Properties

Label 177.5.b.a.119.1
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.1
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.78

$q$-expansion

\(f(q)\) \(=\) \(q-7.85862i q^{2} +(1.36439 + 8.89598i) q^{3} -45.7580 q^{4} +33.8616i q^{5} +(69.9102 - 10.7222i) q^{6} +13.8137 q^{7} +233.857i q^{8} +(-77.2769 + 24.2751i) q^{9} +O(q^{10})\) \(q-7.85862i q^{2} +(1.36439 + 8.89598i) q^{3} -45.7580 q^{4} +33.8616i q^{5} +(69.9102 - 10.7222i) q^{6} +13.8137 q^{7} +233.857i q^{8} +(-77.2769 + 24.2751i) q^{9} +266.105 q^{10} -192.320i q^{11} +(-62.4316 - 407.062i) q^{12} -170.965 q^{13} -108.557i q^{14} +(-301.232 + 46.2003i) q^{15} +1105.66 q^{16} -492.040i q^{17} +(190.769 + 607.290i) q^{18} +210.495 q^{19} -1549.44i q^{20} +(18.8472 + 122.886i) q^{21} -1511.37 q^{22} -115.548i q^{23} +(-2080.38 + 319.071i) q^{24} -521.606 q^{25} +1343.55i q^{26} +(-321.387 - 654.333i) q^{27} -632.087 q^{28} -439.260i q^{29} +(363.071 + 2367.27i) q^{30} +175.455 q^{31} -4947.30i q^{32} +(1710.88 - 262.400i) q^{33} -3866.76 q^{34} +467.753i q^{35} +(3536.03 - 1110.78i) q^{36} +1951.00 q^{37} -1654.20i q^{38} +(-233.263 - 1520.90i) q^{39} -7918.76 q^{40} -1818.50i q^{41} +(965.717 - 148.113i) q^{42} +1528.80 q^{43} +8800.20i q^{44} +(-821.994 - 2616.72i) q^{45} -908.046 q^{46} +1691.29i q^{47} +(1508.56 + 9835.97i) q^{48} -2210.18 q^{49} +4099.10i q^{50} +(4377.18 - 671.334i) q^{51} +7823.03 q^{52} -873.418i q^{53} +(-5142.16 + 2525.66i) q^{54} +6512.27 q^{55} +3230.43i q^{56} +(287.197 + 1872.56i) q^{57} -3451.98 q^{58} +453.188i q^{59} +(13783.8 - 2114.03i) q^{60} -4977.77 q^{61} -1378.83i q^{62} +(-1067.48 + 335.329i) q^{63} -21188.3 q^{64} -5789.15i q^{65} +(-2062.10 - 13445.2i) q^{66} -4017.43 q^{67} +22514.8i q^{68} +(1027.91 - 157.652i) q^{69} +3675.90 q^{70} -233.784i q^{71} +(-5676.91 - 18071.7i) q^{72} -2072.57 q^{73} -15332.1i q^{74} +(-711.672 - 4640.19i) q^{75} -9631.84 q^{76} -2656.66i q^{77} +(-11952.2 + 1833.13i) q^{78} +336.550 q^{79} +37439.5i q^{80} +(5382.44 - 3751.81i) q^{81} -14290.9 q^{82} +687.683i q^{83} +(-862.412 - 5623.03i) q^{84} +16661.3 q^{85} -12014.3i q^{86} +(3907.65 - 599.322i) q^{87} +44975.4 q^{88} -5666.49i q^{89} +(-20563.8 + 6459.74i) q^{90} -2361.66 q^{91} +5287.23i q^{92} +(239.388 + 1560.84i) q^{93} +13291.2 q^{94} +7127.70i q^{95} +(44011.0 - 6750.03i) q^{96} -3420.98 q^{97} +17369.0i q^{98} +(4668.61 + 14861.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.85862i 1.96466i −0.187167 0.982328i \(-0.559931\pi\)
0.187167 0.982328i \(-0.440069\pi\)
\(3\) 1.36439 + 8.89598i 0.151599 + 0.988442i
\(4\) −45.7580 −2.85987
\(5\) 33.8616i 1.35446i 0.735770 + 0.677231i \(0.236820\pi\)
−0.735770 + 0.677231i \(0.763180\pi\)
\(6\) 69.9102 10.7222i 1.94195 0.297839i
\(7\) 13.8137 0.281912 0.140956 0.990016i \(-0.454982\pi\)
0.140956 + 0.990016i \(0.454982\pi\)
\(8\) 233.857i 3.65401i
\(9\) −77.2769 + 24.2751i −0.954036 + 0.299693i
\(10\) 266.105 2.66105
\(11\) 192.320i 1.58943i −0.606986 0.794713i \(-0.707621\pi\)
0.606986 0.794713i \(-0.292379\pi\)
\(12\) −62.4316 407.062i −0.433553 2.82682i
\(13\) −170.965 −1.01163 −0.505815 0.862642i \(-0.668808\pi\)
−0.505815 + 0.862642i \(0.668808\pi\)
\(14\) 108.557i 0.553860i
\(15\) −301.232 + 46.2003i −1.33881 + 0.205335i
\(16\) 1105.66 4.31900
\(17\) 492.040i 1.70256i −0.524711 0.851281i \(-0.675826\pi\)
0.524711 0.851281i \(-0.324174\pi\)
\(18\) 190.769 + 607.290i 0.588794 + 1.87435i
\(19\) 210.495 0.583089 0.291545 0.956557i \(-0.405831\pi\)
0.291545 + 0.956557i \(0.405831\pi\)
\(20\) 1549.44i 3.87359i
\(21\) 18.8472 + 122.886i 0.0427375 + 0.278654i
\(22\) −1511.37 −3.12267
\(23\) 115.548i 0.218427i −0.994018 0.109213i \(-0.965167\pi\)
0.994018 0.109213i \(-0.0348332\pi\)
\(24\) −2080.38 + 319.071i −3.61178 + 0.553943i
\(25\) −521.606 −0.834569
\(26\) 1343.55i 1.98750i
\(27\) −321.387 654.333i −0.440860 0.897576i
\(28\) −632.087 −0.806233
\(29\) 439.260i 0.522307i −0.965297 0.261154i \(-0.915897\pi\)
0.965297 0.261154i \(-0.0841029\pi\)
\(30\) 363.071 + 2367.27i 0.403412 + 2.63030i
\(31\) 175.455 0.182575 0.0912876 0.995825i \(-0.470902\pi\)
0.0912876 + 0.995825i \(0.470902\pi\)
\(32\) 4947.30i 4.83134i
\(33\) 1710.88 262.400i 1.57106 0.240955i
\(34\) −3866.76 −3.34495
\(35\) 467.753i 0.381839i
\(36\) 3536.03 1110.78i 2.72842 0.857084i
\(37\) 1951.00 1.42512 0.712562 0.701609i \(-0.247534\pi\)
0.712562 + 0.701609i \(0.247534\pi\)
\(38\) 1654.20i 1.14557i
\(39\) −233.263 1520.90i −0.153362 0.999937i
\(40\) −7918.76 −4.94922
\(41\) 1818.50i 1.08179i −0.841089 0.540897i \(-0.818085\pi\)
0.841089 0.540897i \(-0.181915\pi\)
\(42\) 965.717 148.113i 0.547459 0.0839645i
\(43\) 1528.80 0.826825 0.413413 0.910544i \(-0.364337\pi\)
0.413413 + 0.910544i \(0.364337\pi\)
\(44\) 8800.20i 4.54556i
\(45\) −821.994 2616.72i −0.405923 1.29221i
\(46\) −908.046 −0.429133
\(47\) 1691.29i 0.765637i 0.923824 + 0.382819i \(0.125047\pi\)
−0.923824 + 0.382819i \(0.874953\pi\)
\(48\) 1508.56 + 9835.97i 0.654755 + 4.26908i
\(49\) −2210.18 −0.920526
\(50\) 4099.10i 1.63964i
\(51\) 4377.18 671.334i 1.68288 0.258106i
\(52\) 7823.03 2.89313
\(53\) 873.418i 0.310936i −0.987841 0.155468i \(-0.950312\pi\)
0.987841 0.155468i \(-0.0496885\pi\)
\(54\) −5142.16 + 2525.66i −1.76343 + 0.866138i
\(55\) 6512.27 2.15282
\(56\) 3230.43i 1.03011i
\(57\) 287.197 + 1872.56i 0.0883956 + 0.576350i
\(58\) −3451.98 −1.02615
\(59\) 453.188i 0.130189i
\(60\) 13783.8 2114.03i 3.82882 0.587231i
\(61\) −4977.77 −1.33775 −0.668876 0.743374i \(-0.733224\pi\)
−0.668876 + 0.743374i \(0.733224\pi\)
\(62\) 1378.83i 0.358697i
\(63\) −1067.48 + 335.329i −0.268954 + 0.0844871i
\(64\) −21188.3 −5.17293
\(65\) 5789.15i 1.37021i
\(66\) −2062.10 13445.2i −0.473393 3.08658i
\(67\) −4017.43 −0.894951 −0.447475 0.894296i \(-0.647677\pi\)
−0.447475 + 0.894296i \(0.647677\pi\)
\(68\) 22514.8i 4.86911i
\(69\) 1027.91 157.652i 0.215902 0.0331132i
\(70\) 3675.90 0.750183
\(71\) 233.784i 0.0463765i −0.999731 0.0231883i \(-0.992618\pi\)
0.999731 0.0231883i \(-0.00738172\pi\)
\(72\) −5676.91 18071.7i −1.09508 3.48606i
\(73\) −2072.57 −0.388924 −0.194462 0.980910i \(-0.562296\pi\)
−0.194462 + 0.980910i \(0.562296\pi\)
\(74\) 15332.1i 2.79988i
\(75\) −711.672 4640.19i −0.126520 0.824923i
\(76\) −9631.84 −1.66756
\(77\) 2656.66i 0.448078i
\(78\) −11952.2 + 1833.13i −1.96453 + 0.301303i
\(79\) 336.550 0.0539257 0.0269628 0.999636i \(-0.491416\pi\)
0.0269628 + 0.999636i \(0.491416\pi\)
\(80\) 37439.5i 5.84993i
\(81\) 5382.44 3751.81i 0.820368 0.571836i
\(82\) −14290.9 −2.12535
\(83\) 687.683i 0.0998234i 0.998754 + 0.0499117i \(0.0158940\pi\)
−0.998754 + 0.0499117i \(0.984106\pi\)
\(84\) −862.412 5623.03i −0.122224 0.796915i
\(85\) 16661.3 2.30606
\(86\) 12014.3i 1.62443i
\(87\) 3907.65 599.322i 0.516270 0.0791811i
\(88\) 44975.4 5.80778
\(89\) 5666.49i 0.715376i −0.933841 0.357688i \(-0.883565\pi\)
0.933841 0.357688i \(-0.116435\pi\)
\(90\) −20563.8 + 6459.74i −2.53874 + 0.797499i
\(91\) −2361.66 −0.285191
\(92\) 5287.23i 0.624673i
\(93\) 239.388 + 1560.84i 0.0276782 + 0.180465i
\(94\) 13291.2 1.50421
\(95\) 7127.70i 0.789773i
\(96\) 44011.0 6750.03i 4.77550 0.732425i
\(97\) −3420.98 −0.363586 −0.181793 0.983337i \(-0.558190\pi\)
−0.181793 + 0.983337i \(0.558190\pi\)
\(98\) 17369.0i 1.80852i
\(99\) 4668.61 + 14861.9i 0.476340 + 1.51637i
\(100\) 23867.6 2.38676
\(101\) 584.413i 0.0572898i −0.999590 0.0286449i \(-0.990881\pi\)
0.999590 0.0286449i \(-0.00911920\pi\)
\(102\) −5275.76 34398.6i −0.507090 3.30629i
\(103\) −19980.2 −1.88332 −0.941662 0.336560i \(-0.890737\pi\)
−0.941662 + 0.336560i \(0.890737\pi\)
\(104\) 39981.4i 3.69651i
\(105\) −4161.12 + 638.197i −0.377426 + 0.0578864i
\(106\) −6863.87 −0.610882
\(107\) 10860.0i 0.948556i −0.880375 0.474278i \(-0.842709\pi\)
0.880375 0.474278i \(-0.157291\pi\)
\(108\) 14706.0 + 29940.9i 1.26080 + 2.56695i
\(109\) −5033.51 −0.423660 −0.211830 0.977306i \(-0.567942\pi\)
−0.211830 + 0.977306i \(0.567942\pi\)
\(110\) 51177.5i 4.22955i
\(111\) 2661.92 + 17356.0i 0.216047 + 1.40865i
\(112\) 15273.3 1.21758
\(113\) 16750.8i 1.31183i −0.754833 0.655917i \(-0.772282\pi\)
0.754833 0.655917i \(-0.227718\pi\)
\(114\) 14715.8 2256.98i 1.13233 0.173667i
\(115\) 3912.63 0.295851
\(116\) 20099.7i 1.49373i
\(117\) 13211.7 4150.21i 0.965130 0.303178i
\(118\) 3561.43 0.255776
\(119\) 6796.89i 0.479973i
\(120\) −10804.3 70445.1i −0.750296 4.89202i
\(121\) −22346.2 −1.52627
\(122\) 39118.5i 2.62822i
\(123\) 16177.3 2481.13i 1.06929 0.163999i
\(124\) −8028.45 −0.522142
\(125\) 3501.10i 0.224070i
\(126\) 2635.23 + 8388.92i 0.165988 + 0.528402i
\(127\) 8026.58 0.497649 0.248825 0.968549i \(-0.419956\pi\)
0.248825 + 0.968549i \(0.419956\pi\)
\(128\) 87354.2i 5.33168i
\(129\) 2085.88 + 13600.2i 0.125346 + 0.817269i
\(130\) −45494.8 −2.69200
\(131\) 21267.7i 1.23931i −0.784876 0.619653i \(-0.787273\pi\)
0.784876 0.619653i \(-0.212727\pi\)
\(132\) −78286.4 + 12006.9i −4.49302 + 0.689100i
\(133\) 2907.72 0.164380
\(134\) 31571.5i 1.75827i
\(135\) 22156.7 10882.7i 1.21573 0.597128i
\(136\) 115067. 6.22118
\(137\) 32442.8i 1.72853i −0.503034 0.864266i \(-0.667783\pi\)
0.503034 0.864266i \(-0.332217\pi\)
\(138\) −1238.93 8077.96i −0.0650561 0.424173i
\(139\) 18614.4 0.963428 0.481714 0.876329i \(-0.340014\pi\)
0.481714 + 0.876329i \(0.340014\pi\)
\(140\) 21403.4i 1.09201i
\(141\) −15045.7 + 2307.58i −0.756788 + 0.116070i
\(142\) −1837.22 −0.0911139
\(143\) 32880.1i 1.60791i
\(144\) −85442.3 + 26840.2i −4.12048 + 1.29438i
\(145\) 14874.0 0.707446
\(146\) 16287.6i 0.764101i
\(147\) −3015.55 19661.7i −0.139550 0.909886i
\(148\) −89273.6 −4.07568
\(149\) 4095.47i 0.184472i 0.995737 + 0.0922362i \(0.0294015\pi\)
−0.995737 + 0.0922362i \(0.970599\pi\)
\(150\) −36465.5 + 5592.77i −1.62069 + 0.248567i
\(151\) −25391.9 −1.11363 −0.556816 0.830636i \(-0.687977\pi\)
−0.556816 + 0.830636i \(0.687977\pi\)
\(152\) 49225.7i 2.13062i
\(153\) 11944.3 + 38023.3i 0.510246 + 1.62430i
\(154\) −20877.7 −0.880320
\(155\) 5941.17i 0.247291i
\(156\) 10673.6 + 69593.5i 0.438595 + 2.85969i
\(157\) −11978.8 −0.485975 −0.242988 0.970029i \(-0.578127\pi\)
−0.242988 + 0.970029i \(0.578127\pi\)
\(158\) 2644.82i 0.105945i
\(159\) 7769.91 1191.68i 0.307342 0.0471374i
\(160\) 167523. 6.54387
\(161\) 1596.14i 0.0615771i
\(162\) −29484.1 42298.5i −1.12346 1.61174i
\(163\) −5885.26 −0.221509 −0.110754 0.993848i \(-0.535327\pi\)
−0.110754 + 0.993848i \(0.535327\pi\)
\(164\) 83210.7i 3.09379i
\(165\) 8885.27 + 57933.0i 0.326364 + 2.12794i
\(166\) 5404.24 0.196119
\(167\) 16035.8i 0.574987i 0.957783 + 0.287493i \(0.0928219\pi\)
−0.957783 + 0.287493i \(0.907178\pi\)
\(168\) −28737.8 + 4407.55i −1.01820 + 0.156163i
\(169\) 668.154 0.0233939
\(170\) 130935.i 4.53061i
\(171\) −16266.4 + 5109.80i −0.556288 + 0.174748i
\(172\) −69954.8 −2.36462
\(173\) 26851.9i 0.897187i 0.893736 + 0.448593i \(0.148075\pi\)
−0.893736 + 0.448593i \(0.851925\pi\)
\(174\) −4709.84 30708.8i −0.155564 1.01429i
\(175\) −7205.30 −0.235275
\(176\) 212642.i 6.86473i
\(177\) −4031.55 + 618.324i −0.128684 + 0.0197365i
\(178\) −44530.8 −1.40547
\(179\) 36640.6i 1.14355i −0.820410 0.571776i \(-0.806255\pi\)
0.820410 0.571776i \(-0.193745\pi\)
\(180\) 37612.8 + 119736.i 1.16089 + 3.69554i
\(181\) 40626.2 1.24008 0.620039 0.784571i \(-0.287117\pi\)
0.620039 + 0.784571i \(0.287117\pi\)
\(182\) 18559.4i 0.560301i
\(183\) −6791.62 44282.2i −0.202801 1.32229i
\(184\) 27021.6 0.798134
\(185\) 66063.8i 1.93028i
\(186\) 12266.1 1881.26i 0.354552 0.0543781i
\(187\) −94629.4 −2.70609
\(188\) 77390.1i 2.18963i
\(189\) −4439.54 9038.75i −0.124284 0.253038i
\(190\) 56013.9 1.55163
\(191\) 14680.3i 0.402409i 0.979549 + 0.201204i \(0.0644855\pi\)
−0.979549 + 0.201204i \(0.935514\pi\)
\(192\) −28909.1 188491.i −0.784209 5.11314i
\(193\) 70347.1 1.88856 0.944282 0.329137i \(-0.106758\pi\)
0.944282 + 0.329137i \(0.106758\pi\)
\(194\) 26884.2i 0.714321i
\(195\) 51500.2 7898.65i 1.35438 0.207723i
\(196\) 101133. 2.63259
\(197\) 63492.6i 1.63603i 0.575198 + 0.818014i \(0.304925\pi\)
−0.575198 + 0.818014i \(0.695075\pi\)
\(198\) 116794. 36688.8i 2.97914 0.935844i
\(199\) 20815.5 0.525630 0.262815 0.964846i \(-0.415349\pi\)
0.262815 + 0.964846i \(0.415349\pi\)
\(200\) 121981.i 3.04952i
\(201\) −5481.34 35739.0i −0.135673 0.884607i
\(202\) −4592.68 −0.112555
\(203\) 6067.81i 0.147245i
\(204\) −200291. + 30718.9i −4.81283 + 0.738151i
\(205\) 61577.1 1.46525
\(206\) 157017.i 3.70008i
\(207\) 2804.94 + 8929.17i 0.0654610 + 0.208387i
\(208\) −189030. −4.36923
\(209\) 40482.5i 0.926777i
\(210\) 5015.35 + 32700.7i 0.113727 + 0.741513i
\(211\) 49115.2 1.10319 0.551596 0.834112i \(-0.314019\pi\)
0.551596 + 0.834112i \(0.314019\pi\)
\(212\) 39965.8i 0.889237i
\(213\) 2079.74 318.972i 0.0458405 0.00703062i
\(214\) −85344.8 −1.86359
\(215\) 51767.6i 1.11990i
\(216\) 153020. 75158.5i 3.27975 1.61091i
\(217\) 2423.68 0.0514701
\(218\) 39556.4i 0.832347i
\(219\) −2827.80 18437.6i −0.0589603 0.384429i
\(220\) −297988. −6.15679
\(221\) 84121.8i 1.72236i
\(222\) 136394. 20919.0i 2.76752 0.424458i
\(223\) 6583.44 0.132386 0.0661932 0.997807i \(-0.478915\pi\)
0.0661932 + 0.997807i \(0.478915\pi\)
\(224\) 68340.4i 1.36201i
\(225\) 40308.1 12662.0i 0.796208 0.250115i
\(226\) −131638. −2.57730
\(227\) 627.937i 0.0121861i −0.999981 0.00609305i \(-0.998061\pi\)
0.999981 0.00609305i \(-0.00193949\pi\)
\(228\) −13141.6 85684.6i −0.252800 1.64829i
\(229\) 28854.0 0.550219 0.275110 0.961413i \(-0.411286\pi\)
0.275110 + 0.961413i \(0.411286\pi\)
\(230\) 30747.9i 0.581245i
\(231\) 23633.6 3624.71i 0.442899 0.0679281i
\(232\) 102724. 1.90852
\(233\) 22896.0i 0.421742i 0.977514 + 0.210871i \(0.0676300\pi\)
−0.977514 + 0.210871i \(0.932370\pi\)
\(234\) −32614.9 103826.i −0.595641 1.89615i
\(235\) −57269.8 −1.03703
\(236\) 20736.9i 0.372324i
\(237\) 459.185 + 2993.94i 0.00817506 + 0.0533024i
\(238\) −53414.2 −0.942981
\(239\) 106275.i 1.86053i −0.366887 0.930266i \(-0.619576\pi\)
0.366887 0.930266i \(-0.380424\pi\)
\(240\) −333061. + 51082.1i −5.78231 + 0.886841i
\(241\) −88624.7 −1.52588 −0.762941 0.646468i \(-0.776245\pi\)
−0.762941 + 0.646468i \(0.776245\pi\)
\(242\) 175610.i 2.99860i
\(243\) 40719.8 + 42763.1i 0.689593 + 0.724197i
\(244\) 227773. 3.82580
\(245\) 74840.2i 1.24682i
\(246\) −19498.3 127131.i −0.322201 2.10079i
\(247\) −35987.4 −0.589870
\(248\) 41031.3i 0.667132i
\(249\) −6117.61 + 938.267i −0.0986696 + 0.0151331i
\(250\) 27513.8 0.440221
\(251\) 39392.8i 0.625273i −0.949873 0.312636i \(-0.898788\pi\)
0.949873 0.312636i \(-0.101212\pi\)
\(252\) 48845.7 15344.0i 0.769175 0.241622i
\(253\) −22222.2 −0.347173
\(254\) 63077.9i 0.977709i
\(255\) 22732.4 + 148218.i 0.349595 + 2.27940i
\(256\) 347471. 5.30198
\(257\) 47148.3i 0.713838i 0.934135 + 0.356919i \(0.116173\pi\)
−0.934135 + 0.356919i \(0.883827\pi\)
\(258\) 106879. 16392.1i 1.60565 0.246261i
\(259\) 26950.5 0.401760
\(260\) 264900.i 3.91864i
\(261\) 10663.1 + 33944.7i 0.156532 + 0.498300i
\(262\) −167135. −2.43481
\(263\) 11954.9i 0.172836i −0.996259 0.0864181i \(-0.972458\pi\)
0.996259 0.0864181i \(-0.0275421\pi\)
\(264\) 61364.0 + 400101.i 0.880452 + 5.74065i
\(265\) 29575.3 0.421151
\(266\) 22850.7i 0.322950i
\(267\) 50409.0 7731.29i 0.707107 0.108450i
\(268\) 183830. 2.55945
\(269\) 31888.6i 0.440688i 0.975422 + 0.220344i \(0.0707180\pi\)
−0.975422 + 0.220344i \(0.929282\pi\)
\(270\) −85522.7 174121.i −1.17315 2.38850i
\(271\) −76590.4 −1.04288 −0.521441 0.853287i \(-0.674606\pi\)
−0.521441 + 0.853287i \(0.674606\pi\)
\(272\) 544032.i 7.35337i
\(273\) −3222.23 21009.3i −0.0432345 0.281894i
\(274\) −254956. −3.39597
\(275\) 100315.i 1.32649i
\(276\) −47035.1 + 7213.83i −0.617453 + 0.0946996i
\(277\) 50328.2 0.655922 0.327961 0.944691i \(-0.393639\pi\)
0.327961 + 0.944691i \(0.393639\pi\)
\(278\) 146284.i 1.89280i
\(279\) −13558.6 + 4259.19i −0.174183 + 0.0547165i
\(280\) −109387. −1.39525
\(281\) 22681.3i 0.287247i 0.989632 + 0.143624i \(0.0458755\pi\)
−0.989632 + 0.143624i \(0.954124\pi\)
\(282\) 18134.4 + 118239.i 0.228037 + 1.48683i
\(283\) 20552.3 0.256619 0.128309 0.991734i \(-0.459045\pi\)
0.128309 + 0.991734i \(0.459045\pi\)
\(284\) 10697.5i 0.132631i
\(285\) −63407.9 + 9724.95i −0.780645 + 0.119729i
\(286\) 258393. 3.15899
\(287\) 25120.1i 0.304971i
\(288\) 120096. + 382312.i 1.44792 + 4.60927i
\(289\) −158583. −1.89872
\(290\) 116890.i 1.38989i
\(291\) −4667.54 30433.0i −0.0551191 0.359384i
\(292\) 94836.8 1.11227
\(293\) 78542.5i 0.914891i 0.889238 + 0.457446i \(0.151236\pi\)
−0.889238 + 0.457446i \(0.848764\pi\)
\(294\) −154514. + 23698.0i −1.78761 + 0.274169i
\(295\) −15345.6 −0.176336
\(296\) 456254.i 5.20742i
\(297\) −125842. + 61809.3i −1.42663 + 0.700714i
\(298\) 32184.8 0.362425
\(299\) 19754.7i 0.220967i
\(300\) 32564.7 + 212326.i 0.361830 + 2.35918i
\(301\) 21118.4 0.233092
\(302\) 199546.i 2.18790i
\(303\) 5198.93 797.366i 0.0566276 0.00868505i
\(304\) 232737. 2.51836
\(305\) 168555.i 1.81193i
\(306\) 298811. 93866.1i 3.19120 1.00246i
\(307\) −143095. −1.51827 −0.759135 0.650934i \(-0.774378\pi\)
−0.759135 + 0.650934i \(0.774378\pi\)
\(308\) 121563.i 1.28145i
\(309\) −27260.7 177743.i −0.285510 1.86156i
\(310\) 46689.4 0.485842
\(311\) 63503.8i 0.656567i −0.944579 0.328283i \(-0.893530\pi\)
0.944579 0.328283i \(-0.106470\pi\)
\(312\) 355674. 54550.2i 3.65378 0.560385i
\(313\) 119628. 1.22108 0.610542 0.791984i \(-0.290952\pi\)
0.610542 + 0.791984i \(0.290952\pi\)
\(314\) 94136.9i 0.954774i
\(315\) −11354.8 36146.5i −0.114435 0.364288i
\(316\) −15399.9 −0.154221
\(317\) 137237.i 1.36569i −0.730561 0.682847i \(-0.760741\pi\)
0.730561 0.682847i \(-0.239259\pi\)
\(318\) −9364.98 61060.8i −0.0926088 0.603821i
\(319\) −84478.8 −0.830168
\(320\) 717469.i 7.00653i
\(321\) 96610.5 14817.3i 0.937593 0.143800i
\(322\) −12543.5 −0.120978
\(323\) 103572.i 0.992745i
\(324\) −246289. + 171675.i −2.34615 + 1.63538i
\(325\) 89176.5 0.844274
\(326\) 46250.1i 0.435188i
\(327\) −6867.66 44778.0i −0.0642263 0.418764i
\(328\) 425267. 3.95289
\(329\) 23363.0i 0.215842i
\(330\) 455274. 69826.0i 4.18066 0.641194i
\(331\) −118240. −1.07921 −0.539607 0.841917i \(-0.681427\pi\)
−0.539607 + 0.841917i \(0.681427\pi\)
\(332\) 31467.0i 0.285482i
\(333\) −150767. + 47360.7i −1.35962 + 0.427100i
\(334\) 126019. 1.12965
\(335\) 136037.i 1.21218i
\(336\) 20838.7 + 135871.i 0.184583 + 1.20351i
\(337\) 47426.4 0.417600 0.208800 0.977958i \(-0.433044\pi\)
0.208800 + 0.977958i \(0.433044\pi\)
\(338\) 5250.77i 0.0459610i
\(339\) 149015. 22854.6i 1.29667 0.198872i
\(340\) −762385. −6.59503
\(341\) 33743.5i 0.290190i
\(342\) 40156.0 + 127832.i 0.343319 + 1.09291i
\(343\) −63697.5 −0.541419
\(344\) 357520.i 3.02123i
\(345\) 5338.34 + 34806.6i 0.0448506 + 0.292431i
\(346\) 211019. 1.76266
\(347\) 38766.0i 0.321953i −0.986958 0.160976i \(-0.948536\pi\)
0.986958 0.160976i \(-0.0514643\pi\)
\(348\) −178806. + 27423.7i −1.47647 + 0.226448i
\(349\) −174398. −1.43183 −0.715914 0.698189i \(-0.753990\pi\)
−0.715914 + 0.698189i \(0.753990\pi\)
\(350\) 56623.7i 0.462235i
\(351\) 54946.0 + 111868.i 0.445987 + 0.908014i
\(352\) −951466. −7.67906
\(353\) 122807.i 0.985536i −0.870161 0.492768i \(-0.835985\pi\)
0.870161 0.492768i \(-0.164015\pi\)
\(354\) 4859.17 + 31682.4i 0.0387754 + 0.252820i
\(355\) 7916.29 0.0628153
\(356\) 259287.i 2.04588i
\(357\) 60465.0 9273.60i 0.474425 0.0727632i
\(358\) −287944. −2.24669
\(359\) 19827.2i 0.153841i 0.997037 + 0.0769204i \(0.0245087\pi\)
−0.997037 + 0.0769204i \(0.975491\pi\)
\(360\) 611937. 192229.i 4.72173 1.48325i
\(361\) −86012.8 −0.660007
\(362\) 319266.i 2.43633i
\(363\) −30488.9 198791.i −0.231381 1.50863i
\(364\) 108065. 0.815609
\(365\) 70180.6i 0.526783i
\(366\) −347997. + 53372.8i −2.59784 + 0.398435i
\(367\) 3598.99 0.0267207 0.0133604 0.999911i \(-0.495747\pi\)
0.0133604 + 0.999911i \(0.495747\pi\)
\(368\) 127757.i 0.943386i
\(369\) 44144.2 + 140528.i 0.324206 + 1.03207i
\(370\) 519170. 3.79233
\(371\) 12065.1i 0.0876565i
\(372\) −10953.9 71421.0i −0.0791560 0.516107i
\(373\) −51310.8 −0.368800 −0.184400 0.982851i \(-0.559034\pi\)
−0.184400 + 0.982851i \(0.559034\pi\)
\(374\) 743657.i 5.31655i
\(375\) −31145.7 + 4776.86i −0.221481 + 0.0339688i
\(376\) −395520. −2.79765
\(377\) 75098.3i 0.528381i
\(378\) −71032.2 + 34888.7i −0.497132 + 0.244175i
\(379\) 134311. 0.935046 0.467523 0.883981i \(-0.345147\pi\)
0.467523 + 0.883981i \(0.345147\pi\)
\(380\) 326149.i 2.25865i
\(381\) 10951.4 + 71404.3i 0.0754429 + 0.491897i
\(382\) 115367. 0.790595
\(383\) 19879.1i 0.135518i −0.997702 0.0677592i \(-0.978415\pi\)
0.997702 0.0677592i \(-0.0215850\pi\)
\(384\) −777101. + 119185.i −5.27005 + 0.808275i
\(385\) 89958.5 0.606905
\(386\) 552832.i 3.71038i
\(387\) −118141. + 37111.8i −0.788821 + 0.247794i
\(388\) 156537. 1.03981
\(389\) 63588.9i 0.420225i 0.977677 + 0.210113i \(0.0673831\pi\)
−0.977677 + 0.210113i \(0.932617\pi\)
\(390\) −62072.6 404721.i −0.408104 2.66089i
\(391\) −56854.1 −0.371885
\(392\) 516866.i 3.36361i
\(393\) 189197. 29017.4i 1.22498 0.187877i
\(394\) 498965. 3.21423
\(395\) 11396.1i 0.0730403i
\(396\) −213626. 680052.i −1.36227 4.33662i
\(397\) 88252.9 0.559948 0.279974 0.960008i \(-0.409674\pi\)
0.279974 + 0.960008i \(0.409674\pi\)
\(398\) 163581.i 1.03268i
\(399\) 3967.25 + 25867.0i 0.0249198 + 0.162480i
\(400\) −576721. −3.60451
\(401\) 129776.i 0.807062i 0.914966 + 0.403531i \(0.132217\pi\)
−0.914966 + 0.403531i \(0.867783\pi\)
\(402\) −280859. + 43075.8i −1.73795 + 0.266551i
\(403\) −29996.7 −0.184698
\(404\) 26741.6i 0.163841i
\(405\) 127042. + 182258.i 0.774530 + 1.11116i
\(406\) −47684.6 −0.289285
\(407\) 375217.i 2.26513i
\(408\) 156996. + 1.02363e6i 0.943123 + 6.14928i
\(409\) 226902. 1.35641 0.678207 0.734871i \(-0.262757\pi\)
0.678207 + 0.734871i \(0.262757\pi\)
\(410\) 483911.i 2.87871i
\(411\) 288611. 44264.6i 1.70855 0.262043i
\(412\) 914253. 5.38607
\(413\) 6260.19i 0.0367018i
\(414\) 70171.0 22042.9i 0.409409 0.128608i
\(415\) −23286.0 −0.135207
\(416\) 845816.i 4.88753i
\(417\) 25397.3 + 165593.i 0.146054 + 0.952293i
\(418\) −318137. −1.82080
\(419\) 333074.i 1.89720i −0.316477 0.948600i \(-0.602500\pi\)
0.316477 0.948600i \(-0.397500\pi\)
\(420\) 190405. 29202.6i 1.07939 0.165548i
\(421\) −109937. −0.620267 −0.310133 0.950693i \(-0.600374\pi\)
−0.310133 + 0.950693i \(0.600374\pi\)
\(422\) 385978.i 2.16739i
\(423\) −41056.4 130698.i −0.229456 0.730445i
\(424\) 204255. 1.13616
\(425\) 256651.i 1.42090i
\(426\) −2506.68 16343.9i −0.0138128 0.0900608i
\(427\) −68761.4 −0.377128
\(428\) 496933.i 2.71275i
\(429\) −292501. + 44861.3i −1.58933 + 0.243757i
\(430\) 406822. 2.20023
\(431\) 216245.i 1.16410i 0.813153 + 0.582050i \(0.197749\pi\)
−0.813153 + 0.582050i \(0.802251\pi\)
\(432\) −355346. 723473.i −1.90407 3.87663i
\(433\) 107632. 0.574071 0.287035 0.957920i \(-0.407330\pi\)
0.287035 + 0.957920i \(0.407330\pi\)
\(434\) 19046.8i 0.101121i
\(435\) 20294.0 + 132319.i 0.107248 + 0.699269i
\(436\) 230323. 1.21161
\(437\) 24322.2i 0.127362i
\(438\) −144894. + 22222.6i −0.755270 + 0.115837i
\(439\) 148945. 0.772853 0.386427 0.922320i \(-0.373709\pi\)
0.386427 + 0.922320i \(0.373709\pi\)
\(440\) 1.52294e6i 7.86642i
\(441\) 170796. 53652.5i 0.878214 0.275875i
\(442\) 661082. 3.38385
\(443\) 9322.46i 0.0475032i −0.999718 0.0237516i \(-0.992439\pi\)
0.999718 0.0237516i \(-0.00756108\pi\)
\(444\) −121804. 794176.i −0.617867 4.02857i
\(445\) 191876. 0.968949
\(446\) 51736.8i 0.260094i
\(447\) −36433.2 + 5587.81i −0.182340 + 0.0279658i
\(448\) −292689. −1.45831
\(449\) 153270.i 0.760266i 0.924932 + 0.380133i \(0.124122\pi\)
−0.924932 + 0.380133i \(0.875878\pi\)
\(450\) −99506.3 316766.i −0.491389 1.56428i
\(451\) −349734. −1.71943
\(452\) 766483.i 3.75168i
\(453\) −34644.5 225886.i −0.168825 1.10076i
\(454\) −4934.72 −0.0239415
\(455\) 79969.6i 0.386280i
\(456\) −437911. + 67163.0i −2.10599 + 0.322998i
\(457\) 27315.8 0.130792 0.0653961 0.997859i \(-0.479169\pi\)
0.0653961 + 0.997859i \(0.479169\pi\)
\(458\) 226753.i 1.08099i
\(459\) −321958. + 158135.i −1.52818 + 0.750591i
\(460\) −179034. −0.846096
\(461\) 175848.i 0.827436i −0.910405 0.413718i \(-0.864230\pi\)
0.910405 0.413718i \(-0.135770\pi\)
\(462\) −28485.2 185727.i −0.133455 0.870145i
\(463\) −189562. −0.884278 −0.442139 0.896946i \(-0.645780\pi\)
−0.442139 + 0.896946i \(0.645780\pi\)
\(464\) 485675.i 2.25585i
\(465\) −52852.5 + 8106.07i −0.244433 + 0.0374890i
\(466\) 179931. 0.828578
\(467\) 121958.i 0.559213i −0.960115 0.279607i \(-0.909796\pi\)
0.960115 0.279607i \(-0.0902041\pi\)
\(468\) −604539. + 189905.i −2.76015 + 0.867052i
\(469\) −55495.6 −0.252297
\(470\) 450062.i 2.03740i
\(471\) −16343.7 106563.i −0.0736732 0.480358i
\(472\) −105981. −0.475712
\(473\) 294020.i 1.31418i
\(474\) 23528.3 3608.56i 0.104721 0.0160612i
\(475\) −109795. −0.486628
\(476\) 311012.i 1.37266i
\(477\) 21202.3 + 67495.0i 0.0931853 + 0.296644i
\(478\) −835178. −3.65530
\(479\) 304764.i 1.32829i 0.747604 + 0.664145i \(0.231204\pi\)
−0.747604 + 0.664145i \(0.768796\pi\)
\(480\) 228567. + 1.49028e6i 0.992043 + 6.46824i
\(481\) −333553. −1.44170
\(482\) 696469.i 2.99783i
\(483\) 14199.2 2177.76i 0.0608654 0.00933501i
\(484\) 1.02252e6 4.36495
\(485\) 115840.i 0.492463i
\(486\) 336059. 320002.i 1.42280 1.35481i
\(487\) −187435. −0.790302 −0.395151 0.918616i \(-0.629308\pi\)
−0.395151 + 0.918616i \(0.629308\pi\)
\(488\) 1.16409e6i 4.88816i
\(489\) −8029.78 52355.2i −0.0335804 0.218948i
\(490\) −588141. −2.44957
\(491\) 463302.i 1.92177i 0.276950 + 0.960884i \(0.410676\pi\)
−0.276950 + 0.960884i \(0.589324\pi\)
\(492\) −740240. + 113532.i −3.05804 + 0.469015i
\(493\) −216134. −0.889260
\(494\) 282811.i 1.15889i
\(495\) −503248. + 158086.i −2.05386 + 0.645184i
\(496\) 193994. 0.788543
\(497\) 3229.42i 0.0130741i
\(498\) 7373.49 + 48076.0i 0.0297313 + 0.193852i
\(499\) 92062.3 0.369727 0.184863 0.982764i \(-0.440816\pi\)
0.184863 + 0.982764i \(0.440816\pi\)
\(500\) 160203.i 0.640813i
\(501\) −142654. + 21879.1i −0.568341 + 0.0871672i
\(502\) −309573. −1.22845
\(503\) 325821.i 1.28778i 0.765116 + 0.643892i \(0.222681\pi\)
−0.765116 + 0.643892i \(0.777319\pi\)
\(504\) −78419.0 249637.i −0.308717 0.982762i
\(505\) 19789.1 0.0775968
\(506\) 174636.i 0.682076i
\(507\) 911.621 + 5943.88i 0.00354649 + 0.0231235i
\(508\) −367280. −1.42321
\(509\) 392471.i 1.51486i −0.652917 0.757429i \(-0.726455\pi\)
0.652917 0.757429i \(-0.273545\pi\)
\(510\) 1.16479e6 178646.i 4.47824 0.686834i
\(511\) −28629.9 −0.109642
\(512\) 1.33298e6i 5.08490i
\(513\) −67650.4 137734.i −0.257061 0.523367i
\(514\) 370521. 1.40245
\(515\) 676560.i 2.55089i
\(516\) −95445.5 622316.i −0.358473 2.33729i
\(517\) 325270. 1.21692
\(518\) 211794.i 0.789320i
\(519\) −238874. + 36636.4i −0.886817 + 0.136012i
\(520\) 1.35383e6 5.00678
\(521\) 513011.i 1.88995i 0.327137 + 0.944977i \(0.393916\pi\)
−0.327137 + 0.944977i \(0.606084\pi\)
\(522\) 266758. 83797.3i 0.978988 0.307531i
\(523\) −290306. −1.06133 −0.530667 0.847580i \(-0.678059\pi\)
−0.530667 + 0.847580i \(0.678059\pi\)
\(524\) 973168.i 3.54426i
\(525\) −9830.83 64098.2i −0.0356674 0.232556i
\(526\) −93949.1 −0.339564
\(527\) 86330.8i 0.310845i
\(528\) 1.89166e6 290126.i 6.78539 1.04068i
\(529\) 266490. 0.952290
\(530\) 232421.i 0.827416i
\(531\) −11001.2 35020.9i −0.0390167 0.124205i
\(532\) −133051. −0.470106
\(533\) 310900.i 1.09437i
\(534\) −60757.3 396145.i −0.213067 1.38922i
\(535\) 367737. 1.28478
\(536\) 939504.i 3.27016i
\(537\) 325954. 49992.0i 1.13034 0.173361i
\(538\) 250601. 0.865800
\(539\) 425063.i 1.46311i
\(540\) −1.01385e6 + 497968.i −3.47684 + 1.70771i
\(541\) −42782.2 −0.146173 −0.0730867 0.997326i \(-0.523285\pi\)
−0.0730867 + 0.997326i \(0.523285\pi\)
\(542\) 601895.i 2.04891i
\(543\) 55429.9 + 361410.i 0.187994 + 1.22575i
\(544\) −2.43427e6 −8.22566
\(545\) 170442.i 0.573832i
\(546\) −165104. + 25322.3i −0.553825 + 0.0849410i
\(547\) 348295. 1.16405 0.582026 0.813170i \(-0.302260\pi\)
0.582026 + 0.813170i \(0.302260\pi\)
\(548\) 1.48452e6i 4.94339i
\(549\) 384667. 120836.i 1.27626 0.400915i
\(550\) 788341. 2.60609
\(551\) 92462.2i 0.304552i
\(552\) 36868.0 + 240384.i 0.120996 + 0.788909i
\(553\) 4649.00 0.0152023
\(554\) 395511.i 1.28866i
\(555\) −587702. + 90136.6i −1.90797 + 0.292628i
\(556\) −851757. −2.75528
\(557\) 570919.i 1.84020i −0.391689 0.920098i \(-0.628109\pi\)
0.391689 0.920098i \(-0.371891\pi\)
\(558\) 33471.4 + 106552.i 0.107499 + 0.342210i
\(559\) −261372. −0.836441
\(560\) 517178.i 1.64917i
\(561\) −129111. 841821.i −0.410240 2.67482i
\(562\) 178244. 0.564343
\(563\) 65361.5i 0.206208i 0.994671 + 0.103104i \(0.0328774\pi\)
−0.994671 + 0.103104i \(0.967123\pi\)
\(564\) 688461. 105590.i 2.16432 0.331944i
\(565\) 567208. 1.77683
\(566\) 161513.i 0.504168i
\(567\) 74351.3 51826.4i 0.231272 0.161207i
\(568\) 54672.0 0.169460
\(569\) 384477.i 1.18753i 0.804637 + 0.593767i \(0.202360\pi\)
−0.804637 + 0.593767i \(0.797640\pi\)
\(570\) 76424.7 + 498298.i 0.235225 + 1.53370i
\(571\) −54990.0 −0.168660 −0.0843298 0.996438i \(-0.526875\pi\)
−0.0843298 + 0.996438i \(0.526875\pi\)
\(572\) 1.50453e6i 4.59842i
\(573\) −130595. + 20029.6i −0.397758 + 0.0610046i
\(574\) −197410. −0.599163
\(575\) 60270.3i 0.182292i
\(576\) 1.63737e6 514349.i 4.93516 1.55029i
\(577\) 421721. 1.26670 0.633350 0.773866i \(-0.281680\pi\)
0.633350 + 0.773866i \(0.281680\pi\)
\(578\) 1.24624e6i 3.73032i
\(579\) 95980.8 + 625807.i 0.286304 + 1.86674i
\(580\) −680606. −2.02320
\(581\) 9499.44i 0.0281414i
\(582\) −239161. + 36680.5i −0.706065 + 0.108290i
\(583\) −167976. −0.494209
\(584\) 484686.i 1.42113i
\(585\) 140533. + 447368.i 0.410644 + 1.30723i
\(586\) 617236. 1.79745
\(587\) 228158.i 0.662156i −0.943603 0.331078i \(-0.892588\pi\)
0.943603 0.331078i \(-0.107412\pi\)
\(588\) 137985. + 899681.i 0.399097 + 2.60216i
\(589\) 36932.4 0.106458
\(590\) 120596.i 0.346440i
\(591\) −564829. + 86628.6i −1.61712 + 0.248020i
\(592\) 2.15715e6 6.15512
\(593\) 205389.i 0.584073i 0.956407 + 0.292037i \(0.0943329\pi\)
−0.956407 + 0.292037i \(0.905667\pi\)
\(594\) 485736. + 988942.i 1.37666 + 2.80284i
\(595\) 230153. 0.650105
\(596\) 187401.i 0.527568i
\(597\) 28400.4 + 185174.i 0.0796848 + 0.519554i
\(598\) 155244. 0.434124
\(599\) 88620.3i 0.246990i 0.992345 + 0.123495i \(0.0394103\pi\)
−0.992345 + 0.123495i \(0.960590\pi\)
\(600\) 1.08514e6 166429.i 3.01428 0.462304i
\(601\) −363771. −1.00711 −0.503557 0.863962i \(-0.667976\pi\)
−0.503557 + 0.863962i \(0.667976\pi\)
\(602\) 165961.i 0.457946i
\(603\) 310455. 97523.7i 0.853815 0.268210i
\(604\) 1.16188e6 3.18485
\(605\) 756676.i 2.06728i
\(606\) −6266.20 40856.4i −0.0170631 0.111254i
\(607\) −150200. −0.407653 −0.203827 0.979007i \(-0.565338\pi\)
−0.203827 + 0.979007i \(0.565338\pi\)
\(608\) 1.04138e6i 2.81710i
\(609\) 53979.1 8278.85i 0.145543 0.0223221i
\(610\) −1.32461e6 −3.55983
\(611\) 289152.i 0.774541i
\(612\) −546549. 1.73987e6i −1.45924 4.64530i
\(613\) 90472.5 0.240766 0.120383 0.992728i \(-0.461588\pi\)
0.120383 + 0.992728i \(0.461588\pi\)
\(614\) 1.12453e6i 2.98288i
\(615\) 84015.1 + 547789.i 0.222130 + 1.44831i
\(616\) 621277. 1.63728
\(617\) 42407.5i 0.111397i −0.998448 0.0556984i \(-0.982261\pi\)
0.998448 0.0556984i \(-0.0177385\pi\)
\(618\) −1.39682e6 + 214232.i −3.65732 + 0.560928i
\(619\) 57960.9 0.151270 0.0756352 0.997136i \(-0.475902\pi\)
0.0756352 + 0.997136i \(0.475902\pi\)
\(620\) 271856.i 0.707222i
\(621\) −75606.7 + 37135.5i −0.196055 + 0.0962956i
\(622\) −499052. −1.28993
\(623\) 78275.2i 0.201673i
\(624\) −257911. 1.68161e6i −0.662370 4.31873i
\(625\) −444556. −1.13806
\(626\) 940114.i 2.39901i
\(627\) 360132. 55233.9i 0.916065 0.140498i
\(628\) 548126. 1.38983
\(629\) 959969.i 2.42636i
\(630\) −284062. + 89232.9i −0.715701 + 0.224825i
\(631\) −214265. −0.538136 −0.269068 0.963121i \(-0.586716\pi\)
−0.269068 + 0.963121i \(0.586716\pi\)
\(632\) 78704.5i 0.197045i
\(633\) 67012.2 + 436928.i 0.167242 + 1.09044i
\(634\) −1.07850e6 −2.68312
\(635\) 271793.i 0.674047i
\(636\) −355535. + 54528.9i −0.878959 + 0.134807i
\(637\) 377865. 0.931231
\(638\) 663887.i 1.63100i
\(639\) 5675.14 + 18066.1i 0.0138987 + 0.0442449i
\(640\) −2.95795e6 −7.22156
\(641\) 55617.2i 0.135361i −0.997707 0.0676804i \(-0.978440\pi\)
0.997707 0.0676804i \(-0.0215598\pi\)
\(642\) −116443. 759226.i −0.282517 1.84205i
\(643\) 173926. 0.420672 0.210336 0.977629i \(-0.432544\pi\)
0.210336 + 0.977629i \(0.432544\pi\)
\(644\) 73036.2i 0.176103i
\(645\) −460523. + 70631.0i −1.10696 + 0.169776i
\(646\) −813934. −1.95040
\(647\) 698038.i 1.66752i 0.552128 + 0.833759i \(0.313816\pi\)
−0.552128 + 0.833759i \(0.686184\pi\)
\(648\) 877387. + 1.25872e6i 2.08949 + 2.99763i
\(649\) 87157.3 0.206926
\(650\) 700804.i 1.65871i
\(651\) 3306.84 + 21561.0i 0.00780281 + 0.0508753i
\(652\) 269298. 0.633487
\(653\) 13267.9i 0.0311154i 0.999879 + 0.0155577i \(0.00495237\pi\)
−0.999879 + 0.0155577i \(0.995048\pi\)
\(654\) −351893. + 53970.4i −0.822727 + 0.126183i
\(655\) 720159. 1.67859
\(656\) 2.01065e6i 4.67227i
\(657\) 160162. 50312.0i 0.371047 0.116558i
\(658\) 183601. 0.424056
\(659\) 481694.i 1.10917i −0.832125 0.554587i \(-0.812876\pi\)
0.832125 0.554587i \(-0.187124\pi\)
\(660\) −406572. 2.65090e6i −0.933361 6.08563i
\(661\) 586120. 1.34148 0.670739 0.741693i \(-0.265977\pi\)
0.670739 + 0.741693i \(0.265977\pi\)
\(662\) 929201.i 2.12028i
\(663\) −748346. + 114775.i −1.70245 + 0.261108i
\(664\) −160819. −0.364756
\(665\) 98459.8i 0.222646i
\(666\) 372190. + 1.18482e6i 0.839105 + 2.67119i
\(667\) −50755.5 −0.114086
\(668\) 733766.i 1.64439i
\(669\) 8982.37 + 58566.2i 0.0200696 + 0.130856i
\(670\) −1.06906e6 −2.38151
\(671\) 957328.i 2.12626i
\(672\) 607955. 93242.9i 1.34627 0.206480i
\(673\) 148675. 0.328251 0.164126 0.986439i \(-0.447520\pi\)
0.164126 + 0.986439i \(0.447520\pi\)
\(674\) 372706.i 0.820440i
\(675\) 167637. + 341304.i 0.367928 + 0.749089i
\(676\) −30573.4 −0.0669037
\(677\) 315103.i 0.687504i 0.939060 + 0.343752i \(0.111698\pi\)
−0.939060 + 0.343752i \(0.888302\pi\)
\(678\) −179606. 1.17105e6i −0.390716 2.54751i
\(679\) −47256.4 −0.102499
\(680\) 3.89635e6i 8.42635i
\(681\) 5586.12 856.750i 0.0120452 0.00184740i
\(682\) −265178. −0.570123
\(683\) 71563.2i 0.153408i −0.997054 0.0767040i \(-0.975560\pi\)
0.997054 0.0767040i \(-0.0244397\pi\)
\(684\) 744318. 233814.i 1.59091 0.499757i
\(685\) 1.09857e6 2.34123
\(686\) 500574.i 1.06370i
\(687\) 39368.1 + 256685.i 0.0834125 + 0.543860i
\(688\) 1.69034e6 3.57106
\(689\) 149324.i 0.314552i
\(690\) 273532. 41952.0i 0.574527 0.0881160i
\(691\) −600494. −1.25763 −0.628814 0.777556i \(-0.716459\pi\)
−0.628814 + 0.777556i \(0.716459\pi\)
\(692\) 1.22869e6i 2.56584i
\(693\) 64490.7 + 205298.i 0.134286 + 0.427483i
\(694\) −304648. −0.632527
\(695\) 630312.i 1.30493i
\(696\) 140155. + 913831.i 0.289329 + 1.88646i
\(697\) −894773. −1.84182
\(698\) 1.37053e6i 2.81305i
\(699\) −203682. + 31239.0i −0.416868 + 0.0639355i
\(700\) 329700. 0.672857
\(701\) 743521.i 1.51306i −0.653957 0.756531i \(-0.726892\pi\)
0.653957 0.756531i \(-0.273108\pi\)
\(702\) 879131. 431800.i 1.78394 0.876211i
\(703\) 410675. 0.830975
\(704\) 4.07494e6i 8.22198i
\(705\) −78138.3 509471.i −0.157212 1.02504i
\(706\) −965091. −1.93624
\(707\) 8072.90i 0.0161507i
\(708\) 184475. 28293.2i 0.368021 0.0564438i
\(709\) 578585. 1.15100 0.575499 0.817802i \(-0.304808\pi\)
0.575499 + 0.817802i \(0.304808\pi\)
\(710\) 62211.2i 0.123410i
\(711\) −26007.5 + 8169.80i −0.0514470 + 0.0161612i
\(712\) 1.32515e6 2.61399
\(713\) 20273.4i 0.0398793i
\(714\) −72877.7 475172.i −0.142955 0.932082i
\(715\) −1.11337e6 −2.17785
\(716\) 1.67660e6i 3.27042i
\(717\) 945424. 145001.i 1.83903 0.282054i
\(718\) 155814. 0.302244
\(719\) 754589.i 1.45966i 0.683627 + 0.729832i \(0.260402\pi\)
−0.683627 + 0.729832i \(0.739598\pi\)
\(720\) −908850. 2.89321e6i −1.75318 5.58104i
\(721\) −276000. −0.530932
\(722\) 675942.i 1.29669i
\(723\) −120919. 788404.i −0.231322 1.50825i
\(724\) −1.85897e6 −3.54647
\(725\) 229121.i 0.435901i
\(726\) −1.56222e6 + 239600.i −2.96395 + 0.454584i
\(727\) −239352. −0.452864 −0.226432 0.974027i \(-0.572706\pi\)
−0.226432 + 0.974027i \(0.572706\pi\)
\(728\) 552291.i 1.04209i
\(729\) −324862. + 420588.i −0.611285 + 0.791410i
\(730\) −551523. −1.03495
\(731\) 752231.i 1.40772i
\(732\) 310771. + 2.02626e6i 0.579986 + 3.78158i
\(733\) 231674. 0.431191 0.215595 0.976483i \(-0.430831\pi\)
0.215595 + 0.976483i \(0.430831\pi\)
\(734\) 28283.1i 0.0524970i
\(735\) 665777. 102111.i 1.23241 0.189016i
\(736\) −571649. −1.05529
\(737\) 772635.i 1.42246i
\(738\) 1.10435e6 346913.i 2.02766 0.636954i
\(739\) −731305. −1.33909 −0.669545 0.742772i \(-0.733511\pi\)
−0.669545 + 0.742772i \(0.733511\pi\)
\(740\) 3.02294e6i 5.52035i
\(741\) −49100.8 320143.i −0.0894236 0.583053i
\(742\) −94815.3 −0.172215
\(743\) 797019.i 1.44375i −0.692025 0.721873i \(-0.743281\pi\)
0.692025 0.721873i \(-0.256719\pi\)
\(744\) −365013. + 55982.6i −0.659421 + 0.101136i
\(745\) −138679. −0.249861
\(746\) 403232.i 0.724565i
\(747\) −16693.6 53142.0i −0.0299164 0.0952350i
\(748\) 4.33005e6 7.73909
\(749\) 150017.i 0.267410i
\(750\) 37539.5 + 244762.i 0.0667369 + 0.435133i
\(751\) 1.02196e6 1.81198 0.905991 0.423296i \(-0.139127\pi\)
0.905991 + 0.423296i \(0.139127\pi\)
\(752\) 1.87000e6i 3.30679i
\(753\) 350438. 53747.1i 0.618046 0.0947906i
\(754\) 590169. 1.03809
\(755\) 859811.i 1.50837i
\(756\) 203144. + 413595.i 0.355436 + 0.723655i
\(757\) 711548. 1.24169 0.620844 0.783934i \(-0.286790\pi\)
0.620844 + 0.783934i \(0.286790\pi\)
\(758\) 1.05550e6i 1.83704i
\(759\) −30319.7 197688.i −0.0526310 0.343160i
\(760\) −1.66686e6 −2.88584
\(761\) 1.11176e6i 1.91973i 0.280459 + 0.959866i \(0.409513\pi\)
−0.280459 + 0.959866i \(0.590487\pi\)
\(762\) 561140. 86062.7i 0.966409 0.148219i
\(763\) −69531.3 −0.119435
\(764\) 671740.i 1.15084i
\(765\) −1.28753e6 + 404454.i −2.20006 + 0.691109i
\(766\) −156222. −0.266247
\(767\) 77479.4i 0.131703i
\(768\) 474085. + 3.09109e6i 0.803774 + 5.24070i
\(769\) 864703. 1.46223 0.731113 0.682257i \(-0.239001\pi\)
0.731113 + 0.682257i \(0.239001\pi\)
\(770\) 706950.i 1.19236i
\(771\) −419430. + 64328.6i −0.705588 + 0.108217i
\(772\) −3.21894e6 −5.40105
\(773\) 770578.i 1.28961i −0.764348 0.644804i \(-0.776939\pi\)
0.764348 0.644804i \(-0.223061\pi\)
\(774\) 291648. + 928425.i 0.486830 + 1.54976i
\(775\) −91518.2 −0.152372
\(776\) 800019.i 1.32855i
\(777\) 36770.9 + 239751.i 0.0609063 + 0.397116i
\(778\) 499721. 0.825598
\(779\) 382785.i 0.630782i
\(780\) −2.35654e6 + 361426.i −3.87335 + 0.594061i
\(781\) −44961.5 −0.0737120
\(782\) 446795.i 0.730626i