Properties

Label 441.2.h.c.214.1
Level $441$
Weight $2$
Character 441.214
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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.c.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 \(-0.636409\pi\)
0.995485 0.0949156i \(-0.0302581\pi\)
\(6\) −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 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 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 −0.802954 0.596041i \(-0.796740\pi\)
0.917663 + 0.397359i \(0.130073\pi\)
\(18\) 4.25729 + 6.03011i 1.00345 + 1.42131i
\(19\) 2.02704 + 3.51094i 0.465035 + 0.805465i 0.999203 0.0399136i \(-0.0127083\pi\)
−0.534168 + 0.845378i \(0.679375\pi\)
\(20\) 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 \(-0.432976\pi\)
0.209009 + 0.977914i \(0.432976\pi\)
\(32\) −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 \(9.46187e-5\pi\)
−0.499743 + 0.866174i \(0.666572\pi\)
\(42\) 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 \(-0.847231\pi\)
−0.887023 + 0.461724i \(0.847231\pi\)
\(48\) 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 \(-0.556798\pi\)
−0.177490 + 0.984123i \(0.556798\pi\)
\(60\) −9.81498 15.3407i −1.26711 1.98047i
\(61\) −2.27335 −0.291072 −0.145536 0.989353i \(-0.546491\pi\)
−0.145536 + 0.989353i \(0.546491\pi\)
\(62\) −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 −0.818543 0.574446i \(-0.805218\pi\)
0.906756 + 0.421656i \(0.138551\pi\)
\(74\) 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 −0.838901 0.544285i \(-0.816801\pi\)
0.890815 + 0.454367i \(0.150135\pi\)
\(84\) 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 \(0.108575\pi\)
−0.181489 + 0.983393i \(0.558092\pi\)
\(90\) 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 \(-0.635094\pi\)
0.995085 0.0990246i \(-0.0315722\pi\)
\(98\) 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 0.942926 0.333002i \(-0.108061\pi\)
−0.759851 + 0.650097i \(0.774728\pi\)
\(102\) 2.17257 + 3.39569i 0.215116 + 0.336224i
\(103\) 4.86333 8.42353i 0.479198 0.829995i −0.520518 0.853851i \(-0.674261\pi\)
0.999715 + 0.0238560i \(0.00759431\pi\)
\(104\) 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 −0.985484 0.169770i \(-0.945697\pi\)
0.639767 + 0.768569i \(0.279031\pi\)
\(132\) −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 0.906289 0.422658i \(-0.138903\pi\)
−0.819177 + 0.573541i \(0.805569\pi\)
\(140\) 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 \(-0.422333\pi\)
0.241584 + 0.970380i \(0.422333\pi\)
\(158\) −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 0.982040 0.188672i \(-0.0604183\pi\)
−0.654415 + 0.756136i \(0.727085\pi\)
\(168\) 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 \(-0.270641\pi\)
0.659799 + 0.751442i \(0.270641\pi\)
\(174\) −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 \(-0.197562\pi\)
0.813495 + 0.581572i \(0.197562\pi\)
\(182\) 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 \(0.464391\pi\)
−0.916430 + 0.400194i \(0.868943\pi\)
\(200\) 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 −0.998131 0.0611159i \(-0.980534\pi\)
0.551993 + 0.833849i \(0.313867\pi\)
\(224\) 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 0.842191 0.539179i \(-0.181265\pi\)
−0.888038 + 0.459769i \(0.847932\pi\)
\(228\) 28.4377 1.29690i 1.88334 0.0858896i
\(229\) 8.98968 15.5706i 0.594055 1.02893i −0.399625 0.916679i \(-0.630859\pi\)
0.993679 0.112254i \(-0.0358072\pi\)
\(230\) 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 \(0.152271\pi\)
−0.0452094 + 0.998978i \(0.514396\pi\)
\(242\) 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 \(-0.302068\pi\)
0.582516 + 0.812819i \(0.302068\pi\)
\(252\) 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 −0.622962 0.782252i \(-0.714071\pi\)
0.988931 + 0.148375i \(0.0474044\pi\)
\(258\) 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 \(-0.638651\pi\)
0.996129 0.0879017i \(-0.0280161\pi\)
\(270\) 12.5110 30.7086i 0.761395 1.86886i
\(271\) 11.9911 + 20.7693i 0.728410 + 1.26164i 0.957555 + 0.288251i \(0.0930738\pi\)
−0.229145 + 0.973392i \(0.573593\pi\)
\(272\) 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 \(-0.297409\pi\)
0.594351 + 0.804205i \(0.297409\pi\)
\(284\) 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 0.557625 0.830093i \(-0.311713\pi\)
−0.997694 + 0.0678705i \(0.978380\pi\)
\(294\) 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 \(-0.783868\pi\)
−0.778203 + 0.628013i \(0.783868\pi\)
\(308\) 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 \(-0.649695\pi\)
−0.453136 + 0.891441i \(0.649695\pi\)
\(312\) 8.74484 0.398809i 0.495079 0.0225781i
\(313\) 11.5979 0.655549 0.327775 0.944756i \(-0.393701\pi\)
0.327775 + 0.944756i \(0.393701\pi\)
\(314\) −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 \(0.397285\pi\)
−0.979885 + 0.199561i \(0.936049\pi\)
\(350\) 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 \(0.180037\pi\)
0.0419914 + 0.999118i \(0.486630\pi\)
\(354\) 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 \(-0.912433\pi\)
0.245949 0.969283i \(-0.420900\pi\)
\(368\) 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 −0.662296 0.749242i \(-0.730418\pi\)
0.980011 + 0.198944i \(0.0637512\pi\)
\(384\) 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 \(0.0354521\pi\)
−0.400647 + 0.916233i \(0.631215\pi\)
\(398\) 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 \(-0.822565\pi\)
−0.848619 + 0.529005i \(0.822565\pi\)
\(410\) −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 0.812213 0.583361i \(-0.198263\pi\)
−0.911312 + 0.411717i \(0.864929\pi\)
\(420\) 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 \(-0.481496\pi\)
0.0580982 + 0.998311i \(0.481496\pi\)
\(434\) 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 \(-0.689411\pi\)
−0.560551 + 0.828120i \(0.689411\pi\)
\(440\) 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 −0.792579 0.609769i \(-0.791262\pi\)
0.924365 + 0.381509i \(0.124595\pi\)
\(462\) 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 \(0.00330013\pi\)
−0.490995 + 0.871163i \(0.663367\pi\)
\(468\) −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 \(-0.973389\pi\)
0.425937 0.904753i \(-0.359945\pi\)
\(480\) 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 \(-0.665677\pi\)
−0.497305 + 0.867576i \(0.665677\pi\)
\(504\) 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 −0.634413 0.772994i \(-0.718758\pi\)
0.986639 + 0.162920i \(0.0520914\pi\)
\(510\) 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 −0.910348 0.413843i \(-0.864186\pi\)
0.813573 + 0.581463i \(0.197520\pi\)
\(522\) −18.0869 + 1.65314i −0.791640 + 0.0723561i
\(523\) −12.6367 21.8874i −0.552563 0.957067i −0.998089 0.0617982i \(-0.980316\pi\)
0.445526 0.895269i \(-0.353017\pi\)
\(524\) −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 \(-0.147074\pi\)
0.895142 + 0.445781i \(0.147074\pi\)
\(564\) −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 −0.963137 0.269013i \(-0.913303\pi\)
0.714540 + 0.699595i \(0.246636\pi\)
\(578\) −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 −0.999962 0.00875568i \(-0.997213\pi\)
0.507563 + 0.861614i \(0.330546\pi\)
\(588\) 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 0.591941 0.805981i \(-0.298362\pi\)
−0.993971 + 0.109645i \(0.965029\pi\)
\(594\) −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 −0.618577 0.785724i \(-0.712290\pi\)
0.989746 + 0.142841i \(0.0456238\pi\)
\(602\) 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 −0.545795 0.837919i \(-0.683772\pi\)
0.998556 + 0.0537125i \(0.0171055\pi\)
\(608\) −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 0.766141 0.642672i \(-0.222174\pi\)
−0.939641 + 0.342161i \(0.888841\pi\)
\(620\) 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 0.952852 0.303437i \(-0.0981341\pi\)
−0.739210 + 0.673475i \(0.764801\pi\)
\(644\) 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 \(0.391093\pi\)
−0.983582 + 0.180464i \(0.942240\pi\)
\(648\) 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 \(-0.607397\pi\)
−0.331032 + 0.943620i \(0.607397\pi\)
\(662\) 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 \(-0.537007\pi\)
−0.115998 + 0.993249i \(0.537007\pi\)
\(678\) 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 \(-0.592116\pi\)
−0.285369 + 0.958418i \(0.592116\pi\)
\(692\) 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 \(0.0225644\pi\)
−0.437405 + 0.899265i \(0.644102\pi\)
\(720\) −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 −0.896291 0.443466i \(-0.853749\pi\)
0.832199 + 0.554478i \(0.187082\pi\)
\(728\) 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 \(0.418649\pi\)
−0.964295 + 0.264829i \(0.914685\pi\)
\(734\) 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 −0.995585 0.0938675i \(-0.970077\pi\)
0.579084 + 0.815268i \(0.303410\pi\)
\(762\) −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 0.805923 0.592021i \(-0.201670\pi\)
−0.915666 + 0.401939i \(0.868336\pi\)
\(770\) 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 \(-0.562372\pi\)
0.946801 0.321821i \(-0.104295\pi\)
\(774\) 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 + 16.1704i −0.299978 + 0.578991i
\(781\)