Properties

Label 76.5.j.a.13.6
Level $76$
Weight $5$
Character 76.13
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) \(=\) 76.13
Dual form 76.5.j.a.41.6

$q$-expansion

\(f(q)\) \(=\) \(q+(3.28951 - 9.03787i) q^{3} +(7.51461 + 42.6175i) q^{5} +(-18.8739 + 32.6905i) q^{7} +(-8.81253 - 7.39459i) q^{9} +O(q^{10})\) \(q+(3.28951 - 9.03787i) q^{3} +(7.51461 + 42.6175i) q^{5} +(-18.8739 + 32.6905i) q^{7} +(-8.81253 - 7.39459i) q^{9} +(103.948 + 180.042i) q^{11} +(-76.3894 - 209.878i) q^{13} +(409.891 + 72.2748i) q^{15} +(361.904 - 303.674i) q^{17} +(-54.7631 + 356.822i) q^{19} +(233.366 + 278.115i) q^{21} +(-61.0806 + 346.405i) q^{23} +(-1172.47 + 426.745i) q^{25} +(578.857 - 334.203i) q^{27} +(-524.525 + 625.105i) q^{29} +(162.613 + 93.8845i) q^{31} +(1969.14 - 347.212i) q^{33} +(-1535.02 - 558.700i) q^{35} -914.694i q^{37} -2148.13 q^{39} +(819.137 - 2250.56i) q^{41} +(-232.697 - 1319.69i) q^{43} +(248.916 - 431.135i) q^{45} +(670.959 + 563.001i) q^{47} +(488.055 + 845.336i) q^{49} +(-1554.07 - 4269.78i) q^{51} +(-4531.29 - 798.988i) q^{53} +(-6891.83 + 5782.93i) q^{55} +(3044.77 + 1668.71i) q^{57} +(2507.79 + 2988.66i) q^{59} +(173.586 - 984.457i) q^{61} +(408.059 - 148.521i) q^{63} +(8370.44 - 4832.68i) q^{65} +(1694.50 - 2019.42i) q^{67} +(2929.84 + 1691.54i) q^{69} +(-2943.73 + 519.059i) q^{71} +(455.176 + 165.670i) q^{73} +12000.4i q^{75} -7847.56 q^{77} +(847.785 - 2329.27i) q^{79} +(-1278.13 - 7248.66i) q^{81} +(1815.81 - 3145.08i) q^{83} +(15661.4 + 13141.5i) q^{85} +(3924.18 + 6796.88i) q^{87} +(-2615.57 - 7186.22i) q^{89} +(8302.78 + 1464.00i) q^{91} +(1383.43 - 1160.84i) q^{93} +(-15618.4 + 347.516i) q^{95} +(125.731 + 149.840i) q^{97} +(415.299 - 2355.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.28951 9.03787i 0.365502 1.00421i −0.611550 0.791206i \(-0.709454\pi\)
0.977052 0.213002i \(-0.0683240\pi\)
\(4\) 0 0
\(5\) 7.51461 + 42.6175i 0.300585 + 1.70470i 0.643594 + 0.765367i \(0.277443\pi\)
−0.343009 + 0.939332i \(0.611446\pi\)
\(6\) 0 0
\(7\) −18.8739 + 32.6905i −0.385181 + 0.667153i −0.991794 0.127844i \(-0.959194\pi\)
0.606613 + 0.794997i \(0.292528\pi\)
\(8\) 0 0
\(9\) −8.81253 7.39459i −0.108797 0.0912912i
\(10\) 0 0
\(11\) 103.948 + 180.042i 0.859070 + 1.48795i 0.872817 + 0.488048i \(0.162291\pi\)
−0.0137466 + 0.999906i \(0.504376\pi\)
\(12\) 0 0
\(13\) −76.3894 209.878i −0.452008 1.24188i −0.931309 0.364231i \(-0.881332\pi\)
0.479300 0.877651i \(-0.340890\pi\)
\(14\) 0 0
\(15\) 409.891 + 72.2748i 1.82174 + 0.321221i
\(16\) 0 0
\(17\) 361.904 303.674i 1.25226 1.05077i 0.255802 0.966729i \(-0.417660\pi\)
0.996462 0.0840453i \(-0.0267841\pi\)
\(18\) 0 0
\(19\) −54.7631 + 356.822i −0.151698 + 0.988427i
\(20\) 0 0
\(21\) 233.366 + 278.115i 0.529175 + 0.630647i
\(22\) 0 0
\(23\) −61.0806 + 346.405i −0.115464 + 0.654831i 0.871055 + 0.491186i \(0.163436\pi\)
−0.986519 + 0.163645i \(0.947675\pi\)
\(24\) 0 0
\(25\) −1172.47 + 426.745i −1.87596 + 0.682792i
\(26\) 0 0
\(27\) 578.857 334.203i 0.794042 0.458440i
\(28\) 0 0
\(29\) −524.525 + 625.105i −0.623692 + 0.743287i −0.981701 0.190431i \(-0.939011\pi\)
0.358009 + 0.933718i \(0.383456\pi\)
\(30\) 0 0
\(31\) 162.613 + 93.8845i 0.169212 + 0.0976946i 0.582214 0.813035i \(-0.302187\pi\)
−0.413002 + 0.910730i \(0.635520\pi\)
\(32\) 0 0
\(33\) 1969.14 347.212i 1.80821 0.318835i
\(34\) 0 0
\(35\) −1535.02 558.700i −1.25307 0.456082i
\(36\) 0 0
\(37\) 914.694i 0.668148i −0.942547 0.334074i \(-0.891577\pi\)
0.942547 0.334074i \(-0.108423\pi\)
\(38\) 0 0
\(39\) −2148.13 −1.41232
\(40\) 0 0
\(41\) 819.137 2250.56i 0.487292 1.33882i −0.415832 0.909442i \(-0.636509\pi\)
0.903123 0.429381i \(-0.141268\pi\)
\(42\) 0 0
\(43\) −232.697 1319.69i −0.125850 0.713733i −0.980799 0.195020i \(-0.937523\pi\)
0.854949 0.518712i \(-0.173588\pi\)
\(44\) 0 0
\(45\) 248.916 431.135i 0.122921 0.212906i
\(46\) 0 0
\(47\) 670.959 + 563.001i 0.303739 + 0.254867i 0.781898 0.623406i \(-0.214252\pi\)
−0.478160 + 0.878273i \(0.658696\pi\)
\(48\) 0 0
\(49\) 488.055 + 845.336i 0.203272 + 0.352077i
\(50\) 0 0
\(51\) −1554.07 4269.78i −0.597491 1.64159i
\(52\) 0 0
\(53\) −4531.29 798.988i −1.61313 0.284439i −0.706930 0.707283i \(-0.749920\pi\)
−0.906202 + 0.422845i \(0.861032\pi\)
\(54\) 0 0
\(55\) −6891.83 + 5782.93i −2.27829 + 1.91171i
\(56\) 0 0
\(57\) 3044.77 + 1668.71i 0.937140 + 0.513608i
\(58\) 0 0
\(59\) 2507.79 + 2988.66i 0.720421 + 0.858565i 0.994672 0.103094i \(-0.0328741\pi\)
−0.274250 + 0.961658i \(0.588430\pi\)
\(60\) 0 0
\(61\) 173.586 984.457i 0.0466504 0.264568i −0.952558 0.304358i \(-0.901558\pi\)
0.999208 + 0.0397906i \(0.0126691\pi\)
\(62\) 0 0
\(63\) 408.059 148.521i 0.102812 0.0374203i
\(64\) 0 0
\(65\) 8370.44 4832.68i 1.98117 1.14383i
\(66\) 0 0
\(67\) 1694.50 2019.42i 0.377477 0.449860i −0.543539 0.839384i \(-0.682916\pi\)
0.921016 + 0.389524i \(0.127360\pi\)
\(68\) 0 0
\(69\) 2929.84 + 1691.54i 0.615384 + 0.355292i
\(70\) 0 0
\(71\) −2943.73 + 519.059i −0.583958 + 0.102968i −0.457819 0.889045i \(-0.651369\pi\)
−0.126138 + 0.992013i \(0.540258\pi\)
\(72\) 0 0
\(73\) 455.176 + 165.670i 0.0854148 + 0.0310885i 0.384374 0.923177i \(-0.374417\pi\)
−0.298959 + 0.954266i \(0.596639\pi\)
\(74\) 0 0
\(75\) 12000.4i 2.13341i
\(76\) 0 0
\(77\) −7847.56 −1.32359
\(78\) 0 0
\(79\) 847.785 2329.27i 0.135841 0.373221i −0.853056 0.521819i \(-0.825254\pi\)
0.988898 + 0.148598i \(0.0474760\pi\)
\(80\) 0 0
\(81\) −1278.13 7248.66i −0.194808 1.10481i
\(82\) 0 0
\(83\) 1815.81 3145.08i 0.263581 0.456536i −0.703610 0.710587i \(-0.748430\pi\)
0.967191 + 0.254051i \(0.0817630\pi\)
\(84\) 0 0
\(85\) 15661.4 + 13141.5i 2.16767 + 1.81889i
\(86\) 0 0
\(87\) 3924.18 + 6796.88i 0.518454 + 0.897989i
\(88\) 0 0
\(89\) −2615.57 7186.22i −0.330207 0.907236i −0.988057 0.154087i \(-0.950756\pi\)
0.657850 0.753149i \(-0.271466\pi\)
\(90\) 0 0
\(91\) 8302.78 + 1464.00i 1.00263 + 0.176791i
\(92\) 0 0
\(93\) 1383.43 1160.84i 0.159953 0.134216i
\(94\) 0 0
\(95\) −15618.4 + 347.516i −1.73057 + 0.0385059i
\(96\) 0 0
\(97\) 125.731 + 149.840i 0.0133628 + 0.0159252i 0.772684 0.634790i \(-0.218914\pi\)
−0.759322 + 0.650715i \(0.774469\pi\)
\(98\) 0 0
\(99\) 415.299 2355.28i 0.0423731 0.240310i
\(100\) 0 0
\(101\) 5764.46 2098.09i 0.565088 0.205675i −0.0436498 0.999047i \(-0.513899\pi\)
0.608737 + 0.793372i \(0.291676\pi\)
\(102\) 0 0
\(103\) 10806.4 6239.10i 1.01861 0.588095i 0.104909 0.994482i \(-0.466545\pi\)
0.913701 + 0.406387i \(0.133212\pi\)
\(104\) 0 0
\(105\) −10098.9 + 12035.4i −0.916001 + 1.09165i
\(106\) 0 0
\(107\) −1213.06 700.358i −0.105953 0.0611720i 0.446087 0.894990i \(-0.352817\pi\)
−0.552040 + 0.833818i \(0.686150\pi\)
\(108\) 0 0
\(109\) 11058.0 1949.82i 0.930727 0.164112i 0.312326 0.949975i \(-0.398892\pi\)
0.618401 + 0.785863i \(0.287781\pi\)
\(110\) 0 0
\(111\) −8266.88 3008.90i −0.670959 0.244209i
\(112\) 0 0
\(113\) 5242.34i 0.410552i −0.978704 0.205276i \(-0.934191\pi\)
0.978704 0.205276i \(-0.0658092\pi\)
\(114\) 0 0
\(115\) −15221.9 −1.15100
\(116\) 0 0
\(117\) −878.778 + 2414.42i −0.0641960 + 0.176377i
\(118\) 0 0
\(119\) 3096.71 + 17562.3i 0.218679 + 1.24019i
\(120\) 0 0
\(121\) −14289.7 + 24750.4i −0.976004 + 1.69049i
\(122\) 0 0
\(123\) −17645.7 14806.5i −1.16635 0.978684i
\(124\) 0 0
\(125\) −13474.1 23337.8i −0.862340 1.49362i
\(126\) 0 0
\(127\) −2155.34 5921.76i −0.133632 0.367150i 0.854771 0.519005i \(-0.173697\pi\)
−0.988403 + 0.151855i \(0.951475\pi\)
\(128\) 0 0
\(129\) −12692.7 2238.06i −0.762734 0.134491i
\(130\) 0 0
\(131\) 21564.8 18095.0i 1.25662 1.05443i 0.260583 0.965451i \(-0.416085\pi\)
0.996034 0.0889757i \(-0.0283594\pi\)
\(132\) 0 0
\(133\) −10631.1 8524.84i −0.601000 0.481929i
\(134\) 0 0
\(135\) 18592.8 + 22158.0i 1.02018 + 1.21580i
\(136\) 0 0
\(137\) 4797.81 27209.7i 0.255624 1.44972i −0.538842 0.842407i \(-0.681138\pi\)
0.794466 0.607309i \(-0.207751\pi\)
\(138\) 0 0
\(139\) −7874.43 + 2866.06i −0.407558 + 0.148339i −0.537660 0.843162i \(-0.680692\pi\)
0.130102 + 0.991501i \(0.458469\pi\)
\(140\) 0 0
\(141\) 7295.46 4212.03i 0.366956 0.211862i
\(142\) 0 0
\(143\) 29846.5 35569.6i 1.45956 1.73943i
\(144\) 0 0
\(145\) −30582.0 17656.5i −1.45455 0.839787i
\(146\) 0 0
\(147\) 9245.50 1630.23i 0.427854 0.0754422i
\(148\) 0 0
\(149\) 11813.3 + 4299.70i 0.532108 + 0.193671i 0.594079 0.804407i \(-0.297517\pi\)
−0.0619716 + 0.998078i \(0.519739\pi\)
\(150\) 0 0
\(151\) 1094.46i 0.0480005i −0.999712 0.0240002i \(-0.992360\pi\)
0.999712 0.0240002i \(-0.00764025\pi\)
\(152\) 0 0
\(153\) −5434.83 −0.232169
\(154\) 0 0
\(155\) −2779.15 + 7635.65i −0.115677 + 0.317821i
\(156\) 0 0
\(157\) 2873.20 + 16294.7i 0.116565 + 0.661071i 0.985964 + 0.166960i \(0.0533951\pi\)
−0.869399 + 0.494111i \(0.835494\pi\)
\(158\) 0 0
\(159\) −22126.9 + 38324.9i −0.875238 + 1.51596i
\(160\) 0 0
\(161\) −10171.3 8534.76i −0.392397 0.329261i
\(162\) 0 0
\(163\) 8971.48 + 15539.1i 0.337667 + 0.584857i 0.983993 0.178204i \(-0.0570288\pi\)
−0.646326 + 0.763061i \(0.723695\pi\)
\(164\) 0 0
\(165\) 29594.6 + 81310.4i 1.08704 + 2.98661i
\(166\) 0 0
\(167\) −31190.3 5499.70i −1.11837 0.197199i −0.416247 0.909252i \(-0.636655\pi\)
−0.702127 + 0.712052i \(0.747766\pi\)
\(168\) 0 0
\(169\) −16334.5 + 13706.3i −0.571915 + 0.479894i
\(170\) 0 0
\(171\) 3121.15 2739.55i 0.106739 0.0936888i
\(172\) 0 0
\(173\) 715.042 + 852.154i 0.0238913 + 0.0284725i 0.777858 0.628440i \(-0.216306\pi\)
−0.753967 + 0.656913i \(0.771862\pi\)
\(174\) 0 0
\(175\) 8178.58 46383.0i 0.267056 1.51455i
\(176\) 0 0
\(177\) 35260.5 12833.8i 1.12549 0.409646i
\(178\) 0 0
\(179\) −18126.2 + 10465.1i −0.565718 + 0.326617i −0.755437 0.655221i \(-0.772575\pi\)
0.189719 + 0.981838i \(0.439242\pi\)
\(180\) 0 0
\(181\) −21860.1 + 26051.8i −0.667259 + 0.795209i −0.988408 0.151820i \(-0.951487\pi\)
0.321149 + 0.947029i \(0.395931\pi\)
\(182\) 0 0
\(183\) −8326.37 4807.23i −0.248630 0.143547i
\(184\) 0 0
\(185\) 38982.0 6873.57i 1.13899 0.200835i
\(186\) 0 0
\(187\) 92293.2 + 33592.0i 2.63929 + 0.960622i
\(188\) 0 0
\(189\) 25230.8i 0.706330i
\(190\) 0 0
\(191\) 42570.4 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(192\) 0 0
\(193\) −15357.1 + 42193.2i −0.412281 + 1.13273i 0.543693 + 0.839284i \(0.317025\pi\)
−0.955975 + 0.293449i \(0.905197\pi\)
\(194\) 0 0
\(195\) −16142.4 91548.1i −0.424521 2.40758i
\(196\) 0 0
\(197\) 7105.29 12306.7i 0.183083 0.317110i −0.759846 0.650104i \(-0.774725\pi\)
0.942929 + 0.332994i \(0.108059\pi\)
\(198\) 0 0
\(199\) −22313.5 18723.2i −0.563457 0.472797i 0.316010 0.948756i \(-0.397657\pi\)
−0.879467 + 0.475959i \(0.842101\pi\)
\(200\) 0 0
\(201\) −12677.2 21957.6i −0.313784 0.543490i
\(202\) 0 0
\(203\) −10535.2 28945.1i −0.255652 0.702398i
\(204\) 0 0
\(205\) 102069. + 17997.5i 2.42876 + 0.428256i
\(206\) 0 0
\(207\) 3099.80 2601.04i 0.0723424 0.0607025i
\(208\) 0 0
\(209\) −69935.6 + 27231.1i −1.60105 + 0.623408i
\(210\) 0 0
\(211\) 19420.0 + 23143.9i 0.436200 + 0.519843i 0.938700 0.344734i \(-0.112031\pi\)
−0.502501 + 0.864577i \(0.667587\pi\)
\(212\) 0 0
\(213\) −4992.26 + 28312.5i −0.110037 + 0.624049i
\(214\) 0 0
\(215\) 54493.3 19833.9i 1.17887 0.429074i
\(216\) 0 0
\(217\) −6138.26 + 3543.92i −0.130354 + 0.0752601i
\(218\) 0 0
\(219\) 2994.61 3568.84i 0.0624385 0.0744113i
\(220\) 0 0
\(221\) −91380.1 52758.3i −1.87097 1.08021i
\(222\) 0 0
\(223\) −80813.3 + 14249.6i −1.62507 + 0.286544i −0.910653 0.413171i \(-0.864421\pi\)
−0.714421 + 0.699716i \(0.753310\pi\)
\(224\) 0 0
\(225\) 13488.1 + 4909.25i 0.266431 + 0.0969728i
\(226\) 0 0
\(227\) 47803.2i 0.927695i 0.885915 + 0.463847i \(0.153531\pi\)
−0.885915 + 0.463847i \(0.846469\pi\)
\(228\) 0 0
\(229\) 32706.7 0.623686 0.311843 0.950134i \(-0.399054\pi\)
0.311843 + 0.950134i \(0.399054\pi\)
\(230\) 0 0
\(231\) −25814.7 + 70925.2i −0.483774 + 1.32916i
\(232\) 0 0
\(233\) −8373.17 47486.6i −0.154233 0.874701i −0.959483 0.281765i \(-0.909080\pi\)
0.805250 0.592935i \(-0.202031\pi\)
\(234\) 0 0
\(235\) −18951.7 + 32825.3i −0.343172 + 0.594392i
\(236\) 0 0
\(237\) −18262.8 15324.3i −0.325141 0.272826i
\(238\) 0 0
\(239\) −39420.4 68278.1i −0.690121 1.19532i −0.971798 0.235815i \(-0.924224\pi\)
0.281677 0.959509i \(-0.409109\pi\)
\(240\) 0 0
\(241\) −30298.5 83244.4i −0.521659 1.43325i −0.868672 0.495387i \(-0.835026\pi\)
0.347013 0.937860i \(-0.387196\pi\)
\(242\) 0 0
\(243\) −16398.5 2891.49i −0.277709 0.0489677i
\(244\) 0 0
\(245\) −32358.5 + 27152.0i −0.539084 + 0.452346i
\(246\) 0 0
\(247\) 79072.5 15763.9i 1.29608 0.258386i
\(248\) 0 0
\(249\) −22451.6 26756.8i −0.362117 0.431555i
\(250\) 0 0
\(251\) −16099.8 + 91306.6i −0.255548 + 1.44929i 0.539112 + 0.842234i \(0.318760\pi\)
−0.794661 + 0.607054i \(0.792351\pi\)
\(252\) 0 0
\(253\) −68716.8 + 25010.9i −1.07355 + 0.390740i
\(254\) 0 0
\(255\) 170289. 98316.5i 2.61883 1.51198i
\(256\) 0 0
\(257\) −57015.0 + 67947.8i −0.863223 + 1.02875i 0.136053 + 0.990702i \(0.456558\pi\)
−0.999276 + 0.0380473i \(0.987886\pi\)
\(258\) 0 0
\(259\) 29901.8 + 17263.8i 0.445756 + 0.257358i
\(260\) 0 0
\(261\) 9244.78 1630.10i 0.135711 0.0239295i
\(262\) 0 0
\(263\) 61111.7 + 22242.9i 0.883513 + 0.321573i 0.743627 0.668595i \(-0.233104\pi\)
0.139887 + 0.990168i \(0.455326\pi\)
\(264\) 0 0
\(265\) 199116.i 2.83540i
\(266\) 0 0
\(267\) −73552.0 −1.03174
\(268\) 0 0
\(269\) −16485.4 + 45293.3i −0.227822 + 0.625936i −0.999955 0.00952562i \(-0.996968\pi\)
0.772133 + 0.635461i \(0.219190\pi\)
\(270\) 0 0
\(271\) 3910.58 + 22178.0i 0.0532479 + 0.301984i 0.999788 0.0206031i \(-0.00655864\pi\)
−0.946540 + 0.322587i \(0.895448\pi\)
\(272\) 0 0
\(273\) 40543.6 70223.5i 0.543997 0.942231i
\(274\) 0 0
\(275\) −198708. 166736.i −2.62754 2.20477i
\(276\) 0 0
\(277\) −6433.92 11143.9i −0.0838525 0.145237i 0.821049 0.570858i \(-0.193389\pi\)
−0.904902 + 0.425621i \(0.860056\pi\)
\(278\) 0 0
\(279\) −738.791 2029.81i −0.00949103 0.0260764i
\(280\) 0 0
\(281\) 86611.2 + 15271.9i 1.09689 + 0.193411i 0.692671 0.721254i \(-0.256434\pi\)
0.404215 + 0.914664i \(0.367545\pi\)
\(282\) 0 0
\(283\) −89003.0 + 74682.4i −1.11130 + 0.932493i −0.998133 0.0610832i \(-0.980544\pi\)
−0.113169 + 0.993576i \(0.536100\pi\)
\(284\) 0 0
\(285\) −48236.1 + 142300.i −0.593858 + 1.75192i
\(286\) 0 0
\(287\) 58111.7 + 69254.8i 0.705504 + 0.840787i
\(288\) 0 0
\(289\) 24253.7 137550.i 0.290391 1.64689i
\(290\) 0 0
\(291\) 1767.83 643.437i 0.0208763 0.00759837i
\(292\) 0 0
\(293\) 64975.6 37513.7i 0.756859 0.436973i −0.0713079 0.997454i \(-0.522717\pi\)
0.828167 + 0.560482i \(0.189384\pi\)
\(294\) 0 0
\(295\) −108524. + 129334.i −1.24705 + 1.48617i
\(296\) 0 0
\(297\) 120341. + 69479.1i 1.36428 + 0.787665i
\(298\) 0 0
\(299\) 77368.8 13642.2i 0.865413 0.152596i
\(300\) 0 0
\(301\) 47533.3 + 17300.7i 0.524644 + 0.190955i
\(302\) 0 0
\(303\) 59000.1i 0.642640i
\(304\) 0 0
\(305\) 43259.5 0.465031
\(306\) 0 0
\(307\) −36832.6 + 101197.i −0.390801 + 1.07372i 0.575836 + 0.817565i \(0.304677\pi\)
−0.966637 + 0.256151i \(0.917545\pi\)
\(308\) 0 0
\(309\) −20840.2 118191.i −0.218265 1.23785i
\(310\) 0 0
\(311\) 33480.2 57989.4i 0.346152 0.599553i −0.639410 0.768866i \(-0.720821\pi\)
0.985562 + 0.169313i \(0.0541548\pi\)
\(312\) 0 0
\(313\) 34053.8 + 28574.5i 0.347597 + 0.291669i 0.799824 0.600234i \(-0.204926\pi\)
−0.452227 + 0.891903i \(0.649370\pi\)
\(314\) 0 0
\(315\) 9396.01 + 16274.4i 0.0946940 + 0.164015i
\(316\) 0 0
\(317\) 35448.9 + 97395.0i 0.352764 + 0.969211i 0.981478 + 0.191574i \(0.0613593\pi\)
−0.628714 + 0.777636i \(0.716418\pi\)
\(318\) 0 0
\(319\) −167068. 29458.7i −1.64177 0.289489i
\(320\) 0 0
\(321\) −10320.1 + 8659.60i −0.100155 + 0.0840403i
\(322\) 0 0
\(323\) 88538.5 + 145766.i 0.848647 + 1.39717i
\(324\) 0 0
\(325\) 179129. + 213478.i 1.69590 + 2.02109i
\(326\) 0 0
\(327\) 18753.1 106354.i 0.175379 0.994626i
\(328\) 0 0
\(329\) −31068.4 + 11308.0i −0.287029 + 0.104470i
\(330\) 0 0
\(331\) 59041.4 34087.6i 0.538891 0.311129i −0.205739 0.978607i \(-0.565960\pi\)
0.744629 + 0.667478i \(0.232626\pi\)
\(332\) 0 0
\(333\) −6763.78 + 8060.76i −0.0609960 + 0.0726922i
\(334\) 0 0
\(335\) 98796.2 + 57040.0i 0.880340 + 0.508265i
\(336\) 0 0
\(337\) 74850.9 13198.2i 0.659079 0.116213i 0.165902 0.986142i \(-0.446947\pi\)
0.493177 + 0.869929i \(0.335835\pi\)
\(338\) 0 0
\(339\) −47379.5 17244.7i −0.412279 0.150057i
\(340\) 0 0
\(341\) 39036.2i 0.335706i
\(342\) 0 0
\(343\) −127478. −1.08355
\(344\) 0 0
\(345\) −50072.8 + 137574.i −0.420691 + 1.15584i
\(346\) 0 0
\(347\) 7554.18 + 42841.9i 0.0627377 + 0.355803i 0.999975 + 0.00711023i \(0.00226328\pi\)
−0.937237 + 0.348693i \(0.886626\pi\)
\(348\) 0 0
\(349\) 78844.4 136562.i 0.647321 1.12119i −0.336439 0.941705i \(-0.609223\pi\)
0.983760 0.179488i \(-0.0574441\pi\)
\(350\) 0 0
\(351\) −114360. 95959.7i −0.928242 0.778888i
\(352\) 0 0
\(353\) −19855.9 34391.5i −0.159346 0.275995i 0.775287 0.631609i \(-0.217605\pi\)
−0.934633 + 0.355614i \(0.884272\pi\)
\(354\) 0 0
\(355\) −44242.0 121554.i −0.351057 0.964522i
\(356\) 0 0
\(357\) 168913. + 29783.9i 1.32534 + 0.233692i
\(358\) 0 0
\(359\) −113432. + 95180.6i −0.880128 + 0.738515i −0.966205 0.257773i \(-0.917011\pi\)
0.0860774 + 0.996288i \(0.472567\pi\)
\(360\) 0 0
\(361\) −124323. 39081.3i −0.953975 0.299885i
\(362\) 0 0
\(363\) 176685. + 210565.i 1.34087 + 1.59799i
\(364\) 0 0
\(365\) −3639.99 + 20643.4i −0.0273221 + 0.154951i
\(366\) 0 0
\(367\) 9866.08 3590.96i 0.0732508 0.0266611i −0.305135 0.952309i \(-0.598702\pi\)
0.378386 + 0.925648i \(0.376479\pi\)
\(368\) 0 0
\(369\) −23860.6 + 13775.9i −0.175238 + 0.101174i
\(370\) 0 0
\(371\) 111642. 133050.i 0.811112 0.966645i
\(372\) 0 0
\(373\) −88926.0 51341.5i −0.639162 0.369021i 0.145129 0.989413i \(-0.453640\pi\)
−0.784292 + 0.620392i \(0.786973\pi\)
\(374\) 0 0
\(375\) −255247. + 45006.9i −1.81509 + 0.320049i
\(376\) 0 0
\(377\) 171264. + 62335.0i 1.20499 + 0.438580i
\(378\) 0 0
\(379\) 193364.i 1.34616i −0.739570 0.673080i \(-0.764971\pi\)
0.739570 0.673080i \(-0.235029\pi\)
\(380\) 0 0
\(381\) −60610.1 −0.417537
\(382\) 0 0
\(383\) −31138.5 + 85552.4i −0.212276 + 0.583223i −0.999438 0.0335230i \(-0.989327\pi\)
0.787162 + 0.616746i \(0.211550\pi\)
\(384\) 0 0
\(385\) −58971.4 334443.i −0.397850 2.25632i
\(386\) 0 0
\(387\) −7707.93 + 13350.5i −0.0514654 + 0.0891407i
\(388\) 0 0
\(389\) 22260.3 + 18678.6i 0.147107 + 0.123437i 0.713371 0.700787i \(-0.247167\pi\)
−0.566264 + 0.824224i \(0.691612\pi\)
\(390\) 0 0
\(391\) 83088.9 + 143914.i 0.543488 + 0.941348i
\(392\) 0 0
\(393\) −92602.7 254424.i −0.599568 1.64730i
\(394\) 0 0
\(395\) 105638. + 18626.9i 0.677061 + 0.119384i
\(396\) 0 0
\(397\) 211925. 177826.i 1.34462 1.12827i 0.364212 0.931316i \(-0.381338\pi\)
0.980412 0.196957i \(-0.0631061\pi\)
\(398\) 0 0
\(399\) −112018. + 68039.8i −0.703623 + 0.427383i
\(400\) 0 0
\(401\) −187594. 223565.i −1.16662 1.39032i −0.905140 0.425114i \(-0.860234\pi\)
−0.261479 0.965209i \(-0.584210\pi\)
\(402\) 0 0
\(403\) 7282.41 41300.6i 0.0448400 0.254300i
\(404\) 0 0
\(405\) 299315. 108942.i 1.82481 0.664177i
\(406\) 0 0
\(407\) 164684. 95080.2i 0.994172 0.573986i
\(408\) 0 0
\(409\) −184229. + 219556.i −1.10131 + 1.31250i −0.155483 + 0.987839i \(0.549693\pi\)
−0.945832 + 0.324658i \(0.894751\pi\)
\(410\) 0 0
\(411\) −230135. 132869.i −1.36238 0.786573i
\(412\) 0 0
\(413\) −145032. + 25573.1i −0.850286 + 0.149928i
\(414\) 0 0
\(415\) 147680. + 53751.3i 0.857485 + 0.312099i
\(416\) 0 0
\(417\) 80596.0i 0.463491i
\(418\) 0 0
\(419\) −87412.0 −0.497901 −0.248951 0.968516i \(-0.580086\pi\)
−0.248951 + 0.968516i \(0.580086\pi\)
\(420\) 0 0
\(421\) −97498.4 + 267875.i −0.550090 + 1.51136i 0.283499 + 0.958973i \(0.408505\pi\)
−0.833588 + 0.552386i \(0.813717\pi\)
\(422\) 0 0
\(423\) −1749.68 9922.92i −0.00977862 0.0554573i
\(424\) 0 0
\(425\) −294732. + 510490.i −1.63173 + 2.82624i
\(426\) 0 0
\(427\) 28906.1 + 24255.1i 0.158538 + 0.133029i
\(428\) 0 0
\(429\) −223293. 386755.i −1.21328 2.10146i
\(430\) 0 0
\(431\) 102913. + 282752.i 0.554010 + 1.52213i 0.828188 + 0.560451i \(0.189372\pi\)
−0.274178 + 0.961679i \(0.588406\pi\)
\(432\) 0 0
\(433\) −260545. 45941.1i −1.38966 0.245034i −0.571769 0.820414i \(-0.693743\pi\)
−0.817886 + 0.575381i \(0.804854\pi\)
\(434\) 0 0
\(435\) −260177. + 218315.i −1.37496 + 1.15373i
\(436\) 0 0
\(437\) −120260. 40765.1i −0.629737 0.213465i
\(438\) 0 0
\(439\) −132702. 158148.i −0.688570 0.820605i 0.302612 0.953114i \(-0.402141\pi\)
−0.991182 + 0.132509i \(0.957697\pi\)
\(440\) 0 0
\(441\) 1949.91 11058.5i 0.0100262 0.0568616i
\(442\) 0 0
\(443\) 64757.2 23569.7i 0.329975 0.120101i −0.171720 0.985146i \(-0.554932\pi\)
0.501695 + 0.865045i \(0.332710\pi\)
\(444\) 0 0
\(445\) 286603. 165471.i 1.44731 0.835605i
\(446\) 0 0
\(447\) 77720.2 92623.3i 0.388972 0.463559i
\(448\) 0 0
\(449\) −217623. 125644.i −1.07947 0.623233i −0.148718 0.988880i \(-0.547515\pi\)
−0.930754 + 0.365646i \(0.880848\pi\)
\(450\) 0 0
\(451\) 490344. 86460.8i 2.41072 0.425076i
\(452\) 0 0
\(453\) −9891.57 3600.24i −0.0482024 0.0175442i
\(454\) 0 0
\(455\) 364845.i 1.76232i
\(456\) 0 0
\(457\) 358067. 1.71448 0.857238 0.514921i \(-0.172179\pi\)
0.857238 + 0.514921i \(0.172179\pi\)
\(458\) 0 0
\(459\) 108002. 296733.i 0.512633 1.40845i
\(460\) 0 0
\(461\) 54042.7 + 306491.i 0.254293 + 1.44217i 0.797880 + 0.602817i \(0.205955\pi\)
−0.543586 + 0.839353i \(0.682934\pi\)
\(462\) 0 0
\(463\) 5432.68 9409.69i 0.0253427 0.0438948i −0.853076 0.521787i \(-0.825266\pi\)
0.878419 + 0.477892i \(0.158599\pi\)
\(464\) 0 0
\(465\) 59867.9 + 50235.2i 0.276878 + 0.232328i
\(466\) 0 0
\(467\) −109600. 189833.i −0.502547 0.870437i −0.999996 0.00294375i \(-0.999063\pi\)
0.497448 0.867494i \(-0.334270\pi\)
\(468\) 0 0
\(469\) 34034.2 + 93508.2i 0.154728 + 0.425113i
\(470\) 0 0
\(471\) 156721. + 27634.2i 0.706457 + 0.124567i
\(472\) 0 0
\(473\) 213412. 179074.i 0.953887 0.800406i
\(474\) 0 0
\(475\) −88063.9 441734.i −0.390311 1.95782i
\(476\) 0 0
\(477\) 34023.9 + 40548.1i 0.149537 + 0.178211i
\(478\) 0 0
\(479\) 53014.1 300658.i 0.231058 1.31039i −0.619701 0.784838i \(-0.712746\pi\)
0.850759 0.525556i \(-0.176143\pi\)
\(480\) 0 0
\(481\) −191974. + 69872.9i −0.829761 + 0.302008i
\(482\) 0 0
\(483\) −110595. + 63851.9i −0.474068 + 0.273703i
\(484\) 0 0
\(485\) −5440.99 + 6484.32i −0.0231310 + 0.0275665i
\(486\) 0 0
\(487\) −4289.91 2476.78i −0.0180880 0.0104431i 0.490929 0.871200i \(-0.336658\pi\)
−0.509017 + 0.860757i \(0.669991\pi\)
\(488\) 0 0
\(489\) 169952. 29967.1i 0.710735 0.125322i
\(490\) 0 0
\(491\) 184130. + 67017.8i 0.763768 + 0.277989i 0.694387 0.719601i \(-0.255675\pi\)
0.0693808 + 0.997590i \(0.477898\pi\)
\(492\) 0 0
\(493\) 385513.i 1.58615i
\(494\) 0 0
\(495\) 103497. 0.422393
\(496\) 0 0
\(497\) 38591.3 106029.i 0.156234 0.429250i
\(498\) 0 0
\(499\) 176.716 + 1002.21i 0.000709701 + 0.00402492i 0.985161 0.171635i \(-0.0549051\pi\)
−0.984451 + 0.175660i \(0.943794\pi\)
\(500\) 0 0
\(501\) −152307. + 263803.i −0.606797 + 1.05100i
\(502\) 0 0
\(503\) −114887. 96401.4i −0.454081 0.381020i 0.386866 0.922136i \(-0.373557\pi\)
−0.840948 + 0.541116i \(0.818002\pi\)
\(504\) 0 0
\(505\) 132733. + 229900.i 0.520471 + 0.901482i
\(506\) 0 0
\(507\) 70142.8 + 192716.i 0.272877 + 0.749724i
\(508\) 0 0
\(509\) 140606. + 24792.6i 0.542709 + 0.0956943i 0.438281 0.898838i \(-0.355588\pi\)
0.104428 + 0.994532i \(0.466699\pi\)
\(510\) 0 0
\(511\) −14006.8 + 11753.1i −0.0536409 + 0.0450101i
\(512\) 0 0
\(513\) 87551.1 + 224851.i 0.332680 + 0.854397i
\(514\) 0 0
\(515\) 347101. + 413659.i 1.30870 + 1.55965i
\(516\) 0 0
\(517\) −31619.6 + 179324.i −0.118297 + 0.670898i
\(518\) 0 0
\(519\) 10053.8 3659.28i 0.0373246 0.0135851i
\(520\) 0 0
\(521\) −105137. + 60701.1i −0.387331 + 0.223625i −0.681003 0.732281i \(-0.738456\pi\)
0.293672 + 0.955906i \(0.405123\pi\)
\(522\) 0 0
\(523\) 38925.4 46389.5i 0.142308 0.169596i −0.690182 0.723635i \(-0.742470\pi\)
0.832491 + 0.554039i \(0.186914\pi\)
\(524\) 0 0
\(525\) −392300. 226495.i −1.42331 0.821749i
\(526\) 0 0
\(527\) 87360.5 15404.0i 0.314553 0.0554642i
\(528\) 0 0
\(529\) 146699. + 53393.9i 0.524221 + 0.190801i
\(530\) 0 0
\(531\) 44881.7i 0.159177i
\(532\) 0 0
\(533\) −534917. −1.88292
\(534\) 0 0
\(535\) 20731.8 56960.3i 0.0724320 0.199005i
\(536\) 0 0
\(537\) 34956.3 + 198247.i 0.121221 + 0.687477i
\(538\) 0 0
\(539\) −101464. + 175741.i −0.349249 + 0.604917i
\(540\) 0 0
\(541\) −322743. 270814.i −1.10271 0.925286i −0.105109 0.994461i \(-0.533519\pi\)
−0.997605 + 0.0691745i \(0.977963\pi\)
\(542\) 0 0
\(543\) 163544. + 283266.i 0.554670 + 0.960717i
\(544\) 0 0
\(545\) 166193. + 456610.i 0.559524 + 1.53728i
\(546\) 0 0
\(547\) −329113. 58031.6i −1.09994 0.193950i −0.405925 0.913906i \(-0.633051\pi\)
−0.694019 + 0.719956i \(0.744162\pi\)
\(548\) 0 0
\(549\) −8809.38 + 7391.95i −0.0292281 + 0.0245253i
\(550\) 0 0
\(551\) −194327. 221395.i −0.640072 0.729229i
\(552\) 0 0
\(553\) 60144.0 + 71676.8i 0.196672 + 0.234384i
\(554\) 0 0
\(555\) 66109.3 374924.i 0.214623 1.21719i
\(556\) 0 0
\(557\) 371939. 135375.i 1.19884 0.436342i 0.336021 0.941855i \(-0.390919\pi\)
0.862819 + 0.505512i \(0.168697\pi\)
\(558\) 0 0
\(559\) −259199. + 149648.i −0.829487 + 0.478904i
\(560\) 0 0
\(561\) 607200. 723632.i 1.92933 2.29928i
\(562\) 0 0
\(563\) 267894. + 154669.i 0.845175 + 0.487962i 0.859020 0.511942i \(-0.171074\pi\)
−0.0138446 + 0.999904i \(0.504407\pi\)
\(564\) 0 0
\(565\) 223415. 39394.1i 0.699867 0.123406i
\(566\) 0 0
\(567\) 261085. + 95027.3i 0.812113 + 0.295585i
\(568\) 0 0
\(569\) 282436.i 0.872360i −0.899859 0.436180i \(-0.856331\pi\)
0.899859 0.436180i \(-0.143669\pi\)
\(570\) 0 0
\(571\) −162080. −0.497114 −0.248557 0.968617i \(-0.579956\pi\)
−0.248557 + 0.968617i \(0.579956\pi\)
\(572\) 0 0
\(573\) 140036. 384746.i 0.426511 1.17183i
\(574\) 0 0
\(575\) −76211.5 432217.i −0.230507 1.30727i
\(576\) 0 0
\(577\) −320896. + 555808.i −0.963857 + 1.66945i −0.251202 + 0.967935i \(0.580826\pi\)
−0.712655 + 0.701515i \(0.752507\pi\)
\(578\) 0 0
\(579\) 330819. + 277590.i 0.986810 + 0.828032i
\(580\) 0 0
\(581\) 68542.7 + 118719.i 0.203053 + 0.351698i
\(582\) 0 0
\(583\) −327164. 898877.i −0.962562 2.64462i
\(584\) 0 0
\(585\) −109500. 19307.9i −0.319966 0.0564186i
\(586\) 0 0
\(587\) 342332. 287251.i 0.993509 0.833653i 0.00743718 0.999972i \(-0.497633\pi\)
0.986072 + 0.166319i \(0.0531882\pi\)
\(588\) 0 0
\(589\) −42405.2 + 52882.4i −0.122233 + 0.152434i
\(590\) 0 0
\(591\) −87853.5 104700.i −0.251527 0.299758i
\(592\) 0 0
\(593\) −4325.64 + 24531.9i −0.0123010 + 0.0697625i −0.990340 0.138658i \(-0.955721\pi\)
0.978039 + 0.208420i \(0.0668322\pi\)
\(594\) 0 0
\(595\) −725192. + 263948.i −2.04842 + 0.745564i
\(596\) 0 0
\(597\) −242619. + 140076.i −0.680731 + 0.393020i
\(598\) 0 0
\(599\) −362000. + 431415.i −1.00892 + 1.20238i −0.0296996 + 0.999559i \(0.509455\pi\)
−0.979216 + 0.202820i \(0.934989\pi\)
\(600\) 0 0
\(601\) −108967. 62911.9i −0.301679 0.174174i 0.341518 0.939875i \(-0.389059\pi\)
−0.643197 + 0.765701i \(0.722392\pi\)
\(602\) 0 0
\(603\) −29865.6 + 5266.11i −0.0821365 + 0.0144829i
\(604\) 0 0
\(605\) −1.16218e6 423000.i −3.17514 1.15566i
\(606\) 0 0
\(607\) 421927.i 1.14514i 0.819855 + 0.572571i \(0.194054\pi\)
−0.819855 + 0.572571i \(0.805946\pi\)
\(608\) 0 0
\(609\) −296258. −0.798794
\(610\) 0 0
\(611\) 66907.5 183827.i 0.179222 0.492410i
\(612\) 0 0
\(613\) −11873.9 67340.2i −0.0315989 0.179206i 0.964924 0.262531i \(-0.0845572\pi\)
−0.996522 + 0.0833248i \(0.973446\pi\)
\(614\) 0 0
\(615\) 498415. 863281.i 1.31777 2.28245i
\(616\) 0 0
\(617\) 260713. + 218764.i 0.684845 + 0.574653i 0.917417 0.397926i \(-0.130270\pi\)
−0.232573 + 0.972579i \(0.574714\pi\)
\(618\) 0 0
\(619\) −68974.6 119468.i −0.180015 0.311795i 0.761871 0.647729i \(-0.224281\pi\)
−0.941885 + 0.335935i \(0.890948\pi\)
\(620\) 0 0
\(621\) 80412.8 + 220932.i 0.208517 + 0.572897i
\(622\) 0 0
\(623\) 284287. + 50127.4i 0.732454 + 0.129151i
\(624\) 0 0
\(625\) 295964. 248344.i 0.757669 0.635760i
\(626\) 0 0
\(627\) 16056.9 + 721645.i 0.0408439 + 1.83565i
\(628\) 0 0
\(629\) −277769. 331032.i −0.702072 0.836697i
\(630\) 0 0
\(631\) 14222.2 80658.1i 0.0357197 0.202577i −0.961725 0.274016i \(-0.911648\pi\)
0.997445 + 0.0714390i \(0.0227591\pi\)
\(632\) 0 0
\(633\) 273054. 99383.6i 0.681462 0.248032i
\(634\) 0 0
\(635\) 236174. 136355.i 0.585713 0.338161i
\(636\) 0 0
\(637\) 140135. 167007.i 0.345357 0.411581i
\(638\) 0 0
\(639\) 29779.9 + 17193.5i 0.0729327 + 0.0421077i
\(640\) 0 0
\(641\) −583030. + 102804.i −1.41897 + 0.250204i −0.829917 0.557887i \(-0.811612\pi\)
−0.589058 + 0.808091i \(0.700501\pi\)
\(642\) 0 0
\(643\) −640784. 233226.i −1.54985 0.564100i −0.581468 0.813569i \(-0.697522\pi\)
−0.968383 + 0.249470i \(0.919744\pi\)
\(644\) 0 0
\(645\) 557747.i 1.34066i
\(646\) 0 0
\(647\) 21537.2 0.0514493 0.0257247 0.999669i \(-0.491811\pi\)
0.0257247 + 0.999669i \(0.491811\pi\)
\(648\) 0 0
\(649\) −277408. + 762172.i −0.658612 + 1.80952i
\(650\) 0 0
\(651\) 11837.6 + 67134.5i 0.0279321 + 0.158411i
\(652\) 0 0
\(653\) 220827. 382483.i 0.517876 0.896987i −0.481909 0.876221i \(-0.660056\pi\)
0.999784 0.0207656i \(-0.00661036\pi\)
\(654\) 0 0
\(655\) 933216. + 783061.i 2.17520 + 1.82521i
\(656\) 0 0
\(657\) −2786.18 4825.81i −0.00645474 0.0111799i
\(658\) 0 0
\(659\) 40628.8 + 111627.i 0.0935542 + 0.257038i 0.977640 0.210287i \(-0.0674399\pi\)
−0.884085 + 0.467325i \(0.845218\pi\)
\(660\) 0 0
\(661\) −258721. 45619.5i −0.592146 0.104411i −0.130458 0.991454i \(-0.541645\pi\)
−0.461688 + 0.887043i \(0.652756\pi\)
\(662\) 0 0
\(663\) −777419. + 652332.i −1.76859 + 1.48403i
\(664\) 0 0
\(665\) 283419. 517131.i 0.640893 1.16939i
\(666\) 0 0
\(667\) −184501. 219880.i −0.414713 0.494236i
\(668\) 0 0
\(669\) −137051. + 777254.i −0.306217 + 1.73664i
\(670\) 0 0
\(671\) 195288. 71078.9i 0.433740 0.157869i
\(672\) 0 0
\(673\) 577163. 333225.i 1.27429 0.735712i 0.298497 0.954410i \(-0.403515\pi\)
0.975792 + 0.218699i \(0.0701813\pi\)
\(674\) 0 0
\(675\) −536074. + 638868.i −1.17657 + 1.40218i
\(676\) 0 0
\(677\) 58995.1 + 34060.8i 0.128718 + 0.0743153i 0.562976 0.826473i \(-0.309656\pi\)
−0.434258 + 0.900788i \(0.642990\pi\)
\(678\) 0 0
\(679\) −7271.37 + 1282.14i −0.0157716 + 0.00278097i
\(680\) 0 0
\(681\) 432039. + 157249.i 0.931598 + 0.339074i
\(682\) 0 0
\(683\) 573992.i 1.23045i −0.788351 0.615225i \(-0.789065\pi\)
0.788351 0.615225i \(-0.210935\pi\)
\(684\) 0 0
\(685\) 1.19566e6 2.54817
\(686\) 0 0
\(687\) 107589. 295599.i 0.227958 0.626310i
\(688\) 0 0
\(689\) 178452. + 1.01205e6i 0.375909 + 2.13189i
\(690\) 0 0
\(691\) 102921. 178264.i 0.215549 0.373342i −0.737893 0.674917i \(-0.764179\pi\)
0.953442 + 0.301576i \(0.0975126\pi\)
\(692\) 0 0
\(693\) 69156.8 + 58029.5i 0.144002 + 0.120832i
\(694\) 0 0
\(695\) −181317. 314051.i −0.375379 0.650176i
\(696\) 0 0
\(697\) −386987. 1.06324e6i −0.796583 2.18859i
\(698\) 0 0
\(699\) −456722. 80532.3i −0.934754 0.164822i
\(700\) 0 0
\(701\) −360259. + 302293.i −0.733127 + 0.615167i −0.930982 0.365065i \(-0.881047\pi\)
0.197855 + 0.980231i \(0.436602\pi\)
\(702\) 0 0
\(703\) 326383. + 50091.4i 0.660415 + 0.101357i
\(704\) 0 0
\(705\) 234329. + 279262.i 0.471463 + 0.561868i
\(706\) 0 0
\(707\) −40210.0 + 228042.i −0.0804442 + 0.456222i
\(708\) 0 0
\(709\) −173573. + 63175.4i −0.345295 + 0.125677i −0.508845 0.860858i \(-0.669928\pi\)
0.163551 + 0.986535i \(0.447705\pi\)
\(710\) 0 0
\(711\) −24695.1 + 14257.7i −0.0488508 + 0.0282040i
\(712\) 0 0
\(713\) −42454.6 + 50595.4i −0.0835114 + 0.0995250i
\(714\) 0 0
\(715\) 1.74017e6 + 1.00469e6i 3.40393 + 1.96526i
\(716\) 0 0
\(717\) −746762. + 131674.i −1.45259 + 0.256131i
\(718\) 0 0
\(719\) −117349. 42711.4i −0.226997 0.0826201i 0.226018 0.974123i \(-0.427429\pi\)
−0.453015 + 0.891503i \(0.649651\pi\)
\(720\) 0 0
\(721\) 471023.i 0.906091i
\(722\) 0 0
\(723\) −852019. −1.62994
\(724\) 0 0
\(725\) 348231. 956757.i 0.662508 1.82023i
\(726\) 0 0
\(727\) 8299.90 + 47071.1i 0.0157038 + 0.0890605i 0.991652 0.128940i \(-0.0411576\pi\)
−0.975949 + 0.218001i \(0.930046\pi\)
\(728\) 0 0
\(729\) 218023. 377628.i 0.410250 0.710573i
\(730\) 0 0
\(731\) −484970. 406938.i −0.907570 0.761542i
\(732\) 0 0
\(733\) 379709. + 657676.i 0.706713 + 1.22406i 0.966070 + 0.258282i \(0.0831563\pi\)
−0.259356 + 0.965782i \(0.583510\pi\)
\(734\) 0 0
\(735\) 138953. + 381769.i 0.257213 + 0.706686i
\(736\) 0 0
\(737\) 539720. + 95167.2i 0.993651 + 0.175207i
\(738\) 0 0
\(739\) 257352. 215944.i 0.471236 0.395414i −0.376009 0.926616i \(-0.622704\pi\)
0.847245 + 0.531202i \(0.178259\pi\)
\(740\) 0 0
\(741\) 117638. 766502.i 0.214246 1.39597i
\(742\) 0 0
\(743\) −469418. 559431.i −0.850320 1.01337i −0.999698 0.0245920i \(-0.992171\pi\)
0.149377 0.988780i \(-0.452273\pi\)
\(744\) 0 0
\(745\) −94469.7 + 535765.i −0.170208 + 0.965298i
\(746\) 0 0
\(747\) −39258.4 + 14288.9i −0.0703545 + 0.0256069i
\(748\) 0 0
\(749\) 45790.1 26436.9i 0.0816221 0.0471245i
\(750\) 0 0
\(751\) 38755.9 46187.5i 0.0687160 0.0818925i −0.730591 0.682815i \(-0.760756\pi\)
0.799307 + 0.600922i \(0.205200\pi\)
\(752\) 0 0
\(753\) 772256. + 445862.i 1.36198 + 0.786341i
\(754\) 0 0
\(755\) 46643.1 8224.43i 0.0818264 0.0144282i
\(756\) 0 0
\(757\) 614099. + 223514.i 1.07163 + 0.390043i 0.816788 0.576938i \(-0.195753\pi\)
0.254847 + 0.966981i \(0.417975\pi\)
\(758\) 0 0
\(759\) 703327.i 1.22088i
\(760\) 0 0
\(761\) 149877. 0.258800 0.129400 0.991592i \(-0.458695\pi\)
0.129400 + 0.991592i \(0.458695\pi\)
\(762\) 0 0
\(763\) −144966. + 398291.i −0.249010 + 0.684150i
\(764\) 0 0
\(765\) −40840.7 231619.i −0.0697863 0.395778i
\(766\) 0 0
\(767\) 435687. 754632.i 0.740600 1.28276i
\(768\) 0 0
\(769\) −264461. 221909.i −0.447208 0.375252i 0.391191 0.920310i \(-0.372063\pi\)
−0.838398 + 0.545058i \(0.816508\pi\)
\(770\) 0 0
\(771\) 426552. + 738809.i 0.717568 + 1.24286i
\(772\) 0 0
\(773\) −257582. 707701.i −0.431079 1.18438i −0.945151 0.326633i \(-0.894086\pi\)
0.514072 0.857747i \(-0.328136\pi\)
\(774\) 0 0
\(775\) −230724. 40682.8i −0.384139 0.0677341i
\(776\) 0 0
\(777\) 254390. 213459.i 0.421365 0.353567i
\(778\) 0 0
\(779\) 758192. + 415534.i 1.24941 + 0.684749i
\(780\) 0 0
\(781\) −399446. 476041.i −0.654872 0.780446i
\(782\) 0 0
\(783\) −94712.9 + 537144.i −0.154485 + 0.876127i
\(784\) 0 0
\(785\) −672850. + 244897.i −1.09189 + 0.397415i
\(786\) 0 0
\(787\) −982271. + 567114.i −1.58592 + 0.915632i −0.591952 + 0.805973i \(0.701643\pi\)
−0.993969 + 0.109659i \(0.965024\pi\)
\(788\) 0 0
\(789\) 402056. 479152.i 0.645851 0.769695i
\(790\) 0 0
\(791\) 171374. + 98943.1i 0.273901 + 0.158137i
\(792\) 0 0