Properties

Label 637.2.f.c.393.1
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $0$
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.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.1
Root \(0.809017 + 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.c.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30902 - 2.26728i) q^{2} +(-1.30902 - 2.26728i) q^{3} +(-2.42705 + 4.20378i) q^{4} -2.61803 q^{5} +(-3.42705 + 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 + 3.33775i) q^{9} +O(q^{10})\) \(q+(-1.30902 - 2.26728i) q^{2} +(-1.30902 - 2.26728i) q^{3} +(-2.42705 + 4.20378i) q^{4} -2.61803 q^{5} +(-3.42705 + 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 + 3.33775i) q^{9} +(3.42705 + 5.93583i) q^{10} +(-0.927051 - 1.60570i) q^{11} +12.7082 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} +10.0902 q^{18} +(-0.927051 + 1.60570i) q^{19} +(6.35410 - 11.0056i) q^{20} +(-2.42705 + 4.20378i) q^{22} +(2.23607 + 3.87298i) q^{23} +(-9.78115 - 16.9415i) q^{24} +1.85410 q^{25} +(2.61803 - 9.06914i) q^{26} +2.23607 q^{27} +(-3.54508 - 6.14027i) q^{29} +(8.97214 - 15.5402i) q^{30} +4.70820 q^{31} +(-5.42705 + 9.39993i) q^{32} +(-2.42705 + 4.20378i) q^{33} +3.85410 q^{34} +(-9.35410 - 16.2018i) q^{36} +(-2.00000 - 3.46410i) q^{37} +4.85410 q^{38} +(2.61803 - 9.06914i) q^{39} -19.5623 q^{40} +(0.381966 + 0.661585i) q^{41} +(-6.28115 + 10.8793i) q^{43} +9.00000 q^{44} +(5.04508 - 8.73834i) q^{45} +(5.85410 - 10.1396i) q^{46} +2.23607 q^{47} +(-12.8992 + 22.3420i) q^{48} +(-2.42705 - 4.20378i) q^{50} +3.85410 q^{51} +(-16.9894 + 4.20378i) q^{52} +3.76393 q^{53} +(-2.92705 - 5.06980i) q^{54} +(2.42705 + 4.20378i) q^{55} +4.85410 q^{57} +(-9.28115 + 16.0754i) q^{58} +(-1.11803 + 1.93649i) q^{59} -33.2705 q^{60} +(-3.00000 + 5.19615i) q^{61} +(-6.16312 - 10.6748i) q^{62} +8.70820 q^{64} +(-6.54508 - 6.80185i) q^{65} +12.7082 q^{66} +(6.35410 + 11.0056i) q^{67} +(-3.57295 - 6.18853i) q^{68} +(5.85410 - 10.1396i) q^{69} +(7.09017 - 12.2805i) q^{71} +(-14.3992 + 24.9401i) q^{72} +2.00000 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} +4.00000 q^{79} +(12.8992 + 22.3420i) q^{80} +(2.85410 + 4.94345i) q^{81} +(1.00000 - 1.73205i) q^{82} -6.70820 q^{83} +(1.92705 - 3.33775i) q^{85} +32.8885 q^{86} +(-9.28115 + 16.0754i) q^{87} +(-6.92705 - 11.9980i) q^{88} +(2.45492 + 4.25204i) q^{89} -26.4164 q^{90} -21.7082 q^{92} +(-6.16312 - 10.6748i) q^{93} +(-2.92705 - 5.06980i) q^{94} +(2.42705 - 4.20378i) q^{95} +28.4164 q^{96} +(9.42705 - 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{2} - 3q^{3} - 3q^{4} - 6q^{5} - 7q^{6} + 12q^{8} - q^{9} + O(q^{10}) \) \( 4q - 3q^{2} - 3q^{3} - 3q^{4} - 6q^{5} - 7q^{6} + 12q^{8} - q^{9} + 7q^{10} + 3q^{11} + 24q^{12} + 10q^{13} + 7q^{15} - 13q^{16} + 6q^{17} + 18q^{18} + 3q^{19} + 12q^{20} - 3q^{22} - 19q^{24} - 6q^{25} + 6q^{26} - 3q^{29} + 18q^{30} - 8q^{31} - 15q^{32} - 3q^{33} + 2q^{34} - 24q^{36} - 8q^{37} + 6q^{38} + 6q^{39} - 38q^{40} + 6q^{41} - 5q^{43} + 36q^{44} + 9q^{45} + 10q^{46} - 27q^{48} - 3q^{50} + 2q^{51} - 21q^{52} + 24q^{53} - 5q^{54} + 3q^{55} + 6q^{57} - 17q^{58} - 66q^{60} - 12q^{61} - 9q^{62} + 8q^{64} - 15q^{65} + 24q^{66} + 12q^{67} - 21q^{68} + 10q^{69} + 6q^{71} - 33q^{72} + 8q^{73} - 12q^{74} - 3q^{75} - 18q^{76} - 49q^{78} + 16q^{79} + 27q^{80} - 2q^{81} + 4q^{82} + q^{85} + 60q^{86} - 17q^{87} - 21q^{88} + 21q^{89} - 52q^{90} - 60q^{92} - 9q^{93} - 5q^{94} + 3q^{95} + 60q^{96} + 31q^{97} + 42q^{99} + O(q^{100}) \)

Character values

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

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

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 \(-0.543118\pi\)
\(3\) −1.30902 2.26728i −0.755761 1.30902i −0.944995 0.327085i \(-0.893934\pi\)
0.189234 0.981932i \(-0.439400\pi\)
\(4\) −2.42705 + 4.20378i −1.21353 + 2.10189i
\(5\) −2.61803 −1.17082 −0.585410 0.810737i \(-0.699067\pi\)
−0.585410 + 0.810737i \(0.699067\pi\)
\(6\) −3.42705 + 5.93583i −1.39909 + 2.42329i
\(7\) 0 0
\(8\) 7.47214 2.64180
\(9\) −1.92705 + 3.33775i −0.642350 + 1.11258i
\(10\) 3.42705 + 5.93583i 1.08373 + 1.87707i
\(11\) −0.927051 1.60570i −0.279516 0.484137i 0.691748 0.722139i \(-0.256841\pi\)
−0.971265 + 0.238002i \(0.923507\pi\)
\(12\) 12.7082 3.66854
\(13\) 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 \(-0.890465\pi\)
0.762852 + 0.646573i \(0.223798\pi\)
\(18\) 10.0902 2.37828
\(19\) −0.927051 + 1.60570i −0.212680 + 0.368373i −0.952552 0.304375i \(-0.901553\pi\)
0.739872 + 0.672747i \(0.234886\pi\)
\(20\) 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 \(0.678937\pi\)
\(24\) −9.78115 16.9415i −1.99657 3.45816i
\(25\) 1.85410 0.370820
\(26\) 2.61803 9.06914i 0.513439 1.77860i
\(27\) 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 \(-0.395393\pi\)
\(30\) 8.97214 15.5402i 1.63808 2.83724i
\(31\) 4.70820 0.845618 0.422809 0.906219i \(-0.361044\pi\)
0.422809 + 0.906219i \(0.361044\pi\)
\(32\) −5.42705 + 9.39993i −0.959376 + 1.66169i
\(33\) −2.42705 + 4.20378i −0.422495 + 0.731783i
\(34\) 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 \(0.939977\pi\)
\(38\) 4.85410 0.787439
\(39\) 2.61803 9.06914i 0.419221 1.45222i
\(40\) −19.5623 −3.09307
\(41\) 0.381966 + 0.661585i 0.0596531 + 0.103322i 0.894310 0.447449i \(-0.147667\pi\)
−0.834657 + 0.550771i \(0.814334\pi\)
\(42\) 0 0
\(43\) −6.28115 + 10.8793i −0.957867 + 1.65907i −0.230200 + 0.973143i \(0.573938\pi\)
−0.727667 + 0.685931i \(0.759395\pi\)
\(44\) 9.00000 1.35680
\(45\) 5.04508 8.73834i 0.752077 1.30264i
\(46\) 5.85410 10.1396i 0.863140 1.49500i
\(47\) 2.23607 0.326164 0.163082 0.986613i \(-0.447856\pi\)
0.163082 + 0.986613i \(0.447856\pi\)
\(48\) −12.8992 + 22.3420i −1.86184 + 3.22480i
\(49\) 0 0
\(50\) −2.42705 4.20378i −0.343237 0.594504i
\(51\) 3.85410 0.539682
\(52\) −16.9894 + 4.20378i −2.35600 + 0.582959i
\(53\) 3.76393 0.517016 0.258508 0.966009i \(-0.416769\pi\)
0.258508 + 0.966009i \(0.416769\pi\)
\(54\) −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
\(58\) −9.28115 + 16.0754i −1.21868 + 2.11081i
\(59\) −1.11803 + 1.93649i −0.145556 + 0.252110i −0.929580 0.368620i \(-0.879830\pi\)
0.784024 + 0.620730i \(0.213164\pi\)
\(60\) −33.2705 −4.29520
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) −6.16312 10.6748i −0.782717 1.35571i
\(63\) 0 0
\(64\) 8.70820 1.08853
\(65\) −6.54508 6.80185i −0.811818 0.843666i
\(66\) 12.7082 1.56427
\(67\) 6.35410 + 11.0056i 0.776277 + 1.34455i 0.934074 + 0.357080i \(0.116228\pi\)
−0.157797 + 0.987472i \(0.550439\pi\)
\(68\) −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 \(-0.151630\pi\)
\(72\) −14.3992 + 24.9401i −1.69696 + 2.93922i
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −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
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 12.8992 + 22.3420i 1.44217 + 2.49792i
\(81\) 2.85410 + 4.94345i 0.317122 + 0.549272i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) −6.70820 −0.736321 −0.368161 0.929762i \(-0.620012\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(84\) 0 0
\(85\) 1.92705 3.33775i 0.209018 0.362030i
\(86\) 32.8885 3.54646
\(87\) −9.28115 + 16.0754i −0.995044 + 1.72347i
\(88\) −6.92705 11.9980i −0.738426 1.27899i
\(89\) 2.45492 + 4.25204i 0.260220 + 0.450715i 0.966300 0.257417i \(-0.0828714\pi\)
−0.706080 + 0.708132i \(0.749538\pi\)
\(90\) −26.4164 −2.78453
\(91\) 0 0
\(92\) −21.7082 −2.26324
\(93\) −6.16312 10.6748i −0.639086 1.10693i
\(94\) −2.92705 5.06980i −0.301902 0.522910i
\(95\) 2.42705 4.20378i 0.249010 0.431298i
\(96\) 28.4164 2.90024
\(97\) 9.42705 16.3281i 0.957172 1.65787i 0.227854 0.973695i \(-0.426829\pi\)
0.729318 0.684175i \(-0.239838\pi\)
\(98\) 0 0
\(99\) 7.14590 0.718190
\(100\) −4.50000 + 7.79423i −0.450000 + 0.779423i
\(101\) −5.78115 10.0133i −0.575246 0.996356i −0.996015 0.0891877i \(-0.971573\pi\)
0.420769 0.907168i \(-0.361760\pi\)
\(102\) −5.04508 8.73834i −0.499538 0.865225i
\(103\) 8.70820 0.858045 0.429022 0.903294i \(-0.358858\pi\)
0.429022 + 0.903294i \(0.358858\pi\)
\(104\) 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
\(109\) −2.70820 −0.259399 −0.129699 0.991553i \(-0.541401\pi\)
−0.129699 + 0.991553i \(0.541401\pi\)
\(110\) 6.35410 11.0056i 0.605840 1.04935i
\(111\) −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
\(115\) −5.85410 10.1396i −0.545898 0.945523i
\(116\) 34.4164 3.19548
\(117\) −13.4894 + 3.33775i −1.24709 + 0.308575i
\(118\) 5.85410 0.538914
\(119\) 0 0
\(120\) 25.6074 + 44.3533i 2.33762 + 4.04888i
\(121\) 3.78115 6.54915i 0.343741 0.595377i
\(122\) 15.7082 1.42215
\(123\) 1.00000 1.73205i 0.0901670 0.156174i
\(124\) −11.4271 + 19.7922i −1.02618 + 1.77739i
\(125\) 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
\(129\) 32.8885 2.89567
\(130\) −6.85410 + 23.7433i −0.601145 + 2.08243i
\(131\) 15.3262 1.33906 0.669530 0.742785i \(-0.266496\pi\)
0.669530 + 0.742785i \(0.266496\pi\)
\(132\) −11.7812 20.4056i −1.02542 1.77608i
\(133\) 0 0
\(134\) 16.6353 28.8131i 1.43707 2.48907i
\(135\) −5.85410 −0.503841
\(136\) −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 \(0.130993\pi\)
\(138\) −30.6525 −2.60931
\(139\) 2.28115 3.95107i 0.193485 0.335126i −0.752918 0.658114i \(-0.771354\pi\)
0.946403 + 0.322989i \(0.104688\pi\)
\(140\) 0 0
\(141\) −2.92705 5.06980i −0.246502 0.426954i
\(142\) −37.1246 −3.11543
\(143\) 1.85410 6.42280i 0.155048 0.537101i
\(144\) 37.9787 3.16489
\(145\) 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
\(149\) −0.927051 + 1.60570i −0.0759470 + 0.131544i −0.901498 0.432784i \(-0.857531\pi\)
0.825551 + 0.564328i \(0.190865\pi\)
\(150\) −6.35410 + 11.0056i −0.518810 + 0.898606i
\(151\) −1.29180 −0.105125 −0.0525624 0.998618i \(-0.516739\pi\)
−0.0525624 + 0.998618i \(0.516739\pi\)
\(152\) −6.92705 + 11.9980i −0.561858 + 0.973167i
\(153\) −2.83688 4.91362i −0.229348 0.397243i
\(154\) 0 0
\(155\) −12.3262 −0.990067
\(156\) 31.7705 + 33.0169i 2.54368 + 2.64347i
\(157\) −14.8541 −1.18549 −0.592743 0.805392i \(-0.701955\pi\)
−0.592743 + 0.805392i \(0.701955\pi\)
\(158\) −5.23607 9.06914i −0.416559 0.721502i
\(159\) −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
\(163\) 1.85410 3.21140i 0.145224 0.251536i −0.784232 0.620467i \(-0.786943\pi\)
0.929457 + 0.368931i \(0.120276\pi\)
\(164\) −3.70820 −0.289562
\(165\) 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 \(0.0190144\pi\)
−0.447406 + 0.894331i \(0.647652\pi\)
\(168\) 0 0
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) −10.0902 −0.773881
\(171\) −3.57295 6.18853i −0.273230 0.473249i
\(172\) −30.4894 52.8091i −2.32479 4.02666i
\(173\) −4.50000 + 7.79423i −0.342129 + 0.592584i −0.984828 0.173534i \(-0.944481\pi\)
0.642699 + 0.766119i \(0.277815\pi\)
\(174\) 48.5967 3.68411
\(175\) 0 0
\(176\) −9.13525 + 15.8227i −0.688596 + 1.19268i
\(177\) 5.85410 0.440021
\(178\) 6.42705 11.1320i 0.481728 0.834377i
\(179\) 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) 24.4894 + 42.4168i 1.82533 + 3.16156i
\(181\) −9.70820 −0.721605 −0.360803 0.932642i \(-0.617497\pi\)
−0.360803 + 0.932642i \(0.617497\pi\)
\(182\) 0 0
\(183\) 15.7082 1.16118
\(184\) 16.7082 + 28.9395i 1.23175 + 2.13345i
\(185\) 5.23607 + 9.06914i 0.384963 + 0.666776i
\(186\) −16.1353 + 27.9471i −1.18309 + 2.04918i
\(187\) 2.72949 0.199600
\(188\) −5.42705 + 9.39993i −0.395808 + 0.685560i
\(189\) 0 0
\(190\) −12.7082 −0.921950
\(191\) −10.6910 + 18.5173i −0.773572 + 1.33987i 0.162021 + 0.986787i \(0.448199\pi\)
−0.935593 + 0.353079i \(0.885135\pi\)
\(192\) −11.3992 19.7440i −0.822665 1.42490i
\(193\) 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) −49.3607 −3.54389
\(195\) −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 0.00121626 + 0.999999i \(0.499613\pi\)
−0.866633 + 0.498946i \(0.833720\pi\)
\(200\) 13.8541 0.979633
\(201\) 16.6353 28.8131i 1.17336 2.03232i
\(202\) −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
\(206\) −11.3992 19.7440i −0.794219 1.37563i
\(207\) −17.2361 −1.19799
\(208\) 9.85410 34.1356i 0.683259 2.36688i
\(209\) 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 \(0.885148\pi\)
\(212\) −9.13525 + 15.8227i −0.627412 + 1.08671i
\(213\) −37.1246 −2.54374
\(214\) 4.42705 7.66788i 0.302627 0.524165i
\(215\) 16.4443 28.4823i 1.12149 1.94248i
\(216\) 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
\(220\) −23.5623 −1.58857
\(221\) −5.15248 + 1.27491i −0.346593 + 0.0857595i
\(222\) 27.4164 1.84007
\(223\) 10.1353 + 17.5548i 0.678707 + 1.17555i 0.975371 + 0.220573i \(0.0707926\pi\)
−0.296664 + 0.954982i \(0.595874\pi\)
\(224\) 0 0
\(225\) −3.57295 + 6.18853i −0.238197 + 0.412569i
\(226\) 3.85410 0.256371
\(227\) 0.736068 1.27491i 0.0488545 0.0846186i −0.840564 0.541712i \(-0.817776\pi\)
0.889419 + 0.457094i \(0.151110\pi\)
\(228\) −11.7812 + 20.4056i −0.780226 + 1.35139i
\(229\) 13.1246 0.867299 0.433649 0.901082i \(-0.357226\pi\)
0.433649 + 0.901082i \(0.357226\pi\)
\(230\) −15.3262 + 26.5458i −1.01058 + 1.75038i
\(231\) 0 0
\(232\) −26.4894 45.8809i −1.73911 3.01223i
\(233\) 2.61803 0.171513 0.0857566 0.996316i \(-0.472669\pi\)
0.0857566 + 0.996316i \(0.472669\pi\)
\(234\) 25.2254 + 26.2150i 1.64904 + 1.71373i
\(235\) −5.85410 −0.381880
\(236\) −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 \(0.794701\pi\)
\(240\) 33.7705 58.4922i 2.17988 3.77566i
\(241\) 12.2812 21.2716i 0.791099 1.37022i −0.134189 0.990956i \(-0.542843\pi\)
0.925287 0.379267i \(-0.123824\pi\)
\(242\) −19.7984 −1.27269
\(243\) 10.8262 18.7516i 0.694503 1.20292i
\(244\) −14.5623 25.2227i −0.932256 1.61471i
\(245\) 0 0
\(246\) −5.23607 −0.333840
\(247\) −6.48936 + 1.60570i −0.412908 + 0.102168i
\(248\) 35.1803 2.23395
\(249\) 8.78115 + 15.2094i 0.556483 + 0.963857i
\(250\) −10.7812 18.6735i −0.681860 1.18102i
\(251\) 0.381966 0.661585i 0.0241095 0.0417588i −0.853719 0.520734i \(-0.825658\pi\)
0.877828 + 0.478975i \(0.158992\pi\)
\(252\) 0 0
\(253\) 4.14590 7.18091i 0.260650 0.451460i
\(254\) 27.2984 47.2822i 1.71285 2.96675i
\(255\) −10.0902 −0.631871
\(256\) 7.28115 12.6113i 0.455072 0.788208i
\(257\) 8.37132 + 14.4996i 0.522189 + 0.904457i 0.999667 + 0.0258138i \(0.00821769\pi\)
−0.477478 + 0.878644i \(0.658449\pi\)
\(258\) −43.0517 74.5677i −2.68028 4.64238i
\(259\) 0 0
\(260\) 44.4787 11.0056i 2.75845 0.682540i
\(261\) 27.3262 1.69145
\(262\) −20.0623 34.7489i −1.23945 2.14680i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) −18.1353 + 31.4112i −1.11615 + 1.93322i
\(265\) −9.85410 −0.605333
\(266\) 0 0
\(267\) 6.42705 11.1320i 0.393329 0.681266i
\(268\) −61.6869 −3.76813
\(269\) −14.3713 + 24.8919i −0.876235 + 1.51768i −0.0207937 + 0.999784i \(0.506619\pi\)
−0.855441 + 0.517900i \(0.826714\pi\)
\(270\) 7.66312 + 13.2729i 0.466363 + 0.807764i
\(271\) −4.20820 7.28882i −0.255630 0.442764i 0.709436 0.704770i \(-0.248950\pi\)
−0.965066 + 0.262005i \(0.915616\pi\)
\(272\) 14.5066 0.879590
\(273\) 0 0
\(274\) −6.85410 −0.414071
\(275\) −1.71885 2.97713i −0.103650 0.179528i
\(276\) 28.4164 + 49.2187i 1.71047 + 2.96262i
\(277\) 2.50000 4.33013i 0.150210 0.260172i −0.781094 0.624413i \(-0.785338\pi\)
0.931305 + 0.364241i \(0.118672\pi\)
\(278\) −11.9443 −0.716370
\(279\) −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 \(0.294399\pi\)
\(282\) −7.66312 + 13.2729i −0.456332 + 0.790390i
\(283\) 6.70820 + 11.6190i 0.398761 + 0.690675i 0.993573 0.113190i \(-0.0361069\pi\)
−0.594812 + 0.803865i \(0.702774\pi\)
\(284\) 34.4164 + 59.6110i 2.04224 + 3.53726i
\(285\) −12.7082 −0.752769
\(286\) −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
\(291\) −49.3607 −2.89357
\(292\) −4.85410 + 8.40755i −0.284065 + 0.492015i
\(293\) −3.38197 + 5.85774i −0.197577 + 0.342213i −0.947742 0.319037i \(-0.896640\pi\)
0.750166 + 0.661250i \(0.229974\pi\)
\(294\) 0 0
\(295\) 2.92705 5.06980i 0.170419 0.295175i
\(296\) −14.9443 25.8842i −0.868618 1.50449i
\(297\) −2.07295 3.59045i −0.120285 0.208339i
\(298\) 4.85410 0.281191
\(299\) −4.47214 + 15.4919i −0.258630 + 0.895922i
\(300\) 23.5623 1.36037
\(301\) 0 0
\(302\) 1.69098 + 2.92887i 0.0973051 + 0.168537i
\(303\) −15.1353 + 26.2150i −0.869498 + 1.50601i
\(304\) 18.2705 1.04789
\(305\) 7.85410 13.6037i 0.449725 0.778946i
\(306\) −7.42705 + 12.8640i −0.424576 + 0.735388i
\(307\) 4.85410 0.277038 0.138519 0.990360i \(-0.455766\pi\)
0.138519 + 0.990360i \(0.455766\pi\)
\(308\) 0 0
\(309\) −11.3992 19.7440i −0.648477 1.12320i
\(310\) 16.1353 + 27.9471i 0.916421 + 1.58729i
\(311\) −3.32624 −0.188614 −0.0943068 0.995543i \(-0.530063\pi\)
−0.0943068 + 0.995543i \(0.530063\pi\)
\(312\) 19.5623 67.7658i 1.10750 3.83648i
\(313\) −25.1246 −1.42013 −0.710064 0.704138i \(-0.751334\pi\)
−0.710064 + 0.704138i \(0.751334\pi\)
\(314\) 19.4443 + 33.6785i 1.09730 + 1.90059i
\(315\) 0 0
\(316\) −9.70820 + 16.8151i −0.546129 + 0.945923i
\(317\) 26.2361 1.47356 0.736782 0.676130i \(-0.236344\pi\)
0.736782 + 0.676130i \(0.236344\pi\)
\(318\) −12.8992 + 22.3420i −0.723350 + 1.25288i
\(319\) −6.57295 + 11.3847i −0.368014 + 0.637420i
\(320\) −22.7984 −1.27447
\(321\) 4.42705 7.66788i 0.247094 0.427979i
\(322\) 0 0
\(323\) −1.36475 2.36381i −0.0759364 0.131526i
\(324\) −27.7082 −1.53934
\(325\) 4.63525 + 4.81710i 0.257118 + 0.267205i
\(326\) −9.70820 −0.537688
\(327\) 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
\(331\) 5.07295 8.78661i 0.278834 0.482956i −0.692261 0.721647i \(-0.743385\pi\)
0.971095 + 0.238692i \(0.0767186\pi\)
\(332\) 16.2812 28.1998i 0.893544 1.54766i
\(333\) 15.4164 0.844814
\(334\) 18.6353 32.2772i 1.01968 1.76613i
\(335\) −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 \(0.601978\pi\)
\(338\) 30.1074 15.8710i 1.63763 0.863268i
\(339\) 3.85410 0.209326
\(340\) 9.35410 + 16.2018i 0.507297 + 0.878665i
\(341\) −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
\(345\) −15.3262 + 26.5458i −0.825137 + 1.42918i
\(346\) 23.5623 1.26672
\(347\) −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 0.997962 + 0.0638103i \(0.0203253\pi\)
−0.443720 + 0.896166i \(0.646341\pi\)
\(350\) 0 0
\(351\) 5.59017 + 5.80948i 0.298381 + 0.310087i
\(352\) 20.1246 1.07265
\(353\) 11.0729 + 19.1789i 0.589354 + 1.02079i 0.994317 + 0.106458i \(0.0339508\pi\)
−0.404964 + 0.914333i \(0.632716\pi\)
\(354\) −7.66312 13.2729i −0.407290 0.705447i
\(355\) −18.5623 + 32.1509i −0.985185 + 1.70639i
\(356\) −23.8328 −1.26314
\(357\) 0 0
\(358\) 11.7812 20.4056i 0.622653 1.07847i
\(359\) −22.0902 −1.16587 −0.582937 0.812517i \(-0.698097\pi\)
−0.582937 + 0.812517i \(0.698097\pi\)
\(360\) 37.6976 65.2941i 1.98684 3.44130i
\(361\) 7.78115 + 13.4774i 0.409534 + 0.709334i
\(362\) 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
\(367\) −0.708204 1.22665i −0.0369679 0.0640304i 0.846949 0.531673i \(-0.178437\pi\)
−0.883917 + 0.467643i \(0.845103\pi\)
\(368\) 22.0344 38.1648i 1.14862 1.98948i
\(369\) −2.94427 −0.153273
\(370\) 13.7082 23.7433i 0.712656 1.23436i
\(371\) 0 0
\(372\) 59.8328 3.10219
\(373\) 10.2812 17.8075i 0.532338 0.922036i −0.466949 0.884284i \(-0.654647\pi\)
0.999287 0.0377522i \(-0.0120198\pi\)
\(374\) −3.57295 6.18853i −0.184753 0.320001i
\(375\) −10.7812 18.6735i −0.556736 0.964296i
\(376\) 16.7082 0.861660
\(377\) 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
\(382\) 55.9787 2.86412
\(383\) −10.9894 + 19.0341i −0.561530 + 0.972598i 0.435833 + 0.900027i \(0.356454\pi\)
−0.997363 + 0.0725709i \(0.976880\pi\)
\(384\) −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
\(388\) 45.7599 + 79.2584i 2.32311 + 4.02374i
\(389\) −11.8885 −0.602773 −0.301387 0.953502i \(-0.597449\pi\)
−0.301387 + 0.953502i \(0.597449\pi\)
\(390\) 62.8050 15.5402i 3.18025 0.786908i
\(391\) −6.58359 −0.332947
\(392\) 0 0
\(393\) −20.0623 34.7489i −1.01201 1.75285i
\(394\) 21.9894 38.0867i 1.10781 1.91878i
\(395\) −10.4721 −0.526910
\(396\) −17.3435 + 30.0398i −0.871542 + 1.50955i
\(397\) 0.708204 1.22665i 0.0355437 0.0615636i −0.847706 0.530466i \(-0.822017\pi\)
0.883250 + 0.468902i \(0.155350\pi\)
\(398\) 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 \(-0.512622\pi\)
\(402\) −87.1033 −4.34432
\(403\) 11.7705 + 12.2323i 0.586331 + 0.609333i
\(404\) 56.1246 2.79230
\(405\) −7.47214 12.9421i −0.371293 0.643099i
\(406\) 0 0
\(407\) −3.70820 + 6.42280i −0.183809 + 0.318366i
\(408\) 28.7984 1.42573
\(409\) 7.21885 12.5034i 0.356949 0.618254i −0.630500 0.776189i \(-0.717150\pi\)
0.987450 + 0.157935i \(0.0504837\pi\)
\(410\) −2.61803 + 4.53457i −0.129295 + 0.223946i
\(411\) −6.85410 −0.338088
\(412\) −21.1353 + 36.6073i −1.04126 + 1.80351i
\(413\) 0 0
\(414\) 22.5623 + 39.0791i 1.10888 + 1.92063i
\(415\) 17.5623 0.862100
\(416\) −37.9894 + 9.39993i −1.86258 + 0.460869i
\(417\) −11.9443 −0.584914
\(418\) −4.50000 7.79423i −0.220102 0.381228i
\(419\) −5.97214 10.3440i −0.291758 0.505340i 0.682468 0.730916i \(-0.260907\pi\)
−0.974226 + 0.225576i \(0.927574\pi\)
\(420\) 0 0
\(421\) 1.41641 0.0690315 0.0345157 0.999404i \(-0.489011\pi\)
0.0345157 + 0.999404i \(0.489011\pi\)
\(422\) −6.16312 + 10.6748i −0.300016 + 0.519643i
\(423\) −4.30902 + 7.46344i −0.209512 + 0.362885i
\(424\) 28.1246 1.36585
\(425\) −1.36475 + 2.36381i −0.0661999 + 0.114662i
\(426\) 48.5967 + 84.1720i 2.35452 + 4.07815i
\(427\) 0 0
\(428\) −16.4164 −0.793517
\(429\) −16.9894 + 4.20378i −0.820254 + 0.202960i
\(430\) −86.1033 −4.15227
\(431\) −3.89919 6.75359i −0.187817 0.325309i 0.756705 0.653756i \(-0.226808\pi\)
−0.944522 + 0.328448i \(0.893475\pi\)
\(432\) −11.0172 19.0824i −0.530066 0.918102i
\(433\) 0.500000 0.866025i 0.0240285 0.0416185i −0.853761 0.520665i \(-0.825684\pi\)
0.877790 + 0.479046i \(0.159017\pi\)
\(434\) 0 0
\(435\) 24.2984 42.0860i 1.16502 2.01787i
\(436\) 6.57295 11.3847i 0.314787 0.545227i
\(437\) −8.29180 −0.396650
\(438\) −6.85410 + 11.8717i −0.327502 + 0.567250i
\(439\) 7.42705 + 12.8640i 0.354474 + 0.613967i 0.987028 0.160550i \(-0.0513267\pi\)
−0.632554 + 0.774516i \(0.717993\pi\)
\(440\) 18.1353 + 31.4112i 0.864564 + 1.49747i
\(441\) 0 0
\(442\) 9.63525 + 10.0133i 0.458302 + 0.476282i
\(443\) −5.23607 −0.248773 −0.124387 0.992234i \(-0.539696\pi\)
−0.124387 + 0.992234i \(0.539696\pi\)
\(444\) −25.4164 44.0225i −1.20621 2.08922i
\(445\) −6.42705 11.1320i −0.304671 0.527706i
\(446\) 26.5344 45.9590i 1.25644 2.17622i
\(447\) 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 \(0.319100\pi\)
\(450\) 18.7082 0.881913
\(451\) 0.708204 1.22665i 0.0333480 0.0577605i
\(452\) −3.57295 6.18853i −0.168057 0.291084i
\(453\) 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 \(0.950753\pi\)
\(458\) −17.1803 29.7572i −0.802785 1.39046i
\(459\) −1.64590 + 2.85078i −0.0768239 + 0.133063i
\(460\) 56.8328 2.64984
\(461\) −6.10739 + 10.5783i −0.284450 + 0.492681i −0.972476 0.233005i \(-0.925144\pi\)
0.688026 + 0.725686i \(0.258477\pi\)
\(462\) 0 0
\(463\) 6.70820 0.311757 0.155878 0.987776i \(-0.450179\pi\)
0.155878 + 0.987776i \(0.450179\pi\)
\(464\) −34.9336 + 60.5068i −1.62175 + 2.80896i
\(465\) 16.1353 + 27.9471i 0.748255 + 1.29601i
\(466\) −3.42705 5.93583i −0.158755 0.274972i
\(467\) −2.34752 −0.108630 −0.0543152 0.998524i \(-0.517298\pi\)
−0.0543152 + 0.998524i \(0.517298\pi\)
\(468\) 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
\(473\) 23.2918 1.07096
\(474\) −13.7082 + 23.7433i −0.629639 + 1.09057i
\(475\) −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
\(479\) 12.4894 + 21.6322i 0.570653 + 0.988400i 0.996499 + 0.0836047i \(0.0266433\pi\)
−0.425846 + 0.904796i \(0.640023\pi\)
\(480\) −74.3951 −3.39566
\(481\) 4.00000 13.8564i 0.182384 0.631798i
\(482\) −64.3050 −2.92901
\(483\) 0 0
\(484\) 18.3541 + 31.7902i 0.834277 + 1.44501i
\(485\) −24.6803 + 42.7476i −1.12068 + 1.94107i
\(486\) −56.6869 −2.57137
\(487\) −14.9894 + 25.9623i −0.679233 + 1.17647i 0.295980 + 0.955194i \(0.404354\pi\)
−0.975212 + 0.221271i \(0.928979\pi\)
\(488\) −22.4164 + 38.8264i −1.01474 + 1.75759i
\(489\) −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
\(493\) 10.4377 0.470090
\(494\) 12.1353 + 12.6113i 0.545991 + 0.567410i
\(495\) −18.7082 −0.840871
\(496\) −23.1976 40.1794i −1.04160 1.80411i
\(497\) 0 0
\(498\) 22.9894 39.8187i 1.03018 1.78432i
\(499\) 14.8541 0.664961 0.332480 0.943110i \(-0.392114\pi\)
0.332480 + 0.943110i \(0.392114\pi\)
\(500\) −19.9894 + 34.6226i −0.893951 + 1.54837i
\(501\) 18.6353 32.2772i 0.832562 1.44204i
\(502\) −2.00000 −0.0892644
\(503\) 13.3090 23.0519i 0.593420 1.02783i −0.400348 0.916363i \(-0.631111\pi\)
0.993768 0.111470i \(-0.0355559\pi\)
\(504\) 0 0
\(505\) 15.1353 + 26.2150i 0.673510 + 1.16655i
\(506\) −21.7082 −0.965047
\(507\) 30.1074 15.8710i 1.33712 0.704855i
\(508\) −101.228 −4.49126
\(509\) −9.29837 16.1053i −0.412143 0.713853i 0.582981 0.812486i \(-0.301886\pi\)
−0.995124 + 0.0986331i \(0.968553\pi\)
\(510\) 13.2082 + 22.8773i 0.584869 + 1.01302i
\(511\) 0 0
\(512\) −40.3050 −1.78124
\(513\) −2.07295 + 3.59045i −0.0915229 + 0.158522i
\(514\) 21.9164 37.9603i 0.966691 1.67436i
\(515\) −22.7984 −1.00462
\(516\) −79.8222 + 138.256i −3.51398 + 6.08638i
\(517\) −2.07295 3.59045i −0.0911682 0.157908i
\(518\) 0 0
\(519\) 23.5623 1.03427
\(520\) −48.9058 50.8244i −2.14466 2.22880i
\(521\) −18.6525 −0.817180 −0.408590 0.912718i \(-0.633979\pi\)
−0.408590 + 0.912718i \(0.633979\pi\)
\(522\) −35.7705 61.9563i −1.56563 2.71176i
\(523\) 0.562306 + 0.973942i 0.0245879 + 0.0425875i 0.878058 0.478555i \(-0.158839\pi\)
−0.853470 + 0.521143i \(0.825506\pi\)
\(524\) −37.1976 + 64.4281i −1.62498 + 2.81455i
\(525\) 0 0
\(526\) −11.7812 + 20.4056i −0.513683 + 0.889724i
\(527\) −3.46556 + 6.00252i −0.150962 + 0.261474i
\(528\) 47.8328 2.08166
\(529\) 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
\(534\) −33.6525 −1.45629
\(535\) −4.42705 7.66788i −0.191398 0.331511i
\(536\) 47.4787 + 82.2355i 2.05077 + 3.55203i
\(537\) 11.7812 20.4056i 0.508394 0.880565i
\(538\) 75.2492 3.24422
\(539\) 0 0
\(540\) 14.2082 24.6093i 0.611424 1.05902i
\(541\) 35.2705 1.51640 0.758199 0.652023i \(-0.226080\pi\)
0.758199 + 0.652023i \(0.226080\pi\)
\(542\) −11.0172 + 19.0824i −0.473230 + 0.819659i
\(543\) 12.7082 + 22.0113i 0.545361 + 0.944593i
\(544\) −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
\(549\) −11.5623 20.0265i −0.493467 0.854710i
\(550\) −4.50000 + 7.79423i −0.191881 + 0.332347i
\(551\) 13.1459 0.560034
\(552\) 43.7426 75.7645i 1.86181 3.22475i
\(553\) 0 0
\(554\) −13.0902 −0.556148
\(555\) 13.7082 23.7433i 0.581881 1.00785i
\(556\) 11.0729 + 19.1789i 0.469598 + 0.813367i
\(557\) 13.9894 + 24.2303i 0.592748 + 1.02667i 0.993860 + 0.110641i \(0.0352904\pi\)
−0.401112 + 0.916029i \(0.631376\pi\)
\(558\) 47.5066 2.01111
\(559\) −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 \(-0.979667\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(564\) 28.4164 1.19655
\(565\) 1.92705 3.33775i 0.0810716 0.140420i
\(566\) 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 \(0.934751\pi\)
\(570\) 16.6353 + 28.8131i 0.696774 + 1.20685i
\(571\) 24.6869 1.03312 0.516558 0.856252i \(-0.327213\pi\)
0.516558 + 0.856252i \(0.327213\pi\)
\(572\) 22.5000 + 23.3827i 0.940772 + 0.977679i
\(573\) 55.9787 2.33854
\(574\) 0 0
\(575\) 4.14590 + 7.18091i 0.172896 + 0.299464i
\(576\) −16.7812 + 29.0658i −0.699215 + 1.21108i
\(577\) 43.8328 1.82478 0.912392 0.409318i \(-0.134233\pi\)
0.912392 + 0.409318i \(0.134233\pi\)
\(578\) 19.4164 33.6302i 0.807616 1.39883i
\(579\) 7.85410 13.6037i 0.326405 0.565351i
\(580\) −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
\(584\) 14.9443 0.618398
\(585\) 35.3156 8.73834i 1.46012 0.361286i
\(586\) 17.7082 0.731519
\(587\) −9.95492 17.2424i −0.410883 0.711671i 0.584103 0.811679i \(-0.301446\pi\)
−0.994987 + 0.100009i \(0.968113\pi\)
\(588\) 0 0
\(589\) −4.36475 + 7.55996i −0.179846 + 0.311503i
\(590\) −15.3262 −0.630971
\(591\) 21.9894 38.0867i 0.904521 1.56668i
\(592\) −19.7082 + 34.1356i −0.810002 + 1.40296i
\(593\) −43.7984 −1.79858 −0.899292 0.437349i \(-0.855917\pi\)
−0.899292 + 0.437349i \(0.855917\pi\)
\(594\) −5.42705 + 9.39993i −0.222675 + 0.385684i
\(595\) 0 0
\(596\) −4.50000 7.79423i −0.184327 0.319264i
\(597\) 63.9230 2.61619
\(598\) 40.9787 10.1396i 1.67574 0.414639i
\(599\) 29.5066 1.20561 0.602803 0.797890i \(-0.294050\pi\)
0.602803 + 0.797890i \(0.294050\pi\)
\(600\) −18.1353 31.4112i −0.740369 1.28236i
\(601\) 20.1976 + 34.9832i 0.823876 + 1.42699i 0.902776 + 0.430112i \(0.141526\pi\)
−0.0788998 + 0.996883i \(0.525141\pi\)
\(602\) 0 0
\(603\) −48.9787 −1.99457
\(604\) 3.13525 5.43042i 0.127572 0.220961i
\(605\) −9.89919 + 17.1459i −0.402459 + 0.697080i
\(606\) 79.2492 3.21928
\(607\) −11.5000 + 19.9186i −0.466771 + 0.808470i −0.999279 0.0379540i \(-0.987916\pi\)
0.532509 + 0.846424i \(0.321249\pi\)
\(608\) −10.0623 17.4284i −0.408080 0.706816i
\(609\) 0 0
\(610\) −41.1246 −1.66509
\(611\) 5.59017 + 5.80948i 0.226154 + 0.235026i
\(612\) 27.5410 1.11328
\(613\) −17.2812 29.9318i −0.697979 1.20894i −0.969166 0.246409i \(-0.920749\pi\)
0.271187 0.962527i \(-0.412584\pi\)
\(614\) −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 \(0.167024\pi\)
\(618\) −29.8435 + 51.6904i −1.20048 + 2.07929i
\(619\) −9.41641 −0.378477 −0.189239 0.981931i \(-0.560602\pi\)
−0.189239 + 0.981931i \(0.560602\pi\)
\(620\) 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
\(625\) −30.8328 −1.23331
\(626\) 32.8885 + 56.9646i 1.31449 + 2.27676i
\(627\) −4.50000 7.79423i −0.179713 0.311272i
\(628\) 36.0517 62.4433i 1.43862 2.49176i
\(629\) 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 \(0.926633\pi\)
\(632\) 29.8885 1.18890
\(633\) −6.16312 + 10.6748i −0.244962 + 0.424287i
\(634\) −34.3435 59.4846i −1.36395 2.36244i
\(635\) −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
\(640\) 1.42705 + 2.47172i 0.0564091 + 0.0977035i
\(641\) 23.7533 41.1419i 0.938199 1.62501i 0.169370 0.985553i \(-0.445827\pi\)
0.768829 0.639455i \(-0.220840\pi\)
\(642\) −23.1803 −0.914855
\(643\) −3.50000 + 6.06218i −0.138027 + 0.239069i −0.926750 0.375680i \(-0.877409\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 0 0
\(645\) −86.1033 −3.39032
\(646\) −3.57295 + 6.18853i −0.140576 + 0.243484i
\(647\) 12.3820 + 21.4462i 0.486785 + 0.843137i 0.999885 0.0151924i \(-0.00483607\pi\)
−0.513099 + 0.858329i \(0.671503\pi\)
\(648\) 21.3262 + 36.9381i 0.837774 + 1.45107i
\(649\) 4.14590 0.162741
\(650\) 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
\(655\) −40.1246 −1.56780
\(656\) 3.76393 6.51932i 0.146957 0.254537i
\(657\) −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
\(661\) −24.2705 42.0378i −0.944013 1.63508i −0.757715 0.652586i \(-0.773684\pi\)
−0.186299 0.982493i \(-0.559649\pi\)
\(662\) −26.5623 −1.03237
\(663\) 9.63525 + 10.0133i 0.374202 + 0.388882i
\(664\) −50.1246 −1.94521
\(665\) 0 0
\(666\) −20.1803 34.9534i −0.781972 1.35442i
\(667\) 15.8541 27.4601i 0.613873 1.06326i
\(668\) −69.1033 −2.67369
\(669\) 26.5344 45.9590i 1.02588 1.77688i
\(670\) −43.5517 + 75.4337i −1.68255 + 2.91426i
\(671\) 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
\(675\) 4.14590 0.159576
\(676\) −53.3951 33.6302i −2.05366 1.29347i
\(677\) −43.7426 −1.68117 −0.840583 0.541682i \(-0.817788\pi\)
−0.840583 + 0.541682i \(0.817788\pi\)
\(678\) −5.04508 8.73834i −0.193755 0.335594i
\(679\) 0 0
\(680\) 14.3992 24.9401i 0.552184 0.956410i
\(681\) −3.85410 −0.147690
\(682\) −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 \(0.175633\pi\)
\(684\) 34.6869 1.32629
\(685\) −3.42705 + 5.93583i −0.130941 + 0.226796i
\(686\) 0 0
\(687\) −17.1803 29.7572i −0.655471 1.13531i
\(688\) 123.790 4.71946
\(689\) 9.40983 + 9.77898i 0.358486 + 0.372550i
\(690\) 80.2492 3.05504
\(691\) −2.92705 5.06980i −0.111350 0.192864i 0.804965 0.593323i \(-0.202184\pi\)
−0.916315 + 0.400458i \(0.868851\pi\)
\(692\) −21.8435 37.8340i −0.830364 1.43823i
\(693\) 0 0
\(694\) 80.5410 3.05730
\(695\) −5.97214 + 10.3440i −0.226536 + 0.392372i
\(696\) −69.3500 + 120.118i −2.62871 + 4.55305i
\(697\) −1.12461 −0.0425977
\(698\) 27.1074 46.9514i 1.02603 1.77714i
\(699\) −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 \(0.431940\pi\)
\(702\) 5.85410 20.2792i 0.220949 0.765389i
\(703\) 7.41641 0.279715
\(704\) −8.07295 13.9828i −0.304261 0.526995i
\(705\) 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
\(709\) −11.7812 + 20.4056i −0.442450 + 0.766347i −0.997871 0.0652231i \(-0.979224\pi\)
0.555420 + 0.831570i \(0.312557\pi\)
\(710\) 97.1935 3.64761
\(711\) −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
\(716\) −43.6869 −1.63266
\(717\) 32.3435 + 56.0205i 1.20789 + 2.09212i
\(718\) 28.9164 + 50.0847i 1.07915 + 1.86914i
\(719\) 4.06231 7.03612i 0.151498 0.262403i −0.780280 0.625430i \(-0.784923\pi\)
0.931779 + 0.363027i \(0.118257\pi\)
\(720\) −99.4296 −3.70552
\(721\) 0 0
\(722\) 20.3713 35.2842i 0.758142 1.31314i
\(723\) −64.3050 −2.39153
\(724\) 23.5623 40.8111i 0.875686 1.51673i
\(725\) −6.57295 11.3847i −0.244113 0.422816i
\(726\) 25.9164 + 44.8885i 0.961848 + 1.66597i
\(727\) 30.7082 1.13890 0.569452 0.822025i \(-0.307155\pi\)
0.569452 + 0.822025i \(0.307155\pi\)
\(728\) 0 0
\(729\) −39.5623 −1.46527
\(730\) 6.85410 + 11.8717i 0.253682 + 0.439390i
\(731\) −9.24671 16.0158i −0.342002 0.592365i
\(732\) −38.1246 + 66.0338i −1.40913 + 2.44068i
\(733\) 32.2705 1.19194 0.595969 0.803007i \(-0.296768\pi\)
0.595969 + 0.803007i \(0.296768\pi\)
\(734\) −1.85410 + 3.21140i −0.0684362 + 0.118535i
\(735\) 0 0
\(736\) −48.5410 −1.78925
\(737\) 11.7812 20.4056i 0.433964 0.751648i
\(738\) 3.85410 + 6.67550i 0.141871 + 0.245729i
\(739\) 3.43769 + 5.95426i 0.126458 + 0.219031i 0.922302 0.386470i \(-0.126306\pi\)
−0.795844 + 0.605502i \(0.792973\pi\)
\(740\) −50.8328 −1.86865
\(741\) 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
\(746\) −53.8328 −1.97096
\(747\) 12.9271 22.3903i 0.472976 0.819219i
\(748\) −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 \(0.969313\pi\)
\(752\) −11.0172 19.0824i −0.401757 0.695863i
\(753\) −2.00000 −0.0728841
\(754\) −64.9681 + 16.0754i −2.36600 + 0.585433i
\(755\) 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 \(-0.336592\pi\)
\(758\) 8.04508 13.9345i 0.292211 0.506124i
\(759\) −21.7082 −0.787958
\(760\) 18.1353 31.4112i 0.657835 1.13940i
\(761\) −14.4271 + 24.9884i −0.522980 + 0.905828i 0.476662 + 0.879087i \(0.341846\pi\)
−0.999642 + 0.0267417i \(0.991487\pi\)
\(762\) −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
\(766\) 57.5410 2.07904
\(767\) −7.82624 + 1.93649i −0.282589 + 0.0699227i
\(768\) −38.1246 −1.37570
\(769\) −9.20820 15.9491i −0.332056 0.575138i 0.650859 0.759199i \(-0.274409\pi\)
−0.982915 + 0.184061i \(0.941076\pi\)
\(770\) 0 0
\(771\) 21.9164 37.9603i 0.789300 1.36711i
\(772\) −29.1246 −1.04822
\(773\) 12.6803 21.9630i 0.456080 0.789954i −0.542669 0.839946i \(-0.682586\pi\)
0.998750 + 0.0499924i \(0.0159197\pi\)
\(774\) −63.3779 + 109.774i −2.27807 + 3.94574i
\(775\) 8.72949 0.313573
\(776\) 70.4402 122.006i 2.52866 4.37976i
\(777\) 0 0
\(778\) 15.5623 + 26.9547i 0.557936 + 0.966373i
\(779\) −1.41641 −0.0507481
\(780\) −83.1763 86.4393i −2.97819 3.09502i
\(781\) −26.2918 −0.940794
\(782\)