Properties

Label 1950.2.bc.k.751.2
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + 115386 x^{4} - 135130 x^{3} + 113253 x^{2} - 54888 x + 14089\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.2
Root \(0.500000 + 0.414256i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.k.901.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.242731 + 0.140141i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.242731 + 0.140141i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.663862 - 0.383281i) q^{11} +1.00000 q^{12} +(-2.77303 + 2.30441i) q^{13} -0.280281 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.10917 + 1.92113i) q^{17} -1.00000i q^{18} +(-4.57097 - 2.63905i) q^{19} +0.280281i q^{21} +(-0.383281 + 0.663862i) q^{22} +(-0.725885 - 1.25727i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.24931 - 3.38219i) q^{26} -1.00000 q^{27} +(0.242731 - 0.140141i) q^{28} +(-3.03030 - 5.24863i) q^{29} +3.28110i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.663862 + 0.383281i) q^{33} -2.21833i q^{34} +(0.500000 + 0.866025i) q^{36} +(-3.07097 + 1.77303i) q^{37} +5.27811 q^{38} +(-3.38219 - 1.24931i) q^{39} +(1.92113 - 1.10917i) q^{41} +(-0.140141 - 0.242731i) q^{42} +(-1.80441 + 3.12533i) q^{43} -0.766562i q^{44} +(1.25727 + 0.725885i) q^{46} +1.06277i q^{47} +(0.500000 - 0.866025i) q^{48} +(-3.46072 - 5.99414i) q^{49} -2.21833 q^{51} +(0.609166 + 3.55372i) q^{52} +3.28110 q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.140141 + 0.242731i) q^{56} -5.27811i q^{57} +(5.24863 + 3.03030i) q^{58} +(-4.32824 - 2.49891i) q^{59} +(-0.773028 + 1.33892i) q^{61} +(-1.64055 - 2.84152i) q^{62} +(-0.242731 + 0.140141i) q^{63} -1.00000 q^{64} -0.766562 q^{66} +(-6.43963 + 3.71792i) q^{67} +(1.10917 + 1.92113i) q^{68} +(0.725885 - 1.25727i) q^{69} +(-2.09811 - 1.21135i) q^{71} +(-0.866025 - 0.500000i) q^{72} +14.2630i q^{73} +(1.77303 - 3.07097i) q^{74} +(-4.57097 + 2.63905i) q^{76} +0.214853 q^{77} +(3.55372 - 0.609166i) q^{78} -14.4715 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.10917 + 1.92113i) q^{82} -4.42419i q^{83} +(0.242731 + 0.140141i) q^{84} -3.60882i q^{86} +(3.03030 - 5.24863i) q^{87} +(0.383281 + 0.663862i) q^{88} +(-4.60275 + 2.65740i) q^{89} +(-0.996041 + 0.170738i) q^{91} -1.45177 q^{92} +(-2.84152 + 1.64055i) q^{93} +(-0.531385 - 0.920385i) q^{94} +1.00000i q^{96} +(1.09737 + 0.633565i) q^{97} +(5.99414 + 3.46072i) q^{98} +0.766562i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{3} + 6q^{4} + 6q^{7} - 6q^{9} + O(q^{10}) \) \( 12q + 6q^{3} + 6q^{4} + 6q^{7} - 6q^{9} - 12q^{11} + 12q^{12} + 8q^{14} - 6q^{16} - 6q^{19} + 4q^{22} - 4q^{23} - 4q^{26} - 12q^{27} + 6q^{28} - 12q^{33} + 6q^{36} + 12q^{37} - 24q^{38} + 6q^{39} + 4q^{42} + 10q^{43} + 12q^{46} + 6q^{48} + 32q^{49} - 6q^{52} + 16q^{53} + 4q^{56} + 24q^{61} - 8q^{62} - 6q^{63} - 12q^{64} + 8q^{66} - 6q^{67} + 4q^{69} + 12q^{71} - 12q^{74} - 6q^{76} + 48q^{77} - 8q^{78} + 52q^{79} - 6q^{81} + 6q^{84} - 4q^{88} + 24q^{89} - 54q^{91} - 8q^{92} - 8q^{94} - 12q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 0.242731 + 0.140141i 0.0917436 + 0.0529682i 0.545170 0.838326i \(-0.316465\pi\)
−0.453426 + 0.891294i \(0.649798\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0.663862 0.383281i 0.200162 0.115564i −0.396569 0.918005i \(-0.629799\pi\)
0.596731 + 0.802441i \(0.296466\pi\)
\(12\) 1.00000 0.288675
\(13\) −2.77303 + 2.30441i −0.769100 + 0.639129i
\(14\) −0.280281 −0.0749083
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.10917 + 1.92113i −0.269012 + 0.465943i −0.968607 0.248597i \(-0.920031\pi\)
0.699595 + 0.714540i \(0.253364\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −4.57097 2.63905i −1.04865 0.605440i −0.126381 0.991982i \(-0.540336\pi\)
−0.922272 + 0.386541i \(0.873670\pi\)
\(20\) 0 0
\(21\) 0.280281i 0.0611624i
\(22\) −0.383281 + 0.663862i −0.0817158 + 0.141536i
\(23\) −0.725885 1.25727i −0.151357 0.262159i 0.780369 0.625319i \(-0.215031\pi\)
−0.931727 + 0.363160i \(0.881698\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) 1.24931 3.38219i 0.245009 0.663303i
\(27\) −1.00000 −0.192450
\(28\) 0.242731 0.140141i 0.0458718 0.0264841i
\(29\) −3.03030 5.24863i −0.562712 0.974646i −0.997259 0.0739965i \(-0.976425\pi\)
0.434546 0.900649i \(-0.356909\pi\)
\(30\) 0 0
\(31\) 3.28110i 0.589303i 0.955605 + 0.294652i \(0.0952036\pi\)
−0.955605 + 0.294652i \(0.904796\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0.663862 + 0.383281i 0.115564 + 0.0667207i
\(34\) 2.21833i 0.380441i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −3.07097 + 1.77303i −0.504865 + 0.291484i −0.730720 0.682677i \(-0.760816\pi\)
0.225855 + 0.974161i \(0.427482\pi\)
\(38\) 5.27811 0.856222
\(39\) −3.38219 1.24931i −0.541584 0.200049i
\(40\) 0 0
\(41\) 1.92113 1.10917i 0.300030 0.173223i −0.342426 0.939545i \(-0.611249\pi\)
0.642457 + 0.766322i \(0.277915\pi\)
\(42\) −0.140141 0.242731i −0.0216242 0.0374542i
\(43\) −1.80441 + 3.12533i −0.275170 + 0.476609i −0.970178 0.242393i \(-0.922068\pi\)
0.695008 + 0.719002i \(0.255401\pi\)
\(44\) 0.766562i 0.115564i
\(45\) 0 0
\(46\) 1.25727 + 0.725885i 0.185374 + 0.107026i
\(47\) 1.06277i 0.155021i 0.996992 + 0.0775104i \(0.0246971\pi\)
−0.996992 + 0.0775104i \(0.975303\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −3.46072 5.99414i −0.494389 0.856306i
\(50\) 0 0
\(51\) −2.21833 −0.310629
\(52\) 0.609166 + 3.55372i 0.0844761 + 0.492812i
\(53\) 3.28110 0.450694 0.225347 0.974279i \(-0.427648\pi\)
0.225347 + 0.974279i \(0.427648\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −0.140141 + 0.242731i −0.0187271 + 0.0324362i
\(57\) 5.27811i 0.699102i
\(58\) 5.24863 + 3.03030i 0.689179 + 0.397898i
\(59\) −4.32824 2.49891i −0.563489 0.325331i 0.191055 0.981579i \(-0.438809\pi\)
−0.754545 + 0.656249i \(0.772142\pi\)
\(60\) 0 0
\(61\) −0.773028 + 1.33892i −0.0989761 + 0.171432i −0.911261 0.411829i \(-0.864890\pi\)
0.812285 + 0.583261i \(0.198223\pi\)
\(62\) −1.64055 2.84152i −0.208350 0.360873i
\(63\) −0.242731 + 0.140141i −0.0305812 + 0.0176561i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −0.766562 −0.0943573
\(67\) −6.43963 + 3.71792i −0.786726 + 0.454216i −0.838809 0.544426i \(-0.816747\pi\)
0.0520827 + 0.998643i \(0.483414\pi\)
\(68\) 1.10917 + 1.92113i 0.134506 + 0.232971i
\(69\) 0.725885 1.25727i 0.0873863 0.151357i
\(70\) 0 0
\(71\) −2.09811 1.21135i −0.249000 0.143760i 0.370306 0.928910i \(-0.379253\pi\)
−0.619306 + 0.785149i \(0.712586\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 14.2630i 1.66936i 0.550737 + 0.834679i \(0.314347\pi\)
−0.550737 + 0.834679i \(0.685653\pi\)
\(74\) 1.77303 3.07097i 0.206110 0.356994i
\(75\) 0 0
\(76\) −4.57097 + 2.63905i −0.524327 + 0.302720i
\(77\) 0.214853 0.0244848
\(78\) 3.55372 0.609166i 0.402379 0.0689744i
\(79\) −14.4715 −1.62817 −0.814085 0.580746i \(-0.802761\pi\)
−0.814085 + 0.580746i \(0.802761\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.10917 + 1.92113i −0.122487 + 0.212153i
\(83\) 4.42419i 0.485617i −0.970074 0.242809i \(-0.921931\pi\)
0.970074 0.242809i \(-0.0780687\pi\)
\(84\) 0.242731 + 0.140141i 0.0264841 + 0.0152906i
\(85\) 0 0
\(86\) 3.60882i 0.389150i
\(87\) 3.03030 5.24863i 0.324882 0.562712i
\(88\) 0.383281 + 0.663862i 0.0408579 + 0.0707679i
\(89\) −4.60275 + 2.65740i −0.487890 + 0.281683i −0.723699 0.690116i \(-0.757559\pi\)
0.235809 + 0.971799i \(0.424226\pi\)
\(90\) 0 0
\(91\) −0.996041 + 0.170738i −0.104413 + 0.0178982i
\(92\) −1.45177 −0.151357
\(93\) −2.84152 + 1.64055i −0.294652 + 0.170117i
\(94\) −0.531385 0.920385i −0.0548081 0.0949305i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 1.09737 + 0.633565i 0.111421 + 0.0643288i 0.554675 0.832067i \(-0.312843\pi\)
−0.443254 + 0.896396i \(0.646176\pi\)
\(98\) 5.99414 + 3.46072i 0.605500 + 0.349586i
\(99\) 0.766562i 0.0770424i
\(100\) 0 0
\(101\) −2.26374 3.92090i −0.225250 0.390145i 0.731144 0.682223i \(-0.238987\pi\)
−0.956394 + 0.292078i \(0.905653\pi\)
\(102\) 1.92113 1.10917i 0.190220 0.109824i
\(103\) 2.94271 0.289954 0.144977 0.989435i \(-0.453689\pi\)
0.144977 + 0.989435i \(0.453689\pi\)
\(104\) −2.30441 2.77303i −0.225966 0.271918i
\(105\) 0 0
\(106\) −2.84152 + 1.64055i −0.275992 + 0.159344i
\(107\) −9.52440 16.4967i −0.920758 1.59480i −0.798245 0.602333i \(-0.794238\pi\)
−0.122513 0.992467i \(-0.539095\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 9.04549i 0.866401i −0.901298 0.433200i \(-0.857384\pi\)
0.901298 0.433200i \(-0.142616\pi\)
\(110\) 0 0
\(111\) −3.07097 1.77303i −0.291484 0.168288i
\(112\) 0.280281i 0.0264841i
\(113\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(114\) 2.63905 + 4.57097i 0.247170 + 0.428111i
\(115\) 0 0
\(116\) −6.06059 −0.562712
\(117\) −0.609166 3.55372i −0.0563174 0.328541i
\(118\) 4.99783 0.460087
\(119\) −0.538457 + 0.310878i −0.0493603 + 0.0284982i
\(120\) 0 0
\(121\) −5.20619 + 9.01739i −0.473290 + 0.819763i
\(122\) 1.54606i 0.139973i
\(123\) 1.92113 + 1.10917i 0.173223 + 0.100010i
\(124\) 2.84152 + 1.64055i 0.255176 + 0.147326i
\(125\) 0 0
\(126\) 0.140141 0.242731i 0.0124847 0.0216242i
\(127\) 1.58585 + 2.74678i 0.140722 + 0.243737i 0.927769 0.373156i \(-0.121724\pi\)
−0.787047 + 0.616893i \(0.788391\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −3.60882 −0.317739
\(130\) 0 0
\(131\) 15.4345 1.34852 0.674259 0.738495i \(-0.264463\pi\)
0.674259 + 0.738495i \(0.264463\pi\)
\(132\) 0.663862 0.383281i 0.0577818 0.0333603i
\(133\) −0.739677 1.28116i −0.0641381 0.111091i
\(134\) 3.71792 6.43963i 0.321180 0.556299i
\(135\) 0 0
\(136\) −1.92113 1.10917i −0.164736 0.0951102i
\(137\) −1.44478 0.834145i −0.123436 0.0712658i 0.437011 0.899456i \(-0.356037\pi\)
−0.560447 + 0.828191i \(0.689371\pi\)
\(138\) 1.45177i 0.123583i
\(139\) −1.05395 + 1.82549i −0.0893949 + 0.154836i −0.907256 0.420580i \(-0.861827\pi\)
0.817861 + 0.575416i \(0.195160\pi\)
\(140\) 0 0
\(141\) −0.920385 + 0.531385i −0.0775104 + 0.0447507i
\(142\) 2.42269 0.203308
\(143\) −0.957671 + 2.59266i −0.0800844 + 0.216809i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −7.13150 12.3521i −0.590207 1.02227i
\(147\) 3.46072 5.99414i 0.285435 0.494389i
\(148\) 3.54606i 0.291484i
\(149\) −4.97167 2.87039i −0.407295 0.235152i 0.282332 0.959317i \(-0.408892\pi\)
−0.689627 + 0.724165i \(0.742225\pi\)
\(150\) 0 0
\(151\) 16.1710i 1.31598i 0.753029 + 0.657988i \(0.228592\pi\)
−0.753029 + 0.657988i \(0.771408\pi\)
\(152\) 2.63905 4.57097i 0.214055 0.370755i
\(153\) −1.10917 1.92113i −0.0896707 0.155314i
\(154\) −0.186068 + 0.107426i −0.0149938 + 0.00865667i
\(155\) 0 0
\(156\) −2.77303 + 2.30441i −0.222020 + 0.184501i
\(157\) −15.8401 −1.26418 −0.632088 0.774896i \(-0.717802\pi\)
−0.632088 + 0.774896i \(0.717802\pi\)
\(158\) 12.5327 7.23574i 0.997046 0.575645i
\(159\) 1.64055 + 2.84152i 0.130104 + 0.225347i
\(160\) 0 0
\(161\) 0.406904i 0.0320685i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) −9.79890 5.65740i −0.767509 0.443121i 0.0644763 0.997919i \(-0.479462\pi\)
−0.831985 + 0.554798i \(0.812796\pi\)
\(164\) 2.21833i 0.173223i
\(165\) 0 0
\(166\) 2.21209 + 3.83146i 0.171692 + 0.297379i
\(167\) 1.25727 0.725885i 0.0972904 0.0561707i −0.450565 0.892743i \(-0.648778\pi\)
0.547856 + 0.836573i \(0.315444\pi\)
\(168\) −0.280281 −0.0216242
\(169\) 2.37937 12.7804i 0.183028 0.983108i
\(170\) 0 0
\(171\) 4.57097 2.63905i 0.349551 0.201813i
\(172\) 1.80441 + 3.12533i 0.137585 + 0.238304i
\(173\) 6.67010 11.5530i 0.507118 0.878355i −0.492848 0.870116i \(-0.664044\pi\)
0.999966 0.00823921i \(-0.00262265\pi\)
\(174\) 6.06059i 0.459452i
\(175\) 0 0
\(176\) −0.663862 0.383281i −0.0500405 0.0288909i
\(177\) 4.99783i 0.375660i
\(178\) 2.65740 4.60275i 0.199180 0.344990i
\(179\) 12.6266 + 21.8699i 0.943755 + 1.63463i 0.758226 + 0.651992i \(0.226067\pi\)
0.185529 + 0.982639i \(0.440600\pi\)
\(180\) 0 0
\(181\) −0.314792 −0.0233983 −0.0116992 0.999932i \(-0.503724\pi\)
−0.0116992 + 0.999932i \(0.503724\pi\)
\(182\) 0.777228 0.645884i 0.0576119 0.0478761i
\(183\) −1.54606 −0.114288
\(184\) 1.25727 0.725885i 0.0926871 0.0535129i
\(185\) 0 0
\(186\) 1.64055 2.84152i 0.120291 0.208350i
\(187\) 1.70049i 0.124352i
\(188\) 0.920385 + 0.531385i 0.0671260 + 0.0387552i
\(189\) −0.242731 0.140141i −0.0176561 0.0101937i
\(190\) 0 0
\(191\) 11.2666 19.5143i 0.815223 1.41201i −0.0939445 0.995577i \(-0.529948\pi\)
0.909168 0.416430i \(-0.136719\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −8.47286 + 4.89181i −0.609890 + 0.352120i −0.772922 0.634501i \(-0.781206\pi\)
0.163032 + 0.986621i \(0.447872\pi\)
\(194\) −1.26713 −0.0909746
\(195\) 0 0
\(196\) −6.92144 −0.494389
\(197\) −10.7883 + 6.22862i −0.768634 + 0.443771i −0.832387 0.554195i \(-0.813026\pi\)
0.0637530 + 0.997966i \(0.479693\pi\)
\(198\) −0.383281 0.663862i −0.0272386 0.0471786i
\(199\) 7.53195 13.0457i 0.533926 0.924787i −0.465289 0.885159i \(-0.654050\pi\)
0.999215 0.0396276i \(-0.0126171\pi\)
\(200\) 0 0
\(201\) −6.43963 3.71792i −0.454216 0.262242i
\(202\) 3.92090 + 2.26374i 0.275874 + 0.159276i
\(203\) 1.69867i 0.119223i
\(204\) −1.10917 + 1.92113i −0.0776571 + 0.134506i
\(205\) 0 0
\(206\) −2.54846 + 1.47135i −0.177560 + 0.102514i
\(207\) 1.45177 0.100905
\(208\) 3.38219 + 1.24931i 0.234513 + 0.0866238i
\(209\) −4.04600 −0.279867
\(210\) 0 0
\(211\) −7.53876 13.0575i −0.518989 0.898916i −0.999756 0.0220676i \(-0.992975\pi\)
0.480767 0.876848i \(-0.340358\pi\)
\(212\) 1.64055 2.84152i 0.112673 0.195156i
\(213\) 2.42269i 0.166000i
\(214\) 16.4967 + 9.52440i 1.12769 + 0.651074i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −0.459815 + 0.796424i −0.0312143 + 0.0540648i
\(218\) 4.52274 + 7.83362i 0.306319 + 0.530560i
\(219\) −12.3521 + 7.13150i −0.834679 + 0.481902i
\(220\) 0 0
\(221\) −1.35133 7.88333i −0.0909004 0.530290i
\(222\) 3.54606 0.237996
\(223\) −4.03252 + 2.32817i −0.270037 + 0.155906i −0.628905 0.777482i \(-0.716496\pi\)
0.358867 + 0.933389i \(0.383163\pi\)
\(224\) 0.140141 + 0.242731i 0.00936354 + 0.0162181i
\(225\) 0 0
\(226\) 0 0
\(227\) 5.37313 + 3.10218i 0.356627 + 0.205899i 0.667600 0.744520i \(-0.267322\pi\)
−0.310973 + 0.950419i \(0.600655\pi\)
\(228\) −4.57097 2.63905i −0.302720 0.174776i
\(229\) 12.8610i 0.849878i −0.905222 0.424939i \(-0.860296\pi\)
0.905222 0.424939i \(-0.139704\pi\)
\(230\) 0 0
\(231\) 0.107426 + 0.186068i 0.00706814 + 0.0122424i
\(232\) 5.24863 3.03030i 0.344589 0.198949i
\(233\) −0.970923 −0.0636073 −0.0318036 0.999494i \(-0.510125\pi\)
−0.0318036 + 0.999494i \(0.510125\pi\)
\(234\) 2.30441 + 2.77303i 0.150644 + 0.181279i
\(235\) 0 0
\(236\) −4.32824 + 2.49891i −0.281745 + 0.162665i
\(237\) −7.23574 12.5327i −0.470012 0.814085i
\(238\) 0.310878 0.538457i 0.0201512 0.0349030i
\(239\) 14.7984i 0.957231i 0.878025 + 0.478616i \(0.158861\pi\)
−0.878025 + 0.478616i \(0.841139\pi\)
\(240\) 0 0
\(241\) 1.89795 + 1.09578i 0.122258 + 0.0705856i 0.559882 0.828572i \(-0.310847\pi\)
−0.437624 + 0.899158i \(0.644180\pi\)
\(242\) 10.4124i 0.669333i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0.773028 + 1.33892i 0.0494880 + 0.0857158i
\(245\) 0 0
\(246\) −2.21833 −0.141436
\(247\) 18.7569 3.21524i 1.19347 0.204581i
\(248\) −3.28110 −0.208350
\(249\) 3.83146 2.21209i 0.242809 0.140186i
\(250\) 0 0
\(251\) 5.29487 9.17098i 0.334209 0.578867i −0.649124 0.760683i \(-0.724864\pi\)
0.983333 + 0.181816i \(0.0581975\pi\)
\(252\) 0.280281i 0.0176561i
\(253\) −0.963775 0.556436i −0.0605920 0.0349828i
\(254\) −2.74678 1.58585i −0.172348 0.0995053i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.42396 5.93047i −0.213581 0.369933i 0.739252 0.673429i \(-0.235179\pi\)
−0.952833 + 0.303496i \(0.901846\pi\)
\(258\) 3.12533 1.80441i 0.194575 0.112338i
\(259\) −0.993893 −0.0617575
\(260\) 0 0
\(261\) 6.06059 0.375141
\(262\) −13.3667 + 7.71724i −0.825795 + 0.476773i
\(263\) −13.1181 22.7212i −0.808898 1.40105i −0.913628 0.406551i \(-0.866731\pi\)
0.104730 0.994501i \(-0.466602\pi\)
\(264\) −0.383281 + 0.663862i −0.0235893 + 0.0408579i
\(265\) 0 0
\(266\) 1.28116 + 0.739677i 0.0785529 + 0.0453525i
\(267\) −4.60275 2.65740i −0.281683 0.162630i
\(268\) 7.43584i 0.454216i
\(269\) −3.24938 + 5.62808i −0.198118 + 0.343150i −0.947918 0.318514i \(-0.896816\pi\)
0.749800 + 0.661664i \(0.230150\pi\)
\(270\) 0 0
\(271\) 5.35904 3.09404i 0.325539 0.187950i −0.328320 0.944567i \(-0.606482\pi\)
0.653859 + 0.756617i \(0.273149\pi\)
\(272\) 2.21833 0.134506
\(273\) −0.645884 0.777228i −0.0390906 0.0470400i
\(274\) 1.66829 0.100785
\(275\) 0 0
\(276\) −0.725885 1.25727i −0.0436931 0.0756787i
\(277\) −14.5289 + 25.1647i −0.872955 + 1.51200i −0.0140299 + 0.999902i \(0.504466\pi\)
−0.858925 + 0.512101i \(0.828867\pi\)
\(278\) 2.10790i 0.126423i
\(279\) −2.84152 1.64055i −0.170117 0.0982172i
\(280\) 0 0
\(281\) 14.1438i 0.843746i 0.906655 + 0.421873i \(0.138627\pi\)
−0.906655 + 0.421873i \(0.861373\pi\)
\(282\) 0.531385 0.920385i 0.0316435 0.0548081i
\(283\) 4.37290 + 7.57409i 0.259942 + 0.450233i 0.966226 0.257696i \(-0.0829632\pi\)
−0.706284 + 0.707928i \(0.749630\pi\)
\(284\) −2.09811 + 1.21135i −0.124500 + 0.0718802i
\(285\) 0 0
\(286\) −0.466963 2.72415i −0.0276121 0.161082i
\(287\) 0.621757 0.0367011
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 6.03950 + 10.4607i 0.355265 + 0.615337i
\(290\) 0 0
\(291\) 1.26713i 0.0742805i
\(292\) 12.3521 + 7.13150i 0.722853 + 0.417339i
\(293\) −27.2798 15.7500i −1.59371 0.920126i −0.992664 0.120909i \(-0.961419\pi\)
−0.601042 0.799217i \(-0.705248\pi\)
\(294\) 6.92144i 0.403667i
\(295\) 0 0
\(296\) −1.77303 3.07097i −0.103055 0.178497i
\(297\) −0.663862 + 0.383281i −0.0385212 + 0.0222402i
\(298\) 5.74079 0.332555
\(299\) 4.91017 + 1.81370i 0.283962 + 0.104889i
\(300\) 0 0
\(301\) −0.875972 + 0.505743i −0.0504902 + 0.0291505i
\(302\) −8.08549 14.0045i −0.465268 0.805867i
\(303\) 2.26374 3.92090i 0.130048 0.225250i
\(304\) 5.27811i 0.302720i
\(305\) 0 0
\(306\) 1.92113 + 1.10917i 0.109824 + 0.0634068i
\(307\) 7.03152i 0.401310i 0.979662 + 0.200655i \(0.0643070\pi\)
−0.979662 + 0.200655i \(0.935693\pi\)
\(308\) 0.107426 0.186068i 0.00612119 0.0106022i
\(309\) 1.47135 + 2.54846i 0.0837025 + 0.144977i
\(310\) 0 0
\(311\) 8.79844 0.498914 0.249457 0.968386i \(-0.419748\pi\)
0.249457 + 0.968386i \(0.419748\pi\)
\(312\) 1.24931 3.38219i 0.0707280 0.191479i
\(313\) 9.34134 0.528004 0.264002 0.964522i \(-0.414958\pi\)
0.264002 + 0.964522i \(0.414958\pi\)
\(314\) 13.7179 7.92004i 0.774147 0.446954i
\(315\) 0 0
\(316\) −7.23574 + 12.5327i −0.407042 + 0.705018i
\(317\) 19.4697i 1.09353i 0.837287 + 0.546763i \(0.184140\pi\)
−0.837287 + 0.546763i \(0.815860\pi\)
\(318\) −2.84152 1.64055i −0.159344 0.0919975i
\(319\) −4.02340 2.32291i −0.225267 0.130058i
\(320\) 0 0
\(321\) 9.52440 16.4967i 0.531600 0.920758i
\(322\) 0.203452 + 0.352389i 0.0113379 + 0.0196379i
\(323\) 10.1399 5.85429i 0.564201 0.325742i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 11.3148 0.626668
\(327\) 7.83362 4.52274i 0.433200 0.250108i
\(328\) 1.10917 + 1.92113i 0.0612434 + 0.106077i
\(329\) −0.148937 + 0.257967i −0.00821117 + 0.0142222i
\(330\) 0 0
\(331\) 16.4081 + 9.47320i 0.901869 + 0.520694i 0.877806 0.479016i \(-0.159007\pi\)
0.0240626 + 0.999710i \(0.492340\pi\)
\(332\) −3.83146 2.21209i −0.210279 0.121404i
\(333\) 3.54606i 0.194323i
\(334\) −0.725885 + 1.25727i −0.0397186 + 0.0687947i
\(335\) 0 0
\(336\) 0.242731 0.140141i 0.0132420 0.00764530i
\(337\) −2.72966 −0.148694 −0.0743469 0.997232i \(-0.523687\pi\)
−0.0743469 + 0.997232i \(0.523687\pi\)
\(338\) 4.32961 + 12.2578i 0.235500 + 0.666738i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.25758 + 2.17820i 0.0681020 + 0.117956i
\(342\) −2.63905 + 4.57097i −0.142704 + 0.247170i
\(343\) 3.90192i 0.210684i
\(344\) −3.12533 1.80441i −0.168507 0.0972874i
\(345\) 0 0
\(346\) 13.3402i 0.717174i
\(347\) 6.34600 10.9916i 0.340671 0.590059i −0.643887 0.765121i \(-0.722679\pi\)
0.984557 + 0.175062i \(0.0560125\pi\)
\(348\) −3.03030 5.24863i −0.162441 0.281356i
\(349\) 1.04906 0.605676i 0.0561549 0.0324211i −0.471660 0.881781i \(-0.656345\pi\)
0.527815 + 0.849360i \(0.323012\pi\)
\(350\) 0 0
\(351\) 2.77303 2.30441i 0.148013 0.123000i
\(352\) 0.766562 0.0408579
\(353\) −29.0813 + 16.7901i −1.54784 + 0.893647i −0.549535 + 0.835471i \(0.685195\pi\)
−0.998306 + 0.0581762i \(0.981471\pi\)
\(354\) 2.49891 + 4.32824i 0.132816 + 0.230044i
\(355\) 0 0
\(356\) 5.31479i 0.281683i
\(357\) −0.538457 0.310878i −0.0284982 0.0164534i
\(358\) −21.8699 12.6266i −1.15586 0.667335i
\(359\) 22.0423i 1.16335i 0.813423 + 0.581673i \(0.197602\pi\)
−0.813423 + 0.581673i \(0.802398\pi\)
\(360\) 0 0
\(361\) 4.42920 + 7.67161i 0.233116 + 0.403769i
\(362\) 0.272618 0.157396i 0.0143285 0.00827256i
\(363\) −10.4124 −0.546508
\(364\) −0.350157 + 0.947965i −0.0183532 + 0.0496869i
\(365\) 0 0
\(366\) 1.33892 0.773028i 0.0699867 0.0404068i
\(367\) 4.82908 + 8.36421i 0.252076 + 0.436608i 0.964097 0.265550i \(-0.0855534\pi\)
−0.712021 + 0.702158i \(0.752220\pi\)
\(368\) −0.725885 + 1.25727i −0.0378394 + 0.0655397i
\(369\) 2.21833i 0.115482i
\(370\) 0 0
\(371\) 0.796424 + 0.459815i 0.0413483 + 0.0238724i
\(372\) 3.28110i 0.170117i
\(373\) −6.12153 + 10.6028i −0.316961 + 0.548992i −0.979852 0.199723i \(-0.935996\pi\)
0.662892 + 0.748715i \(0.269329\pi\)
\(374\) −0.850244 1.47267i −0.0439651 0.0761498i
\(375\) 0 0
\(376\) −1.06277 −0.0548081
\(377\) 20.4981 + 7.57154i 1.05571 + 0.389954i
\(378\) 0.280281 0.0144161
\(379\) 11.7669 6.79362i 0.604425 0.348965i −0.166355 0.986066i \(-0.553200\pi\)
0.770780 + 0.637101i \(0.219867\pi\)
\(380\) 0 0
\(381\) −1.58585 + 2.74678i −0.0812458 + 0.140722i
\(382\) 22.5332i 1.15290i
\(383\) −13.3487 7.70686i −0.682086 0.393802i 0.118555 0.992948i \(-0.462174\pi\)
−0.800640 + 0.599145i \(0.795507\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 4.89181 8.47286i 0.248987 0.431257i
\(387\) −1.80441 3.12533i −0.0917234 0.158870i
\(388\) 1.09737 0.633565i 0.0557103 0.0321644i
\(389\) 6.06059 0.307284 0.153642 0.988127i \(-0.450900\pi\)
0.153642 + 0.988127i \(0.450900\pi\)
\(390\) 0 0
\(391\) 3.22051 0.162868
\(392\) 5.99414 3.46072i 0.302750 0.174793i
\(393\) 7.71724 + 13.3667i 0.389283 + 0.674259i
\(394\) 6.22862 10.7883i 0.313794 0.543506i
\(395\) 0 0
\(396\) 0.663862 + 0.383281i 0.0333603 + 0.0192606i
\(397\) 14.7131 + 8.49464i 0.738432 + 0.426334i 0.821499 0.570210i \(-0.193138\pi\)
−0.0830670 + 0.996544i \(0.526472\pi\)
\(398\) 15.0639i 0.755085i
\(399\) 0.739677 1.28116i 0.0370302 0.0641381i
\(400\) 0 0
\(401\) −16.8156 + 9.70852i −0.839733 + 0.484820i −0.857174 0.515028i \(-0.827782\pi\)
0.0174403 + 0.999848i \(0.494448\pi\)
\(402\) 7.43584 0.370866
\(403\) −7.56101 9.09858i −0.376641 0.453233i
\(404\) −4.52747 −0.225250
\(405\) 0 0
\(406\) 0.849335 + 1.47109i 0.0421518 + 0.0730091i
\(407\) −1.35914 + 2.35409i −0.0673699 + 0.116688i
\(408\) 2.21833i 0.109824i
\(409\) −0.803328 0.463802i −0.0397220 0.0229335i 0.480007 0.877264i \(-0.340634\pi\)
−0.519730 + 0.854331i \(0.673967\pi\)
\(410\) 0 0
\(411\) 1.66829i 0.0822907i
\(412\) 1.47135 2.54846i 0.0724885 0.125554i
\(413\) −0.700398 1.21313i −0.0344643 0.0596940i
\(414\) −1.25727 + 0.725885i −0.0617914 + 0.0356753i
\(415\) 0 0
\(416\) −3.55372 + 0.609166i −0.174235 + 0.0298668i
\(417\) −2.10790 −0.103224
\(418\) 3.50393 2.02300i 0.171383 0.0989481i
\(419\) 12.5907 + 21.8077i 0.615096 + 1.06538i 0.990368 + 0.138463i \(0.0442163\pi\)
−0.375271 + 0.926915i \(0.622450\pi\)
\(420\) 0 0
\(421\) 27.6912i 1.34958i 0.738008 + 0.674792i \(0.235767\pi\)
−0.738008 + 0.674792i \(0.764233\pi\)
\(422\) 13.0575 + 7.53876i 0.635630 + 0.366981i
\(423\) −0.920385 0.531385i −0.0447507 0.0258368i
\(424\) 3.28110i 0.159344i
\(425\) 0 0
\(426\) 1.21135 + 2.09811i 0.0586899 + 0.101654i
\(427\) −0.375275 + 0.216665i −0.0181608 + 0.0104852i
\(428\) −19.0488 −0.920758
\(429\) −2.72415 + 0.466963i −0.131523 + 0.0225452i
\(430\) 0 0
\(431\) 0.0798174 0.0460826i 0.00384467 0.00221972i −0.498076 0.867133i \(-0.665960\pi\)
0.501921 + 0.864913i \(0.332627\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 2.01113 3.48337i 0.0966486 0.167400i −0.813647 0.581359i \(-0.802521\pi\)
0.910295 + 0.413959i \(0.135854\pi\)
\(434\) 0.919631i 0.0441437i
\(435\) 0 0
\(436\) −7.83362 4.52274i −0.375162 0.216600i
\(437\) 7.66259i 0.366552i
\(438\) 7.13150 12.3521i 0.340756 0.590207i
\(439\) 12.9742 + 22.4719i 0.619223 + 1.07253i 0.989628 + 0.143656i \(0.0458858\pi\)
−0.370404 + 0.928871i \(0.620781\pi\)
\(440\) 0 0
\(441\) 6.92144 0.329592
\(442\) 5.11195 + 6.15150i 0.243151 + 0.292597i
\(443\) 15.0646 0.715740 0.357870 0.933771i \(-0.383503\pi\)
0.357870 + 0.933771i \(0.383503\pi\)
\(444\) −3.07097 + 1.77303i −0.145742 + 0.0841442i
\(445\) 0 0
\(446\) 2.32817 4.03252i 0.110242 0.190945i
\(447\) 5.74079i 0.271530i
\(448\) −0.242731 0.140141i −0.0114679 0.00662102i
\(449\) 29.8460 + 17.2316i 1.40852 + 0.813208i 0.995245 0.0973991i \(-0.0310523\pi\)
0.413273 + 0.910607i \(0.364386\pi\)
\(450\) 0 0
\(451\) 0.850244 1.47267i 0.0400364 0.0693451i
\(452\) 0 0
\(453\) −14.0045 + 8.08549i −0.657988 + 0.379889i
\(454\) −6.20436 −0.291185
\(455\) 0 0
\(456\) 5.27811 0.247170
\(457\) −36.0525 + 20.8149i −1.68646 + 0.973680i −0.729273 + 0.684223i \(0.760141\pi\)
−0.957191 + 0.289457i \(0.906525\pi\)
\(458\) 6.43049 + 11.1379i 0.300477 + 0.520442i
\(459\) 1.10917 1.92113i 0.0517714 0.0896707i
\(460\) 0 0
\(461\) 6.02737 + 3.47990i 0.280722 + 0.162075i 0.633750 0.773538i \(-0.281515\pi\)
−0.353028 + 0.935613i \(0.614848\pi\)
\(462\) −0.186068 0.107426i −0.00865667 0.00499793i
\(463\) 11.9289i 0.554382i 0.960815 + 0.277191i \(0.0894035\pi\)
−0.960815 + 0.277191i \(0.910597\pi\)
\(464\) −3.03030 + 5.24863i −0.140678 + 0.243661i
\(465\) 0 0
\(466\) 0.840844 0.485461i 0.0389513 0.0224886i
\(467\) 34.4406 1.59372 0.796860 0.604164i \(-0.206493\pi\)
0.796860 + 0.604164i \(0.206493\pi\)
\(468\) −3.38219 1.24931i −0.156342 0.0577492i
\(469\) −2.08413 −0.0962361
\(470\) 0 0
\(471\) −7.92004 13.7179i −0.364936 0.632088i
\(472\) 2.49891 4.32824i 0.115022 0.199224i
\(473\) 2.76639i 0.127199i
\(474\) 12.5327 + 7.23574i 0.575645 + 0.332349i
\(475\) 0 0
\(476\) 0.621757i 0.0284982i
\(477\) −1.64055 + 2.84152i −0.0751156 + 0.130104i
\(478\) −7.39922 12.8158i −0.338432 0.586182i
\(479\) −11.8896 + 6.86444i −0.543248 + 0.313644i −0.746394 0.665504i \(-0.768217\pi\)
0.203146 + 0.979148i \(0.434883\pi\)
\(480\) 0 0
\(481\) 4.43011 11.9934i 0.201996 0.546854i
\(482\) −2.19157 −0.0998231
\(483\) 0.352389 0.203452i 0.0160343 0.00925738i
\(484\) 5.20619 + 9.01739i 0.236645 + 0.409881i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 8.25303 + 4.76489i 0.373981 + 0.215918i 0.675196 0.737638i \(-0.264059\pi\)
−0.301215 + 0.953556i \(0.597392\pi\)
\(488\) −1.33892 0.773028i −0.0606102 0.0349933i
\(489\) 11.3148i 0.511673i
\(490\) 0 0
\(491\) 16.7409 + 28.9960i 0.755505 + 1.30857i 0.945123 + 0.326715i \(0.105942\pi\)
−0.189618 + 0.981858i \(0.560725\pi\)
\(492\) 1.92113 1.10917i 0.0866113 0.0500051i
\(493\) 13.4444 0.605506
\(494\) −14.6363 + 12.1629i −0.658520 + 0.547236i
\(495\) 0 0
\(496\) 2.84152 1.64055i 0.127588 0.0736629i
\(497\) −0.339518 0.588062i −0.0152294 0.0263782i
\(498\) −2.21209 + 3.83146i −0.0991262 + 0.171692i
\(499\) 15.0882i 0.675439i −0.941247 0.337720i \(-0.890344\pi\)
0.941247 0.337720i \(-0.109656\pi\)
\(500\) 0 0
\(501\) 1.25727 + 0.725885i 0.0561707 + 0.0324301i
\(502\) 10.5897i 0.472643i
\(503\) 9.74919 16.8861i 0.434695 0.752914i −0.562576 0.826746i \(-0.690189\pi\)
0.997271 + 0.0738319i \(0.0235228\pi\)
\(504\) −0.140141 0.242731i −0.00624236 0.0108121i
\(505\) 0 0
\(506\) 1.11287 0.0494732
\(507\) 12.2578 4.32961i 0.544390 0.192285i
\(508\) 3.17171 0.140722
\(509\) 29.5101 17.0377i 1.30801 0.755181i 0.326248 0.945284i \(-0.394215\pi\)
0.981764 + 0.190103i \(0.0608821\pi\)
\(510\) 0 0
\(511\) −1.99883 + 3.46207i −0.0884228 + 0.153153i
\(512\) 1.00000i 0.0441942i
\(513\) 4.57097 + 2.63905i 0.201813 + 0.116517i
\(514\) 5.93047 + 3.42396i 0.261582 + 0.151024i
\(515\) 0 0
\(516\) −1.80441 + 3.12533i −0.0794348 + 0.137585i
\(517\) 0.407339 + 0.705532i 0.0179148 + 0.0310293i
\(518\) 0.860736 0.496946i 0.0378186 0.0218346i
\(519\) 13.3402 0.585570
\(520\) 0 0
\(521\) −1.10626 −0.0484660 −0.0242330 0.999706i \(-0.507714\pi\)
−0.0242330 + 0.999706i \(0.507714\pi\)
\(522\) −5.24863 + 3.03030i −0.229726 + 0.132633i
\(523\) −5.32920 9.23044i −0.233030 0.403619i 0.725669 0.688044i \(-0.241531\pi\)
−0.958698 + 0.284425i \(0.908197\pi\)
\(524\) 7.71724 13.3667i 0.337129 0.583925i
\(525\) 0 0
\(526\) 22.7212 + 13.1181i 0.990693 + 0.571977i
\(527\) −6.30343 3.63928i −0.274582 0.158530i
\(528\) 0.766562i 0.0333603i
\(529\) 10.4462 18.0933i 0.454182 0.786666i
\(530\) 0 0
\(531\) 4.32824 2.49891i 0.187830 0.108444i
\(532\) −1.47935 −0.0641381
\(533\) −2.77138 + 7.50283i −0.120042 + 0.324983i
\(534\) 5.31479 0.229994
\(535\) 0 0
\(536\) −3.71792 6.43963i −0.160590 0.278150i
\(537\) −12.6266 + 21.8699i −0.544877 + 0.943755i
\(538\) 6.49875i 0.280181i
\(539\) −4.59488 2.65286i −0.197916 0.114267i
\(540\) 0 0
\(541\) 38.1486i 1.64013i 0.572267 + 0.820067i \(0.306064\pi\)
−0.572267 + 0.820067i \(0.693936\pi\)
\(542\) −3.09404 + 5.35904i −0.132901 + 0.230191i
\(543\) −0.157396 0.272618i −0.00675452 0.0116992i
\(544\) −1.92113 + 1.10917i −0.0823678 + 0.0475551i
\(545\) 0 0
\(546\) 0.947965 + 0.350157i 0.0405692 + 0.0149853i
\(547\) 26.9609 1.15277 0.576383 0.817180i \(-0.304464\pi\)
0.576383 + 0.817180i \(0.304464\pi\)
\(548\) −1.44478 + 0.834145i −0.0617180 + 0.0356329i
\(549\) −0.773028 1.33892i −0.0329920 0.0571439i
\(550\) 0 0
\(551\) 31.9885i 1.36275i
\(552\) 1.25727 + 0.725885i 0.0535129 + 0.0308957i
\(553\) −3.51267 2.02804i −0.149374 0.0862411i
\(554\) 29.0577i 1.23454i
\(555\) 0 0
\(556\) 1.05395 + 1.82549i 0.0446974 + 0.0774182i
\(557\) 30.5249 17.6236i 1.29338 0.746735i 0.314130 0.949380i \(-0.398287\pi\)
0.979252 + 0.202645i \(0.0649539\pi\)
\(558\) 3.28110 0.138900
\(559\) −2.19837 12.8247i −0.0929812 0.542429i
\(560\) 0 0
\(561\) −1.47267 + 0.850244i −0.0621760 + 0.0358973i
\(562\) −7.07188 12.2489i −0.298309 0.516687i
\(563\) 8.50830 14.7368i 0.358582 0.621082i −0.629142 0.777290i \(-0.716594\pi\)
0.987724 + 0.156208i \(0.0499270\pi\)
\(564\) 1.06277i 0.0447507i
\(565\) 0 0
\(566\) −7.57409 4.37290i −0.318363 0.183807i
\(567\) 0.280281i 0.0117707i
\(568\) 1.21135 2.09811i 0.0508270 0.0880349i
\(569\) 17.6968 + 30.6518i 0.741889 + 1.28499i 0.951634 + 0.307233i \(0.0994030\pi\)
−0.209746 + 0.977756i \(0.567264\pi\)
\(570\) 0 0
\(571\) −17.5185 −0.733125 −0.366563 0.930393i \(-0.619465\pi\)
−0.366563 + 0.930393i \(0.619465\pi\)
\(572\) 1.76647 + 2.12570i 0.0738600 + 0.0888799i
\(573\) 22.5332 0.941339
\(574\) −0.538457 + 0.310878i −0.0224748 + 0.0129758i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 26.6215i 1.10827i 0.832428 + 0.554133i \(0.186950\pi\)
−0.832428 + 0.554133i \(0.813050\pi\)
\(578\) −10.4607 6.03950i −0.435109 0.251210i
\(579\) −8.47286 4.89181i −0.352120 0.203297i
\(580\) 0 0
\(581\) 0.620008 1.07389i 0.0257223 0.0445523i
\(582\) −0.633565 1.09737i −0.0262621 0.0454873i
\(583\) 2.17820 1.25758i 0.0902118 0.0520838i
\(584\) −14.2630 −0.590207
\(585\) 0 0
\(586\) 31.5001 1.30126
\(587\) −14.4115 + 8.32051i −0.594828 + 0.343424i −0.767004 0.641642i \(-0.778254\pi\)
0.172176 + 0.985066i \(0.444920\pi\)
\(588\) −3.46072 5.99414i −0.142718 0.247194i
\(589\) 8.65900 14.9978i 0.356788 0.617975i
\(590\) 0 0
\(591\) −10.7883 6.22862i −0.443771 0.256211i
\(592\) 3.07097 + 1.77303i 0.126216 + 0.0728710i
\(593\) 24.7460i 1.01620i 0.861300 + 0.508098i \(0.169651\pi\)
−0.861300 + 0.508098i \(0.830349\pi\)
\(594\) 0.383281 0.663862i 0.0157262 0.0272386i
\(595\) 0 0
\(596\) −4.97167 + 2.87039i −0.203647 + 0.117576i
\(597\) 15.0639 0.616524
\(598\) −5.15918 + 0.884368i −0.210975 + 0.0361645i
\(599\) −23.2517 −0.950037 −0.475019 0.879976i \(-0.657559\pi\)
−0.475019 + 0.879976i \(0.657559\pi\)
\(600\) 0 0
\(601\) −16.5985 28.7494i −0.677067 1.17271i −0.975860 0.218396i \(-0.929917\pi\)
0.298793 0.954318i \(-0.403416\pi\)
\(602\) 0.505743 0.875972i 0.0206125 0.0357020i
\(603\) 7.43584i 0.302811i
\(604\) 14.0045 + 8.08549i 0.569834 + 0.328994i
\(605\) 0 0
\(606\) 4.52747i 0.183916i
\(607\) 19.7130 34.1440i 0.800128 1.38586i −0.119404 0.992846i \(-0.538098\pi\)
0.919532 0.393016i \(-0.128568\pi\)
\(608\) −2.63905 4.57097i −0.107028 0.185377i
\(609\) 1.47109 0.849335i 0.0596117 0.0344168i
\(610\) 0 0
\(611\) −2.44906 2.94709i −0.0990783 0.119226i
\(612\) −2.21833 −0.0896707
\(613\) −9.03087 + 5.21398i −0.364753 + 0.210591i −0.671164 0.741309i \(-0.734205\pi\)
0.306410 + 0.951899i \(0.400872\pi\)
\(614\) −3.51576 6.08947i −0.141884 0.245751i
\(615\) 0 0
\(616\) 0.214853i 0.00865667i
\(617\) 17.5464 + 10.1304i 0.706393 + 0.407836i 0.809724 0.586811i \(-0.199617\pi\)
−0.103331 + 0.994647i \(0.532950\pi\)
\(618\) −2.54846 1.47135i −0.102514 0.0591866i
\(619\) 27.8009i 1.11741i 0.829365 + 0.558707i \(0.188702\pi\)
−0.829365 + 0.558707i \(0.811298\pi\)
\(620\) 0 0
\(621\) 0.725885 + 1.25727i 0.0291288 + 0.0504525i
\(622\) −7.61967 + 4.39922i −0.305521 + 0.176393i
\(623\) −1.48964 −0.0596810
\(624\) 0.609166 + 3.55372i 0.0243861 + 0.142263i
\(625\) 0 0
\(626\) −8.08984 + 4.67067i −0.323335 + 0.186677i
\(627\) −2.02300 3.50393i −0.0807907 0.139934i
\(628\) −7.92004 + 13.7179i −0.316044 + 0.547405i
\(629\) 7.86633i 0.313651i
\(630\) 0 0
\(631\) −31.6461 18.2709i −1.25981 0.727352i −0.286773 0.957999i \(-0.592583\pi\)
−0.973038 + 0.230646i \(0.925916\pi\)
\(632\) 14.4715i 0.575645i
\(633\) 7.53876 13.0575i 0.299639 0.518989i
\(634\) −9.73484 16.8612i −0.386620 0.669645i
\(635\) 0 0
\(636\) 3.28110 0.130104
\(637\) 23.4097 + 8.64700i 0.927524 + 0.342607i
\(638\) 4.64582 0.183930
\(639\) 2.09811 1.21135i 0.0830001 0.0479201i
\(640\) 0 0
\(641\) −21.9295 + 37.9830i −0.866163 + 1.50024i −0.000274574 1.00000i \(0.500087\pi\)
−0.865888 + 0.500238i \(0.833246\pi\)
\(642\) 19.0488i 0.751796i
\(643\) 14.4213 + 8.32615i 0.568721 + 0.328351i 0.756638 0.653834i \(-0.226840\pi\)
−0.187917 + 0.982185i \(0.560174\pi\)
\(644\) −0.352389 0.203452i −0.0138861 0.00801713i
\(645\) 0 0
\(646\) −5.85429 + 10.1399i −0.230334 + 0.398950i
\(647\) 4.69543 + 8.13271i 0.184596 + 0.319730i 0.943440 0.331542i \(-0.107569\pi\)
−0.758844 + 0.651272i \(0.774236\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −3.83114 −0.150386
\(650\) 0 0
\(651\) −0.919631 −0.0360432
\(652\) −9.79890 + 5.65740i −0.383754 + 0.221561i
\(653\) −20.5572 35.6061i −0.804465 1.39337i −0.916652 0.399686i \(-0.869119\pi\)
0.112187 0.993687i \(-0.464214\pi\)
\(654\) −4.52274 + 7.83362i −0.176853 + 0.306319i
\(655\) 0 0
\(656\) −1.92113 1.10917i −0.0750076 0.0433056i
\(657\) −12.3521 7.13150i −0.481902 0.278226i
\(658\) 0.297874i 0.0116123i
\(659\) 1.72663 2.99061i 0.0672600 0.116498i −0.830434 0.557117i \(-0.811908\pi\)
0.897694 + 0.440619i \(0.145241\pi\)
\(660\) 0 0
\(661\) 21.3306 12.3152i 0.829665 0.479007i −0.0240732 0.999710i \(-0.507663\pi\)
0.853738 + 0.520703i \(0.174330\pi\)
\(662\) −18.9464 −0.736373
\(663\) 6.15150 5.11195i 0.238904 0.198532i
\(664\) 4.42419 0.171692
\(665\) 0 0
\(666\) 1.77303 + 3.07097i 0.0687034 + 0.118998i
\(667\) −4.39929 + 7.61980i −0.170341 + 0.295040i
\(668\) 1.45177i 0.0561707i
\(669\) −4.03252 2.32817i −0.155906 0.0900124i
\(670\) 0 0
\(671\) 1.18515i 0.0457521i
\(672\) −0.140141 + 0.242731i −0.00540604 + 0.00936354i
\(673\) 8.52052 + 14.7580i 0.328442 + 0.568878i 0.982203 0.187823i \(-0.0601431\pi\)
−0.653761 + 0.756701i \(0.726810\pi\)
\(674\) 2.36395 1.36483i 0.0910560 0.0525712i
\(675\) 0 0
\(676\) −9.87847 8.45079i −0.379941 0.325030i
\(677\) −16.6324 −0.639236 −0.319618 0.947546i \(-0.603555\pi\)
−0.319618 + 0.947546i \(0.603555\pi\)
\(678\) 0 0
\(679\) 0.177576 + 0.307571i 0.00681475 + 0.0118035i
\(680\) 0 0
\(681\) 6.20436i 0.237752i
\(682\) −2.17820 1.25758i −0.0834075 0.0481554i
\(683\) 42.3252 + 24.4365i 1.61953 + 0.935035i 0.987042 + 0.160463i \(0.0512987\pi\)
0.632486 + 0.774572i \(0.282035\pi\)
\(684\) 5.27811i 0.201813i
\(685\) 0 0
\(686\) 1.95096 + 3.37916i 0.0744880 + 0.129017i
\(687\) 11.1379 6.43049i 0.424939 0.245339i
\(688\) 3.60882 0.137585
\(689\) −9.09858 + 7.56101i −0.346628 + 0.288051i
\(690\) 0 0
\(691\) 31.0699 17.9382i 1.18195 0.682401i 0.225488 0.974246i \(-0.427602\pi\)
0.956466 + 0.291845i \(0.0942690\pi\)
\(692\) −6.67010 11.5530i −0.253559 0.439177i
\(693\) −0.107426 + 0.186068i −0.00408079 + 0.00706814i
\(694\) 12.6920i 0.481781i
\(695\) 0 0
\(696\) 5.24863 + 3.03030i 0.198949 + 0.114863i
\(697\) 4.92099i 0.186396i
\(698\) −0.605676 + 1.04906i −0.0229252 + 0.0397075i
\(699\) −0.485461 0.840844i −0.0183618 0.0318036i
\(700\) 0 0
\(701\) −31.0288 −1.17194 −0.585971 0.810332i \(-0.699287\pi\)
−0.585971 + 0.810332i \(0.699287\pi\)
\(702\) −1.24931 + 3.38219i −0.0471520 + 0.127653i
\(703\) 18.7165 0.705905
\(704\) −0.663862 + 0.383281i −0.0250202 + 0.0144454i
\(705\) 0 0
\(706\) 16.7901 29.0813i 0.631904 1.09449i
\(707\) 1.26896i 0.0477243i
\(708\) −4.32824 2.49891i −0.162665 0.0939149i
\(709\) 9.78339 + 5.64844i 0.367423 + 0.212132i 0.672332 0.740250i \(-0.265293\pi\)
−0.304909 + 0.952381i \(0.598626\pi\)
\(710\) 0 0
\(711\) 7.23574 12.5327i 0.271362 0.470012i
\(712\) −2.65740 4.60275i −0.0995901 0.172495i
\(713\) 4.12523 2.38170i 0.154491 0.0891954i
\(714\) 0.621757 0.0232687
\(715\) 0 0
\(716\) 25.2532 0.943755
\(717\) −12.8158 + 7.39922i −0.478616 + 0.276329i
\(718\) −11.0211 19.0892i −0.411305 0.712401i
\(719\) −6.01084 + 10.4111i −0.224167 + 0.388268i −0.956069 0.293141i \(-0.905299\pi\)
0.731902 + 0.681409i \(0.238633\pi\)
\(720\) 0 0
\(721\) 0.714286 + 0.412393i 0.0266014 + 0.0153583i
\(722\) −7.67161 4.42920i −0.285508 0.164838i
\(723\) 2.19157i 0.0815052i
\(724\) −0.157396 + 0.272618i −0.00584958 + 0.0101318i
\(725\) 0 0
\(726\) 9.01739 5.20619i 0.334667 0.193220i
\(727\) −4.18908 −0.155364 −0.0776822 0.996978i \(-0.524752\pi\)
−0.0776822 + 0.996978i \(0.524752\pi\)
\(728\) −0.170738 0.996041i −0.00632796 0.0369157i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.00278 6.93303i −0.148048 0.256427i
\(732\) −0.773028 + 1.33892i −0.0285719 + 0.0494880i
\(733\) 11.3923i 0.420783i 0.977617 + 0.210391i \(0.0674738\pi\)
−0.977617 + 0.210391i \(0.932526\pi\)
\(734\) −8.36421 4.82908i −0.308729 0.178244i
\(735\) 0 0
\(736\) 1.45177i 0.0535129i
\(737\) −2.85002 + 4.93637i −0.104982 + 0.181834i
\(738\) −1.10917 1.92113i −0.0408290 0.0707178i
\(739\) −17.6996 + 10.2189i −0.651090 + 0.375907i −0.788874 0.614555i \(-0.789336\pi\)
0.137783 + 0.990462i \(0.456002\pi\)
\(740\) 0 0
\(741\) 12.1629 + 14.6363i 0.446817 + 0.537679i
\(742\) −0.919631 −0.0337607
\(743\) −8.79255 + 5.07638i −0.322567 + 0.186234i −0.652536 0.757757i \(-0.726295\pi\)
0.329969 + 0.943992i \(0.392962\pi\)
\(744\) −1.64055 2.84152i −0.0601455 0.104175i
\(745\) 0 0
\(746\) 12.2431i 0.448250i
\(747\) 3.83146 + 2.21209i 0.140186 + 0.0809362i
\(748\) 1.47267 + 0.850244i 0.0538460 + 0.0310880i
\(749\) 5.33902i 0.195083i
\(750\) 0 0
\(751\) −8.99084 15.5726i −0.328080 0.568252i 0.654051 0.756451i \(-0.273068\pi\)
−0.982131 + 0.188199i \(0.939735\pi\)
\(752\) 0.920385 0.531385i 0.0335630 0.0193776i
\(753\) 10.5897 0.385911
\(754\) −21.5376 + 3.69191i −0.784355 + 0.134451i
\(755\) 0 0
\(756\) −0.242731 + 0.140141i −0.00882803 + 0.00509686i
\(757\) −22.4916 38.9566i −0.817470 1.41590i −0.907540 0.419965i \(-0.862042\pi\)
0.0900700 0.995935i \(-0.471291\pi\)
\(758\) −6.79362 + 11.7669i −0.246755 + 0.427393i
\(759\) 1.11287i 0.0403947i
\(760\) 0 0
\(761\) −39.1697 22.6146i −1.41990 0.819779i −0.423610 0.905845i \(-0.639237\pi\)
−0.996289 + 0.0860657i \(0.972571\pi\)
\(762\) 3.17171i 0.114899i
\(763\) 1.26764 2.19562i 0.0458917 0.0794867i
\(764\) −11.2666 19.5143i −0.407612 0.706004i
\(765\) 0 0
\(766\) 15.4137 0.556921
\(767\) 17.7609 3.04450i 0.641308 0.109931i
\(768\) −1.00000 −0.0360844
\(769\) 31.3010 18.0716i 1.12874 0.651680i 0.185125 0.982715i \(-0.440731\pi\)
0.943619 + 0.331035i \(0.107398\pi\)
\(770\) 0 0
\(771\) 3.42396 5.93047i 0.123311 0.213581i
\(772\) 9.78362i 0.352120i
\(773\) 14.1829 + 8.18850i 0.510123 + 0.294520i 0.732884 0.680353i \(-0.238174\pi\)
−0.222761 + 0.974873i \(0.571507\pi\)
\(774\) 3.12533 + 1.80441i 0.112338 + 0.0648583i
\(775\) 0 0
\(776\) −0.633565 + 1.09737i −0.0227437 + 0.0393932i
\(777\) −0.496946 0.860736i −0.0178279 0.0308787i
\(778\) −5.24863 + 3.03030i −0.188172 + 0.108641i
\(779\) −11.7086 −0.419504
\(780\) 0 0
\(781\) −1.85714 −0.0664538
\(782\) −2.78904 + 1.61025i −0.0997359 + 0.0575825i
\(783\) 3.03030 + 5.24863i 0.108294 + 0.187571i
\(784\) −3.46072 + 5.99414i −0.123597 + 0.214077i