Properties

Label 117.4.g.f.100.3
Level $117$
Weight $4$
Character 117.100
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 100.3
Root \(-1.37814 + 2.38701i\) of defining polynomial
Character \(\chi\) \(=\) 117.100
Dual form 117.4.g.f.55.3

$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(-0.995332\pi\)
0.512647 + 0.858600i \(0.328665\pi\)
\(3\) 0 0
\(4\) 0.201468 + 0.348954i 0.0251836 + 0.0436192i
\(5\) 0.313209 0.0280143 0.0140071 0.999902i \(-0.495541\pi\)
0.0140071 + 0.999902i \(0.495541\pi\)
\(6\) 0 0
\(7\) −14.2830 24.7388i −0.771208 1.33577i −0.936901 0.349595i \(-0.886319\pi\)
0.165693 0.986177i \(-0.447014\pi\)
\(8\) −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 −0.000743312 1.00000i \(0.500237\pi\)
−0.865654 + 0.500644i \(0.833097\pi\)
\(12\) 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 −0.966701 0.255907i \(-0.917626\pi\)
0.261729 0.965142i \(-0.415708\pi\)
\(18\) 0 0
\(19\) 7.24486 + 12.5485i 0.0874782 + 0.151517i 0.906445 0.422325i \(-0.138786\pi\)
−0.818966 + 0.573842i \(0.805453\pi\)
\(20\) 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 \(-0.812556\pi\)
0.896795 + 0.442446i \(0.145889\pi\)
\(24\) 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 −0.359439 0.933169i \(-0.617032\pi\)
0.987867 0.155301i \(-0.0496347\pi\)
\(30\) 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 0.256302 + 0.966597i \(0.417496\pi\)
−0.965248 + 0.261335i \(0.915837\pi\)
\(38\) −39.9377 −0.170493
\(39\) 0 0
\(40\) −7.25418 −0.0286747
\(41\) −173.053 + 299.737i −0.659180 + 1.14173i 0.321649 + 0.946859i \(0.395763\pi\)
−0.980828 + 0.194873i \(0.937570\pi\)
\(42\) 0 0
\(43\) 34.7427 + 60.1761i 0.123214 + 0.213413i 0.921033 0.389483i \(-0.127346\pi\)
−0.797819 + 0.602897i \(0.794013\pi\)
\(44\) −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 \(-0.550532\pi\)
−0.158085 + 0.987426i \(0.550532\pi\)
\(48\) 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 \(-0.780145\pi\)
−0.770804 + 0.637072i \(0.780145\pi\)
\(54\) 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 \(-0.0942342\pi\)
−0.730903 + 0.682481i \(0.760901\pi\)
\(60\) 0 0
\(61\) 107.989 + 187.043i 0.226666 + 0.392596i 0.956818 0.290688i \(-0.0938842\pi\)
−0.730152 + 0.683285i \(0.760551\pi\)
\(62\) −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 −0.895604 0.444853i \(-0.853256\pi\)
0.833056 + 0.553189i \(0.186589\pi\)
\(68\) 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 −0.925452 0.378864i \(-0.876315\pi\)
0.134620 0.990897i \(-0.457019\pi\)
\(72\) 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 \(-0.308593\pi\)
0.565733 + 0.824588i \(0.308593\pi\)
\(84\) 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 0.193731 + 0.981055i \(0.437941\pi\)
−0.946484 + 0.322751i \(0.895392\pi\)
\(90\) 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 0.639022 0.769188i \(-0.279339\pi\)
−0.985648 + 0.168815i \(0.946006\pi\)
\(98\) −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 \(-0.705495\pi\)
0.992569 + 0.121680i \(0.0388281\pi\)
\(102\) 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 \(-0.714716\pi\)
0.988628 + 0.150379i \(0.0480494\pi\)
\(108\) 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 \(-0.174137\pi\)
−0.877520 + 0.479539i \(0.840804\pi\)
\(114\) 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 0.412965 + 0.910747i \(0.364493\pi\)
−0.995212 + 0.0977357i \(0.968840\pi\)
\(128\) −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 \(-0.564407\pi\)
−0.200962 + 0.979599i \(0.564407\pi\)
\(132\) 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 \(-0.208638\pi\)
−0.924246 + 0.381799i \(0.875305\pi\)
\(138\) 0 0
\(139\) −14.5851 25.2622i −0.00889995 0.0154152i 0.861541 0.507688i \(-0.169500\pi\)
−0.870441 + 0.492273i \(0.836166\pi\)
\(140\) 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 −0.994390 0.105778i \(-0.966267\pi\)
0.405588 0.914056i \(-0.367067\pi\)
\(150\) 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 0.792581 0.609767i \(-0.208737\pi\)
−0.924364 + 0.381511i \(0.875404\pi\)
\(164\) −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 0.115712 0.993283i \(-0.463085\pi\)
0.802352 0.596851i \(-0.203582\pi\)
\(168\) 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 \(-0.0425762\pi\)
−0.611026 + 0.791611i \(0.709243\pi\)
\(174\) 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 \(-0.931435\pi\)
0.673550 + 0.739141i \(0.264768\pi\)
\(180\) 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 \(-0.281832\pi\)
−0.986939 + 0.161091i \(0.948499\pi\)
\(192\) 0 0
\(193\) −2078.26 + 3599.66i −0.775112 + 1.34253i 0.159620 + 0.987179i \(0.448973\pi\)
−0.934732 + 0.355354i \(0.884360\pi\)
\(194\) 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 \(-0.744571\pi\)
0.970200 + 0.242306i \(0.0779038\pi\)
\(198\) 0 0
\(199\) −404.065 699.861i −0.143937 0.249306i 0.785039 0.619446i \(-0.212643\pi\)
−0.928976 + 0.370141i \(0.879309\pi\)
\(200\) 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 −0.0156511 0.999878i \(-0.504982\pi\)
0.873745 0.486384i \(-0.161685\pi\)
\(212\) −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 −0.262657 0.964889i \(-0.584599\pi\)
0.966947 0.254977i \(-0.0820678\pi\)
\(224\) −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 0.999715 + 0.0238849i \(0.00760352\pi\)
−0.479172 + 0.877721i \(0.659063\pi\)
\(228\) 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 \(-0.461757\pi\)
0.119854 + 0.992792i \(0.461757\pi\)
\(234\) 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 \(-0.595742\pi\)
−0.296267 + 0.955105i \(0.595742\pi\)
\(240\) 0 0
\(241\) −3164.99 5481.92i −0.845954 1.46523i −0.884791 0.465989i \(-0.845699\pi\)
0.0388369 0.999246i \(-0.487635\pi\)
\(242\) 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 \(-0.316321\pi\)
−0.998572 + 0.0534200i \(0.982988\pi\)
\(252\) 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 \(-0.711700\pi\)
0.990009 + 0.141005i \(0.0450334\pi\)
\(258\) 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 \(-0.969680\pi\)
0.580100 + 0.814545i \(0.303014\pi\)
\(264\) 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 0.978285 + 0.207263i \(0.0664557\pi\)
−0.309647 + 0.950852i \(0.600211\pi\)
\(270\) 0 0
\(271\) 1054.76 1826.90i 0.236429 0.409507i −0.723258 0.690578i \(-0.757356\pi\)
0.959687 + 0.281071i \(0.0906896\pi\)
\(272\) −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 −0.927235 0.374480i \(-0.877821\pi\)
0.139308 0.990249i \(-0.455512\pi\)
\(278\) 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 \(-0.330951\pi\)
0.506469 + 0.862258i \(0.330951\pi\)
\(282\) 0 0
\(283\) −1018.13 + 1763.45i −0.213857 + 0.370411i −0.952918 0.303227i \(-0.901936\pi\)
0.739061 + 0.673638i \(0.235269\pi\)
\(284\) 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 \(-0.287571\pi\)
−0.989683 + 0.143273i \(0.954237\pi\)
\(294\) 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 \(-0.636764\pi\)
−0.416560 + 0.909108i \(0.636764\pi\)
\(312\) 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 \(-0.651093\pi\)
−0.457047 + 0.889442i \(0.651093\pi\)
\(318\) 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 0.987722 + 0.156220i \(0.0499309\pi\)
−0.358570 + 0.933503i \(0.616736\pi\)
\(332\) 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 0.988117 + 0.153703i \(0.0491198\pi\)
−0.360948 + 0.932586i \(0.617547\pi\)
\(348\) 0 0
\(349\) −4343.19 + 7522.62i −0.666148 + 1.15380i 0.312825 + 0.949811i \(0.398725\pi\)
−0.978973 + 0.203991i \(0.934609\pi\)
\(350\) −9834.24 −1.50189
\(351\) 0 0
\(352\) 1151.64 0.174383
\(353\) 4525.12 7837.73i 0.682288 1.18176i −0.291993 0.956421i \(-0.594318\pi\)
0.974281 0.225337i \(-0.0723483\pi\)
\(354\) 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 \(-0.673237\pi\)
−0.517768 + 0.855521i \(0.673237\pi\)
\(360\) 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 −0.333491 + 0.942753i \(0.608227\pi\)
−0.649703 + 0.760188i \(0.725107\pi\)
\(368\) −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 0.555837 0.831291i \(-0.312398\pi\)
−0.997838 + 0.0657238i \(0.979064\pi\)
\(374\) −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 −0.937059 0.349171i \(-0.886463\pi\)
0.770920 + 0.636932i \(0.219797\pi\)
\(380\) −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 0.959995 + 0.280018i \(0.0903405\pi\)
−0.237494 + 0.971389i \(0.576326\pi\)
\(384\) 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 \(-0.394831\pi\)
0.324419 + 0.945914i \(0.394831\pi\)
\(390\) 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 −0.993207 0.116361i \(-0.962877\pi\)
0.395832 0.918323i \(-0.370456\pi\)
\(398\) 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 −0.452013 0.892011i \(-0.649294\pi\)
0.998511 0.0545506i \(-0.0173726\pi\)
\(402\) 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 0.969689 0.244342i \(-0.0785719\pi\)
−0.696451 + 0.717605i \(0.745239\pi\)
\(410\) −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 −0.268541 0.963268i \(-0.586542\pi\)
0.968485 0.249070i \(-0.0801251\pi\)
\(420\) 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 \(-0.907115\pi\)
0.728003 + 0.685574i \(0.240449\pi\)
\(432\) 0 0
\(433\) −1453.03 2516.72i −0.161266 0.279321i 0.774057 0.633116i \(-0.218224\pi\)
−0.935323 + 0.353795i \(0.884891\pi\)
\(434\) 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 −0.999796 0.0201788i \(-0.993576\pi\)
0.517374 + 0.855760i \(0.326910\pi\)
\(440\) 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 \(-0.737085\pi\)
−0.677843 + 0.735207i \(0.737085\pi\)
\(444\) 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 \(-0.196391\pi\)
−0.908875 + 0.417069i \(0.863057\pi\)
\(450\) 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 −0.979590 0.201008i \(-0.935578\pi\)
0.663873 + 0.747845i \(0.268912\pi\)
\(458\) 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 \(-0.289576\pi\)
−0.990566 + 0.137036i \(0.956243\pi\)
\(462\) 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 \(-0.563374\pi\)
−0.197782 + 0.980246i \(0.563374\pi\)
\(468\) 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 \(-0.785305\pi\)
0.931343 + 0.364143i \(0.118638\pi\)
\(480\) 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 0.942517 0.334157i \(-0.108452\pi\)
−0.760647 + 0.649166i \(0.775118\pi\)
\(488\) −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 \(-0.734547\pi\)
0.977348 + 0.211641i \(0.0678806\pi\)
\(492\) 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 \(-0.00530250\pi\)
−0.514356 + 0.857576i \(0.671969\pi\)
\(504\) 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 \(-0.994230\pi\)
0.515616 + 0.856820i \(0.327563\pi\)
\(510\) 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 \(-0.532220\pi\)
−0.101048 + 0.994882i \(0.532220\pi\)
\(522\) 0 0
\(523\) −2125.86 + 3682.10i −0.177739 + 0.307853i −0.941106 0.338113i \(-0.890212\pi\)
0.763367 + 0.645965i \(0.223545\pi\)
\(524\) −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 \(-0.803457\pi\)
0.909074 + 0.416635i \(0.136791\pi\)
\(558\) 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 0.976523 + 0.215413i \(0.0691098\pi\)
−0.301708 + 0.953400i \(0.597557\pi\)
\(564\) 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 \(-0.688565\pi\)
0.997635 + 0.0687410i \(0.0218982\pi\)
\(570\) 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 \(-0.990889\pi\)
0.524579 + 0.851362i \(0.324223\pi\)
\(588\) 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 \(-0.684659\pi\)
−0.548126 + 0.836396i \(0.684659\pi\)
\(594\) 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 \(-0.435351\pi\)
0.201706 + 0.979446i \(0.435351\pi\)
\(600\) 0 0
\(601\) −4946.10 + 8566.89i −0.335700 + 0.581449i −0.983619 0.180260i \(-0.942306\pi\)
0.647919 + 0.761709i \(0.275639\pi\)
\(602\) 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 0.997401 + 0.0720510i \(0.0229544\pi\)
−0.436302 + 0.899800i \(0.643712\pi\)
\(608\) 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 −0.994137 0.108132i \(-0.965513\pi\)
0.590713 + 0.806882i \(0.298847\pi\)
\(614\) 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 \(-0.0604031\pi\)
−0.654379 + 0.756167i \(0.727070\pi\)
\(618\) 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 0.657373 0.753566i \(-0.271668\pi\)
−0.981293 + 0.192519i \(0.938334\pi\)
\(632\) −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 \(-0.304909\pi\)
−0.996016 + 0.0891780i \(0.971576\pi\)
\(642\) 0 0
\(643\) −12335.8 21366.2i −0.756572 1.31042i −0.944589 0.328256i \(-0.893539\pi\)
0.188017 0.982166i \(-0.439794\pi\)
\(644\) −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 0.498326 + 0.866990i \(0.333948\pi\)
−0.999998 + 0.00193194i \(0.999385\pi\)
\(648\) 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 0.112412 0.993662i \(-0.464142\pi\)
0.804330 0.594182i \(-0.202524\pi\)
\(654\) 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 \(-0.188395\pi\)
−0.898113 + 0.439765i \(0.855062\pi\)
\(660\) 0 0
\(661\) 13811.2 23921.7i 0.812700 1.40764i −0.0982684 0.995160i \(-0.531330\pi\)
0.910968 0.412477i \(-0.135336\pi\)
\(662\) −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 −0.657484 0.753469i \(-0.728379\pi\)
0.981265 + 0.192663i \(0.0617125\pi\)
\(674\) 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 \(-0.644564\pi\)
−0.438710 + 0.898629i \(0.644564\pi\)
\(678\) 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 \(-0.0102819\pi\)
−0.527708 + 0.849426i \(0.676949\pi\)
\(684\) 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 −0.282751 0.959193i \(-0.591247\pi\)
0.972061 0.234727i \(-0.0754195\pi\)
\(692\) −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 \(-0.223905\pi\)
0.762635 + 0.646829i \(0.223905\pi\)
\(702\) 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 0.925029 0.379895i \(-0.124040\pi\)
−0.791514 + 0.611151i \(0.790707\pi\)
\(710\) 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 \(-0.0673269\pi\)
−0.670671 + 0.741755i \(0.733994\pi\)
\(720\) 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 −0.0684357 0.997656i \(-0.521801\pi\)
0.898213 0.439561i \(-0.144866\pi\)
\(740\) −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 \(-0.817404\pi\)
0.889952 + 0.456054i \(0.150738\pi\)
\(744\) 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 0.00829952 + 0.999966i \(0.497358\pi\)
−0.870145 + 0.492795i \(0.835975\pi\)
\(752\) −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 −0.893379 0.449304i \(-0.851672\pi\)
0.835798 + 0.549037i \(0.185005\pi\)
\(758\) −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 \(-0.204702\pi\)
−0.919454 + 0.393198i \(0.871369\pi\)
\(762\) 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 −0.982673 0.185346i \(-0.940659\pi\)
0.651851 + 0.758347i \(0.273993\pi\)
\(770\) −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 \(-0.262402\pi\)
−0.975274 + 0.220997i \(0.929069\pi\)
\(774\) 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
\(786\)