Properties

Label 76.5.j.a.13.4
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 13.4
Character \(\chi\) \(=\) 76.13
Dual form 76.5.j.a.41.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.180467 + 0.495829i) q^{3} +(-0.550159 - 3.12011i) q^{5} +(-25.9990 + 45.0316i) q^{7} +(61.8363 + 51.8868i) q^{9} +O(q^{10})\) \(q+(-0.180467 + 0.495829i) q^{3} +(-0.550159 - 3.12011i) q^{5} +(-25.9990 + 45.0316i) q^{7} +(61.8363 + 51.8868i) q^{9} +(-19.1428 - 33.1563i) q^{11} +(71.6974 + 196.987i) q^{13} +(1.64632 + 0.290291i) q^{15} +(-302.594 + 253.907i) q^{17} +(210.294 + 293.424i) q^{19} +(-17.6360 - 21.0178i) q^{21} +(-80.8917 + 458.759i) q^{23} +(577.875 - 210.329i) q^{25} +(-73.9000 + 42.6662i) q^{27} +(277.497 - 330.708i) q^{29} +(-1061.61 - 612.923i) q^{31} +(19.8945 - 3.50794i) q^{33} +(154.807 + 56.3452i) q^{35} +963.274i q^{37} -110.611 q^{39} +(866.860 - 2381.68i) q^{41} +(-372.808 - 2114.30i) q^{43} +(127.873 - 221.482i) q^{45} +(-1913.69 - 1605.78i) q^{47} +(-151.397 - 262.228i) q^{49} +(-71.2860 - 195.857i) q^{51} +(3624.29 + 639.061i) q^{53} +(-92.9197 + 77.9689i) q^{55} +(-183.439 + 51.3167i) q^{57} +(-897.018 - 1069.02i) q^{59} +(-83.2176 + 471.950i) q^{61} +(-3944.23 + 1435.58i) q^{63} +(575.175 - 332.078i) q^{65} +(-1813.84 + 2161.65i) q^{67} +(-212.868 - 122.899i) q^{69} +(5130.43 - 904.634i) q^{71} +(3346.39 + 1217.99i) q^{73} +324.485i q^{75} +1990.78 q^{77} +(-2475.89 + 6802.45i) q^{79} +(1127.57 + 6394.77i) q^{81} +(-3492.18 + 6048.63i) q^{83} +(958.691 + 804.437i) q^{85} +(113.895 + 197.273i) q^{87} +(-194.356 - 533.990i) q^{89} +(-10734.7 - 1892.82i) q^{91} +(495.491 - 415.766i) q^{93} +(799.817 - 817.570i) q^{95} +(6980.90 + 8319.52i) q^{97} +(536.656 - 3043.53i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

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
\(3\) −0.180467 + 0.495829i −0.0200519 + 0.0550921i −0.949315 0.314327i \(-0.898221\pi\)
0.929263 + 0.369419i \(0.120443\pi\)
\(4\) 0 0
\(5\) −0.550159 3.12011i −0.0220064 0.124804i 0.971826 0.235701i \(-0.0757387\pi\)
−0.993832 + 0.110897i \(0.964628\pi\)
\(6\) 0 0
\(7\) −25.9990 + 45.0316i −0.530592 + 0.919013i 0.468771 + 0.883320i \(0.344697\pi\)
−0.999363 + 0.0356926i \(0.988636\pi\)
\(8\) 0 0
\(9\) 61.8363 + 51.8868i 0.763411 + 0.640578i
\(10\) 0 0
\(11\) −19.1428 33.1563i −0.158205 0.274019i 0.776016 0.630713i \(-0.217237\pi\)
−0.934221 + 0.356693i \(0.883904\pi\)
\(12\) 0 0
\(13\) 71.6974 + 196.987i 0.424245 + 1.16560i 0.949255 + 0.314507i \(0.101839\pi\)
−0.525010 + 0.851096i \(0.675939\pi\)
\(14\) 0 0
\(15\) 1.64632 + 0.290291i 0.00731700 + 0.00129018i
\(16\) 0 0
\(17\) −302.594 + 253.907i −1.04704 + 0.878570i −0.992779 0.119957i \(-0.961724\pi\)
−0.0542595 + 0.998527i \(0.517280\pi\)
\(18\) 0 0
\(19\) 210.294 + 293.424i 0.582532 + 0.812808i
\(20\) 0 0
\(21\) −17.6360 21.0178i −0.0399910 0.0476594i
\(22\) 0 0
\(23\) −80.8917 + 458.759i −0.152914 + 0.867220i 0.807754 + 0.589520i \(0.200683\pi\)
−0.960668 + 0.277700i \(0.910428\pi\)
\(24\) 0 0
\(25\) 577.875 210.329i 0.924601 0.336527i
\(26\) 0 0
\(27\) −73.9000 + 42.6662i −0.101372 + 0.0585270i
\(28\) 0 0
\(29\) 277.497 330.708i 0.329960 0.393231i −0.575402 0.817870i \(-0.695155\pi\)
0.905363 + 0.424639i \(0.139599\pi\)
\(30\) 0 0
\(31\) −1061.61 612.923i −1.10470 0.637797i −0.167246 0.985915i \(-0.553487\pi\)
−0.937451 + 0.348118i \(0.886821\pi\)
\(32\) 0 0
\(33\) 19.8945 3.50794i 0.0182686 0.00322125i
\(34\) 0 0
\(35\) 154.807 + 56.3452i 0.126373 + 0.0459960i
\(36\) 0 0
\(37\) 963.274i 0.703634i 0.936069 + 0.351817i \(0.114436\pi\)
−0.936069 + 0.351817i \(0.885564\pi\)
\(38\) 0 0
\(39\) −110.611 −0.0727224
\(40\) 0 0
\(41\) 866.860 2381.68i 0.515681 1.41682i −0.359554 0.933124i \(-0.617071\pi\)
0.875235 0.483698i \(-0.160707\pi\)
\(42\) 0 0
\(43\) −372.808 2114.30i −0.201627 1.14348i −0.902660 0.430354i \(-0.858389\pi\)
0.701034 0.713128i \(-0.252722\pi\)
\(44\) 0 0
\(45\) 127.873 221.482i 0.0631470 0.109374i
\(46\) 0 0
\(47\) −1913.69 1605.78i −0.866316 0.726925i 0.0970031 0.995284i \(-0.469074\pi\)
−0.963319 + 0.268359i \(0.913519\pi\)
\(48\) 0 0
\(49\) −151.397 262.228i −0.0630560 0.109216i
\(50\) 0 0
\(51\) −71.2860 195.857i −0.0274072 0.0753005i
\(52\) 0 0
\(53\) 3624.29 + 639.061i 1.29024 + 0.227505i 0.776324 0.630334i \(-0.217082\pi\)
0.513919 + 0.857839i \(0.328193\pi\)
\(54\) 0 0
\(55\) −92.9197 + 77.9689i −0.0307173 + 0.0257748i
\(56\) 0 0
\(57\) −183.439 + 51.3167i −0.0564601 + 0.0157946i
\(58\) 0 0
\(59\) −897.018 1069.02i −0.257690 0.307103i 0.621652 0.783293i \(-0.286462\pi\)
−0.879342 + 0.476191i \(0.842017\pi\)
\(60\) 0 0
\(61\) −83.2176 + 471.950i −0.0223643 + 0.126834i −0.993946 0.109871i \(-0.964956\pi\)
0.971582 + 0.236705i \(0.0760675\pi\)
\(62\) 0 0
\(63\) −3944.23 + 1435.58i −0.993759 + 0.361699i
\(64\) 0 0
\(65\) 575.175 332.078i 0.136136 0.0785983i
\(66\) 0 0
\(67\) −1813.84 + 2161.65i −0.404063 + 0.481544i −0.929254 0.369441i \(-0.879549\pi\)
0.525191 + 0.850984i \(0.323994\pi\)
\(68\) 0 0
\(69\) −212.868 122.899i −0.0447107 0.0258138i
\(70\) 0 0
\(71\) 5130.43 904.634i 1.01774 0.179455i 0.360201 0.932875i \(-0.382708\pi\)
0.657540 + 0.753419i \(0.271597\pi\)
\(72\) 0 0
\(73\) 3346.39 + 1217.99i 0.627959 + 0.228558i 0.636343 0.771406i \(-0.280446\pi\)
−0.00838368 + 0.999965i \(0.502669\pi\)
\(74\) 0 0
\(75\) 324.485i 0.0576862i
\(76\) 0 0
\(77\) 1990.78 0.335770
\(78\) 0 0
\(79\) −2475.89 + 6802.45i −0.396714 + 1.08996i 0.567161 + 0.823607i \(0.308042\pi\)
−0.963875 + 0.266355i \(0.914181\pi\)
\(80\) 0 0
\(81\) 1127.57 + 6394.77i 0.171860 + 0.974664i
\(82\) 0 0
\(83\) −3492.18 + 6048.63i −0.506921 + 0.878012i 0.493047 + 0.870003i \(0.335883\pi\)
−0.999968 + 0.00800975i \(0.997450\pi\)
\(84\) 0 0
\(85\) 958.691 + 804.437i 0.132691 + 0.111341i
\(86\) 0 0
\(87\) 113.895 + 197.273i 0.0150476 + 0.0260632i
\(88\) 0 0
\(89\) −194.356 533.990i −0.0245368 0.0674144i 0.926819 0.375507i \(-0.122531\pi\)
−0.951356 + 0.308093i \(0.900309\pi\)
\(90\) 0 0
\(91\) −10734.7 1892.82i −1.29630 0.228574i
\(92\) 0 0
\(93\) 495.491 415.766i 0.0572888 0.0480710i
\(94\) 0 0
\(95\) 799.817 817.570i 0.0886224 0.0905895i
\(96\) 0 0
\(97\) 6980.90 + 8319.52i 0.741939 + 0.884208i 0.996564 0.0828316i \(-0.0263964\pi\)
−0.254625 + 0.967040i \(0.581952\pi\)
\(98\) 0 0
\(99\) 536.656 3043.53i 0.0547552 0.310532i
\(100\) 0 0
\(101\) 6626.34 2411.79i 0.649578 0.236427i 0.00384764 0.999993i \(-0.498775\pi\)
0.645730 + 0.763566i \(0.276553\pi\)
\(102\) 0 0
\(103\) 4953.12 2859.68i 0.466879 0.269553i −0.248053 0.968746i \(-0.579791\pi\)
0.714932 + 0.699194i \(0.246458\pi\)
\(104\) 0 0
\(105\) −55.8751 + 66.5894i −0.00506804 + 0.00603985i
\(106\) 0 0
\(107\) 1251.39 + 722.488i 0.109301 + 0.0631049i 0.553654 0.832747i \(-0.313233\pi\)
−0.444353 + 0.895852i \(0.646566\pi\)
\(108\) 0 0
\(109\) −11571.3 + 2040.33i −0.973931 + 0.171730i −0.637899 0.770120i \(-0.720196\pi\)
−0.336032 + 0.941850i \(0.609085\pi\)
\(110\) 0 0
\(111\) −477.619 173.839i −0.0387646 0.0141092i
\(112\) 0 0
\(113\) 17403.4i 1.36294i −0.731845 0.681471i \(-0.761341\pi\)
0.731845 0.681471i \(-0.238659\pi\)
\(114\) 0 0
\(115\) 1475.88 0.111598
\(116\) 0 0
\(117\) −5787.53 + 15901.1i −0.422787 + 1.16160i
\(118\) 0 0
\(119\) −3566.68 20227.6i −0.251866 1.42840i
\(120\) 0 0
\(121\) 6587.60 11410.1i 0.449942 0.779323i
\(122\) 0 0
\(123\) 1024.47 + 859.628i 0.0677153 + 0.0568199i
\(124\) 0 0
\(125\) −1964.25 3402.18i −0.125712 0.217739i
\(126\) 0 0
\(127\) −525.524 1443.87i −0.0325826 0.0895199i 0.922335 0.386392i \(-0.126279\pi\)
−0.954917 + 0.296872i \(0.904057\pi\)
\(128\) 0 0
\(129\) 1115.61 + 196.712i 0.0670398 + 0.0118209i
\(130\) 0 0
\(131\) 1467.97 1231.77i 0.0855409 0.0717774i −0.599014 0.800738i \(-0.704441\pi\)
0.684555 + 0.728961i \(0.259996\pi\)
\(132\) 0 0
\(133\) −18680.8 + 1841.16i −1.05607 + 0.104085i
\(134\) 0 0
\(135\) 173.780 + 207.103i 0.00953525 + 0.0113637i
\(136\) 0 0
\(137\) 5865.24 33263.4i 0.312496 1.77225i −0.273434 0.961891i \(-0.588160\pi\)
0.585930 0.810362i \(-0.300729\pi\)
\(138\) 0 0
\(139\) 13242.3 4819.79i 0.685382 0.249459i 0.0242252 0.999707i \(-0.492288\pi\)
0.661157 + 0.750248i \(0.270066\pi\)
\(140\) 0 0
\(141\) 1141.55 659.074i 0.0574191 0.0331509i
\(142\) 0 0
\(143\) 5158.88 6148.11i 0.252280 0.300656i
\(144\) 0 0
\(145\) −1184.51 683.877i −0.0563382 0.0325269i
\(146\) 0 0
\(147\) 157.342 27.7437i 0.00728134 0.00128390i
\(148\) 0 0
\(149\) 17675.3 + 6433.30i 0.796151 + 0.289775i 0.707890 0.706322i \(-0.249647\pi\)
0.0882604 + 0.996097i \(0.471869\pi\)
\(150\) 0 0
\(151\) 24175.2i 1.06027i 0.847913 + 0.530135i \(0.177859\pi\)
−0.847913 + 0.530135i \(0.822141\pi\)
\(152\) 0 0
\(153\) −31885.7 −1.36211
\(154\) 0 0
\(155\) −1328.33 + 3649.55i −0.0552894 + 0.151906i
\(156\) 0 0
\(157\) 1620.67 + 9191.29i 0.0657500 + 0.372887i 0.999873 + 0.0159357i \(0.00507269\pi\)
−0.934123 + 0.356951i \(0.883816\pi\)
\(158\) 0 0
\(159\) −970.930 + 1681.70i −0.0384055 + 0.0665203i
\(160\) 0 0
\(161\) −18555.6 15570.0i −0.715851 0.600670i
\(162\) 0 0
\(163\) −10154.6 17588.2i −0.382196 0.661982i 0.609180 0.793032i \(-0.291499\pi\)
−0.991376 + 0.131050i \(0.958165\pi\)
\(164\) 0 0
\(165\) −21.8903 60.1431i −0.000804051 0.00220911i
\(166\) 0 0
\(167\) 37747.3 + 6655.86i 1.35348 + 0.238655i 0.802894 0.596121i \(-0.203292\pi\)
0.550588 + 0.834777i \(0.314403\pi\)
\(168\) 0 0
\(169\) −11784.3 + 9888.23i −0.412602 + 0.346215i
\(170\) 0 0
\(171\) −2221.00 + 29055.7i −0.0759549 + 0.993664i
\(172\) 0 0
\(173\) 16752.5 + 19964.8i 0.559741 + 0.667074i 0.969492 0.245124i \(-0.0788287\pi\)
−0.409751 + 0.912198i \(0.634384\pi\)
\(174\) 0 0
\(175\) −5552.72 + 31491.0i −0.181313 + 1.02828i
\(176\) 0 0
\(177\) 691.935 251.844i 0.0220861 0.00803868i
\(178\) 0 0
\(179\) 46834.0 27039.6i 1.46169 0.843907i 0.462600 0.886567i \(-0.346917\pi\)
0.999090 + 0.0426605i \(0.0135834\pi\)
\(180\) 0 0
\(181\) −30865.0 + 36783.5i −0.942127 + 1.12278i 0.0501495 + 0.998742i \(0.484030\pi\)
−0.992277 + 0.124042i \(0.960414\pi\)
\(182\) 0 0
\(183\) −218.989 126.433i −0.00653912 0.00377536i
\(184\) 0 0
\(185\) 3005.52 529.954i 0.0878165 0.0154844i
\(186\) 0 0
\(187\) 14211.1 + 5172.42i 0.406392 + 0.147915i
\(188\) 0 0
\(189\) 4437.12i 0.124216i
\(190\) 0 0
\(191\) 20431.6 0.560061 0.280030 0.959991i \(-0.409655\pi\)
0.280030 + 0.959991i \(0.409655\pi\)
\(192\) 0 0
\(193\) −4955.27 + 13614.5i −0.133031 + 0.365499i −0.988266 0.152740i \(-0.951190\pi\)
0.855236 + 0.518240i \(0.173412\pi\)
\(194\) 0 0
\(195\) 60.8535 + 345.118i 0.00160036 + 0.00907607i
\(196\) 0 0
\(197\) −27348.9 + 47369.8i −0.704706 + 1.22059i 0.262091 + 0.965043i \(0.415588\pi\)
−0.966797 + 0.255544i \(0.917745\pi\)
\(198\) 0 0
\(199\) −49582.7 41604.8i −1.25206 1.05060i −0.996482 0.0838097i \(-0.973291\pi\)
−0.255574 0.966790i \(-0.582264\pi\)
\(200\) 0 0
\(201\) −744.470 1289.46i −0.0184270 0.0319165i
\(202\) 0 0
\(203\) 7677.66 + 21094.2i 0.186310 + 0.511883i
\(204\) 0 0
\(205\) −7908.00 1394.39i −0.188174 0.0331801i
\(206\) 0 0
\(207\) −28805.6 + 24170.8i −0.672259 + 0.564092i
\(208\) 0 0
\(209\) 5703.23 12589.5i 0.130565 0.288215i
\(210\) 0 0
\(211\) 32105.5 + 38261.8i 0.721131 + 0.859411i 0.994740 0.102430i \(-0.0326619\pi\)
−0.273609 + 0.961841i \(0.588217\pi\)
\(212\) 0 0
\(213\) −477.330 + 2707.07i −0.0105211 + 0.0596679i
\(214\) 0 0
\(215\) −6391.73 + 2326.40i −0.138274 + 0.0503278i
\(216\) 0 0
\(217\) 55201.8 31870.8i 1.17229 0.676820i
\(218\) 0 0
\(219\) −1207.83 + 1439.43i −0.0251835 + 0.0300126i
\(220\) 0 0
\(221\) −71711.5 41402.6i −1.46826 0.847703i
\(222\) 0 0
\(223\) 74551.7 13145.5i 1.49916 0.264342i 0.636955 0.770901i \(-0.280194\pi\)
0.862205 + 0.506559i \(0.169083\pi\)
\(224\) 0 0
\(225\) 46647.0 + 16978.1i 0.921423 + 0.335370i
\(226\) 0 0
\(227\) 13420.6i 0.260448i −0.991485 0.130224i \(-0.958430\pi\)
0.991485 0.130224i \(-0.0415697\pi\)
\(228\) 0 0
\(229\) −19611.7 −0.373977 −0.186988 0.982362i \(-0.559873\pi\)
−0.186988 + 0.982362i \(0.559873\pi\)
\(230\) 0 0
\(231\) −359.270 + 987.085i −0.00673281 + 0.0184983i
\(232\) 0 0
\(233\) −15352.7 87069.6i −0.282796 1.60382i −0.713053 0.701110i \(-0.752688\pi\)
0.430256 0.902707i \(-0.358423\pi\)
\(234\) 0 0
\(235\) −3957.36 + 6854.36i −0.0716589 + 0.124117i
\(236\) 0 0
\(237\) −2926.04 2455.24i −0.0520934 0.0437116i
\(238\) 0 0
\(239\) −24137.8 41807.8i −0.422572 0.731917i 0.573618 0.819123i \(-0.305539\pi\)
−0.996190 + 0.0872061i \(0.972206\pi\)
\(240\) 0 0
\(241\) −12652.2 34761.5i −0.217836 0.598501i 0.781852 0.623464i \(-0.214275\pi\)
−0.999688 + 0.0249635i \(0.992053\pi\)
\(242\) 0 0
\(243\) −10181.1 1795.21i −0.172418 0.0304020i
\(244\) 0 0
\(245\) −734.887 + 616.643i −0.0122430 + 0.0102731i
\(246\) 0 0
\(247\) −42723.1 + 62462.9i −0.700275 + 1.02383i
\(248\) 0 0
\(249\) −2368.86 2823.10i −0.0382068 0.0455331i
\(250\) 0 0
\(251\) 17755.8 100698.i 0.281833 1.59835i −0.434551 0.900647i \(-0.643093\pi\)
0.716384 0.697706i \(-0.245796\pi\)
\(252\) 0 0
\(253\) 16759.3 6099.88i 0.261827 0.0952972i
\(254\) 0 0
\(255\) −571.875 + 330.172i −0.00879470 + 0.00507762i
\(256\) 0 0
\(257\) −1331.43 + 1586.74i −0.0201582 + 0.0240237i −0.776029 0.630697i \(-0.782769\pi\)
0.755871 + 0.654720i \(0.227214\pi\)
\(258\) 0 0
\(259\) −43377.8 25044.2i −0.646648 0.373342i
\(260\) 0 0
\(261\) 34318.7 6051.32i 0.503791 0.0888319i
\(262\) 0 0
\(263\) 71950.3 + 26187.8i 1.04021 + 0.378606i 0.804960 0.593329i \(-0.202187\pi\)
0.235251 + 0.971935i \(0.424409\pi\)
\(264\) 0 0
\(265\) 11659.8i 0.166034i
\(266\) 0 0
\(267\) 299.842 0.00420601
\(268\) 0 0
\(269\) −40959.5 + 112535.i −0.566044 + 1.55519i 0.244582 + 0.969629i \(0.421349\pi\)
−0.810626 + 0.585565i \(0.800873\pi\)
\(270\) 0 0
\(271\) −23494.3 133243.i −0.319908 1.81429i −0.543279 0.839552i \(-0.682817\pi\)
0.223371 0.974733i \(-0.428294\pi\)
\(272\) 0 0
\(273\) 2875.77 4980.98i 0.0385859 0.0668328i
\(274\) 0 0
\(275\) −18035.9 15133.9i −0.238492 0.200118i
\(276\) 0 0
\(277\) 18417.5 + 31900.1i 0.240033 + 0.415750i 0.960724 0.277507i \(-0.0895083\pi\)
−0.720690 + 0.693257i \(0.756175\pi\)
\(278\) 0 0
\(279\) −33843.6 92984.6i −0.434779 1.19455i
\(280\) 0 0
\(281\) 28595.8 + 5042.22i 0.362152 + 0.0638571i 0.351763 0.936089i \(-0.385582\pi\)
0.0103881 + 0.999946i \(0.496693\pi\)
\(282\) 0 0
\(283\) −29691.9 + 24914.4i −0.370736 + 0.311084i −0.809053 0.587736i \(-0.800019\pi\)
0.438317 + 0.898821i \(0.355575\pi\)
\(284\) 0 0
\(285\) 261.034 + 544.117i 0.00321372 + 0.00669889i
\(286\) 0 0
\(287\) 84713.3 + 100957.i 1.02846 + 1.22567i
\(288\) 0 0
\(289\) 12591.4 71409.2i 0.150757 0.854985i
\(290\) 0 0
\(291\) −5384.88 + 1959.94i −0.0635902 + 0.0231449i
\(292\) 0 0
\(293\) 26114.1 15077.0i 0.304187 0.175622i −0.340136 0.940376i \(-0.610473\pi\)
0.644322 + 0.764754i \(0.277140\pi\)
\(294\) 0 0
\(295\) −2841.97 + 3386.93i −0.0326569 + 0.0389190i
\(296\) 0 0
\(297\) 2829.31 + 1633.50i 0.0320751 + 0.0185186i
\(298\) 0 0
\(299\) −96169.3 + 16957.2i −1.07571 + 0.189676i
\(300\) 0 0
\(301\) 104903. + 38181.5i 1.15786 + 0.421425i
\(302\) 0 0
\(303\) 3720.78i 0.0405274i
\(304\) 0 0
\(305\) 1518.32 0.0163216
\(306\) 0 0
\(307\) −60034.4 + 164943.i −0.636977 + 1.75008i 0.0240437 + 0.999711i \(0.492346\pi\)
−0.661020 + 0.750368i \(0.729876\pi\)
\(308\) 0 0
\(309\) 524.040 + 2971.98i 0.00548842 + 0.0311264i
\(310\) 0 0
\(311\) −59834.2 + 103636.i −0.618626 + 1.07149i 0.371110 + 0.928589i \(0.378977\pi\)
−0.989737 + 0.142904i \(0.954356\pi\)
\(312\) 0 0
\(313\) −59356.0 49805.6i −0.605865 0.508381i 0.287460 0.957793i \(-0.407189\pi\)
−0.893325 + 0.449412i \(0.851634\pi\)
\(314\) 0 0
\(315\) 6649.13 + 11516.6i 0.0670106 + 0.116066i
\(316\) 0 0
\(317\) 50069.0 + 137564.i 0.498254 + 1.36894i 0.892961 + 0.450134i \(0.148624\pi\)
−0.394707 + 0.918807i \(0.629154\pi\)
\(318\) 0 0
\(319\) −16277.1 2870.10i −0.159954 0.0282043i
\(320\) 0 0
\(321\) −584.064 + 490.088i −0.00566827 + 0.00475624i
\(322\) 0 0
\(323\) −138136. 35393.1i −1.32404 0.339246i
\(324\) 0 0
\(325\) 82864.3 + 98753.8i 0.784514 + 0.934948i
\(326\) 0 0
\(327\) 1076.58 6105.59i 0.0100682 0.0570994i
\(328\) 0 0
\(329\) 122065. 44428.0i 1.12771 0.410454i
\(330\) 0 0
\(331\) 171009. 98731.9i 1.56085 0.901160i 0.563683 0.825991i \(-0.309384\pi\)
0.997171 0.0751687i \(-0.0239495\pi\)
\(332\) 0 0
\(333\) −49981.3 + 59565.3i −0.450732 + 0.537162i
\(334\) 0 0
\(335\) 7742.48 + 4470.12i 0.0689907 + 0.0398318i
\(336\) 0 0
\(337\) 47042.1 8294.80i 0.414216 0.0730375i 0.0373435 0.999302i \(-0.488110\pi\)
0.376873 + 0.926265i \(0.376999\pi\)
\(338\) 0 0
\(339\) 8629.11 + 3140.74i 0.0750873 + 0.0273295i
\(340\) 0 0
\(341\) 46932.3i 0.403611i
\(342\) 0 0
\(343\) −109103. −0.927356
\(344\) 0 0
\(345\) −266.348 + 731.785i −0.00223775 + 0.00614816i
\(346\) 0 0
\(347\) 27447.3 + 155661.i 0.227950 + 1.29277i 0.856964 + 0.515377i \(0.172348\pi\)
−0.629013 + 0.777394i \(0.716541\pi\)
\(348\) 0 0
\(349\) −19980.7 + 34607.6i −0.164044 + 0.284133i −0.936315 0.351160i \(-0.885787\pi\)
0.772271 + 0.635293i \(0.219121\pi\)
\(350\) 0 0
\(351\) −13703.1 11498.3i −0.111226 0.0933295i
\(352\) 0 0
\(353\) −102732. 177938.i −0.824438 1.42797i −0.902348 0.431009i \(-0.858158\pi\)
0.0779095 0.996960i \(-0.475175\pi\)
\(354\) 0 0
\(355\) −5645.11 15509.8i −0.0447936 0.123069i
\(356\) 0 0
\(357\) 10673.1 + 1881.96i 0.0837441 + 0.0147664i
\(358\) 0 0
\(359\) −46.7711 + 39.2456i −0.000362901 + 0.000304510i −0.642969 0.765892i \(-0.722298\pi\)
0.642606 + 0.766197i \(0.277853\pi\)
\(360\) 0 0
\(361\) −41873.7 + 123411.i −0.321312 + 0.946973i
\(362\) 0 0
\(363\) 4468.60 + 5325.46i 0.0339123 + 0.0404152i
\(364\) 0 0
\(365\) 1959.20 11111.2i 0.0147060 0.0834017i
\(366\) 0 0
\(367\) 42648.2 15522.7i 0.316642 0.115248i −0.178810 0.983884i \(-0.557225\pi\)
0.495452 + 0.868635i \(0.335002\pi\)
\(368\) 0 0
\(369\) 177181. 102296.i 1.30126 0.751284i
\(370\) 0 0
\(371\) −123006. + 146593.i −0.893673 + 1.06504i
\(372\) 0 0
\(373\) −2182.83 1260.26i −0.0156893 0.00905820i 0.492135 0.870519i \(-0.336217\pi\)
−0.507824 + 0.861461i \(0.669550\pi\)
\(374\) 0 0
\(375\) 2041.38 359.950i 0.0145165 0.00255965i
\(376\) 0 0
\(377\) 85040.9 + 30952.3i 0.598336 + 0.217776i
\(378\) 0 0
\(379\) 141908.i 0.987936i −0.869480 0.493968i \(-0.835546\pi\)
0.869480 0.493968i \(-0.164454\pi\)
\(380\) 0 0
\(381\) 810.750 0.00558518
\(382\) 0 0
\(383\) −52054.1 + 143018.i −0.354860 + 0.974971i 0.625925 + 0.779883i \(0.284721\pi\)
−0.980786 + 0.195088i \(0.937501\pi\)
\(384\) 0 0
\(385\) −1095.24 6211.44i −0.00738907 0.0419055i
\(386\) 0 0
\(387\) 86651.2 150084.i 0.578566 1.00210i
\(388\) 0 0
\(389\) −216517. 181680.i −1.43085 1.20062i −0.945210 0.326464i \(-0.894143\pi\)
−0.485638 0.874160i \(-0.661413\pi\)
\(390\) 0 0
\(391\) −92004.7 159357.i −0.601806 1.04236i
\(392\) 0 0
\(393\) 345.828 + 950.155i 0.00223911 + 0.00615190i
\(394\) 0 0
\(395\) 22586.5 + 3982.61i 0.144762 + 0.0255255i
\(396\) 0 0
\(397\) −39373.6 + 33038.4i −0.249818 + 0.209622i −0.759094 0.650981i \(-0.774358\pi\)
0.509276 + 0.860603i \(0.329913\pi\)
\(398\) 0 0
\(399\) 2458.36 9594.74i 0.0154419 0.0602681i
\(400\) 0 0
\(401\) 11830.4 + 14098.9i 0.0735717 + 0.0876794i 0.801575 0.597894i \(-0.203996\pi\)
−0.728003 + 0.685574i \(0.759551\pi\)
\(402\) 0 0
\(403\) 44622.9 253069.i 0.274756 1.55822i
\(404\) 0 0
\(405\) 19332.0 7036.28i 0.117860 0.0428976i
\(406\) 0 0
\(407\) 31938.7 18439.8i 0.192809 0.111318i
\(408\) 0 0
\(409\) 121640. 144965.i 0.727158 0.866593i −0.268147 0.963378i \(-0.586411\pi\)
0.995305 + 0.0967849i \(0.0308559\pi\)
\(410\) 0 0
\(411\) 15434.5 + 8911.10i 0.0913710 + 0.0527531i
\(412\) 0 0
\(413\) 71461.5 12600.6i 0.418959 0.0738738i
\(414\) 0 0
\(415\) 20793.6 + 7568.26i 0.120735 + 0.0439440i
\(416\) 0 0
\(417\) 7435.71i 0.0427612i
\(418\) 0 0
\(419\) −133497. −0.760400 −0.380200 0.924904i \(-0.624145\pi\)
−0.380200 + 0.924904i \(0.624145\pi\)
\(420\) 0 0
\(421\) 24810.7 68166.9i 0.139983 0.384600i −0.849814 0.527082i \(-0.823286\pi\)
0.989797 + 0.142482i \(0.0455083\pi\)
\(422\) 0 0
\(423\) −35016.9 198591.i −0.195703 1.10989i
\(424\) 0 0
\(425\) −121458. + 210371.i −0.672430 + 1.16468i
\(426\) 0 0
\(427\) −19089.1 16017.7i −0.104696 0.0878503i
\(428\) 0 0
\(429\) 2117.40 + 3667.45i 0.0115051 + 0.0199274i
\(430\) 0 0
\(431\) 12011.1 + 33000.3i 0.0646590 + 0.177649i 0.967815 0.251664i \(-0.0809778\pi\)
−0.903156 + 0.429313i \(0.858756\pi\)
\(432\) 0 0
\(433\) 241750. + 42627.0i 1.28941 + 0.227357i 0.775970 0.630770i \(-0.217261\pi\)
0.513437 + 0.858127i \(0.328372\pi\)
\(434\) 0 0
\(435\) 552.851 463.897i 0.00292166 0.00245156i
\(436\) 0 0
\(437\) −151622. + 72738.9i −0.793960 + 0.380894i
\(438\) 0 0
\(439\) 66870.5 + 79693.2i 0.346981 + 0.413516i 0.911105 0.412174i \(-0.135230\pi\)
−0.564124 + 0.825690i \(0.690786\pi\)
\(440\) 0 0
\(441\) 4244.32 24070.8i 0.0218238 0.123769i
\(442\) 0 0
\(443\) 103744. 37759.7i 0.528634 0.192407i −0.0638940 0.997957i \(-0.520352\pi\)
0.592529 + 0.805549i \(0.298130\pi\)
\(444\) 0 0
\(445\) −1559.18 + 900.192i −0.00787364 + 0.00454585i
\(446\) 0 0
\(447\) −6379.63 + 7602.95i −0.0319286 + 0.0380511i
\(448\) 0 0
\(449\) −286945. 165668.i −1.42333 0.821760i −0.426748 0.904371i \(-0.640341\pi\)
−0.996582 + 0.0826112i \(0.973674\pi\)
\(450\) 0 0
\(451\) −95561.9 + 16850.1i −0.469820 + 0.0828419i
\(452\) 0 0
\(453\) −11986.8 4362.83i −0.0584125 0.0212604i
\(454\) 0 0
\(455\) 34534.8i 0.166814i
\(456\) 0 0
\(457\) 5096.81 0.0244043 0.0122021 0.999926i \(-0.496116\pi\)
0.0122021 + 0.999926i \(0.496116\pi\)
\(458\) 0 0
\(459\) 11528.5 31674.3i 0.0547201 0.150342i
\(460\) 0 0
\(461\) −47130.4 267290.i −0.221768 1.25771i −0.868768 0.495220i \(-0.835088\pi\)
0.646999 0.762490i \(-0.276024\pi\)
\(462\) 0 0
\(463\) 27622.4 47843.5i 0.128855 0.223183i −0.794378 0.607423i \(-0.792203\pi\)
0.923233 + 0.384240i \(0.125537\pi\)
\(464\) 0 0
\(465\) −1569.83 1317.25i −0.00726019 0.00609202i
\(466\) 0 0
\(467\) 188119. + 325832.i 0.862580 + 1.49403i 0.869430 + 0.494056i \(0.164486\pi\)
−0.00684959 + 0.999977i \(0.502180\pi\)
\(468\) 0 0
\(469\) −50184.5 137881.i −0.228152 0.626842i
\(470\) 0 0
\(471\) −4849.79 855.148i −0.0218615 0.00385478i
\(472\) 0 0
\(473\) −62965.8 + 52834.6i −0.281438 + 0.236154i
\(474\) 0 0
\(475\) 183239. + 125331.i 0.812142 + 0.555484i
\(476\) 0 0
\(477\) 190954. + 227570.i 0.839252 + 1.00018i
\(478\) 0 0
\(479\) −37162.5 + 210759.i −0.161970 + 0.918576i 0.790164 + 0.612895i \(0.209995\pi\)
−0.952134 + 0.305681i \(0.901116\pi\)
\(480\) 0 0
\(481\) −189752. + 69064.2i −0.820157 + 0.298513i
\(482\) 0 0
\(483\) 11068.7 6390.52i 0.0474463 0.0273932i
\(484\) 0 0
\(485\) 22117.2 26358.2i 0.0940256 0.112055i
\(486\) 0 0
\(487\) 56468.3 + 32602.0i 0.238093 + 0.137463i 0.614300 0.789073i \(-0.289439\pi\)
−0.376207 + 0.926536i \(0.622772\pi\)
\(488\) 0 0
\(489\) 10553.3 1860.83i 0.0441337 0.00778197i
\(490\) 0 0
\(491\) 349139. + 127076.i 1.44822 + 0.527110i 0.942094 0.335348i \(-0.108854\pi\)
0.506128 + 0.862458i \(0.331076\pi\)
\(492\) 0 0
\(493\) 170528.i 0.701622i
\(494\) 0 0
\(495\) −9791.37 −0.0399607
\(496\) 0 0
\(497\) −92649.1 + 254551.i −0.375084 + 1.03053i
\(498\) 0 0
\(499\) −24132.3 136861.i −0.0969165 0.549641i −0.994143 0.108071i \(-0.965533\pi\)
0.897227 0.441570i \(-0.145578\pi\)
\(500\) 0 0
\(501\) −10112.3 + 17515.0i −0.0402879 + 0.0697807i
\(502\) 0 0
\(503\) 55026.8 + 46173.0i 0.217490 + 0.182495i 0.745023 0.667039i \(-0.232439\pi\)
−0.527533 + 0.849534i \(0.676883\pi\)
\(504\) 0 0
\(505\) −11170.6 19348.0i −0.0438020 0.0758672i
\(506\) 0 0
\(507\) −2776.19 7627.51i −0.0108002 0.0296734i
\(508\) 0 0
\(509\) −433988. 76523.8i −1.67510 0.295366i −0.746210 0.665710i \(-0.768129\pi\)
−0.928895 + 0.370344i \(0.879240\pi\)
\(510\) 0 0
\(511\) −141851. + 119027.i −0.543238 + 0.455831i
\(512\) 0 0
\(513\) −28060.0 12711.6i −0.106624 0.0483019i
\(514\) 0 0
\(515\) −11647.5 13881.0i −0.0439156 0.0523366i
\(516\) 0 0
\(517\) −16608.3 + 94190.2i −0.0621360 + 0.352391i
\(518\) 0 0
\(519\) −12922.4 + 4703.38i −0.0479743 + 0.0174612i
\(520\) 0 0
\(521\) −261584. + 151025.i −0.963685 + 0.556384i −0.897305 0.441411i \(-0.854478\pi\)
−0.0663798 + 0.997794i \(0.521145\pi\)
\(522\) 0 0
\(523\) −222308. + 264936.i −0.812739 + 0.968584i −0.999906 0.0137438i \(-0.995625\pi\)
0.187167 + 0.982328i \(0.440070\pi\)
\(524\) 0 0
\(525\) −14612.1 8436.29i −0.0530143 0.0306078i
\(526\) 0 0
\(527\) 476863. 84083.8i 1.71701 0.302755i
\(528\) 0 0
\(529\) 59047.8 + 21491.7i 0.211005 + 0.0767995i
\(530\) 0 0
\(531\) 112648.i 0.399516i
\(532\) 0 0
\(533\) 531311. 1.87023
\(534\) 0 0
\(535\) 1565.78 4301.94i 0.00547045 0.0150299i
\(536\) 0 0
\(537\) 4955.04 + 28101.4i 0.0171830 + 0.0974495i
\(538\) 0 0
\(539\) −5796.35 + 10039.6i −0.0199516 + 0.0345571i
\(540\) 0 0
\(541\) 85186.7 + 71480.1i 0.291057 + 0.244225i 0.776610 0.629981i \(-0.216938\pi\)
−0.485554 + 0.874207i \(0.661382\pi\)
\(542\) 0 0
\(543\) −12668.2 21942.0i −0.0429651 0.0744177i
\(544\) 0 0
\(545\) 12732.1 + 34981.1i 0.0428654 + 0.117772i
\(546\) 0 0
\(547\) 185387. + 32688.7i 0.619591 + 0.109251i 0.474628 0.880187i \(-0.342583\pi\)
0.144963 + 0.989437i \(0.453694\pi\)
\(548\) 0 0
\(549\) −29633.9 + 24865.8i −0.0983204 + 0.0825006i
\(550\) 0 0
\(551\) 155393. + 11878.2i 0.511834 + 0.0391242i
\(552\) 0 0
\(553\) −241955. 288350.i −0.791195 0.942910i
\(554\) 0 0
\(555\) −279.630 + 1585.86i −0.000907817 + 0.00514849i
\(556\) 0 0
\(557\) −100049. + 36414.7i −0.322478 + 0.117372i −0.498187 0.867070i \(-0.666001\pi\)
0.175709 + 0.984442i \(0.443778\pi\)
\(558\) 0 0
\(559\) 389760. 225028.i 1.24731 0.720133i
\(560\) 0 0
\(561\) −5129.28 + 6112.83i −0.0162978 + 0.0194230i
\(562\) 0 0
\(563\) −234974. 135662.i −0.741315 0.427998i 0.0812322 0.996695i \(-0.474114\pi\)
−0.822547 + 0.568697i \(0.807448\pi\)
\(564\) 0 0
\(565\) −54300.5 + 9574.64i −0.170101 + 0.0299934i
\(566\) 0 0
\(567\) −317283. 115481.i −0.986916 0.359208i
\(568\) 0 0
\(569\) 31356.3i 0.0968501i −0.998827 0.0484250i \(-0.984580\pi\)
0.998827 0.0484250i \(-0.0154202\pi\)
\(570\) 0 0
\(571\) −208073. −0.638180 −0.319090 0.947724i \(-0.603377\pi\)
−0.319090 + 0.947724i \(0.603377\pi\)
\(572\) 0 0
\(573\) −3687.22 + 10130.6i −0.0112303 + 0.0308549i
\(574\) 0 0
\(575\) 49745.3 + 282120.i 0.150458 + 0.853292i
\(576\) 0 0
\(577\) −113879. + 197245.i −0.342053 + 0.592454i −0.984814 0.173613i \(-0.944456\pi\)
0.642761 + 0.766067i \(0.277789\pi\)
\(578\) 0 0
\(579\) −5856.19 4913.93i −0.0174686 0.0146579i
\(580\) 0 0
\(581\) −181586. 314517.i −0.537936 0.931733i
\(582\) 0 0
\(583\) −48190.3 132402.i −0.141782 0.389544i
\(584\) 0 0
\(585\) 52797.2 + 9309.57i 0.154276 + 0.0272031i
\(586\) 0 0
\(587\) 39581.8 33213.1i 0.114873 0.0963903i −0.583542 0.812083i \(-0.698333\pi\)
0.698415 + 0.715693i \(0.253889\pi\)
\(588\) 0 0
\(589\) −43405.2 440396.i −0.125115 1.26944i
\(590\) 0 0
\(591\) −18551.7 22109.1i −0.0531140 0.0632988i
\(592\) 0 0
\(593\) 38149.6 216357.i 0.108488 0.615264i −0.881282 0.472590i \(-0.843319\pi\)
0.989770 0.142673i \(-0.0455699\pi\)
\(594\) 0 0
\(595\) −61150.1 + 22256.8i −0.172728 + 0.0628679i
\(596\) 0 0
\(597\) 29576.9 17076.2i 0.0829858 0.0479119i
\(598\) 0 0
\(599\) 172539. 205624.i 0.480877 0.573086i −0.469996 0.882668i \(-0.655745\pi\)
0.950873 + 0.309582i \(0.100189\pi\)
\(600\) 0 0
\(601\) 352411. + 203465.i 0.975664 + 0.563300i 0.900958 0.433906i \(-0.142865\pi\)
0.0747060 + 0.997206i \(0.476198\pi\)
\(602\) 0 0
\(603\) −224322. + 39554.1i −0.616933 + 0.108782i
\(604\) 0 0
\(605\) −39224.9 14276.7i −0.107164 0.0390047i
\(606\) 0 0
\(607\) 169315.i 0.459535i −0.973246 0.229768i \(-0.926203\pi\)
0.973246 0.229768i \(-0.0737966\pi\)
\(608\) 0 0
\(609\) −11844.7 −0.0319366
\(610\) 0 0
\(611\) 179111. 492102.i 0.479776 1.31817i
\(612\) 0 0
\(613\) 21097.6 + 119651.i 0.0561452 + 0.318415i 0.999926 0.0121563i \(-0.00386957\pi\)
−0.943781 + 0.330572i \(0.892758\pi\)
\(614\) 0 0
\(615\) 2118.51 3669.37i 0.00560120 0.00970156i
\(616\) 0 0
\(617\) −105120. 88206.3i −0.276131 0.231702i 0.494196 0.869351i \(-0.335463\pi\)
−0.770327 + 0.637649i \(0.779907\pi\)
\(618\) 0 0
\(619\) 26097.4 + 45202.1i 0.0681108 + 0.117971i 0.898070 0.439853i \(-0.144970\pi\)
−0.829959 + 0.557825i \(0.811636\pi\)
\(620\) 0 0
\(621\) −13595.6 37353.7i −0.0352546 0.0968613i
\(622\) 0 0
\(623\) 29099.5 + 5131.03i 0.0749738 + 0.0132199i
\(624\) 0 0
\(625\) 284896. 239056.i 0.729333 0.611983i
\(626\) 0 0
\(627\) 5213.01 + 5099.82i 0.0132603 + 0.0129724i
\(628\) 0 0
\(629\) −244582. 291481.i −0.618191 0.736731i
\(630\) 0 0
\(631\) −23375.9 + 132571.i −0.0587097 + 0.332960i −0.999989 0.00466924i \(-0.998514\pi\)
0.941279 + 0.337629i \(0.109625\pi\)
\(632\) 0 0
\(633\) −24765.3 + 9013.83i −0.0618068 + 0.0224958i
\(634\) 0 0
\(635\) −4215.90 + 2434.05i −0.0104554 + 0.00603645i
\(636\) 0 0
\(637\) 40800.7 48624.4i 0.100552 0.119833i
\(638\) 0 0
\(639\) 364186. + 210263.i 0.891911 + 0.514945i
\(640\) 0 0
\(641\) −204371. + 36036.2i −0.497398 + 0.0877046i −0.416719 0.909036i \(-0.636820\pi\)
−0.0806789 + 0.996740i \(0.525709\pi\)
\(642\) 0 0
\(643\) −198736. 72334.0i −0.480679 0.174953i 0.0903050 0.995914i \(-0.471216\pi\)
−0.570984 + 0.820961i \(0.693438\pi\)
\(644\) 0 0
\(645\) 3589.04i 0.00862699i
\(646\) 0 0
\(647\) −212208. −0.506936 −0.253468 0.967344i \(-0.581571\pi\)
−0.253468 + 0.967344i \(0.581571\pi\)
\(648\) 0 0
\(649\) −18273.5 + 50206.0i −0.0433842 + 0.119197i
\(650\) 0 0
\(651\) 5840.35 + 33122.3i 0.0137809 + 0.0781552i
\(652\) 0 0
\(653\) 327740. 567662.i 0.768604 1.33126i −0.169716 0.985493i \(-0.554285\pi\)
0.938320 0.345769i \(-0.112382\pi\)
\(654\) 0 0
\(655\) −4650.87 3902.55i −0.0108406 0.00909631i
\(656\) 0 0
\(657\) 143731. + 248950.i 0.332982 + 0.576741i
\(658\) 0 0
\(659\) −60523.7 166288.i −0.139365 0.382903i 0.850300 0.526298i \(-0.176420\pi\)
−0.989666 + 0.143395i \(0.954198\pi\)
\(660\) 0 0
\(661\) −29843.7 5262.25i −0.0683045 0.0120439i 0.139391 0.990237i \(-0.455485\pi\)
−0.207696 + 0.978193i \(0.566596\pi\)
\(662\) 0 0
\(663\) 33470.2 28084.8i 0.0761432 0.0638917i
\(664\) 0 0
\(665\) 16022.0 + 57273.1i 0.0362305 + 0.129511i
\(666\) 0 0
\(667\) 129268. + 154056.i 0.290563 + 0.346279i
\(668\) 0 0
\(669\) −6936.22 + 39337.2i −0.0154978 + 0.0878925i
\(670\) 0 0
\(671\) 17241.2 6275.27i 0.0382932 0.0139376i
\(672\) 0 0
\(673\) −763517. + 440817.i −1.68573 + 0.973258i −0.728010 + 0.685566i \(0.759555\pi\)
−0.957723 + 0.287692i \(0.907112\pi\)
\(674\) 0 0
\(675\) −33731.1 + 40199.1i −0.0740325 + 0.0882285i
\(676\) 0 0
\(677\) 93382.7 + 53914.5i 0.203746 + 0.117633i 0.598402 0.801196i \(-0.295803\pi\)
−0.394656 + 0.918829i \(0.629136\pi\)
\(678\) 0 0
\(679\) −556138. + 98062.1i −1.20627 + 0.212697i
\(680\) 0 0
\(681\) 6654.34 + 2421.98i 0.0143486 + 0.00522248i
\(682\) 0 0
\(683\) 275330.i 0.590217i 0.955464 + 0.295109i \(0.0953559\pi\)
−0.955464 + 0.295109i \(0.904644\pi\)
\(684\) 0 0
\(685\) −107012. −0.228062
\(686\) 0 0
\(687\) 3539.27 9724.06i 0.00749894 0.0206032i
\(688\) 0 0
\(689\) 133966. + 759757.i 0.282199 + 1.60043i
\(690\) 0 0
\(691\) 248965. 431220.i 0.521413 0.903113i −0.478277 0.878209i \(-0.658739\pi\)
0.999690 0.0249044i \(-0.00792815\pi\)
\(692\) 0 0
\(693\) 123102. + 103295.i 0.256330 + 0.215087i
\(694\) 0 0
\(695\) −22323.6 38665.6i −0.0462162 0.0800489i
\(696\) 0 0
\(697\) 342417. + 940783.i 0.704839 + 1.93653i
\(698\) 0 0
\(699\) 45942.3 + 8100.87i 0.0940283 + 0.0165797i
\(700\) 0 0
\(701\) 707525. 593684.i 1.43981 1.20815i 0.500197 0.865912i \(-0.333261\pi\)
0.939615 0.342234i \(-0.111184\pi\)
\(702\) 0 0
\(703\) −282647. + 202571.i −0.571919 + 0.409889i
\(704\) 0 0
\(705\) −2684.41 3199.16i −0.00540097 0.00643662i
\(706\) 0 0
\(707\) −63671.5 + 361099.i −0.127382 + 0.722417i
\(708\) 0 0
\(709\) 844331. 307311.i 1.67966 0.611345i 0.686394 0.727230i \(-0.259193\pi\)
0.993263 + 0.115885i \(0.0369705\pi\)
\(710\) 0 0
\(711\) −506058. + 292172.i −1.00106 + 0.577963i
\(712\) 0 0
\(713\) 367060. 437445.i 0.722034 0.860487i
\(714\) 0 0
\(715\) −22021.0 12713.8i −0.0430749 0.0248693i
\(716\) 0 0
\(717\) 25085.6 4423.27i 0.0487962 0.00860409i
\(718\) 0 0
\(719\) −697825. 253987.i −1.34986 0.491309i −0.436955 0.899483i \(-0.643943\pi\)
−0.912904 + 0.408175i \(0.866165\pi\)
\(720\) 0 0
\(721\) 297396.i 0.572090i
\(722\) 0 0
\(723\) 19519.1 0.0373407
\(724\) 0 0
\(725\) 90801.0 249474.i 0.172749 0.474623i
\(726\) 0 0
\(727\) 10629.1 + 60280.8i 0.0201108 + 0.114054i 0.993211 0.116330i \(-0.0371130\pi\)
−0.973100 + 0.230384i \(0.926002\pi\)
\(728\) 0 0
\(729\) −260256. + 450777.i −0.489718 + 0.848216i
\(730\) 0 0
\(731\) 649644. + 545116.i 1.21574 + 1.02013i
\(732\) 0 0
\(733\) 313840. + 543587.i 0.584118 + 1.01172i 0.994985 + 0.100027i \(0.0318929\pi\)
−0.410866 + 0.911696i \(0.634774\pi\)
\(734\) 0 0
\(735\) −173.127 475.662i −0.000320472 0.000880488i
\(736\) 0 0
\(737\) 106394. + 18760.2i 0.195877 + 0.0345384i
\(738\) 0 0
\(739\) −681044. + 571463.i −1.24706 + 1.04640i −0.250118 + 0.968215i \(0.580469\pi\)
−0.996939 + 0.0781890i \(0.975086\pi\)
\(740\) 0 0
\(741\) −23260.8 32455.8i −0.0423632 0.0591093i
\(742\) 0 0
\(743\) −202266. 241051.i −0.366392 0.436649i 0.551078 0.834453i \(-0.314217\pi\)
−0.917470 + 0.397805i \(0.869772\pi\)
\(744\) 0 0
\(745\) 10348.3 58688.3i 0.0186448 0.105740i
\(746\) 0 0
\(747\) −529787. + 192827.i −0.949424 + 0.345562i
\(748\) 0 0
\(749\) −65069.6 + 37568.0i −0.115988 + 0.0669659i
\(750\) 0 0
\(751\) 9165.30 10922.8i 0.0162505 0.0193666i −0.757858 0.652420i \(-0.773754\pi\)
0.774108 + 0.633053i \(0.218198\pi\)
\(752\) 0 0
\(753\) 46724.6 + 26976.5i 0.0824054 + 0.0475768i
\(754\) 0 0
\(755\) 75429.3 13300.2i 0.132326 0.0233327i
\(756\) 0 0
\(757\) −644273. 234496.i −1.12429 0.409208i −0.288073 0.957608i \(-0.593015\pi\)
−0.836216 + 0.548401i \(0.815237\pi\)
\(758\) 0 0
\(759\) 9410.56i 0.0163355i
\(760\) 0 0
\(761\) −184923. −0.319317 −0.159658 0.987172i \(-0.551039\pi\)
−0.159658 + 0.987172i \(0.551039\pi\)
\(762\) 0 0
\(763\) 208963. 574120.i 0.358938 0.986174i
\(764\) 0 0
\(765\) 17542.2 + 99486.9i 0.0299752 + 0.169998i
\(766\) 0 0
\(767\) 146270. 253347.i 0.248636 0.430651i
\(768\) 0 0
\(769\) 585144. + 490994.i 0.989486 + 0.830277i 0.985493 0.169715i \(-0.0542846\pi\)
0.00399290 + 0.999992i \(0.498729\pi\)
\(770\) 0 0
\(771\) −546.471 946.516i −0.000919303 0.00159228i
\(772\) 0 0
\(773\) 178470. + 490342.i 0.298680 + 0.820616i 0.994721 + 0.102615i \(0.0327209\pi\)
−0.696041 + 0.718002i \(0.745057\pi\)
\(774\) 0 0
\(775\) −742396. 130904.i −1.23604 0.217947i
\(776\) 0 0
\(777\) 20245.9 16988.3i 0.0335347 0.0281390i
\(778\) 0 0
\(779\) 881136. 246496.i 1.45200 0.406195i
\(780\) 0 0
\(781\) −128205. 152789.i −0.210186 0.250490i
\(782\) 0 0
\(783\) −6396.97 + 36279.0i −0.0104340 + 0.0591742i
\(784\) 0 0
\(785\) 27786.2 10113.3i 0.0450910 0.0164118i
\(786\) 0 0
\(787\) −519955. + 300196.i −0.839491 + 0.484680i −0.857091 0.515165i \(-0.827731\pi\)
0.0176001 + 0.999845i \(0.494397\pi\)
\(788\) 0 0
\(789\) −25969.3 + 30949.0i −0.0417164 + 0.0497156i
\(790\) 0 0
\(791\) 783703. + 452471.i 1.25256 + 0.723166i
\(792\) 0