Properties

Label 1110.2.o.a.253.13
Level $1110$
Weight $2$
Character 1110.253
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.o (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 253.13
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.13

$q$-expansion

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

Character values

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

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) −1.65797 1.50038i −0.741467 0.670989i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) −1.06172 + 1.06172i −0.401294 + 0.401294i −0.878689 0.477395i \(-0.841581\pi\)
0.477395 + 0.878689i \(0.341581\pi\)
\(8\) −1.00000 −0.353553
\(9\) 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
\(13\) 4.56074 1.26492 0.632460 0.774593i \(-0.282045\pi\)
0.632460 + 0.774593i \(0.282045\pi\)
\(14\) 1.06172 1.06172i 0.283758 0.283758i
\(15\) −2.23329 + 0.111436i −0.576633 + 0.0287725i
\(16\) 1.00000 0.250000
\(17\) 3.41073i 0.827223i 0.910453 + 0.413611i \(0.135733\pi\)
−0.910453 + 0.413611i \(0.864267\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.26022 3.26022i −0.747945 0.747945i 0.226148 0.974093i \(-0.427387\pi\)
−0.974093 + 0.226148i \(0.927387\pi\)
\(20\) −1.65797 1.50038i −0.370734 0.335495i
\(21\) 1.50150i 0.327655i
\(22\) 4.34528i 0.926416i
\(23\) −3.95501 −0.824676 −0.412338 0.911031i \(-0.635288\pi\)
−0.412338 + 0.911031i \(0.635288\pi\)
\(24\) −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 −0.858128 0.513437i \(-0.828372\pi\)
0.513437 + 0.858128i \(0.328372\pi\)
\(30\) 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 \(0.592843\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.07257 + 3.07257i 0.534867 + 0.534867i
\(34\) 3.41073i 0.584935i
\(35\) 3.35329 0.167321i 0.566810 0.0282824i
\(36\) 1.00000i 0.166667i
\(37\) 5.73924 2.01522i 0.943526 0.331300i
\(38\) 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 \(0.593315\pi\)
\(42\) 1.50150i 0.231687i
\(43\) 2.82236 0.430406 0.215203 0.976569i \(-0.430959\pi\)
0.215203 + 0.976569i \(0.430959\pi\)
\(44\) 4.34528i 0.655075i
\(45\) −1.50038 + 1.65797i −0.223663 + 0.247156i
\(46\) 3.95501 0.583134
\(47\) 5.10670 5.10670i 0.744889 0.744889i −0.228626 0.973514i \(-0.573423\pi\)
0.973514 + 0.228626i \(0.0734232\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 4.74548i 0.677926i
\(50\) −0.497735 4.97516i −0.0703904 0.703594i
\(51\) 2.41175 + 2.41175i 0.337712 + 0.337712i
\(52\) 4.56074 0.632460
\(53\) 4.58664 + 4.58664i 0.630023 + 0.630023i 0.948074 0.318051i \(-0.103028\pi\)
−0.318051 + 0.948074i \(0.603028\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 6.51956 7.20434i 0.879097 0.971433i
\(56\) 1.06172 1.06172i 0.141879 0.141879i
\(57\) −4.61064 −0.610694
\(58\) 1.85622 1.85622i 0.243733 0.243733i
\(59\) −2.79480 2.79480i −0.363852 0.363852i 0.501377 0.865229i \(-0.332827\pi\)
−0.865229 + 0.501377i \(0.832827\pi\)
\(60\) −2.23329 + 0.111436i −0.288316 + 0.0143863i
\(61\) 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 \(-0.161452\pi\)
−0.485745 + 0.874101i \(0.661452\pi\)
\(68\) 3.41073i 0.413611i
\(69\) −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 \(0.312821\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 6.35469 6.35469i 0.743760 0.743760i −0.229539 0.973299i \(-0.573722\pi\)
0.973299 + 0.229539i \(0.0737219\pi\)
\(74\) −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 0.695452 0.718573i \(-0.255204\pi\)
−0.718573 + 0.695452i \(0.755204\pi\)
\(80\) −1.65797 1.50038i −0.185367 0.167747i
\(81\) −1.00000 −0.111111
\(82\) 12.2599i 1.35388i
\(83\) −2.55799 2.55799i −0.280776 0.280776i 0.552643 0.833418i \(-0.313619\pi\)
−0.833418 + 0.552643i \(0.813619\pi\)
\(84\) 1.50150i 0.163828i
\(85\) 5.11738 5.65489i 0.555058 0.613359i
\(86\) −2.82236 −0.304343
\(87\) 2.62509i 0.281439i
\(88\) 4.34528i 0.463208i
\(89\) −4.88031 + 4.88031i −0.517311 + 0.517311i −0.916757 0.399445i \(-0.869203\pi\)
0.399445 + 0.916757i \(0.369203\pi\)
\(90\) 1.50038 1.65797i 0.158154 0.174765i
\(91\) −4.84224 + 4.84224i −0.507605 + 0.507605i
\(92\) −3.95501 −0.412338
\(93\) 5.27722 0.547222
\(94\) −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
\(97\) 7.85190i 0.797240i 0.917116 + 0.398620i \(0.130511\pi\)
−0.917116 + 0.398620i \(0.869489\pi\)
\(98\) 4.74548i 0.479366i
\(99\) 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
\(103\) 13.8674i 1.36640i 0.730231 + 0.683200i \(0.239412\pi\)
−0.730231 + 0.683200i \(0.760588\pi\)
\(104\) −4.56074 −0.447217
\(105\) 2.25282 2.48945i 0.219853 0.242946i
\(106\) −4.58664 4.58664i −0.445494 0.445494i
\(107\) 13.3916 13.3916i 1.29462 1.29462i 0.362716 0.931900i \(-0.381850\pi\)
0.931900 0.362716i \(-0.118150\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 5.95541 + 5.95541i 0.570424 + 0.570424i 0.932247 0.361823i \(-0.117845\pi\)
−0.361823 + 0.932247i \(0.617845\pi\)
\(110\) −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
\(113\) 9.16869i 0.862518i −0.902228 0.431259i \(-0.858070\pi\)
0.902228 0.431259i \(-0.141930\pi\)
\(114\) 4.61064 0.431826
\(115\) 6.55729 + 5.93401i 0.611471 + 0.553349i
\(116\) −1.85622 + 1.85622i −0.172346 + 0.172346i
\(117\) 4.56074i 0.421640i
\(118\) 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
\(125\) 6.63939 8.99547i 0.593845 0.804579i
\(126\) −1.06172 1.06172i −0.0945859 0.0945859i
\(127\) −0.349491 + 0.349491i −0.0310123 + 0.0310123i −0.722443 0.691431i \(-0.756981\pi\)
0.691431 + 0.722443i \(0.256981\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.99571 1.99571i 0.175712 0.175712i
\(130\) 7.56157 + 6.84283i 0.663193 + 0.600155i
\(131\) −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
\(133\) 6.92290 0.600291
\(134\) −3.17883 3.17883i −0.274609 0.274609i
\(135\) 0.111436 + 2.23329i 0.00959084 + 0.192211i
\(136\) 3.41073i 0.292467i
\(137\) −5.52765 + 5.52765i −0.472259 + 0.472259i −0.902645 0.430386i \(-0.858377\pi\)
0.430386 + 0.902645i \(0.358377\pi\)
\(138\) 2.79661 2.79661i 0.238064 0.238064i
\(139\) −13.4120 −1.13759 −0.568797 0.822478i \(-0.692591\pi\)
−0.568797 + 0.822478i \(0.692591\pi\)
\(140\) 3.35329 0.167321i 0.283405 0.0141412i
\(141\) 7.22196i 0.608199i
\(142\) −9.34849 −0.784508
\(143\) 19.8177i 1.65724i
\(144\) 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
\(148\) 5.73924 2.01522i 0.471763 0.165650i
\(149\) 21.3340i 1.74775i 0.486149 + 0.873876i \(0.338401\pi\)
−0.486149 + 0.873876i \(0.661599\pi\)
\(150\) −3.86992 3.16602i −0.315978 0.258504i
\(151\) 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
\(153\) 3.41073 0.275741
\(154\) 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 −0.620653 0.784085i \(-0.713133\pi\)
0.784085 + 0.620653i \(0.213133\pi\)
\(158\) 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
\(162\) 1.00000 0.0785674
\(163\) 12.1359i 0.950560i −0.879835 0.475280i \(-0.842347\pi\)
0.879835 0.475280i \(-0.157653\pi\)
\(164\) 12.2599i 0.957337i
\(165\) −0.484218 9.70426i −0.0376963 0.755476i
\(166\) 2.55799 + 2.55799i 0.198539 + 0.198539i
\(167\) 8.95519i 0.692973i −0.938055 0.346487i \(-0.887375\pi\)
0.938055 0.346487i \(-0.112625\pi\)
\(168\) 1.50150i 0.115844i
\(169\) 7.80032 0.600024
\(170\) −5.11738 + 5.65489i −0.392485 + 0.433710i
\(171\) −3.26022 + 3.26022i −0.249315 + 0.249315i
\(172\) 2.82236 0.215203
\(173\) −14.6997 + 14.6997i −1.11760 + 1.11760i −0.125506 + 0.992093i \(0.540055\pi\)
−0.992093 + 0.125506i \(0.959945\pi\)
\(174\) 2.62509i 0.199007i
\(175\) −5.81071 4.75379i −0.439248 0.359353i
\(176\) 4.34528i 0.327538i
\(177\) −3.95245 −0.297084
\(178\) 4.88031 4.88031i 0.365794 0.365794i
\(179\) 6.65594 6.65594i 0.497488 0.497488i −0.413167 0.910655i \(-0.635577\pi\)
0.910655 + 0.413167i \(0.135577\pi\)
\(180\) −1.50038 + 1.65797i −0.111832 + 0.123578i
\(181\) −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
\(183\) 2.01684 0.149089
\(184\) 3.95501 0.291567
\(185\) −12.5391 5.26986i −0.921892 0.387448i
\(186\) −5.27722 −0.386945
\(187\) −14.8206 −1.08379
\(188\) 5.10670 5.10670i 0.372444 0.372444i
\(189\) 1.50150 0.109218
\(190\) −0.513789 10.2969i −0.0372742 0.747015i
\(191\) −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
\(193\) 9.97235 0.717826 0.358913 0.933371i \(-0.383148\pi\)
0.358913 + 0.933371i \(0.383148\pi\)
\(194\) 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 −0.957969 0.286870i \(-0.907385\pi\)
0.286870 + 0.957969i \(0.407385\pi\)
\(198\) −4.34528 −0.308805
\(199\) 8.39214 8.39214i 0.594903 0.594903i −0.344049 0.938952i \(-0.611798\pi\)
0.938952 + 0.344049i \(0.111798\pi\)
\(200\) −0.497735 4.97516i −0.0351952 0.351797i
\(201\) 4.49554 0.317091
\(202\) 3.02340i 0.212726i
\(203\) 3.94158i 0.276645i
\(204\) 2.41175 + 2.41175i 0.168856 + 0.168856i
\(205\) 18.3945 20.3265i 1.28472 1.41967i
\(206\) 13.8674i 0.966190i
\(207\) 3.95501i 0.274892i
\(208\) 4.56074 0.316230
\(209\) 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
\(217\) −7.92377 −0.537900
\(218\) −5.95541 5.95541i −0.403351 0.403351i
\(219\) 8.98689i 0.607278i
\(220\) 6.51956 7.20434i 0.439548 0.485717i
\(221\) 15.5554i 1.04637i
\(222\) −2.63328 + 5.48323i −0.176734 + 0.368010i
\(223\) 0.189445 + 0.189445i 0.0126862 + 0.0126862i 0.713421 0.700735i \(-0.247145\pi\)
−0.700735 + 0.713421i \(0.747145\pi\)
\(224\) 1.06172 1.06172i 0.0709394 0.0709394i
\(225\) 4.97516 0.497735i 0.331678 0.0331824i
\(226\) 9.16869i 0.609892i
\(227\) 22.4161i 1.48781i 0.668285 + 0.743905i \(0.267029\pi\)
−0.668285 + 0.743905i \(0.732971\pi\)
\(228\) −4.61064 −0.305347
\(229\) 6.71069i 0.443455i −0.975109 0.221727i \(-0.928831\pi\)
0.975109 0.221727i \(-0.0711695\pi\)
\(230\) −6.55729 5.93401i −0.432375 0.391277i
\(231\) −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 \(-0.813765\pi\)
0.552263 + 0.833670i \(0.313765\pi\)
\(234\) 4.56074i 0.298145i
\(235\) −16.1287 + 0.804783i −1.05212 + 0.0524983i
\(236\) −2.79480 2.79480i −0.181926 0.181926i
\(237\) −0.290621 −0.0188779
\(238\) 3.62125 + 3.62125i 0.234731 + 0.234731i
\(239\) −2.69780 2.69780i −0.174506 0.174506i 0.614450 0.788956i \(-0.289378\pi\)
−0.788956 + 0.614450i \(0.789378\pi\)
\(240\) −2.23329 + 0.111436i −0.144158 + 0.00719313i
\(241\) −13.6895 + 13.6895i −0.881820 + 0.881820i −0.993719 0.111900i \(-0.964306\pi\)
0.111900 + 0.993719i \(0.464306\pi\)
\(242\) 7.88143 0.506638
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 1.42612 + 1.42612i 0.0912980 + 0.0912980i
\(245\) 7.12002 7.86788i 0.454881 0.502660i
\(246\) −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
\(253\) 17.1856i 1.08045i
\(254\) 0.349491 0.349491i 0.0219290 0.0219290i
\(255\) −0.380076 7.61714i −0.0238013 0.477004i
\(256\) 1.00000 0.0625000
\(257\) 24.5293i 1.53010i −0.643974 0.765048i \(-0.722715\pi\)
0.643974 0.765048i \(-0.277285\pi\)
\(258\) −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 \(-0.771992\pi\)
0.656605 + 0.754235i \(0.271992\pi\)
\(264\) −3.07257 3.07257i −0.189104 0.189104i
\(265\) −0.722825 14.4862i −0.0444028 0.889880i
\(266\) −6.92290 −0.424470
\(267\) 6.90180i 0.422383i
\(268\) 3.17883 + 3.17883i 0.194178 + 0.194178i
\(269\) 6.02812i 0.367541i −0.982969 0.183771i \(-0.941170\pi\)
0.982969 0.183771i \(-0.0588304\pi\)
\(270\) −0.111436 2.23329i −0.00678175 0.135914i
\(271\) −22.2398 −1.35097 −0.675485 0.737374i \(-0.736066\pi\)
−0.675485 + 0.737374i \(0.736066\pi\)
\(272\) 3.41073i 0.206806i
\(273\) 6.84797i 0.414458i
\(274\) 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
\(277\) 1.53430 0.0921869 0.0460934 0.998937i \(-0.485323\pi\)
0.0460934 + 0.998937i \(0.485323\pi\)
\(278\) 13.4120 0.804400
\(279\) 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 \(-0.0349433\pi\)
\(282\) 7.22196i 0.430062i
\(283\) 13.7302i 0.816174i −0.912943 0.408087i \(-0.866196\pi\)
0.912943 0.408087i \(-0.133804\pi\)
\(284\) 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
\(288\) 1.00000i 0.0589256i
\(289\) 5.36694 0.315702
\(290\) −5.86258 + 0.292528i −0.344263 + 0.0171778i
\(291\) 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 0.991508 0.130043i \(-0.0415114\pi\)
−0.130043 + 0.991508i \(0.541511\pi\)
\(294\) −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
\(298\) 21.3340i 1.23585i
\(299\) −18.0378 −1.04315
\(300\) 3.86992 + 3.16602i 0.223430 + 0.182790i
\(301\) −2.99657 + 2.99657i −0.172719 + 0.172719i
\(302\) 21.4210i 1.23264i
\(303\) 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 −0.914324 0.404982i \(-0.867278\pi\)
−0.404982 0.914324i \(-0.632722\pi\)
\(308\) −4.61348 4.61348i −0.262878 0.262878i
\(309\) 9.80576 + 9.80576i 0.557830 + 0.557830i
\(310\) 0.588070 + 11.7856i 0.0334001 + 0.669375i
\(311\) −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
\(313\) −15.9823 −0.903373 −0.451687 0.892177i \(-0.649177\pi\)
−0.451687 + 0.892177i \(0.649177\pi\)
\(314\) −2.04779 + 2.04779i −0.115564 + 0.115564i
\(315\) −0.167321 3.35329i −0.00942746 0.188937i
\(316\) −0.205500 0.205500i −0.0115603 0.0115603i
\(317\) 11.2092 + 11.2092i 0.629569 + 0.629569i 0.947960 0.318391i \(-0.103142\pi\)
−0.318391 + 0.947960i \(0.603142\pi\)
\(318\) −6.48649 −0.363744
\(319\) −8.06578 8.06578i −0.451597 0.451597i
\(320\) −1.65797 1.50038i −0.0926834 0.0838736i
\(321\) 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
\(325\) 2.27004 + 22.6904i 0.125919 + 1.25864i
\(326\) 12.1359i 0.672147i
\(327\) 8.42221 0.465750
\(328\) 12.2599i 0.676939i
\(329\) 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
\(333\) −2.01522 5.73924i −0.110433 0.314509i
\(334\) 8.95519i 0.490006i
\(335\) −0.500963 10.0398i −0.0273705 0.548535i
\(336\) 1.50150i 0.0819138i
\(337\) −13.0929 13.0929i −0.713214 0.713214i 0.253992 0.967206i \(-0.418256\pi\)
−0.967206 + 0.253992i \(0.918256\pi\)
\(338\) −7.80032 −0.424281
\(339\) −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
\(347\) 20.6489 1.10849 0.554247 0.832352i \(-0.313006\pi\)
0.554247 + 0.832352i \(0.313006\pi\)
\(348\) 2.62509i 0.140720i
\(349\) 9.13035i 0.488737i 0.969683 + 0.244368i \(0.0785806\pi\)
−0.969683 + 0.244368i \(0.921419\pi\)
\(350\) 5.81071 + 4.75379i 0.310595 + 0.254101i
\(351\) −3.22493 3.22493i −0.172134 0.172134i
\(352\) 4.34528i 0.231604i
\(353\) 2.40807i 0.128169i 0.997944 + 0.0640843i \(0.0204127\pi\)
−0.997944 + 0.0640843i \(0.979587\pi\)
\(354\) 3.95245 0.210070
\(355\) −15.4995 14.0263i −0.822630 0.744437i
\(356\) −4.88031 + 4.88031i −0.258656 + 0.258656i
\(357\) −5.12122 −0.271044
\(358\) −6.65594 + 6.65594i −0.351777 + 0.351777i
\(359\) 33.5658i 1.77153i 0.464131 + 0.885767i \(0.346367\pi\)
−0.464131 + 0.885767i \(0.653633\pi\)
\(360\) 1.50038 1.65797i 0.0790768 0.0873827i
\(361\) 2.25801i 0.118843i
\(362\) 12.8467 0.675206
\(363\) −5.57302 + 5.57302i −0.292507 + 0.292507i
\(364\) −4.84224 + 4.84224i −0.253802 + 0.253802i
\(365\) −20.0703 + 1.00146i −1.05053 + 0.0524187i
\(366\) −2.01684 −0.105422
\(367\) 7.30745 7.30745i 0.381446 0.381446i −0.490177 0.871623i \(-0.663068\pi\)
0.871623 + 0.490177i \(0.163068\pi\)
\(368\) −3.95501 −0.206169
\(369\) 12.2599 0.638224
\(370\) 12.5391 + 5.26986i 0.651876 + 0.273967i
\(371\) −9.73949 −0.505649
\(372\) 5.27722 0.273611
\(373\) 12.9730 12.9730i 0.671717 0.671717i −0.286395 0.958112i \(-0.592457\pi\)
0.958112 + 0.286395i \(0.0924568\pi\)
\(374\) 14.8206 0.766353
\(375\) −1.66600 11.0555i −0.0860317 0.570904i
\(376\) −5.10670 + 5.10670i −0.263358 + 0.263358i
\(377\) −8.46572 + 8.46572i −0.436007 + 0.436007i
\(378\) −1.50150 −0.0772291
\(379\) 23.8917i 1.22724i 0.789603 + 0.613618i \(0.210286\pi\)
−0.789603 + 0.613618i \(0.789714\pi\)
\(380\) 0.513789 + 10.2969i 0.0263568 + 0.528220i
\(381\) 0.494255i 0.0253215i
\(382\) 7.31029 7.31029i 0.374027 0.374027i
\(383\) 5.61859 0.287097 0.143548 0.989643i \(-0.454149\pi\)
0.143548 + 0.989643i \(0.454149\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 0.727056 + 14.5710i 0.0370542 + 0.742607i
\(386\) −9.97235 −0.507579
\(387\) 2.82236i 0.143469i
\(388\) 7.85190i 0.398620i
\(389\) −19.5391 19.5391i −0.990671 0.990671i 0.00928635 0.999957i \(-0.497044\pi\)
−0.999957 + 0.00928635i \(0.997044\pi\)
\(390\) 10.1854 0.508228i 0.515760 0.0257351i
\(391\) 13.4895i 0.682191i
\(392\) 4.74548i 0.239683i
\(393\) −14.4366 −0.728229
\(394\) 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 \(-0.244804\pi\)
−0.695471 + 0.718554i \(0.744804\pi\)
\(398\) −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 \(0.708483\pi\)
\(402\) −4.49554 −0.224217
\(403\) 17.0187 + 17.0187i 0.847759 + 0.847759i
\(404\) 3.02340i 0.150420i
\(405\) 1.65797 + 1.50038i 0.0823852 + 0.0745544i
\(406\) 3.94158i 0.195617i
\(407\) 8.75668 + 24.9386i 0.434052 + 1.23616i
\(408\) −2.41175 2.41175i −0.119399 0.119399i
\(409\) −23.4462 + 23.4462i −1.15934 + 1.15934i −0.174722 + 0.984618i \(0.555903\pi\)
−0.984618 + 0.174722i \(0.944097\pi\)
\(410\) −18.3945 + 20.3265i −0.908438 + 1.00386i
\(411\) 7.81728i 0.385598i
\(412\) 13.8674i 0.683200i
\(413\) 5.93462 0.292024
\(414\) 3.95501i 0.194378i
\(415\) 0.403123 + 8.07902i 0.0197885 + 0.396584i
\(416\) −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 \(-0.778302\pi\)
0.767102 0.641525i \(-0.221698\pi\)
\(420\) 2.25282 2.48945i 0.109927 0.121473i
\(421\) 15.2941 + 15.2941i 0.745387 + 0.745387i 0.973609 0.228222i \(-0.0732912\pi\)
−0.228222 + 0.973609i \(0.573291\pi\)
\(422\) 23.7130 1.15433
\(423\) −5.10670 5.10670i −0.248296 0.248296i
\(424\) −4.58664 4.58664i −0.222747 0.222747i
\(425\) −16.9689 + 1.69764i −0.823114 + 0.0823476i
\(426\) −6.61038 + 6.61038i −0.320274 + 0.320274i
\(427\) −3.02829 −0.146549
\(428\) 13.3916 13.3916i 0.647308 0.647308i
\(429\) 14.0132 + 14.0132i 0.676564 + 0.676564i
\(430\) 4.67939 + 4.23460i 0.225660 + 0.204211i
\(431\) −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 0.997500 0.0706638i \(-0.0225118\pi\)
−0.0706638 + 0.997500i \(0.522512\pi\)
\(434\) 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
\(438\) 8.98689i 0.429410i
\(439\) 18.1003 18.1003i 0.863882 0.863882i −0.127904 0.991787i \(-0.540825\pi\)
0.991787 + 0.127904i \(0.0408250\pi\)
\(440\) −6.51956 + 7.20434i −0.310808 + 0.343454i
\(441\) 4.74548 0.225975
\(442\) 15.5554i 0.739896i
\(443\) 7.18587 7.18587i 0.341411 0.341411i −0.515487 0.856898i \(-0.672389\pi\)
0.856898 + 0.515487i \(0.172389\pi\)
\(444\) 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 0.753939 0.656945i \(-0.228152\pi\)
−0.656945 + 0.753939i \(0.728152\pi\)
\(450\) −4.97516 + 0.497735i −0.234531 + 0.0234635i
\(451\) −53.2726 −2.50851
\(452\) 9.16869i 0.431259i
\(453\) 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
\(457\) 29.9149i 1.39936i 0.714456 + 0.699681i \(0.246674\pi\)
−0.714456 + 0.699681i \(0.753326\pi\)
\(458\) 6.71069i 0.313570i
\(459\) 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 \(0.0555119\pi\)
\(462\) 6.52445 0.303545
\(463\) 21.2696 0.988484 0.494242 0.869324i \(-0.335446\pi\)
0.494242 + 0.869324i \(0.335446\pi\)
\(464\) −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
\(467\) 11.3616i 0.525754i −0.964829 0.262877i \(-0.915329\pi\)
0.964829 0.262877i \(-0.0846714\pi\)
\(468\) 4.56074i 0.210820i
\(469\) −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
\(473\) 12.2639i 0.563896i
\(474\) 0.290621 0.0133487
\(475\) 14.5974 17.8428i 0.669774 0.818685i
\(476\) −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 0.867573 0.497309i \(-0.165678\pi\)
−0.497309 + 0.867573i \(0.665678\pi\)
\(480\) 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
\(483\) 5.93846i 0.270209i
\(484\) −7.88143 −0.358247
\(485\) 11.7808 13.0182i 0.534939 0.591127i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 13.1026i 0.593738i −0.954918 0.296869i \(-0.904058\pi\)
0.954918 0.296869i \(-0.0959424\pi\)
\(488\) −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
\(495\) −7.20434 6.51956i −0.323811 0.293032i
\(496\) 3.73156 + 3.73156i 0.167552 + 0.167552i
\(497\) −9.92552 + 9.92552i −0.445220 + 0.445220i
\(498\) 3.61754 0.162106
\(499\) −5.96339 + 5.96339i −0.266958 + 0.266958i −0.827873 0.560915i \(-0.810449\pi\)
0.560915 + 0.827873i \(0.310449\pi\)
\(500\) 6.63939 8.99547i 0.296923 0.402290i
\(501\) −6.33227 6.33227i −0.282905 0.282905i
\(502\) −5.86904 5.86904i −0.261948 0.261948i
\(503\) 23.5927 1.05195 0.525973 0.850501i \(-0.323701\pi\)
0.525973 + 0.850501i \(0.323701\pi\)
\(504\) −1.06172 1.06172i −0.0472929 0.0472929i
\(505\) 4.53624 5.01271i 0.201860 0.223063i
\(506\) 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 \(-0.105907\pi\)
0.945159 + 0.326611i \(0.105907\pi\)
\(510\) 0.380076 + 7.61714i 0.0168301 + 0.337293i
\(511\) 13.4939i 0.596933i
\(512\) −1.00000 −0.0441942
\(513\) 4.61064i 0.203565i
\(514\) 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
\(518\) 3.95389 8.23310i 0.173724 0.361741i
\(519\) 20.7885i 0.912516i
\(520\) 7.56157 + 6.84283i 0.331597 + 0.300078i
\(521\) 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
\(523\) 14.0079 0.612523 0.306262 0.951947i \(-0.400922\pi\)
0.306262 + 0.951947i \(0.400922\pi\)
\(524\) −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
\(532\) 6.92290 0.300146
\(533\) 55.9141i 2.42191i
\(534\) 6.90180i 0.298670i
\(535\) −42.2954 + 2.11043i −1.82859 + 0.0912419i
\(536\) −3.17883 3.17883i −0.137304 0.137304i
\(537\) 9.41292i 0.406198i
\(538\) 6.02812i 0.259891i
\(539\) −20.6204 −0.888185
\(540\) 0.111436 + 2.23329i 0.00479542 + 0.0961055i
\(541\) 10.6677 10.6677i 0.458641 0.458641i −0.439568 0.898209i \(-0.644869\pi\)
0.898209 + 0.439568i \(0.144869\pi\)
\(542\) 22.2398 0.955280
\(543\) −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
\(547\) −17.2017 −0.735490 −0.367745 0.929927i \(-0.619870\pi\)
−0.367745 + 0.929927i \(0.619870\pi\)
\(548\) −5.52765 + 5.52765i −0.236129 + 0.236129i
\(549\) 1.42612 1.42612i 0.0608653 0.0608653i
\(550\) 21.6185 2.16280i 0.921815 0.0922220i
\(551\) 12.1033 0.515620
\(552\) 2.79661 2.79661i 0.119032 0.119032i
\(553\) 0.436369 0.0185563
\(554\) −1.53430 −0.0651860
\(555\) −12.5928 + 5.14012i −0.534536 + 0.218186i
\(556\) −13.4120 −0.568797
\(557\) 29.7084 1.25879 0.629393 0.777087i \(-0.283303\pi\)
0.629393 + 0.777087i \(0.283303\pi\)
\(558\) −3.73156 + 3.73156i −0.157969 + 0.157969i
\(559\) 12.8720 0.544429
\(560\) 3.35329 0.167321i 0.141703 0.00707060i
\(561\) −10.4797 + 10.4797i −0.442454 + 0.442454i
\(562\) −18.4987 + 18.4987i −0.780319 + 0.780319i
\(563\) −18.1294 −0.764062 −0.382031 0.924149i \(-0.624775\pi\)
−0.382031 + 0.924149i \(0.624775\pi\)
\(564\) 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
\(568\) −9.34849 −0.392254
\(569\) −8.90810 + 8.90810i −0.373447 + 0.373447i −0.868731 0.495284i \(-0.835064\pi\)
0.495284 + 0.868731i \(0.335064\pi\)
\(570\) −7.64431 6.91770i −0.320185 0.289751i
\(571\) 45.2926 1.89544 0.947718 0.319109i \(-0.103384\pi\)
0.947718 + 0.319109i \(0.103384\pi\)
\(572\) 19.8177i 0.828618i
\(573\) 10.3383i 0.431889i
\(574\) 13.0166 + 13.0166i 0.543303 + 0.543303i
\(575\) −1.96855 19.6768i −0.0820941 0.820580i
\(576\) 1.00000i 0.0416667i
\(577\) 3.80406i 0.158365i −0.996860 0.0791826i \(-0.974769\pi\)
0.996860 0.0791826i \(-0.0252310\pi\)
\(578\) −5.36694 −0.223235
\(579\) 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
\(587\) 30.4191 1.25553 0.627766 0.778402i \(-0.283969\pi\)
0.627766 + 0.778402i \(0.283969\pi\)
\(588\) 3.35556 + 3.35556i 0.138381 + 0.138381i
\(589\) 24.3314i 1.00256i
\(590\) −0.440443 8.82696i −0.0181328 0.363400i
\(591\) 13.3209i 0.547950i
\(592\) 5.73924 2.01522i 0.235881 0.0828249i
\(593\) −4.86429 4.86429i −0.199752 0.199752i 0.600142 0.799894i \(-0.295111\pi\)
−0.799894 + 0.600142i \(0.795111\pi\)
\(594\) −3.07257 + 3.07257i −0.126069 + 0.126069i
\(595\) 0.570686 + 11.4372i 0.0233958 + 0.468878i
\(596\) 21.3340i 0.873876i
\(597\) 11.8683i 0.485736i
\(598\) 18.0378 0.737619
\(599\) 44.2957i 1.80987i 0.425545 + 0.904937i \(0.360082\pi\)
−0.425545 + 0.904937i \(0.639918\pi\)
\(600\) −3.86992 3.16602i −0.157989 0.129252i
\(601\) 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
\(605\) 13.0672 + 11.8251i 0.531257 + 0.480760i
\(606\) −2.13787 2.13787i −0.0868449 0.0868449i
\(607\) −42.7185 −1.73389 −0.866945 0.498404i \(-0.833919\pi\)
−0.866945 + 0.498404i \(0.833919\pi\)
\(608\) 3.26022 + 3.26022i 0.132219 + 0.132219i
\(609\) −2.78712 2.78712i −0.112940 0.112940i
\(610\) 0.224747 + 4.50418i 0.00909976 + 0.182369i
\(611\) 23.2903 23.2903i 0.942225 0.942225i
\(612\) 3.41073 0.137870
\(613\) −14.3851 + 14.3851i −0.581008 + 0.581008i −0.935180 0.354172i \(-0.884763\pi\)
0.354172 + 0.935180i \(0.384763\pi\)
\(614\) 23.1161 + 23.1161i 0.932891 + 0.932891i
\(615\) −1.36619 27.3799i −0.0550900 1.10406i
\(616\) 4.61348 + 4.61348i 0.185883 + 0.185883i
\(617\) −25.2866 25.2866i −1.01800 1.01800i −0.999835 0.0181641i \(-0.994218\pi\)
−0.0181641 0.999835i \(-0.505782\pi\)
\(618\) −9.80576 9.80576i −0.394446 0.394446i
\(619\) −27.8054 −1.11759 −0.558797 0.829305i \(-0.688737\pi\)
−0.558797 + 0.829305i \(0.688737\pi\)
\(620\) −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
\(623\) 10.3631i 0.415188i
\(624\) 3.22493 3.22493i 0.129100 0.129100i
\(625\) −24.5045 + 4.95263i −0.980181 + 0.198105i
\(626\) 15.9823 0.638781
\(627\) 20.0345i 0.800101i
\(628\) 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
\(635\) 1.10381 0.0550776i 0.0438036 0.00218569i
\(636\) 6.48649 0.257206
\(637\) 21.6429i 0.857523i
\(638\) 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 \(0.277598\pi\)
\(642\) 18.9386i 0.747447i
\(643\) 12.0685i 0.475934i 0.971273 + 0.237967i \(0.0764810\pi\)
−0.971273 + 0.237967i \(0.923519\pi\)
\(644\) 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
\(647\) −29.2633 −1.15046 −0.575229 0.817993i \(-0.695087\pi\)
−0.575229 + 0.817993i \(0.695087\pi\)
\(648\) 1.00000 0.0392837
\(649\) 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
\(652\) 12.1359i 0.475280i
\(653\) 16.0675i 0.628769i −0.949296 0.314384i \(-0.898202\pi\)
0.949296 0.314384i \(-0.101798\pi\)
\(654\) −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
\(658\) 10.8438i 0.422736i
\(659\) −30.0316 −1.16987 −0.584933 0.811081i \(-0.698879\pi\)
−0.584933 + 0.811081i \(0.698879\pi\)
\(660\) −0.484218 9.70426i −0.0188482 0.377738i
\(661\) 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
\(668\) 8.95519i 0.346487i
\(669\) 0.267916 0.0103582
\(670\) 0.500963 + 10.0398i 0.0193539 + 0.387873i
\(671\) −6.19689 + 6.19689i −0.239228 + 0.239228i
\(672\) 1.50150i 0.0579218i
\(673\) −30.1779 30.1779i −1.16327 1.16327i −0.983755 0.179516i \(-0.942547\pi\)
−0.179516 0.983755i \(-0.557453\pi\)
\(674\) 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 0.965723 + 0.259574i \(0.0835821\pi\)
0.259574 + 0.965723i \(0.416418\pi\)
\(678\) 6.48324 + 6.48324i 0.248987 + 0.248987i
\(679\) −8.33655 8.33655i −0.319928 0.319928i
\(680\) −5.11738 + 5.65489i −0.196243 + 0.216855i
\(681\) 15.8506 + 15.8506i 0.607396 + 0.607396i
\(682\) 16.2147 16.2147i 0.620891 0.620891i
\(683\) −18.9583 −0.725421 −0.362710 0.931902i \(-0.618149\pi\)
−0.362710 + 0.931902i \(0.618149\pi\)
\(684\) −3.26022 + 3.26022i −0.124657 + 0.124657i
\(685\) 17.4582 0.871122i 0.667045 0.0332839i
\(686\) 12.4705 + 12.4705i 0.476124 + 0.476124i
\(687\) −4.74517 4.74517i −0.181040 0.181040i
\(688\) 2.82236 0.107601
\(689\) 20.9184 + 20.9184i 0.796929 + 0.796929i
\(690\) −8.83268 + 0.440728i −0.336254 + 0.0167782i
\(691\) 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
\(695\) 22.2368 + 20.1231i 0.843488 + 0.763313i
\(696\) 2.62509i 0.0995037i
\(697\) −41.8151 −1.58386
\(698\) 9.13035i 0.345589i
\(699\) 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
\(703\) −25.2812 12.1411i −0.953499 0.457911i
\(704\) 4.34528i 0.163769i
\(705\) −10.8357 + 11.9738i −0.408095 + 0.450960i
\(706\) 2.40807i 0.0906289i
\(707\) −3.21002 3.21002i −0.120725 0.120725i
\(708\) −3.95245 −0.148542
\(709\) −18.8499 18.8499i −0.707923 0.707923i 0.258175 0.966098i \(-0.416879\pi\)
−0.966098 + 0.258175i \(0.916879\pi\)
\(710\) 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
\(717\) −3.81527 −0.142484
\(718\) 33.5658i 1.25266i
\(719\) 40.4350i 1.50797i −0.656892 0.753985i \(-0.728129\pi\)
0.656892 0.753985i \(-0.271871\pi\)
\(720\) −1.50038 + 1.65797i −0.0559158 + 0.0617889i
\(721\) −14.7234 14.7234i −0.548328 0.548328i
\(722\) 2.25801i 0.0840346i
\(723\) 19.3599i 0.720003i
\(724\) −12.8467 −0.477443
\(725\) −10.1589 8.31108i −0.377292 0.308666i
\(726\) 5.57302 5.57302i 0.206834 0.206834i
\(727\) −24.3164 −0.901846 −0.450923 0.892563i \(-0.648905\pi\)
−0.450923 + 0.892563i \(0.648905\pi\)
\(728\) 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
\(732\) 2.01684 0.0745445
\(733\) 23.5268 23.5268i 0.868981 0.868981i −0.123379 0.992360i \(-0.539373\pi\)
0.992360 + 0.123379i \(0.0393730\pi\)
\(734\) −7.30745 + 7.30745i −0.269723 + 0.269723i
\(735\) −0.528815 10.5980i −0.0195057 0.390915i
\(736\) 3.95501 0.145784
\(737\) −13.8129 + 13.8129i −0.508804 + 0.508804i
\(738\) −12.2599 −0.451293
\(739\) −22.6050 −0.831539 −0.415769 0.909470i \(-0.636488\pi\)
−0.415769 + 0.909470i \(0.636488\pi\)
\(740\) −12.5391 5.26986i −0.460946 0.193724i
\(741\) −21.0279 −0.772480
\(742\) 9.73949 0.357548
\(743\) −10.1178 + 10.1178i −0.371187 + 0.371187i −0.867909 0.496722i \(-0.834537\pi\)
0.496722 + 0.867909i \(0.334537\pi\)
\(744\) −5.27722 −0.193472
\(745\) 32.0091 35.3712i 1.17272 1.29590i
\(746\) −12.9730 + 12.9730i −0.474976 + 0.474976i
\(747\) −2.55799 + 2.55799i −0.0935920 + 0.0935920i
\(748\) −14.8206 −0.541893
\(749\) 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
\(753\) 8.30008 0.302472
\(754\) 8.46572 8.46572i 0.308303 0.308303i
\(755\) 32.1396 35.5154i 1.16968 1.29254i
\(756\) 1.50150 0.0546092
\(757\) 27.1295i 0.986039i 0.870018 + 0.493020i \(0.164107\pi\)
−0.870018 + 0.493020i \(0.835893\pi\)
\(758\) 23.8917i 0.867787i
\(759\) −12.1521 12.1521i −0.441092 0.441092i
\(760\) −0.513789 10.2969i −0.0186371 0.373508i
\(761\) 17.0293i 0.617311i −0.951174 0.308655i \(-0.900121\pi\)
0.951174 0.308655i \(-0.0998790\pi\)
\(762\) 0.494255i 0.0179050i
\(763\) −12.6460 −0.457816
\(764\) −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 −0.352601 0.935774i \(-0.614703\pi\)
0.935774 + 0.352601i \(0.114703\pi\)
\(770\) −0.727056 14.5710i −0.0262013 0.525102i
\(771\) −17.3448 17.3448i −0.624659 0.624659i
\(772\) 9.97235 0.358913
\(773\) −18.0786 18.0786i −0.650241 0.650241i 0.302810 0.953051i \(-0.402075\pi\)
−0.953051 + 0.302810i \(0.902075\pi\)
\(774\) 2.82236i 0.101448i
\(775\) −16.7078 + 20.4224i −0.600161 + 0.733596i
\(776\) 7.85190i 0.281867i
\(777\) 3.02586 + 8.61750i 0.108552 + 0.309151i
\(778\) 19.5391 + 19.5391i 0.700510 + 0.700510i
\(779\) 39.9699 39.9699i 1.43207 1.43207i
\(780\) −10.1854