Properties

Label 76.5.j.a.13.5
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 13.5
Character \(\chi\) \(=\) 76.13
Dual form 76.5.j.a.41.5

$q$-expansion

\(f(q)\) \(=\) \(q+(2.65366 - 7.29088i) q^{3} +(0.405227 + 2.29816i) q^{5} +(23.2726 - 40.3094i) q^{7} +(15.9346 + 13.3707i) q^{9} +O(q^{10})\) \(q+(2.65366 - 7.29088i) q^{3} +(0.405227 + 2.29816i) q^{5} +(23.2726 - 40.3094i) q^{7} +(15.9346 + 13.3707i) q^{9} +(-88.3294 - 152.991i) q^{11} +(-37.7242 - 103.646i) q^{13} +(17.8309 + 3.14407i) q^{15} +(-57.1483 + 47.9531i) q^{17} +(-192.492 - 305.398i) q^{19} +(-232.133 - 276.646i) q^{21} +(15.6411 - 88.7052i) q^{23} +(582.191 - 211.900i) q^{25} +(684.034 - 394.927i) q^{27} +(-121.887 + 145.259i) q^{29} +(670.369 + 387.038i) q^{31} +(-1349.84 + 238.013i) q^{33} +(102.068 + 37.1497i) q^{35} +1355.70i q^{37} -855.781 q^{39} +(-316.776 + 870.336i) q^{41} +(298.395 + 1692.28i) q^{43} +(-24.2709 + 42.0384i) q^{45} +(1738.43 + 1458.72i) q^{47} +(117.269 + 203.116i) q^{49} +(197.968 + 543.913i) q^{51} +(-1141.83 - 201.336i) q^{53} +(315.804 - 264.991i) q^{55} +(-2737.43 + 593.012i) q^{57} +(2592.52 + 3089.64i) q^{59} +(702.333 - 3983.13i) q^{61} +(909.805 - 331.142i) q^{63} +(222.909 - 128.697i) q^{65} +(1781.28 - 2122.85i) q^{67} +(-605.233 - 349.431i) q^{69} +(5745.13 - 1013.02i) q^{71} +(-4484.03 - 1632.05i) q^{73} -4806.99i q^{75} -8222.63 q^{77} +(1602.75 - 4403.53i) q^{79} +(-771.592 - 4375.92i) q^{81} +(-3711.86 + 6429.14i) q^{83} +(-133.362 - 111.904i) q^{85} +(735.618 + 1274.13i) q^{87} +(-1547.47 - 4251.63i) q^{89} +(-5055.87 - 891.486i) q^{91} +(4600.78 - 3860.51i) q^{93} +(623.850 - 566.132i) q^{95} +(3365.63 + 4011.01i) q^{97} +(638.106 - 3618.88i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

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
\(3\) 2.65366 7.29088i 0.294851 0.810098i −0.700488 0.713664i \(-0.747034\pi\)
0.995339 0.0964336i \(-0.0307435\pi\)
\(4\) 0 0
\(5\) 0.405227 + 2.29816i 0.0162091 + 0.0919263i 0.991839 0.127496i \(-0.0406939\pi\)
−0.975630 + 0.219422i \(0.929583\pi\)
\(6\) 0 0
\(7\) 23.2726 40.3094i 0.474952 0.822641i −0.524637 0.851326i \(-0.675799\pi\)
0.999588 + 0.0286856i \(0.00913217\pi\)
\(8\) 0 0
\(9\) 15.9346 + 13.3707i 0.196723 + 0.165070i
\(10\) 0 0
\(11\) −88.3294 152.991i −0.729995 1.26439i −0.956885 0.290468i \(-0.906189\pi\)
0.226889 0.973921i \(-0.427144\pi\)
\(12\) 0 0
\(13\) −37.7242 103.646i −0.223220 0.613293i 0.776641 0.629943i \(-0.216922\pi\)
−0.999861 + 0.0166508i \(0.994700\pi\)
\(14\) 0 0
\(15\) 17.8309 + 3.14407i 0.0792486 + 0.0139737i
\(16\) 0 0
\(17\) −57.1483 + 47.9531i −0.197745 + 0.165928i −0.736284 0.676673i \(-0.763421\pi\)
0.538539 + 0.842601i \(0.318977\pi\)
\(18\) 0 0
\(19\) −192.492 305.398i −0.533218 0.845978i
\(20\) 0 0
\(21\) −232.133 276.646i −0.526379 0.627314i
\(22\) 0 0
\(23\) 15.6411 88.7052i 0.0295673 0.167685i −0.966449 0.256860i \(-0.917312\pi\)
0.996016 + 0.0891754i \(0.0284232\pi\)
\(24\) 0 0
\(25\) 582.191 211.900i 0.931505 0.339040i
\(26\) 0 0
\(27\) 684.034 394.927i 0.938318 0.541738i
\(28\) 0 0
\(29\) −121.887 + 145.259i −0.144931 + 0.172721i −0.833626 0.552329i \(-0.813739\pi\)
0.688696 + 0.725051i \(0.258184\pi\)
\(30\) 0 0
\(31\) 670.369 + 387.038i 0.697574 + 0.402745i 0.806443 0.591311i \(-0.201390\pi\)
−0.108869 + 0.994056i \(0.534723\pi\)
\(32\) 0 0
\(33\) −1349.84 + 238.013i −1.23952 + 0.218561i
\(34\) 0 0
\(35\) 102.068 + 37.1497i 0.0833208 + 0.0303263i
\(36\) 0 0
\(37\) 1355.70i 0.990283i 0.868812 + 0.495141i \(0.164884\pi\)
−0.868812 + 0.495141i \(0.835116\pi\)
\(38\) 0 0
\(39\) −855.781 −0.562644
\(40\) 0 0
\(41\) −316.776 + 870.336i −0.188445 + 0.517749i −0.997553 0.0699111i \(-0.977728\pi\)
0.809108 + 0.587660i \(0.199951\pi\)
\(42\) 0 0
\(43\) 298.395 + 1692.28i 0.161382 + 0.915243i 0.952717 + 0.303860i \(0.0982754\pi\)
−0.791335 + 0.611383i \(0.790613\pi\)
\(44\) 0 0
\(45\) −24.2709 + 42.0384i −0.0119856 + 0.0207597i
\(46\) 0 0
\(47\) 1738.43 + 1458.72i 0.786978 + 0.660353i 0.944995 0.327083i \(-0.106066\pi\)
−0.158018 + 0.987436i \(0.550510\pi\)
\(48\) 0 0
\(49\) 117.269 + 203.116i 0.0488417 + 0.0845962i
\(50\) 0 0
\(51\) 197.968 + 543.913i 0.0761123 + 0.209117i
\(52\) 0 0
\(53\) −1141.83 201.336i −0.406491 0.0716753i −0.0333356 0.999444i \(-0.510613\pi\)
−0.373155 + 0.927769i \(0.621724\pi\)
\(54\) 0 0
\(55\) 315.804 264.991i 0.104398 0.0876004i
\(56\) 0 0
\(57\) −2737.43 + 593.012i −0.842545 + 0.182521i
\(58\) 0 0
\(59\) 2592.52 + 3089.64i 0.744763 + 0.887574i 0.996783 0.0801483i \(-0.0255394\pi\)
−0.252020 + 0.967722i \(0.581095\pi\)
\(60\) 0 0
\(61\) 702.333 3983.13i 0.188749 1.07045i −0.732295 0.680987i \(-0.761551\pi\)
0.921044 0.389459i \(-0.127338\pi\)
\(62\) 0 0
\(63\) 909.805 331.142i 0.229228 0.0834321i
\(64\) 0 0
\(65\) 222.909 128.697i 0.0527595 0.0304607i
\(66\) 0 0
\(67\) 1781.28 2122.85i 0.396811 0.472900i −0.530234 0.847851i \(-0.677896\pi\)
0.927045 + 0.374951i \(0.122340\pi\)
\(68\) 0 0
\(69\) −605.233 349.431i −0.127123 0.0733945i
\(70\) 0 0
\(71\) 5745.13 1013.02i 1.13968 0.200956i 0.428215 0.903677i \(-0.359143\pi\)
0.711466 + 0.702721i \(0.248032\pi\)
\(72\) 0 0
\(73\) −4484.03 1632.05i −0.841440 0.306259i −0.114895 0.993378i \(-0.536653\pi\)
−0.726545 + 0.687119i \(0.758875\pi\)
\(74\) 0 0
\(75\) 4806.99i 0.854577i
\(76\) 0 0
\(77\) −8222.63 −1.38685
\(78\) 0 0
\(79\) 1602.75 4403.53i 0.256810 0.705581i −0.742549 0.669792i \(-0.766383\pi\)
0.999359 0.0357890i \(-0.0113944\pi\)
\(80\) 0 0
\(81\) −771.592 4375.92i −0.117603 0.666959i
\(82\) 0 0
\(83\) −3711.86 + 6429.14i −0.538810 + 0.933247i 0.460158 + 0.887837i \(0.347793\pi\)
−0.998968 + 0.0454098i \(0.985541\pi\)
\(84\) 0 0
\(85\) −133.362 111.904i −0.0184584 0.0154884i
\(86\) 0 0
\(87\) 735.618 + 1274.13i 0.0971883 + 0.168335i
\(88\) 0 0
\(89\) −1547.47 4251.63i −0.195362 0.536754i 0.802872 0.596152i \(-0.203304\pi\)
−0.998234 + 0.0593976i \(0.981082\pi\)
\(90\) 0 0
\(91\) −5055.87 891.486i −0.610538 0.107654i
\(92\) 0 0
\(93\) 4600.78 3860.51i 0.531943 0.446353i
\(94\) 0 0
\(95\) 623.850 566.132i 0.0691246 0.0627293i
\(96\) 0 0
\(97\) 3365.63 + 4011.01i 0.357704 + 0.426295i 0.914646 0.404257i \(-0.132470\pi\)
−0.556942 + 0.830552i \(0.688025\pi\)
\(98\) 0 0
\(99\) 638.106 3618.88i 0.0651062 0.369235i
\(100\) 0 0
\(101\) −6086.56 + 2215.33i −0.596663 + 0.217168i −0.622658 0.782494i \(-0.713947\pi\)
0.0259944 + 0.999662i \(0.491725\pi\)
\(102\) 0 0
\(103\) 12871.6 7431.44i 1.21327 0.700484i 0.249803 0.968297i \(-0.419634\pi\)
0.963471 + 0.267812i \(0.0863007\pi\)
\(104\) 0 0
\(105\) 541.708 645.583i 0.0491346 0.0585563i
\(106\) 0 0
\(107\) −13745.2 7935.81i −1.20056 0.693144i −0.239881 0.970802i \(-0.577108\pi\)
−0.960680 + 0.277658i \(0.910442\pi\)
\(108\) 0 0
\(109\) 10969.9 1934.29i 0.923314 0.162805i 0.308271 0.951299i \(-0.400250\pi\)
0.615043 + 0.788493i \(0.289139\pi\)
\(110\) 0 0
\(111\) 9884.23 + 3597.56i 0.802226 + 0.291986i
\(112\) 0 0
\(113\) 24537.3i 1.92163i 0.277193 + 0.960814i \(0.410596\pi\)
−0.277193 + 0.960814i \(0.589404\pi\)
\(114\) 0 0
\(115\) 210.197 0.0158939
\(116\) 0 0
\(117\) 784.706 2155.96i 0.0573239 0.157496i
\(118\) 0 0
\(119\) 602.969 + 3419.61i 0.0425796 + 0.241481i
\(120\) 0 0
\(121\) −8283.67 + 14347.7i −0.565786 + 0.979970i
\(122\) 0 0
\(123\) 5504.89 + 4619.16i 0.363864 + 0.305318i
\(124\) 0 0
\(125\) 1452.15 + 2515.20i 0.0929378 + 0.160973i
\(126\) 0 0
\(127\) −1306.34 3589.15i −0.0809935 0.222528i 0.892586 0.450878i \(-0.148889\pi\)
−0.973579 + 0.228350i \(0.926667\pi\)
\(128\) 0 0
\(129\) 13130.1 + 2315.19i 0.789020 + 0.139125i
\(130\) 0 0
\(131\) −25945.5 + 21770.9i −1.51189 + 1.26862i −0.651905 + 0.758301i \(0.726030\pi\)
−0.859983 + 0.510323i \(0.829526\pi\)
\(132\) 0 0
\(133\) −16790.2 + 651.813i −0.949189 + 0.0368485i
\(134\) 0 0
\(135\) 1184.79 + 1411.98i 0.0650092 + 0.0774750i
\(136\) 0 0
\(137\) −771.241 + 4373.93i −0.0410912 + 0.233040i −0.998436 0.0559085i \(-0.982194\pi\)
0.957345 + 0.288948i \(0.0933056\pi\)
\(138\) 0 0
\(139\) 9764.51 3553.99i 0.505383 0.183944i −0.0767305 0.997052i \(-0.524448\pi\)
0.582114 + 0.813107i \(0.302226\pi\)
\(140\) 0 0
\(141\) 15248.6 8803.77i 0.766992 0.442823i
\(142\) 0 0
\(143\) −12524.8 + 14926.5i −0.612491 + 0.729938i
\(144\) 0 0
\(145\) −383.219 221.252i −0.0182268 0.0105233i
\(146\) 0 0
\(147\) 1792.08 315.993i 0.0829323 0.0146232i
\(148\) 0 0
\(149\) 17999.4 + 6551.26i 0.810748 + 0.295088i 0.713933 0.700214i \(-0.246912\pi\)
0.0968155 + 0.995302i \(0.469134\pi\)
\(150\) 0 0
\(151\) 16772.4i 0.735598i 0.929905 + 0.367799i \(0.119889\pi\)
−0.929905 + 0.367799i \(0.880111\pi\)
\(152\) 0 0
\(153\) −1551.80 −0.0662909
\(154\) 0 0
\(155\) −617.822 + 1697.45i −0.0257158 + 0.0706535i
\(156\) 0 0
\(157\) −6522.77 36992.5i −0.264626 1.50077i −0.770097 0.637926i \(-0.779792\pi\)
0.505471 0.862844i \(-0.331319\pi\)
\(158\) 0 0
\(159\) −4497.96 + 7790.69i −0.177918 + 0.308164i
\(160\) 0 0
\(161\) −3211.64 2694.89i −0.123901 0.103965i
\(162\) 0 0
\(163\) −11507.2 19931.0i −0.433105 0.750160i 0.564034 0.825752i \(-0.309249\pi\)
−0.997139 + 0.0755914i \(0.975916\pi\)
\(164\) 0 0
\(165\) −1093.98 3005.69i −0.0401829 0.110402i
\(166\) 0 0
\(167\) −7735.07 1363.90i −0.277352 0.0489046i 0.0332420 0.999447i \(-0.489417\pi\)
−0.310594 + 0.950543i \(0.600528\pi\)
\(168\) 0 0
\(169\) 12559.5 10538.7i 0.439744 0.368989i
\(170\) 0 0
\(171\) 1016.11 7440.14i 0.0347494 0.254442i
\(172\) 0 0
\(173\) 11562.8 + 13780.0i 0.386341 + 0.460424i 0.923805 0.382863i \(-0.125062\pi\)
−0.537464 + 0.843287i \(0.680617\pi\)
\(174\) 0 0
\(175\) 5007.55 28399.2i 0.163512 0.927321i
\(176\) 0 0
\(177\) 29405.9 10702.9i 0.938616 0.341628i
\(178\) 0 0
\(179\) 19162.8 11063.7i 0.598072 0.345297i −0.170211 0.985408i \(-0.554445\pi\)
0.768283 + 0.640111i \(0.221111\pi\)
\(180\) 0 0
\(181\) 20579.6 24525.8i 0.628175 0.748629i −0.354278 0.935140i \(-0.615273\pi\)
0.982453 + 0.186511i \(0.0597179\pi\)
\(182\) 0 0
\(183\) −27176.8 15690.5i −0.811513 0.468527i
\(184\) 0 0
\(185\) −3115.61 + 549.365i −0.0910330 + 0.0160516i
\(186\) 0 0
\(187\) 12384.3 + 4507.51i 0.354150 + 0.128900i
\(188\) 0 0
\(189\) 36764.0i 1.02920i
\(190\) 0 0
\(191\) −54589.8 −1.49639 −0.748196 0.663478i \(-0.769080\pi\)
−0.748196 + 0.663478i \(0.769080\pi\)
\(192\) 0 0
\(193\) −18704.7 + 51390.8i −0.502154 + 1.37966i 0.387013 + 0.922074i \(0.373507\pi\)
−0.889167 + 0.457582i \(0.848716\pi\)
\(194\) 0 0
\(195\) −346.786 1966.72i −0.00911994 0.0517218i
\(196\) 0 0
\(197\) 3388.48 5869.03i 0.0873118 0.151229i −0.819062 0.573705i \(-0.805506\pi\)
0.906374 + 0.422476i \(0.138839\pi\)
\(198\) 0 0
\(199\) −49441.1 41486.0i −1.24848 1.04760i −0.996812 0.0797869i \(-0.974576\pi\)
−0.251669 0.967813i \(-0.580980\pi\)
\(200\) 0 0
\(201\) −10750.5 18620.4i −0.266095 0.460891i
\(202\) 0 0
\(203\) 3018.67 + 8293.73i 0.0732527 + 0.201260i
\(204\) 0 0
\(205\) −2128.53 375.318i −0.0506492 0.00893083i
\(206\) 0 0
\(207\) 1435.29 1204.35i 0.0334964 0.0281068i
\(208\) 0 0
\(209\) −29720.5 + 56425.1i −0.680398 + 1.29175i
\(210\) 0 0
\(211\) 43222.2 + 51510.2i 0.970827 + 1.15699i 0.987578 + 0.157127i \(0.0502233\pi\)
−0.0167510 + 0.999860i \(0.505332\pi\)
\(212\) 0 0
\(213\) 7859.82 44575.3i 0.173242 0.982505i
\(214\) 0 0
\(215\) −3768.22 + 1371.52i −0.0815190 + 0.0296705i
\(216\) 0 0
\(217\) 31202.5 18014.8i 0.662628 0.382569i
\(218\) 0 0
\(219\) −23798.2 + 28361.6i −0.496200 + 0.591348i
\(220\) 0 0
\(221\) 7126.05 + 4114.23i 0.145903 + 0.0842371i
\(222\) 0 0
\(223\) 3287.92 579.750i 0.0661168 0.0116582i −0.140492 0.990082i \(-0.544868\pi\)
0.206609 + 0.978424i \(0.433757\pi\)
\(224\) 0 0
\(225\) 12110.2 + 4407.76i 0.239214 + 0.0870669i
\(226\) 0 0
\(227\) 74854.6i 1.45267i −0.687341 0.726335i \(-0.741222\pi\)
0.687341 0.726335i \(-0.258778\pi\)
\(228\) 0 0
\(229\) 69586.5 1.32695 0.663474 0.748199i \(-0.269081\pi\)
0.663474 + 0.748199i \(0.269081\pi\)
\(230\) 0 0
\(231\) −21820.1 + 59950.2i −0.408915 + 1.12348i
\(232\) 0 0
\(233\) 5567.08 + 31572.5i 0.102545 + 0.581563i 0.992172 + 0.124876i \(0.0398532\pi\)
−0.889627 + 0.456688i \(0.849036\pi\)
\(234\) 0 0
\(235\) −2647.91 + 4586.31i −0.0479476 + 0.0830477i
\(236\) 0 0
\(237\) −27852.4 23371.0i −0.495869 0.416083i
\(238\) 0 0
\(239\) 12567.6 + 21767.7i 0.220017 + 0.381081i 0.954813 0.297207i \(-0.0960553\pi\)
−0.734796 + 0.678289i \(0.762722\pi\)
\(240\) 0 0
\(241\) 10430.9 + 28658.6i 0.179592 + 0.493425i 0.996524 0.0833092i \(-0.0265489\pi\)
−0.816932 + 0.576735i \(0.804327\pi\)
\(242\) 0 0
\(243\) 29054.4 + 5123.07i 0.492038 + 0.0867596i
\(244\) 0 0
\(245\) −419.271 + 351.810i −0.00698494 + 0.00586106i
\(246\) 0 0
\(247\) −24391.8 + 31472.0i −0.399807 + 0.515858i
\(248\) 0 0
\(249\) 37024.0 + 44123.5i 0.597152 + 0.711658i
\(250\) 0 0
\(251\) 7734.70 43865.7i 0.122771 0.696269i −0.859836 0.510571i \(-0.829434\pi\)
0.982607 0.185699i \(-0.0594548\pi\)
\(252\) 0 0
\(253\) −14952.7 + 5442.33i −0.233603 + 0.0850244i
\(254\) 0 0
\(255\) −1169.78 + 675.371i −0.0179896 + 0.0103863i
\(256\) 0 0
\(257\) −65549.4 + 78118.7i −0.992436 + 1.18274i −0.00928251 + 0.999957i \(0.502955\pi\)
−0.983153 + 0.182782i \(0.941490\pi\)
\(258\) 0 0
\(259\) 54647.3 + 31550.6i 0.814647 + 0.470337i
\(260\) 0 0
\(261\) −3884.43 + 684.929i −0.0570224 + 0.0100546i
\(262\) 0 0
\(263\) 113180. + 41194.3i 1.63629 + 0.595560i 0.986384 0.164456i \(-0.0525870\pi\)
0.649904 + 0.760017i \(0.274809\pi\)
\(264\) 0 0
\(265\) 2705.70i 0.0385290i
\(266\) 0 0
\(267\) −35104.6 −0.492426
\(268\) 0 0
\(269\) −47107.1 + 129426.i −0.651001 + 1.78861i −0.0369886 + 0.999316i \(0.511777\pi\)
−0.614013 + 0.789296i \(0.710446\pi\)
\(270\) 0 0
\(271\) −15656.1 88790.1i −0.213179 1.20900i −0.884038 0.467414i \(-0.845186\pi\)
0.670859 0.741585i \(-0.265925\pi\)
\(272\) 0 0
\(273\) −19916.3 + 34496.0i −0.267229 + 0.462854i
\(274\) 0 0
\(275\) −83843.4 70352.9i −1.10867 0.930287i
\(276\) 0 0
\(277\) −62079.9 107525.i −0.809080 1.40137i −0.913502 0.406834i \(-0.866633\pi\)
0.104423 0.994533i \(-0.466701\pi\)
\(278\) 0 0
\(279\) 5507.09 + 15130.6i 0.0707479 + 0.194378i
\(280\) 0 0
\(281\) 47169.6 + 8317.28i 0.597379 + 0.105334i 0.464158 0.885752i \(-0.346357\pi\)
0.133221 + 0.991086i \(0.457468\pi\)
\(282\) 0 0
\(283\) −22734.0 + 19076.1i −0.283860 + 0.238187i −0.773589 0.633688i \(-0.781540\pi\)
0.489729 + 0.871875i \(0.337096\pi\)
\(284\) 0 0
\(285\) −2472.11 6050.74i −0.0304354 0.0744935i
\(286\) 0 0
\(287\) 27710.5 + 33024.1i 0.336419 + 0.400928i
\(288\) 0 0
\(289\) −13536.8 + 76771.2i −0.162077 + 0.919185i
\(290\) 0 0
\(291\) 38175.0 13894.6i 0.450810 0.164081i
\(292\) 0 0
\(293\) 121893. 70375.0i 1.41986 0.819754i 0.423570 0.905864i \(-0.360777\pi\)
0.996286 + 0.0861098i \(0.0274436\pi\)
\(294\) 0 0
\(295\) −6049.93 + 7210.03i −0.0695194 + 0.0828500i
\(296\) 0 0
\(297\) −120841. 69767.3i −1.36993 0.790932i
\(298\) 0 0
\(299\) −9784.03 + 1725.19i −0.109440 + 0.0192972i
\(300\) 0 0
\(301\) 75159.4 + 27355.8i 0.829564 + 0.301937i
\(302\) 0 0
\(303\) 50255.1i 0.547388i
\(304\) 0 0
\(305\) 9438.46 0.101462
\(306\) 0 0
\(307\) −33386.2 + 91727.9i −0.354234 + 0.973251i 0.626760 + 0.779213i \(0.284381\pi\)
−0.980994 + 0.194038i \(0.937841\pi\)
\(308\) 0 0
\(309\) −20024.8 113566.i −0.209725 1.18941i
\(310\) 0 0
\(311\) 72667.7 125864.i 0.751313 1.30131i −0.195874 0.980629i \(-0.562754\pi\)
0.947187 0.320682i \(-0.103912\pi\)
\(312\) 0 0
\(313\) −101844. 85457.2i −1.03955 0.872288i −0.0475958 0.998867i \(-0.515156\pi\)
−0.991957 + 0.126579i \(0.959600\pi\)
\(314\) 0 0
\(315\) 1129.69 + 1956.69i 0.0113852 + 0.0197197i
\(316\) 0 0
\(317\) −54530.5 149821.i −0.542651 1.49092i −0.843436 0.537230i \(-0.819471\pi\)
0.300784 0.953692i \(-0.402752\pi\)
\(318\) 0 0
\(319\) 32989.5 + 5816.93i 0.324186 + 0.0571627i
\(320\) 0 0
\(321\) −94334.2 + 79155.8i −0.915502 + 0.768197i
\(322\) 0 0
\(323\) 25645.4 + 8222.39i 0.245813 + 0.0788122i
\(324\) 0 0
\(325\) −43925.4 52348.2i −0.415861 0.495604i
\(326\) 0 0
\(327\) 15007.7 85113.1i 0.140352 0.795978i
\(328\) 0 0
\(329\) 99258.0 36127.0i 0.917010 0.333764i
\(330\) 0 0
\(331\) 78104.0 45093.4i 0.712881 0.411582i −0.0992457 0.995063i \(-0.531643\pi\)
0.812127 + 0.583481i \(0.198310\pi\)
\(332\) 0 0
\(333\) −18126.6 + 21602.5i −0.163466 + 0.194812i
\(334\) 0 0
\(335\) 5600.47 + 3233.43i 0.0499039 + 0.0288120i
\(336\) 0 0
\(337\) −9306.78 + 1641.04i −0.0819482 + 0.0144497i −0.214472 0.976730i \(-0.568803\pi\)
0.132524 + 0.991180i \(0.457692\pi\)
\(338\) 0 0
\(339\) 178898. + 65113.7i 1.55671 + 0.566595i
\(340\) 0 0
\(341\) 136747.i 1.17601i
\(342\) 0 0
\(343\) 122672. 1.04269
\(344\) 0 0
\(345\) 557.791 1532.52i 0.00468634 0.0128756i
\(346\) 0 0
\(347\) −30236.7 171481.i −0.251117 1.42415i −0.805847 0.592124i \(-0.798289\pi\)
0.554730 0.832031i \(-0.312822\pi\)
\(348\) 0 0
\(349\) −85890.6 + 148767.i −0.705172 + 1.22139i 0.261458 + 0.965215i \(0.415797\pi\)
−0.966630 + 0.256178i \(0.917537\pi\)
\(350\) 0 0
\(351\) −66737.4 55999.3i −0.541695 0.454536i
\(352\) 0 0
\(353\) −52519.6 90966.6i −0.421475 0.730016i 0.574609 0.818428i \(-0.305154\pi\)
−0.996084 + 0.0884119i \(0.971821\pi\)
\(354\) 0 0
\(355\) 4656.17 + 12792.7i 0.0369464 + 0.101509i
\(356\) 0 0
\(357\) 26532.0 + 4678.32i 0.208178 + 0.0367074i
\(358\) 0 0
\(359\) −131354. + 110219.i −1.01919 + 0.855200i −0.989525 0.144360i \(-0.953888\pi\)
−0.0296621 + 0.999560i \(0.509443\pi\)
\(360\) 0 0
\(361\) −56214.8 + 117573.i −0.431356 + 0.902182i
\(362\) 0 0
\(363\) 82625.6 + 98469.4i 0.627049 + 0.747288i
\(364\) 0 0
\(365\) 1933.67 10966.4i 0.0145143 0.0823146i
\(366\) 0 0
\(367\) −41854.0 + 15233.6i −0.310745 + 0.113102i −0.492685 0.870208i \(-0.663985\pi\)
0.181940 + 0.983310i \(0.441762\pi\)
\(368\) 0 0
\(369\) −16684.7 + 9632.92i −0.122537 + 0.0707465i
\(370\) 0 0
\(371\) −34689.2 + 41341.0i −0.252027 + 0.300354i
\(372\) 0 0
\(373\) −192034. 110871.i −1.38026 0.796894i −0.388070 0.921630i \(-0.626858\pi\)
−0.992190 + 0.124736i \(0.960192\pi\)
\(374\) 0 0
\(375\) 22191.6 3912.97i 0.157807 0.0278256i
\(376\) 0 0
\(377\) 19653.6 + 7153.34i 0.138280 + 0.0503299i
\(378\) 0 0
\(379\) 146879.i 1.02254i 0.859419 + 0.511271i \(0.170825\pi\)
−0.859419 + 0.511271i \(0.829175\pi\)
\(380\) 0 0
\(381\) −29634.7 −0.204150
\(382\) 0 0
\(383\) −946.882 + 2601.54i −0.00645503 + 0.0177351i −0.942878 0.333137i \(-0.891893\pi\)
0.936423 + 0.350872i \(0.114115\pi\)
\(384\) 0 0
\(385\) −3332.04 18896.9i −0.0224796 0.127488i
\(386\) 0 0
\(387\) −17872.2 + 30955.6i −0.119332 + 0.206689i
\(388\) 0 0
\(389\) 35161.7 + 29504.2i 0.232365 + 0.194977i 0.751534 0.659694i \(-0.229314\pi\)
−0.519169 + 0.854671i \(0.673759\pi\)
\(390\) 0 0
\(391\) 3359.83 + 5819.39i 0.0219768 + 0.0380649i
\(392\) 0 0
\(393\) 89878.1 + 246938.i 0.581927 + 1.59883i
\(394\) 0 0
\(395\) 10769.5 + 1898.95i 0.0690241 + 0.0121708i
\(396\) 0 0
\(397\) 91174.4 76504.4i 0.578485 0.485406i −0.305964 0.952043i \(-0.598979\pi\)
0.884449 + 0.466637i \(0.154534\pi\)
\(398\) 0 0
\(399\) −39803.2 + 124145.i −0.250019 + 0.779800i
\(400\) 0 0
\(401\) 130832. + 155920.i 0.813628 + 0.969644i 0.999917 0.0128506i \(-0.00409060\pi\)
−0.186289 + 0.982495i \(0.559646\pi\)
\(402\) 0 0
\(403\) 14825.9 84082.0i 0.0912876 0.517718i
\(404\) 0 0
\(405\) 9743.87 3546.48i 0.0594048 0.0216216i
\(406\) 0 0
\(407\) 207410. 119748.i 1.25210 0.722902i
\(408\) 0 0
\(409\) −67298.2 + 80202.8i −0.402306 + 0.479450i −0.928722 0.370778i \(-0.879091\pi\)
0.526416 + 0.850227i \(0.323536\pi\)
\(410\) 0 0
\(411\) 29843.2 + 17230.0i 0.176669 + 0.102000i
\(412\) 0 0
\(413\) 184876. 32598.7i 1.08388 0.191117i
\(414\) 0 0
\(415\) −16279.3 5925.19i −0.0945236 0.0344038i
\(416\) 0 0
\(417\) 80622.9i 0.463646i
\(418\) 0 0
\(419\) −214521. −1.22192 −0.610959 0.791662i \(-0.709216\pi\)
−0.610959 + 0.791662i \(0.709216\pi\)
\(420\) 0 0
\(421\) −76569.4 + 210373.i −0.432007 + 1.18693i 0.512571 + 0.858645i \(0.328693\pi\)
−0.944579 + 0.328286i \(0.893529\pi\)
\(422\) 0 0
\(423\) 8197.12 + 46488.2i 0.0458122 + 0.259814i
\(424\) 0 0
\(425\) −23109.9 + 40027.6i −0.127944 + 0.221606i
\(426\) 0 0
\(427\) −144212. 121009.i −0.790946 0.663682i
\(428\) 0 0
\(429\) 75590.7 + 130927.i 0.410727 + 0.711400i
\(430\) 0 0
\(431\) −37160.5 102098.i −0.200045 0.549618i 0.798589 0.601877i \(-0.205580\pi\)
−0.998634 + 0.0522588i \(0.983358\pi\)
\(432\) 0 0
\(433\) 117896. + 20788.3i 0.628818 + 0.110878i 0.478970 0.877832i \(-0.341010\pi\)
0.149848 + 0.988709i \(0.452122\pi\)
\(434\) 0 0
\(435\) −2630.06 + 2206.88i −0.0138991 + 0.0116627i
\(436\) 0 0
\(437\) −30101.2 + 12298.3i −0.157623 + 0.0643992i
\(438\) 0 0
\(439\) 146363. + 174429.i 0.759456 + 0.905084i 0.997813 0.0660931i \(-0.0210534\pi\)
−0.238357 + 0.971177i \(0.576609\pi\)
\(440\) 0 0
\(441\) −847.169 + 4804.53i −0.00435605 + 0.0247044i
\(442\) 0 0
\(443\) −67184.3 + 24453.1i −0.342342 + 0.124602i −0.507469 0.861670i \(-0.669419\pi\)
0.165127 + 0.986272i \(0.447197\pi\)
\(444\) 0 0
\(445\) 9143.84 5279.20i 0.0461752 0.0266592i
\(446\) 0 0
\(447\) 95528.8 113847.i 0.478101 0.569778i
\(448\) 0 0
\(449\) −14220.1 8210.00i −0.0705361 0.0407240i 0.464317 0.885669i \(-0.346300\pi\)
−0.534853 + 0.844945i \(0.679633\pi\)
\(450\) 0 0
\(451\) 161134. 28412.3i 0.792200 0.139686i
\(452\) 0 0
\(453\) 122285. + 44508.2i 0.595907 + 0.216892i
\(454\) 0 0
\(455\) 11980.4i 0.0578695i
\(456\) 0 0
\(457\) −236201. −1.13097 −0.565483 0.824760i \(-0.691310\pi\)
−0.565483 + 0.824760i \(0.691310\pi\)
\(458\) 0 0
\(459\) −20153.4 + 55371.0i −0.0956583 + 0.262819i
\(460\) 0 0
\(461\) 8044.64 + 45623.4i 0.0378534 + 0.214677i 0.997867 0.0652750i \(-0.0207925\pi\)
−0.960014 + 0.279952i \(0.909681\pi\)
\(462\) 0 0
\(463\) −107047. + 185410.i −0.499358 + 0.864913i −1.00000 0.000741640i \(-0.999764\pi\)
0.500642 + 0.865654i \(0.333097\pi\)
\(464\) 0 0
\(465\) 10736.4 + 9008.93i 0.0496539 + 0.0416646i
\(466\) 0 0
\(467\) −90821.3 157307.i −0.416441 0.721298i 0.579137 0.815230i \(-0.303390\pi\)
−0.995579 + 0.0939325i \(0.970056\pi\)
\(468\) 0 0
\(469\) −44115.6 121207.i −0.200561 0.551037i
\(470\) 0 0
\(471\) −287017. 50608.8i −1.29380 0.228131i
\(472\) 0 0
\(473\) 232547. 195130.i 1.03941 0.872172i
\(474\) 0 0
\(475\) −176781. 137011.i −0.783516 0.607250i
\(476\) 0 0
\(477\) −15502.6 18475.3i −0.0681348 0.0811999i
\(478\) 0 0
\(479\) 37321.6 211661.i 0.162663 0.922508i −0.788778 0.614678i \(-0.789286\pi\)
0.951441 0.307830i \(-0.0996028\pi\)
\(480\) 0 0
\(481\) 140513. 51142.6i 0.607333 0.221051i
\(482\) 0 0
\(483\) −28170.7 + 16264.4i −0.120755 + 0.0697177i
\(484\) 0 0
\(485\) −7854.08 + 9360.13i −0.0333896 + 0.0397922i
\(486\) 0 0
\(487\) 127784. + 73775.9i 0.538787 + 0.311069i 0.744587 0.667525i \(-0.232646\pi\)
−0.205800 + 0.978594i \(0.565980\pi\)
\(488\) 0 0
\(489\) −175851. + 31007.2i −0.735405 + 0.129672i
\(490\) 0 0
\(491\) −256367. 93309.9i −1.06341 0.387048i −0.249698 0.968324i \(-0.580331\pi\)
−0.813707 + 0.581276i \(0.802554\pi\)
\(492\) 0 0
\(493\) 14146.1i 0.0582028i
\(494\) 0 0
\(495\) 8575.33 0.0349978
\(496\) 0 0
\(497\) 92870.0 255158.i 0.375978 1.03299i
\(498\) 0 0
\(499\) 29635.6 + 168072.i 0.119018 + 0.674985i 0.984682 + 0.174360i \(0.0557856\pi\)
−0.865664 + 0.500626i \(0.833103\pi\)
\(500\) 0 0
\(501\) −30470.3 + 52776.1i −0.121395 + 0.210263i
\(502\) 0 0
\(503\) 12725.1 + 10677.7i 0.0502952 + 0.0422027i 0.667589 0.744530i \(-0.267326\pi\)
−0.617294 + 0.786733i \(0.711771\pi\)
\(504\) 0 0
\(505\) −7557.61 13090.2i −0.0296348 0.0513290i
\(506\) 0 0
\(507\) −43507.6 119536.i −0.169258 0.465033i
\(508\) 0 0
\(509\) 182544. + 32187.4i 0.704581 + 0.124237i 0.514448 0.857522i \(-0.327997\pi\)
0.190133 + 0.981758i \(0.439108\pi\)
\(510\) 0 0
\(511\) −170142. + 142766.i −0.651584 + 0.546744i
\(512\) 0 0
\(513\) −252281. 132882.i −0.958626 0.504931i
\(514\) 0 0
\(515\) 22294.5 + 26569.6i 0.0840590 + 0.100178i
\(516\) 0 0
\(517\) 69616.1 394813.i 0.260453 1.47710i
\(518\) 0 0
\(519\) 131152. 47735.5i 0.486902 0.177218i
\(520\) 0 0
\(521\) 376417. 217325.i 1.38674 0.800633i 0.393790 0.919200i \(-0.371164\pi\)
0.992946 + 0.118568i \(0.0378303\pi\)
\(522\) 0 0
\(523\) 12503.6 14901.2i 0.0457122 0.0544776i −0.742704 0.669620i \(-0.766457\pi\)
0.788416 + 0.615142i \(0.210901\pi\)
\(524\) 0 0
\(525\) −193767. 111871.i −0.703009 0.405883i
\(526\) 0 0
\(527\) −56870.1 + 10027.7i −0.204768 + 0.0361062i
\(528\) 0 0
\(529\) 255341. + 92936.4i 0.912449 + 0.332104i
\(530\) 0 0
\(531\) 83896.0i 0.297545i
\(532\) 0 0
\(533\) 102157. 0.359596
\(534\) 0 0
\(535\) 12667.8 34804.5i 0.0442582 0.121598i
\(536\) 0 0
\(537\) −29812.2 169073.i −0.103382 0.586308i
\(538\) 0 0
\(539\) 20716.6 35882.2i 0.0713084 0.123510i
\(540\) 0 0
\(541\) 346656. + 290879.i 1.18442 + 0.993844i 0.999939 + 0.0110070i \(0.00350370\pi\)
0.184477 + 0.982837i \(0.440941\pi\)
\(542\) 0 0
\(543\) −124204. 215127.i −0.421245 0.729617i
\(544\) 0 0
\(545\) 8890.60 + 24426.7i 0.0299322 + 0.0822379i
\(546\) 0 0
\(547\) −312719. 55140.9i −1.04515 0.184289i −0.375393 0.926866i \(-0.622492\pi\)
−0.669761 + 0.742577i \(0.733603\pi\)
\(548\) 0 0
\(549\) 64448.7 54078.8i 0.213830 0.179425i
\(550\) 0 0
\(551\) 67823.9 + 9262.78i 0.223398 + 0.0305097i
\(552\) 0 0
\(553\) −140203. 167088.i −0.458467 0.546379i
\(554\) 0 0
\(555\) −4262.41 + 24173.3i −0.0138379 + 0.0784785i
\(556\) 0 0
\(557\) −63243.6 + 23018.8i −0.203848 + 0.0741945i −0.441926 0.897051i \(-0.645705\pi\)
0.238078 + 0.971246i \(0.423482\pi\)
\(558\) 0 0
\(559\) 164142. 94767.7i 0.525288 0.303275i
\(560\) 0 0
\(561\) 65727.4 78330.9i 0.208843 0.248890i
\(562\) 0 0
\(563\) 178538. + 103079.i 0.563268 + 0.325203i 0.754456 0.656351i \(-0.227901\pi\)
−0.191188 + 0.981553i \(0.561234\pi\)
\(564\) 0 0
\(565\) −56390.5 + 9943.17i −0.176648 + 0.0311478i
\(566\) 0 0
\(567\) −194347. 70736.7i −0.604523 0.220028i
\(568\) 0 0
\(569\) 532584.i 1.64499i 0.568771 + 0.822496i \(0.307419\pi\)
−0.568771 + 0.822496i \(0.692581\pi\)
\(570\) 0 0
\(571\) −197356. −0.605309 −0.302654 0.953100i \(-0.597873\pi\)
−0.302654 + 0.953100i \(0.597873\pi\)
\(572\) 0 0
\(573\) −144863. + 398008.i −0.441213 + 1.21222i
\(574\) 0 0
\(575\) −9690.52 54957.7i −0.0293097 0.166224i
\(576\) 0 0
\(577\) 50452.7 87386.6i 0.151542 0.262478i −0.780253 0.625464i \(-0.784910\pi\)
0.931794 + 0.362986i \(0.118243\pi\)
\(578\) 0 0
\(579\) 325048. + 272748.i 0.969596 + 0.813588i
\(580\) 0 0
\(581\) 172770. + 299246.i 0.511818 + 0.886494i
\(582\) 0 0
\(583\) 70054.8 + 192474.i 0.206111 + 0.566285i
\(584\) 0 0
\(585\) 5272.73 + 929.724i 0.0154072 + 0.00271670i
\(586\) 0 0
\(587\) −368685. + 309363.i −1.06999 + 0.897826i −0.995051 0.0993621i \(-0.968320\pi\)
−0.0749363 + 0.997188i \(0.523875\pi\)
\(588\) 0 0
\(589\) −10840.0 279231.i −0.0312464 0.804883i
\(590\) 0 0
\(591\) −33798.5 40279.5i −0.0967659 0.115321i
\(592\) 0 0
\(593\) −65332.1 + 370517.i −0.185788 + 1.05366i 0.739151 + 0.673540i \(0.235227\pi\)
−0.924939 + 0.380116i \(0.875884\pi\)
\(594\) 0 0
\(595\) −7614.46 + 2771.44i −0.0215083 + 0.00782837i
\(596\) 0 0
\(597\) −433670. + 250379.i −1.21678 + 0.702505i
\(598\) 0 0
\(599\) −51498.6 + 61373.7i −0.143530 + 0.171052i −0.833020 0.553243i \(-0.813390\pi\)
0.689490 + 0.724295i \(0.257835\pi\)
\(600\) 0 0
\(601\) −206392. 119160.i −0.571403 0.329900i 0.186306 0.982492i \(-0.440348\pi\)
−0.757710 + 0.652592i \(0.773682\pi\)
\(602\) 0 0
\(603\) 56768.0 10009.7i 0.156124 0.0275288i
\(604\) 0 0
\(605\) −36330.2 13223.1i −0.0992559 0.0361262i
\(606\) 0 0
\(607\) 46881.4i 0.127240i 0.997974 + 0.0636199i \(0.0202645\pi\)
−0.997974 + 0.0636199i \(0.979735\pi\)
\(608\) 0 0
\(609\) 68479.1 0.184639
\(610\) 0 0
\(611\) 85610.0 235212.i 0.229320 0.630052i
\(612\) 0 0
\(613\) 62444.3 + 354139.i 0.166177 + 0.942438i 0.947842 + 0.318740i \(0.103260\pi\)
−0.781665 + 0.623698i \(0.785629\pi\)
\(614\) 0 0
\(615\) −8384.81 + 14522.9i −0.0221689 + 0.0383976i
\(616\) 0 0
\(617\) −34916.8 29298.6i −0.0917199 0.0769622i 0.595775 0.803152i \(-0.296845\pi\)
−0.687495 + 0.726189i \(0.741290\pi\)
\(618\) 0 0
\(619\) 179541. + 310975.i 0.468579 + 0.811603i 0.999355 0.0359092i \(-0.0114327\pi\)
−0.530776 + 0.847512i \(0.678099\pi\)
\(620\) 0 0
\(621\) −24333.0 66854.4i −0.0630976 0.173359i
\(622\) 0 0
\(623\) −207394. 36569.2i −0.534343 0.0942191i
\(624\) 0 0
\(625\) 291437. 244545.i 0.746079 0.626034i
\(626\) 0 0
\(627\) 332521. + 366422.i 0.845832 + 0.932065i
\(628\) 0 0
\(629\) −65009.9 77475.8i −0.164315 0.195824i
\(630\) 0 0
\(631\) −68745.3 + 389874.i −0.172657 + 0.979187i 0.768156 + 0.640262i \(0.221174\pi\)
−0.940814 + 0.338925i \(0.889937\pi\)
\(632\) 0 0
\(633\) 490252. 178437.i 1.22352 0.445326i
\(634\) 0 0
\(635\) 7719.07 4456.61i 0.0191433 0.0110524i
\(636\) 0 0
\(637\) 16628.3 19816.9i 0.0409798 0.0488378i
\(638\) 0 0
\(639\) 105091. + 60674.4i 0.257374 + 0.148595i
\(640\) 0 0
\(641\) −9953.74 + 1755.11i −0.0242254 + 0.00427158i −0.185748 0.982597i \(-0.559471\pi\)
0.161522 + 0.986869i \(0.448360\pi\)
\(642\) 0 0
\(643\) 147595. + 53720.0i 0.356984 + 0.129931i 0.514285 0.857619i \(-0.328057\pi\)
−0.157302 + 0.987551i \(0.550279\pi\)
\(644\) 0 0
\(645\) 31113.2i 0.0747868i
\(646\) 0 0
\(647\) 63979.4 0.152838 0.0764190 0.997076i \(-0.475651\pi\)
0.0764190 + 0.997076i \(0.475651\pi\)
\(648\) 0 0
\(649\) 243692. 669539.i 0.578565 1.58959i
\(650\) 0 0
\(651\) −48542.6 275299.i −0.114541 0.649595i
\(652\) 0 0
\(653\) −365655. + 633333.i −0.857522 + 1.48527i 0.0167642 + 0.999859i \(0.494664\pi\)
−0.874286 + 0.485411i \(0.838670\pi\)
\(654\) 0 0
\(655\) −60546.7 50804.7i −0.141126 0.118419i
\(656\) 0 0
\(657\) −49629.5 85960.8i −0.114977 0.199145i
\(658\) 0 0
\(659\) −47157.2 129563.i −0.108587 0.298340i 0.873484 0.486853i \(-0.161855\pi\)
−0.982071 + 0.188513i \(0.939633\pi\)
\(660\) 0 0
\(661\) 474797. + 83719.5i 1.08669 + 0.191612i 0.688171 0.725549i \(-0.258414\pi\)
0.398517 + 0.917161i \(0.369525\pi\)
\(662\) 0 0
\(663\) 48906.5 41037.4i 0.111260 0.0933582i
\(664\) 0 0
\(665\) −8301.81 38322.4i −0.0187728 0.0866581i
\(666\) 0 0
\(667\) 10978.8 + 13084.0i 0.0246775 + 0.0294095i
\(668\) 0 0
\(669\) 4498.16 25510.3i 0.0100504 0.0569985i
\(670\) 0 0
\(671\) −671420. + 244377.i −1.49125 + 0.542769i
\(672\) 0 0
\(673\) −680011. + 392605.i −1.50136 + 0.866813i −0.501365 + 0.865236i \(0.667168\pi\)
−0.999999 + 0.00157637i \(0.999498\pi\)
\(674\) 0 0
\(675\) 314553. 374869.i 0.690377 0.822759i
\(676\) 0 0
\(677\) 139771. + 80696.9i 0.304958 + 0.176068i 0.644668 0.764463i \(-0.276996\pi\)
−0.339710 + 0.940530i \(0.610329\pi\)
\(678\) 0 0
\(679\) 240008. 42320.0i 0.520579 0.0917922i
\(680\) 0 0
\(681\) −545756. 198639.i −1.17681 0.428322i
\(682\) 0 0
\(683\) 328136.i 0.703417i −0.936110 0.351708i \(-0.885601\pi\)
0.936110 0.351708i \(-0.114399\pi\)
\(684\) 0 0
\(685\) −10364.5 −0.0220886
\(686\) 0 0
\(687\) 184659. 507347.i 0.391253 1.07496i
\(688\) 0 0
\(689\) 22207.0 + 125942.i 0.0467790 + 0.265297i
\(690\) 0 0
\(691\) 397198. 687967.i 0.831862 1.44083i −0.0646987 0.997905i \(-0.520609\pi\)
0.896560 0.442922i \(-0.146058\pi\)
\(692\) 0 0
\(693\) −131024. 109942.i −0.272826 0.228928i
\(694\) 0 0
\(695\) 12124.5 + 21000.2i 0.0251011 + 0.0434764i
\(696\) 0 0
\(697\) −23632.1 64928.6i −0.0486448 0.133651i
\(698\) 0 0
\(699\) 244964. + 43193.8i 0.501359 + 0.0884031i
\(700\) 0 0
\(701\) −94166.3 + 79014.9i −0.191628 + 0.160795i −0.733554 0.679631i \(-0.762140\pi\)
0.541926 + 0.840426i \(0.317695\pi\)
\(702\) 0 0
\(703\) 414027. 260961.i 0.837757 0.528037i
\(704\) 0 0
\(705\) 26411.6 + 31476.1i 0.0531393 + 0.0633290i
\(706\) 0 0
\(707\) −52351.8 + 296902.i −0.104735 + 0.593984i
\(708\) 0 0
\(709\) −809937. + 294793.i −1.61124 + 0.586442i −0.981684 0.190517i \(-0.938984\pi\)
−0.629551 + 0.776959i \(0.716761\pi\)
\(710\) 0 0
\(711\) 84417.5 48738.5i 0.166991 0.0964124i
\(712\) 0 0
\(713\) 44817.6 53411.5i 0.0881595 0.105064i
\(714\) 0 0
\(715\) −39378.8 22735.4i −0.0770284 0.0444724i
\(716\) 0 0
\(717\) 192056. 33864.7i 0.373585 0.0658732i
\(718\) 0 0
\(719\) −512487. 186530.i −0.991346 0.360821i −0.205105 0.978740i \(-0.565754\pi\)
−0.786241 + 0.617919i \(0.787976\pi\)
\(720\) 0 0
\(721\) 691797.i 1.33078i
\(722\) 0 0
\(723\) 236627. 0.452676
\(724\) 0 0
\(725\) −40180.9 + 110396.i −0.0764440 + 0.210028i
\(726\) 0 0
\(727\) 38500.0 + 218344.i 0.0728437 + 0.413117i 0.999324 + 0.0367730i \(0.0117078\pi\)
−0.926480 + 0.376344i \(0.877181\pi\)
\(728\) 0 0
\(729\) 294411. 509934.i 0.553986 0.959532i
\(730\) 0 0
\(731\) −98203.1 82402.2i −0.183777 0.154207i
\(732\) 0 0
\(733\) −77402.2 134065.i −0.144061 0.249521i 0.784961 0.619545i \(-0.212683\pi\)
−0.929022 + 0.370024i \(0.879349\pi\)
\(734\) 0 0
\(735\) 1452.40 + 3990.44i 0.00268851 + 0.00738663i
\(736\) 0 0
\(737\) −482117. 85010.2i −0.887600 0.156508i
\(738\) 0 0
\(739\) 360117. 302174.i 0.659409 0.553310i −0.250501 0.968116i \(-0.580595\pi\)
0.909910 + 0.414807i \(0.136151\pi\)
\(740\) 0 0
\(741\) 164731. + 261354.i 0.300012 + 0.475984i
\(742\) 0 0
\(743\) −514022. 612588.i −0.931117 1.10966i −0.993750 0.111626i \(-0.964394\pi\)
0.0626329 0.998037i \(-0.480050\pi\)
\(744\) 0 0
\(745\) −7761.96 + 44020.3i −0.0139849 + 0.0793122i
\(746\) 0 0
\(747\) −145109. + 52815.4i −0.260048 + 0.0946498i
\(748\) 0 0
\(749\) −639775. + 369374.i −1.14042 + 0.658420i
\(750\) 0 0
\(751\) −502229. + 598533.i −0.890475 + 1.06123i 0.107278 + 0.994229i \(0.465787\pi\)
−0.997753 + 0.0669978i \(0.978658\pi\)
\(752\) 0 0
\(753\) −299294. 172797.i −0.527847 0.304753i
\(754\) 0 0
\(755\) −38545.6 + 6796.62i −0.0676208 + 0.0119234i
\(756\) 0 0
\(757\) −187799. 68353.4i −0.327719 0.119280i 0.172920 0.984936i \(-0.444680\pi\)
−0.500640 + 0.865656i \(0.666902\pi\)
\(758\) 0 0
\(759\) 123460.i 0.214311i
\(760\) 0 0
\(761\) 718953. 1.24146 0.620728 0.784026i \(-0.286837\pi\)
0.620728 + 0.784026i \(0.286837\pi\)
\(762\) 0 0
\(763\) 177328. 487206.i 0.304600 0.836880i
\(764\) 0 0
\(765\) −628.833 3566.29i −0.00107451 0.00609387i
\(766\) 0 0
\(767\) 222430. 385260.i 0.378096 0.654882i
\(768\) 0 0
\(769\) −307970. 258418.i −0.520782 0.436988i 0.344122 0.938925i \(-0.388177\pi\)
−0.864904 + 0.501937i \(0.832621\pi\)
\(770\) 0 0
\(771\) 395608. + 685214.i 0.665513 + 1.15270i
\(772\) 0 0
\(773\) 341555. + 938415.i 0.571612 + 1.57049i 0.801956 + 0.597383i \(0.203793\pi\)
−0.230344 + 0.973109i \(0.573985\pi\)
\(774\) 0 0
\(775\) 472296. + 83278.5i 0.786340 + 0.138653i
\(776\) 0 0
\(777\) 375048. 314702.i 0.621218 0.521264i
\(778\) 0 0
\(779\) 326776. 70789.7i 0.538486 0.116653i
\(780\) 0 0
\(781\) −662447. 789474.i −1.08605 1.29430i
\(782\) 0 0
\(783\) −26007.9 + 147498.i −0.0424211 + 0.240582i
\(784\) 0 0
\(785\) 82371.3 29980.7i 0.133671 0.0486522i
\(786\) 0 0
\(787\) −113438. + 65493.7i −0.183152 + 0.105743i −0.588773 0.808299i \(-0.700389\pi\)
0.405621 + 0.914041i \(0.367055\pi\)
\(788\) 0 0
\(789\) 600685. 715869.i 0.964924 1.14995i
\(790\) 0 0
\(791\) 989082. + 571047.i 1.58081 + 0.912681i
\(792\) 0