Properties

Label 637.2.h.g.471.2
Level $637$
Weight $2$
Character 637.471
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 471.2
Root \(0.809017 + 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.g.165.2

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 −0.189234 0.981932i \(-0.560600\pi\)
0.944995 0.327085i \(-0.106066\pi\)
\(4\) 4.85410 2.42705
\(5\) −1.30902 + 2.26728i −0.585410 + 1.01396i 0.409414 + 0.912349i \(0.365733\pi\)
−0.994824 + 0.101611i \(0.967600\pi\)
\(6\) 3.42705 5.93583i 1.39909 2.42329i
\(7\) 0 0
\(8\) 7.47214 2.64180
\(9\) −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 −0.971265 0.238002i \(-0.923507\pi\)
0.691748 + 0.722139i \(0.256841\pi\)
\(12\) 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 0.952552 0.304375i \(-0.0984475\pi\)
−0.739872 + 0.672747i \(0.765114\pi\)
\(20\) −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 −0.981054 0.193734i \(-0.937940\pi\)
0.322748 0.946485i \(-0.395393\pi\)
\(30\) 8.97214 + 15.5402i 1.63808 + 2.83724i
\(31\) 2.35410 + 4.07742i 0.422809 + 0.732327i 0.996213 0.0869459i \(-0.0277107\pi\)
−0.573404 + 0.819273i \(0.694377\pi\)
\(32\) 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 0.834657 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
\(45\) 10.0902 1.50415
\(46\) −11.7082 −1.72628
\(47\) 1.11803 1.93649i 0.163082 0.282466i −0.772890 0.634539i \(-0.781190\pi\)
0.935973 + 0.352073i \(0.114523\pi\)
\(48\) 12.8992 22.3420i 1.86184 3.22480i
\(49\) 0 0
\(50\) −2.42705 4.20378i −0.343237 0.594504i
\(51\) −1.92705 + 3.33775i −0.269841 + 0.467379i
\(52\) −12.1353 12.6113i −1.68286 1.74888i
\(53\) −1.88197 3.25966i −0.258508 0.447749i 0.707334 0.706879i \(-0.249897\pi\)
−0.965842 + 0.259130i \(0.916564\pi\)
\(54\) −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 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) 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 −0.157797 0.987472i \(-0.550439\pi\)
0.934074 0.357080i \(-0.116228\pi\)
\(68\) −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 −0.0472218 0.998884i \(-0.515037\pi\)
0.888670 0.458547i \(-0.151630\pi\)
\(72\) −14.3992 24.9401i −1.69696 2.93922i
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) 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 −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) −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 −0.227854 + 0.973695i \(0.573171\pi\)
−0.729318 + 0.684175i \(0.760162\pi\)
\(98\) 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 −0.420769 0.907168i \(-0.638240\pi\)
0.996015 0.0891877i \(-0.0284271\pi\)
\(102\) −5.04508 + 8.73834i −0.499538 + 0.865225i
\(103\) 4.35410 7.54153i 0.429022 0.743089i −0.567764 0.823191i \(-0.692191\pi\)
0.996787 + 0.0801026i \(0.0255248\pi\)
\(104\) −18.6803 19.4132i −1.83176 1.90362i
\(105\) 0 0
\(106\) −4.92705 8.53390i −0.478557 0.828886i
\(107\) −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 0.923560 0.383454i \(-0.125265\pi\)
−0.793861 + 0.608100i \(0.791932\pi\)
\(110\) −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 \(0.188725\pi\)
\(114\) 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 0.791157 + 0.611613i \(0.209479\pi\)
0.134094 + 0.990969i \(0.457187\pi\)
\(128\) 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 −0.308506 0.951222i \(-0.599829\pi\)
0.978036 0.208437i \(-0.0668377\pi\)
\(132\) 11.7812 + 20.4056i 1.02542 + 1.77608i
\(133\) 0 0
\(134\) 16.6353 28.8131i 1.43707 2.48907i
\(135\) 2.92705 5.06980i 0.251920 0.436339i
\(136\) −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 −0.946403 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
\(143\) 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 0.825551 0.564328i \(-0.190865\pi\)
−0.901498 + 0.432784i \(0.857531\pi\)
\(150\) −12.7082 −1.03762
\(151\) 0.645898 + 1.11873i 0.0525624 + 0.0910408i 0.891109 0.453788i \(-0.149928\pi\)
−0.838547 + 0.544829i \(0.816594\pi\)
\(152\) 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 −0.993861 0.110635i \(-0.964712\pi\)
0.401118 0.916026i \(-0.368622\pi\)
\(158\) −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 0.929457 0.368931i \(-0.120276\pi\)
−0.784232 + 0.620467i \(0.786943\pi\)
\(164\) −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 −0.998216 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
\(171\) 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 \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) −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 −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) 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 −0.935593 0.353079i \(-0.885135\pi\)
0.162021 0.986787i \(-0.448199\pi\)
\(192\) 11.3992 19.7440i 0.822665 1.42490i
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) −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 \(0.629130\pi\)
\(198\) 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 0.773545 0.633741i \(-0.218481\pi\)
−0.935608 + 0.353039i \(0.885148\pi\)
\(212\) −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 −0.975371 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
\(227\) 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 −0.563535 0.826092i \(-0.690559\pi\)
0.997184 + 0.0749895i \(0.0238923\pi\)
\(230\) 15.3262 26.5458i 1.01058 1.75038i
\(231\) 0 0
\(232\) −26.4894 45.8809i −1.73911 3.01223i
\(233\) −1.30902 + 2.26728i −0.0857566 + 0.148535i −0.905713 0.423891i \(-0.860664\pi\)
0.819957 + 0.572425i \(0.193997\pi\)
\(234\) −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 −0.877828 0.478975i \(-0.841008\pi\)
0.853719 + 0.520734i \(0.174342\pi\)
\(252\) 0 0
\(253\) 4.14590 7.18091i 0.260650 0.451460i
\(254\) 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 −0.970758 0.240059i \(-0.922833\pi\)
0.693276 + 0.720672i \(0.256167\pi\)
\(264\) 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 −0.993573 0.113190i \(-0.963893\pi\)
0.594812 + 0.803865i \(0.297226\pi\)
\(284\) 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 −0.750166 0.661250i \(-0.770026\pi\)
0.947742 + 0.319037i \(0.103360\pi\)
\(294\) 0 0
\(295\) 2.92705 5.06980i 0.170419 0.295175i
\(296\) 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 0.815012 0.579444i \(-0.196730\pi\)
−0.909319 + 0.416099i \(0.863397\pi\)
\(312\) −68.4681 + 16.9415i −3.87624 + 0.959121i
\(313\) −12.5623 + 21.7586i −0.710064 + 1.22987i 0.254769 + 0.967002i \(0.418000\pi\)
−0.964833 + 0.262864i \(0.915333\pi\)
\(314\) −19.4443 33.6785i −1.09730 1.90059i
\(315\) 0 0
\(316\) −9.70820 + 16.8151i −0.546129 + 0.945923i
\(317\) −13.1180 + 22.7211i −0.736782 + 1.27614i 0.217155 + 0.976137i \(0.430322\pi\)
−0.953937 + 0.300007i \(0.903011\pi\)
\(318\) −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 0.971095 0.238692i \(-0.0767186\pi\)
−0.692261 + 0.721647i \(0.743385\pi\)
\(332\) 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 −0.997962 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
\(353\) −11.0729 + 19.1789i −0.589354 + 1.02079i 0.404964 + 0.914333i \(0.367284\pi\)
−0.994317 + 0.106458i \(0.966049\pi\)
\(354\) −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 −0.412192 0.911097i \(-0.635237\pi\)
0.995129 0.0985799i \(-0.0314300\pi\)
\(360\) 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 −0.846949 0.531673i \(-0.821563\pi\)
0.883917 + 0.467643i \(0.154897\pi\)
\(368\) −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 0.999287 + 0.0377522i \(0.0120198\pi\)
−0.466949 + 0.884284i \(0.654647\pi\)
\(374\) 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 0.934092 0.357032i \(-0.116211\pi\)
−0.776245 + 0.630431i \(0.782878\pi\)
\(380\) −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 0.997363 + 0.0725709i \(0.0231204\pi\)
−0.435833 + 0.900027i \(0.643546\pi\)
\(384\) 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 0.976450 0.215743i \(-0.0692172\pi\)
−0.675064 + 0.737759i \(0.735884\pi\)
\(390\) 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 0.847706 0.530466i \(-0.177983\pi\)
−0.883250 + 0.468902i \(0.844650\pi\)
\(398\) −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 0.974226 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 \(0.489011\pi\)
\(422\) −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 −0.944522 0.328448i \(-0.893475\pi\)
0.756705 + 0.653756i \(0.226808\pi\)
\(432\) −22.0344 −1.06013
\(433\) −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
\(436\) 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 −0.797106 0.603839i \(-0.793637\pi\)
0.921493 + 0.388395i \(0.126970\pi\)
\(444\) 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 \(0.319100\pi\)
\(450\) −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 −0.688026 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 \(0.450179\pi\)
\(464\) −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 −0.891905 0.452224i \(-0.850631\pi\)
0.837589 + 0.546300i \(0.183964\pi\)
\(468\) −18.7082 + 64.8071i −0.864787 + 2.99571i
\(469\) 0 0
\(470\) 7.66312 + 13.2729i 0.353473 + 0.612234i
\(471\) −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 0.425846 + 0.904796i \(0.359977\pi\)
−0.996499 + 0.0836047i \(0.973357\pi\)
\(480\) 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 0.691839 0.722051i \(-0.256801\pi\)
−0.971235 + 0.238125i \(0.923467\pi\)
\(492\) −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 −0.982998 0.183619i \(-0.941219\pi\)
0.650517 + 0.759492i \(0.274552\pi\)
\(500\) −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 0.400348 + 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
\(507\) 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 0.586142 0.810208i \(-0.300646\pi\)
−0.994732 + 0.102510i \(0.967313\pi\)
\(522\) −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 0.185569 + 0.982631i \(0.440587\pi\)
−0.943768 + 0.330608i \(0.892746\pi\)
\(542\) −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 −0.401112 0.916029i \(-0.631376\pi\)
0.993860 0.110641i \(-0.0352904\pi\)
\(558\) 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 −0.999815 0.0192259i \(-0.993880\pi\)
0.483257 0.875478i \(-0.339453\pi\)
\(572\) 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 0.810675 + 0.585496i \(0.199100\pi\)
0.101717 + 0.994813i \(0.467567\pi\)
\(578\) −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 0.994987 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
\(591\) 43.9787 1.80904
\(592\) 39.4164 1.62000
\(593\) −21.8992 + 37.9305i −0.899292 + 1.55762i −0.0708905 + 0.997484i \(0.522584\pi\)
−0.828401 + 0.560135i \(0.810749\pi\)
\(594\) 5.42705 9.39993i 0.222675 0.385684i
\(595\) 0 0
\(596\) −4.50000 7.79423i −0.184327 0.319264i
\(597\) −31.9615 + 55.3589i −1.30810 + 2.26569i
\(598\) 29.2705 + 30.4188i 1.19696 + 1.24392i
\(599\) −14.7533 25.5534i −0.602803 1.04409i −0.992395 0.123098i \(-0.960717\pi\)
0.389592 0.920988i \(-0.372616\pi\)
\(600\) −36.2705 −1.48074
\(601\) −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
\(604\) 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 0.999279 0.0379540i \(-0.0120840\pi\)
−0.532509 + 0.846424i \(0.678751\pi\)
\(608\) 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 0.271187 + 0.962527i \(0.412584\pi\)
−0.969166 + 0.246409i \(0.920749\pi\)
\(614\) −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 −0.866586 0.499028i \(-0.833690\pi\)
0.865464 + 0.500971i \(0.167024\pi\)
\(618\) −29.8435 51.6904i −1.20048 2.07929i
\(619\) −4.70820 8.15485i −0.189239 0.327771i 0.755758 0.654851i \(-0.227269\pi\)
−0.944997 + 0.327080i \(0.893935\pi\)
\(620\) −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 0.288931 + 0.957350i \(0.406700\pi\)
−0.973555 + 0.228454i \(0.926633\pi\)
\(632\) −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 −0.788723 0.614749i \(-0.789257\pi\)
0.926750 + 0.375680i \(0.122591\pi\)
\(644\) 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 \(-0.995164\pi\)
0.513099 + 0.858329i \(0.328497\pi\)
\(648\) 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 −0.533931 0.845528i \(-0.679286\pi\)
0.999214 + 0.0396343i \(0.0126193\pi\)
\(660\) −61.6869 −2.40116
\(661\) 24.2705 42.0378i 0.944013 1.63508i 0.186299 0.982493i \(-0.440351\pi\)
0.757715 0.652586i \(-0.226316\pi\)
\(662\) 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 0.944639 + 0.328113i \(0.106413\pi\)
−0.188165 + 0.982137i \(0.560254\pi\)
\(674\) −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 0.0488191 + 0.998808i \(0.484454\pi\)
−0.889402 + 0.457125i \(0.848879\pi\)
\(678\) 5.04508 + 8.73834i 0.193755 + 0.335594i
\(679\) 0 0
\(680\) 14.3992 24.9401i 0.552184 0.956410i
\(681\) 1.92705 3.33775i 0.0738448 0.127903i
\(682\) −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 0.555420 0.831570i \(-0.312557\pi\)
−0.997871 + 0.0652231i \(0.979224\pi\)
\(710\) 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 0.780280 0.625430i \(-0.215077\pi\)
−0.931779 + 0.363027i \(0.881743\pi\)
\(720\) 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 −0.397440 0.917628i \(-0.630101\pi\)
0.993409 0.114621i \(-0.0365653\pi\)
\(734\) 1.85410 3.21140i 0.0684362 0.118535i
\(735\) 0 0
\(736\) −48.5410 −1.78925
\(737\) 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 −0.795844 0.605502i \(-0.792973\pi\)
0.922302 + 0.386470i \(0.126306\pi\)
\(740\) −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 \(-0.423154\pi\)
\(744\) 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 −0.999948 0.0102362i \(-0.996742\pi\)
0.491109 0.871098i \(-0.336592\pi\)
\(758\) 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 0.999642 + 0.0267417i \(0.00851317\pi\)
−0.476662 + 0.879087i \(0.658154\pi\)
\(762\) 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 0.982915 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
\(773\) 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 0.616