Properties

Label 76.5.j.a.29.3
Level $76$
Weight $5$
Character 76.29
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 29.3
Character \(\chi\) \(=\) 76.29
Dual form 76.5.j.a.21.3

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

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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 0.737306 0.675558i \(-0.236097\pi\)
−0.793327 + 0.608796i \(0.791653\pi\)
\(4\) 0 0
\(5\) −8.75235 3.18559i −0.350094 0.127424i 0.160987 0.986957i \(-0.448532\pi\)
−0.511081 + 0.859533i \(0.670755\pi\)
\(6\) 0 0
\(7\) −3.87876 + 6.71820i −0.0791583 + 0.137106i −0.902887 0.429878i \(-0.858557\pi\)
0.823729 + 0.566984i \(0.191890\pi\)
\(8\) 0 0
\(9\) 13.9587 79.1635i 0.172329 0.977328i
\(10\) 0 0
\(11\) −94.7123 164.047i −0.782746 1.35576i −0.930336 0.366708i \(-0.880485\pi\)
0.147590 0.989049i \(-0.452849\pi\)
\(12\) 0 0
\(13\) −152.490 + 181.730i −0.902307 + 1.07533i 0.0945038 + 0.995524i \(0.469874\pi\)
−0.996811 + 0.0798029i \(0.974571\pi\)
\(14\) 0 0
\(15\) 2.49870 + 6.86512i 0.0111053 + 0.0305117i
\(16\) 0 0
\(17\) −73.3453 415.962i −0.253790 1.43931i −0.799160 0.601118i \(-0.794722\pi\)
0.545370 0.838195i \(-0.316389\pi\)
\(18\) 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 −0.885717 0.464226i \(-0.846333\pi\)
−0.380100 + 0.924945i \(0.624110\pi\)
\(24\) 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 0.984717 0.174160i \(-0.0557211\pi\)
0.865765 + 0.500450i \(0.166832\pi\)
\(30\) 0 0
\(31\) −389.047 224.616i −0.404835 0.233732i 0.283733 0.958903i \(-0.408427\pi\)
−0.688568 + 0.725172i \(0.741760\pi\)
\(32\) 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 \(0.109464\pi\)
−0.941450 + 0.337153i \(0.890536\pi\)
\(38\) 0 0
\(39\) 186.079 0.122340
\(40\) 0 0
\(41\) 1592.45 + 1897.81i 0.947322 + 1.12897i 0.991520 + 0.129952i \(0.0414822\pi\)
−0.0441984 + 0.999023i \(0.514073\pi\)
\(42\) 0 0
\(43\) 374.881 + 136.446i 0.202748 + 0.0737942i 0.441398 0.897311i \(-0.354483\pi\)
−0.238650 + 0.971106i \(0.576705\pi\)
\(44\) 0 0
\(45\) −374.354 + 648.400i −0.184866 + 0.320198i
\(46\) 0 0
\(47\) 189.007 1071.91i 0.0855623 0.485248i −0.911672 0.410920i \(-0.865208\pi\)
0.997234 0.0743281i \(-0.0236812\pi\)
\(48\) 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 0.876335 0.481703i \(-0.159982\pi\)
−0.980944 + 0.194291i \(0.937759\pi\)
\(54\) 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 −0.494978 0.868906i \(-0.664824\pi\)
−0.167944 + 0.985797i \(0.553713\pi\)
\(60\) 0 0
\(61\) 5176.31 1884.02i 1.39111 0.506321i 0.465580 0.885006i \(-0.345846\pi\)
0.925526 + 0.378684i \(0.123623\pi\)
\(62\) 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 −0.603193 0.797596i \(-0.706105\pi\)
−0.839609 + 0.543191i \(0.817216\pi\)
\(68\) 0 0
\(69\) 484.055 + 279.469i 0.101671 + 0.0586997i
\(70\) 0 0
\(71\) 877.159 2409.97i 0.174005 0.478075i −0.821779 0.569807i \(-0.807018\pi\)
0.995784 + 0.0917320i \(0.0292403\pi\)
\(72\) 0 0
\(73\) −3639.17 + 3053.62i −0.682898 + 0.573020i −0.916852 0.399228i \(-0.869278\pi\)
0.233953 + 0.972248i \(0.424834\pi\)
\(74\) 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 −0.885158 0.465291i \(-0.845950\pi\)
−0.304516 0.952507i \(-0.598495\pi\)
\(80\) 0 0
\(81\) −6025.19 2192.99i −0.918334 0.334246i
\(82\) 0 0
\(83\) 5155.43 8929.47i 0.748357 1.29619i −0.200253 0.979744i \(-0.564176\pi\)
0.948610 0.316448i \(-0.102490\pi\)
\(84\) 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 −0.670236 0.742148i \(-0.733807\pi\)
0.847259 + 0.531181i \(0.178251\pi\)
\(90\) 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 0.178131 0.984007i \(-0.442995\pi\)
0.503939 + 0.863739i \(0.331884\pi\)
\(98\) 0 0
\(99\) −14308.6 + 5207.89i −1.45991 + 0.531363i
\(100\) 0 0
\(101\) 826.363 + 693.401i 0.0810081 + 0.0679738i 0.682393 0.730986i \(-0.260940\pi\)
−0.601384 + 0.798960i \(0.705384\pi\)
\(102\) 0 0
\(103\) −3188.70 + 1841.00i −0.300566 + 0.173532i −0.642697 0.766120i \(-0.722185\pi\)
0.342131 + 0.939652i \(0.388851\pi\)
\(104\) 0 0
\(105\) −55.8131 9.84136i −0.00506242 0.000892641i
\(106\) 0 0
\(107\) 13571.7 + 7835.61i 1.18540 + 0.684393i 0.957258 0.289234i \(-0.0934007\pi\)
0.228145 + 0.973627i \(0.426734\pi\)
\(108\) 0 0
\(109\) 4348.57 11947.6i 0.366010 1.00561i −0.610853 0.791744i \(-0.709174\pi\)
0.976864 0.213862i \(-0.0686042\pi\)
\(110\) 0 0
\(111\) 554.673 465.426i 0.0450185 0.0377750i
\(112\) 0 0
\(113\) 9061.84i 0.709675i −0.934928 0.354837i \(-0.884536\pi\)
0.934928 0.354837i \(-0.115464\pi\)
\(114\) 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 0.0678790 + 0.997694i \(0.478377\pi\)
−0.994323 + 0.106400i \(0.966068\pi\)
\(128\) 0 0
\(129\) −107.024 294.047i −0.00643137 0.0176700i
\(130\) 0 0
\(131\) −2940.86 16678.4i −0.171369 0.971880i −0.942252 0.334904i \(-0.891296\pi\)
0.770884 0.636976i \(-0.219815\pi\)
\(132\) 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 −0.0821812 0.996617i \(-0.526189\pi\)
0.577659 + 0.816278i \(0.303966\pi\)
\(138\) 0 0
\(139\) 15521.6 + 13024.2i 0.803356 + 0.674096i 0.949012 0.315240i \(-0.102085\pi\)
−0.145656 + 0.989335i \(0.546529\pi\)
\(140\) 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 −0.578457 0.815713i \(-0.696345\pi\)
0.702872 + 0.711316i \(0.251901\pi\)
\(150\) 0 0
\(151\) 17076.6i 0.748940i 0.927239 + 0.374470i \(0.122175\pi\)
−0.927239 + 0.374470i \(0.877825\pi\)
\(152\) 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 −0.185188 0.982703i \(-0.559289\pi\)
−0.773532 + 0.633758i \(0.781512\pi\)
\(158\) 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 0.998097 0.0616580i \(-0.0196388\pi\)
−0.552446 + 0.833549i \(0.686305\pi\)
\(164\) 0 0
\(165\) 889.542 1060.11i 0.0326737 0.0389390i
\(166\) 0 0
\(167\) −13247.0 36395.9i −0.474991 1.30503i −0.913697 0.406397i \(-0.866785\pi\)
0.438706 0.898631i \(-0.355437\pi\)
\(168\) 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 −0.101596 0.994826i \(-0.532395\pi\)
0.244782 + 0.969578i \(0.421284\pi\)
\(174\) 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 0.212220 0.977222i \(-0.431931\pi\)
0.952409 + 0.304823i \(0.0985975\pi\)
\(180\) 0 0
\(181\) −10363.9 1827.44i −0.316349 0.0557808i 0.0132194 0.999913i \(-0.495792\pi\)
−0.329568 + 0.944132i \(0.606903\pi\)
\(182\) 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 −0.999010 0.0444917i \(-0.985833\pi\)
0.129660 0.991558i \(-0.458611\pi\)
\(194\) 0 0
\(195\) −1628.63 592.772i −0.0428304 0.0155890i
\(196\) 0 0
\(197\) 11238.5 19465.7i 0.289585 0.501576i −0.684126 0.729364i \(-0.739816\pi\)
0.973711 + 0.227788i \(0.0731493\pi\)
\(198\) 0 0
\(199\) 8018.46 45475.0i 0.202481 1.14833i −0.698873 0.715246i \(-0.746315\pi\)
0.901354 0.433083i \(-0.142574\pi\)
\(200\) 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 0.391684 0.920100i \(-0.371893\pi\)
0.682755 + 0.730647i \(0.260782\pi\)
\(212\) 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 −0.665613 0.746297i \(-0.731830\pi\)
0.989600 0.143848i \(-0.0459478\pi\)
\(224\) 0 0
\(225\) −33144.4 + 27811.5i −0.654705 + 0.549362i
\(226\) 0 0
\(227\) 11619.6i 0.225497i −0.993624 0.112748i \(-0.964035\pi\)
0.993624 0.112748i \(-0.0359654\pi\)
\(228\) 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 −0.307480 0.951554i \(-0.599486\pi\)
−0.847191 + 0.531289i \(0.821708\pi\)
\(234\) 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 0.997638 0.0686844i \(-0.0218801\pi\)
−0.558302 + 0.829638i \(0.688547\pi\)
\(240\) 0 0
\(241\) −45715.6 + 54481.7i −0.787100 + 0.938030i −0.999231 0.0392116i \(-0.987515\pi\)
0.212131 + 0.977241i \(0.431960\pi\)
\(242\) 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 −0.0677358 0.997703i \(-0.521578\pi\)
0.589423 + 0.807825i \(0.299355\pi\)
\(252\) 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 0.801926 0.597423i \(-0.203809\pi\)
0.549233 + 0.835669i \(0.314920\pi\)
\(258\) 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 −0.748101 0.663585i \(-0.769034\pi\)
0.523597 + 0.851966i \(0.324590\pi\)
\(264\) 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 0.660734 0.750620i \(-0.270245\pi\)
−0.853952 + 0.520352i \(0.825801\pi\)
\(270\) 0 0
\(271\) −104267. 37950.1i −1.41974 0.516743i −0.485766 0.874089i \(-0.661459\pi\)
−0.933972 + 0.357346i \(0.883682\pi\)
\(272\) 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 0.953241 + 0.302212i \(0.0977250\pi\)
−0.214897 + 0.976637i \(0.568942\pi\)
\(278\) 0 0
\(279\) −23212.0 + 27663.0i −0.298197 + 0.355378i
\(280\) 0 0
\(281\) −12444.0 34189.7i −0.157597 0.432995i 0.835614 0.549317i \(-0.185112\pi\)
−0.993212 + 0.116321i \(0.962890\pi\)
\(282\) 0 0
\(283\) −20132.3 114176.i −0.251374 1.42562i −0.805210 0.592990i \(-0.797948\pi\)
0.553836 0.832626i \(-0.313164\pi\)
\(284\) 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 −0.489588 0.871954i \(-0.662853\pi\)
0.510340 + 0.859973i \(0.329520\pi\)
\(294\) 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 0.998399 0.0565673i \(-0.0180156\pi\)
−0.229078 + 0.973408i \(0.573571\pi\)
\(308\) 0 0
\(309\) 2713.89 + 987.776i 0.0284234 + 0.0103453i
\(310\) 0 0
\(311\) −8320.72 + 14411.9i −0.0860281 + 0.149005i −0.905829 0.423644i \(-0.860751\pi\)
0.819801 + 0.572649i \(0.194084\pi\)
\(312\) 0 0
\(313\) 27818.3 157766.i 0.283950 1.61036i −0.425060 0.905165i \(-0.639747\pi\)
0.709011 0.705198i \(-0.249142\pi\)
\(314\) 0 0
\(315\) −2904.06 5029.97i −0.0292674 0.0506926i
\(316\) 0 0
\(317\) −101170. + 120569.i −1.00677 + 1.19982i −0.0270146 + 0.999635i \(0.508600\pi\)
−0.979757 + 0.200189i \(0.935844\pi\)
\(318\) 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 −0.866663 0.498895i \(-0.833739\pi\)
−0.00127600 + 0.999999i \(0.500406\pi\)
\(332\) 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 −0.983213 0.182459i \(-0.941594\pi\)
0.870468 + 0.492226i \(0.163817\pi\)
\(338\) 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 −0.479950 0.877296i \(-0.659345\pi\)
−0.931578 + 0.363542i \(0.881567\pi\)
\(348\) 0 0
\(349\) 66787.2 115679.i 0.548330 0.949736i −0.450059 0.892999i \(-0.648597\pi\)
0.998389 0.0567371i \(-0.0180697\pi\)
\(350\) 0 0
\(351\) 5214.70 29574.1i 0.0423268 0.240047i
\(352\) 0 0
\(353\) 19867.3 + 34411.1i 0.159437 + 0.276153i 0.934666 0.355528i \(-0.115699\pi\)
−0.775229 + 0.631680i \(0.782366\pi\)
\(354\) 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 −0.993151 0.116835i \(-0.962725\pi\)
0.893297 0.449467i \(-0.148386\pi\)
\(360\) 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 0.798109 0.602514i \(-0.205834\pi\)
−0.454770 + 0.890609i \(0.650279\pi\)
\(368\) 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 0.871046 0.491201i \(-0.163442\pi\)
0.0101310 + 0.999949i \(0.496775\pi\)
\(374\) 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 \(0.139149\pi\)
−0.905963 + 0.423358i \(0.860851\pi\)
\(380\) 0 0
\(381\) 18234.0 0.125613
\(382\) 0 0
\(383\) −51324.3 61165.9i −0.349885 0.416977i 0.562185 0.827012i \(-0.309961\pi\)
−0.912070 + 0.410035i \(0.865517\pi\)
\(384\) 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 −0.958982 0.283467i \(-0.908515\pi\)
0.998100 + 0.0616190i \(0.0196264\pi\)
\(390\) 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 0.992301 + 0.123849i \(0.0395240\pi\)
−0.890099 + 0.455767i \(0.849365\pi\)
\(398\) 0 0
\(399\) 691.219 2085.02i 0.00434180 0.0130968i
\(400\) 0 0
\(401\) 20240.3 3568.92i 0.125872 0.0221946i −0.110357 0.993892i \(-0.535199\pi\)
0.236229 + 0.971697i \(0.424088\pi\)
\(402\) 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 0.717277 0.696788i \(-0.245388\pi\)
0.435704 + 0.900090i \(0.356499\pi\)
\(410\) 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 0.496949 0.867780i \(-0.334454\pi\)
−0.940891 + 0.338711i \(0.890009\pi\)
\(422\) 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 −0.909365 0.415998i \(-0.863432\pi\)
0.567588 + 0.823313i \(0.307877\pi\)
\(432\) 0 0
\(433\) −6334.35 17403.5i −0.0337852 0.0928240i 0.921653 0.388015i \(-0.126839\pi\)
−0.955438 + 0.295191i \(0.904617\pi\)
\(434\) 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 −0.0479832 0.998848i \(-0.515279\pi\)
0.296537 + 0.955021i \(0.404168\pi\)
\(440\) 0 0
\(441\) 176819. 64356.7i 0.909181 0.330915i
\(442\) 0 0
\(443\) 133793. + 112265.i 0.681749 + 0.572055i 0.916517 0.399996i \(-0.130989\pi\)
−0.234768 + 0.972051i \(0.575433\pi\)
\(444\) 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 −0.0188626 0.999822i \(-0.506005\pi\)
−0.875303 + 0.483576i \(0.839338\pi\)
\(450\) 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 0.160272 0.987073i \(-0.448763\pi\)
−0.511703 + 0.859162i \(0.670985\pi\)
\(462\) 0 0
\(463\) −70223.0 + 121630.i −0.327580 + 0.567385i −0.982031 0.188719i \(-0.939566\pi\)
0.654451 + 0.756104i \(0.272900\pi\)
\(464\) 0 0
\(465\) 569.906 3232.10i 0.00263571 0.0149479i
\(466\) 0 0
\(467\) −18527.0 32089.7i −0.0849514 0.147140i 0.820419 0.571763i \(-0.193740\pi\)
−0.905371 + 0.424622i \(0.860407\pi\)
\(468\) 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 −0.938538 0.345176i \(-0.887819\pi\)
−0.497087 + 0.867701i \(0.665597\pi\)
\(480\) 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 0.938371 0.345629i \(-0.112334\pi\)
0.169862 + 0.985468i \(0.445668\pi\)
\(488\) 0 0
\(489\) 6352.95 17454.6i 0.0265679 0.0729948i
\(490\) 0 0
\(491\) −37420.5 + 31399.5i −0.155220 + 0.130245i −0.717090 0.696980i \(-0.754526\pi\)
0.561870 + 0.827225i \(0.310082\pi\)
\(492\) 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 0.275471 0.961309i \(-0.411166\pi\)
−0.406895 + 0.913475i \(0.633388\pi\)
\(500\) 0 0
\(501\) −15190.1 + 26310.0i −0.0605180 + 0.104820i
\(502\) 0 0
\(503\) 46195.2 261986.i 0.182583 1.03548i −0.746438 0.665455i \(-0.768238\pi\)
0.929021 0.370026i \(-0.120651\pi\)
\(504\) 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 −0.897837 0.440327i \(-0.854862\pi\)
0.404746 0.914429i \(-0.367360\pi\)
\(510\) 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 −0.770905 0.636950i \(-0.780196\pi\)
0.166162 + 0.986098i \(0.446862\pi\)
\(522\) 0 0
\(523\) 83466.4 + 14717.4i 0.305147 + 0.0538056i 0.324125 0.946014i \(-0.394930\pi\)
−0.0189782 + 0.999820i \(0.506041\pi\)
\(524\) 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 0.436794 + 0.899562i \(0.356114\pi\)
−0.718120 + 0.695919i \(0.754997\pi\)
\(542\) 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 0.999928 0.0120041i \(-0.00382113\pi\)
−0.773705 + 0.633546i \(0.781599\pi\)
\(548\) 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 0.982440 + 0.186576i \(0.0597391\pi\)
0.354341 + 0.935116i \(0.384705\pi\)
\(558\) 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 0.606019 0.795450i \(-0.292765\pi\)
−0.385870 + 0.922553i \(0.626099\pi\)
\(564\) 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 \(0.110215\pi\)
−0.940651 + 0.339374i \(0.889785\pi\)
\(570\) 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 −0.784480 0.620154i \(-0.787070\pi\)
0.929309 + 0.369303i \(0.120403\pi\)
\(578\) 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 0.912790 + 0.408428i \(0.133923\pi\)
−0.718052 + 0.695990i \(0.754966\pi\)
\(588\) 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 −0.180945 0.983493i \(-0.557916\pi\)
0.493565 + 0.869709i \(0.335693\pi\)
\(594\) 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 −0.00727514 0.999974i \(-0.502316\pi\)
−0.348847 + 0.937180i \(0.613427\pi\)
\(600\) 0 0
\(601\) 30321.7 + 17506.3i 0.0839470 + 0.0484668i 0.541386 0.840774i \(-0.317900\pi\)
−0.457439 + 0.889241i \(0.651233\pi\)
\(602\) 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 \(0.220005\pi\)
−0.770504 + 0.637435i \(0.779995\pi\)
\(608\) 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 0.623426 0.781883i \(-0.285740\pi\)
−0.0250126 + 0.999687i \(0.507963\pi\)
\(614\) 0 0
\(615\) −9049.62 + 15674.4i −0.0239265 + 0.0414420i
\(616\) 0 0
\(617\) 49410.0 280218.i 0.129791 0.736081i −0.848555 0.529107i \(-0.822527\pi\)
0.978346 0.206974i \(-0.0663617\pi\)
\(618\) 0 0
\(619\) −176197. 305181.i −0.459850 0.796484i 0.539103 0.842240i \(-0.318763\pi\)
−0.998953 + 0.0457565i \(0.985430\pi\)
\(620\) 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 0.217578 0.976043i \(-0.430184\pi\)
0.794062 + 0.607836i \(0.207962\pi\)
\(632\) 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 −0.924898 0.380215i \(-0.875850\pi\)
0.952911 + 0.303251i \(0.0980722\pi\)
\(642\) 0 0
\(643\) −15196.8 + 12751.6i −0.0367562 + 0.0308421i −0.660981 0.750403i \(-0.729859\pi\)
0.624225 + 0.781245i \(0.285415\pi\)
\(644\) 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 0.200863 + 0.979619i \(0.435626\pi\)
−0.948807 + 0.315858i \(0.897708\pi\)
\(654\) 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 −0.482327 0.875991i \(-0.660208\pi\)
0.946438 + 0.322885i \(0.104653\pi\)
\(660\) 0 0
\(661\) 160266. + 440328.i 0.366808 + 1.00780i 0.976568 + 0.215211i \(0.0690440\pi\)
−0.609759 + 0.792587i \(0.708734\pi\)
\(662\) 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 0.0397942 0.999208i \(-0.487330\pi\)
0.885237 + 0.465141i \(0.153996\pi\)
\(674\) 0 0
\(675\) 67099.6 + 11831.5i 0.147269 + 0.0259676i
\(676\) 0 0
\(677\) −439608. 253808.i −0.959154 0.553768i −0.0632415 0.997998i \(-0.520144\pi\)
−0.895913 + 0.444230i \(0.853477\pi\)
\(678\) 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 \(-0.794920\pi\)
0.799533 0.600622i \(-0.205080\pi\)
\(684\) 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 −0.581301 0.813689i \(-0.697456\pi\)
0.995325 + 0.0965773i \(0.0307895\pi\)
\(692\) 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 0.994238 + 0.107197i \(0.0341874\pi\)
−0.897615 + 0.440781i \(0.854701\pi\)
\(702\) 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 0.392960 0.919556i \(-0.371451\pi\)
−0.837349 + 0.546669i \(0.815895\pi\)
\(710\) 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 −0.583444 0.812154i \(-0.698295\pi\)
0.698501 + 0.715609i \(0.253851\pi\)
\(720\) 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 −0.454872 0.890557i \(-0.650315\pi\)
−0.920891 + 0.389821i \(0.872537\pi\)
\(728\) 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 −0.694368 0.719620i \(-0.744316\pi\)
−0.276025 0.961150i \(-0.589017\pi\)
\(734\) 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 0.991512 + 0.130017i \(0.0415031\pi\)
−0.887248 + 0.461293i \(0.847386\pi\)
\(740\) 0 0
\(741\) 31889.1 59122.7i 0.0580773 0.107676i
\(742\) 0 0
\(743\) 336541. 59341.2i 0.609621 0.107493i 0.139689 0.990195i \(-0.455390\pi\)
0.469932 + 0.882703i \(0.344278\pi\)
\(744\) 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 −0.363522 0.931586i \(-0.618426\pi\)
−0.660220 + 0.751073i \(0.729537\pi\)
\(752\) 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 −0.292534 0.956255i \(-0.594499\pi\)
0.890929 + 0.454142i \(0.150054\pi\)
\(758\) 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 0.851653 + 0.524107i \(0.175601\pi\)
−0.979547 + 0.201217i \(0.935510\pi\)
\(770\) 0 0
\(771\) −35539.8 61556.7i −0.0597869 0.103554i
\(772\) 0 0
\(773\) 260878. 310902.i 0.436595 0.520313i −0.502218 0.864741i \(-0.667483\pi\)
0.938813 + 0.344428i \(0.111927\pi\)
\(774\) 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 −0.204811 0.978802i \(-0.565658\pi\)
0.745262 + 0.666772i \(0.232325\pi\)
\(788\) 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