Properties

Label 76.5.j.a.21.3
Level $76$
Weight $5$
Character 76.21
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 21.3
Character \(\chi\) \(=\) 76.21
Dual form 76.5.j.a.29.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.504186 + 0.600866i) q^{3} +(-8.75235 + 3.18559i) q^{5} +(-3.87876 - 6.71820i) q^{7} +(13.9587 + 79.1635i) q^{9} +O(q^{10})\) \(q+(-0.504186 + 0.600866i) q^{3} +(-8.75235 + 3.18559i) q^{5} +(-3.87876 - 6.71820i) q^{7} +(13.9587 + 79.1635i) q^{9} +(-94.7123 + 164.047i) q^{11} +(-152.490 - 181.730i) q^{13} +(2.49870 - 6.86512i) q^{15} +(-73.3453 + 415.962i) q^{17} +(171.374 + 317.729i) q^{19} +(5.99236 + 1.05661i) q^{21} +(-669.617 - 243.721i) q^{23} +(-412.322 + 345.979i) q^{25} +(-109.627 - 63.2931i) q^{27} +(1556.26 - 274.410i) q^{29} +(-389.047 + 224.616i) q^{31} +(-50.8173 - 139.619i) q^{33} +(55.3497 + 46.4439i) q^{35} -923.124i q^{37} +186.079 q^{39} +(1592.45 - 1897.81i) q^{41} +(374.881 - 136.446i) q^{43} +(-374.354 - 648.400i) q^{45} +(189.007 + 1071.91i) q^{47} +(1170.41 - 2027.21i) q^{49} +(-212.957 - 253.793i) q^{51} +(-293.848 + 807.340i) q^{53} +(306.370 - 1737.51i) q^{55} +(-277.317 - 57.2217i) q^{57} +(-2307.63 - 406.897i) q^{59} +(5176.31 + 1884.02i) q^{61} +(477.695 - 400.833i) q^{63} +(1913.56 + 1104.80i) q^{65} +(-6476.74 + 1142.02i) q^{67} +(484.055 - 279.469i) q^{69} +(877.159 + 2409.97i) q^{71} +(-3639.17 - 3053.62i) q^{73} -422.188i q^{75} +1469.46 q^{77} +(-7424.75 + 8848.48i) q^{79} +(-6025.19 + 2192.99i) q^{81} +(5155.43 + 8929.47i) q^{83} +(-683.142 - 3874.29i) q^{85} +(-619.759 + 1073.45i) q^{87} +(1402.20 + 1671.08i) q^{89} +(-629.430 + 1729.35i) q^{91} +(61.1878 - 347.013i) q^{93} +(-2512.09 - 2234.95i) q^{95} +(6417.59 + 1131.59i) q^{97} +(-14308.6 - 5207.89i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −0.504186 + 0.600866i −0.0560207 + 0.0667629i −0.793327 0.608796i \(-0.791653\pi\)
0.737306 + 0.675558i \(0.236097\pi\)
\(4\) 0 0
\(5\) −8.75235 + 3.18559i −0.350094 + 0.127424i −0.511081 0.859533i \(-0.670755\pi\)
0.160987 + 0.986957i \(0.448532\pi\)
\(6\) 0 0
\(7\) −3.87876 6.71820i −0.0791583 0.137106i 0.823729 0.566984i \(-0.191890\pi\)
−0.902887 + 0.429878i \(0.858557\pi\)
\(8\) 0 0
\(9\) 13.9587 + 79.1635i 0.172329 + 0.977328i
\(10\) 0 0
\(11\) −94.7123 + 164.047i −0.782746 + 1.35576i 0.147590 + 0.989049i \(0.452849\pi\)
−0.930336 + 0.366708i \(0.880485\pi\)
\(12\) 0 0
\(13\) −152.490 181.730i −0.902307 1.07533i −0.996811 0.0798029i \(-0.974571\pi\)
0.0945038 0.995524i \(-0.469874\pi\)
\(14\) 0 0
\(15\) 2.49870 6.86512i 0.0111053 0.0305117i
\(16\) 0 0
\(17\) −73.3453 + 415.962i −0.253790 + 1.43931i 0.545370 + 0.838195i \(0.316389\pi\)
−0.799160 + 0.601118i \(0.794722\pi\)
\(18\) 0 0
\(19\) 171.374 + 317.729i 0.474721 + 0.880136i
\(20\) 0 0
\(21\) 5.99236 + 1.05661i 0.0135881 + 0.00239595i
\(22\) 0 0
\(23\) −669.617 243.721i −1.26582 0.460720i −0.380100 0.924945i \(-0.624110\pi\)
−0.885717 + 0.464226i \(0.846333\pi\)
\(24\) 0 0
\(25\) −412.322 + 345.979i −0.659715 + 0.553567i
\(26\) 0 0
\(27\) −109.627 63.2931i −0.150380 0.0868217i
\(28\) 0 0
\(29\) 1556.26 274.410i 1.85048 0.326290i 0.865765 0.500450i \(-0.166832\pi\)
0.984717 + 0.174160i \(0.0557211\pi\)
\(30\) 0 0
\(31\) −389.047 + 224.616i −0.404835 + 0.233732i −0.688568 0.725172i \(-0.741760\pi\)
0.283733 + 0.958903i \(0.408427\pi\)
\(32\) 0 0
\(33\) −50.8173 139.619i −0.0466642 0.128209i
\(34\) 0 0
\(35\) 55.3497 + 46.4439i 0.0451834 + 0.0379134i
\(36\) 0 0
\(37\) 923.124i 0.674305i −0.941450 0.337153i \(-0.890536\pi\)
0.941450 0.337153i \(-0.109464\pi\)
\(38\) 0 0
\(39\) 186.079 0.122340
\(40\) 0 0
\(41\) 1592.45 1897.81i 0.947322 1.12897i −0.0441984 0.999023i \(-0.514073\pi\)
0.991520 0.129952i \(-0.0414822\pi\)
\(42\) 0 0
\(43\) 374.881 136.446i 0.202748 0.0737942i −0.238650 0.971106i \(-0.576705\pi\)
0.441398 + 0.897311i \(0.354483\pi\)
\(44\) 0 0
\(45\) −374.354 648.400i −0.184866 0.320198i
\(46\) 0 0
\(47\) 189.007 + 1071.91i 0.0855623 + 0.485248i 0.997234 + 0.0743281i \(0.0236812\pi\)
−0.911672 + 0.410920i \(0.865208\pi\)
\(48\) 0 0
\(49\) 1170.41 2027.21i 0.487468 0.844319i
\(50\) 0 0
\(51\) −212.957 253.793i −0.0818752 0.0975751i
\(52\) 0 0
\(53\) −293.848 + 807.340i −0.104609 + 0.287412i −0.980944 0.194291i \(-0.937759\pi\)
0.876335 + 0.481703i \(0.159982\pi\)
\(54\) 0 0
\(55\) 306.370 1737.51i 0.101279 0.574383i
\(56\) 0 0
\(57\) −277.317 57.2217i −0.0853546 0.0176121i
\(58\) 0 0
\(59\) −2307.63 406.897i −0.662921 0.116891i −0.167944 0.985797i \(-0.553713\pi\)
−0.494978 + 0.868906i \(0.664824\pi\)
\(60\) 0 0
\(61\) 5176.31 + 1884.02i 1.39111 + 0.506321i 0.925526 0.378684i \(-0.123623\pi\)
0.465580 + 0.885006i \(0.345846\pi\)
\(62\) 0 0
\(63\) 477.695 400.833i 0.120356 0.100991i
\(64\) 0 0
\(65\) 1913.56 + 1104.80i 0.452915 + 0.261490i
\(66\) 0 0
\(67\) −6476.74 + 1142.02i −1.44280 + 0.254405i −0.839609 0.543191i \(-0.817216\pi\)
−0.603193 + 0.797596i \(0.706105\pi\)
\(68\) 0 0
\(69\) 484.055 279.469i 0.101671 0.0586997i
\(70\) 0 0
\(71\) 877.159 + 2409.97i 0.174005 + 0.478075i 0.995784 0.0917320i \(-0.0292403\pi\)
−0.821779 + 0.569807i \(0.807018\pi\)
\(72\) 0 0
\(73\) −3639.17 3053.62i −0.682898 0.573020i 0.233953 0.972248i \(-0.424834\pi\)
−0.916852 + 0.399228i \(0.869278\pi\)
\(74\) 0 0
\(75\) 422.188i 0.0750557i
\(76\) 0 0
\(77\) 1469.46 0.247844
\(78\) 0 0
\(79\) −7424.75 + 8848.48i −1.18967 + 1.41780i −0.304516 + 0.952507i \(0.598495\pi\)
−0.885158 + 0.465291i \(0.845950\pi\)
\(80\) 0 0
\(81\) −6025.19 + 2192.99i −0.918334 + 0.334246i
\(82\) 0 0
\(83\) 5155.43 + 8929.47i 0.748357 + 1.29619i 0.948610 + 0.316448i \(0.102490\pi\)
−0.200253 + 0.979744i \(0.564176\pi\)
\(84\) 0 0
\(85\) −683.142 3874.29i −0.0945525 0.536234i
\(86\) 0 0
\(87\) −619.759 + 1073.45i −0.0818813 + 0.141823i
\(88\) 0 0
\(89\) 1402.20 + 1671.08i 0.177023 + 0.210968i 0.847259 0.531181i \(-0.178251\pi\)
−0.670236 + 0.742148i \(0.733807\pi\)
\(90\) 0 0
\(91\) −629.430 + 1729.35i −0.0760090 + 0.208833i
\(92\) 0 0
\(93\) 61.1878 347.013i 0.00707455 0.0401218i
\(94\) 0 0
\(95\) −2512.09 2234.95i −0.278347 0.247640i
\(96\) 0 0
\(97\) 6417.59 + 1131.59i 0.682070 + 0.120267i 0.503939 0.863739i \(-0.331884\pi\)
0.178131 + 0.984007i \(0.442995\pi\)
\(98\) 0 0
\(99\) −14308.6 5207.89i −1.45991 0.531363i
\(100\) 0 0
\(101\) 826.363 693.401i 0.0810081 0.0679738i −0.601384 0.798960i \(-0.705384\pi\)
0.682393 + 0.730986i \(0.260940\pi\)
\(102\) 0 0
\(103\) −3188.70 1841.00i −0.300566 0.173532i 0.342131 0.939652i \(-0.388851\pi\)
−0.642697 + 0.766120i \(0.722185\pi\)
\(104\) 0 0
\(105\) −55.8131 + 9.84136i −0.00506242 + 0.000892641i
\(106\) 0 0
\(107\) 13571.7 7835.61i 1.18540 0.684393i 0.228145 0.973627i \(-0.426734\pi\)
0.957258 + 0.289234i \(0.0934007\pi\)
\(108\) 0 0
\(109\) 4348.57 + 11947.6i 0.366010 + 1.00561i 0.976864 + 0.213862i \(0.0686042\pi\)
−0.610853 + 0.791744i \(0.709174\pi\)
\(110\) 0 0
\(111\) 554.673 + 465.426i 0.0450185 + 0.0377750i
\(112\) 0 0
\(113\) 9061.84i 0.709675i 0.934928 + 0.354837i \(0.115464\pi\)
−0.934928 + 0.354837i \(0.884536\pi\)
\(114\) 0 0
\(115\) 6637.12 0.501862
\(116\) 0 0
\(117\) 12257.9 14608.3i 0.895453 1.06716i
\(118\) 0 0
\(119\) 3079.00 1120.67i 0.217428 0.0791375i
\(120\) 0 0
\(121\) −10620.3 18395.0i −0.725384 1.25640i
\(122\) 0 0
\(123\) 337.436 + 1913.70i 0.0223039 + 0.126492i
\(124\) 0 0
\(125\) 5417.28 9383.00i 0.346706 0.600512i
\(126\) 0 0
\(127\) −14942.6 17807.9i −0.926444 1.10409i −0.994323 0.106400i \(-0.966068\pi\)
0.0678790 0.997694i \(-0.478377\pi\)
\(128\) 0 0
\(129\) −107.024 + 294.047i −0.00643137 + 0.0176700i
\(130\) 0 0
\(131\) −2940.86 + 16678.4i −0.171369 + 0.971880i 0.770884 + 0.636976i \(0.219815\pi\)
−0.942252 + 0.334904i \(0.891296\pi\)
\(132\) 0 0
\(133\) 1469.85 2383.72i 0.0830940 0.134757i
\(134\) 0 0
\(135\) 1161.12 + 204.736i 0.0637102 + 0.0112338i
\(136\) 0 0
\(137\) 9299.62 + 3384.78i 0.495478 + 0.180339i 0.577659 0.816278i \(-0.303966\pi\)
−0.0821812 + 0.996617i \(0.526189\pi\)
\(138\) 0 0
\(139\) 15521.6 13024.2i 0.803356 0.674096i −0.145656 0.989335i \(-0.546529\pi\)
0.949012 + 0.315240i \(0.102085\pi\)
\(140\) 0 0
\(141\) −739.370 426.876i −0.0371898 0.0214715i
\(142\) 0 0
\(143\) 44254.9 7803.33i 2.16416 0.381600i
\(144\) 0 0
\(145\) −12746.7 + 7359.33i −0.606266 + 0.350028i
\(146\) 0 0
\(147\) 627.977 + 1725.35i 0.0290609 + 0.0798441i
\(148\) 0 0
\(149\) 2762.13 + 2317.70i 0.124415 + 0.104396i 0.702872 0.711316i \(-0.251901\pi\)
−0.578457 + 0.815713i \(0.696345\pi\)
\(150\) 0 0
\(151\) 17076.6i 0.748940i −0.927239 0.374470i \(-0.877825\pi\)
0.927239 0.374470i \(-0.122175\pi\)
\(152\) 0 0
\(153\) −33952.8 −1.45042
\(154\) 0 0
\(155\) 2689.54 3205.26i 0.111947 0.133414i
\(156\) 0 0
\(157\) −23631.5 + 8601.16i −0.958720 + 0.348945i −0.773532 0.633758i \(-0.781512\pi\)
−0.185188 + 0.982703i \(0.559289\pi\)
\(158\) 0 0
\(159\) −336.949 583.613i −0.0133282 0.0230850i
\(160\) 0 0
\(161\) 959.917 + 5443.96i 0.0370324 + 0.210021i
\(162\) 0 0
\(163\) 11840.5 20508.4i 0.445651 0.771891i −0.552446 0.833549i \(-0.686305\pi\)
0.998097 + 0.0616580i \(0.0196388\pi\)
\(164\) 0 0
\(165\) 889.542 + 1060.11i 0.0326737 + 0.0389390i
\(166\) 0 0
\(167\) −13247.0 + 36395.9i −0.474991 + 1.30503i 0.438706 + 0.898631i \(0.355437\pi\)
−0.913697 + 0.406397i \(0.866785\pi\)
\(168\) 0 0
\(169\) −4813.19 + 27297.0i −0.168523 + 0.955743i
\(170\) 0 0
\(171\) −22760.4 + 18001.7i −0.778373 + 0.615631i
\(172\) 0 0
\(173\) 4285.42 + 755.635i 0.143186 + 0.0252476i 0.244782 0.969578i \(-0.421284\pi\)
−0.101596 + 0.994826i \(0.532395\pi\)
\(174\) 0 0
\(175\) 3923.66 + 1428.09i 0.128119 + 0.0466317i
\(176\) 0 0
\(177\) 1407.97 1181.42i 0.0449413 0.0377102i
\(178\) 0 0
\(179\) 37315.9 + 21544.3i 1.16463 + 0.672399i 0.952409 0.304823i \(-0.0985975\pi\)
0.212220 + 0.977222i \(0.431931\pi\)
\(180\) 0 0
\(181\) −10363.9 + 1827.44i −0.316349 + 0.0557808i −0.329568 0.944132i \(-0.606903\pi\)
0.0132194 + 0.999913i \(0.495792\pi\)
\(182\) 0 0
\(183\) −3741.87 + 2160.37i −0.111734 + 0.0645098i
\(184\) 0 0
\(185\) 2940.70 + 8079.50i 0.0859225 + 0.236070i
\(186\) 0 0
\(187\) −61290.4 51428.7i −1.75271 1.47070i
\(188\) 0 0
\(189\) 981.994i 0.0274907i
\(190\) 0 0
\(191\) 10198.0 0.279543 0.139772 0.990184i \(-0.455363\pi\)
0.139772 + 0.990184i \(0.455363\pi\)
\(192\) 0 0
\(193\) −32382.4 + 38591.8i −0.869349 + 1.03605i 0.129660 + 0.991558i \(0.458611\pi\)
−0.999010 + 0.0444917i \(0.985833\pi\)
\(194\) 0 0
\(195\) −1628.63 + 592.772i −0.0428304 + 0.0155890i
\(196\) 0 0
\(197\) 11238.5 + 19465.7i 0.289585 + 0.501576i 0.973711 0.227788i \(-0.0731493\pi\)
−0.684126 + 0.729364i \(0.739816\pi\)
\(198\) 0 0
\(199\) 8018.46 + 45475.0i 0.202481 + 1.14833i 0.901354 + 0.433083i \(0.142574\pi\)
−0.698873 + 0.715246i \(0.746315\pi\)
\(200\) 0 0
\(201\) 2579.28 4467.44i 0.0638420 0.110578i
\(202\) 0 0
\(203\) −7879.88 9390.88i −0.191217 0.227884i
\(204\) 0 0
\(205\) −7892.02 + 21683.2i −0.187794 + 0.515958i
\(206\) 0 0
\(207\) 9946.83 56411.3i 0.232137 1.31651i
\(208\) 0 0
\(209\) −68353.6 1979.49i −1.56484 0.0453169i
\(210\) 0 0
\(211\) 47835.1 + 8434.62i 1.07444 + 0.189453i 0.682755 0.730647i \(-0.260782\pi\)
0.391684 + 0.920100i \(0.371893\pi\)
\(212\) 0 0
\(213\) −1890.32 688.021i −0.0416655 0.0151650i
\(214\) 0 0
\(215\) −2846.43 + 2388.44i −0.0615777 + 0.0516698i
\(216\) 0 0
\(217\) 3018.03 + 1742.46i 0.0640921 + 0.0370036i
\(218\) 0 0
\(219\) 3669.63 647.056i 0.0765129 0.0134913i
\(220\) 0 0
\(221\) 86777.3 50100.9i 1.77673 1.02580i
\(222\) 0 0
\(223\) 16111.5 + 44266.0i 0.323986 + 0.890145i 0.989600 + 0.143848i \(0.0459478\pi\)
−0.665613 + 0.746297i \(0.731830\pi\)
\(224\) 0 0
\(225\) −33144.4 27811.5i −0.654705 0.549362i
\(226\) 0 0
\(227\) 11619.6i 0.225497i 0.993624 + 0.112748i \(0.0359654\pi\)
−0.993624 + 0.112748i \(0.964035\pi\)
\(228\) 0 0
\(229\) 38184.6 0.728145 0.364072 0.931371i \(-0.381386\pi\)
0.364072 + 0.931371i \(0.381386\pi\)
\(230\) 0 0
\(231\) −740.884 + 882.951i −0.0138844 + 0.0165467i
\(232\) 0 0
\(233\) −62685.9 + 22815.8i −1.15467 + 0.420266i −0.847191 0.531289i \(-0.821708\pi\)
−0.307480 + 0.951554i \(0.599486\pi\)
\(234\) 0 0
\(235\) −5068.93 8779.65i −0.0917870 0.158980i
\(236\) 0 0
\(237\) −1573.29 8922.56i −0.0280099 0.158852i
\(238\) 0 0
\(239\) 25095.4 43466.4i 0.439337 0.760954i −0.558302 0.829638i \(-0.688547\pi\)
0.997638 + 0.0686844i \(0.0218801\pi\)
\(240\) 0 0
\(241\) −45715.6 54481.7i −0.787100 0.938030i 0.212131 0.977241i \(-0.431960\pi\)
−0.999231 + 0.0392116i \(0.987515\pi\)
\(242\) 0 0
\(243\) 5227.02 14361.1i 0.0885201 0.243207i
\(244\) 0 0
\(245\) −3785.97 + 21471.3i −0.0630732 + 0.357706i
\(246\) 0 0
\(247\) 31608.2 79594.4i 0.518090 1.30463i
\(248\) 0 0
\(249\) −7964.71 1404.39i −0.128461 0.0226511i
\(250\) 0 0
\(251\) 32866.8 + 11962.5i 0.521687 + 0.189878i 0.589423 0.807825i \(-0.299355\pi\)
−0.0677358 + 0.997703i \(0.521578\pi\)
\(252\) 0 0
\(253\) 103403. 86765.0i 1.61544 1.35551i
\(254\) 0 0
\(255\) 2672.36 + 1542.89i 0.0410974 + 0.0237276i
\(256\) 0 0
\(257\) 89242.7 15735.9i 1.35116 0.238246i 0.549233 0.835669i \(-0.314920\pi\)
0.801926 + 0.597423i \(0.203809\pi\)
\(258\) 0 0
\(259\) −6201.73 + 3580.57i −0.0924514 + 0.0533769i
\(260\) 0 0
\(261\) 43446.5 + 119368.i 0.637784 + 1.75230i
\(262\) 0 0
\(263\) −15528.7 13030.1i −0.224504 0.188381i 0.523597 0.851966i \(-0.324590\pi\)
−0.748101 + 0.663585i \(0.769034\pi\)
\(264\) 0 0
\(265\) 8002.20i 0.113951i
\(266\) 0 0
\(267\) −1711.06 −0.0240018
\(268\) 0 0
\(269\) −13981.4 + 16662.4i −0.193218 + 0.230268i −0.853952 0.520352i \(-0.825801\pi\)
0.660734 + 0.750620i \(0.270245\pi\)
\(270\) 0 0
\(271\) −104267. + 37950.1i −1.41974 + 0.516743i −0.933972 0.357346i \(-0.883682\pi\)
−0.485766 + 0.874089i \(0.661459\pi\)
\(272\) 0 0
\(273\) −721.755 1250.12i −0.00968421 0.0167735i
\(274\) 0 0
\(275\) −17704.7 100409.i −0.234112 1.32772i
\(276\) 0 0
\(277\) 56652.4 98124.8i 0.738344 1.27885i −0.214897 0.976637i \(-0.568942\pi\)
0.953241 0.302212i \(-0.0977250\pi\)
\(278\) 0 0
\(279\) −23212.0 27663.0i −0.298197 0.355378i
\(280\) 0 0
\(281\) −12444.0 + 34189.7i −0.157597 + 0.432995i −0.993212 0.116321i \(-0.962890\pi\)
0.835614 + 0.549317i \(0.185112\pi\)
\(282\) 0 0
\(283\) −20132.3 + 114176.i −0.251374 + 1.42562i 0.553836 + 0.832626i \(0.313164\pi\)
−0.805210 + 0.592990i \(0.797948\pi\)
\(284\) 0 0
\(285\) 2609.46 382.596i 0.0321263 0.00471033i
\(286\) 0 0
\(287\) −18926.6 3337.26i −0.229778 0.0405160i
\(288\) 0 0
\(289\) −89160.5 32451.8i −1.06752 0.388546i
\(290\) 0 0
\(291\) −3915.60 + 3285.58i −0.0462394 + 0.0387995i
\(292\) 0 0
\(293\) 1781.50 + 1028.55i 0.0207515 + 0.0119809i 0.510340 0.859973i \(-0.329520\pi\)
−0.489588 + 0.871954i \(0.662853\pi\)
\(294\) 0 0
\(295\) 21493.4 3789.86i 0.246979 0.0435491i
\(296\) 0 0
\(297\) 20766.0 11989.3i 0.235418 0.135919i
\(298\) 0 0
\(299\) 57818.4 + 158855.i 0.646731 + 1.77688i
\(300\) 0 0
\(301\) −2370.74 1989.29i −0.0261668 0.0219566i
\(302\) 0 0
\(303\) 846.137i 0.00921627i
\(304\) 0 0
\(305\) −51306.6 −0.551535
\(306\) 0 0
\(307\) 72507.7 86411.3i 0.769321 0.916841i −0.229078 0.973408i \(-0.573571\pi\)
0.998399 + 0.0565673i \(0.0180156\pi\)
\(308\) 0 0
\(309\) 2713.89 987.776i 0.0284234 0.0103453i
\(310\) 0 0
\(311\) −8320.72 14411.9i −0.0860281 0.149005i 0.819801 0.572649i \(-0.194084\pi\)
−0.905829 + 0.423644i \(0.860751\pi\)
\(312\) 0 0
\(313\) 27818.3 + 157766.i 0.283950 + 1.61036i 0.709011 + 0.705198i \(0.249142\pi\)
−0.425060 + 0.905165i \(0.639747\pi\)
\(314\) 0 0
\(315\) −2904.06 + 5029.97i −0.0292674 + 0.0506926i
\(316\) 0 0
\(317\) −101170. 120569.i −1.00677 1.19982i −0.979757 0.200189i \(-0.935844\pi\)
−0.0270146 0.999635i \(-0.508600\pi\)
\(318\) 0 0
\(319\) −102381. + 281288.i −1.00609 + 2.76421i
\(320\) 0 0
\(321\) −2134.50 + 12105.4i −0.0207151 + 0.117481i
\(322\) 0 0
\(323\) −144733. + 47981.3i −1.38727 + 0.459903i
\(324\) 0 0
\(325\) 125750. + 22173.1i 1.19053 + 0.209923i
\(326\) 0 0
\(327\) −9371.39 3410.91i −0.0876413 0.0318988i
\(328\) 0 0
\(329\) 6468.21 5427.48i 0.0597575 0.0501425i
\(330\) 0 0
\(331\) −95092.2 54901.5i −0.867939 0.501105i −0.00127600 0.999999i \(-0.500406\pi\)
−0.866663 + 0.498895i \(0.833739\pi\)
\(332\) 0 0
\(333\) 73077.7 12885.6i 0.659017 0.116202i
\(334\) 0 0
\(335\) 53048.7 30627.7i 0.472699 0.272913i
\(336\) 0 0
\(337\) −12804.4 35179.9i −0.112746 0.309767i 0.870468 0.492226i \(-0.163817\pi\)
−0.983213 + 0.182459i \(0.941594\pi\)
\(338\) 0 0
\(339\) −5444.95 4568.85i −0.0473799 0.0397565i
\(340\) 0 0
\(341\) 85095.7i 0.731811i
\(342\) 0 0
\(343\) −36784.7 −0.312665
\(344\) 0 0
\(345\) −3346.34 + 3988.02i −0.0281146 + 0.0335057i
\(346\) 0 0
\(347\) −169961. + 61860.6i −1.41153 + 0.513754i −0.931578 0.363542i \(-0.881567\pi\)
−0.479950 + 0.877296i \(0.659345\pi\)
\(348\) 0 0
\(349\) 66787.2 + 115679.i 0.548330 + 0.949736i 0.998389 + 0.0567371i \(0.0180697\pi\)
−0.450059 + 0.892999i \(0.648597\pi\)
\(350\) 0 0
\(351\) 5214.70 + 29574.1i 0.0423268 + 0.240047i
\(352\) 0 0
\(353\) 19867.3 34411.1i 0.159437 0.276153i −0.775229 0.631680i \(-0.782366\pi\)
0.934666 + 0.355528i \(0.115699\pi\)
\(354\) 0 0
\(355\) −15354.4 18298.7i −0.121836 0.145199i
\(356\) 0 0
\(357\) −879.022 + 2415.09i −0.00689705 + 0.0189495i
\(358\) 0 0
\(359\) −12869.3 + 72985.6i −0.0998543 + 0.566302i 0.893297 + 0.449467i \(0.148386\pi\)
−0.993151 + 0.116835i \(0.962725\pi\)
\(360\) 0 0
\(361\) −71582.6 + 108901.i −0.549279 + 0.835639i
\(362\) 0 0
\(363\) 16407.6 + 2893.09i 0.124518 + 0.0219558i
\(364\) 0 0
\(365\) 41578.9 + 15133.5i 0.312095 + 0.113593i
\(366\) 0 0
\(367\) 46243.9 38803.3i 0.343339 0.288095i −0.454770 0.890609i \(-0.650279\pi\)
0.798109 + 0.602514i \(0.205834\pi\)
\(368\) 0 0
\(369\) 172465. + 99573.0i 1.26663 + 0.731289i
\(370\) 0 0
\(371\) 6563.64 1157.35i 0.0476867 0.00840845i
\(372\) 0 0
\(373\) 122597. 70781.6i 0.881178 0.508748i 0.0101310 0.999949i \(-0.496775\pi\)
0.871046 + 0.491201i \(0.163442\pi\)
\(374\) 0 0
\(375\) 2906.61 + 7985.84i 0.0206692 + 0.0567882i
\(376\) 0 0
\(377\) −287182. 240974.i −2.02057 1.69546i
\(378\) 0 0
\(379\) 121623.i 0.846715i −0.905963 0.423358i \(-0.860851\pi\)
0.905963 0.423358i \(-0.139149\pi\)
\(380\) 0 0
\(381\) 18234.0 0.125613
\(382\) 0 0
\(383\) −51324.3 + 61165.9i −0.349885 + 0.416977i −0.912070 0.410035i \(-0.865517\pi\)
0.562185 + 0.827012i \(0.309961\pi\)
\(384\) 0 0
\(385\) −12861.3 + 4681.12i −0.0867685 + 0.0315812i
\(386\) 0 0
\(387\) 16034.3 + 27772.3i 0.107061 + 0.185434i
\(388\) 0 0
\(389\) 5919.35 + 33570.3i 0.0391178 + 0.221848i 0.998100 0.0616190i \(-0.0196264\pi\)
−0.958982 + 0.283467i \(0.908515\pi\)
\(390\) 0 0
\(391\) 150492. 260659.i 0.984372 1.70498i
\(392\) 0 0
\(393\) −8538.76 10176.1i −0.0552853 0.0658865i
\(394\) 0 0
\(395\) 36796.4 101097.i 0.235836 0.647955i
\(396\) 0 0
\(397\) 16108.0 91352.8i 0.102202 0.579617i −0.890099 0.455767i \(-0.849365\pi\)
0.992301 0.123849i \(-0.0395240\pi\)
\(398\) 0 0
\(399\) 691.219 + 2085.02i 0.00434180 + 0.0130968i
\(400\) 0 0
\(401\) 20240.3 + 3568.92i 0.125872 + 0.0221946i 0.236229 0.971697i \(-0.424088\pi\)
−0.110357 + 0.993892i \(0.535199\pi\)
\(402\) 0 0
\(403\) 100145. + 36449.9i 0.616624 + 0.224433i
\(404\) 0 0
\(405\) 45748.6 38387.6i 0.278912 0.234035i
\(406\) 0 0
\(407\) 151435. + 87431.2i 0.914194 + 0.527810i
\(408\) 0 0
\(409\) 192872. 34008.5i 1.15298 0.203302i 0.435704 0.900090i \(-0.356499\pi\)
0.717277 + 0.696788i \(0.245388\pi\)
\(410\) 0 0
\(411\) −6722.54 + 3881.26i −0.0397970 + 0.0229768i
\(412\) 0 0
\(413\) 6217.11 + 17081.4i 0.0364493 + 0.100144i
\(414\) 0 0
\(415\) −73567.8 61730.7i −0.427161 0.358431i
\(416\) 0 0
\(417\) 15893.0i 0.0913977i
\(418\) 0 0
\(419\) 71668.6 0.408226 0.204113 0.978947i \(-0.434569\pi\)
0.204113 + 0.978947i \(0.434569\pi\)
\(420\) 0 0
\(421\) −78684.7 + 93772.7i −0.443942 + 0.529069i −0.940891 0.338711i \(-0.890009\pi\)
0.496949 + 0.867780i \(0.334454\pi\)
\(422\) 0 0
\(423\) −82218.1 + 29924.9i −0.459501 + 0.167245i
\(424\) 0 0
\(425\) −113672. 196886.i −0.629328 1.09003i
\(426\) 0 0
\(427\) −7420.39 42083.1i −0.0406978 0.230809i
\(428\) 0 0
\(429\) −17624.0 + 30525.6i −0.0957611 + 0.165863i
\(430\) 0 0
\(431\) −63488.9 75663.1i −0.341777 0.407314i 0.567588 0.823313i \(-0.307877\pi\)
−0.909365 + 0.415998i \(0.863432\pi\)
\(432\) 0 0
\(433\) −6334.35 + 17403.5i −0.0337852 + 0.0928240i −0.955438 0.295191i \(-0.904617\pi\)
0.921653 + 0.388015i \(0.126839\pi\)
\(434\) 0 0
\(435\) 2004.76 11369.6i 0.0105946 0.0600848i
\(436\) 0 0
\(437\) −37318.1 254524.i −0.195414 1.33280i
\(438\) 0 0
\(439\) 47901.5 + 8446.33i 0.248554 + 0.0438267i 0.296537 0.955021i \(-0.404168\pi\)
−0.0479832 + 0.998848i \(0.515279\pi\)
\(440\) 0 0
\(441\) 176819. + 64356.7i 0.909181 + 0.330915i
\(442\) 0 0
\(443\) 133793. 112265.i 0.681749 0.572055i −0.234768 0.972051i \(-0.575433\pi\)
0.916517 + 0.399996i \(0.130989\pi\)
\(444\) 0 0
\(445\) −17595.9 10159.0i −0.0888570 0.0513016i
\(446\) 0 0
\(447\) −2785.26 + 491.116i −0.0139396 + 0.00245793i
\(448\) 0 0
\(449\) −180265. + 104076.i −0.894165 + 0.516247i −0.875303 0.483576i \(-0.839338\pi\)
−0.0188626 + 0.999822i \(0.506005\pi\)
\(450\) 0 0
\(451\) 160504. + 440981.i 0.789102 + 2.16804i
\(452\) 0 0
\(453\) 10260.7 + 8609.78i 0.0500014 + 0.0419562i
\(454\) 0 0
\(455\) 17141.0i 0.0827965i
\(456\) 0 0
\(457\) 78903.9 0.377804 0.188902 0.981996i \(-0.439507\pi\)
0.188902 + 0.981996i \(0.439507\pi\)
\(458\) 0 0
\(459\) 34368.1 40958.3i 0.163129 0.194409i
\(460\) 0 0
\(461\) −74686.5 + 27183.7i −0.351431 + 0.127910i −0.511703 0.859162i \(-0.670985\pi\)
0.160272 + 0.987073i \(0.448763\pi\)
\(462\) 0 0
\(463\) −70223.0 121630.i −0.327580 0.567385i 0.654451 0.756104i \(-0.272900\pi\)
−0.982031 + 0.188719i \(0.939566\pi\)
\(464\) 0 0
\(465\) 569.906 + 3232.10i 0.00263571 + 0.0149479i
\(466\) 0 0
\(467\) −18527.0 + 32089.7i −0.0849514 + 0.147140i −0.905371 0.424622i \(-0.860407\pi\)
0.820419 + 0.571763i \(0.193740\pi\)
\(468\) 0 0
\(469\) 32794.0 + 39082.4i 0.149090 + 0.177679i
\(470\) 0 0
\(471\) 6746.53 18535.9i 0.0304116 0.0835551i
\(472\) 0 0
\(473\) −13122.4 + 74421.0i −0.0586532 + 0.332639i
\(474\) 0 0
\(475\) −180589. 71714.8i −0.800395 0.317849i
\(476\) 0 0
\(477\) −68013.6 11992.6i −0.298923 0.0527082i
\(478\) 0 0
\(479\) −329391. 119889.i −1.43563 0.522525i −0.497087 0.867701i \(-0.665597\pi\)
−0.938538 + 0.345176i \(0.887819\pi\)
\(480\) 0 0
\(481\) −167760. + 140767.i −0.725099 + 0.608430i
\(482\) 0 0
\(483\) −3755.07 2167.99i −0.0160962 0.00929314i
\(484\) 0 0
\(485\) −59773.8 + 10539.7i −0.254113 + 0.0448071i
\(486\) 0 0
\(487\) 262839. 151750.i 1.10823 0.639839i 0.169862 0.985468i \(-0.445668\pi\)
0.938371 + 0.345629i \(0.112334\pi\)
\(488\) 0 0
\(489\) 6352.95 + 17454.6i 0.0265679 + 0.0729948i
\(490\) 0 0
\(491\) −37420.5 31399.5i −0.155220 0.130245i 0.561870 0.827225i \(-0.310082\pi\)
−0.717090 + 0.696980i \(0.754526\pi\)
\(492\) 0 0
\(493\) 667470.i 2.74623i
\(494\) 0 0
\(495\) 141824. 0.578814
\(496\) 0 0
\(497\) 12788.4 15240.6i 0.0517731 0.0617007i
\(498\) 0 0
\(499\) −32724.7 + 11910.8i −0.131424 + 0.0478345i −0.406895 0.913475i \(-0.633388\pi\)
0.275471 + 0.961309i \(0.411166\pi\)
\(500\) 0 0
\(501\) −15190.1 26310.0i −0.0605180 0.104820i
\(502\) 0 0
\(503\) 46195.2 + 261986.i 0.182583 + 1.03548i 0.929021 + 0.370026i \(0.120651\pi\)
−0.746438 + 0.665455i \(0.768238\pi\)
\(504\) 0 0
\(505\) −5023.73 + 8701.35i −0.0196990 + 0.0341196i
\(506\) 0 0
\(507\) −13975.1 16654.8i −0.0543673 0.0647925i
\(508\) 0 0
\(509\) −127751. + 350992.i −0.493091 + 1.35476i 0.404746 + 0.914429i \(0.367360\pi\)
−0.897837 + 0.440327i \(0.854862\pi\)
\(510\) 0 0
\(511\) −6399.42 + 36292.9i −0.0245075 + 0.138989i
\(512\) 0 0
\(513\) 1322.82 45678.4i 0.00502652 0.173571i
\(514\) 0 0
\(515\) 33773.3 + 5955.15i 0.127338 + 0.0224532i
\(516\) 0 0
\(517\) −193745. 70517.4i −0.724852 0.263824i
\(518\) 0 0
\(519\) −2614.68 + 2193.98i −0.00970699 + 0.00814513i
\(520\) 0 0
\(521\) −164152. 94773.2i −0.604743 0.349149i 0.166162 0.986098i \(-0.446862\pi\)
−0.770905 + 0.636950i \(0.780196\pi\)
\(522\) 0 0
\(523\) 83466.4 14717.4i 0.305147 0.0538056i −0.0189782 0.999820i \(-0.506041\pi\)
0.324125 + 0.946014i \(0.394930\pi\)
\(524\) 0 0
\(525\) −2836.35 + 1637.57i −0.0102906 + 0.00594128i
\(526\) 0 0
\(527\) −64897.0 178303.i −0.233670 0.642004i
\(528\) 0 0
\(529\) 174617. + 146521.i 0.623985 + 0.523586i
\(530\) 0 0
\(531\) 188360.i 0.668035i
\(532\) 0 0
\(533\) −587721. −2.06879
\(534\) 0 0
\(535\) −93823.0 + 111814.i −0.327795 + 0.390650i
\(536\) 0 0
\(537\) −31759.4 + 11559.5i −0.110135 + 0.0400857i
\(538\) 0 0
\(539\) 221705. + 384004.i 0.763128 + 1.32178i
\(540\) 0 0
\(541\) −82338.9 466967.i −0.281326 1.59548i −0.718120 0.695919i \(-0.754997\pi\)
0.436794 0.899562i \(-0.356114\pi\)
\(542\) 0 0
\(543\) 4127.29 7148.68i 0.0139980 0.0242452i
\(544\) 0 0
\(545\) −76120.4 90716.8i −0.256276 0.305418i
\(546\) 0 0
\(547\) 67687.8 185971.i 0.226223 0.621541i −0.773705 0.633546i \(-0.781599\pi\)
0.999928 + 0.0120041i \(0.00382113\pi\)
\(548\) 0 0
\(549\) −76891.4 + 436073.i −0.255113 + 1.44682i
\(550\) 0 0
\(551\) 353890. + 447441.i 1.16564 + 1.47378i
\(552\) 0 0
\(553\) 88244.7 + 15559.9i 0.288561 + 0.0508812i
\(554\) 0 0
\(555\) −6337.36 2306.61i −0.0205742 0.00748838i
\(556\) 0 0
\(557\) 414735. 348004.i 1.33678 1.12169i 0.354341 0.935116i \(-0.384705\pi\)
0.982440 0.186576i \(-0.0597391\pi\)
\(558\) 0 0
\(559\) −81961.8 47320.7i −0.262294 0.151435i
\(560\) 0 0
\(561\) 61803.5 10897.6i 0.196376 0.0346263i
\(562\) 0 0
\(563\) 69780.4 40287.7i 0.220149 0.127103i −0.385870 0.922553i \(-0.626099\pi\)
0.606019 + 0.795450i \(0.292765\pi\)
\(564\) 0 0
\(565\) −28867.3 79312.4i −0.0904295 0.248453i
\(566\) 0 0
\(567\) 38103.2 + 31972.4i 0.118521 + 0.0994510i
\(568\) 0 0
\(569\) 219752.i 0.678749i −0.940651 0.339374i \(-0.889785\pi\)
0.940651 0.339374i \(-0.110215\pi\)
\(570\) 0 0
\(571\) −71941.6 −0.220652 −0.110326 0.993895i \(-0.535190\pi\)
−0.110326 + 0.993895i \(0.535190\pi\)
\(572\) 0 0
\(573\) −5141.70 + 6127.64i −0.0156602 + 0.0186631i
\(574\) 0 0
\(575\) 360420. 131182.i 1.09012 0.396771i
\(576\) 0 0
\(577\) 48217.9 + 83515.8i 0.144829 + 0.250852i 0.929309 0.369303i \(-0.120403\pi\)
−0.784480 + 0.620154i \(0.787070\pi\)
\(578\) 0 0
\(579\) −6861.76 38914.9i −0.0204681 0.116081i
\(580\) 0 0
\(581\) 39993.3 69270.5i 0.118477 0.205209i
\(582\) 0 0
\(583\) −104610. 124670.i −0.307778 0.366796i
\(584\) 0 0
\(585\) −60748.8 + 166906.i −0.177511 + 0.487708i
\(586\) 0 0
\(587\) 67100.9 380548.i 0.194739 1.10442i −0.718052 0.695990i \(-0.754966\pi\)
0.912790 0.408428i \(-0.133923\pi\)
\(588\) 0 0
\(589\) −138040. 85118.0i −0.397900 0.245353i
\(590\) 0 0
\(591\) −17362.6 3061.49i −0.0497094 0.00876511i
\(592\) 0 0
\(593\) 109933. + 40012.2i 0.312620 + 0.113784i 0.493565 0.869709i \(-0.335693\pi\)
−0.180945 + 0.983493i \(0.557916\pi\)
\(594\) 0 0
\(595\) −23378.5 + 19616.9i −0.0660364 + 0.0554111i
\(596\) 0 0
\(597\) −31367.1 18109.8i −0.0880089 0.0508119i
\(598\) 0 0
\(599\) −127777. + 22530.6i −0.356123 + 0.0627940i −0.348847 0.937180i \(-0.613427\pi\)
−0.00727514 + 0.999974i \(0.502316\pi\)
\(600\) 0 0
\(601\) 30321.7 17506.3i 0.0839470 0.0484668i −0.457439 0.889241i \(-0.651233\pi\)
0.541386 + 0.840774i \(0.317900\pi\)
\(602\) 0 0
\(603\) −180813. 496780.i −0.497274 1.36625i
\(604\) 0 0
\(605\) 151552. + 127167.i 0.414048 + 0.347428i
\(606\) 0 0
\(607\) 469725.i 1.27487i −0.770504 0.637435i \(-0.779995\pi\)
0.770504 0.637435i \(-0.220005\pi\)
\(608\) 0 0
\(609\) 9615.58 0.0259263
\(610\) 0 0
\(611\) 165977. 197804.i 0.444597 0.529850i
\(612\) 0 0
\(613\) 224865. 81844.2i 0.598413 0.217805i −0.0250126 0.999687i \(-0.507963\pi\)
0.623426 + 0.781883i \(0.285740\pi\)
\(614\) 0 0
\(615\) −9049.62 15674.4i −0.0239265 0.0414420i
\(616\) 0 0
\(617\) 49410.0 + 280218.i 0.129791 + 0.736081i 0.978346 + 0.206974i \(0.0663617\pi\)
−0.848555 + 0.529107i \(0.822527\pi\)
\(618\) 0 0
\(619\) −176197. + 305181.i −0.459850 + 0.796484i −0.998953 0.0457565i \(-0.985430\pi\)
0.539103 + 0.842240i \(0.318763\pi\)
\(620\) 0 0
\(621\) 57982.1 + 69100.4i 0.150353 + 0.179183i
\(622\) 0 0
\(623\) 5787.84 15902.0i 0.0149122 0.0409708i
\(624\) 0 0
\(625\) 40892.7 231914.i 0.104685 0.593699i
\(626\) 0 0
\(627\) 35652.4 40073.3i 0.0906887 0.101934i
\(628\) 0 0
\(629\) 383984. + 67706.8i 0.970537 + 0.171132i
\(630\) 0 0
\(631\) 402796. + 146606.i 1.01164 + 0.368207i 0.794062 0.607836i \(-0.207962\pi\)
0.217578 + 0.976043i \(0.430184\pi\)
\(632\) 0 0
\(633\) −29185.9 + 24489.8i −0.0728392 + 0.0611193i
\(634\) 0 0
\(635\) 187512. + 108260.i 0.465030 + 0.268485i
\(636\) 0 0
\(637\) −546881. + 96429.9i −1.34777 + 0.237647i
\(638\) 0 0
\(639\) −178538. + 103079.i −0.437249 + 0.252446i
\(640\) 0 0
\(641\) 11509.8 + 31622.9i 0.0280125 + 0.0769637i 0.952911 0.303251i \(-0.0980722\pi\)
−0.924898 + 0.380215i \(0.875850\pi\)
\(642\) 0 0
\(643\) −15196.8 12751.6i −0.0367562 0.0308421i 0.624225 0.781245i \(-0.285415\pi\)
−0.660981 + 0.750403i \(0.729859\pi\)
\(644\) 0 0
\(645\) 2914.54i 0.00700568i
\(646\) 0 0
\(647\) 609119. 1.45510 0.727551 0.686053i \(-0.240658\pi\)
0.727551 + 0.686053i \(0.240658\pi\)
\(648\) 0 0
\(649\) 285311. 340020.i 0.677375 0.807264i
\(650\) 0 0
\(651\) −2568.64 + 934.908i −0.00606095 + 0.00220601i
\(652\) 0 0
\(653\) −318930. 552403.i −0.747944 1.29548i −0.948807 0.315858i \(-0.897708\pi\)
0.200863 0.979619i \(-0.435626\pi\)
\(654\) 0 0
\(655\) −27391.3 155344.i −0.0638455 0.362086i
\(656\) 0 0
\(657\) 190938. 330714.i 0.442345 0.766163i
\(658\) 0 0
\(659\) 201555. + 240204.i 0.464111 + 0.553106i 0.946438 0.322885i \(-0.104653\pi\)
−0.482327 + 0.875991i \(0.660208\pi\)
\(660\) 0 0
\(661\) 160266. 440328.i 0.366808 1.00780i −0.609759 0.792587i \(-0.708734\pi\)
0.976568 0.215211i \(-0.0690440\pi\)
\(662\) 0 0
\(663\) −13648.0 + 77401.7i −0.0310486 + 0.176085i
\(664\) 0 0
\(665\) −5271.07 + 25545.5i −0.0119194 + 0.0577659i
\(666\) 0 0
\(667\) −1.10897e6 195542.i −2.49270 0.439530i
\(668\) 0 0
\(669\) −34721.1 12637.5i −0.0775786 0.0282363i
\(670\) 0 0
\(671\) −799327. + 670715.i −1.77533 + 1.48968i
\(672\) 0 0
\(673\) 418973. + 241894.i 0.925031 + 0.534067i 0.885237 0.465141i \(-0.153996\pi\)
0.0397942 + 0.999208i \(0.487330\pi\)
\(674\) 0 0
\(675\) 67099.6 11831.5i 0.147269 0.0259676i
\(676\) 0 0
\(677\) −439608. + 253808.i −0.959154 + 0.553768i −0.895913 0.444230i \(-0.853477\pi\)
−0.0632415 + 0.997998i \(0.520144\pi\)
\(678\) 0 0
\(679\) −17290.0 47503.9i −0.0375021 0.103036i
\(680\) 0 0
\(681\) −6981.83 5858.45i −0.0150548 0.0126325i
\(682\) 0 0
\(683\) 560367.i 1.20124i 0.799533 + 0.600622i \(0.205080\pi\)
−0.799533 + 0.600622i \(0.794920\pi\)
\(684\) 0 0
\(685\) −92176.1 −0.196443
\(686\) 0 0
\(687\) −19252.2 + 22943.8i −0.0407912 + 0.0486130i
\(688\) 0 0
\(689\) 191527. 69710.1i 0.403452 0.146844i
\(690\) 0 0
\(691\) 197689. + 342407.i 0.414024 + 0.717111i 0.995325 0.0965773i \(-0.0307895\pi\)
−0.581301 + 0.813689i \(0.697456\pi\)
\(692\) 0 0
\(693\) 20511.8 + 116328.i 0.0427107 + 0.242224i
\(694\) 0 0
\(695\) −94361.0 + 163438.i −0.195354 + 0.338364i
\(696\) 0 0
\(697\) 672616. + 801593.i 1.38453 + 1.65002i
\(698\) 0 0
\(699\) 17896.1 49169.3i 0.0366273 0.100633i
\(700\) 0 0
\(701\) 47480.8 269277.i 0.0966233 0.547978i −0.897615 0.440781i \(-0.854701\pi\)
0.994238 0.107197i \(-0.0341874\pi\)
\(702\) 0 0
\(703\) 293303. 158200.i 0.593480 0.320107i
\(704\) 0 0
\(705\) 7831.08 + 1380.83i 0.0157559 + 0.00277819i
\(706\) 0 0
\(707\) −7863.67 2862.14i −0.0157321 0.00572602i
\(708\) 0 0
\(709\) −223386. + 187443.i −0.444389 + 0.372886i −0.837349 0.546669i \(-0.815895\pi\)
0.392960 + 0.919556i \(0.371451\pi\)
\(710\) 0 0
\(711\) −804116. 464257.i −1.59067 0.918373i
\(712\) 0 0
\(713\) 315256. 55588.1i 0.620132 0.109346i
\(714\) 0 0
\(715\) −362476. + 209276.i −0.709034 + 0.409361i
\(716\) 0 0
\(717\) 13464.8 + 36994.1i 0.0261915 + 0.0719605i
\(718\) 0 0
\(719\) 59480.3 + 49909.9i 0.115058 + 0.0965448i 0.698501 0.715609i \(-0.253851\pi\)
−0.583444 + 0.812154i \(0.698295\pi\)
\(720\) 0 0
\(721\) 28563.1i 0.0549459i
\(722\) 0 0
\(723\) 55785.4 0.106719
\(724\) 0 0
\(725\) −546739. + 651578.i −1.04017 + 1.23962i
\(726\) 0 0
\(727\) −727130. + 264654.i −1.37576 + 0.500737i −0.920891 0.389821i \(-0.872537\pi\)
−0.454872 + 0.890557i \(0.650315\pi\)
\(728\) 0 0
\(729\) −253687. 439399.i −0.477357 0.826807i
\(730\) 0 0
\(731\) 29260.4 + 165944.i 0.0547577 + 0.310546i
\(732\) 0 0
\(733\) −521382. + 903059.i −0.970393 + 1.68077i −0.276025 + 0.961150i \(0.589017\pi\)
−0.694368 + 0.719620i \(0.744316\pi\)
\(734\) 0 0
\(735\) −10992.5 13100.4i −0.0203481 0.0242499i
\(736\) 0 0
\(737\) 426082. 1.17065e6i 0.784437 2.15522i
\(738\) 0 0
\(739\) 56940.7 322926.i 0.104264 0.591309i −0.887248 0.461293i \(-0.847386\pi\)
0.991512 0.130017i \(-0.0415031\pi\)
\(740\) 0 0
\(741\) 31889.1 + 59122.7i 0.0580773 + 0.107676i
\(742\) 0 0
\(743\) 336541. + 59341.2i 0.609621 + 0.107493i 0.469932 0.882703i \(-0.344278\pi\)
0.139689 + 0.990195i \(0.455390\pi\)
\(744\) 0 0
\(745\) −31558.4 11486.3i −0.0568594 0.0206951i
\(746\) 0 0
\(747\) −634925. + 532766.i −1.13784 + 0.954762i
\(748\) 0 0
\(749\) −105283. 60784.9i −0.187669 0.108351i
\(750\) 0 0
\(751\) −577391. + 101810.i −1.02374 + 0.180513i −0.660220 0.751073i \(-0.729537\pi\)
−0.363522 + 0.931586i \(0.618426\pi\)
\(752\) 0 0
\(753\) −23758.9 + 13717.2i −0.0419021 + 0.0241922i
\(754\) 0 0
\(755\) 54399.1 + 149460.i 0.0954328 + 0.262200i
\(756\) 0 0
\(757\) 342910. + 287735.i 0.598395 + 0.502113i 0.890929 0.454142i \(-0.150054\pi\)
−0.292534 + 0.956255i \(0.594499\pi\)
\(758\) 0 0
\(759\) 105877.i 0.183788i
\(760\) 0 0
\(761\) 741840. 1.28098 0.640488 0.767968i \(-0.278732\pi\)
0.640488 + 0.767968i \(0.278732\pi\)
\(762\) 0 0
\(763\) 63399.4 75556.4i 0.108902 0.129784i
\(764\) 0 0
\(765\) 297167. 108160.i 0.507782 0.184818i
\(766\) 0 0
\(767\) 277944. + 481414.i 0.472462 + 0.818329i
\(768\) 0 0
\(769\) −75631.6 428928.i −0.127894 0.725323i −0.979547 0.201217i \(-0.935510\pi\)
0.851653 0.524107i \(-0.175601\pi\)
\(770\) 0 0
\(771\) −35539.8 + 61556.7i −0.0597869 + 0.103554i
\(772\) 0 0
\(773\) 260878. + 310902.i 0.436595 + 0.520313i 0.938813 0.344428i \(-0.111927\pi\)
−0.502218 + 0.864741i \(0.667483\pi\)
\(774\) 0 0
\(775\) 82700.0 227216.i 0.137690 0.378300i
\(776\) 0 0
\(777\) 975.385 5531.69i 0.00161560 0.00916253i
\(778\) 0 0
\(779\) 875893. + 180732.i 1.44337 + 0.297824i
\(780\) 0 0
\(781\) −478426. 84359.4i −0.784355 0.138303i
\(782\) 0 0
\(783\) −187976. 68417.5i −0.306604 0.111595i
\(784\) 0 0
\(785\) 179431. 150561.i 0.291178 0.244327i
\(786\) 0 0
\(787\) 334739. + 193261.i 0.540451 + 0.312030i 0.745262 0.666772i \(-0.232325\pi\)
−0.204811 + 0.978802i \(0.565658\pi\)
\(788\) 0 0
\(789\) 15658.7 2761.06i 0.0251537 0.00443528i
\(790\) 0 0
\(791\) 60879.3 35148.7i 0.0973008 0.0561767i
\(792\) 0