Properties

Label 546.2.o.b.265.3
Level $546$
Weight $2$
Character 546.265
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.836829184.2
Defining polynomial: \(x^{8} + 14 x^{6} + 61 x^{4} + 84 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 265.3
Root \(2.63640i\) of defining polynomial
Character \(\chi\) \(=\) 546.265
Dual form 546.2.o.b.307.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-1.15711 - 1.15711i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.02133 - 1.70711i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-1.15711 - 1.15711i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.02133 - 1.70711i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -1.63640 q^{10} +(1.37930 + 1.37930i) q^{11} -1.00000 q^{12} +(-1.50062 - 3.27843i) q^{13} +(0.222191 - 2.63640i) q^{14} +(-1.15711 + 1.15711i) q^{15} -1.00000 q^{16} -1.50625 q^{17} +(-0.707107 + 0.707107i) q^{18} +(-0.934922 - 0.934922i) q^{19} +(-1.15711 + 1.15711i) q^{20} +(-1.70711 - 2.02133i) q^{21} +1.95063 q^{22} +4.19327i q^{23} +(-0.707107 + 0.707107i) q^{24} -2.32218i q^{25} +(-3.37930 - 1.25710i) q^{26} +1.00000i q^{27} +(-1.70711 - 2.02133i) q^{28} -0.406261 q^{29} +1.63640i q^{30} +(-2.31423 - 2.31423i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.37930 - 1.37930i) q^{33} +(-1.06508 + 1.06508i) q^{34} +(-4.31423 - 0.363595i) q^{35} +1.00000i q^{36} +(0.257101 + 0.257101i) q^{37} -1.32218 q^{38} +(-3.27843 + 1.50062i) q^{39} +1.63640i q^{40} +(3.60624 + 3.60624i) q^{41} +(-2.63640 - 0.222191i) q^{42} -2.46483i q^{43} +(1.37930 - 1.37930i) q^{44} +(1.15711 + 1.15711i) q^{45} +(2.96509 + 2.96509i) q^{46} +(-1.41421 + 1.41421i) q^{47} +1.00000i q^{48} +(1.17157 - 6.90126i) q^{49} +(-1.64203 - 1.64203i) q^{50} +1.50625i q^{51} +(-3.27843 + 1.50062i) q^{52} +13.4456 q^{53} +(0.707107 + 0.707107i) q^{54} -3.19202i q^{55} +(-2.63640 - 0.222191i) q^{56} +(-0.934922 + 0.934922i) q^{57} +(-0.287270 + 0.287270i) q^{58} +(8.75986 - 8.75986i) q^{59} +(1.15711 + 1.15711i) q^{60} +11.7394i q^{61} -3.27281 q^{62} +(-2.02133 + 1.70711i) q^{63} +1.00000i q^{64} +(-2.05713 + 5.52991i) q^{65} -1.95063i q^{66} +(11.1012 - 11.1012i) q^{67} +1.50625i q^{68} +4.19327 q^{69} +(-3.30772 + 2.79352i) q^{70} +(-5.18078 + 5.18078i) q^{71} +(0.707107 + 0.707107i) q^{72} +(-2.56008 + 2.56008i) q^{73} +0.363595 q^{74} -2.32218 q^{75} +(-0.934922 + 0.934922i) q^{76} +(5.14265 + 0.433413i) q^{77} +(-1.25710 + 3.37930i) q^{78} +1.42546 q^{79} +(1.15711 + 1.15711i) q^{80} +1.00000 q^{81} +5.09999 q^{82} +(4.90797 + 4.90797i) q^{83} +(-2.02133 + 1.70711i) q^{84} +(1.74290 + 1.74290i) q^{85} +(-1.74290 - 1.74290i) q^{86} +0.406261i q^{87} -1.95063i q^{88} +(2.03017 - 2.03017i) q^{89} +1.63640 q^{90} +(-8.62990 - 4.06508i) q^{91} +4.19327 q^{92} +(-2.31423 + 2.31423i) q^{93} +2.00000i q^{94} +2.16362i q^{95} +(0.707107 + 0.707107i) q^{96} +(10.2741 + 10.2741i) q^{97} +(-4.05150 - 5.70836i) q^{98} +(-1.37930 - 1.37930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 8q^{9} + O(q^{10}) \) \( 8q - 4q^{5} - 8q^{9} + 4q^{10} - 8q^{12} + 16q^{13} - 4q^{14} - 4q^{15} - 8q^{16} + 4q^{17} - 8q^{19} - 4q^{20} - 8q^{21} - 12q^{22} - 16q^{26} - 8q^{28} + 12q^{29} - 8q^{31} - 8q^{34} - 24q^{35} - 4q^{37} - 4q^{38} - 4q^{39} + 12q^{41} - 4q^{42} + 4q^{45} + 24q^{46} + 32q^{49} - 8q^{50} - 4q^{52} + 40q^{53} - 4q^{56} - 8q^{57} + 4q^{58} - 8q^{59} + 4q^{60} + 8q^{62} - 12q^{65} + 32q^{67} - 28q^{69} + 8q^{70} - 12q^{71} + 20q^{73} + 20q^{74} - 12q^{75} - 8q^{76} + 8q^{77} - 4q^{78} + 24q^{79} + 4q^{80} + 8q^{81} + 40q^{82} + 44q^{83} + 20q^{85} - 20q^{86} + 16q^{89} - 4q^{90} - 28q^{91} - 28q^{92} - 8q^{93} - 8q^{97} - 16q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 1.00000i 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) −1.15711 1.15711i −0.517477 0.517477i 0.399330 0.916807i \(-0.369243\pi\)
−0.916807 + 0.399330i \(0.869243\pi\)
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) 2.02133 1.70711i 0.763992 0.645226i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.00000 −0.333333
\(10\) −1.63640 −0.517477
\(11\) 1.37930 + 1.37930i 0.415876 + 0.415876i 0.883780 0.467904i \(-0.154991\pi\)
−0.467904 + 0.883780i \(0.654991\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.50062 3.27843i −0.416198 0.909274i
\(14\) 0.222191 2.63640i 0.0593831 0.704609i
\(15\) −1.15711 + 1.15711i −0.298765 + 0.298765i
\(16\) −1.00000 −0.250000
\(17\) −1.50625 −0.365319 −0.182659 0.983176i \(-0.558471\pi\)
−0.182659 + 0.983176i \(0.558471\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) −0.934922 0.934922i −0.214486 0.214486i 0.591684 0.806170i \(-0.298463\pi\)
−0.806170 + 0.591684i \(0.798463\pi\)
\(20\) −1.15711 + 1.15711i −0.258738 + 0.258738i
\(21\) −1.70711 2.02133i −0.372521 0.441091i
\(22\) 1.95063 0.415876
\(23\) 4.19327i 0.874358i 0.899375 + 0.437179i \(0.144022\pi\)
−0.899375 + 0.437179i \(0.855978\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 2.32218i 0.464436i
\(26\) −3.37930 1.25710i −0.662736 0.246538i
\(27\) 1.00000i 0.192450i
\(28\) −1.70711 2.02133i −0.322613 0.381996i
\(29\) −0.406261 −0.0754407 −0.0377204 0.999288i \(-0.512010\pi\)
−0.0377204 + 0.999288i \(0.512010\pi\)
\(30\) 1.63640i 0.298765i
\(31\) −2.31423 2.31423i −0.415647 0.415647i 0.468053 0.883700i \(-0.344956\pi\)
−0.883700 + 0.468053i \(0.844956\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 1.37930 1.37930i 0.240106 0.240106i
\(34\) −1.06508 + 1.06508i −0.182659 + 0.182659i
\(35\) −4.31423 0.363595i −0.729237 0.0614588i
\(36\) 1.00000i 0.166667i
\(37\) 0.257101 + 0.257101i 0.0422671 + 0.0422671i 0.727924 0.685657i \(-0.240485\pi\)
−0.685657 + 0.727924i \(0.740485\pi\)
\(38\) −1.32218 −0.214486
\(39\) −3.27843 + 1.50062i −0.524969 + 0.240292i
\(40\) 1.63640i 0.258738i
\(41\) 3.60624 + 3.60624i 0.563199 + 0.563199i 0.930215 0.367015i \(-0.119620\pi\)
−0.367015 + 0.930215i \(0.619620\pi\)
\(42\) −2.63640 0.222191i −0.406806 0.0342849i
\(43\) 2.46483i 0.375883i −0.982180 0.187942i \(-0.939818\pi\)
0.982180 0.187942i \(-0.0601816\pi\)
\(44\) 1.37930 1.37930i 0.207938 0.207938i
\(45\) 1.15711 + 1.15711i 0.172492 + 0.172492i
\(46\) 2.96509 + 2.96509i 0.437179 + 0.437179i
\(47\) −1.41421 + 1.41421i −0.206284 + 0.206284i −0.802686 0.596402i \(-0.796597\pi\)
0.596402 + 0.802686i \(0.296597\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 1.17157 6.90126i 0.167368 0.985895i
\(50\) −1.64203 1.64203i −0.232218 0.232218i
\(51\) 1.50625i 0.210917i
\(52\) −3.27843 + 1.50062i −0.454637 + 0.208099i
\(53\) 13.4456 1.84690 0.923450 0.383719i \(-0.125357\pi\)
0.923450 + 0.383719i \(0.125357\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 3.19202i 0.430412i
\(56\) −2.63640 0.222191i −0.352304 0.0296916i
\(57\) −0.934922 + 0.934922i −0.123833 + 0.123833i
\(58\) −0.287270 + 0.287270i −0.0377204 + 0.0377204i
\(59\) 8.75986 8.75986i 1.14044 1.14044i 0.152066 0.988370i \(-0.451407\pi\)
0.988370 0.152066i \(-0.0485927\pi\)
\(60\) 1.15711 + 1.15711i 0.149383 + 0.149383i
\(61\) 11.7394i 1.50308i 0.659689 + 0.751539i \(0.270688\pi\)
−0.659689 + 0.751539i \(0.729312\pi\)
\(62\) −3.27281 −0.415647
\(63\) −2.02133 + 1.70711i −0.254664 + 0.215075i
\(64\) 1.00000i 0.125000i
\(65\) −2.05713 + 5.52991i −0.255155 + 0.685901i
\(66\) 1.95063i 0.240106i
\(67\) 11.1012 11.1012i 1.35623 1.35623i 0.477720 0.878512i \(-0.341464\pi\)
0.878512 0.477720i \(-0.158536\pi\)
\(68\) 1.50625i 0.182659i
\(69\) 4.19327 0.504811
\(70\) −3.30772 + 2.79352i −0.395348 + 0.333889i
\(71\) −5.18078 + 5.18078i −0.614845 + 0.614845i −0.944205 0.329360i \(-0.893167\pi\)
0.329360 + 0.944205i \(0.393167\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) −2.56008 + 2.56008i −0.299635 + 0.299635i −0.840871 0.541236i \(-0.817957\pi\)
0.541236 + 0.840871i \(0.317957\pi\)
\(74\) 0.363595 0.0422671
\(75\) −2.32218 −0.268142
\(76\) −0.934922 + 0.934922i −0.107243 + 0.107243i
\(77\) 5.14265 + 0.433413i 0.586060 + 0.0493920i
\(78\) −1.25710 + 3.37930i −0.142339 + 0.382631i
\(79\) 1.42546 0.160377 0.0801884 0.996780i \(-0.474448\pi\)
0.0801884 + 0.996780i \(0.474448\pi\)
\(80\) 1.15711 + 1.15711i 0.129369 + 0.129369i
\(81\) 1.00000 0.111111
\(82\) 5.09999 0.563199
\(83\) 4.90797 + 4.90797i 0.538719 + 0.538719i 0.923153 0.384434i \(-0.125603\pi\)
−0.384434 + 0.923153i \(0.625603\pi\)
\(84\) −2.02133 + 1.70711i −0.220545 + 0.186261i
\(85\) 1.74290 + 1.74290i 0.189044 + 0.189044i
\(86\) −1.74290 1.74290i −0.187942 0.187942i
\(87\) 0.406261i 0.0435557i
\(88\) 1.95063i 0.207938i
\(89\) 2.03017 2.03017i 0.215198 0.215198i −0.591274 0.806471i \(-0.701375\pi\)
0.806471 + 0.591274i \(0.201375\pi\)
\(90\) 1.63640 0.172492
\(91\) −8.62990 4.06508i −0.904659 0.426136i
\(92\) 4.19327 0.437179
\(93\) −2.31423 + 2.31423i −0.239974 + 0.239974i
\(94\) 2.00000i 0.206284i
\(95\) 2.16362i 0.221983i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) 10.2741 + 10.2741i 1.04317 + 1.04317i 0.999025 + 0.0441477i \(0.0140572\pi\)
0.0441477 + 0.999025i \(0.485943\pi\)
\(98\) −4.05150 5.70836i −0.409264 0.576631i
\(99\) −1.37930 1.37930i −0.138625 0.138625i
\(100\) −2.32218 −0.232218
\(101\) −1.93018 −0.192060 −0.0960301 0.995378i \(-0.530615\pi\)
−0.0960301 + 0.995378i \(0.530615\pi\)
\(102\) 1.06508 + 1.06508i 0.105458 + 0.105458i
\(103\) 7.94886 0.783225 0.391612 0.920130i \(-0.371917\pi\)
0.391612 + 0.920130i \(0.371917\pi\)
\(104\) −1.25710 + 3.37930i −0.123269 + 0.331368i
\(105\) −0.363595 + 4.31423i −0.0354832 + 0.421025i
\(106\) 9.50750 9.50750i 0.923450 0.923450i
\(107\) −3.33315 −0.322228 −0.161114 0.986936i \(-0.551509\pi\)
−0.161114 + 0.986936i \(0.551509\pi\)
\(108\) 1.00000 0.0962250
\(109\) 9.58382 9.58382i 0.917964 0.917964i −0.0789174 0.996881i \(-0.525146\pi\)
0.996881 + 0.0789174i \(0.0251463\pi\)
\(110\) −2.25710 2.25710i −0.215206 0.215206i
\(111\) 0.257101 0.257101i 0.0244029 0.0244029i
\(112\) −2.02133 + 1.70711i −0.190998 + 0.161306i
\(113\) −10.3865 −0.977084 −0.488542 0.872540i \(-0.662471\pi\)
−0.488542 + 0.872540i \(0.662471\pi\)
\(114\) 1.32218i 0.123833i
\(115\) 4.85209 4.85209i 0.452460 0.452460i
\(116\) 0.406261i 0.0377204i
\(117\) 1.50062 + 3.27843i 0.138733 + 0.303091i
\(118\) 12.3883i 1.14044i
\(119\) −3.04463 + 2.57133i −0.279101 + 0.235713i
\(120\) 1.63640 0.149383
\(121\) 7.19504i 0.654094i
\(122\) 8.30102 + 8.30102i 0.751539 + 0.751539i
\(123\) 3.60624 3.60624i 0.325163 0.325163i
\(124\) −2.31423 + 2.31423i −0.207824 + 0.207824i
\(125\) −8.47259 + 8.47259i −0.757811 + 0.757811i
\(126\) −0.222191 + 2.63640i −0.0197944 + 0.234870i
\(127\) 9.12016i 0.809283i −0.914475 0.404642i \(-0.867396\pi\)
0.914475 0.404642i \(-0.132604\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −2.46483 −0.217016
\(130\) 2.45563 + 5.36484i 0.215373 + 0.470528i
\(131\) 3.98205i 0.347913i −0.984753 0.173957i \(-0.944345\pi\)
0.984753 0.173957i \(-0.0556553\pi\)
\(132\) −1.37930 1.37930i −0.120053 0.120053i
\(133\) −3.48580 0.293777i −0.302257 0.0254737i
\(134\) 15.6995i 1.35623i
\(135\) 1.15711 1.15711i 0.0995884 0.0995884i
\(136\) 1.06508 + 1.06508i 0.0913297 + 0.0913297i
\(137\) 13.8868 + 13.8868i 1.18643 + 1.18643i 0.978047 + 0.208382i \(0.0668197\pi\)
0.208382 + 0.978047i \(0.433180\pi\)
\(138\) 2.96509 2.96509i 0.252405 0.252405i
\(139\) 7.37155i 0.625247i −0.949877 0.312623i \(-0.898792\pi\)
0.949877 0.312623i \(-0.101208\pi\)
\(140\) −0.363595 + 4.31423i −0.0307294 + 0.364619i
\(141\) 1.41421 + 1.41421i 0.119098 + 0.119098i
\(142\) 7.32672i 0.614845i
\(143\) 2.45214 6.59178i 0.205058 0.551232i
\(144\) 1.00000 0.0833333
\(145\) 0.470090 + 0.470090i 0.0390388 + 0.0390388i
\(146\) 3.62050i 0.299635i
\(147\) −6.90126 1.17157i −0.569206 0.0966297i
\(148\) 0.257101 0.257101i 0.0211335 0.0211335i
\(149\) −11.7376 + 11.7376i −0.961585 + 0.961585i −0.999289 0.0377039i \(-0.987996\pi\)
0.0377039 + 0.999289i \(0.487996\pi\)
\(150\) −1.64203 + 1.64203i −0.134071 + 0.134071i
\(151\) 2.79529 + 2.79529i 0.227477 + 0.227477i 0.811638 0.584161i \(-0.198576\pi\)
−0.584161 + 0.811638i \(0.698576\pi\)
\(152\) 1.32218i 0.107243i
\(153\) 1.50625 0.121773
\(154\) 3.94287 3.32994i 0.317726 0.268334i
\(155\) 5.35564i 0.430176i
\(156\) 1.50062 + 3.27843i 0.120146 + 0.262485i
\(157\) 10.4472i 0.833774i 0.908958 + 0.416887i \(0.136879\pi\)
−0.908958 + 0.416887i \(0.863121\pi\)
\(158\) 1.00795 1.00795i 0.0801884 0.0801884i
\(159\) 13.4456i 1.06631i
\(160\) 1.63640 0.129369
\(161\) 7.15836 + 8.47600i 0.564158 + 0.668002i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 9.07232 + 9.07232i 0.710599 + 0.710599i 0.966660 0.256062i \(-0.0824250\pi\)
−0.256062 + 0.966660i \(0.582425\pi\)
\(164\) 3.60624 3.60624i 0.281600 0.281600i
\(165\) −3.19202 −0.248499
\(166\) 6.94091 0.538719
\(167\) −9.04741 + 9.04741i −0.700109 + 0.700109i −0.964434 0.264325i \(-0.914851\pi\)
0.264325 + 0.964434i \(0.414851\pi\)
\(168\) −0.222191 + 2.63640i −0.0171424 + 0.203403i
\(169\) −8.49625 + 9.83940i −0.653558 + 0.756877i
\(170\) 2.46483 0.189044
\(171\) 0.934922 + 0.934922i 0.0714952 + 0.0714952i
\(172\) −2.46483 −0.187942
\(173\) −0.0159057 −0.00120928 −0.000604642 1.00000i \(-0.500192\pi\)
−0.000604642 1.00000i \(0.500192\pi\)
\(174\) 0.287270 + 0.287270i 0.0217779 + 0.0217779i
\(175\) −3.96421 4.69390i −0.299666 0.354825i
\(176\) −1.37930 1.37930i −0.103969 0.103969i
\(177\) −8.75986 8.75986i −0.658431 0.658431i
\(178\) 2.87109i 0.215198i
\(179\) 10.3710i 0.775167i −0.921835 0.387584i \(-0.873310\pi\)
0.921835 0.387584i \(-0.126690\pi\)
\(180\) 1.15711 1.15711i 0.0862461 0.0862461i
\(181\) 1.42973 0.106271 0.0531354 0.998587i \(-0.483079\pi\)
0.0531354 + 0.998587i \(0.483079\pi\)
\(182\) −8.97670 + 3.22781i −0.665398 + 0.239262i
\(183\) 11.7394 0.867802
\(184\) 2.96509 2.96509i 0.218589 0.218589i
\(185\) 0.594989i 0.0437444i
\(186\) 3.27281i 0.239974i
\(187\) −2.07757 2.07757i −0.151927 0.151927i
\(188\) 1.41421 + 1.41421i 0.103142 + 0.103142i
\(189\) 1.70711 + 2.02133i 0.124174 + 0.147030i
\(190\) 1.52991 + 1.52991i 0.110991 + 0.110991i
\(191\) −23.1833 −1.67748 −0.838741 0.544530i \(-0.816708\pi\)
−0.838741 + 0.544530i \(0.816708\pi\)
\(192\) 1.00000 0.0721688
\(193\) 13.6264 + 13.6264i 0.980850 + 0.980850i 0.999820 0.0189698i \(-0.00603863\pi\)
−0.0189698 + 0.999820i \(0.506039\pi\)
\(194\) 14.5297 1.04317
\(195\) 5.52991 + 2.05713i 0.396005 + 0.147314i
\(196\) −6.90126 1.17157i −0.492947 0.0836838i
\(197\) 10.1950 10.1950i 0.726366 0.726366i −0.243528 0.969894i \(-0.578305\pi\)
0.969894 + 0.243528i \(0.0783046\pi\)
\(198\) −1.95063 −0.138625
\(199\) −1.42518 −0.101029 −0.0505143 0.998723i \(-0.516086\pi\)
−0.0505143 + 0.998723i \(0.516086\pi\)
\(200\) −1.64203 + 1.64203i −0.116109 + 0.116109i
\(201\) −11.1012 11.1012i −0.783021 0.783021i
\(202\) −1.36484 + 1.36484i −0.0960301 + 0.0960301i
\(203\) −0.821188 + 0.693530i −0.0576361 + 0.0486763i
\(204\) 1.50625 0.105458
\(205\) 8.34564i 0.582885i
\(206\) 5.62070 5.62070i 0.391612 0.391612i
\(207\) 4.19327i 0.291453i
\(208\) 1.50062 + 3.27843i 0.104050 + 0.227318i
\(209\) 2.57908i 0.178399i
\(210\) 2.79352 + 3.30772i 0.192771 + 0.228254i
\(211\) 5.45234 0.375354 0.187677 0.982231i \(-0.439904\pi\)
0.187677 + 0.982231i \(0.439904\pi\)
\(212\) 13.4456i 0.923450i
\(213\) 5.18078 + 5.18078i 0.354981 + 0.354981i
\(214\) −2.35689 + 2.35689i −0.161114 + 0.161114i
\(215\) −2.85209 + 2.85209i −0.194511 + 0.194511i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) −8.62845 0.727190i −0.585737 0.0493649i
\(218\) 13.5536i 0.917964i
\(219\) 2.56008 + 2.56008i 0.172994 + 0.172994i
\(220\) −3.19202 −0.215206
\(221\) 2.26031 + 4.93813i 0.152045 + 0.332175i
\(222\) 0.363595i 0.0244029i
\(223\) −18.3548 18.3548i −1.22913 1.22913i −0.964293 0.264839i \(-0.914681\pi\)
−0.264839 0.964293i \(-0.585319\pi\)
\(224\) −0.222191 + 2.63640i −0.0148458 + 0.176152i
\(225\) 2.32218i 0.154812i
\(226\) −7.34440 + 7.34440i −0.488542 + 0.488542i
\(227\) −6.91251 6.91251i −0.458799 0.458799i 0.439462 0.898261i \(-0.355169\pi\)
−0.898261 + 0.439462i \(0.855169\pi\)
\(228\) 0.934922 + 0.934922i 0.0619167 + 0.0619167i
\(229\) −2.96035 + 2.96035i −0.195625 + 0.195625i −0.798122 0.602496i \(-0.794173\pi\)
0.602496 + 0.798122i \(0.294173\pi\)
\(230\) 6.86189i 0.452460i
\(231\) 0.433413 5.14265i 0.0285165 0.338362i
\(232\) 0.287270 + 0.287270i 0.0188602 + 0.0188602i
\(233\) 6.59953i 0.432350i −0.976355 0.216175i \(-0.930642\pi\)
0.976355 0.216175i \(-0.0693581\pi\)
\(234\) 3.37930 + 1.25710i 0.220912 + 0.0821792i
\(235\) 3.27281 0.213495
\(236\) −8.75986 8.75986i −0.570218 0.570218i
\(237\) 1.42546i 0.0925936i
\(238\) −0.334675 + 3.97108i −0.0216938 + 0.257407i
\(239\) −10.9611 + 10.9611i −0.709014 + 0.709014i −0.966328 0.257314i \(-0.917162\pi\)
0.257314 + 0.966328i \(0.417162\pi\)
\(240\) 1.15711 1.15711i 0.0746913 0.0746913i
\(241\) −20.1598 + 20.1598i −1.29861 + 1.29861i −0.369295 + 0.929312i \(0.620401\pi\)
−0.929312 + 0.369295i \(0.879599\pi\)
\(242\) −5.08766 5.08766i −0.327047 0.327047i
\(243\) 1.00000i 0.0641500i
\(244\) 11.7394 0.751539
\(245\) −9.34118 + 6.62990i −0.596786 + 0.423569i
\(246\) 5.09999i 0.325163i
\(247\) −1.66211 + 4.46804i −0.105758 + 0.284295i
\(248\) 3.27281i 0.207824i
\(249\) 4.90797 4.90797i 0.311030 0.311030i
\(250\) 11.9820i 0.757811i
\(251\) −6.62641 −0.418255 −0.209128 0.977888i \(-0.567062\pi\)
−0.209128 + 0.977888i \(0.567062\pi\)
\(252\) 1.70711 + 2.02133i 0.107538 + 0.127332i
\(253\) −5.78380 + 5.78380i −0.363624 + 0.363624i
\(254\) −6.44893 6.44893i −0.404642 0.404642i
\(255\) 1.74290 1.74290i 0.109145 0.109145i
\(256\) 1.00000 0.0625000
\(257\) −10.5297 −0.656826 −0.328413 0.944534i \(-0.606514\pi\)
−0.328413 + 0.944534i \(0.606514\pi\)
\(258\) −1.74290 + 1.74290i −0.108508 + 0.108508i
\(259\) 0.958584 + 0.0807877i 0.0595635 + 0.00501990i
\(260\) 5.52991 + 2.05713i 0.342950 + 0.127578i
\(261\) 0.406261 0.0251469
\(262\) −2.81573 2.81573i −0.173957 0.173957i
\(263\) 11.3310 0.698699 0.349349 0.936993i \(-0.386403\pi\)
0.349349 + 0.936993i \(0.386403\pi\)
\(264\) −1.95063 −0.120053
\(265\) −15.5581 15.5581i −0.955727 0.955727i
\(266\) −2.67256 + 2.25710i −0.163865 + 0.138392i
\(267\) −2.03017 2.03017i −0.124244 0.124244i
\(268\) −11.1012 11.1012i −0.678116 0.678116i
\(269\) 11.6504i 0.710339i −0.934802 0.355170i \(-0.884423\pi\)
0.934802 0.355170i \(-0.115577\pi\)
\(270\) 1.63640i 0.0995884i
\(271\) −9.41876 + 9.41876i −0.572149 + 0.572149i −0.932728 0.360580i \(-0.882579\pi\)
0.360580 + 0.932728i \(0.382579\pi\)
\(272\) 1.50625 0.0913297
\(273\) −4.06508 + 8.62990i −0.246030 + 0.522305i
\(274\) 19.6389 1.18643
\(275\) 3.20299 3.20299i 0.193148 0.193148i
\(276\) 4.19327i 0.252405i
\(277\) 5.99357i 0.360119i 0.983656 + 0.180059i \(0.0576290\pi\)
−0.983656 + 0.180059i \(0.942371\pi\)
\(278\) −5.21247 5.21247i −0.312623 0.312623i
\(279\) 2.31423 + 2.31423i 0.138549 + 0.138549i
\(280\) 2.79352 + 3.30772i 0.166945 + 0.197674i
\(281\) 12.4581 + 12.4581i 0.743190 + 0.743190i 0.973190 0.230001i \(-0.0738729\pi\)
−0.230001 + 0.973190i \(0.573873\pi\)
\(282\) 2.00000 0.119098
\(283\) 12.9995 0.772739 0.386370 0.922344i \(-0.373729\pi\)
0.386370 + 0.922344i \(0.373729\pi\)
\(284\) 5.18078 + 5.18078i 0.307422 + 0.307422i
\(285\) 2.16362 0.128162
\(286\) −2.92717 6.39501i −0.173087 0.378145i
\(287\) 13.4456 + 1.13317i 0.793671 + 0.0668891i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) −14.7312 −0.866542
\(290\) 0.664807 0.0390388
\(291\) 10.2741 10.2741i 0.602276 0.602276i
\(292\) 2.56008 + 2.56008i 0.149817 + 0.149817i
\(293\) −1.51545 + 1.51545i −0.0885336 + 0.0885336i −0.749987 0.661453i \(-0.769940\pi\)
0.661453 + 0.749987i \(0.269940\pi\)
\(294\) −5.70836 + 4.05150i −0.332918 + 0.236288i
\(295\) −20.2723 −1.18030
\(296\) 0.363595i 0.0211335i
\(297\) −1.37930 + 1.37930i −0.0800354 + 0.0800354i
\(298\) 16.5995i 0.961585i
\(299\) 13.7474 6.29253i 0.795030 0.363906i
\(300\) 2.32218i 0.134071i
\(301\) −4.20773 4.98225i −0.242530 0.287172i
\(302\) 3.95313 0.227477
\(303\) 1.93018i 0.110886i
\(304\) 0.934922 + 0.934922i 0.0536214 + 0.0536214i
\(305\) 13.5838 13.5838i 0.777807 0.777807i
\(306\) 1.06508 1.06508i 0.0608865 0.0608865i
\(307\) 4.87286 4.87286i 0.278109 0.278109i −0.554245 0.832354i \(-0.686993\pi\)
0.832354 + 0.554245i \(0.186993\pi\)
\(308\) 0.433413 5.14265i 0.0246960 0.293030i
\(309\) 7.94886i 0.452195i
\(310\) 3.78701 + 3.78701i 0.215088 + 0.215088i
\(311\) −26.8179 −1.52070 −0.760352 0.649511i \(-0.774974\pi\)
−0.760352 + 0.649511i \(0.774974\pi\)
\(312\) 3.37930 + 1.25710i 0.191315 + 0.0711693i
\(313\) 1.96858i 0.111271i 0.998451 + 0.0556354i \(0.0177184\pi\)
−0.998451 + 0.0556354i \(0.982282\pi\)
\(314\) 7.38726 + 7.38726i 0.416887 + 0.416887i
\(315\) 4.31423 + 0.363595i 0.243079 + 0.0204863i
\(316\) 1.42546i 0.0801884i
\(317\) 9.47705 9.47705i 0.532284 0.532284i −0.388967 0.921252i \(-0.627168\pi\)
0.921252 + 0.388967i \(0.127168\pi\)
\(318\) −9.50750 9.50750i −0.533154 0.533154i
\(319\) −0.560357 0.560357i −0.0313740 0.0313740i
\(320\) 1.15711 1.15711i 0.0646846 0.0646846i
\(321\) 3.33315i 0.186038i
\(322\) 11.0552 + 0.931709i 0.616080 + 0.0519221i
\(323\) 1.40822 + 1.40822i 0.0783557 + 0.0783557i
\(324\) 1.00000i 0.0555556i
\(325\) −7.61311 + 3.48472i −0.422299 + 0.193297i
\(326\) 12.8302 0.710599
\(327\) −9.58382 9.58382i −0.529987 0.529987i
\(328\) 5.09999i 0.281600i
\(329\) −0.444383 + 5.27281i −0.0244996 + 0.290699i
\(330\) −2.25710 + 2.25710i −0.124249 + 0.124249i
\(331\) −13.2853 + 13.2853i −0.730226 + 0.730226i −0.970664 0.240438i \(-0.922709\pi\)
0.240438 + 0.970664i \(0.422709\pi\)
\(332\) 4.90797 4.90797i 0.269360 0.269360i
\(333\) −0.257101 0.257101i −0.0140890 0.0140890i
\(334\) 12.7950i 0.700109i
\(335\) −25.6908 −1.40364
\(336\) 1.70711 + 2.02133i 0.0931303 + 0.110273i
\(337\) 10.6200i 0.578507i 0.957252 + 0.289254i \(0.0934071\pi\)
−0.957252 + 0.289254i \(0.906593\pi\)
\(338\) 0.949747 + 12.9653i 0.0516595 + 0.705217i
\(339\) 10.3865i 0.564120i
\(340\) 1.74290 1.74290i 0.0945220 0.0945220i
\(341\) 6.38404i 0.345715i
\(342\) 1.32218 0.0714952
\(343\) −9.41305 15.9497i −0.508257 0.861205i
\(344\) −1.74290 + 1.74290i −0.0939708 + 0.0939708i
\(345\) −4.85209 4.85209i −0.261228 0.261228i
\(346\) −0.0112470 + 0.0112470i −0.000604642 + 0.000604642i
\(347\) −33.6050 −1.80401 −0.902007 0.431722i \(-0.857906\pi\)
−0.902007 + 0.431722i \(0.857906\pi\)
\(348\) 0.406261 0.0217779
\(349\) 22.5833 22.5833i 1.20886 1.20886i 0.237462 0.971397i \(-0.423684\pi\)
0.971397 0.237462i \(-0.0763156\pi\)
\(350\) −6.12220 0.515968i −0.327246 0.0275797i
\(351\) 3.27843 1.50062i 0.174990 0.0800974i
\(352\) −1.95063 −0.103969
\(353\) 10.4681 + 10.4681i 0.557162 + 0.557162i 0.928498 0.371336i \(-0.121100\pi\)
−0.371336 + 0.928498i \(0.621100\pi\)
\(354\) −12.3883 −0.658431
\(355\) 11.9895 0.636336
\(356\) −2.03017 2.03017i −0.107599 0.107599i
\(357\) 2.57133 + 3.04463i 0.136089 + 0.161139i
\(358\) −7.33343 7.33343i −0.387584 0.387584i
\(359\) −2.68248 2.68248i −0.141576 0.141576i 0.632767 0.774343i \(-0.281919\pi\)
−0.774343 + 0.632767i \(0.781919\pi\)
\(360\) 1.63640i 0.0862461i
\(361\) 17.2518i 0.907992i
\(362\) 1.01097 1.01097i 0.0531354 0.0531354i
\(363\) −7.19504 −0.377642
\(364\) −4.06508 + 8.62990i −0.213068 + 0.452330i
\(365\) 5.92460 0.310108
\(366\) 8.30102 8.30102i 0.433901 0.433901i
\(367\) 8.08749i 0.422164i 0.977468 + 0.211082i \(0.0676986\pi\)
−0.977468 + 0.211082i \(0.932301\pi\)
\(368\) 4.19327i 0.218589i
\(369\) −3.60624 3.60624i −0.187733 0.187733i
\(370\) −0.420721 0.420721i −0.0218722 0.0218722i
\(371\) 27.1781 22.9531i 1.41102 1.19167i
\(372\) 2.31423 + 2.31423i 0.119987 + 0.119987i
\(373\) −27.5920 −1.42866 −0.714331 0.699808i \(-0.753269\pi\)
−0.714331 + 0.699808i \(0.753269\pi\)
\(374\) −2.93813 −0.151927
\(375\) 8.47259 + 8.47259i 0.437523 + 0.437523i
\(376\) 2.00000 0.103142
\(377\) 0.609645 + 1.33190i 0.0313983 + 0.0685963i
\(378\) 2.63640 + 0.222191i 0.135602 + 0.0114283i
\(379\) −7.79457 + 7.79457i −0.400380 + 0.400380i −0.878367 0.477987i \(-0.841367\pi\)
0.477987 + 0.878367i \(0.341367\pi\)
\(380\) 2.16362 0.110991
\(381\) −9.12016 −0.467240
\(382\) −16.3931 + 16.3931i −0.838741 + 0.838741i
\(383\) −11.3366 11.3366i −0.579275 0.579275i 0.355428 0.934704i \(-0.384335\pi\)
−0.934704 + 0.355428i \(0.884335\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) −5.44912 6.45214i −0.277713 0.328831i
\(386\) 19.2707 0.980850
\(387\) 2.46483i 0.125294i
\(388\) 10.2741 10.2741i 0.521586 0.521586i
\(389\) 17.5669i 0.890675i −0.895363 0.445338i \(-0.853084\pi\)
0.895363 0.445338i \(-0.146916\pi\)
\(390\) 5.36484 2.45563i 0.271659 0.124346i
\(391\) 6.31611i 0.319419i
\(392\) −5.70836 + 4.05150i −0.288316 + 0.204632i
\(393\) −3.98205 −0.200868
\(394\) 14.4180i 0.726366i
\(395\) −1.64942 1.64942i −0.0829913 0.0829913i
\(396\) −1.37930 + 1.37930i −0.0693127 + 0.0693127i
\(397\) −24.6394 + 24.6394i −1.23662 + 1.23662i −0.275242 + 0.961375i \(0.588758\pi\)
−0.961375 + 0.275242i \(0.911242\pi\)
\(398\) −1.00776 + 1.00776i −0.0505143 + 0.0505143i
\(399\) −0.293777 + 3.48580i −0.0147072 + 0.174508i
\(400\) 2.32218i 0.116109i
\(401\) 20.8486 + 20.8486i 1.04113 + 1.04113i 0.999117 + 0.0420122i \(0.0133769\pi\)
0.0420122 + 0.999117i \(0.486623\pi\)
\(402\) −15.6995 −0.783021
\(403\) −4.11425 + 11.0598i −0.204945 + 0.550929i
\(404\) 1.93018i 0.0960301i
\(405\) −1.15711 1.15711i −0.0574974 0.0574974i
\(406\) −0.0902676 + 1.07107i −0.00447991 + 0.0531562i
\(407\) 0.709240i 0.0351557i
\(408\) 1.06508 1.06508i 0.0527292 0.0527292i
\(409\) 13.8170 + 13.8170i 0.683206 + 0.683206i 0.960721 0.277515i \(-0.0895109\pi\)
−0.277515 + 0.960721i \(0.589511\pi\)
\(410\) −5.90126 5.90126i −0.291443 0.291443i
\(411\) 13.8868 13.8868i 0.684985 0.684985i
\(412\) 7.94886i 0.391612i
\(413\) 2.75258 32.6606i 0.135445 1.60712i
\(414\) −2.96509 2.96509i −0.145726 0.145726i
\(415\) 11.3581i 0.557549i
\(416\) 3.37930 + 1.25710i 0.165684 + 0.0616344i
\(417\) −7.37155 −0.360986
\(418\) −1.82369 1.82369i −0.0891995 0.0891995i
\(419\) 16.3845i 0.800435i −0.916420 0.400218i \(-0.868935\pi\)
0.916420 0.400218i \(-0.131065\pi\)
\(420\) 4.31423 + 0.363595i 0.210513 + 0.0177416i
\(421\) −17.2214 + 17.2214i −0.839319 + 0.839319i −0.988769 0.149450i \(-0.952250\pi\)
0.149450 + 0.988769i \(0.452250\pi\)
\(422\) 3.85538 3.85538i 0.187677 0.187677i
\(423\) 1.41421 1.41421i 0.0687614 0.0687614i
\(424\) −9.50750 9.50750i −0.461725 0.461725i
\(425\) 3.49778i 0.169667i
\(426\) 7.32672 0.354981
\(427\) 20.0404 + 23.7293i 0.969824 + 1.14834i
\(428\) 3.33315i 0.161114i
\(429\) −6.59178 2.45214i −0.318254 0.118390i
\(430\) 4.03346i 0.194511i
\(431\) 22.5749 22.5749i 1.08739 1.08739i 0.0915975 0.995796i \(-0.470803\pi\)
0.995796 0.0915975i \(-0.0291973\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 35.8075 1.72080 0.860400 0.509620i \(-0.170214\pi\)
0.860400 + 0.509620i \(0.170214\pi\)
\(434\) −6.61544 + 5.58704i −0.317551 + 0.268186i
\(435\) 0.470090 0.470090i 0.0225391 0.0225391i
\(436\) −9.58382 9.58382i −0.458982 0.458982i
\(437\) 3.92038 3.92038i 0.187537 0.187537i
\(438\) 3.62050 0.172994
\(439\) 9.78979 0.467241 0.233621 0.972328i \(-0.424943\pi\)
0.233621 + 0.972328i \(0.424943\pi\)
\(440\) −2.25710 + 2.25710i −0.107603 + 0.107603i
\(441\) −1.17157 + 6.90126i −0.0557892 + 0.328632i
\(442\) 5.09007 + 1.89351i 0.242110 + 0.0900649i
\(443\) −2.71378 −0.128936 −0.0644679 0.997920i \(-0.520535\pi\)
−0.0644679 + 0.997920i \(0.520535\pi\)
\(444\) −0.257101 0.257101i −0.0122015 0.0122015i
\(445\) −4.69827 −0.222719
\(446\) −25.9577 −1.22913
\(447\) 11.7376 + 11.7376i 0.555171 + 0.555171i
\(448\) 1.70711 + 2.02133i 0.0806532 + 0.0954990i
\(449\) 14.7825 + 14.7825i 0.697632 + 0.697632i 0.963899 0.266268i \(-0.0857905\pi\)
−0.266268 + 0.963899i \(0.585790\pi\)
\(450\) 1.64203 + 1.64203i 0.0774060 + 0.0774060i
\(451\) 9.94819i 0.468442i
\(452\) 10.3865i 0.488542i
\(453\) 2.79529 2.79529i 0.131334 0.131334i
\(454\) −9.77576 −0.458799
\(455\) 5.28201 + 14.6895i 0.247625 + 0.688655i
\(456\) 1.32218 0.0619167
\(457\) −17.9920 + 17.9920i −0.841632 + 0.841632i −0.989071 0.147439i \(-0.952897\pi\)
0.147439 + 0.989071i \(0.452897\pi\)
\(458\) 4.18657i 0.195625i
\(459\) 1.50625i 0.0703056i
\(460\) −4.85209 4.85209i −0.226230 0.226230i
\(461\) 23.4424 + 23.4424i 1.09182 + 1.09182i 0.995334 + 0.0964882i \(0.0307610\pi\)
0.0964882 + 0.995334i \(0.469239\pi\)
\(462\) −3.32994 3.94287i −0.154923 0.183439i
\(463\) 12.4486 + 12.4486i 0.578536 + 0.578536i 0.934500 0.355964i \(-0.115847\pi\)
−0.355964 + 0.934500i \(0.615847\pi\)
\(464\) 0.406261 0.0188602
\(465\) 5.35564 0.248362
\(466\) −4.66657 4.66657i −0.216175 0.216175i
\(467\) 27.6932 1.28149 0.640744 0.767754i \(-0.278626\pi\)
0.640744 + 0.767754i \(0.278626\pi\)
\(468\) 3.27843 1.50062i 0.151546 0.0693664i
\(469\) 3.48830 41.3903i 0.161075 1.91123i
\(470\) 2.31423 2.31423i 0.106747 0.106747i
\(471\) 10.4472 0.481380
\(472\) −12.3883 −0.570218
\(473\) 3.39975 3.39975i 0.156321 0.156321i
\(474\) −1.00795 1.00795i −0.0462968 0.0462968i
\(475\) −2.17106 + 2.17106i −0.0996148 + 0.0996148i
\(476\) 2.57133 + 3.04463i 0.117857 + 0.139550i
\(477\) −13.4456 −0.615633
\(478\) 15.5013i 0.709014i
\(479\) 7.69426 7.69426i 0.351560 0.351560i −0.509130 0.860690i \(-0.670033\pi\)
0.860690 + 0.509130i \(0.170033\pi\)
\(480\) 1.63640i 0.0746913i
\(481\) 0.457076 1.22870i 0.0208409 0.0560238i
\(482\) 28.5103i 1.29861i
\(483\) 8.47600 7.15836i 0.385671 0.325717i
\(484\) −7.19504 −0.327047
\(485\) 23.7765i 1.07964i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) −3.65436 + 3.65436i −0.165595 + 0.165595i −0.785040 0.619445i \(-0.787358\pi\)
0.619445 + 0.785040i \(0.287358\pi\)
\(488\) 8.30102 8.30102i 0.375769 0.375769i
\(489\) 9.07232 9.07232i 0.410264 0.410264i
\(490\) −1.91717 + 11.2933i −0.0866088 + 0.510177i
\(491\) 12.9652i 0.585110i 0.956249 + 0.292555i \(0.0945055\pi\)
−0.956249 + 0.292555i \(0.905495\pi\)
\(492\) −3.60624 3.60624i −0.162582 0.162582i
\(493\) 0.611930 0.0275599
\(494\) 1.98409 + 4.33468i 0.0892686 + 0.195026i
\(495\) 3.19202i 0.143471i
\(496\) 2.31423 + 2.31423i 0.103912 + 0.103912i
\(497\) −1.62793 + 19.3162i −0.0730228 + 0.866450i
\(498\) 6.94091i 0.311030i
\(499\) 15.8982 15.8982i 0.711703 0.711703i −0.255188 0.966891i \(-0.582137\pi\)
0.966891 + 0.255188i \(0.0821374\pi\)
\(500\) 8.47259 + 8.47259i 0.378906 + 0.378906i
\(501\) 9.04741 + 9.04741i 0.404208 + 0.404208i
\(502\) −4.68558 + 4.68558i −0.209128 + 0.209128i
\(503\) 7.72073i 0.344250i 0.985075 + 0.172125i \(0.0550633\pi\)
−0.985075 + 0.172125i \(0.944937\pi\)
\(504\) 2.63640 + 0.222191i 0.117435 + 0.00989719i
\(505\) 2.23344 + 2.23344i 0.0993867 + 0.0993867i
\(506\) 8.17953i 0.363624i
\(507\) 9.83940 + 8.49625i 0.436983 + 0.377332i
\(508\) −9.12016 −0.404642
\(509\) 23.7432 + 23.7432i 1.05240 + 1.05240i 0.998549 + 0.0538516i \(0.0171498\pi\)
0.0538516 + 0.998549i \(0.482850\pi\)
\(510\) 2.46483i 0.109145i
\(511\) −0.804444 + 9.54510i −0.0355865 + 0.422250i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0.934922 0.934922i 0.0412778 0.0412778i
\(514\) −7.44563 + 7.44563i −0.328413 + 0.328413i
\(515\) −9.19773 9.19773i −0.405301 0.405301i
\(516\) 2.46483i 0.108508i
\(517\) −3.90126 −0.171577
\(518\) 0.734947 0.620696i 0.0322917 0.0272718i
\(519\) 0.0159057i 0.000698181i
\(520\) 5.36484 2.45563i 0.235264 0.107686i
\(521\) 11.2520i 0.492958i −0.969148 0.246479i \(-0.920726\pi\)
0.969148 0.246479i \(-0.0792736\pi\)
\(522\) 0.287270 0.287270i 0.0125735 0.0125735i
\(523\) 39.7356i 1.73752i 0.495237 + 0.868758i \(0.335081\pi\)
−0.495237 + 0.868758i \(0.664919\pi\)
\(524\) −3.98205 −0.173957
\(525\) −4.69390 + 3.96421i −0.204858 + 0.173012i
\(526\) 8.01222 8.01222i 0.349349 0.349349i
\(527\) 3.48580 + 3.48580i 0.151844 + 0.151844i
\(528\) −1.37930 + 1.37930i −0.0600265 + 0.0600265i
\(529\) 5.41647 0.235499
\(530\) −22.0025 −0.955727
\(531\) −8.75986 + 8.75986i −0.380145 + 0.380145i
\(532\) −0.293777 + 3.48580i −0.0127368 + 0.151129i
\(533\) 6.41120 17.2344i 0.277700 0.746505i
\(534\) −2.87109 −0.124244
\(535\) 3.85683 + 3.85683i 0.166745 + 0.166745i
\(536\) −15.6995 −0.678116
\(537\) −10.3710 −0.447543
\(538\) −8.23810 8.23810i −0.355170 0.355170i
\(539\) 11.1349 7.90299i 0.479614 0.340406i
\(540\) −1.15711 1.15711i −0.0497942 0.0497942i
\(541\) −10.4751 10.4751i −0.450359 0.450359i 0.445114 0.895474i \(-0.353163\pi\)
−0.895474 + 0.445114i \(0.853163\pi\)
\(542\) 13.3201i 0.572149i
\(543\) 1.42973i 0.0613554i
\(544\) 1.06508 1.06508i 0.0456649 0.0456649i
\(545\) −22.1791 −0.950050
\(546\) 3.22781 + 8.97670i 0.138138 + 0.384167i
\(547\) 17.4124 0.744502 0.372251 0.928132i \(-0.378586\pi\)
0.372251 + 0.928132i \(0.378586\pi\)
\(548\) 13.8868 13.8868i 0.593215 0.593215i
\(549\) 11.7394i 0.501026i
\(550\) 4.52971i 0.193148i
\(551\) 0.379822 + 0.379822i 0.0161810 + 0.0161810i
\(552\) −2.96509 2.96509i −0.126203 0.126203i
\(553\) 2.88133 2.43341i 0.122527 0.103479i
\(554\) 4.23810 + 4.23810i 0.180059 + 0.180059i
\(555\) −0.594989 −0.0252559
\(556\) −7.37155 −0.312623
\(557\) 6.23417 + 6.23417i 0.264150 + 0.264150i 0.826738 0.562587i \(-0.190194\pi\)
−0.562587 + 0.826738i \(0.690194\pi\)
\(558\) 3.27281 0.138549
\(559\) −8.08079 + 3.69879i −0.341781 + 0.156442i
\(560\) 4.31423 + 0.363595i 0.182309 + 0.0153647i
\(561\) −2.07757 + 2.07757i −0.0877153 + 0.0877153i
\(562\) 17.6185 0.743190
\(563\) 32.2131 1.35762 0.678809 0.734315i \(-0.262496\pi\)
0.678809 + 0.734315i \(0.262496\pi\)
\(564\) 1.41421 1.41421i 0.0595491 0.0595491i
\(565\) 12.0184 + 12.0184i 0.505618 + 0.505618i
\(566\) 9.19202 9.19202i 0.386370 0.386370i
\(567\) 2.02133 1.70711i 0.0848880 0.0716917i
\(568\) 7.32672 0.307422
\(569\) 25.5422i 1.07079i −0.844603 0.535393i \(-0.820164\pi\)
0.844603 0.535393i \(-0.179836\pi\)
\(570\) 1.52991 1.52991i 0.0640809 0.0640809i
\(571\) 34.8620i 1.45893i −0.684020 0.729464i \(-0.739770\pi\)
0.684020 0.729464i \(-0.260230\pi\)
\(572\) −6.59178 2.45214i −0.275616 0.102529i
\(573\) 23.1833i 0.968495i
\(574\) 10.3088 8.70622i 0.430280 0.363391i
\(575\) 9.73753 0.406083
\(576\) 1.00000i 0.0416667i
\(577\) 11.7404 + 11.7404i 0.488760 + 0.488760i 0.907915 0.419155i \(-0.137674\pi\)
−0.419155 + 0.907915i \(0.637674\pi\)
\(578\) −10.4165 + 10.4165i −0.433271 + 0.433271i
\(579\) 13.6264 13.6264i 0.566294 0.566294i
\(580\) 0.470090 0.470090i 0.0195194 0.0195194i
\(581\) 18.2991 + 1.54221i 0.759173 + 0.0639817i
\(582\) 14.5297i 0.602276i
\(583\) 18.5456 + 18.5456i 0.768081 + 0.768081i
\(584\) 3.62050 0.149817
\(585\) 2.05713 5.52991i 0.0850517 0.228634i
\(586\) 2.14317i 0.0885336i
\(587\) 25.6920 + 25.6920i 1.06042 + 1.06042i 0.998053 + 0.0623701i \(0.0198659\pi\)
0.0623701 + 0.998053i \(0.480134\pi\)
\(588\) −1.17157 + 6.90126i −0.0483149 + 0.284603i
\(589\) 4.32724i 0.178301i
\(590\) −14.3347 + 14.3347i −0.590149 + 0.590149i
\(591\) −10.1950 10.1950i −0.419368 0.419368i
\(592\) −0.257101 0.257101i −0.0105668 0.0105668i
\(593\) 6.06857 6.06857i 0.249206 0.249206i −0.571439 0.820645i \(-0.693614\pi\)
0.820645 + 0.571439i \(0.193614\pi\)
\(594\) 1.95063i 0.0800354i
\(595\) 6.49830 + 0.547664i 0.266404 + 0.0224521i
\(596\) 11.7376 + 11.7376i 0.480793 + 0.480793i
\(597\) 1.42518i 0.0583289i
\(598\) 5.27136 14.1703i 0.215562 0.579468i
\(599\) −42.6492 −1.74260 −0.871300 0.490750i \(-0.836723\pi\)
−0.871300 + 0.490750i \(0.836723\pi\)
\(600\) 1.64203 + 1.64203i 0.0670355 + 0.0670355i
\(601\) 4.02249i 0.164081i −0.996629 0.0820405i \(-0.973856\pi\)
0.996629 0.0820405i \(-0.0261437\pi\)
\(602\) −6.49830 0.547664i −0.264851 0.0223211i
\(603\) −11.1012 + 11.1012i −0.452077 + 0.452077i
\(604\) 2.79529 2.79529i 0.113739 0.113739i
\(605\) −8.32547 + 8.32547i −0.338479 + 0.338479i
\(606\) 1.36484 + 1.36484i 0.0554430 + 0.0554430i
\(607\) 39.1674i 1.58975i 0.606770 + 0.794877i \(0.292465\pi\)
−0.606770 + 0.794877i \(0.707535\pi\)
\(608\) 1.32218 0.0536214
\(609\) 0.693530 + 0.821188i 0.0281033 + 0.0332762i
\(610\) 19.2104i 0.777807i
\(611\) 6.75861 + 2.51420i 0.273424 + 0.101714i
\(612\) 1.50625i 0.0608865i
\(613\) −15.7609 + 15.7609i −0.636577 + 0.636577i −0.949710 0.313132i \(-0.898622\pi\)
0.313132 + 0.949710i \(0.398622\pi\)
\(614\) 6.89126i 0.278109i
\(615\) −8.34564 −0.336529
\(616\) −3.32994 3.94287i −0.134167 0.158863i
\(617\) −19.4135 + 19.4135i −0.781558 + 0.781558i −0.980094 0.198536i \(-0.936381\pi\)
0.198536 + 0.980094i \(0.436381\pi\)
\(618\) −5.62070 5.62070i −0.226098 0.226098i
\(619\) 28.9913 28.9913i 1.16526 1.16526i 0.181953 0.983307i \(-0.441758\pi\)
0.983307 0.181953i \(-0.0582418\pi\)
\(620\) 5.35564 0.215088
\(621\) −4.19327 −0.168270
\(622\) −18.9631 + 18.9631i −0.760352 + 0.760352i
\(623\) 0.637932 7.56936i 0.0255582 0.303260i
\(624\) 3.27843 1.50062i 0.131242 0.0600731i
\(625\) 7.99659 0.319864
\(626\) 1.39200 + 1.39200i 0.0556354 + 0.0556354i
\(627\) −2.57908 −0.102999
\(628\) 10.4472 0.416887
\(629\) −0.387257 0.387257i −0.0154410 0.0154410i
\(630\) 3.30772 2.79352i 0.131783 0.111296i
\(631\) −14.3025 14.3025i −0.569375 0.569375i 0.362578 0.931953i \(-0.381897\pi\)
−0.931953 + 0.362578i \(0.881897\pi\)
\(632\) −1.00795 1.00795i −0.0400942 0.0400942i
\(633\) 5.45234i 0.216711i
\(634\) 13.4026i 0.532284i
\(635\) −10.5531 + 10.5531i −0.418785 + 0.418785i
\(636\) −13.4456 −0.533154
\(637\) −24.3834 + 6.51528i −0.966106 + 0.258145i
\(638\) −0.792465 −0.0313740
\(639\) 5.18078 5.18078i 0.204948 0.204948i
\(640\) 1.63640i 0.0646846i
\(641\) 41.5501i 1.64113i 0.571553 + 0.820565i \(0.306341\pi\)
−0.571553 + 0.820565i \(0.693659\pi\)
\(642\) 2.35689 + 2.35689i 0.0930191 + 0.0930191i
\(643\) 23.7094 + 23.7094i 0.935009 + 0.935009i 0.998013 0.0630044i \(-0.0200682\pi\)
−0.0630044 + 0.998013i \(0.520068\pi\)
\(644\) 8.47600 7.15836i 0.334001 0.282079i
\(645\) 2.85209 + 2.85209i 0.112301 + 0.112301i
\(646\) 1.99153 0.0783557
\(647\) −26.3735 −1.03685 −0.518425 0.855123i \(-0.673482\pi\)
−0.518425 + 0.855123i \(0.673482\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) 24.1650 0.948560
\(650\) −2.91921 + 7.84735i −0.114501 + 0.307798i
\(651\) −0.727190 + 8.62845i −0.0285008 + 0.338176i
\(652\) 9.07232 9.07232i 0.355299 0.355299i
\(653\) −12.3520 −0.483369 −0.241685 0.970355i \(-0.577700\pi\)
−0.241685 + 0.970355i \(0.577700\pi\)
\(654\) −13.5536 −0.529987
\(655\) −4.60768 + 4.60768i −0.180037 + 0.180037i
\(656\) −3.60624 3.60624i −0.140800 0.140800i
\(657\) 2.56008 2.56008i 0.0998782 0.0998782i
\(658\) 3.41421 + 4.04267i 0.133100 + 0.157600i
\(659\) −40.1732 −1.56492 −0.782462 0.622698i \(-0.786036\pi\)
−0.782462 + 0.622698i \(0.786036\pi\)
\(660\) 3.19202i 0.124249i
\(661\) 26.5576 26.5576i 1.03297 1.03297i 0.0335333 0.999438i \(-0.489324\pi\)
0.999438 0.0335333i \(-0.0106760\pi\)
\(662\) 18.7883i 0.730226i
\(663\) 4.93813 2.26031i 0.191781 0.0877833i
\(664\) 6.94091i 0.269360i
\(665\) 3.69353 + 4.37340i 0.143229 + 0.169593i
\(666\) −0.363595 −0.0140890
\(667\) 1.70356i 0.0659622i
\(668\) 9.04741 + 9.04741i 0.350055 + 0.350055i
\(669\) −18.3548 + 18.3548i −0.709639 + 0.709639i
\(670\) −18.1661 + 18.1661i −0.701818 + 0.701818i
\(671\) −16.1922 + 16.1922i −0.625094 + 0.625094i
\(672\) 2.63640 + 0.222191i 0.101702 + 0.00857122i
\(673\) 3.49388i 0.134679i −0.997730 0.0673395i \(-0.978549\pi\)
0.997730 0.0673395i \(-0.0214511\pi\)
\(674\) 7.50946 + 7.50946i 0.289254 + 0.289254i
\(675\) 2.32218 0.0893807
\(676\) 9.83940 + 8.49625i 0.378438 + 0.326779i
\(677\) 25.1586i 0.966922i −0.875366 0.483461i \(-0.839380\pi\)
0.875366 0.483461i \(-0.160620\pi\)
\(678\) 7.34440 + 7.34440i 0.282060 + 0.282060i
\(679\) 38.3062 + 3.22838i 1.47006 + 0.123894i
\(680\) 2.46483i 0.0945220i
\(681\) −6.91251 + 6.91251i −0.264888 + 0.264888i
\(682\) −4.51420 4.51420i −0.172858 0.172858i
\(683\) −26.5689 26.5689i −1.01663 1.01663i −0.999859 0.0167709i \(-0.994661\pi\)
−0.0167709 0.999859i \(-0.505339\pi\)
\(684\) 0.934922 0.934922i 0.0357476 0.0357476i
\(685\) 32.1372i 1.22790i
\(686\) −17.9342 4.62214i −0.684731 0.176474i
\(687\) 2.96035 + 2.96035i 0.112944 + 0.112944i
\(688\) 2.46483i 0.0939708i
\(689\) −20.1768 44.0806i −0.768677 1.67934i
\(690\) −6.86189 −0.261228
\(691\) −1.14265 1.14265i −0.0434686 0.0434686i 0.685038 0.728507i \(-0.259785\pi\)
−0.728507 + 0.685038i \(0.759785\pi\)
\(692\) 0.0159057i 0.000604642i
\(693\) −5.14265 0.433413i −0.195353 0.0164640i
\(694\) −23.7624 + 23.7624i −0.902007 + 0.902007i
\(695\) −8.52971 + 8.52971i −0.323550 + 0.323550i
\(696\) 0.287270 0.287270i 0.0108889 0.0108889i
\(697\) −5.43189 5.43189i −0.205747 0.205747i
\(698\) 31.9377i 1.20886i
\(699\) −6.59953 −0.249617
\(700\) −4.69390 + 3.96421i −0.177413 + 0.149833i
\(701\) 21.5853i 0.815264i −0.913146 0.407632i \(-0.866355\pi\)
0.913146 0.407632i \(-0.133645\pi\)
\(702\) 1.25710 3.37930i 0.0474462 0.127544i
\(703\) 0.480738i 0.0181314i
\(704\) −1.37930 + 1.37930i −0.0519845 + 0.0519845i
\(705\) 3.27281i 0.123261i
\(706\) 14.8042 0.557162
\(707\) −3.90154 + 3.29503i −0.146732 + 0.123922i
\(708\) −8.75986 + 8.75986i −0.329216 + 0.329216i
\(709\) 29.2210 + 29.2210i 1.09742 + 1.09742i 0.994712 + 0.102706i \(0.0327501\pi\)
0.102706 + 0.994712i \(0.467250\pi\)
\(710\) 8.47785 8.47785i 0.318168 0.318168i
\(711\) −1.42546 −0.0534589
\(712\) −2.87109 −0.107599
\(713\) 9.70418 9.70418i 0.363424 0.363424i
\(714\) 3.97108 + 0.334675i 0.148614 + 0.0125249i
\(715\) −10.4648 + 4.79003i −0.391363 + 0.179137i
\(716\) −10.3710 −0.387584
\(717\) 10.9611 + 10.9611i 0.409349 + 0.409349i
\(718\) −3.79360 −0.141576
\(719\) −13.2373 −0.493668 −0.246834 0.969058i \(-0.579390\pi\)
−0.246834 + 0.969058i \(0.579390\pi\)
\(720\) −1.15711 1.15711i −0.0431231 0.0431231i
\(721\) 16.0673 13.5696i 0.598378 0.505357i
\(722\) −12.1989 12.1989i −0.453996 0.453996i
\(723\) 20.1598 + 20.1598i 0.749751 + 0.749751i
\(724\) 1.42973i 0.0531354i
\(725\) 0.943410i 0.0350374i
\(726\) −5.08766 + 5.08766i −0.188821 + 0.188821i
\(727\) −17.2911 −0.641291 −0.320646 0.947199i \(-0.603900\pi\)
−0.320646 + 0.947199i \(0.603900\pi\)
\(728\) 3.22781 + 8.97670i 0.119631 + 0.332699i
\(729\) −1.00000 −0.0370370
\(730\) 4.18933 4.18933i 0.155054 0.155054i
\(731\) 3.71265i 0.137317i
\(732\) 11.7394i 0.433901i
\(733\) −14.5279 14.5279i −0.536602 0.536602i 0.385927 0.922529i \(-0.373882\pi\)
−0.922529 + 0.385927i \(0.873882\pi\)
\(734\) 5.71872 + 5.71872i 0.211082 + 0.211082i
\(735\) 6.62990 + 9.34118i 0.244547 + 0.344555i
\(736\) −2.96509 2.96509i −0.109295 0.109295i
\(737\) 30.6240 1.12805
\(738\) −5.09999 −0.187733
\(739\) −12.3646 12.3646i −0.454838 0.454838i 0.442119 0.896957i \(-0.354227\pi\)
−0.896957 + 0.442119i \(0.854227\pi\)
\(740\) −0.594989 −0.0218722
\(741\) 4.46804 + 1.66211i 0.164138 + 0.0610592i
\(742\) 2.98750 35.4481i 0.109675 1.30134i
\(743\) −12.6873 + 12.6873i −0.465452 + 0.465452i −0.900437 0.434986i \(-0.856753\pi\)
0.434986 + 0.900437i \(0.356753\pi\)
\(744\) 3.27281 0.119987
\(745\) 27.1636 0.995196
\(746\) −19.5105 + 19.5105i −0.714331 + 0.714331i
\(747\) −4.90797 4.90797i −0.179573 0.179573i
\(748\) −2.07757 + 2.07757i −0.0759637 + 0.0759637i
\(749\) −6.73740 + 5.69004i −0.246179 + 0.207910i
\(750\) 11.9820 0.437523
\(751\) 15.8031i 0.576663i −0.957531 0.288331i \(-0.906900\pi\)
0.957531 0.288331i \(-0.0931004\pi\)
\(752\) 1.41421 1.41421i 0.0515711 0.0515711i
\(753\) 6.62641i 0.241480i
\(754\) 1.37288 + 0.510711i 0.0499973 + 0.0185990i
\(755\) 6.46892i 0.235428i
\(756\) 2.02133 1.70711i 0.0735152 0.0620869i
\(757\) 36.8200 1.33825 0.669123 0.743152i \(-0.266670\pi\)
0.669123 + 0.743152i \(0.266670\pi\)
\(758\) 11.0232i 0.400380i
\(759\) 5.78380 + 5.78380i 0.209939 + 0.209939i
\(760\) 1.52991 1.52991i 0.0554957 0.0554957i
\(761\) 29.9773 29.9773i 1.08668 1.08668i 0.0908090 0.995868i \(-0.471055\pi\)
0.995868 0.0908090i \(-0.0289453\pi\)
\(762\) −6.44893 + 6.44893i −0.233620 + 0.233620i
\(763\) 3.01149 35.7327i 0.109023 1.29361i
\(764\) 23.1833i 0.838741i
\(765\) −1.74290 1.74290i −0.0630147 0.0630147i
\(766\) −16.0324 −0.579275
\(767\) −41.8639 15.5734i −1.51162 0.562321i
\(768\) 1.00000i 0.0360844i
\(769\) −28.6613 28.6613i −1.03355 1.03355i −0.999417 0.0341363i \(-0.989132\pi\)
−0.0341363 0.999417i \(-0.510868\pi\)
\(770\) −8.41546 0.709240i −0.303272 0.0255592i
\(771\) 10.5297i 0.379218i
\(772\) 13.6264 13.6264i 0.490425 0.490425i
\(773\) −31.7211 31.7211i −1.14093 1.14093i −0.988280 0.152650i \(-0.951219\pi\)
−0.152650 0.988280i \(-0.548781\pi\)
\(774\) 1.74290 + 1.74290i 0.0626472 + 0.0626472i
\(775\) −5.37405 + 5.37405i −0.193041 + 0.193041i
\(776\) 14.5297i 0.521586i
\(777\) 0.0807877 0.958584i 0.00289824 0.0343890i
\(778\) −12.4216 12.4216i −0.445338 0.445338i