Properties

Label 546.2.o.b.307.3
Level $546$
Weight $2$
Character 546.307
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 307.3
Root \(-2.63640i\) of defining polynomial
Character \(\chi\) \(=\) 546.307
Dual form 546.2.o.b.265.3

$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

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

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 −0.916807 0.399330i \(-0.869243\pi\)
0.399330 + 0.916807i \(0.369243\pi\)
\(6\) −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 −0.467904 0.883780i \(-0.654991\pi\)
0.883780 + 0.467904i \(0.154991\pi\)
\(12\) −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 −0.806170 0.591684i \(-0.798463\pi\)
0.591684 + 0.806170i \(0.298463\pi\)
\(20\) −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 \(-0.855978\pi\)
0.899375 0.437179i \(-0.144022\pi\)
\(24\) −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 −0.883700 0.468053i \(-0.844956\pi\)
0.468053 + 0.883700i \(0.344956\pi\)
\(32\) −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 −0.685657 0.727924i \(-0.740485\pi\)
0.727924 + 0.685657i \(0.240485\pi\)
\(38\) −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 −0.367015 0.930215i \(-0.619620\pi\)
0.930215 + 0.367015i \(0.119620\pi\)
\(42\) −2.63640 + 0.222191i −0.406806 + 0.0342849i
\(43\) 2.46483i 0.375883i 0.982180 + 0.187942i \(0.0601816\pi\)
−0.982180 + 0.187942i \(0.939818\pi\)
\(44\) 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 0.596402 0.802686i \(-0.296597\pi\)
−0.802686 + 0.596402i \(0.796597\pi\)
\(48\) 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 0.988370 + 0.152066i \(0.0485927\pi\)
0.152066 + 0.988370i \(0.451407\pi\)
\(60\) 1.15711 1.15711i 0.149383 0.149383i
\(61\) 11.7394i 1.50308i −0.659689 0.751539i \(-0.729312\pi\)
0.659689 0.751539i \(-0.270688\pi\)
\(62\) −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 0.878512 + 0.477720i \(0.158536\pi\)
0.477720 + 0.878512i \(0.341464\pi\)
\(68\) 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 0.329360 0.944205i \(-0.393167\pi\)
−0.944205 + 0.329360i \(0.893167\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) −2.56008 2.56008i −0.299635 0.299635i 0.541236 0.840871i \(-0.317957\pi\)
−0.840871 + 0.541236i \(0.817957\pi\)
\(74\) 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 −0.384434 0.923153i \(-0.625603\pi\)
0.923153 + 0.384434i \(0.125603\pi\)
\(84\) −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 0.806471 0.591274i \(-0.201375\pi\)
−0.591274 + 0.806471i \(0.701375\pi\)
\(90\) 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 0.0441477 0.999025i \(-0.485943\pi\)
0.999025 0.0441477i \(-0.0140572\pi\)
\(98\) −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 0.996881 0.0789174i \(-0.0251463\pi\)
−0.0789174 + 0.996881i \(0.525146\pi\)
\(110\) −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 \(0.132604\pi\)
−0.914475 + 0.404642i \(0.867396\pi\)
\(128\) 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 \(0.0556553\pi\)
−0.984753 + 0.173957i \(0.944345\pi\)
\(132\) −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 0.208382 0.978047i \(-0.433180\pi\)
0.978047 0.208382i \(-0.0668197\pi\)
\(138\) 2.96509 + 2.96509i 0.252405 + 0.252405i
\(139\) 7.37155i 0.625247i 0.949877 + 0.312623i \(0.101208\pi\)
−0.949877 + 0.312623i \(0.898792\pi\)
\(140\) −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 0.0377039 0.999289i \(-0.487996\pi\)
−0.999289 + 0.0377039i \(0.987996\pi\)
\(150\) −1.64203 1.64203i −0.134071 0.134071i
\(151\) 2.79529 2.79529i 0.227477 0.227477i −0.584161 0.811638i \(-0.698576\pi\)
0.811638 + 0.584161i \(0.198576\pi\)
\(152\) 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 \(-0.863121\pi\)
0.908958 0.416887i \(-0.136879\pi\)
\(158\) 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 −0.256062 0.966660i \(-0.582425\pi\)
0.966660 + 0.256062i \(0.0824250\pi\)
\(164\) 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 0.264325 0.964434i \(-0.414851\pi\)
−0.964434 + 0.264325i \(0.914851\pi\)
\(168\) −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 \(0.126690\pi\)
−0.921835 + 0.387584i \(0.873310\pi\)
\(180\) 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 −0.0189698 0.999820i \(-0.506039\pi\)
0.999820 + 0.0189698i \(0.00603863\pi\)
\(194\) 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 0.969894 0.243528i \(-0.0783046\pi\)
−0.243528 + 0.969894i \(0.578305\pi\)
\(198\) −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 −0.264839 + 0.964293i \(0.585319\pi\)
−0.964293 + 0.264839i \(0.914681\pi\)
\(224\) −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 −0.898261 0.439462i \(-0.855169\pi\)
0.439462 + 0.898261i \(0.355169\pi\)
\(228\) 0.934922 0.934922i 0.0619167 0.0619167i
\(229\) −2.96035 2.96035i −0.195625 0.195625i 0.602496 0.798122i \(-0.294173\pi\)
−0.798122 + 0.602496i \(0.794173\pi\)
\(230\) 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 \(0.0693581\pi\)
−0.976355 + 0.216175i \(0.930642\pi\)
\(234\) 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 0.257314 0.966328i \(-0.417162\pi\)
−0.966328 + 0.257314i \(0.917162\pi\)
\(240\) 1.15711 + 1.15711i 0.0746913 + 0.0746913i
\(241\) −20.1598 20.1598i −1.29861 1.29861i −0.929312 0.369295i \(-0.879599\pi\)
−0.369295 0.929312i \(-0.620401\pi\)
\(242\) −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 \(0.115577\pi\)
−0.934802 + 0.355170i \(0.884423\pi\)
\(270\) 1.63640i 0.0995884i
\(271\) −9.41876 9.41876i −0.572149 0.572149i 0.360580 0.932728i \(-0.382579\pi\)
−0.932728 + 0.360580i \(0.882579\pi\)
\(272\) 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 \(-0.942371\pi\)
0.983656 0.180059i \(-0.0576290\pi\)
\(278\) −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 −0.230001 0.973190i \(-0.573873\pi\)
0.973190 + 0.230001i \(0.0738729\pi\)
\(282\) 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 0.661453 0.749987i \(-0.269940\pi\)
−0.749987 + 0.661453i \(0.769940\pi\)
\(294\) −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 0.832354 0.554245i \(-0.186993\pi\)
−0.554245 + 0.832354i \(0.686993\pi\)
\(308\) 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 \(-0.982282\pi\)
0.998451 0.0556354i \(-0.0177184\pi\)
\(314\) 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 0.921252 0.388967i \(-0.127168\pi\)
−0.388967 + 0.921252i \(0.627168\pi\)
\(318\) −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 0.240438 0.970664i \(-0.422709\pi\)
−0.970664 + 0.240438i \(0.922709\pi\)
\(332\) 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 \(-0.906593\pi\)
0.957252 0.289254i \(-0.0934071\pi\)
\(338\) 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 0.971397 + 0.237462i \(0.0763156\pi\)
0.237462 + 0.971397i \(0.423684\pi\)
\(350\) −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 −0.371336 0.928498i \(-0.621100\pi\)
0.928498 + 0.371336i \(0.121100\pi\)
\(354\) −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 −0.774343 0.632767i \(-0.781919\pi\)
0.632767 + 0.774343i \(0.281919\pi\)
\(360\) 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 \(-0.932301\pi\)
0.977468 0.211082i \(-0.0676986\pi\)
\(368\) 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 0.477987 0.878367i \(-0.341367\pi\)
−0.878367 + 0.477987i \(0.841367\pi\)
\(380\) 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 −0.934704 0.355428i \(-0.884335\pi\)
0.355428 + 0.934704i \(0.384335\pi\)
\(384\) 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 \(0.146916\pi\)
−0.895363 + 0.445338i \(0.853084\pi\)
\(390\) 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 −0.961375 0.275242i \(-0.911242\pi\)
−0.275242 0.961375i \(-0.588758\pi\)
\(398\) −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 0.0420122 0.999117i \(-0.486623\pi\)
0.999117 0.0420122i \(-0.0133769\pi\)
\(402\) −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 −0.277515 0.960721i \(-0.589511\pi\)
0.960721 + 0.277515i \(0.0895109\pi\)
\(410\) −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 \(0.131065\pi\)
−0.916420 + 0.400218i \(0.868935\pi\)
\(420\) 4.31423 0.363595i 0.210513 0.0177416i
\(421\) −17.2214 17.2214i −0.839319 0.839319i 0.149450 0.988769i \(-0.452250\pi\)
−0.988769 + 0.149450i \(0.952250\pi\)
\(422\) 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 0.995796 + 0.0915975i \(0.0291973\pi\)
0.0915975 + 0.995796i \(0.470803\pi\)
\(432\) 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 −0.266268 0.963899i \(-0.585790\pi\)
0.963899 + 0.266268i \(0.0857905\pi\)
\(450\) 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 0.147439 0.989071i \(-0.452897\pi\)
−0.989071 + 0.147439i \(0.952897\pi\)
\(458\) 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 0.0964882 0.995334i \(-0.469239\pi\)
0.995334 0.0964882i \(-0.0307610\pi\)
\(462\) −3.32994 + 3.94287i −0.154923 + 0.183439i
\(463\) 12.4486 12.4486i 0.578536 0.578536i −0.355964 0.934500i \(-0.615847\pi\)
0.934500 + 0.355964i \(0.115847\pi\)
\(464\) 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 0.860690 0.509130i \(-0.170033\pi\)
−0.509130 + 0.860690i \(0.670033\pi\)
\(480\) 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 0.619445 0.785040i \(-0.287358\pi\)
−0.785040 + 0.619445i \(0.787358\pi\)
\(488\) 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 \(-0.905495\pi\)
0.956249 0.292555i \(-0.0945055\pi\)
\(492\) −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 0.966891 0.255188i \(-0.0821374\pi\)
−0.255188 + 0.966891i \(0.582137\pi\)
\(500\) 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 \(-0.944937\pi\)
0.985075 0.172125i \(-0.0550633\pi\)
\(504\) 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 0.0538516 0.998549i \(-0.482850\pi\)
0.998549 0.0538516i \(-0.0171498\pi\)
\(510\) 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 \(0.0792736\pi\)
−0.969148 + 0.246479i \(0.920726\pi\)
\(522\) 0.287270 + 0.287270i 0.0125735 + 0.0125735i
\(523\) 39.7356i 1.73752i −0.495237 0.868758i \(-0.664919\pi\)
0.495237 0.868758i \(-0.335081\pi\)
\(524\) −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 −0.895474 0.445114i \(-0.853163\pi\)
0.445114 + 0.895474i \(0.353163\pi\)
\(542\) 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 −0.562587 0.826738i \(-0.690194\pi\)
0.826738 + 0.562587i \(0.190194\pi\)
\(558\) 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 \(0.179836\pi\)
−0.844603 + 0.535393i \(0.820164\pi\)
\(570\) 1.52991 + 1.52991i 0.0640809 + 0.0640809i
\(571\) 34.8620i 1.45893i 0.684020 + 0.729464i \(0.260230\pi\)
−0.684020 + 0.729464i \(0.739770\pi\)
\(572\) −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 −0.419155 0.907915i \(-0.637674\pi\)
0.907915 + 0.419155i \(0.137674\pi\)
\(578\) −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 0.0623701 0.998053i \(-0.480134\pi\)
0.998053 0.0623701i \(-0.0198659\pi\)
\(588\) −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 0.820645 0.571439i \(-0.193614\pi\)
−0.571439 + 0.820645i \(0.693614\pi\)
\(594\) 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 \(0.0261437\pi\)
−0.996629 + 0.0820405i \(0.973856\pi\)
\(602\) −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 \(-0.707535\pi\)
0.606770 0.794877i \(-0.292465\pi\)
\(608\) 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 0.313132 0.949710i \(-0.398622\pi\)
−0.949710 + 0.313132i \(0.898622\pi\)
\(614\) 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 0.198536 0.980094i \(-0.436381\pi\)
−0.980094 + 0.198536i \(0.936381\pi\)
\(618\) −5.62070 + 5.62070i −0.226098 + 0.226098i
\(619\) 28.9913 + 28.9913i 1.16526 + 1.16526i 0.983307 + 0.181953i \(0.0582418\pi\)
0.181953 + 0.983307i \(0.441758\pi\)
\(620\) 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 −0.931953 0.362578i \(-0.881897\pi\)
0.362578 + 0.931953i \(0.381897\pi\)
\(632\) −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 \(-0.693659\pi\)
0.571553 0.820565i \(-0.306341\pi\)
\(642\) 2.35689 2.35689i 0.0930191 0.0930191i
\(643\) 23.7094 23.7094i 0.935009 0.935009i −0.0630044 0.998013i \(-0.520068\pi\)
0.998013 + 0.0630044i \(0.0200682\pi\)
\(644\) 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 0.999438 + 0.0335333i \(0.0106760\pi\)
0.0335333 + 0.999438i \(0.489324\pi\)
\(662\) 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 \(0.0214511\pi\)
−0.997730 + 0.0673395i \(0.978549\pi\)
\(674\) 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 \(0.160620\pi\)
−0.875366 + 0.483461i \(0.839380\pi\)
\(678\) 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 −0.0167709 + 0.999859i \(0.505339\pi\)
−0.999859 + 0.0167709i \(0.994661\pi\)
\(684\) 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 −0.728507 0.685038i \(-0.759785\pi\)
0.685038 + 0.728507i \(0.259785\pi\)
\(692\) 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 \(0.133645\pi\)
−0.913146 + 0.407632i \(0.866355\pi\)
\(702\) 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 0.102706 0.994712i \(-0.467250\pi\)
0.994712 0.102706i \(-0.0327501\pi\)
\(710\) 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 −0.922529 0.385927i \(-0.873882\pi\)
0.385927 + 0.922529i \(0.373882\pi\)
\(734\) 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 −0.896957 0.442119i \(-0.854227\pi\)
0.442119 + 0.896957i \(0.354227\pi\)
\(740\) −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 0.434986 0.900437i \(-0.356753\pi\)
−0.900437 + 0.434986i \(0.856753\pi\)
\(744\) 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 \(0.0931004\pi\)
−0.957531 + 0.288331i \(0.906900\pi\)
\(752\) 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 0.995868 + 0.0908090i \(0.0289453\pi\)
0.0908090 + 0.995868i \(0.471055\pi\)
\(762\) −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 −0.0341363 + 0.999417i \(0.510868\pi\)
−0.999417 + 0.0341363i \(0.989132\pi\)
\(770\) −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 −0.152650 + 0.988280i \(0.548781\pi\)
−0.988280 + 0.152650i \(0.951219\pi\)
\(774\) 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 +