35410 - 11.0056i) q^{20} +(-2.42705 - 4.20378i) q^{22} +(2.23607 + 3.87298i) q^{23} -19.5623 q^{24} +(-0.927051 - 1.60570i) q^{25} +(9.16312 + 2.26728i) q^{26} -2.23607 q^{27} +(-3.54508 + 6.14027i) q^{29} -17.9443 q^{30} +(2.35410 + 4.07742i) q^{31} +(-5.42705 + 9.39993i) q^{32} -4.85410 q^{33} -3.85410 q^{34} +(-9.35410 + 16.2018i) q^{36} +(-2.00000 - 3.46410i) q^{37} +(2.42705 + 4.20378i) q^{38} +(6.54508 - 6.80185i) q^{39} +(-9.78115 + 16.9415i) q^{40} +(-0.381966 + 0.661585i) q^{41} +(-6.28115 - 10.8793i) q^{43} +(-4.50000 + 7.79423i) q^{44} +(-5.04508 + 8.73834i) q^{45} +(5.85410 - 10.1396i) q^{46} +(1.11803 - 1.93649i) q^{47} +(12.8992 + 22.3420i) q^{48} +(-2.42705 + 4.20378i) q^{50} +(-1.92705 + 3.33775i) q^{51} +(-4.85410 - 16.8151i) q^{52} +(-1.88197 - 3.25966i) q^{53} +(2.92705 + 5.06980i) q^{54} +(-2.42705 + 4.20378i) q^{55} +4.85410 q^{57} +18.5623 q^{58} +(1.11803 - 1.93649i) q^{59} +(16.6353 + 28.8131i) q^{60} -6.00000 q^{61} +(6.16312 - 10.6748i) q^{62} +8.70820 q^{64} +(-2.61803 - 9.06914i) q^{65} +(6.35410 + 11.0056i) q^{66} -12.7082 q^{67} +(3.57295 + 6.18853i) q^{68} +(-5.85410 - 10.1396i) q^{69} +(7.09017 + 12.2805i) q^{71} +28.7984 q^{72} +(1.00000 + 1.73205i) q^{73} +(-5.23607 + 9.06914i) q^{74} +(2.42705 + 4.20378i) q^{75} +(4.50000 - 7.79423i) q^{76} +(-23.9894 - 5.93583i) q^{78} +(-2.00000 + 3.46410i) q^{79} +25.7984 q^{80} -5.70820 q^{81} +2.00000 q^{82} +6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} +(-16.4443 + 28.4823i) q^{86} +(9.28115 - 16.0754i) q^{87} +13.8541 q^{88} +(-2.45492 - 4.25204i) q^{89} +26.4164 q^{90} -21.7082 q^{92} +(-6.16312 - 10.6748i) q^{93} -5.85410 q^{94} +(2.42705 - 4.20378i) q^{95} +(14.2082 - 24.6093i) q^{96} +(-9.42705 - 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{2} - 6q^{3} - 3q^{4} - 3q^{5} + 7q^{6} + 12q^{8} + 2q^{9} + O(q^{10}) \) \( 4q - 3q^{2} - 6q^{3} - 3q^{4} - 3q^{5} + 7q^{6} + 12q^{8} + 2q^{9} + 14q^{10} - 6q^{11} + 12q^{12} - 10q^{13} + 7q^{15} - 13q^{16} - 6q^{17} - 9q^{18} + 6q^{19} - 12q^{20} - 3q^{22} - 38q^{24} + 3q^{25} + 21q^{26} - 3q^{29} - 36q^{30} - 4q^{31} - 15q^{32} - 6q^{33} - 2q^{34} - 24q^{36} - 8q^{37} + 3q^{38} + 15q^{39} - 19q^{40} - 6q^{41} - 5q^{43} - 18q^{44} - 9q^{45} + 10q^{46} + 27q^{48} - 3q^{50} - q^{51} - 6q^{52} - 12q^{53} + 5q^{54} - 3q^{55} + 6q^{57} + 34q^{58} + 33q^{60} - 24q^{61} + 9q^{62} + 8q^{64} - 6q^{65} + 12q^{66} - 24q^{67} + 21q^{68} - 10q^{69} + 6q^{71} + 66q^{72} + 4q^{73} - 12q^{74} + 3q^{75} + 18q^{76} - 49q^{78} - 8q^{79} + 54q^{80} + 4q^{81} + 8q^{82} + q^{85} - 30q^{86} + 17q^{87} + 42q^{88} - 21q^{89} + 52q^{90} - 60q^{92} - 9q^{93} - 10q^{94} + 3q^{95} + 30q^{96} - 31q^{97} + 42q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30902 2.26728i −0.925615 1.60321i −0.790569 0.612372i \(-0.790215\pi\)
−0.135045 0.990839i \(-0.543118\pi\)
\(3\) −2.61803 −1.51152 −0.755761 0.654847i \(-0.772733\pi\)
−0.755761 + 0.654847i \(0.772733\pi\)
\(4\) −2.42705 + 4.20378i −1.21353 + 2.10189i
\(5\) −1.30902 + 2.26728i −0.585410 + 1.01396i 0.409414 + 0.912349i \(0.365733\pi\)
−0.994824 + 0.101611i \(0.967600\pi\)
\(6\) 3.42705 + 5.93583i 1.39909 + 2.42329i
\(7\) 0 0
\(8\) 7.47214 2.64180
\(9\) 3.85410 1.28470
\(10\) 6.85410 2.16746
\(11\) 1.85410 0.559033 0.279516 0.960141i \(-0.409826\pi\)
0.279516 + 0.960141i \(0.409826\pi\)
\(12\) 6.35410 11.0056i 1.83427 3.17705i
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 0 0
\(15\) 3.42705 5.93583i 0.884861 1.53262i
\(16\) −4.92705 8.53390i −1.23176 2.13348i
\(17\) 0.736068 1.27491i 0.178523 0.309210i −0.762852 0.646573i \(-0.776202\pi\)
0.941375 + 0.337363i \(0.109535\pi\)
\(18\) −5.04508 8.73834i −1.18914 2.05965i
\(19\) −1.85410 −0.425360 −0.212680 0.977122i \(-0.568219\pi\)
−0.212680 + 0.977122i \(0.568219\pi\)
\(20\) −6.35410 11.0056i −1.42082 2.46093i
\(21\) 0 0
\(22\) −2.42705 4.20378i −0.517449 0.896248i
\(23\) 2.23607 + 3.87298i 0.466252 + 0.807573i 0.999257 0.0385394i \(-0.0122705\pi\)
−0.533005 + 0.846112i \(0.678937\pi\)
\(24\) −19.5623 −3.99314
\(25\) −0.927051 1.60570i −0.185410 0.321140i
\(26\) 9.16312 + 2.26728i 1.79704 + 0.444651i
\(27\) −2.23607 −0.430331
\(28\) 0 0
\(29\) −3.54508 + 6.14027i −0.658306 + 1.14022i 0.322748 + 0.946485i \(0.395393\pi\)
−0.981054 + 0.193734i \(0.937940\pi\)
\(30\) −17.9443 −3.27616
\(31\) 2.35410 + 4.07742i 0.422809 + 0.732327i 0.996213 0.0869459i \(-0.0277107\pi\)
−0.573404 + 0.819273i \(0.694377\pi\)
\(32\) −5.42705 + 9.39993i −0.959376 + 1.66169i
\(33\) −4.85410 −0.844991
\(34\) −3.85410 −0.660973
\(35\) 0 0
\(36\) −9.35410 + 16.2018i −1.55902 + 2.70030i
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 2.42705 + 4.20378i 0.393720 + 0.681942i
\(39\) 6.54508 6.80185i 1.04805 1.08917i
\(40\) −9.78115 + 16.9415i −1.54654 + 2.67868i
\(41\) −0.381966 + 0.661585i −0.0596531 + 0.103322i −0.894310 0.447449i \(-0.852333\pi\)
0.834657 + 0.550771i \(0.185666\pi\)
\(42\) 0 0
\(43\) −6.28115 10.8793i −0.957867 1.65907i −0.727667 0.685931i \(-0.759395\pi\)
−0.230200 0.973143i \(-0.573938\pi\)
\(44\) −4.50000 + 7.79423i −0.678401 + 1.17502i
\(45\) −5.04508 + 8.73834i −0.752077 + 1.30264i
\(46\) 5.85410 10.1396i 0.863140 1.49500i
\(47\) 1.11803 1.93649i 0.163082 0.282466i −0.772890 0.634539i \(-0.781190\pi\)
0.935973 + 0.352073i \(0.114523\pi\)
\(48\) 12.8992 + 22.3420i 1.86184 + 3.22480i
\(49\) 0 0
\(50\) −2.42705 + 4.20378i −0.343237 + 0.594504i
\(51\) −1.92705 + 3.33775i −0.269841 + 0.467379i
\(52\) −4.85410 16.8151i −0.673143 2.33184i
\(53\) −1.88197 3.25966i −0.258508 0.447749i 0.707334 0.706879i \(-0.249897\pi\)
−0.965842 + 0.259130i \(0.916564\pi\)
\(54\) 2.92705 + 5.06980i 0.398321 + 0.689913i
\(55\) −2.42705 + 4.20378i −0.327263 + 0.566837i
\(56\) 0 0
\(57\) 4.85410 0.642942
\(58\) 18.5623 2.43735
\(59\) 1.11803 1.93649i 0.145556 0.252110i −0.784024 0.620730i \(-0.786836\pi\)
0.929580 + 0.368620i \(0.120170\pi\)
\(60\) 16.6353 + 28.8131i 2.14760 + 3.71976i
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 6.16312 10.6748i 0.782717 1.35571i
\(63\) 0 0
\(64\) 8.70820 1.08853
\(65\) −2.61803 9.06914i −0.324727 1.12489i
\(66\) 6.35410 + 11.0056i 0.782136 + 1.35470i
\(67\) −12.7082 −1.55255 −0.776277 0.630392i \(-0.782894\pi\)
−0.776277 + 0.630392i \(0.782894\pi\)
\(68\) 3.57295 + 6.18853i 0.433284 + 0.750469i
\(69\) −5.85410 10.1396i −0.704751 1.22066i
\(70\) 0 0
\(71\) 7.09017 + 12.2805i 0.841448 + 1.45743i 0.888670 + 0.458547i \(0.151630\pi\)
−0.0472218 + 0.998884i \(0.515037\pi\)
\(72\) 28.7984 3.39392
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) −5.23607 + 9.06914i −0.608681 + 1.05427i
\(75\) 2.42705 + 4.20378i 0.280252 + 0.485410i
\(76\) 4.50000 7.79423i 0.516185 0.894059i
\(77\) 0 0
\(78\) −23.9894 5.93583i −2.71626 0.672100i
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 25.7984 2.88435
\(81\) −5.70820 −0.634245
\(82\) 2.00000 0.220863
\(83\) 6.70820 0.736321 0.368161 0.929762i \(-0.379988\pi\)
0.368161 + 0.929762i \(0.379988\pi\)
\(84\) 0 0
\(85\) 1.92705 + 3.33775i 0.209018 + 0.362030i
\(86\) −16.4443 + 28.4823i −1.77323 + 3.07133i
\(87\) 9.28115 16.0754i 0.995044 1.72347i
\(88\) 13.8541 1.47685
\(89\) −2.45492 4.25204i −0.260220 0.450715i 0.706080 0.708132i \(-0.250462\pi\)
−0.966300 + 0.257417i \(0.917129\pi\)
\(90\) 26.4164 2.78453
\(91\) 0 0
\(92\) −21.7082 −2.26324
\(93\) −6.16312 10.6748i −0.639086 1.10693i
\(94\) −5.85410 −0.603805
\(95\) 2.42705 4.20378i 0.249010 0.431298i
\(96\) 14.2082 24.6093i 1.45012 2.51168i
\(97\) −9.42705 16.3281i −0.957172 1.65787i −0.729318 0.684175i \(-0.760162\pi\)
−0.227854 0.973695i \(-0.573171\pi\)
\(98\) 0 0
\(99\) 7.14590 0.718190
\(100\) 9.00000 0.900000
\(101\) −11.5623 −1.15049 −0.575246 0.817980i \(-0.695094\pi\)
−0.575246 + 0.817980i \(0.695094\pi\)
\(102\) 10.0902 0.999076
\(103\) 4.35410 7.54153i 0.429022 0.743089i −0.567764 0.823191i \(-0.692191\pi\)
0.996787 + 0.0801026i \(0.0255248\pi\)
\(104\) −18.6803 + 19.4132i −1.83176 + 1.90362i
\(105\) 0 0
\(106\) −4.92705 + 8.53390i −0.478557 + 0.828886i
\(107\) 1.69098 + 2.92887i 0.163473 + 0.283144i 0.936112 0.351702i \(-0.114397\pi\)
−0.772639 + 0.634846i \(0.781064\pi\)
\(108\) 5.42705 9.39993i 0.522218 0.904508i
\(109\) 1.35410 + 2.34537i 0.129699 + 0.224646i 0.923560 0.383454i \(-0.125265\pi\)
−0.793861 + 0.608100i \(0.791932\pi\)
\(110\) 12.7082 1.21168
\(111\) 5.23607 + 9.06914i 0.496986 + 0.860804i
\(112\) 0 0
\(113\) −0.736068 1.27491i −0.0692435 0.119933i 0.829325 0.558766i \(-0.188725\pi\)
−0.898568 + 0.438833i \(0.855392\pi\)
\(114\) −6.35410 11.0056i −0.595116 1.03077i
\(115\) −11.7082 −1.09180
\(116\) −17.2082 29.8055i −1.59774 2.76737i
\(117\) −9.63525 + 10.0133i −0.890780 + 0.925725i
\(118\) −5.85410 −0.538914
\(119\) 0 0
\(120\) 25.6074 44.3533i 2.33762 4.04888i
\(121\) −7.56231 −0.687482
\(122\) 7.85410 + 13.6037i 0.711077 + 1.23162i
\(123\) 1.00000 1.73205i 0.0901670 0.156174i
\(124\) −22.8541 −2.05236
\(125\) −8.23607 −0.736656
\(126\) 0 0
\(127\) 10.4271 18.0602i 0.925251 1.60258i 0.134094 0.990969i \(-0.457187\pi\)
0.791157 0.611613i \(-0.209479\pi\)
\(128\) −0.545085 0.944115i −0.0481792 0.0834488i
\(129\) 16.4443 + 28.4823i 1.44784 + 2.50773i
\(130\) −17.1353 + 17.8075i −1.50286 + 1.56182i
\(131\) 7.66312 13.2729i 0.669530 1.15966i −0.308506 0.951222i \(-0.599829\pi\)
0.978036 0.208437i \(-0.0668377\pi\)
\(132\) 11.7812 20.4056i 1.02542 1.77608i
\(133\) 0 0
\(134\) 16.6353 + 28.8131i 1.43707 + 2.48907i
\(135\) 2.92705 5.06980i 0.251920 0.436339i
\(136\) 5.50000 9.52628i 0.471621 0.816872i
\(137\) 1.30902 2.26728i 0.111837 0.193707i −0.804674 0.593717i \(-0.797660\pi\)
0.916511 + 0.400010i \(0.130993\pi\)
\(138\) −15.3262 + 26.5458i −1.30466 + 2.25973i
\(139\) −2.28115 3.95107i −0.193485 0.335126i 0.752918 0.658114i \(-0.228646\pi\)
−0.946403 + 0.322989i \(0.895312\pi\)
\(140\) 0 0
\(141\) −2.92705 + 5.06980i −0.246502 + 0.426954i
\(142\) 18.5623 32.1509i 1.55771 2.69804i
\(143\) −4.63525 + 4.81710i −0.387619 + 0.402826i
\(144\) −18.9894 32.8905i −1.58245 2.74088i
\(145\) −9.28115 16.0754i −0.770758 1.33499i
\(146\) 2.61803 4.53457i 0.216670 0.375284i
\(147\) 0 0
\(148\) 19.4164 1.59602
\(149\) 1.85410 0.151894 0.0759470 0.997112i \(-0.475802\pi\)
0.0759470 + 0.997112i \(0.475802\pi\)
\(150\) 6.35410 11.0056i 0.518810 0.898606i
\(151\) 0.645898 + 1.11873i 0.0525624 + 0.0910408i 0.891109 0.453788i \(-0.149928\pi\)
−0.838547 + 0.544829i \(0.816594\pi\)
\(152\) −13.8541 −1.12372
\(153\) 2.83688 4.91362i 0.229348 0.397243i
\(154\) 0 0
\(155\) −12.3262 −0.990067
\(156\) 12.7082 + 44.0225i 1.01747 + 3.52462i
\(157\) −7.42705 12.8640i −0.592743 1.02666i −0.993861 0.110635i \(-0.964712\pi\)
0.401118 0.916026i \(-0.368622\pi\)
\(158\) 10.4721 0.833118
\(159\) 4.92705 + 8.53390i 0.390741 + 0.676783i
\(160\) −14.2082 24.6093i −1.12326 1.94554i
\(161\) 0 0
\(162\) 7.47214 + 12.9421i 0.587066 + 1.01683i
\(163\) −3.70820 −0.290449 −0.145224 0.989399i \(-0.546390\pi\)
−0.145224 + 0.989399i \(0.546390\pi\)
\(164\) −1.85410 3.21140i −0.144781 0.250768i
\(165\) 6.35410 11.0056i 0.494666 0.856787i
\(166\) −8.78115 15.2094i −0.681550 1.18048i
\(167\) −7.11803 + 12.3288i −0.550810 + 0.954031i 0.447406 + 0.894331i \(0.352348\pi\)
−0.998216 + 0.0597001i \(0.980986\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 5.04508 8.73834i 0.386940 0.670200i
\(171\) −7.14590 −0.546460
\(172\) 60.9787 4.64958
\(173\) −9.00000 −0.684257 −0.342129 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) −48.5967 −3.68411
\(175\) 0 0
\(176\) −9.13525 15.8227i −0.688596 1.19268i
\(177\) −2.92705 + 5.06980i −0.220011 + 0.381070i
\(178\) −6.42705 + 11.1320i −0.481728 + 0.834377i
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −24.4894 42.4168i −1.82533 3.16156i
\(181\) 9.70820 0.721605 0.360803 0.932642i \(-0.382503\pi\)
0.360803 + 0.932642i \(0.382503\pi\)
\(182\) 0 0
\(183\) 15.7082 1.16118
\(184\) 16.7082 + 28.9395i 1.23175 + 2.13345i
\(185\) 10.4721 0.769927
\(186\) −16.1353 + 27.9471i −1.18309 + 2.04918i
\(187\) 1.36475 2.36381i 0.0998000 0.172859i
\(188\) 5.42705 + 9.39993i 0.395808 + 0.685560i
\(189\) 0 0
\(190\) −12.7082 −0.921950
\(191\) 21.3820 1.54714 0.773572 0.633708i \(-0.218468\pi\)
0.773572 + 0.633708i \(0.218468\pi\)
\(192\) −22.7984 −1.64533
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) −24.6803 + 42.7476i −1.77195 + 3.06910i
\(195\) 6.85410 + 23.7433i 0.490832 + 1.70029i
\(196\) 0 0
\(197\) 8.39919 14.5478i 0.598417 1.03649i −0.394638 0.918837i \(-0.629130\pi\)
0.993055 0.117652i \(-0.0375368\pi\)
\(198\) −9.35410 16.2018i −0.664767 1.15141i
\(199\) 12.2082 21.1452i 0.865417 1.49895i −0.00121626 0.999999i \(-0.500387\pi\)
0.866633 0.498946i \(-0.166280\pi\)
\(200\) −6.92705 11.9980i −0.489816 0.848387i
\(201\) 33.2705 2.34672
\(202\) 15.1353 + 26.2150i 1.06491 + 1.84448i
\(203\) 0 0
\(204\) −9.35410 16.2018i −0.654918 1.13435i
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) −22.7984 −1.58844
\(207\) 8.61803 + 14.9269i 0.598995 + 1.03749i
\(208\) 34.4894 + 8.53390i 2.39141 + 0.591720i
\(209\) −3.43769 −0.237790
\(210\) 0 0
\(211\) −2.35410 + 4.07742i −0.162063 + 0.280701i −0.935608 0.353039i \(-0.885148\pi\)
0.773545 + 0.633741i \(0.218481\pi\)
\(212\) 18.2705 1.25482
\(213\) −18.5623 32.1509i −1.27187 2.20294i
\(214\) 4.42705 7.66788i 0.302627 0.524165i
\(215\) 32.8885 2.24298
\(216\) −16.7082 −1.13685
\(217\) 0 0
\(218\) 3.54508 6.14027i 0.240103 0.415871i
\(219\) −2.61803 4.53457i −0.176910 0.306418i
\(220\) −11.7812 20.4056i −0.794285 1.37574i
\(221\) 1.47214 + 5.09963i 0.0990266 + 0.343038i
\(222\) 13.7082 23.7433i 0.920034 1.59355i
\(223\) −10.1353 + 17.5548i −0.678707 + 1.17555i 0.296664 + 0.954982i \(0.404126\pi\)
−0.975371 + 0.220573i \(0.929207\pi\)
\(224\) 0 0
\(225\) −3.57295 6.18853i −0.238197 0.412569i
\(226\) −1.92705 + 3.33775i −0.128186 + 0.222024i
\(227\) −0.736068 + 1.27491i −0.0488545 + 0.0846186i −0.889419 0.457094i \(-0.848890\pi\)
0.840564 + 0.541712i \(0.182224\pi\)
\(228\) −11.7812 + 20.4056i −0.780226 + 1.35139i
\(229\) 6.56231 11.3662i 0.433649 0.751103i −0.563535 0.826092i \(-0.690559\pi\)
0.997184 + 0.0749895i \(0.0238923\pi\)
\(230\) 15.3262 + 26.5458i 1.01058 + 1.75038i
\(231\) 0 0
\(232\) −26.4894 + 45.8809i −1.73911 + 3.01223i
\(233\) −1.30902 + 2.26728i −0.0857566 + 0.148535i −0.905713 0.423891i \(-0.860664\pi\)
0.819957 + 0.572425i \(0.193997\pi\)
\(234\) 35.3156 + 8.73834i 2.30865 + 0.571243i
\(235\) 2.92705 + 5.06980i 0.190940 + 0.330717i
\(236\) 5.42705 + 9.39993i 0.353271 + 0.611883i
\(237\) 5.23607 9.06914i 0.340119 0.589104i
\(238\) 0 0
\(239\) −24.7082 −1.59824 −0.799120 0.601171i \(-0.794701\pi\)
−0.799120 + 0.601171i \(0.794701\pi\)
\(240\) −67.5410 −4.35975
\(241\) −12.2812 + 21.2716i −0.791099 + 1.37022i 0.134189 + 0.990956i \(0.457157\pi\)
−0.925287 + 0.379267i \(0.876176\pi\)
\(242\) 9.89919 + 17.1459i 0.636344 + 1.10218i
\(243\) 21.6525 1.38901
\(244\) 14.5623 25.2227i 0.932256 1.61471i
\(245\) 0 0
\(246\) −5.23607 −0.333840
\(247\) 4.63525 4.81710i 0.294934 0.306505i
\(248\) 17.5902 + 30.4671i 1.11698 + 1.93466i
\(249\) −17.5623 −1.11297
\(250\) 10.7812 + 18.6735i 0.681860 + 1.18102i
\(251\) −0.381966 0.661585i −0.0241095 0.0417588i 0.853719 0.520734i \(-0.174342\pi\)
−0.877828 + 0.478975i \(0.841008\pi\)
\(252\) 0 0
\(253\) 4.14590 + 7.18091i 0.260650 + 0.451460i
\(254\) −54.5967 −3.42570
\(255\) −5.04508 8.73834i −0.315935 0.547216i
\(256\) 7.28115 12.6113i 0.455072 0.788208i
\(257\) −8.37132 14.4996i −0.522189 0.904457i −0.999667 0.0258138i \(-0.991782\pi\)
0.477478 0.878644i \(-0.341551\pi\)
\(258\) 43.0517 74.5677i 2.68028 4.64238i
\(259\) 0 0
\(260\) 44.4787 + 11.0056i 2.75845 + 0.682540i
\(261\) −13.6631 + 23.6652i −0.845726 + 1.46484i
\(262\) −40.1246 −2.47891
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) −36.2705 −2.23230
\(265\) 9.85410 0.605333
\(266\) 0 0
\(267\) 6.42705 + 11.1320i 0.393329 + 0.681266i
\(268\) 30.8435 53.4224i 1.88406 3.26329i
\(269\) 14.3713 24.8919i 0.876235 1.51768i 0.0207937 0.999784i \(-0.493381\pi\)
0.855441 0.517900i \(-0.173286\pi\)
\(270\) −15.3262 −0.932725
\(271\) 4.20820 + 7.28882i 0.255630 + 0.442764i 0.965066 0.262005i \(-0.0843837\pi\)
−0.709436 + 0.704770i \(0.751050\pi\)
\(272\) −14.5066 −0.879590
\(273\) 0 0
\(274\) −6.85410 −0.414071
\(275\) −1.71885 2.97713i −0.103650 0.179528i
\(276\) 56.8328 3.42093
\(277\) 2.50000 4.33013i 0.150210 0.260172i −0.781094 0.624413i \(-0.785338\pi\)
0.931305 + 0.364241i \(0.118672\pi\)
\(278\) −5.97214 + 10.3440i −0.358185 + 0.620394i
\(279\) 9.07295 + 15.7148i 0.543183 + 0.940821i
\(280\) 0 0
\(281\) 20.1803 1.20386 0.601929 0.798550i \(-0.294399\pi\)
0.601929 + 0.798550i \(0.294399\pi\)
\(282\) 15.3262 0.912664
\(283\) 13.4164 0.797523 0.398761 0.917055i \(-0.369440\pi\)
0.398761 + 0.917055i \(0.369440\pi\)
\(284\) −68.8328 −4.08448
\(285\) −6.35410 + 11.0056i −0.376385 + 0.651917i
\(286\) 16.9894 + 4.20378i 1.00460 + 0.248574i
\(287\) 0 0
\(288\) −20.9164 + 36.2283i −1.23251 + 2.13477i
\(289\) 7.41641 + 12.8456i 0.436259 + 0.755623i
\(290\) −24.2984 + 42.0860i −1.42685 + 2.47138i
\(291\) 24.6803 + 42.7476i 1.44679 + 2.50591i
\(292\) −9.70820 −0.568130
\(293\) 3.38197 + 5.85774i 0.197577 + 0.342213i 0.947742 0.319037i \(-0.103360\pi\)
−0.750166 + 0.661250i \(0.770026\pi\)
\(294\) 0 0
\(295\) 2.92705 + 5.06980i 0.170419 + 0.295175i
\(296\) −14.9443 25.8842i −0.868618 1.50449i
\(297\) −4.14590 −0.240569
\(298\) −2.42705 4.20378i −0.140595 0.243518i
\(299\) −15.6525 3.87298i −0.905206 0.223980i
\(300\) −23.5623 −1.36037
\(301\) 0 0
\(302\) 1.69098 2.92887i 0.0973051 0.168537i
\(303\) 30.2705 1.73900
\(304\) 9.13525 + 15.8227i 0.523943 + 0.907496i
\(305\) 7.85410 13.6037i 0.449725 0.778946i
\(306\) −14.8541 −0.849152
\(307\) −4.85410 −0.277038 −0.138519 0.990360i \(-0.544234\pi\)
−0.138519 + 0.990360i \(0.544234\pi\)
\(308\) 0 0
\(309\) −11.3992 + 19.7440i −0.648477 + 1.12320i
\(310\) 16.1353 + 27.9471i 0.916421 + 1.58729i
\(311\) −1.66312 2.88061i −0.0943068 0.163344i 0.815012 0.579444i \(-0.196730\pi\)
−0.909319 + 0.416099i \(0.863397\pi\)
\(312\) 48.9058 50.8244i 2.76874 2.87736i
\(313\) −12.5623 + 21.7586i −0.710064 + 1.22987i 0.254769 + 0.967002i \(0.418000\pi\)
−0.964833 + 0.262864i \(0.915333\pi\)
\(314\) −19.4443 + 33.6785i −1.09730 + 1.90059i
\(315\) 0 0
\(316\) −9.70820 16.8151i −0.546129 0.945923i
\(317\) −13.1180 + 22.7211i −0.736782 + 1.27614i 0.217155 + 0.976137i \(0.430322\pi\)
−0.953937 + 0.300007i \(0.903011\pi\)
\(318\) 12.8992 22.3420i 0.723350 1.25288i
\(319\) −6.57295 + 11.3847i −0.368014 + 0.637420i
\(320\) −11.3992 + 19.7440i −0.637234 + 1.10372i
\(321\) −4.42705 7.66788i −0.247094 0.427979i
\(322\) 0 0
\(323\) −1.36475 + 2.36381i −0.0759364 + 0.131526i
\(324\) 13.8541 23.9960i 0.769672 1.33311i
\(325\) 6.48936 + 1.60570i 0.359965 + 0.0890682i
\(326\) 4.85410 + 8.40755i 0.268844 + 0.465651i
\(327\) −3.54508 6.14027i −0.196044 0.339558i
\(328\) −2.85410 + 4.94345i −0.157591 + 0.272956i
\(329\) 0 0
\(330\) −33.2705 −1.83148
\(331\) −10.1459 −0.557669 −0.278834 0.960339i \(-0.589948\pi\)
−0.278834 + 0.960339i \(0.589948\pi\)
\(332\) −16.2812 + 28.1998i −0.893544 + 1.54766i
\(333\) −7.70820 13.3510i −0.422407 0.731630i
\(334\) 37.2705 2.03935
\(335\) 16.6353 28.8131i 0.908881 1.57423i
\(336\) 0 0
\(337\) −11.5623 −0.629839 −0.314919 0.949118i \(-0.601978\pi\)
−0.314919 + 0.949118i \(0.601978\pi\)
\(338\) −28.7984 + 18.1383i −1.56643 + 0.986592i
\(339\) 1.92705 + 3.33775i 0.104663 + 0.181282i
\(340\) −18.7082 −1.01459
\(341\) 4.36475 + 7.55996i 0.236364 + 0.409395i
\(342\) 9.35410 + 16.2018i 0.505812 + 0.876092i
\(343\) 0 0
\(344\) −46.9336 81.2914i −2.53049 4.38294i
\(345\) 30.6525 1.65027
\(346\) 11.7812 + 20.4056i 0.633359 + 1.09701i
\(347\) −15.3820 + 26.6423i −0.825747 + 1.43024i 0.0755997 + 0.997138i \(0.475913\pi\)
−0.901347 + 0.433098i \(0.857420\pi\)
\(348\) 45.0517 + 78.0318i 2.41502 + 4.18294i
\(349\) −10.3541 + 17.9338i −0.554242 + 0.959976i 0.443720 + 0.896166i \(0.353659\pi\)
−0.997962 + 0.0638103i \(0.979675\pi\)
\(350\) 0 0
\(351\) 5.59017 5.80948i 0.298381 0.310087i
\(352\) −10.0623 + 17.4284i −0.536323 + 0.928938i
\(353\) 22.1459 1.17871 0.589354 0.807875i \(-0.299382\pi\)
0.589354 + 0.807875i \(0.299382\pi\)
\(354\) 15.3262 0.814580
\(355\) −37.1246 −1.97037
\(356\) 23.8328 1.26314
\(357\) 0 0
\(358\) 11.7812 + 20.4056i 0.622653 + 1.07847i
\(359\) 11.0451 19.1306i 0.582937 1.00968i −0.412192 0.911097i \(-0.635237\pi\)
0.995129 0.0985799i \(-0.0314300\pi\)
\(360\) −37.6976 + 65.2941i −1.98684 + 3.44130i
\(361\) −15.5623 −0.819069
\(362\) −12.7082 22.0113i −0.667928 1.15689i
\(363\) 19.7984 1.03915
\(364\) 0 0
\(365\) −5.23607 −0.274068
\(366\) −20.5623 35.6150i −1.07481 1.86162i
\(367\) −1.41641 −0.0739359 −0.0369679 0.999316i \(-0.511770\pi\)
−0.0369679 + 0.999316i \(0.511770\pi\)
\(368\) 22.0344 38.1648i 1.14862 1.98948i
\(369\) −1.47214 + 2.54981i −0.0766363 + 0.132738i
\(370\) −13.7082 23.7433i −0.712656 1.23436i
\(371\) 0 0
\(372\) 59.8328 3.10219
\(373\) −20.5623 −1.06468 −0.532338 0.846532i \(-0.678686\pi\)
−0.532338 + 0.846532i \(0.678686\pi\)
\(374\) −7.14590 −0.369506
\(375\) 21.5623 1.11347
\(376\) 8.35410 14.4697i 0.430830 0.746219i
\(377\) −7.09017 24.5611i −0.365162 1.26496i
\(378\) 0 0
\(379\) 3.07295 5.32250i 0.157847 0.273399i −0.776245 0.630431i \(-0.782878\pi\)
0.934092 + 0.357032i \(0.116211\pi\)
\(380\) 11.7812 + 20.4056i 0.604360 + 1.04678i
\(381\) −27.2984 + 47.2822i −1.39854 + 2.42234i
\(382\) −27.9894 48.4790i −1.43206 2.48040i
\(383\) −21.9787 −1.12306 −0.561530 0.827456i \(-0.689787\pi\)
−0.561530 + 0.827456i \(0.689787\pi\)
\(384\) 1.42705 + 2.47172i 0.0728239 + 0.126135i
\(385\) 0 0
\(386\) 7.85410 + 13.6037i 0.399763 + 0.692410i
\(387\) −24.2082 41.9298i −1.23057 2.13141i
\(388\) 91.5197 4.64621
\(389\) 5.94427 + 10.2958i 0.301387 + 0.522017i 0.976450 0.215743i \(-0.0692172\pi\)
−0.675064 + 0.737759i \(0.735884\pi\)
\(390\) 44.8607 46.6206i 2.27161 2.36073i
\(391\) 6.58359 0.332947
\(392\) 0 0
\(393\) −20.0623 + 34.7489i −1.01201 + 1.75285i
\(394\) −43.9787 −2.21562
\(395\) −5.23607 9.06914i −0.263455 0.456318i
\(396\) −17.3435 + 30.0398i −0.871542 + 1.50955i
\(397\) 1.41641 0.0710875 0.0355437 0.999368i \(-0.488684\pi\)
0.0355437 + 0.999368i \(0.488684\pi\)
\(398\) −63.9230 −3.20417
\(399\) 0 0
\(400\) −9.13525 + 15.8227i −0.456763 + 0.791136i
\(401\) −17.7254 30.7013i −0.885165 1.53315i −0.845524 0.533938i \(-0.820712\pi\)
−0.0396416 0.999214i \(-0.512622\pi\)
\(402\) −43.5517 75.4337i −2.17216 3.76229i
\(403\) −16.4787 4.07742i −0.820863 0.203111i
\(404\) 28.0623 48.6053i 1.39615 2.41821i
\(405\) 7.47214 12.9421i 0.371293 0.643099i
\(406\) 0 0
\(407\) −3.70820 6.42280i −0.183809 0.318366i
\(408\) −14.3992 + 24.9401i −0.712866 + 1.23472i
\(409\) −7.21885 + 12.5034i −0.356949 + 0.618254i −0.987450 0.157935i \(-0.949516\pi\)
0.630500 + 0.776189i \(0.282850\pi\)
\(410\) −2.61803 + 4.53457i −0.129295 + 0.223946i
\(411\) −3.42705 + 5.93583i −0.169044 + 0.292793i
\(412\) 21.1353 + 36.6073i 1.04126 + 1.80351i
\(413\) 0 0
\(414\) 22.5623 39.0791i 1.10888 1.92063i
\(415\) −8.78115 + 15.2094i −0.431050 + 0.746600i
\(416\) −10.8541 37.5997i −0.532166 1.84348i
\(417\) 5.97214 + 10.3440i 0.292457 + 0.506550i
\(418\) 4.50000 + 7.79423i 0.220102 + 0.381228i
\(419\) 5.97214 10.3440i 0.291758 0.505340i −0.682468 0.730916i \(-0.739093\pi\)
0.974226 + 0.225576i \(0.0724265\pi\)
\(420\) 0 0
\(421\) 1.41641 0.0690315 0.0345157 0.999404i \(-0.489011\pi\)
0.0345157 + 0.999404i \(0.489011\pi\)
\(422\) 12.3262 0.600032
\(423\) 4.30902 7.46344i 0.209512 0.362885i
\(424\) −14.0623 24.3566i −0.682926 1.18286i
\(425\) −2.72949 −0.132400
\(426\) −48.5967 + 84.1720i −2.35452 + 4.07815i
\(427\) 0 0
\(428\) −16.4164 −0.793517
\(429\) 12.1353 12.6113i 0.585896 0.608881i
\(430\) −43.0517 74.5677i −2.07614 3.59597i
\(431\) 7.79837 0.375634 0.187817 0.982204i \(-0.439859\pi\)
0.187817 + 0.982204i \(0.439859\pi\)
\(432\) 11.0172 + 19.0824i 0.530066 + 0.918102i
\(433\) −0.500000 0.866025i −0.0240285 0.0416185i 0.853761 0.520665i \(-0.174316\pi\)
−0.877790 + 0.479046i \(0.840983\pi\)
\(434\) 0 0
\(435\) 24.2984 + 42.0860i 1.16502 + 2.01787i
\(436\) −13.1459 −0.629574
\(437\) −4.14590 7.18091i −0.198325 0.343509i
\(438\) −6.85410 + 11.8717i −0.327502 + 0.567250i
\(439\) −7.42705 12.8640i −0.354474 0.613967i 0.632554 0.774516i \(-0.282007\pi\)
−0.987028 + 0.160550i \(0.948673\pi\)
\(440\) −18.1353 + 31.4112i −0.864564 + 1.49747i
\(441\) 0 0
\(442\) 9.63525 10.0133i 0.458302 0.476282i
\(443\) 2.61803 4.53457i 0.124387 0.215444i −0.797106 0.603839i \(-0.793637\pi\)
0.921493 + 0.388395i \(0.126970\pi\)
\(444\) −50.8328 −2.41242
\(445\) 12.8541 0.609343
\(446\) 53.0689 2.51288
\(447\) −4.85410 −0.229591
\(448\) 0 0
\(449\) −9.76393 16.9116i −0.460788 0.798109i 0.538212 0.842809i \(-0.319100\pi\)
−0.999000 + 0.0447005i \(0.985767\pi\)
\(450\) −9.35410 + 16.2018i −0.440957 + 0.763759i
\(451\) −0.708204 + 1.22665i −0.0333480 + 0.0577605i
\(452\) 7.14590 0.336115
\(453\) −1.69098 2.92887i −0.0794493 0.137610i
\(454\) 3.85410 0.180882
\(455\) 0 0
\(456\) 36.2705 1.69852
\(457\) −7.70820 13.3510i −0.360575 0.624533i 0.627481 0.778632i \(-0.284086\pi\)
−0.988055 + 0.154098i \(0.950753\pi\)
\(458\) −34.3607 −1.60557
\(459\) −1.64590 + 2.85078i −0.0768239 + 0.133063i
\(460\) 28.4164 49.2187i 1.32492 2.29483i
\(461\) 6.10739 + 10.5783i 0.284450 + 0.492681i 0.972476 0.233005i \(-0.0748558\pi\)
−0.688026 + 0.725686i \(0.741523\pi\)
\(462\) 0 0
\(463\) 6.70820 0.311757 0.155878 0.987776i \(-0.450179\pi\)
0.155878 + 0.987776i \(0.450179\pi\)
\(464\) 69.8673 3.24351
\(465\) 32.2705 1.49651
\(466\) 6.85410 0.317510
\(467\) −1.17376 + 2.03302i −0.0543152 + 0.0940767i −0.891905 0.452224i \(-0.850631\pi\)
0.837589 + 0.546300i \(0.183964\pi\)
\(468\) −18.7082 64.8071i −0.864787 2.99571i
\(469\) 0 0
\(470\) 7.66312 13.2729i 0.353473 0.612234i
\(471\) 19.4443 + 33.6785i 0.895945 + 1.55182i
\(472\) 8.35410 14.4697i 0.384529 0.666023i
\(473\) −11.6459 20.1713i −0.535479 0.927477i
\(474\) −27.4164 −1.25928
\(475\) 1.71885 + 2.97713i 0.0788661 + 0.136600i
\(476\) 0 0
\(477\) −7.25329 12.5631i −0.332105 0.575223i
\(478\) 32.3435 + 56.0205i 1.47936 + 2.56232i
\(479\) 24.9787 1.14131 0.570653 0.821191i \(-0.306690\pi\)
0.570653 + 0.821191i \(0.306690\pi\)
\(480\) 37.1976 + 64.4281i 1.69783 + 2.94073i
\(481\) 14.0000 + 3.46410i 0.638345 + 0.157949i
\(482\) 64.3050 2.92901
\(483\) 0 0
\(484\) 18.3541 31.7902i 0.834277 1.44501i
\(485\) 49.3607 2.24135
\(486\) −28.3435 49.0923i −1.28569 2.22687i
\(487\) −14.9894 + 25.9623i −0.679233 + 1.17647i 0.295980 + 0.955194i \(0.404354\pi\)
−0.975212 + 0.221271i \(0.928979\pi\)
\(488\) −44.8328 −2.02949
\(489\) 9.70820 0.439020
\(490\) 0 0
\(491\) −6.19098 + 10.7231i −0.279395 + 0.483927i −0.971235 0.238125i \(-0.923467\pi\)
0.691839 + 0.722051i \(0.256801\pi\)
\(492\) 4.85410 + 8.40755i 0.218840 + 0.379042i
\(493\) 5.21885 + 9.03931i 0.235045 + 0.407110i
\(494\) −16.9894 4.20378i −0.764387 0.189137i
\(495\) −9.35410 + 16.2018i −0.420436 + 0.728216i
\(496\) 23.1976 40.1794i 1.04160 1.80411i
\(497\) 0 0
\(498\) 22.9894 + 39.8187i 1.03018 + 1.78432i
\(499\) −7.42705 + 12.8640i −0.332480 + 0.575873i −0.982998 0.183619i \(-0.941219\pi\)
0.650517 + 0.759492i \(0.274552\pi\)
\(500\) 19.9894 34.6226i 0.893951 1.54837i
\(501\) 18.6353 32.2772i 0.832562 1.44204i
\(502\) −1.00000 + 1.73205i −0.0446322 + 0.0773052i
\(503\) −13.3090 23.0519i −0.593420 1.02783i −0.993768 0.111470i \(-0.964444\pi\)
0.400348 0.916363i \(-0.368889\pi\)
\(504\) 0 0
\(505\) 15.1353 26.2150i 0.673510 1.16655i
\(506\) 10.8541 18.7999i 0.482524 0.835756i
\(507\) 1.30902 + 34.0093i 0.0581355 + 1.51040i
\(508\) 50.6140 + 87.6660i 2.24563 + 3.88955i
\(509\) 9.29837 + 16.1053i 0.412143 + 0.713853i 0.995124 0.0986331i \(-0.0314470\pi\)
−0.582981 + 0.812486i \(0.698114\pi\)
\(510\) −13.2082 + 22.8773i −0.584869 + 1.01302i
\(511\) 0 0
\(512\) −40.3050 −1.78124
\(513\) 4.14590 0.183046
\(514\) −21.9164 + 37.9603i −0.966691 + 1.67436i
\(515\) 11.3992 + 19.7440i 0.502308 + 0.870023i
\(516\) −159.644 −7.02795
\(517\) 2.07295 3.59045i 0.0911682 0.157908i
\(518\) 0 0
\(519\) 23.5623 1.03427
\(520\) −19.5623 67.7658i −0.857864 2.97173i
\(521\) −9.32624 16.1535i −0.408590 0.707698i 0.586142 0.810208i \(-0.300646\pi\)
−0.994732 + 0.102510i \(0.967313\pi\)
\(522\) 71.5410 3.13127
\(523\) −0.562306 0.973942i −0.0245879 0.0425875i 0.853470 0.521143i \(-0.174494\pi\)
−0.878058 + 0.478555i \(0.841161\pi\)
\(524\) 37.1976 + 64.4281i 1.62498 + 2.81455i
\(525\) 0 0
\(526\) −11.7812 20.4056i −0.513683 0.889724i
\(527\) 6.93112 0.301924
\(528\) 23.9164 + 41.4244i 1.04083 + 1.80277i
\(529\) 1.50000 2.59808i 0.0652174 0.112960i
\(530\) −12.8992 22.3420i −0.560305 0.970477i
\(531\) 4.30902 7.46344i 0.186995 0.323886i
\(532\) 0 0
\(533\) −0.763932 2.64634i −0.0330896 0.114626i
\(534\) 16.8262 29.1439i 0.728143 1.26118i
\(535\) −8.85410 −0.382796
\(536\) −94.9574 −4.10154
\(537\) 23.5623 1.01679
\(538\) −75.2492 −3.24422
\(539\) 0 0
\(540\) 14.2082 + 24.6093i 0.611424 + 1.05902i
\(541\) −17.6353 + 30.5452i −0.758199 + 1.31324i 0.185569 + 0.982631i \(0.440587\pi\)
−0.943768 + 0.330608i \(0.892746\pi\)
\(542\) 11.0172 19.0824i 0.473230 0.819659i
\(543\) −25.4164 −1.09072
\(544\) 7.98936 + 13.8380i 0.342541 + 0.593298i
\(545\) −7.09017 −0.303710
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) 6.35410 + 11.0056i 0.271434 + 0.470137i
\(549\) −23.1246 −0.986934
\(550\) −4.50000 + 7.79423i −0.191881 + 0.332347i
\(551\) 6.57295 11.3847i 0.280017 0.485004i
\(552\) −43.7426 75.7645i −1.86181 3.22475i
\(553\) 0 0
\(554\) −13.0902 −0.556148
\(555\) −27.4164 −1.16376
\(556\) 22.1459 0.939195
\(557\) −27.9787 −1.18550 −0.592748 0.805388i \(-0.701957\pi\)
−0.592748 + 0.805388i \(0.701957\pi\)
\(558\) 23.7533 41.1419i 1.00556 1.74168i
\(559\) 43.9681 + 10.8793i 1.85965 + 0.460144i
\(560\) 0 0
\(561\) −3.57295 + 6.18853i −0.150850 + 0.261280i
\(562\) −26.4164 45.7546i −1.11431 1.93004i
\(563\) 10.5279 18.2348i 0.443697 0.768505i −0.554264 0.832341i \(-0.687000\pi\)
0.997960 + 0.0638360i \(0.0203335\pi\)
\(564\) −14.2082 24.6093i −0.598273 1.03624i
\(565\) 3.85410 0.162143
\(566\) −17.5623 30.4188i −0.738199 1.27860i
\(567\) 0 0
\(568\) 52.9787 + 91.7618i 2.22294 + 3.85024i
\(569\) −7.47214 12.9421i −0.313248 0.542562i 0.665815 0.746117i \(-0.268084\pi\)
−0.979064 + 0.203555i \(0.934751\pi\)
\(570\) 33.2705 1.39355
\(571\) −12.3435 21.3795i −0.516558 0.894704i −0.999815 0.0192259i \(-0.993880\pi\)
0.483257 0.875478i \(-0.339453\pi\)
\(572\) −9.00000 31.1769i −0.376309 1.30357i
\(573\) −55.9787 −2.33854
\(574\) 0 0
\(575\) 4.14590 7.18091i 0.172896 0.299464i
\(576\) 33.5623 1.39843
\(577\) 21.9164 + 37.9603i 0.912392 + 1.58031i 0.810675 + 0.585496i \(0.199100\pi\)
0.101717 + 0.994813i \(0.467567\pi\)
\(578\) 19.4164 33.6302i 0.807616 1.39883i
\(579\) 15.7082 0.652811
\(580\) 90.1033 3.74134
\(581\) 0 0
\(582\) 64.6140 111.915i 2.67834 4.63901i
\(583\) −3.48936 6.04374i −0.144514 0.250306i
\(584\) 7.47214 + 12.9421i 0.309199 + 0.535549i
\(585\) −10.0902 34.9534i −0.417177 1.44514i
\(586\) 8.85410 15.3358i 0.365760 0.633514i
\(587\) 9.95492 17.2424i 0.410883 0.711671i −0.584103 0.811679i \(-0.698554\pi\)
0.994987 + 0.100009i \(0.0318870\pi\)
\(588\) 0 0
\(589\) −4.36475 7.55996i −0.179846 0.311503i
\(590\) 7.66312 13.2729i 0.315486 0.546437i
\(591\) −21.9894 + 38.0867i −0.904521 + 1.56668i
\(592\) −19.7082 + 34.1356i −0.810002 + 1.40296i
\(593\) −21.8992 + 37.9305i −0.899292 + 1.55762i −0.0708905 + 0.997484i \(0.522584\pi\)
−0.828401 + 0.560135i \(0.810749\pi\)
\(594\) 5.42705 + 9.39993i 0.222675 + 0.385684i
\(595\) 0 0
\(596\) −4.50000 + 7.79423i −0.184327 + 0.319264i
\(597\) −31.9615 + 55.3589i −1.30810 + 2.26569i
\(598\) 11.7082 + 40.5584i 0.478784 + 1.65856i
\(599\) −14.7533 25.5534i −0.602803 1.04409i −0.992395 0.123098i \(-0.960717\pi\)
0.389592 0.920988i \(-0.372616\pi\)
\(600\) 18.1353 + 31.4112i 0.740369 + 1.28236i
\(601\) −20.1976 + 34.9832i −0.823876 + 1.42699i 0.0788998 + 0.996883i \(0.474859\pi\)
−0.902776 + 0.430112i \(0.858474\pi\)
\(602\) 0 0
\(603\) −48.9787 −1.99457
\(604\) −6.27051 −0.255143
\(605\) 9.89919 17.1459i 0.402459 0.697080i
\(606\) −39.6246 68.6318i −1.60964 2.78798i
\(607\) −23.0000 −0.933541 −0.466771 0.884378i \(-0.654583\pi\)
−0.466771 + 0.884378i \(0.654583\pi\)
\(608\) 10.0623 17.4284i 0.408080 0.706816i
\(609\) 0 0
\(610\) −41.1246 −1.66509
\(611\) 2.23607 + 7.74597i 0.0904616 + 0.313368i
\(612\) 13.7705 + 23.8512i 0.556640 + 0.964129i
\(613\) 34.5623 1.39596 0.697979 0.716118i \(-0.254083\pi\)
0.697979 + 0.716118i \(0.254083\pi\)
\(614\) 6.35410 + 11.0056i 0.256431 + 0.444151i
\(615\) 2.61803 + 4.53457i 0.105569 + 0.182851i
\(616\) 0 0
\(617\) −0.0278640 0.0482619i −0.00112176 0.00194295i 0.865464 0.500971i \(-0.167024\pi\)
−0.866586 + 0.499028i \(0.833690\pi\)
\(618\) 59.6869 2.40096
\(619\) −4.70820 8.15485i −0.189239 0.327771i 0.755758 0.654851i \(-0.227269\pi\)
−0.944997 + 0.327080i \(0.893935\pi\)
\(620\) 29.9164 51.8167i 1.20147 2.08101i
\(621\) −5.00000 8.66025i −0.200643 0.347524i
\(622\) −4.35410 + 7.54153i −0.174584 + 0.302388i
\(623\) 0 0
\(624\) −90.2943 22.3420i −3.61467 0.894398i
\(625\) 15.4164 26.7020i 0.616656 1.06808i
\(626\) 65.7771 2.62898
\(627\) 9.00000 0.359425
\(628\) 72.1033 2.87724
\(629\) −5.88854 −0.234792
\(630\) 0 0
\(631\) −17.1976 29.7870i −0.684624 1.18580i −0.973555 0.228454i \(-0.926633\pi\)
0.288931 0.957350i \(-0.406700\pi\)
\(632\) −14.9443 + 25.8842i −0.594451 + 1.02962i
\(633\) 6.16312 10.6748i 0.244962 0.424287i
\(634\) 68.6869 2.72791
\(635\) 27.2984 + 47.2822i 1.08330 + 1.87634i
\(636\) −47.8328 −1.89669
\(637\) 0 0
\(638\) 34.4164 1.36256
\(639\) 27.3262 + 47.3304i 1.08101 + 1.87236i
\(640\) 2.85410 0.112818
\(641\) 23.7533 41.1419i 0.938199 1.62501i 0.169370 0.985553i \(-0.445827\pi\)
0.768829 0.639455i \(-0.220840\pi\)
\(642\) −11.5902 + 20.0748i −0.457428 + 0.792288i
\(643\) 3.50000 + 6.06218i 0.138027 + 0.239069i 0.926750 0.375680i \(-0.122591\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 0 0
\(645\) −86.1033 −3.39032
\(646\) 7.14590 0.281152
\(647\) 24.7639 0.973571 0.486785 0.873522i \(-0.338169\pi\)
0.486785 + 0.873522i \(0.338169\pi\)
\(648\) −42.6525 −1.67555
\(649\) 2.07295 3.59045i 0.0813704 0.140938i
\(650\) −4.85410 16.8151i −0.190394 0.659543i
\(651\) 0 0
\(652\) 9.00000 15.5885i 0.352467 0.610491i
\(653\) 0.190983 + 0.330792i 0.00747374 + 0.0129449i 0.869738 0.493514i \(-0.164288\pi\)
−0.862264 + 0.506458i \(0.830954\pi\)
\(654\) −9.28115 + 16.0754i −0.362922 + 0.628599i
\(655\) 20.0623 + 34.7489i 0.783899 + 1.35775i
\(656\) 7.52786 0.293914
\(657\) 3.85410 + 6.67550i 0.150363 + 0.260436i
\(658\) 0 0
\(659\) 11.9443 + 20.6881i 0.465283 + 0.805893i 0.999214 0.0396343i \(-0.0126193\pi\)
−0.533931 + 0.845528i \(0.679286\pi\)
\(660\) 30.8435 + 53.4224i 1.20058 + 2.07947i
\(661\) −48.5410 −1.88803 −0.944013 0.329907i \(-0.892983\pi\)
−0.944013 + 0.329907i \(0.892983\pi\)
\(662\) 13.2812 + 23.0036i 0.516187 + 0.894062i
\(663\) −3.85410 13.3510i −0.149681 0.518510i
\(664\) 50.1246 1.94521
\(665\) 0 0
\(666\) −20.1803 + 34.9534i −0.781972 + 1.35442i
\(667\) −31.7082 −1.22775
\(668\) −34.5517 59.8452i −1.33684 2.31548i
\(669\) 26.5344 45.9590i 1.02588 1.77688i
\(670\) −87.1033 −3.36510
\(671\) −11.1246 −0.429461
\(672\) 0 0
\(673\) 19.6246 33.9908i 0.756473 1.31025i −0.188165 0.982137i \(-0.560254\pi\)
0.944639 0.328113i \(-0.106413\pi\)
\(674\) 15.1353 + 26.2150i 0.582988 + 1.00977i
\(675\) 2.07295 + 3.59045i 0.0797878 + 0.138197i
\(676\) 55.8222 + 29.4264i 2.14701 + 1.13179i
\(677\) −21.8713 + 37.8822i −0.840583 + 1.45593i 0.0488191 + 0.998808i \(0.484454\pi\)
−0.889402 + 0.457125i \(0.848879\pi\)
\(678\) 5.04508 8.73834i 0.193755 0.335594i
\(679\) 0 0
\(680\) 14.3992 + 24.9401i 0.552184 + 0.956410i
\(681\) 1.92705 3.33775i 0.0738448 0.127903i
\(682\) 11.4271 19.7922i 0.437564 0.757884i
\(683\) −0.736068 + 1.27491i −0.0281649 + 0.0487830i −0.879764 0.475410i \(-0.842300\pi\)
0.851599 + 0.524193i \(0.175633\pi\)
\(684\) 17.3435 30.0398i 0.663144 1.14860i
\(685\) 3.42705 + 5.93583i 0.130941 + 0.226796i
\(686\) 0 0
\(687\) −17.1803 + 29.7572i −0.655471 + 1.13531i
\(688\) −61.8951 + 107.205i −2.35973 + 4.08717i
\(689\) 13.1738 + 3.25966i 0.501880 + 0.124183i
\(690\) −40.1246 69.4979i −1.52752 2.64574i
\(691\) 2.92705 + 5.06980i 0.111350 + 0.192864i 0.916315 0.400458i \(-0.131149\pi\)
−0.804965 + 0.593323i \(0.797816\pi\)
\(692\) 21.8435 37.8340i 0.830364 1.43823i
\(693\) 0 0
\(694\) 80.5410 3.05730
\(695\) 11.9443 0.453072
\(696\) 69.3500 120.118i 2.62871 4.55305i
\(697\) 0.562306 + 0.973942i 0.0212989 + 0.0368907i
\(698\) 54.2148 2.05206
\(699\) 3.42705 5.93583i 0.129623 0.224514i
\(700\) 0 0
\(701\) 11.2361 0.424380 0.212190 0.977228i \(-0.431940\pi\)
0.212190 + 0.977228i \(0.431940\pi\)
\(702\) −20.4894 5.06980i −0.773321 0.191347i
\(703\) 3.70820 + 6.42280i 0.139858 + 0.242240i
\(704\) 16.1459 0.608521
\(705\) −7.66312 13.2729i −0.288610 0.499887i
\(706\) −28.9894 50.2110i −1.09103 1.88972i
\(707\) 0 0
\(708\) −14.2082 24.6093i −0.533977 0.924875i
\(709\) 23.5623 0.884901 0.442450 0.896793i \(-0.354109\pi\)
0.442450 + 0.896793i \(0.354109\pi\)
\(710\) 48.5967 + 84.1720i 1.82380 + 3.15892i
\(711\) −7.70820 + 13.3510i −0.289080 + 0.500702i
\(712\) −18.3435 31.7718i −0.687450 1.19070i
\(713\) −10.5279 + 18.2348i −0.394272 + 0.682898i
\(714\) 0 0
\(715\) −4.85410 16.8151i −0.181533 0.628849i
\(716\) 21.8435 37.8340i 0.816328 1.41392i
\(717\) 64.6869 2.41578
\(718\) −57.8328 −2.15830
\(719\) 8.12461 0.302997 0.151498 0.988457i \(-0.451590\pi\)
0.151498 + 0.988457i \(0.451590\pi\)
\(720\) 99.4296 3.70552
\(721\) 0 0
\(722\) 20.3713 + 35.2842i 0.758142 + 1.31314i
\(723\) 32.1525 55.6897i 1.19576 2.07112i
\(724\) −23.5623 + 40.8111i −0.875686 + 1.51673i
\(725\) 13.1459 0.488226
\(726\) −25.9164 44.8885i −0.961848 1.66597i
\(727\) −30.7082 −1.13890 −0.569452 0.822025i \(-0.692845\pi\)
−0.569452 + 0.822025i \(0.692845\pi\)
\(728\) 0 0
\(729\) −39.5623 −1.46527
\(730\) 6.85410 + 11.8717i 0.253682 + 0.439390i
\(731\) −18.4934 −0.684004
\(732\) −38.1246 + 66.0338i −1.40913 + 2.44068i
\(733\) 16.1353 27.9471i 0.595969 1.03225i −0.397440 0.917628i \(-0.630101\pi\)
0.993409 0.114621i \(-0.0365653\pi\)
\(734\) 1.85410 + 3.21140i 0.0684362 + 0.118535i
\(735\) 0 0
\(736\) −48.5410 −1.78925
\(737\) −23.5623 −0.867929
\(738\) 7.70820 0.283743
\(739\) −6.87539 −0.252915 −0.126458 0.991972i \(-0.540361\pi\)
−0.126458 + 0.991972i \(0.540361\pi\)
\(740\) −25.4164 + 44.0225i −0.934326 + 1.61830i
\(741\) −12.1353 + 12.6113i −0.445800 + 0.463289i
\(742\) 0 0
\(743\) −19.6631 + 34.0575i −0.721370 + 1.24945i 0.239081 + 0.971000i \(0.423154\pi\)
−0.960451 + 0.278450i \(0.910179\pi\)
\(744\) −46.0517 79.7638i −1.68834 2.92428i
\(745\) −2.42705 + 4.20378i −0.0889203 + 0.154014i
\(746\) 26.9164 + 46.6206i 0.985480 + 1.70690i
\(747\) 25.8541 0.945952
\(748\) 6.62461 + 11.4742i 0.242220 + 0.419537i
\(749\) 0 0
\(750\) −28.2254 48.8879i −1.03065 1.78513i
\(751\) −11.3541 19.6659i −0.414317 0.717618i 0.581039 0.813875i \(-0.302646\pi\)
−0.995356 + 0.0962572i \(0.969313\pi\)
\(752\) −22.0344 −0.803513
\(753\) 1.00000 + 1.73205i 0.0364420 + 0.0631194i
\(754\) −46.4058 + 48.2263i −1.69000 + 1.75630i
\(755\) −3.38197 −0.123082
\(756\) 0 0
\(757\) −14.0000 + 24.2487i −0.508839 + 0.881334i 0.491109 + 0.871098i \(0.336592\pi\)
−0.999948 + 0.0102362i \(0.996742\pi\)
\(758\) −16.0902 −0.584421
\(759\) −10.8541 18.7999i −0.393979 0.682392i
\(760\) 18.1353 31.4112i 0.657835 1.13940i
\(761\) −28.8541 −1.04596 −0.522980 0.852345i \(-0.675180\pi\)
−0.522980 + 0.852345i \(0.675180\pi\)
\(762\) 142.936 5.17803
\(763\) 0 0
\(764\) −51.8951 + 89.8850i −1.87750 + 3.25192i
\(765\) 7.42705 + 12.8640i 0.268526 + 0.465100i
\(766\) 28.7705 + 49.8320i 1.03952 + 1.80050i
\(767\) 2.23607 + 7.74597i 0.0807397 + 0.279691i
\(768\) −19.0623 + 33.0169i −0.687852 + 1.19139i
\(769\) 9.20820 15.9491i 0.332056 0.575138i −0.650859 0.759199i \(-0.725591\pi\)
0.982915 + 0.184061i \(0.0589243\pi\)
\(770\) 0 0
\(771\) 21.9164 + 37.9603i 0.789300 + 1.36711i
\(772\) 14.5623 25.2227i 0.524109 0.907783i
\(773\) −12.6803 + 21.9630i −0.456080 + 0.789954i −0.998750 0.0499924i \(-0.984080\pi\)
0.542669 + 0.839946i \(0.317414\pi\)
\(774\) −63.3779 + 109.774i −2.27807 + 3.94574i
\(775\) 4.36475 7.55996i 0.156786 0.271562i
\(776\) −70.4402 122.006i −2.52866 4.37976i
\(777\) 0 0
\(778\) 15.5623 26.9547i 0.557936 0.966373i
\(779\) 0.708204 1.22665i 0.0253740 0.0439491i
\(780\) −116.447 28.8131i −4.16946 1.03167i
\(781\) 13.1459 + 22.7694i 0.470397 +