Properties

Label 117.4.g.f.55.6
Level $117$
Weight $4$
Character 117.55
Analytic conductor $6.903$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 52 x^{14} + 1899 x^{12} + 33440 x^{10} + 424113 x^{8} + 2869882 x^{6} + 13705540 x^{4} + 21016320 x^{2} + 24920064 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.6
Root \(1.37814 + 2.38701i\) of defining polynomial
Character \(\chi\) \(=\) 117.55
Dual form 117.4.g.f.100.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.37814 + 2.38701i) q^{2} +(0.201468 - 0.348954i) q^{4} -0.313209 q^{5} +(-14.2830 + 24.7388i) q^{7} +23.1608 q^{8} +O(q^{10})\) \(q+(1.37814 + 2.38701i) q^{2} +(0.201468 - 0.348954i) q^{4} -0.313209 q^{5} +(-14.2830 + 24.7388i) q^{7} +23.1608 q^{8} +(-0.431646 - 0.747632i) q^{10} +(31.6086 + 54.7478i) q^{11} +(-2.26982 + 46.8172i) q^{13} -78.7357 q^{14} +(30.3071 + 52.4934i) q^{16} +(49.4135 - 85.5867i) q^{17} +(7.24486 - 12.5485i) q^{19} +(-0.0631018 + 0.109295i) q^{20} +(-87.1222 + 150.900i) q^{22} +(-7.19499 - 12.4621i) q^{23} -124.902 q^{25} +(-114.881 + 59.1025i) q^{26} +(5.75514 + 9.96819i) q^{28} +(-98.1415 - 169.986i) q^{29} +118.691 q^{31} +(9.10860 - 15.7766i) q^{32} +272.395 q^{34} +(4.47356 - 7.74843i) q^{35} +(-159.557 - 276.361i) q^{37} +39.9377 q^{38} -7.25418 q^{40} +(173.053 + 299.737i) q^{41} +(34.7427 - 60.1761i) q^{43} +25.4726 q^{44} +(19.8314 - 34.3490i) q^{46} +101.875 q^{47} +(-236.507 - 409.642i) q^{49} +(-172.132 - 298.142i) q^{50} +(15.8797 + 10.2242i) q^{52} +594.823 q^{53} +(-9.90012 - 17.1475i) q^{55} +(-330.806 + 572.972i) q^{56} +(270.505 - 468.529i) q^{58} +(-102.237 + 177.079i) q^{59} +(107.989 - 187.043i) q^{61} +(163.572 + 283.315i) q^{62} +535.125 q^{64} +(0.710929 - 14.6636i) q^{65} +(-34.3025 - 59.4136i) q^{67} +(-19.9105 - 34.4860i) q^{68} +24.6607 q^{70} +(473.121 - 819.469i) q^{71} -779.872 q^{73} +(439.784 - 761.727i) q^{74} +(-2.91922 - 5.05624i) q^{76} -1805.86 q^{77} +240.022 q^{79} +(-9.49245 - 16.4414i) q^{80} +(-476.982 + 826.158i) q^{82} -855.576 q^{83} +(-15.4768 + 26.8065i) q^{85} +191.521 q^{86} +(732.082 + 1268.00i) q^{88} +(632.029 + 1094.71i) q^{89} +(-1125.78 - 724.842i) q^{91} -5.79825 q^{92} +(140.398 + 243.176i) q^{94} +(-2.26916 + 3.93030i) q^{95} +(-331.145 + 573.560i) q^{97} +(651.879 - 1129.09i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 40 q^{4} + 22 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 40 q^{4} + 22 q^{7} - 36 q^{10} + 36 q^{13} - 204 q^{16} - 244 q^{19} - 136 q^{22} + 708 q^{25} + 452 q^{28} + 484 q^{31} - 2584 q^{34} - 1018 q^{37} + 3400 q^{40} - 74 q^{43} + 896 q^{46} - 298 q^{49} - 1676 q^{52} - 1300 q^{55} - 812 q^{58} - 1148 q^{61} + 7272 q^{64} + 2198 q^{67} + 4400 q^{70} - 4352 q^{73} - 6936 q^{76} + 3724 q^{79} - 5436 q^{82} + 890 q^{85} - 3528 q^{88} - 4754 q^{91} + 3104 q^{94} + 4370 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37814 + 2.38701i 0.487246 + 0.843934i 0.999892 0.0146655i \(-0.00466834\pi\)
−0.512647 + 0.858600i \(0.671335\pi\)
\(3\) 0 0
\(4\) 0.201468 0.348954i 0.0251836 0.0436192i
\(5\) −0.313209 −0.0280143 −0.0140071 0.999902i \(-0.504459\pi\)
−0.0140071 + 0.999902i \(0.504459\pi\)
\(6\) 0 0
\(7\) −14.2830 + 24.7388i −0.771208 + 1.33577i 0.165693 + 0.986177i \(0.447014\pi\)
−0.936901 + 0.349595i \(0.886319\pi\)
\(8\) 23.1608 1.02357
\(9\) 0 0
\(10\) −0.431646 0.747632i −0.0136498 0.0236422i
\(11\) 31.6086 + 54.7478i 0.866397 + 1.50064i 0.865654 + 0.500644i \(0.166903\pi\)
0.000743312 1.00000i \(0.499763\pi\)
\(12\) 0 0
\(13\) −2.26982 + 46.8172i −0.0484258 + 0.998827i
\(14\) −78.7357 −1.50307
\(15\) 0 0
\(16\) 30.3071 + 52.4934i 0.473548 + 0.820209i
\(17\) 49.4135 85.5867i 0.704973 1.22105i −0.261729 0.965142i \(-0.584292\pi\)
0.966701 0.255907i \(-0.0823742\pi\)
\(18\) 0 0
\(19\) 7.24486 12.5485i 0.0874782 0.151517i −0.818966 0.573842i \(-0.805453\pi\)
0.906445 + 0.422325i \(0.138786\pi\)
\(20\) −0.0631018 + 0.109295i −0.000705499 + 0.00122196i
\(21\) 0 0
\(22\) −87.1222 + 150.900i −0.844296 + 1.46236i
\(23\) −7.19499 12.4621i −0.0652286 0.112979i 0.831567 0.555425i \(-0.187444\pi\)
−0.896795 + 0.442446i \(0.854111\pi\)
\(24\) 0 0
\(25\) −124.902 −0.999215
\(26\) −114.881 + 59.1025i −0.866539 + 0.445806i
\(27\) 0 0
\(28\) 5.75514 + 9.96819i 0.0388435 + 0.0672790i
\(29\) −98.1415 169.986i −0.628428 1.08847i −0.987867 0.155301i \(-0.950365\pi\)
0.359439 0.933169i \(-0.382968\pi\)
\(30\) 0 0
\(31\) 118.691 0.687661 0.343830 0.939032i \(-0.388276\pi\)
0.343830 + 0.939032i \(0.388276\pi\)
\(32\) 9.10860 15.7766i 0.0503184 0.0871540i
\(33\) 0 0
\(34\) 272.395 1.37398
\(35\) 4.47356 7.74843i 0.0216048 0.0374207i
\(36\) 0 0
\(37\) −159.557 276.361i −0.708947 1.22793i −0.965248 0.261335i \(-0.915837\pi\)
0.256302 0.966597i \(-0.417496\pi\)
\(38\) 39.9377 0.170493
\(39\) 0 0
\(40\) −7.25418 −0.0286747
\(41\) 173.053 + 299.737i 0.659180 + 1.14173i 0.980828 + 0.194873i \(0.0624296\pi\)
−0.321649 + 0.946859i \(0.604237\pi\)
\(42\) 0 0
\(43\) 34.7427 60.1761i 0.123214 0.213413i −0.797819 0.602897i \(-0.794013\pi\)
0.921033 + 0.389483i \(0.127346\pi\)
\(44\) 25.4726 0.0872758
\(45\) 0 0
\(46\) 19.8314 34.3490i 0.0635647 0.110097i
\(47\) 101.875 0.316170 0.158085 0.987426i \(-0.449468\pi\)
0.158085 + 0.987426i \(0.449468\pi\)
\(48\) 0 0
\(49\) −236.507 409.642i −0.689525 1.19429i
\(50\) −172.132 298.142i −0.486863 0.843272i
\(51\) 0 0
\(52\) 15.8797 + 10.2242i 0.0423485 + 0.0272663i
\(53\) 594.823 1.54161 0.770804 0.637072i \(-0.219855\pi\)
0.770804 + 0.637072i \(0.219855\pi\)
\(54\) 0 0
\(55\) −9.90012 17.1475i −0.0242715 0.0420394i
\(56\) −330.806 + 572.972i −0.789388 + 1.36726i
\(57\) 0 0
\(58\) 270.505 468.529i 0.612398 1.06070i
\(59\) −102.237 + 177.079i −0.225595 + 0.390741i −0.956498 0.291740i \(-0.905766\pi\)
0.730903 + 0.682481i \(0.239099\pi\)
\(60\) 0 0
\(61\) 107.989 187.043i 0.226666 0.392596i −0.730152 0.683285i \(-0.760551\pi\)
0.956818 + 0.290688i \(0.0938842\pi\)
\(62\) 163.572 + 283.315i 0.335060 + 0.580340i
\(63\) 0 0
\(64\) 535.125 1.04517
\(65\) 0.710929 14.6636i 0.00135661 0.0279814i
\(66\) 0 0
\(67\) −34.3025 59.4136i −0.0625480 0.108336i 0.833056 0.553189i \(-0.186589\pi\)
−0.895604 + 0.444853i \(0.853256\pi\)
\(68\) −19.9105 34.4860i −0.0355074 0.0615007i
\(69\) 0 0
\(70\) 24.6607 0.0421075
\(71\) 473.121 819.469i 0.790832 1.36976i −0.134620 0.990897i \(-0.542981\pi\)
0.925452 0.378864i \(-0.123685\pi\)
\(72\) 0 0
\(73\) −779.872 −1.25037 −0.625185 0.780476i \(-0.714977\pi\)
−0.625185 + 0.780476i \(0.714977\pi\)
\(74\) 439.784 761.727i 0.690862 1.19661i
\(75\) 0 0
\(76\) −2.91922 5.05624i −0.00440602 0.00763145i
\(77\) −1805.86 −2.67269
\(78\) 0 0
\(79\) 240.022 0.341831 0.170915 0.985286i \(-0.445328\pi\)
0.170915 + 0.985286i \(0.445328\pi\)
\(80\) −9.49245 16.4414i −0.0132661 0.0229776i
\(81\) 0 0
\(82\) −476.982 + 826.158i −0.642365 + 1.11261i
\(83\) −855.576 −1.13147 −0.565733 0.824588i \(-0.691407\pi\)
−0.565733 + 0.824588i \(0.691407\pi\)
\(84\) 0 0
\(85\) −15.4768 + 26.8065i −0.0197493 + 0.0342068i
\(86\) 191.521 0.240142
\(87\) 0 0
\(88\) 732.082 + 1268.00i 0.886821 + 1.53602i
\(89\) 632.029 + 1094.71i 0.752753 + 1.30381i 0.946484 + 0.322751i \(0.104608\pi\)
−0.193731 + 0.981055i \(0.562059\pi\)
\(90\) 0 0
\(91\) −1125.78 724.842i −1.29686 0.834989i
\(92\) −5.79825 −0.00657075
\(93\) 0 0
\(94\) 140.398 + 243.176i 0.154052 + 0.266826i
\(95\) −2.26916 + 3.93030i −0.00245064 + 0.00424463i
\(96\) 0 0
\(97\) −331.145 + 573.560i −0.346625 + 0.600373i −0.985648 0.168815i \(-0.946006\pi\)
0.639022 + 0.769188i \(0.279339\pi\)
\(98\) 651.879 1129.09i 0.671936 1.16383i
\(99\) 0 0
\(100\) −25.1638 + 43.5850i −0.0251638 + 0.0435850i
\(101\) −396.785 687.252i −0.390907 0.677071i 0.601662 0.798751i \(-0.294505\pi\)
−0.992569 + 0.121680i \(0.961172\pi\)
\(102\) 0 0
\(103\) 980.791 0.938254 0.469127 0.883131i \(-0.344569\pi\)
0.469127 + 0.883131i \(0.344569\pi\)
\(104\) −52.5710 + 1084.32i −0.0495674 + 1.02237i
\(105\) 0 0
\(106\) 819.749 + 1419.85i 0.751142 + 1.30102i
\(107\) −402.972 697.968i −0.364082 0.630609i 0.624546 0.780988i \(-0.285284\pi\)
−0.988628 + 0.150379i \(0.951951\pi\)
\(108\) 0 0
\(109\) 845.184 0.742697 0.371348 0.928494i \(-0.378896\pi\)
0.371348 + 0.928494i \(0.378896\pi\)
\(110\) 27.2875 47.2633i 0.0236523 0.0409671i
\(111\) 0 0
\(112\) −1731.50 −1.46082
\(113\) 28.1887 48.8243i 0.0234670 0.0406460i −0.854053 0.520185i \(-0.825863\pi\)
0.877520 + 0.479539i \(0.159196\pi\)
\(114\) 0 0
\(115\) 2.25354 + 3.90324i 0.00182733 + 0.00316503i
\(116\) −79.0896 −0.0633042
\(117\) 0 0
\(118\) −563.585 −0.439680
\(119\) 1411.54 + 2444.87i 1.08736 + 1.88337i
\(120\) 0 0
\(121\) −1332.71 + 2308.33i −1.00129 + 1.73428i
\(122\) 595.296 0.441767
\(123\) 0 0
\(124\) 23.9124 41.4175i 0.0173177 0.0299952i
\(125\) 78.2716 0.0560066
\(126\) 0 0
\(127\) −833.323 1443.36i −0.582248 1.00848i −0.995212 0.0977357i \(-0.968840\pi\)
0.412965 0.910747i \(-0.364493\pi\)
\(128\) 664.607 + 1151.13i 0.458934 + 0.794897i
\(129\) 0 0
\(130\) 35.9818 18.5114i 0.0242755 0.0124889i
\(131\) 602.630 0.401924 0.200962 0.979599i \(-0.435593\pi\)
0.200962 + 0.979599i \(0.435593\pi\)
\(132\) 0 0
\(133\) 206.956 + 358.459i 0.134928 + 0.233702i
\(134\) 94.5471 163.760i 0.0609524 0.105573i
\(135\) 0 0
\(136\) 1144.46 1982.26i 0.721591 1.24983i
\(137\) 210.827 365.163i 0.131476 0.227722i −0.792770 0.609521i \(-0.791362\pi\)
0.924246 + 0.381799i \(0.124695\pi\)
\(138\) 0 0
\(139\) −14.5851 + 25.2622i −0.00889995 + 0.0154152i −0.870441 0.492273i \(-0.836166\pi\)
0.861541 + 0.507688i \(0.169500\pi\)
\(140\) −1.80256 3.12213i −0.00108817 0.00188477i
\(141\) 0 0
\(142\) 2608.10 1.54132
\(143\) −2634.88 + 1355.56i −1.54084 + 0.792710i
\(144\) 0 0
\(145\) 30.7388 + 53.2412i 0.0176050 + 0.0304927i
\(146\) −1074.77 1861.56i −0.609238 1.05523i
\(147\) 0 0
\(148\) −128.583 −0.0714152
\(149\) 1070.90 1854.85i 0.588802 1.01983i −0.405588 0.914056i \(-0.632933\pi\)
0.994390 0.105778i \(-0.0337334\pi\)
\(150\) 0 0
\(151\) 1459.30 0.786462 0.393231 0.919440i \(-0.371357\pi\)
0.393231 + 0.919440i \(0.371357\pi\)
\(152\) 167.797 290.633i 0.0895403 0.155088i
\(153\) 0 0
\(154\) −2488.73 4310.60i −1.30226 2.25557i
\(155\) −37.1750 −0.0192643
\(156\) 0 0
\(157\) 2008.20 1.02084 0.510419 0.859926i \(-0.329490\pi\)
0.510419 + 0.859926i \(0.329490\pi\)
\(158\) 330.784 + 572.935i 0.166555 + 0.288482i
\(159\) 0 0
\(160\) −2.85290 + 4.94136i −0.00140963 + 0.00244156i
\(161\) 411.063 0.201219
\(162\) 0 0
\(163\) −274.248 + 475.011i −0.131784 + 0.228256i −0.924364 0.381511i \(-0.875404\pi\)
0.792581 + 0.609767i \(0.208737\pi\)
\(164\) 139.459 0.0664019
\(165\) 0 0
\(166\) −1179.10 2042.27i −0.551302 0.954883i
\(167\) −1981.29 3431.69i −0.918064 1.59013i −0.802352 0.596851i \(-0.796418\pi\)
−0.115712 0.993283i \(-0.536915\pi\)
\(168\) 0 0
\(169\) −2186.70 212.533i −0.995310 0.0967380i
\(170\) −85.3165 −0.0384910
\(171\) 0 0
\(172\) −13.9991 24.2472i −0.00620594 0.0107490i
\(173\) −864.771 + 1497.83i −0.380042 + 0.658252i −0.991068 0.133358i \(-0.957424\pi\)
0.611026 + 0.791611i \(0.290757\pi\)
\(174\) 0 0
\(175\) 1783.97 3089.93i 0.770603 1.33472i
\(176\) −1915.93 + 3318.49i −0.820561 + 1.42125i
\(177\) 0 0
\(178\) −1742.05 + 3017.32i −0.733551 + 1.27055i
\(179\) 726.456 + 1258.26i 0.303340 + 0.525400i 0.976890 0.213741i \(-0.0685649\pi\)
−0.673550 + 0.739141i \(0.735232\pi\)
\(180\) 0 0
\(181\) −550.329 −0.225998 −0.112999 0.993595i \(-0.536046\pi\)
−0.112999 + 0.993595i \(0.536046\pi\)
\(182\) 178.716 3686.18i 0.0727875 1.50131i
\(183\) 0 0
\(184\) −166.642 288.632i −0.0667663 0.115643i
\(185\) 49.9747 + 86.5588i 0.0198606 + 0.0343996i
\(186\) 0 0
\(187\) 6247.58 2.44314
\(188\) 20.5246 35.5496i 0.00796228 0.0137911i
\(189\) 0 0
\(190\) −12.5089 −0.00477625
\(191\) 934.340 1618.32i 0.353960 0.613078i −0.632979 0.774169i \(-0.718168\pi\)
0.986939 + 0.161091i \(0.0515014\pi\)
\(192\) 0 0
\(193\) −2078.26 3599.66i −0.775112 1.34253i −0.934732 0.355354i \(-0.884360\pi\)
0.159620 0.987179i \(-0.448973\pi\)
\(194\) −1825.45 −0.675567
\(195\) 0 0
\(196\) −190.595 −0.0694587
\(197\) −761.092 1318.25i −0.275257 0.476758i 0.694943 0.719065i \(-0.255429\pi\)
−0.970200 + 0.242306i \(0.922096\pi\)
\(198\) 0 0
\(199\) −404.065 + 699.861i −0.143937 + 0.249306i −0.928976 0.370141i \(-0.879309\pi\)
0.785039 + 0.619446i \(0.212643\pi\)
\(200\) −2892.83 −1.02277
\(201\) 0 0
\(202\) 1093.65 1894.26i 0.380935 0.659800i
\(203\) 5607.01 1.93860
\(204\) 0 0
\(205\) −54.2018 93.8803i −0.0184664 0.0319848i
\(206\) 1351.67 + 2341.15i 0.457160 + 0.791825i
\(207\) 0 0
\(208\) −2526.38 + 1299.74i −0.842179 + 0.433273i
\(209\) 916.001 0.303163
\(210\) 0 0
\(211\) 2630.02 + 4555.32i 0.858094 + 1.48626i 0.873745 + 0.486384i \(0.161685\pi\)
−0.0156511 + 0.999878i \(0.504982\pi\)
\(212\) 119.838 207.566i 0.0388232 0.0672437i
\(213\) 0 0
\(214\) 1110.70 1923.79i 0.354795 0.614523i
\(215\) −10.8817 + 18.8477i −0.00345176 + 0.00597862i
\(216\) 0 0
\(217\) −1695.26 + 2936.27i −0.530330 + 0.918558i
\(218\) 1164.78 + 2017.46i 0.361876 + 0.626787i
\(219\) 0 0
\(220\) −7.97824 −0.00244497
\(221\) 3894.77 + 2507.67i 1.18548 + 0.763276i
\(222\) 0 0
\(223\) 2345.36 + 4062.28i 0.704290 + 1.21987i 0.966947 + 0.254977i \(0.0820678\pi\)
−0.262657 + 0.964889i \(0.584599\pi\)
\(224\) 260.196 + 450.672i 0.0776119 + 0.134428i
\(225\) 0 0
\(226\) 155.392 0.0457368
\(227\) −1780.31 + 3083.58i −0.520542 + 0.901606i 0.479172 + 0.877721i \(0.340937\pi\)
−0.999715 + 0.0238849i \(0.992396\pi\)
\(228\) 0 0
\(229\) −3144.82 −0.907490 −0.453745 0.891131i \(-0.649912\pi\)
−0.453745 + 0.891131i \(0.649912\pi\)
\(230\) −6.21137 + 10.7584i −0.00178072 + 0.00308430i
\(231\) 0 0
\(232\) −2273.04 3937.02i −0.643242 1.11413i
\(233\) −852.543 −0.239708 −0.119854 0.992792i \(-0.538243\pi\)
−0.119854 + 0.992792i \(0.538243\pi\)
\(234\) 0 0
\(235\) −31.9081 −0.00885727
\(236\) 41.1949 + 71.3517i 0.0113625 + 0.0196805i
\(237\) 0 0
\(238\) −3890.61 + 6738.73i −1.05962 + 1.83532i
\(239\) 2189.33 0.592534 0.296267 0.955105i \(-0.404258\pi\)
0.296267 + 0.955105i \(0.404258\pi\)
\(240\) 0 0
\(241\) −3164.99 + 5481.92i −0.845954 + 1.46523i 0.0388369 + 0.999246i \(0.487635\pi\)
−0.884791 + 0.465989i \(0.845699\pi\)
\(242\) −7346.65 −1.95149
\(243\) 0 0
\(244\) −43.5128 75.3664i −0.0114165 0.0197739i
\(245\) 74.0762 + 128.304i 0.0193165 + 0.0334572i
\(246\) 0 0
\(247\) 571.039 + 367.667i 0.147103 + 0.0947129i
\(248\) 2748.97 0.703871
\(249\) 0 0
\(250\) 107.869 + 186.835i 0.0272890 + 0.0472659i
\(251\) 1801.49 3120.27i 0.453023 0.784659i −0.545549 0.838079i \(-0.683679\pi\)
0.998572 + 0.0534200i \(0.0170122\pi\)
\(252\) 0 0
\(253\) 454.848 787.819i 0.113028 0.195770i
\(254\) 2296.87 3978.29i 0.567395 0.982757i
\(255\) 0 0
\(256\) 308.657 534.610i 0.0753558 0.130520i
\(257\) −1536.32 2660.98i −0.372891 0.645865i 0.617118 0.786870i \(-0.288300\pi\)
−0.990009 + 0.141005i \(0.954967\pi\)
\(258\) 0 0
\(259\) 9115.80 2.18698
\(260\) −4.97367 3.20233i −0.00118636 0.000763846i
\(261\) 0 0
\(262\) 830.507 + 1438.48i 0.195836 + 0.339197i
\(263\) 1771.60 + 3068.50i 0.415367 + 0.719437i 0.995467 0.0951084i \(-0.0303198\pi\)
−0.580100 + 0.814545i \(0.696986\pi\)
\(264\) 0 0
\(265\) −186.304 −0.0431871
\(266\) −570.429 + 988.012i −0.131486 + 0.227740i
\(267\) 0 0
\(268\) −27.6435 −0.00630072
\(269\) −2949.98 + 5109.52i −0.668638 + 1.15811i 0.309647 + 0.950852i \(0.399789\pi\)
−0.978285 + 0.207263i \(0.933544\pi\)
\(270\) 0 0
\(271\) 1054.76 + 1826.90i 0.236429 + 0.409507i 0.959687 0.281071i \(-0.0906896\pi\)
−0.723258 + 0.690578i \(0.757356\pi\)
\(272\) 5990.32 1.33535
\(273\) 0 0
\(274\) 1162.19 0.256244
\(275\) −3947.98 6838.10i −0.865717 1.49947i
\(276\) 0 0
\(277\) −3632.50 + 6291.67i −0.787927 + 1.36473i 0.139308 + 0.990249i \(0.455512\pi\)
−0.927235 + 0.374480i \(0.877821\pi\)
\(278\) −80.4012 −0.0173458
\(279\) 0 0
\(280\) 103.611 179.460i 0.0221141 0.0383028i
\(281\) −4771.36 −1.01294 −0.506469 0.862258i \(-0.669049\pi\)
−0.506469 + 0.862258i \(0.669049\pi\)
\(282\) 0 0
\(283\) −1018.13 1763.45i −0.213857 0.370411i 0.739061 0.673638i \(-0.235269\pi\)
−0.952918 + 0.303227i \(0.901936\pi\)
\(284\) −190.638 330.194i −0.0398319 0.0689909i
\(285\) 0 0
\(286\) −6866.96 4421.33i −1.41976 0.914122i
\(287\) −9886.86 −2.03346
\(288\) 0 0
\(289\) −2426.89 4203.50i −0.493973 0.855587i
\(290\) −84.7247 + 146.747i −0.0171559 + 0.0297148i
\(291\) 0 0
\(292\) −157.119 + 272.139i −0.0314888 + 0.0545402i
\(293\) 1859.51 3220.77i 0.370764 0.642182i −0.618920 0.785454i \(-0.712429\pi\)
0.989683 + 0.143273i \(0.0457626\pi\)
\(294\) 0 0
\(295\) 32.0215 55.4628i 0.00631987 0.0109463i
\(296\) −3695.47 6400.75i −0.725659 1.25688i
\(297\) 0 0
\(298\) 5903.39 1.14756
\(299\) 599.771 308.562i 0.116005 0.0596810i
\(300\) 0 0
\(301\) 992.458 + 1718.99i 0.190048 + 0.329172i
\(302\) 2011.11 + 3483.35i 0.383200 + 0.663722i
\(303\) 0 0
\(304\) 878.282 0.165700
\(305\) −33.8232 + 58.5835i −0.00634987 + 0.0109983i
\(306\) 0 0
\(307\) −7282.24 −1.35381 −0.676905 0.736070i \(-0.736679\pi\)
−0.676905 + 0.736070i \(0.736679\pi\)
\(308\) −363.824 + 630.162i −0.0673078 + 0.116581i
\(309\) 0 0
\(310\) −51.2323 88.7370i −0.00938645 0.0162578i
\(311\) 4569.28 0.833120 0.416560 0.909108i \(-0.363236\pi\)
0.416560 + 0.909108i \(0.363236\pi\)
\(312\) 0 0
\(313\) 21.0294 0.00379761 0.00189880 0.999998i \(-0.499396\pi\)
0.00189880 + 0.999998i \(0.499396\pi\)
\(314\) 2767.57 + 4793.58i 0.497399 + 0.861520i
\(315\) 0 0
\(316\) 48.3569 83.7566i 0.00860851 0.0149104i
\(317\) 5159.17 0.914095 0.457047 0.889442i \(-0.348907\pi\)
0.457047 + 0.889442i \(0.348907\pi\)
\(318\) 0 0
\(319\) 6204.24 10746.1i 1.08894 1.88609i
\(320\) −167.606 −0.0292796
\(321\) 0 0
\(322\) 566.502 + 981.211i 0.0980433 + 0.169816i
\(323\) −715.988 1240.13i −0.123339 0.213630i
\(324\) 0 0
\(325\) 283.505 5847.55i 0.0483878 0.998043i
\(326\) −1511.80 −0.256844
\(327\) 0 0
\(328\) 4008.05 + 6942.15i 0.674719 + 1.16865i
\(329\) −1455.08 + 2520.27i −0.243833 + 0.422331i
\(330\) 0 0
\(331\) 3788.76 6562.33i 0.629152 1.08972i −0.358570 0.933503i \(-0.616736\pi\)
0.987722 0.156220i \(-0.0499309\pi\)
\(332\) −172.372 + 298.556i −0.0284943 + 0.0493536i
\(333\) 0 0
\(334\) 5460.98 9458.70i 0.894645 1.54957i
\(335\) 10.7438 + 18.6089i 0.00175224 + 0.00303496i
\(336\) 0 0
\(337\) −2109.79 −0.341032 −0.170516 0.985355i \(-0.554543\pi\)
−0.170516 + 0.985355i \(0.554543\pi\)
\(338\) −2506.25 5512.56i −0.403320 0.887111i
\(339\) 0 0
\(340\) 6.23616 + 10.8013i 0.000994715 + 0.00172290i
\(341\) 3751.65 + 6498.05i 0.595787 + 1.03193i
\(342\) 0 0
\(343\) 3713.98 0.584653
\(344\) 804.669 1393.73i 0.126119 0.218444i
\(345\) 0 0
\(346\) −4767.09 −0.740695
\(347\) −4053.95 + 7021.65i −0.627169 + 1.08629i 0.360948 + 0.932586i \(0.382453\pi\)
−0.988117 + 0.153703i \(0.950880\pi\)
\(348\) 0 0
\(349\) −4343.19 7522.62i −0.666148 1.15380i −0.978973 0.203991i \(-0.934609\pi\)
0.312825 0.949811i \(-0.398725\pi\)
\(350\) 9834.24 1.50189
\(351\) 0 0
\(352\) 1151.64 0.174383
\(353\) −4525.12 7837.73i −0.682288 1.18176i −0.974281 0.225337i \(-0.927652\pi\)
0.291993 0.956421i \(-0.405682\pi\)
\(354\) 0 0
\(355\) −148.186 + 256.665i −0.0221546 + 0.0383729i
\(356\) 509.336 0.0758279
\(357\) 0 0
\(358\) −2002.31 + 3468.11i −0.295602 + 0.511998i
\(359\) 7043.80 1.03554 0.517768 0.855521i \(-0.326763\pi\)
0.517768 + 0.855521i \(0.326763\pi\)
\(360\) 0 0
\(361\) 3324.52 + 5758.24i 0.484695 + 0.839517i
\(362\) −758.429 1313.64i −0.110116 0.190727i
\(363\) 0 0
\(364\) −479.746 + 246.813i −0.0690811 + 0.0355399i
\(365\) 244.263 0.0350282
\(366\) 0 0
\(367\) −6912.55 11972.9i −0.983194 1.70294i −0.649703 0.760188i \(-0.725107\pi\)
−0.333491 0.942753i \(-0.608227\pi\)
\(368\) 436.118 755.378i 0.0617778 0.107002i
\(369\) 0 0
\(370\) −137.744 + 238.580i −0.0193540 + 0.0335221i
\(371\) −8495.85 + 14715.2i −1.18890 + 2.05924i
\(372\) 0 0
\(373\) −3184.09 + 5515.01i −0.442000 + 0.765567i −0.997838 0.0657238i \(-0.979064\pi\)
0.555837 + 0.831291i \(0.312398\pi\)
\(374\) 8610.03 + 14913.0i 1.19041 + 2.06185i
\(375\) 0 0
\(376\) 2359.51 0.323623
\(377\) 8181.03 4208.87i 1.11762 0.574981i
\(378\) 0 0
\(379\) −1225.83 2123.20i −0.166139 0.287761i 0.770920 0.636932i \(-0.219797\pi\)
−0.937059 + 0.349171i \(0.886463\pi\)
\(380\) 0.914327 + 1.58366i 0.000123432 + 0.000213790i
\(381\) 0 0
\(382\) 5150.60 0.689863
\(383\) −5415.47 + 9379.87i −0.722500 + 1.25141i 0.237494 + 0.971389i \(0.423674\pi\)
−0.959995 + 0.280018i \(0.909659\pi\)
\(384\) 0 0
\(385\) 565.613 0.0748735
\(386\) 5728.27 9921.65i 0.755340 1.30829i
\(387\) 0 0
\(388\) 133.430 + 231.108i 0.0174585 + 0.0302390i
\(389\) −4978.07 −0.648838 −0.324419 0.945914i \(-0.605169\pi\)
−0.324419 + 0.945914i \(0.605169\pi\)
\(390\) 0 0
\(391\) −1422.12 −0.183938
\(392\) −5477.70 9487.65i −0.705779 1.22245i
\(393\) 0 0
\(394\) 2097.78 3633.46i 0.268235 0.464597i
\(395\) −75.1772 −0.00957614
\(396\) 0 0
\(397\) −4725.34 + 8184.52i −0.597375 + 1.03468i 0.395832 + 0.918323i \(0.370456\pi\)
−0.993207 + 0.116361i \(0.962877\pi\)
\(398\) −2227.43 −0.280530
\(399\) 0 0
\(400\) −3785.41 6556.52i −0.473176 0.819566i
\(401\) −4388.39 7600.91i −0.546498 0.946562i −0.998511 0.0545506i \(-0.982627\pi\)
0.452013 0.892011i \(-0.350706\pi\)
\(402\) 0 0
\(403\) −269.407 + 5556.76i −0.0333005 + 0.686854i
\(404\) −319.759 −0.0393777
\(405\) 0 0
\(406\) 7727.24 + 13384.0i 0.944572 + 1.63605i
\(407\) 10086.8 17470.8i 1.22846 2.12775i
\(408\) 0 0
\(409\) 2260.10 3914.60i 0.273238 0.473263i −0.696451 0.717605i \(-0.745239\pi\)
0.969689 + 0.244342i \(0.0785719\pi\)
\(410\) 149.395 258.760i 0.0179954 0.0311689i
\(411\) 0 0
\(412\) 197.598 342.250i 0.0236286 0.0409259i
\(413\) −2920.49 5058.43i −0.347961 0.602686i
\(414\) 0 0
\(415\) 267.974 0.0316972
\(416\) 717.939 + 462.249i 0.0846150 + 0.0544798i
\(417\) 0 0
\(418\) 1262.38 + 2186.50i 0.147715 + 0.255850i
\(419\) −6003.22 10397.9i −0.699944 1.21234i −0.968485 0.249070i \(-0.919875\pi\)
0.268541 0.963268i \(-0.413458\pi\)
\(420\) 0 0
\(421\) −9731.52 −1.12657 −0.563284 0.826263i \(-0.690462\pi\)
−0.563284 + 0.826263i \(0.690462\pi\)
\(422\) −7249.05 + 12555.7i −0.836205 + 1.44835i
\(423\) 0 0
\(424\) 13776.6 1.57795
\(425\) −6171.84 + 10689.9i −0.704420 + 1.22009i
\(426\) 0 0
\(427\) 3084.82 + 5343.06i 0.349613 + 0.605547i
\(428\) −324.745 −0.0366755
\(429\) 0 0
\(430\) −59.9861 −0.00672741
\(431\) 2055.51 + 3560.25i 0.229723 + 0.397892i 0.957726 0.287682i \(-0.0928846\pi\)
−0.728003 + 0.685574i \(0.759551\pi\)
\(432\) 0 0
\(433\) −1453.03 + 2516.72i −0.161266 + 0.279321i −0.935323 0.353795i \(-0.884891\pi\)
0.774057 + 0.633116i \(0.218224\pi\)
\(434\) −9345.19 −1.03360
\(435\) 0 0
\(436\) 170.278 294.930i 0.0187037 0.0323958i
\(437\) −208.507 −0.0228243
\(438\) 0 0
\(439\) −4437.36 7685.73i −0.482423 0.835581i 0.517374 0.855760i \(-0.326910\pi\)
−0.999796 + 0.0201788i \(0.993576\pi\)
\(440\) −229.295 397.150i −0.0248436 0.0430305i
\(441\) 0 0
\(442\) −618.288 + 12752.7i −0.0665361 + 1.37237i
\(443\) 12640.5 1.35569 0.677843 0.735207i \(-0.262915\pi\)
0.677843 + 0.735207i \(0.262915\pi\)
\(444\) 0 0
\(445\) −197.957 342.872i −0.0210878 0.0365252i
\(446\) −6464.45 + 11196.8i −0.686324 + 1.18875i
\(447\) 0 0
\(448\) −7643.18 + 13238.4i −0.806041 + 1.39610i
\(449\) 887.147 1536.58i 0.0932451 0.161505i −0.815630 0.578574i \(-0.803609\pi\)
0.908875 + 0.417069i \(0.136943\pi\)
\(450\) 0 0
\(451\) −10940.0 + 18948.6i −1.14222 + 1.97839i
\(452\) −11.3583 19.6731i −0.00118197 0.00204722i
\(453\) 0 0
\(454\) −9814.04 −1.01453
\(455\) 352.606 + 227.027i 0.0363306 + 0.0233916i
\(456\) 0 0
\(457\) −3084.41 5342.35i −0.315717 0.546837i 0.663873 0.747845i \(-0.268912\pi\)
−0.979590 + 0.201008i \(0.935578\pi\)
\(458\) −4333.99 7506.69i −0.442171 0.765862i
\(459\) 0 0
\(460\) 1.81607 0.000184075
\(461\) 3727.69 6456.55i 0.376607 0.652302i −0.613959 0.789338i \(-0.710424\pi\)
0.990566 + 0.137036i \(0.0437574\pi\)
\(462\) 0 0
\(463\) 5399.78 0.542006 0.271003 0.962578i \(-0.412645\pi\)
0.271003 + 0.962578i \(0.412645\pi\)
\(464\) 5948.76 10303.6i 0.595182 1.03088i
\(465\) 0 0
\(466\) −1174.92 2035.03i −0.116797 0.202298i
\(467\) 3992.01 0.395564 0.197782 0.980246i \(-0.436626\pi\)
0.197782 + 0.980246i \(0.436626\pi\)
\(468\) 0 0
\(469\) 1959.77 0.192950
\(470\) −43.9738 76.1649i −0.00431566 0.00747495i
\(471\) 0 0
\(472\) −2367.89 + 4101.30i −0.230913 + 0.399952i
\(473\) 4392.68 0.427009
\(474\) 0 0
\(475\) −904.897 + 1567.33i −0.0874095 + 0.151398i
\(476\) 1137.53 0.109535
\(477\) 0 0
\(478\) 3017.19 + 5225.93i 0.288710 + 0.500060i
\(479\) −1575.81 2729.39i −0.150315 0.260352i 0.781029 0.624495i \(-0.214695\pi\)
−0.931343 + 0.364143i \(0.881362\pi\)
\(480\) 0 0
\(481\) 13300.6 6842.72i 1.26082 0.648651i
\(482\) −17447.2 −1.64875
\(483\) 0 0
\(484\) 536.999 + 930.110i 0.0504319 + 0.0873507i
\(485\) 103.718 179.644i 0.00971046 0.0168190i
\(486\) 0 0
\(487\) 1954.59 3385.45i 0.181870 0.315009i −0.760647 0.649166i \(-0.775118\pi\)
0.942517 + 0.334157i \(0.108452\pi\)
\(488\) 2501.12 4332.07i 0.232009 0.401851i
\(489\) 0 0
\(490\) −204.174 + 353.641i −0.0188238 + 0.0326038i
\(491\) −3322.57 5754.86i −0.305388 0.528947i 0.671960 0.740588i \(-0.265453\pi\)
−0.977348 + 0.211641i \(0.932119\pi\)
\(492\) 0 0
\(493\) −19398.1 −1.77210
\(494\) −90.6515 + 1869.77i −0.00825628 + 0.170293i
\(495\) 0 0
\(496\) 3597.17 + 6230.48i 0.325640 + 0.564026i
\(497\) 13515.1 + 23408.9i 1.21979 + 2.11274i
\(498\) 0 0
\(499\) 6111.83 0.548303 0.274151 0.961687i \(-0.411603\pi\)
0.274151 + 0.961687i \(0.411603\pi\)
\(500\) 15.7692 27.3131i 0.00141044 0.00244296i
\(501\) 0 0
\(502\) 9930.79 0.882934
\(503\) −5477.03 + 9486.50i −0.485505 + 0.840919i −0.999861 0.0166575i \(-0.994698\pi\)
0.514356 + 0.857576i \(0.328031\pi\)
\(504\) 0 0
\(505\) 124.277 + 215.254i 0.0109510 + 0.0189677i
\(506\) 2507.37 0.220289
\(507\) 0 0
\(508\) −671.553 −0.0586523
\(509\) 5560.57 + 9631.18i 0.484220 + 0.838693i 0.999836 0.0181268i \(-0.00577025\pi\)
−0.515616 + 0.856820i \(0.672437\pi\)
\(510\) 0 0
\(511\) 11138.9 19293.1i 0.964296 1.67021i
\(512\) 12335.2 1.06473
\(513\) 0 0
\(514\) 4234.52 7334.40i 0.363379 0.629390i
\(515\) −307.193 −0.0262845
\(516\) 0 0
\(517\) 3220.13 + 5577.42i 0.273928 + 0.474458i
\(518\) 12562.8 + 21759.5i 1.06560 + 1.84567i
\(519\) 0 0
\(520\) 16.4657 339.620i 0.00138859 0.0286410i
\(521\) 2403.33 0.202096 0.101048 0.994882i \(-0.467780\pi\)
0.101048 + 0.994882i \(0.467780\pi\)
\(522\) 0 0
\(523\) −2125.86 3682.10i −0.177739 0.307853i 0.763367 0.645965i \(-0.223545\pi\)
−0.941106 + 0.338113i \(0.890212\pi\)
\(524\) 121.411 210.290i 0.0101219 0.0175316i
\(525\) 0 0
\(526\) −4883.02 + 8457.64i −0.404772 + 0.701085i
\(527\) 5864.92 10158.3i 0.484782 0.839667i
\(528\) 0 0
\(529\) 5979.96 10357.6i 0.491490 0.851286i
\(530\) −256.753 444.709i −0.0210427 0.0364470i
\(531\) 0 0
\(532\) 166.781 0.0135918
\(533\) −14425.6 + 7421.51i −1.17231 + 0.603117i
\(534\) 0 0
\(535\) 126.215 + 218.610i 0.0101995 + 0.0176661i
\(536\) −794.473 1376.07i −0.0640224 0.110890i
\(537\) 0 0
\(538\) −16261.9 −1.30316
\(539\) 14951.3 25896.5i 1.19480 2.06946i
\(540\) 0 0
\(541\) −8924.44 −0.709227 −0.354613 0.935013i \(-0.615388\pi\)
−0.354613 + 0.935013i \(0.615388\pi\)
\(542\) −2907.22 + 5035.45i −0.230398 + 0.399061i
\(543\) 0 0
\(544\) −900.176 1559.15i −0.0709462 0.122882i
\(545\) −264.719 −0.0208061
\(546\) 0 0
\(547\) −14696.0 −1.14873 −0.574367 0.818598i \(-0.694752\pi\)
−0.574367 + 0.818598i \(0.694752\pi\)
\(548\) −84.9499 147.138i −0.00662204 0.0114697i
\(549\) 0 0
\(550\) 10881.7 18847.7i 0.843633 1.46122i
\(551\) −2844.09 −0.219895
\(552\) 0 0
\(553\) −3428.23 + 5937.87i −0.263623 + 0.456608i
\(554\) −20024.3 −1.53566
\(555\) 0 0
\(556\) 5.87688 + 10.1791i 0.000448265 + 0.000776417i
\(557\) −1232.01 2133.91i −0.0937202 0.162328i 0.815354 0.578963i \(-0.196543\pi\)
−0.909074 + 0.416635i \(0.863209\pi\)
\(558\) 0 0
\(559\) 2738.41 + 1763.14i 0.207196 + 0.133404i
\(560\) 542.322 0.0409237
\(561\) 0 0
\(562\) −6575.59 11389.3i −0.493549 0.854852i
\(563\) −9014.61 + 15613.8i −0.674815 + 1.16881i 0.301708 + 0.953400i \(0.402443\pi\)
−0.976523 + 0.215413i \(0.930890\pi\)
\(564\) 0 0
\(565\) −8.82897 + 15.2922i −0.000657411 + 0.00113867i
\(566\) 2806.25 4860.57i 0.208402 0.360963i
\(567\) 0 0
\(568\) 10957.9 18979.6i 0.809475 1.40205i
\(569\) −5962.32 10327.0i −0.439286 0.760865i 0.558349 0.829606i \(-0.311435\pi\)
−0.997635 + 0.0687410i \(0.978102\pi\)
\(570\) 0 0
\(571\) 5834.77 0.427632 0.213816 0.976874i \(-0.431411\pi\)
0.213816 + 0.976874i \(0.431411\pi\)
\(572\) −57.8182 + 1192.55i −0.00422640 + 0.0871734i
\(573\) 0 0
\(574\) −13625.5 23600.0i −0.990794 1.71611i
\(575\) 898.667 + 1556.54i 0.0651774 + 0.112891i
\(576\) 0 0
\(577\) 15927.5 1.14917 0.574586 0.818444i \(-0.305163\pi\)
0.574586 + 0.818444i \(0.305163\pi\)
\(578\) 6689.19 11586.0i 0.481373 0.833762i
\(579\) 0 0
\(580\) 24.7716 0.00177342
\(581\) 12220.2 21166.0i 0.872596 1.51138i
\(582\) 0 0
\(583\) 18801.6 + 32565.3i 1.33564 + 2.31340i
\(584\) −18062.5 −1.27985
\(585\) 0 0
\(586\) 10250.7 0.722612
\(587\) 6755.55 + 11701.0i 0.475011 + 0.822743i 0.999590 0.0286184i \(-0.00911075\pi\)
−0.524579 + 0.851362i \(0.675777\pi\)
\(588\) 0 0
\(589\) 859.898 1489.39i 0.0601553 0.104192i
\(590\) 176.520 0.0123173
\(591\) 0 0
\(592\) 9671.42 16751.4i 0.671441 1.16297i
\(593\) 15830.4 1.09625 0.548126 0.836396i \(-0.315341\pi\)
0.548126 + 0.836396i \(0.315341\pi\)
\(594\) 0 0
\(595\) −442.109 765.755i −0.0304617 0.0527611i
\(596\) −431.505 747.388i −0.0296562 0.0513661i
\(597\) 0 0
\(598\) 1563.11 + 1006.42i 0.106890 + 0.0688217i
\(599\) −5914.12 −0.403413 −0.201706 0.979446i \(-0.564649\pi\)
−0.201706 + 0.979446i \(0.564649\pi\)
\(600\) 0 0
\(601\) −4946.10 8566.89i −0.335700 0.581449i 0.647919 0.761709i \(-0.275639\pi\)
−0.983619 + 0.180260i \(0.942306\pi\)
\(602\) −2735.49 + 4738.01i −0.185200 + 0.320775i
\(603\) 0 0
\(604\) 294.002 509.226i 0.0198059 0.0343048i
\(605\) 417.418 722.989i 0.0280503 0.0485846i
\(606\) 0 0
\(607\) 8391.16 14533.9i 0.561098 0.971851i −0.436302 0.899800i \(-0.643712\pi\)
0.997401 0.0720510i \(-0.0229544\pi\)
\(608\) −131.981 228.598i −0.00880352 0.0152481i
\(609\) 0 0
\(610\) −186.452 −0.0123758
\(611\) −231.238 + 4769.49i −0.0153108 + 0.315799i
\(612\) 0 0
\(613\) −6122.83 10605.0i −0.403424 0.698750i 0.590713 0.806882i \(-0.298847\pi\)
−0.994137 + 0.108132i \(0.965513\pi\)
\(614\) −10035.9 17382.8i −0.659638 1.14253i
\(615\) 0 0
\(616\) −41825.3 −2.73569
\(617\) −5021.86 + 8698.12i −0.327670 + 0.567542i −0.982049 0.188625i \(-0.939597\pi\)
0.654379 + 0.756167i \(0.272930\pi\)
\(618\) 0 0
\(619\) −9942.69 −0.645607 −0.322803 0.946466i \(-0.604625\pi\)
−0.322803 + 0.946466i \(0.604625\pi\)
\(620\) −7.48959 + 12.9724i −0.000485144 + 0.000840294i
\(621\) 0 0
\(622\) 6297.10 + 10906.9i 0.405934 + 0.703098i
\(623\) −36109.1 −2.32212
\(624\) 0 0
\(625\) 15588.2 0.997646
\(626\) 28.9814 + 50.1973i 0.00185037 + 0.00320493i
\(627\) 0 0
\(628\) 404.588 700.767i 0.0257083 0.0445281i
\(629\) −31537.1 −1.99915
\(630\) 0 0
\(631\) −5134.31 + 8892.89i −0.323920 + 0.561047i −0.981293 0.192519i \(-0.938334\pi\)
0.657373 + 0.753566i \(0.271668\pi\)
\(632\) 5559.11 0.349889
\(633\) 0 0
\(634\) 7110.05 + 12315.0i 0.445389 + 0.771436i
\(635\) 261.004 + 452.073i 0.0163113 + 0.0282519i
\(636\) 0 0
\(637\) 19715.1 10142.8i 1.22628 0.630881i
\(638\) 34201.2 2.12232
\(639\) 0 0
\(640\) −208.161 360.546i −0.0128567 0.0222685i
\(641\) 6828.72 11827.7i 0.420777 0.728808i −0.575238 0.817986i \(-0.695091\pi\)
0.996016 + 0.0891780i \(0.0284240\pi\)
\(642\) 0 0
\(643\) −12335.8 + 21366.2i −0.756572 + 1.31042i 0.188017 + 0.982166i \(0.439794\pi\)
−0.944589 + 0.328256i \(0.893539\pi\)
\(644\) 82.8163 143.442i 0.00506742 0.00877703i
\(645\) 0 0
\(646\) 1973.46 3418.14i 0.120193 0.208181i
\(647\) 8256.13 + 14300.0i 0.501672 + 0.868922i 0.999998 + 0.00193194i \(0.000614955\pi\)
−0.498326 + 0.866990i \(0.666052\pi\)
\(648\) 0 0
\(649\) −12926.3 −0.781818
\(650\) 14348.9 7382.01i 0.865859 0.445456i
\(651\) 0 0
\(652\) 110.504 + 191.399i 0.00663756 + 0.0114966i
\(653\) −15297.4 26495.8i −0.916742 1.58784i −0.804330 0.594182i \(-0.797476\pi\)
−0.112412 0.993662i \(-0.535858\pi\)
\(654\) 0 0
\(655\) −188.749 −0.0112596
\(656\) −10489.5 + 18168.3i −0.624306 + 1.08133i
\(657\) 0 0
\(658\) −8021.19 −0.475226
\(659\) 1153.89 1998.60i 0.0682084 0.118140i −0.829904 0.557906i \(-0.811605\pi\)
0.898113 + 0.439765i \(0.144938\pi\)
\(660\) 0 0
\(661\) 13811.2 + 23921.7i 0.812700 + 1.40764i 0.910968 + 0.412477i \(0.135336\pi\)
−0.0982684 + 0.995160i \(0.531330\pi\)
\(662\) 20885.8 1.22621
\(663\) 0 0
\(664\) −19815.9 −1.15814
\(665\) −64.8206 112.273i −0.00377991 0.00654699i
\(666\) 0 0
\(667\) −1412.25 + 2446.09i −0.0819830 + 0.141999i
\(668\) −1596.67 −0.0924805
\(669\) 0 0
\(670\) −29.6130 + 51.2913i −0.00170754 + 0.00295754i
\(671\) 13653.6 0.785530
\(672\) 0 0
\(673\) 5652.94 + 9791.17i 0.323781 + 0.560805i 0.981265 0.192663i \(-0.0617125\pi\)
−0.657484 + 0.753469i \(0.728379\pi\)
\(674\) −2907.58 5036.08i −0.166166 0.287808i
\(675\) 0 0
\(676\) −514.714 + 720.236i −0.0292851 + 0.0409784i
\(677\) 15455.8 0.877419 0.438710 0.898629i \(-0.355436\pi\)
0.438710 + 0.898629i \(0.355436\pi\)
\(678\) 0 0
\(679\) −9459.47 16384.3i −0.534641 0.926025i
\(680\) −358.455 + 620.862i −0.0202149 + 0.0350132i
\(681\) 0 0
\(682\) −10340.6 + 17910.4i −0.580589 + 1.00561i
\(683\) −8420.96 + 14585.5i −0.471770 + 0.817130i −0.999478 0.0322958i \(-0.989718\pi\)
0.527708 + 0.849426i \(0.323051\pi\)
\(684\) 0 0
\(685\) −66.0329 + 114.372i −0.00368319 + 0.00637948i
\(686\) 5118.37 + 8865.28i 0.284869 + 0.493408i
\(687\) 0 0
\(688\) 4211.80 0.233391
\(689\) −1350.14 + 27847.9i −0.0746537 + 1.53980i
\(690\) 0 0
\(691\) 12520.8 + 21686.6i 0.689310 + 1.19392i 0.972061 + 0.234727i \(0.0754195\pi\)
−0.282751 + 0.959193i \(0.591247\pi\)
\(692\) 348.448 + 603.529i 0.0191416 + 0.0331543i
\(693\) 0 0
\(694\) −22347.6 −1.22234
\(695\) 4.56819 7.91234i 0.000249326 0.000431845i
\(696\) 0 0
\(697\) 34204.7 1.85881
\(698\) 11971.0 20734.4i 0.649155 1.12437i
\(699\) 0 0
\(700\) −718.828 1245.05i −0.0388131 0.0672262i
\(701\) −28309.0 −1.52527 −0.762635 0.646829i \(-0.776095\pi\)
−0.762635 + 0.646829i \(0.776095\pi\)
\(702\) 0 0
\(703\) −4623.88 −0.248069
\(704\) 16914.6 + 29296.9i 0.905528 + 1.56842i
\(705\) 0 0
\(706\) 12472.5 21603.0i 0.664884 1.15161i
\(707\) 22669.1 1.20588
\(708\) 0 0
\(709\) 2520.59 4365.78i 0.133516 0.231256i −0.791514 0.611151i \(-0.790707\pi\)
0.925029 + 0.379895i \(0.124040\pi\)
\(710\) −816.882 −0.0431789
\(711\) 0 0
\(712\) 14638.3 + 25354.3i 0.770498 + 1.33454i
\(713\) −853.978 1479.13i −0.0448552 0.0776914i
\(714\) 0 0
\(715\) 825.269 424.574i 0.0431655 0.0222072i
\(716\) 585.431 0.0305567
\(717\) 0 0
\(718\) 9707.33 + 16813.6i 0.504560 + 0.873924i
\(719\) −5919.62 + 10253.1i −0.307044 + 0.531815i −0.977714 0.209940i \(-0.932673\pi\)
0.670671 + 0.741755i \(0.266006\pi\)
\(720\) 0 0
\(721\) −14008.6 + 24263.6i −0.723590 + 1.25329i
\(722\) −9163.31 + 15871.3i −0.472331 + 0.818101i
\(723\) 0 0
\(724\) −110.874 + 192.039i −0.00569143 + 0.00985784i
\(725\) 12258.1 + 21231.6i 0.627935 + 1.08762i
\(726\) 0 0
\(727\) −31004.9 −1.58172 −0.790858 0.611999i \(-0.790365\pi\)
−0.790858 + 0.611999i \(0.790365\pi\)
\(728\) −26074.1 16787.9i −1.32743 0.854673i
\(729\) 0 0
\(730\) 336.628 + 583.057i 0.0170674 + 0.0295615i
\(731\) −3433.52 5947.02i −0.173725 0.300901i
\(732\) 0 0
\(733\) 15666.0 0.789411 0.394706 0.918808i \(-0.370847\pi\)
0.394706 + 0.918808i \(0.370847\pi\)
\(734\) 19052.9 33000.6i 0.958114 1.65950i
\(735\) 0 0
\(736\) −262.145 −0.0131288
\(737\) 2168.51 3755.97i 0.108383 0.187724i
\(738\) 0 0
\(739\) 16669.7 + 28872.8i 0.829777 + 1.43722i 0.898213 + 0.439561i \(0.144866\pi\)
−0.0684357 + 0.997656i \(0.521801\pi\)
\(740\) 40.2733 0.00200064
\(741\) 0 0
\(742\) −46833.8 −2.31715
\(743\) −1013.07 1754.69i −0.0500215 0.0866397i 0.839931 0.542694i \(-0.182596\pi\)
−0.889952 + 0.456054i \(0.849262\pi\)
\(744\) 0 0
\(745\) −335.415 + 580.956i −0.0164949 + 0.0285699i
\(746\) −17552.5 −0.861451
\(747\) 0 0
\(748\) 1258.69 2180.11i 0.0615271 0.106568i
\(749\) 23022.6 1.12313
\(750\) 0 0
\(751\) −17737.4 30722.0i −0.861846 1.49276i −0.870145 0.492795i \(-0.835975\pi\)
0.00829952 0.999966i \(-0.497358\pi\)
\(752\) 3087.53 + 5347.76i 0.149722 + 0.259325i
\(753\) 0 0
\(754\) 21321.2 + 13727.8i 1.02980 + 0.663044i
\(755\) −457.065 −0.0220322
\(756\) 0 0
\(757\) −1199.29 2077.23i −0.0575811 0.0997333i 0.835798 0.549037i \(-0.185005\pi\)
−0.893379 + 0.449304i \(0.851672\pi\)
\(758\) 3378.73 5852.13i 0.161901 0.280421i
\(759\) 0 0
\(760\) −52.5555 + 91.0289i −0.00250841 + 0.00434469i
\(761\) 2502.53 4334.52i 0.119207 0.206473i −0.800246 0.599671i \(-0.795298\pi\)
0.919454 + 0.393198i \(0.128631\pi\)
\(762\) 0 0
\(763\) −12071.7 + 20908.9i −0.572774 + 0.992074i
\(764\) −376.480 652.082i −0.0178280 0.0308789i
\(765\) 0 0
\(766\) −29853.1 −1.40814
\(767\) −8058.28 5188.37i −0.379358 0.244252i
\(768\) 0 0
\(769\) −7054.78 12219.2i −0.330822 0.573000i 0.651851 0.758347i \(-0.273993\pi\)
−0.982673 + 0.185346i \(0.940659\pi\)
\(770\) 779.493 + 1350.12i 0.0364818 + 0.0631883i
\(771\) 0 0
\(772\) −1674.82 −0.0780803
\(773\) 6366.85 11027.7i 0.296248 0.513116i −0.679027 0.734114i \(-0.737598\pi\)
0.975274 + 0.220997i \(0.0709312\pi\)
\(774\) 0 0
\(775\) −14824.7 −0.687121
\(776\) −7669.59 + 13284.1i −0.354796 + 0.614526i
\(777\) 0 0
\(778\) −6860.46 11882.7i −0.316143 0.547576i
\(779\) 5014.98 0.230655
\(780\) 0 0
\(781\) 59818.8 2.74070
\(782\) −1959.88 3394.60i −0.0896228 0.155231i
\(783\) 0 0
\(784\) 14335.7 24830.1i 0.653046 1.13111i
\(785\) −628.986 −0.0285980
\(786\) 0