Properties

Label 177.5.b.a.119.17
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 119.17
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.62

$q$-expansion

\(f(q)\) \(=\) \(q-5.25412i q^{2} +(4.74448 - 7.64787i) q^{3} -11.6058 q^{4} -7.04330i q^{5} +(-40.1829 - 24.9281i) q^{6} +35.8552 q^{7} -23.0875i q^{8} +(-35.9798 - 72.5703i) q^{9} +O(q^{10})\) \(q-5.25412i q^{2} +(4.74448 - 7.64787i) q^{3} -11.6058 q^{4} -7.04330i q^{5} +(-40.1829 - 24.9281i) q^{6} +35.8552 q^{7} -23.0875i q^{8} +(-35.9798 - 72.5703i) q^{9} -37.0064 q^{10} -53.7614i q^{11} +(-55.0636 + 88.7598i) q^{12} +72.1398 q^{13} -188.388i q^{14} +(-53.8662 - 33.4168i) q^{15} -306.998 q^{16} -83.3038i q^{17} +(-381.294 + 189.042i) q^{18} -387.051 q^{19} +81.7433i q^{20} +(170.114 - 274.216i) q^{21} -282.469 q^{22} +137.560i q^{23} +(-176.570 - 109.538i) q^{24} +575.392 q^{25} -379.032i q^{26} +(-725.714 - 69.1399i) q^{27} -416.129 q^{28} +105.343i q^{29} +(-175.576 + 283.020i) q^{30} -942.385 q^{31} +1243.61i q^{32} +(-411.160 - 255.070i) q^{33} -437.689 q^{34} -252.539i q^{35} +(417.575 + 842.239i) q^{36} +2041.28 q^{37} +2033.61i q^{38} +(342.266 - 551.716i) q^{39} -162.612 q^{40} -119.053i q^{41} +(-1440.76 - 893.802i) q^{42} +3203.63 q^{43} +623.946i q^{44} +(-511.134 + 253.416i) q^{45} +722.756 q^{46} +1973.51i q^{47} +(-1456.55 + 2347.88i) q^{48} -1115.41 q^{49} -3023.18i q^{50} +(-637.097 - 395.233i) q^{51} -837.242 q^{52} +1181.07i q^{53} +(-363.269 + 3812.99i) q^{54} -378.658 q^{55} -827.808i q^{56} +(-1836.36 + 2960.11i) q^{57} +553.483 q^{58} -453.188i q^{59} +(625.162 + 387.829i) q^{60} -3111.42 q^{61} +4951.41i q^{62} +(-1290.06 - 2602.02i) q^{63} +1622.09 q^{64} -508.102i q^{65} +(-1340.17 + 2160.29i) q^{66} +4166.52 q^{67} +966.810i q^{68} +(1052.04 + 652.650i) q^{69} -1326.87 q^{70} -1448.75i q^{71} +(-1675.47 + 830.685i) q^{72} -2159.42 q^{73} -10725.2i q^{74} +(2729.94 - 4400.52i) q^{75} +4492.04 q^{76} -1927.63i q^{77} +(-2898.78 - 1798.31i) q^{78} +2141.63 q^{79} +2162.28i q^{80} +(-3971.91 + 5222.13i) q^{81} -625.522 q^{82} -4416.32i q^{83} +(-1974.32 + 3182.50i) q^{84} -586.733 q^{85} -16832.3i q^{86} +(805.646 + 499.796i) q^{87} -1241.22 q^{88} -13821.0i q^{89} +(1331.48 + 2685.56i) q^{90} +2586.59 q^{91} -1596.50i q^{92} +(-4471.13 + 7207.24i) q^{93} +10369.1 q^{94} +2726.11i q^{95} +(9510.93 + 5900.26i) q^{96} +10753.5 q^{97} +5860.48i q^{98} +(-3901.48 + 1934.32i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.25412i 1.31353i −0.754095 0.656766i \(-0.771924\pi\)
0.754095 0.656766i \(-0.228076\pi\)
\(3\) 4.74448 7.64787i 0.527165 0.849763i
\(4\) −11.6058 −0.725364
\(5\) 7.04330i 0.281732i −0.990029 0.140866i \(-0.955011\pi\)
0.990029 0.140866i \(-0.0449886\pi\)
\(6\) −40.1829 24.9281i −1.11619 0.692447i
\(7\) 35.8552 0.731738 0.365869 0.930666i \(-0.380772\pi\)
0.365869 + 0.930666i \(0.380772\pi\)
\(8\) 23.0875i 0.360743i
\(9\) −35.9798 72.5703i −0.444195 0.895930i
\(10\) −37.0064 −0.370064
\(11\) 53.7614i 0.444309i −0.975011 0.222155i \(-0.928691\pi\)
0.975011 0.222155i \(-0.0713090\pi\)
\(12\) −55.0636 + 88.7598i −0.382386 + 0.616388i
\(13\) 72.1398 0.426863 0.213431 0.976958i \(-0.431536\pi\)
0.213431 + 0.976958i \(0.431536\pi\)
\(14\) 188.388i 0.961161i
\(15\) −53.8662 33.4168i −0.239405 0.148519i
\(16\) −306.998 −1.19921
\(17\) 83.3038i 0.288248i −0.989560 0.144124i \(-0.953964\pi\)
0.989560 0.144124i \(-0.0460365\pi\)
\(18\) −381.294 + 189.042i −1.17683 + 0.583464i
\(19\) −387.051 −1.07216 −0.536081 0.844166i \(-0.680096\pi\)
−0.536081 + 0.844166i \(0.680096\pi\)
\(20\) 81.7433i 0.204358i
\(21\) 170.114 274.216i 0.385747 0.621804i
\(22\) −282.469 −0.583614
\(23\) 137.560i 0.260037i 0.991512 + 0.130019i \(0.0415037\pi\)
−0.991512 + 0.130019i \(0.958496\pi\)
\(24\) −176.570 109.538i −0.306546 0.190171i
\(25\) 575.392 0.920627
\(26\) 379.032i 0.560698i
\(27\) −725.714 69.1399i −0.995492 0.0948421i
\(28\) −416.129 −0.530777
\(29\) 105.343i 0.125259i 0.998037 + 0.0626293i \(0.0199486\pi\)
−0.998037 + 0.0626293i \(0.980051\pi\)
\(30\) −175.576 + 283.020i −0.195084 + 0.314466i
\(31\) −942.385 −0.980630 −0.490315 0.871545i \(-0.663118\pi\)
−0.490315 + 0.871545i \(0.663118\pi\)
\(32\) 1243.61i 1.21446i
\(33\) −411.160 255.070i −0.377558 0.234224i
\(34\) −437.689 −0.378623
\(35\) 252.539i 0.206154i
\(36\) 417.575 + 842.239i 0.322203 + 0.649876i
\(37\) 2041.28 1.49108 0.745538 0.666463i \(-0.232193\pi\)
0.745538 + 0.666463i \(0.232193\pi\)
\(38\) 2033.61i 1.40832i
\(39\) 342.266 551.716i 0.225027 0.362732i
\(40\) −162.612 −0.101633
\(41\) 119.053i 0.0708230i −0.999373 0.0354115i \(-0.988726\pi\)
0.999373 0.0354115i \(-0.0112742\pi\)
\(42\) −1440.76 893.802i −0.816760 0.506690i
\(43\) 3203.63 1.73263 0.866315 0.499498i \(-0.166482\pi\)
0.866315 + 0.499498i \(0.166482\pi\)
\(44\) 623.946i 0.322286i
\(45\) −511.134 + 253.416i −0.252412 + 0.125144i
\(46\) 722.756 0.341567
\(47\) 1973.51i 0.893396i 0.894685 + 0.446698i \(0.147400\pi\)
−0.894685 + 0.446698i \(0.852600\pi\)
\(48\) −1456.55 + 2347.88i −0.632182 + 1.01905i
\(49\) −1115.41 −0.464559
\(50\) 3023.18i 1.20927i
\(51\) −637.097 395.233i −0.244943 0.151954i
\(52\) −837.242 −0.309631
\(53\) 1181.07i 0.420461i 0.977652 + 0.210230i \(0.0674214\pi\)
−0.977652 + 0.210230i \(0.932579\pi\)
\(54\) −363.269 + 3812.99i −0.124578 + 1.30761i
\(55\) −378.658 −0.125176
\(56\) 827.808i 0.263969i
\(57\) −1836.36 + 2960.11i −0.565206 + 0.911085i
\(58\) 553.483 0.164531
\(59\) 453.188i 0.130189i
\(60\) 625.162 + 387.829i 0.173656 + 0.107730i
\(61\) −3111.42 −0.836179 −0.418090 0.908406i \(-0.637300\pi\)
−0.418090 + 0.908406i \(0.637300\pi\)
\(62\) 4951.41i 1.28809i
\(63\) −1290.06 2602.02i −0.325035 0.655587i
\(64\) 1622.09 0.396018
\(65\) 508.102i 0.120261i
\(66\) −1340.17 + 2160.29i −0.307661 + 0.495934i
\(67\) 4166.52 0.928162 0.464081 0.885793i \(-0.346385\pi\)
0.464081 + 0.885793i \(0.346385\pi\)
\(68\) 966.810i 0.209085i
\(69\) 1052.04 + 652.650i 0.220970 + 0.137083i
\(70\) −1326.87 −0.270790
\(71\) 1448.75i 0.287393i −0.989622 0.143696i \(-0.954101\pi\)
0.989622 0.143696i \(-0.0458989\pi\)
\(72\) −1675.47 + 830.685i −0.323200 + 0.160240i
\(73\) −2159.42 −0.405220 −0.202610 0.979260i \(-0.564942\pi\)
−0.202610 + 0.979260i \(0.564942\pi\)
\(74\) 10725.2i 1.95858i
\(75\) 2729.94 4400.52i 0.485322 0.782315i
\(76\) 4492.04 0.777709
\(77\) 1927.63i 0.325118i
\(78\) −2898.78 1798.31i −0.476460 0.295580i
\(79\) 2141.63 0.343155 0.171578 0.985171i \(-0.445114\pi\)
0.171578 + 0.985171i \(0.445114\pi\)
\(80\) 2162.28i 0.337856i
\(81\) −3971.91 + 5222.13i −0.605382 + 0.795935i
\(82\) −625.522 −0.0930282
\(83\) 4416.32i 0.641068i −0.947237 0.320534i \(-0.896138\pi\)
0.947237 0.320534i \(-0.103862\pi\)
\(84\) −1974.32 + 3182.50i −0.279807 + 0.451035i
\(85\) −586.733 −0.0812088
\(86\) 16832.3i 2.27586i
\(87\) 805.646 + 499.796i 0.106440 + 0.0660319i
\(88\) −1241.22 −0.160281
\(89\) 13821.0i 1.74485i −0.488749 0.872425i \(-0.662547\pi\)
0.488749 0.872425i \(-0.337453\pi\)
\(90\) 1331.48 + 2685.56i 0.164380 + 0.331551i
\(91\) 2586.59 0.312352
\(92\) 1596.50i 0.188622i
\(93\) −4471.13 + 7207.24i −0.516953 + 0.833303i
\(94\) 10369.1 1.17350
\(95\) 2726.11i 0.302062i
\(96\) 9510.93 + 5900.26i 1.03200 + 0.640219i
\(97\) 10753.5 1.14290 0.571448 0.820638i \(-0.306382\pi\)
0.571448 + 0.820638i \(0.306382\pi\)
\(98\) 5860.48i 0.610212i
\(99\) −3901.48 + 1934.32i −0.398070 + 0.197360i
\(100\) −6677.90 −0.667790
\(101\) 6746.90i 0.661396i −0.943737 0.330698i \(-0.892716\pi\)
0.943737 0.330698i \(-0.107284\pi\)
\(102\) −2076.61 + 3347.38i −0.199597 + 0.321740i
\(103\) 4079.24 0.384508 0.192254 0.981345i \(-0.438420\pi\)
0.192254 + 0.981345i \(0.438420\pi\)
\(104\) 1665.53i 0.153988i
\(105\) −1931.38 1198.16i −0.175182 0.108677i
\(106\) 6205.51 0.552288
\(107\) 10692.5i 0.933926i −0.884277 0.466963i \(-0.845348\pi\)
0.884277 0.466963i \(-0.154652\pi\)
\(108\) 8422.51 + 802.425i 0.722095 + 0.0687950i
\(109\) −3718.61 −0.312988 −0.156494 0.987679i \(-0.550019\pi\)
−0.156494 + 0.987679i \(0.550019\pi\)
\(110\) 1989.51i 0.164423i
\(111\) 9684.83 15611.5i 0.786043 1.26706i
\(112\) −11007.5 −0.877509
\(113\) 12359.6i 0.967936i −0.875086 0.483968i \(-0.839195\pi\)
0.875086 0.483968i \(-0.160805\pi\)
\(114\) 15552.8 + 9648.44i 1.19674 + 0.742416i
\(115\) 968.874 0.0732608
\(116\) 1222.59i 0.0908582i
\(117\) −2595.58 5235.21i −0.189610 0.382439i
\(118\) −2381.10 −0.171007
\(119\) 2986.87i 0.210922i
\(120\) −771.511 + 1243.64i −0.0535772 + 0.0863637i
\(121\) 11750.7 0.802589
\(122\) 16347.8i 1.09835i
\(123\) −910.505 564.847i −0.0601828 0.0373354i
\(124\) 10937.2 0.711314
\(125\) 8454.72i 0.541102i
\(126\) −13671.4 + 6778.15i −0.861133 + 0.426943i
\(127\) 6349.54 0.393672 0.196836 0.980436i \(-0.436933\pi\)
0.196836 + 0.980436i \(0.436933\pi\)
\(128\) 11375.0i 0.694276i
\(129\) 15199.6 24501.0i 0.913381 1.47233i
\(130\) −2669.63 −0.157966
\(131\) 14041.4i 0.818216i −0.912486 0.409108i \(-0.865840\pi\)
0.912486 0.409108i \(-0.134160\pi\)
\(132\) 4771.86 + 2960.30i 0.273867 + 0.169898i
\(133\) −13877.8 −0.784543
\(134\) 21891.4i 1.21917i
\(135\) −486.972 + 5111.42i −0.0267200 + 0.280462i
\(136\) −1923.28 −0.103984
\(137\) 13528.0i 0.720765i 0.932805 + 0.360383i \(0.117354\pi\)
−0.932805 + 0.360383i \(0.882646\pi\)
\(138\) 3429.10 5527.55i 0.180062 0.290251i
\(139\) 2624.62 0.135843 0.0679214 0.997691i \(-0.478363\pi\)
0.0679214 + 0.997691i \(0.478363\pi\)
\(140\) 2930.92i 0.149537i
\(141\) 15093.2 + 9363.29i 0.759175 + 0.470967i
\(142\) −7611.89 −0.377499
\(143\) 3878.34i 0.189659i
\(144\) 11045.7 + 22279.0i 0.532684 + 1.07441i
\(145\) 741.959 0.0352894
\(146\) 11345.8i 0.532269i
\(147\) −5292.02 + 8530.48i −0.244899 + 0.394765i
\(148\) −23690.8 −1.08157
\(149\) 27527.8i 1.23994i 0.784627 + 0.619968i \(0.212854\pi\)
−0.784627 + 0.619968i \(0.787146\pi\)
\(150\) −23120.9 14343.4i −1.02760 0.637486i
\(151\) −17919.6 −0.785915 −0.392958 0.919557i \(-0.628548\pi\)
−0.392958 + 0.919557i \(0.628548\pi\)
\(152\) 8936.05i 0.386775i
\(153\) −6045.39 + 2997.25i −0.258250 + 0.128039i
\(154\) −10128.0 −0.427053
\(155\) 6637.50i 0.276275i
\(156\) −3972.28 + 6403.12i −0.163227 + 0.263113i
\(157\) −18785.5 −0.762118 −0.381059 0.924551i \(-0.624441\pi\)
−0.381059 + 0.924551i \(0.624441\pi\)
\(158\) 11252.4i 0.450745i
\(159\) 9032.70 + 5603.58i 0.357292 + 0.221652i
\(160\) 8759.08 0.342152
\(161\) 4932.23i 0.190279i
\(162\) 27437.7 + 20868.9i 1.04549 + 0.795188i
\(163\) 29203.1 1.09914 0.549570 0.835447i \(-0.314791\pi\)
0.549570 + 0.835447i \(0.314791\pi\)
\(164\) 1381.71i 0.0513725i
\(165\) −1796.53 + 2895.92i −0.0659884 + 0.106370i
\(166\) −23203.9 −0.842063
\(167\) 14056.6i 0.504018i 0.967725 + 0.252009i \(0.0810913\pi\)
−0.967725 + 0.252009i \(0.918909\pi\)
\(168\) −6330.97 3927.52i −0.224311 0.139155i
\(169\) −23356.8 −0.817788
\(170\) 3082.77i 0.106670i
\(171\) 13926.0 + 28088.4i 0.476249 + 0.960583i
\(172\) −37180.8 −1.25679
\(173\) 10847.8i 0.362452i 0.983441 + 0.181226i \(0.0580066\pi\)
−0.983441 + 0.181226i \(0.941993\pi\)
\(174\) 2625.99 4232.96i 0.0867350 0.139813i
\(175\) 20630.8 0.673658
\(176\) 16504.6i 0.532821i
\(177\) −3465.92 2150.14i −0.110630 0.0686310i
\(178\) −72617.0 −2.29191
\(179\) 17664.8i 0.551317i −0.961256 0.275659i \(-0.911104\pi\)
0.961256 0.275659i \(-0.0888960\pi\)
\(180\) 5932.14 2941.11i 0.183091 0.0907749i
\(181\) 53290.1 1.62663 0.813316 0.581823i \(-0.197660\pi\)
0.813316 + 0.581823i \(0.197660\pi\)
\(182\) 13590.2i 0.410284i
\(183\) −14762.1 + 23795.8i −0.440804 + 0.710554i
\(184\) 3175.92 0.0938066
\(185\) 14377.4i 0.420084i
\(186\) 37867.7 + 23491.9i 1.09457 + 0.679034i
\(187\) −4478.53 −0.128071
\(188\) 22904.2i 0.648037i
\(189\) −26020.6 2479.02i −0.728440 0.0693996i
\(190\) 14323.3 0.396768
\(191\) 45052.3i 1.23495i 0.786589 + 0.617476i \(0.211845\pi\)
−0.786589 + 0.617476i \(0.788155\pi\)
\(192\) 7695.97 12405.5i 0.208767 0.336521i
\(193\) 46146.6 1.23887 0.619434 0.785048i \(-0.287362\pi\)
0.619434 + 0.785048i \(0.287362\pi\)
\(194\) 56500.3i 1.50123i
\(195\) −3885.90 2410.68i −0.102193 0.0633973i
\(196\) 12945.2 0.336974
\(197\) 46937.7i 1.20945i −0.796433 0.604727i \(-0.793282\pi\)
0.796433 0.604727i \(-0.206718\pi\)
\(198\) 10163.2 + 20498.9i 0.259238 + 0.522877i
\(199\) 2813.95 0.0710575 0.0355288 0.999369i \(-0.488688\pi\)
0.0355288 + 0.999369i \(0.488688\pi\)
\(200\) 13284.4i 0.332110i
\(201\) 19768.0 31865.0i 0.489294 0.788718i
\(202\) −35449.1 −0.868764
\(203\) 3777.08i 0.0916566i
\(204\) 7394.03 + 4587.01i 0.177673 + 0.110222i
\(205\) −838.528 −0.0199531
\(206\) 21432.8i 0.505063i
\(207\) 9982.76 4949.37i 0.232975 0.115507i
\(208\) −22146.8 −0.511899
\(209\) 20808.4i 0.476372i
\(210\) −6295.31 + 10147.7i −0.142751 + 0.230107i
\(211\) −15688.9 −0.352392 −0.176196 0.984355i \(-0.556379\pi\)
−0.176196 + 0.984355i \(0.556379\pi\)
\(212\) 13707.3i 0.304987i
\(213\) −11079.8 6873.55i −0.244216 0.151503i
\(214\) −56179.8 −1.22674
\(215\) 22564.1i 0.488137i
\(216\) −1596.27 + 16754.9i −0.0342136 + 0.359117i
\(217\) −33789.4 −0.717565
\(218\) 19538.0i 0.411119i
\(219\) −10245.3 + 16514.9i −0.213617 + 0.344341i
\(220\) 4394.63 0.0907982
\(221\) 6009.52i 0.123043i
\(222\) −82024.6 50885.3i −1.66433 1.03249i
\(223\) 13217.8 0.265797 0.132898 0.991130i \(-0.457572\pi\)
0.132898 + 0.991130i \(0.457572\pi\)
\(224\) 44589.7i 0.888666i
\(225\) −20702.5 41756.4i −0.408938 0.824818i
\(226\) −64938.7 −1.27141
\(227\) 74384.0i 1.44354i 0.692135 + 0.721768i \(0.256670\pi\)
−0.692135 + 0.721768i \(0.743330\pi\)
\(228\) 21312.4 34354.6i 0.409980 0.660868i
\(229\) −23594.8 −0.449930 −0.224965 0.974367i \(-0.572227\pi\)
−0.224965 + 0.974367i \(0.572227\pi\)
\(230\) 5090.59i 0.0962304i
\(231\) −14742.2 9145.58i −0.276273 0.171391i
\(232\) 2432.10 0.0451862
\(233\) 37798.5i 0.696246i 0.937449 + 0.348123i \(0.113181\pi\)
−0.937449 + 0.348123i \(0.886819\pi\)
\(234\) −27506.5 + 13637.5i −0.502346 + 0.249059i
\(235\) 13900.0 0.251698
\(236\) 5259.62i 0.0944344i
\(237\) 10160.9 16378.9i 0.180899 0.291601i
\(238\) −15693.4 −0.277053
\(239\) 64531.0i 1.12972i 0.825185 + 0.564862i \(0.191071\pi\)
−0.825185 + 0.564862i \(0.808929\pi\)
\(240\) 16536.8 + 10258.9i 0.287097 + 0.178106i
\(241\) 55960.1 0.963483 0.481742 0.876313i \(-0.340004\pi\)
0.481742 + 0.876313i \(0.340004\pi\)
\(242\) 61739.7i 1.05423i
\(243\) 21093.5 + 55152.9i 0.357221 + 0.934020i
\(244\) 36110.6 0.606534
\(245\) 7856.13i 0.130881i
\(246\) −2967.78 + 4783.91i −0.0490412 + 0.0790519i
\(247\) −27921.8 −0.457666
\(248\) 21757.4i 0.353755i
\(249\) −33775.4 20953.1i −0.544756 0.337948i
\(250\) −44422.1 −0.710754
\(251\) 65007.8i 1.03185i −0.856633 0.515927i \(-0.827448\pi\)
0.856633 0.515927i \(-0.172552\pi\)
\(252\) 14972.2 + 30198.6i 0.235768 + 0.475539i
\(253\) 7395.41 0.115537
\(254\) 33361.3i 0.517101i
\(255\) −2783.74 + 4487.26i −0.0428104 + 0.0690082i
\(256\) 85719.2 1.30797
\(257\) 88880.8i 1.34568i −0.739788 0.672840i \(-0.765074\pi\)
0.739788 0.672840i \(-0.234926\pi\)
\(258\) −128731. 79860.5i −1.93395 1.19975i
\(259\) 73190.6 1.09108
\(260\) 5896.94i 0.0872329i
\(261\) 7644.74 3790.20i 0.112223 0.0556393i
\(262\) −73775.3 −1.07475
\(263\) 31758.9i 0.459149i 0.973291 + 0.229574i \(0.0737334\pi\)
−0.973291 + 0.229574i \(0.926267\pi\)
\(264\) −5888.94 + 9492.68i −0.0844946 + 0.136201i
\(265\) 8318.65 0.118457
\(266\) 72915.6i 1.03052i
\(267\) −105701. 65573.2i −1.48271 0.919823i
\(268\) −48355.9 −0.673256
\(269\) 27028.4i 0.373521i 0.982405 + 0.186761i \(0.0597989\pi\)
−0.982405 + 0.186761i \(0.940201\pi\)
\(270\) 26856.0 + 2558.61i 0.368395 + 0.0350976i
\(271\) 101687. 1.38461 0.692304 0.721606i \(-0.256596\pi\)
0.692304 + 0.721606i \(0.256596\pi\)
\(272\) 25574.1i 0.345671i
\(273\) 12272.0 19781.9i 0.164661 0.265425i
\(274\) 71078.0 0.946748
\(275\) 30933.9i 0.409043i
\(276\) −12209.8 7574.54i −0.160284 0.0994348i
\(277\) 80803.4 1.05310 0.526551 0.850144i \(-0.323485\pi\)
0.526551 + 0.850144i \(0.323485\pi\)
\(278\) 13790.1i 0.178434i
\(279\) 33906.8 + 68389.2i 0.435591 + 0.878576i
\(280\) −5830.49 −0.0743685
\(281\) 1181.63i 0.0149647i 0.999972 + 0.00748236i \(0.00238173\pi\)
−0.999972 + 0.00748236i \(0.997618\pi\)
\(282\) 49195.9 79301.3i 0.618629 0.997200i
\(283\) 108188. 1.35085 0.675425 0.737429i \(-0.263960\pi\)
0.675425 + 0.737429i \(0.263960\pi\)
\(284\) 16813.9i 0.208464i
\(285\) 20849.0 + 12934.0i 0.256682 + 0.159237i
\(286\) −20377.3 −0.249123
\(287\) 4268.68i 0.0518239i
\(288\) 90248.9 44744.7i 1.08807 0.539456i
\(289\) 76581.5 0.916913
\(290\) 3898.34i 0.0463537i
\(291\) 51019.9 82241.5i 0.602495 0.971192i
\(292\) 25061.8 0.293932
\(293\) 39113.3i 0.455606i 0.973707 + 0.227803i \(0.0731542\pi\)
−0.973707 + 0.227803i \(0.926846\pi\)
\(294\) 44820.2 + 27804.9i 0.518536 + 0.321682i
\(295\) −3191.93 −0.0366784
\(296\) 47128.2i 0.537895i
\(297\) −3717.06 + 39015.4i −0.0421392 + 0.442306i
\(298\) 144635. 1.62869
\(299\) 9923.54i 0.111000i
\(300\) −31683.2 + 51071.7i −0.352035 + 0.567463i
\(301\) 114867. 1.26783
\(302\) 94152.1i 1.03232i
\(303\) −51599.4 32010.5i −0.562030 0.348664i
\(304\) 118824. 1.28575
\(305\) 21914.7i 0.235578i
\(306\) 15747.9 + 31763.2i 0.168183 + 0.339220i
\(307\) −19295.0 −0.204724 −0.102362 0.994747i \(-0.532640\pi\)
−0.102362 + 0.994747i \(0.532640\pi\)
\(308\) 22371.7i 0.235829i
\(309\) 19353.9 31197.5i 0.202699 0.326740i
\(310\) 34874.2 0.362895
\(311\) 158346.i 1.63714i 0.574406 + 0.818571i \(0.305233\pi\)
−0.574406 + 0.818571i \(0.694767\pi\)
\(312\) −12737.8 7902.08i −0.130853 0.0811768i
\(313\) −80665.2 −0.823375 −0.411687 0.911325i \(-0.635060\pi\)
−0.411687 + 0.911325i \(0.635060\pi\)
\(314\) 98701.1i 1.00107i
\(315\) −18326.8 + 9086.29i −0.184700 + 0.0915726i
\(316\) −24855.4 −0.248913
\(317\) 7574.70i 0.0753784i 0.999290 + 0.0376892i \(0.0119997\pi\)
−0.999290 + 0.0376892i \(0.988000\pi\)
\(318\) 29441.9 47458.9i 0.291147 0.469314i
\(319\) 5663.37 0.0556536
\(320\) 11424.9i 0.111571i
\(321\) −81775.0 50730.5i −0.793616 0.492333i
\(322\) 25914.6 0.249938
\(323\) 32242.8i 0.309049i
\(324\) 46097.3 60607.2i 0.439122 0.577343i
\(325\) 41508.7 0.392982
\(326\) 153437.i 1.44376i
\(327\) −17642.9 + 28439.4i −0.164996 + 0.265965i
\(328\) −2748.65 −0.0255489
\(329\) 70760.6i 0.653732i
\(330\) 15215.5 + 9439.21i 0.139720 + 0.0866778i
\(331\) 17348.1 0.158342 0.0791708 0.996861i \(-0.474773\pi\)
0.0791708 + 0.996861i \(0.474773\pi\)
\(332\) 51255.0i 0.465008i
\(333\) −73445.0 148137.i −0.662329 1.33590i
\(334\) 73854.9 0.662043
\(335\) 29346.0i 0.261493i
\(336\) −52224.7 + 84183.7i −0.462592 + 0.745675i
\(337\) −58282.4 −0.513189 −0.256595 0.966519i \(-0.582601\pi\)
−0.256595 + 0.966519i \(0.582601\pi\)
\(338\) 122720.i 1.07419i
\(339\) −94524.4 58639.7i −0.822516 0.510261i
\(340\) 6809.52 0.0589059
\(341\) 50664.0i 0.435703i
\(342\) 147580. 73169.0i 1.26176 0.625568i
\(343\) −126081. −1.07167
\(344\) 73964.0i 0.625034i
\(345\) 4596.81 7409.82i 0.0386205 0.0622543i
\(346\) 56995.8 0.476092
\(347\) 51313.4i 0.426160i 0.977035 + 0.213080i \(0.0683494\pi\)
−0.977035 + 0.213080i \(0.931651\pi\)
\(348\) −9350.19 5800.54i −0.0772079 0.0478972i
\(349\) −127375. −1.04576 −0.522882 0.852405i \(-0.675143\pi\)
−0.522882 + 0.852405i \(0.675143\pi\)
\(350\) 108397.i 0.884871i
\(351\) −52352.9 4987.74i −0.424939 0.0404845i
\(352\) 66858.0 0.539595
\(353\) 55186.9i 0.442881i −0.975174 0.221440i \(-0.928924\pi\)
0.975174 0.221440i \(-0.0710758\pi\)
\(354\) −11297.1 + 18210.4i −0.0901489 + 0.145316i
\(355\) −10203.9 −0.0809677
\(356\) 160404.i 1.26565i
\(357\) −22843.2 14171.2i −0.179234 0.111191i
\(358\) −92812.9 −0.724173
\(359\) 53361.3i 0.414035i 0.978337 + 0.207018i \(0.0663757\pi\)
−0.978337 + 0.207018i \(0.933624\pi\)
\(360\) 5850.76 + 11800.8i 0.0451447 + 0.0910558i
\(361\) 19487.3 0.149533
\(362\) 279993.i 2.13663i
\(363\) 55751.0 89867.9i 0.423097 0.682011i
\(364\) −30019.5 −0.226569
\(365\) 15209.4i 0.114163i
\(366\) 125026. + 77561.8i 0.933335 + 0.579010i
\(367\) −133555. −0.991584 −0.495792 0.868441i \(-0.665122\pi\)
−0.495792 + 0.868441i \(0.665122\pi\)
\(368\) 42230.6i 0.311840i
\(369\) −8639.75 + 4283.52i −0.0634524 + 0.0314592i
\(370\) −75540.4 −0.551793
\(371\) 42347.6i 0.307667i
\(372\) 51891.2 83646.0i 0.374979 0.604448i
\(373\) 17826.7 0.128131 0.0640653 0.997946i \(-0.479593\pi\)
0.0640653 + 0.997946i \(0.479593\pi\)
\(374\) 23530.8i 0.168226i
\(375\) −64660.6 40113.2i −0.459808 0.285250i
\(376\) 45563.5 0.322286
\(377\) 7599.39i 0.0534683i
\(378\) −13025.1 + 136716.i −0.0911585 + 0.956829i
\(379\) −272993. −1.90052 −0.950261 0.311456i \(-0.899183\pi\)
−0.950261 + 0.311456i \(0.899183\pi\)
\(380\) 31638.8i 0.219105i
\(381\) 30125.3 48560.5i 0.207530 0.334528i
\(382\) 236710. 1.62215
\(383\) 142000.i 0.968032i −0.875059 0.484016i \(-0.839178\pi\)
0.875059 0.484016i \(-0.160822\pi\)
\(384\) 86994.7 + 53968.6i 0.589971 + 0.365998i
\(385\) −13576.8 −0.0915961
\(386\) 242460.i 1.62729i
\(387\) −115266. 232489.i −0.769626 1.55232i
\(388\) −124803. −0.829016
\(389\) 213755.i 1.41259i 0.707916 + 0.706297i \(0.249636\pi\)
−0.707916 + 0.706297i \(0.750364\pi\)
\(390\) −12666.0 + 20417.0i −0.0832743 + 0.134234i
\(391\) 11459.3 0.0749554
\(392\) 25752.0i 0.167586i
\(393\) −107387. 66619.1i −0.695289 0.431334i
\(394\) −246617. −1.58866
\(395\) 15084.1i 0.0966777i
\(396\) 45280.0 22449.4i 0.288746 0.143158i
\(397\) 153201. 0.972032 0.486016 0.873950i \(-0.338450\pi\)
0.486016 + 0.873950i \(0.338450\pi\)
\(398\) 14784.8i 0.0933363i
\(399\) −65842.9 + 106135.i −0.413583 + 0.666676i
\(400\) −176644. −1.10403
\(401\) 127864.i 0.795171i −0.917565 0.397585i \(-0.869848\pi\)
0.917565 0.397585i \(-0.130152\pi\)
\(402\) −167423. 103863.i −1.03601 0.642703i
\(403\) −67983.5 −0.418594
\(404\) 78303.3i 0.479753i
\(405\) 36781.0 + 27975.3i 0.224240 + 0.170555i
\(406\) 19845.2 0.120394
\(407\) 109742.i 0.662499i
\(408\) −9124.96 + 14709.0i −0.0548164 + 0.0883614i
\(409\) −38312.6 −0.229031 −0.114516 0.993421i \(-0.536532\pi\)
−0.114516 + 0.993421i \(0.536532\pi\)
\(410\) 4405.73i 0.0262090i
\(411\) 103461. + 64183.6i 0.612480 + 0.379962i
\(412\) −47343.0 −0.278908
\(413\) 16249.1i 0.0952642i
\(414\) −26004.6 52450.7i −0.151722 0.306020i
\(415\) −31105.4 −0.180609
\(416\) 89713.5i 0.518407i
\(417\) 12452.5 20072.8i 0.0716115 0.115434i
\(418\) 109330. 0.625729
\(419\) 242130.i 1.37918i 0.724201 + 0.689589i \(0.242209\pi\)
−0.724201 + 0.689589i \(0.757791\pi\)
\(420\) 22415.3 + 13905.7i 0.127071 + 0.0788305i
\(421\) −278724. −1.57257 −0.786285 0.617863i \(-0.787998\pi\)
−0.786285 + 0.617863i \(0.787998\pi\)
\(422\) 82431.2i 0.462878i
\(423\) 143218. 71006.5i 0.800420 0.396842i
\(424\) 27268.1 0.151678
\(425\) 47932.3i 0.265369i
\(426\) −36114.5 + 58214.8i −0.199004 + 0.320785i
\(427\) −111561. −0.611864
\(428\) 124096.i 0.677437i
\(429\) −29661.0 18400.7i −0.161165 0.0999816i
\(430\) −118555. −0.641183
\(431\) 189524.i 1.02025i −0.860099 0.510127i \(-0.829598\pi\)
0.860099 0.510127i \(-0.170402\pi\)
\(432\) 222793. + 21225.8i 1.19381 + 0.113736i
\(433\) −117183. −0.625012 −0.312506 0.949916i \(-0.601168\pi\)
−0.312506 + 0.949916i \(0.601168\pi\)
\(434\) 177534.i 0.942543i
\(435\) 3520.21 5674.40i 0.0186033 0.0299876i
\(436\) 43157.5 0.227030
\(437\) 53242.6i 0.278803i
\(438\) 86771.5 + 53830.1i 0.452302 + 0.280593i
\(439\) −340406. −1.76632 −0.883158 0.469075i \(-0.844587\pi\)
−0.883158 + 0.469075i \(0.844587\pi\)
\(440\) 8742.27i 0.0451563i
\(441\) 40132.1 + 80945.4i 0.206355 + 0.416212i
\(442\) −31574.8 −0.161620
\(443\) 114277.i 0.582307i 0.956676 + 0.291154i \(0.0940391\pi\)
−0.956676 + 0.291154i \(0.905961\pi\)
\(444\) −112400. + 181184.i −0.570167 + 0.919081i
\(445\) −97345.0 −0.491580
\(446\) 69448.0i 0.349132i
\(447\) 210529. + 130605.i 1.05365 + 0.653650i
\(448\) 58160.3 0.289782
\(449\) 336617.i 1.66972i 0.550462 + 0.834860i \(0.314452\pi\)
−0.550462 + 0.834860i \(0.685548\pi\)
\(450\) −219393. + 108773.i −1.08342 + 0.537153i
\(451\) −6400.48 −0.0314673
\(452\) 143443.i 0.702106i
\(453\) −85019.4 + 137047.i −0.414307 + 0.667842i
\(454\) 390823. 1.89613
\(455\) 18218.1i 0.0879995i
\(456\) 68341.7 + 42396.9i 0.328667 + 0.203894i
\(457\) 131255. 0.628469 0.314234 0.949345i \(-0.398252\pi\)
0.314234 + 0.949345i \(0.398252\pi\)
\(458\) 123970.i 0.590997i
\(459\) −5759.61 + 60454.7i −0.0273381 + 0.286949i
\(460\) −11244.6 −0.0531408
\(461\) 210787.i 0.991841i −0.868368 0.495920i \(-0.834831\pi\)
0.868368 0.495920i \(-0.165169\pi\)
\(462\) −48052.0 + 77457.5i −0.225127 + 0.362894i
\(463\) −4070.47 −0.0189882 −0.00949408 0.999955i \(-0.503022\pi\)
−0.00949408 + 0.999955i \(0.503022\pi\)
\(464\) 32340.0i 0.150212i
\(465\) 50762.7 + 31491.5i 0.234768 + 0.145642i
\(466\) 198598. 0.914541
\(467\) 131302.i 0.602057i −0.953615 0.301029i \(-0.902670\pi\)
0.953615 0.301029i \(-0.0973299\pi\)
\(468\) 30123.8 + 60759.0i 0.137537 + 0.277408i
\(469\) 149391. 0.679172
\(470\) 73032.5i 0.330613i
\(471\) −89127.2 + 143669.i −0.401762 + 0.647620i
\(472\) −10463.0 −0.0469647
\(473\) 172232.i 0.769824i
\(474\) −86056.9 53386.8i −0.383027 0.237617i
\(475\) −222706. −0.987062
\(476\) 34665.1i 0.152996i
\(477\) 85710.9 42494.8i 0.376703 0.186767i
\(478\) 339054. 1.48393
\(479\) 229631.i 1.00083i 0.865786 + 0.500415i \(0.166819\pi\)
−0.865786 + 0.500415i \(0.833181\pi\)
\(480\) 41557.3 66988.3i 0.180370 0.290748i
\(481\) 147258. 0.636485
\(482\) 294021.i 1.26557i
\(483\) 37721.1 + 23400.9i 0.161692 + 0.100309i
\(484\) −136377. −0.582170
\(485\) 75740.2i 0.321990i
\(486\) 289780. 110828.i 1.22686 0.469221i
\(487\) −325.460 −0.00137227 −0.000686136 1.00000i \(-0.500218\pi\)
−0.000686136 1.00000i \(0.500218\pi\)
\(488\) 71835.1i 0.301646i
\(489\) 138553. 223341.i 0.579428 0.934009i
\(490\) 41277.1 0.171916
\(491\) 428306.i 1.77661i 0.459257 + 0.888304i \(0.348116\pi\)
−0.459257 + 0.888304i \(0.651884\pi\)
\(492\) 10567.2 + 6555.51i 0.0436544 + 0.0270817i
\(493\) 8775.44 0.0361056
\(494\) 146704.i 0.601159i
\(495\) 13624.0 + 27479.3i 0.0556026 + 0.112149i
\(496\) 289310. 1.17598
\(497\) 51945.1i 0.210296i
\(498\) −110090. + 177460.i −0.443906 + 0.715554i
\(499\) −209527. −0.841471 −0.420735 0.907183i \(-0.638228\pi\)
−0.420735 + 0.907183i \(0.638228\pi\)
\(500\) 98124.0i 0.392496i
\(501\) 107503. + 66691.1i 0.428296 + 0.265700i
\(502\) −341559. −1.35537
\(503\) 328979.i 1.30026i −0.759821 0.650132i \(-0.774713\pi\)
0.759821 0.650132i \(-0.225287\pi\)
\(504\) −60074.3 + 29784.4i −0.236498 + 0.117254i
\(505\) −47520.4 −0.186336
\(506\) 38856.4i 0.151762i
\(507\) −110816. + 178630.i −0.431109 + 0.694926i
\(508\) −73691.7 −0.285556
\(509\) 361912.i 1.39691i 0.715655 + 0.698454i \(0.246128\pi\)
−0.715655 + 0.698454i \(0.753872\pi\)
\(510\) 23576.6 + 14626.1i 0.0906444 + 0.0562328i
\(511\) −77426.2 −0.296515
\(512\) 268379.i 1.02379i
\(513\) 280888. + 26760.6i 1.06733 + 0.101686i
\(514\) −466991. −1.76759
\(515\) 28731.3i 0.108328i
\(516\) −176404. + 284354.i −0.662534 + 1.06797i
\(517\) 106099. 0.396944
\(518\) 384552.i 1.43316i
\(519\) 82962.8 + 51467.3i 0.307998 + 0.191072i
\(520\) −11730.8 −0.0433832
\(521\) 268878.i 0.990559i −0.868734 0.495280i \(-0.835066\pi\)
0.868734 0.495280i \(-0.164934\pi\)
\(522\) −19914.2 40166.4i −0.0730839 0.147408i
\(523\) 25969.9 0.0949439 0.0474719 0.998873i \(-0.484884\pi\)
0.0474719 + 0.998873i \(0.484884\pi\)
\(524\) 162962.i 0.593504i
\(525\) 97882.4 157782.i 0.355129 0.572450i
\(526\) 166865. 0.603106
\(527\) 78504.3i 0.282665i
\(528\) 126225. + 78306.0i 0.452771 + 0.280884i
\(529\) 260918. 0.932381
\(530\) 43707.2i 0.155597i
\(531\) −32888.0 + 16305.6i −0.116640 + 0.0578293i
\(532\) 161063. 0.569079
\(533\) 8588.49i 0.0302317i
\(534\) −344530. + 555365.i −1.20822 + 1.94758i
\(535\) −75310.6 −0.263117
\(536\) 96194.7i 0.334828i
\(537\) −135098. 83810.1i −0.468489 0.290635i
\(538\) 142010. 0.490632
\(539\) 59965.8i 0.206408i
\(540\) 5651.72 59322.2i 0.0193817 0.203437i
\(541\) 88195.2 0.301335 0.150668 0.988584i \(-0.451858\pi\)
0.150668 + 0.988584i \(0.451858\pi\)
\(542\) 534276.i 1.81873i
\(543\) 252834. 407555.i 0.857502 1.38225i
\(544\) 103597. 0.350066
\(545\) 26191.2i 0.0881786i
\(546\) −103936. 64478.7i −0.348644 0.216287i
\(547\) −553062. −1.84841 −0.924206 0.381894i \(-0.875272\pi\)
−0.924206 + 0.381894i \(0.875272\pi\)
\(548\) 157004.i 0.522817i
\(549\) 111948. + 225797.i 0.371427 + 0.749158i
\(550\) −162531. −0.537291
\(551\) 40772.9i 0.134298i
\(552\) 15068.1 24289.0i 0.0494515 0.0797134i
\(553\) 76788.6 0.251100
\(554\) 424551.i 1.38328i
\(555\) −109956. 68213.1i −0.356972 0.221453i
\(556\) −30460.9 −0.0985356
\(557\) 460127.i 1.48309i 0.670903 + 0.741545i \(0.265906\pi\)
−0.670903 + 0.741545i \(0.734094\pi\)
\(558\) 359326. 178151.i 1.15404 0.572162i
\(559\) 231109. 0.739595
\(560\) 77528.9i 0.247222i
\(561\) −21248.3 + 34251.2i −0.0675147 + 0.108830i
\(562\) 6208.43 0.0196566
\(563\) 596909.i 1.88318i 0.336763 + 0.941589i \(0.390668\pi\)
−0.336763 + 0.941589i \(0.609332\pi\)
\(564\) −175169. 108669.i −0.550678 0.341622i
\(565\) −87052.1 −0.272698
\(566\) 568434.i 1.77438i
\(567\) −142414. + 187241.i −0.442981 + 0.582417i
\(568\) −33448.0 −0.103675
\(569\) 303832.i 0.938444i −0.883080 0.469222i \(-0.844534\pi\)
0.883080 0.469222i \(-0.155466\pi\)
\(570\) 67956.8 109543.i 0.209162 0.337159i
\(571\) 49273.8 0.151128 0.0755638 0.997141i \(-0.475924\pi\)
0.0755638 + 0.997141i \(0.475924\pi\)
\(572\) 45011.3i 0.137572i
\(573\) 344554. + 213750.i 1.04942 + 0.651023i
\(574\) −22428.2 −0.0680723
\(575\) 79150.8i 0.239398i
\(576\) −58362.4 117716.i −0.175909 0.354804i
\(577\) 220702. 0.662909 0.331455 0.943471i \(-0.392461\pi\)
0.331455 + 0.943471i \(0.392461\pi\)
\(578\) 402369.i 1.20439i
\(579\) 218942. 352923.i 0.653088 1.05275i
\(580\) −8611.04 −0.0255976
\(581\) 158348.i 0.469094i
\(582\) −432107. 268065.i −1.27569 0.791396i
\(583\) 63496.2 0.186815
\(584\) 49855.6i 0.146180i
\(585\) −36873.1 + 18281.4i −0.107745 + 0.0534193i
\(586\) 205506. 0.598453
\(587\) 158765.i 0.460764i 0.973100 + 0.230382i \(0.0739976\pi\)
−0.973100 + 0.230382i \(0.926002\pi\)
\(588\) 61418.3 99003.2i 0.177641 0.286348i
\(589\) 364751. 1.05139
\(590\) 16770.8i 0.0481782i
\(591\) −358973. 222695.i −1.02775 0.637582i
\(592\) −626670. −1.78811
\(593\) 16441.0i 0.0467540i −0.999727 0.0233770i \(-0.992558\pi\)
0.999727 0.0233770i \(-0.00744180\pi\)
\(594\) 204992. + 19529.9i 0.580983 + 0.0553512i
\(595\) −21037.4 −0.0594236
\(596\) 319483.i 0.899405i
\(597\) 13350.7 21520.7i 0.0374590 0.0603821i
\(598\) 52139.5 0.145802
\(599\) 233718.i 0.651385i 0.945476 + 0.325693i \(0.105597\pi\)
−0.945476 + 0.325693i \(0.894403\pi\)
\(600\) −101597. 63027.5i −0.282214 0.175076i
\(601\) −164717. −0.456026 −0.228013 0.973658i \(-0.573223\pi\)
−0.228013 + 0.973658i \(0.573223\pi\)
\(602\) 603525.i 1.66534i
\(603\) −149911. 302366.i −0.412285 0.831569i
\(604\) 207972. 0.570075
\(605\) 82763.7i 0.226115i
\(606\) −168187. + 271110.i −0.457982 + 0.738244i
\(607\) −270098. −0.733068 −0.366534 0.930405i \(-0.619456\pi\)
−0.366534 + 0.930405i \(0.619456\pi\)
\(608\) 481338.i 1.30210i
\(609\) 28886.6 + 17920.3i 0.0778864 + 0.0483181i
\(610\) 115142. 0.309439
\(611\) 142369.i 0.381357i
\(612\) 70161.7 34785.6i 0.187326 0.0928746i
\(613\) 448318. 1.19307 0.596534 0.802588i \(-0.296544\pi\)
0.596534 + 0.802588i \(0.296544\pi\)
\(614\) 101378.i 0.268911i
\(615\) −3978.38 + 6412.96i −0.0105186 + 0.0169554i
\(616\) −44504.1 −0.117284
\(617\) 716557.i 1.88226i −0.338040 0.941132i \(-0.609764\pi\)
0.338040 0.941132i \(-0.390236\pi\)
\(618\) −163916. 101688.i −0.429184 0.266251i
\(619\) 47548.8 0.124096 0.0620481 0.998073i \(-0.480237\pi\)
0.0620481 + 0.998073i \(0.480237\pi\)
\(620\) 77033.7i 0.200400i
\(621\) 9510.87 99829.1i 0.0246625 0.258865i
\(622\) 831969. 2.15044
\(623\) 495553.i 1.27677i
\(624\) −105075. + 169376.i −0.269855 + 0.434993i
\(625\) 300071. 0.768182
\(626\) 423825.i 1.08153i
\(627\) 159140. + 98725.1i 0.404803 + 0.251126i
\(628\) 218021. 0.552813
\(629\) 170047.i 0.429800i
\(630\) 47740.5 + 96291.4i 0.120283 + 0.242609i
\(631\) −118486. −0.297583 −0.148791 0.988869i \(-0.547538\pi\)
−0.148791 + 0.988869i \(0.547538\pi\)
\(632\) 49445.0i 0.123791i
\(633\) −74435.5 + 119986.i −0.185769 + 0.299450i
\(634\) 39798.4 0.0990118
\(635\) 44721.7i 0.110910i
\(636\) −104832. 65034.2i −0.259167 0.160778i
\(637\) −80465.2 −0.198303
\(638\) 29756.0i 0.0731027i
\(639\) −105136. + 52125.6i −0.257484 + 0.127658i
\(640\) 80117.7 0.195600
\(641\) 464057.i 1.12942i 0.825290 + 0.564709i \(0.191012\pi\)
−0.825290 + 0.564709i \(0.808988\pi\)
\(642\) −266544. + 429656.i −0.646694 + 1.04244i
\(643\) 671136. 1.62326 0.811630 0.584171i \(-0.198580\pi\)
0.811630 + 0.584171i \(0.198580\pi\)
\(644\) 57242.6i 0.138022i
\(645\) −172568. 107055.i −0.414801 0.257329i
\(646\) 169408. 0.405946
\(647\) 163162.i 0.389773i 0.980826 + 0.194886i \(0.0624338\pi\)
−0.980826 + 0.194886i \(0.937566\pi\)
\(648\) 120566. + 91701.6i 0.287128 + 0.218387i
\(649\) −24364.0 −0.0578441
\(650\) 218092.i 0.516193i
\(651\) −160313. + 258417.i −0.378275 + 0.609760i
\(652\) −338926. −0.797277
\(653\) 696228.i 1.63277i 0.577507 + 0.816385i \(0.304025\pi\)
−0.577507 + 0.816385i \(0.695975\pi\)
\(654\) 149424. + 92697.8i 0.349354 + 0.216727i
\(655\) −98897.7 −0.230517
\(656\) 36549.2i 0.0849317i
\(657\) 77695.3 + 156710.i 0.179997 + 0.363048i
\(658\) 371785. 0.858697
\(659\) 337529.i 0.777213i 0.921404 + 0.388607i \(0.127043\pi\)
−0.921404 + 0.388607i \(0.872957\pi\)
\(660\) 20850.3 33609.6i 0.0478656 0.0771570i
\(661\) 766349. 1.75398 0.876988 0.480513i \(-0.159550\pi\)
0.876988 + 0.480513i \(0.159550\pi\)
\(662\) 91148.8i 0.207987i
\(663\) −45960.0 28512.1i −0.104557 0.0648637i
\(664\) −101962. −0.231261
\(665\) 97745.3i 0.221031i
\(666\) −778328. + 385889.i −1.75475 + 0.869989i
\(667\) −14490.9 −0.0325719
\(668\) 163138.i 0.365597i
\(669\) 62711.7 101088.i 0.140119 0.225864i
\(670\) −154188. −0.343479
\(671\) 167275.i 0.371522i
\(672\) 341016. + 211555.i 0.755156 + 0.468473i
\(673\) −91779.6 −0.202636 −0.101318 0.994854i \(-0.532306\pi\)
−0.101318 + 0.994854i \(0.532306\pi\)
\(674\) 306223.i 0.674090i
\(675\) −417570. 39782.5i −0.916477 0.0873142i
\(676\) 271076. 0.593194
\(677\) 665195.i 1.45135i −0.688039 0.725674i \(-0.741528\pi\)
0.688039 0.725674i \(-0.258472\pi\)
\(678\) −308101. + 496643.i −0.670244 + 1.08040i
\(679\) 385569. 0.836302
\(680\) 13546.2i 0.0292955i
\(681\) 568879. + 352913.i 1.22666 + 0.760981i
\(682\) 266195. 0.572309
\(683\) 919287.i 1.97065i 0.170688 + 0.985325i \(0.445401\pi\)
−0.170688 + 0.985325i \(0.554599\pi\)
\(684\) −161623. 325989.i −0.345454 0.696773i
\(685\) 95282.0 0.203063
\(686\) 662447.i 1.40768i
\(687\) −111945. + 180450.i −0.237187 + 0.382334i
\(688\) −983509. −2.07779
\(689\) 85202.5i 0.179479i
\(690\) −38932.1 24152.2i −0.0817730 0.0507292i
\(691\) −431736. −0.904194 −0.452097 0.891969i \(-0.649324\pi\)
−0.452097 + 0.891969i \(0.649324\pi\)
\(692\) 125898.i 0.262910i
\(693\) −139888. + 69355.6i −0.291283 + 0.144416i
\(694\) 269607. 0.559774
\(695\) 18486.0i 0.0382713i
\(696\) 11539.1 18600.4i 0.0238205 0.0383975i
\(697\) −9917.60 −0.0204146
\(698\) 669244.i 1.37364i
\(699\) 289078. + 179334.i 0.591645 + 0.367036i
\(700\) −239437. −0.488648
\(701\) 792305.i 1.61234i −0.591684 0.806170i \(-0.701537\pi\)
0.591684 0.806170i \(-0.298463\pi\)
\(702\) −26206.2 + 275069.i −0.0531777 + 0.558170i
\(703\) −790080. −1.59868
\(704\) 87205.8i 0.175954i
\(705\) 65948.4 106306.i 0.132686 0.213884i
\(706\) −289959. −0.581738
\(707\) 241911.i 0.483969i
\(708\) 40224.9 + 24954.2i 0.0802469 + 0.0497825i
\(709\) 313982. 0.624616 0.312308 0.949981i \(-0.398898\pi\)
0.312308 + 0.949981i \(0.398898\pi\)
\(710\) 53612.8i 0.106354i
\(711\) −77055.5 155419.i −0.152428 0.307443i
\(712\) −319092. −0.629442
\(713\) 129634.i 0.255000i
\(714\) −74457.1 + 120021.i −0.146053 + 0.235430i
\(715\) −27316.3 −0.0534330
\(716\) 205014.i 0.399906i
\(717\) 493525. + 306166.i 0.959999 + 0.595551i
\(718\) 280367. 0.543848
\(719\) 169678.i 0.328223i 0.986442 + 0.164111i \(0.0524757\pi\)
−0.986442 + 0.164111i \(0.947524\pi\)
\(720\) 156917. 77798.3i 0.302695 0.150074i
\(721\) 146262. 0.281359
\(722\) 102389.i 0.196417i
\(723\) 265502. 427975.i 0.507914 0.818733i
\(724\) −618475. −1.17990
\(725\) 60613.3i 0.115317i
\(726\) −472177. 292923.i −0.895843 0.555751i
\(727\) 6078.79 0.0115013 0.00575067 0.999983i \(-0.498169\pi\)
0.00575067 + 0.999983i \(0.498169\pi\)
\(728\) 59717.9i 0.112679i
\(729\) 521880. + 100352.i 0.982010 + 0.188829i
\(730\) 79912.1 0.149957
\(731\) 266875.i 0.499428i
\(732\) 171326. 276169.i 0.319743 0.515411i
\(733\) 924119. 1.71997 0.859983 0.510323i \(-0.170474\pi\)
0.859983 + 0.510323i \(0.170474\pi\)
\(734\) 701717.i 1.30248i
\(735\) 60082.7 + 37273.3i 0.111218 + 0.0689958i
\(736\) −171070. −0.315805
\(737\) 223998.i 0.412391i
\(738\) 22506.1 + 45394.3i 0.0413227 + 0.0833468i
\(739\) 91156.8 0.166917 0.0834585 0.996511i \(-0.473403\pi\)
0.0834585 + 0.996511i \(0.473403\pi\)
\(740\) 166861.i 0.304714i
\(741\) −132474. + 213542.i −0.241266 + 0.388908i
\(742\) 222500. 0.404131
\(743\) 268211.i 0.485846i −0.970046 0.242923i \(-0.921894\pi\)
0.970046 0.242923i \(-0.0781063\pi\)
\(744\) 166397. + 103227.i 0.300608 + 0.186487i
\(745\) 193886. 0.349329
\(746\) 93663.7i 0.168304i
\(747\) −320494. + 158898.i −0.574352 + 0.284759i
\(748\) 51977.1 0.0928984
\(749\) 383382.i 0.683390i
\(750\) −210760. + 339735.i −0.374684 + 0.603973i
\(751\) 2579.41 0.00457342 0.00228671 0.999997i \(-0.499272\pi\)
0.00228671 + 0.999997i \(0.499272\pi\)
\(752\) 605864.i 1.07137i
\(753\) −497171. 308428.i −0.876831 0.543956i
\(754\) 39928.2 0.0702322
\(755\) 126213.i 0.221417i
\(756\) 301991. + 28771.1i 0.528384 + 0.0503400i
\(757\) −403700. −0.704478 −0.352239 0.935910i \(-0.614579\pi\)
−0.352239 + 0.935910i \(0.614579\pi\)
\(758\) 1.43434e6i 2.49639i
\(759\) 35087.4 56559.1i 0.0609070 0.0981791i
\(760\) 62939.2 0.108967
\(761\) 68694.9i 0.118619i −0.998240 0.0593096i \(-0.981110\pi\)
0.998240 0.0593096i \(-0.0188899\pi\)
\(762\) −255143. 158282.i −0.439413 0.272597i
\(763\) −133331. −0.229025
\(764\) 522869.i 0.895791i
\(765\) 21110.5 + 42579.4i 0.0360725 + 0.0727574i
\(766\) −746084. −1.27154
\(767\) 32692.9i 0.0555728i
\(768\) 406693. 655569.i 0.689516 1.11147i
\(769\) −904654. −1.52978 −0.764891 0.644160i \(-0.777207\pi\)
−0.764891 + 0.644160i \(0.777207\pi\)
\(770\) 71334.4i 0.120314i
\(771\) −679748. 421693.i −1.14351 0.709394i
\(772\) −535570. −0.898631
\(773\) 54079.3i 0.0905049i −0.998976 0.0452525i \(-0.985591\pi\)
0.998976 0.0452525i \(-0.0144092\pi\)
\(774\) −1.22152e6 + 605622.i −2.03901 + 1.01093i
\(775\) −542241. −0.902795
\(776\) 248272.i 0.412292i
\(777\) 347251. 559752.i 0.575178 0.927158i
\(778\) 1.12310e6 1.85549
\(779\) 46079.7i 0.0759338i
\(780\) 45099.1 + 27977.9i 0.0741273 + 0.0459861i
\(781\) −77886.7 −0.127691
\(782\) 60208.4i