Properties

Label 76.5.j.a.41.4
Level $76$
Weight $5$
Character 76.41
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 41.4
Character \(\chi\) \(=\) 76.41
Dual form 76.5.j.a.13.4

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

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\)

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 0.929263 0.369419i \(-0.120443\pi\)
−0.949315 + 0.314327i \(0.898221\pi\)
\(4\) 0 0
\(5\) −0.550159 + 3.12011i −0.0220064 + 0.124804i −0.993832 0.110897i \(-0.964628\pi\)
0.971826 + 0.235701i \(0.0757387\pi\)
\(6\) 0 0
\(7\) −25.9990 45.0316i −0.530592 0.919013i −0.999363 0.0356926i \(-0.988636\pi\)
0.468771 0.883320i \(-0.344697\pi\)
\(8\) 0 0
\(9\) 61.8363 51.8868i 0.763411 0.640578i
\(10\) 0 0
\(11\) −19.1428 + 33.1563i −0.158205 + 0.274019i −0.934221 0.356693i \(-0.883904\pi\)
0.776016 + 0.630713i \(0.217237\pi\)
\(12\) 0 0
\(13\) 71.6974 196.987i 0.424245 1.16560i −0.525010 0.851096i \(-0.675939\pi\)
0.949255 0.314507i \(-0.101839\pi\)
\(14\) 0 0
\(15\) 1.64632 0.290291i 0.00731700 0.00129018i
\(16\) 0 0
\(17\) −302.594 253.907i −1.04704 0.878570i −0.0542595 0.998527i \(-0.517280\pi\)
−0.992779 + 0.119957i \(0.961724\pi\)
\(18\) 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 −0.960668 0.277700i \(-0.910428\pi\)
0.807754 0.589520i \(-0.200683\pi\)
\(24\) 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 0.905363 0.424639i \(-0.139599\pi\)
−0.575402 + 0.817870i \(0.695155\pi\)
\(30\) 0 0
\(31\) −1061.61 + 612.923i −1.10470 + 0.637797i −0.937451 0.348118i \(-0.886821\pi\)
−0.167246 + 0.985915i \(0.553487\pi\)
\(32\) 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 \(-0.885564\pi\)
0.936069 0.351817i \(-0.114436\pi\)
\(38\) 0 0
\(39\) −110.611 −0.0727224
\(40\) 0 0
\(41\) 866.860 + 2381.68i 0.515681 + 1.41682i 0.875235 + 0.483698i \(0.160707\pi\)
−0.359554 + 0.933124i \(0.617071\pi\)
\(42\) 0 0
\(43\) −372.808 + 2114.30i −0.201627 + 1.14348i 0.701034 + 0.713128i \(0.252722\pi\)
−0.902660 + 0.430354i \(0.858389\pi\)
\(44\) 0 0
\(45\) 127.873 + 221.482i 0.0631470 + 0.109374i
\(46\) 0 0
\(47\) −1913.69 + 1605.78i −0.866316 + 0.726925i −0.963319 0.268359i \(-0.913519\pi\)
0.0970031 + 0.995284i \(0.469074\pi\)
\(48\) 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 0.513919 0.857839i \(-0.328193\pi\)
0.776324 + 0.630334i \(0.217082\pi\)
\(54\) 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 −0.879342 0.476191i \(-0.842017\pi\)
0.621652 + 0.783293i \(0.286462\pi\)
\(60\) 0 0
\(61\) −83.2176 471.950i −0.0223643 0.126834i 0.971582 0.236705i \(-0.0760675\pi\)
−0.993946 + 0.109871i \(0.964956\pi\)
\(62\) 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 0.525191 0.850984i \(-0.323994\pi\)
−0.929254 + 0.369441i \(0.879549\pi\)
\(68\) 0 0
\(69\) −212.868 + 122.899i −0.0447107 + 0.0258138i
\(70\) 0 0
\(71\) 5130.43 + 904.634i 1.01774 + 0.179455i 0.657540 0.753419i \(-0.271597\pi\)
0.360201 + 0.932875i \(0.382708\pi\)
\(72\) 0 0
\(73\) 3346.39 1217.99i 0.627959 0.228558i −0.00838368 0.999965i \(-0.502669\pi\)
0.636343 + 0.771406i \(0.280446\pi\)
\(74\) 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 −0.963875 0.266355i \(-0.914181\pi\)
0.567161 0.823607i \(-0.308042\pi\)
\(80\) 0 0
\(81\) 1127.57 6394.77i 0.171860 0.974664i
\(82\) 0 0
\(83\) −3492.18 6048.63i −0.506921 0.878012i −0.999968 0.00800975i \(-0.997450\pi\)
0.493047 0.870003i \(-0.335883\pi\)
\(84\) 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 −0.951356 0.308093i \(-0.900309\pi\)
0.926819 + 0.375507i \(0.122531\pi\)
\(90\) 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 −0.254625 0.967040i \(-0.581952\pi\)
0.996564 + 0.0828316i \(0.0263964\pi\)
\(98\) 0 0
\(99\) 536.656 + 3043.53i 0.0547552 + 0.310532i
\(100\) 0 0
\(101\) 6626.34 + 2411.79i 0.649578 + 0.236427i 0.645730 0.763566i \(-0.276553\pi\)
0.00384764 + 0.999993i \(0.498775\pi\)
\(102\) 0 0
\(103\) 4953.12 + 2859.68i 0.466879 + 0.269553i 0.714932 0.699194i \(-0.246458\pi\)
−0.248053 + 0.968746i \(0.579791\pi\)
\(104\) 0 0
\(105\) −55.8751 66.5894i −0.00506804 0.00603985i
\(106\) 0 0
\(107\) 1251.39 722.488i 0.109301 0.0631049i −0.444353 0.895852i \(-0.646566\pi\)
0.553654 + 0.832747i \(0.313233\pi\)
\(108\) 0 0
\(109\) −11571.3 2040.33i −0.973931 0.171730i −0.336032 0.941850i \(-0.609085\pi\)
−0.637899 + 0.770120i \(0.720196\pi\)
\(110\) 0 0
\(111\) −477.619 + 173.839i −0.0387646 + 0.0141092i
\(112\) 0 0
\(113\) 17403.4i 1.36294i 0.731845 + 0.681471i \(0.238659\pi\)
−0.731845 + 0.681471i \(0.761341\pi\)
\(114\) 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 −0.954917 0.296872i \(-0.904057\pi\)
0.922335 + 0.386392i \(0.126279\pi\)
\(128\) 0 0
\(129\) 1115.61 196.712i 0.0670398 0.0118209i
\(130\) 0 0
\(131\) 1467.97 + 1231.77i 0.0855409 + 0.0717774i 0.684555 0.728961i \(-0.259996\pi\)
−0.599014 + 0.800738i \(0.704441\pi\)
\(132\) 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 0.585930 + 0.810362i \(0.300729\pi\)
−0.273434 + 0.961891i \(0.588160\pi\)
\(138\) 0 0
\(139\) 13242.3 + 4819.79i 0.685382 + 0.249459i 0.661157 0.750248i \(-0.270066\pi\)
0.0242252 + 0.999707i \(0.492288\pi\)
\(140\) 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 0.0882604 0.996097i \(-0.471869\pi\)
0.707890 + 0.706322i \(0.249647\pi\)
\(150\) 0 0
\(151\) 24175.2i 1.06027i −0.847913 0.530135i \(-0.822141\pi\)
0.847913 0.530135i \(-0.177859\pi\)
\(152\) 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 −0.934123 0.356951i \(-0.883816\pi\)
0.999873 0.0159357i \(-0.00507269\pi\)
\(158\) 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 −0.991376 0.131050i \(-0.958165\pi\)
0.609180 + 0.793032i \(0.291499\pi\)
\(164\) 0 0
\(165\) −21.8903 + 60.1431i −0.000804051 + 0.00220911i
\(166\) 0 0
\(167\) 37747.3 6655.86i 1.35348 0.238655i 0.550588 0.834777i \(-0.314403\pi\)
0.802894 + 0.596121i \(0.203292\pi\)
\(168\) 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 −0.409751 0.912198i \(-0.634384\pi\)
0.969492 + 0.245124i \(0.0788287\pi\)
\(174\) 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 0.999090 0.0426605i \(-0.0135834\pi\)
0.462600 + 0.886567i \(0.346917\pi\)
\(180\) 0 0
\(181\) −30865.0 36783.5i −0.942127 1.12278i −0.992277 0.124042i \(-0.960414\pi\)
0.0501495 0.998742i \(-0.484030\pi\)
\(182\) 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 0.855236 0.518240i \(-0.173412\pi\)
−0.988266 + 0.152740i \(0.951190\pi\)
\(194\) 0 0
\(195\) 60.8535 345.118i 0.00160036 0.00907607i
\(196\) 0 0
\(197\) −27348.9 47369.8i −0.704706 1.22059i −0.966797 0.255544i \(-0.917745\pi\)
0.262091 0.965043i \(-0.415588\pi\)
\(198\) 0 0
\(199\) −49582.7 + 41604.8i −1.25206 + 1.05060i −0.255574 + 0.966790i \(0.582264\pi\)
−0.996482 + 0.0838097i \(0.973291\pi\)
\(200\) 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 −0.273609 0.961841i \(-0.588217\pi\)
0.994740 + 0.102430i \(0.0326619\pi\)
\(212\) 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 0.862205 0.506559i \(-0.169083\pi\)
0.636955 + 0.770901i \(0.280194\pi\)
\(224\) 0 0
\(225\) 46647.0 16978.1i 0.921423 0.335370i
\(226\) 0 0
\(227\) 13420.6i 0.260448i 0.991485 + 0.130224i \(0.0415697\pi\)
−0.991485 + 0.130224i \(0.958430\pi\)
\(228\) 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 0.430256 + 0.902707i \(0.358423\pi\)
−0.713053 + 0.701110i \(0.752688\pi\)
\(234\) 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 −0.996190 0.0872061i \(-0.972206\pi\)
0.573618 + 0.819123i \(0.305539\pi\)
\(240\) 0 0
\(241\) −12652.2 + 34761.5i −0.217836 + 0.598501i −0.999688 0.0249635i \(-0.992053\pi\)
0.781852 + 0.623464i \(0.214275\pi\)
\(242\) 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 0.716384 + 0.697706i \(0.245796\pi\)
−0.434551 + 0.900647i \(0.643093\pi\)
\(252\) 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 0.755871 0.654720i \(-0.227214\pi\)
−0.776029 + 0.630697i \(0.782769\pi\)
\(258\) 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 0.235251 0.971935i \(-0.424409\pi\)
0.804960 + 0.593329i \(0.202187\pi\)
\(264\) 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 −0.810626 0.585565i \(-0.800873\pi\)
0.244582 0.969629i \(-0.421349\pi\)
\(270\) 0 0
\(271\) −23494.3 + 133243.i −0.319908 + 1.81429i 0.223371 + 0.974733i \(0.428294\pi\)
−0.543279 + 0.839552i \(0.682817\pi\)
\(272\) 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 −0.720690 0.693257i \(-0.756175\pi\)
0.960724 + 0.277507i \(0.0895083\pi\)
\(278\) 0 0
\(279\) −33843.6 + 92984.6i −0.434779 + 1.19455i
\(280\) 0 0
\(281\) 28595.8 5042.22i 0.362152 0.0638571i 0.0103881 0.999946i \(-0.496693\pi\)
0.351763 + 0.936089i \(0.385582\pi\)
\(282\) 0 0
\(283\) −29691.9 24914.4i −0.370736 0.311084i 0.438317 0.898821i \(-0.355575\pi\)
−0.809053 + 0.587736i \(0.800019\pi\)
\(284\) 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 0.644322 0.764754i \(-0.277140\pi\)
−0.340136 + 0.940376i \(0.610473\pi\)
\(294\) 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 −0.661020 0.750368i \(-0.729876\pi\)
0.0240437 0.999711i \(-0.492346\pi\)
\(308\) 0 0
\(309\) 524.040 2971.98i 0.00548842 0.0311264i
\(310\) 0 0
\(311\) −59834.2 103636.i −0.618626 1.07149i −0.989737 0.142904i \(-0.954356\pi\)
0.371110 0.928589i \(-0.378977\pi\)
\(312\) 0 0
\(313\) −59356.0 + 49805.6i −0.605865 + 0.508381i −0.893325 0.449412i \(-0.851634\pi\)
0.287460 + 0.957793i \(0.407189\pi\)
\(314\) 0 0
\(315\) 6649.13 11516.6i 0.0670106 0.116066i
\(316\) 0 0
\(317\) 50069.0 137564.i 0.498254 1.36894i −0.394707 0.918807i \(-0.629154\pi\)
0.892961 0.450134i \(-0.148624\pi\)
\(318\) 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 0.997171 + 0.0751687i \(0.0239495\pi\)
0.563683 + 0.825991i \(0.309384\pi\)
\(332\) 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 0.376873 0.926265i \(-0.376999\pi\)
0.0373435 + 0.999302i \(0.488110\pi\)
\(338\) 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 −0.629013 0.777394i \(-0.716541\pi\)
0.856964 0.515377i \(-0.172348\pi\)
\(348\) 0 0
\(349\) −19980.7 34607.6i −0.164044 0.284133i 0.772271 0.635293i \(-0.219121\pi\)
−0.936315 + 0.351160i \(0.885787\pi\)
\(350\) 0 0
\(351\) −13703.1 + 11498.3i −0.111226 + 0.0933295i
\(352\) 0 0
\(353\) −102732. + 177938.i −0.824438 + 1.42797i 0.0779095 + 0.996960i \(0.475175\pi\)
−0.902348 + 0.431009i \(0.858158\pi\)
\(354\) 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 0.642606 0.766197i \(-0.277853\pi\)
−0.642969 + 0.765892i \(0.722298\pi\)
\(360\) 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 0.495452 0.868635i \(-0.335002\pi\)
−0.178810 + 0.983884i \(0.557225\pi\)
\(368\) 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 −0.507824 0.861461i \(-0.669550\pi\)
0.492135 + 0.870519i \(0.336217\pi\)
\(374\) 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 \(0.164454\pi\)
−0.869480 + 0.493968i \(0.835546\pi\)
\(380\) 0 0
\(381\) 810.750 0.00558518
\(382\) 0 0
\(383\) −52054.1 143018.i −0.354860 0.974971i −0.980786 0.195088i \(-0.937501\pi\)
0.625925 0.779883i \(-0.284721\pi\)
\(384\) 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 −0.485638 + 0.874160i \(0.661413\pi\)
−0.945210 + 0.326464i \(0.894143\pi\)
\(390\) 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 0.509276 0.860603i \(-0.329913\pi\)
−0.759094 + 0.650981i \(0.774358\pi\)
\(398\) 0 0
\(399\) 2458.36 + 9594.74i 0.0154419 + 0.0602681i
\(400\) 0 0
\(401\) 11830.4 14098.9i 0.0735717 0.0876794i −0.728003 0.685574i \(-0.759551\pi\)
0.801575 + 0.597894i \(0.203996\pi\)
\(402\) 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 0.995305 0.0967849i \(-0.0308559\pi\)
−0.268147 + 0.963378i \(0.586411\pi\)
\(410\) 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 0.989797 0.142482i \(-0.0455083\pi\)
−0.849814 + 0.527082i \(0.823286\pi\)
\(422\) 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 −0.903156 0.429313i \(-0.858756\pi\)
0.967815 + 0.251664i \(0.0809778\pi\)
\(432\) 0 0
\(433\) 241750. 42627.0i 1.28941 0.227357i 0.513437 0.858127i \(-0.328372\pi\)
0.775970 + 0.630770i \(0.217261\pi\)
\(434\) 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 −0.564124 0.825690i \(-0.690786\pi\)
0.911105 + 0.412174i \(0.135230\pi\)
\(440\) 0 0
\(441\) 4244.32 + 24070.8i 0.0218238 + 0.123769i
\(442\) 0 0
\(443\) 103744. + 37759.7i 0.528634 + 0.192407i 0.592529 0.805549i \(-0.298130\pi\)
−0.0638940 + 0.997957i \(0.520352\pi\)
\(444\) 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 −0.996582 0.0826112i \(-0.973674\pi\)
−0.426748 + 0.904371i \(0.640341\pi\)
\(450\) 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 0.646999 + 0.762490i \(0.276024\pi\)
−0.868768 + 0.495220i \(0.835088\pi\)
\(462\) 0 0
\(463\) 27622.4 + 47843.5i 0.128855 + 0.223183i 0.923233 0.384240i \(-0.125537\pi\)
−0.794378 + 0.607423i \(0.792203\pi\)
\(464\) 0 0
\(465\) −1569.83 + 1317.25i −0.00726019 + 0.00609202i
\(466\) 0 0
\(467\) 188119. 325832.i 0.862580 1.49403i −0.00684959 0.999977i \(-0.502180\pi\)
0.869430 0.494056i \(-0.164486\pi\)
\(468\) 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 −0.952134 0.305681i \(-0.901116\pi\)
0.790164 0.612895i \(-0.209995\pi\)
\(480\) 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 −0.376207 0.926536i \(-0.622772\pi\)
0.614300 + 0.789073i \(0.289439\pi\)
\(488\) 0 0
\(489\) 10553.3 + 1860.83i 0.0441337 + 0.00778197i
\(490\) 0 0
\(491\) 349139. 127076.i 1.44822 0.527110i 0.506128 0.862458i \(-0.331076\pi\)
0.942094 + 0.335348i \(0.108854\pi\)
\(492\) 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 0.897227 + 0.441570i \(0.145578\pi\)
−0.994143 + 0.108071i \(0.965533\pi\)
\(500\) 0 0
\(501\) −10112.3 17515.0i −0.0402879 0.0697807i
\(502\) 0 0
\(503\) 55026.8 46173.0i 0.217490 0.182495i −0.527533 0.849534i \(-0.676883\pi\)
0.745023 + 0.667039i \(0.232439\pi\)
\(504\) 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 −0.928895 0.370344i \(-0.879240\pi\)
−0.746210 + 0.665710i \(0.768129\pi\)
\(510\) 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 −0.0663798 0.997794i \(-0.521145\pi\)
−0.897305 + 0.441411i \(0.854478\pi\)
\(522\) 0 0
\(523\) −222308. 264936.i −0.812739 0.968584i 0.187167 0.982328i \(-0.440070\pi\)
−0.999906 + 0.0137438i \(0.995625\pi\)
\(524\) 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 −0.485554 0.874207i \(-0.661382\pi\)
0.776610 + 0.629981i \(0.216938\pi\)
\(542\) 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 0.144963 0.989437i \(-0.453694\pi\)
0.474628 + 0.880187i \(0.342583\pi\)
\(548\) 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 0.175709 0.984442i \(-0.443778\pi\)
−0.498187 + 0.867070i \(0.666001\pi\)
\(558\) 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 −0.822547 0.568697i \(-0.807448\pi\)
0.0812322 + 0.996695i \(0.474114\pi\)
\(564\) 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 \(0.0154202\pi\)
−0.998827 + 0.0484250i \(0.984580\pi\)
\(570\) 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 0.642761 0.766067i \(-0.277789\pi\)
−0.984814 + 0.173613i \(0.944456\pi\)
\(578\) 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 0.698415 0.715693i \(-0.253889\pi\)
−0.583542 + 0.812083i \(0.698333\pi\)
\(588\) 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 0.989770 + 0.142673i \(0.0455699\pi\)
−0.881282 + 0.472590i \(0.843319\pi\)
\(594\) 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 0.950873 0.309582i \(-0.100189\pi\)
−0.469996 + 0.882668i \(0.655745\pi\)
\(600\) 0 0
\(601\) 352411. 203465.i 0.975664 0.563300i 0.0747060 0.997206i \(-0.476198\pi\)
0.900958 + 0.433906i \(0.142865\pi\)
\(602\) 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 \(0.0737966\pi\)
−0.973246 + 0.229768i \(0.926203\pi\)
\(608\) 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 −0.943781 0.330572i \(-0.892758\pi\)
0.999926 + 0.0121563i \(0.00386957\pi\)
\(614\) 0 0
\(615\) 2118.51 + 3669.37i 0.00560120 + 0.00970156i
\(616\) 0 0
\(617\) −105120. + 88206.3i −0.276131 + 0.231702i −0.770327 0.637649i \(-0.779907\pi\)
0.494196 + 0.869351i \(0.335463\pi\)
\(618\) 0 0
\(619\) 26097.4 45202.1i 0.0681108 0.117971i −0.829959 0.557825i \(-0.811636\pi\)
0.898070 + 0.439853i \(0.144970\pi\)
\(620\) 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 0.941279 0.337629i \(-0.109625\pi\)
−0.999989 + 0.00466924i \(0.998514\pi\)
\(632\) 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 −0.0806789 0.996740i \(-0.525709\pi\)
−0.416719 + 0.909036i \(0.636820\pi\)
\(642\) 0 0
\(643\) −198736. + 72334.0i −0.480679 + 0.174953i −0.570984 0.820961i \(-0.693438\pi\)
0.0903050 + 0.995914i \(0.471216\pi\)
\(644\) 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 0.938320 + 0.345769i \(0.112382\pi\)
−0.169716 + 0.985493i \(0.554285\pi\)
\(654\) 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 −0.989666 0.143395i \(-0.954198\pi\)
0.850300 + 0.526298i \(0.176420\pi\)
\(660\) 0 0
\(661\) −29843.7 + 5262.25i −0.0683045 + 0.0120439i −0.207696 0.978193i \(-0.566596\pi\)
0.139391 + 0.990237i \(0.455485\pi\)
\(662\) 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 −0.957723 0.287692i \(-0.907112\pi\)
−0.728010 0.685566i \(-0.759555\pi\)
\(674\) 0 0
\(675\) −33731.1 40199.1i −0.0740325 0.0882285i
\(676\) 0 0
\(677\) 93382.7 53914.5i 0.203746 0.117633i −0.394656 0.918829i \(-0.629136\pi\)
0.598402 + 0.801196i \(0.295803\pi\)
\(678\) 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 \(-0.904644\pi\)
0.955464 0.295109i \(-0.0953559\pi\)
\(684\) 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 0.999690 + 0.0249044i \(0.00792815\pi\)
−0.478277 + 0.878209i \(0.658739\pi\)
\(692\) 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 0.939615 + 0.342234i \(0.111184\pi\)
0.500197 + 0.865912i \(0.333261\pi\)
\(702\) 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 0.993263 0.115885i \(-0.0369705\pi\)
0.686394 + 0.727230i \(0.259193\pi\)
\(710\) 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 −0.912904 0.408175i \(-0.866165\pi\)
−0.436955 + 0.899483i \(0.643943\pi\)
\(720\) 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 −0.973100 0.230384i \(-0.926002\pi\)
0.993211 + 0.116330i \(0.0371130\pi\)
\(728\) 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 −0.410866 0.911696i \(-0.634774\pi\)
0.994985 0.100027i \(-0.0318929\pi\)
\(734\) 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 −0.996939 0.0781890i \(-0.975086\pi\)
−0.250118 0.968215i \(-0.580469\pi\)
\(740\) 0 0
\(741\) −23260.8 + 32455.8i −0.0423632 + 0.0591093i
\(742\) 0 0
\(743\) −202266. + 241051.i −0.366392 + 0.436649i −0.917470 0.397805i \(-0.869772\pi\)
0.551078 + 0.834453i \(0.314217\pi\)
\(744\) 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 0.774108 0.633053i \(-0.218198\pi\)
−0.757858 + 0.652420i \(0.773754\pi\)
\(752\) 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 −0.836216 0.548401i \(-0.815237\pi\)
−0.288073 + 0.957608i \(0.593015\pi\)
\(758\) 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 0.00399290 0.999992i \(-0.498729\pi\)
0.985493 + 0.169715i \(0.0542846\pi\)
\(770\) 0 0
\(771\) −546.471 + 946.516i −0.000919303 + 0.00159228i
\(772\) 0 0
\(773\) 178470. 490342.i 0.298680 0.820616i −0.696041 0.718002i \(-0.745057\pi\)
0.994721 0.102615i \(-0.0327209\pi\)
\(774\) 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 0.0176001 0.999845i \(-0.494397\pi\)
−0.857091 + 0.515165i \(0.827731\pi\)
\(788\) 0 0
\(789\) −25969.3 30949.0i −0.0417164 0.0497156i
\(790\) 0 0
\(791\) 783703. 452471.i 1.25256 0.723166i