Properties

Label 637.2.g.b.263.1
Level $637$
Weight $2$
Character 637.263
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 263.1
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.b.373.1

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30902 + 2.26728i −0.925615 + 1.60321i −0.135045 + 0.990839i \(0.543118\pi\)
−0.790569 + 0.612372i \(0.790215\pi\)
\(3\) −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 −0.994824 0.101611i \(-0.967600\pi\)
0.409414 0.912349i \(-0.365733\pi\)
\(6\) 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 0.941375 0.337363i \(-0.109535\pi\)
−0.762852 + 0.646573i \(0.776202\pi\)
\(18\) −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 −0.533005 0.846112i \(-0.678937\pi\)
0.999257 + 0.0385394i \(0.0122705\pi\)
\(24\) −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 −0.981054 0.193734i \(-0.937940\pi\)
0.322748 0.946485i \(-0.395393\pi\)
\(30\) −17.9443 −3.27616
\(31\) 2.35410 4.07742i 0.422809 0.732327i −0.573404 0.819273i \(-0.694377\pi\)
0.996213 + 0.0869459i \(0.0277107\pi\)
\(32\) −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 −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 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 0.834657 0.550771i \(-0.185666\pi\)
−0.894310 + 0.447449i \(0.852333\pi\)
\(42\) 0 0
\(43\) −6.28115 + 10.8793i −0.957867 + 1.65907i −0.230200 + 0.973143i \(0.573938\pi\)
−0.727667 + 0.685931i \(0.759395\pi\)
\(44\) −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 0.935973 0.352073i \(-0.114523\pi\)
−0.772890 + 0.634539i \(0.781190\pi\)
\(48\) 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 −0.965842 0.259130i \(-0.916564\pi\)
0.707334 + 0.706879i \(0.249897\pi\)
\(54\) 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 0.929580 0.368620i \(-0.120170\pi\)
−0.784024 + 0.620730i \(0.786836\pi\)
\(60\) 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 −0.0472218 0.998884i \(-0.515037\pi\)
0.888670 0.458547i \(-0.151630\pi\)
\(72\) 28.7984 3.39392
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) −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 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 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 −0.966300 0.257417i \(-0.917129\pi\)
0.706080 + 0.708132i \(0.250462\pi\)
\(90\) 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 −0.227854 + 0.973695i \(0.573171\pi\)
−0.729318 + 0.684175i \(0.760162\pi\)
\(98\) 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 0.996787 0.0801026i \(-0.0255248\pi\)
−0.567764 + 0.823191i \(0.692191\pi\)
\(104\) −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 −0.772639 0.634846i \(-0.781064\pi\)
0.936112 + 0.351702i \(0.114397\pi\)
\(108\) 5.42705 + 9.39993i 0.522218 + 0.904508i
\(109\) 1.35410 2.34537i 0.129699 0.224646i −0.793861 0.608100i \(-0.791932\pi\)
0.923560 + 0.383454i \(0.125265\pi\)
\(110\) 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 −0.898568 0.438833i \(-0.855392\pi\)
0.829325 + 0.558766i \(0.188725\pi\)
\(114\) −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 0.791157 + 0.611613i \(0.209479\pi\)
0.134094 + 0.990969i \(0.457187\pi\)
\(128\) −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 0.978036 + 0.208437i \(0.0668377\pi\)
−0.308506 + 0.951222i \(0.599829\pi\)
\(132\) 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 0.916511 0.400010i \(-0.130993\pi\)
−0.804674 + 0.593717i \(0.797660\pi\)
\(138\) −15.3262 26.5458i −1.30466 2.25973i
\(139\) −2.28115 + 3.95107i −0.193485 + 0.335126i −0.946403 0.322989i \(-0.895312\pi\)
0.752918 + 0.658114i \(0.228646\pi\)
\(140\) 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 −0.838547 0.544829i \(-0.816594\pi\)
0.891109 + 0.453788i \(0.149928\pi\)
\(152\) −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 0.401118 + 0.916026i \(0.368622\pi\)
−0.993861 + 0.110635i \(0.964712\pi\)
\(158\) 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 −0.998216 0.0597001i \(-0.980986\pi\)
0.447406 0.894331i \(-0.352348\pi\)
\(168\) 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 0.993055 + 0.117652i \(0.0375368\pi\)
−0.394638 + 0.918837i \(0.629130\pi\)
\(198\) −9.35410 + 16.2018i −0.664767 + 1.15141i
\(199\) 12.2082 + 21.1452i 0.865417 + 1.49895i 0.866633 + 0.498946i \(0.166280\pi\)
−0.00121626 + 0.999999i \(0.500387\pi\)
\(200\) −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 0.773545 0.633741i \(-0.218481\pi\)
−0.935608 + 0.353039i \(0.885148\pi\)
\(212\) 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 −0.975371 0.220573i \(-0.929207\pi\)
0.296664 0.954982i \(-0.404126\pi\)
\(224\) 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 0.840564 0.541712i \(-0.182224\pi\)
−0.889419 + 0.457094i \(0.848890\pi\)
\(228\) −11.7812 20.4056i −0.780226 1.35139i
\(229\) 6.56231 + 11.3662i 0.433649 + 0.751103i 0.997184 0.0749895i \(-0.0238923\pi\)
−0.563535 + 0.826092i \(0.690559\pi\)
\(230\) 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 0.819957 0.572425i \(-0.193997\pi\)
−0.905713 + 0.423891i \(0.860664\pi\)
\(234\) 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 −0.925287 0.379267i \(-0.876176\pi\)
0.134189 0.990956i \(-0.457157\pi\)
\(242\) 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 −0.877828 0.478975i \(-0.841008\pi\)
0.853719 + 0.520734i \(0.174342\pi\)
\(252\) 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 0.477478 + 0.878644i \(0.341551\pi\)
−0.999667 + 0.0258138i \(0.991782\pi\)
\(258\) 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 0.855441 + 0.517900i \(0.173286\pi\)
0.0207937 + 0.999784i \(0.493381\pi\)
\(270\) −15.3262 −0.932725
\(271\) 4.20820 7.28882i 0.255630 0.442764i −0.709436 0.704770i \(-0.751050\pi\)
0.965066 + 0.262005i \(0.0843837\pi\)
\(272\) −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 0.931305 0.364241i \(-0.118672\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) −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 −0.750166 0.661250i \(-0.770026\pi\)
0.947742 + 0.319037i \(0.103360\pi\)
\(294\) 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 −0.909319 0.416099i \(-0.863397\pi\)
0.815012 + 0.579444i \(0.196730\pi\)
\(312\) 48.9058 + 50.8244i 2.76874 + 2.87736i
\(313\) −12.5623 21.7586i −0.710064 1.22987i −0.964833 0.262864i \(-0.915333\pi\)
0.254769 0.967002i \(-0.418000\pi\)
\(314\) −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 −0.953937 0.300007i \(-0.903011\pi\)
0.217155 0.976137i \(-0.430322\pi\)
\(318\) 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 −0.901347 0.433098i \(-0.857420\pi\)
0.0755997 0.997138i \(-0.475913\pi\)
\(348\) 45.0517 78.0318i 2.41502 4.18294i
\(349\) −10.3541 17.9338i −0.554242 0.959976i −0.997962 0.0638103i \(-0.979675\pi\)
0.443720 0.896166i \(-0.353659\pi\)
\(350\) 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 0.995129 + 0.0985799i \(0.0314300\pi\)
−0.412192 + 0.911097i \(0.635237\pi\)
\(360\) −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 0.934092 0.357032i \(-0.116211\pi\)
−0.776245 + 0.630431i \(0.782878\pi\)
\(380\) 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 −0.675064 0.737759i \(-0.735884\pi\)
0.976450 + 0.215743i \(0.0692172\pi\)
\(390\) 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 −0.0396416 + 0.999214i \(0.512622\pi\)
−0.845524 + 0.533938i \(0.820712\pi\)
\(402\) −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 0.630500 0.776189i \(-0.282850\pi\)
−0.987450 + 0.157935i \(0.949516\pi\)
\(410\) −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 0.974226 0.225576i \(-0.0724265\pi\)
−0.682468 + 0.730916i \(0.739093\pi\)
\(420\) 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 −0.877790 0.479046i \(-0.840983\pi\)
0.853761 + 0.520665i \(0.174316\pi\)
\(434\) 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 −0.987028 0.160550i \(-0.948673\pi\)
0.632554 + 0.774516i \(0.282007\pi\)
\(440\) −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 0.921493 0.388395i \(-0.126970\pi\)
−0.797106 + 0.603839i \(0.793637\pi\)
\(444\) −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 −0.999000 0.0447005i \(-0.985767\pi\)
0.538212 + 0.842809i \(0.319100\pi\)
\(450\) −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 −0.988055 0.154098i \(-0.950753\pi\)
0.627481 + 0.778632i \(0.284086\pi\)
\(458\) −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 −0.688026 0.725686i \(-0.741523\pi\)
0.972476 + 0.233005i \(0.0748558\pi\)
\(462\) 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 0.837589 0.546300i \(-0.183964\pi\)
−0.891905 + 0.452224i \(0.850631\pi\)
\(468\) −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 −0.975212 0.221271i \(-0.928979\pi\)
0.295980 0.955194i \(-0.404354\pi\)
\(488\) −44.8328 −2.02949
\(489\) 9.70820 0.439020
\(490\) 0 0
\(491\) −6.19098 10.7231i −0.279395 0.483927i 0.691839 0.722051i \(-0.256801\pi\)
−0.971235 + 0.238125i \(0.923467\pi\)
\(492\) 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 0.650517 0.759492i \(-0.274552\pi\)
−0.982998 + 0.183619i \(0.941219\pi\)
\(500\) 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 0.400348 + 0.916363i \(0.368889\pi\)
−0.993768 + 0.111470i \(0.964444\pi\)
\(504\) 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 −0.582981 0.812486i \(-0.698114\pi\)
0.995124 + 0.0986331i \(0.0314470\pi\)
\(510\) −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 −0.994732 0.102510i \(-0.967313\pi\)
0.586142 + 0.810208i \(0.300646\pi\)
\(522\) 71.5410 3.13127
\(523\) −0.562306 + 0.973942i −0.0245879 + 0.0425875i −0.878058 0.478555i \(-0.841161\pi\)
0.853470 + 0.521143i \(0.174494\pi\)
\(524\) 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 −0.943768 0.330608i \(-0.892746\pi\)
0.185569 0.982631i \(-0.440587\pi\)
\(542\) 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 0.997960 0.0638360i \(-0.0203335\pi\)
−0.554264 + 0.832341i \(0.687000\pi\)
\(564\) −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 −0.979064 0.203555i \(-0.934751\pi\)
0.665815 + 0.746117i \(0.268084\pi\)
\(570\) 33.2705 1.39355
\(571\) −12.3435 + 21.3795i −0.516558 + 0.894704i 0.483257 + 0.875478i \(0.339453\pi\)
−0.999815 + 0.0192259i \(0.993880\pi\)
\(572\) −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 0.101717 0.994813i \(-0.467567\pi\)
0.810675 0.585496i \(-0.199100\pi\)
\(578\) 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 0.994987 0.100009i \(-0.0318870\pi\)
−0.584103 + 0.811679i \(0.698554\pi\)
\(588\) 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 −0.828401 0.560135i \(-0.810749\pi\)
−0.0708905 0.997484i \(-0.522584\pi\)
\(594\) 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 0.389592 + 0.920988i \(0.372616\pi\)
−0.992395 + 0.123098i \(0.960717\pi\)
\(600\) 18.1353 31.4112i 0.740369 1.28236i
\(601\) −20.1976 34.9832i −0.823876 1.42699i −0.902776 0.430112i \(-0.858474\pi\)
0.0788998 0.996883i \(-0.474859\pi\)
\(602\) 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 −0.866586 0.499028i \(-0.833690\pi\)
0.865464 + 0.500971i \(0.167024\pi\)
\(618\) 59.6869 2.40096
\(619\) −4.70820 + 8.15485i −0.189239 + 0.327771i −0.944997 0.327080i \(-0.893935\pi\)
0.755758 + 0.654851i \(0.227269\pi\)
\(620\) 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 0.288931 + 0.957350i \(0.406700\pi\)
−0.973555 + 0.228454i \(0.926633\pi\)
\(632\) −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 0.768829 + 0.639455i \(0.220840\pi\)
0.169370 + 0.985553i \(0.445827\pi\)
\(642\) −11.5902 20.0748i −0.457428 0.792288i
\(643\) 3.50000 6.06218i 0.138027 0.239069i −0.788723 0.614749i \(-0.789257\pi\)
0.926750 + 0.375680i \(0.122591\pi\)
\(644\) 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 −0.862264 0.506458i \(-0.830954\pi\)
0.869738 + 0.493514i \(0.164288\pi\)
\(654\) −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 −0.533931 0.845528i \(-0.679286\pi\)
0.999214 + 0.0396343i \(0.0126193\pi\)
\(660\) 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 0.944639 + 0.328113i \(0.106413\pi\)
−0.188165 + 0.982137i \(0.560254\pi\)
\(674\) 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 −0.889402 0.457125i \(-0.848879\pi\)
0.0488191 0.998808i \(-0.484454\pi\)
\(678\) 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 0.851599 0.524193i \(-0.175633\pi\)
−0.879764 + 0.475410i \(0.842300\pi\)
\(684\) 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 −0.804965 0.593323i \(-0.797816\pi\)
0.916315 + 0.400458i \(0.131149\pi\)
\(692\) 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 0.993409 + 0.114621i \(0.0365653\pi\)
−0.397440 + 0.917628i \(0.630101\pi\)
\(734\) 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 −0.960451 0.278450i \(-0.910179\pi\)
0.239081 0.971000i \(-0.423154\pi\)
\(744\) −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 −0.995356 0.0962572i \(-0.969313\pi\)
0.581039 + 0.813875i \(0.302646\pi\)
\(752\) −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 −0.999948 0.0102362i \(-0.996742\pi\)
0.491109 0.871098i \(-0.336592\pi\)
\(758\) −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 0.982915 0.184061i \(-0.0589243\pi\)
−0.650859 + 0.759199i \(0.725591\pi\)
\(770\) 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 0.542669 0.839946i \(-0.317414\pi\)
−0.998750 + 0.0499924i \(0.984080\pi\)
\(774\) −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 0.814752i