Properties

Label 637.2.h.g.165.2
Level $637$
Weight $2$
Character 637.165
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.h (of order \(3\), degree \(2\), not 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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.2
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 637.165
Dual form 637.2.h.g.471.2

$q$-expansion

\(f(q)\) \(=\) \(q+2.61803 q^{2} +(1.30902 + 2.26728i) q^{3} +4.85410 q^{4} +(-1.30902 - 2.26728i) q^{5} +(3.42705 + 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 + 3.33775i) q^{9} +O(q^{10})\) \(q+2.61803 q^{2} +(1.30902 + 2.26728i) q^{3} +4.85410 q^{4} +(-1.30902 - 2.26728i) 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} +(6.35410 + 11.0056i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(3.42705 - 5.93583i) q^{15} +9.85410 q^{16} -1.47214 q^{17} +(-5.04508 + 8.73834i) q^{18} +(0.927051 - 1.60570i) q^{19} +(-6.35410 - 11.0056i) q^{20} +(-2.42705 - 4.20378i) q^{22} -4.47214 q^{23} +(9.78115 + 16.9415i) q^{24} +(-0.927051 + 1.60570i) q^{25} +(-6.54508 + 6.80185i) q^{26} -2.23607 q^{27} +(-3.54508 + 6.14027i) q^{29} +(8.97214 - 15.5402i) q^{30} +(2.35410 - 4.07742i) q^{31} +10.8541 q^{32} +(2.42705 - 4.20378i) q^{33} -3.85410 q^{34} +(-9.35410 + 16.2018i) q^{36} +4.00000 q^{37} +(2.42705 - 4.20378i) q^{38} +(-9.16312 - 2.26728i) 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} +10.0902 q^{45} -11.7082 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} +(-12.1353 + 12.6113i) q^{52} +(-1.88197 + 3.25966i) q^{53} -5.85410 q^{54} +(-2.42705 + 4.20378i) q^{55} +4.85410 q^{57} +(-9.28115 + 16.0754i) q^{58} -2.23607 q^{59} +(16.6353 - 28.8131i) q^{60} +(3.00000 - 5.19615i) q^{61} +(6.16312 - 10.6748i) q^{62} +8.70820 q^{64} +(9.16312 + 2.26728i) q^{65} +(6.35410 - 11.0056i) q^{66} +(6.35410 + 11.0056i) q^{67} -7.14590 q^{68} +(-5.85410 - 10.1396i) q^{69} +(7.09017 + 12.2805i) q^{71} +(-14.3992 + 24.9401i) q^{72} +(1.00000 - 1.73205i) q^{73} +10.4721 q^{74} -4.85410 q^{75} +(4.50000 - 7.79423i) q^{76} +(-23.9894 - 5.93583i) q^{78} +(-2.00000 - 3.46410i) 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} +(-16.4443 - 28.4823i) q^{86} -18.5623 q^{87} +(-6.92705 - 11.9980i) q^{88} +4.90983 q^{89} +26.4164 q^{90} -21.7082 q^{92} +12.3262 q^{93} +(2.92705 + 5.06980i) q^{94} -4.85410 q^{95} +(14.2082 + 24.6093i) q^{96} +(-9.42705 - 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{2} + 3q^{3} + 6q^{4} - 3q^{5} + 7q^{6} + 12q^{8} - q^{9} + O(q^{10}) \) \( 4q + 6q^{2} + 3q^{3} + 6q^{4} - 3q^{5} + 7q^{6} + 12q^{8} - q^{9} - 7q^{10} + 3q^{11} + 12q^{12} - 10q^{13} + 7q^{15} + 26q^{16} + 12q^{17} - 9q^{18} - 3q^{19} - 12q^{20} - 3q^{22} + 19q^{24} + 3q^{25} - 15q^{26} - 3q^{29} + 18q^{30} - 4q^{31} + 30q^{32} + 3q^{33} - 2q^{34} - 24q^{36} + 16q^{37} + 3q^{38} - 21q^{39} - 19q^{40} - 6q^{41} - 5q^{43} - 18q^{44} + 18q^{45} - 20q^{46} + 27q^{48} - 3q^{50} - q^{51} - 15q^{52} - 12q^{53} - 10q^{54} - 3q^{55} + 6q^{57} - 17q^{58} + 33q^{60} + 12q^{61} + 9q^{62} + 8q^{64} + 21q^{65} + 12q^{66} + 12q^{67} - 42q^{68} - 10q^{69} + 6q^{71} - 33q^{72} + 4q^{73} + 24q^{74} - 6q^{75} + 18q^{76} - 49q^{78} - 8q^{79} - 27q^{80} - 2q^{81} - 4q^{82} + q^{85} - 30q^{86} - 34q^{87} - 21q^{88} + 42q^{89} + 52q^{90} - 60q^{92} + 18q^{93} + 5q^{94} - 6q^{95} + 30q^{96} - 31q^{97} + 42q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.61803 1.85123 0.925615 0.378467i \(-0.123549\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) 1.30902 + 2.26728i 0.755761 + 1.30902i 0.944995 + 0.327085i \(0.106066\pi\)
−0.189234 + 0.981932i \(0.560600\pi\)
\(4\) 4.85410 2.42705
\(5\) −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
\(9\) −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 \(0.923507\pi\)
\(12\) 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
\(16\) 9.85410 2.46353
\(17\) −1.47214 −0.357045 −0.178523 0.983936i \(-0.557132\pi\)
−0.178523 + 0.983936i \(0.557132\pi\)
\(18\) −5.04508 + 8.73834i −1.18914 + 2.05965i
\(19\) 0.927051 1.60570i 0.212680 0.368373i −0.739872 0.672747i \(-0.765114\pi\)
0.952552 + 0.304375i \(0.0984475\pi\)
\(20\) −6.35410 11.0056i −1.42082 2.46093i
\(21\) 0 0
\(22\) −2.42705 4.20378i −0.517449 0.896248i
\(23\) −4.47214 −0.932505 −0.466252 0.884652i \(-0.654396\pi\)
−0.466252 + 0.884652i \(0.654396\pi\)
\(24\) 9.78115 + 16.9415i 1.99657 + 3.45816i
\(25\) −0.927051 + 1.60570i −0.185410 + 0.321140i
\(26\) −6.54508 + 6.80185i −1.28360 + 1.33395i
\(27\) −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 \(0.937940\pi\)
\(30\) 8.97214 15.5402i 1.63808 2.83724i
\(31\) 2.35410 4.07742i 0.422809 0.732327i −0.573404 0.819273i \(-0.694377\pi\)
0.996213 + 0.0869459i \(0.0277107\pi\)
\(32\) 10.8541 1.91875
\(33\) 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
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 2.42705 4.20378i 0.393720 0.681942i
\(39\) −9.16312 2.26728i −1.46727 0.363056i
\(40\) −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
\(45\) 10.0902 1.50415
\(46\) −11.7082 −1.72628
\(47\) 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
\(52\) −12.1353 + 12.6113i −1.68286 + 1.74888i
\(53\) −1.88197 + 3.25966i −0.258508 + 0.447749i −0.965842 0.259130i \(-0.916564\pi\)
0.707334 + 0.706879i \(0.249897\pi\)
\(54\) −5.85410 −0.796642
\(55\) −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
\(59\) −2.23607 −0.291111 −0.145556 0.989350i \(-0.546497\pi\)
−0.145556 + 0.989350i \(0.546497\pi\)
\(60\) 16.6353 28.8131i 2.14760 3.71976i
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) 6.16312 10.6748i 0.782717 1.35571i
\(63\) 0 0
\(64\) 8.70820 1.08853
\(65\) 9.16312 + 2.26728i 1.13655 + 0.281222i
\(66\) 6.35410 11.0056i 0.782136 1.35470i
\(67\) 6.35410 + 11.0056i 0.776277 + 1.34455i 0.934074 + 0.357080i \(0.116228\pi\)
−0.157797 + 0.987472i \(0.550439\pi\)
\(68\) −7.14590 −0.866567
\(69\) −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 \(0.515037\pi\)
\(72\) −14.3992 + 24.9401i −1.69696 + 2.93922i
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) 10.4721 1.21736
\(75\) −4.85410 −0.560503
\(76\) 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 \(0.905577\pi\)
\(80\) −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 \(-0.379988\pi\)
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
\(87\) −18.5623 −1.99009
\(88\) −6.92705 11.9980i −0.738426 1.27899i
\(89\) 4.90983 0.520441 0.260220 0.965549i \(-0.416205\pi\)
0.260220 + 0.965549i \(0.416205\pi\)
\(90\) 26.4164 2.78453
\(91\) 0 0
\(92\) −21.7082 −2.26324
\(93\) 12.3262 1.27817
\(94\) 2.92705 + 5.06980i 0.301902 + 0.522910i
\(95\) −4.85410 −0.498020
\(96\) 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
\(100\) −4.50000 + 7.79423i −0.450000 + 0.779423i
\(101\) 5.78115 + 10.0133i 0.575246 + 0.996356i 0.996015 + 0.0891877i \(0.0284271\pi\)
−0.420769 + 0.907168i \(0.638240\pi\)
\(102\) −5.04508 8.73834i −0.499538 0.865225i
\(103\) 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
\(107\) −3.38197 −0.326947 −0.163473 0.986548i \(-0.552270\pi\)
−0.163473 + 0.986548i \(0.552270\pi\)
\(108\) −10.8541 −1.04444
\(109\) 1.35410 2.34537i 0.129699 0.224646i −0.793861 0.608100i \(-0.791932\pi\)
0.923560 + 0.383454i \(0.125265\pi\)
\(110\) −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 0.829325 0.558766i \(-0.188725\pi\)
−0.898568 + 0.438833i \(0.855392\pi\)
\(114\) 12.7082 1.19023
\(115\) 5.85410 + 10.1396i 0.545898 + 0.945523i
\(116\) −17.2082 + 29.8055i −1.59774 + 2.76737i
\(117\) −3.85410 13.3510i −0.356312 1.23430i
\(118\) −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
\(122\) 7.85410 13.6037i 0.711077 1.23162i
\(123\) −2.00000 −0.180334
\(124\) 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 0.134094 0.990969i \(-0.457187\pi\)
0.791157 0.611613i \(-0.209479\pi\)
\(128\) 1.09017 0.0963583
\(129\) 16.4443 28.4823i 1.44784 2.50773i
\(130\) 23.9894 + 5.93583i 2.10401 + 0.520606i
\(131\) 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
\(136\) −11.0000 −0.943242
\(137\) −2.61803 −0.223674 −0.111837 0.993727i \(-0.535673\pi\)
−0.111837 + 0.993727i \(0.535673\pi\)
\(138\) −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
\(143\) 6.48936 + 1.60570i 0.542667 + 0.134275i
\(144\) −18.9894 + 32.8905i −1.58245 + 2.74088i
\(145\) 18.5623 1.54152
\(146\) 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 \(0.190865\pi\)
\(150\) −12.7082 −1.03762
\(151\) 0.645898 1.11873i 0.0525624 0.0910408i −0.838547 0.544829i \(-0.816594\pi\)
0.891109 + 0.453788i \(0.149928\pi\)
\(152\) 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
\(156\) −44.4787 11.0056i −3.56115 0.881155i
\(157\) −7.42705 + 12.8640i −0.592743 + 1.02666i 0.401118 + 0.916026i \(0.368622\pi\)
−0.993861 + 0.110635i \(0.964712\pi\)
\(158\) −5.23607 9.06914i −0.416559 0.721502i
\(159\) −9.85410 −0.781481
\(160\) −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 \(0.120276\pi\)
\(164\) −1.85410 + 3.21140i −0.144781 + 0.250768i
\(165\) −12.7082 −0.989332
\(166\) 17.5623 1.36310
\(167\) −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
\(171\) 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 −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) −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
\(178\) 12.8541 0.963456
\(179\) 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) 48.9787 3.65066
\(181\) 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
\(184\) −33.4164 −2.46349
\(185\) −5.23607 9.06914i −0.384963 0.666776i
\(186\) 32.2705 2.36619
\(187\) 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
\(191\) −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 \(0.764050\pi\)
\(194\) −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 \(-0.0375368\pi\)
\(198\) 18.7082 1.32953
\(199\) −24.4164 −1.73083 −0.865417 0.501053i \(-0.832946\pi\)
−0.865417 + 0.501053i \(0.832946\pi\)
\(200\) −6.92705 + 11.9980i −0.489816 + 0.848387i
\(201\) −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
\(205\) 2.00000 0.139686
\(206\) 11.3992 + 19.7440i 0.794219 + 1.37563i
\(207\) 8.61803 14.9269i 0.598995 1.03749i
\(208\) −24.6353 + 25.6017i −1.70815 + 1.77516i
\(209\) −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 \(0.218481\pi\)
\(212\) −9.13525 + 15.8227i −0.627412 + 1.08671i
\(213\) −18.5623 + 32.1509i −1.27187 + 2.20294i
\(214\) −8.85410 −0.605254
\(215\) −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
\(219\) 5.23607 0.353821
\(220\) −11.7812 + 20.4056i −0.794285 + 1.37574i
\(221\) 3.68034 3.82472i 0.247566 0.257279i
\(222\) 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
\(227\) 1.47214 0.0977091 0.0488545 0.998806i \(-0.484443\pi\)
0.0488545 + 0.998806i \(0.484443\pi\)
\(228\) 23.5623 1.56045
\(229\) 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 \(0.860664\pi\)
\(234\) −10.0902 34.9534i −0.659615 2.28497i
\(235\) 2.92705 5.06980i 0.190940 0.330717i
\(236\) −10.8541 −0.706542
\(237\) 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
\(241\) 24.5623 1.58220 0.791099 0.611689i \(-0.209509\pi\)
0.791099 + 0.611689i \(0.209509\pi\)
\(242\) 9.89919 17.1459i 0.636344 1.10218i
\(243\) −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
\(247\) 1.85410 + 6.42280i 0.117974 + 0.408673i
\(248\) 17.5902 30.4671i 1.11698 1.93466i
\(249\) 8.78115 + 15.2094i 0.556483 + 0.963857i
\(250\) −21.5623 −1.36372
\(251\) −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
\(254\) 27.2984 47.2822i 1.71285 2.96675i
\(255\) −5.04508 + 8.73834i −0.315935 + 0.547216i
\(256\) −14.5623 −0.910144
\(257\) 16.7426 1.04438 0.522189 0.852830i \(-0.325116\pi\)
0.522189 + 0.852830i \(0.325116\pi\)
\(258\) 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
\(262\) 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
\(268\) 30.8435 + 53.4224i 1.88406 + 3.26329i
\(269\) −28.7426 −1.75247 −0.876235 0.481884i \(-0.839953\pi\)
−0.876235 + 0.481884i \(0.839953\pi\)
\(270\) 7.66312 + 13.2729i 0.466363 + 0.807764i
\(271\) −8.41641 −0.511260 −0.255630 0.966775i \(-0.582283\pi\)
−0.255630 + 0.966775i \(0.582283\pi\)
\(272\) −14.5066 −0.879590
\(273\) 0 0
\(274\) −6.85410 −0.414071
\(275\) 3.43769 0.207301
\(276\) −28.4164 49.2187i −1.71047 2.96262i
\(277\) −5.00000 −0.300421 −0.150210 0.988654i \(-0.547995\pi\)
−0.150210 + 0.988654i \(0.547995\pi\)
\(278\) −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 \(0.294399\pi\)
\(282\) −7.66312 + 13.2729i −0.456332 + 0.790390i
\(283\) −6.70820 11.6190i −0.398761 0.690675i 0.594812 0.803865i \(-0.297226\pi\)
−0.993573 + 0.113190i \(0.963893\pi\)
\(284\) 34.4164 + 59.6110i 2.04224 + 3.53726i
\(285\) −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
\(289\) −14.8328 −0.872519
\(290\) 48.5967 2.85370
\(291\) 24.6803 42.7476i 1.44679 2.50591i
\(292\) 4.85410 8.40755i 0.284065 0.492015i
\(293\) 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
\(296\) 29.8885 1.73724
\(297\) 2.07295 + 3.59045i 0.120285 + 0.208339i
\(298\) −2.42705 + 4.20378i −0.140595 + 0.243518i
\(299\) 11.1803 11.6190i 0.646576 0.671941i
\(300\) −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
\(304\) 9.13525 15.8227i 0.523943 0.907496i
\(305\) −15.7082 −0.899449
\(306\) 7.42705 12.8640i 0.424576 0.735388i
\(307\) −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
\(310\) −32.2705 −1.83284
\(311\) −1.66312 + 2.88061i −0.0943068 + 0.163344i −0.909319 0.416099i \(-0.863397\pi\)
0.815012 + 0.579444i \(0.196730\pi\)
\(312\) −68.4681 16.9415i −3.87624 0.959121i
\(313\) −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 \(-0.430322\pi\)
\(318\) −25.7984 −1.44670
\(319\) 13.1459 0.736029
\(320\) −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
\(325\) −1.85410 6.42280i −0.102847 0.356273i
\(326\) 4.85410 8.40755i 0.268844 0.465651i
\(327\) 7.09017 0.392087
\(328\) −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 \(0.0767186\pi\)
\(332\) 32.5623 1.78709
\(333\) −7.70820 + 13.3510i −0.422407 + 0.731630i
\(334\) −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 \(0.601978\pi\)
\(338\) −1.30902 34.0093i −0.0712011 1.84986i
\(339\) 1.92705 3.33775i 0.104663 0.181282i
\(340\) 9.35410 + 16.2018i 0.507297 + 0.878665i
\(341\) −8.72949 −0.472728
\(342\) 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
\(346\) 11.7812 20.4056i 0.633359 1.09701i
\(347\) 30.7639 1.65149 0.825747 0.564040i \(-0.190754\pi\)
0.825747 + 0.564040i \(0.190754\pi\)
\(348\) −90.1033 −4.83005
\(349\) −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
\(353\) −11.0729 19.1789i −0.589354 1.02079i −0.994317 0.106458i \(-0.966049\pi\)
0.404964 0.914333i \(-0.367284\pi\)
\(354\) −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
\(359\) 11.0451 + 19.1306i 0.582937 + 1.00968i 0.995129 + 0.0985799i \(0.0314300\pi\)
−0.412192 + 0.911097i \(0.635237\pi\)
\(360\) 75.3951 3.97367
\(361\) 7.78115 + 13.4774i 0.409534 + 0.709334i
\(362\) 25.4164 1.33586
\(363\) 19.7984 1.03915
\(364\) 0 0
\(365\) −5.23607 −0.274068
\(366\) 41.1246 2.14962
\(367\) 0.708204 + 1.22665i 0.0369679 + 0.0640304i 0.883917 0.467643i \(-0.154897\pi\)
−0.846949 + 0.531673i \(0.821563\pi\)
\(368\) −44.0689 −2.29725
\(369\) −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
\(373\) 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
\(376\) 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 \(0.116211\pi\)
\(380\) −23.5623 −1.20872
\(381\) 54.5967 2.79708
\(382\) −27.9894 + 48.4790i −1.43206 + 2.48040i
\(383\) 10.9894 19.0341i 0.561530 0.972598i −0.435833 0.900027i \(-0.643546\pi\)
0.997363 0.0725709i \(-0.0231204\pi\)
\(384\) 1.42705 + 2.47172i 0.0728239 + 0.126135i
\(385\) 0 0
\(386\) 7.85410 + 13.6037i 0.399763 + 0.692410i
\(387\) 48.4164 2.46114
\(388\) −45.7599 79.2584i −2.32311 4.02374i
\(389\) 5.94427 10.2958i 0.301387 0.522017i −0.675064 0.737759i \(-0.735884\pi\)
0.976450 + 0.215743i \(0.0692172\pi\)
\(390\) 17.9443 + 62.1608i 0.908644 + 3.14763i
\(391\) 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
\(395\) −5.23607 + 9.06914i −0.263455 + 0.456318i
\(396\) 34.6869 1.74308
\(397\) −0.708204 + 1.22665i −0.0355437 + 0.0615636i −0.883250 0.468902i \(-0.844650\pi\)
0.847706 + 0.530466i \(0.177983\pi\)
\(398\) −63.9230 −3.20417
\(399\) 0 0
\(400\) −9.13525 + 15.8227i −0.456763 + 0.791136i
\(401\) 35.4508 1.77033 0.885165 0.465276i \(-0.154045\pi\)
0.885165 + 0.465276i \(0.154045\pi\)
\(402\) −43.5517 + 75.4337i −2.17216 + 3.76229i
\(403\) 4.70820 + 16.3097i 0.234532 + 0.812444i
\(404\) 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
\(409\) 14.4377 0.713898 0.356949 0.934124i \(-0.383817\pi\)
0.356949 + 0.934124i \(0.383817\pi\)
\(410\) 5.23607 0.258591
\(411\) −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
\(416\) −27.1353 + 28.1998i −1.33042 + 1.38261i
\(417\) 5.97214 10.3440i 0.292457 0.506550i
\(418\) −9.00000 −0.440204
\(419\) 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 \(0.489011\pi\)
\(422\) −6.16312 + 10.6748i −0.300016 + 0.519643i
\(423\) −8.61803 −0.419023
\(424\) −14.0623 + 24.3566i −0.682926 + 1.18286i
\(425\) 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
\(429\) 4.85410 + 16.8151i 0.234358 + 0.811841i
\(430\) −43.0517 + 74.5677i −2.07614 + 3.59597i
\(431\) −3.89919 6.75359i −0.187817 0.325309i 0.756705 0.653756i \(-0.226808\pi\)
−0.944522 + 0.328448i \(0.893475\pi\)
\(432\) −22.0344 −1.06013
\(433\) −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
\(436\) 6.57295 11.3847i 0.314787 0.545227i
\(437\) −4.14590 + 7.18091i −0.198325 + 0.343509i
\(438\) 13.7082 0.655003
\(439\) 14.8541 0.708948 0.354474 0.935066i \(-0.384660\pi\)
0.354474 + 0.935066i \(0.384660\pi\)
\(440\) −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 \(0.793637\pi\)
\(444\) 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 0.538212 0.842809i \(-0.319100\pi\)
−0.999000 + 0.0447005i \(0.985767\pi\)
\(450\) −9.35410 16.2018i −0.440957 0.763759i
\(451\) 1.41641 0.0666960
\(452\) −3.57295 6.18853i −0.168057 0.291084i
\(453\) 3.38197 0.158899
\(454\) 3.85410 0.180882
\(455\) 0 0
\(456\) 36.2705 1.69852
\(457\) 15.4164 0.721149 0.360575 0.932730i \(-0.382581\pi\)
0.360575 + 0.932730i \(0.382581\pi\)
\(458\) 17.1803 + 29.7572i 0.802785 + 1.39046i
\(459\) 3.29180 0.153648
\(460\) 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 \(0.450179\pi\)
\(464\) −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
\(467\) −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
\(471\) −38.8885 −1.79189
\(472\) −16.7082 −0.769057
\(473\) −11.6459 + 20.1713i −0.535479 + 0.927477i
\(474\) 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
\(478\) −64.6869 −2.95871
\(479\) −12.4894 21.6322i −0.570653 0.988400i −0.996499 0.0836047i \(-0.973357\pi\)
0.425846 0.904796i \(-0.359977\pi\)
\(480\) 37.1976 64.4281i 1.69783 2.94073i
\(481\) −10.0000 + 10.3923i −0.455961 + 0.473848i
\(482\) 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
\(486\) −28.3435 + 49.0923i −1.28569 + 2.22687i
\(487\) 29.9787 1.35847 0.679233 0.733923i \(-0.262313\pi\)
0.679233 + 0.733923i \(0.262313\pi\)
\(488\) 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 −0.971235 0.238125i \(-0.923467\pi\)
0.691839 + 0.722051i \(0.256801\pi\)
\(492\) −9.70820 −0.437680
\(493\) 5.21885 9.03931i 0.235045 0.407110i
\(494\) 4.85410 + 16.8151i 0.218396 + 0.756547i
\(495\) −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 \(0.941219\pi\)
\(500\) −39.9787 −1.78790
\(501\) −37.2705 −1.66512
\(502\) −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
\(507\) 28.7984 18.1383i 1.27898 0.805549i
\(508\) 50.6140 87.6660i 2.24563 3.88955i
\(509\) −18.5967 −0.824286 −0.412143 0.911119i \(-0.635220\pi\)
−0.412143 + 0.911119i \(0.635220\pi\)
\(510\) −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
\(514\) 43.8328 1.93338
\(515\) 11.3992 19.7440i 0.502308 0.870023i
\(516\) 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
\(520\) 68.4681 + 16.9415i 3.00252 + 0.742932i
\(521\) −9.32624 + 16.1535i −0.408590 + 0.707698i −0.994732 0.102510i \(-0.967313\pi\)
0.586142 + 0.810208i \(0.300646\pi\)
\(522\) −35.7705 61.9563i −1.56563 2.71176i
\(523\) 1.12461 0.0491758 0.0245879 0.999698i \(-0.492173\pi\)
0.0245879 + 0.999698i \(0.492173\pi\)
\(524\) 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
\(528\) 23.9164 41.4244i 1.04083 1.80277i
\(529\) −3.00000 −0.130435
\(530\) 25.7984 1.12061
\(531\) 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
\(535\) 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
\(541\) −17.6353 30.5452i −0.758199 1.31324i −0.943768 0.330608i \(-0.892746\pi\)
0.185569 0.982631i \(-0.440587\pi\)
\(542\) −22.0344 −0.946460
\(543\) 12.7082 + 22.0113i 0.545361 + 0.944593i
\(544\) −15.9787 −0.685082
\(545\) −7.09017 −0.303710
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) −12.7082 −0.542868
\(549\) 11.5623 + 20.0265i 0.493467 + 0.854710i
\(550\) 9.00000 0.383761
\(551\) 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
\(555\) 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 \(0.631376\pi\)
\(558\) 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
\(562\) 52.8328 2.22862
\(563\) −21.0557 −0.887393 −0.443697 0.896177i \(-0.646333\pi\)
−0.443697 + 0.896177i \(0.646333\pi\)
\(564\) −14.2082 + 24.6093i −0.598273 + 1.03624i
\(565\) −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
\(569\) 14.9443 0.626496 0.313248 0.949671i \(-0.398583\pi\)
0.313248 + 0.949671i \(0.398583\pi\)
\(570\) −16.6353 28.8131i −0.696774 1.20685i
\(571\) −12.3435 + 21.3795i −0.516558 + 0.894704i 0.483257 + 0.875478i \(0.339453\pi\)
−0.999815 + 0.0192259i \(0.993880\pi\)
\(572\) 31.5000 + 7.79423i 1.31708 + 0.325893i
\(573\) −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
\(577\) 21.9164 37.9603i 0.912392 1.58031i 0.101717 0.994813i \(-0.467567\pi\)
0.810675 0.585496i \(-0.199100\pi\)
\(578\) −38.8328 −1.61523
\(579\) −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
\(583\) 6.97871 0.289029
\(584\) 7.47214 12.9421i 0.309199 0.535549i
\(585\) −25.2254 + 26.2150i −1.04294 + 1.08386i
\(586\) 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
\(591\) 43.9787 1.80904
\(592\) 39.4164 1.62000
\(593\) −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
\(598\) 29.2705 30.4188i 1.19696 1.24392i
\(599\) −14.7533 + 25.5534i −0.602803 + 1.04409i 0.389592 + 0.920988i \(0.372616\pi\)
−0.992395 + 0.123098i \(0.960717\pi\)
\(600\) −36.2705 −1.48074
\(601\) −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
\(604\) 3.13525 5.43042i 0.127572 0.220961i
\(605\) −19.7984 −0.804918
\(606\) −39.6246 + 68.6318i −1.60964 + 2.78798i
\(607\) 11.5000 19.9186i 0.466771 0.808470i −0.532509 0.846424i \(-0.678751\pi\)
0.999279 + 0.0379540i \(0.0120840\pi\)
\(608\) 10.0623 17.4284i 0.408080 0.706816i
\(609\) 0 0
\(610\) −41.1246 −1.66509
\(611\) −7.82624 1.93649i −0.316616 0.0783421i
\(612\) 13.7705 23.8512i 0.556640 0.964129i
\(613\) −17.2812 29.9318i −0.697979 1.20894i −0.969166 0.246409i \(-0.920749\pi\)
0.271187 0.962527i \(-0.412584\pi\)
\(614\) −12.7082 −0.512861
\(615\) 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 \(0.833690\pi\)
\(618\) −29.8435 + 51.6904i −1.20048 + 2.07929i
\(619\) −4.70820 + 8.15485i −0.189239 + 0.327771i −0.944997 0.327080i \(-0.893935\pi\)
0.755758 + 0.654851i \(0.227269\pi\)
\(620\) −59.8328 −2.40294
\(621\) 10.0000 0.401286
\(622\) −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
\(626\) −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 −0.973555 0.228454i \(-0.926633\pi\)
0.288931 0.957350i \(-0.406700\pi\)
\(632\) −14.9443 25.8842i −0.594451 1.02962i
\(633\) −12.3262 −0.489924
\(634\) −34.3435 59.4846i −1.36395 2.36244i
\(635\) −54.5967 −2.16661
\(636\) −47.8328 −1.89669
\(637\) 0 0
\(638\) 34.4164 1.36256
\(639\) −54.6525 −2.16202
\(640\) −1.42705 2.47172i −0.0564091 0.0977035i
\(641\) −47.5066 −1.87640 −0.938199 0.346098i \(-0.887507\pi\)
−0.938199 + 0.346098i \(0.887507\pi\)
\(642\) −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
\(646\) −3.57295 + 6.18853i −0.140576 + 0.243484i
\(647\) −12.3820 21.4462i −0.486785 0.843137i 0.513099 0.858329i \(-0.328497\pi\)
−0.999885 + 0.0151924i \(0.995164\pi\)
\(648\) 21.3262 + 36.9381i 0.837774 + 1.45107i
\(649\) 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
\(653\) −0.381966 −0.0149475 −0.00747374 0.999972i \(-0.502379\pi\)
−0.00747374 + 0.999972i \(0.502379\pi\)
\(654\) 18.5623 0.725844
\(655\) 20.0623 34.7489i 0.783899 1.35775i
\(656\) −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 0.999214 0.0396343i \(-0.0126193\pi\)
−0.533931 + 0.845528i \(0.679286\pi\)
\(660\) −61.6869 −2.40116
\(661\) 24.2705 + 42.0378i 0.944013 + 1.63508i 0.757715 + 0.652586i \(0.226316\pi\)
0.186299 + 0.982493i \(0.440351\pi\)
\(662\) 13.2812 23.0036i 0.516187 0.894062i
\(663\) 13.4894 + 3.33775i 0.523883 + 0.129627i
\(664\) 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
\(668\) −34.5517 + 59.8452i −1.33684 + 2.31548i
\(669\) −53.0689 −2.05176
\(670\) 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 −0.188165 0.982137i \(-0.560254\pi\)
0.944639 0.328113i \(-0.106413\pi\)
\(674\) −30.2705 −1.16598
\(675\) 2.07295 3.59045i 0.0797878 0.138197i
\(676\) −2.42705 63.0566i −0.0933481 2.42526i
\(677\) −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
\(682\) −22.8541 −0.875129
\(683\) 1.47214 0.0563297 0.0281649 0.999603i \(-0.491034\pi\)
0.0281649 + 0.999603i \(0.491034\pi\)
\(684\) 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
\(689\) −3.76393 13.0386i −0.143394 0.496733i
\(690\) −40.1246 + 69.4979i −1.52752 + 2.64574i
\(691\) −5.85410 −0.222701 −0.111350 0.993781i \(-0.535518\pi\)
−0.111350 + 0.993781i \(0.535518\pi\)
\(692\) 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
\(696\) −138.700 −5.25741
\(697\) 0.562306 0.973942i 0.0212989 0.0368907i
\(698\) −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 \(0.431940\pi\)
\(702\) 14.6353 15.2094i 0.552372 0.574042i
\(703\) 3.70820 6.42280i 0.139858 0.242240i
\(704\) −8.07295 13.9828i −0.304261 0.526995i
\(705\) 15.3262 0.577220
\(706\) −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 \(0.312557\pi\)
\(710\) 48.5967 84.1720i 1.82380 3.15892i
\(711\) 15.4164 0.578160
\(712\) 36.6869 1.37490
\(713\) −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
\(717\) −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 −0.931779 0.363027i \(-0.881743\pi\)
0.780280 + 0.625430i \(0.215077\pi\)
\(720\) 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
\(724\) 47.1246 1.75137
\(725\) −6.57295 11.3847i −0.244113 0.422816i
\(726\) 51.8328 1.92370
\(727\) −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
\(730\) −13.7082 −0.507363
\(731\) 9.24671 + 16.0158i 0.342002 + 0.592365i
\(732\) 76.2492 2.81825
\(733\) 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
\(737\) 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 \(0.792973\pi\)
\(740\) −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 \(0.910179\pi\)
\(744\) 92.1033 3.37667
\(745\) 4.85410 0.177841
\(746\) 26.9164 46.6206i 0.985480 1.70690i
\(747\) −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
\(751\) 22.7082 0.828634 0.414317 0.910133i \(-0.364020\pi\)
0.414317 + 0.910133i \(0.364020\pi\)
\(752\) 11.0172 + 19.0824i 0.401757 + 0.695863i
\(753\) 1.00000 1.73205i 0.0364420 0.0631194i
\(754\) −18.5623 64.3017i −0.675999 2.34173i
\(755\) −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 \(0.996742\pi\)
\(758\) 8.04508 13.9345i 0.292211 0.506124i
\(759\) −10.8541 + 18.7999i −0.393979 + 0.682392i
\(760\) −36.2705 −1.31567
\(761\) 14.4271 24.9884i 0.522980 0.905828i −0.476662 0.879087i \(-0.658154\pi\)
0.999642 0.0267417i \(-0.00851317\pi\)
\(762\) 142.936 5.17803
\(763\) 0 0
\(764\) −51.8951 + 89.8850i −1.87750 + 3.25192i
\(765\) −14.8541 −0.537051
\(766\) 28.7705 49.8320i 1.03952 1.80050i
\(767\) 5.59017 5.80948i 0.201849 0.209768i
\(768\) −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
\(773\) 25.3607 0.912160 0.456080 0.889939i \(-0.349253\pi\)
0.456080 + 0.889939i \(0.349253\pi\)
\(774\) 126.756 4.55614
\(775\) 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
\(780\) 33.2705 + 115.252i 1.19128 + 4.12670i
\(781\) 13.1459 22.7694i 0.470397 0.814752i
\(782\) 17.2361