Properties

Label 76.5.j.a.41.6
Level $76$
Weight $5$
Character 76.41
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 41.6
Character \(\chi\) \(=\) 76.41
Dual form 76.5.j.a.13.6

$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\)

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 0.977052 + 0.213002i \(0.0683240\pi\)
−0.611550 + 0.791206i \(0.709454\pi\)
\(4\) 0 0
\(5\) 7.51461 42.6175i 0.300585 1.70470i −0.343009 0.939332i \(-0.611446\pi\)
0.643594 0.765367i \(-0.277443\pi\)
\(6\) 0 0
\(7\) −18.8739 32.6905i −0.385181 0.667153i 0.606613 0.794997i \(-0.292528\pi\)
−0.991794 + 0.127844i \(0.959194\pi\)
\(8\) 0 0
\(9\) −8.81253 + 7.39459i −0.108797 + 0.0912912i
\(10\) 0 0
\(11\) 103.948 180.042i 0.859070 1.48795i −0.0137466 0.999906i \(-0.504376\pi\)
0.872817 0.488048i \(-0.162291\pi\)
\(12\) 0 0
\(13\) −76.3894 + 209.878i −0.452008 + 1.24188i 0.479300 + 0.877651i \(0.340890\pi\)
−0.931309 + 0.364231i \(0.881332\pi\)
\(14\) 0 0
\(15\) 409.891 72.2748i 1.82174 0.321221i
\(16\) 0 0
\(17\) 361.904 + 303.674i 1.25226 + 1.05077i 0.996462 + 0.0840453i \(0.0267841\pi\)
0.255802 + 0.966729i \(0.417660\pi\)
\(18\) 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 −0.986519 0.163645i \(-0.947675\pi\)
0.871055 0.491186i \(-0.163436\pi\)
\(24\) 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 0.358009 0.933718i \(-0.383456\pi\)
−0.981701 + 0.190431i \(0.939011\pi\)
\(30\) 0 0
\(31\) 162.613 93.8845i 0.169212 0.0976946i −0.413002 0.910730i \(-0.635520\pi\)
0.582214 + 0.813035i \(0.302187\pi\)
\(32\) 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 \(0.108423\pi\)
−0.942547 + 0.334074i \(0.891577\pi\)
\(38\) 0 0
\(39\) −2148.13 −1.41232
\(40\) 0 0
\(41\) 819.137 + 2250.56i 0.487292 + 1.33882i 0.903123 + 0.429381i \(0.141268\pi\)
−0.415832 + 0.909442i \(0.636509\pi\)
\(42\) 0 0
\(43\) −232.697 + 1319.69i −0.125850 + 0.713733i 0.854949 + 0.518712i \(0.173588\pi\)
−0.980799 + 0.195020i \(0.937523\pi\)
\(44\) 0 0
\(45\) 248.916 + 431.135i 0.122921 + 0.212906i
\(46\) 0 0
\(47\) 670.959 563.001i 0.303739 0.254867i −0.478160 0.878273i \(-0.658696\pi\)
0.781898 + 0.623406i \(0.214252\pi\)
\(48\) 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 −0.906202 0.422845i \(-0.861032\pi\)
−0.706930 + 0.707283i \(0.749920\pi\)
\(54\) 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 −0.274250 0.961658i \(-0.588430\pi\)
0.994672 + 0.103094i \(0.0328741\pi\)
\(60\) 0 0
\(61\) 173.586 + 984.457i 0.0466504 + 0.264568i 0.999208 0.0397906i \(-0.0126691\pi\)
−0.952558 + 0.304358i \(0.901558\pi\)
\(62\) 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 0.921016 0.389524i \(-0.127360\pi\)
−0.543539 + 0.839384i \(0.682916\pi\)
\(68\) 0 0
\(69\) 2929.84 1691.54i 0.615384 0.355292i
\(70\) 0 0
\(71\) −2943.73 519.059i −0.583958 0.102968i −0.126138 0.992013i \(-0.540258\pi\)
−0.457819 + 0.889045i \(0.651369\pi\)
\(72\) 0 0
\(73\) 455.176 165.670i 0.0854148 0.0310885i −0.298959 0.954266i \(-0.596639\pi\)
0.384374 + 0.923177i \(0.374417\pi\)
\(74\) 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 0.988898 0.148598i \(-0.0474760\pi\)
−0.853056 + 0.521819i \(0.825254\pi\)
\(80\) 0 0
\(81\) −1278.13 + 7248.66i −0.194808 + 1.10481i
\(82\) 0 0
\(83\) 1815.81 + 3145.08i 0.263581 + 0.456536i 0.967191 0.254051i \(-0.0817630\pi\)
−0.703610 + 0.710587i \(0.748430\pi\)
\(84\) 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 0.657850 + 0.753149i \(0.271466\pi\)
−0.988057 + 0.154087i \(0.950756\pi\)
\(90\) 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 −0.759322 0.650715i \(-0.774469\pi\)
0.772684 + 0.634790i \(0.218914\pi\)
\(98\) 0 0
\(99\) 415.299 + 2355.28i 0.0423731 + 0.240310i
\(100\) 0 0
\(101\) 5764.46 + 2098.09i 0.565088 + 0.205675i 0.608737 0.793372i \(-0.291676\pi\)
−0.0436498 + 0.999047i \(0.513899\pi\)
\(102\) 0 0
\(103\) 10806.4 + 6239.10i 1.01861 + 0.588095i 0.913701 0.406387i \(-0.133212\pi\)
0.104909 + 0.994482i \(0.466545\pi\)
\(104\) 0 0
\(105\) −10098.9 12035.4i −0.916001 1.09165i
\(106\) 0 0
\(107\) −1213.06 + 700.358i −0.105953 + 0.0611720i −0.552040 0.833818i \(-0.686150\pi\)
0.446087 + 0.894990i \(0.352817\pi\)
\(108\) 0 0
\(109\) 11058.0 + 1949.82i 0.930727 + 0.164112i 0.618401 0.785863i \(-0.287781\pi\)
0.312326 + 0.949975i \(0.398892\pi\)
\(110\) 0 0
\(111\) −8266.88 + 3008.90i −0.670959 + 0.244209i
\(112\) 0 0
\(113\) 5242.34i 0.410552i 0.978704 + 0.205276i \(0.0658092\pi\)
−0.978704 + 0.205276i \(0.934191\pi\)
\(114\) 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 −0.988403 0.151855i \(-0.951475\pi\)
0.854771 + 0.519005i \(0.173697\pi\)
\(128\) 0 0
\(129\) −12692.7 + 2238.06i −0.762734 + 0.134491i
\(130\) 0 0
\(131\) 21564.8 + 18095.0i 1.25662 + 1.05443i 0.996034 + 0.0889757i \(0.0283594\pi\)
0.260583 + 0.965451i \(0.416085\pi\)
\(132\) 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 0.794466 + 0.607309i \(0.207751\pi\)
−0.538842 + 0.842407i \(0.681138\pi\)
\(138\) 0 0
\(139\) −7874.43 2866.06i −0.407558 0.148339i 0.130102 0.991501i \(-0.458469\pi\)
−0.537660 + 0.843162i \(0.680692\pi\)
\(140\) 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 −0.0619716 0.998078i \(-0.519739\pi\)
0.594079 + 0.804407i \(0.297517\pi\)
\(150\) 0 0
\(151\) 1094.46i 0.0480005i 0.999712 + 0.0240002i \(0.00764025\pi\)
−0.999712 + 0.0240002i \(0.992360\pi\)
\(152\) 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 −0.869399 0.494111i \(-0.835494\pi\)
0.985964 0.166960i \(-0.0533951\pi\)
\(158\) 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 −0.646326 0.763061i \(-0.723695\pi\)
0.983993 + 0.178204i \(0.0570288\pi\)
\(164\) 0 0
\(165\) 29594.6 81310.4i 1.08704 2.98661i
\(166\) 0 0
\(167\) −31190.3 + 5499.70i −1.11837 + 0.197199i −0.702127 0.712052i \(-0.747766\pi\)
−0.416247 + 0.909252i \(0.636655\pi\)
\(168\) 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 −0.753967 0.656913i \(-0.771862\pi\)
0.777858 + 0.628440i \(0.216306\pi\)
\(174\) 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 0.189719 0.981838i \(-0.439242\pi\)
−0.755437 + 0.655221i \(0.772575\pi\)
\(180\) 0 0
\(181\) −21860.1 26051.8i −0.667259 0.795209i 0.321149 0.947029i \(-0.395931\pi\)
−0.988408 + 0.151820i \(0.951487\pi\)
\(182\) 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 −0.955975 0.293449i \(-0.905197\pi\)
0.543693 0.839284i \(-0.317025\pi\)
\(194\) 0 0
\(195\) −16142.4 + 91548.1i −0.424521 + 2.40758i
\(196\) 0 0
\(197\) 7105.29 + 12306.7i 0.183083 + 0.317110i 0.942929 0.332994i \(-0.108059\pi\)
−0.759846 + 0.650104i \(0.774725\pi\)
\(198\) 0 0
\(199\) −22313.5 + 18723.2i −0.563457 + 0.472797i −0.879467 0.475959i \(-0.842101\pi\)
0.316010 + 0.948756i \(0.397657\pi\)
\(200\) 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 −0.502501 0.864577i \(-0.667587\pi\)
0.938700 + 0.344734i \(0.112031\pi\)
\(212\) 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 −0.714421 0.699716i \(-0.753310\pi\)
−0.910653 + 0.413171i \(0.864421\pi\)
\(224\) 0 0
\(225\) 13488.1 4909.25i 0.266431 0.0969728i
\(226\) 0 0
\(227\) 47803.2i 0.927695i −0.885915 0.463847i \(-0.846469\pi\)
0.885915 0.463847i \(-0.153531\pi\)
\(228\) 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 0.805250 + 0.592935i \(0.202031\pi\)
−0.959483 + 0.281765i \(0.909080\pi\)
\(234\) 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 0.281677 + 0.959509i \(0.409109\pi\)
−0.971798 + 0.235815i \(0.924224\pi\)
\(240\) 0 0
\(241\) −30298.5 + 83244.4i −0.521659 + 1.43325i 0.347013 + 0.937860i \(0.387196\pi\)
−0.868672 + 0.495387i \(0.835026\pi\)
\(242\) 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 −0.794661 0.607054i \(-0.792351\pi\)
0.539112 0.842234i \(-0.318760\pi\)
\(252\) 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 −0.999276 0.0380473i \(-0.987886\pi\)
0.136053 0.990702i \(-0.456558\pi\)
\(258\) 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 0.139887 0.990168i \(-0.455326\pi\)
0.743627 + 0.668595i \(0.233104\pi\)
\(264\) 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 0.772133 0.635461i \(-0.219190\pi\)
−0.999955 + 0.00952562i \(0.996968\pi\)
\(270\) 0 0
\(271\) 3910.58 22178.0i 0.0532479 0.301984i −0.946540 0.322587i \(-0.895448\pi\)
0.999788 + 0.0206031i \(0.00655864\pi\)
\(272\) 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 −0.904902 0.425621i \(-0.860056\pi\)
0.821049 + 0.570858i \(0.193389\pi\)
\(278\) 0 0
\(279\) −738.791 + 2029.81i −0.00949103 + 0.0260764i
\(280\) 0 0
\(281\) 86611.2 15271.9i 1.09689 0.193411i 0.404215 0.914664i \(-0.367545\pi\)
0.692671 + 0.721254i \(0.256434\pi\)
\(282\) 0 0
\(283\) −89003.0 74682.4i −1.11130 0.932493i −0.113169 0.993576i \(-0.536100\pi\)
−0.998133 + 0.0610832i \(0.980544\pi\)
\(284\) 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 0.828167 0.560482i \(-0.189384\pi\)
−0.0713079 + 0.997454i \(0.522717\pi\)
\(294\) 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 −0.966637 0.256151i \(-0.917545\pi\)
0.575836 0.817565i \(-0.304677\pi\)
\(308\) 0 0
\(309\) −20840.2 + 118191.i −0.218265 + 1.23785i
\(310\) 0 0
\(311\) 33480.2 + 57989.4i 0.346152 + 0.599553i 0.985562 0.169313i \(-0.0541548\pi\)
−0.639410 + 0.768866i \(0.720821\pi\)
\(312\) 0 0
\(313\) 34053.8 28574.5i 0.347597 0.291669i −0.452227 0.891903i \(-0.649370\pi\)
0.799824 + 0.600234i \(0.204926\pi\)
\(314\) 0 0
\(315\) 9396.01 16274.4i 0.0946940 0.164015i
\(316\) 0 0
\(317\) 35448.9 97395.0i 0.352764 0.969211i −0.628714 0.777636i \(-0.716418\pi\)
0.981478 0.191574i \(-0.0613593\pi\)
\(318\) 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 0.744629 0.667478i \(-0.232626\pi\)
−0.205739 + 0.978607i \(0.565960\pi\)
\(332\) 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 0.493177 0.869929i \(-0.335835\pi\)
0.165902 + 0.986142i \(0.446947\pi\)
\(338\) 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 −0.937237 0.348693i \(-0.886626\pi\)
0.999975 0.00711023i \(-0.00226328\pi\)
\(348\) 0 0
\(349\) 78844.4 + 136562.i 0.647321 + 1.12119i 0.983760 + 0.179488i \(0.0574441\pi\)
−0.336439 + 0.941705i \(0.609223\pi\)
\(350\) 0 0
\(351\) −114360. + 95959.7i −0.928242 + 0.778888i
\(352\) 0 0
\(353\) −19855.9 + 34391.5i −0.159346 + 0.275995i −0.934633 0.355614i \(-0.884272\pi\)
0.775287 + 0.631609i \(0.217605\pi\)
\(354\) 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 0.0860774 0.996288i \(-0.472567\pi\)
−0.966205 + 0.257773i \(0.917011\pi\)
\(360\) 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 0.378386 0.925648i \(-0.376479\pi\)
−0.305135 + 0.952309i \(0.598702\pi\)
\(368\) 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 −0.784292 0.620392i \(-0.786973\pi\)
0.145129 + 0.989413i \(0.453640\pi\)
\(374\) 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 \(0.235029\pi\)
−0.739570 + 0.673080i \(0.764971\pi\)
\(380\) 0 0
\(381\) −60610.1 −0.417537
\(382\) 0 0
\(383\) −31138.5 85552.4i −0.212276 0.583223i 0.787162 0.616746i \(-0.211550\pi\)
−0.999438 + 0.0335230i \(0.989327\pi\)
\(384\) 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 −0.566264 0.824224i \(-0.691612\pi\)
0.713371 + 0.700787i \(0.247167\pi\)
\(390\) 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 0.980412 + 0.196957i \(0.0631061\pi\)
0.364212 + 0.931316i \(0.381338\pi\)
\(398\) 0 0
\(399\) −112018. 68039.8i −0.703623 0.427383i
\(400\) 0 0
\(401\) −187594. + 223565.i −1.16662 + 1.39032i −0.261479 + 0.965209i \(0.584210\pi\)
−0.905140 + 0.425114i \(0.860234\pi\)
\(402\) 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 −0.945832 0.324658i \(-0.894751\pi\)
−0.155483 0.987839i \(-0.549693\pi\)
\(410\) 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 −0.833588 0.552386i \(-0.813717\pi\)
0.283499 0.958973i \(-0.408505\pi\)
\(422\) 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 −0.274178 0.961679i \(-0.588406\pi\)
0.828188 0.560451i \(-0.189372\pi\)
\(432\) 0 0
\(433\) −260545. + 45941.1i −1.38966 + 0.245034i −0.817886 0.575381i \(-0.804854\pi\)
−0.571769 + 0.820414i \(0.693743\pi\)
\(434\) 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 −0.991182 0.132509i \(-0.957697\pi\)
0.302612 + 0.953114i \(0.402141\pi\)
\(440\) 0 0
\(441\) 1949.91 + 11058.5i 0.0100262 + 0.0568616i
\(442\) 0 0
\(443\) 64757.2 + 23569.7i 0.329975 + 0.120101i 0.501695 0.865045i \(-0.332710\pi\)
−0.171720 + 0.985146i \(0.554932\pi\)
\(444\) 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 −0.930754 0.365646i \(-0.880848\pi\)
−0.148718 + 0.988880i \(0.547515\pi\)
\(450\) 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 −0.543586 0.839353i \(-0.682934\pi\)
0.797880 0.602817i \(-0.205955\pi\)
\(462\) 0 0
\(463\) 5432.68 + 9409.69i 0.0253427 + 0.0438948i 0.878419 0.477892i \(-0.158599\pi\)
−0.853076 + 0.521787i \(0.825266\pi\)
\(464\) 0 0
\(465\) 59867.9 50235.2i 0.276878 0.232328i
\(466\) 0 0
\(467\) −109600. + 189833.i −0.502547 + 0.870437i 0.497448 + 0.867494i \(0.334270\pi\)
−0.999996 + 0.00294375i \(0.999063\pi\)
\(468\) 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 0.850759 + 0.525556i \(0.176143\pi\)
−0.619701 + 0.784838i \(0.712746\pi\)
\(480\) 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 −0.509017 0.860757i \(-0.669991\pi\)
0.490929 + 0.871200i \(0.336658\pi\)
\(488\) 0 0
\(489\) 169952. + 29967.1i 0.710735 + 0.125322i
\(490\) 0 0
\(491\) 184130. 67017.8i 0.763768 0.277989i 0.0693808 0.997590i \(-0.477898\pi\)
0.694387 + 0.719601i \(0.255675\pi\)
\(492\) 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 −0.984451 0.175660i \(-0.943794\pi\)
0.985161 + 0.171635i \(0.0549051\pi\)
\(500\) 0 0
\(501\) −152307. 263803.i −0.606797 1.05100i
\(502\) 0 0
\(503\) −114887. + 96401.4i −0.454081 + 0.381020i −0.840948 0.541116i \(-0.818002\pi\)
0.386866 + 0.922136i \(0.373557\pi\)
\(504\) 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 0.104428 0.994532i \(-0.466699\pi\)
0.438281 + 0.898838i \(0.355588\pi\)
\(510\) 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 0.293672 0.955906i \(-0.405123\pi\)
−0.681003 + 0.732281i \(0.738456\pi\)
\(522\) 0 0
\(523\) 38925.4 + 46389.5i 0.142308 + 0.169596i 0.832491 0.554039i \(-0.186914\pi\)
−0.690182 + 0.723635i \(0.742470\pi\)
\(524\) 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 −0.997605 0.0691745i \(-0.977963\pi\)
−0.105109 + 0.994461i \(0.533519\pi\)
\(542\) 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 −0.694019 0.719956i \(-0.744162\pi\)
−0.405925 + 0.913906i \(0.633051\pi\)
\(548\) 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 0.862819 0.505512i \(-0.168697\pi\)
0.336021 + 0.941855i \(0.390919\pi\)
\(558\) 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 −0.0138446 0.999904i \(-0.504407\pi\)
0.859020 + 0.511942i \(0.171074\pi\)
\(564\) 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 \(0.143669\pi\)
−0.899859 + 0.436180i \(0.856331\pi\)
\(570\) 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 −0.712655 0.701515i \(-0.752507\pi\)
−0.251202 0.967935i \(-0.580826\pi\)
\(578\) 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 0.986072 0.166319i \(-0.0531882\pi\)
0.00743718 + 0.999972i \(0.497633\pi\)
\(588\) 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 0.978039 0.208420i \(-0.0668322\pi\)
−0.990340 + 0.138658i \(0.955721\pi\)
\(594\) 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 −0.979216 0.202820i \(-0.934989\pi\)
−0.0296996 0.999559i \(-0.509455\pi\)
\(600\) 0 0
\(601\) −108967. + 62911.9i −0.301679 + 0.174174i −0.643197 0.765701i \(-0.722392\pi\)
0.341518 + 0.939875i \(0.389059\pi\)
\(602\) 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 \(-0.805946\pi\)
0.819855 0.572571i \(-0.194054\pi\)
\(608\) 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 −0.996522 0.0833248i \(-0.973446\pi\)
0.964924 + 0.262531i \(0.0845572\pi\)
\(614\) 0 0
\(615\) 498415. + 863281.i 1.31777 + 2.28245i
\(616\) 0 0
\(617\) 260713. 218764.i 0.684845 0.574653i −0.232573 0.972579i \(-0.574714\pi\)
0.917417 + 0.397926i \(0.130270\pi\)
\(618\) 0 0
\(619\) −68974.6 + 119468.i −0.180015 + 0.311795i −0.941885 0.335935i \(-0.890948\pi\)
0.761871 + 0.647729i \(0.224281\pi\)
\(620\) 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 0.997445 0.0714390i \(-0.0227591\pi\)
−0.961725 + 0.274016i \(0.911648\pi\)
\(632\) 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 −0.589058 0.808091i \(-0.700501\pi\)
−0.829917 + 0.557887i \(0.811612\pi\)
\(642\) 0 0
\(643\) −640784. + 233226.i −1.54985 + 0.564100i −0.968383 0.249470i \(-0.919744\pi\)
−0.581468 + 0.813569i \(0.697522\pi\)
\(644\) 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 0.999784 + 0.0207656i \(0.00661036\pi\)
−0.481909 + 0.876221i \(0.660056\pi\)
\(654\) 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 −0.884085 0.467325i \(-0.845218\pi\)
0.977640 + 0.210287i \(0.0674399\pi\)
\(660\) 0 0
\(661\) −258721. + 45619.5i −0.592146 + 0.104411i −0.461688 0.887043i \(-0.652756\pi\)
−0.130458 + 0.991454i \(0.541645\pi\)
\(662\) 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 0.975792 0.218699i \(-0.0701813\pi\)
0.298497 + 0.954410i \(0.403515\pi\)
\(674\) 0 0
\(675\) −536074. 638868.i −1.17657 1.40218i
\(676\) 0 0
\(677\) 58995.1 34060.8i 0.128718 0.0743153i −0.434258 0.900788i \(-0.642990\pi\)
0.562976 + 0.826473i \(0.309656\pi\)
\(678\) 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 \(0.210935\pi\)
−0.788351 + 0.615225i \(0.789065\pi\)
\(684\) 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 0.953442 0.301576i \(-0.0975126\pi\)
−0.737893 + 0.674917i \(0.764179\pi\)
\(692\) 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 0.197855 0.980231i \(-0.436602\pi\)
−0.930982 + 0.365065i \(0.881047\pi\)
\(702\) 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 0.163551 0.986535i \(-0.447705\pi\)
−0.508845 + 0.860858i \(0.669928\pi\)
\(710\) 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 −0.453015 0.891503i \(-0.649651\pi\)
0.226018 + 0.974123i \(0.427429\pi\)
\(720\) 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 −0.975949 0.218001i \(-0.930046\pi\)
0.991652 + 0.128940i \(0.0411576\pi\)
\(728\) 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 −0.259356 0.965782i \(-0.583510\pi\)
0.966070 0.258282i \(-0.0831563\pi\)
\(734\) 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 0.847245 0.531202i \(-0.178259\pi\)
−0.376009 + 0.926616i \(0.622704\pi\)
\(740\) 0 0
\(741\) 117638. + 766502.i 0.214246 + 1.39597i
\(742\) 0 0
\(743\) −469418. + 559431.i −0.850320 + 1.01337i 0.149377 + 0.988780i \(0.452273\pi\)
−0.999698 + 0.0245920i \(0.992171\pi\)
\(744\) 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 0.799307 0.600922i \(-0.205200\pi\)
−0.730591 + 0.682815i \(0.760756\pi\)
\(752\) 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 0.254847 0.966981i \(-0.417975\pi\)
0.816788 + 0.576938i \(0.195753\pi\)
\(758\) 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 −0.838398 0.545058i \(-0.816508\pi\)
0.391191 + 0.920310i \(0.372063\pi\)
\(770\) 0 0
\(771\) 426552. 738809.i 0.717568 1.24286i
\(772\) 0 0
\(773\) −257582. + 707701.i −0.431079 + 1.18438i 0.514072 + 0.857747i \(0.328136\pi\)
−0.945151 + 0.326633i \(0.894086\pi\)
\(774\) 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 −0.993969 0.109659i \(-0.965024\pi\)
−0.591952 0.805973i \(-0.701643\pi\)
\(788\) 0 0
\(789\) 402056. + 479152.i 0.645851 + 0.769695i
\(790\) 0 0
\(791\) 171374. 98943.1i 0.273901 0.158137i
\(792\) 0 0