Properties

Label 441.2.f.d.295.3
Level $441$
Weight $2$
Character 441.295
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 295.3
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.d.148.3

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.00784213 0.999969i \(-0.497504\pi\)
0.862078 0.506776i \(-0.169163\pi\)
\(3\) 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 −0.995485 0.0949156i \(-0.969742\pi\)
0.415543 0.909573i \(-0.363591\pi\)
\(6\) 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 0.294198 + 0.955744i \(0.404947\pi\)
−0.974798 + 0.223089i \(0.928386\pi\)
\(12\) −3.78434 5.91486i −1.09244 1.70747i
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 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 0.879923 0.475117i \(-0.157594\pi\)
−0.851425 + 0.524477i \(0.824261\pi\)
\(24\) −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 −0.957350 0.288932i \(-0.906700\pi\)
0.728897 + 0.684623i \(0.240033\pi\)
\(30\) −11.0416 + 0.503554i −2.01592 + 0.0919360i
\(31\) 1.16372 + 2.01561i 0.209009 + 0.362015i 0.951403 0.307949i \(-0.0996427\pi\)
−0.742393 + 0.669964i \(0.766309\pi\)
\(32\) 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 −1.00000 0.000297253i \(-0.999905\pi\)
0.499743 0.866174i \(-0.333428\pi\)
\(42\) 0 0
\(43\) 5.21780 9.03749i 0.795707 1.37820i −0.126682 0.991943i \(-0.540433\pi\)
0.922389 0.386262i \(-0.126234\pi\)
\(44\) 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 −0.0436467 + 0.999047i \(0.513898\pi\)
−0.843377 + 0.537323i \(0.819436\pi\)
\(48\) −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 0.763530 0.645772i \(-0.223464\pi\)
−0.941020 + 0.338350i \(0.890131\pi\)
\(60\) −8.37792 + 16.1704i −1.08158 + 2.08758i
\(61\) −1.13667 + 1.96878i −0.145536 + 0.252076i −0.929573 0.368639i \(-0.879824\pi\)
0.784037 + 0.620714i \(0.213157\pi\)
\(62\) 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 0.706400 + 0.707813i \(0.250318\pi\)
0.259784 + 0.965667i \(0.416349\pi\)
\(68\) −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 0.0725952 + 0.997361i \(0.476872\pi\)
−0.900038 + 0.435811i \(0.856461\pi\)
\(80\) 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 −0.890815 0.454367i \(-0.849865\pi\)
0.838901 + 0.544285i \(0.183199\pi\)
\(84\) 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 0.411785 + 0.911281i \(0.364906\pi\)
−0.995085 + 0.0990246i \(0.968428\pi\)
\(98\) 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 −0.942926 0.333002i \(-0.891939\pi\)
0.759851 + 0.650097i \(0.225272\pi\)
\(102\) 1.85447 3.57935i 0.183620 0.354408i
\(103\) −4.86333 8.42353i −0.479198 0.829995i 0.520518 0.853851i \(-0.325739\pi\)
−0.999715 + 0.0238560i \(0.992406\pi\)
\(104\) −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 0.511271 0.859420i \(-0.329175\pi\)
−0.999915 + 0.0130636i \(0.995842\pi\)
\(114\) 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 0.985484 0.169770i \(-0.0543026\pi\)
−0.639767 + 0.768569i \(0.720969\pi\)
\(132\) 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 −0.776859 0.629674i \(-0.783188\pi\)
0.933744 + 0.357943i \(0.116522\pi\)
\(138\) 1.16372 0.0530713i 0.0990620 0.00451773i
\(139\) −1.02704 1.77889i −0.0871126 0.150883i 0.819177 0.573541i \(-0.194431\pi\)
−0.906289 + 0.422658i \(0.861097\pi\)
\(140\) 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 0.997921 + 0.0644482i \(0.0205287\pi\)
−0.443147 + 0.896449i \(0.646138\pi\)
\(150\) 3.96576 + 6.19843i 0.323803 + 0.506099i
\(151\) −4.96410 + 8.59808i −0.403973 + 0.699702i −0.994201 0.107535i \(-0.965704\pi\)
0.590228 + 0.807236i \(0.299038\pi\)
\(152\) −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 0.961166 0.275972i \(-0.0889996\pi\)
−0.719581 + 0.694408i \(0.755666\pi\)
\(158\) 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 0.654415 0.756136i \(-0.272915\pi\)
−0.982040 + 0.188672i \(0.939582\pi\)
\(168\) 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 −0.320868 0.947124i \(-0.603975\pi\)
0.980667 0.195682i \(-0.0626920\pi\)
\(174\) 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 −0.853052 0.521826i \(-0.825251\pi\)
0.878440 + 0.477852i \(0.158584\pi\)
\(192\) −12.6783 + 0.578195i −0.914978 + 0.0417276i
\(193\) −6.07227 10.5175i −0.437092 0.757065i 0.560372 0.828241i \(-0.310658\pi\)
−0.997464 + 0.0711760i \(0.977325\pi\)
\(194\) 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 0.776778 0.629775i \(-0.216853\pi\)
−0.933790 + 0.357822i \(0.883520\pi\)
\(212\) 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 −0.551993 0.833849i \(-0.686133\pi\)
0.998131 + 0.0611159i \(0.0194659\pi\)
\(224\) 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 −0.842191 0.539179i \(-0.818735\pi\)
0.888038 + 0.459769i \(0.152068\pi\)
\(228\) −15.3420 23.9793i −1.01605 1.58807i
\(229\) −8.98968 15.5706i −0.594055 1.02893i −0.993679 0.112254i \(-0.964193\pi\)
0.399625 0.916679i \(-0.369141\pi\)
\(230\) −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 0.776011 0.630719i \(-0.217240\pi\)
−0.934224 + 0.356686i \(0.883907\pi\)
\(240\) 19.4195 0.885629i 1.25353 0.0571671i
\(241\) −13.0797 + 22.6546i −0.842535 + 1.45931i 0.0452094 + 0.998978i \(0.485604\pi\)
−0.887745 + 0.460336i \(0.847729\pi\)
\(242\) −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 0.622962 0.782252i \(-0.285929\pi\)
−0.988931 + 0.148375i \(0.952596\pi\)
\(258\) −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 −0.726463 0.687206i \(-0.758837\pi\)
0.958369 + 0.285532i \(0.0921703\pi\)
\(264\) 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 −0.953325 0.301947i \(-0.902364\pi\)
0.738156 + 0.674630i \(0.235697\pi\)
\(278\) −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 −0.997974 0.0636271i \(-0.979733\pi\)
0.554090 + 0.832457i \(0.313067\pi\)
\(282\) 27.9341 + 43.6606i 1.66345 + 2.59995i
\(283\) 9.99854 + 17.3180i 0.594351 + 1.02945i 0.993638 + 0.112621i \(0.0359245\pi\)
−0.399287 + 0.916826i \(0.630742\pi\)
\(284\) −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 0.997694 0.0678705i \(-0.0216205\pi\)
−0.557625 + 0.830093i \(0.688287\pi\)
\(294\) 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 0.545443 0.838148i \(-0.316362\pi\)
−0.998579 + 0.0532931i \(0.983028\pi\)
\(312\) −4.71780 7.37385i −0.267093 0.417462i
\(313\) 5.79893 10.0440i 0.327775 0.567722i −0.654295 0.756239i \(-0.727035\pi\)
0.982070 + 0.188517i \(0.0603680\pi\)
\(314\) 14.8961 0.840636
\(315\) 0 0
\(316\) 59.6313 3.35452
\(317\) 1.00885 1.74739i 0.0566629 0.0981430i −0.836303 0.548268i \(-0.815287\pi\)
0.892965 + 0.450125i \(0.148621\pi\)
\(318\) −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 −0.457159 0.889385i \(-0.651133\pi\)
0.998809 0.0487815i \(-0.0155338\pi\)
\(332\) 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 0.925188 + 0.379509i \(0.123907\pi\)
−0.133929 + 0.990991i \(0.542759\pi\)
\(338\) −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 −0.931572 0.363557i \(-0.881562\pi\)
0.150936 0.988544i \(-0.451771\pi\)
\(348\) 17.2594 0.787117i 0.925203 0.0421939i
\(349\) 12.3815 21.4454i 0.662767 1.14795i −0.317118 0.948386i \(-0.602715\pi\)
0.979885 0.199561i \(-0.0639515\pi\)
\(350\) 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 −0.0419914 + 0.999118i \(0.513370\pi\)
−0.844266 + 0.535925i \(0.819963\pi\)
\(354\) −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 −0.245949 0.969283i \(-0.579100\pi\)
0.962398 0.271644i \(-0.0875672\pi\)
\(368\) −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 0.573502 0.819204i \(-0.305585\pi\)
−0.996203 + 0.0870646i \(0.972251\pi\)
\(374\) 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 0.662296 0.749242i \(-0.269582\pi\)
−0.980011 + 0.198944i \(0.936249\pi\)
\(384\) −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 0.477414 + 0.878678i \(0.341574\pi\)
−0.999665 + 0.0258860i \(0.991759\pi\)
\(390\) −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 0.896263 0.443522i \(-0.146271\pi\)
−0.832233 + 0.554426i \(0.812938\pi\)
\(402\) 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 −0.882441 0.470423i \(-0.844101\pi\)
0.0338223 0.999428i \(-0.489232\pi\)
\(410\) 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 0.911312 0.411717i \(-0.135071\pi\)
−0.812213 + 0.583361i \(0.801737\pi\)
\(420\) 0 0
\(421\) 10.5344 18.2462i 0.513417 0.889264i −0.486462 0.873702i \(-0.661713\pi\)
0.999879 0.0155624i \(-0.00495387\pi\)
\(422\) −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 0.436898 + 0.899511i \(0.356077\pi\)
−0.997448 + 0.0713911i \(0.977256\pi\)
\(440\) −59.1780 −2.82120
\(441\) 0 0
\(442\) 2.32743 0.110705
\(443\) 6.70895 11.6202i 0.318752 0.552094i −0.661476 0.749966i \(-0.730070\pi\)
0.980228 + 0.197872i \(0.0634031\pi\)
\(444\) −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 −0.950522 0.310658i \(-0.899451\pi\)
0.744298 + 0.667847i \(0.232784\pi\)
\(458\) −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 −0.924365 0.381509i \(-0.875405\pi\)
0.792579 + 0.609769i \(0.208738\pi\)
\(462\) 0 0
\(463\) −7.86333 13.6197i −0.365440 0.632960i 0.623407 0.781898i \(-0.285748\pi\)
−0.988847 + 0.148937i \(0.952415\pi\)
\(464\) −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 −0.425937 0.904753i \(-0.640055\pi\)
0.996507 0.0835043i \(-0.0266112\pi\)
\(480\) 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 0.667358 0.744737i \(-0.267425\pi\)
−0.978640 + 0.205580i \(0.934092\pi\)
\(492\) −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 0.681564 0.731758i \(-0.261300\pi\)
−0.974503 + 0.224373i \(0.927967\pi\)
\(500\) 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 0.634413 0.772994i \(-0.281242\pi\)
−0.986639 + 0.162920i \(0.947909\pi\)
\(510\) −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 −0.782416 0.622756i \(-0.786013\pi\)
0.930531 + 0.366214i \(0.119346\pi\)
\(548\) −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 0.833629 + 0.552325i \(0.186259\pi\)
0.0615128 + 0.998106i \(0.480407\pi\)
\(564\) 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 −0.954217 0.299114i \(-0.903309\pi\)
0.736149 + 0.676820i \(0.236642\pi\)
\(570\) −44.7637 + 2.04145i −1.87495 + 0.0855070i
\(571\) −8.92480 15.4582i −0.373491 0.646906i 0.616609 0.787270i \(-0.288506\pi\)
−0.990100 + 0.140364i \(0.955173\pi\)
\(572\) 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 −0.507563 0.861614i \(-0.669454\pi\)
0.999962 + 0.00875568i \(0.00278706\pi\)
\(588\) 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 0.612004 0.790855i \(-0.290364\pi\)
−0.990902 + 0.134583i \(0.957030\pi\)
\(600\) 6.95331 13.4207i 0.283868 0.547897i
\(601\) −9.09931 + 15.7605i −0.371169 + 0.642883i −0.989746 0.142841i \(-0.954376\pi\)
0.618577 + 0.785724i \(0.287710\pi\)
\(602\) 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 0.545795 0.837919i \(-0.316228\pi\)
−0.998556 + 0.0537125i \(0.982895\pi\)
\(608\) 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 0.957219 0.289364i \(-0.0934439\pi\)
−0.729206 + 0.684294i \(0.760111\pi\)
\(618\) −41.4092 + 1.88847i −1.66572 + 0.0759654i
\(619\) 4.31663 7.47663i 0.173500 0.300511i −0.766141 0.642672i \(-0.777826\pi\)
0.939641 + 0.342161i \(0.111159\pi\)
\(620\) −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 −0.301978 0.953315i \(-0.597647\pi\)
0.976584 0.215137i \(-0.0690199\pi\)
\(642\) −2.69436 + 5.20042i −0.106338 + 0.205244i
\(643\) −5.41741 9.38323i −0.213642 0.370039i 0.739210 0.673475i \(-0.235199\pi\)
−0.952852 + 0.303437i \(0.901866\pi\)
\(644\) 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 0.901919 0.431905i \(-0.142159\pi\)
−0.825000 + 0.565132i \(0.808825\pi\)
\(654\) −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 −0.982025 0.188749i \(-0.939557\pi\)
0.654474 + 0.756084i \(0.272890\pi\)
\(660\) −44.3106 69.2568i −1.72479 2.69582i
\(661\) −8.51080 14.7411i −0.331032 0.573364i 0.651683 0.758492i \(-0.274063\pi\)
−0.982714 + 0.185128i \(0.940730\pi\)
\(662\) −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 0.443953 + 0.896050i \(0.353576\pi\)
−0.997979 + 0.0635501i \(0.979758\pi\)
\(674\) 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 −0.918178 0.396167i \(-0.870340\pi\)
0.802180 + 0.597082i \(0.203673\pi\)
\(678\) −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 −0.972699 0.232072i \(-0.925450\pi\)
0.687330 + 0.726346i \(0.258783\pi\)
\(692\) −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 −0.928799 0.370584i \(-0.879158\pi\)
0.785334 + 0.619072i \(0.212491\pi\)
\(710\) −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 −0.832199 0.554478i \(-0.812918\pi\)
0.896291 + 0.443466i \(0.146251\pi\)
\(728\) 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 0.964295 + 0.264829i \(0.0853155\pi\)
−0.252799 + 0.967519i \(0.581351\pi\)
\(734\) −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 0.765803 0.643075i \(-0.222342\pi\)
−0.939821 + 0.341668i \(0.889008\pi\)
\(744\) −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 0.941670 0.336537i \(-0.109256\pi\)
−0.762285 + 0.647242i \(0.775922\pi\)
\(752\) −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 0.995585 0.0938675i \(-0.0299230\pi\)
−0.579084 + 0.815268i \(0.696590\pi\)
\(762\) 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 0.915666 0.401939i \(-0.131664\pi\)
−0.805923 + 0.592021i \(0.798330\pi\)
\(770\) 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
\(781\)