Properties

Label 76.2.d.a.75.4
Level $76$
Weight $2$
Character 76.75
Analytic conductor $0.607$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.14453810176.1
Defining polynomial: \(x^{8} + 3 x^{6} + 6 x^{4} + 12 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 75.4
Root \(-0.331077 + 1.37491i\) of defining polynomial
Character \(\chi\) \(=\) 76.75
Dual form 76.2.d.a.75.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.331077 + 1.37491i) q^{2} -2.35829 q^{3} +(-1.78078 - 0.910404i) q^{4} -2.56155 q^{5} +(0.780776 - 3.24245i) q^{6} +4.15286i q^{7} +(1.84130 - 2.14700i) q^{8} +2.56155 q^{9} +O(q^{10})\) \(q+(-0.331077 + 1.37491i) q^{2} -2.35829 q^{3} +(-1.78078 - 0.910404i) q^{4} -2.56155 q^{5} +(0.780776 - 3.24245i) q^{6} +4.15286i q^{7} +(1.84130 - 2.14700i) q^{8} +2.56155 q^{9} +(0.848071 - 3.52191i) q^{10} -2.33205i q^{11} +(4.19960 + 2.14700i) q^{12} +4.29400i q^{13} +(-5.70982 - 1.37491i) q^{14} +6.04090 q^{15} +(2.34233 + 3.24245i) q^{16} -1.00000 q^{17} +(-0.848071 + 3.52191i) q^{18} +(-3.68260 + 2.33205i) q^{19} +(4.56155 + 2.33205i) q^{20} -9.79366i q^{21} +(3.20636 + 0.772087i) q^{22} -1.82081i q^{23} +(-4.34233 + 5.06326i) q^{24} +1.56155 q^{25} +(-5.90388 - 1.42164i) q^{26} +1.03399 q^{27} +(3.78078 - 7.39531i) q^{28} +1.20565i q^{29} +(-2.00000 + 8.30571i) q^{30} +1.32431 q^{31} +(-5.23358 + 2.14700i) q^{32} +5.49966i q^{33} +(0.331077 - 1.37491i) q^{34} -10.6378i q^{35} +(-4.56155 - 2.33205i) q^{36} -5.49966i q^{37} +(-1.98714 - 5.83535i) q^{38} -10.1265i q^{39} +(-4.71659 + 5.49966i) q^{40} +5.49966i q^{41} +(13.4654 + 3.24245i) q^{42} +1.30957i q^{43} +(-2.12311 + 4.15286i) q^{44} -6.56155 q^{45} +(2.50345 + 0.602827i) q^{46} +6.99614i q^{47} +(-5.52390 - 7.64666i) q^{48} -10.2462 q^{49} +(-0.516994 + 2.14700i) q^{50} +2.35829 q^{51} +(3.90928 - 7.64666i) q^{52} +9.79366i q^{53} +(-0.342329 + 1.42164i) q^{54} +5.97366i q^{55} +(8.91618 + 7.64666i) q^{56} +(8.68466 - 5.49966i) q^{57} +(-1.65767 - 0.399164i) q^{58} -6.33122 q^{59} +(-10.7575 - 5.49966i) q^{60} +11.6847 q^{61} +(-0.438447 + 1.82081i) q^{62} +10.6378i q^{63} +(-1.21922 - 7.90655i) q^{64} -10.9993i q^{65} +(-7.56155 - 1.82081i) q^{66} +0.290319 q^{67} +(1.78078 + 0.910404i) q^{68} +4.29400i q^{69} +(14.6260 + 3.52191i) q^{70} -2.06798 q^{71} +(4.71659 - 5.49966i) q^{72} -0.123106 q^{73} +(7.56155 + 1.82081i) q^{74} -3.68260 q^{75} +(8.68100 - 0.800201i) q^{76} +9.68466 q^{77} +(13.9231 + 3.35265i) q^{78} +13.4061 q^{79} +(-6.00000 - 8.30571i) q^{80} -10.1231 q^{81} +(-7.56155 - 1.82081i) q^{82} +11.9473i q^{83} +(-8.91618 + 17.4403i) q^{84} +2.56155 q^{85} +(-1.80054 - 0.433567i) q^{86} -2.84329i q^{87} +(-5.00691 - 4.29400i) q^{88} -14.0877i q^{89} +(2.17238 - 9.02157i) q^{90} -17.8324 q^{91} +(-1.65767 + 3.24245i) q^{92} -3.12311 q^{93} +(-9.61909 - 2.31626i) q^{94} +(9.43318 - 5.97366i) q^{95} +(12.3423 - 5.06326i) q^{96} -2.41131i q^{97} +(3.39228 - 14.0877i) q^{98} -5.97366i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{4} - 4q^{5} - 2q^{6} + 4q^{9} + O(q^{10}) \) \( 8q - 6q^{4} - 4q^{5} - 2q^{6} + 4q^{9} - 6q^{16} - 8q^{17} + 20q^{20} - 10q^{24} - 4q^{25} - 6q^{26} + 22q^{28} - 16q^{30} - 20q^{36} + 18q^{38} + 50q^{42} + 16q^{44} - 36q^{45} - 16q^{49} + 22q^{54} + 20q^{57} - 38q^{58} + 44q^{61} - 20q^{62} - 18q^{64} - 44q^{66} + 6q^{68} + 32q^{73} + 44q^{74} - 16q^{76} + 28q^{77} - 48q^{80} - 48q^{81} - 44q^{82} + 4q^{85} - 38q^{92} + 8q^{93} + 74q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.331077 + 1.37491i −0.234107 + 0.972211i
\(3\) −2.35829 −1.36156 −0.680781 0.732487i \(-0.738359\pi\)
−0.680781 + 0.732487i \(0.738359\pi\)
\(4\) −1.78078 0.910404i −0.890388 0.455202i
\(5\) −2.56155 −1.14556 −0.572781 0.819709i \(-0.694135\pi\)
−0.572781 + 0.819709i \(0.694135\pi\)
\(6\) 0.780776 3.24245i 0.318751 1.32373i
\(7\) 4.15286i 1.56963i 0.619729 + 0.784816i \(0.287243\pi\)
−0.619729 + 0.784816i \(0.712757\pi\)
\(8\) 1.84130 2.14700i 0.650998 0.759079i
\(9\) 2.56155 0.853851
\(10\) 0.848071 3.52191i 0.268183 1.11373i
\(11\) 2.33205i 0.703139i −0.936162 0.351569i \(-0.885648\pi\)
0.936162 0.351569i \(-0.114352\pi\)
\(12\) 4.19960 + 2.14700i 1.21232 + 0.619786i
\(13\) 4.29400i 1.19094i 0.803377 + 0.595471i \(0.203034\pi\)
−0.803377 + 0.595471i \(0.796966\pi\)
\(14\) −5.70982 1.37491i −1.52601 0.367461i
\(15\) 6.04090 1.55975
\(16\) 2.34233 + 3.24245i 0.585582 + 0.810613i
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) −0.848071 + 3.52191i −0.199892 + 0.830123i
\(19\) −3.68260 + 2.33205i −0.844847 + 0.535008i
\(20\) 4.56155 + 2.33205i 1.01999 + 0.521462i
\(21\) 9.79366i 2.13715i
\(22\) 3.20636 + 0.772087i 0.683599 + 0.164609i
\(23\) 1.82081i 0.379665i −0.981817 0.189832i \(-0.939206\pi\)
0.981817 0.189832i \(-0.0607944\pi\)
\(24\) −4.34233 + 5.06326i −0.886374 + 1.03353i
\(25\) 1.56155 0.312311
\(26\) −5.90388 1.42164i −1.15785 0.278807i
\(27\) 1.03399 0.198991
\(28\) 3.78078 7.39531i 0.714500 1.39758i
\(29\) 1.20565i 0.223884i 0.993715 + 0.111942i \(0.0357071\pi\)
−0.993715 + 0.111942i \(0.964293\pi\)
\(30\) −2.00000 + 8.30571i −0.365148 + 1.51641i
\(31\) 1.32431 0.237853 0.118926 0.992903i \(-0.462055\pi\)
0.118926 + 0.992903i \(0.462055\pi\)
\(32\) −5.23358 + 2.14700i −0.925175 + 0.379540i
\(33\) 5.49966i 0.957367i
\(34\) 0.331077 1.37491i 0.0567792 0.235796i
\(35\) 10.6378i 1.79811i
\(36\) −4.56155 2.33205i −0.760259 0.388675i
\(37\) 5.49966i 0.904138i −0.891983 0.452069i \(-0.850686\pi\)
0.891983 0.452069i \(-0.149314\pi\)
\(38\) −1.98714 5.83535i −0.322357 0.946618i
\(39\) 10.1265i 1.62154i
\(40\) −4.71659 + 5.49966i −0.745758 + 0.869572i
\(41\) 5.49966i 0.858902i 0.903090 + 0.429451i \(0.141293\pi\)
−0.903090 + 0.429451i \(0.858707\pi\)
\(42\) 13.4654 + 3.24245i 2.07776 + 0.500321i
\(43\) 1.30957i 0.199707i 0.995002 + 0.0998536i \(0.0318375\pi\)
−0.995002 + 0.0998536i \(0.968163\pi\)
\(44\) −2.12311 + 4.15286i −0.320070 + 0.626067i
\(45\) −6.56155 −0.978139
\(46\) 2.50345 + 0.602827i 0.369114 + 0.0888820i
\(47\) 6.99614i 1.02049i 0.860028 + 0.510246i \(0.170446\pi\)
−0.860028 + 0.510246i \(0.829554\pi\)
\(48\) −5.52390 7.64666i −0.797307 1.10370i
\(49\) −10.2462 −1.46374
\(50\) −0.516994 + 2.14700i −0.0731140 + 0.303632i
\(51\) 2.35829 0.330227
\(52\) 3.90928 7.64666i 0.542119 1.06040i
\(53\) 9.79366i 1.34526i 0.739978 + 0.672631i \(0.234836\pi\)
−0.739978 + 0.672631i \(0.765164\pi\)
\(54\) −0.342329 + 1.42164i −0.0465851 + 0.193461i
\(55\) 5.97366i 0.805489i
\(56\) 8.91618 + 7.64666i 1.19148 + 1.02183i
\(57\) 8.68466 5.49966i 1.15031 0.728447i
\(58\) −1.65767 0.399164i −0.217663 0.0524128i
\(59\) −6.33122 −0.824254 −0.412127 0.911126i \(-0.635214\pi\)
−0.412127 + 0.911126i \(0.635214\pi\)
\(60\) −10.7575 5.49966i −1.38879 0.710002i
\(61\) 11.6847 1.49607 0.748034 0.663661i \(-0.230998\pi\)
0.748034 + 0.663661i \(0.230998\pi\)
\(62\) −0.438447 + 1.82081i −0.0556828 + 0.231243i
\(63\) 10.6378i 1.34023i
\(64\) −1.21922 7.90655i −0.152403 0.988318i
\(65\) 10.9993i 1.36430i
\(66\) −7.56155 1.82081i −0.930763 0.224126i
\(67\) 0.290319 0.0354681 0.0177341 0.999843i \(-0.494355\pi\)
0.0177341 + 0.999843i \(0.494355\pi\)
\(68\) 1.78078 + 0.910404i 0.215951 + 0.110403i
\(69\) 4.29400i 0.516937i
\(70\) 14.6260 + 3.52191i 1.74814 + 0.420949i
\(71\) −2.06798 −0.245423 −0.122712 0.992442i \(-0.539159\pi\)
−0.122712 + 0.992442i \(0.539159\pi\)
\(72\) 4.71659 5.49966i 0.555855 0.648141i
\(73\) −0.123106 −0.0144084 −0.00720421 0.999974i \(-0.502293\pi\)
−0.00720421 + 0.999974i \(0.502293\pi\)
\(74\) 7.56155 + 1.82081i 0.879013 + 0.211665i
\(75\) −3.68260 −0.425230
\(76\) 8.68100 0.800201i 0.995778 0.0917893i
\(77\) 9.68466 1.10367
\(78\) 13.9231 + 3.35265i 1.57648 + 0.379613i
\(79\) 13.4061 1.50830 0.754152 0.656700i \(-0.228048\pi\)
0.754152 + 0.656700i \(0.228048\pi\)
\(80\) −6.00000 8.30571i −0.670820 0.928607i
\(81\) −10.1231 −1.12479
\(82\) −7.56155 1.82081i −0.835034 0.201075i
\(83\) 11.9473i 1.31139i 0.755026 + 0.655695i \(0.227624\pi\)
−0.755026 + 0.655695i \(0.772376\pi\)
\(84\) −8.91618 + 17.4403i −0.972835 + 1.90289i
\(85\) 2.56155 0.277839
\(86\) −1.80054 0.433567i −0.194158 0.0467528i
\(87\) 2.84329i 0.304832i
\(88\) −5.00691 4.29400i −0.533738 0.457742i
\(89\) 14.0877i 1.49329i −0.665223 0.746644i \(-0.731664\pi\)
0.665223 0.746644i \(-0.268336\pi\)
\(90\) 2.17238 9.02157i 0.228989 0.950957i
\(91\) −17.8324 −1.86934
\(92\) −1.65767 + 3.24245i −0.172824 + 0.338049i
\(93\) −3.12311 −0.323851
\(94\) −9.61909 2.31626i −0.992134 0.238904i
\(95\) 9.43318 5.97366i 0.967824 0.612885i
\(96\) 12.3423 5.06326i 1.25968 0.516767i
\(97\) 2.41131i 0.244831i −0.992479 0.122416i \(-0.960936\pi\)
0.992479 0.122416i \(-0.0390641\pi\)
\(98\) 3.39228 14.0877i 0.342672 1.42307i
\(99\) 5.97366i 0.600376i
\(100\) −2.78078 1.42164i −0.278078 0.142164i
\(101\) −8.24621 −0.820529 −0.410264 0.911967i \(-0.634564\pi\)
−0.410264 + 0.911967i \(0.634564\pi\)
\(102\) −0.780776 + 3.24245i −0.0773084 + 0.321051i
\(103\) −12.0818 −1.19045 −0.595227 0.803557i \(-0.702938\pi\)
−0.595227 + 0.803557i \(0.702938\pi\)
\(104\) 9.21922 + 7.90655i 0.904019 + 0.775301i
\(105\) 25.0870i 2.44824i
\(106\) −13.4654 3.24245i −1.30788 0.314935i
\(107\) 5.75058 0.555929 0.277965 0.960591i \(-0.410340\pi\)
0.277965 + 0.960591i \(0.410340\pi\)
\(108\) −1.84130 0.941346i −0.177179 0.0905811i
\(109\) 12.2050i 1.16902i 0.811385 + 0.584512i \(0.198714\pi\)
−0.811385 + 0.584512i \(0.801286\pi\)
\(110\) −8.21327 1.97774i −0.783105 0.188570i
\(111\) 12.9698i 1.23104i
\(112\) −13.4654 + 9.72736i −1.27236 + 0.919149i
\(113\) 5.49966i 0.517364i −0.965963 0.258682i \(-0.916712\pi\)
0.965963 0.258682i \(-0.0832882\pi\)
\(114\) 4.68626 + 13.7615i 0.438909 + 1.28888i
\(115\) 4.66410i 0.434929i
\(116\) 1.09763 2.14700i 0.101913 0.199344i
\(117\) 10.9993i 1.01689i
\(118\) 2.09612 8.70488i 0.192963 0.801349i
\(119\) 4.15286i 0.380692i
\(120\) 11.1231 12.9698i 1.01540 1.18398i
\(121\) 5.56155 0.505596
\(122\) −3.86852 + 16.0654i −0.350239 + 1.45449i
\(123\) 12.9698i 1.16945i
\(124\) −2.35829 1.20565i −0.211781 0.108271i
\(125\) 8.80776 0.787790
\(126\) −14.6260 3.52191i −1.30299 0.313757i
\(127\) −6.04090 −0.536043 −0.268021 0.963413i \(-0.586370\pi\)
−0.268021 + 0.963413i \(0.586370\pi\)
\(128\) 11.2745 + 0.941346i 0.996533 + 0.0832041i
\(129\) 3.08835i 0.271914i
\(130\) 15.1231 + 3.64162i 1.32638 + 0.319391i
\(131\) 5.97366i 0.521921i −0.965349 0.260961i \(-0.915961\pi\)
0.965349 0.260961i \(-0.0840393\pi\)
\(132\) 5.00691 9.79366i 0.435795 0.852428i
\(133\) −9.68466 15.2933i −0.839766 1.32610i
\(134\) −0.0961180 + 0.399164i −0.00830333 + 0.0344825i
\(135\) −2.64861 −0.227956
\(136\) −1.84130 + 2.14700i −0.157890 + 0.184104i
\(137\) −12.1231 −1.03575 −0.517873 0.855457i \(-0.673276\pi\)
−0.517873 + 0.855457i \(0.673276\pi\)
\(138\) −5.90388 1.42164i −0.502572 0.121018i
\(139\) 18.9435i 1.60676i −0.595464 0.803382i \(-0.703032\pi\)
0.595464 0.803382i \(-0.296968\pi\)
\(140\) −9.68466 + 18.9435i −0.818503 + 1.60102i
\(141\) 16.4990i 1.38946i
\(142\) 0.684658 2.84329i 0.0574553 0.238603i
\(143\) 10.0138 0.837397
\(144\) 6.00000 + 8.30571i 0.500000 + 0.692143i
\(145\) 3.08835i 0.256473i
\(146\) 0.0407574 0.169260i 0.00337311 0.0140080i
\(147\) 24.1636 1.99298
\(148\) −5.00691 + 9.79366i −0.411565 + 0.805034i
\(149\) 2.80776 0.230021 0.115010 0.993364i \(-0.463310\pi\)
0.115010 + 0.993364i \(0.463310\pi\)
\(150\) 1.21922 5.06326i 0.0995492 0.413413i
\(151\) 8.85254 0.720409 0.360205 0.932873i \(-0.382707\pi\)
0.360205 + 0.932873i \(0.382707\pi\)
\(152\) −1.77387 + 12.2005i −0.143880 + 0.989595i
\(153\) −2.56155 −0.207089
\(154\) −3.20636 + 13.3156i −0.258376 + 1.07300i
\(155\) −3.39228 −0.272475
\(156\) −9.21922 + 18.0331i −0.738129 + 1.44380i
\(157\) 6.00000 0.478852 0.239426 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) −4.43845 + 18.4322i −0.353104 + 1.46639i
\(159\) 23.0963i 1.83166i
\(160\) 13.4061 5.49966i 1.05985 0.434786i
\(161\) 7.56155 0.595934
\(162\) 3.35152 13.9184i 0.263321 1.09353i
\(163\) 17.6339i 1.38119i 0.723240 + 0.690597i \(0.242652\pi\)
−0.723240 + 0.690597i \(0.757348\pi\)
\(164\) 5.00691 9.79366i 0.390974 0.764756i
\(165\) 14.0877i 1.09672i
\(166\) −16.4265 3.95548i −1.27495 0.307005i
\(167\) 10.7575 0.832439 0.416220 0.909264i \(-0.363355\pi\)
0.416220 + 0.909264i \(0.363355\pi\)
\(168\) −21.0270 18.0331i −1.62227 1.39128i
\(169\) −5.43845 −0.418342
\(170\) −0.848071 + 3.52191i −0.0650440 + 0.270119i
\(171\) −9.43318 + 5.97366i −0.721373 + 0.456817i
\(172\) 1.19224 2.33205i 0.0909071 0.177817i
\(173\) 2.41131i 0.183328i −0.995790 0.0916642i \(-0.970781\pi\)
0.995790 0.0916642i \(-0.0292186\pi\)
\(174\) 3.90928 + 0.941346i 0.296361 + 0.0713633i
\(175\) 6.48490i 0.490213i
\(176\) 7.56155 5.46242i 0.569973 0.411746i
\(177\) 14.9309 1.12227
\(178\) 19.3693 + 4.66410i 1.45179 + 0.349589i
\(179\) 8.10887 0.606085 0.303043 0.952977i \(-0.401998\pi\)
0.303043 + 0.952977i \(0.401998\pi\)
\(180\) 11.6847 + 5.97366i 0.870923 + 0.445251i
\(181\) 19.5873i 1.45591i 0.685623 + 0.727957i \(0.259530\pi\)
−0.685623 + 0.727957i \(0.740470\pi\)
\(182\) 5.90388 24.5180i 0.437625 1.81739i
\(183\) −27.5559 −2.03699
\(184\) −3.90928 3.35265i −0.288196 0.247161i
\(185\) 14.0877i 1.03575i
\(186\) 1.03399 4.29400i 0.0758156 0.314851i
\(187\) 2.33205i 0.170536i
\(188\) 6.36932 12.4586i 0.464530 0.908634i
\(189\) 4.29400i 0.312343i
\(190\) 5.09017 + 14.9475i 0.369280 + 1.08441i
\(191\) 7.79447i 0.563988i 0.959416 + 0.281994i \(0.0909959\pi\)
−0.959416 + 0.281994i \(0.909004\pi\)
\(192\) 2.87529 + 18.6460i 0.207506 + 1.34566i
\(193\) 5.49966i 0.395874i 0.980215 + 0.197937i \(0.0634241\pi\)
−0.980215 + 0.197937i \(0.936576\pi\)
\(194\) 3.31534 + 0.798328i 0.238028 + 0.0573166i
\(195\) 25.9396i 1.85757i
\(196\) 18.2462 + 9.32819i 1.30330 + 0.666299i
\(197\) −22.4924 −1.60252 −0.801259 0.598317i \(-0.795836\pi\)
−0.801259 + 0.598317i \(0.795836\pi\)
\(198\) 8.21327 + 1.97774i 0.583692 + 0.140552i
\(199\) 5.17534i 0.366870i −0.983032 0.183435i \(-0.941278\pi\)
0.983032 0.183435i \(-0.0587217\pi\)
\(200\) 2.87529 3.35265i 0.203314 0.237069i
\(201\) −0.684658 −0.0482921
\(202\) 2.73013 11.3378i 0.192091 0.797727i
\(203\) −5.00691 −0.351416
\(204\) −4.19960 2.14700i −0.294030 0.150320i
\(205\) 14.0877i 0.983925i
\(206\) 4.00000 16.6114i 0.278693 1.15737i
\(207\) 4.66410i 0.324177i
\(208\) −13.9231 + 10.0580i −0.965393 + 0.697394i
\(209\) 5.43845 + 8.58800i 0.376185 + 0.594045i
\(210\) −34.4924 8.30571i −2.38020 0.573149i
\(211\) 25.1976 1.73467 0.867336 0.497723i \(-0.165830\pi\)
0.867336 + 0.497723i \(0.165830\pi\)
\(212\) 8.91618 17.4403i 0.612366 1.19781i
\(213\) 4.87689 0.334159
\(214\) −1.90388 + 7.90655i −0.130147 + 0.540480i
\(215\) 3.35453i 0.228777i
\(216\) 1.90388 2.21997i 0.129543 0.151050i
\(217\) 5.49966i 0.373341i
\(218\) −16.7808 4.04078i −1.13654 0.273676i
\(219\) 0.290319 0.0196180
\(220\) 5.43845 10.6378i 0.366660 0.717198i
\(221\) 4.29400i 0.288846i
\(222\) −17.8324 4.29400i −1.19683 0.288194i
\(223\) −22.2586 −1.49055 −0.745274 0.666758i \(-0.767681\pi\)
−0.745274 + 0.666758i \(0.767681\pi\)
\(224\) −8.91618 21.7343i −0.595738 1.45218i
\(225\) 4.00000 0.266667
\(226\) 7.56155 + 1.82081i 0.502987 + 0.121118i
\(227\) −24.6169 −1.63388 −0.816942 0.576720i \(-0.804332\pi\)
−0.816942 + 0.576720i \(0.804332\pi\)
\(228\) −20.4723 + 1.88711i −1.35581 + 0.124977i
\(229\) −6.56155 −0.433600 −0.216800 0.976216i \(-0.569562\pi\)
−0.216800 + 0.976216i \(0.569562\pi\)
\(230\) −6.41273 1.54417i −0.422843 0.101820i
\(231\) −22.8393 −1.50271
\(232\) 2.58854 + 2.21997i 0.169946 + 0.145748i
\(233\) 10.8078 0.708040 0.354020 0.935238i \(-0.384814\pi\)
0.354020 + 0.935238i \(0.384814\pi\)
\(234\) −15.1231 3.64162i −0.988628 0.238060i
\(235\) 17.9210i 1.16904i
\(236\) 11.2745 + 5.76396i 0.733906 + 0.375202i
\(237\) −31.6155 −2.05365
\(238\) 5.70982 + 1.37491i 0.370113 + 0.0891224i
\(239\) 9.83943i 0.636460i 0.948014 + 0.318230i \(0.103088\pi\)
−0.948014 + 0.318230i \(0.896912\pi\)
\(240\) 14.1498 + 19.5873i 0.913364 + 1.26436i
\(241\) 22.6757i 1.46067i 0.683090 + 0.730334i \(0.260635\pi\)
−0.683090 + 0.730334i \(0.739365\pi\)
\(242\) −1.84130 + 7.64666i −0.118363 + 0.491546i
\(243\) 20.7713 1.33248
\(244\) −20.8078 10.6378i −1.33208 0.681013i
\(245\) 26.2462 1.67681
\(246\) 17.8324 + 4.29400i 1.13695 + 0.273776i
\(247\) −10.0138 15.8131i −0.637164 1.00616i
\(248\) 2.43845 2.84329i 0.154842 0.180549i
\(249\) 28.1753i 1.78554i
\(250\) −2.91605 + 12.1099i −0.184427 + 0.765898i
\(251\) 21.5626i 1.36102i 0.732739 + 0.680510i \(0.238242\pi\)
−0.732739 + 0.680510i \(0.761758\pi\)
\(252\) 9.68466 18.9435i 0.610076 1.19333i
\(253\) −4.24621 −0.266957
\(254\) 2.00000 8.30571i 0.125491 0.521147i
\(255\) −6.04090 −0.378296
\(256\) −5.02699 + 15.1898i −0.314187 + 0.949361i
\(257\) 17.1760i 1.07141i −0.844405 0.535705i \(-0.820046\pi\)
0.844405 0.535705i \(-0.179954\pi\)
\(258\) 4.24621 + 1.02248i 0.264358 + 0.0636568i
\(259\) 22.8393 1.41916
\(260\) −10.0138 + 19.5873i −0.621031 + 1.21475i
\(261\) 3.08835i 0.191164i
\(262\) 8.21327 + 1.97774i 0.507418 + 0.122185i
\(263\) 14.2794i 0.880504i 0.897874 + 0.440252i \(0.145111\pi\)
−0.897874 + 0.440252i \(0.854889\pi\)
\(264\) 11.8078 + 10.1265i 0.726718 + 0.623244i
\(265\) 25.0870i 1.54108i
\(266\) 24.2334 8.25231i 1.48584 0.505982i
\(267\) 33.2228i 2.03321i
\(268\) −0.516994 0.264308i −0.0315804 0.0161452i
\(269\) 5.49966i 0.335320i 0.985845 + 0.167660i \(0.0536211\pi\)
−0.985845 + 0.167660i \(0.946379\pi\)
\(270\) 0.876894 3.64162i 0.0533661 0.221622i
\(271\) 22.0738i 1.34089i −0.741959 0.670445i \(-0.766103\pi\)
0.741959 0.670445i \(-0.233897\pi\)
\(272\) −2.34233 3.24245i −0.142025 0.196603i
\(273\) 42.0540 2.54522
\(274\) 4.01368 16.6682i 0.242475 1.00696i
\(275\) 3.64162i 0.219598i
\(276\) 3.90928 7.64666i 0.235311 0.460275i
\(277\) 13.0540 0.784337 0.392169 0.919893i \(-0.371725\pi\)
0.392169 + 0.919893i \(0.371725\pi\)
\(278\) 26.0456 + 6.27174i 1.56211 + 0.376154i
\(279\) 3.39228 0.203091
\(280\) −22.8393 19.5873i −1.36491 1.17057i
\(281\) 28.1753i 1.68080i 0.541968 + 0.840399i \(0.317679\pi\)
−0.541968 + 0.840399i \(0.682321\pi\)
\(282\) 22.6847 + 5.46242i 1.35085 + 0.325283i
\(283\) 5.97366i 0.355097i −0.984112 0.177549i \(-0.943183\pi\)
0.984112 0.177549i \(-0.0568167\pi\)
\(284\) 3.68260 + 1.88269i 0.218522 + 0.111717i
\(285\) −22.2462 + 14.0877i −1.31775 + 0.834481i
\(286\) −3.31534 + 13.7681i −0.196040 + 0.814127i
\(287\) −22.8393 −1.34816
\(288\) −13.4061 + 5.49966i −0.789962 + 0.324070i
\(289\) −16.0000 −0.941176
\(290\) 4.24621 + 1.02248i 0.249346 + 0.0600421i
\(291\) 5.68658i 0.333353i
\(292\) 0.219224 + 0.112076i 0.0128291 + 0.00655874i
\(293\) 4.29400i 0.250858i −0.992103 0.125429i \(-0.959969\pi\)
0.992103 0.125429i \(-0.0400308\pi\)
\(294\) −8.00000 + 33.2228i −0.466569 + 1.93760i
\(295\) 16.2177 0.944233
\(296\) −11.8078 10.1265i −0.686312 0.588592i
\(297\) 2.41131i 0.139918i
\(298\) −0.929585 + 3.86043i −0.0538494 + 0.223629i
\(299\) 7.81855 0.452159
\(300\) 6.55789 + 3.35265i 0.378620 + 0.193566i
\(301\) −5.43845 −0.313467
\(302\) −2.93087 + 12.1715i −0.168653 + 0.700390i
\(303\) 19.4470 1.11720
\(304\) −16.1874 6.47823i −0.928412 0.371552i
\(305\) −29.9309 −1.71384
\(306\) 0.848071 3.52191i 0.0484810 0.201334i
\(307\) 13.4061 0.765126 0.382563 0.923929i \(-0.375041\pi\)
0.382563 + 0.923929i \(0.375041\pi\)
\(308\) −17.2462 8.81695i −0.982694 0.502392i
\(309\) 28.4924 1.62088
\(310\) 1.12311 4.66410i 0.0637881 0.264903i
\(311\) 4.15286i 0.235487i 0.993044 + 0.117743i \(0.0375660\pi\)
−0.993044 + 0.117743i \(0.962434\pi\)
\(312\) −21.7416 18.6460i −1.23088 1.05562i
\(313\) −0.438447 −0.0247825 −0.0123913 0.999923i \(-0.503944\pi\)
−0.0123913 + 0.999923i \(0.503944\pi\)
\(314\) −1.98646 + 8.24948i −0.112102 + 0.465545i
\(315\) 27.2492i 1.53532i
\(316\) −23.8733 12.2050i −1.34298 0.686583i
\(317\) 4.29400i 0.241175i 0.992703 + 0.120588i \(0.0384779\pi\)
−0.992703 + 0.120588i \(0.961522\pi\)
\(318\) 31.7555 + 7.64666i 1.78076 + 0.428803i
\(319\) 2.81164 0.157422
\(320\) 3.12311 + 20.2530i 0.174587 + 1.13218i
\(321\) −13.5616 −0.756932
\(322\) −2.50345 + 10.3965i −0.139512 + 0.579373i
\(323\) 3.68260 2.33205i 0.204905 0.129759i
\(324\) 18.0270 + 9.21612i 1.00150 + 0.512006i
\(325\) 6.70531i 0.371944i
\(326\) −24.2451 5.83817i −1.34281 0.323347i
\(327\) 28.7829i 1.59170i
\(328\) 11.8078 + 10.1265i 0.651975 + 0.559144i
\(329\) −29.0540 −1.60180
\(330\) 19.3693 + 4.66410i 1.06625 + 0.256750i
\(331\) 23.8733 1.31219 0.656097 0.754677i \(-0.272206\pi\)
0.656097 + 0.754677i \(0.272206\pi\)
\(332\) 10.8769 21.2755i 0.596947 1.16765i
\(333\) 14.0877i 0.771999i
\(334\) −3.56155 + 14.7906i −0.194879 + 0.809306i
\(335\) −0.743668 −0.0406309
\(336\) 31.7555 22.9400i 1.73240 1.25148i
\(337\) 6.17669i 0.336466i −0.985747 0.168233i \(-0.946194\pi\)
0.985747 0.168233i \(-0.0538061\pi\)
\(338\) 1.80054 7.47740i 0.0979366 0.406717i
\(339\) 12.9698i 0.704423i
\(340\) −4.56155 2.33205i −0.247385 0.126473i
\(341\) 3.08835i 0.167243i
\(342\) −5.09017 14.9475i −0.275245 0.808271i
\(343\) 13.4810i 0.727908i
\(344\) 2.81164 + 2.41131i 0.151594 + 0.130009i
\(345\) 10.9993i 0.592183i
\(346\) 3.31534 + 0.798328i 0.178234 + 0.0429184i
\(347\) 29.8683i 1.60342i −0.597716 0.801708i \(-0.703925\pi\)
0.597716 0.801708i \(-0.296075\pi\)
\(348\) −2.58854 + 5.06326i −0.138760 + 0.271419i
\(349\) 9.05398 0.484648 0.242324 0.970195i \(-0.422090\pi\)
0.242324 + 0.970195i \(0.422090\pi\)
\(350\) −8.91618 2.14700i −0.476590 0.114762i
\(351\) 4.43994i 0.236987i
\(352\) 5.00691 + 12.2050i 0.266869 + 0.650527i
\(353\) 18.6847 0.994484 0.497242 0.867612i \(-0.334346\pi\)
0.497242 + 0.867612i \(0.334346\pi\)
\(354\) −4.94326 + 20.5287i −0.262731 + 1.09109i
\(355\) 5.29723 0.281148
\(356\) −12.8255 + 25.0870i −0.679748 + 1.32961i
\(357\) 9.79366i 0.518335i
\(358\) −2.68466 + 11.1490i −0.141889 + 0.589243i
\(359\) 6.19782i 0.327108i 0.986534 + 0.163554i \(0.0522958\pi\)
−0.986534 + 0.163554i \(0.947704\pi\)
\(360\) −12.0818 + 14.0877i −0.636766 + 0.742485i
\(361\) 8.12311 17.1760i 0.427532 0.904000i
\(362\) −26.9309 6.48490i −1.41546 0.340839i
\(363\) −13.1158 −0.688400
\(364\) 31.7555 + 16.2347i 1.66444 + 0.850927i
\(365\) 0.315342 0.0165057
\(366\) 9.12311 37.8869i 0.476872 1.98038i
\(367\) 1.02248i 0.0533730i 0.999644 + 0.0266865i \(0.00849559\pi\)
−0.999644 + 0.0266865i \(0.991504\pi\)
\(368\) 5.90388 4.26493i 0.307761 0.222325i
\(369\) 14.0877i 0.733374i
\(370\) −19.3693 4.66410i −1.00696 0.242475i
\(371\) −40.6716 −2.11157
\(372\) 5.56155 + 2.84329i 0.288353 + 0.147418i
\(373\) 6.70531i 0.347188i 0.984817 + 0.173594i \(0.0555380\pi\)
−0.984817 + 0.173594i \(0.944462\pi\)
\(374\) −3.20636 0.772087i −0.165797 0.0399237i
\(375\) −20.7713 −1.07263
\(376\) 15.0207 + 12.8820i 0.774635 + 0.664339i
\(377\) −5.17708 −0.266633
\(378\) −5.90388 1.42164i −0.303663 0.0731215i
\(379\) −15.7644 −0.809762 −0.404881 0.914369i \(-0.632687\pi\)
−0.404881 + 0.914369i \(0.632687\pi\)
\(380\) −22.2368 + 2.04976i −1.14073 + 0.105150i
\(381\) 14.2462 0.729856
\(382\) −10.7167 2.58057i −0.548315 0.132033i
\(383\) 22.2586 1.13736 0.568682 0.822558i \(-0.307454\pi\)
0.568682 + 0.822558i \(0.307454\pi\)
\(384\) −26.5885 2.21997i −1.35684 0.113287i
\(385\) −24.8078 −1.26432
\(386\) −7.56155 1.82081i −0.384873 0.0926767i
\(387\) 3.35453i 0.170520i
\(388\) −2.19526 + 4.29400i −0.111448 + 0.217995i
\(389\) 14.8078 0.750783 0.375392 0.926866i \(-0.377508\pi\)
0.375392 + 0.926866i \(0.377508\pi\)
\(390\) −35.6647 8.58800i −1.80595 0.434870i
\(391\) 1.82081i 0.0920822i
\(392\) −18.8664 + 21.9986i −0.952895 + 1.11110i
\(393\) 14.0877i 0.710628i
\(394\) 7.44672 30.9251i 0.375160 1.55799i
\(395\) −34.3404 −1.72785
\(396\) −5.43845 + 10.6378i −0.273292 + 0.534568i
\(397\) −3.93087 −0.197285 −0.0986423 0.995123i \(-0.531450\pi\)
−0.0986423 + 0.995123i \(0.531450\pi\)
\(398\) 7.11564 + 1.71343i 0.356675 + 0.0858866i
\(399\) 22.8393 + 36.0661i 1.14339 + 1.80557i
\(400\) 3.65767 + 5.06326i 0.182884 + 0.253163i
\(401\) 7.91096i 0.395055i 0.980297 + 0.197527i \(0.0632911\pi\)
−0.980297 + 0.197527i \(0.936709\pi\)
\(402\) 0.226674 0.941346i 0.0113055 0.0469501i
\(403\) 5.68658i 0.283269i
\(404\) 14.6847 + 7.50738i 0.730589 + 0.373506i
\(405\) 25.9309 1.28852
\(406\) 1.65767 6.88407i 0.0822688 0.341651i
\(407\) −12.8255 −0.635734
\(408\) 4.34233 5.06326i 0.214977 0.250669i
\(409\) 27.4983i 1.35970i −0.733350 0.679851i \(-0.762044\pi\)
0.733350 0.679851i \(-0.237956\pi\)
\(410\) 19.3693 + 4.66410i 0.956582 + 0.230343i
\(411\) 28.5899 1.41023
\(412\) 21.5150 + 10.9993i 1.05997 + 0.541897i
\(413\) 26.2926i 1.29378i
\(414\) 6.41273 + 1.54417i 0.315168 + 0.0758920i
\(415\) 30.6037i 1.50228i
\(416\) −9.21922 22.4730i −0.452010 1.10183i
\(417\) 44.6743i 2.18771i
\(418\) −13.6083 + 4.63411i −0.665604 + 0.226662i
\(419\) 39.9319i 1.95080i −0.220440 0.975401i \(-0.570749\pi\)
0.220440 0.975401i \(-0.429251\pi\)
\(420\) 22.8393 44.6743i 1.11444 2.17988i
\(421\) 23.2043i 1.13091i −0.824780 0.565454i \(-0.808701\pi\)
0.824780 0.565454i \(-0.191299\pi\)
\(422\) −8.34233 + 34.6445i −0.406098 + 1.68647i
\(423\) 17.9210i 0.871348i
\(424\) 21.0270 + 18.0331i 1.02116 + 0.875763i
\(425\) −1.56155 −0.0757464
\(426\) −1.61463 + 6.70531i −0.0782289 + 0.324873i
\(427\) 48.5247i 2.34827i
\(428\) −10.2405 5.23535i −0.494993 0.253060i
\(429\) −23.6155 −1.14017
\(430\) 4.61219 + 1.11061i 0.222419 + 0.0535582i
\(431\) 5.29723 0.255158 0.127579 0.991828i \(-0.459279\pi\)
0.127579 + 0.991828i \(0.459279\pi\)
\(432\) 2.42194 + 3.35265i 0.116526 + 0.161305i
\(433\) 18.9103i 0.908770i −0.890805 0.454385i \(-0.849859\pi\)
0.890805 0.454385i \(-0.150141\pi\)
\(434\) −7.56155 1.82081i −0.362966 0.0874016i
\(435\) 7.28323i 0.349204i
\(436\) 11.1114 21.7343i 0.532142 1.04088i
\(437\) 4.24621 + 6.70531i 0.203124 + 0.320758i
\(438\) −0.0961180 + 0.399164i −0.00459269 + 0.0190728i
\(439\) −19.6100 −0.935935 −0.467968 0.883746i \(-0.655014\pi\)
−0.467968 + 0.883746i \(0.655014\pi\)
\(440\) 12.8255 + 10.9993i 0.611430 + 0.524372i
\(441\) −26.2462 −1.24982
\(442\) 5.90388 + 1.42164i 0.280819 + 0.0676207i
\(443\) 12.2344i 0.581275i 0.956833 + 0.290637i \(0.0938673\pi\)
−0.956833 + 0.290637i \(0.906133\pi\)
\(444\) 11.8078 23.0963i 0.560372 1.09610i
\(445\) 36.0863i 1.71065i
\(446\) 7.36932 30.6037i 0.348947 1.44913i
\(447\) −6.62153 −0.313188
\(448\) 32.8348 5.06326i 1.55130 0.239217i
\(449\) 14.7647i 0.696789i 0.937348 + 0.348395i \(0.113273\pi\)
−0.937348 + 0.348395i \(0.886727\pi\)
\(450\) −1.32431 + 5.49966i −0.0624284 + 0.259256i
\(451\) 12.8255 0.603927
\(452\) −5.00691 + 9.79366i −0.235505 + 0.460655i
\(453\) −20.8769 −0.980882
\(454\) 8.15009 33.8462i 0.382503 1.58848i
\(455\) 45.6786 2.14144
\(456\) 4.18330 28.7725i 0.195901 1.34740i
\(457\) 3.87689 0.181353 0.0906767 0.995880i \(-0.471097\pi\)
0.0906767 + 0.995880i \(0.471097\pi\)
\(458\) 2.17238 9.02157i 0.101509 0.421550i
\(459\) −1.03399 −0.0482624
\(460\) 4.24621 8.30571i 0.197981 0.387256i
\(461\) 31.6847 1.47570 0.737851 0.674964i \(-0.235841\pi\)
0.737851 + 0.674964i \(0.235841\pi\)
\(462\) 7.56155 31.4020i 0.351795 1.46096i
\(463\) 16.3243i 0.758656i 0.925262 + 0.379328i \(0.123845\pi\)
−0.925262 + 0.379328i \(0.876155\pi\)
\(464\) −3.90928 + 2.82404i −0.181484 + 0.131103i
\(465\) 8.00000 0.370991
\(466\) −3.57820 + 14.8597i −0.165757 + 0.688364i
\(467\) 2.33205i 0.107914i −0.998543 0.0539572i \(-0.982817\pi\)
0.998543 0.0539572i \(-0.0171834\pi\)
\(468\) 10.0138 19.5873i 0.462889 0.905424i
\(469\) 1.20565i 0.0556719i
\(470\) 24.6398 + 5.93322i 1.13655 + 0.273679i
\(471\) −14.1498 −0.651987
\(472\) −11.6577 + 13.5931i −0.536588 + 0.625674i
\(473\) 3.05398 0.140422
\(474\) 10.4672 43.4686i 0.480773 1.99658i
\(475\) −5.75058 + 3.64162i −0.263855 + 0.167089i
\(476\) −3.78078 + 7.39531i −0.173292 + 0.338963i
\(477\) 25.0870i 1.14865i
\(478\) −13.5284 3.25761i −0.618773 0.148999i
\(479\) 41.5286i 1.89749i 0.316045 + 0.948744i \(0.397645\pi\)
−0.316045 + 0.948744i \(0.602355\pi\)
\(480\) −31.6155 + 12.9698i −1.44304 + 0.591988i
\(481\) 23.6155 1.07678
\(482\) −31.1771 7.50738i −1.42008 0.341952i
\(483\) −17.8324 −0.811401
\(484\) −9.90388 5.06326i −0.450176 0.230148i
\(485\) 6.17669i 0.280469i
\(486\) −6.87689 + 28.5588i −0.311942 + 1.29545i
\(487\) −18.8664 −0.854916 −0.427458 0.904035i \(-0.640591\pi\)
−0.427458 + 0.904035i \(0.640591\pi\)
\(488\) 21.5150 25.0870i 0.973937 1.13563i
\(489\) 41.5859i 1.88058i
\(490\) −8.68951 + 36.0863i −0.392552 + 1.63021i
\(491\) 21.2755i 0.960151i −0.877227 0.480075i \(-0.840609\pi\)
0.877227 0.480075i \(-0.159391\pi\)
\(492\) −11.8078 + 23.0963i −0.532335 + 1.04126i
\(493\) 1.20565i 0.0542999i
\(494\) 25.0570 8.53279i 1.12737 0.383908i
\(495\) 15.3019i 0.687767i
\(496\) 3.10196 + 4.29400i 0.139282 + 0.192806i
\(497\) 8.58800i 0.385225i
\(498\) 38.7386 + 9.32819i 1.73592 + 0.418006i
\(499\) 1.30957i 0.0586243i 0.999570 + 0.0293122i \(0.00933169\pi\)
−0.999570 + 0.0293122i \(0.990668\pi\)
\(500\) −15.6847 8.01862i −0.701439 0.358604i
\(501\) −25.3693 −1.13342
\(502\) −29.6467 7.13888i −1.32320 0.318624i
\(503\) 16.3873i 0.730672i −0.930876 0.365336i \(-0.880954\pi\)
0.930876 0.365336i \(-0.119046\pi\)
\(504\) 22.8393 + 19.5873i 1.01734 + 0.872488i
\(505\) 21.1231 0.939966
\(506\) 1.40582 5.83817i 0.0624964 0.259539i
\(507\) 12.8255 0.569599
\(508\) 10.7575 + 5.49966i 0.477286 + 0.244008i
\(509\) 8.58800i 0.380657i −0.981721 0.190328i \(-0.939045\pi\)
0.981721 0.190328i \(-0.0609552\pi\)
\(510\) 2.00000 8.30571i 0.0885615 0.367783i
\(511\) 0.511240i 0.0226159i
\(512\) −19.2203 11.9407i −0.849426 0.527707i
\(513\) −3.80776 + 2.41131i −0.168117 + 0.106462i
\(514\) 23.6155 + 5.68658i 1.04164 + 0.250824i
\(515\) 30.9481 1.36374
\(516\) −2.81164 + 5.49966i −0.123776 + 0.242109i
\(517\) 16.3153 0.717548
\(518\) −7.56155 + 31.4020i −0.332236 + 1.37973i
\(519\) 5.68658i 0.249613i
\(520\) −23.6155 20.2530i −1.03561 0.888155i
\(521\) 22.6757i 0.993439i −0.867911 0.496719i \(-0.834538\pi\)
0.867911 0.496719i \(-0.165462\pi\)
\(522\) −4.24621 1.02248i −0.185852 0.0447527i
\(523\) −2.19526 −0.0959922 −0.0479961 0.998848i \(-0.515284\pi\)
−0.0479961 + 0.998848i \(0.515284\pi\)
\(524\) −5.43845 + 10.6378i −0.237580 + 0.464713i
\(525\) 15.2933i 0.667455i
\(526\) −19.6329 4.72757i −0.856036 0.206132i
\(527\) −1.32431 −0.0576877
\(528\) −17.8324 + 12.8820i −0.776054 + 0.560617i
\(529\) 19.6847 0.855855
\(530\) 34.4924 + 8.30571i 1.49826 + 0.360777i
\(531\) −16.2177 −0.703790
\(532\) 3.32312 + 36.0509i 0.144075 + 1.56301i
\(533\) −23.6155 −1.02290
\(534\) −45.6786 10.9993i −1.97670 0.475987i
\(535\) −14.7304 −0.636851
\(536\) 0.534565 0.623316i 0.0230897 0.0269231i
\(537\) −19.1231 −0.825223
\(538\) −7.56155 1.82081i −0.326002 0.0785006i
\(539\) 23.8947i 1.02922i
\(540\) 4.71659 + 2.41131i 0.202970 + 0.103766i
\(541\) −32.8078 −1.41052 −0.705258 0.708951i \(-0.749169\pi\)
−0.705258 + 0.708951i \(0.749169\pi\)
\(542\) 30.3496 + 7.30814i 1.30363 + 0.313911i
\(543\) 46.1927i 1.98232i
\(544\) 5.23358 2.14700i 0.224388 0.0920519i
\(545\) 31.2637i 1.33919i
\(546\) −13.9231 + 57.8206i −0.595853 + 2.47449i
\(547\) −0.580639 −0.0248263 −0.0124132 0.999923i \(-0.503951\pi\)
−0.0124132 + 0.999923i \(0.503951\pi\)
\(548\) 21.5885 + 11.0369i 0.922217 + 0.471474i
\(549\) 29.9309 1.27742
\(550\) 5.00691 + 1.20565i 0.213495 + 0.0514093i
\(551\) −2.81164 4.43994i −0.119780 0.189148i
\(552\) 9.21922 + 7.90655i 0.392396 + 0.336525i
\(553\) 55.6736i 2.36748i
\(554\) −4.32187 + 17.9481i −0.183619 + 0.762541i
\(555\) 33.2228i 1.41023i
\(556\) −17.2462 + 33.7341i −0.731402 + 1.43064i
\(557\) 9.93087 0.420784 0.210392 0.977617i \(-0.432526\pi\)
0.210392 + 0.977617i \(0.432526\pi\)
\(558\) −1.12311 + 4.66410i −0.0475449 + 0.197447i
\(559\) −5.62329 −0.237840
\(560\) 34.4924 24.9171i 1.45757 1.05294i
\(561\) 5.49966i 0.232196i
\(562\) −38.7386 9.32819i −1.63409 0.393486i
\(563\) −21.3519 −0.899877 −0.449938 0.893060i \(-0.648554\pi\)
−0.449938 + 0.893060i \(0.648554\pi\)
\(564\) −15.0207 + 29.3810i −0.632487 + 1.23716i
\(565\) 14.0877i 0.592672i
\(566\) 8.21327 + 1.97774i 0.345230 + 0.0831307i
\(567\) 42.0398i 1.76551i
\(568\) −3.80776 + 4.43994i −0.159770 + 0.186296i
\(569\) 41.5859i 1.74337i 0.490064 + 0.871687i \(0.336973\pi\)
−0.490064 + 0.871687i \(0.663027\pi\)
\(570\) −12.0041 35.2507i −0.502797 1.47649i
\(571\) 15.5889i 0.652377i −0.945305 0.326188i \(-0.894236\pi\)
0.945305 0.326188i \(-0.105764\pi\)
\(572\) −17.8324 9.11662i −0.745609 0.381185i
\(573\) 18.3817i 0.767905i
\(574\) 7.56155 31.4020i 0.315613 1.31070i
\(575\) 2.84329i 0.118573i
\(576\) −3.12311 20.2530i −0.130129 0.843877i
\(577\) 27.0000 1.12402 0.562012 0.827129i \(-0.310027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(578\) 5.29723 21.9986i 0.220336 0.915022i
\(579\) 12.9698i 0.539007i
\(580\) −2.81164 + 5.49966i −0.116747 + 0.228361i
\(581\) −49.6155 −2.05840
\(582\) −7.81855 1.88269i −0.324089 0.0780401i
\(583\) 22.8393 0.945906
\(584\) −0.226674 + 0.264308i −0.00937986 + 0.0109371i
\(585\) 28.1753i 1.16491i
\(586\) 5.90388 + 1.42164i 0.243887 + 0.0587276i
\(587\) 5.97366i 0.246559i −0.992372 0.123280i \(-0.960659\pi\)
0.992372 0.123280i \(-0.0393412\pi\)
\(588\) −43.0299 21.9986i −1.77452 0.907208i
\(589\) −4.87689 + 3.08835i −0.200949 + 0.127253i
\(590\) −5.36932 + 22.2980i −0.221051 + 0.917994i
\(591\) 53.0438 2.18193
\(592\) 17.8324 12.8820i 0.732906 0.529447i
\(593\) 12.7386 0.523113 0.261556 0.965188i \(-0.415764\pi\)
0.261556 + 0.965188i \(0.415764\pi\)
\(594\) 3.31534 + 0.798328i 0.136030 + 0.0327558i
\(595\) 10.6378i 0.436106i
\(596\) −5.00000 2.55620i −0.204808 0.104706i
\(597\) 12.2050i 0.499516i
\(598\) −2.58854 + 10.7498i −0.105853 + 0.439593i
\(599\) 24.9073 1.01768 0.508841 0.860860i \(-0.330074\pi\)
0.508841 + 0.860860i \(0.330074\pi\)
\(600\) −6.78078 + 7.90655i −0.276824 + 0.322783i
\(601\) 35.4092i 1.44437i 0.691698 + 0.722187i \(0.256863\pi\)
−0.691698 + 0.722187i \(0.743137\pi\)
\(602\) 1.80054 7.47740i 0.0733847 0.304756i
\(603\) 0.743668 0.0302845
\(604\) −15.7644 8.05939i −0.641444 0.327932i
\(605\) −14.2462 −0.579191
\(606\) −6.43845 + 26.7379i −0.261544 + 1.08615i
\(607\) −31.5288 −1.27971 −0.639857 0.768494i \(-0.721006\pi\)
−0.639857 + 0.768494i \(0.721006\pi\)
\(608\) 14.2663 20.1115i 0.578574 0.815630i
\(609\) 11.8078 0.478475
\(610\) 9.90941 41.1524i 0.401220 1.66621i
\(611\) −30.0414 −1.21535
\(612\) 4.56155 + 2.33205i 0.184390 + 0.0942674i
\(613\) −29.3002 −1.18342 −0.591712 0.806150i \(-0.701548\pi\)
−0.591712 + 0.806150i \(0.701548\pi\)
\(614\) −4.43845 + 18.4322i −0.179121 + 0.743864i
\(615\) 33.2228i 1.33967i
\(616\) 17.8324 20.7930i 0.718487 0.837773i
\(617\) 41.5464 1.67259 0.836297 0.548276i \(-0.184716\pi\)
0.836297 + 0.548276i \(0.184716\pi\)
\(618\) −9.43318 + 39.1746i −0.379458 + 1.57583i
\(619\) 6.70906i 0.269660i −0.990869 0.134830i \(-0.956951\pi\)
0.990869 0.134830i \(-0.0430488\pi\)
\(620\) 6.04090 + 3.08835i 0.242608 + 0.124031i
\(621\) 1.88269i 0.0755499i
\(622\) −5.70982 1.37491i −0.228943 0.0551290i
\(623\) 58.5040 2.34391
\(624\) 32.8348 23.7196i 1.31444 0.949546i
\(625\) −30.3693 −1.21477
\(626\) 0.145160 0.602827i 0.00580175 0.0240938i
\(627\) −12.8255 20.2530i −0.512200 0.808828i
\(628\) −10.6847 5.46242i −0.426364 0.217974i
\(629\) 5.49966i 0.219286i
\(630\) 37.4653 + 9.02157i 1.49265 + 0.359428i
\(631\) 9.61528i 0.382778i −0.981514 0.191389i \(-0.938701\pi\)
0.981514 0.191389i \(-0.0612992\pi\)
\(632\) 24.6847 28.7829i 0.981903 1.14492i
\(633\) −59.4233 −2.36186
\(634\) −5.90388 1.42164i −0.234473 0.0564607i
\(635\) 15.4741 0.614070
\(636\) −21.0270 + 41.1294i −0.833774 + 1.63089i
\(637\) 43.9972i 1.74323i
\(638\) −0.930870 + 3.86577i −0.0368535 + 0.153047i
\(639\) −5.29723 −0.209555
\(640\) −28.8802 2.41131i −1.14159 0.0953153i
\(641\) 26.8212i 1.05938i −0.848193 0.529688i \(-0.822309\pi\)
0.848193 0.529688i \(-0.177691\pi\)
\(642\) 4.48991 18.6460i 0.177203 0.735898i
\(643\) 14.2794i 0.563124i 0.959543 + 0.281562i \(0.0908524\pi\)
−0.959543 + 0.281562i \(0.909148\pi\)
\(644\) −13.4654 6.88407i −0.530612 0.271270i
\(645\) 7.91096i 0.311494i
\(646\) 1.98714 + 5.83535i 0.0781830 + 0.229589i
\(647\) 32.1374i 1.26345i 0.775191 + 0.631726i \(0.217653\pi\)
−0.775191 + 0.631726i \(0.782347\pi\)
\(648\) −18.6397 + 21.7343i −0.732236 + 0.853805i
\(649\) 14.7647i 0.579565i
\(650\) −9.21922 2.21997i −0.361608 0.0870745i
\(651\) 12.9698i 0.508327i
\(652\) 16.0540 31.4020i 0.628722 1.22980i
\(653\) −25.1922 −0.985848 −0.492924 0.870072i \(-0.664072\pi\)
−0.492924 + 0.870072i \(0.664072\pi\)
\(654\) 39.5740 + 9.52935i 1.54747 + 0.372627i
\(655\) 15.3019i 0.597893i
\(656\) −17.8324 + 12.8820i −0.696237 + 0.502958i
\(657\) −0.315342 −0.0123026
\(658\) 9.61909 39.9467i 0.374991 1.55729i
\(659\) −41.9960 −1.63593 −0.817965 0.575268i \(-0.804898\pi\)
−0.817965 + 0.575268i \(0.804898\pi\)
\(660\) −12.8255 + 25.0870i −0.499230 + 0.976509i
\(661\) 37.2919i 1.45049i −0.688492 0.725244i \(-0.741727\pi\)
0.688492 0.725244i \(-0.258273\pi\)
\(662\) −7.90388 + 32.8237i −0.307193 + 1.27573i
\(663\) 10.1265i 0.393281i
\(664\) 25.6509 + 21.9986i 0.995449 + 0.853712i
\(665\) 24.8078 + 39.1746i 0.962004 + 1.51913i
\(666\) 19.3693 + 4.66410i 0.750546 + 0.180730i
\(667\) 2.19526 0.0850010
\(668\) −19.1567 9.79366i −0.741194 0.378928i
\(669\) 52.4924 2.02947
\(670\) 0.246211 1.02248i 0.00951197 0.0395018i
\(671\) 27.2492i 1.05194i
\(672\) 21.0270 + 51.2559i 0.811134 + 1.97724i
\(673\) 24.4099i 0.940934i 0.882418 + 0.470467i \(0.155914\pi\)
−0.882418 + 0.470467i \(0.844086\pi\)
\(674\) 8.49242 + 2.04496i 0.327116 + 0.0787689i
\(675\) 1.61463 0.0621470
\(676\) 9.68466 + 4.95118i 0.372487 + 0.190430i
\(677\) 40.3803i 1.55194i −0.630770 0.775970i \(-0.717261\pi\)
0.630770 0.775970i \(-0.282739\pi\)
\(678\) −17.8324 4.29400i −0.684848 0.164910i
\(679\) 10.0138 0.384295
\(680\) 4.71659 5.49966i 0.180873 0.210902i
\(681\) 58.0540 2.22463
\(682\) 4.24621 + 1.02248i 0.162596 + 0.0391528i
\(683\) 31.5288 1.20642 0.603208 0.797584i \(-0.293889\pi\)
0.603208 + 0.797584i \(0.293889\pi\)
\(684\) 22.2368 2.04976i 0.850246 0.0783744i
\(685\) 31.0540 1.18651
\(686\) 18.5353 + 4.46326i 0.707680 + 0.170408i
\(687\) 15.4741 0.590373
\(688\) −4.24621 + 3.06744i −0.161885 + 0.116945i
\(689\) −42.0540 −1.60213
\(690\) 15.1231 + 3.64162i 0.575727 + 0.138634i
\(691\) 8.01862i 0.305043i −0.988300 0.152521i \(-0.951261\pi\)
0.988300 0.152521i \(-0.0487393\pi\)
\(692\) −2.19526 + 4.29400i −0.0834514 + 0.163233i
\(693\) 24.8078 0.942369
\(694\) 41.0664 + 9.88871i 1.55886 + 0.375370i
\(695\) 48.5247i 1.84065i
\(696\) −6.10454 5.23535i −0.231392 0.198445i
\(697\) 5.49966i 0.208314i
\(698\) −2.99756 + 12.4484i −0.113459 + 0.471180i
\(699\) −25.4879 −0.964041
\(700\) 5.90388 11.5482i 0.223146 0.436480i
\(701\) 4.63068 0.174898 0.0874492 0.996169i \(-0.472128\pi\)
0.0874492 + 0.996169i \(0.472128\pi\)
\(702\) −6.10454 1.46996i −0.230401 0.0554801i
\(703\) 12.8255 + 20.2530i 0.483721 + 0.763858i
\(704\) −18.4384 + 2.84329i −0.694925 + 0.107160i
\(705\) 42.2630i 1.59172i
\(706\) −6.18606 + 25.6898i −0.232815 + 0.966848i
\(707\) 34.2453i 1.28793i
\(708\) −26.5885 13.5931i −0.999259 0.510861i
\(709\) 12.6307 0.474355 0.237178 0.971466i \(-0.423778\pi\)
0.237178 + 0.971466i \(0.423778\pi\)
\(710\) −1.75379 + 7.28323i −0.0658185 + 0.273335i
\(711\) 34.3404 1.28787
\(712\) −30.2462 25.9396i −1.13352 0.972128i
\(713\) 2.41131i 0.0903042i
\(714\) −13.4654 3.24245i −0.503931 0.121346i
\(715\) −25.6509 −0.959290
\(716\) −14.4401 7.38235i −0.539651 0.275891i
\(717\) 23.2043i 0.866580i
\(718\) −8.52146 2.05195i −0.318018 0.0765782i
\(719\) 26.4509i 0.986450i 0.869902 + 0.493225i \(0.164182\pi\)
−0.869902 + 0.493225i \(0.835818\pi\)
\(720\) −15.3693 21.2755i −0.572781 0.792892i
\(721\) 50.1739i 1.86858i
\(722\) 20.9262 + 16.8551i 0.778791 + 0.627284i
\(723\) 53.4759i 1.98879i
\(724\) 17.8324 34.8806i 0.662735 1.29633i
\(725\) 1.88269i 0.0699215i
\(726\) 4.34233 18.0331i 0.161159 0.669270i
\(727\) 44.6589i 1.65631i 0.560500 + 0.828154i \(0.310609\pi\)
−0.560500 + 0.828154i \(0.689391\pi\)
\(728\) −32.8348 + 38.2861i −1.21694 + 1.41898i
\(729\) −18.6155 −0.689464
\(730\) −0.104402 + 0.433567i −0.00386410 + 0.0160471i
\(731\) 1.30957i 0.0484361i
\(732\) 49.0708 + 25.0870i 1.81371 + 0.927241i
\(733\) −5.12311 −0.189226 −0.0946131 0.995514i \(-0.530161\pi\)
−0.0946131 + 0.995514i \(0.530161\pi\)
\(734\) −1.40582 0.338519i −0.0518898 0.0124950i
\(735\) −61.8963 −2.28308
\(736\) 3.90928 + 9.52935i 0.144098 + 0.351256i
\(737\) 0.677039i 0.0249390i
\(738\) −19.3693 4.66410i −0.712994 0.171688i
\(739\) 25.2042i 0.927152i 0.886057 + 0.463576i \(0.153434\pi\)
−0.886057 + 0.463576i \(0.846566\pi\)
\(740\) 12.8255 25.0870i 0.471473 0.922215i
\(741\) 23.6155 + 37.2919i 0.867538 + 1.36995i
\(742\) 13.4654 55.9200i 0.494332 2.05289i
\(743\) 11.9188 0.437257 0.218628 0.975808i \(-0.429842\pi\)
0.218628 + 0.975808i \(0.429842\pi\)
\(744\) −5.75058 + 6.70531i −0.210826 + 0.245829i
\(745\) −7.19224 −0.263503
\(746\) −9.21922 2.21997i −0.337540 0.0812789i
\(747\) 30.6037i 1.11973i
\(748\) 2.12311 4.15286i 0.0776284 0.151843i
\(749\) 23.8813i 0.872604i
\(750\) 6.87689 28.5588i 0.251109 1.04282i
\(751\) −35.6647 −1.30142 −0.650712 0.759324i \(-0.725530\pi\)
−0.650712 + 0.759324i \(0.725530\pi\)
\(752\) −22.6847 + 16.3873i −0.827224 + 0.597582i
\(753\) 50.8510i 1.85311i
\(754\) 1.71401 7.11804i 0.0624206 0.259224i
\(755\) −22.6762 −0.825273
\(756\) 3.90928 7.64666i 0.142179 0.278106i
\(757\) −44.8078 −1.62857 −0.814283 0.580468i \(-0.802870\pi\)
−0.814283 + 0.580468i \(0.802870\pi\)
\(758\) 5.21922 21.6747i 0.189571 0.787260i
\(759\) 10.0138 0.363479
\(760\) 4.54386 31.2524i 0.164823 1.13364i
\(761\) 30.6155 1.10981 0.554906 0.831913i \(-0.312754\pi\)
0.554906 + 0.831913i \(0.312754\pi\)
\(762\) −4.71659 + 19.5873i −0.170864 + 0.709574i
\(763\) −50.6855 −1.83494
\(764\) 7.09612 13.8802i 0.256729 0.502168i
\(765\) 6.56155 0.237233
\(766\) −7.36932 + 30.6037i −0.266264 + 1.10576i
\(767\) 27.1862i 0.981638i
\(768\) 11.8551 35.8220i 0.427785 1.29261i
\(769\) −28.2311 −1.01804 −0.509019 0.860755i \(-0.669992\pi\)
−0.509019 + 0.860755i \(0.669992\pi\)
\(770\) 8.21327 34.1085i 0.295986 1.22919i
\(771\) 40.5061i 1.45879i
\(772\) 5.00691 9.79366i 0.180203 0.352481i
\(773\) 41.0573i 1.47673i 0.674402 + 0.738365i \(0.264402\pi\)
−0.674402 + 0.738365i \(0.735598\pi\)
\(774\) −4.61219 1.11061i −0.165782 0.0399199i
\(775\) 2.06798 0.0742839
\(776\) −5.17708 4.43994i −0.185846 0.159385i
\(777\) −53.8617 −1.93228
\(778\) −4.90251 + 20.3594i −0.175763 + 0.729920i
\(779\) −12.8255 20.2530i −0.459520 0.725640i
\(780\) 23.6155 46.1927i 0.845572 1.65396i
\(781\) 4.82262i 0.172567i