Properties

Label 76.5.j.a.13.3
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 13.3
Character \(\chi\) \(=\) 76.13
Dual form 76.5.j.a.41.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.28730 + 6.28431i) q^{3} +(-2.03045 - 11.5152i) q^{5} +(38.6373 - 66.9218i) q^{7} +(27.7888 + 23.3175i) q^{9} +O(q^{10})\) \(q+(-2.28730 + 6.28431i) q^{3} +(-2.03045 - 11.5152i) q^{5} +(38.6373 - 66.9218i) q^{7} +(27.7888 + 23.3175i) q^{9} +(79.3551 + 137.447i) q^{11} +(65.1618 + 179.031i) q^{13} +(77.0097 + 13.5789i) q^{15} +(343.501 - 288.231i) q^{17} +(-191.484 + 306.031i) q^{19} +(332.182 + 395.879i) q^{21} +(99.9867 - 567.053i) q^{23} +(458.830 - 167.000i) q^{25} +(-679.220 + 392.148i) q^{27} +(447.390 - 533.179i) q^{29} +(533.474 + 308.001i) q^{31} +(-1045.27 + 184.309i) q^{33} +(-849.072 - 309.037i) q^{35} -2288.40i q^{37} -1274.13 q^{39} +(-792.647 + 2177.78i) q^{41} +(465.909 + 2642.30i) q^{43} +(212.083 - 367.339i) q^{45} +(-1399.04 - 1173.94i) q^{47} +(-1785.19 - 3092.03i) q^{49} +(1025.65 + 2817.94i) q^{51} +(-1889.93 - 333.245i) q^{53} +(1421.61 - 1192.87i) q^{55} +(-1485.21 - 1903.33i) q^{57} +(-1322.44 - 1576.02i) q^{59} +(228.828 - 1297.75i) q^{61} +(2634.13 - 958.747i) q^{63} +(1929.27 - 1113.87i) q^{65} +(-3218.45 + 3835.60i) q^{67} +(3334.84 + 1925.37i) q^{69} +(-4665.83 + 822.711i) q^{71} +(6554.25 + 2385.55i) q^{73} +3265.41i q^{75} +12264.3 q^{77} +(-2018.56 + 5545.94i) q^{79} +(-400.563 - 2271.71i) q^{81} +(2417.78 - 4187.71i) q^{83} +(-4016.51 - 3370.26i) q^{85} +(2327.35 + 4031.08i) q^{87} +(-1672.93 - 4596.33i) q^{89} +(14498.7 + 2556.52i) q^{91} +(-3155.80 + 2648.03i) q^{93} +(3912.82 + 1583.61i) q^{95} +(42.3160 + 50.4302i) q^{97} +(-999.747 + 5669.85i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

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
\(3\) −2.28730 + 6.28431i −0.254145 + 0.698257i 0.745356 + 0.666667i \(0.232279\pi\)
−0.999501 + 0.0315905i \(0.989943\pi\)
\(4\) 0 0
\(5\) −2.03045 11.5152i −0.0812179 0.460610i −0.998109 0.0614718i \(-0.980421\pi\)
0.916891 0.399138i \(-0.130691\pi\)
\(6\) 0 0
\(7\) 38.6373 66.9218i 0.788517 1.36575i −0.138359 0.990382i \(-0.544183\pi\)
0.926876 0.375369i \(-0.122484\pi\)
\(8\) 0 0
\(9\) 27.7888 + 23.3175i 0.343071 + 0.287871i
\(10\) 0 0
\(11\) 79.3551 + 137.447i 0.655827 + 1.13593i 0.981686 + 0.190508i \(0.0610134\pi\)
−0.325858 + 0.945419i \(0.605653\pi\)
\(12\) 0 0
\(13\) 65.1618 + 179.031i 0.385573 + 1.05935i 0.968973 + 0.247168i \(0.0794999\pi\)
−0.583400 + 0.812185i \(0.698278\pi\)
\(14\) 0 0
\(15\) 77.0097 + 13.5789i 0.342265 + 0.0603506i
\(16\) 0 0
\(17\) 343.501 288.231i 1.18858 0.997340i 0.188701 0.982035i \(-0.439572\pi\)
0.999883 0.0153052i \(-0.00487200\pi\)
\(18\) 0 0
\(19\) −191.484 + 306.031i −0.530427 + 0.847731i
\(20\) 0 0
\(21\) 332.182 + 395.879i 0.753248 + 0.897686i
\(22\) 0 0
\(23\) 99.9867 567.053i 0.189011 1.07193i −0.731682 0.681646i \(-0.761265\pi\)
0.920693 0.390287i \(-0.127624\pi\)
\(24\) 0 0
\(25\) 458.830 167.000i 0.734128 0.267201i
\(26\) 0 0
\(27\) −679.220 + 392.148i −0.931715 + 0.537926i
\(28\) 0 0
\(29\) 447.390 533.179i 0.531974 0.633982i −0.431394 0.902164i \(-0.641978\pi\)
0.963368 + 0.268181i \(0.0864226\pi\)
\(30\) 0 0
\(31\) 533.474 + 308.001i 0.555124 + 0.320501i 0.751186 0.660090i \(-0.229482\pi\)
−0.196062 + 0.980591i \(0.562815\pi\)
\(32\) 0 0
\(33\) −1045.27 + 184.309i −0.959844 + 0.169246i
\(34\) 0 0
\(35\) −849.072 309.037i −0.693120 0.252275i
\(36\) 0 0
\(37\) 2288.40i 1.67159i −0.549043 0.835794i \(-0.685008\pi\)
0.549043 0.835794i \(-0.314992\pi\)
\(38\) 0 0
\(39\) −1274.13 −0.837692
\(40\) 0 0
\(41\) −792.647 + 2177.78i −0.471533 + 1.29553i 0.444987 + 0.895537i \(0.353208\pi\)
−0.916520 + 0.399989i \(0.869014\pi\)
\(42\) 0 0
\(43\) 465.909 + 2642.30i 0.251979 + 1.42904i 0.803709 + 0.595022i \(0.202857\pi\)
−0.551730 + 0.834023i \(0.686032\pi\)
\(44\) 0 0
\(45\) 212.083 367.339i 0.104733 0.181402i
\(46\) 0 0
\(47\) −1399.04 1173.94i −0.633338 0.531433i 0.268626 0.963244i \(-0.413430\pi\)
−0.901964 + 0.431811i \(0.857875\pi\)
\(48\) 0 0
\(49\) −1785.19 3092.03i −0.743517 1.28781i
\(50\) 0 0
\(51\) 1025.65 + 2817.94i 0.394327 + 1.08341i
\(52\) 0 0
\(53\) −1889.93 333.245i −0.672812 0.118635i −0.173203 0.984886i \(-0.555412\pi\)
−0.499609 + 0.866251i \(0.666523\pi\)
\(54\) 0 0
\(55\) 1421.61 1192.87i 0.469954 0.394338i
\(56\) 0 0
\(57\) −1485.21 1903.33i −0.457129 0.585821i
\(58\) 0 0
\(59\) −1322.44 1576.02i −0.379902 0.452750i 0.541881 0.840455i \(-0.317712\pi\)
−0.921783 + 0.387705i \(0.873268\pi\)
\(60\) 0 0
\(61\) 228.828 1297.75i 0.0614964 0.348763i −0.938498 0.345286i \(-0.887782\pi\)
0.999994 0.00347754i \(-0.00110694\pi\)
\(62\) 0 0
\(63\) 2634.13 958.747i 0.663677 0.241559i
\(64\) 0 0
\(65\) 1929.27 1113.87i 0.456633 0.263637i
\(66\) 0 0
\(67\) −3218.45 + 3835.60i −0.716964 + 0.854445i −0.994332 0.106319i \(-0.966094\pi\)
0.277368 + 0.960764i \(0.410538\pi\)
\(68\) 0 0
\(69\) 3334.84 + 1925.37i 0.700449 + 0.404404i
\(70\) 0 0
\(71\) −4665.83 + 822.711i −0.925576 + 0.163204i −0.616068 0.787693i \(-0.711275\pi\)
−0.309508 + 0.950897i \(0.600164\pi\)
\(72\) 0 0
\(73\) 6554.25 + 2385.55i 1.22992 + 0.447655i 0.873571 0.486698i \(-0.161799\pi\)
0.356351 + 0.934352i \(0.384021\pi\)
\(74\) 0 0
\(75\) 3265.41i 0.580517i
\(76\) 0 0
\(77\) 12264.3 2.06852
\(78\) 0 0
\(79\) −2018.56 + 5545.94i −0.323435 + 0.888630i 0.666296 + 0.745687i \(0.267879\pi\)
−0.989731 + 0.142943i \(0.954344\pi\)
\(80\) 0 0
\(81\) −400.563 2271.71i −0.0610521 0.346244i
\(82\) 0 0
\(83\) 2417.78 4187.71i 0.350962 0.607884i −0.635457 0.772137i \(-0.719188\pi\)
0.986418 + 0.164253i \(0.0525214\pi\)
\(84\) 0 0
\(85\) −4016.51 3370.26i −0.555919 0.466471i
\(86\) 0 0
\(87\) 2327.35 + 4031.08i 0.307484 + 0.532578i
\(88\) 0 0
\(89\) −1672.93 4596.33i −0.211202 0.580271i 0.788180 0.615445i \(-0.211024\pi\)
−0.999381 + 0.0351738i \(0.988802\pi\)
\(90\) 0 0
\(91\) 14498.7 + 2556.52i 1.75084 + 0.308721i
\(92\) 0 0
\(93\) −3155.80 + 2648.03i −0.364874 + 0.306166i
\(94\) 0 0
\(95\) 3912.82 + 1583.61i 0.433553 + 0.175469i
\(96\) 0 0
\(97\) 42.3160 + 50.4302i 0.00449740 + 0.00535979i 0.768288 0.640104i \(-0.221109\pi\)
−0.763791 + 0.645464i \(0.776664\pi\)
\(98\) 0 0
\(99\) −999.747 + 5669.85i −0.102005 + 0.578497i
\(100\) 0 0
\(101\) −4545.64 + 1654.48i −0.445607 + 0.162188i −0.555071 0.831803i \(-0.687309\pi\)
0.109464 + 0.993991i \(0.465087\pi\)
\(102\) 0 0
\(103\) −9097.21 + 5252.27i −0.857499 + 0.495077i −0.863174 0.504907i \(-0.831527\pi\)
0.00567497 + 0.999984i \(0.498194\pi\)
\(104\) 0 0
\(105\) 3884.17 4628.97i 0.352306 0.419862i
\(106\) 0 0
\(107\) −15452.5 8921.49i −1.34968 0.779237i −0.361475 0.932382i \(-0.617727\pi\)
−0.988204 + 0.153145i \(0.951060\pi\)
\(108\) 0 0
\(109\) 6680.09 1177.88i 0.562250 0.0991399i 0.114702 0.993400i \(-0.463409\pi\)
0.447548 + 0.894260i \(0.352297\pi\)
\(110\) 0 0
\(111\) 14381.1 + 5234.27i 1.16720 + 0.424826i
\(112\) 0 0
\(113\) 9283.02i 0.726996i −0.931595 0.363498i \(-0.881582\pi\)
0.931595 0.363498i \(-0.118418\pi\)
\(114\) 0 0
\(115\) −6732.77 −0.509094
\(116\) 0 0
\(117\) −2363.79 + 6494.45i −0.172678 + 0.474429i
\(118\) 0 0
\(119\) −6017.01 34124.2i −0.424900 2.40973i
\(120\) 0 0
\(121\) −5273.97 + 9134.78i −0.360219 + 0.623918i
\(122\) 0 0
\(123\) −11872.8 9962.48i −0.784773 0.658502i
\(124\) 0 0
\(125\) −6508.71 11273.4i −0.416557 0.721498i
\(126\) 0 0
\(127\) 1182.46 + 3248.78i 0.0733126 + 0.201425i 0.970936 0.239338i \(-0.0769303\pi\)
−0.897624 + 0.440763i \(0.854708\pi\)
\(128\) 0 0
\(129\) −17670.7 3115.83i −1.06188 0.187238i
\(130\) 0 0
\(131\) −12314.9 + 10333.5i −0.717612 + 0.602148i −0.926723 0.375744i \(-0.877387\pi\)
0.209112 + 0.977892i \(0.432943\pi\)
\(132\) 0 0
\(133\) 13081.7 + 24638.7i 0.739538 + 1.39288i
\(134\) 0 0
\(135\) 5894.80 + 7025.15i 0.323446 + 0.385468i
\(136\) 0 0
\(137\) −2118.53 + 12014.8i −0.112874 + 0.640140i 0.874907 + 0.484291i \(0.160922\pi\)
−0.987781 + 0.155849i \(0.950189\pi\)
\(138\) 0 0
\(139\) −7828.89 + 2849.48i −0.405201 + 0.147481i −0.536577 0.843852i \(-0.680283\pi\)
0.131376 + 0.991333i \(0.458061\pi\)
\(140\) 0 0
\(141\) 10577.4 6106.88i 0.532037 0.307171i
\(142\) 0 0
\(143\) −19436.3 + 23163.3i −0.950478 + 1.13274i
\(144\) 0 0
\(145\) −7048.09 4069.22i −0.335224 0.193542i
\(146\) 0 0
\(147\) 23514.6 4146.25i 1.08818 0.191876i
\(148\) 0 0
\(149\) −19199.2 6987.94i −0.864791 0.314758i −0.128735 0.991679i \(-0.541092\pi\)
−0.736056 + 0.676921i \(0.763314\pi\)
\(150\) 0 0
\(151\) 32736.5i 1.43575i −0.696172 0.717875i \(-0.745115\pi\)
0.696172 0.717875i \(-0.254885\pi\)
\(152\) 0 0
\(153\) 16266.3 0.694874
\(154\) 0 0
\(155\) 2463.52 6768.47i 0.102540 0.281726i
\(156\) 0 0
\(157\) 2557.89 + 14506.5i 0.103772 + 0.588523i 0.991704 + 0.128546i \(0.0410311\pi\)
−0.887931 + 0.459976i \(0.847858\pi\)
\(158\) 0 0
\(159\) 6417.06 11114.7i 0.253829 0.439645i
\(160\) 0 0
\(161\) −34085.0 28600.7i −1.31496 1.10338i
\(162\) 0 0
\(163\) 4902.49 + 8491.36i 0.184519 + 0.319597i 0.943414 0.331616i \(-0.107594\pi\)
−0.758895 + 0.651213i \(0.774261\pi\)
\(164\) 0 0
\(165\) 4244.73 + 11662.3i 0.155913 + 0.428368i
\(166\) 0 0
\(167\) 28741.8 + 5067.95i 1.03058 + 0.181719i 0.663269 0.748381i \(-0.269168\pi\)
0.367308 + 0.930099i \(0.380280\pi\)
\(168\) 0 0
\(169\) −5926.92 + 4973.28i −0.207518 + 0.174128i
\(170\) 0 0
\(171\) −12457.0 + 4039.27i −0.426011 + 0.138137i
\(172\) 0 0
\(173\) 27666.0 + 32971.0i 0.924388 + 1.10164i 0.994566 + 0.104108i \(0.0331987\pi\)
−0.0701785 + 0.997534i \(0.522357\pi\)
\(174\) 0 0
\(175\) 6551.99 37158.2i 0.213942 1.21333i
\(176\) 0 0
\(177\) 12929.0 4705.79i 0.412686 0.150206i
\(178\) 0 0
\(179\) 53187.6 30707.9i 1.65998 0.958392i 0.687265 0.726407i \(-0.258811\pi\)
0.972719 0.231986i \(-0.0745223\pi\)
\(180\) 0 0
\(181\) 7862.80 9370.52i 0.240005 0.286027i −0.632574 0.774500i \(-0.718002\pi\)
0.872579 + 0.488473i \(0.162446\pi\)
\(182\) 0 0
\(183\) 7632.06 + 4406.37i 0.227898 + 0.131577i
\(184\) 0 0
\(185\) −26351.5 + 4646.49i −0.769950 + 0.135763i
\(186\) 0 0
\(187\) 66875.1 + 24340.5i 1.91241 + 0.696060i
\(188\) 0 0
\(189\) 60606.2i 1.69665i
\(190\) 0 0
\(191\) −34351.9 −0.941638 −0.470819 0.882230i \(-0.656042\pi\)
−0.470819 + 0.882230i \(0.656042\pi\)
\(192\) 0 0
\(193\) −18862.0 + 51823.0i −0.506377 + 1.39126i 0.378573 + 0.925571i \(0.376415\pi\)
−0.884950 + 0.465687i \(0.845807\pi\)
\(194\) 0 0
\(195\) 2587.05 + 14671.9i 0.0680356 + 0.385849i
\(196\) 0 0
\(197\) −1530.25 + 2650.47i −0.0394303 + 0.0682953i −0.885067 0.465464i \(-0.845888\pi\)
0.845637 + 0.533759i \(0.179221\pi\)
\(198\) 0 0
\(199\) 22659.0 + 19013.2i 0.572183 + 0.480119i 0.882370 0.470557i \(-0.155947\pi\)
−0.310186 + 0.950676i \(0.600391\pi\)
\(200\) 0 0
\(201\) −16742.6 28999.0i −0.414409 0.717778i
\(202\) 0 0
\(203\) −18395.3 50540.8i −0.446391 1.22645i
\(204\) 0 0
\(205\) 26687.1 + 4705.65i 0.635029 + 0.111973i
\(206\) 0 0
\(207\) 16000.8 13426.2i 0.373422 0.313339i
\(208\) 0 0
\(209\) −57258.3 2033.84i −1.31083 0.0465613i
\(210\) 0 0
\(211\) 7223.13 + 8608.19i 0.162241 + 0.193351i 0.841040 0.540973i \(-0.181944\pi\)
−0.678799 + 0.734324i \(0.737499\pi\)
\(212\) 0 0
\(213\) 5501.99 31203.3i 0.121272 0.687767i
\(214\) 0 0
\(215\) 29480.8 10730.1i 0.637767 0.232128i
\(216\) 0 0
\(217\) 41224.0 23800.7i 0.875449 0.505441i
\(218\) 0 0
\(219\) −29983.1 + 35732.5i −0.625156 + 0.745032i
\(220\) 0 0
\(221\) 73985.4 + 42715.5i 1.51482 + 0.874582i
\(222\) 0 0
\(223\) −32675.5 + 5761.57i −0.657072 + 0.115859i −0.492236 0.870462i \(-0.663820\pi\)
−0.164835 + 0.986321i \(0.552709\pi\)
\(224\) 0 0
\(225\) 16644.3 + 6058.05i 0.328777 + 0.119665i
\(226\) 0 0
\(227\) 37637.2i 0.730408i −0.930928 0.365204i \(-0.880999\pi\)
0.930928 0.365204i \(-0.119001\pi\)
\(228\) 0 0
\(229\) −83612.9 −1.59442 −0.797209 0.603703i \(-0.793691\pi\)
−0.797209 + 0.603703i \(0.793691\pi\)
\(230\) 0 0
\(231\) −28052.1 + 77072.6i −0.525704 + 1.44436i
\(232\) 0 0
\(233\) −15577.1 88342.4i −0.286930 1.62726i −0.698309 0.715797i \(-0.746064\pi\)
0.411379 0.911465i \(-0.365047\pi\)
\(234\) 0 0
\(235\) −10677.5 + 18493.9i −0.193345 + 0.334883i
\(236\) 0 0
\(237\) −30235.4 25370.5i −0.538293 0.451681i
\(238\) 0 0
\(239\) −24342.8 42162.9i −0.426161 0.738133i 0.570367 0.821390i \(-0.306801\pi\)
−0.996528 + 0.0832570i \(0.973468\pi\)
\(240\) 0 0
\(241\) 5701.60 + 15665.0i 0.0981664 + 0.269710i 0.979049 0.203625i \(-0.0652723\pi\)
−0.880883 + 0.473335i \(0.843050\pi\)
\(242\) 0 0
\(243\) −47370.5 8352.70i −0.802224 0.141454i
\(244\) 0 0
\(245\) −31980.8 + 26835.1i −0.532791 + 0.447065i
\(246\) 0 0
\(247\) −67266.3 14340.0i −1.10256 0.235048i
\(248\) 0 0
\(249\) 20786.7 + 24772.6i 0.335264 + 0.399552i
\(250\) 0 0
\(251\) 11781.3 66815.0i 0.187002 1.06054i −0.736355 0.676595i \(-0.763455\pi\)
0.923357 0.383943i \(-0.125434\pi\)
\(252\) 0 0
\(253\) 85874.2 31255.6i 1.34160 0.488301i
\(254\) 0 0
\(255\) 30366.7 17532.2i 0.467001 0.269623i
\(256\) 0 0
\(257\) 14598.8 17398.2i 0.221030 0.263413i −0.644122 0.764923i \(-0.722777\pi\)
0.865152 + 0.501509i \(0.167222\pi\)
\(258\) 0 0
\(259\) −153144. 88417.8i −2.28297 1.31808i
\(260\) 0 0
\(261\) 24864.8 4384.34i 0.365010 0.0643611i
\(262\) 0 0
\(263\) −41218.9 15002.5i −0.595916 0.216896i 0.0264136 0.999651i \(-0.491591\pi\)
−0.622329 + 0.782756i \(0.713814\pi\)
\(264\) 0 0
\(265\) 22439.6i 0.319539i
\(266\) 0 0
\(267\) 32711.3 0.458854
\(268\) 0 0
\(269\) −20443.1 + 56166.9i −0.282515 + 0.776204i 0.714546 + 0.699589i \(0.246633\pi\)
−0.997061 + 0.0766150i \(0.975589\pi\)
\(270\) 0 0
\(271\) 6645.37 + 37687.8i 0.0904859 + 0.513171i 0.996037 + 0.0889346i \(0.0283462\pi\)
−0.905552 + 0.424236i \(0.860543\pi\)
\(272\) 0 0
\(273\) −49229.0 + 85267.1i −0.660534 + 1.14408i
\(274\) 0 0
\(275\) 59364.2 + 49812.5i 0.784981 + 0.658677i
\(276\) 0 0
\(277\) 2220.77 + 3846.49i 0.0289431 + 0.0501308i 0.880134 0.474725i \(-0.157453\pi\)
−0.851191 + 0.524856i \(0.824119\pi\)
\(278\) 0 0
\(279\) 7642.75 + 20998.3i 0.0981841 + 0.269759i
\(280\) 0 0
\(281\) −115129. 20300.3i −1.45805 0.257093i −0.612278 0.790642i \(-0.709747\pi\)
−0.845769 + 0.533549i \(0.820858\pi\)
\(282\) 0 0
\(283\) −46915.8 + 39367.1i −0.585796 + 0.491541i −0.886845 0.462067i \(-0.847108\pi\)
0.301049 + 0.953609i \(0.402663\pi\)
\(284\) 0 0
\(285\) −18901.7 + 20967.2i −0.232708 + 0.258137i
\(286\) 0 0
\(287\) 115115. + 137189.i 1.39755 + 1.66554i
\(288\) 0 0
\(289\) 20412.2 115763.i 0.244395 1.38604i
\(290\) 0 0
\(291\) −413.709 + 150.578i −0.00488550 + 0.00177818i
\(292\) 0 0
\(293\) 132814. 76680.1i 1.54706 0.893197i 0.548699 0.836020i \(-0.315123\pi\)
0.998364 0.0571772i \(-0.0182100\pi\)
\(294\) 0 0
\(295\) −15463.1 + 18428.3i −0.177686 + 0.211758i
\(296\) 0 0
\(297\) −107799. 62237.9i −1.22209 0.705573i
\(298\) 0 0
\(299\) 108035. 19049.5i 1.20843 0.213079i
\(300\) 0 0
\(301\) 194829. + 70912.0i 2.15041 + 0.782685i
\(302\) 0 0
\(303\) 32350.5i 0.352367i
\(304\) 0 0
\(305\) −15408.5 −0.165638
\(306\) 0 0
\(307\) 10545.7 28974.0i 0.111892 0.307420i −0.871090 0.491123i \(-0.836586\pi\)
0.982982 + 0.183704i \(0.0588086\pi\)
\(308\) 0 0
\(309\) −12198.9 69183.2i −0.127762 0.724576i
\(310\) 0 0
\(311\) −66618.9 + 115387.i −0.688774 + 1.19299i 0.283460 + 0.958984i \(0.408518\pi\)
−0.972235 + 0.234008i \(0.924816\pi\)
\(312\) 0 0
\(313\) −129680. 108815.i −1.32369 1.11070i −0.985509 0.169621i \(-0.945746\pi\)
−0.338176 0.941083i \(-0.609810\pi\)
\(314\) 0 0
\(315\) −16388.7 28386.0i −0.165167 0.286077i
\(316\) 0 0
\(317\) −5024.10 13803.6i −0.0499965 0.137364i 0.912181 0.409787i \(-0.134397\pi\)
−0.962178 + 0.272423i \(0.912175\pi\)
\(318\) 0 0
\(319\) 108787. + 19182.0i 1.06904 + 0.188501i
\(320\) 0 0
\(321\) 91409.9 76702.0i 0.887122 0.744383i
\(322\) 0 0
\(323\) 22432.7 + 160313.i 0.215019 + 1.53661i
\(324\) 0 0
\(325\) 59796.4 + 71262.5i 0.566120 + 0.674675i
\(326\) 0 0
\(327\) −7877.23 + 44674.0i −0.0736678 + 0.417791i
\(328\) 0 0
\(329\) −132617. + 48268.7i −1.22520 + 0.445937i
\(330\) 0 0
\(331\) 69493.7 40122.2i 0.634292 0.366209i −0.148120 0.988969i \(-0.547322\pi\)
0.782412 + 0.622761i \(0.213989\pi\)
\(332\) 0 0
\(333\) 53360.0 63591.9i 0.481202 0.573474i
\(334\) 0 0
\(335\) 50702.8 + 29273.3i 0.451796 + 0.260845i
\(336\) 0 0
\(337\) 199558. 35187.5i 1.75715 0.309834i 0.800126 0.599832i \(-0.204766\pi\)
0.957027 + 0.289998i \(0.0936546\pi\)
\(338\) 0 0
\(339\) 58337.4 + 21233.1i 0.507630 + 0.184762i
\(340\) 0 0
\(341\) 97766.0i 0.840773i
\(342\) 0 0
\(343\) −90362.7 −0.768070
\(344\) 0 0
\(345\) 15399.9 42310.8i 0.129384 0.355478i
\(346\) 0 0
\(347\) −22885.2 129789.i −0.190062 1.07790i −0.919277 0.393612i \(-0.871225\pi\)
0.729214 0.684285i \(-0.239886\pi\)
\(348\) 0 0
\(349\) −40374.8 + 69931.2i −0.331482 + 0.574143i −0.982803 0.184659i \(-0.940882\pi\)
0.651321 + 0.758802i \(0.274215\pi\)
\(350\) 0 0
\(351\) −114466. 96048.2i −0.929097 0.779605i
\(352\) 0 0
\(353\) 67250.4 + 116481.i 0.539691 + 0.934773i 0.998920 + 0.0464551i \(0.0147924\pi\)
−0.459229 + 0.888318i \(0.651874\pi\)
\(354\) 0 0
\(355\) 18947.4 + 52057.7i 0.150347 + 0.413074i
\(356\) 0 0
\(357\) 228210. + 40239.5i 1.79060 + 0.315730i
\(358\) 0 0
\(359\) −96425.6 + 80910.7i −0.748175 + 0.627794i −0.935020 0.354596i \(-0.884618\pi\)
0.186844 + 0.982390i \(0.440174\pi\)
\(360\) 0 0
\(361\) −56988.6 117200.i −0.437294 0.899319i
\(362\) 0 0
\(363\) −45342.7 54037.3i −0.344107 0.410091i
\(364\) 0 0
\(365\) 14162.1 80317.5i 0.106302 0.602871i
\(366\) 0 0
\(367\) 102088. 37157.1i 0.757955 0.275873i 0.0660056 0.997819i \(-0.478974\pi\)
0.691949 + 0.721946i \(0.256752\pi\)
\(368\) 0 0
\(369\) −72807.1 + 42035.2i −0.534714 + 0.308717i
\(370\) 0 0
\(371\) −95323.1 + 113602.i −0.692549 + 0.825348i
\(372\) 0 0
\(373\) −202445. 116882.i −1.45509 0.840096i −0.456325 0.889813i \(-0.650835\pi\)
−0.998763 + 0.0497171i \(0.984168\pi\)
\(374\) 0 0
\(375\) 85733.0 15117.0i 0.609657 0.107499i
\(376\) 0 0
\(377\) 124608. + 45353.7i 0.876726 + 0.319102i
\(378\) 0 0
\(379\) 127119.i 0.884979i 0.896774 + 0.442490i \(0.145905\pi\)
−0.896774 + 0.442490i \(0.854095\pi\)
\(380\) 0 0
\(381\) −23121.0 −0.159278
\(382\) 0 0
\(383\) −48655.0 + 133679.i −0.331688 + 0.911306i 0.655985 + 0.754774i \(0.272254\pi\)
−0.987673 + 0.156532i \(0.949969\pi\)
\(384\) 0 0
\(385\) −24902.0 141226.i −0.168001 0.952782i
\(386\) 0 0
\(387\) −48665.0 + 84290.2i −0.324934 + 0.562801i
\(388\) 0 0
\(389\) −58248.9 48876.7i −0.384936 0.323000i 0.429700 0.902971i \(-0.358619\pi\)
−0.814637 + 0.579972i \(0.803064\pi\)
\(390\) 0 0
\(391\) −129097. 223602.i −0.844427 1.46259i
\(392\) 0 0
\(393\) −36770.7 101027.i −0.238077 0.654110i
\(394\) 0 0
\(395\) 67961.4 + 11983.4i 0.435580 + 0.0768046i
\(396\) 0 0
\(397\) −112650. + 94524.9i −0.714746 + 0.599743i −0.925926 0.377704i \(-0.876714\pi\)
0.211180 + 0.977447i \(0.432269\pi\)
\(398\) 0 0
\(399\) −184759. + 25853.3i −1.16054 + 0.162394i
\(400\) 0 0
\(401\) 110099. + 131211.i 0.684692 + 0.815984i 0.990703 0.136044i \(-0.0434390\pi\)
−0.306011 + 0.952028i \(0.598995\pi\)
\(402\) 0 0
\(403\) −20379.6 + 115578.i −0.125483 + 0.711649i
\(404\) 0 0
\(405\) −25345.9 + 9225.16i −0.154525 + 0.0562424i
\(406\) 0 0
\(407\) 314535. 181597.i 1.89880 1.09627i
\(408\) 0 0
\(409\) −151405. + 180438.i −0.905097 + 1.07865i 0.0914657 + 0.995808i \(0.470845\pi\)
−0.996563 + 0.0828441i \(0.973600\pi\)
\(410\) 0 0
\(411\) −70658.9 40794.9i −0.418296 0.241503i
\(412\) 0 0
\(413\) −156566. + 27606.8i −0.917903 + 0.161851i
\(414\) 0 0
\(415\) −53131.7 19338.3i −0.308501 0.112285i
\(416\) 0 0
\(417\) 55716.8i 0.320416i
\(418\) 0 0
\(419\) −28749.7 −0.163759 −0.0818795 0.996642i \(-0.526092\pi\)
−0.0818795 + 0.996642i \(0.526092\pi\)
\(420\) 0 0
\(421\) 7598.61 20877.0i 0.0428716 0.117789i −0.916409 0.400242i \(-0.868926\pi\)
0.959281 + 0.282453i \(0.0911482\pi\)
\(422\) 0 0
\(423\) −11504.4 65244.5i −0.0642957 0.364639i
\(424\) 0 0
\(425\) 109474. 189614.i 0.606082 1.04976i
\(426\) 0 0
\(427\) −78006.4 65455.1i −0.427833 0.358995i
\(428\) 0 0
\(429\) −101109. 175125.i −0.549381 0.951557i
\(430\) 0 0
\(431\) −68732.4 188841.i −0.370005 1.01658i −0.975359 0.220623i \(-0.929191\pi\)
0.605354 0.795956i \(-0.293031\pi\)
\(432\) 0 0
\(433\) −273497. 48224.8i −1.45873 0.257214i −0.612688 0.790325i \(-0.709912\pi\)
−0.846046 + 0.533111i \(0.821023\pi\)
\(434\) 0 0
\(435\) 41693.4 34984.9i 0.220337 0.184885i
\(436\) 0 0
\(437\) 154390. + 139181.i 0.808454 + 0.728813i
\(438\) 0 0
\(439\) 447.225 + 532.982i 0.00232058 + 0.00276556i 0.767203 0.641404i \(-0.221648\pi\)
−0.764883 + 0.644169i \(0.777203\pi\)
\(440\) 0 0
\(441\) 22490.5 127550.i 0.115644 0.655847i
\(442\) 0 0
\(443\) 117220. 42664.7i 0.597303 0.217401i −0.0256353 0.999671i \(-0.508161\pi\)
0.622939 + 0.782271i \(0.285939\pi\)
\(444\) 0 0
\(445\) −49531.1 + 28596.8i −0.250125 + 0.144410i
\(446\) 0 0
\(447\) 87828.9 104670.i 0.439564 0.523852i
\(448\) 0 0
\(449\) 66839.9 + 38590.0i 0.331545 + 0.191418i 0.656527 0.754302i \(-0.272025\pi\)
−0.324982 + 0.945720i \(0.605358\pi\)
\(450\) 0 0
\(451\) −362230. + 63870.9i −1.78087 + 0.314015i
\(452\) 0 0
\(453\) 205727. + 74878.4i 1.00252 + 0.364888i
\(454\) 0 0
\(455\) 172147.i 0.831529i
\(456\) 0 0
\(457\) 203300. 0.973432 0.486716 0.873560i \(-0.338195\pi\)
0.486716 + 0.873560i \(0.338195\pi\)
\(458\) 0 0
\(459\) −120283. + 330475.i −0.570926 + 1.56861i
\(460\) 0 0
\(461\) 41048.6 + 232798.i 0.193151 + 1.09541i 0.915028 + 0.403391i \(0.132169\pi\)
−0.721877 + 0.692022i \(0.756720\pi\)
\(462\) 0 0
\(463\) 65503.2 113455.i 0.305563 0.529250i −0.671824 0.740711i \(-0.734489\pi\)
0.977386 + 0.211461i \(0.0678220\pi\)
\(464\) 0 0
\(465\) 36900.4 + 30963.1i 0.170657 + 0.143198i
\(466\) 0 0
\(467\) 75152.4 + 130168.i 0.344595 + 0.596856i 0.985280 0.170948i \(-0.0546829\pi\)
−0.640685 + 0.767804i \(0.721350\pi\)
\(468\) 0 0
\(469\) 132333. + 363582.i 0.601621 + 1.65294i
\(470\) 0 0
\(471\) −97014.0 17106.2i −0.437313 0.0771101i
\(472\) 0 0
\(473\) −326205. + 273718.i −1.45803 + 1.22344i
\(474\) 0 0
\(475\) −36751.4 + 172394.i −0.162887 + 0.764073i
\(476\) 0 0
\(477\) −44748.3 53328.9i −0.196671 0.234383i
\(478\) 0 0
\(479\) −607.917 + 3447.67i −0.00264956 + 0.0150264i −0.986104 0.166130i \(-0.946873\pi\)
0.983454 + 0.181156i \(0.0579840\pi\)
\(480\) 0 0
\(481\) 409695. 149117.i 1.77080 0.644519i
\(482\) 0 0
\(483\) 257698. 148782.i 1.10463 0.637759i
\(484\) 0 0
\(485\) 494.796 589.675i 0.00210350 0.00250686i
\(486\) 0 0
\(487\) 291020. + 168020.i 1.22706 + 0.708442i 0.966413 0.256993i \(-0.0827319\pi\)
0.260644 + 0.965435i \(0.416065\pi\)
\(488\) 0 0
\(489\) −64575.9 + 11386.5i −0.270055 + 0.0476180i
\(490\) 0 0
\(491\) 5044.74 + 1836.14i 0.0209255 + 0.00761626i 0.352462 0.935826i \(-0.385345\pi\)
−0.331536 + 0.943443i \(0.607567\pi\)
\(492\) 0 0
\(493\) 312099.i 1.28410i
\(494\) 0 0
\(495\) 67319.6 0.274746
\(496\) 0 0
\(497\) −125218. + 344033.i −0.506936 + 1.39280i
\(498\) 0 0
\(499\) −55118.2 312591.i −0.221357 1.25538i −0.869528 0.493884i \(-0.835577\pi\)
0.648171 0.761495i \(-0.275534\pi\)
\(500\) 0 0
\(501\) −97589.7 + 169030.i −0.388802 + 0.673425i
\(502\) 0 0
\(503\) 166647. + 139833.i 0.658659 + 0.552681i 0.909685 0.415300i \(-0.136323\pi\)
−0.251025 + 0.967980i \(0.580768\pi\)
\(504\) 0 0
\(505\) 28281.4 + 48984.8i 0.110897 + 0.192078i
\(506\) 0 0
\(507\) −17697.0 48622.0i −0.0688467 0.189155i
\(508\) 0 0
\(509\) 141631. + 24973.3i 0.546666 + 0.0963919i 0.440159 0.897920i \(-0.354922\pi\)
0.106507 + 0.994312i \(0.466033\pi\)
\(510\) 0 0
\(511\) 412884. 346451.i 1.58120 1.32678i
\(512\) 0 0
\(513\) 10050.6 282952.i 0.0381907 1.07517i
\(514\) 0 0
\(515\) 78952.6 + 94092.1i 0.297682 + 0.354763i
\(516\) 0 0
\(517\) 50332.9 285452.i 0.188309 1.06795i
\(518\) 0 0
\(519\) −270481. + 98447.0i −1.00416 + 0.365484i
\(520\) 0 0
\(521\) −147332. + 85062.1i −0.542777 + 0.313372i −0.746204 0.665718i \(-0.768125\pi\)
0.203427 + 0.979090i \(0.434792\pi\)
\(522\) 0 0
\(523\) 79213.6 94403.1i 0.289599 0.345130i −0.601555 0.798831i \(-0.705452\pi\)
0.891154 + 0.453701i \(0.149897\pi\)
\(524\) 0 0
\(525\) 218527. + 126167.i 0.792842 + 0.457748i
\(526\) 0 0
\(527\) 272024. 47965.2i 0.979460 0.172705i
\(528\) 0 0
\(529\) −48586.8 17684.1i −0.173623 0.0631935i
\(530\) 0 0
\(531\) 74631.8i 0.264688i
\(532\) 0 0
\(533\) −441540. −1.55423
\(534\) 0 0
\(535\) −71357.7 + 196054.i −0.249306 + 0.684963i
\(536\) 0 0
\(537\) 71321.7 + 404485.i 0.247328 + 1.40267i
\(538\) 0 0
\(539\) 283327. 490737.i 0.975238 1.68916i
\(540\) 0 0
\(541\) −222820. 186969.i −0.761308 0.638813i 0.177159 0.984182i \(-0.443309\pi\)
−0.938467 + 0.345369i \(0.887754\pi\)
\(542\) 0 0
\(543\) 40902.7 + 70845.5i 0.138724 + 0.240277i
\(544\) 0 0
\(545\) −27127.2 74531.3i −0.0913296 0.250926i
\(546\) 0 0
\(547\) 186506. + 32886.0i 0.623329 + 0.109910i 0.476388 0.879235i \(-0.341946\pi\)
0.146942 + 0.989145i \(0.453057\pi\)
\(548\) 0 0
\(549\) 36619.2 30727.1i 0.121496 0.101948i
\(550\) 0 0
\(551\) 77501.0 + 239011.i 0.255272 + 0.787252i
\(552\) 0 0
\(553\) 293153. + 349366.i 0.958613 + 1.14243i
\(554\) 0 0
\(555\) 31074.0 176229.i 0.100881 0.572127i
\(556\) 0 0
\(557\) −177494. + 64602.5i −0.572101 + 0.208228i −0.611839 0.790982i \(-0.709570\pi\)
0.0397378 + 0.999210i \(0.487348\pi\)
\(558\) 0 0
\(559\) −442694. + 255589.i −1.41671 + 0.817936i
\(560\) 0 0
\(561\) −305927. + 364590.i −0.972058 + 1.15845i
\(562\) 0 0
\(563\) 238656. + 137788.i 0.752931 + 0.434705i 0.826752 0.562566i \(-0.190186\pi\)
−0.0738207 + 0.997272i \(0.523519\pi\)
\(564\) 0 0
\(565\) −106896. + 18848.7i −0.334862 + 0.0590452i
\(566\) 0 0
\(567\) −167503. 60966.2i −0.521023 0.189637i
\(568\) 0 0
\(569\) 201455.i 0.622233i −0.950372 0.311116i \(-0.899297\pi\)
0.950372 0.311116i \(-0.100703\pi\)
\(570\) 0 0
\(571\) 206021. 0.631885 0.315943 0.948778i \(-0.397679\pi\)
0.315943 + 0.948778i \(0.397679\pi\)
\(572\) 0 0
\(573\) 78573.2 215878.i 0.239312 0.657506i
\(574\) 0 0
\(575\) −48821.1 276878.i −0.147663 0.837439i
\(576\) 0 0
\(577\) 51593.6 89362.8i 0.154969 0.268414i −0.778079 0.628167i \(-0.783806\pi\)
0.933048 + 0.359753i \(0.117139\pi\)
\(578\) 0 0
\(579\) −282529. 237070.i −0.842763 0.707162i
\(580\) 0 0
\(581\) −186833. 323604.i −0.553478 0.958653i
\(582\) 0 0
\(583\) −104172. 286210.i −0.306488 0.842068i
\(584\) 0 0
\(585\) 79584.8 + 14032.9i 0.232551 + 0.0410050i
\(586\) 0 0
\(587\) 101118. 84847.8i 0.293461 0.246243i −0.484155 0.874982i \(-0.660873\pi\)
0.777616 + 0.628739i \(0.216429\pi\)
\(588\) 0 0
\(589\) −196410. + 104282.i −0.566151 + 0.300593i
\(590\) 0 0
\(591\) −13156.2 15679.0i −0.0376666 0.0448894i
\(592\) 0 0
\(593\) −87272.3 + 494946.i −0.248180 + 1.40750i 0.564809 + 0.825221i \(0.308950\pi\)
−0.812990 + 0.582278i \(0.802161\pi\)
\(594\) 0 0
\(595\) −380731. + 138575.i −1.07543 + 0.391426i
\(596\) 0 0
\(597\) −171313. + 98907.5i −0.480664 + 0.277511i
\(598\) 0 0
\(599\) −68182.5 + 81256.7i −0.190029 + 0.226467i −0.852644 0.522493i \(-0.825002\pi\)
0.662615 + 0.748960i \(0.269447\pi\)
\(600\) 0 0
\(601\) −370588. 213959.i −1.02599 0.592355i −0.110156 0.993914i \(-0.535135\pi\)
−0.915833 + 0.401559i \(0.868468\pi\)
\(602\) 0 0
\(603\) −178874. + 31540.3i −0.491940 + 0.0867422i
\(604\) 0 0
\(605\) 115898. + 42183.3i 0.316639 + 0.115247i
\(606\) 0 0
\(607\) 158805.i 0.431009i 0.976503 + 0.215504i \(0.0691395\pi\)
−0.976503 + 0.215504i \(0.930860\pi\)
\(608\) 0 0
\(609\) 359690. 0.969825
\(610\) 0 0
\(611\) 119006. 326967.i 0.318778 0.875835i
\(612\) 0 0
\(613\) 32986.8 + 187077.i 0.0877848 + 0.497852i 0.996721 + 0.0809167i \(0.0257848\pi\)
−0.908936 + 0.416935i \(0.863104\pi\)
\(614\) 0 0
\(615\) −90613.3 + 156947.i −0.239575 + 0.414956i
\(616\) 0 0
\(617\) −98890.7 82979.1i −0.259768 0.217971i 0.503597 0.863939i \(-0.332010\pi\)
−0.763365 + 0.645968i \(0.776454\pi\)
\(618\) 0 0
\(619\) 156923. + 271799.i 0.409549 + 0.709359i 0.994839 0.101465i \(-0.0323528\pi\)
−0.585290 + 0.810824i \(0.699020\pi\)
\(620\) 0 0
\(621\) 154456. + 424363.i 0.400516 + 1.10041i
\(622\) 0 0
\(623\) −372232. 65634.6i −0.959042 0.169105i
\(624\) 0 0
\(625\) 117175. 98321.8i 0.299969 0.251704i
\(626\) 0 0
\(627\) 143748. 355177.i 0.365652 0.903462i
\(628\) 0 0
\(629\) −659590. 786068.i −1.66714 1.98682i
\(630\) 0 0
\(631\) −102049. + 578750.i −0.256301 + 1.45356i 0.536408 + 0.843959i \(0.319781\pi\)
−0.792710 + 0.609599i \(0.791330\pi\)
\(632\) 0 0
\(633\) −70618.1 + 25702.9i −0.176242 + 0.0641467i
\(634\) 0 0
\(635\) 35009.6 20212.8i 0.0868239 0.0501278i
\(636\) 0 0
\(637\) 437243. 521085.i 1.07757 1.28419i
\(638\) 0 0
\(639\) −148841. 85933.5i −0.364520 0.210456i
\(640\) 0 0
\(641\) 242434. 42747.6i 0.590034 0.104039i 0.129344 0.991600i \(-0.458713\pi\)
0.460690 + 0.887561i \(0.347602\pi\)
\(642\) 0 0
\(643\) −448205. 163133.i −1.08406 0.394567i −0.262646 0.964892i \(-0.584595\pi\)
−0.821419 + 0.570325i \(0.806817\pi\)
\(644\) 0 0
\(645\) 209809.i 0.504319i
\(646\) 0 0
\(647\) 104424. 0.249454 0.124727 0.992191i \(-0.460195\pi\)
0.124727 + 0.992191i \(0.460195\pi\)
\(648\) 0 0
\(649\) 111677. 306831.i 0.265140 0.728467i
\(650\) 0 0
\(651\) 55279.2 + 313504.i 0.130437 + 0.739744i
\(652\) 0 0
\(653\) −136854. + 237038.i −0.320945 + 0.555893i −0.980683 0.195602i \(-0.937334\pi\)
0.659738 + 0.751495i \(0.270667\pi\)
\(654\) 0 0
\(655\) 143997. + 120828.i 0.335638 + 0.281634i
\(656\) 0 0
\(657\) 126509. + 219120.i 0.293084 + 0.507636i
\(658\) 0 0
\(659\) −169164. 464776.i −0.389528 1.07022i −0.967215 0.253960i \(-0.918267\pi\)
0.577687 0.816258i \(-0.303955\pi\)
\(660\) 0 0
\(661\) 123889. + 21845.0i 0.283550 + 0.0499975i 0.313614 0.949550i \(-0.398460\pi\)
−0.0300643 + 0.999548i \(0.509571\pi\)
\(662\) 0 0
\(663\) −437664. + 367244.i −0.995667 + 0.835464i
\(664\) 0 0
\(665\) 257159. 200666.i 0.581511 0.453765i
\(666\) 0 0
\(667\) −257607. 307005.i −0.579038 0.690070i
\(668\) 0 0
\(669\) 38531.3 218522.i 0.0860916 0.488250i
\(670\) 0 0
\(671\) 196530. 71531.2i 0.436501 0.158873i
\(672\) 0 0
\(673\) 365687. 211130.i 0.807383 0.466143i −0.0386634 0.999252i \(-0.512310\pi\)
0.846046 + 0.533110i \(0.178977\pi\)
\(674\) 0 0
\(675\) −246158. + 293359.i −0.540263 + 0.643861i
\(676\) 0 0
\(677\) −553872. 319778.i −1.20846 0.697704i −0.246036 0.969261i \(-0.579128\pi\)
−0.962422 + 0.271557i \(0.912461\pi\)
\(678\) 0 0
\(679\) 5009.86 883.373i 0.0108664 0.00191604i
\(680\) 0 0
\(681\) 236524. + 86087.6i 0.510012 + 0.185629i
\(682\) 0 0
\(683\) 23651.0i 0.0507000i −0.999679 0.0253500i \(-0.991930\pi\)
0.999679 0.0253500i \(-0.00807003\pi\)
\(684\) 0 0
\(685\) 142655. 0.304022
\(686\) 0 0
\(687\) 191248. 525450.i 0.405213 1.11331i
\(688\) 0 0
\(689\) −63490.0 360070.i −0.133742 0.758487i
\(690\) 0 0
\(691\) −263775. + 456872.i −0.552430 + 0.956837i 0.445668 + 0.895198i \(0.352966\pi\)
−0.998098 + 0.0616392i \(0.980367\pi\)
\(692\) 0 0
\(693\) 340809. + 285973.i 0.709651 + 0.595468i
\(694\) 0 0
\(695\) 48708.7 + 84365.9i 0.100841 + 0.174661i
\(696\) 0 0
\(697\) 355429. + 976534.i 0.731624 + 2.01012i
\(698\) 0 0
\(699\) 590801. + 104174.i 1.20917 + 0.213209i
\(700\) 0 0
\(701\) 77321.9 64880.8i 0.157350 0.132032i −0.560714 0.828010i \(-0.689473\pi\)
0.718064 + 0.695978i \(0.245029\pi\)
\(702\) 0 0
\(703\) 700322. + 438193.i 1.41706 + 0.886656i
\(704\) 0 0
\(705\) −91799.1 109402.i −0.184697 0.220113i
\(706\) 0 0
\(707\) −64910.7 + 368127.i −0.129861 + 0.736476i
\(708\) 0 0
\(709\) 241224. 87798.4i 0.479875 0.174660i −0.0907454 0.995874i \(-0.528925\pi\)
0.570621 + 0.821214i \(0.306703\pi\)
\(710\) 0 0
\(711\) −185411. + 107047.i −0.366772 + 0.211756i
\(712\) 0 0
\(713\) 227993. 271712.i 0.448480 0.534478i
\(714\) 0 0
\(715\) 306196. + 176782.i 0.598945 + 0.345801i
\(716\) 0 0
\(717\) 320644. 56538.2i 0.623713 0.109978i
\(718\) 0 0
\(719\) 82282.6 + 29948.4i 0.159166 + 0.0579317i 0.420374 0.907351i \(-0.361899\pi\)
−0.261208 + 0.965282i \(0.584121\pi\)
\(720\) 0 0
\(721\) 811735.i 1.56151i
\(722\) 0 0
\(723\) −111485. −0.213275
\(724\) 0 0
\(725\) 116235. 319353.i 0.221137 0.607568i
\(726\) 0 0
\(727\) 5021.81 + 28480.1i 0.00950148 + 0.0538856i 0.989190 0.146640i \(-0.0468460\pi\)
−0.979688 + 0.200526i \(0.935735\pi\)
\(728\) 0 0
\(729\) 254265. 440400.i 0.478445 0.828690i
\(730\) 0 0
\(731\) 921635. + 773343.i 1.72474 + 1.44723i
\(732\) 0 0
\(733\) −239223. 414347.i −0.445241 0.771180i 0.552828 0.833295i \(-0.313549\pi\)
−0.998069 + 0.0621152i \(0.980215\pi\)
\(734\) 0 0
\(735\) −95490.2 262357.i −0.176760 0.485644i
\(736\) 0 0
\(737\) −782593. 137992.i −1.44079 0.254050i
\(738\) 0 0
\(739\) −547603. + 459493.i −1.00271 + 0.841376i −0.987358 0.158506i \(-0.949332\pi\)
−0.0153548 + 0.999882i \(0.504888\pi\)
\(740\) 0 0
\(741\) 243976. 389923.i 0.444335 0.710137i
\(742\) 0 0
\(743\) 59406.1 + 70797.5i 0.107610 + 0.128245i 0.817161 0.576409i \(-0.195547\pi\)
−0.709551 + 0.704654i \(0.751102\pi\)
\(744\) 0 0
\(745\) −41484.9 + 235272.i −0.0747441 + 0.423895i
\(746\) 0 0
\(747\) 164834. 59994.7i 0.295397 0.107516i
\(748\) 0 0
\(749\) −1.19408e6 + 689405.i −2.12849 + 1.22888i
\(750\) 0 0
\(751\) 486298. 579548.i 0.862229 1.02757i −0.137086 0.990559i \(-0.543774\pi\)
0.999315 0.0370059i \(-0.0117820\pi\)
\(752\) 0 0
\(753\) 392939. + 226863.i 0.693003 + 0.400105i
\(754\) 0 0
\(755\) −376969. + 66469.8i −0.661321 + 0.116609i
\(756\) 0 0
\(757\) −451854. 164461.i −0.788509 0.286994i −0.0837927 0.996483i \(-0.526703\pi\)
−0.704716 + 0.709490i \(0.748926\pi\)
\(758\) 0 0
\(759\) 611151.i 1.06088i
\(760\) 0 0
\(761\) 738590. 1.27536 0.637682 0.770299i \(-0.279893\pi\)
0.637682 + 0.770299i \(0.279893\pi\)
\(762\) 0 0
\(763\) 179275. 492554.i 0.307943 0.846067i
\(764\) 0 0
\(765\) −33027.9 187310.i −0.0564362 0.320066i
\(766\) 0 0
\(767\) 195984. 339454.i 0.333142 0.577019i
\(768\) 0 0
\(769\) 468069. + 392756.i 0.791511 + 0.664157i 0.946119 0.323819i \(-0.104967\pi\)
−0.154608 + 0.987976i \(0.549411\pi\)
\(770\) 0 0
\(771\) 75943.7 + 131538.i 0.127757 + 0.221281i
\(772\) 0 0
\(773\) −60864.5 167224.i −0.101860 0.279859i 0.878286 0.478136i \(-0.158688\pi\)
−0.980146 + 0.198277i \(0.936465\pi\)
\(774\) 0 0
\(775\) 296210. + 52229.9i 0.493170 + 0.0869592i
\(776\) 0 0
\(777\) 905932. 760168.i 1.50056 1.25912i
\(778\) 0 0
\(779\) −514688. 659585.i −0.848143 1.08692i
\(780\) 0 0
\(781\) −483337. 576018.i −0.792406 0.944352i
\(782\) 0 0
\(783\) −94791.4 + 537589.i −0.154613 + 0.876853i
\(784\) 0 0
\(785\) 161852. 58909.4i 0.262651 0.0955972i
\(786\) 0 0
\(787\) −415176. + 239702.i −0.670321 + 0.387010i −0.796198 0.605036i \(-0.793159\pi\)
0.125877 + 0.992046i \(0.459825\pi\)
\(788\) 0 0
\(789\) 188560. 224717.i 0.302898 0.360980i
\(790\) 0 0
\(791\) −621236. 358671.i −0.992896 0.573249i
\(792\) 0 0