Properties

Label 1110.2.l.b.697.8
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
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: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 697.8
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.8

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.220830 + 2.22514i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.18593 - 1.18593i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.220830 + 2.22514i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.18593 - 1.18593i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.22514 - 0.220830i) q^{10} +4.79879i q^{11} +(0.707107 + 0.707107i) q^{12} -4.44661i q^{13} +(1.18593 - 1.18593i) q^{14} +(1.72956 - 1.41726i) q^{15} +1.00000 q^{16} -1.30290 q^{17} -1.00000 q^{18} +(-4.46151 - 4.46151i) q^{19} +(0.220830 - 2.22514i) q^{20} +1.67716i q^{21} -4.79879 q^{22} +0.933219i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.90247 - 0.982756i) q^{25} +4.44661 q^{26} +(0.707107 - 0.707107i) q^{27} +(1.18593 + 1.18593i) q^{28} +(-3.66959 + 3.66959i) q^{29} +(1.41726 + 1.72956i) q^{30} +(4.54367 + 4.54367i) q^{31} +1.00000i q^{32} +(3.39326 - 3.39326i) q^{33} -1.30290i q^{34} +(2.90075 - 2.37697i) q^{35} -1.00000i q^{36} +(3.31197 - 5.10204i) q^{37} +(4.46151 - 4.46151i) q^{38} +(-3.14423 + 3.14423i) q^{39} +(2.22514 + 0.220830i) q^{40} -7.79237i q^{41} -1.67716 q^{42} -2.02422i q^{43} -4.79879i q^{44} +(-2.22514 - 0.220830i) q^{45} -0.933219 q^{46} +(-6.81249 - 6.81249i) q^{47} +(-0.707107 - 0.707107i) q^{48} -4.18713i q^{49} +(0.982756 - 4.90247i) q^{50} +(0.921286 + 0.921286i) q^{51} +4.44661i q^{52} +(5.08803 - 5.08803i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-10.6780 - 1.05972i) q^{55} +(-1.18593 + 1.18593i) q^{56} +6.30953i q^{57} +(-3.66959 - 3.66959i) q^{58} +(-3.87716 - 3.87716i) q^{59} +(-1.72956 + 1.41726i) q^{60} +(-6.36168 - 6.36168i) q^{61} +(-4.54367 + 4.54367i) q^{62} +(1.18593 - 1.18593i) q^{63} -1.00000 q^{64} +(9.89431 + 0.981946i) q^{65} +(3.39326 + 3.39326i) q^{66} +(0.639879 - 0.639879i) q^{67} +1.30290 q^{68} +(0.659885 - 0.659885i) q^{69} +(2.37697 + 2.90075i) q^{70} -8.94910 q^{71} +1.00000 q^{72} +(-1.06393 - 1.06393i) q^{73} +(5.10204 + 3.31197i) q^{74} +(2.77166 + 4.16148i) q^{75} +(4.46151 + 4.46151i) q^{76} +(5.69104 - 5.69104i) q^{77} +(-3.14423 - 3.14423i) q^{78} +(-2.21244 - 2.21244i) q^{79} +(-0.220830 + 2.22514i) q^{80} -1.00000 q^{81} +7.79237 q^{82} +(-6.32708 + 6.32708i) q^{83} -1.67716i q^{84} +(0.287719 - 2.89912i) q^{85} +2.02422 q^{86} +5.18959 q^{87} +4.79879 q^{88} +(3.11309 - 3.11309i) q^{89} +(0.220830 - 2.22514i) q^{90} +(-5.27338 + 5.27338i) q^{91} -0.933219i q^{92} -6.42572i q^{93} +(6.81249 - 6.81249i) q^{94} +(10.9127 - 8.94223i) q^{95} +(0.707107 - 0.707107i) q^{96} +0.0235287 q^{97} +4.18713 q^{98} -4.79879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

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
\(5\) −0.220830 + 2.22514i −0.0987584 + 0.995111i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −1.18593 1.18593i −0.448240 0.448240i 0.446529 0.894769i \(-0.352660\pi\)
−0.894769 + 0.446529i \(0.852660\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −2.22514 0.220830i −0.703650 0.0698327i
\(11\) 4.79879i 1.44689i 0.690382 + 0.723445i \(0.257443\pi\)
−0.690382 + 0.723445i \(0.742557\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 4.44661i 1.23327i −0.787250 0.616634i \(-0.788496\pi\)
0.787250 0.616634i \(-0.211504\pi\)
\(14\) 1.18593 1.18593i 0.316954 0.316954i
\(15\) 1.72956 1.41726i 0.446570 0.365935i
\(16\) 1.00000 0.250000
\(17\) −1.30290 −0.315999 −0.157999 0.987439i \(-0.550504\pi\)
−0.157999 + 0.987439i \(0.550504\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.46151 4.46151i −1.02354 1.02354i −0.999716 0.0238243i \(-0.992416\pi\)
−0.0238243 0.999716i \(-0.507584\pi\)
\(20\) 0.220830 2.22514i 0.0493792 0.497556i
\(21\) 1.67716i 0.365987i
\(22\) −4.79879 −1.02311
\(23\) 0.933219i 0.194590i 0.995256 + 0.0972948i \(0.0310190\pi\)
−0.995256 + 0.0972948i \(0.968981\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) −4.90247 0.982756i −0.980494 0.196551i
\(26\) 4.44661 0.872052
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 1.18593 + 1.18593i 0.224120 + 0.224120i
\(29\) −3.66959 + 3.66959i −0.681426 + 0.681426i −0.960322 0.278895i \(-0.910032\pi\)
0.278895 + 0.960322i \(0.410032\pi\)
\(30\) 1.41726 + 1.72956i 0.258755 + 0.315773i
\(31\) 4.54367 + 4.54367i 0.816067 + 0.816067i 0.985536 0.169468i \(-0.0542051\pi\)
−0.169468 + 0.985536i \(0.554205\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.39326 3.39326i 0.590691 0.590691i
\(34\) 1.30290i 0.223445i
\(35\) 2.90075 2.37697i 0.490316 0.401781i
\(36\) 1.00000i 0.166667i
\(37\) 3.31197 5.10204i 0.544484 0.838771i
\(38\) 4.46151 4.46151i 0.723752 0.723752i
\(39\) −3.14423 + 3.14423i −0.503479 + 0.503479i
\(40\) 2.22514 + 0.220830i 0.351825 + 0.0349164i
\(41\) 7.79237i 1.21696i −0.793568 0.608482i \(-0.791779\pi\)
0.793568 0.608482i \(-0.208221\pi\)
\(42\) −1.67716 −0.258792
\(43\) 2.02422i 0.308690i −0.988017 0.154345i \(-0.950673\pi\)
0.988017 0.154345i \(-0.0493268\pi\)
\(44\) 4.79879i 0.723445i
\(45\) −2.22514 0.220830i −0.331704 0.0329195i
\(46\) −0.933219 −0.137596
\(47\) −6.81249 6.81249i −0.993704 0.993704i 0.00627644 0.999980i \(-0.498002\pi\)
−0.999980 + 0.00627644i \(0.998002\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 4.18713i 0.598162i
\(50\) 0.982756 4.90247i 0.138983 0.693314i
\(51\) 0.921286 + 0.921286i 0.129006 + 0.129006i
\(52\) 4.44661i 0.616634i
\(53\) 5.08803 5.08803i 0.698895 0.698895i −0.265277 0.964172i \(-0.585463\pi\)
0.964172 + 0.265277i \(0.0854634\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −10.6780 1.05972i −1.43982 0.142893i
\(56\) −1.18593 + 1.18593i −0.158477 + 0.158477i
\(57\) 6.30953i 0.835717i
\(58\) −3.66959 3.66959i −0.481841 0.481841i
\(59\) −3.87716 3.87716i −0.504763 0.504763i 0.408151 0.912914i \(-0.366174\pi\)
−0.912914 + 0.408151i \(0.866174\pi\)
\(60\) −1.72956 + 1.41726i −0.223285 + 0.182967i
\(61\) −6.36168 6.36168i −0.814529 0.814529i 0.170780 0.985309i \(-0.445371\pi\)
−0.985309 + 0.170780i \(0.945371\pi\)
\(62\) −4.54367 + 4.54367i −0.577047 + 0.577047i
\(63\) 1.18593 1.18593i 0.149413 0.149413i
\(64\) −1.00000 −0.125000
\(65\) 9.89431 + 0.981946i 1.22724 + 0.121795i
\(66\) 3.39326 + 3.39326i 0.417681 + 0.417681i
\(67\) 0.639879 0.639879i 0.0781737 0.0781737i −0.666939 0.745112i \(-0.732396\pi\)
0.745112 + 0.666939i \(0.232396\pi\)
\(68\) 1.30290 0.157999
\(69\) 0.659885 0.659885i 0.0794409 0.0794409i
\(70\) 2.37697 + 2.90075i 0.284102 + 0.346706i
\(71\) −8.94910 −1.06206 −0.531031 0.847352i \(-0.678195\pi\)
−0.531031 + 0.847352i \(0.678195\pi\)
\(72\) 1.00000 0.117851
\(73\) −1.06393 1.06393i −0.124524 0.124524i 0.642098 0.766622i \(-0.278064\pi\)
−0.766622 + 0.642098i \(0.778064\pi\)
\(74\) 5.10204 + 3.31197i 0.593101 + 0.385009i
\(75\) 2.77166 + 4.16148i 0.320043 + 0.480526i
\(76\) 4.46151 + 4.46151i 0.511770 + 0.511770i
\(77\) 5.69104 5.69104i 0.648554 0.648554i
\(78\) −3.14423 3.14423i −0.356014 0.356014i
\(79\) −2.21244 2.21244i −0.248919 0.248919i 0.571608 0.820527i \(-0.306320\pi\)
−0.820527 + 0.571608i \(0.806320\pi\)
\(80\) −0.220830 + 2.22514i −0.0246896 + 0.248778i
\(81\) −1.00000 −0.111111
\(82\) 7.79237 0.860524
\(83\) −6.32708 + 6.32708i −0.694488 + 0.694488i −0.963216 0.268728i \(-0.913397\pi\)
0.268728 + 0.963216i \(0.413397\pi\)
\(84\) 1.67716i 0.182993i
\(85\) 0.287719 2.89912i 0.0312075 0.314454i
\(86\) 2.02422 0.218277
\(87\) 5.18959 0.556382
\(88\) 4.79879 0.511553
\(89\) 3.11309 3.11309i 0.329987 0.329987i −0.522594 0.852582i \(-0.675036\pi\)
0.852582 + 0.522594i \(0.175036\pi\)
\(90\) 0.220830 2.22514i 0.0232776 0.234550i
\(91\) −5.27338 + 5.27338i −0.552800 + 0.552800i
\(92\) 0.933219i 0.0972948i
\(93\) 6.42572i 0.666316i
\(94\) 6.81249 6.81249i 0.702655 0.702655i
\(95\) 10.9127 8.94223i 1.11962 0.917454i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 0.0235287 0.00238898 0.00119449 0.999999i \(-0.499620\pi\)
0.00119449 + 0.999999i \(0.499620\pi\)
\(98\) 4.18713 0.422964
\(99\) −4.79879 −0.482297
\(100\) 4.90247 + 0.982756i 0.490247 + 0.0982756i
\(101\) 3.95084i 0.393124i 0.980491 + 0.196562i \(0.0629776\pi\)
−0.980491 + 0.196562i \(0.937022\pi\)
\(102\) −0.921286 + 0.921286i −0.0912209 + 0.0912209i
\(103\) −10.4171 −1.02642 −0.513212 0.858262i \(-0.671545\pi\)
−0.513212 + 0.858262i \(0.671545\pi\)
\(104\) −4.44661 −0.436026
\(105\) −3.73191 0.370368i −0.364197 0.0361442i
\(106\) 5.08803 + 5.08803i 0.494194 + 0.494194i
\(107\) −3.87605 3.87605i −0.374712 0.374712i 0.494478 0.869190i \(-0.335359\pi\)
−0.869190 + 0.494478i \(0.835359\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −0.670005 0.670005i −0.0641748 0.0641748i 0.674291 0.738466i \(-0.264449\pi\)
−0.738466 + 0.674291i \(0.764449\pi\)
\(110\) 1.05972 10.6780i 0.101040 1.01810i
\(111\) −5.94961 + 1.26577i −0.564712 + 0.120142i
\(112\) −1.18593 1.18593i −0.112060 0.112060i
\(113\) 10.2693 0.966056 0.483028 0.875605i \(-0.339537\pi\)
0.483028 + 0.875605i \(0.339537\pi\)
\(114\) −6.30953 −0.590941
\(115\) −2.07654 0.206083i −0.193638 0.0192173i
\(116\) 3.66959 3.66959i 0.340713 0.340713i
\(117\) 4.44661 0.411089
\(118\) 3.87716 3.87716i 0.356921 0.356921i
\(119\) 1.54515 + 1.54515i 0.141643 + 0.141643i
\(120\) −1.41726 1.72956i −0.129377 0.157887i
\(121\) −12.0284 −1.09349
\(122\) 6.36168 6.36168i 0.575959 0.575959i
\(123\) −5.51004 + 5.51004i −0.496824 + 0.496824i
\(124\) −4.54367 4.54367i −0.408034 0.408034i
\(125\) 3.26938 10.6916i 0.292422 0.956289i
\(126\) 1.18593 + 1.18593i 0.105651 + 0.105651i
\(127\) 13.8004 + 13.8004i 1.22459 + 1.22459i 0.965983 + 0.258607i \(0.0832636\pi\)
0.258607 + 0.965983i \(0.416736\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.43134 + 1.43134i −0.126022 + 0.126022i
\(130\) −0.981946 + 9.89431i −0.0861224 + 0.867789i
\(131\) −7.14423 7.14423i −0.624194 0.624194i 0.322407 0.946601i \(-0.395508\pi\)
−0.946601 + 0.322407i \(0.895508\pi\)
\(132\) −3.39326 + 3.39326i −0.295345 + 0.295345i
\(133\) 10.5821i 0.917584i
\(134\) 0.639879 + 0.639879i 0.0552771 + 0.0552771i
\(135\) 1.41726 + 1.72956i 0.121978 + 0.148857i
\(136\) 1.30290i 0.111722i
\(137\) 6.54303 + 6.54303i 0.559008 + 0.559008i 0.929025 0.370017i \(-0.120648\pi\)
−0.370017 + 0.929025i \(0.620648\pi\)
\(138\) 0.659885 + 0.659885i 0.0561732 + 0.0561732i
\(139\) −13.1631 −1.11648 −0.558241 0.829679i \(-0.688524\pi\)
−0.558241 + 0.829679i \(0.688524\pi\)
\(140\) −2.90075 + 2.37697i −0.245158 + 0.200891i
\(141\) 9.63432i 0.811356i
\(142\) 8.94910i 0.750992i
\(143\) 21.3384 1.78440
\(144\) 1.00000i 0.0833333i
\(145\) −7.35499 8.97570i −0.610798 0.745392i
\(146\) 1.06393 1.06393i 0.0880517 0.0880517i
\(147\) −2.96075 + 2.96075i −0.244198 + 0.244198i
\(148\) −3.31197 + 5.10204i −0.272242 + 0.419385i
\(149\) 5.19216i 0.425359i 0.977122 + 0.212679i \(0.0682189\pi\)
−0.977122 + 0.212679i \(0.931781\pi\)
\(150\) −4.16148 + 2.77166i −0.339784 + 0.226305i
\(151\) 11.5161i 0.937170i 0.883419 + 0.468585i \(0.155236\pi\)
−0.883419 + 0.468585i \(0.844764\pi\)
\(152\) −4.46151 + 4.46151i −0.361876 + 0.361876i
\(153\) 1.30290i 0.105333i
\(154\) 5.69104 + 5.69104i 0.458597 + 0.458597i
\(155\) −11.1137 + 9.10691i −0.892671 + 0.731484i
\(156\) 3.14423 3.14423i 0.251740 0.251740i
\(157\) −2.32320 2.32320i −0.185411 0.185411i 0.608298 0.793709i \(-0.291853\pi\)
−0.793709 + 0.608298i \(0.791853\pi\)
\(158\) 2.21244 2.21244i 0.176012 0.176012i
\(159\) −7.19557 −0.570646
\(160\) −2.22514 0.220830i −0.175913 0.0174582i
\(161\) 1.10673 1.10673i 0.0872229 0.0872229i
\(162\) 1.00000i 0.0785674i
\(163\) 0.310642 0.0243314 0.0121657 0.999926i \(-0.496127\pi\)
0.0121657 + 0.999926i \(0.496127\pi\)
\(164\) 7.79237i 0.608482i
\(165\) 6.80113 + 8.29980i 0.529467 + 0.646139i
\(166\) −6.32708 6.32708i −0.491077 0.491077i
\(167\) 21.2856 1.64713 0.823563 0.567225i \(-0.191983\pi\)
0.823563 + 0.567225i \(0.191983\pi\)
\(168\) 1.67716 0.129396
\(169\) −6.77233 −0.520948
\(170\) 2.89912 + 0.287719i 0.222352 + 0.0220670i
\(171\) 4.46151 4.46151i 0.341180 0.341180i
\(172\) 2.02422i 0.154345i
\(173\) −13.5623 13.5623i −1.03112 1.03112i −0.999500 0.0316231i \(-0.989932\pi\)
−0.0316231 0.999500i \(-0.510068\pi\)
\(174\) 5.18959i 0.393422i
\(175\) 4.64851 + 6.97947i 0.351394 + 0.527599i
\(176\) 4.79879i 0.361723i
\(177\) 5.48313i 0.412137i
\(178\) 3.11309 + 3.11309i 0.233336 + 0.233336i
\(179\) −9.91196 + 9.91196i −0.740854 + 0.740854i −0.972742 0.231888i \(-0.925510\pi\)
0.231888 + 0.972742i \(0.425510\pi\)
\(180\) 2.22514 + 0.220830i 0.165852 + 0.0164597i
\(181\) −1.52458 −0.113321 −0.0566606 0.998393i \(-0.518045\pi\)
−0.0566606 + 0.998393i \(0.518045\pi\)
\(182\) −5.27338 5.27338i −0.390889 0.390889i
\(183\) 8.99677i 0.665060i
\(184\) 0.933219 0.0687978
\(185\) 10.6214 + 8.49627i 0.780898 + 0.624658i
\(186\) 6.42572 0.471157
\(187\) 6.25232i 0.457215i
\(188\) 6.81249 + 6.81249i 0.496852 + 0.496852i
\(189\) −1.67716 −0.121996
\(190\) 8.94223 + 10.9127i 0.648738 + 0.791691i
\(191\) −15.7574 + 15.7574i −1.14016 + 1.14016i −0.151745 + 0.988420i \(0.548489\pi\)
−0.988420 + 0.151745i \(0.951511\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 16.8985i 1.21638i 0.793790 + 0.608192i \(0.208105\pi\)
−0.793790 + 0.608192i \(0.791895\pi\)
\(194\) 0.0235287i 0.00168926i
\(195\) −6.30199 7.69068i −0.451295 0.550741i
\(196\) 4.18713i 0.299081i
\(197\) −5.46379 5.46379i −0.389279 0.389279i 0.485151 0.874430i \(-0.338764\pi\)
−0.874430 + 0.485151i \(0.838764\pi\)
\(198\) 4.79879i 0.341035i
\(199\) −11.6938 + 11.6938i −0.828949 + 0.828949i −0.987371 0.158423i \(-0.949359\pi\)
0.158423 + 0.987371i \(0.449359\pi\)
\(200\) −0.982756 + 4.90247i −0.0694913 + 0.346657i
\(201\) −0.904926 −0.0638285
\(202\) −3.95084 −0.277980
\(203\) 8.70377 0.610885
\(204\) −0.921286 0.921286i −0.0645029 0.0645029i
\(205\) 17.3391 + 1.72079i 1.21101 + 0.120185i
\(206\) 10.4171i 0.725792i
\(207\) −0.933219 −0.0648632
\(208\) 4.44661i 0.308317i
\(209\) 21.4099 21.4099i 1.48095 1.48095i
\(210\) 0.370368 3.73191i 0.0255578 0.257526i
\(211\) 25.9385 1.78568 0.892841 0.450371i \(-0.148708\pi\)
0.892841 + 0.450371i \(0.148708\pi\)
\(212\) −5.08803 + 5.08803i −0.349448 + 0.349448i
\(213\) 6.32797 + 6.32797i 0.433585 + 0.433585i
\(214\) 3.87605 3.87605i 0.264962 0.264962i
\(215\) 4.50416 + 0.447009i 0.307181 + 0.0304857i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 10.7770i 0.731588i
\(218\) 0.670005 0.670005i 0.0453784 0.0453784i
\(219\) 1.50463i 0.101673i
\(220\) 10.6780 + 1.05972i 0.719909 + 0.0714463i
\(221\) 5.79347i 0.389711i
\(222\) −1.26577 5.94961i −0.0849532 0.399311i
\(223\) −10.7674 + 10.7674i −0.721039 + 0.721039i −0.968817 0.247778i \(-0.920300\pi\)
0.247778 + 0.968817i \(0.420300\pi\)
\(224\) 1.18593 1.18593i 0.0792384 0.0792384i
\(225\) 0.982756 4.90247i 0.0655170 0.326831i
\(226\) 10.2693i 0.683105i
\(227\) −9.50039 −0.630563 −0.315282 0.948998i \(-0.602099\pi\)
−0.315282 + 0.948998i \(0.602099\pi\)
\(228\) 6.30953i 0.417859i
\(229\) 4.84055i 0.319873i −0.987127 0.159936i \(-0.948871\pi\)
0.987127 0.159936i \(-0.0511289\pi\)
\(230\) 0.206083 2.07654i 0.0135887 0.136923i
\(231\) −8.04835 −0.529542
\(232\) 3.66959 + 3.66959i 0.240921 + 0.240921i
\(233\) −4.19880 4.19880i −0.275072 0.275072i 0.556066 0.831138i \(-0.312310\pi\)
−0.831138 + 0.556066i \(0.812310\pi\)
\(234\) 4.44661i 0.290684i
\(235\) 16.6631 13.6543i 1.08698 0.890710i
\(236\) 3.87716 + 3.87716i 0.252382 + 0.252382i
\(237\) 3.12886i 0.203241i
\(238\) −1.54515 + 1.54515i −0.100157 + 0.100157i
\(239\) 5.62269 + 5.62269i 0.363701 + 0.363701i 0.865174 0.501472i \(-0.167208\pi\)
−0.501472 + 0.865174i \(0.667208\pi\)
\(240\) 1.72956 1.41726i 0.111643 0.0914837i
\(241\) 10.8325 10.8325i 0.697784 0.697784i −0.266148 0.963932i \(-0.585751\pi\)
0.963932 + 0.266148i \(0.0857510\pi\)
\(242\) 12.0284i 0.773216i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 6.36168 + 6.36168i 0.407265 + 0.407265i
\(245\) 9.31694 + 0.924646i 0.595237 + 0.0590734i
\(246\) −5.51004 5.51004i −0.351307 0.351307i
\(247\) −19.8386 + 19.8386i −1.26230 + 1.26230i
\(248\) 4.54367 4.54367i 0.288523 0.288523i
\(249\) 8.94785 0.567047
\(250\) 10.6916 + 3.26938i 0.676199 + 0.206774i
\(251\) 14.8022 + 14.8022i 0.934305 + 0.934305i 0.997971 0.0636664i \(-0.0202794\pi\)
−0.0636664 + 0.997971i \(0.520279\pi\)
\(252\) −1.18593 + 1.18593i −0.0747067 + 0.0747067i
\(253\) −4.47832 −0.281550
\(254\) −13.8004 + 13.8004i −0.865916 + 0.865916i
\(255\) −2.25344 + 1.84654i −0.141116 + 0.115635i
\(256\) 1.00000 0.0625000
\(257\) 11.2517 0.701861 0.350931 0.936401i \(-0.385865\pi\)
0.350931 + 0.936401i \(0.385865\pi\)
\(258\) −1.43134 1.43134i −0.0891112 0.0891112i
\(259\) −9.97845 + 2.12291i −0.620031 + 0.131911i
\(260\) −9.89431 0.981946i −0.613619 0.0608977i
\(261\) −3.66959 3.66959i −0.227142 0.227142i
\(262\) 7.14423 7.14423i 0.441372 0.441372i
\(263\) −10.1672 10.1672i −0.626937 0.626937i 0.320359 0.947296i \(-0.396196\pi\)
−0.947296 + 0.320359i \(0.896196\pi\)
\(264\) −3.39326 3.39326i −0.208841 0.208841i
\(265\) 10.1980 + 12.4452i 0.626457 + 0.764500i
\(266\) −10.5821 −0.648830
\(267\) −4.40258 −0.269434
\(268\) −0.639879 + 0.639879i −0.0390868 + 0.0390868i
\(269\) 24.8306i 1.51395i 0.653445 + 0.756974i \(0.273323\pi\)
−0.653445 + 0.756974i \(0.726677\pi\)
\(270\) −1.72956 + 1.41726i −0.105258 + 0.0862516i
\(271\) 3.95334 0.240148 0.120074 0.992765i \(-0.461687\pi\)
0.120074 + 0.992765i \(0.461687\pi\)
\(272\) −1.30290 −0.0789996
\(273\) 7.45768 0.451359
\(274\) −6.54303 + 6.54303i −0.395279 + 0.395279i
\(275\) 4.71604 23.5259i 0.284388 1.41867i
\(276\) −0.659885 + 0.659885i −0.0397204 + 0.0397204i
\(277\) 2.77329i 0.166631i −0.996523 0.0833154i \(-0.973449\pi\)
0.996523 0.0833154i \(-0.0265509\pi\)
\(278\) 13.1631i 0.789472i
\(279\) −4.54367 + 4.54367i −0.272022 + 0.272022i
\(280\) −2.37697 2.90075i −0.142051 0.173353i
\(281\) −12.9824 + 12.9824i −0.774467 + 0.774467i −0.978884 0.204417i \(-0.934470\pi\)
0.204417 + 0.978884i \(0.434470\pi\)
\(282\) −9.63432 −0.573715
\(283\) −26.5212 −1.57652 −0.788261 0.615341i \(-0.789018\pi\)
−0.788261 + 0.615341i \(0.789018\pi\)
\(284\) 8.94910 0.531031
\(285\) −14.0396 1.39334i −0.831632 0.0825341i
\(286\) 21.3384i 1.26176i
\(287\) −9.24122 + 9.24122i −0.545492 + 0.545492i
\(288\) −1.00000 −0.0589256
\(289\) −15.3025 −0.900145
\(290\) 8.97570 7.35499i 0.527071 0.431900i
\(291\) −0.0166373 0.0166373i −0.000975297 0.000975297i
\(292\) 1.06393 + 1.06393i 0.0622619 + 0.0622619i
\(293\) −18.1427 + 18.1427i −1.05991 + 1.05991i −0.0618185 + 0.998087i \(0.519690\pi\)
−0.998087 + 0.0618185i \(0.980310\pi\)
\(294\) −2.96075 2.96075i −0.172674 0.172674i
\(295\) 9.48340 7.77102i 0.552145 0.452446i
\(296\) −5.10204 3.31197i −0.296550 0.192504i
\(297\) 3.39326 + 3.39326i 0.196897 + 0.196897i
\(298\) −5.19216 −0.300774
\(299\) 4.14966 0.239981
\(300\) −2.77166 4.16148i −0.160022 0.240263i
\(301\) −2.40058 + 2.40058i −0.138367 + 0.138367i
\(302\) −11.5161 −0.662679
\(303\) 2.79367 2.79367i 0.160492 0.160492i
\(304\) −4.46151 4.46151i −0.255885 0.255885i
\(305\) 15.5605 12.7507i 0.890989 0.730106i
\(306\) 1.30290 0.0744816
\(307\) −2.44662 + 2.44662i −0.139636 + 0.139636i −0.773470 0.633833i \(-0.781480\pi\)
0.633833 + 0.773470i \(0.281480\pi\)
\(308\) −5.69104 + 5.69104i −0.324277 + 0.324277i
\(309\) 7.36598 + 7.36598i 0.419036 + 0.419036i
\(310\) −9.10691 11.1137i −0.517238 0.631214i
\(311\) −22.4050 22.4050i −1.27047 1.27047i −0.945841 0.324631i \(-0.894760\pi\)
−0.324631 0.945841i \(-0.605240\pi\)
\(312\) 3.14423 + 3.14423i 0.178007 + 0.178007i
\(313\) 1.26968i 0.0717668i 0.999356 + 0.0358834i \(0.0114245\pi\)
−0.999356 + 0.0358834i \(0.988576\pi\)
\(314\) 2.32320 2.32320i 0.131106 0.131106i
\(315\) 2.37697 + 2.90075i 0.133927 + 0.163439i
\(316\) 2.21244 + 2.21244i 0.124459 + 0.124459i
\(317\) 11.5508 11.5508i 0.648757 0.648757i −0.303936 0.952693i \(-0.598301\pi\)
0.952693 + 0.303936i \(0.0983008\pi\)
\(318\) 7.19557i 0.403507i
\(319\) −17.6096 17.6096i −0.985949 0.985949i
\(320\) 0.220830 2.22514i 0.0123448 0.124389i
\(321\) 5.48157i 0.305951i
\(322\) 1.10673 + 1.10673i 0.0616759 + 0.0616759i
\(323\) 5.81288 + 5.81288i 0.323437 + 0.323437i
\(324\) 1.00000 0.0555556
\(325\) −4.36993 + 21.7994i −0.242400 + 1.20921i
\(326\) 0.310642i 0.0172049i
\(327\) 0.947530i 0.0523985i
\(328\) −7.79237 −0.430262
\(329\) 16.1583i 0.890836i
\(330\) −8.29980 + 6.80113i −0.456889 + 0.374390i
\(331\) −14.6794 + 14.6794i −0.806851 + 0.806851i −0.984156 0.177305i \(-0.943262\pi\)
0.177305 + 0.984156i \(0.443262\pi\)
\(332\) 6.32708 6.32708i 0.347244 0.347244i
\(333\) 5.10204 + 3.31197i 0.279590 + 0.181495i
\(334\) 21.2856i 1.16469i
\(335\) 1.28251 + 1.56512i 0.0700712 + 0.0855118i
\(336\) 1.67716i 0.0914966i
\(337\) 3.80408 3.80408i 0.207222 0.207222i −0.595864 0.803085i \(-0.703190\pi\)
0.803085 + 0.595864i \(0.203190\pi\)
\(338\) 6.77233i 0.368366i
\(339\) −7.26150 7.26150i −0.394391 0.394391i
\(340\) −0.287719 + 2.89912i −0.0156037 + 0.157227i
\(341\) −21.8041 + 21.8041i −1.18076 + 1.18076i
\(342\) 4.46151 + 4.46151i 0.241251 + 0.241251i
\(343\) −13.2672 + 13.2672i −0.716360 + 0.716360i
\(344\) −2.02422 −0.109138
\(345\) 1.32261 + 1.61406i 0.0712071 + 0.0868980i
\(346\) 13.5623 13.5623i 0.729114 0.729114i
\(347\) 32.1513i 1.72597i −0.505226 0.862987i \(-0.668591\pi\)
0.505226 0.862987i \(-0.331409\pi\)
\(348\) −5.18959 −0.278191
\(349\) 4.32501i 0.231512i 0.993278 + 0.115756i \(0.0369291\pi\)
−0.993278 + 0.115756i \(0.963071\pi\)
\(350\) −6.97947 + 4.64851i −0.373069 + 0.248473i
\(351\) −3.14423 3.14423i −0.167826 0.167826i
\(352\) −4.79879 −0.255777
\(353\) −16.0457 −0.854028 −0.427014 0.904245i \(-0.640434\pi\)
−0.427014 + 0.904245i \(0.640434\pi\)
\(354\) −5.48313 −0.291425
\(355\) 1.97623 19.9130i 0.104888 1.05687i
\(356\) −3.11309 + 3.11309i −0.164994 + 0.164994i
\(357\) 2.18517i 0.115651i
\(358\) −9.91196 9.91196i −0.523863 0.523863i
\(359\) 15.7185i 0.829591i −0.909915 0.414795i \(-0.863853\pi\)
0.909915 0.414795i \(-0.136147\pi\)
\(360\) −0.220830 + 2.22514i −0.0116388 + 0.117275i
\(361\) 20.8101i 1.09527i
\(362\) 1.52458i 0.0801302i
\(363\) 8.50537 + 8.50537i 0.446416 + 0.446416i
\(364\) 5.27338 5.27338i 0.276400 0.276400i
\(365\) 2.60234 2.13245i 0.136213 0.111617i
\(366\) −8.99677 −0.470269
\(367\) 17.3935 + 17.3935i 0.907935 + 0.907935i 0.996105 0.0881705i \(-0.0281020\pi\)
−0.0881705 + 0.996105i \(0.528102\pi\)
\(368\) 0.933219i 0.0486474i
\(369\) 7.79237 0.405655
\(370\) −8.49627 + 10.6214i −0.441700 + 0.552178i
\(371\) −12.0681 −0.626546
\(372\) 6.42572i 0.333158i
\(373\) −24.4469 24.4469i −1.26581 1.26581i −0.948231 0.317582i \(-0.897129\pi\)
−0.317582 0.948231i \(-0.602871\pi\)
\(374\) 6.25232 0.323300
\(375\) −9.87193 + 5.24833i −0.509784 + 0.271023i
\(376\) −6.81249 + 6.81249i −0.351327 + 0.351327i
\(377\) 16.3172 + 16.3172i 0.840381 + 0.840381i
\(378\) 1.67716i 0.0862639i
\(379\) 28.8766i 1.48329i −0.670793 0.741645i \(-0.734046\pi\)
0.670793 0.741645i \(-0.265954\pi\)
\(380\) −10.9127 + 8.94223i −0.559810 + 0.458727i
\(381\) 19.5168i 0.999873i
\(382\) −15.7574 15.7574i −0.806218 0.806218i
\(383\) 36.9567i 1.88840i −0.329374 0.944200i \(-0.606838\pi\)
0.329374 0.944200i \(-0.393162\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 11.4066 + 13.9201i 0.581334 + 0.709434i
\(386\) −16.8985 −0.860113
\(387\) 2.02422 0.102897
\(388\) −0.0235287 −0.00119449
\(389\) 21.5492 + 21.5492i 1.09259 + 1.09259i 0.995252 + 0.0973355i \(0.0310320\pi\)
0.0973355 + 0.995252i \(0.468968\pi\)
\(390\) 7.69068 6.30199i 0.389433 0.319114i
\(391\) 1.21589i 0.0614900i
\(392\) −4.18713 −0.211482
\(393\) 10.1035i 0.509652i
\(394\) 5.46379 5.46379i 0.275262 0.275262i
\(395\) 5.41155 4.43441i 0.272285 0.223119i
\(396\) 4.79879 0.241148
\(397\) 26.8752 26.8752i 1.34883 1.34883i 0.461894 0.886935i \(-0.347170\pi\)
0.886935 0.461894i \(-0.152830\pi\)
\(398\) −11.6938 11.6938i −0.586155 0.586155i
\(399\) 7.48267 7.48267i 0.374602 0.374602i
\(400\) −4.90247 0.982756i −0.245123 0.0491378i
\(401\) 16.3614 + 16.3614i 0.817048 + 0.817048i 0.985679 0.168631i \(-0.0539346\pi\)
−0.168631 + 0.985679i \(0.553935\pi\)
\(402\) 0.904926i 0.0451336i
\(403\) 20.2039 20.2039i 1.00643 1.00643i
\(404\) 3.95084i 0.196562i
\(405\) 0.220830 2.22514i 0.0109732 0.110568i
\(406\) 8.70377i 0.431961i
\(407\) 24.4837 + 15.8935i 1.21361 + 0.787809i
\(408\) 0.921286 0.921286i 0.0456105 0.0456105i
\(409\) −1.75957 + 1.75957i −0.0870050 + 0.0870050i −0.749270 0.662265i \(-0.769595\pi\)
0.662265 + 0.749270i \(0.269595\pi\)
\(410\) −1.72079 + 17.3391i −0.0849839 + 0.856317i
\(411\) 9.25324i 0.456429i
\(412\) 10.4171 0.513212
\(413\) 9.19609i 0.452510i
\(414\) 0.933219i 0.0458652i
\(415\) −12.6814 15.4758i −0.622506 0.759679i
\(416\) 4.44661 0.218013
\(417\) 9.30774 + 9.30774i 0.455802 + 0.455802i
\(418\) 21.4099 + 21.4099i 1.04719 + 1.04719i
\(419\) 10.0390i 0.490439i 0.969468 + 0.245220i \(0.0788601\pi\)
−0.969468 + 0.245220i \(0.921140\pi\)
\(420\) 3.73191 + 0.370368i 0.182099 + 0.0180721i
\(421\) −6.87930 6.87930i −0.335277 0.335277i 0.519310 0.854586i \(-0.326189\pi\)
−0.854586 + 0.519310i \(0.826189\pi\)
\(422\) 25.9385i 1.26267i
\(423\) 6.81249 6.81249i 0.331235 0.331235i
\(424\) −5.08803 5.08803i −0.247097 0.247097i
\(425\) 6.38740 + 1.28043i 0.309835 + 0.0621099i
\(426\) −6.32797 + 6.32797i −0.306591 + 0.306591i
\(427\) 15.0890i 0.730209i
\(428\) 3.87605 + 3.87605i 0.187356 + 0.187356i
\(429\) −15.0885 15.0885i −0.728479 0.728479i
\(430\) −0.447009 + 4.50416i −0.0215567 + 0.217210i
\(431\) 6.62805 + 6.62805i 0.319262 + 0.319262i 0.848484 0.529222i \(-0.177516\pi\)
−0.529222 + 0.848484i \(0.677516\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 11.5273 11.5273i 0.553968 0.553968i −0.373616 0.927584i \(-0.621882\pi\)
0.927584 + 0.373616i \(0.121882\pi\)
\(434\) 10.7770 0.517311
\(435\) −1.14602 + 11.5475i −0.0549474 + 0.553662i
\(436\) 0.670005 + 0.670005i 0.0320874 + 0.0320874i
\(437\) 4.16356 4.16356i 0.199170 0.199170i
\(438\) −1.50463 −0.0718939
\(439\) 25.1084 25.1084i 1.19836 1.19836i 0.223702 0.974658i \(-0.428186\pi\)
0.974658 0.223702i \(-0.0718144\pi\)
\(440\) −1.05972 + 10.6780i −0.0505201 + 0.509052i
\(441\) 4.18713 0.199387
\(442\) −5.79347 −0.275567
\(443\) 10.8396 + 10.8396i 0.515004 + 0.515004i 0.916056 0.401051i \(-0.131355\pi\)
−0.401051 + 0.916056i \(0.631355\pi\)
\(444\) 5.94961 1.26577i 0.282356 0.0600710i
\(445\) 6.23959 + 7.61453i 0.295785 + 0.360963i
\(446\) −10.7674 10.7674i −0.509852 0.509852i
\(447\) 3.67141 3.67141i 0.173652 0.173652i
\(448\) 1.18593 + 1.18593i 0.0560300 + 0.0560300i
\(449\) −16.9181 16.9181i −0.798413 0.798413i 0.184433 0.982845i \(-0.440955\pi\)
−0.982845 + 0.184433i \(0.940955\pi\)
\(450\) 4.90247 + 0.982756i 0.231105 + 0.0463275i
\(451\) 37.3940 1.76081
\(452\) −10.2693 −0.483028
\(453\) 8.14314 8.14314i 0.382598 0.382598i
\(454\) 9.50039i 0.445876i
\(455\) −10.5695 12.8985i −0.495504 0.604691i
\(456\) 6.30953 0.295471
\(457\) 17.9114 0.837860 0.418930 0.908018i \(-0.362405\pi\)
0.418930 + 0.908018i \(0.362405\pi\)
\(458\) 4.84055 0.226184
\(459\) −0.921286 + 0.921286i −0.0430020 + 0.0430020i
\(460\) 2.07654 + 0.206083i 0.0968192 + 0.00960867i
\(461\) 2.45180 2.45180i 0.114192 0.114192i −0.647702 0.761894i \(-0.724270\pi\)
0.761894 + 0.647702i \(0.224270\pi\)
\(462\) 8.04835i 0.374443i
\(463\) 36.5028i 1.69643i −0.529654 0.848214i \(-0.677678\pi\)
0.529654 0.848214i \(-0.322322\pi\)
\(464\) −3.66959 + 3.66959i −0.170357 + 0.170357i
\(465\) 14.2981 + 1.41899i 0.663059 + 0.0658043i
\(466\) 4.19880 4.19880i 0.194505 0.194505i
\(467\) −20.8160 −0.963252 −0.481626 0.876377i \(-0.659954\pi\)
−0.481626 + 0.876377i \(0.659954\pi\)
\(468\) −4.44661 −0.205545
\(469\) −1.51771 −0.0700812
\(470\) 13.6543 + 16.6631i 0.629827 + 0.768613i
\(471\) 3.28550i 0.151388i
\(472\) −3.87716 + 3.87716i −0.178461 + 0.178461i
\(473\) 9.71380 0.446641
\(474\) −3.12886 −0.143713
\(475\) 17.4878 + 26.2570i 0.802397 + 1.20475i
\(476\) −1.54515 1.54515i −0.0708216 0.0708216i
\(477\) 5.08803 + 5.08803i 0.232965 + 0.232965i
\(478\) −5.62269 + 5.62269i −0.257176 + 0.257176i
\(479\) −21.3099 21.3099i −0.973672 0.973672i 0.0259899 0.999662i \(-0.491726\pi\)
−0.999662 + 0.0259899i \(0.991726\pi\)
\(480\) 1.41726 + 1.72956i 0.0646887 + 0.0789433i
\(481\) −22.6868 14.7270i −1.03443 0.671495i
\(482\) 10.8325 + 10.8325i 0.493408 + 0.493408i
\(483\) −1.56516 −0.0712172
\(484\) 12.0284 0.546746
\(485\) −0.00519586 + 0.0523546i −0.000235932 + 0.00237730i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) −31.2190 −1.41467 −0.707334 0.706880i \(-0.750102\pi\)
−0.707334 + 0.706880i \(0.750102\pi\)
\(488\) −6.36168 + 6.36168i −0.287980 + 0.287980i
\(489\) −0.219657 0.219657i −0.00993323 0.00993323i
\(490\) −0.924646 + 9.31694i −0.0417712 + 0.420896i
\(491\) 1.46818 0.0662579 0.0331289 0.999451i \(-0.489453\pi\)
0.0331289 + 0.999451i \(0.489453\pi\)
\(492\) 5.51004 5.51004i 0.248412 0.248412i
\(493\) 4.78109 4.78109i 0.215330 0.215330i
\(494\) −19.8386 19.8386i −0.892580 0.892580i
\(495\) 1.05972 10.6780i 0.0476308 0.479939i
\(496\) 4.54367 + 4.54367i 0.204017 + 0.204017i
\(497\) 10.6130 + 10.6130i 0.476059 + 0.476059i
\(498\) 8.94785i 0.400963i
\(499\) 1.77906 1.77906i 0.0796419 0.0796419i −0.666164 0.745806i \(-0.732065\pi\)
0.745806 + 0.666164i \(0.232065\pi\)
\(500\) −3.26938 + 10.6916i −0.146211 + 0.478145i
\(501\) −15.0512 15.0512i −0.672436 0.672436i
\(502\) −14.8022 + 14.8022i −0.660653 + 0.660653i
\(503\) 10.5966i 0.472478i −0.971695 0.236239i \(-0.924085\pi\)
0.971695 0.236239i \(-0.0759148\pi\)
\(504\) −1.18593 1.18593i −0.0528256 0.0528256i
\(505\) −8.79117 0.872466i −0.391202 0.0388242i
\(506\) 4.47832i 0.199086i
\(507\) 4.78876 + 4.78876i 0.212676 + 0.212676i
\(508\) −13.8004 13.8004i −0.612295 0.612295i
\(509\) −7.39583 −0.327814 −0.163907 0.986476i \(-0.552410\pi\)
−0.163907 + 0.986476i \(0.552410\pi\)
\(510\) −1.84654 2.25344i −0.0817661 0.0997838i
\(511\) 2.52350i 0.111633i
\(512\) 1.00000i 0.0441942i
\(513\) −6.30953 −0.278572
\(514\) 11.2517i 0.496291i
\(515\) 2.30041 23.1794i 0.101368 1.02141i
\(516\) 1.43134 1.43134i 0.0630111 0.0630111i
\(517\) 32.6917 32.6917i 1.43778 1.43778i
\(518\) −2.12291 9.97845i −0.0932752 0.438428i
\(519\) 19.1800i 0.841908i
\(520\) 0.981946 9.89431i 0.0430612 0.433894i
\(521\) 42.7186i 1.87154i 0.352614 + 0.935769i \(0.385293\pi\)
−0.352614 + 0.935769i \(0.614707\pi\)
\(522\) 3.66959 3.66959i 0.160614 0.160614i
\(523\) 28.4562i 1.24430i 0.782897 + 0.622151i \(0.213741\pi\)
−0.782897 + 0.622151i \(0.786259\pi\)
\(524\) 7.14423 + 7.14423i 0.312097 + 0.312097i
\(525\) 1.64824 8.22223i 0.0719351 0.358847i
\(526\) 10.1672 10.1672i 0.443311 0.443311i
\(527\) −5.91993 5.91993i −0.257876 0.257876i
\(528\) 3.39326 3.39326i 0.147673 0.147673i
\(529\) 22.1291 0.962135
\(530\) −12.4452 + 10.1980i −0.540583 + 0.442972i
\(531\) 3.87716 3.87716i 0.168254 0.168254i
\(532\) 10.5821i 0.458792i
\(533\) −34.6496 −1.50084
\(534\) 4.40258i 0.190518i
\(535\) 9.48070 7.76880i 0.409887 0.335875i
\(536\) −0.639879 0.639879i −0.0276386 0.0276386i
\(537\) 14.0176 0.604905
\(538\) −24.8306 −1.07052
\(539\) 20.0932 0.865474
\(540\) −1.41726 1.72956i −0.0609891 0.0744284i
\(541\) −18.6520 + 18.6520i −0.801912 + 0.801912i −0.983394 0.181482i \(-0.941910\pi\)
0.181482 + 0.983394i \(0.441910\pi\)
\(542\) 3.95334i 0.169810i
\(543\) 1.07804 + 1.07804i 0.0462632 + 0.0462632i
\(544\) 1.30290i 0.0558612i
\(545\) 1.63881 1.34289i 0.0701989 0.0575233i
\(546\) 7.45768i 0.319159i
\(547\) 4.88671i 0.208941i −0.994528 0.104470i \(-0.966685\pi\)
0.994528 0.104470i \(-0.0333147\pi\)
\(548\) −6.54303 6.54303i −0.279504 0.279504i
\(549\) 6.36168 6.36168i 0.271510 0.271510i
\(550\) 23.5259 + 4.71604i 1.00315 + 0.201093i
\(551\) 32.7438 1.39493
\(552\) −0.659885 0.659885i −0.0280866 0.0280866i
\(553\) 5.24761i 0.223151i
\(554\) 2.77329 0.117826
\(555\) −1.50267 13.5182i −0.0637847 0.573816i
\(556\) 13.1631 0.558241
\(557\) 41.5104i 1.75885i −0.476037 0.879425i \(-0.657927\pi\)
0.476037 0.879425i \(-0.342073\pi\)
\(558\) −4.54367 4.54367i −0.192349 0.192349i
\(559\) −9.00090 −0.380698
\(560\) 2.90075 2.37697i 0.122579 0.100445i
\(561\) −4.42106 + 4.42106i −0.186657 + 0.186657i
\(562\) −12.9824 12.9824i −0.547631 0.547631i
\(563\) 34.6086i 1.45858i −0.684206 0.729288i \(-0.739851\pi\)
0.684206 0.729288i \(-0.260149\pi\)
\(564\) 9.63432i 0.405678i
\(565\) −2.26778 + 22.8506i −0.0954061 + 0.961333i
\(566\) 26.5212i 1.11477i
\(567\) 1.18593 + 1.18593i 0.0498045 + 0.0498045i
\(568\) 8.94910i 0.375496i
\(569\) −4.46452 + 4.46452i −0.187162 + 0.187162i −0.794468 0.607306i \(-0.792250\pi\)
0.607306 + 0.794468i \(0.292250\pi\)
\(570\) 1.39334 14.0396i 0.0583604 0.588053i
\(571\) −16.6857 −0.698274 −0.349137 0.937072i \(-0.613525\pi\)
−0.349137 + 0.937072i \(0.613525\pi\)
\(572\) −21.3384 −0.892201
\(573\) 22.2843 0.930940
\(574\) −9.24122 9.24122i −0.385721 0.385721i
\(575\) 0.917126 4.57508i 0.0382468 0.190794i
\(576\) 1.00000i 0.0416667i
\(577\) 17.2889 0.719745 0.359872 0.933002i \(-0.382820\pi\)
0.359872 + 0.933002i \(0.382820\pi\)
\(578\) 15.3025i 0.636499i
\(579\) 11.9491 11.9491i 0.496587 0.496587i
\(580\) 7.35499 + 8.97570i 0.305399 + 0.372696i
\(581\) 15.0070 0.622595
\(582\) 0.0166373 0.0166373i 0.000689639 0.000689639i
\(583\) 24.4164 + 24.4164i 1.01122 + 1.01122i
\(584\) −1.06393 + 1.06393i −0.0440258 + 0.0440258i
\(585\) −0.981946 + 9.89431i −0.0405985 + 0.409079i
\(586\) −18.1427 18.1427i −0.749467 0.749467i
\(587\) 28.9501i 1.19490i 0.801907 + 0.597449i \(0.203819\pi\)
−0.801907 + 0.597449i \(0.796181\pi\)
\(588\) 2.96075 2.96075i 0.122099 0.122099i
\(589\) 40.5433i 1.67056i
\(590\) 7.77102 + 9.48340i 0.319928 + 0.390426i
\(591\) 7.72696i 0.317845i
\(592\) 3.31197 5.10204i 0.136121 0.209693i
\(593\) 33.1096 33.1096i 1.35965 1.35965i 0.485300 0.874347i \(-0.338710\pi\)
0.874347 0.485300i \(-0.161290\pi\)
\(594\) −3.39326 + 3.39326i −0.139227 + 0.139227i
\(595\) −3.77937 + 3.09694i −0.154939 + 0.126962i
\(596\) 5.19216i 0.212679i
\(597\) 16.5375 0.676834
\(598\) 4.14966i 0.169692i
\(599\) 19.5074i 0.797053i 0.917157 + 0.398526i \(0.130478\pi\)
−0.917157 + 0.398526i \(0.869522\pi\)
\(600\) 4.16148 2.77166i 0.169892 0.113152i
\(601\) 41.8679 1.70783 0.853913 0.520415i \(-0.174223\pi\)
0.853913 + 0.520415i \(0.174223\pi\)
\(602\) −2.40058 2.40058i −0.0978405 0.0978405i
\(603\) 0.639879 + 0.639879i 0.0260579 + 0.0260579i
\(604\) 11.5161i 0.468585i
\(605\) 2.65624 26.7649i 0.107992 1.08815i
\(606\) 2.79367 + 2.79367i 0.113485 + 0.113485i
\(607\) 28.0484i 1.13845i −0.822182 0.569225i \(-0.807243\pi\)
0.822182 0.569225i \(-0.192757\pi\)
\(608\) 4.46151 4.46151i 0.180938 0.180938i
\(609\) −6.15450 6.15450i −0.249393 0.249393i
\(610\) 12.7507 + 15.5605i 0.516263 + 0.630024i
\(611\) −30.2925 + 30.2925i −1.22550 + 1.22550i
\(612\) 1.30290i 0.0526664i
\(613\) 23.0006 + 23.0006i 0.928986 + 0.928986i 0.997640 0.0686549i \(-0.0218707\pi\)
−0.0686549 + 0.997640i \(0.521871\pi\)
\(614\) −2.44662 2.44662i −0.0987377 0.0987377i
\(615\) −11.0438 13.4774i −0.445329 0.543460i
\(616\) −5.69104 5.69104i −0.229299 0.229299i
\(617\) −14.0932 + 14.0932i −0.567369 + 0.567369i −0.931391 0.364022i \(-0.881403\pi\)
0.364022 + 0.931391i \(0.381403\pi\)
\(618\) −7.36598 + 7.36598i −0.296303 + 0.296303i
\(619\) 22.6414 0.910037 0.455018 0.890482i \(-0.349633\pi\)
0.455018 + 0.890482i \(0.349633\pi\)
\(620\) 11.1137 9.10691i 0.446336 0.365742i
\(621\) 0.659885 + 0.659885i 0.0264803 + 0.0264803i
\(622\) 22.4050 22.4050i 0.898359 0.898359i
\(623\) −7.38384 −0.295827
\(624\) −3.14423 + 3.14423i −0.125870 + 0.125870i
\(625\) 23.0684 + 9.63586i 0.922735 + 0.385434i
\(626\) −1.26968 −0.0507468
\(627\) −30.2781 −1.20919
\(628\) 2.32320 + 2.32320i 0.0927057 + 0.0927057i
\(629\) −4.31515 + 6.64743i −0.172056 + 0.265050i
\(630\) −2.90075 + 2.37697i −0.115569 + 0.0947008i
\(631\) 5.51471 + 5.51471i 0.219537 + 0.219537i 0.808303 0.588766i \(-0.200386\pi\)
−0.588766 + 0.808303i \(0.700386\pi\)
\(632\) −2.21244 + 2.21244i −0.0880061 + 0.0880061i
\(633\) −18.3413 18.3413i −0.729002 0.729002i
\(634\) 11.5508 + 11.5508i 0.458740 + 0.458740i
\(635\) −33.7554 + 27.6603i −1.33954 + 1.09766i
\(636\) 7.19557 0.285323
\(637\) −18.6185 −0.737693
\(638\) 17.6096 17.6096i 0.697171 0.697171i
\(639\) 8.94910i 0.354021i
\(640\) 2.22514 + 0.220830i 0.0879563 + 0.00872909i
\(641\) 22.8591 0.902878 0.451439 0.892302i \(-0.350911\pi\)
0.451439 + 0.892302i \(0.350911\pi\)
\(642\) −5.48157 −0.216340
\(643\) −4.05269 −0.159822 −0.0799112 0.996802i \(-0.525464\pi\)
−0.0799112 + 0.996802i \(0.525464\pi\)
\(644\) −1.10673 + 1.10673i −0.0436114 + 0.0436114i
\(645\) −2.86884 3.50101i −0.112960 0.137852i
\(646\) −5.81288 + 5.81288i −0.228705 + 0.228705i
\(647\) 40.5162i 1.59285i 0.604734 + 0.796427i \(0.293279\pi\)
−0.604734 + 0.796427i \(0.706721\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 18.6057 18.6057i 0.730337 0.730337i
\(650\) −21.7994 4.36993i −0.855041 0.171403i
\(651\) −7.62047 + 7.62047i −0.298670 + 0.298670i
\(652\) −0.310642 −0.0121657
\(653\) −3.85391 −0.150815 −0.0754076 0.997153i \(-0.524026\pi\)
−0.0754076 + 0.997153i \(0.524026\pi\)
\(654\) −0.947530 −0.0370513
\(655\) 17.4745 14.3192i 0.682787 0.559498i
\(656\) 7.79237i 0.304241i
\(657\) 1.06393 1.06393i 0.0415079 0.0415079i
\(658\) −16.1583 −0.629916
\(659\) −38.4968 −1.49962 −0.749812 0.661651i \(-0.769856\pi\)
−0.749812 + 0.661651i \(0.769856\pi\)
\(660\) −6.80113 8.29980i −0.264734 0.323069i
\(661\) −34.7273 34.7273i −1.35073 1.35073i −0.884841 0.465894i \(-0.845733\pi\)
−0.465894 0.884841i \(-0.654267\pi\)
\(662\) −14.6794 14.6794i −0.570530 0.570530i
\(663\) 4.09660 4.09660i 0.159099 0.159099i
\(664\) 6.32708 + 6.32708i 0.245539 + 0.245539i
\(665\) −23.5466 2.33685i −0.913098 0.0906191i
\(666\) −3.31197 + 5.10204i −0.128336 + 0.197700i
\(667\) −3.42453 3.42453i −0.132598 0.132598i
\(668\) −21.2856 −0.823563
\(669\) 15.2274 0.588726
\(670\) −1.56512 + 1.28251i −0.0604660 + 0.0495478i
\(671\) 30.5284 30.5284i 1.17853 1.17853i
\(672\) −1.67716 −0.0646979
\(673\) 0.532326 0.532326i 0.0205197 0.0205197i −0.696773 0.717292i \(-0.745381\pi\)
0.717292 + 0.696773i \(0.245381\pi\)
\(674\) 3.80408 + 3.80408i 0.146528 + 0.146528i
\(675\) −4.16148 + 2.77166i −0.160175 + 0.106681i
\(676\) 6.77233 0.260474
\(677\) −5.75332 + 5.75332i −0.221118 + 0.221118i −0.808969 0.587851i \(-0.799974\pi\)
0.587851 + 0.808969i \(0.299974\pi\)
\(678\) 7.26150 7.26150i 0.278876 0.278876i
\(679\) −0.0279035 0.0279035i −0.00107084 0.00107084i
\(680\) −2.89912 0.287719i −0.111176 0.0110335i
\(681\) 6.71779 + 6.71779i 0.257426 + 0.257426i
\(682\) −21.8041 21.8041i −0.834923 0.834923i
\(683\) 39.9256i 1.52771i 0.645388 + 0.763855i \(0.276696\pi\)
−0.645388 + 0.763855i \(0.723304\pi\)
\(684\) −4.46151 + 4.46151i −0.170590 + 0.170590i
\(685\) −16.0040 + 13.1142i −0.611482 + 0.501069i
\(686\) −13.2672 13.2672i −0.506543 0.506543i
\(687\) −3.42279 + 3.42279i −0.130587 + 0.130587i
\(688\) 2.02422i 0.0771726i
\(689\) −22.6245 22.6245i −0.861925 0.861925i
\(690\) −1.61406 + 1.32261i −0.0614461 + 0.0503510i
\(691\) 17.1171i 0.651166i 0.945513 + 0.325583i \(0.105561\pi\)
−0.945513 + 0.325583i \(0.894439\pi\)
\(692\) 13.5623 + 13.5623i 0.515562 + 0.515562i
\(693\) 5.69104 + 5.69104i 0.216185 + 0.216185i
\(694\) 32.1513 1.22045
\(695\) 2.90682 29.2898i 0.110262 1.11102i
\(696\) 5.18959i 0.196711i
\(697\) 10.1526i 0.384559i
\(698\) −4.32501 −0.163704
\(699\) 5.93799i 0.224596i
\(700\) −4.64851 6.97947i −0.175697 0.263799i
\(701\) −22.1259 + 22.1259i −0.835684 + 0.835684i −0.988288 0.152603i \(-0.951234\pi\)
0.152603 + 0.988288i \(0.451234\pi\)
\(702\) 3.14423 3.14423i 0.118671 0.118671i
\(703\) −37.5392 + 7.98644i −1.41582 + 0.301214i
\(704\) 4.79879i 0.180861i
\(705\) −21.4377 2.12755i −0.807389 0.0801282i
\(706\) 16.0457i 0.603889i
\(707\) 4.68543 4.68543i 0.176214 0.176214i
\(708\) 5.48313i 0.206069i
\(709\) −28.0496 28.0496i −1.05342 1.05342i −0.998490 0.0549332i \(-0.982505\pi\)
−0.0549332 0.998490i \(-0.517495\pi\)
\(710\) 19.9130 + 1.97623i 0.747321 + 0.0741667i
\(711\) 2.21244 2.21244i 0.0829730 0.0829730i
\(712\) −3.11309 3.11309i −0.116668 0.116668i
\(713\) −4.24024 + 4.24024i −0.158798 + 0.158798i
\(714\) 2.18517 0.0817778
\(715\) −4.71216 + 47.4808i −0.176225 + 1.77568i
\(716\) 9.91196 9.91196i 0.370427 0.370427i
\(717\) 7.95168i 0.296961i
\(718\) 15.7185 0.586609
\(719\) 22.1676i 0.826713i 0.910569 + 0.413357i \(0.135644\pi\)
−0.910569 + 0.413357i \(0.864356\pi\)
\(720\) −2.22514 0.220830i −0.0829260 0.00822986i
\(721\) 12.3539 + 12.3539i 0.460085 + 0.460085i
\(722\) −20.8101 −0.774473
\(723\) −15.3195 −0.569738
\(724\) 1.52458 0.0566606
\(725\) 21.5964 14.3837i 0.802069 0.534199i
\(726\) −8.50537 + 8.50537i −0.315664 + 0.315664i
\(727\) 29.7685i 1.10405i 0.833827 + 0.552026i \(0.186145\pi\)
−0.833827 + 0.552026i \(0.813855\pi\)
\(728\) 5.27338 + 5.27338i 0.195444 + 0.195444i
\(729\) 1.00000i 0.0370370i
\(730\) 2.13245 + 2.60234i 0.0789254 + 0.0963170i
\(731\) 2.63734i 0.0975457i
\(732\) 8.99677i 0.332530i
\(733\) −27.3738 27.3738i −1.01108 1.01108i −0.999938 0.0111379i \(-0.996455\pi\)
−0.0111379 0.999938i \(-0.503545\pi\)
\(734\) −17.3935 + 17.3935i −0.642007 + 0.642007i
\(735\) −5.93425 7.24189i −0.218888 0.267121i
\(736\) −0.933219 −0.0343989
\(737\) 3.07065 + 3.07065i 0.113109 + 0.113109i
\(738\) 7.79237i 0.286841i
\(739\) 3.45235 0.126997 0.0634984 0.997982i \(-0.479774\pi\)
0.0634984 + 0.997982i \(0.479774\pi\)
\(740\) −10.6214 8.49627i −0.390449 0.312329i
\(741\) 28.0560 1.03066
\(742\) 12.0681i 0.443035i
\(743\) 6.95019 + 6.95019i 0.254978 + 0.254978i 0.823008 0.568030i \(-0.192294\pi\)
−0.568030 + 0.823008i \(0.692294\pi\)
\(744\) −6.42572 −0.235578
\(745\) −11.5533 1.14659i −0.423279 0.0420077i
\(746\) 24.4469 24.4469i 0.895065 0.895065i
\(747\) −6.32708 6.32708i −0.231496 0.231496i
\(748\) 6.25232i 0.228608i
\(749\) 9.19347i 0.335922i
\(750\) −5.24833 9.87193i −0.191642 0.360472i
\(751\) 48.5947i 1.77325i −0.462491 0.886624i \(-0.653044\pi\)
0.462491 0.886624i \(-0.346956\pi\)
\(752\) −6.81249 6.81249i −0.248426 0.248426i
\(753\) 20.9334i 0.762857i
\(754\) −16.3172 + 16.3172i −0.594239 + 0.594239i
\(755\) −25.6250 2.54311i −0.932588 0.0925533i
\(756\) 1.67716 0.0609978
\(757\) −24.9414 −0.906511 −0.453256 0.891381i \(-0.649737\pi\)
−0.453256 + 0.891381i \(0.649737\pi\)
\(758\) 28.8766 1.04884
\(759\) 3.16665 + 3.16665i 0.114942 + 0.114942i
\(760\) −8.94223 10.9127i −0.324369 0.395845i
\(761\) 38.6923i 1.40260i 0.712868 + 0.701298i \(0.247396\pi\)
−0.712868 + 0.701298i \(0.752604\pi\)
\(762\) 19.5168 0.707017
\(763\) 1.58916i 0.0575315i
\(764\) 15.7574 15.7574i 0.570082 0.570082i
\(765\) 2.89912 + 0.287719i 0.104818 + 0.0104025i
\(766\) 36.9567 1.33530
\(767\) −17.2402 + 17.2402i −0.622508 + 0.622508i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 15.3838 15.3838i 0.554755 0.554755i −0.373055 0.927809i \(-0.621690\pi\)
0.927809 + 0.373055i \(0.121690\pi\)
\(770\) −13.9201 + 11.4066i −0.501646 + 0.411065i
\(771\) −7.95615 7.95615i −0.286534 0.286534i
\(772\) 16.8985i 0.608192i
\(773\) −19.3766 + 19.3766i −0.696929 + 0.696929i −0.963747 0.266818i \(-0.914028\pi\)
0.266818 + 0.963747i \(0.414028\pi\)
\(774\) 2.02422i 0.0727590i
\(775\) −17.8099 26.7405i −0.639750 0.960548i
\(776\) 0.0235287i 0.000844632i
\(777\) 8.55695 + 5.55471i 0.306979 + 0.199274i
\(778\) −21.5492 + 21.5492i −0.772576 + 0.772576i
\(779\) −34.7657 + 34.7657i −1.24561 + 1.24561i
\(780\) 6.30199