Properties

Label 441.2.f.d.148.3
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.3
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.d.295.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.23025 + 2.13086i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-2.02704 + 3.51094i) q^{4} +(-1.29679 + 2.24611i) q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(2.98755 + 0.273062i) q^{9} +O(q^{10})\) \(q+(1.23025 + 2.13086i) q^{2} +(1.73025 + 0.0789082i) q^{3} +(-2.02704 + 3.51094i) q^{4} +(-1.29679 + 2.24611i) q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(2.98755 + 0.273062i) q^{9} -6.38151 q^{10} +(-2.25729 - 3.90975i) q^{11} +(-3.78434 + 5.91486i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-2.42101 + 3.78400i) q^{15} +(-2.16372 - 3.74766i) q^{16} +0.945916 q^{17} +(3.09358 + 6.70198i) q^{18} +4.05408 q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +(0.136673 - 0.236725i) q^{23} +(-8.74484 - 0.398809i) q^{24} +(-0.863327 - 1.49533i) q^{25} +2.46050 q^{26} +(5.14766 + 0.708209i) q^{27} +(-1.23025 - 2.13086i) q^{29} +(-11.0416 - 0.503554i) q^{30} +(1.16372 - 2.01561i) q^{31} +(0.269748 - 0.467216i) q^{32} +(-3.59718 - 6.94297i) q^{33} +(1.16372 + 2.01561i) q^{34} +(-7.01459 + 9.93559i) q^{36} +1.78074 q^{37} +(4.98755 + 8.63868i) q^{38} +(0.933463 - 1.45899i) q^{39} +(6.55408 - 11.3520i) q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +18.3025 q^{44} +(-4.48755 + 6.35624i) q^{45} +0.672570 q^{46} +(-6.08113 - 10.5328i) q^{47} +(-3.44805 - 6.65514i) q^{48} +(2.12422 - 3.67926i) q^{50} +(1.63667 + 0.0746406i) q^{51} +(2.02704 + 3.51094i) q^{52} -6.27335 q^{53} +(4.82383 + 11.8402i) q^{54} +11.7089 q^{55} +(7.01459 + 0.319901i) q^{57} +(3.02704 - 5.24299i) q^{58} +(-1.36333 + 2.36135i) q^{59} +(-8.37792 - 16.1704i) q^{60} +(-1.13667 - 1.96878i) q^{61} +5.72665 q^{62} -7.32743 q^{64} +(1.29679 + 2.24611i) q^{65} +(10.3691 - 16.2067i) q^{66} +(7.90856 - 13.6980i) q^{67} +(-1.91741 + 3.32105i) q^{68} +(0.255158 - 0.398809i) q^{69} +3.27335 q^{71} +(-15.0993 - 1.38008i) q^{72} +1.50739 q^{73} +(2.19076 + 3.79450i) q^{74} +(-1.37578 - 2.65542i) q^{75} +(-8.21780 + 14.2336i) q^{76} +(4.25729 + 0.194154i) q^{78} +(-7.35447 - 12.7383i) q^{79} +11.2235 q^{80} +(8.85087 + 1.63157i) q^{81} -15.7630 q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(-12.8384 + 22.2368i) q^{86} +(-1.96050 - 3.78400i) q^{87} +(11.4086 + 19.7602i) q^{88} +14.3566 q^{89} +(-19.0651 - 1.74255i) q^{90} +(0.554084 + 0.959702i) q^{92} +(2.17257 - 3.39569i) q^{93} +(14.9626 - 25.9161i) q^{94} +(-5.25729 + 9.10590i) q^{95} +(0.503599 - 0.787117i) q^{96} +(-5.74484 - 9.95036i) q^{97} +(-5.67617 - 12.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} + 4q^{3} - 3q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + O(q^{10}) \) \( 6q + q^{2} + 4q^{3} - 3q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + 2q^{11} + 2q^{12} + 3q^{13} + 11q^{15} - 3q^{16} + 24q^{17} + 13q^{18} + 6q^{19} - 16q^{20} + 15q^{22} - 15q^{24} - 6q^{25} + 2q^{26} + 7q^{27} - q^{29} - 26q^{30} - 3q^{31} + 8q^{32} - 8q^{33} - 3q^{34} - 11q^{36} - 6q^{37} + 8q^{38} + 2q^{39} + 21q^{40} - 22q^{41} + 3q^{43} + 46q^{44} - 5q^{45} + 24q^{46} - 9q^{47} + 14q^{48} - 10q^{50} + 9q^{51} + 3q^{52} - 36q^{53} + 17q^{54} + 12q^{55} + 11q^{57} + 9q^{58} - 9q^{59} - 20q^{60} - 6q^{61} + 36q^{62} - 24q^{64} + 5q^{65} + 2q^{66} + 6q^{68} + 39q^{69} + 18q^{71} - 24q^{72} - 6q^{73} - 6q^{74} - 31q^{75} - 21q^{76} + 10q^{78} - 15q^{79} - 22q^{80} + 32q^{81} - 18q^{82} - 12q^{83} - 9q^{85} - 34q^{86} + q^{87} + 21q^{88} + 4q^{89} - 73q^{90} - 15q^{92} + 33q^{93} + 24q^{94} - 16q^{95} - 5q^{96} + 3q^{97} - 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23025 + 2.13086i 0.869920 + 1.50675i 0.862078 + 0.506776i \(0.169163\pi\)
0.00784213 + 0.999969i \(0.497504\pi\)
\(3\) 1.73025 + 0.0789082i 0.998962 + 0.0455577i
\(4\) −2.02704 + 3.51094i −1.01352 + 1.75547i
\(5\) −1.29679 + 2.24611i −0.579942 + 1.00449i 0.415543 + 0.909573i \(0.363591\pi\)
−0.995485 + 0.0949156i \(0.969742\pi\)
\(6\) 1.96050 + 3.78400i 0.800373 + 1.54481i
\(7\) 0 0
\(8\) −5.05408 −1.78689
\(9\) 2.98755 + 0.273062i 0.995849 + 0.0910208i
\(10\) −6.38151 −2.01801
\(11\) −2.25729 3.90975i −0.680600 1.17883i −0.974798 0.223089i \(-0.928386\pi\)
0.294198 0.955744i \(-0.404947\pi\)
\(12\) −3.78434 + 5.91486i −1.09244 + 1.70747i
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) −2.42101 + 3.78400i −0.625102 + 0.977025i
\(16\) −2.16372 3.74766i −0.540929 0.936916i
\(17\) 0.945916 0.229418 0.114709 0.993399i \(-0.463406\pi\)
0.114709 + 0.993399i \(0.463406\pi\)
\(18\) 3.09358 + 6.70198i 0.729164 + 1.57967i
\(19\) 4.05408 0.930071 0.465035 0.885292i \(-0.346042\pi\)
0.465035 + 0.885292i \(0.346042\pi\)
\(20\) −5.25729 9.10590i −1.17557 2.03614i
\(21\) 0 0
\(22\) 5.55408 9.61996i 1.18413 2.05098i
\(23\) 0.136673 0.236725i 0.0284983 0.0493605i −0.851425 0.524477i \(-0.824261\pi\)
0.879923 + 0.475117i \(0.157594\pi\)
\(24\) −8.74484 0.398809i −1.78503 0.0814065i
\(25\) −0.863327 1.49533i −0.172665 0.299065i
\(26\) 2.46050 0.482545
\(27\) 5.14766 + 0.708209i 0.990668 + 0.136295i
\(28\) 0 0
\(29\) −1.23025 2.13086i −0.228452 0.395691i 0.728897 0.684623i \(-0.240033\pi\)
−0.957350 + 0.288932i \(0.906700\pi\)
\(30\) −11.0416 0.503554i −2.01592 0.0919360i
\(31\) 1.16372 2.01561i 0.209009 0.362015i −0.742393 0.669964i \(-0.766309\pi\)
0.951403 + 0.307949i \(0.0996427\pi\)
\(32\) 0.269748 0.467216i 0.0476851 0.0825930i
\(33\) −3.59718 6.94297i −0.626188 1.20862i
\(34\) 1.16372 + 2.01561i 0.199576 + 0.345675i
\(35\) 0 0
\(36\) −7.01459 + 9.93559i −1.16910 + 1.65593i
\(37\) 1.78074 0.292752 0.146376 0.989229i \(-0.453239\pi\)
0.146376 + 0.989229i \(0.453239\pi\)
\(38\) 4.98755 + 8.63868i 0.809087 + 1.40138i
\(39\) 0.933463 1.45899i 0.149474 0.233625i
\(40\) 6.55408 11.3520i 1.03629 1.79491i
\(41\) −3.20321 + 5.54812i −0.500257 + 0.866471i 0.499743 + 0.866174i \(0.333428\pi\)
−1.00000 0.000297253i \(0.999905\pi\)
\(42\) 0 0
\(43\) 5.21780 + 9.03749i 0.795707 + 1.37820i 0.922389 + 0.386262i \(0.126234\pi\)
−0.126682 + 0.991943i \(0.540433\pi\)
\(44\) 18.3025 2.75921
\(45\) −4.48755 + 6.35624i −0.668964 + 0.947533i
\(46\) 0.672570 0.0991650
\(47\) −6.08113 10.5328i −0.887023 1.53637i −0.843377 0.537323i \(-0.819436\pi\)
−0.0436467 0.999047i \(-0.513898\pi\)
\(48\) −3.44805 6.65514i −0.497683 0.960587i
\(49\) 0 0
\(50\) 2.12422 3.67926i 0.300410 0.520326i
\(51\) 1.63667 + 0.0746406i 0.229180 + 0.0104518i
\(52\) 2.02704 + 3.51094i 0.281100 + 0.486880i
\(53\) −6.27335 −0.861710 −0.430855 0.902421i \(-0.641788\pi\)
−0.430855 + 0.902421i \(0.641788\pi\)
\(54\) 4.82383 + 11.8402i 0.656440 + 1.61125i
\(55\) 11.7089 1.57883
\(56\) 0 0
\(57\) 7.01459 + 0.319901i 0.929105 + 0.0423719i
\(58\) 3.02704 5.24299i 0.397470 0.688438i
\(59\) −1.36333 + 2.36135i −0.177490 + 0.307422i −0.941020 0.338350i \(-0.890131\pi\)
0.763530 + 0.645772i \(0.223464\pi\)
\(60\) −8.37792 16.1704i −1.08158 2.08758i
\(61\) −1.13667 1.96878i −0.145536 0.252076i 0.784037 0.620714i \(-0.213157\pi\)
−0.929573 + 0.368639i \(0.879824\pi\)
\(62\) 5.72665 0.727286
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) 1.29679 + 2.24611i 0.160847 + 0.278595i
\(66\) 10.3691 16.2067i 1.27634 1.99491i
\(67\) 7.90856 13.6980i 0.966184 1.67348i 0.259784 0.965667i \(-0.416349\pi\)
0.706400 0.707813i \(-0.250318\pi\)
\(68\) −1.91741 + 3.32105i −0.232520 + 0.402737i
\(69\) 0.255158 0.398809i 0.0307175 0.0480110i
\(70\) 0 0
\(71\) 3.27335 0.388475 0.194237 0.980955i \(-0.437777\pi\)
0.194237 + 0.980955i \(0.437777\pi\)
\(72\) −15.0993 1.38008i −1.77947 0.162644i
\(73\) 1.50739 0.176427 0.0882134 0.996102i \(-0.471884\pi\)
0.0882134 + 0.996102i \(0.471884\pi\)
\(74\) 2.19076 + 3.79450i 0.254670 + 0.441102i
\(75\) −1.37578 2.65542i −0.158861 0.306621i
\(76\) −8.21780 + 14.2336i −0.942646 + 1.63271i
\(77\) 0 0
\(78\) 4.25729 + 0.194154i 0.482044 + 0.0219836i
\(79\) −7.35447 12.7383i −0.827443 1.43317i −0.900038 0.435811i \(-0.856461\pi\)
0.0725952 0.997361i \(-0.476872\pi\)
\(80\) 11.2235 1.25483
\(81\) 8.85087 + 1.63157i 0.983430 + 0.181286i
\(82\) −15.7630 −1.74074
\(83\) −0.472958 0.819187i −0.0519139 0.0899175i 0.838901 0.544285i \(-0.183199\pi\)
−0.890815 + 0.454367i \(0.849865\pi\)
\(84\) 0 0
\(85\) −1.22665 + 2.12463i −0.133049 + 0.230448i
\(86\) −12.8384 + 22.2368i −1.38440 + 2.39786i
\(87\) −1.96050 3.78400i −0.210188 0.405688i
\(88\) 11.4086 + 19.7602i 1.21616 + 2.10644i
\(89\) 14.3566 1.52180 0.760899 0.648871i \(-0.224758\pi\)
0.760899 + 0.648871i \(0.224758\pi\)
\(90\) −19.0651 1.74255i −2.00964 0.183681i
\(91\) 0 0
\(92\) 0.554084 + 0.959702i 0.0577673 + 0.100056i
\(93\) 2.17257 3.39569i 0.225285 0.352117i
\(94\) 14.9626 25.9161i 1.54328 2.67304i
\(95\) −5.25729 + 9.10590i −0.539387 + 0.934246i
\(96\) 0.503599 0.787117i 0.0513983 0.0803348i
\(97\) −5.74484 9.95036i −0.583300 1.01031i −0.995085 0.0990246i \(-0.968428\pi\)
0.411785 0.911281i \(-0.364906\pi\)
\(98\) 0 0
\(99\) −5.67617 12.2969i −0.570476 1.23589i
\(100\) 7.00000 0.700000
\(101\) −1.83988 3.18677i −0.183075 0.317096i 0.759851 0.650097i \(-0.225272\pi\)
−0.942926 + 0.333002i \(0.891939\pi\)
\(102\) 1.85447 + 3.57935i 0.183620 + 0.354408i
\(103\) −4.86333 + 8.42353i −0.479198 + 0.829995i −0.999715 0.0238560i \(-0.992406\pi\)
0.520518 + 0.853851i \(0.325739\pi\)
\(104\) −2.52704 + 4.37697i −0.247797 + 0.429197i
\(105\) 0 0
\(106\) −7.71780 13.3676i −0.749619 1.29838i
\(107\) −1.37432 −0.132860 −0.0664301 0.997791i \(-0.521161\pi\)
−0.0664301 + 0.997791i \(0.521161\pi\)
\(108\) −12.9210 + 16.6376i −1.24332 + 1.60095i
\(109\) −3.39922 −0.325587 −0.162793 0.986660i \(-0.552050\pi\)
−0.162793 + 0.986660i \(0.552050\pi\)
\(110\) 14.4050 + 24.9501i 1.37346 + 2.37890i
\(111\) 3.08113 + 0.140515i 0.292448 + 0.0133371i
\(112\) 0 0
\(113\) −5.19436 + 8.99689i −0.488644 + 0.846356i −0.999915 0.0130636i \(-0.995842\pi\)
0.511271 + 0.859420i \(0.329175\pi\)
\(114\) 7.94805 + 15.3407i 0.744403 + 1.43678i
\(115\) 0.354473 + 0.613964i 0.0330547 + 0.0572525i
\(116\) 9.97509 0.926164
\(117\) 1.73025 2.45076i 0.159962 0.226573i
\(118\) −6.70895 −0.617608
\(119\) 0 0
\(120\) 12.2360 19.1247i 1.11699 1.74584i
\(121\) −4.69076 + 8.12463i −0.426432 + 0.738603i
\(122\) 2.79679 4.84418i 0.253209 0.438572i
\(123\) −5.98016 + 9.34689i −0.539212 + 0.842781i
\(124\) 4.71780 + 8.17147i 0.423671 + 0.733820i
\(125\) −8.48968 −0.759340
\(126\) 0 0
\(127\) 0.672570 0.0596809 0.0298405 0.999555i \(-0.490500\pi\)
0.0298405 + 0.999555i \(0.490500\pi\)
\(128\) −9.55408 16.5482i −0.844470 1.46266i
\(129\) 8.31498 + 16.0489i 0.732093 + 1.41302i
\(130\) −3.19076 + 5.52655i −0.279848 + 0.484711i
\(131\) 3.95691 6.85356i 0.345717 0.598799i −0.639767 0.768569i \(-0.720969\pi\)
0.985484 + 0.169770i \(0.0543026\pi\)
\(132\) 31.6680 + 1.44422i 2.75634 + 0.125703i
\(133\) 0 0
\(134\) 38.9181 3.36201
\(135\) −8.26615 + 10.6438i −0.711437 + 0.916072i
\(136\) −4.78074 −0.409945
\(137\) 1.83628 + 3.18054i 0.156884 + 0.271732i 0.933744 0.357943i \(-0.116522\pi\)
−0.776859 + 0.629674i \(0.783188\pi\)
\(138\) 1.16372 + 0.0530713i 0.0990620 + 0.00451773i
\(139\) −1.02704 + 1.77889i −0.0871126 + 0.150883i −0.906289 0.422658i \(-0.861097\pi\)
0.819177 + 0.573541i \(0.194431\pi\)
\(140\) 0 0
\(141\) −9.69076 18.7043i −0.816109 1.57519i
\(142\) 4.02704 + 6.97504i 0.337942 + 0.585332i
\(143\) −4.51459 −0.377529
\(144\) −5.44085 11.7872i −0.453405 0.982263i
\(145\) 6.38151 0.529956
\(146\) 1.85447 + 3.21204i 0.153477 + 0.265830i
\(147\) 0 0
\(148\) −3.60963 + 6.25206i −0.296710 + 0.513917i
\(149\) 6.77188 11.7292i 0.554774 0.960897i −0.443147 0.896449i \(-0.646138\pi\)
0.997921 0.0644482i \(-0.0205287\pi\)
\(150\) 3.96576 6.19843i 0.323803 0.506099i
\(151\) −4.96410 8.59808i −0.403973 0.699702i 0.590228 0.807236i \(-0.299038\pi\)
−0.994201 + 0.107535i \(0.965704\pi\)
\(152\) −20.4897 −1.66193
\(153\) 2.82597 + 0.258294i 0.228466 + 0.0208818i
\(154\) 0 0
\(155\) 3.01819 + 5.22765i 0.242427 + 0.419895i
\(156\) 3.23025 + 6.23476i 0.258627 + 0.499181i
\(157\) 3.02704 5.24299i 0.241584 0.418436i −0.719581 0.694408i \(-0.755666\pi\)
0.961166 + 0.275972i \(0.0889996\pi\)
\(158\) 18.0957 31.3427i 1.43962 2.49349i
\(159\) −10.8545 0.495019i −0.860816 0.0392575i
\(160\) 0.699612 + 1.21176i 0.0553092 + 0.0957983i
\(161\) 0 0
\(162\) 7.41216 + 20.8672i 0.582354 + 1.63948i
\(163\) 17.8171 1.39554 0.697772 0.716320i \(-0.254175\pi\)
0.697772 + 0.716320i \(0.254175\pi\)
\(164\) −12.9861 22.4926i −1.01404 1.75637i
\(165\) 20.2594 + 0.923932i 1.57719 + 0.0719280i
\(166\) 1.16372 2.01561i 0.0903218 0.156442i
\(167\) −4.23385 + 7.33325i −0.327625 + 0.567464i −0.982040 0.188672i \(-0.939582\pi\)
0.654415 + 0.756136i \(0.272915\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) −6.03638 −0.462969
\(171\) 12.1118 + 1.10702i 0.926210 + 0.0846558i
\(172\) −42.3068 −3.22586
\(173\) 8.67830 + 15.0313i 0.659799 + 1.14281i 0.980667 + 0.195682i \(0.0626920\pi\)
−0.320868 + 0.947124i \(0.603975\pi\)
\(174\) 5.65126 8.83284i 0.428421 0.669616i
\(175\) 0 0
\(176\) −9.76829 + 16.9192i −0.736312 + 1.27533i
\(177\) −2.54523 + 3.97816i −0.191311 + 0.299017i
\(178\) 17.6623 + 30.5919i 1.32384 + 2.29296i
\(179\) −11.3494 −0.848295 −0.424147 0.905593i \(-0.639426\pi\)
−0.424147 + 0.905593i \(0.639426\pi\)
\(180\) −13.2199 28.6399i −0.985356 2.13469i
\(181\) −21.8889 −1.62699 −0.813495 0.581572i \(-0.802438\pi\)
−0.813495 + 0.581572i \(0.802438\pi\)
\(182\) 0 0
\(183\) −1.81138 3.49617i −0.133901 0.258444i
\(184\) −0.690757 + 1.19643i −0.0509233 + 0.0882018i
\(185\) −2.30924 + 3.99973i −0.169779 + 0.294066i
\(186\) 9.90856 + 0.451880i 0.726531 + 0.0331335i
\(187\) −2.13521 3.69829i −0.156142 0.270446i
\(188\) 49.3068 3.59607
\(189\) 0 0
\(190\) −25.8712 −1.87689
\(191\) 0.350874 + 0.607731i 0.0253883 + 0.0439739i 0.878440 0.477852i \(-0.158584\pi\)
−0.853052 + 0.521826i \(0.825251\pi\)
\(192\) −12.6783 0.578195i −0.914978 0.0417276i
\(193\) −6.07227 + 10.5175i −0.437092 + 0.757065i −0.997464 0.0711760i \(-0.977325\pi\)
0.560372 + 0.828241i \(0.310658\pi\)
\(194\) 14.1352 24.4829i 1.01485 1.75777i
\(195\) 2.06654 + 3.98866i 0.147988 + 0.285634i
\(196\) 0 0
\(197\) −16.4107 −1.16921 −0.584607 0.811317i \(-0.698751\pi\)
−0.584607 + 0.811317i \(0.698751\pi\)
\(198\) 19.2199 27.2235i 1.36590 1.93469i
\(199\) −22.7060 −1.60959 −0.804794 0.593555i \(-0.797724\pi\)
−0.804794 + 0.593555i \(0.797724\pi\)
\(200\) 4.36333 + 7.55750i 0.308534 + 0.534396i
\(201\) 14.7647 23.0770i 1.04142 1.62773i
\(202\) 4.52704 7.84107i 0.318522 0.551696i
\(203\) 0 0
\(204\) −3.57966 + 5.59496i −0.250627 + 0.391726i
\(205\) −8.30778 14.3895i −0.580241 1.00501i
\(206\) −23.9325 −1.66745
\(207\) 0.472958 0.669906i 0.0328728 0.0465617i
\(208\) −4.32743 −0.300053
\(209\) −9.15126 15.8505i −0.633006 1.09640i
\(210\) 0 0
\(211\) −2.28074 + 3.95035i −0.157012 + 0.271954i −0.933790 0.357822i \(-0.883520\pi\)
0.776778 + 0.629775i \(0.216853\pi\)
\(212\) 12.7163 22.0253i 0.873362 1.51271i
\(213\) 5.66372 + 0.258294i 0.388071 + 0.0176980i
\(214\) −1.69076 2.92848i −0.115578 0.200187i
\(215\) −27.0656 −1.84586
\(216\) −26.0167 3.57935i −1.77021 0.243544i
\(217\) 0 0
\(218\) −4.18190 7.24327i −0.283234 0.490576i
\(219\) 2.60817 + 0.118946i 0.176244 + 0.00803760i
\(220\) −23.7345 + 41.1094i −1.60018 + 2.77160i
\(221\) 0.472958 0.819187i 0.0318146 0.0551045i
\(222\) 3.49115 + 6.73832i 0.234310 + 0.452246i
\(223\) 6.66225 + 11.5394i 0.446137 + 0.772733i 0.998131 0.0611159i \(-0.0194659\pi\)
−0.551993 + 0.833849i \(0.686133\pi\)
\(224\) 0 0
\(225\) −2.17091 4.70310i −0.144727 0.313540i
\(226\) −25.5615 −1.70032
\(227\) 0.690757 + 1.19643i 0.0458472 + 0.0794096i 0.888038 0.459769i \(-0.152068\pi\)
−0.842191 + 0.539179i \(0.818735\pi\)
\(228\) −15.3420 + 23.9793i −1.01605 + 1.58807i
\(229\) −8.98968 + 15.5706i −0.594055 + 1.02893i 0.399625 + 0.916679i \(0.369141\pi\)
−0.993679 + 0.112254i \(0.964193\pi\)
\(230\) −0.872181 + 1.51066i −0.0575099 + 0.0996101i
\(231\) 0 0
\(232\) 6.21780 + 10.7695i 0.408219 + 0.707055i
\(233\) −18.9823 −1.24357 −0.621786 0.783187i \(-0.713592\pi\)
−0.621786 + 0.783187i \(0.713592\pi\)
\(234\) 7.35087 + 0.671871i 0.480542 + 0.0439216i
\(235\) 31.5438 2.05769
\(236\) −5.52704 9.57312i −0.359780 0.623157i
\(237\) −11.7199 22.6208i −0.761292 1.46938i
\(238\) 0 0
\(239\) −2.44592 + 4.23645i −0.158213 + 0.274033i −0.934224 0.356686i \(-0.883907\pi\)
0.776011 + 0.630719i \(0.217240\pi\)
\(240\) 19.4195 + 0.885629i 1.25353 + 0.0571671i
\(241\) −13.0797 22.6546i −0.842535 1.45931i −0.887745 0.460336i \(-0.847729\pi\)
0.0452094 0.998978i \(-0.485604\pi\)
\(242\) −23.0833 −1.48385
\(243\) 15.1855 + 3.52144i 0.974150 + 0.225901i
\(244\) 9.21634 0.590016
\(245\) 0 0
\(246\) −27.2740 1.24383i −1.73893 0.0793039i
\(247\) 2.02704 3.51094i 0.128978 0.223396i
\(248\) −5.88151 + 10.1871i −0.373477 + 0.646880i
\(249\) −0.753696 1.45472i −0.0477635 0.0921892i
\(250\) −10.4445 18.0903i −0.660565 1.14413i
\(251\) −18.4576 −1.16503 −0.582516 0.812819i \(-0.697932\pi\)
−0.582516 + 0.812819i \(0.697932\pi\)
\(252\) 0 0
\(253\) −1.23405 −0.0775838
\(254\) 0.827430 + 1.43315i 0.0519176 + 0.0899239i
\(255\) −2.29007 + 3.57935i −0.143410 + 0.224147i
\(256\) 16.1804 28.0253i 1.01128 1.75158i
\(257\) −5.86693 + 10.1618i −0.365969 + 0.633876i −0.988931 0.148375i \(-0.952596\pi\)
0.622962 + 0.782252i \(0.285929\pi\)
\(258\) −23.9684 + 37.4622i −1.49221 + 2.33230i
\(259\) 0 0
\(260\) −10.5146 −0.652087
\(261\) −3.09358 6.70198i −0.191488 0.414842i
\(262\) 19.4720 1.20298
\(263\) 3.76089 + 6.51406i 0.231907 + 0.401674i 0.958369 0.285532i \(-0.0921703\pi\)
−0.726463 + 0.687206i \(0.758837\pi\)
\(264\) 18.1804 + 35.0904i 1.11893 + 2.15966i
\(265\) 8.13521 14.0906i 0.499742 0.865579i
\(266\) 0 0
\(267\) 24.8406 + 1.13285i 1.52022 + 0.0693296i
\(268\) 32.0620 + 55.5329i 1.95850 + 3.39221i
\(269\) 18.8348 1.14838 0.574190 0.818722i \(-0.305317\pi\)
0.574190 + 0.818722i \(0.305317\pi\)
\(270\) −32.8499 4.51945i −1.99918 0.275045i
\(271\) 23.9823 1.45682 0.728410 0.685141i \(-0.240260\pi\)
0.728410 + 0.685141i \(0.240260\pi\)
\(272\) −2.04669 3.54498i −0.124099 0.214946i
\(273\) 0 0
\(274\) −4.51819 + 7.82573i −0.272954 + 0.472770i
\(275\) −3.89757 + 6.75078i −0.235032 + 0.407088i
\(276\) 0.882977 + 1.70425i 0.0531490 + 0.102584i
\(277\) −3.58113 6.20269i −0.215169 0.372684i 0.738156 0.674630i \(-0.235697\pi\)
−0.953325 + 0.301947i \(0.902364\pi\)
\(278\) −5.05408 −0.303124
\(279\) 4.02704 5.70397i 0.241093 0.341488i
\(280\) 0 0
\(281\) −7.44085 12.8879i −0.443884 0.768830i 0.554090 0.832457i \(-0.313067\pi\)
−0.997974 + 0.0636271i \(0.979733\pi\)
\(282\) 27.9341 43.6606i 1.66345 2.59995i
\(283\) 9.99854 17.3180i 0.594351 1.02945i −0.399287 0.916826i \(-0.630742\pi\)
0.993638 0.112621i \(-0.0359245\pi\)
\(284\) −6.63521 + 11.4925i −0.393727 + 0.681956i
\(285\) −9.81498 + 15.3407i −0.581389 + 0.908703i
\(286\) −5.55408 9.61996i −0.328420 0.568840i
\(287\) 0 0
\(288\) 0.933463 1.32217i 0.0550048 0.0779098i
\(289\) −16.1052 −0.947367
\(290\) 7.85087 + 13.5981i 0.461019 + 0.798509i
\(291\) −9.15486 17.6699i −0.536667 1.03583i
\(292\) −3.05555 + 5.29236i −0.178812 + 0.309712i
\(293\) 7.53278 13.0472i 0.440070 0.762223i −0.557625 0.830093i \(-0.688287\pi\)
0.997694 + 0.0678705i \(0.0216205\pi\)
\(294\) 0 0
\(295\) −3.53590 6.12435i −0.205868 0.356574i
\(296\) −9.00000 −0.523114
\(297\) −8.85087 21.7247i −0.513580 1.26060i
\(298\) 33.3245 1.93044
\(299\) −0.136673 0.236725i −0.00790401 0.0136901i
\(300\) 12.1118 + 0.552358i 0.699273 + 0.0318904i
\(301\) 0 0
\(302\) 12.2142 21.1556i 0.702848 1.21737i
\(303\) −2.93200 5.65910i −0.168439 0.325107i
\(304\) −8.77188 15.1933i −0.503102 0.871398i
\(305\) 5.89610 0.337610
\(306\) 2.92627 + 6.33951i 0.167283 + 0.362406i
\(307\) 27.2704 1.55641 0.778203 0.628013i \(-0.216132\pi\)
0.778203 + 0.628013i \(0.216132\pi\)
\(308\) 0 0
\(309\) −9.07947 + 14.1911i −0.516513 + 0.807302i
\(310\) −7.42627 + 12.8627i −0.421784 + 0.730551i
\(311\) −7.99115 + 13.8411i −0.453136 + 0.784855i −0.998579 0.0532931i \(-0.983028\pi\)
0.545443 + 0.838148i \(0.316362\pi\)
\(312\) −4.71780 + 7.37385i −0.267093 + 0.417462i
\(313\) 5.79893 + 10.0440i 0.327775 + 0.567722i 0.982070 0.188517i \(-0.0603680\pi\)
−0.654295 + 0.756239i \(0.727035\pi\)
\(314\) 14.8961 0.840636
\(315\) 0 0
\(316\) 59.6313 3.35452
\(317\) 1.00885 + 1.74739i 0.0566629 + 0.0981430i 0.892965 0.450125i \(-0.148621\pi\)
−0.836303 + 0.548268i \(0.815287\pi\)
\(318\) −12.2989 23.7384i −0.689690 1.33118i
\(319\) −5.55408 + 9.61996i −0.310969 + 0.538614i
\(320\) 9.50214 16.4582i 0.531186 0.920040i
\(321\) −2.37792 0.108445i −0.132722 0.00605281i
\(322\) 0 0
\(323\) 3.83482 0.213375
\(324\) −23.6694 + 27.7676i −1.31497 + 1.54265i
\(325\) −1.72665 −0.0957775
\(326\) 21.9195 + 37.9658i 1.21401 + 2.10273i
\(327\) −5.88151 0.268227i −0.325249 0.0148330i
\(328\) 16.1893 28.0407i 0.893904 1.54829i
\(329\) 0 0
\(330\) 22.9554 + 44.3067i 1.26366 + 2.43900i
\(331\) 9.85447 + 17.0684i 0.541651 + 0.938167i 0.998809 + 0.0487815i \(0.0155338\pi\)
−0.457159 + 0.889385i \(0.651133\pi\)
\(332\) 3.83482 0.210463
\(333\) 5.32004 + 0.486253i 0.291536 + 0.0266465i
\(334\) −20.8348 −1.14003
\(335\) 20.5115 + 35.5269i 1.12066 + 1.94104i
\(336\) 0 0
\(337\) 14.5256 25.1590i 0.791259 1.37050i −0.133929 0.990991i \(-0.542759\pi\)
0.925188 0.379509i \(-0.123907\pi\)
\(338\) −14.7630 + 25.5703i −0.803003 + 1.39084i
\(339\) −9.69748 + 15.1570i −0.526695 + 0.823216i
\(340\) −4.97296 8.61342i −0.269697 0.467128i
\(341\) −10.5074 −0.569007
\(342\) 12.5416 + 27.1704i 0.678174 + 1.46921i
\(343\) 0 0
\(344\) −26.3712 45.6763i −1.42184 2.46270i
\(345\) 0.564880 + 1.09028i 0.0304121 + 0.0586989i
\(346\) −21.3530 + 36.9845i −1.14794 + 1.98830i
\(347\) −14.5416 + 25.1868i −0.780636 + 1.35210i 0.150936 + 0.988544i \(0.451771\pi\)
−0.931572 + 0.363557i \(0.881562\pi\)
\(348\) 17.2594 + 0.787117i 0.925203 + 0.0421939i
\(349\) 12.3815 + 21.4454i 0.662767 + 1.14795i 0.979885 + 0.199561i \(0.0639515\pi\)
−0.317118 + 0.948386i \(0.602715\pi\)
\(350\) 0 0
\(351\) 3.18716 4.10390i 0.170118 0.219050i
\(352\) −2.43560 −0.129818
\(353\) −16.6513 28.8408i −0.886257 1.53504i −0.844266 0.535925i \(-0.819963\pi\)
−0.0419914 0.999118i \(-0.513370\pi\)
\(354\) −11.6082 0.529391i −0.616967 0.0281368i
\(355\) −4.24484 + 7.35228i −0.225293 + 0.390219i
\(356\) −29.1015 + 50.4052i −1.54237 + 2.67147i
\(357\) 0 0
\(358\) −13.9626 24.1840i −0.737949 1.27816i
\(359\) 25.5366 1.34777 0.673884 0.738837i \(-0.264625\pi\)
0.673884 + 0.738837i \(0.264625\pi\)
\(360\) 22.6804 32.1250i 1.19536 1.69314i
\(361\) −2.56440 −0.134968
\(362\) −26.9289 46.6422i −1.41535 2.45146i
\(363\) −8.75729 + 13.6875i −0.459639 + 0.718409i
\(364\) 0 0
\(365\) −1.95477 + 3.38576i −0.102317 + 0.177219i
\(366\) 5.22140 8.16097i 0.272927 0.426581i
\(367\) 13.7252 + 23.7727i 0.716449 + 1.24093i 0.962398 + 0.271644i \(0.0875672\pi\)
−0.245949 + 0.969283i \(0.579100\pi\)
\(368\) −1.18289 −0.0616622
\(369\) −11.0847 + 15.7006i −0.577048 + 0.817341i
\(370\) −11.3638 −0.590776
\(371\) 0 0
\(372\) 7.51819 + 14.5110i 0.389800 + 0.752359i
\(373\) −8.16372 + 14.1400i −0.422701 + 0.732140i −0.996203 0.0870646i \(-0.972251\pi\)
0.573502 + 0.819204i \(0.305585\pi\)
\(374\) 5.25370 9.09967i 0.271662 0.470533i
\(375\) −14.6893 0.669906i −0.758552 0.0345938i
\(376\) 30.7345 + 53.2338i 1.58501 + 2.74532i
\(377\) −2.46050 −0.126722
\(378\) 0 0
\(379\) 12.0364 0.618267 0.309134 0.951019i \(-0.399961\pi\)
0.309134 + 0.951019i \(0.399961\pi\)
\(380\) −21.3135 36.9161i −1.09336 1.89376i
\(381\) 1.16372 + 0.0530713i 0.0596189 + 0.00271892i
\(382\) −0.863327 + 1.49533i −0.0441716 + 0.0765075i
\(383\) −6.21780 + 10.7695i −0.317715 + 0.550298i −0.980011 0.198944i \(-0.936249\pi\)
0.662296 + 0.749242i \(0.269582\pi\)
\(384\) −15.2252 29.3864i −0.776957 1.49962i
\(385\) 0 0
\(386\) −29.8817 −1.52094
\(387\) 13.1206 + 28.4247i 0.666959 + 1.44491i
\(388\) 46.5801 2.36475
\(389\) −10.3004 17.8408i −0.522250 0.904564i −0.999665 0.0258860i \(-0.991759\pi\)
0.477414 0.878678i \(-0.341574\pi\)
\(390\) −5.95691 + 9.31056i −0.301640 + 0.471458i
\(391\) 0.129281 0.223922i 0.00653803 0.0113242i
\(392\) 0 0
\(393\) 7.38725 11.5462i 0.372637 0.582427i
\(394\) −20.1893 34.9689i −1.01712 1.76171i
\(395\) 38.1488 1.91948
\(396\) 54.6797 + 4.99773i 2.74776 + 0.251145i
\(397\) 23.6372 1.18631 0.593157 0.805087i \(-0.297881\pi\)
0.593157 + 0.805087i \(0.297881\pi\)
\(398\) −27.9341 48.3833i −1.40021 2.42524i
\(399\) 0 0
\(400\) −3.73599 + 6.47092i −0.186799 + 0.323546i
\(401\) 1.28220 2.22084i 0.0640300 0.110903i −0.832233 0.554426i \(-0.812938\pi\)
0.896263 + 0.443522i \(0.146271\pi\)
\(402\) 67.3381 + 3.07096i 3.35852 + 0.153165i
\(403\) −1.16372 2.01561i −0.0579688 0.100405i
\(404\) 14.9181 0.742202
\(405\) −15.1424 + 17.7642i −0.752432 + 0.882710i
\(406\) 0 0
\(407\) −4.01965 6.96224i −0.199247 0.345105i
\(408\) −8.27188 0.377240i −0.409519 0.0186761i
\(409\) −17.1623 + 29.7259i −0.848619 + 1.46985i 0.0338223 + 0.999428i \(0.489232\pi\)
−0.882441 + 0.470423i \(0.844101\pi\)
\(410\) 20.4413 35.4054i 1.00953 1.74855i
\(411\) 2.92627 + 5.64803i 0.144342 + 0.278597i
\(412\) −19.7163 34.1497i −0.971354 1.68243i
\(413\) 0 0
\(414\) 2.00933 + 0.183653i 0.0987533 + 0.00902607i
\(415\) 2.45331 0.120428
\(416\) −0.269748 0.467216i −0.0132255 0.0229072i
\(417\) −1.91741 + 2.99689i −0.0938960 + 0.146758i
\(418\) 22.5167 39.0001i 1.10133 1.90756i
\(419\) 2.02850 3.51347i 0.0990989 0.171644i −0.812213 0.583361i \(-0.801737\pi\)
0.911312 + 0.411717i \(0.135071\pi\)
\(420\) 0 0
\(421\) 10.5344 + 18.2462i 0.513417 + 0.889264i 0.999879 + 0.0155624i \(0.00495387\pi\)
−0.486462 + 0.873702i \(0.661713\pi\)
\(422\) −11.2235 −0.546353
\(423\) −15.2915 33.1278i −0.743500 1.61073i
\(424\) 31.7060 1.53978
\(425\) −0.816635 1.41445i −0.0396126 0.0686110i
\(426\) 6.41741 + 12.3863i 0.310925 + 0.600121i
\(427\) 0 0
\(428\) 2.78580 4.82515i 0.134657 0.233232i
\(429\) −7.81138 0.356238i −0.377137 0.0171993i
\(430\) −33.2975 57.6729i −1.60575 2.78123i
\(431\) 22.6185 1.08949 0.544747 0.838600i \(-0.316626\pi\)
0.544747 + 0.838600i \(0.316626\pi\)
\(432\) −8.48395 20.8241i −0.408184 1.00190i
\(433\) −2.41789 −0.116196 −0.0580982 0.998311i \(-0.518504\pi\)
−0.0580982 + 0.998311i \(0.518504\pi\)
\(434\) 0 0
\(435\) 11.0416 + 0.503554i 0.529406 + 0.0241436i
\(436\) 6.89037 11.9345i 0.329989 0.571557i
\(437\) 0.554084 0.959702i 0.0265054 0.0459088i
\(438\) 2.95525 + 5.70397i 0.141207 + 0.272546i
\(439\) −11.7448 20.3427i −0.560551 0.970902i −0.997448 0.0713911i \(-0.977256\pi\)
0.436898 0.899511i \(-0.356077\pi\)
\(440\) −59.1780 −2.82120
\(441\) 0 0
\(442\) 2.32743 0.110705
\(443\) 6.70895 + 11.6202i 0.318752 + 0.552094i 0.980228 0.197872i \(-0.0634031\pi\)
−0.661476 + 0.749966i \(0.730070\pi\)
\(444\) −6.73891 + 10.5328i −0.319815 + 0.499866i
\(445\) −18.6175 + 32.2465i −0.882554 + 1.52863i
\(446\) −16.3925 + 28.3927i −0.776208 + 1.34443i
\(447\) 12.6426 19.7602i 0.597975 0.934625i
\(448\) 0 0
\(449\) −9.16225 −0.432393 −0.216197 0.976350i \(-0.569365\pi\)
−0.216197 + 0.976350i \(0.569365\pi\)
\(450\) 7.35087 10.4119i 0.346524 0.490822i
\(451\) 28.9224 1.36190
\(452\) −21.0584 36.4741i −0.990502 1.71560i
\(453\) −7.91069 15.2686i −0.371677 0.717379i
\(454\) −1.69961 + 2.94381i −0.0797667 + 0.138160i
\(455\) 0 0
\(456\) −35.4523 1.61680i −1.66021 0.0757138i
\(457\) −4.40856 7.63584i −0.206224 0.357190i 0.744298 0.667847i \(-0.232784\pi\)
−0.950522 + 0.310658i \(0.899451\pi\)
\(458\) −44.2383 −2.06712
\(459\) 4.86926 + 0.669906i 0.227277 + 0.0312685i
\(460\) −2.87412 −0.134007
\(461\) −2.82957 4.90095i −0.131786 0.228260i 0.792579 0.609769i \(-0.208738\pi\)
−0.924365 + 0.381509i \(0.875405\pi\)
\(462\) 0 0
\(463\) −7.86333 + 13.6197i −0.365440 + 0.632960i −0.988847 0.148937i \(-0.952415\pi\)
0.623407 + 0.781898i \(0.285748\pi\)
\(464\) −5.32383 + 9.22115i −0.247153 + 0.428081i
\(465\) 4.80972 + 9.28332i 0.223045 + 0.430504i
\(466\) −23.3530 40.4486i −1.08181 1.87375i
\(467\) 21.9971 1.01790 0.508952 0.860795i \(-0.330033\pi\)
0.508952 + 0.860795i \(0.330033\pi\)
\(468\) 5.09718 + 11.0426i 0.235617 + 0.510445i
\(469\) 0 0
\(470\) 38.8068 + 67.2153i 1.79002 + 3.10041i
\(471\) 5.65126 8.83284i 0.260396 0.406996i
\(472\) 6.89037 11.9345i 0.317155 0.549328i
\(473\) 23.5562 40.8006i 1.08312 1.87601i
\(474\) 33.7834 52.8029i 1.55172 2.42532i
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) −18.7419 1.71301i −0.858133 0.0784336i
\(478\) −12.0364 −0.550531
\(479\) 12.4875 + 21.6291i 0.570571 + 0.988257i 0.996507 + 0.0835043i \(0.0266112\pi\)
−0.425937 + 0.904753i \(0.640055\pi\)
\(480\) 1.11489 + 2.15186i 0.0508874 + 0.0982186i
\(481\) 0.890369 1.54216i 0.0405973 0.0703166i
\(482\) 32.1826 55.7419i 1.46588 2.53897i
\(483\) 0 0
\(484\) −19.0167 32.9379i −0.864397 1.49718i
\(485\) 29.7994 1.35312
\(486\) 11.1783 + 36.6904i 0.507058 + 1.66431i
\(487\) −17.5979 −0.797435 −0.398717 0.917074i \(-0.630545\pi\)
−0.398717 + 0.917074i \(0.630545\pi\)
\(488\) 5.74484 + 9.95036i 0.260057 + 0.450432i
\(489\) 30.8281 + 1.40592i 1.39410 + 0.0635778i
\(490\) 0 0
\(491\) −6.89757 + 11.9469i −0.311283 + 0.539158i −0.978640 0.205580i \(-0.934092\pi\)
0.667358 + 0.744737i \(0.267425\pi\)
\(492\) −20.6944 39.9425i −0.932974 1.80075i
\(493\) −1.16372 2.01561i −0.0524111 0.0907787i
\(494\) 9.97509 0.448801
\(495\) 34.9810 + 3.19727i 1.57228 + 0.143707i
\(496\) −10.0718 −0.452237
\(497\) 0 0
\(498\) 2.17257 3.39569i 0.0973552 0.152165i
\(499\) −6.54377 + 11.3341i −0.292939 + 0.507386i −0.974503 0.224373i \(-0.927967\pi\)
0.681564 + 0.731758i \(0.261300\pi\)
\(500\) 17.2089 29.8068i 0.769607 1.33300i
\(501\) −7.90428 + 12.3543i −0.353137 + 0.551949i
\(502\) −22.7075 39.3305i −1.01348 1.75541i
\(503\) 22.3068 0.994611 0.497305 0.867576i \(-0.334323\pi\)
0.497305 + 0.867576i \(0.334323\pi\)
\(504\) 0 0
\(505\) 9.54377 0.424692
\(506\) −1.51819 2.62958i −0.0674917 0.116899i
\(507\) 9.56148 + 18.4548i 0.424640 + 0.819605i
\(508\) −1.36333 + 2.36135i −0.0604879 + 0.104768i
\(509\) −7.94659 + 13.7639i −0.352226 + 0.610074i −0.986639 0.162920i \(-0.947909\pi\)
0.634413 + 0.772994i \(0.281242\pi\)
\(510\) −10.4445 0.476320i −0.462488 0.0210918i
\(511\) 0 0
\(512\) 41.4078 1.82998
\(513\) 20.8691 + 2.87114i 0.921392 + 0.126764i
\(514\) −28.8712 −1.27345
\(515\) −12.6134 21.8471i −0.555814 0.962698i
\(516\) −73.2014 3.33836i −3.22251 0.146963i
\(517\) −27.4538 + 47.5514i −1.20742 + 2.09131i
\(518\) 0 0
\(519\) 13.8296 + 26.6927i 0.607051 + 1.17168i
\(520\) −6.55408 11.3520i −0.287416 0.497818i
\(521\) −4.41789 −0.193551 −0.0967756 0.995306i \(-0.530853\pi\)
−0.0967756 + 0.995306i \(0.530853\pi\)
\(522\) 10.4751 14.8371i 0.458482 0.649403i
\(523\) −25.2733 −1.10513 −0.552563 0.833471i \(-0.686350\pi\)
−0.552563 + 0.833471i \(0.686350\pi\)
\(524\) 16.0416 + 27.7849i 0.700782 + 1.21379i
\(525\) 0 0
\(526\) −9.25370 + 16.0279i −0.403480 + 0.698848i
\(527\) 1.10078 1.90660i 0.0479506 0.0830528i
\(528\) −18.2367 + 28.5036i −0.793649 + 1.24046i
\(529\) 11.4626 + 19.8539i 0.498376 + 0.863212i
\(530\) 40.0335 1.73894
\(531\) −4.71780 + 6.68238i −0.204735 + 0.289990i
\(532\) 0 0
\(533\) 3.20321 + 5.54812i 0.138746 + 0.240316i
\(534\) 28.1462 + 54.3254i 1.21801 + 2.35089i
\(535\) 1.78220 3.08686i 0.0770513 0.133457i
\(536\) −39.9705 + 69.2310i −1.72646 + 2.99032i
\(537\) −19.6373 0.895562i −0.847414 0.0386464i
\(538\) 23.1716 + 40.1344i 0.998998 + 1.73032i
\(539\) 0 0
\(540\) −20.6139 50.5974i −0.887081 2.17736i
\(541\) −3.43852 −0.147834 −0.0739168 0.997264i \(-0.523550\pi\)
−0.0739168 + 0.997264i \(0.523550\pi\)
\(542\) 29.5043 + 51.1029i 1.26732 + 2.19506i
\(543\) −37.8733 1.72722i −1.62530 0.0741219i
\(544\) 0.255158 0.441947i 0.0109398 0.0189483i
\(545\) 4.40808 7.63501i 0.188821 0.327048i
\(546\) 0 0
\(547\) 3.46410 + 6.00000i 0.148114 + 0.256542i 0.930531 0.366214i \(-0.119346\pi\)
−0.782416 + 0.622756i \(0.786013\pi\)
\(548\) −14.8889 −0.636023
\(549\) −2.85827 6.19219i −0.121988 0.264276i
\(550\) −19.1800 −0.817836
\(551\) −4.98755 8.63868i −0.212477 0.368020i
\(552\) −1.28959 + 2.01561i −0.0548887 + 0.0857902i
\(553\) 0 0
\(554\) 8.81138 15.2618i 0.374360 0.648410i
\(555\) −4.31118 + 6.73832i −0.183000 + 0.286026i
\(556\) −4.16372 7.21177i −0.176581 0.305847i
\(557\) 33.5835 1.42298 0.711488 0.702698i \(-0.248021\pi\)
0.711488 + 0.702698i \(0.248021\pi\)
\(558\) 17.1086 + 1.56373i 0.724267 + 0.0661981i
\(559\) 10.4356 0.441379
\(560\) 0 0
\(561\) −3.40263 6.56747i −0.143659 0.277279i
\(562\) 18.3083 31.7108i 0.772287 1.33764i
\(563\) 21.2396 36.7880i 0.895142 1.55043i 0.0615128 0.998106i \(-0.480407\pi\)
0.833629 0.552325i \(-0.186259\pi\)
\(564\) 85.3132 + 3.89071i 3.59233 + 0.163829i
\(565\) −13.4720 23.3341i −0.566770 0.981675i
\(566\) 49.2029 2.06815
\(567\) 0 0
\(568\) −16.5438 −0.694161
\(569\) −5.20175 9.00969i −0.218069 0.377706i 0.736149 0.676820i \(-0.236642\pi\)
−0.954217 + 0.299114i \(0.903309\pi\)
\(570\) −44.7637 2.04145i −1.87495 0.0855070i
\(571\) −8.92480 + 15.4582i −0.373491 + 0.646906i −0.990100 0.140364i \(-0.955173\pi\)
0.616609 + 0.787270i \(0.288506\pi\)
\(572\) 9.15126 15.8505i 0.382633 0.662741i
\(573\) 0.559145 + 1.07922i 0.0233586 + 0.0450849i
\(574\) 0 0
\(575\) −0.471974 −0.0196827
\(576\) −21.8910 2.00085i −0.912127 0.0833686i
\(577\) −11.9430 −0.497193 −0.248597 0.968607i \(-0.579969\pi\)
−0.248597 + 0.968607i \(0.579969\pi\)
\(578\) −19.8135 34.3180i −0.824134 1.42744i
\(579\) −11.3365 + 17.7187i −0.471128 + 0.736366i
\(580\) −12.9356 + 22.4051i −0.537122 + 0.930322i
\(581\) 0 0
\(582\) 26.3894 41.2462i 1.09388 1.70971i
\(583\) 14.1608 + 24.5272i 0.586480 + 1.01581i
\(584\) −7.61849 −0.315255
\(585\) 3.26089 + 7.06445i 0.134821 + 0.292079i
\(586\) 37.0689 1.53130
\(587\) 11.9299 + 20.6631i 0.492398 + 0.852859i 0.999962 0.00875568i \(-0.00278706\pi\)
−0.507563 + 0.861614i \(0.669454\pi\)
\(588\) 0 0
\(589\) 4.71780 8.17147i 0.194394 0.336699i
\(590\) 8.70009 15.0690i 0.358177 0.620381i
\(591\) −28.3946 1.29494i −1.16800 0.0532667i
\(592\) −3.85301 6.67361i −0.158358 0.274284i
\(593\) −19.5801 −0.804060 −0.402030 0.915626i \(-0.631695\pi\)
−0.402030 + 0.915626i \(0.631695\pi\)
\(594\) 35.4035 45.5868i 1.45262 1.87045i
\(595\) 0 0
\(596\) 27.4538 + 47.5514i 1.12455 + 1.94778i
\(597\) −39.2871 1.79169i −1.60792 0.0733291i
\(598\) 0.336285 0.582462i 0.0137517 0.0238187i
\(599\) −9.27335 + 16.0619i −0.378899 + 0.656272i −0.990902 0.134583i \(-0.957030\pi\)
0.612004 + 0.790855i \(0.290364\pi\)
\(600\) 6.95331 + 13.4207i 0.283868 + 0.547897i
\(601\) −9.09931 15.7605i −0.371169 0.642883i 0.618577 0.785724i \(-0.287710\pi\)
−0.989746 + 0.142841i \(0.954376\pi\)
\(602\) 0 0
\(603\) 27.3676 38.7640i 1.11449 1.57859i
\(604\) 40.2498 1.63774
\(605\) −12.1659 21.0719i −0.494612 0.856693i
\(606\) 8.45165 13.2098i 0.343325 0.536612i
\(607\) −11.1549 + 19.3208i −0.452762 + 0.784206i −0.998556 0.0537125i \(-0.982895\pi\)
0.545795 + 0.837919i \(0.316228\pi\)
\(608\) 1.09358 1.89413i 0.0443505 0.0768173i
\(609\) 0 0
\(610\) 7.25370 + 12.5638i 0.293694 + 0.508692i
\(611\) −12.1623 −0.492032
\(612\) −6.63521 + 9.39823i −0.268212 + 0.379901i
\(613\) 10.2370 0.413467 0.206734 0.978397i \(-0.433717\pi\)
0.206734 + 0.978397i \(0.433717\pi\)
\(614\) 33.5495 + 58.1094i 1.35395 + 2.34511i
\(615\) −13.2391 25.5530i −0.533852 1.03040i
\(616\) 0 0
\(617\) 5.66372 9.80984i 0.228013 0.394929i −0.729206 0.684294i \(-0.760111\pi\)
0.957219 + 0.289364i \(0.0934439\pi\)
\(618\) −41.4092 1.88847i −1.66572 0.0759654i
\(619\) 4.31663 + 7.47663i 0.173500 + 0.300511i 0.939641 0.342161i \(-0.111159\pi\)
−0.766141 + 0.642672i \(0.777826\pi\)
\(620\) −24.4720 −0.982818
\(621\) 0.871198 1.12179i 0.0349600 0.0450157i
\(622\) −39.3245 −1.57677
\(623\) 0 0
\(624\) −7.48755 0.341470i −0.299742 0.0136697i
\(625\) 15.3260 26.5454i 0.613039 1.06181i
\(626\) −14.2683 + 24.7134i −0.570275 + 0.987746i
\(627\) −14.5833 28.1474i −0.582399 1.12410i
\(628\) 12.2719 + 21.2555i 0.489701 + 0.848188i
\(629\) 1.68443 0.0671626
\(630\) 0 0
\(631\) −14.8535 −0.591308 −0.295654 0.955295i \(-0.595538\pi\)
−0.295654 + 0.955295i \(0.595538\pi\)
\(632\) 37.1701 + 64.3805i 1.47855 + 2.56092i
\(633\) −4.25797 + 6.65514i −0.169239 + 0.264518i
\(634\) −2.48229 + 4.29945i −0.0985844 + 0.170753i
\(635\) −0.872181 + 1.51066i −0.0346115 + 0.0599488i
\(636\) 23.7405 37.1060i 0.941370 1.47135i
\(637\) 0 0
\(638\) −27.3317 −1.08207
\(639\) 9.77928 + 0.893828i 0.386862 + 0.0353593i
\(640\) 49.5586 1.95897
\(641\) 17.0797 + 29.5828i 0.674606 + 1.16845i 0.976584 + 0.215137i \(0.0690199\pi\)
−0.301978 + 0.953315i \(0.597647\pi\)
\(642\) −2.69436 5.20042i −0.106338 0.205244i
\(643\) −5.41741 + 9.38323i −0.213642 + 0.370039i −0.952852 0.303437i \(-0.901866\pi\)
0.739210 + 0.673475i \(0.235199\pi\)
\(644\) 0 0
\(645\) −46.8302 2.13570i −1.84394 0.0840929i
\(646\) 4.71780 + 8.17147i 0.185619 + 0.321502i
\(647\) −32.9692 −1.29615 −0.648077 0.761575i \(-0.724427\pi\)
−0.648077 + 0.761575i \(0.724427\pi\)
\(648\) −44.7331 8.24611i −1.75728 0.323938i
\(649\) 12.3097 0.483199
\(650\) −2.12422 3.67926i −0.0833188 0.144312i
\(651\) 0 0
\(652\) −36.1160 + 62.5548i −1.41441 + 2.44984i
\(653\) 1.96557 3.40446i 0.0769185 0.133227i −0.825000 0.565132i \(-0.808825\pi\)
0.901919 + 0.431905i \(0.142159\pi\)
\(654\) −6.66419 12.8627i −0.260591 0.502970i
\(655\) 10.2626 + 17.7753i 0.400991 + 0.694537i
\(656\) 27.7233 1.08241
\(657\) 4.50340 + 0.411612i 0.175695 + 0.0160585i
\(658\) 0 0
\(659\) −8.40856 14.5640i −0.327551 0.567335i 0.654474 0.756084i \(-0.272890\pi\)
−0.982025 + 0.188749i \(0.939557\pi\)
\(660\) −44.3106 + 69.2568i −1.72479 + 2.69582i
\(661\) −8.51080 + 14.7411i −0.331032 + 0.573364i −0.982714 0.185128i \(-0.940730\pi\)
0.651683 + 0.758492i \(0.274063\pi\)
\(662\) −24.2470 + 41.9970i −0.942386 + 1.63226i
\(663\) 0.882977 1.38008i 0.0342920 0.0535979i
\(664\) 2.39037 + 4.14024i 0.0927643 + 0.160672i
\(665\) 0 0
\(666\) 5.50885 + 11.9345i 0.213464 + 0.462451i
\(667\) −0.672570 −0.0260420
\(668\) −17.1644 29.7296i −0.664110 1.15027i
\(669\) 10.6168 + 20.4917i 0.410470 + 0.792255i
\(670\) −50.4686 + 87.4141i −1.94977 + 3.37710i
\(671\) −5.13161 + 8.88821i −0.198104 + 0.343126i
\(672\) 0 0
\(673\) −14.3727 24.8942i −0.554025 0.959600i −0.997979 0.0635501i \(-0.979758\pi\)
0.443953 0.896050i \(-0.353576\pi\)
\(674\) 71.4805 2.75333
\(675\) −3.38511 8.30885i −0.130293 0.319808i
\(676\) −48.6490 −1.87112
\(677\) −3.01819 5.22765i −0.115998 0.200915i 0.802180 0.597082i \(-0.203673\pi\)
−0.918178 + 0.396167i \(0.870340\pi\)
\(678\) −44.2278 2.01701i −1.69856 0.0774628i
\(679\) 0 0
\(680\) 6.19961 10.7380i 0.237744 0.411785i
\(681\) 1.10078 + 2.12463i 0.0421818 + 0.0814159i
\(682\) −12.9267 22.3898i −0.494991 0.857349i
\(683\) 20.5113 0.784842 0.392421 0.919786i \(-0.371638\pi\)
0.392421 + 0.919786i \(0.371638\pi\)
\(684\) −28.4377 + 40.2797i −1.08734 + 1.54013i
\(685\) −9.52510 −0.363935
\(686\) 0 0
\(687\) −16.7831 + 26.2317i −0.640314 + 1.00080i
\(688\) 22.5797 39.1091i 0.860842 1.49102i
\(689\) −3.13667 + 5.43288i −0.119498 + 0.206976i
\(690\) −1.62830 + 2.54500i −0.0619882 + 0.0968867i
\(691\) −7.50146 12.9929i −0.285369 0.494274i 0.687330 0.726346i \(-0.258783\pi\)
−0.972699 + 0.232072i \(0.925450\pi\)
\(692\) −70.3652 −2.67488
\(693\) 0 0
\(694\) −71.5595 −2.71636
\(695\) −2.66372 4.61369i −0.101040 0.175007i
\(696\) 9.90856 + 19.1247i 0.375583 + 0.724919i
\(697\) −3.02997 + 5.24806i −0.114768 + 0.198784i
\(698\) −30.4648 + 52.7665i −1.15311 + 1.99724i
\(699\) −32.8442 1.49786i −1.24228 0.0566542i
\(700\) 0 0
\(701\) 38.5113 1.45455 0.727275 0.686346i \(-0.240786\pi\)
0.727275 + 0.686346i \(0.240786\pi\)
\(702\) 12.6659 + 1.74255i 0.478042 + 0.0657684i
\(703\) 7.21926 0.272280
\(704\) 16.5402 + 28.6484i 0.623381 + 1.07973i
\(705\) 54.5787 + 2.48906i 2.05555 + 0.0937435i
\(706\) 40.9705 70.9630i 1.54195 2.67073i
\(707\) 0 0
\(708\) −8.80778 17.0000i −0.331017 0.638901i
\(709\) −3.82004 6.61650i −0.143465 0.248488i 0.785334 0.619072i \(-0.212491\pi\)
−0.928799 + 0.370584i \(0.879158\pi\)
\(710\) −20.8889 −0.783947
\(711\) −18.4935 40.0646i −0.693560 1.50254i
\(712\) −72.5595 −2.71928
\(713\) −0.318097 0.550960i −0.0119128 0.0206336i
\(714\) 0 0
\(715\) 5.85447 10.1402i 0.218945 0.379224i
\(716\) 23.0057 39.8471i 0.859765 1.48916i
\(717\) −4.56634 + 7.13713i −0.170533 + 0.266541i
\(718\) 31.4164 + 54.4148i 1.17245 + 2.03074i
\(719\) 30.0364 1.12017 0.560084 0.828436i \(-0.310769\pi\)
0.560084 + 0.828436i \(0.310769\pi\)
\(720\) 33.5308 + 3.06472i 1.24962 + 0.114216i
\(721\) 0 0
\(722\) −3.15486 5.46438i −0.117412 0.203363i
\(723\) −20.8435 40.2303i −0.775177 1.49618i
\(724\) 44.3697 76.8506i 1.64899 2.85613i
\(725\) −2.12422 + 3.67926i −0.0788916 + 0.136644i
\(726\) −39.9399 1.82146i −1.48231 0.0676007i
\(727\) 1.72812 + 2.99319i 0.0640923 + 0.111011i 0.896291 0.443466i \(-0.146251\pi\)
−0.832199 + 0.554478i \(0.812918\pi\)
\(728\) 0 0
\(729\) 25.9969 + 7.29124i 0.962847 + 0.270046i
\(730\) −9.61944 −0.356032
\(731\) 4.93560 + 8.54871i 0.182550 + 0.316185i
\(732\) 15.9466 + 0.727245i 0.589403 + 0.0268797i
\(733\) 19.2630 33.3645i 0.711496 1.23235i −0.252799 0.967519i \(-0.581351\pi\)
0.964295 0.264829i \(-0.0853155\pi\)
\(734\) −33.7709 + 58.4929i −1.24651 + 2.15901i
\(735\) 0 0
\(736\) −0.0737345 0.127712i −0.00271789 0.00470752i
\(737\) −71.4078 −2.63034
\(738\) −47.0928 4.30429i −1.73351 0.158443i
\(739\) 45.1239 1.65991 0.829955 0.557830i \(-0.188366\pi\)
0.829955 + 0.557830i \(0.188366\pi\)
\(740\) −9.36186 16.2152i −0.344149 0.596084i
\(741\) 3.78434 5.91486i 0.139021 0.217288i
\(742\) 0 0
\(743\) −4.74338 + 8.21577i −0.174018 + 0.301407i −0.939821 0.341668i \(-0.889008\pi\)
0.765803 + 0.643075i \(0.222342\pi\)
\(744\) −10.9803 + 17.1621i −0.402559 + 0.629194i
\(745\) 17.5634 + 30.4207i 0.643474 + 1.11453i
\(746\) −40.1737 −1.47086
\(747\) −1.18929 2.57651i −0.0435140 0.0942695i
\(748\) 17.3126 0.633013
\(749\) 0 0
\(750\) −16.6441 32.1250i −0.607755 1.17304i
\(751\) 4.91595 8.51467i 0.179386 0.310705i −0.762285 0.647242i \(-0.775922\pi\)
0.941670 + 0.336537i \(0.109256\pi\)
\(752\) −26.3157 + 45.5800i −0.959633 + 1.66213i
\(753\) −31.9363 1.45646i −1.16382 0.0530762i
\(754\) −3.02704 5.24299i −0.110238 0.190938i
\(755\) 25.7496 0.937124
\(756\) 0 0
\(757\) −41.8171 −1.51987 −0.759934 0.650000i \(-0.774769\pi\)
−0.759934 + 0.650000i \(0.774769\pi\)
\(758\) 14.8078 + 25.6478i 0.537843 + 0.931571i
\(759\) −2.13521 0.0973764i −0.0775032 0.00353454i
\(760\) 26.5708 46.0220i 0.963825 1.66939i
\(761\) 11.4897 19.9007i 0.416501 0.721400i −0.579084 0.815268i \(-0.696590\pi\)
0.995585 + 0.0938675i \(0.0299230\pi\)
\(762\) 1.31858 + 2.54500i 0.0477670 + 0.0921958i
\(763\) 0 0
\(764\) −2.84494 −0.102926
\(765\) −4.24484 + 6.01247i −0.153473 + 0.217381i
\(766\) −30.5979 −1.10555
\(767\) 1.36333 + 2.36135i 0.0492269 + 0.0852635i
\(768\) 30.2077 47.2142i 1.09003 1.70369i
\(769\) 3.04329 5.27113i 0.109744 0.190082i −0.805923 0.592021i \(-0.798330\pi\)
0.915666 + 0.401939i \(0.131664\pi\)
\(770\) 0 0
\(771\) −10.9531 + 17.1196i −0.394467 + 0.616546i
\(772\) −24.6175 42.6388i −0.886003 1.53460i
\(773\) 41.8214 1.50421 0.752105 0.659043i \(-0.229038\pi\)
0.752105 + 0.659043i \(0.229038\pi\)
\(774\) −44.4274 + 62.9278i −1.59691 + 2.26189i
\(775\) −4.01867 −0.144355
\(776\) 29.0349 + 50.2899i 1.04229 + 1.80530i
\(777\) 0 0
\(778\) 25.3442 43.8974i 0.908632 1.57380i
\(779\) −12.9861 + 22.4926i −0.465275 + 0.805880i
\(780\) −18.1929 0.829688i −0.651410 0.0297076i
\(781\) −7.38891 </