Properties

Label 177.3.b.a.119.16
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.16
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.23

$q$-expansion

\(f(q)\) \(=\) \(q-1.19271i q^{2} +(0.625113 + 2.93415i) q^{3} +2.57744 q^{4} +0.192711i q^{5} +(3.49960 - 0.745581i) q^{6} +6.00162 q^{7} -7.84499i q^{8} +(-8.21847 + 3.66835i) q^{9} +O(q^{10})\) \(q-1.19271i q^{2} +(0.625113 + 2.93415i) q^{3} +2.57744 q^{4} +0.192711i q^{5} +(3.49960 - 0.745581i) q^{6} +6.00162 q^{7} -7.84499i q^{8} +(-8.21847 + 3.66835i) q^{9} +0.229849 q^{10} +7.32965i q^{11} +(1.61119 + 7.56258i) q^{12} +9.24069 q^{13} -7.15821i q^{14} +(-0.565443 + 0.120466i) q^{15} +0.952916 q^{16} +9.92749i q^{17} +(4.37529 + 9.80227i) q^{18} +0.266471 q^{19} +0.496700i q^{20} +(3.75169 + 17.6097i) q^{21} +8.74217 q^{22} +9.30188i q^{23} +(23.0184 - 4.90401i) q^{24} +24.9629 q^{25} -11.0215i q^{26} +(-15.9010 - 21.8211i) q^{27} +15.4688 q^{28} -28.6314i q^{29} +(0.143682 + 0.674411i) q^{30} -36.4525 q^{31} -32.5165i q^{32} +(-21.5063 + 4.58186i) q^{33} +11.8406 q^{34} +1.15658i q^{35} +(-21.1826 + 9.45494i) q^{36} +9.90726 q^{37} -0.317824i q^{38} +(5.77648 + 27.1136i) q^{39} +1.51182 q^{40} -38.7065i q^{41} +(21.0033 - 4.47469i) q^{42} -39.2418 q^{43} +18.8917i q^{44} +(-0.706931 - 1.58379i) q^{45} +11.0945 q^{46} +17.9574i q^{47} +(0.595680 + 2.79600i) q^{48} -12.9805 q^{49} -29.7735i q^{50} +(-29.1287 + 6.20581i) q^{51} +23.8173 q^{52} -23.3905i q^{53} +(-26.0263 + 18.9653i) q^{54} -1.41250 q^{55} -47.0827i q^{56} +(0.166575 + 0.781867i) q^{57} -34.1490 q^{58} +7.68115i q^{59} +(-1.45739 + 0.310494i) q^{60} -71.8344 q^{61} +43.4774i q^{62} +(-49.3241 + 22.0161i) q^{63} -34.9712 q^{64} +1.78078i q^{65} +(5.46485 + 25.6508i) q^{66} -58.1753 q^{67} +25.5875i q^{68} +(-27.2931 + 5.81473i) q^{69} +1.37947 q^{70} -25.1511i q^{71} +(28.7782 + 64.4738i) q^{72} -68.2547 q^{73} -11.8165i q^{74} +(15.6046 + 73.2448i) q^{75} +0.686812 q^{76} +43.9898i q^{77} +(32.3387 - 6.88968i) q^{78} +72.5230 q^{79} +0.183637i q^{80} +(54.0864 - 60.2964i) q^{81} -46.1657 q^{82} -85.5760i q^{83} +(9.66975 + 45.3878i) q^{84} -1.91314 q^{85} +46.8042i q^{86} +(84.0088 - 17.8979i) q^{87} +57.5011 q^{88} -94.8794i q^{89} +(-1.88900 + 0.843166i) q^{90} +55.4591 q^{91} +23.9750i q^{92} +(-22.7869 - 106.957i) q^{93} +21.4181 q^{94} +0.0513519i q^{95} +(95.4084 - 20.3265i) q^{96} -150.163 q^{97} +15.4821i q^{98} +(-26.8877 - 60.2385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19271i 0.596357i −0.954510 0.298178i \(-0.903621\pi\)
0.954510 0.298178i \(-0.0963790\pi\)
\(3\) 0.625113 + 2.93415i 0.208371 + 0.978050i
\(4\) 2.57744 0.644359
\(5\) 0.192711i 0.0385422i 0.999814 + 0.0192711i \(0.00613456\pi\)
−0.999814 + 0.0192711i \(0.993865\pi\)
\(6\) 3.49960 0.745581i 0.583266 0.124263i
\(7\) 6.00162 0.857375 0.428687 0.903453i \(-0.358976\pi\)
0.428687 + 0.903453i \(0.358976\pi\)
\(8\) 7.84499i 0.980624i
\(9\) −8.21847 + 3.66835i −0.913163 + 0.407595i
\(10\) 0.229849 0.0229849
\(11\) 7.32965i 0.666332i 0.942868 + 0.333166i \(0.108117\pi\)
−0.942868 + 0.333166i \(0.891883\pi\)
\(12\) 1.61119 + 7.56258i 0.134266 + 0.630215i
\(13\) 9.24069 0.710822 0.355411 0.934710i \(-0.384341\pi\)
0.355411 + 0.934710i \(0.384341\pi\)
\(14\) 7.15821i 0.511301i
\(15\) −0.565443 + 0.120466i −0.0376962 + 0.00803108i
\(16\) 0.952916 0.0595572
\(17\) 9.92749i 0.583970i 0.956423 + 0.291985i \(0.0943157\pi\)
−0.956423 + 0.291985i \(0.905684\pi\)
\(18\) 4.37529 + 9.80227i 0.243072 + 0.544571i
\(19\) 0.266471 0.0140248 0.00701240 0.999975i \(-0.497768\pi\)
0.00701240 + 0.999975i \(0.497768\pi\)
\(20\) 0.496700i 0.0248350i
\(21\) 3.75169 + 17.6097i 0.178652 + 0.838555i
\(22\) 8.74217 0.397371
\(23\) 9.30188i 0.404430i 0.979341 + 0.202215i \(0.0648139\pi\)
−0.979341 + 0.202215i \(0.935186\pi\)
\(24\) 23.0184 4.90401i 0.959099 0.204334i
\(25\) 24.9629 0.998515
\(26\) 11.0215i 0.423903i
\(27\) −15.9010 21.8211i −0.588925 0.808188i
\(28\) 15.4688 0.552457
\(29\) 28.6314i 0.987290i −0.869664 0.493645i \(-0.835664\pi\)
0.869664 0.493645i \(-0.164336\pi\)
\(30\) 0.143682 + 0.674411i 0.00478938 + 0.0224804i
\(31\) −36.4525 −1.17589 −0.587944 0.808902i \(-0.700062\pi\)
−0.587944 + 0.808902i \(0.700062\pi\)
\(32\) 32.5165i 1.01614i
\(33\) −21.5063 + 4.58186i −0.651706 + 0.138844i
\(34\) 11.8406 0.348254
\(35\) 1.15658i 0.0330451i
\(36\) −21.1826 + 9.45494i −0.588405 + 0.262637i
\(37\) 9.90726 0.267764 0.133882 0.990997i \(-0.457256\pi\)
0.133882 + 0.990997i \(0.457256\pi\)
\(38\) 0.317824i 0.00836378i
\(39\) 5.77648 + 27.1136i 0.148115 + 0.695219i
\(40\) 1.51182 0.0377954
\(41\) 38.7065i 0.944061i −0.881582 0.472030i \(-0.843521\pi\)
0.881582 0.472030i \(-0.156479\pi\)
\(42\) 21.0033 4.47469i 0.500078 0.106540i
\(43\) −39.2418 −0.912599 −0.456300 0.889826i \(-0.650825\pi\)
−0.456300 + 0.889826i \(0.650825\pi\)
\(44\) 18.8917i 0.429357i
\(45\) −0.706931 1.58379i −0.0157096 0.0351953i
\(46\) 11.0945 0.241184
\(47\) 17.9574i 0.382073i 0.981583 + 0.191037i \(0.0611849\pi\)
−0.981583 + 0.191037i \(0.938815\pi\)
\(48\) 0.595680 + 2.79600i 0.0124100 + 0.0582499i
\(49\) −12.9805 −0.264909
\(50\) 29.7735i 0.595471i
\(51\) −29.1287 + 6.20581i −0.571152 + 0.121682i
\(52\) 23.8173 0.458024
\(53\) 23.3905i 0.441331i −0.975350 0.220665i \(-0.929177\pi\)
0.975350 0.220665i \(-0.0708229\pi\)
\(54\) −26.0263 + 18.9653i −0.481968 + 0.351209i
\(55\) −1.41250 −0.0256819
\(56\) 47.0827i 0.840762i
\(57\) 0.166575 + 0.781867i 0.00292236 + 0.0137170i
\(58\) −34.1490 −0.588777
\(59\) 7.68115i 0.130189i
\(60\) −1.45739 + 0.310494i −0.0242899 + 0.00517489i
\(61\) −71.8344 −1.17761 −0.588807 0.808274i \(-0.700402\pi\)
−0.588807 + 0.808274i \(0.700402\pi\)
\(62\) 43.4774i 0.701248i
\(63\) −49.3241 + 22.0161i −0.782923 + 0.349461i
\(64\) −34.9712 −0.546425
\(65\) 1.78078i 0.0273966i
\(66\) 5.46485 + 25.6508i 0.0828007 + 0.388649i
\(67\) −58.1753 −0.868288 −0.434144 0.900843i \(-0.642949\pi\)
−0.434144 + 0.900843i \(0.642949\pi\)
\(68\) 25.5875i 0.376286i
\(69\) −27.2931 + 5.81473i −0.395552 + 0.0842714i
\(70\) 1.37947 0.0197067
\(71\) 25.1511i 0.354241i −0.984189 0.177121i \(-0.943322\pi\)
0.984189 0.177121i \(-0.0566783\pi\)
\(72\) 28.7782 + 64.4738i 0.399697 + 0.895470i
\(73\) −68.2547 −0.934996 −0.467498 0.883994i \(-0.654844\pi\)
−0.467498 + 0.883994i \(0.654844\pi\)
\(74\) 11.8165i 0.159683i
\(75\) 15.6046 + 73.2448i 0.208062 + 0.976597i
\(76\) 0.686812 0.00903701
\(77\) 43.9898i 0.571296i
\(78\) 32.3387 6.88968i 0.414599 0.0883292i
\(79\) 72.5230 0.918012 0.459006 0.888433i \(-0.348206\pi\)
0.459006 + 0.888433i \(0.348206\pi\)
\(80\) 0.183637i 0.00229547i
\(81\) 54.0864 60.2964i 0.667733 0.744401i
\(82\) −46.1657 −0.562997
\(83\) 85.5760i 1.03104i −0.856879 0.515518i \(-0.827599\pi\)
0.856879 0.515518i \(-0.172401\pi\)
\(84\) 9.66975 + 45.3878i 0.115116 + 0.540330i
\(85\) −1.91314 −0.0225075
\(86\) 46.8042i 0.544235i
\(87\) 84.0088 17.8979i 0.965619 0.205723i
\(88\) 57.5011 0.653421
\(89\) 94.8794i 1.06606i −0.846096 0.533030i \(-0.821053\pi\)
0.846096 0.533030i \(-0.178947\pi\)
\(90\) −1.88900 + 0.843166i −0.0209889 + 0.00936851i
\(91\) 55.4591 0.609441
\(92\) 23.9750i 0.260598i
\(93\) −22.7869 106.957i −0.245021 1.15008i
\(94\) 21.4181 0.227852
\(95\) 0.0513519i 0.000540546i
\(96\) 95.4084 20.3265i 0.993837 0.211735i
\(97\) −150.163 −1.54807 −0.774034 0.633144i \(-0.781764\pi\)
−0.774034 + 0.633144i \(0.781764\pi\)
\(98\) 15.4821i 0.157980i
\(99\) −26.8877 60.2385i −0.271593 0.608470i
\(100\) 64.3402 0.643402
\(101\) 106.598i 1.05543i 0.849422 + 0.527714i \(0.176951\pi\)
−0.849422 + 0.527714i \(0.823049\pi\)
\(102\) 7.40175 + 34.7422i 0.0725661 + 0.340610i
\(103\) 45.3370 0.440165 0.220083 0.975481i \(-0.429367\pi\)
0.220083 + 0.975481i \(0.429367\pi\)
\(104\) 72.4931i 0.697049i
\(105\) −3.39357 + 0.722992i −0.0323197 + 0.00688564i
\(106\) −27.8982 −0.263190
\(107\) 27.3786i 0.255875i −0.991782 0.127938i \(-0.959164\pi\)
0.991782 0.127938i \(-0.0408357\pi\)
\(108\) −40.9837 56.2424i −0.379479 0.520763i
\(109\) 170.671 1.56579 0.782896 0.622152i \(-0.213741\pi\)
0.782896 + 0.622152i \(0.213741\pi\)
\(110\) 1.68471i 0.0153156i
\(111\) 6.19316 + 29.0694i 0.0557943 + 0.261886i
\(112\) 5.71904 0.0510628
\(113\) 172.039i 1.52247i −0.648477 0.761234i \(-0.724594\pi\)
0.648477 0.761234i \(-0.275406\pi\)
\(114\) 0.932542 0.198676i 0.00818020 0.00174277i
\(115\) −1.79257 −0.0155876
\(116\) 73.7956i 0.636169i
\(117\) −75.9443 + 33.8981i −0.649096 + 0.289727i
\(118\) 9.16140 0.0776390
\(119\) 59.5810i 0.500681i
\(120\) 0.945056 + 4.43589i 0.00787547 + 0.0369658i
\(121\) 67.2762 0.556002
\(122\) 85.6779i 0.702278i
\(123\) 113.571 24.1959i 0.923339 0.196715i
\(124\) −93.9540 −0.757693
\(125\) 9.62839i 0.0770271i
\(126\) 26.2588 + 58.8295i 0.208404 + 0.466901i
\(127\) 70.8372 0.557773 0.278887 0.960324i \(-0.410035\pi\)
0.278887 + 0.960324i \(0.410035\pi\)
\(128\) 88.3555i 0.690277i
\(129\) −24.5306 115.141i −0.190159 0.892568i
\(130\) 2.12396 0.0163382
\(131\) 231.671i 1.76848i 0.467035 + 0.884239i \(0.345322\pi\)
−0.467035 + 0.884239i \(0.654678\pi\)
\(132\) −55.4311 + 11.8095i −0.419932 + 0.0894655i
\(133\) 1.59926 0.0120245
\(134\) 69.3865i 0.517810i
\(135\) 4.20516 3.06429i 0.0311493 0.0226984i
\(136\) 77.8811 0.572655
\(137\) 57.1816i 0.417384i 0.977981 + 0.208692i \(0.0669206\pi\)
−0.977981 + 0.208692i \(0.933079\pi\)
\(138\) 6.93530 + 32.5528i 0.0502558 + 0.235890i
\(139\) 274.608 1.97560 0.987799 0.155735i \(-0.0497746\pi\)
0.987799 + 0.155735i \(0.0497746\pi\)
\(140\) 2.98101i 0.0212929i
\(141\) −52.6898 + 11.2254i −0.373686 + 0.0796130i
\(142\) −29.9981 −0.211254
\(143\) 67.7310i 0.473643i
\(144\) −7.83150 + 3.49563i −0.0543855 + 0.0242752i
\(145\) 5.51758 0.0380523
\(146\) 81.4083i 0.557591i
\(147\) −8.11430 38.0868i −0.0551993 0.259094i
\(148\) 25.5353 0.172536
\(149\) 195.063i 1.30915i 0.755997 + 0.654576i \(0.227153\pi\)
−0.755997 + 0.654576i \(0.772847\pi\)
\(150\) 87.3600 18.6118i 0.582400 0.124079i
\(151\) −23.0021 −0.152332 −0.0761659 0.997095i \(-0.524268\pi\)
−0.0761659 + 0.997095i \(0.524268\pi\)
\(152\) 2.09047i 0.0137531i
\(153\) −36.4175 81.5888i −0.238023 0.533260i
\(154\) 52.4672 0.340696
\(155\) 7.02479i 0.0453213i
\(156\) 14.8885 + 69.8834i 0.0954391 + 0.447971i
\(157\) −102.811 −0.654848 −0.327424 0.944878i \(-0.606180\pi\)
−0.327424 + 0.944878i \(0.606180\pi\)
\(158\) 86.4991i 0.547463i
\(159\) 68.6313 14.6217i 0.431643 0.0919606i
\(160\) 6.26629 0.0391643
\(161\) 55.8264i 0.346748i
\(162\) −71.9164 64.5096i −0.443928 0.398207i
\(163\) −205.066 −1.25807 −0.629036 0.777376i \(-0.716550\pi\)
−0.629036 + 0.777376i \(0.716550\pi\)
\(164\) 99.7635i 0.608314i
\(165\) −0.882975 4.14450i −0.00535136 0.0251182i
\(166\) −102.068 −0.614865
\(167\) 307.058i 1.83867i 0.393476 + 0.919335i \(0.371272\pi\)
−0.393476 + 0.919335i \(0.628728\pi\)
\(168\) 138.148 29.4320i 0.822307 0.175191i
\(169\) −83.6097 −0.494732
\(170\) 2.28182i 0.0134225i
\(171\) −2.18999 + 0.977510i −0.0128069 + 0.00571643i
\(172\) −101.143 −0.588041
\(173\) 6.42487i 0.0371380i 0.999828 + 0.0185690i \(0.00591103\pi\)
−0.999828 + 0.0185690i \(0.994089\pi\)
\(174\) −21.3470 100.198i −0.122684 0.575853i
\(175\) 149.818 0.856101
\(176\) 6.98454i 0.0396849i
\(177\) −22.5376 + 4.80159i −0.127331 + 0.0271276i
\(178\) −113.164 −0.635752
\(179\) 219.882i 1.22839i 0.789153 + 0.614196i \(0.210520\pi\)
−0.789153 + 0.614196i \(0.789480\pi\)
\(180\) −1.82207 4.08211i −0.0101226 0.0226784i
\(181\) −61.5411 −0.340006 −0.170003 0.985444i \(-0.554378\pi\)
−0.170003 + 0.985444i \(0.554378\pi\)
\(182\) 66.1468i 0.363444i
\(183\) −44.9046 210.773i −0.245381 1.15176i
\(184\) 72.9732 0.396593
\(185\) 1.90924i 0.0103202i
\(186\) −127.569 + 27.1783i −0.685855 + 0.146120i
\(187\) −72.7650 −0.389118
\(188\) 46.2841i 0.246192i
\(189\) −95.4316 130.962i −0.504929 0.692920i
\(190\) 0.0612481 0.000322358
\(191\) 32.8865i 0.172181i −0.996287 0.0860904i \(-0.972563\pi\)
0.996287 0.0860904i \(-0.0274374\pi\)
\(192\) −21.8610 102.611i −0.113859 0.534431i
\(193\) −117.139 −0.606937 −0.303468 0.952841i \(-0.598145\pi\)
−0.303468 + 0.952841i \(0.598145\pi\)
\(194\) 179.101i 0.923200i
\(195\) −5.22508 + 1.11319i −0.0267953 + 0.00570867i
\(196\) −33.4565 −0.170696
\(197\) 21.5523i 0.109402i −0.998503 0.0547012i \(-0.982579\pi\)
0.998503 0.0547012i \(-0.0174206\pi\)
\(198\) −71.8472 + 32.0693i −0.362865 + 0.161966i
\(199\) 169.225 0.850378 0.425189 0.905105i \(-0.360208\pi\)
0.425189 + 0.905105i \(0.360208\pi\)
\(200\) 195.833i 0.979167i
\(201\) −36.3662 170.695i −0.180926 0.849229i
\(202\) 127.141 0.629411
\(203\) 171.835i 0.846477i
\(204\) −75.0775 + 15.9951i −0.368027 + 0.0784072i
\(205\) 7.45916 0.0363862
\(206\) 54.0741i 0.262495i
\(207\) −34.1226 76.4472i −0.164843 0.369310i
\(208\) 8.80559 0.0423346
\(209\) 1.95314i 0.00934517i
\(210\) 0.862322 + 4.04756i 0.00410630 + 0.0192741i
\(211\) 201.272 0.953893 0.476947 0.878932i \(-0.341743\pi\)
0.476947 + 0.878932i \(0.341743\pi\)
\(212\) 60.2876i 0.284375i
\(213\) 73.7972 15.7223i 0.346466 0.0738136i
\(214\) −32.6549 −0.152593
\(215\) 7.56232i 0.0351736i
\(216\) −171.186 + 124.743i −0.792529 + 0.577514i
\(217\) −218.774 −1.00818
\(218\) 203.562i 0.933771i
\(219\) −42.6669 200.269i −0.194826 0.914473i
\(220\) −3.64064 −0.0165483
\(221\) 91.7368i 0.415099i
\(222\) 34.6715 7.38667i 0.156178 0.0332733i
\(223\) 25.6377 0.114967 0.0574837 0.998346i \(-0.481692\pi\)
0.0574837 + 0.998346i \(0.481692\pi\)
\(224\) 195.152i 0.871214i
\(225\) −205.156 + 91.5726i −0.911806 + 0.406989i
\(226\) −205.193 −0.907934
\(227\) 87.6856i 0.386280i −0.981171 0.193140i \(-0.938133\pi\)
0.981171 0.193140i \(-0.0618672\pi\)
\(228\) 0.429336 + 2.01521i 0.00188305 + 0.00883864i
\(229\) 149.568 0.653137 0.326568 0.945174i \(-0.394108\pi\)
0.326568 + 0.945174i \(0.394108\pi\)
\(230\) 2.13803i 0.00929577i
\(231\) −129.073 + 27.4986i −0.558756 + 0.119042i
\(232\) −224.613 −0.968160
\(233\) 102.416i 0.439552i −0.975550 0.219776i \(-0.929467\pi\)
0.975550 0.219776i \(-0.0705326\pi\)
\(234\) 40.4307 + 90.5797i 0.172781 + 0.387093i
\(235\) −3.46059 −0.0147259
\(236\) 19.7977i 0.0838884i
\(237\) 45.3351 + 212.793i 0.191287 + 0.897862i
\(238\) 71.0631 0.298584
\(239\) 20.5515i 0.0859896i 0.999075 + 0.0429948i \(0.0136899\pi\)
−0.999075 + 0.0429948i \(0.986310\pi\)
\(240\) −0.538819 + 0.114794i −0.00224508 + 0.000478309i
\(241\) 391.721 1.62540 0.812700 0.582682i \(-0.197997\pi\)
0.812700 + 0.582682i \(0.197997\pi\)
\(242\) 80.2413i 0.331575i
\(243\) 210.729 + 121.005i 0.867197 + 0.497965i
\(244\) −185.149 −0.758806
\(245\) 2.50149i 0.0102102i
\(246\) −28.8588 135.457i −0.117312 0.550639i
\(247\) 2.46238 0.00996914
\(248\) 285.970i 1.15310i
\(249\) 251.093 53.4947i 1.00840 0.214838i
\(250\) 11.4839 0.0459356
\(251\) 226.561i 0.902634i 0.892364 + 0.451317i \(0.149046\pi\)
−0.892364 + 0.451317i \(0.850954\pi\)
\(252\) −127.130 + 56.7450i −0.504483 + 0.225178i
\(253\) −68.1795 −0.269484
\(254\) 84.4884i 0.332632i
\(255\) −1.19593 5.61343i −0.00468991 0.0220134i
\(256\) −245.268 −0.958077
\(257\) 430.021i 1.67323i 0.547788 + 0.836617i \(0.315470\pi\)
−0.547788 + 0.836617i \(0.684530\pi\)
\(258\) −137.330 + 29.2579i −0.532289 + 0.113403i
\(259\) 59.4597 0.229574
\(260\) 4.58985i 0.0176533i
\(261\) 105.030 + 235.306i 0.402414 + 0.901556i
\(262\) 276.317 1.05464
\(263\) 90.6588i 0.344710i −0.985035 0.172355i \(-0.944862\pi\)
0.985035 0.172355i \(-0.0551377\pi\)
\(264\) 35.9447 + 168.717i 0.136154 + 0.639078i
\(265\) 4.50761 0.0170098
\(266\) 1.90746i 0.00717089i
\(267\) 278.390 59.3104i 1.04266 0.222136i
\(268\) −149.943 −0.559489
\(269\) 177.836i 0.661099i −0.943789 0.330549i \(-0.892766\pi\)
0.943789 0.330549i \(-0.107234\pi\)
\(270\) −3.65482 5.01555i −0.0135364 0.0185761i
\(271\) −430.864 −1.58990 −0.794952 0.606672i \(-0.792504\pi\)
−0.794952 + 0.606672i \(0.792504\pi\)
\(272\) 9.46006i 0.0347796i
\(273\) 34.6682 + 162.725i 0.126990 + 0.596063i
\(274\) 68.2012 0.248910
\(275\) 182.969i 0.665342i
\(276\) −70.3462 + 14.9871i −0.254878 + 0.0543010i
\(277\) −310.975 −1.12265 −0.561327 0.827594i \(-0.689709\pi\)
−0.561327 + 0.827594i \(0.689709\pi\)
\(278\) 327.529i 1.17816i
\(279\) 299.584 133.721i 1.07378 0.479285i
\(280\) 9.07335 0.0324048
\(281\) 113.386i 0.403509i −0.979436 0.201755i \(-0.935336\pi\)
0.979436 0.201755i \(-0.0646644\pi\)
\(282\) 13.3887 + 62.8438i 0.0474777 + 0.222850i
\(283\) 331.753 1.17227 0.586135 0.810213i \(-0.300649\pi\)
0.586135 + 0.810213i \(0.300649\pi\)
\(284\) 64.8254i 0.228258i
\(285\) −0.150674 + 0.0321008i −0.000528681 + 0.000112634i
\(286\) 80.7836 0.282460
\(287\) 232.302i 0.809414i
\(288\) 119.282 + 267.236i 0.414174 + 0.927903i
\(289\) 190.445 0.658979
\(290\) 6.58089i 0.0226927i
\(291\) −93.8686 440.599i −0.322573 1.51409i
\(292\) −175.922 −0.602473
\(293\) 300.701i 1.02628i 0.858304 + 0.513142i \(0.171519\pi\)
−0.858304 + 0.513142i \(0.828481\pi\)
\(294\) −45.4267 + 9.67804i −0.154512 + 0.0329185i
\(295\) −1.48024 −0.00501776
\(296\) 77.7224i 0.262576i
\(297\) 159.941 116.548i 0.538521 0.392419i
\(298\) 232.655 0.780721
\(299\) 85.9558i 0.287477i
\(300\) 40.2199 + 188.784i 0.134066 + 0.629279i
\(301\) −235.514 −0.782439
\(302\) 27.4349i 0.0908441i
\(303\) −312.775 + 66.6359i −1.03226 + 0.219921i
\(304\) 0.253925 0.000835278
\(305\) 13.8433i 0.0453878i
\(306\) −97.3120 + 43.4357i −0.318013 + 0.141947i
\(307\) 242.499 0.789899 0.394950 0.918703i \(-0.370762\pi\)
0.394950 + 0.918703i \(0.370762\pi\)
\(308\) 113.381i 0.368120i
\(309\) 28.3408 + 133.026i 0.0917177 + 0.430504i
\(310\) −8.37856 −0.0270276
\(311\) 356.024i 1.14477i −0.819985 0.572386i \(-0.806018\pi\)
0.819985 0.572386i \(-0.193982\pi\)
\(312\) 212.706 45.3164i 0.681749 0.145245i
\(313\) −295.350 −0.943611 −0.471806 0.881703i \(-0.656398\pi\)
−0.471806 + 0.881703i \(0.656398\pi\)
\(314\) 122.624i 0.390523i
\(315\) −4.24273 9.50530i −0.0134690 0.0301755i
\(316\) 186.923 0.591529
\(317\) 67.0964i 0.211660i 0.994384 + 0.105830i \(0.0337500\pi\)
−0.994384 + 0.105830i \(0.966250\pi\)
\(318\) −17.4395 81.8575i −0.0548413 0.257413i
\(319\) 209.858 0.657862
\(320\) 6.73934i 0.0210604i
\(321\) 80.3330 17.1147i 0.250259 0.0533170i
\(322\) 66.5848 0.206785
\(323\) 2.64539i 0.00819006i
\(324\) 139.404 155.410i 0.430260 0.479661i
\(325\) 230.674 0.709766
\(326\) 244.585i 0.750260i
\(327\) 106.689 + 500.775i 0.326266 + 1.53142i
\(328\) −303.652 −0.925769
\(329\) 107.774i 0.327580i
\(330\) −4.94319 + 1.05314i −0.0149794 + 0.00319132i
\(331\) 608.621 1.83873 0.919367 0.393402i \(-0.128702\pi\)
0.919367 + 0.393402i \(0.128702\pi\)
\(332\) 220.567i 0.664357i
\(333\) −81.4225 + 36.3433i −0.244512 + 0.109139i
\(334\) 366.232 1.09650
\(335\) 11.2110i 0.0334657i
\(336\) 3.57505 + 16.7805i 0.0106400 + 0.0499420i
\(337\) 39.1038 0.116035 0.0580175 0.998316i \(-0.481522\pi\)
0.0580175 + 0.998316i \(0.481522\pi\)
\(338\) 99.7224i 0.295037i
\(339\) 504.788 107.544i 1.48905 0.317238i
\(340\) −4.93098 −0.0145029
\(341\) 267.184i 0.783531i
\(342\) 1.16589 + 2.61202i 0.00340903 + 0.00763750i
\(343\) −371.984 −1.08450
\(344\) 307.851i 0.894917i
\(345\) −1.12056 5.25968i −0.00324800 0.0152454i
\(346\) 7.66303 0.0221475
\(347\) 294.930i 0.849941i 0.905207 + 0.424971i \(0.139716\pi\)
−0.905207 + 0.424971i \(0.860284\pi\)
\(348\) 216.527 46.1306i 0.622205 0.132559i
\(349\) −320.108 −0.917216 −0.458608 0.888639i \(-0.651652\pi\)
−0.458608 + 0.888639i \(0.651652\pi\)
\(350\) 178.689i 0.510541i
\(351\) −146.936 201.642i −0.418621 0.574478i
\(352\) 238.335 0.677087
\(353\) 428.068i 1.21266i −0.795214 0.606329i \(-0.792642\pi\)
0.795214 0.606329i \(-0.207358\pi\)
\(354\) 5.72691 + 26.8809i 0.0161777 + 0.0759348i
\(355\) 4.84690 0.0136532
\(356\) 244.545i 0.686926i
\(357\) −174.820 + 37.2449i −0.489691 + 0.104327i
\(358\) 262.256 0.732560
\(359\) 390.412i 1.08750i −0.839248 0.543749i \(-0.817004\pi\)
0.839248 0.543749i \(-0.182996\pi\)
\(360\) −12.4248 + 5.54587i −0.0345134 + 0.0154052i
\(361\) −360.929 −0.999803
\(362\) 73.4009i 0.202765i
\(363\) 42.0553 + 197.399i 0.115855 + 0.543798i
\(364\) 142.942 0.392699
\(365\) 13.1534i 0.0360368i
\(366\) −251.392 + 53.5584i −0.686862 + 0.146334i
\(367\) 287.119 0.782340 0.391170 0.920318i \(-0.372070\pi\)
0.391170 + 0.920318i \(0.372070\pi\)
\(368\) 8.86391i 0.0240867i
\(369\) 141.989 + 318.108i 0.384794 + 0.862081i
\(370\) 2.27717 0.00615452
\(371\) 140.381i 0.378386i
\(372\) −58.7319 275.675i −0.157881 0.741062i
\(373\) −488.823 −1.31052 −0.655259 0.755404i \(-0.727441\pi\)
−0.655259 + 0.755404i \(0.727441\pi\)
\(374\) 86.7878i 0.232053i
\(375\) −28.2511 + 6.01883i −0.0753363 + 0.0160502i
\(376\) 140.876 0.374670
\(377\) 264.574i 0.701787i
\(378\) −156.200 + 113.822i −0.413227 + 0.301118i
\(379\) 371.086 0.979119 0.489559 0.871970i \(-0.337158\pi\)
0.489559 + 0.871970i \(0.337158\pi\)
\(380\) 0.132356i 0.000348306i
\(381\) 44.2813 + 207.847i 0.116224 + 0.545530i
\(382\) −39.2242 −0.102681
\(383\) 474.681i 1.23938i 0.784849 + 0.619688i \(0.212741\pi\)
−0.784849 + 0.619688i \(0.787259\pi\)
\(384\) 259.248 55.2322i 0.675125 0.143834i
\(385\) −8.47731 −0.0220190
\(386\) 139.713i 0.361951i
\(387\) 322.507 143.953i 0.833352 0.371971i
\(388\) −387.034 −0.997511
\(389\) 605.349i 1.55617i −0.628161 0.778083i \(-0.716192\pi\)
0.628161 0.778083i \(-0.283808\pi\)
\(390\) 1.32772 + 6.23202i 0.00340440 + 0.0159795i
\(391\) −92.3443 −0.236175
\(392\) 101.832i 0.259776i
\(393\) −679.756 + 144.820i −1.72966 + 0.368500i
\(394\) −25.7057 −0.0652429
\(395\) 13.9760i 0.0353822i
\(396\) −69.3014 155.261i −0.175004 0.392073i
\(397\) 520.491 1.31106 0.655530 0.755169i \(-0.272445\pi\)
0.655530 + 0.755169i \(0.272445\pi\)
\(398\) 201.837i 0.507128i
\(399\) 0.999718 + 4.69247i 0.00250556 + 0.0117606i
\(400\) 23.7875 0.0594687
\(401\) 550.265i 1.37223i −0.727493 0.686115i \(-0.759314\pi\)
0.727493 0.686115i \(-0.240686\pi\)
\(402\) −203.590 + 43.3744i −0.506444 + 0.107897i
\(403\) −336.846 −0.835846
\(404\) 274.750i 0.680074i
\(405\) 11.6198 + 10.4230i 0.0286908 + 0.0257359i
\(406\) −204.950 −0.504802
\(407\) 72.6168i 0.178420i
\(408\) 48.6845 + 228.515i 0.119325 + 0.560085i
\(409\) −386.335 −0.944585 −0.472293 0.881442i \(-0.656573\pi\)
−0.472293 + 0.881442i \(0.656573\pi\)
\(410\) 8.89664i 0.0216991i
\(411\) −167.779 + 35.7450i −0.408222 + 0.0869707i
\(412\) 116.853 0.283624
\(413\) 46.0993i 0.111621i
\(414\) −91.1796 + 40.6984i −0.220241 + 0.0983054i
\(415\) 16.4914 0.0397384
\(416\) 300.475i 0.722296i
\(417\) 171.661 + 805.741i 0.411657 + 1.93223i
\(418\) 2.32954 0.00557305
\(419\) 666.029i 1.58957i 0.606893 + 0.794784i \(0.292416\pi\)
−0.606893 + 0.794784i \(0.707584\pi\)
\(420\) −8.74671 + 1.86347i −0.0208255 + 0.00443682i
\(421\) −702.025 −1.66752 −0.833759 0.552129i \(-0.813816\pi\)
−0.833759 + 0.552129i \(0.813816\pi\)
\(422\) 240.059i 0.568861i
\(423\) −65.8742 147.583i −0.155731 0.348895i
\(424\) −183.499 −0.432780
\(425\) 247.819i 0.583103i
\(426\) −18.7522 88.0188i −0.0440192 0.206617i
\(427\) −431.123 −1.00966
\(428\) 70.5667i 0.164875i
\(429\) −198.733 + 42.3395i −0.463247 + 0.0986936i
\(430\) −9.01967 −0.0209760
\(431\) 709.664i 1.64655i −0.567641 0.823276i \(-0.692144\pi\)
0.567641 0.823276i \(-0.307856\pi\)
\(432\) −15.1523 20.7936i −0.0350747 0.0481334i
\(433\) −52.7210 −0.121757 −0.0608787 0.998145i \(-0.519390\pi\)
−0.0608787 + 0.998145i \(0.519390\pi\)
\(434\) 260.935i 0.601232i
\(435\) 3.44911 + 16.1894i 0.00792900 + 0.0372170i
\(436\) 439.895 1.00893
\(437\) 2.47868i 0.00567205i
\(438\) −238.864 + 50.8894i −0.545352 + 0.116186i
\(439\) −26.6734 −0.0607594 −0.0303797 0.999538i \(-0.509672\pi\)
−0.0303797 + 0.999538i \(0.509672\pi\)
\(440\) 11.0811i 0.0251843i
\(441\) 106.680 47.6172i 0.241905 0.107975i
\(442\) 109.416 0.247547
\(443\) 281.292i 0.634972i 0.948263 + 0.317486i \(0.102839\pi\)
−0.948263 + 0.317486i \(0.897161\pi\)
\(444\) 15.9625 + 74.9245i 0.0359515 + 0.168749i
\(445\) 18.2843 0.0410883
\(446\) 30.5785i 0.0685616i
\(447\) −572.345 + 121.937i −1.28041 + 0.272789i
\(448\) −209.884 −0.468491
\(449\) 813.712i 1.81228i −0.422983 0.906138i \(-0.639017\pi\)
0.422983 0.906138i \(-0.360983\pi\)
\(450\) 109.220 + 244.693i 0.242711 + 0.543762i
\(451\) 283.705 0.629058
\(452\) 443.419i 0.981016i
\(453\) −14.3789 67.4916i −0.0317416 0.148988i
\(454\) −104.584 −0.230361
\(455\) 10.6876i 0.0234892i
\(456\) 6.13374 1.30678i 0.0134512 0.00286574i
\(457\) 152.151 0.332935 0.166467 0.986047i \(-0.446764\pi\)
0.166467 + 0.986047i \(0.446764\pi\)
\(458\) 178.392i 0.389502i
\(459\) 216.629 157.857i 0.471958 0.343914i
\(460\) −4.62024 −0.0100440
\(461\) 151.258i 0.328108i 0.986451 + 0.164054i \(0.0524571\pi\)
−0.986451 + 0.164054i \(0.947543\pi\)
\(462\) 32.7979 + 153.947i 0.0709912 + 0.333218i
\(463\) −188.686 −0.407530 −0.203765 0.979020i \(-0.565318\pi\)
−0.203765 + 0.979020i \(0.565318\pi\)
\(464\) 27.2833i 0.0588002i
\(465\) 20.6118 4.39129i 0.0443264 0.00944364i
\(466\) −122.152 −0.262130
\(467\) 555.701i 1.18994i −0.803749 0.594968i \(-0.797165\pi\)
0.803749 0.594968i \(-0.202835\pi\)
\(468\) −195.741 + 87.3701i −0.418251 + 0.186688i
\(469\) −349.146 −0.744448
\(470\) 4.12749i 0.00878190i
\(471\) −64.2686 301.663i −0.136451 0.640474i
\(472\) 60.2585 0.127666
\(473\) 287.628i 0.608094i
\(474\) 253.801 54.0717i 0.535446 0.114075i
\(475\) 6.65189 0.0140040
\(476\) 153.566i 0.322618i
\(477\) 85.8047 + 192.234i 0.179884 + 0.403007i
\(478\) 24.5121 0.0512805
\(479\) 264.217i 0.551601i 0.961215 + 0.275800i \(0.0889429\pi\)
−0.961215 + 0.275800i \(0.911057\pi\)
\(480\) 3.91714 + 18.3862i 0.00816071 + 0.0383046i
\(481\) 91.5499 0.190332
\(482\) 467.211i 0.969318i
\(483\) −163.803 + 34.8978i −0.339136 + 0.0722522i
\(484\) 173.400 0.358265
\(485\) 28.9380i 0.0596659i
\(486\) 144.325 251.339i 0.296965 0.517159i
\(487\) −163.268 −0.335252 −0.167626 0.985851i \(-0.553610\pi\)
−0.167626 + 0.985851i \(0.553610\pi\)
\(488\) 563.541i 1.15480i
\(489\) −128.189 601.694i −0.262146 1.23046i
\(490\) −2.98356 −0.00608890
\(491\) 884.367i 1.80116i 0.434695 + 0.900578i \(0.356856\pi\)
−0.434695 + 0.900578i \(0.643144\pi\)
\(492\) 292.721 62.3635i 0.594961 0.126755i
\(493\) 284.238 0.576548
\(494\) 2.93691i 0.00594516i
\(495\) 11.6086 5.18156i 0.0234517 0.0104678i
\(496\) −34.7362 −0.0700326
\(497\) 150.948i 0.303717i
\(498\) −63.8038 299.482i −0.128120 0.601369i
\(499\) 543.803 1.08979 0.544893 0.838506i \(-0.316570\pi\)
0.544893 + 0.838506i \(0.316570\pi\)
\(500\) 24.8165i 0.0496331i
\(501\) −900.953 + 191.946i −1.79831 + 0.383126i
\(502\) 270.222 0.538292
\(503\) 243.208i 0.483514i 0.970337 + 0.241757i \(0.0777238\pi\)
−0.970337 + 0.241757i \(0.922276\pi\)
\(504\) 172.716 + 386.947i 0.342690 + 0.767753i
\(505\) −20.5426 −0.0406785
\(506\) 81.3186i 0.160709i
\(507\) −52.2655 245.323i −0.103088 0.483873i
\(508\) 182.578 0.359406
\(509\) 807.215i 1.58588i 0.609297 + 0.792942i \(0.291452\pi\)
−0.609297 + 0.792942i \(0.708548\pi\)
\(510\) −6.69521 + 1.42640i −0.0131279 + 0.00279686i
\(511\) −409.639 −0.801642
\(512\) 60.8880i 0.118922i
\(513\) −4.23715 5.81469i −0.00825955 0.0113347i
\(514\) 512.892 0.997844
\(515\) 8.73694i 0.0169649i
\(516\) −63.2259 296.769i −0.122531 0.575134i
\(517\) −131.622 −0.254587
\(518\) 70.9183i 0.136908i
\(519\) −18.8515 + 4.01627i −0.0363228 + 0.00773848i
\(520\) 13.9702 0.0268658
\(521\) 260.497i 0.499993i 0.968247 + 0.249997i \(0.0804295\pi\)
−0.968247 + 0.249997i \(0.919570\pi\)
\(522\) 280.653 125.271i 0.537649 0.239982i
\(523\) −619.355 −1.18424 −0.592118 0.805851i \(-0.701708\pi\)
−0.592118 + 0.805851i \(0.701708\pi\)
\(524\) 597.116i 1.13953i
\(525\) 93.6530 + 439.587i 0.178387 + 0.837309i
\(526\) −108.130 −0.205570
\(527\) 361.882i 0.686683i
\(528\) −20.4937 + 4.36613i −0.0388138 + 0.00826918i
\(529\) 442.475 0.836437
\(530\) 5.37629i 0.0101439i
\(531\) −28.1771 63.1272i −0.0530643 0.118884i
\(532\) 4.12199 0.00774810
\(533\) 357.675i 0.671059i
\(534\) −70.7402 332.040i −0.132472 0.621797i
\(535\) 5.27616 0.00986199
\(536\) 456.385i 0.851465i
\(537\) −645.167 + 137.451i −1.20143 + 0.255961i
\(538\) −212.107 −0.394250
\(539\) 95.1428i 0.176517i
\(540\) 10.8385 7.89801i 0.0200713 0.0146259i
\(541\) 74.4432 0.137603 0.0688015 0.997630i \(-0.478082\pi\)
0.0688015 + 0.997630i \(0.478082\pi\)
\(542\) 513.897i 0.948150i
\(543\) −38.4702 180.571i −0.0708474 0.332543i
\(544\) 322.808 0.593396
\(545\) 32.8902i 0.0603491i
\(546\) 194.085 41.3492i 0.355466 0.0757312i
\(547\) −451.226 −0.824911 −0.412455 0.910978i \(-0.635329\pi\)
−0.412455 + 0.910978i \(0.635329\pi\)
\(548\) 147.382i 0.268945i
\(549\) 590.369 263.514i 1.07535 0.479989i
\(550\) 218.230 0.396781
\(551\) 7.62945i 0.0138465i
\(552\) 45.6165 + 214.114i 0.0826386 + 0.387888i
\(553\) 435.255 0.787080
\(554\) 370.904i 0.669502i
\(555\) −5.60199 + 1.19349i −0.0100937 + 0.00215043i
\(556\) 707.785 1.27299
\(557\) 731.546i 1.31337i −0.754166 0.656684i \(-0.771958\pi\)
0.754166 0.656684i \(-0.228042\pi\)
\(558\) −159.490 357.317i −0.285825 0.640354i
\(559\) −362.621 −0.648696
\(560\) 1.10212i 0.00196807i
\(561\) −45.4864 213.503i −0.0810809 0.380577i
\(562\) −135.237 −0.240635
\(563\) 938.349i 1.66669i 0.552750 + 0.833347i \(0.313579\pi\)
−0.552750 + 0.833347i \(0.686421\pi\)
\(564\) −135.805 + 28.9328i −0.240788 + 0.0512993i
\(565\) 33.1538 0.0586792
\(566\) 395.686i 0.699091i
\(567\) 324.606 361.876i 0.572498 0.638230i
\(568\) −197.310 −0.347377
\(569\) 262.597i 0.461505i 0.973012 + 0.230753i \(0.0741188\pi\)
−0.973012 + 0.230753i \(0.925881\pi\)
\(570\) 0.0382870 + 0.179711i 6.71702e−5 + 0.000315283i
\(571\) −305.783 −0.535521 −0.267761 0.963485i \(-0.586284\pi\)
−0.267761 + 0.963485i \(0.586284\pi\)
\(572\) 174.572i 0.305196i
\(573\) 96.4940 20.5578i 0.168401 0.0358775i
\(574\) −277.069 −0.482699
\(575\) 232.202i 0.403829i
\(576\) 287.410 128.287i 0.498975 0.222720i
\(577\) 631.668 1.09475 0.547373 0.836889i \(-0.315628\pi\)
0.547373 + 0.836889i \(0.315628\pi\)
\(578\) 227.146i 0.392986i
\(579\) −73.2250 343.703i −0.126468 0.593615i
\(580\) 14.2212 0.0245193
\(581\) 513.595i 0.883984i
\(582\) −525.509 + 111.958i −0.902936 + 0.192368i
\(583\) 171.444 0.294073
\(584\) 535.458i 0.916880i
\(585\) −6.53253 14.6353i −0.0111667 0.0250176i
\(586\) 358.650 0.612031
\(587\) 588.946i 1.00331i −0.865066 0.501657i \(-0.832724\pi\)
0.865066 0.501657i \(-0.167276\pi\)
\(588\) −20.9141 98.1663i −0.0355682 0.166950i
\(589\) −9.71354 −0.0164916
\(590\) 1.76550i 0.00299238i
\(591\) 63.2376 13.4726i 0.107001 0.0227963i
\(592\) 9.44079 0.0159473
\(593\) 123.195i 0.207749i −0.994590 0.103875i \(-0.966876\pi\)
0.994590 0.103875i \(-0.0331241\pi\)
\(594\) −139.009 190.764i −0.234022 0.321151i
\(595\) −11.4819 −0.0192973
\(596\) 502.764i 0.843563i
\(597\) 105.785 + 496.532i 0.177194 + 0.831712i
\(598\) 102.521 0.171439
\(599\) 1039.18i 1.73485i 0.497564 + 0.867427i \(0.334228\pi\)
−0.497564 + 0.867427i \(0.665772\pi\)
\(600\) 574.605 122.418i 0.957675 0.204030i
\(601\) 703.372 1.17034 0.585168 0.810912i \(-0.301029\pi\)
0.585168 + 0.810912i \(0.301029\pi\)
\(602\) 280.901i 0.466613i
\(603\) 478.112 213.408i 0.792889 0.353910i
\(604\) −59.2864 −0.0981564
\(605\) 12.9649i 0.0214295i
\(606\) 79.4775 + 373.051i 0.131151 + 0.615595i
\(607\) −290.004 −0.477766 −0.238883 0.971048i \(-0.576781\pi\)
−0.238883 + 0.971048i \(0.576781\pi\)
\(608\) 8.66472i 0.0142512i
\(609\) 504.189 107.416i 0.827897 0.176381i
\(610\) −16.5111 −0.0270673
\(611\) 165.939i 0.271586i
\(612\) −93.8638 210.290i −0.153372 0.343611i
\(613\) −637.904 −1.04063 −0.520313 0.853976i \(-0.674185\pi\)
−0.520313 + 0.853976i \(0.674185\pi\)
\(614\) 289.232i 0.471062i
\(615\) 4.66282 + 21.8863i 0.00758182 + 0.0355875i
\(616\) 345.100 0.560227
\(617\) 871.415i 1.41234i −0.708041 0.706171i \(-0.750421\pi\)
0.708041 0.706171i \(-0.249579\pi\)
\(618\) 158.661 33.8024i 0.256734 0.0546965i
\(619\) 529.878 0.856023 0.428011 0.903773i \(-0.359214\pi\)
0.428011 + 0.903773i \(0.359214\pi\)
\(620\) 18.1060i 0.0292032i
\(621\) 202.977 147.909i 0.326855 0.238179i
\(622\) −424.634 −0.682692
\(623\) 569.430i 0.914013i
\(624\) 5.50449 + 25.8369i 0.00882130 + 0.0414053i
\(625\) 622.216 0.995546
\(626\) 352.268i 0.562729i
\(627\) −5.73081 + 1.22093i −0.00914004 + 0.00194726i
\(628\) −264.989 −0.421957
\(629\) 98.3543i 0.156366i
\(630\) −11.3371 + 5.06037i −0.0179954 + 0.00803233i
\(631\) 79.4381 0.125892 0.0629462 0.998017i \(-0.479950\pi\)
0.0629462 + 0.998017i \(0.479950\pi\)
\(632\) 568.942i 0.900225i
\(633\) 125.817 + 590.561i 0.198764 + 0.932955i
\(634\) 80.0267 0.126225
\(635\) 13.6511i 0.0214978i
\(636\) 176.893 37.6866i 0.278133 0.0592556i
\(637\) −119.949 −0.188303
\(638\) 250.301i 0.392321i
\(639\) 92.2632 + 206.704i 0.144387 + 0.323480i
\(640\) 17.0271 0.0266048
\(641\) 617.174i 0.962830i 0.876493 + 0.481415i \(0.159877\pi\)
−0.876493 + 0.481415i \(0.840123\pi\)
\(642\) −20.4130 95.8142i −0.0317959 0.149243i
\(643\) 478.843 0.744701 0.372351 0.928092i \(-0.378552\pi\)
0.372351 + 0.928092i \(0.378552\pi\)
\(644\) 143.889i 0.223430i
\(645\) 22.1890 4.72730i 0.0344015 0.00732915i
\(646\) 3.15519 0.00488420
\(647\) 952.499i 1.47218i 0.676885 + 0.736088i \(0.263329\pi\)
−0.676885 + 0.736088i \(0.736671\pi\)
\(648\) −473.025 424.307i −0.729977 0.654795i
\(649\) −56.3001 −0.0867490
\(650\) 275.128i 0.423274i
\(651\) −136.759 641.916i −0.210075 0.986046i
\(652\) −528.544 −0.810650
\(653\) 838.343i 1.28383i 0.766775 + 0.641916i \(0.221860\pi\)
−0.766775 + 0.641916i \(0.778140\pi\)
\(654\) 597.281 127.249i 0.913274 0.194571i
\(655\) −44.6454 −0.0681610
\(656\) 36.8840i 0.0562256i
\(657\) 560.949 250.382i 0.853804 0.381099i
\(658\) 128.543 0.195354
\(659\) 697.326i 1.05816i −0.848572 0.529079i \(-0.822537\pi\)
0.848572 0.529079i \(-0.177463\pi\)
\(660\) −2.27581 10.6822i −0.00344820 0.0161851i
\(661\) 122.681 0.185599 0.0927997 0.995685i \(-0.470418\pi\)
0.0927997 + 0.995685i \(0.470418\pi\)
\(662\) 725.910i 1.09654i
\(663\) −269.170 + 57.3459i −0.405987 + 0.0864946i
\(664\) −671.343 −1.01106
\(665\) 0.308195i 0.000463451i
\(666\) 43.3472 + 97.1137i 0.0650858 + 0.145816i
\(667\) 266.326 0.399289
\(668\) 791.422i 1.18476i
\(669\) 16.0265 + 75.2250i 0.0239559 + 0.112444i
\(670\) −13.3715 −0.0199575
\(671\) 526.521i 0.784681i
\(672\) 572.605 121.992i 0.852091 0.181536i
\(673\) 415.437 0.617291 0.308645 0.951177i \(-0.400124\pi\)
0.308645 + 0.951177i \(0.400124\pi\)
\(674\) 46.6396i 0.0691982i
\(675\) −396.934 544.717i −0.588050 0.806987i
\(676\) −215.499 −0.318785
\(677\) 605.231i 0.893990i −0.894536 0.446995i \(-0.852494\pi\)
0.894536 0.446995i \(-0.147506\pi\)
\(678\) −128.269 602.067i −0.189187 0.888004i
\(679\) −901.219 −1.32727
\(680\) 15.0085i 0.0220714i
\(681\) 257.283 54.8134i 0.377801 0.0804896i
\(682\) −318.674 −0.467264
\(683\) 155.804i 0.228118i 0.993474 + 0.114059i \(0.0363853\pi\)
−0.993474 + 0.114059i \(0.963615\pi\)
\(684\) −5.64455 + 2.51947i −0.00825226 + 0.00368343i
\(685\) −11.0195 −0.0160869
\(686\) 443.670i 0.646749i
\(687\) 93.4971 + 438.856i 0.136095 + 0.638800i
\(688\) −37.3941 −0.0543519
\(689\) 216.145i 0.313708i
\(690\) −6.27329 + 1.33651i −0.00909172 + 0.00193697i
\(691\) −58.8402 −0.0851523 −0.0425761 0.999093i \(-0.513557\pi\)
−0.0425761 + 0.999093i \(0.513557\pi\)
\(692\) 16.5597i 0.0239302i
\(693\) −161.370 361.529i −0.232857 0.521686i
\(694\) 351.766 0.506868
\(695\) 52.9200i 0.0761438i
\(696\) −140.409 659.049i −0.201737 0.946909i
\(697\) 384.258 0.551303
\(698\) 381.798i 0.546988i
\(699\) 300.503 64.0213i 0.429903 0.0915899i
\(700\) 386.145 0.551636
\(701\) 1175.46i 1.67683i 0.545032 + 0.838416i \(0.316518\pi\)
−0.545032 + 0.838416i \(0.683482\pi\)
\(702\) −240.501 + 175.252i −0.342594 + 0.249647i
\(703\) 2.64000 0.00375534
\(704\) 256.327i 0.364101i
\(705\) −2.16326 10.1539i −0.00306846 0.0144027i
\(706\) −510.562 −0.723176
\(707\) 639.762i 0.904897i
\(708\) −58.0893 + 12.3758i −0.0820470 + 0.0174799i
\(709\) 1266.22 1.78592 0.892961 0.450135i \(-0.148624\pi\)
0.892961 + 0.450135i \(0.148624\pi\)
\(710\) 5.78096i 0.00814219i
\(711\) −596.028 + 266.040i −0.838295 + 0.374177i
\(712\) −744.328 −1.04540
\(713\) 339.077i 0.475564i
\(714\) 44.4225 + 208.510i 0.0622164 + 0.292030i
\(715\) −13.0525 −0.0182552
\(716\) 566.732i 0.791525i
\(717\) −60.3012 + 12.8470i −0.0841021 + 0.0179177i
\(718\) −465.649 −0.648537
\(719\) 419.586i 0.583570i 0.956484 + 0.291785i \(0.0942491\pi\)
−0.956484 + 0.291785i \(0.905751\pi\)
\(720\) −0.673646 1.50922i −0.000935619 0.00209613i
\(721\) 272.096 0.377386
\(722\) 430.485i 0.596239i
\(723\) 244.870 + 1149.37i 0.338686 + 1.58972i
\(724\) −158.618 −0.219086
\(725\) 714.722i 0.985823i
\(726\) 235.440 50.1599i 0.324297 0.0690907i
\(727\) −862.945 −1.18699 −0.593497 0.804836i \(-0.702253\pi\)
−0.593497 + 0.804836i \(0.702253\pi\)
\(728\) 435.076i 0.597632i
\(729\) −223.319 + 693.952i −0.306336 + 0.951924i
\(730\) −15.6883 −0.0214908
\(731\) 389.572i 0.532931i
\(732\) −115.739 543.254i −0.158113 0.742150i
\(733\) −161.777 −0.220705 −0.110352 0.993893i \(-0.535198\pi\)
−0.110352 + 0.993893i \(0.535198\pi\)
\(734\) 342.451i 0.466554i
\(735\) 7.33975 1.56371i 0.00998605 0.00212750i
\(736\) 302.465 0.410958
\(737\) 426.405i 0.578568i
\(738\) 379.412 169.352i 0.514108 0.229474i
\(739\) −346.715 −0.469168 −0.234584 0.972096i \(-0.575373\pi\)
−0.234584 + 0.972096i \(0.575373\pi\)
\(740\) 4.92094i 0.00664992i
\(741\) 1.53926 + 7.22498i 0.00207728 + 0.00975031i
\(742\) −167.434 −0.225653
\(743\) 658.712i 0.886557i 0.896384 + 0.443279i \(0.146185\pi\)
−0.896384 + 0.443279i \(0.853815\pi\)
\(744\) −839.078 + 178.763i −1.12779 + 0.240273i
\(745\) −37.5909 −0.0504575
\(746\) 583.026i 0.781536i
\(747\) 313.923 + 703.304i 0.420245 + 0.941504i
\(748\) −187.547 −0.250732
\(749\) 164.316i 0.219381i
\(750\) 7.17874 + 33.6955i 0.00957165 + 0.0449273i
\(751\) −518.163 −0.689964 −0.344982 0.938609i \(-0.612115\pi\)
−0.344982 + 0.938609i \(0.612115\pi\)
\(752\) 17.1119i 0.0227552i
\(753\) −664.764 + 141.626i −0.882821 + 0.188083i
\(754\) −315.561 −0.418515
\(755\) 4.43276i 0.00587120i
\(756\) −245.969 337.546i −0.325355 0.446489i
\(757\) −396.939 −0.524358 −0.262179 0.965019i \(-0.584441\pi\)
−0.262179 + 0.965019i \(0.584441\pi\)
\(758\) 442.599i 0.583904i
\(759\) −42.6199 200.049i −0.0561527 0.263569i
\(760\) 0.402855 0.000530073
\(761\) 143.135i 0.188088i −0.995568 0.0940442i \(-0.970020\pi\)
0.995568 0.0940442i \(-0.0299795\pi\)
\(762\) 247.902 52.8148i 0.325330 0.0693108i
\(763\) 1024.31 1.34247
\(764\) 84.7629i 0.110946i
\(765\) 15.7230 7.01805i 0.0205530 0.00917393i
\(766\) 566.158 0.739110
\(767\) 70.9791i 0.0925411i
\(768\) −153.320 719.652i −0.199635 0.937047i
\(769\) −1406.57 −1.82909 −0.914546 0.404482i \(-0.867452\pi\)
−0.914546 + 0.404482i \(0.867452\pi\)
\(770\) 10.1110i 0.0131312i
\(771\) −1261.75 + 268.812i −1.63651 + 0.348654i
\(772\) −301.918 −0.391085
\(773\) 1460.02i 1.88877i 0.328840 + 0.944386i \(0.393342\pi\)
−0.328840 + 0.944386i \(0.606658\pi\)
\(774\) −171.694 384.659i −0.221827 0.496975i
\(775\) −909.959 −1.17414
\(776\) 1178.02i 1.51807i
\(777\) 37.1690 + 174.464i 0.0478366 + 0.224535i
\(778\) −722.007 −0.928030
\(779\) 10.3142i 0.0132403i
\(780\) −13.4673 + 2.86917i −0.0172658 + 0.00367843i
\(781\) 184.349 0.236042
\(782\) 110.140i 0.140844i
\(783\) −624.768 + 455.267i −0.797916 + 0.581439i
\(784\) −12.3694 −0.0157772
\(785\) 19.8128i 0.0252393i