Properties

Label 1110.2.l.a.697.6
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 697.6
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.a.43.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.50038 + 1.65797i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.06172 - 1.06172i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.50038 + 1.65797i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.06172 - 1.06172i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(1.65797 - 1.50038i) q^{10} +4.34528i q^{11} +(0.707107 + 0.707107i) q^{12} -4.56074i q^{13} +(-1.06172 + 1.06172i) q^{14} +(0.111436 - 2.23329i) q^{15} +1.00000 q^{16} -3.41073 q^{17} +1.00000 q^{18} +(3.26022 + 3.26022i) q^{19} +(-1.50038 - 1.65797i) q^{20} +1.50150i q^{21} +4.34528 q^{22} +3.95501i q^{23} +(0.707107 - 0.707107i) q^{24} +(-0.497735 + 4.97516i) q^{25} -4.56074 q^{26} +(0.707107 - 0.707107i) q^{27} +(1.06172 + 1.06172i) q^{28} +(1.85622 - 1.85622i) q^{29} +(-2.23329 - 0.111436i) q^{30} +(3.73156 + 3.73156i) q^{31} -1.00000i q^{32} +(3.07257 - 3.07257i) q^{33} +3.41073i q^{34} +(0.167321 - 3.35329i) q^{35} -1.00000i q^{36} +(2.01522 + 5.73924i) q^{37} +(3.26022 - 3.26022i) q^{38} +(-3.22493 + 3.22493i) q^{39} +(-1.65797 + 1.50038i) q^{40} +12.2599i q^{41} +1.50150 q^{42} -2.82236i q^{43} -4.34528i q^{44} +(-1.65797 + 1.50038i) q^{45} +3.95501 q^{46} +(5.10670 + 5.10670i) q^{47} +(-0.707107 - 0.707107i) q^{48} -4.74548i q^{49} +(4.97516 + 0.497735i) q^{50} +(2.41175 + 2.41175i) q^{51} +4.56074i q^{52} +(4.58664 - 4.58664i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-7.20434 + 6.51956i) q^{55} +(1.06172 - 1.06172i) q^{56} -4.61064i q^{57} +(-1.85622 - 1.85622i) q^{58} +(2.79480 + 2.79480i) q^{59} +(-0.111436 + 2.23329i) q^{60} +(1.42612 + 1.42612i) q^{61} +(3.73156 - 3.73156i) q^{62} +(1.06172 - 1.06172i) q^{63} -1.00000 q^{64} +(7.56157 - 6.84283i) q^{65} +(-3.07257 - 3.07257i) q^{66} +(-3.17883 + 3.17883i) q^{67} +3.41073 q^{68} +(2.79661 - 2.79661i) q^{69} +(-3.35329 - 0.167321i) q^{70} +9.34849 q^{71} -1.00000 q^{72} +(-6.35469 - 6.35469i) q^{73} +(5.73924 - 2.01522i) q^{74} +(3.86992 - 3.16602i) q^{75} +(-3.26022 - 3.26022i) q^{76} +(4.61348 - 4.61348i) q^{77} +(3.22493 + 3.22493i) q^{78} +(0.205500 + 0.205500i) q^{79} +(1.50038 + 1.65797i) q^{80} -1.00000 q^{81} +12.2599 q^{82} +(-2.55799 + 2.55799i) q^{83} -1.50150i q^{84} +(-5.11738 - 5.65489i) q^{85} -2.82236 q^{86} -2.62509 q^{87} -4.34528 q^{88} +(4.88031 - 4.88031i) q^{89} +(1.50038 + 1.65797i) q^{90} +(-4.84224 + 4.84224i) q^{91} -3.95501i q^{92} -5.27722i q^{93} +(5.10670 - 5.10670i) q^{94} +(-0.513789 + 10.2969i) q^{95} +(-0.707107 + 0.707107i) q^{96} -7.85190 q^{97} -4.74548 q^{98} -4.34528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{4} + 4q^{7} + O(q^{10}) \) \( 36q - 36q^{4} + 4q^{7} - 4q^{10} + 4q^{14} + 36q^{16} - 32q^{17} + 36q^{18} + 4q^{19} + 8q^{22} - 4q^{25} + 8q^{26} - 4q^{28} + 36q^{29} - 4q^{31} + 4q^{33} - 12q^{35} - 4q^{37} + 4q^{38} + 4q^{39} + 4q^{40} - 16q^{42} + 4q^{45} + 16q^{47} - 16q^{50} - 8q^{53} + 16q^{55} - 4q^{56} - 36q^{58} - 4q^{59} - 4q^{61} - 4q^{62} - 4q^{63} - 36q^{64} + 52q^{65} - 4q^{66} + 16q^{67} + 32q^{68} - 8q^{69} - 28q^{70} - 8q^{71} - 36q^{72} - 4q^{73} + 28q^{74} + 16q^{75} - 4q^{76} + 8q^{77} - 4q^{78} - 12q^{79} - 36q^{81} - 8q^{82} + 8q^{83} + 8q^{85} + 32q^{86} - 8q^{87} - 8q^{88} - 24q^{89} + 56q^{91} + 16q^{94} - 20q^{95} + 40q^{97} - 12q^{98} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.00000 −0.500000
\(5\) 1.50038 + 1.65797i 0.670989 + 0.741467i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) −1.06172 1.06172i −0.401294 0.401294i 0.477395 0.878689i \(-0.341581\pi\)
−0.878689 + 0.477395i \(0.841581\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 1.65797 1.50038i 0.524296 0.474461i
\(11\) 4.34528i 1.31015i 0.755564 + 0.655075i \(0.227363\pi\)
−0.755564 + 0.655075i \(0.772637\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 4.56074i 1.26492i −0.774593 0.632460i \(-0.782045\pi\)
0.774593 0.632460i \(-0.217955\pi\)
\(14\) −1.06172 + 1.06172i −0.283758 + 0.283758i
\(15\) 0.111436 2.23329i 0.0287725 0.576633i
\(16\) 1.00000 0.250000
\(17\) −3.41073 −0.827223 −0.413611 0.910453i \(-0.635733\pi\)
−0.413611 + 0.910453i \(0.635733\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.26022 + 3.26022i 0.747945 + 0.747945i 0.974093 0.226148i \(-0.0726133\pi\)
−0.226148 + 0.974093i \(0.572613\pi\)
\(20\) −1.50038 1.65797i −0.335495 0.370734i
\(21\) 1.50150i 0.327655i
\(22\) 4.34528 0.926416
\(23\) 3.95501i 0.824676i 0.911031 + 0.412338i \(0.135288\pi\)
−0.911031 + 0.412338i \(0.864712\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) −0.497735 + 4.97516i −0.0995471 + 0.995033i
\(26\) −4.56074 −0.894434
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 1.06172 + 1.06172i 0.200647 + 0.200647i
\(29\) 1.85622 1.85622i 0.344691 0.344691i −0.513437 0.858128i \(-0.671628\pi\)
0.858128 + 0.513437i \(0.171628\pi\)
\(30\) −2.23329 0.111436i −0.407741 0.0203452i
\(31\) 3.73156 + 3.73156i 0.670208 + 0.670208i 0.957764 0.287556i \(-0.0928428\pi\)
−0.287556 + 0.957764i \(0.592843\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.07257 3.07257i 0.534867 0.534867i
\(34\) 3.41073i 0.584935i
\(35\) 0.167321 3.35329i 0.0282824 0.566810i
\(36\) 1.00000i 0.166667i
\(37\) 2.01522 + 5.73924i 0.331300 + 0.943526i
\(38\) 3.26022 3.26022i 0.528877 0.528877i
\(39\) −3.22493 + 3.22493i −0.516402 + 0.516402i
\(40\) −1.65797 + 1.50038i −0.262148 + 0.237230i
\(41\) 12.2599i 1.91467i 0.288975 + 0.957337i \(0.406685\pi\)
−0.288975 + 0.957337i \(0.593315\pi\)
\(42\) 1.50150 0.231687
\(43\) 2.82236i 0.430406i −0.976569 0.215203i \(-0.930959\pi\)
0.976569 0.215203i \(-0.0690413\pi\)
\(44\) 4.34528i 0.655075i
\(45\) −1.65797 + 1.50038i −0.247156 + 0.223663i
\(46\) 3.95501 0.583134
\(47\) 5.10670 + 5.10670i 0.744889 + 0.744889i 0.973514 0.228626i \(-0.0734232\pi\)
−0.228626 + 0.973514i \(0.573423\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 4.74548i 0.677926i
\(50\) 4.97516 + 0.497735i 0.703594 + 0.0703904i
\(51\) 2.41175 + 2.41175i 0.337712 + 0.337712i
\(52\) 4.56074i 0.632460i
\(53\) 4.58664 4.58664i 0.630023 0.630023i −0.318051 0.948074i \(-0.603028\pi\)
0.948074 + 0.318051i \(0.103028\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) −7.20434 + 6.51956i −0.971433 + 0.879097i
\(56\) 1.06172 1.06172i 0.141879 0.141879i
\(57\) 4.61064i 0.610694i
\(58\) −1.85622 1.85622i −0.243733 0.243733i
\(59\) 2.79480 + 2.79480i 0.363852 + 0.363852i 0.865229 0.501377i \(-0.167173\pi\)
−0.501377 + 0.865229i \(0.667173\pi\)
\(60\) −0.111436 + 2.23329i −0.0143863 + 0.288316i
\(61\) 1.42612 + 1.42612i 0.182596 + 0.182596i 0.792486 0.609890i \(-0.208786\pi\)
−0.609890 + 0.792486i \(0.708786\pi\)
\(62\) 3.73156 3.73156i 0.473908 0.473908i
\(63\) 1.06172 1.06172i 0.133765 0.133765i
\(64\) −1.00000 −0.125000
\(65\) 7.56157 6.84283i 0.937897 0.848748i
\(66\) −3.07257 3.07257i −0.378208 0.378208i
\(67\) −3.17883 + 3.17883i −0.388355 + 0.388355i −0.874101 0.485745i \(-0.838548\pi\)
0.485745 + 0.874101i \(0.338548\pi\)
\(68\) 3.41073 0.413611
\(69\) 2.79661 2.79661i 0.336673 0.336673i
\(70\) −3.35329 0.167321i −0.400795 0.0199987i
\(71\) 9.34849 1.10946 0.554731 0.832030i \(-0.312821\pi\)
0.554731 + 0.832030i \(0.312821\pi\)
\(72\) −1.00000 −0.117851
\(73\) −6.35469 6.35469i −0.743760 0.743760i 0.229539 0.973299i \(-0.426278\pi\)
−0.973299 + 0.229539i \(0.926278\pi\)
\(74\) 5.73924 2.01522i 0.667173 0.234264i
\(75\) 3.86992 3.16602i 0.446860 0.365581i
\(76\) −3.26022 3.26022i −0.373972 0.373972i
\(77\) 4.61348 4.61348i 0.525755 0.525755i
\(78\) 3.22493 + 3.22493i 0.365151 + 0.365151i
\(79\) 0.205500 + 0.205500i 0.0231206 + 0.0231206i 0.718573 0.695452i \(-0.244796\pi\)
−0.695452 + 0.718573i \(0.744796\pi\)
\(80\) 1.50038 + 1.65797i 0.167747 + 0.185367i
\(81\) −1.00000 −0.111111
\(82\) 12.2599 1.35388
\(83\) −2.55799 + 2.55799i −0.280776 + 0.280776i −0.833418 0.552643i \(-0.813619\pi\)
0.552643 + 0.833418i \(0.313619\pi\)
\(84\) 1.50150i 0.163828i
\(85\) −5.11738 5.65489i −0.555058 0.613359i
\(86\) −2.82236 −0.304343
\(87\) −2.62509 −0.281439
\(88\) −4.34528 −0.463208
\(89\) 4.88031 4.88031i 0.517311 0.517311i −0.399445 0.916757i \(-0.630797\pi\)
0.916757 + 0.399445i \(0.130797\pi\)
\(90\) 1.50038 + 1.65797i 0.158154 + 0.174765i
\(91\) −4.84224 + 4.84224i −0.507605 + 0.507605i
\(92\) 3.95501i 0.412338i
\(93\) 5.27722i 0.547222i
\(94\) 5.10670 5.10670i 0.526716 0.526716i
\(95\) −0.513789 + 10.2969i −0.0527137 + 1.05644i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) −7.85190 −0.797240 −0.398620 0.917116i \(-0.630511\pi\)
−0.398620 + 0.917116i \(0.630511\pi\)
\(98\) −4.74548 −0.479366
\(99\) −4.34528 −0.436717
\(100\) 0.497735 4.97516i 0.0497735 0.497516i
\(101\) 3.02340i 0.300840i 0.988622 + 0.150420i \(0.0480625\pi\)
−0.988622 + 0.150420i \(0.951937\pi\)
\(102\) 2.41175 2.41175i 0.238799 0.238799i
\(103\) 13.8674 1.36640 0.683200 0.730231i \(-0.260588\pi\)
0.683200 + 0.730231i \(0.260588\pi\)
\(104\) 4.56074 0.447217
\(105\) −2.48945 + 2.25282i −0.242946 + 0.219853i
\(106\) −4.58664 4.58664i −0.445494 0.445494i
\(107\) 13.3916 + 13.3916i 1.29462 + 1.29462i 0.931900 + 0.362716i \(0.118150\pi\)
0.362716 + 0.931900i \(0.381850\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −5.95541 5.95541i −0.570424 0.570424i 0.361823 0.932247i \(-0.382155\pi\)
−0.932247 + 0.361823i \(0.882155\pi\)
\(110\) 6.51956 + 7.20434i 0.621615 + 0.686907i
\(111\) 2.63328 5.48323i 0.249940 0.520445i
\(112\) −1.06172 1.06172i −0.100323 0.100323i
\(113\) −9.16869 −0.862518 −0.431259 0.902228i \(-0.641930\pi\)
−0.431259 + 0.902228i \(0.641930\pi\)
\(114\) −4.61064 −0.431826
\(115\) −6.55729 + 5.93401i −0.611471 + 0.553349i
\(116\) −1.85622 + 1.85622i −0.172346 + 0.172346i
\(117\) 4.56074 0.421640
\(118\) 2.79480 2.79480i 0.257282 0.257282i
\(119\) 3.62125 + 3.62125i 0.331960 + 0.331960i
\(120\) 2.23329 + 0.111436i 0.203871 + 0.0101726i
\(121\) −7.88143 −0.716494
\(122\) 1.42612 1.42612i 0.129115 0.129115i
\(123\) 8.66905 8.66905i 0.781662 0.781662i
\(124\) −3.73156 3.73156i −0.335104 0.335104i
\(125\) −8.99547 + 6.63939i −0.804579 + 0.593845i
\(126\) −1.06172 1.06172i −0.0945859 0.0945859i
\(127\) −0.349491 0.349491i −0.0310123 0.0310123i 0.691431 0.722443i \(-0.256981\pi\)
−0.722443 + 0.691431i \(0.756981\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.99571 + 1.99571i −0.175712 + 0.175712i
\(130\) −6.84283 7.56157i −0.600155 0.663193i
\(131\) −10.2082 10.2082i −0.891895 0.891895i 0.102807 0.994701i \(-0.467218\pi\)
−0.994701 + 0.102807i \(0.967218\pi\)
\(132\) −3.07257 + 3.07257i −0.267433 + 0.267433i
\(133\) 6.92290i 0.600291i
\(134\) 3.17883 + 3.17883i 0.274609 + 0.274609i
\(135\) 2.23329 + 0.111436i 0.192211 + 0.00959084i
\(136\) 3.41073i 0.292467i
\(137\) −5.52765 5.52765i −0.472259 0.472259i 0.430386 0.902645i \(-0.358377\pi\)
−0.902645 + 0.430386i \(0.858377\pi\)
\(138\) −2.79661 2.79661i −0.238064 0.238064i
\(139\) 13.4120 1.13759 0.568797 0.822478i \(-0.307409\pi\)
0.568797 + 0.822478i \(0.307409\pi\)
\(140\) −0.167321 + 3.35329i −0.0141412 + 0.283405i
\(141\) 7.22196i 0.608199i
\(142\) 9.34849i 0.784508i
\(143\) 19.8177 1.65724
\(144\) 1.00000i 0.0833333i
\(145\) 5.86258 + 0.292528i 0.486861 + 0.0242931i
\(146\) −6.35469 + 6.35469i −0.525918 + 0.525918i
\(147\) −3.35556 + 3.35556i −0.276762 + 0.276762i
\(148\) −2.01522 5.73924i −0.165650 0.471763i
\(149\) 21.3340i 1.74775i −0.486149 0.873876i \(-0.661599\pi\)
0.486149 0.873876i \(-0.338401\pi\)
\(150\) −3.16602 3.86992i −0.258504 0.315978i
\(151\) 21.4210i 1.74322i 0.490202 + 0.871609i \(0.336923\pi\)
−0.490202 + 0.871609i \(0.663077\pi\)
\(152\) −3.26022 + 3.26022i −0.264438 + 0.264438i
\(153\) 3.41073i 0.275741i
\(154\) −4.61348 4.61348i −0.371765 0.371765i
\(155\) −0.588070 + 11.7856i −0.0472349 + 0.946639i
\(156\) 3.22493 3.22493i 0.258201 0.258201i
\(157\) 2.04779 + 2.04779i 0.163432 + 0.163432i 0.784085 0.620653i \(-0.213133\pi\)
−0.620653 + 0.784085i \(0.713133\pi\)
\(158\) 0.205500 0.205500i 0.0163487 0.0163487i
\(159\) −6.48649 −0.514412
\(160\) 1.65797 1.50038i 0.131074 0.118615i
\(161\) 4.19913 4.19913i 0.330938 0.330938i
\(162\) 1.00000i 0.0785674i
\(163\) −12.1359 −0.950560 −0.475280 0.879835i \(-0.657653\pi\)
−0.475280 + 0.879835i \(0.657653\pi\)
\(164\) 12.2599i 0.957337i
\(165\) 9.70426 + 0.484218i 0.755476 + 0.0376963i
\(166\) 2.55799 + 2.55799i 0.198539 + 0.198539i
\(167\) 8.95519 0.692973 0.346487 0.938055i \(-0.387375\pi\)
0.346487 + 0.938055i \(0.387375\pi\)
\(168\) −1.50150 −0.115844
\(169\) −7.80032 −0.600024
\(170\) −5.65489 + 5.11738i −0.433710 + 0.392485i
\(171\) −3.26022 + 3.26022i −0.249315 + 0.249315i
\(172\) 2.82236i 0.215203i
\(173\) 14.6997 + 14.6997i 1.11760 + 1.11760i 0.992093 + 0.125506i \(0.0400554\pi\)
0.125506 + 0.992093i \(0.459945\pi\)
\(174\) 2.62509i 0.199007i
\(175\) 5.81071 4.75379i 0.439248 0.359353i
\(176\) 4.34528i 0.327538i
\(177\) 3.95245i 0.297084i
\(178\) −4.88031 4.88031i −0.365794 0.365794i
\(179\) −6.65594 + 6.65594i −0.497488 + 0.497488i −0.910655 0.413167i \(-0.864423\pi\)
0.413167 + 0.910655i \(0.364423\pi\)
\(180\) 1.65797 1.50038i 0.123578 0.111832i
\(181\) −12.8467 −0.954886 −0.477443 0.878663i \(-0.658436\pi\)
−0.477443 + 0.878663i \(0.658436\pi\)
\(182\) 4.84224 + 4.84224i 0.358931 + 0.358931i
\(183\) 2.01684i 0.149089i
\(184\) −3.95501 −0.291567
\(185\) −6.49191 + 11.9522i −0.477295 + 0.878743i
\(186\) −5.27722 −0.386945
\(187\) 14.8206i 1.08379i
\(188\) −5.10670 5.10670i −0.372444 0.372444i
\(189\) −1.50150 −0.109218
\(190\) 10.2969 + 0.513789i 0.747015 + 0.0372742i
\(191\) −7.31029 + 7.31029i −0.528954 + 0.528954i −0.920260 0.391307i \(-0.872023\pi\)
0.391307 + 0.920260i \(0.372023\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 9.97235i 0.717826i −0.933371 0.358913i \(-0.883148\pi\)
0.933371 0.358913i \(-0.116852\pi\)
\(194\) 7.85190i 0.563734i
\(195\) −10.1854 0.508228i −0.729395 0.0363950i
\(196\) 4.74548i 0.338963i
\(197\) −9.41933 9.41933i −0.671099 0.671099i 0.286870 0.957969i \(-0.407385\pi\)
−0.957969 + 0.286870i \(0.907385\pi\)
\(198\) 4.34528i 0.308805i
\(199\) −8.39214 + 8.39214i −0.594903 + 0.594903i −0.938952 0.344049i \(-0.888202\pi\)
0.344049 + 0.938952i \(0.388202\pi\)
\(200\) −4.97516 0.497735i −0.351797 0.0351952i
\(201\) 4.49554 0.317091
\(202\) 3.02340 0.212726
\(203\) −3.94158 −0.276645
\(204\) −2.41175 2.41175i −0.168856 0.168856i
\(205\) −20.3265 + 18.3945i −1.41967 + 1.28472i
\(206\) 13.8674i 0.966190i
\(207\) −3.95501 −0.274892
\(208\) 4.56074i 0.316230i
\(209\) −14.1665 + 14.1665i −0.979920 + 0.979920i
\(210\) 2.25282 + 2.48945i 0.155460 + 0.171788i
\(211\) −23.7130 −1.63247 −0.816237 0.577718i \(-0.803943\pi\)
−0.816237 + 0.577718i \(0.803943\pi\)
\(212\) −4.58664 + 4.58664i −0.315012 + 0.315012i
\(213\) −6.61038 6.61038i −0.452936 0.452936i
\(214\) 13.3916 13.3916i 0.915432 0.915432i
\(215\) 4.67939 4.23460i 0.319132 0.288798i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 7.92377i 0.537900i
\(218\) −5.95541 + 5.95541i −0.403351 + 0.403351i
\(219\) 8.98689i 0.607278i
\(220\) 7.20434 6.51956i 0.485717 0.439548i
\(221\) 15.5554i 1.04637i
\(222\) −5.48323 2.63328i −0.368010 0.176734i
\(223\) 0.189445 0.189445i 0.0126862 0.0126862i −0.700735 0.713421i \(-0.747145\pi\)
0.713421 + 0.700735i \(0.247145\pi\)
\(224\) −1.06172 + 1.06172i −0.0709394 + 0.0709394i
\(225\) −4.97516 0.497735i −0.331678 0.0331824i
\(226\) 9.16869i 0.609892i
\(227\) −22.4161 −1.48781 −0.743905 0.668285i \(-0.767029\pi\)
−0.743905 + 0.668285i \(0.767029\pi\)
\(228\) 4.61064i 0.305347i
\(229\) 6.71069i 0.443455i 0.975109 + 0.221727i \(0.0711695\pi\)
−0.975109 + 0.221727i \(0.928831\pi\)
\(230\) 5.93401 + 6.55729i 0.391277 + 0.432375i
\(231\) −6.52445 −0.429277
\(232\) 1.85622 + 1.85622i 0.121867 + 0.121867i
\(233\) 4.29550 + 4.29550i 0.281407 + 0.281407i 0.833670 0.552263i \(-0.186235\pi\)
−0.552263 + 0.833670i \(0.686235\pi\)
\(234\) 4.56074i 0.298145i
\(235\) −0.804783 + 16.1287i −0.0524983 + 1.05212i
\(236\) −2.79480 2.79480i −0.181926 0.181926i
\(237\) 0.290621i 0.0188779i
\(238\) 3.62125 3.62125i 0.234731 0.234731i
\(239\) 2.69780 + 2.69780i 0.174506 + 0.174506i 0.788956 0.614450i \(-0.210622\pi\)
−0.614450 + 0.788956i \(0.710622\pi\)
\(240\) 0.111436 2.23329i 0.00719313 0.144158i
\(241\) −13.6895 + 13.6895i −0.881820 + 0.881820i −0.993719 0.111900i \(-0.964306\pi\)
0.111900 + 0.993719i \(0.464306\pi\)
\(242\) 7.88143i 0.506638i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) −1.42612 1.42612i −0.0912980 0.0912980i
\(245\) 7.86788 7.12002i 0.502660 0.454881i
\(246\) −8.66905 8.66905i −0.552718 0.552718i
\(247\) 14.8690 14.8690i 0.946091 0.946091i
\(248\) −3.73156 + 3.73156i −0.236954 + 0.236954i
\(249\) 3.61754 0.229253
\(250\) 6.63939 + 8.99547i 0.419912 + 0.568923i
\(251\) 5.86904 + 5.86904i 0.370451 + 0.370451i 0.867641 0.497191i \(-0.165635\pi\)
−0.497191 + 0.867641i \(0.665635\pi\)
\(252\) −1.06172 + 1.06172i −0.0668823 + 0.0668823i
\(253\) −17.1856 −1.08045
\(254\) −0.349491 + 0.349491i −0.0219290 + 0.0219290i
\(255\) −0.380076 + 7.61714i −0.0238013 + 0.477004i
\(256\) 1.00000 0.0625000
\(257\) 24.5293 1.53010 0.765048 0.643974i \(-0.222715\pi\)
0.765048 + 0.643974i \(0.222715\pi\)
\(258\) 1.99571 + 1.99571i 0.124247 + 0.124247i
\(259\) 3.95389 8.23310i 0.245683 0.511580i
\(260\) −7.56157 + 6.84283i −0.468949 + 0.424374i
\(261\) 1.85622 + 1.85622i 0.114897 + 0.114897i
\(262\) −10.2082 + 10.2082i −0.630665 + 0.630665i
\(263\) 1.58329 + 1.58329i 0.0976299 + 0.0976299i 0.754235 0.656605i \(-0.228008\pi\)
−0.656605 + 0.754235i \(0.728008\pi\)
\(264\) 3.07257 + 3.07257i 0.189104 + 0.189104i
\(265\) 14.4862 + 0.722825i 0.889880 + 0.0444028i
\(266\) −6.92290 −0.424470
\(267\) −6.90180 −0.422383
\(268\) 3.17883 3.17883i 0.194178 0.194178i
\(269\) 6.02812i 0.367541i 0.982969 + 0.183771i \(0.0588304\pi\)
−0.982969 + 0.183771i \(0.941170\pi\)
\(270\) 0.111436 2.23329i 0.00678175 0.135914i
\(271\) −22.2398 −1.35097 −0.675485 0.737374i \(-0.736066\pi\)
−0.675485 + 0.737374i \(0.736066\pi\)
\(272\) −3.41073 −0.206806
\(273\) 6.84797 0.414458
\(274\) −5.52765 + 5.52765i −0.333937 + 0.333937i
\(275\) −21.6185 2.16280i −1.30364 0.130422i
\(276\) −2.79661 + 2.79661i −0.168336 + 0.168336i
\(277\) 1.53430i 0.0921869i 0.998937 + 0.0460934i \(0.0146772\pi\)
−0.998937 + 0.0460934i \(0.985323\pi\)
\(278\) 13.4120i 0.804400i
\(279\) −3.73156 + 3.73156i −0.223403 + 0.223403i
\(280\) 3.35329 + 0.167321i 0.200398 + 0.00999934i
\(281\) 18.4987 18.4987i 1.10354 1.10354i 0.109557 0.993980i \(-0.465057\pi\)
0.993980 0.109557i \(-0.0349433\pi\)
\(282\) −7.22196 −0.430062
\(283\) −13.7302 −0.816174 −0.408087 0.912943i \(-0.633804\pi\)
−0.408087 + 0.912943i \(0.633804\pi\)
\(284\) −9.34849 −0.554731
\(285\) 7.64431 6.91770i 0.452810 0.409769i
\(286\) 19.8177i 1.17184i
\(287\) 13.0166 13.0166i 0.768347 0.768347i
\(288\) 1.00000 0.0589256
\(289\) −5.36694 −0.315702
\(290\) 0.292528 5.86258i 0.0171778 0.344263i
\(291\) 5.55213 + 5.55213i 0.325472 + 0.325472i
\(292\) 6.35469 + 6.35469i 0.371880 + 0.371880i
\(293\) 14.7459 14.7459i 0.861466 0.861466i −0.130043 0.991508i \(-0.541511\pi\)
0.991508 + 0.130043i \(0.0415114\pi\)
\(294\) 3.35556 + 3.35556i 0.195700 + 0.195700i
\(295\) −0.440443 + 8.82696i −0.0256436 + 0.513926i
\(296\) −5.73924 + 2.01522i −0.333587 + 0.117132i
\(297\) 3.07257 + 3.07257i 0.178289 + 0.178289i
\(298\) −21.3340 −1.23585
\(299\) 18.0378 1.04315
\(300\) −3.86992 + 3.16602i −0.223430 + 0.182790i
\(301\) −2.99657 + 2.99657i −0.172719 + 0.172719i
\(302\) 21.4210 1.23264
\(303\) 2.13787 2.13787i 0.122817 0.122817i
\(304\) 3.26022 + 3.26022i 0.186986 + 0.186986i
\(305\) −0.224747 + 4.50418i −0.0128690 + 0.257909i
\(306\) −3.41073 −0.194978
\(307\) 23.1161 23.1161i 1.31931 1.31931i 0.404982 0.914324i \(-0.367278\pi\)
0.914324 0.404982i \(-0.132722\pi\)
\(308\) −4.61348 + 4.61348i −0.262878 + 0.262878i
\(309\) −9.80576 9.80576i −0.557830 0.557830i
\(310\) 11.7856 + 0.588070i 0.669375 + 0.0334001i
\(311\) −15.0521 15.0521i −0.853527 0.853527i 0.137038 0.990566i \(-0.456242\pi\)
−0.990566 + 0.137038i \(0.956242\pi\)
\(312\) −3.22493 3.22493i −0.182576 0.182576i
\(313\) 15.9823i 0.903373i 0.892177 + 0.451687i \(0.149177\pi\)
−0.892177 + 0.451687i \(0.850823\pi\)
\(314\) 2.04779 2.04779i 0.115564 0.115564i
\(315\) 3.35329 + 0.167321i 0.188937 + 0.00942746i
\(316\) −0.205500 0.205500i −0.0115603 0.0115603i
\(317\) −11.2092 + 11.2092i −0.629569 + 0.629569i −0.947960 0.318391i \(-0.896858\pi\)
0.318391 + 0.947960i \(0.396858\pi\)
\(318\) 6.48649i 0.363744i
\(319\) 8.06578 + 8.06578i 0.451597 + 0.451597i
\(320\) −1.50038 1.65797i −0.0838736 0.0926834i
\(321\) 18.9386i 1.05705i
\(322\) −4.19913 4.19913i −0.234008 0.234008i
\(323\) −11.1197 11.1197i −0.618717 0.618717i
\(324\) 1.00000 0.0555556
\(325\) 22.6904 + 2.27004i 1.25864 + 0.125919i
\(326\) 12.1359i 0.672147i
\(327\) 8.42221i 0.465750i
\(328\) −12.2599 −0.676939
\(329\) 10.8438i 0.597839i
\(330\) 0.484218 9.70426i 0.0266553 0.534202i
\(331\) 13.1668 13.1668i 0.723711 0.723711i −0.245648 0.969359i \(-0.579001\pi\)
0.969359 + 0.245648i \(0.0790007\pi\)
\(332\) 2.55799 2.55799i 0.140388 0.140388i
\(333\) −5.73924 + 2.01522i −0.314509 + 0.110433i
\(334\) 8.95519i 0.490006i
\(335\) −10.0398 0.500963i −0.548535 0.0273705i
\(336\) 1.50150i 0.0819138i
\(337\) 13.0929 13.0929i 0.713214 0.713214i −0.253992 0.967206i \(-0.581744\pi\)
0.967206 + 0.253992i \(0.0817437\pi\)
\(338\) 7.80032i 0.424281i
\(339\) 6.48324 + 6.48324i 0.352121 + 0.352121i
\(340\) 5.11738 + 5.65489i 0.277529 + 0.306679i
\(341\) −16.2147 + 16.2147i −0.878073 + 0.878073i
\(342\) 3.26022 + 3.26022i 0.176292 + 0.176292i
\(343\) −12.4705 + 12.4705i −0.673342 + 0.673342i
\(344\) 2.82236 0.152171
\(345\) 8.83268 + 0.440728i 0.475536 + 0.0237280i
\(346\) 14.6997 14.6997i 0.790262 0.790262i
\(347\) 20.6489i 1.10849i 0.832352 + 0.554247i \(0.186994\pi\)
−0.832352 + 0.554247i \(0.813006\pi\)
\(348\) 2.62509 0.140720
\(349\) 9.13035i 0.488737i −0.969683 0.244368i \(-0.921419\pi\)
0.969683 0.244368i \(-0.0785806\pi\)
\(350\) −4.75379 5.81071i −0.254101 0.310595i
\(351\) −3.22493 3.22493i −0.172134 0.172134i
\(352\) 4.34528 0.231604
\(353\) 2.40807 0.128169 0.0640843 0.997944i \(-0.479587\pi\)
0.0640843 + 0.997944i \(0.479587\pi\)
\(354\) −3.95245 −0.210070
\(355\) 14.0263 + 15.4995i 0.744437 + 0.822630i
\(356\) −4.88031 + 4.88031i −0.258656 + 0.258656i
\(357\) 5.12122i 0.271044i
\(358\) 6.65594 + 6.65594i 0.351777 + 0.351777i
\(359\) 33.5658i 1.77153i −0.464131 0.885767i \(-0.653633\pi\)
0.464131 0.885767i \(-0.346367\pi\)
\(360\) −1.50038 1.65797i −0.0790768 0.0873827i
\(361\) 2.25801i 0.118843i
\(362\) 12.8467i 0.675206i
\(363\) 5.57302 + 5.57302i 0.292507 + 0.292507i
\(364\) 4.84224 4.84224i 0.253802 0.253802i
\(365\) 1.00146 20.0703i 0.0524187 1.05053i
\(366\) −2.01684 −0.105422
\(367\) 7.30745 + 7.30745i 0.381446 + 0.381446i 0.871623 0.490177i \(-0.163068\pi\)
−0.490177 + 0.871623i \(0.663068\pi\)
\(368\) 3.95501i 0.206169i
\(369\) −12.2599 −0.638224
\(370\) 11.9522 + 6.49191i 0.621365 + 0.337498i
\(371\) −9.73949 −0.505649
\(372\) 5.27722i 0.273611i
\(373\) −12.9730 12.9730i −0.671717 0.671717i 0.286395 0.958112i \(-0.407543\pi\)
−0.958112 + 0.286395i \(0.907543\pi\)
\(374\) −14.8206 −0.766353
\(375\) 11.0555 + 1.66600i 0.570904 + 0.0860317i
\(376\) −5.10670 + 5.10670i −0.263358 + 0.263358i
\(377\) −8.46572 8.46572i −0.436007 0.436007i
\(378\) 1.50150i 0.0772291i
\(379\) 23.8917i 1.22724i −0.789603 0.613618i \(-0.789714\pi\)
0.789603 0.613618i \(-0.210286\pi\)
\(380\) 0.513789 10.2969i 0.0263568 0.528220i
\(381\) 0.494255i 0.0253215i
\(382\) 7.31029 + 7.31029i 0.374027 + 0.374027i
\(383\) 5.61859i 0.287097i −0.989643 0.143548i \(-0.954149\pi\)
0.989643 0.143548i \(-0.0458512\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 14.5710 + 0.727056i 0.742607 + 0.0370542i
\(386\) −9.97235 −0.507579
\(387\) 2.82236 0.143469
\(388\) 7.85190 0.398620
\(389\) 19.5391 + 19.5391i 0.990671 + 0.990671i 0.999957 0.00928635i \(-0.00295598\pi\)
−0.00928635 + 0.999957i \(0.502956\pi\)
\(390\) −0.508228 + 10.1854i −0.0257351 + 0.515760i
\(391\) 13.4895i 0.682191i
\(392\) 4.74548 0.239683
\(393\) 14.4366i 0.728229i
\(394\) −9.41933 + 9.41933i −0.474539 + 0.474539i
\(395\) −0.0323855 + 0.649041i −0.00162949 + 0.0326568i
\(396\) 4.34528 0.218358
\(397\) −0.459928 + 0.459928i −0.0230831 + 0.0230831i −0.718554 0.695471i \(-0.755196\pi\)
0.695471 + 0.718554i \(0.255196\pi\)
\(398\) 8.39214 + 8.39214i 0.420660 + 0.420660i
\(399\) −4.89523 + 4.89523i −0.245068 + 0.245068i
\(400\) −0.497735 + 4.97516i −0.0248868 + 0.248758i
\(401\) 3.68324 + 3.68324i 0.183932 + 0.183932i 0.793067 0.609135i \(-0.208483\pi\)
−0.609135 + 0.793067i \(0.708483\pi\)
\(402\) 4.49554i 0.224217i
\(403\) 17.0187 17.0187i 0.847759 0.847759i
\(404\) 3.02340i 0.150420i
\(405\) −1.50038 1.65797i −0.0745544 0.0823852i
\(406\) 3.94158i 0.195617i
\(407\) −24.9386 + 8.75668i −1.23616 + 0.434052i
\(408\) −2.41175 + 2.41175i −0.119399 + 0.119399i
\(409\) 23.4462 23.4462i 1.15934 1.15934i 0.174722 0.984618i \(-0.444097\pi\)
0.984618 0.174722i \(-0.0559026\pi\)
\(410\) 18.3945 + 20.3265i 0.908438 + 1.00386i
\(411\) 7.81728i 0.385598i
\(412\) −13.8674 −0.683200
\(413\) 5.93462i 0.292024i
\(414\) 3.95501i 0.194378i
\(415\) −8.07902 0.403123i −0.396584 0.0197885i
\(416\) −4.56074 −0.223608
\(417\) −9.48374 9.48374i −0.464421 0.464421i
\(418\) 14.1665 + 14.1665i 0.692908 + 0.692908i
\(419\) 26.2634i 1.28305i 0.767102 + 0.641525i \(0.221698\pi\)
−0.767102 + 0.641525i \(0.778302\pi\)
\(420\) 2.48945 2.25282i 0.121473 0.109927i
\(421\) 15.2941 + 15.2941i 0.745387 + 0.745387i 0.973609 0.228222i \(-0.0732912\pi\)
−0.228222 + 0.973609i \(0.573291\pi\)
\(422\) 23.7130i 1.15433i
\(423\) −5.10670 + 5.10670i −0.248296 + 0.248296i
\(424\) 4.58664 + 4.58664i 0.222747 + 0.222747i
\(425\) 1.69764 16.9689i 0.0823476 0.823114i
\(426\) −6.61038 + 6.61038i −0.320274 + 0.320274i
\(427\) 3.02829i 0.146549i
\(428\) −13.3916 13.3916i −0.647308 0.647308i
\(429\) −14.0132 14.0132i −0.676564 0.676564i
\(430\) −4.23460 4.67939i −0.204211 0.225660i
\(431\) −25.6410 25.6410i −1.23509 1.23509i −0.961986 0.273100i \(-0.911951\pi\)
−0.273100 0.961986i \(-0.588049\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 19.2862 19.2862i 0.926836 0.926836i −0.0706638 0.997500i \(-0.522512\pi\)
0.997500 + 0.0706638i \(0.0225118\pi\)
\(434\) −7.92377 −0.380353
\(435\) −3.93862 4.35232i −0.188843 0.208678i
\(436\) 5.95541 + 5.95541i 0.285212 + 0.285212i
\(437\) −12.8942 + 12.8942i −0.616812 + 0.616812i
\(438\) 8.98689 0.429410
\(439\) −18.1003 + 18.1003i −0.863882 + 0.863882i −0.991787 0.127904i \(-0.959175\pi\)
0.127904 + 0.991787i \(0.459175\pi\)
\(440\) −6.51956 7.20434i −0.310808 0.343454i
\(441\) 4.74548 0.225975
\(442\) 15.5554 0.739896
\(443\) −7.18587 7.18587i −0.341411 0.341411i 0.515487 0.856898i \(-0.327611\pi\)
−0.856898 + 0.515487i \(0.827611\pi\)
\(444\) −2.63328 + 5.48323i −0.124970 + 0.260223i
\(445\) 15.4137 + 0.769105i 0.730680 + 0.0364591i
\(446\) −0.189445 0.189445i −0.00897049 0.00897049i
\(447\) −15.0854 + 15.0854i −0.713517 + 0.713517i
\(448\) 1.06172 + 1.06172i 0.0501617 + 0.0501617i
\(449\) −2.05526 2.05526i −0.0969938 0.0969938i 0.656945 0.753939i \(-0.271848\pi\)
−0.753939 + 0.656945i \(0.771848\pi\)
\(450\) −0.497735 + 4.97516i −0.0234635 + 0.234531i
\(451\) −53.2726 −2.50851
\(452\) 9.16869 0.431259
\(453\) 15.1469 15.1469i 0.711665 0.711665i
\(454\) 22.4161i 1.05204i
\(455\) −15.2935 0.763106i −0.716970 0.0357750i
\(456\) 4.61064 0.215913
\(457\) −29.9149 −1.39936 −0.699681 0.714456i \(-0.746674\pi\)
−0.699681 + 0.714456i \(0.746674\pi\)
\(458\) 6.71069 0.313570
\(459\) −2.41175 + 2.41175i −0.112571 + 0.112571i
\(460\) 6.55729 5.93401i 0.305735 0.276674i
\(461\) 17.4197 17.4197i 0.811318 0.811318i −0.173513 0.984832i \(-0.555512\pi\)
0.984832 + 0.173513i \(0.0555119\pi\)
\(462\) 6.52445i 0.303545i
\(463\) 21.2696i 0.988484i −0.869324 0.494242i \(-0.835446\pi\)
0.869324 0.494242i \(-0.164554\pi\)
\(464\) 1.85622 1.85622i 0.0861728 0.0861728i
\(465\) 8.74948 7.91782i 0.405747 0.367180i
\(466\) 4.29550 4.29550i 0.198985 0.198985i
\(467\) 11.3616 0.525754 0.262877 0.964829i \(-0.415329\pi\)
0.262877 + 0.964829i \(0.415329\pi\)
\(468\) −4.56074 −0.210820
\(469\) 6.75007 0.311689
\(470\) 16.1287 + 0.804783i 0.743963 + 0.0371219i
\(471\) 2.89602i 0.133441i
\(472\) −2.79480 + 2.79480i −0.128641 + 0.128641i
\(473\) 12.2639 0.563896
\(474\) −0.290621 −0.0133487
\(475\) −17.8428 + 14.5974i −0.818685 + 0.669774i
\(476\) −3.62125 3.62125i −0.165980 0.165980i
\(477\) 4.58664 + 4.58664i 0.210008 + 0.210008i
\(478\) 2.69780 2.69780i 0.123395 0.123395i
\(479\) −8.10363 8.10363i −0.370264 0.370264i 0.497309 0.867573i \(-0.334322\pi\)
−0.867573 + 0.497309i \(0.834322\pi\)
\(480\) −2.23329 0.111436i −0.101935 0.00508631i
\(481\) 26.1752 9.19088i 1.19348 0.419068i
\(482\) 13.6895 + 13.6895i 0.623541 + 0.623541i
\(483\) −5.93846 −0.270209
\(484\) 7.88143 0.358247
\(485\) −11.7808 13.0182i −0.534939 0.591127i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 13.1026 0.593738 0.296869 0.954918i \(-0.404058\pi\)
0.296869 + 0.954918i \(0.404058\pi\)
\(488\) −1.42612 + 1.42612i −0.0645574 + 0.0645574i
\(489\) 8.58140 + 8.58140i 0.388064 + 0.388064i
\(490\) −7.12002 7.86788i −0.321650 0.355434i
\(491\) 33.5415 1.51371 0.756854 0.653584i \(-0.226735\pi\)
0.756854 + 0.653584i \(0.226735\pi\)
\(492\) −8.66905 + 8.66905i −0.390831 + 0.390831i
\(493\) −6.33105 + 6.33105i −0.285136 + 0.285136i
\(494\) −14.8690 14.8690i −0.668987 0.668987i
\(495\) −6.51956 7.20434i −0.293032 0.323811i
\(496\) 3.73156 + 3.73156i 0.167552 + 0.167552i
\(497\) −9.92552 9.92552i −0.445220 0.445220i
\(498\) 3.61754i 0.162106i
\(499\) 5.96339 5.96339i 0.266958 0.266958i −0.560915 0.827873i \(-0.689551\pi\)
0.827873 + 0.560915i \(0.189551\pi\)
\(500\) 8.99547 6.63939i 0.402290 0.296923i
\(501\) −6.33227 6.33227i −0.282905 0.282905i
\(502\) 5.86904 5.86904i 0.261948 0.261948i
\(503\) 23.5927i 1.05195i −0.850501 0.525973i \(-0.823701\pi\)
0.850501 0.525973i \(-0.176299\pi\)
\(504\) 1.06172 + 1.06172i 0.0472929 + 0.0472929i
\(505\) −5.01271 + 4.53624i −0.223063 + 0.201860i
\(506\) 17.1856i 0.763994i
\(507\) 5.51566 + 5.51566i 0.244959 + 0.244959i
\(508\) 0.349491 + 0.349491i 0.0155062 + 0.0155062i
\(509\) −42.6475 −1.89032 −0.945159 0.326611i \(-0.894093\pi\)
−0.945159 + 0.326611i \(0.894093\pi\)
\(510\) 7.61714 + 0.380076i 0.337293 + 0.0168301i
\(511\) 13.4939i 0.596933i
\(512\) 1.00000i 0.0441942i
\(513\) 4.61064 0.203565
\(514\) 24.5293i 1.08194i
\(515\) 20.8064 + 22.9918i 0.916839 + 1.01314i
\(516\) 1.99571 1.99571i 0.0878562 0.0878562i
\(517\) −22.1900 + 22.1900i −0.975916 + 0.975916i
\(518\) −8.23310 3.95389i −0.361741 0.173724i
\(519\) 20.7885i 0.912516i
\(520\) 6.84283 + 7.56157i 0.300078 + 0.331597i
\(521\) 14.3544i 0.628878i −0.949278 0.314439i \(-0.898184\pi\)
0.949278 0.314439i \(-0.101816\pi\)
\(522\) 1.85622 1.85622i 0.0812445 0.0812445i
\(523\) 14.0079i 0.612523i −0.951947 0.306262i \(-0.900922\pi\)
0.951947 0.306262i \(-0.0990783\pi\)
\(524\) 10.2082 + 10.2082i 0.445947 + 0.445947i
\(525\) −7.47023 0.747352i −0.326028 0.0326171i
\(526\) 1.58329 1.58329i 0.0690348 0.0690348i
\(527\) −12.7273 12.7273i −0.554411 0.554411i
\(528\) 3.07257 3.07257i 0.133717 0.133717i
\(529\) 7.35790 0.319909
\(530\) 0.722825 14.4862i 0.0313975 0.629240i
\(531\) −2.79480 + 2.79480i −0.121284 + 0.121284i
\(532\) 6.92290i 0.300146i
\(533\) 55.9141 2.42191
\(534\) 6.90180i 0.298670i
\(535\) −2.11043 + 42.2954i −0.0912419 + 1.82859i
\(536\) −3.17883 3.17883i −0.137304 0.137304i
\(537\) 9.41292 0.406198
\(538\) 6.02812 0.259891
\(539\) 20.6204 0.888185
\(540\) −2.23329 0.111436i −0.0961055 0.00479542i
\(541\) 10.6677 10.6677i 0.458641 0.458641i −0.439568 0.898209i \(-0.644869\pi\)
0.898209 + 0.439568i \(0.144869\pi\)
\(542\) 22.2398i 0.955280i
\(543\) 9.08397 + 9.08397i 0.389831 + 0.389831i
\(544\) 3.41073i 0.146234i
\(545\) 0.938534 18.8092i 0.0402024 0.805699i
\(546\) 6.84797i 0.293066i
\(547\) 17.2017i 0.735490i −0.929927 0.367745i \(-0.880130\pi\)
0.929927 0.367745i \(-0.119870\pi\)
\(548\) 5.52765 + 5.52765i 0.236129 + 0.236129i
\(549\) −1.42612 + 1.42612i −0.0608653 + 0.0608653i
\(550\) −2.16280 + 21.6185i −0.0922220 + 0.921815i
\(551\) 12.1033 0.515620
\(552\) 2.79661 + 2.79661i 0.119032 + 0.119032i
\(553\) 0.436369i 0.0185563i
\(554\) 1.53430 0.0651860
\(555\) 13.0420 3.86101i 0.553600 0.163891i
\(556\) −13.4120 −0.568797
\(557\) 29.7084i 1.25879i 0.777087 + 0.629393i \(0.216697\pi\)
−0.777087 + 0.629393i \(0.783303\pi\)
\(558\) 3.73156 + 3.73156i 0.157969 + 0.157969i
\(559\) −12.8720 −0.544429
\(560\) 0.167321 3.35329i 0.00707060 0.141703i
\(561\) −10.4797 + 10.4797i −0.442454 + 0.442454i
\(562\) −18.4987 18.4987i −0.780319 0.780319i
\(563\) 18.1294i 0.764062i 0.924149 + 0.382031i \(0.124775\pi\)
−0.924149 + 0.382031i \(0.875225\pi\)
\(564\) 7.22196i 0.304100i
\(565\) −13.7565 15.2014i −0.578740 0.639528i
\(566\) 13.7302i 0.577122i
\(567\) 1.06172 + 1.06172i 0.0445882 + 0.0445882i
\(568\) 9.34849i 0.392254i
\(569\) 8.90810 8.90810i 0.373447 0.373447i −0.495284 0.868731i \(-0.664936\pi\)
0.868731 + 0.495284i \(0.164936\pi\)
\(570\) −6.91770 7.64431i −0.289751 0.320185i
\(571\) 45.2926 1.89544 0.947718 0.319109i \(-0.103384\pi\)
0.947718 + 0.319109i \(0.103384\pi\)
\(572\) −19.8177 −0.828618
\(573\) 10.3383 0.431889
\(574\) −13.0166 13.0166i −0.543303 0.543303i
\(575\) −19.6768 1.96855i −0.820580 0.0820941i
\(576\) 1.00000i 0.0416667i
\(577\) 3.80406 0.158365 0.0791826 0.996860i \(-0.474769\pi\)
0.0791826 + 0.996860i \(0.474769\pi\)
\(578\) 5.36694i 0.223235i
\(579\) −7.05152 + 7.05152i −0.293051 + 0.293051i
\(580\) −5.86258 0.292528i −0.243431 0.0121466i
\(581\) 5.43176 0.225347
\(582\) 5.55213 5.55213i 0.230143 0.230143i
\(583\) 19.9302 + 19.9302i 0.825425 + 0.825425i
\(584\) 6.35469 6.35469i 0.262959 0.262959i
\(585\) 6.84283 + 7.56157i 0.282916 + 0.312632i
\(586\) −14.7459 14.7459i −0.609148 0.609148i
\(587\) 30.4191i 1.25553i 0.778402 + 0.627766i \(0.216031\pi\)
−0.778402 + 0.627766i \(0.783969\pi\)
\(588\) 3.35556 3.35556i 0.138381 0.138381i
\(589\) 24.3314i 1.00256i
\(590\) 8.82696 + 0.440443i 0.363400 + 0.0181328i
\(591\) 13.3209i 0.547950i
\(592\) 2.01522 + 5.73924i 0.0828249 + 0.235881i
\(593\) −4.86429 + 4.86429i −0.199752 + 0.199752i −0.799894 0.600142i \(-0.795111\pi\)
0.600142 + 0.799894i \(0.295111\pi\)
\(594\) 3.07257 3.07257i 0.126069 0.126069i
\(595\) −0.570686 + 11.4372i −0.0233958 + 0.468878i
\(596\) 21.3340i 0.873876i
\(597\) 11.8683 0.485736
\(598\) 18.0378i 0.737619i
\(599\) 44.2957i 1.80987i −0.425545 0.904937i \(-0.639918\pi\)
0.425545 0.904937i \(-0.360082\pi\)
\(600\) 3.16602 + 3.86992i 0.129252 + 0.157989i
\(601\) 0.405142 0.0165261 0.00826304 0.999966i \(-0.497370\pi\)
0.00826304 + 0.999966i \(0.497370\pi\)
\(602\) 2.99657 + 2.99657i 0.122131 + 0.122131i
\(603\) −3.17883 3.17883i −0.129452 0.129452i
\(604\) 21.4210i 0.871609i
\(605\) −11.8251 13.0672i −0.480760 0.531257i
\(606\) −2.13787 2.13787i −0.0868449 0.0868449i
\(607\) 42.7185i 1.73389i −0.498404 0.866945i \(-0.666081\pi\)
0.498404 0.866945i \(-0.333919\pi\)
\(608\) 3.26022 3.26022i 0.132219 0.132219i
\(609\) 2.78712 + 2.78712i 0.112940 + 0.112940i
\(610\) 4.50418 + 0.224747i 0.182369 + 0.00909976i
\(611\) 23.2903 23.2903i 0.942225 0.942225i
\(612\) 3.41073i 0.137870i
\(613\) 14.3851 + 14.3851i 0.581008 + 0.581008i 0.935180 0.354172i \(-0.115237\pi\)
−0.354172 + 0.935180i \(0.615237\pi\)
\(614\) −23.1161 23.1161i −0.932891 0.932891i
\(615\) 27.3799 + 1.36619i 1.10406 + 0.0550900i
\(616\) 4.61348 + 4.61348i 0.185883 + 0.185883i
\(617\) 25.2866 25.2866i 1.01800 1.01800i 0.0181641 0.999835i \(-0.494218\pi\)
0.999835 0.0181641i \(-0.00578213\pi\)
\(618\) −9.80576 + 9.80576i −0.394446 + 0.394446i
\(619\) 27.8054 1.11759 0.558797 0.829305i \(-0.311263\pi\)
0.558797 + 0.829305i \(0.311263\pi\)
\(620\) 0.588070 11.7856i 0.0236174 0.473319i
\(621\) 2.79661 + 2.79661i 0.112224 + 0.112224i
\(622\) −15.0521 + 15.0521i −0.603535 + 0.603535i
\(623\) −10.3631 −0.415188
\(624\) −3.22493 + 3.22493i −0.129100 + 0.129100i
\(625\) −24.5045 4.95263i −0.980181 0.198105i
\(626\) 15.9823 0.638781
\(627\) 20.0345 0.800101
\(628\) −2.04779 2.04779i −0.0817159 0.0817159i
\(629\) −6.87336 19.5750i −0.274059 0.780506i
\(630\) 0.167321 3.35329i 0.00666622 0.133598i
\(631\) 24.6071 + 24.6071i 0.979594 + 0.979594i 0.999796 0.0202023i \(-0.00643102\pi\)
−0.0202023 + 0.999796i \(0.506431\pi\)
\(632\) −0.205500 + 0.205500i −0.00817435 + 0.00817435i
\(633\) 16.7677 + 16.7677i 0.666454 + 0.666454i
\(634\) 11.2092 + 11.2092i 0.445173 + 0.445173i
\(635\) 0.0550776 1.10381i 0.00218569 0.0438036i
\(636\) 6.48649 0.257206
\(637\) −21.6429 −0.857523
\(638\) 8.06578 8.06578i 0.319327 0.319327i
\(639\) 9.34849i 0.369821i
\(640\) −1.65797 + 1.50038i −0.0655371 + 0.0593076i
\(641\) 32.5701 1.28644 0.643220 0.765681i \(-0.277598\pi\)
0.643220 + 0.765681i \(0.277598\pi\)
\(642\) −18.9386 −0.747447
\(643\) 12.0685 0.475934 0.237967 0.971273i \(-0.423519\pi\)
0.237967 + 0.971273i \(0.423519\pi\)
\(644\) −4.19913 + 4.19913i −0.165469 + 0.165469i
\(645\) −6.30314 0.314511i −0.248186 0.0123839i
\(646\) −11.1197 + 11.1197i −0.437499 + 0.437499i
\(647\) 29.2633i 1.15046i −0.817993 0.575229i \(-0.804913\pi\)
0.817993 0.575229i \(-0.195087\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −12.1442 + 12.1442i −0.476701 + 0.476701i
\(650\) 2.27004 22.6904i 0.0890383 0.889991i
\(651\) −5.60295 + 5.60295i −0.219597 + 0.219597i
\(652\) 12.1359 0.475280
\(653\) −16.0675 −0.628769 −0.314384 0.949296i \(-0.601798\pi\)
−0.314384 + 0.949296i \(0.601798\pi\)
\(654\) 8.42221 0.329335
\(655\) 1.60875 32.2411i 0.0628590 1.25976i
\(656\) 12.2599i 0.478668i
\(657\) 6.35469 6.35469i 0.247920 0.247920i
\(658\) −10.8438 −0.422736
\(659\) 30.0316 1.16987 0.584933 0.811081i \(-0.301121\pi\)
0.584933 + 0.811081i \(0.301121\pi\)
\(660\) −9.70426 0.484218i −0.377738 0.0188482i
\(661\) 19.5170 + 19.5170i 0.759124 + 0.759124i 0.976163 0.217039i \(-0.0696400\pi\)
−0.217039 + 0.976163i \(0.569640\pi\)
\(662\) −13.1668 13.1668i −0.511741 0.511741i
\(663\) 10.9993 10.9993i 0.427179 0.427179i
\(664\) −2.55799 2.55799i −0.0992693 0.0992693i
\(665\) 11.4780 10.3870i 0.445096 0.402789i
\(666\) 2.01522 + 5.73924i 0.0780881 + 0.222391i
\(667\) 7.34136 + 7.34136i 0.284259 + 0.284259i
\(668\) −8.95519 −0.346487
\(669\) −0.267916 −0.0103582
\(670\) −0.500963 + 10.0398i −0.0193539 + 0.387873i
\(671\) −6.19689 + 6.19689i −0.239228 + 0.239228i
\(672\) 1.50150 0.0579218
\(673\) −30.1779 + 30.1779i −1.16327 + 1.16327i −0.179516 + 0.983755i \(0.557453\pi\)
−0.983755 + 0.179516i \(0.942547\pi\)
\(674\) −13.0929 13.0929i −0.504319 0.504319i
\(675\) 3.16602 + 3.86992i 0.121860 + 0.148953i
\(676\) 7.80032 0.300012
\(677\) −31.8813 + 31.8813i −1.22530 + 1.22530i −0.259574 + 0.965723i \(0.583582\pi\)
−0.965723 + 0.259574i \(0.916418\pi\)
\(678\) 6.48324 6.48324i 0.248987 0.248987i
\(679\) 8.33655 + 8.33655i 0.319928 + 0.319928i
\(680\) 5.65489 5.11738i 0.216855 0.196243i
\(681\) 15.8506 + 15.8506i 0.607396 + 0.607396i
\(682\) 16.2147 + 16.2147i 0.620891 + 0.620891i
\(683\) 18.9583i 0.725421i 0.931902 + 0.362710i \(0.118149\pi\)
−0.931902 + 0.362710i \(0.881851\pi\)
\(684\) 3.26022 3.26022i 0.124657 0.124657i
\(685\) 0.871122 17.4582i 0.0332839 0.667045i
\(686\) 12.4705 + 12.4705i 0.476124 + 0.476124i
\(687\) 4.74517 4.74517i 0.181040 0.181040i
\(688\) 2.82236i 0.107601i
\(689\) −20.9184 20.9184i −0.796929 0.796929i
\(690\) 0.440728 8.83268i 0.0167782 0.336254i
\(691\) 7.08926i 0.269688i −0.990867 0.134844i \(-0.956947\pi\)
0.990867 0.134844i \(-0.0430534\pi\)
\(692\) −14.6997 14.6997i −0.558799 0.558799i
\(693\) 4.61348 + 4.61348i 0.175252 + 0.175252i
\(694\) 20.6489 0.783823
\(695\) 20.1231 + 22.2368i 0.763313 + 0.843488i
\(696\) 2.62509i 0.0995037i
\(697\) 41.8151i 1.58386i
\(698\) −9.13035 −0.345589
\(699\) 6.07475i 0.229768i
\(700\) −5.81071 + 4.75379i −0.219624 + 0.179677i
\(701\) 35.8566 35.8566i 1.35429 1.35429i 0.473485 0.880802i \(-0.342996\pi\)
0.880802 0.473485i \(-0.157004\pi\)
\(702\) −3.22493 + 3.22493i −0.121717 + 0.121717i
\(703\) −12.1411 + 25.2812i −0.457911 + 0.953499i
\(704\) 4.34528i 0.163769i
\(705\) 11.9738 10.8357i 0.450960 0.408095i
\(706\) 2.40807i 0.0906289i
\(707\) 3.21002 3.21002i 0.120725 0.120725i
\(708\) 3.95245i 0.148542i
\(709\) 18.8499 + 18.8499i 0.707923 + 0.707923i 0.966098 0.258175i \(-0.0831210\pi\)
−0.258175 + 0.966098i \(0.583121\pi\)
\(710\) 15.4995 14.0263i 0.581687 0.526396i
\(711\) −0.205500 + 0.205500i −0.00770685 + 0.00770685i
\(712\) 4.88031 + 4.88031i 0.182897 + 0.182897i
\(713\) −14.7583 + 14.7583i −0.552704 + 0.552704i
\(714\) −5.12122 −0.191657
\(715\) 29.7340 + 32.8571i 1.11199 + 1.22879i
\(716\) 6.65594 6.65594i 0.248744 0.248744i
\(717\) 3.81527i 0.142484i
\(718\) −33.5658 −1.25266
\(719\) 40.4350i 1.50797i 0.656892 + 0.753985i \(0.271871\pi\)
−0.656892 + 0.753985i \(0.728129\pi\)
\(720\) −1.65797 + 1.50038i −0.0617889 + 0.0559158i
\(721\) −14.7234 14.7234i −0.548328 0.548328i
\(722\) 2.25801 0.0840346
\(723\) 19.3599 0.720003
\(724\) 12.8467 0.477443
\(725\) 8.31108 + 10.1589i 0.308666 + 0.377292i
\(726\) 5.57302 5.57302i 0.206834 0.206834i
\(727\) 24.3164i 0.901846i −0.892563 0.450923i \(-0.851095\pi\)
0.892563 0.450923i \(-0.148905\pi\)
\(728\) −4.84224 4.84224i −0.179465 0.179465i
\(729\) 1.00000i 0.0370370i
\(730\) −20.0703 1.00146i −0.742836 0.0370656i
\(731\) 9.62630i 0.356042i
\(732\) 2.01684i 0.0745445i
\(733\) −23.5268 23.5268i −0.868981 0.868981i 0.123379 0.992360i \(-0.460627\pi\)
−0.992360 + 0.123379i \(0.960627\pi\)
\(734\) 7.30745 7.30745i 0.269723 0.269723i
\(735\) −10.5980 0.528815i −0.390915 0.0195057i
\(736\) 3.95501 0.145784
\(737\) −13.8129 13.8129i −0.508804 0.508804i
\(738\) 12.2599i 0.451293i
\(739\) 22.6050 0.831539 0.415769 0.909470i \(-0.363512\pi\)
0.415769 + 0.909470i \(0.363512\pi\)
\(740\) 6.49191 11.9522i 0.238647 0.439372i
\(741\) −21.0279 −0.772480
\(742\) 9.73949i 0.357548i
\(743\) 10.1178 + 10.1178i 0.371187 + 0.371187i 0.867909 0.496722i \(-0.165463\pi\)
−0.496722 + 0.867909i \(0.665463\pi\)
\(744\) 5.27722 0.193472
\(745\) 35.3712 32.0091i 1.29590 1.17272i
\(746\) −12.9730 + 12.9730i −0.474976 + 0.474976i
\(747\) −2.55799 2.55799i −0.0935920 0.0935920i
\(748\) 14.8206i 0.541893i
\(749\) 28.4364i 1.03904i
\(750\) 1.66600 11.0555i 0.0608336 0.403690i
\(751\) 15.6348i 0.570520i −0.958450 0.285260i \(-0.907920\pi\)
0.958450 0.285260i \(-0.0920800\pi\)
\(752\) 5.10670 + 5.10670i 0.186222 + 0.186222i
\(753\) 8.30008i 0.302472i
\(754\) −8.46572 + 8.46572i −0.308303 + 0.308303i
\(755\) −35.5154 + 32.1396i −1.29254 + 1.16968i
\(756\) 1.50150 0.0546092
\(757\) −27.1295 −0.986039 −0.493020 0.870018i \(-0.664107\pi\)
−0.493020 + 0.870018i \(0.664107\pi\)
\(758\) −23.8917 −0.867787
\(759\) 12.1521 + 12.1521i 0.441092 + 0.441092i
\(760\) −10.2969 0.513789i −0.373508 0.0186371i
\(761\) 17.0293i 0.617311i −0.951174 0.308655i \(-0.900121\pi\)
0.951174 0.308655i \(-0.0998790\pi\)
\(762\) 0.494255 0.0179050
\(763\) 12.6460i 0.457816i
\(764\) 7.31029 7.31029i 0.264477 0.264477i
\(765\) 5.65489 5.11738i 0.204453 0.185019i
\(766\) −5.61859 −0.203008
\(767\) 12.7464 12.7464i 0.460244 0.460244i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) −16.1719 + 16.1719i −0.583172 + 0.583172i −0.935774 0.352601i \(-0.885297\pi\)
0.352601 + 0.935774i \(0.385297\pi\)
\(770\) 0.727056 14.5710i 0.0262013 0.525102i
\(771\) −17.3448 17.3448i −0.624659 0.624659i
\(772\) 9.97235i 0.358913i
\(773\) −18.0786 + 18.0786i −0.650241 + 0.650241i −0.953051 0.302810i \(-0.902075\pi\)
0.302810 + 0.953051i \(0.402075\pi\)
\(774\) 2.82236i 0.101448i
\(775\) −20.4224 + 16.7078i −0.733596 + 0.600161i
\(776\) 7.85190i 0.281867i
\(777\) −8.61750 + 3.02586i −0.309151 + 0.108552i
\(778\) 19.5391 19.5391i 0.700510 0.700510i
\(779\) −39.9699 + 39.9699i −1.43207 + 1.43207i
\(780\) 10.1854 + 0.508228i 0.364697 +