Properties

Label 177.2.d.c.176.6
Level $177$
Weight $2$
Character 177.176
Analytic conductor $1.413$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.41335211578\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.19298288.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} - 2 x^{3} + 9 x^{2} - 9 x + 27\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.6
Root \(0.321037 - 1.70204i\) of defining polynomial
Character \(\chi\) \(=\) 177.176
Dual form 177.2.d.c.176.5

$q$-expansion

\(f(q)\) \(=\) \(q+2.47283 q^{2} +(-0.321037 + 1.70204i) q^{3} +4.11491 q^{4} -2.50682i q^{5} +(-0.793871 + 4.20886i) q^{6} -2.11491 q^{7} +5.22982 q^{8} +(-2.79387 - 1.09283i) q^{9} +O(q^{10})\) \(q+2.47283 q^{2} +(-0.321037 + 1.70204i) q^{3} +4.11491 q^{4} -2.50682i q^{5} +(-0.793871 + 4.20886i) q^{6} -2.11491 q^{7} +5.22982 q^{8} +(-2.79387 - 1.09283i) q^{9} -6.19895i q^{10} -3.64207 q^{11} +(-1.32104 + 7.00373i) q^{12} +4.69249i q^{13} -5.22982 q^{14} +(4.26670 + 0.804782i) q^{15} +4.70265 q^{16} -2.79487i q^{17} +(-6.90878 - 2.70240i) q^{18} +6.70265 q^{19} -10.3153i q^{20} +(0.678963 - 3.59965i) q^{21} -9.00624 q^{22} -0.885092 q^{23} +(-1.67896 + 8.90135i) q^{24} -1.28415 q^{25} +11.6037i q^{26} +(2.75698 - 4.40444i) q^{27} -8.70265 q^{28} -1.50646i q^{29} +(10.5509 + 1.99009i) q^{30} +6.91126i q^{31} +1.16924 q^{32} +(1.16924 - 6.19895i) q^{33} -6.91126i q^{34} +5.30169i q^{35} +(-11.4965 - 4.49691i) q^{36} -11.6037i q^{37} +16.5745 q^{38} +(-7.98680 - 1.50646i) q^{39} -13.1102i q^{40} +0.288053i q^{41} +(1.67896 - 8.90135i) q^{42} +7.70541i q^{43} -14.9868 q^{44} +(-2.73954 + 7.00373i) q^{45} -2.18869 q^{46} +9.47283 q^{47} +(-1.50972 + 8.00409i) q^{48} -2.52717 q^{49} -3.17548 q^{50} +(4.75698 + 0.897257i) q^{51} +19.3092i q^{52} -9.31497i q^{53} +(6.81756 - 10.8914i) q^{54} +9.13002i q^{55} -11.0606 q^{56} +(-2.15180 + 11.4082i) q^{57} -3.72523i q^{58} +(4.06058 + 6.52010i) q^{59} +(17.5571 + 3.31160i) q^{60} +9.92418i q^{61} +17.0904i q^{62} +(5.90878 + 2.31124i) q^{63} -6.51396 q^{64} +11.7632 q^{65} +(2.89134 - 15.3290i) q^{66} -4.69249i q^{67} -11.5006i q^{68} +(0.284147 - 1.50646i) q^{69} +13.1102i q^{70} +2.69177i q^{71} +(-14.6114 - 5.71532i) q^{72} +2.47372i q^{73} -28.6941i q^{74} +(0.412259 - 2.18567i) q^{75} +27.5808 q^{76} +7.70265 q^{77} +(-19.7500 - 3.72523i) q^{78} -3.56829 q^{79} -11.7887i q^{80} +(6.61143 + 6.10647i) q^{81} +0.712306i q^{82} -14.9868 q^{83} +(2.79387 - 14.8122i) q^{84} -7.00624 q^{85} +19.0542i q^{86} +(2.56406 + 0.483630i) q^{87} -19.0474 q^{88} -5.93246 q^{89} +(-6.77442 + 17.3191i) q^{90} -9.92418i q^{91} -3.64207 q^{92} +(-11.7632 - 2.21877i) q^{93} +23.4247 q^{94} -16.8023i q^{95} +(-0.375369 + 1.99009i) q^{96} -1.67957i q^{97} -6.24926 q^{98} +(10.1755 + 3.98018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 4q^{2} - q^{3} + 12q^{4} + 7q^{6} + 6q^{8} - 5q^{9} + O(q^{10}) \) \( 6q + 4q^{2} - q^{3} + 12q^{4} + 7q^{6} + 6q^{8} - 5q^{9} - 20q^{11} - 7q^{12} - 6q^{14} + 3q^{15} - 8q^{16} - 17q^{18} + 4q^{19} + 5q^{21} + 2q^{22} - 18q^{23} - 11q^{24} - 4q^{25} + 2q^{27} - 16q^{28} + 37q^{30} + 16q^{32} + 16q^{33} - 21q^{36} + 36q^{38} - 8q^{39} + 11q^{42} - 50q^{44} + 17q^{45} - 6q^{46} + 46q^{47} - q^{48} - 26q^{49} + 28q^{50} + 14q^{51} - 8q^{54} - 32q^{56} - 3q^{57} - 10q^{59} + 23q^{60} + 11q^{63} - 10q^{64} - 26q^{66} - 2q^{69} - 27q^{72} + 26q^{75} + 46q^{76} + 10q^{77} - 8q^{78} - 14q^{79} - 21q^{81} - 50q^{83} + 5q^{84} + 14q^{85} + 29q^{87} - 40q^{88} + 26q^{89} - 45q^{90} - 20q^{92} + 52q^{94} - 23q^{96} + 4q^{98} + 14q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.47283 1.74856 0.874279 0.485424i \(-0.161335\pi\)
0.874279 + 0.485424i \(0.161335\pi\)
\(3\) −0.321037 + 1.70204i −0.185351 + 0.982672i
\(4\) 4.11491 2.05745
\(5\) 2.50682i 1.12108i −0.828126 0.560542i \(-0.810593\pi\)
0.828126 0.560542i \(-0.189407\pi\)
\(6\) −0.793871 + 4.20886i −0.324096 + 1.71826i
\(7\) −2.11491 −0.799360 −0.399680 0.916655i \(-0.630879\pi\)
−0.399680 + 0.916655i \(0.630879\pi\)
\(8\) 5.22982 1.84902
\(9\) −2.79387 1.09283i −0.931290 0.364278i
\(10\) 6.19895i 1.96028i
\(11\) −3.64207 −1.09813 −0.549063 0.835781i \(-0.685015\pi\)
−0.549063 + 0.835781i \(0.685015\pi\)
\(12\) −1.32104 + 7.00373i −0.381350 + 2.02180i
\(13\) 4.69249i 1.30146i 0.759308 + 0.650731i \(0.225537\pi\)
−0.759308 + 0.650731i \(0.774463\pi\)
\(14\) −5.22982 −1.39773
\(15\) 4.26670 + 0.804782i 1.10166 + 0.207794i
\(16\) 4.70265 1.17566
\(17\) 2.79487i 0.677856i −0.940812 0.338928i \(-0.889936\pi\)
0.940812 0.338928i \(-0.110064\pi\)
\(18\) −6.90878 2.70240i −1.62841 0.636961i
\(19\) 6.70265 1.53769 0.768847 0.639433i \(-0.220831\pi\)
0.768847 + 0.639433i \(0.220831\pi\)
\(20\) 10.3153i 2.30658i
\(21\) 0.678963 3.59965i 0.148162 0.785509i
\(22\) −9.00624 −1.92014
\(23\) −0.885092 −0.184555 −0.0922773 0.995733i \(-0.529415\pi\)
−0.0922773 + 0.995733i \(0.529415\pi\)
\(24\) −1.67896 + 8.90135i −0.342717 + 1.81698i
\(25\) −1.28415 −0.256829
\(26\) 11.6037i 2.27568i
\(27\) 2.75698 4.40444i 0.530581 0.847634i
\(28\) −8.70265 −1.64465
\(29\) 1.50646i 0.279743i −0.990170 0.139871i \(-0.955331\pi\)
0.990170 0.139871i \(-0.0446689\pi\)
\(30\) 10.5509 + 1.99009i 1.92631 + 0.363339i
\(31\) 6.91126i 1.24130i 0.784088 + 0.620649i \(0.213131\pi\)
−0.784088 + 0.620649i \(0.786869\pi\)
\(32\) 1.16924 0.206694
\(33\) 1.16924 6.19895i 0.203539 1.07910i
\(34\) 6.91126i 1.18527i
\(35\) 5.30169i 0.896150i
\(36\) −11.4965 4.49691i −1.91609 0.749485i
\(37\) 11.6037i 1.90764i −0.300373 0.953822i \(-0.597111\pi\)
0.300373 0.953822i \(-0.402889\pi\)
\(38\) 16.5745 2.68875
\(39\) −7.98680 1.50646i −1.27891 0.241227i
\(40\) 13.1102i 2.07291i
\(41\) 0.288053i 0.0449862i 0.999747 + 0.0224931i \(0.00716039\pi\)
−0.999747 + 0.0224931i \(0.992840\pi\)
\(42\) 1.67896 8.90135i 0.259070 1.37351i
\(43\) 7.70541i 1.17506i 0.809201 + 0.587532i \(0.199900\pi\)
−0.809201 + 0.587532i \(0.800100\pi\)
\(44\) −14.9868 −2.25934
\(45\) −2.73954 + 7.00373i −0.408386 + 1.04405i
\(46\) −2.18869 −0.322704
\(47\) 9.47283 1.38175 0.690877 0.722972i \(-0.257224\pi\)
0.690877 + 0.722972i \(0.257224\pi\)
\(48\) −1.50972 + 8.00409i −0.217910 + 1.15529i
\(49\) −2.52717 −0.361024
\(50\) −3.17548 −0.449081
\(51\) 4.75698 + 0.897257i 0.666111 + 0.125641i
\(52\) 19.3092i 2.67770i
\(53\) 9.31497i 1.27951i −0.768579 0.639755i \(-0.779036\pi\)
0.768579 0.639755i \(-0.220964\pi\)
\(54\) 6.81756 10.8914i 0.927752 1.48214i
\(55\) 9.13002i 1.23109i
\(56\) −11.0606 −1.47803
\(57\) −2.15180 + 11.4082i −0.285012 + 1.51105i
\(58\) 3.72523i 0.489147i
\(59\) 4.06058 + 6.52010i 0.528642 + 0.848845i
\(60\) 17.5571 + 3.31160i 2.26661 + 0.427526i
\(61\) 9.92418i 1.27066i 0.772240 + 0.635330i \(0.219136\pi\)
−0.772240 + 0.635330i \(0.780864\pi\)
\(62\) 17.0904i 2.17048i
\(63\) 5.90878 + 2.31124i 0.744436 + 0.291189i
\(64\) −6.51396 −0.814245
\(65\) 11.7632 1.45905
\(66\) 2.89134 15.3290i 0.355899 1.88687i
\(67\) 4.69249i 0.573279i −0.958039 0.286639i \(-0.907462\pi\)
0.958039 0.286639i \(-0.0925381\pi\)
\(68\) 11.5006i 1.39466i
\(69\) 0.284147 1.50646i 0.0342073 0.181357i
\(70\) 13.1102i 1.56697i
\(71\) 2.69177i 0.319454i 0.987161 + 0.159727i \(0.0510615\pi\)
−0.987161 + 0.159727i \(0.948939\pi\)
\(72\) −14.6114 5.71532i −1.72197 0.673557i
\(73\) 2.47372i 0.289527i 0.989466 + 0.144764i \(0.0462422\pi\)
−0.989466 + 0.144764i \(0.953758\pi\)
\(74\) 28.6941i 3.33563i
\(75\) 0.412259 2.18567i 0.0476035 0.252379i
\(76\) 27.5808 3.16373
\(77\) 7.70265 0.877798
\(78\) −19.7500 3.72523i −2.23625 0.421799i
\(79\) −3.56829 −0.401465 −0.200732 0.979646i \(-0.564332\pi\)
−0.200732 + 0.979646i \(0.564332\pi\)
\(80\) 11.7887i 1.31802i
\(81\) 6.61143 + 6.10647i 0.734603 + 0.678497i
\(82\) 0.712306i 0.0786610i
\(83\) −14.9868 −1.64501 −0.822507 0.568755i \(-0.807425\pi\)
−0.822507 + 0.568755i \(0.807425\pi\)
\(84\) 2.79387 14.8122i 0.304836 1.61615i
\(85\) −7.00624 −0.759934
\(86\) 19.0542i 2.05467i
\(87\) 2.56406 + 0.483630i 0.274896 + 0.0518505i
\(88\) −19.0474 −2.03046
\(89\) −5.93246 −0.628840 −0.314420 0.949284i \(-0.601810\pi\)
−0.314420 + 0.949284i \(0.601810\pi\)
\(90\) −6.77442 + 17.3191i −0.714087 + 1.82559i
\(91\) 9.92418i 1.04034i
\(92\) −3.64207 −0.379712
\(93\) −11.7632 2.21877i −1.21979 0.230075i
\(94\) 23.4247 2.41608
\(95\) 16.8023i 1.72388i
\(96\) −0.375369 + 1.99009i −0.0383109 + 0.203113i
\(97\) 1.67957i 0.170534i −0.996358 0.0852670i \(-0.972826\pi\)
0.996358 0.0852670i \(-0.0271743\pi\)
\(98\) −6.24926 −0.631271
\(99\) 10.1755 + 3.98018i 1.02267 + 0.400023i
\(100\) −5.28415 −0.528415
\(101\) 5.51396 0.548660 0.274330 0.961636i \(-0.411544\pi\)
0.274330 + 0.961636i \(0.411544\pi\)
\(102\) 11.7632 + 2.21877i 1.16473 + 0.219691i
\(103\) 12.3979i 1.22160i −0.791784 0.610801i \(-0.790848\pi\)
0.791784 0.610801i \(-0.209152\pi\)
\(104\) 24.5408i 2.40643i
\(105\) −9.02369 1.70204i −0.880622 0.166102i
\(106\) 23.0344i 2.23730i
\(107\) 4.98054i 0.481487i 0.970589 + 0.240744i \(0.0773913\pi\)
−0.970589 + 0.240744i \(0.922609\pi\)
\(108\) 11.3447 18.1238i 1.09165 1.74397i
\(109\) 5.23169i 0.501105i −0.968103 0.250553i \(-0.919388\pi\)
0.968103 0.250553i \(-0.0806123\pi\)
\(110\) 22.5770i 2.15264i
\(111\) 19.7500 + 3.72523i 1.87459 + 0.353583i
\(112\) −9.94567 −0.939777
\(113\) −6.81756 −0.641342 −0.320671 0.947191i \(-0.603908\pi\)
−0.320671 + 0.947191i \(0.603908\pi\)
\(114\) −5.32104 + 28.2105i −0.498361 + 2.64216i
\(115\) 2.21877i 0.206901i
\(116\) 6.19895i 0.575558i
\(117\) 5.12811 13.1102i 0.474094 1.21204i
\(118\) 10.0411 + 16.1231i 0.924361 + 1.48425i
\(119\) 5.91090i 0.541851i
\(120\) 22.3141 + 4.20886i 2.03699 + 0.384214i
\(121\) 2.26470 0.205882
\(122\) 24.5408i 2.22182i
\(123\) −0.490277 0.0924755i −0.0442067 0.00833823i
\(124\) 28.4392i 2.55391i
\(125\) 9.31497i 0.833157i
\(126\) 14.6114 + 5.71532i 1.30169 + 0.509161i
\(127\) 16.1755 1.43534 0.717671 0.696382i \(-0.245208\pi\)
0.717671 + 0.696382i \(0.245208\pi\)
\(128\) −18.4464 −1.63045
\(129\) −13.1149 2.47372i −1.15470 0.217799i
\(130\) 29.0885 2.55123
\(131\) −1.40530 −0.122781 −0.0613907 0.998114i \(-0.519554\pi\)
−0.0613907 + 0.998114i \(0.519554\pi\)
\(132\) 4.81131 25.5081i 0.418771 2.22020i
\(133\) −14.1755 −1.22917
\(134\) 11.6037i 1.00241i
\(135\) −11.0411 6.91126i −0.950269 0.594826i
\(136\) 14.6167i 1.25337i
\(137\) 15.6870i 1.34023i 0.742256 + 0.670117i \(0.233756\pi\)
−0.742256 + 0.670117i \(0.766244\pi\)
\(138\) 0.702649 3.72523i 0.0598135 0.317113i
\(139\) −11.1560 −0.946243 −0.473121 0.880997i \(-0.656873\pi\)
−0.473121 + 0.880997i \(0.656873\pi\)
\(140\) 21.8160i 1.84379i
\(141\) −3.04113 + 16.1231i −0.256109 + 1.35781i
\(142\) 6.65630i 0.558585i
\(143\) 17.0904i 1.42917i
\(144\) −13.1386 5.13922i −1.09488 0.428268i
\(145\) −3.77643 −0.313615
\(146\) 6.11710i 0.506255i
\(147\) 0.811313 4.30133i 0.0669160 0.354768i
\(148\) 47.7483i 3.92489i
\(149\) 10.1428 0.830933 0.415467 0.909608i \(-0.363618\pi\)
0.415467 + 0.909608i \(0.363618\pi\)
\(150\) 1.01945 5.40479i 0.0832375 0.441300i
\(151\) 2.47372i 0.201309i 0.994921 + 0.100654i \(0.0320936\pi\)
−0.994921 + 0.100654i \(0.967906\pi\)
\(152\) 35.0536 2.84322
\(153\) −3.05433 + 7.80851i −0.246928 + 0.631281i
\(154\) 19.0474 1.53488
\(155\) 17.3253 1.39160
\(156\) −32.8649 6.19895i −2.63130 0.496313i
\(157\) 12.1429i 0.969113i −0.874760 0.484556i \(-0.838981\pi\)
0.874760 0.484556i \(-0.161019\pi\)
\(158\) −8.82380 −0.701984
\(159\) 15.8544 + 2.99045i 1.25734 + 0.237158i
\(160\) 2.93107i 0.231722i
\(161\) 1.87189 0.147525
\(162\) 16.3490 + 15.1003i 1.28450 + 1.18639i
\(163\) −4.90454 −0.384153 −0.192077 0.981380i \(-0.561522\pi\)
−0.192077 + 0.981380i \(0.561522\pi\)
\(164\) 1.18531i 0.0925571i
\(165\) −15.5397 2.93107i −1.20976 0.228184i
\(166\) −37.0599 −2.87640
\(167\) 9.67303i 0.748521i −0.927324 0.374261i \(-0.877897\pi\)
0.927324 0.374261i \(-0.122103\pi\)
\(168\) 3.55085 18.8255i 0.273954 1.45242i
\(169\) −9.01945 −0.693804
\(170\) −17.3253 −1.32879
\(171\) −18.7263 7.32488i −1.43204 0.560148i
\(172\) 31.7071i 2.41764i
\(173\) 3.59398 0.273246 0.136623 0.990623i \(-0.456375\pi\)
0.136623 + 0.990623i \(0.456375\pi\)
\(174\) 6.34048 + 1.19594i 0.480671 + 0.0906637i
\(175\) 2.71585 0.205299
\(176\) −17.1274 −1.29103
\(177\) −12.4011 + 4.81806i −0.932121 + 0.362148i
\(178\) −14.6700 −1.09956
\(179\) −12.1281 −0.906498 −0.453249 0.891384i \(-0.649735\pi\)
−0.453249 + 0.891384i \(0.649735\pi\)
\(180\) −11.2729 + 28.8197i −0.840236 + 2.14809i
\(181\) 4.34472 0.322941 0.161470 0.986878i \(-0.448376\pi\)
0.161470 + 0.986878i \(0.448376\pi\)
\(182\) 24.5408i 1.81909i
\(183\) −16.8913 3.18603i −1.24864 0.235518i
\(184\) −4.62887 −0.341245
\(185\) −29.0885 −2.13863
\(186\) −29.0885 5.48664i −2.13287 0.402300i
\(187\) 10.1791i 0.744372i
\(188\) 38.9798 2.84290
\(189\) −5.83076 + 9.31497i −0.424125 + 0.677565i
\(190\) 41.5494i 3.01431i
\(191\) −6.81756 −0.493301 −0.246651 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(192\) 2.09122 11.0870i 0.150921 0.800136i
\(193\) 6.76322 0.486828 0.243414 0.969923i \(-0.421733\pi\)
0.243414 + 0.969923i \(0.421733\pi\)
\(194\) 4.15329i 0.298189i
\(195\) −3.77643 + 20.0215i −0.270436 + 1.43377i
\(196\) −10.3991 −0.742790
\(197\) 1.35841i 0.0967829i 0.998828 + 0.0483915i \(0.0154095\pi\)
−0.998828 + 0.0483915i \(0.984590\pi\)
\(198\) 25.1623 + 9.84233i 1.78821 + 0.699464i
\(199\) 7.88509 0.558959 0.279480 0.960152i \(-0.409838\pi\)
0.279480 + 0.960152i \(0.409838\pi\)
\(200\) −6.71585 −0.474883
\(201\) 7.98680 + 1.50646i 0.563345 + 0.106258i
\(202\) 13.6351 0.959363
\(203\) 3.18603i 0.223615i
\(204\) 19.5745 + 3.69213i 1.37049 + 0.258501i
\(205\) 0.722096 0.0504334
\(206\) 30.6579i 2.13604i
\(207\) 2.47283 + 0.967259i 0.171874 + 0.0672292i
\(208\) 22.0671i 1.53008i
\(209\) −24.4115 −1.68858
\(210\) −22.3141 4.20886i −1.53982 0.290439i
\(211\) 17.6296i 1.21367i −0.794827 0.606836i \(-0.792439\pi\)
0.794827 0.606836i \(-0.207561\pi\)
\(212\) 38.3303i 2.63253i
\(213\) −4.58150 0.864158i −0.313919 0.0592111i
\(214\) 12.3161i 0.841908i
\(215\) 19.3161 1.31735
\(216\) 14.4185 23.0344i 0.981055 1.56729i
\(217\) 14.6167i 0.992244i
\(218\) 12.9371i 0.876211i
\(219\) −4.21037 0.794155i −0.284510 0.0536641i
\(220\) 37.5692i 2.53292i
\(221\) 13.1149 0.882204
\(222\) 48.8385 + 9.21187i 3.27783 + 0.618260i
\(223\) 20.5808 1.37819 0.689096 0.724671i \(-0.258008\pi\)
0.689096 + 0.724671i \(0.258008\pi\)
\(224\) −2.47283 −0.165223
\(225\) 3.58774 + 1.40336i 0.239183 + 0.0935573i
\(226\) −16.8587 −1.12142
\(227\) −20.0342 −1.32971 −0.664857 0.746970i \(-0.731508\pi\)
−0.664857 + 0.746970i \(0.731508\pi\)
\(228\) −8.85445 + 46.9436i −0.586400 + 3.10891i
\(229\) 4.97674i 0.328872i 0.986388 + 0.164436i \(0.0525804\pi\)
−0.986388 + 0.164436i \(0.947420\pi\)
\(230\) 5.48664i 0.361779i
\(231\) −2.47283 + 13.1102i −0.162701 + 0.862588i
\(232\) 7.87852i 0.517250i
\(233\) 8.68945 0.569264 0.284632 0.958637i \(-0.408129\pi\)
0.284632 + 0.958637i \(0.408129\pi\)
\(234\) 12.6810 32.4194i 0.828981 2.11932i
\(235\) 23.7467i 1.54906i
\(236\) 16.7089 + 26.8296i 1.08766 + 1.74646i
\(237\) 1.14555 6.07337i 0.0744117 0.394508i
\(238\) 14.6167i 0.947458i
\(239\) 7.31426i 0.473120i 0.971617 + 0.236560i \(0.0760200\pi\)
−0.971617 + 0.236560i \(0.923980\pi\)
\(240\) 20.0648 + 3.78461i 1.29518 + 0.244295i
\(241\) 26.5070 1.70747 0.853733 0.520711i \(-0.174333\pi\)
0.853733 + 0.520711i \(0.174333\pi\)
\(242\) 5.60023 0.359996
\(243\) −12.5160 + 9.29250i −0.802900 + 0.596114i
\(244\) 40.8371i 2.61433i
\(245\) 6.33515i 0.404738i
\(246\) −1.21237 0.228676i −0.0772980 0.0145799i
\(247\) 31.4521i 2.00125i
\(248\) 36.1446i 2.29518i
\(249\) 4.81131 25.5081i 0.304905 1.61651i
\(250\) 23.0344i 1.45682i
\(251\) 25.7143i 1.62307i 0.584302 + 0.811536i \(0.301368\pi\)
−0.584302 + 0.811536i \(0.698632\pi\)
\(252\) 24.3141 + 9.51055i 1.53164 + 0.599108i
\(253\) 3.22357 0.202664
\(254\) 39.9993 2.50978
\(255\) 2.24926 11.9249i 0.140854 0.746766i
\(256\) −32.5870 −2.03669
\(257\) 18.4450i 1.15057i −0.817954 0.575284i \(-0.804892\pi\)
0.817954 0.575284i \(-0.195108\pi\)
\(258\) −32.4310 6.11710i −2.01907 0.380834i
\(259\) 24.5408i 1.52489i
\(260\) 48.4046 3.00192
\(261\) −1.64631 + 4.20886i −0.101904 + 0.260522i
\(262\) −3.47507 −0.214690
\(263\) 9.30313i 0.573655i −0.957982 0.286828i \(-0.907399\pi\)
0.957982 0.286828i \(-0.0926007\pi\)
\(264\) 6.11491 32.4194i 0.376347 1.99527i
\(265\) −23.3510 −1.43444
\(266\) −35.0536 −2.14928
\(267\) 1.90454 10.0973i 0.116556 0.617944i
\(268\) 19.3092i 1.17949i
\(269\) 7.45115 0.454305 0.227152 0.973859i \(-0.427058\pi\)
0.227152 + 0.973859i \(0.427058\pi\)
\(270\) −27.3029 17.0904i −1.66160 1.04009i
\(271\) −5.58078 −0.339008 −0.169504 0.985529i \(-0.554217\pi\)
−0.169504 + 0.985529i \(0.554217\pi\)
\(272\) 13.1433i 0.796930i
\(273\) 16.8913 + 3.18603i 1.02231 + 0.192827i
\(274\) 38.7914i 2.34348i
\(275\) 4.67696 0.282031
\(276\) 1.16924 6.19895i 0.0703800 0.373133i
\(277\) −25.7717 −1.54847 −0.774236 0.632897i \(-0.781866\pi\)
−0.774236 + 0.632897i \(0.781866\pi\)
\(278\) −27.5870 −1.65456
\(279\) 7.55286 19.3092i 0.452178 1.15601i
\(280\) 27.7269i 1.65700i
\(281\) 17.2266i 1.02765i 0.857894 + 0.513826i \(0.171772\pi\)
−0.857894 + 0.513826i \(0.828228\pi\)
\(282\) −7.52021 + 39.8698i −0.447822 + 2.37421i
\(283\) 19.0542i 1.13265i −0.824180 0.566327i \(-0.808364\pi\)
0.824180 0.566327i \(-0.191636\pi\)
\(284\) 11.0764i 0.657263i
\(285\) 28.5982 + 5.39417i 1.69401 + 0.319523i
\(286\) 42.2617i 2.49899i
\(287\) 0.609204i 0.0359602i
\(288\) −3.26670 1.27779i −0.192492 0.0752942i
\(289\) 9.18869 0.540511
\(290\) −9.33848 −0.548374
\(291\) 2.85868 + 0.539202i 0.167579 + 0.0316086i
\(292\) 10.1791i 0.595689i
\(293\) 10.7765i 0.629569i 0.949163 + 0.314785i \(0.101932\pi\)
−0.949163 + 0.314785i \(0.898068\pi\)
\(294\) 2.00624 10.6365i 0.117006 0.620332i
\(295\) 16.3447 10.1791i 0.951627 0.592652i
\(296\) 60.6854i 3.52727i
\(297\) −10.0411 + 16.0413i −0.582645 + 0.930809i
\(298\) 25.0815 1.45293
\(299\) 4.15329i 0.240191i
\(300\) 1.69641 8.99382i 0.0979420 0.519259i
\(301\) 16.2962i 0.939299i
\(302\) 6.11710i 0.352000i
\(303\) −1.77018 + 9.38498i −0.101694 + 0.539153i
\(304\) 31.5202 1.80781
\(305\) 24.8781 1.42452
\(306\) −7.55286 + 19.3092i −0.431768 + 1.10383i
\(307\) −1.01945 −0.0581829 −0.0290915 0.999577i \(-0.509261\pi\)
−0.0290915 + 0.999577i \(0.509261\pi\)
\(308\) 31.6957 1.80603
\(309\) 21.1017 + 3.98018i 1.20043 + 0.226425i
\(310\) 42.8425 2.43329
\(311\) 4.84054i 0.274482i 0.990538 + 0.137241i \(0.0438234\pi\)
−0.990538 + 0.137241i \(0.956177\pi\)
\(312\) −41.7695 7.87852i −2.36473 0.446033i
\(313\) 16.0413i 0.906707i 0.891331 + 0.453353i \(0.149772\pi\)
−0.891331 + 0.453353i \(0.850228\pi\)
\(314\) 30.0275i 1.69455i
\(315\) 5.79387 14.8122i 0.326448 0.834575i
\(316\) −14.6832 −0.825995
\(317\) 17.2966i 0.971473i −0.874105 0.485737i \(-0.838551\pi\)
0.874105 0.485737i \(-0.161449\pi\)
\(318\) 39.2054 + 7.39489i 2.19853 + 0.414685i
\(319\) 5.48664i 0.307193i
\(320\) 16.3293i 0.912837i
\(321\) −8.47707 1.59894i −0.473144 0.0892440i
\(322\) 4.62887 0.257957
\(323\) 18.7331i 1.04233i
\(324\) 27.2054 + 25.1276i 1.51141 + 1.39598i
\(325\) 6.02585i 0.334254i
\(326\) −12.1281 −0.671714
\(327\) 8.90454 + 1.67957i 0.492422 + 0.0928802i
\(328\) 1.50646i 0.0831804i
\(329\) −20.0342 −1.10452
\(330\) −38.4270 7.24806i −2.11534 0.398992i
\(331\) −9.45267 −0.519566 −0.259783 0.965667i \(-0.583651\pi\)
−0.259783 + 0.965667i \(0.583651\pi\)
\(332\) −61.6693 −3.38454
\(333\) −12.6810 + 32.4194i −0.694913 + 1.77657i
\(334\) 23.9198i 1.30883i
\(335\) −11.7632 −0.642694
\(336\) 3.19293 16.9279i 0.174188 0.923493i
\(337\) 25.4263i 1.38506i 0.721391 + 0.692528i \(0.243503\pi\)
−0.721391 + 0.692528i \(0.756497\pi\)
\(338\) −22.3036 −1.21316
\(339\) 2.18869 11.6037i 0.118873 0.630229i
\(340\) −28.8300 −1.56353
\(341\) 25.1713i 1.36310i
\(342\) −46.3071 18.1132i −2.50400 0.979451i
\(343\) 20.1491 1.08795
\(344\) 40.2979i 2.17272i
\(345\) −3.77643 0.712306i −0.203316 0.0383493i
\(346\) 8.88733 0.477786
\(347\) 16.9604 0.910481 0.455241 0.890368i \(-0.349553\pi\)
0.455241 + 0.890368i \(0.349553\pi\)
\(348\) 10.5509 + 1.99009i 0.565585 + 0.106680i
\(349\) 7.70541i 0.412461i −0.978503 0.206231i \(-0.933880\pi\)
0.978503 0.206231i \(-0.0661197\pi\)
\(350\) 6.71585 0.358977
\(351\) 20.6678 + 12.9371i 1.10316 + 0.690531i
\(352\) −4.25846 −0.226977
\(353\) 3.79187 0.201821 0.100910 0.994896i \(-0.467824\pi\)
0.100910 + 0.994896i \(0.467824\pi\)
\(354\) −30.6658 + 11.9143i −1.62987 + 0.633236i
\(355\) 6.74779 0.358135
\(356\) −24.4115 −1.29381
\(357\) −10.0606 1.89762i −0.532462 0.100432i
\(358\) −29.9908 −1.58506
\(359\) 8.41772i 0.444270i 0.975016 + 0.222135i \(0.0713026\pi\)
−0.975016 + 0.222135i \(0.928697\pi\)
\(360\) −14.3273 + 36.6282i −0.755114 + 1.93048i
\(361\) 25.9255 1.36450
\(362\) 10.7438 0.564680
\(363\) −0.727052 + 3.85461i −0.0381603 + 0.202314i
\(364\) 40.8371i 2.14044i
\(365\) 6.20117 0.324584
\(366\) −41.7695 7.87852i −2.18333 0.411817i
\(367\) 0.254953i 0.0133084i 0.999978 + 0.00665422i \(0.00211812\pi\)
−0.999978 + 0.00665422i \(0.997882\pi\)
\(368\) −4.16228 −0.216974
\(369\) 0.314794 0.804782i 0.0163875 0.0418953i
\(370\) −71.9310 −3.73952
\(371\) 19.7003i 1.02279i
\(372\) −48.4046 9.13002i −2.50966 0.473370i
\(373\) −3.23606 −0.167557 −0.0837784 0.996484i \(-0.526699\pi\)
−0.0837784 + 0.996484i \(0.526699\pi\)
\(374\) 25.1713i 1.30158i
\(375\) 15.8544 + 2.99045i 0.818720 + 0.154426i
\(376\) 49.5412 2.55489
\(377\) 7.06905 0.364075
\(378\) −14.4185 + 23.0344i −0.741608 + 1.18476i
\(379\) −6.09323 −0.312988 −0.156494 0.987679i \(-0.550019\pi\)
−0.156494 + 0.987679i \(0.550019\pi\)
\(380\) 69.1401i 3.54681i
\(381\) −5.19293 + 27.5313i −0.266042 + 1.41047i
\(382\) −16.8587 −0.862565
\(383\) 30.1306i 1.53960i 0.638284 + 0.769801i \(0.279644\pi\)
−0.638284 + 0.769801i \(0.720356\pi\)
\(384\) 5.92198 31.3965i 0.302205 1.60220i
\(385\) 19.3092i 0.984086i
\(386\) 16.7243 0.851246
\(387\) 8.42074 21.5279i 0.428050 1.09433i
\(388\) 6.91126i 0.350866i
\(389\) 16.0531i 0.813926i −0.913445 0.406963i \(-0.866588\pi\)
0.913445 0.406963i \(-0.133412\pi\)
\(390\) −9.33848 + 49.5097i −0.472872 + 2.50702i
\(391\) 2.47372i 0.125101i
\(392\) −13.2166 −0.667540
\(393\) 0.451152 2.39187i 0.0227576 0.120654i
\(394\) 3.35913i 0.169231i
\(395\) 8.94507i 0.450075i
\(396\) 41.8712 + 16.3781i 2.10411 + 0.823030i
\(397\) 18.5150i 0.929241i −0.885510 0.464621i \(-0.846191\pi\)
0.885510 0.464621i \(-0.153809\pi\)
\(398\) 19.4985 0.977373
\(399\) 4.55085 24.1272i 0.227828 1.20787i
\(400\) −6.03889 −0.301945
\(401\) 30.5591 1.52605 0.763024 0.646370i \(-0.223714\pi\)
0.763024 + 0.646370i \(0.223714\pi\)
\(402\) 19.7500 + 3.72523i 0.985041 + 0.185798i
\(403\) −32.4310 −1.61550
\(404\) 22.6894 1.12884
\(405\) 15.3078 16.5737i 0.760652 0.823552i
\(406\) 7.87852i 0.391004i
\(407\) 42.2617i 2.09483i
\(408\) 24.8781 + 4.69249i 1.23165 + 0.232313i
\(409\) 32.2463i 1.59447i 0.603666 + 0.797237i \(0.293706\pi\)
−0.603666 + 0.797237i \(0.706294\pi\)
\(410\) 1.78562 0.0881856
\(411\) −26.6999 5.03611i −1.31701 0.248413i
\(412\) 51.0162i 2.51339i
\(413\) −8.58774 13.7894i −0.422575 0.678533i
\(414\) 6.11491 + 2.39187i 0.300531 + 0.117554i
\(415\) 37.5692i 1.84420i
\(416\) 5.48664i 0.269005i
\(417\) 3.58150 18.9880i 0.175387 0.929847i
\(418\) −60.3657 −2.95258
\(419\) 20.1476 0.984273 0.492136 0.870518i \(-0.336216\pi\)
0.492136 + 0.870518i \(0.336216\pi\)
\(420\) −37.1316 7.00373i −1.81184 0.341747i
\(421\) 23.1162i 1.12662i −0.826247 0.563308i \(-0.809528\pi\)
0.826247 0.563308i \(-0.190472\pi\)
\(422\) 43.5950i 2.12217i
\(423\) −26.4659 10.3522i −1.28681 0.503343i
\(424\) 48.7156i 2.36584i
\(425\) 3.58903i 0.174093i
\(426\) −11.3293 2.13692i −0.548906 0.103534i
\(427\) 20.9887i 1.01572i
\(428\) 20.4945i 0.990637i
\(429\) 29.0885 + 5.48664i 1.40441 + 0.264898i
\(430\) 47.7655 2.30345
\(431\) −21.0691 −1.01486 −0.507430 0.861693i \(-0.669405\pi\)
−0.507430 + 0.861693i \(0.669405\pi\)
\(432\) 12.9651 20.7125i 0.623784 0.996531i
\(433\) 12.1344 0.583140 0.291570 0.956550i \(-0.405822\pi\)
0.291570 + 0.956550i \(0.405822\pi\)
\(434\) 36.1446i 1.73500i
\(435\) 1.21237 6.42763i 0.0581288 0.308181i
\(436\) 21.5279i 1.03100i
\(437\) −5.93246 −0.283788
\(438\) −10.4115 1.96381i −0.497483 0.0938347i
\(439\) 23.8432 1.13798 0.568988 0.822346i \(-0.307335\pi\)
0.568988 + 0.822346i \(0.307335\pi\)
\(440\) 47.7483i 2.27631i
\(441\) 7.06058 + 2.76177i 0.336218 + 0.131513i
\(442\) 32.4310 1.54258
\(443\) −22.0731 −1.04872 −0.524361 0.851496i \(-0.675696\pi\)
−0.524361 + 0.851496i \(0.675696\pi\)
\(444\) 81.2695 + 15.3290i 3.85688 + 0.727481i
\(445\) 14.8716i 0.704982i
\(446\) 50.8929 2.40985
\(447\) −3.25622 + 17.2635i −0.154014 + 0.816535i
\(448\) 13.7764 0.650875
\(449\) 16.6992i 0.788086i 0.919092 + 0.394043i \(0.128924\pi\)
−0.919092 + 0.394043i \(0.871076\pi\)
\(450\) 8.87189 + 3.47028i 0.418225 + 0.163590i
\(451\) 1.04911i 0.0494006i
\(452\) −28.0536 −1.31953
\(453\) −4.21037 0.794155i −0.197820 0.0373127i
\(454\) −49.5412 −2.32508
\(455\) −24.8781 −1.16630
\(456\) −11.2535 + 59.6626i −0.526993 + 2.79396i
\(457\) 1.04911i 0.0490752i 0.999699 + 0.0245376i \(0.00781135\pi\)
−0.999699 + 0.0245376i \(0.992189\pi\)
\(458\) 12.3066i 0.575052i
\(459\) −12.3098 7.70541i −0.574574 0.359658i
\(460\) 9.13002i 0.425690i
\(461\) 4.35949i 0.203042i −0.994833 0.101521i \(-0.967629\pi\)
0.994833 0.101521i \(-0.0323709\pi\)
\(462\) −6.11491 + 32.4194i −0.284491 + 1.50829i
\(463\) 7.16621i 0.333042i −0.986038 0.166521i \(-0.946747\pi\)
0.986038 0.166521i \(-0.0532534\pi\)
\(464\) 7.08436i 0.328883i
\(465\) −5.56205 + 29.4883i −0.257934 + 1.36749i
\(466\) 21.4876 0.995392
\(467\) 12.7981 0.592226 0.296113 0.955153i \(-0.404310\pi\)
0.296113 + 0.955153i \(0.404310\pi\)
\(468\) 21.1017 53.9473i 0.975427 2.49371i
\(469\) 9.92418i 0.458256i
\(470\) 58.7216i 2.70863i
\(471\) 20.6678 + 3.89833i 0.952320 + 0.179626i
\(472\) 21.2361 + 34.0989i 0.977469 + 1.56953i
\(473\) 28.0637i 1.29037i
\(474\) 2.83276 15.0184i 0.130113 0.689820i
\(475\) −8.60719 −0.394925
\(476\) 24.3228i 1.11483i
\(477\) −10.1797 + 26.0248i −0.466097 + 1.19160i
\(478\) 18.0869i 0.827278i
\(479\) 21.4248i 0.978925i 0.872024 + 0.489463i \(0.162807\pi\)
−0.872024 + 0.489463i \(0.837193\pi\)
\(480\) 4.98880 + 0.940983i 0.227707 + 0.0429498i
\(481\) 54.4504 2.48273
\(482\) 65.5474 2.98560
\(483\) −0.600945 + 3.18603i −0.0273440 + 0.144969i
\(484\) 9.31903 0.423592
\(485\) −4.21037 −0.191183
\(486\) −30.9499 + 22.9788i −1.40392 + 1.04234i
\(487\) −32.3767 −1.46713 −0.733563 0.679621i \(-0.762144\pi\)
−0.733563 + 0.679621i \(0.762144\pi\)
\(488\) 51.9016i 2.34948i
\(489\) 1.57454 8.34772i 0.0712031 0.377497i
\(490\) 15.6658i 0.707708i
\(491\) 20.8525i 0.941061i −0.882384 0.470531i \(-0.844063\pi\)
0.882384 0.470531i \(-0.155937\pi\)
\(492\) −2.01744 0.380528i −0.0909533 0.0171555i
\(493\) −4.21037 −0.189625
\(494\) 77.7758i 3.49930i
\(495\) 9.97760 25.5081i 0.448460 1.14650i
\(496\) 32.5012i 1.45935i
\(497\) 5.69285i 0.255359i
\(498\) 11.8976 63.0773i 0.533143 2.82656i
\(499\) −4.08074 −0.182679 −0.0913395 0.995820i \(-0.529115\pi\)
−0.0913395 + 0.995820i \(0.529115\pi\)
\(500\) 38.3303i 1.71418i
\(501\) 16.4639 + 3.10540i 0.735551 + 0.138739i
\(502\) 63.5872i 2.83804i
\(503\) −36.1748 −1.61295 −0.806477 0.591266i \(-0.798628\pi\)
−0.806477 + 0.591266i \(0.798628\pi\)
\(504\) 30.9018 + 12.0874i 1.37648 + 0.538414i
\(505\) 13.8225i 0.615094i
\(506\) 7.97136 0.354370
\(507\) 2.89557 15.3514i 0.128597 0.681782i
\(508\) 66.5606 2.95315
\(509\) −35.3378 −1.56632 −0.783159 0.621821i \(-0.786393\pi\)
−0.783159 + 0.621821i \(0.786393\pi\)
\(510\) 5.56205 29.4883i 0.246292 1.30576i
\(511\) 5.23169i 0.231436i
\(512\) −43.6894 −1.93082
\(513\) 18.4791 29.5214i 0.815871 1.30340i
\(514\) 45.6114i 2.01183i
\(515\) −31.0793 −1.36952
\(516\) −53.9666 10.1791i −2.37575 0.448111i
\(517\) −34.5008 −1.51734
\(518\) 60.6854i 2.66637i
\(519\) −1.15380 + 6.11710i −0.0506463 + 0.268511i
\(520\) 61.5195 2.69781
\(521\) 29.1964i 1.27912i 0.768742 + 0.639559i \(0.220883\pi\)
−0.768742 + 0.639559i \(0.779117\pi\)
\(522\) −4.07106 + 10.4078i −0.178185 + 0.455537i
\(523\) −25.3121 −1.10682 −0.553410 0.832909i \(-0.686674\pi\)
−0.553410 + 0.832909i \(0.686674\pi\)
\(524\) −5.78267 −0.252617
\(525\) −0.871889 + 4.62249i −0.0380523 + 0.201742i
\(526\) 23.0051i 1.00307i
\(527\) 19.3161 0.841422
\(528\) 5.49852 29.1515i 0.239293 1.26866i
\(529\) −22.2166 −0.965940
\(530\) −57.7431 −2.50820
\(531\) −4.21933 22.6539i −0.183103 0.983094i
\(532\) −58.3308 −2.52896
\(533\) −1.35168 −0.0585479
\(534\) 4.70961 24.9689i 0.203805 1.08051i
\(535\) 12.4853 0.539787
\(536\) 24.5408i 1.06000i
\(537\) 3.89357 20.6425i 0.168020 0.890790i
\(538\) 18.4255 0.794378
\(539\) 9.20412 0.396450
\(540\) −45.4332 28.4392i −1.95513 1.22383i
\(541\) 18.5150i 0.796022i 0.917381 + 0.398011i \(0.130299\pi\)
−0.917381 + 0.398011i \(0.869701\pi\)
\(542\) −13.8003 −0.592776
\(543\) −1.39482 + 7.39489i −0.0598573 + 0.317345i
\(544\) 3.26788i 0.140109i
\(545\) −13.1149 −0.561781
\(546\) 41.7695 + 7.87852i 1.78757 + 0.337169i
\(547\) 9.65679 0.412895 0.206447 0.978458i \(-0.433810\pi\)
0.206447 + 0.978458i \(0.433810\pi\)
\(548\) 64.5507i 2.75747i
\(549\) 10.8455 27.7269i 0.462874 1.18335i
\(550\) 11.5653 0.493148
\(551\) 10.0973i 0.430159i
\(552\) 1.48604 7.87852i 0.0632500 0.335332i
\(553\) 7.54661 0.320915
\(554\) −63.7291 −2.70759
\(555\) 9.33848 49.5097i 0.396396 2.10157i
\(556\) −45.9061 −1.94685
\(557\) 15.5958i 0.660814i −0.943839 0.330407i \(-0.892814\pi\)
0.943839 0.330407i \(-0.107186\pi\)
\(558\) 18.6770 47.7483i 0.790659 2.02135i
\(559\) −36.1576 −1.52930
\(560\) 24.9320i 1.05357i
\(561\) −17.3253 3.26788i −0.731474 0.137970i
\(562\) 42.5985i 1.79691i
\(563\) −4.27567 −0.180198 −0.0900990 0.995933i \(-0.528718\pi\)
−0.0900990 + 0.995933i \(0.528718\pi\)
\(564\) −12.5140 + 66.3452i −0.526933 + 2.79364i
\(565\) 17.0904i 0.718998i
\(566\) 47.1179i 1.98051i
\(567\) −13.9826 12.9146i −0.587212 0.542363i
\(568\) 14.0775i 0.590677i
\(569\) 39.7151 1.66495 0.832473 0.554066i \(-0.186925\pi\)
0.832473 + 0.554066i \(0.186925\pi\)
\(570\) 70.7187 + 13.3389i 2.96208 + 0.558704i
\(571\) 13.7313i 0.574635i 0.957835 + 0.287318i \(0.0927635\pi\)
−0.957835 + 0.287318i \(0.907236\pi\)
\(572\) 70.3254i 2.94045i
\(573\) 2.18869 11.6037i 0.0914337 0.484753i
\(574\) 1.50646i 0.0628785i
\(575\) 1.13659 0.0473990
\(576\) 18.1992 + 7.11868i 0.758299 + 0.296612i
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) 22.7221 0.945115
\(579\) −2.17124 + 11.5113i −0.0902338 + 0.478392i
\(580\) −15.5397 −0.645249
\(581\) 31.6957 1.31496
\(582\) 7.06905 + 1.33336i 0.293022 + 0.0552695i
\(583\) 33.9258i 1.40506i
\(584\) 12.9371i 0.535341i
\(585\) −32.8649 12.8553i −1.35880 0.531499i
\(586\) 26.6485i 1.10084i
\(587\) −43.2074 −1.78336 −0.891680 0.452665i \(-0.850473\pi\)
−0.891680 + 0.452665i \(0.850473\pi\)
\(588\) 3.33848 17.6996i 0.137677 0.729919i
\(589\) 46.3237i 1.90874i
\(590\) 40.4178 25.1713i 1.66397 1.03629i
\(591\) −2.31207 0.436101i −0.0951059 0.0179388i
\(592\) 54.5683i 2.24274i
\(593\) 2.79868i 0.114928i −0.998348 0.0574639i \(-0.981699\pi\)
0.998348 0.0574639i \(-0.0183014\pi\)
\(594\) −24.8300 + 39.6674i −1.01879 + 1.62757i
\(595\) 14.8176 0.607461
\(596\) 41.7368 1.70961
\(597\) −2.53140 + 13.4207i −0.103604 + 0.549274i
\(598\) 10.2704i 0.419987i
\(599\) 24.6108i 1.00557i 0.864411 + 0.502786i \(0.167692\pi\)
−0.864411 + 0.502786i \(0.832308\pi\)
\(600\) 2.15604 11.4306i 0.0880198 0.466654i
\(601\) 28.4392i 1.16006i 0.814596 + 0.580029i \(0.196959\pi\)
−0.814596 + 0.580029i \(0.803041\pi\)
\(602\) 40.2979i 1.64242i
\(603\) −5.12811 + 13.1102i −0.208833 + 0.533889i
\(604\) 10.1791i 0.414183i
\(605\) 5.67720i 0.230811i
\(606\) −4.37737 + 23.2075i −0.177819 + 0.942740i
\(607\) −13.3510 −0.541899 −0.270949 0.962594i \(-0.587338\pi\)
−0.270949 + 0.962594i \(0.587338\pi\)
\(608\) 7.83700 0.317832
\(609\) −5.42274 1.02283i −0.219741 0.0414472i
\(610\) 61.5195 2.49085
\(611\) 44.4512i 1.79830i
\(612\) −12.5683 + 32.1313i −0.508043 + 1.29883i
\(613\) 7.45046i 0.300921i 0.988616 + 0.150461i \(0.0480757\pi\)
−0.988616 + 0.150461i \(0.951924\pi\)
\(614\) −2.52092 −0.101736
\(615\) −0.231819 + 1.22904i −0.00934786 + 0.0495595i
\(616\) 40.2834 1.62307
\(617\) 25.5450i 1.02840i 0.857669 + 0.514202i \(0.171912\pi\)
−0.857669 + 0.514202i \(0.828088\pi\)
\(618\) 52.1810 + 9.84233i 2.09903 + 0.395917i
\(619\) −8.78267 −0.353005 −0.176503 0.984300i \(-0.556478\pi\)
−0.176503 + 0.984300i \(0.556478\pi\)
\(620\) 71.2919 2.86315
\(621\) −2.44018 + 3.89833i −0.0979212 + 0.156435i
\(622\) 11.9698i 0.479947i
\(623\) 12.5466 0.502669
\(624\) −37.5591 7.08436i −1.50357 0.283601i
\(625\) −29.7717 −1.19087
\(626\) 39.6674i 1.58543i
\(627\) 7.83700 41.5494i 0.312980 1.65932i
\(628\) 49.9671i 1.99390i
\(629\) −32.4310 −1.29311
\(630\) 14.3273 36.6282i 0.570812 1.45930i
\(631\) 29.6282 1.17948 0.589739 0.807594i \(-0.299231\pi\)
0.589739 + 0.807594i \(0.299231\pi\)
\(632\) −18.6615 −0.742315
\(633\) 30.0062 + 5.65975i 1.19264 + 0.224955i
\(634\) 42.7716i 1.69868i
\(635\) 40.5490i 1.60914i
\(636\) 65.2396 + 12.3054i 2.58692 + 0.487942i
\(637\) 11.8587i 0.469859i
\(638\) 13.5676i 0.537145i
\(639\) 2.94166 7.52046i 0.116370 0.297505i
\(640\) 46.2419i 1.82787i
\(641\) 41.4501i 1.63718i −0.574378 0.818590i \(-0.694756\pi\)
0.574378 0.818590i \(-0.305244\pi\)
\(642\) −20.9624 3.95391i −0.827320 0.156048i
\(643\) −9.82228 −0.387353 −0.193677 0.981065i \(-0.562041\pi\)
−0.193677 + 0.981065i \(0.562041\pi\)
\(644\) 7.70265 0.303527
\(645\) −6.20117 + 32.8767i −0.244171 + 1.29452i
\(646\) 46.3237i 1.82258i
\(647\) 37.0749i 1.45757i −0.684744 0.728783i \(-0.740086\pi\)
0.684744 0.728783i \(-0.259914\pi\)
\(648\) 34.5765 + 31.9357i 1.35829 + 1.25455i
\(649\) −14.7889 23.7467i −0.580516 0.932139i
\(650\) 14.9009i 0.584462i
\(651\) 24.8781 + 4.69249i 0.975051 + 0.183913i
\(652\) −20.1817 −0.790377
\(653\) 25.7924i 1.00933i −0.863314 0.504666i \(-0.831615\pi\)
0.863314 0.504666i \(-0.168385\pi\)
\(654\) 22.0194 + 4.15329i 0.861029 + 0.162406i
\(655\) 3.52283i 0.137648i
\(656\) 1.35461i 0.0528886i
\(657\) 2.70337 6.91126i 0.105468 0.269634i
\(658\) −49.5412 −1.93132
\(659\) 14.5855 0.568171 0.284085 0.958799i \(-0.408310\pi\)
0.284085 + 0.958799i \(0.408310\pi\)
\(660\) −63.9442 12.0611i −2.48903 0.469478i
\(661\) −3.09947 −0.120555 −0.0602777 0.998182i \(-0.519199\pi\)
−0.0602777 + 0.998182i \(0.519199\pi\)
\(662\) −23.3749 −0.908491
\(663\) −4.21037 + 22.3221i −0.163517 + 0.866918i
\(664\) −78.3782 −3.04166
\(665\) 35.5354i 1.37800i
\(666\) −31.3579 + 80.1677i −1.21509 + 3.10644i
\(667\) 1.33336i 0.0516278i
\(668\) 39.8036i 1.54005i
\(669\) −6.60719 + 35.0293i −0.255449 + 1.35431i
\(670\) −29.0885 −1.12379
\(671\) 36.1446i 1.39535i
\(672\) 0.793871 4.20886i 0.0306242 0.162360i
\(673\) 27.2988i 1.05229i −0.850394 0.526146i \(-0.823637\pi\)
0.850394 0.526146i \(-0.176363\pi\)
\(674\) 62.8749i 2.42185i
\(675\) −3.54037 + 5.65594i −0.136269 + 0.217697i
\(676\) −37.1142 −1.42747
\(677\) 35.2355i 1.35421i 0.735887 + 0.677105i \(0.236766\pi\)
−0.735887 + 0.677105i \(0.763234\pi\)
\(678\) 5.41226 28.6941i 0.207857 1.10199i
\(679\) 3.55213i 0.136318i
\(680\) −36.6414 −1.40513
\(681\) 6.43171 34.0989i 0.246463 1.30667i
\(682\) 62.2445i 2.38346i
\(683\) 8.38433 0.320818 0.160409 0.987051i \(-0.448719\pi\)
0.160409 + 0.987051i \(0.448719\pi\)
\(684\) −77.0571 30.1412i −2.94635 1.15248i
\(685\) 39.3246 1.50251
\(686\) 49.8253 1.90234
\(687\) −8.47060 1.59772i −0.323174 0.0609567i
\(688\) 36.2358i 1.38148i
\(689\) 43.7104 1.66523
\(690\) −9.33848 1.76141i −0.355510 0.0670559i
\(691\) 0.346208i 0.0131704i −0.999978 0.00658518i \(-0.997904\pi\)
0.999978 0.00658518i \(-0.00209614\pi\)
\(692\) 14.7889 0.562190
\(693\) −21.5202 8.41772i −0.817485 0.319763i
\(694\) 41.9402 1.59203
\(695\) 27.9662i 1.06082i
\(696\) 13.4095 + 2.52929i 0.508287 + 0.0958726i
\(697\) 0.805070 0.0304942
\(698\) 19.0542i 0.721212i
\(699\) −2.78963 + 14.7898i −0.105514 + 0.559401i
\(700\) 11.1755 0.422394
\(701\) −5.66376 −0.213917 −0.106959 0.994263i \(-0.534111\pi\)
−0.106959 + 0.994263i \(0.534111\pi\)
\(702\) 51.1079 + 31.9913i 1.92895 + 1.20743i
\(703\) 77.7758i 2.93337i
\(704\) 23.7243 0.894144
\(705\) 40.4178 + 7.62356i 1.52222 + 0.287120i
\(706\) 9.37666 0.352895
\(707\) −11.6615 −0.438577
\(708\) −51.0292 + 19.8259i −1.91780 + 0.745102i
\(709\) −12.5723 −0.472163 −0.236081 0.971733i \(-0.575863\pi\)
−0.236081 + 0.971733i \(0.575863\pi\)
\(710\) 16.6862 0.626220
\(711\) 9.96935 + 3.89955i 0.373880 + 0.146245i
\(712\) −31.0257 −1.16274
\(713\) 6.11710i 0.229087i
\(714\) −24.8781 4.69249i −0.931041 0.175612i
\(715\) −42.8425 −1.60222
\(716\) −49.9061 −1.86508
\(717\) −12.4491 2.34815i −0.464922 0.0876931i
\(718\) 20.8156i 0.776832i
\(719\) 19.7655 0.737127 0.368564 0.929603i \(-0.379850\pi\)
0.368564 + 0.929603i \(0.379850\pi\)
\(720\) −12.8831 + 32.9361i −0.480124 + 1.22746i
\(721\) 26.2204i 0.976499i
\(722\) 64.1095 2.38591
\(723\) −8.50972 + 45.1159i −0.316480 + 1.67788i
\(724\) 17.8781 0.664436
\(725\) 1.93452i 0.0718462i
\(726\) −1.79788 + 9.53180i −0.0667256 + 0.353758i
\(727\) 18.8495 0.699089 0.349544 0.936920i \(-0.386336\pi\)
0.349544 + 0.936920i \(0.386336\pi\)
\(728\) 51.9016i 1.92360i
\(729\) −11.7981 24.2859i −0.436967 0.899478i
\(730\) 15.3345 0.567554
\(731\) 21.5356 0.796525
\(732\) −69.5063 13.1102i −2.56903 0.484567i
\(733\) 45.8146 1.69220 0.846101 0.533023i \(-0.178944\pi\)
0.846101 + 0.533023i \(0.178944\pi\)
\(734\) 0.630457i 0.0232706i
\(735\) −10.7827 2.03382i −0.397725 0.0750185i
\(736\) −1.03489 −0.0381464
\(737\) 17.0904i 0.629533i
\(738\) 0.778432 1.99009i 0.0286545 0.0732563i
\(739\) 35.8896i 1.32022i −0.751168 0.660111i \(-0.770509\pi\)
0.751168 0.660111i \(-0.229491\pi\)
\(740\) −119.696 −4.40013
\(741\) −53.5327 10.0973i −1.96657 0.370933i
\(742\) 48.7156i 1.78841i
\(743\) 30.3737i 1.11430i 0.830411 + 0.557151i \(0.188106\pi\)
−0.830411 + 0.557151i \(0.811894\pi\)
\(744\) −61.5195 11.6037i −2.25541 0.425414i
\(745\) 25.4263i 0.931546i
\(746\) −8.00223 −0.292983
\(747\) 41.8712 + 16.3781i 1.53199 + 0.599243i
\(748\) 41.8862i 1.53151i
\(749\) 10.5334i 0.384881i
\(750\) 39.2054 + 7.39489i 1.43158 + 0.270023i
\(751\) 49.0817i 1.79102i −0.445045 0.895508i \(-0.646812\pi\)
0.445045 0.895508i \(-0.353188\pi\)
\(752\) 44.5474 1.62448
\(753\) −43.7667 8.25524i −1.59495 0.300838i
\(754\) 17.4806 0.636606
\(755\) 6.20117 0.225684
\(756\) −23.9930 + 38.3303i −0.872618 + 1.39406i
\(757\) 45.0272 1.63654 0.818271 0.574833i \(-0.194933\pi\)
0.818271 + 0.574833i \(0.194933\pi\)
\(758\) −15.0675 −0.547278
\(759\) −1.03489 + 5.48664i −0.0375640 + 0.199153i
\(760\) 87.8731i 3.18749i
\(761\) 32.5225i 1.17894i −0.807791 0.589469i \(-0.799337\pi\)
0.807791 0.589469i \(-0.200663\pi\)
\(762\) −12.8412 + 68.0803i −0.465189 + 2.46629i
\(763\) 11.0645i 0.400563i
\(764\) −28.0536 −1.01494
\(765\) 19.5745 + 7.65666i 0.707719 + 0.276827i
\(766\) 74.5079i 2.69208i
\(767\) −30.5955 + 19.0542i −1.10474 + 0.688007i
\(768\) 10.4616 55.4644i 0.377502 2.00140i
\(769\) 13.1921i 0.475718i 0.971300 + 0.237859i \(0.0764456\pi\)
−0.971300 + 0.237859i \(0.923554\pi\)
\(770\) 47.7483i 1.72073i
\(771\) 31.3941 + 5.92152i 1.13063 + 0.213258i
\(772\) 27.8300 1.00163
\(773\) −8.05585 −0.289749 −0.144874 0.989450i \(-0.546278\pi\)
−0.144874 + 0.989450i \(0.546278\pi\)
\(774\) 20.8231 53.2350i 0.748470 1.91349i
\(775\) 8.87507i 0.318802i
\(776\) 8.78382i 0.315321i
\(777\) −41.7695 7.87852i −1.49847 0.282640i
\(778\) 39.6967i 1.42320i
\(779\) 1.93072i 0.0691750i
\(780\) −15.5397 + 82.3865i −0.556409 + 2.94991i
\(781\) 9.80363i 0.350801i
\(782\) 6.11710i 0.218747i
\(783\) −6.63511 4.15329i −0.237120 0.148426i
\(784\) −11.8844 −0.424442