Properties

Label 441.2.h.b.214.1
Level $441$
Weight $2$
Character 441.214
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.h (of order \(3\), degree \(2\), not 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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 214.1
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.b.373.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46050 q^{2} +(-0.796790 + 1.53790i) q^{3} +4.05408 q^{4} +(-1.29679 + 2.24611i) q^{5} +(1.96050 - 3.78400i) q^{6} -5.05408 q^{8} +(-1.73025 - 2.45076i) q^{9} +O(q^{10})\) \(q-2.46050 q^{2} +(-0.796790 + 1.53790i) q^{3} +4.05408 q^{4} +(-1.29679 + 2.24611i) q^{5} +(1.96050 - 3.78400i) q^{6} -5.05408 q^{8} +(-1.73025 - 2.45076i) q^{9} +(3.19076 - 5.52655i) q^{10} +(-2.25729 - 3.90975i) q^{11} +(-3.23025 + 6.23476i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-2.42101 - 3.78400i) q^{15} +4.32743 q^{16} +(-0.472958 + 0.819187i) q^{17} +(4.25729 + 6.03011i) q^{18} +(-2.02704 - 3.51094i) q^{19} +(-5.25729 + 9.10590i) q^{20} +(5.55408 + 9.61996i) q^{22} +(0.136673 - 0.236725i) q^{23} +(4.02704 - 7.77266i) q^{24} +(-0.863327 - 1.49533i) q^{25} +(-1.23025 - 2.13086i) q^{26} +(5.14766 - 0.708209i) q^{27} +(-1.23025 + 2.13086i) q^{29} +(5.95691 + 9.31056i) q^{30} -2.32743 q^{31} -0.539495 q^{32} +(7.81138 - 0.356238i) q^{33} +(1.16372 - 2.01561i) q^{34} +(-7.01459 - 9.93559i) q^{36} +(-0.890369 - 1.54216i) q^{37} +(4.98755 + 8.63868i) q^{38} +(-1.73025 + 0.0789082i) q^{39} +(6.55408 - 11.3520i) q^{40} +(-3.20321 - 5.54812i) q^{41} +(5.21780 - 9.03749i) q^{43} +(-9.15126 - 15.8505i) q^{44} +(7.74844 - 0.708209i) q^{45} +(-0.336285 + 0.582462i) q^{46} +12.1623 q^{47} +(-3.44805 + 6.65514i) q^{48} +(2.12422 + 3.67926i) q^{50} +(-0.882977 - 1.38008i) q^{51} +(2.02704 + 3.51094i) q^{52} +(3.13667 - 5.43288i) q^{53} +(-12.6659 + 1.74255i) q^{54} +11.7089 q^{55} +(7.01459 - 0.319901i) q^{57} +(3.02704 - 5.24299i) q^{58} +2.72665 q^{59} +(-9.81498 - 15.3407i) q^{60} +2.27335 q^{61} +5.72665 q^{62} -7.32743 q^{64} -2.59358 q^{65} +(-19.2199 + 0.876526i) q^{66} -15.8171 q^{67} +(-1.91741 + 3.32105i) q^{68} +(0.255158 + 0.398809i) q^{69} +3.27335 q^{71} +(8.74484 + 12.3863i) q^{72} +(-0.753696 + 1.30544i) q^{73} +(2.19076 + 3.79450i) q^{74} +(2.98755 - 0.136247i) q^{75} +(-8.21780 - 14.2336i) q^{76} +(4.25729 - 0.194154i) q^{78} +14.7089 q^{79} +(-5.61177 + 9.71987i) q^{80} +(-3.01245 + 8.48087i) q^{81} +(7.88151 + 13.6512i) q^{82} +(-0.472958 + 0.819187i) q^{83} +(-1.22665 - 2.12463i) q^{85} +(-12.8384 + 22.2368i) q^{86} +(-2.29679 - 3.58985i) q^{87} +(11.4086 + 19.7602i) q^{88} +(-7.17830 - 12.4332i) q^{89} +(-19.0651 + 1.74255i) q^{90} +(0.554084 - 0.959702i) q^{92} +(1.85447 - 3.57935i) q^{93} -29.9253 q^{94} +10.5146 q^{95} +(0.429864 - 0.829688i) q^{96} +(-5.74484 + 9.95036i) q^{97} +(-5.67617 + 12.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 2q^{2} - 2q^{3} + 6q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + O(q^{10}) \) \( 6q - 2q^{2} - 2q^{3} + 6q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + 2q^{11} - 13q^{12} + 3q^{13} + 11q^{15} + 6q^{16} - 12q^{17} + 10q^{18} - 3q^{19} - 16q^{20} + 15q^{22} + 15q^{24} - 6q^{25} - q^{26} + 7q^{27} - q^{29} + 31q^{30} + 6q^{31} - 16q^{32} + 13q^{33} - 3q^{34} - 11q^{36} + 3q^{37} + 8q^{38} - 4q^{39} + 21q^{40} - 22q^{41} + 3q^{43} - 23q^{44} + q^{45} - 12q^{46} + 18q^{47} + 14q^{48} - 10q^{50} - 12q^{51} + 3q^{52} + 18q^{53} - 13q^{54} + 12q^{55} + 11q^{57} + 9q^{58} + 18q^{59} - 17q^{60} + 12q^{61} + 36q^{62} - 24q^{64} - 10q^{65} - 34q^{66} + 6q^{68} + 39q^{69} + 18q^{71} + 15q^{72} + 3q^{73} - 6q^{74} - 4q^{75} - 21q^{76} + 10q^{78} + 30q^{79} + 11q^{80} - 40q^{81} + 9q^{82} - 12q^{83} - 9q^{85} - 34q^{86} - 11q^{87} + 21q^{88} - 2q^{89} - 73q^{90} - 15q^{92} - 18q^{93} - 48q^{94} + 32q^{95} + 7q^{96} + 3q^{97} - 46q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46050 −1.73984 −0.869920 0.493193i \(-0.835830\pi\)
−0.869920 + 0.493193i \(0.835830\pi\)
\(3\) −0.796790 + 1.53790i −0.460027 + 0.887905i
\(4\) 4.05408 2.02704
\(5\) −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
\(9\) −1.73025 2.45076i −0.576751 0.816920i
\(10\) 3.19076 5.52655i 1.00901 1.74765i
\(11\) −2.25729 3.90975i −0.680600 1.17883i −0.974798 0.223089i \(-0.928386\pi\)
0.294198 0.955744i \(-0.404947\pi\)
\(12\) −3.23025 + 6.23476i −0.932494 + 1.79982i
\(13\) 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
\(16\) 4.32743 1.08186
\(17\) −0.472958 + 0.819187i −0.114709 + 0.198682i −0.917663 0.397359i \(-0.869927\pi\)
0.802954 + 0.596041i \(0.203260\pi\)
\(18\) 4.25729 + 6.03011i 1.00345 + 1.42131i
\(19\) −2.02704 3.51094i −0.465035 0.805465i 0.534168 0.845378i \(-0.320625\pi\)
−0.999203 + 0.0399136i \(0.987292\pi\)
\(20\) −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 \(0.157594\pi\)
\(24\) 4.02704 7.77266i 0.822017 1.58659i
\(25\) −0.863327 1.49533i −0.172665 0.299065i
\(26\) −1.23025 2.13086i −0.241272 0.417896i
\(27\) 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 \(0.240033\pi\)
\(30\) 5.95691 + 9.31056i 1.08758 + 1.69987i
\(31\) −2.32743 −0.418019 −0.209009 0.977914i \(-0.567024\pi\)
−0.209009 + 0.977914i \(0.567024\pi\)
\(32\) −0.539495 −0.0953702
\(33\) 7.81138 0.356238i 1.35979 0.0620131i
\(34\) 1.16372 2.01561i 0.199576 0.345675i
\(35\) 0 0
\(36\) −7.01459 9.93559i −1.16910 1.65593i
\(37\) −0.890369 1.54216i −0.146376 0.253530i 0.783510 0.621380i \(-0.213428\pi\)
−0.929885 + 0.367849i \(0.880094\pi\)
\(38\) 4.98755 + 8.63868i 0.809087 + 1.40138i
\(39\) −1.73025 + 0.0789082i −0.277062 + 0.0126354i
\(40\) 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 \(-0.126234\pi\)
\(44\) −9.15126 15.8505i −1.37960 2.38955i
\(45\) 7.74844 0.708209i 1.15507 0.105574i
\(46\) −0.336285 + 0.582462i −0.0495825 + 0.0858794i
\(47\) 12.1623 1.77405 0.887023 0.461724i \(-0.152769\pi\)
0.887023 + 0.461724i \(0.152769\pi\)
\(48\) −3.44805 + 6.65514i −0.497683 + 0.960587i
\(49\) 0 0
\(50\) 2.12422 + 3.67926i 0.300410 + 0.520326i
\(51\) −0.882977 1.38008i −0.123642 0.193250i
\(52\) 2.02704 + 3.51094i 0.281100 + 0.486880i
\(53\) 3.13667 5.43288i 0.430855 0.746263i −0.566092 0.824342i \(-0.691545\pi\)
0.996947 + 0.0780790i \(0.0248786\pi\)
\(54\) −12.6659 + 1.74255i −1.72360 + 0.237131i
\(55\) 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
\(59\) 2.72665 0.354980 0.177490 0.984123i \(-0.443202\pi\)
0.177490 + 0.984123i \(0.443202\pi\)
\(60\) −9.81498 15.3407i −1.26711 1.98047i
\(61\) 2.27335 0.291072 0.145536 0.989353i \(-0.453509\pi\)
0.145536 + 0.989353i \(0.453509\pi\)
\(62\) 5.72665 0.727286
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) −2.59358 −0.321694
\(66\) −19.2199 + 0.876526i −2.36581 + 0.107893i
\(67\) −15.8171 −1.93237 −0.966184 0.257854i \(-0.916985\pi\)
−0.966184 + 0.257854i \(0.916985\pi\)
\(68\) −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 \(0.437777\pi\)
\(72\) 8.74484 + 12.3863i 1.03059 + 1.45975i
\(73\) −0.753696 + 1.30544i −0.0882134 + 0.152790i −0.906756 0.421656i \(-0.861449\pi\)
0.818543 + 0.574446i \(0.194782\pi\)
\(74\) 2.19076 + 3.79450i 0.254670 + 0.441102i
\(75\) 2.98755 0.136247i 0.344972 0.0157325i
\(76\) −8.21780 14.2336i −0.942646 1.63271i
\(77\) 0 0
\(78\) 4.25729 0.194154i 0.482044 0.0219836i
\(79\) 14.7089 1.65489 0.827443 0.561550i \(-0.189795\pi\)
0.827443 + 0.561550i \(0.189795\pi\)
\(80\) −5.61177 + 9.71987i −0.627415 + 1.08671i
\(81\) −3.01245 + 8.48087i −0.334717 + 0.942319i
\(82\) 7.88151 + 13.6512i 0.870368 + 1.50752i
\(83\) −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
\(87\) −2.29679 3.58985i −0.246242 0.384872i
\(88\) 11.4086 + 19.7602i 1.21616 + 2.10644i
\(89\) −7.17830 12.4332i −0.760899 1.31792i −0.942388 0.334522i \(-0.891425\pi\)
0.181489 0.983393i \(-0.441908\pi\)
\(90\) −19.0651 + 1.74255i −2.00964 + 0.183681i
\(91\) 0 0
\(92\) 0.554084 0.959702i 0.0577673 0.100056i
\(93\) 1.85447 3.57935i 0.192300 0.371161i
\(94\) −29.9253 −3.08656
\(95\) 10.5146 1.07877
\(96\) 0.429864 0.829688i 0.0438728 0.0846797i
\(97\) −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
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) −1.83988 3.18677i −0.183075 0.317096i 0.759851 0.650097i \(-0.225272\pi\)
−0.942926 + 0.333002i \(0.891939\pi\)
\(102\) 2.17257 + 3.39569i 0.215116 + 0.336224i
\(103\) −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
\(107\) 0.687159 + 1.19019i 0.0664301 + 0.115060i 0.897327 0.441365i \(-0.145506\pi\)
−0.830897 + 0.556426i \(0.812172\pi\)
\(108\) 20.8691 2.87114i 2.00813 0.276275i
\(109\) 1.69961 2.94381i 0.162793 0.281966i −0.773076 0.634313i \(-0.781283\pi\)
0.935869 + 0.352347i \(0.114616\pi\)
\(110\) −28.8099 −2.74692
\(111\) 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 \(0.995842\pi\)
\(114\) −17.2594 + 0.787117i −1.61649 + 0.0737203i
\(115\) 0.354473 + 0.613964i 0.0330547 + 0.0572525i
\(116\) −4.98755 + 8.63868i −0.463082 + 0.802082i
\(117\) 1.25729 2.72382i 0.116237 0.251818i
\(118\) −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
\(122\) −5.59358 −0.506419
\(123\) 11.0847 0.505519i 0.999476 0.0455812i
\(124\) −9.43560 −0.847342
\(125\) −8.48968 −0.759340
\(126\) 0 0
\(127\) 0.672570 0.0596809 0.0298405 0.999555i \(-0.490500\pi\)
0.0298405 + 0.999555i \(0.490500\pi\)
\(128\) 19.1082 1.68894
\(129\) 9.74124 + 15.2254i 0.857669 + 1.34052i
\(130\) 6.38151 0.559696
\(131\) 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
\(135\) −5.08472 + 12.4806i −0.437623 + 1.07416i
\(136\) 2.39037 4.14024i 0.204972 0.355023i
\(137\) 1.83628 + 3.18054i 0.156884 + 0.271732i 0.933744 0.357943i \(-0.116522\pi\)
−0.776859 + 0.629674i \(0.783188\pi\)
\(138\) −0.627819 0.981271i −0.0534435 0.0835314i
\(139\) −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
\(142\) −8.05408 −0.675884
\(143\) 2.25729 3.90975i 0.188764 0.326950i
\(144\) −7.48755 10.6055i −0.623962 0.883791i
\(145\) −3.19076 5.52655i −0.264978 0.458955i
\(146\) 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 \(-0.0205287\pi\)
\(150\) −7.35087 + 0.335237i −0.600196 + 0.0273720i
\(151\) −4.96410 8.59808i −0.403973 0.699702i 0.590228 0.807236i \(-0.299038\pi\)
−0.994201 + 0.107535i \(0.965704\pi\)
\(152\) 10.2448 + 17.7446i 0.830966 + 1.43928i
\(153\) 2.82597 0.258294i 0.228466 0.0208818i
\(154\) 0 0
\(155\) 3.01819 5.22765i 0.242427 0.419895i
\(156\) −7.01459 + 0.319901i −0.561617 + 0.0256126i
\(157\) −6.05408 −0.483169 −0.241584 0.970380i \(-0.577667\pi\)
−0.241584 + 0.970380i \(0.577667\pi\)
\(158\) −36.1914 −2.87924
\(159\) 5.85594 + 9.15274i 0.464406 + 0.725859i
\(160\) 0.699612 1.21176i 0.0553092 0.0957983i
\(161\) 0 0
\(162\) 7.41216 20.8672i 0.582354 1.63948i
\(163\) −8.90856 15.4301i −0.697772 1.20858i −0.969237 0.246128i \(-0.920842\pi\)
0.271465 0.962448i \(-0.412492\pi\)
\(164\) −12.9861 22.4926i −1.01404 1.75637i
\(165\) −9.32957 + 18.0071i −0.726306 + 1.40185i
\(166\) 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
\(170\) 3.01819 + 5.22765i 0.231484 + 0.400943i
\(171\) −5.09718 + 11.0426i −0.389791 + 0.844449i
\(172\) 21.1534 36.6388i 1.61293 2.79368i
\(173\) −17.3566 −1.31960 −0.659799 0.751442i \(-0.729359\pi\)
−0.659799 + 0.751442i \(0.729359\pi\)
\(174\) 5.65126 + 8.83284i 0.428421 + 0.669616i
\(175\) 0 0
\(176\) −9.76829 16.9192i −0.736312 1.27533i
\(177\) −2.17257 + 4.19331i −0.163300 + 0.315189i
\(178\) 17.6623 + 30.5919i 1.32384 + 2.29296i
\(179\) 5.67471 9.82888i 0.424147 0.734645i −0.572193 0.820119i \(-0.693907\pi\)
0.996340 + 0.0854741i \(0.0272405\pi\)
\(180\) 31.4128 2.87114i 2.34137 0.214002i
\(181\) −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
\(185\) 4.61849 0.339558
\(186\) −4.56294 + 8.80700i −0.334571 + 0.645761i
\(187\) 4.27042 0.312284
\(188\) 49.3068 3.59607
\(189\) 0 0
\(190\) −25.8712 −1.87689
\(191\) −0.701748 −0.0507767 −0.0253883 0.999678i \(-0.508082\pi\)
−0.0253883 + 0.999678i \(0.508082\pi\)
\(192\) 5.83842 11.2688i 0.421352 0.813258i
\(193\) 12.1445 0.874183 0.437092 0.899417i \(-0.356009\pi\)
0.437092 + 0.899417i \(0.356009\pi\)
\(194\) 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 \(0.698751\pi\)
\(198\) 13.9662 30.2567i 0.992537 2.15025i
\(199\) 11.3530 19.6640i 0.804794 1.39394i −0.111637 0.993749i \(-0.535609\pi\)
0.916430 0.400194i \(-0.131057\pi\)
\(200\) 4.36333 + 7.55750i 0.308534 + 0.534396i
\(201\) 12.6029 24.3251i 0.888941 1.71576i
\(202\) 4.52704 + 7.84107i 0.318522 + 0.551696i
\(203\) 0 0
\(204\) −3.57966 5.59496i −0.250627 0.391726i
\(205\) 16.6156 1.16048
\(206\) 11.9662 20.7261i 0.833727 1.44406i
\(207\) −0.816635 + 0.0746406i −0.0567600 + 0.00518788i
\(208\) 2.16372 + 3.74766i 0.150027 + 0.259854i
\(209\) −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
\(213\) −2.60817 + 5.03407i −0.178709 + 0.344929i
\(214\) −1.69076 2.92848i −0.115578 0.200187i
\(215\) 13.5328 + 23.4395i 0.922928 + 1.59856i
\(216\) −26.0167 + 3.57935i −1.77021 + 0.243544i
\(217\) 0 0
\(218\) −4.18190 + 7.24327i −0.283234 + 0.490576i
\(219\) −1.40709 2.19927i −0.0950826 0.148613i
\(220\) 47.4690 3.20036
\(221\) −0.945916 −0.0636292
\(222\) −7.58113 + 0.345738i −0.508812 + 0.0232044i
\(223\) 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
\(226\) 12.7807 + 22.1369i 0.850162 + 1.47252i
\(227\) 0.690757 + 1.19643i 0.0458472 + 0.0794096i 0.888038 0.459769i \(-0.152068\pi\)
−0.842191 + 0.539179i \(0.818735\pi\)
\(228\) 28.4377 1.29690i 1.88334 0.0858896i
\(229\) −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
\(233\) 9.49115 + 16.4391i 0.621786 + 1.07696i 0.989153 + 0.146888i \(0.0469258\pi\)
−0.367367 + 0.930076i \(0.619741\pi\)
\(234\) −3.09358 + 6.70198i −0.202234 + 0.438122i
\(235\) −15.7719 + 27.3177i −1.02884 + 1.78201i
\(236\) 11.0541 0.719560
\(237\) −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 \(0.883907\pi\)
\(240\) −10.4768 16.3750i −0.676271 1.05700i
\(241\) −13.0797 22.6546i −0.842535 1.45931i −0.887745 0.460336i \(-0.847729\pi\)
0.0452094 0.998978i \(-0.485604\pi\)
\(242\) 11.5416 19.9907i 0.741924 1.28505i
\(243\) −10.6424 11.3903i −0.682711 0.730689i
\(244\) 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
\(248\) 11.7630 0.746953
\(249\) −0.882977 1.38008i −0.0559564 0.0874590i
\(250\) 20.8889 1.32113
\(251\) −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
\(254\) −1.65486 −0.103835
\(255\) 4.24484 0.193586i 0.265822 0.0121228i
\(256\) −32.3609 −2.02256
\(257\) −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
\(261\) 7.35087 0.671871i 0.455008 0.0415878i
\(262\) −9.73599 + 16.8632i −0.601491 + 1.04181i
\(263\) 3.76089 + 6.51406i 0.231907 + 0.401674i 0.958369 0.285532i \(-0.0921703\pi\)
−0.726463 + 0.687206i \(0.758837\pi\)
\(264\) −39.4794 + 1.80046i −2.42979 + 0.110811i
\(265\) 8.13521 + 14.0906i 0.499742 + 0.865579i
\(266\) 0 0
\(267\) 24.8406 1.13285i 1.52022 0.0693296i
\(268\) −64.1239 −3.91699
\(269\) −9.41741 + 16.3114i −0.574190 + 0.994526i 0.421939 + 0.906624i \(0.361349\pi\)
−0.996129 + 0.0879017i \(0.971984\pi\)
\(270\) 12.5110 30.7086i 0.761395 1.86886i
\(271\) −11.9911 20.7693i −0.728410 1.26164i −0.957555 0.288251i \(-0.906926\pi\)
0.229145 0.973392i \(-0.426407\pi\)
\(272\) −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
\(276\) 1.03443 + 1.61680i 0.0622656 + 0.0973202i
\(277\) −3.58113 6.20269i −0.215169 0.372684i 0.738156 0.674630i \(-0.235697\pi\)
−0.953325 + 0.301947i \(0.902364\pi\)
\(278\) 2.52704 + 4.37697i 0.151562 + 0.262513i
\(279\) 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 \(0.313067\pi\)
\(282\) 23.8442 46.0220i 1.41990 2.74057i
\(283\) −19.9971 −1.18870 −0.594351 0.804205i \(-0.702591\pi\)
−0.594351 + 0.804205i \(0.702591\pi\)
\(284\) 13.2704 0.787455
\(285\) −8.37792 + 16.1704i −0.496265 + 0.957849i
\(286\) −5.55408 + 9.61996i −0.328420 + 0.568840i
\(287\) 0 0
\(288\) 0.933463 + 1.32217i 0.0550048 + 0.0779098i
\(289\) 8.05262 + 13.9475i 0.473684 + 0.820444i
\(290\) 7.85087 + 13.5981i 0.461019 + 0.798509i
\(291\) −10.7252 16.7633i −0.628722 0.982683i
\(292\) −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
\(296\) 4.50000 + 7.79423i 0.261557 + 0.453030i
\(297\) −14.3887 18.5274i −0.834918 1.07507i
\(298\) −16.6623 + 28.8599i −0.965218 + 1.67181i
\(299\) 0.273346 0.0158080
\(300\) 12.1118 0.552358i 0.699273 0.0318904i
\(301\) 0 0
\(302\) 12.2142 + 21.1556i 0.702848 + 1.21737i
\(303\) 6.36693 0.290364i 0.365770 0.0166810i
\(304\) −8.77188 15.1933i −0.503102 0.871398i
\(305\) −2.94805 + 5.10618i −0.168805 + 0.292379i
\(306\) −6.95331 + 0.635534i −0.397494 + 0.0363310i
\(307\) 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
\(311\) 15.9823 0.906273 0.453136 0.891441i \(-0.350305\pi\)
0.453136 + 0.891441i \(0.350305\pi\)
\(312\) 8.74484 0.398809i 0.495079 0.0225781i
\(313\) −11.5979 −0.655549 −0.327775 0.944756i \(-0.606299\pi\)
−0.327775 + 0.944756i \(0.606299\pi\)
\(314\) 14.8961 0.840636
\(315\) 0 0
\(316\) 59.6313 3.35452
\(317\) −2.01771 −0.113326 −0.0566629 0.998393i \(-0.518046\pi\)
−0.0566629 + 0.998393i \(0.518046\pi\)
\(318\) −14.4086 22.5204i −0.807992 1.26288i
\(319\) 11.1082 0.621938
\(320\) 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
\(324\) −12.2127 + 34.3822i −0.678485 + 1.91012i
\(325\) 0.863327 1.49533i 0.0478888 0.0829458i
\(326\) 21.9195 + 37.9658i 1.21401 + 2.10273i
\(327\) 3.17305 + 4.95943i 0.175470 + 0.274257i
\(328\) 16.1893 + 28.0407i 0.893904 + 1.54829i
\(329\) 0 0
\(330\) 22.9554 44.3067i 1.26366 2.43900i
\(331\) −19.7089 −1.08330 −0.541651 0.840604i \(-0.682200\pi\)
−0.541651 + 0.840604i \(0.682200\pi\)
\(332\) −1.91741 + 3.32105i −0.105232 + 0.182266i
\(333\) −2.23891 + 4.85041i −0.122692 + 0.265801i
\(334\) 10.4174 + 18.0435i 0.570015 + 0.987296i
\(335\) 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
\(339\) 17.9751 0.819755i 0.976273 0.0445230i
\(340\) −4.97296 8.61342i −0.269697 0.467128i
\(341\) 5.25370 + 9.09967i 0.284504 + 0.492775i
\(342\) 12.5416 27.1704i 0.678174 1.46921i
\(343\) 0 0
\(344\) −26.3712 + 45.6763i −1.42184 + 2.46270i
\(345\) −1.22665 + 0.0559416i −0.0660408 + 0.00301179i
\(346\) 42.7060 2.29589
\(347\) 29.0833 1.56127 0.780636 0.624986i \(-0.214895\pi\)
0.780636 + 0.624986i \(0.214895\pi\)
\(348\) −9.31138 14.5535i −0.499142 0.780152i
\(349\) 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
\(352\) 1.21780 + 2.10929i 0.0649089 + 0.112426i
\(353\) −16.6513 28.8408i −0.886257 1.53504i −0.844266 0.535925i \(-0.819963\pi\)
−0.0419914 0.999118i \(-0.513370\pi\)
\(354\) 5.34562 10.3177i 0.284116 0.548378i
\(355\) −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
\(359\) −12.7683 22.1153i −0.673884 1.16720i −0.976794 0.214182i \(-0.931291\pi\)
0.302909 0.953019i \(-0.402042\pi\)
\(360\) −39.1613 + 3.57935i −2.06398 + 0.188648i
\(361\) 1.28220 2.22084i 0.0674842 0.116886i
\(362\) 53.8578 2.83070
\(363\) −8.75729 13.6875i −0.459639 0.718409i
\(364\) 0 0
\(365\) −1.95477 3.38576i −0.102317 0.177219i
\(366\) 4.45691 8.60235i 0.232966 0.449652i
\(367\) 13.7252 + 23.7727i 0.716449 + 1.24093i 0.962398 + 0.271644i \(0.0875672\pi\)
−0.245949 + 0.969283i \(0.579100\pi\)
\(368\) 0.591443 1.02441i 0.0308311 0.0534011i
\(369\) −8.05476 + 17.4500i −0.419314 + 0.908408i
\(370\) −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 \(0.305585\pi\)
\(374\) −10.5074 −0.543324
\(375\) 6.76449 13.0563i 0.349317 0.674222i
\(376\) −61.4690 −3.17002
\(377\) −2.46050 −0.126722
\(378\) 0 0
\(379\) 12.0364 0.618267 0.309134 0.951019i \(-0.399961\pi\)
0.309134 + 0.951019i \(0.399961\pi\)
\(380\) 42.6270 2.18672
\(381\) −0.535897 + 1.03434i −0.0274548 + 0.0529910i
\(382\) 1.72665 0.0883433
\(383\) −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
\(387\) −31.1768 + 2.84957i −1.58481 + 0.144852i
\(388\) −23.2901 + 40.3396i −1.18237 + 2.04793i
\(389\) −10.3004 17.8408i −0.522250 0.904564i −0.999665 0.0258860i \(-0.991759\pi\)
0.477414 0.878678i \(-0.341574\pi\)
\(390\) −5.08472 + 9.81411i −0.257475 + 0.496957i
\(391\) 0.129281 + 0.223922i 0.00653803 + 0.0113242i
\(392\) 0 0
\(393\) 7.38725 + 11.5462i 0.372637 + 0.582427i
\(394\) 40.3786 2.03424
\(395\) −19.0744 + 33.0378i −0.959738 + 1.66231i
\(396\) −23.0117 + 49.8528i −1.15638 + 2.50520i
\(397\) −11.8186 20.4704i −0.593157 1.02738i −0.993804 0.111146i \(-0.964548\pi\)
0.400647 0.916233i \(-0.368785\pi\)
\(398\) −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 \(0.146271\pi\)
\(402\) −31.0095 + 59.8520i −1.54661 + 2.98515i
\(403\) −1.16372 2.01561i −0.0579688 0.100405i
\(404\) −7.45904 12.9194i −0.371101 0.642766i
\(405\) −15.1424 17.7642i −0.752432 0.882710i
\(406\) 0 0
\(407\) −4.01965 + 6.96224i −0.199247 + 0.345105i
\(408\) 4.46264 + 6.97504i 0.220934 + 0.345316i
\(409\) 34.3245 1.69724 0.848619 0.529005i \(-0.177435\pi\)
0.848619 + 0.529005i \(0.177435\pi\)
\(410\) −40.8827 −2.01905
\(411\) −6.35447 + 0.289796i −0.313443 + 0.0142946i
\(412\) −19.7163 + 34.1497i −0.971354 + 1.68243i
\(413\) 0 0
\(414\) 2.00933 0.183653i 0.0987533 0.00902607i
\(415\) −1.22665 2.12463i −0.0602141 0.104294i
\(416\) −0.269748 0.467216i −0.0132255 0.0229072i
\(417\) 3.55408 0.162084i 0.174044 0.00793730i
\(418\) 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 \(-0.00495387\pi\)
\(422\) 5.61177 + 9.71987i 0.273177 + 0.473156i
\(423\) −21.0438 29.8068i −1.02318 1.44925i
\(424\) −15.8530 + 27.4582i −0.769890 + 1.33349i
\(425\) 1.63327 0.0792252
\(426\) 6.41741 12.3863i 0.310925 0.600121i
\(427\) 0 0
\(428\) 2.78580 + 4.82515i 0.134657 + 0.233232i
\(429\) 4.21420 + 6.58673i 0.203464 + 0.318010i
\(430\) −33.2975 57.6729i −1.60575 2.78123i
\(431\) −11.3092 + 19.5882i −0.544747 + 0.943530i 0.453876 + 0.891065i \(0.350041\pi\)
−0.998623 + 0.0524646i \(0.983292\pi\)
\(432\) 22.2762 3.06472i 1.07176 0.147452i
\(433\) −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
\(437\) −1.10817 −0.0530109
\(438\) 3.46216 + 5.41131i 0.165429 + 0.258562i
\(439\) 23.4897 1.12110 0.560551 0.828120i \(-0.310589\pi\)
0.560551 + 0.828120i \(0.310589\pi\)
\(440\) −59.1780 −2.82120
\(441\) 0 0
\(442\) 2.32743 0.110705
\(443\) −13.4179 −0.637503 −0.318752 0.947838i \(-0.603264\pi\)
−0.318752 + 0.947838i \(0.603264\pi\)
\(444\) 12.4911 0.569659i 0.592804 0.0270348i
\(445\) 37.2350 1.76511
\(446\) −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 \(0.569365\pi\)
\(450\) 5.34154 11.5720i 0.251803 0.545509i
\(451\) −14.4612 + 25.0475i −0.680950 + 1.17944i
\(452\) −21.0584 36.4741i −0.990502 1.71560i
\(453\) 17.1783 0.783417i 0.807107 0.0368082i
\(454\) −1.69961 2.94381i −0.0797667 0.138160i
\(455\) 0 0
\(456\) −35.4523 + 1.61680i −1.66021 + 0.0757138i
\(457\) 8.81711 0.412447 0.206224 0.978505i \(-0.433883\pi\)
0.206224 + 0.978505i \(0.433883\pi\)
\(458\) 22.1192 38.3115i 1.03356 1.79018i
\(459\) −1.85447 + 4.55185i −0.0865594 + 0.212462i
\(460\) 1.43706 + 2.48906i 0.0670033 + 0.116053i
\(461\) −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
\(465\) 5.63473 + 8.80700i 0.261304 + 0.408415i
\(466\) −23.3530 40.4486i −1.08181 1.87375i
\(467\) −10.9985 19.0500i −0.508952 0.881530i −0.999946 0.0103675i \(-0.996700\pi\)
0.490995 0.871163i \(-0.336633\pi\)
\(468\) 5.09718 11.0426i 0.235617 0.510445i
\(469\) 0 0
\(470\) 38.8068 67.2153i 1.79002 3.10041i
\(471\) 4.82383 9.31056i 0.222270 0.429008i
\(472\) −13.7807 −0.634310
\(473\) −47.1124 −2.16623
\(474\) 28.8370 55.6587i 1.32453 2.55649i
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) −18.7419 + 1.71301i −0.858133 + 0.0784336i
\(478\) 6.01819 + 10.4238i 0.275265 + 0.476774i
\(479\) 12.4875 + 21.6291i 0.570571 + 0.988257i 0.996507 + 0.0835043i \(0.0266112\pi\)
−0.425937 + 0.904753i \(0.640055\pi\)
\(480\) 1.30612 + 2.04145i 0.0596161 + 0.0931791i
\(481\) 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
\(485\) −14.8997 25.8070i −0.676561 1.17184i
\(486\) 26.1857 + 28.0259i 1.18781 + 1.27128i
\(487\) 8.79893 15.2402i 0.398717 0.690599i −0.594851 0.803836i \(-0.702789\pi\)
0.993568 + 0.113238i \(0.0361221\pi\)
\(488\) −11.4897 −0.520114
\(489\) 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 \(0.934092\pi\)
\(492\) 44.9384 2.04942i 2.02598 0.0923949i
\(493\) −1.16372 2.01561i −0.0524111 0.0907787i
\(494\) −4.98755 + 8.63868i −0.224400 + 0.388673i
\(495\) −20.2594 28.6958i −0.910594 1.28978i
\(496\) −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 \(0.261300\pi\)
\(500\) −34.4179 −1.53921
\(501\) 14.6513 0.668172i 0.654570 0.0298517i
\(502\) 45.4150 2.02697
\(503\) 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
\(506\) 3.03638 0.134983
\(507\) 11.2016 + 17.5079i 0.497478 + 0.777551i
\(508\) 2.72665 0.120976
\(509\) −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
\(513\) −12.9210 16.6376i −0.570477 0.734567i
\(514\) 14.4356 25.0032i 0.636727 1.10284i
\(515\) −12.6134 21.8471i −0.555814 0.962698i
\(516\) 39.4918 + 61.7251i 1.73853 + 2.71730i
\(517\) −27.4538 47.5514i −1.20742 2.09131i
\(518\) 0 0
\(519\) 13.8296 26.6927i 0.607051 1.17168i
\(520\) 13.1082 0.574831
\(521\) 2.20895 3.82600i 0.0967756 0.167620i −0.813573 0.581463i \(-0.802480\pi\)
0.910348 + 0.413843i \(0.135814\pi\)
\(522\) −18.0869 + 1.65314i −0.791640 + 0.0723561i
\(523\) 12.6367 + 21.8874i 0.552563 + 0.957067i 0.998089 + 0.0617982i \(0.0196835\pi\)
−0.445526 + 0.895269i \(0.646983\pi\)
\(524\) 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
\(528\) 33.8032 1.54160i 1.47110 0.0670894i
\(529\) 11.4626 + 19.8539i 0.498376 + 0.863212i
\(530\) −20.0167 34.6700i −0.869471 1.50597i
\(531\) −4.71780 6.68238i −0.204735 0.289990i
\(532\) 0 0
\(533\) 3.20321 5.54812i 0.138746 0.240316i
\(534\) −61.1203 + 2.78739i −2.64493 + 0.120622i
\(535\) −3.56440 −0.154103
\(536\) 79.9410 3.45293
\(537\) 10.5943 + 16.5587i 0.457176 + 0.714559i
\(538\) 23.1716 40.1344i 0.998998 1.73032i
\(539\) 0 0
\(540\) −20.6139 + 50.5974i −0.887081 + 2.17736i
\(541\) 1.71926 + 2.97785i 0.0739168 + 0.128028i 0.900615 0.434618i \(-0.143117\pi\)
−0.826698 + 0.562646i \(0.809783\pi\)
\(542\) 29.5043 + 51.1029i 1.26732 + 2.19506i
\(543\) 17.4409 33.6629i 0.748459 1.44461i
\(544\) 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 \(0.119346\pi\)
\(548\) 7.44445 + 12.8942i 0.318011 + 0.550812i
\(549\) −3.93346 5.57143i −0.167876 0.237783i
\(550\) 9.58998 16.6103i 0.408918 0.708267i
\(551\) 9.97509 0.424953
\(552\) −1.28959 2.01561i −0.0548887 0.0857902i
\(553\) 0 0
\(554\) 8.81138 + 15.2618i 0.374360 + 0.648410i
\(555\) −3.67996 + 7.10275i −0.156206 + 0.301495i
\(556\) −4.16372 7.21177i −0.176581 0.305847i
\(557\) −16.7917 + 29.0841i −0.711488 + 1.23233i 0.252810 + 0.967516i \(0.418645\pi\)
−0.964298 + 0.264818i \(0.914688\pi\)
\(558\) −9.90856 14.0347i −0.419463 0.594134i
\(559\) 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
\(563\) −42.4792 −1.79028 −0.895142 0.445781i \(-0.852926\pi\)
−0.895142 + 0.445781i \(0.852926\pi\)
\(564\) −39.2871 + 75.8288i −1.65429 + 3.19297i
\(565\) 26.9439 1.13354
\(566\) 49.2029 2.06815
\(567\) 0 0
\(568\) −16.5438 −0.694161
\(569\) 10.4035 0.436137 0.218069 0.975933i \(-0.430024\pi\)
0.218069 + 0.975933i \(0.430024\pi\)
\(570\) 20.6139 39.7872i 0.863421 1.66650i
\(571\) 17.8496 0.746983 0.373491 0.927634i \(-0.378161\pi\)
0.373491 + 0.927634i \(0.378161\pi\)
\(572\) 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
\(576\) 12.6783 + 17.9578i 0.528263 + 0.748241i
\(577\) 5.97150 10.3429i 0.248597 0.430582i −0.714540 0.699595i \(-0.753364\pi\)
0.963137 + 0.269013i \(0.0866973\pi\)
\(578\) −19.8135 34.3180i −0.824134 1.42744i
\(579\) −9.67665 + 18.6771i −0.402148 + 0.776192i
\(580\) −12.9356 22.4051i −0.537122 0.930322i
\(581\) 0 0
\(582\) 26.3894 + 41.2462i 1.09388 + 1.70971i
\(583\) −28.3216 −1.17296
\(584\) 3.80924 6.59780i 0.157628 0.273019i
\(585\) 4.48755 + 6.35624i 0.185537 + 0.262798i
\(586\) −18.5344 32.1026i −0.765650 1.32615i
\(587\) 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
\(591\) 13.0759 25.2380i 0.537869 1.03815i
\(592\) −3.85301 6.67361i −0.158358 0.274284i
\(593\) 9.79007 + 16.9569i 0.402030 + 0.696336i 0.993971 0.109645i \(-0.0349714\pi\)
−0.591941 + 0.805981i \(0.701638\pi\)
\(594\) 35.4035 + 45.5868i 1.45262 + 1.87045i
\(595\) 0 0
\(596\) 27.4538 47.5514i 1.12455 1.94778i
\(597\) 21.1952 + 33.1278i 0.867463 + 1.35583i
\(598\) −0.672570 −0.0275034
\(599\) 18.5467 0.757797 0.378899 0.925438i \(-0.376303\pi\)
0.378899 + 0.925438i \(0.376303\pi\)
\(600\) −15.0993 + 0.688605i −0.616427 + 0.0281122i
\(601\) −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
\(604\) −20.1249 34.8573i −0.818870 1.41832i
\(605\) −12.1659 21.0719i −0.494612 0.856693i
\(606\) −15.6659 + 0.714442i −0.636382 + 0.0290222i
\(607\) −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
\(611\) 6.08113 + 10.5328i 0.246016 + 0.426112i
\(612\) 11.4567 1.04715i 0.463110 0.0423284i
\(613\) −5.11849 + 8.86548i −0.206734 + 0.358073i −0.950684 0.310162i \(-0.899617\pi\)
0.743950 + 0.668235i \(0.232950\pi\)
\(614\) −67.0990 −2.70790
\(615\) −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 \(0.760111\pi\)
\(618\) 22.3401 + 34.9172i 0.898650 + 1.40458i
\(619\) 4.31663 + 7.47663i 0.173500 + 0.300511i 0.939641 0.342161i \(-0.111159\pi\)
−0.766141 + 0.642672i \(0.777826\pi\)
\(620\) 12.2360 21.1934i 0.491409 0.851145i
\(621\) 0.535897 1.31537i 0.0215048 0.0527841i
\(622\) −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
\(626\) 28.5366 1.14055
\(627\) −17.0847 26.7032i −0.682298 1.06642i
\(628\) −24.5438 −0.979403
\(629\) 1.68443 0.0671626
\(630\) 0 0
\(631\) −14.8535 −0.591308 −0.295654 0.955295i \(-0.595538\pi\)
−0.295654 + 0.955295i \(0.595538\pi\)
\(632\) −74.3402 −2.95710
\(633\) 7.89251 0.359938i 0.313699 0.0143063i
\(634\) 4.96458 0.197169
\(635\) −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
\(639\) −5.66372 8.02219i −0.224053 0.317353i
\(640\) −24.7793 + 42.9190i −0.979487 + 1.69652i
\(641\) 17.0797 + 29.5828i 0.674606 + 1.16845i 0.976584 + 0.215137i \(0.0690199\pi\)
−0.301978 + 0.953315i \(0.597647\pi\)
\(642\) 5.85087 0.266829i 0.230916 0.0105309i
\(643\) −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
\(646\) −9.43560 −0.371239
\(647\) 16.4846 28.5522i 0.648077 1.12250i −0.335504 0.942039i \(-0.608907\pi\)
0.983582 0.180464i \(-0.0577600\pi\)
\(648\) 15.2252 42.8630i 0.598102 1.68382i
\(649\) −6.15486 10.6605i −0.241599 0.418462i
\(650\) −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 \(0.142159\pi\)
\(654\) −7.80730 12.2027i −0.305290 0.477163i
\(655\) 10.2626 + 17.7753i 0.400991 + 0.694537i
\(656\) −13.8617 24.0091i −0.541207 0.937399i
\(657\) 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 \(0.272890\pi\)
\(660\) −37.8228 + 73.0025i −1.47225 + 2.84162i
\(661\) 17.0216 0.662063 0.331032 0.943620i \(-0.392603\pi\)
0.331032 + 0.943620i \(0.392603\pi\)
\(662\) 48.4940 1.88477
\(663\) 0.753696 1.45472i 0.0292711 0.0564967i
\(664\) 2.39037 4.14024i 0.0927643 0.160672i
\(665\) 0 0
\(666\) 5.50885 11.9345i 0.213464 0.462451i
\(667\) 0.336285 + 0.582462i 0.0130210 + 0.0225530i
\(668\) −17.1644 29.7296i −0.664110 1.15027i
\(669\) 12.4379 + 19.4403i 0.480878 + 0.751605i
\(670\) −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 \(0.979758\pi\)
\(674\) −35.7403 61.9039i −1.37666 2.38445i
\(675\) −5.50312 7.08602i −0.211815 0.272741i
\(676\) 24.3245 42.1313i 0.935558 1.62043i
\(677\) 6.03638 0.231997 0.115998 0.993249i \(-0.462993\pi\)
0.115998 + 0.993249i \(0.462993\pi\)
\(678\) −44.2278 + 2.01701i −1.69856 + 0.0774628i
\(679\) 0 0
\(680\) 6.19961 + 10.7380i 0.237744 + 0.411785i
\(681\) −2.39037 + 0.109013i −0.0915991 + 0.00417738i
\(682\) −12.9267 22.3898i −0.494991 0.857349i
\(683\) −10.2556 + 17.7633i −0.392421 + 0.679693i −0.992768 0.120046i \(-0.961696\pi\)
0.600347 + 0.799739i \(0.295029\pi\)
\(684\) −20.6644 + 44.7677i −0.790123 + 1.71173i
\(685\) −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
\(689\) 6.27335 0.238995
\(690\) 3.01819 0.137645i 0.114900 0.00524004i
\(691\) 15.0029 0.570738 0.285369 0.958418i \(-0.407884\pi\)
0.285369 + 0.958418i \(0.407884\pi\)
\(692\) −70.3652 −2.67488
\(693\) 0 0
\(694\) −71.5595 −2.71636
\(695\) 5.32743 0.202081
\(696\) 11.6082 + 18.1434i 0.440006 + 0.687724i
\(697\) 6.05993 0.229536
\(698\) −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 \(0.240786\pi\)
\(702\) −7.84202 10.0977i −0.295978 0.381112i
\(703\) −3.60963 + 6.25206i −0.136140 + 0.235801i
\(704\) 16.5402 + 28.6484i 0.623381 + 1.07973i
\(705\) −29.4449 46.0220i −1.10896 1.73329i
\(706\) 40.9705 + 70.9630i 1.54195 + 2.67073i
\(707\) 0 0
\(708\) −8.80778 + 17.0000i −0.331017 + 0.638901i
\(709\) 7.64008 0.286929 0.143465 0.989655i \(-0.454176\pi\)
0.143465 + 0.989655i \(0.454176\pi\)
\(710\) 10.4445 18.0903i 0.391973 0.678918i
\(711\) −25.4502 36.0481i −0.954457 1.35191i
\(712\) 36.2798 + 62.8384i 1.35964 + 2.35497i
\(713\) −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
\(717\) 8.46410 0.386006i 0.316098 0.0144157i
\(718\) 31.4164 + 54.4148i 1.17245 + 2.03074i
\(719\) −15.0182 26.0123i −0.560084 0.970094i −0.997488 0.0708289i \(-0.977436\pi\)
0.437405 0.899265i \(-0.355898\pi\)
\(720\) 33.5308 3.06472i 1.24962 0.114216i
\(721\) 0 0
\(722\) −3.15486 + 5.46438i −0.117412 + 0.203363i
\(723\) 45.2622 2.06419i 1.68332 0.0767679i
\(724\) −88.7395 −3.29798
\(725\) 4.24844 0.157783
\(726\) 21.5474 + 33.6782i 0.799698 + 1.24992i
\(727\) 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
\(730\) 4.80972 + 8.33068i 0.178016 + 0.308332i
\(731\) 4.93560 + 8.54871i 0.182550 + 0.316185i
\(732\) −7.34348 + 14.1738i −0.271423 + 0.523878i
\(733\) 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
\(737\) 35.7039 + 61.8409i 1.31517 + 2.27794i
\(738\) 19.8188 42.9357i 0.729539 1.58048i
\(739\) −22.5620 + 39.0785i −0.829955 + 1.43752i 0.0681179 + 0.997677i \(0.478301\pi\)
−0.898073 + 0.439847i \(0.855033\pi\)
\(740\) 18.7237 0.688298
\(741\) 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 \(0.889008\pi\)
\(744\) −9.37266 + 18.0903i −0.343618 + 0.663223i
\(745\) 17.5634 + 30.4207i 0.643474 + 1.11453i
\(746\) 20.0869 34.7915i 0.735432 1.27381i
\(747\) 2.82597 0.258294i 0.103397 0.00945048i
\(748\) 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 \(0.109256\pi\)
\(752\) 52.6313 1.91927
\(753\) 14.7068 28.3859i 0.535946 1.03444i
\(754\) 6.05408 0.220477
\(755\) 25.7496 0.937124
\(756\) 0 0
\(757\) −41.8171 −1.51987 −0.759934 0.650000i \(-0.774769\pi\)
−0.759934 + 0.650000i \(0.774769\pi\)
\(758\) −29.6156 −1.07569
\(759\) 0.983275 1.89783i 0.0356906 0.0688870i
\(760\) −53.1416 −1.92765
\(761\) 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
\(765\) −3.08453 + 6.68238i −0.111521 + 0.241602i
\(766\) 15.2989 26.4985i 0.552773 0.957430i
\(767\) 1.36333 + 2.36135i 0.0492269 + 0.0852635i
\(768\) 25.7848 49.7677i 0.930429 1.79584i
\(769\) 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
\(772\) 49.2350 1.77201
\(773\) −20.9107 + 36.2184i −0.752105 + 1.30268i 0.194695 + 0.980864i \(0.437628\pi\)
−0.946801 + 0.321821i \(0.895705\pi\)
\(774\) 76.7108 7.01138i 2.75731 0.252019i
\(775\) 2.00933 + 3.48027i 0.0721774 + 0.125015i
\(776\) 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
\(780\) 8.37792