Properties

Label 76.6.d.a.75.9
Level $76$
Weight $6$
Character 76.75
Analytic conductor $12.189$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,6,Mod(75,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.75");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 75.9
Character \(\chi\) \(=\) 76.75
Dual form 76.6.d.a.75.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.77452 - 3.03380i) q^{2} +25.5646 q^{3} +(13.5921 + 28.9699i) q^{4} +94.0869 q^{5} +(-122.059 - 77.5580i) q^{6} -166.433i q^{7} +(22.9933 - 179.553i) q^{8} +410.550 q^{9} +O(q^{10})\) \(q+(-4.77452 - 3.03380i) q^{2} +25.5646 q^{3} +(13.5921 + 28.9699i) q^{4} +94.0869 q^{5} +(-122.059 - 77.5580i) q^{6} -166.433i q^{7} +(22.9933 - 179.553i) q^{8} +410.550 q^{9} +(-449.220 - 285.441i) q^{10} +721.639i q^{11} +(347.476 + 740.605i) q^{12} -430.611i q^{13} +(-504.924 + 794.636i) q^{14} +2405.30 q^{15} +(-654.511 + 787.522i) q^{16} -541.677 q^{17} +(-1960.18 - 1245.53i) q^{18} +(-1417.04 + 684.177i) q^{19} +(1278.84 + 2725.69i) q^{20} -4254.79i q^{21} +(2189.31 - 3445.48i) q^{22} -9.20716i q^{23} +(587.816 - 4590.21i) q^{24} +5727.35 q^{25} +(-1306.39 + 2055.96i) q^{26} +4283.35 q^{27} +(4821.54 - 2262.17i) q^{28} -3732.49i q^{29} +(-11484.1 - 7297.20i) q^{30} -3182.34 q^{31} +(5514.16 - 1774.38i) q^{32} +18448.4i q^{33} +(2586.25 + 1643.34i) q^{34} -15659.1i q^{35} +(5580.23 + 11893.6i) q^{36} +49.0739i q^{37} +(8841.34 + 1032.40i) q^{38} -11008.4i q^{39} +(2163.37 - 16893.6i) q^{40} -798.065i q^{41} +(-12908.2 + 20314.6i) q^{42} +8741.19i q^{43} +(-20905.8 + 9808.57i) q^{44} +38627.4 q^{45} +(-27.9327 + 43.9598i) q^{46} -15993.5i q^{47} +(-16732.3 + 20132.7i) q^{48} -10892.8 q^{49} +(-27345.4 - 17375.7i) q^{50} -13847.8 q^{51} +(12474.8 - 5852.89i) q^{52} +28325.1i q^{53} +(-20451.0 - 12994.8i) q^{54} +67896.8i q^{55} +(-29883.5 - 3826.84i) q^{56} +(-36226.1 + 17490.7i) q^{57} +(-11323.6 + 17820.9i) q^{58} -11895.3 q^{59} +(32693.0 + 69681.2i) q^{60} +19568.1 q^{61} +(15194.1 + 9654.59i) q^{62} -68328.9i q^{63} +(-31710.6 - 8257.05i) q^{64} -40514.9i q^{65} +(55968.9 - 88082.3i) q^{66} +25458.9 q^{67} +(-7362.52 - 15692.3i) q^{68} -235.378i q^{69} +(-47506.7 + 74764.9i) q^{70} +35628.2 q^{71} +(9439.92 - 73715.5i) q^{72} -18156.0 q^{73} +(148.880 - 234.304i) q^{74} +146418. q^{75} +(-39081.1 - 31752.1i) q^{76} +120104. q^{77} +(-33397.3 + 52559.8i) q^{78} -96443.4 q^{79} +(-61580.9 + 74095.6i) q^{80} +9738.65 q^{81} +(-2421.17 + 3810.38i) q^{82} -34700.1i q^{83} +(123261. - 57831.4i) q^{84} -50964.8 q^{85} +(26519.1 - 41735.0i) q^{86} -95419.7i q^{87} +(129572. + 16592.9i) q^{88} +32267.6i q^{89} +(-184427. - 117188. i) q^{90} -71667.7 q^{91} +(266.731 - 125.144i) q^{92} -81355.3 q^{93} +(-48521.1 + 76361.3i) q^{94} +(-133325. + 64372.2i) q^{95} +(140968. - 45361.5i) q^{96} -6031.95i q^{97} +(52008.0 + 33046.7i) q^{98} +296269. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.77452 3.03380i −0.844024 0.536306i
\(3\) 25.5646 1.63997 0.819986 0.572384i \(-0.193981\pi\)
0.819986 + 0.572384i \(0.193981\pi\)
\(4\) 13.5921 + 28.9699i 0.424752 + 0.905310i
\(5\) 94.0869 1.68308 0.841539 0.540196i \(-0.181650\pi\)
0.841539 + 0.540196i \(0.181650\pi\)
\(6\) −122.059 77.5580i −1.38417 0.879526i
\(7\) 166.433i 1.28379i −0.766793 0.641894i \(-0.778149\pi\)
0.766793 0.641894i \(-0.221851\pi\)
\(8\) 22.9933 179.553i 0.127022 0.991900i
\(9\) 410.550 1.68951
\(10\) −449.220 285.441i −1.42056 0.902645i
\(11\) 721.639i 1.79820i 0.437743 + 0.899100i \(0.355778\pi\)
−0.437743 + 0.899100i \(0.644222\pi\)
\(12\) 347.476 + 740.605i 0.696582 + 1.48468i
\(13\) 430.611i 0.706686i −0.935494 0.353343i \(-0.885045\pi\)
0.935494 0.353343i \(-0.114955\pi\)
\(14\) −504.924 + 794.636i −0.688503 + 1.08355i
\(15\) 2405.30 2.76020
\(16\) −654.511 + 787.522i −0.639171 + 0.769065i
\(17\) −541.677 −0.454588 −0.227294 0.973826i \(-0.572988\pi\)
−0.227294 + 0.973826i \(0.572988\pi\)
\(18\) −1960.18 1245.53i −1.42598 0.906092i
\(19\) −1417.04 + 684.177i −0.900529 + 0.434795i
\(20\) 1278.84 + 2725.69i 0.714892 + 1.52371i
\(21\) 4254.79i 2.10538i
\(22\) 2189.31 3445.48i 0.964385 1.51772i
\(23\) 9.20716i 0.00362916i −0.999998 0.00181458i \(-0.999422\pi\)
0.999998 0.00181458i \(-0.000577599\pi\)
\(24\) 587.816 4590.21i 0.208312 1.62669i
\(25\) 5727.35 1.83275
\(26\) −1306.39 + 2055.96i −0.379000 + 0.596460i
\(27\) 4283.35 1.13077
\(28\) 4821.54 2262.17i 1.16223 0.545292i
\(29\) 3732.49i 0.824145i −0.911151 0.412073i \(-0.864805\pi\)
0.911151 0.412073i \(-0.135195\pi\)
\(30\) −11484.1 7297.20i −2.32967 1.48031i
\(31\) −3182.34 −0.594761 −0.297380 0.954759i \(-0.596113\pi\)
−0.297380 + 0.954759i \(0.596113\pi\)
\(32\) 5514.16 1774.38i 0.951929 0.306318i
\(33\) 18448.4i 2.94900i
\(34\) 2586.25 + 1643.34i 0.383684 + 0.243798i
\(35\) 15659.1i 2.16072i
\(36\) 5580.23 + 11893.6i 0.717622 + 1.52953i
\(37\) 49.0739i 0.00589313i 0.999996 + 0.00294656i \(0.000937922\pi\)
−0.999996 + 0.00294656i \(0.999062\pi\)
\(38\) 8841.34 + 1032.40i 0.993251 + 0.115982i
\(39\) 11008.4i 1.15894i
\(40\) 2163.37 16893.6i 0.213787 1.66945i
\(41\) 798.065i 0.0741444i −0.999313 0.0370722i \(-0.988197\pi\)
0.999313 0.0370722i \(-0.0118032\pi\)
\(42\) −12908.2 + 20314.6i −1.12913 + 1.77699i
\(43\) 8741.19i 0.720941i 0.932771 + 0.360470i \(0.117384\pi\)
−0.932771 + 0.360470i \(0.882616\pi\)
\(44\) −20905.8 + 9808.57i −1.62793 + 0.763790i
\(45\) 38627.4 2.84357
\(46\) −27.9327 + 43.9598i −0.00194634 + 0.00306310i
\(47\) 15993.5i 1.05609i −0.849218 0.528043i \(-0.822926\pi\)
0.849218 0.528043i \(-0.177074\pi\)
\(48\) −16732.3 + 20132.7i −1.04822 + 1.26124i
\(49\) −10892.8 −0.648112
\(50\) −27345.4 17375.7i −1.54689 0.982916i
\(51\) −13847.8 −0.745512
\(52\) 12474.8 5852.89i 0.639770 0.300167i
\(53\) 28325.1i 1.38510i 0.721370 + 0.692550i \(0.243513\pi\)
−0.721370 + 0.692550i \(0.756487\pi\)
\(54\) −20451.0 12994.8i −0.954397 0.606439i
\(55\) 67896.8i 3.02651i
\(56\) −29883.5 3826.84i −1.27339 0.163069i
\(57\) −36226.1 + 17490.7i −1.47684 + 0.713052i
\(58\) −11323.6 + 17820.9i −0.441994 + 0.695598i
\(59\) −11895.3 −0.444884 −0.222442 0.974946i \(-0.571403\pi\)
−0.222442 + 0.974946i \(0.571403\pi\)
\(60\) 32693.0 + 69681.2i 1.17240 + 2.49884i
\(61\) 19568.1 0.673324 0.336662 0.941625i \(-0.390702\pi\)
0.336662 + 0.941625i \(0.390702\pi\)
\(62\) 15194.1 + 9654.59i 0.501992 + 0.318973i
\(63\) 68328.9i 2.16897i
\(64\) −31710.6 8257.05i −0.967731 0.251985i
\(65\) 40514.9i 1.18941i
\(66\) 55968.9 88082.3i 1.58156 2.48902i
\(67\) 25458.9 0.692872 0.346436 0.938074i \(-0.387392\pi\)
0.346436 + 0.938074i \(0.387392\pi\)
\(68\) −7362.52 15692.3i −0.193088 0.411543i
\(69\) 235.378i 0.00595172i
\(70\) −47506.7 + 74764.9i −1.15880 + 1.82370i
\(71\) 35628.2 0.838780 0.419390 0.907806i \(-0.362244\pi\)
0.419390 + 0.907806i \(0.362244\pi\)
\(72\) 9439.92 73715.5i 0.214604 1.67582i
\(73\) −18156.0 −0.398761 −0.199381 0.979922i \(-0.563893\pi\)
−0.199381 + 0.979922i \(0.563893\pi\)
\(74\) 148.880 234.304i 0.00316052 0.00497394i
\(75\) 146418. 3.00566
\(76\) −39081.1 31752.1i −0.776126 0.630578i
\(77\) 120104. 2.30851
\(78\) −33397.3 + 52559.8i −0.621549 + 0.978177i
\(79\) −96443.4 −1.73862 −0.869310 0.494267i \(-0.835436\pi\)
−0.869310 + 0.494267i \(0.835436\pi\)
\(80\) −61580.9 + 74095.6i −1.07577 + 1.29440i
\(81\) 9738.65 0.164925
\(82\) −2421.17 + 3810.38i −0.0397641 + 0.0625796i
\(83\) 34700.1i 0.552887i −0.961030 0.276443i \(-0.910844\pi\)
0.961030 0.276443i \(-0.0891558\pi\)
\(84\) 123261. 57831.4i 1.90602 0.894264i
\(85\) −50964.8 −0.765108
\(86\) 26519.1 41735.0i 0.386645 0.608491i
\(87\) 95419.7i 1.35157i
\(88\) 129572. + 16592.9i 1.78363 + 0.228410i
\(89\) 32267.6i 0.431808i 0.976415 + 0.215904i \(0.0692699\pi\)
−0.976415 + 0.215904i \(0.930730\pi\)
\(90\) −184427. 117188.i −2.40004 1.52502i
\(91\) −71667.7 −0.907235
\(92\) 266.731 125.144i 0.00328551 0.00154149i
\(93\) −81355.3 −0.975390
\(94\) −48521.1 + 76361.3i −0.566385 + 0.891361i
\(95\) −133325. + 64372.2i −1.51566 + 0.731794i
\(96\) 140968. 45361.5i 1.56114 0.502353i
\(97\) 6031.95i 0.0650922i −0.999470 0.0325461i \(-0.989638\pi\)
0.999470 0.0325461i \(-0.0103616\pi\)
\(98\) 52008.0 + 33046.7i 0.547022 + 0.347586i
\(99\) 296269.i 3.03807i
\(100\) 77846.6 + 165921.i 0.778466 + 1.65921i
\(101\) −108403. −1.05739 −0.528697 0.848811i \(-0.677319\pi\)
−0.528697 + 0.848811i \(0.677319\pi\)
\(102\) 66116.5 + 42011.4i 0.629230 + 0.399822i
\(103\) −77927.4 −0.723765 −0.361882 0.932224i \(-0.617866\pi\)
−0.361882 + 0.932224i \(0.617866\pi\)
\(104\) −77317.5 9901.18i −0.700962 0.0897643i
\(105\) 400320.i 3.54351i
\(106\) 85932.7 135239.i 0.742837 1.16906i
\(107\) 94800.4 0.800481 0.400240 0.916410i \(-0.368927\pi\)
0.400240 + 0.916410i \(0.368927\pi\)
\(108\) 58219.7 + 124088.i 0.480297 + 1.02370i
\(109\) 226846.i 1.82880i 0.404816 + 0.914398i \(0.367336\pi\)
−0.404816 + 0.914398i \(0.632664\pi\)
\(110\) 205985. 324174.i 1.62314 2.55445i
\(111\) 1254.55i 0.00966456i
\(112\) 131069. + 108932.i 0.987316 + 0.820560i
\(113\) 39331.1i 0.289761i 0.989449 + 0.144880i \(0.0462797\pi\)
−0.989449 + 0.144880i \(0.953720\pi\)
\(114\) 226026. + 26392.9i 1.62890 + 0.190207i
\(115\) 866.274i 0.00610816i
\(116\) 108130. 50732.3i 0.746107 0.350058i
\(117\) 176787.i 1.19395i
\(118\) 56794.6 + 36088.1i 0.375493 + 0.238594i
\(119\) 90152.8i 0.583595i
\(120\) 55305.8 431879.i 0.350605 2.73784i
\(121\) −359711. −2.23352
\(122\) −93428.3 59365.8i −0.568302 0.361108i
\(123\) 20402.2i 0.121595i
\(124\) −43254.6 92192.0i −0.252626 0.538442i
\(125\) 244848. 1.40159
\(126\) −207296. + 326238.i −1.16323 + 1.83066i
\(127\) −164306. −0.903950 −0.451975 0.892031i \(-0.649280\pi\)
−0.451975 + 0.892031i \(0.649280\pi\)
\(128\) 126353. + 135627.i 0.681647 + 0.731681i
\(129\) 223465.i 1.18232i
\(130\) −122914. + 193439.i −0.637886 + 1.00389i
\(131\) 345339.i 1.75819i −0.476642 0.879097i \(-0.658146\pi\)
0.476642 0.879097i \(-0.341854\pi\)
\(132\) −534449. + 250752.i −2.66975 + 1.25259i
\(133\) 113869. + 235842.i 0.558185 + 1.15609i
\(134\) −121554. 77237.3i −0.584800 0.371591i
\(135\) 403008. 1.90318
\(136\) −12455.0 + 97259.8i −0.0577425 + 0.450906i
\(137\) −269095. −1.22491 −0.612455 0.790506i \(-0.709818\pi\)
−0.612455 + 0.790506i \(0.709818\pi\)
\(138\) −714.089 + 1123.81i −0.00319194 + 0.00502339i
\(139\) 105247.i 0.462033i 0.972950 + 0.231016i \(0.0742051\pi\)
−0.972950 + 0.231016i \(0.925795\pi\)
\(140\) 453644. 212840.i 1.95612 0.917770i
\(141\) 408868.i 1.73195i
\(142\) −170108. 108089.i −0.707950 0.449842i
\(143\) 310745. 1.27076
\(144\) −268709. + 323317.i −1.07988 + 1.29934i
\(145\) 351179.i 1.38710i
\(146\) 86686.2 + 55081.7i 0.336564 + 0.213858i
\(147\) −278471. −1.06289
\(148\) −1421.66 + 667.016i −0.00533510 + 0.00250312i
\(149\) 9590.81 0.0353908 0.0176954 0.999843i \(-0.494367\pi\)
0.0176954 + 0.999843i \(0.494367\pi\)
\(150\) −699074. 444202.i −2.53685 1.61195i
\(151\) 93897.3 0.335128 0.167564 0.985861i \(-0.446410\pi\)
0.167564 + 0.985861i \(0.446410\pi\)
\(152\) 90263.7 + 270165.i 0.316887 + 0.948463i
\(153\) −222386. −0.768030
\(154\) −573440. 364373.i −1.94844 1.23807i
\(155\) −299417. −1.00103
\(156\) 318912. 149627.i 1.04920 0.492265i
\(157\) 499368. 1.61686 0.808428 0.588595i \(-0.200319\pi\)
0.808428 + 0.588595i \(0.200319\pi\)
\(158\) 460471. + 292590.i 1.46744 + 0.932432i
\(159\) 724120.i 2.27153i
\(160\) 518811. 166946.i 1.60217 0.515557i
\(161\) −1532.37 −0.00465907
\(162\) −46497.4 29545.1i −0.139201 0.0884501i
\(163\) 225573.i 0.664993i −0.943104 0.332497i \(-0.892109\pi\)
0.943104 0.332497i \(-0.107891\pi\)
\(164\) 23119.9 10847.4i 0.0671236 0.0314930i
\(165\) 1.73576e6i 4.96339i
\(166\) −105273. + 165677.i −0.296516 + 0.466649i
\(167\) 352587. 0.978306 0.489153 0.872198i \(-0.337306\pi\)
0.489153 + 0.872198i \(0.337306\pi\)
\(168\) −763960. 97831.8i −2.08832 0.267428i
\(169\) 185867. 0.500595
\(170\) 243332. + 154617.i 0.645769 + 0.410332i
\(171\) −581765. + 280889.i −1.52145 + 0.734589i
\(172\) −253231. + 118811.i −0.652674 + 0.306221i
\(173\) 542727.i 1.37869i −0.724434 0.689344i \(-0.757899\pi\)
0.724434 0.689344i \(-0.242101\pi\)
\(174\) −289485. + 455583.i −0.724857 + 1.14076i
\(175\) 953219.i 2.35287i
\(176\) −568307. 472320.i −1.38293 1.14936i
\(177\) −304100. −0.729597
\(178\) 97893.4 154062.i 0.231581 0.364457i
\(179\) −429784. −1.00258 −0.501288 0.865280i \(-0.667140\pi\)
−0.501288 + 0.865280i \(0.667140\pi\)
\(180\) 525027. + 1.11903e6i 1.20781 + 2.57431i
\(181\) 175918.i 0.399131i −0.979885 0.199565i \(-0.936047\pi\)
0.979885 0.199565i \(-0.0639530\pi\)
\(182\) 342179. + 217426.i 0.765728 + 0.486555i
\(183\) 500251. 1.10423
\(184\) −1653.17 211.703i −0.00359976 0.000460981i
\(185\) 4617.21i 0.00991860i
\(186\) 388432. + 246816.i 0.823253 + 0.523107i
\(187\) 390895.i 0.817441i
\(188\) 463330. 217385.i 0.956084 0.448575i
\(189\) 712890.i 1.45167i
\(190\) 831855. + 97135.4i 1.67172 + 0.195206i
\(191\) 95349.0i 0.189118i 0.995519 + 0.0945590i \(0.0301441\pi\)
−0.995519 + 0.0945590i \(0.969856\pi\)
\(192\) −810670. 211088.i −1.58705 0.413249i
\(193\) 912221.i 1.76281i 0.472357 + 0.881407i \(0.343403\pi\)
−0.472357 + 0.881407i \(0.656597\pi\)
\(194\) −18299.8 + 28799.7i −0.0349093 + 0.0549393i
\(195\) 1.03575e6i 1.95060i
\(196\) −148056. 315564.i −0.275287 0.586742i
\(197\) 144265. 0.264847 0.132424 0.991193i \(-0.457724\pi\)
0.132424 + 0.991193i \(0.457724\pi\)
\(198\) 898821. 1.41454e6i 1.62933 2.56420i
\(199\) 607857.i 1.08810i 0.839053 + 0.544050i \(0.183110\pi\)
−0.839053 + 0.544050i \(0.816890\pi\)
\(200\) 131691. 1.02836e6i 0.232799 1.81791i
\(201\) 650847. 1.13629
\(202\) 517571. + 328873.i 0.892466 + 0.567086i
\(203\) −621208. −1.05803
\(204\) −188220. 401169.i −0.316658 0.674919i
\(205\) 75087.5i 0.124791i
\(206\) 372066. + 236417.i 0.610875 + 0.388159i
\(207\) 3780.00i 0.00613149i
\(208\) 339116. + 281839.i 0.543487 + 0.451693i
\(209\) −493729. 1.02259e6i −0.781849 1.61933i
\(210\) −1.21449e6 + 1.91134e6i −1.90041 + 2.99081i
\(211\) 778502. 1.20380 0.601899 0.798572i \(-0.294411\pi\)
0.601899 + 0.798572i \(0.294411\pi\)
\(212\) −820575. + 384997.i −1.25394 + 0.588325i
\(213\) 910822. 1.37558
\(214\) −452627. 287606.i −0.675625 0.429302i
\(215\) 822432.i 1.21340i
\(216\) 98488.6 769089.i 0.143632 1.12161i
\(217\) 529645.i 0.763547i
\(218\) 688207. 1.08308e6i 0.980794 1.54355i
\(219\) −464151. −0.653957
\(220\) −1.96696e6 + 922858.i −2.73993 + 1.28552i
\(221\) 233252.i 0.321251i
\(222\) 3806.07 5989.90i 0.00518316 0.00815712i
\(223\) −281144. −0.378588 −0.189294 0.981920i \(-0.560620\pi\)
−0.189294 + 0.981920i \(0.560620\pi\)
\(224\) −295315. 917737.i −0.393248 1.22208i
\(225\) 2.35136e6 3.09645
\(226\) 119323. 187787.i 0.155400 0.244565i
\(227\) 541554. 0.697553 0.348777 0.937206i \(-0.386597\pi\)
0.348777 + 0.937206i \(0.386597\pi\)
\(228\) −999093. 811731.i −1.27282 1.03413i
\(229\) 786356. 0.990901 0.495451 0.868636i \(-0.335003\pi\)
0.495451 + 0.868636i \(0.335003\pi\)
\(230\) −2628.10 + 4136.04i −0.00327584 + 0.00515543i
\(231\) 3.07042e6 3.78589
\(232\) −670180. 85822.5i −0.817470 0.104684i
\(233\) 355481. 0.428969 0.214485 0.976727i \(-0.431193\pi\)
0.214485 + 0.976727i \(0.431193\pi\)
\(234\) −536338. + 844074.i −0.640322 + 1.00772i
\(235\) 1.50478e6i 1.77747i
\(236\) −161682. 344607.i −0.188966 0.402758i
\(237\) −2.46554e6 −2.85129
\(238\) 273506. 430436.i 0.312986 0.492568i
\(239\) 104233.i 0.118034i 0.998257 + 0.0590172i \(0.0187967\pi\)
−0.998257 + 0.0590172i \(0.981203\pi\)
\(240\) −1.57429e6 + 1.89423e6i −1.76424 + 2.12277i
\(241\) 306180.i 0.339574i 0.985481 + 0.169787i \(0.0543080\pi\)
−0.985481 + 0.169787i \(0.945692\pi\)
\(242\) 1.71745e6 + 1.09129e6i 1.88515 + 1.19785i
\(243\) −791890. −0.860298
\(244\) 265971. + 566886.i 0.285996 + 0.609567i
\(245\) −1.02487e6 −1.09082
\(246\) −61896.3 + 97410.8i −0.0652119 + 0.102629i
\(247\) 294614. + 610192.i 0.307264 + 0.636392i
\(248\) −73172.6 + 571399.i −0.0755474 + 0.589943i
\(249\) 887096.i 0.906718i
\(250\) −1.16903e6 742819.i −1.18297 0.751680i
\(251\) 248473.i 0.248940i 0.992223 + 0.124470i \(0.0397231\pi\)
−0.992223 + 0.124470i \(0.960277\pi\)
\(252\) 1.97948e6 928732.i 1.96359 0.921274i
\(253\) 6644.24 0.00652596
\(254\) 784483. + 498472.i 0.762955 + 0.484793i
\(255\) −1.30290e6 −1.25476
\(256\) −191807. 1.03088e6i −0.182921 0.983128i
\(257\) 878165.i 0.829361i −0.909967 0.414680i \(-0.863893\pi\)
0.909967 0.414680i \(-0.136107\pi\)
\(258\) 677950. 1.06694e6i 0.634086 0.997908i
\(259\) 8167.49 0.00756553
\(260\) 1.17371e6 550681.i 1.07678 0.505204i
\(261\) 1.53237e6i 1.39240i
\(262\) −1.04769e6 + 1.64883e6i −0.942930 + 1.48396i
\(263\) 1.28149e6i 1.14242i −0.820804 0.571211i \(-0.806474\pi\)
0.820804 0.571211i \(-0.193526\pi\)
\(264\) 3.31247e6 + 424191.i 2.92511 + 0.374586i
\(265\) 2.66502e6i 2.33123i
\(266\) 171825. 1.47149e6i 0.148896 1.27512i
\(267\) 824908.i 0.708153i
\(268\) 346039. + 737542.i 0.294299 + 0.627263i
\(269\) 1.88601e6i 1.58914i −0.607171 0.794571i \(-0.707696\pi\)
0.607171 0.794571i \(-0.292304\pi\)
\(270\) −1.92417e6 1.22265e6i −1.60633 1.02068i
\(271\) 1.37764e6i 1.13949i −0.821820 0.569747i \(-0.807041\pi\)
0.821820 0.569747i \(-0.192959\pi\)
\(272\) 354534. 426583.i 0.290560 0.349608i
\(273\) −1.83216e6 −1.48784
\(274\) 1.28480e6 + 816381.i 1.03385 + 0.656926i
\(275\) 4.13308e6i 3.29566i
\(276\) 6818.87 3199.27i 0.00538815 0.00252801i
\(277\) 1.34891e6 1.05629 0.528147 0.849153i \(-0.322887\pi\)
0.528147 + 0.849153i \(0.322887\pi\)
\(278\) 319299. 502504.i 0.247791 0.389967i
\(279\) −1.30651e6 −1.00485
\(280\) −2.81165e6 360056.i −2.14321 0.274457i
\(281\) 454809.i 0.343608i −0.985131 0.171804i \(-0.945040\pi\)
0.985131 0.171804i \(-0.0549596\pi\)
\(282\) −1.24042e6 + 1.95215e6i −0.928854 + 1.46181i
\(283\) 1.15530e6i 0.857487i 0.903426 + 0.428744i \(0.141044\pi\)
−0.903426 + 0.428744i \(0.858956\pi\)
\(284\) 484261. + 1.03215e6i 0.356274 + 0.759355i
\(285\) −3.40840e6 + 1.64565e6i −2.48564 + 1.20012i
\(286\) −1.48366e6 942740.i −1.07255 0.681517i
\(287\) −132824. −0.0951857
\(288\) 2.26384e6 728473.i 1.60829 0.517526i
\(289\) −1.12644e6 −0.793349
\(290\) −1.06541e6 + 1.67671e6i −0.743910 + 1.17075i
\(291\) 154205.i 0.106749i
\(292\) −246778. 525978.i −0.169375 0.361002i
\(293\) 2.20787e6i 1.50247i 0.660036 + 0.751234i \(0.270541\pi\)
−0.660036 + 0.751234i \(0.729459\pi\)
\(294\) 1.32957e6 + 844826.i 0.897101 + 0.570032i
\(295\) −1.11920e6 −0.748775
\(296\) 8811.36 + 1128.37i 0.00584539 + 0.000748554i
\(297\) 3.09103e6i 2.03335i
\(298\) −45791.5 29096.6i −0.0298706 0.0189803i
\(299\) −3964.70 −0.00256468
\(300\) 1.99012e6 + 4.24171e6i 1.27666 + 2.72106i
\(301\) 1.45482e6 0.925535
\(302\) −448314. 284866.i −0.282856 0.179731i
\(303\) −2.77128e6 −1.73410
\(304\) 388663. 1.56375e6i 0.241206 0.970474i
\(305\) 1.84110e6 1.13326
\(306\) 1.06178e6 + 674674.i 0.648236 + 0.411899i
\(307\) −2.72997e6 −1.65315 −0.826575 0.562826i \(-0.809714\pi\)
−0.826575 + 0.562826i \(0.809714\pi\)
\(308\) 1.63247e6 + 3.47941e6i 0.980544 + 2.08991i
\(309\) −1.99219e6 −1.18695
\(310\) 1.42957e6 + 908371.i 0.844892 + 0.536857i
\(311\) 102980.i 0.0603741i −0.999544 0.0301870i \(-0.990390\pi\)
0.999544 0.0301870i \(-0.00961030\pi\)
\(312\) −1.97659e6 253120.i −1.14956 0.147211i
\(313\) −1.53929e6 −0.888094 −0.444047 0.896003i \(-0.646458\pi\)
−0.444047 + 0.896003i \(0.646458\pi\)
\(314\) −2.38424e6 1.51498e6i −1.36467 0.867129i
\(315\) 6.42886e6i 3.65054i
\(316\) −1.31087e6 2.79396e6i −0.738483 1.57399i
\(317\) 1.52122e6i 0.850244i −0.905136 0.425122i \(-0.860231\pi\)
0.905136 0.425122i \(-0.139769\pi\)
\(318\) 2.19684e6 3.45732e6i 1.21823 1.91722i
\(319\) 2.69351e6 1.48198
\(320\) −2.98355e6 776881.i −1.62877 0.424111i
\(321\) 2.42354e6 1.31277
\(322\) 7316.34 + 4648.91i 0.00393237 + 0.00249869i
\(323\) 767578. 370603.i 0.409370 0.197653i
\(324\) 132368. + 282128.i 0.0700522 + 0.149308i
\(325\) 2.46626e6i 1.29518i
\(326\) −684343. + 1.07700e6i −0.356640 + 0.561270i
\(327\) 5.79924e6i 2.99917i
\(328\) −143295. 18350.2i −0.0735438 0.00941793i
\(329\) −2.66184e6 −1.35579
\(330\) 5.26594e6 8.28740e6i 2.66190 4.18922i
\(331\) 1.34814e6 0.676338 0.338169 0.941085i \(-0.390192\pi\)
0.338169 + 0.941085i \(0.390192\pi\)
\(332\) 1.00526e6 471647.i 0.500533 0.234840i
\(333\) 20147.3i 0.00995648i
\(334\) −1.68343e6 1.06968e6i −0.825714 0.524671i
\(335\) 2.39535e6 1.16616
\(336\) 3.35074e6 + 2.78480e6i 1.61917 + 1.34569i
\(337\) 3.02702e6i 1.45191i −0.687741 0.725956i \(-0.741397\pi\)
0.687741 0.725956i \(-0.258603\pi\)
\(338\) −887427. 563885.i −0.422514 0.268472i
\(339\) 1.00548e6i 0.475199i
\(340\) −692717. 1.47644e6i −0.324982 0.692660i
\(341\) 2.29650e6i 1.06950i
\(342\) 3.62981e6 + 423852.i 1.67810 + 0.195952i
\(343\) 984312.i 0.451749i
\(344\) 1.56951e6 + 200989.i 0.715101 + 0.0915750i
\(345\) 22146.0i 0.0100172i
\(346\) −1.64653e6 + 2.59126e6i −0.739399 + 1.16365i
\(347\) 1.14412e6i 0.510092i −0.966929 0.255046i \(-0.917909\pi\)
0.966929 0.255046i \(-0.0820906\pi\)
\(348\) 2.76430e6 1.29695e6i 1.22359 0.574085i
\(349\) −1.73948e6 −0.764463 −0.382232 0.924067i \(-0.624844\pi\)
−0.382232 + 0.924067i \(0.624844\pi\)
\(350\) −2.89188e6 + 4.55116e6i −1.26186 + 1.98588i
\(351\) 1.84446e6i 0.799100i
\(352\) 1.28046e6 + 3.97923e6i 0.550821 + 1.71176i
\(353\) 3.46233e6 1.47888 0.739438 0.673225i \(-0.235091\pi\)
0.739438 + 0.673225i \(0.235091\pi\)
\(354\) 1.45193e6 + 922580.i 0.615798 + 0.391287i
\(355\) 3.35215e6 1.41173
\(356\) −934788. + 438583.i −0.390920 + 0.183412i
\(357\) 2.30472e6i 0.957080i
\(358\) 2.05201e6 + 1.30388e6i 0.846199 + 0.537688i
\(359\) 1.15342e6i 0.472336i 0.971712 + 0.236168i \(0.0758916\pi\)
−0.971712 + 0.236168i \(0.924108\pi\)
\(360\) 888173. 6.93567e6i 0.361195 2.82054i
\(361\) 1.53990e6 1.93901e6i 0.621906 0.783092i
\(362\) −533702. + 839926.i −0.214056 + 0.336876i
\(363\) −9.19588e6 −3.66291
\(364\) −974113. 2.07621e6i −0.385350 0.821329i
\(365\) −1.70824e6 −0.671147
\(366\) −2.38846e6 1.51766e6i −0.931999 0.592206i
\(367\) 2.03678e6i 0.789368i 0.918817 + 0.394684i \(0.129146\pi\)
−0.918817 + 0.394684i \(0.870854\pi\)
\(368\) 7250.84 + 6026.19i 0.00279106 + 0.00231965i
\(369\) 327645.i 0.125267i
\(370\) 14007.7 22045.0i 0.00531940 0.00837153i
\(371\) 4.71422e6 1.77818
\(372\) −1.10579e6 2.35685e6i −0.414299 0.883030i
\(373\) 878299.i 0.326867i 0.986554 + 0.163433i \(0.0522568\pi\)
−0.986554 + 0.163433i \(0.947743\pi\)
\(374\) −1.18590e6 + 1.86634e6i −0.438398 + 0.689940i
\(375\) 6.25943e6 2.29857
\(376\) −2.87168e6 367744.i −1.04753 0.134146i
\(377\) −1.60725e6 −0.582412
\(378\) −2.16277e6 + 3.40371e6i −0.778539 + 1.22524i
\(379\) 3.41881e6 1.22258 0.611289 0.791407i \(-0.290651\pi\)
0.611289 + 0.791407i \(0.290651\pi\)
\(380\) −3.67702e6 2.98746e6i −1.30628 1.06131i
\(381\) −4.20042e6 −1.48245
\(382\) 289270. 455246.i 0.101425 0.159620i
\(383\) 1.14090e6 0.397420 0.198710 0.980058i \(-0.436325\pi\)
0.198710 + 0.980058i \(0.436325\pi\)
\(384\) 3.23016e6 + 3.46726e6i 1.11788 + 1.19994i
\(385\) 1.13002e7 3.88540
\(386\) 2.76750e6 4.35542e6i 0.945407 1.48786i
\(387\) 3.58870e6i 1.21803i
\(388\) 174745. 81986.8i 0.0589286 0.0276481i
\(389\) 2.91802e6 0.977719 0.488860 0.872362i \(-0.337413\pi\)
0.488860 + 0.872362i \(0.337413\pi\)
\(390\) −3.14225e6 + 4.94519e6i −1.04612 + 1.64635i
\(391\) 4987.31i 0.00164977i
\(392\) −250463. + 1.95584e6i −0.0823242 + 0.642863i
\(393\) 8.82845e6i 2.88339i
\(394\) −688796. 437671.i −0.223537 0.142039i
\(395\) −9.07406e6 −2.92623
\(396\) −8.58288e6 + 4.02691e6i −2.75039 + 1.29043i
\(397\) −1.50445e6 −0.479072 −0.239536 0.970887i \(-0.576995\pi\)
−0.239536 + 0.970887i \(0.576995\pi\)
\(398\) 1.84412e6 2.90223e6i 0.583554 0.918382i
\(399\) 2.91103e6 + 6.02920e6i 0.915407 + 1.89595i
\(400\) −3.74862e6 + 4.51042e6i −1.17144 + 1.40951i
\(401\) 6.12590e6i 1.90243i 0.308525 + 0.951216i \(0.400165\pi\)
−0.308525 + 0.951216i \(0.599835\pi\)
\(402\) −3.10748e6 1.97454e6i −0.959055 0.609399i
\(403\) 1.37035e6i 0.420309i
\(404\) −1.47342e6 3.14042e6i −0.449131 0.957269i
\(405\) 916280. 0.277581
\(406\) 2.96597e6 + 1.88462e6i 0.893001 + 0.567426i
\(407\) −35413.6 −0.0105970
\(408\) −318407. + 2.48641e6i −0.0946961 + 0.739473i
\(409\) 2.85001e6i 0.842439i 0.906959 + 0.421220i \(0.138398\pi\)
−0.906959 + 0.421220i \(0.861602\pi\)
\(410\) −227801. + 358507.i −0.0669260 + 0.105326i
\(411\) −6.87931e6 −2.00882
\(412\) −1.05920e6 2.25755e6i −0.307421 0.655231i
\(413\) 1.97977e6i 0.571137i
\(414\) −11467.8 + 18047.7i −0.00328835 + 0.00517512i
\(415\) 3.26483e6i 0.930551i
\(416\) −764069. 2.37446e6i −0.216471 0.672715i
\(417\) 2.69060e6i 0.757721i
\(418\) −745020. + 6.38025e6i −0.208558 + 1.78606i
\(419\) 5.03769e6i 1.40183i −0.713244 0.700916i \(-0.752775\pi\)
0.713244 0.700916i \(-0.247225\pi\)
\(420\) 1.15972e7 5.44118e6i 3.20798 1.50512i
\(421\) 2.24346e6i 0.616898i 0.951241 + 0.308449i \(0.0998100\pi\)
−0.951241 + 0.308449i \(0.900190\pi\)
\(422\) −3.71697e6 2.36182e6i −1.01603 0.645603i
\(423\) 6.56613e6i 1.78426i
\(424\) 5.08585e6 + 651288.i 1.37388 + 0.175938i
\(425\) −3.10238e6 −0.833148
\(426\) −4.34874e6 2.76325e6i −1.16102 0.737729i
\(427\) 3.25677e6i 0.864406i
\(428\) 1.28853e6 + 2.74636e6i 0.340006 + 0.724683i
\(429\) 7.94409e6 2.08401
\(430\) 2.49510e6 3.92672e6i 0.650753 1.02414i
\(431\) 5.37467e6 1.39366 0.696832 0.717234i \(-0.254592\pi\)
0.696832 + 0.717234i \(0.254592\pi\)
\(432\) −2.80350e6 + 3.37324e6i −0.722755 + 0.869636i
\(433\) 1.19123e6i 0.305334i 0.988278 + 0.152667i \(0.0487862\pi\)
−0.988278 + 0.152667i \(0.951214\pi\)
\(434\) 1.60684e6 2.52880e6i 0.409494 0.644452i
\(435\) 8.97775e6i 2.27481i
\(436\) −6.57171e6 + 3.08331e6i −1.65563 + 0.776786i
\(437\) 6299.33 + 13046.9i 0.00157794 + 0.00326817i
\(438\) 2.21610e6 + 1.40814e6i 0.551955 + 0.350721i
\(439\) 200583. 0.0496743 0.0248372 0.999692i \(-0.492093\pi\)
0.0248372 + 0.999692i \(0.492093\pi\)
\(440\) 1.21911e7 + 1.56117e6i 3.00200 + 0.384432i
\(441\) −4.47205e6 −1.09499
\(442\) 707641. 1.11367e6i 0.172289 0.271144i
\(443\) 86536.0i 0.0209502i −0.999945 0.0104751i \(-0.996666\pi\)
0.999945 0.0104751i \(-0.00333438\pi\)
\(444\) −36344.3 + 17052.0i −0.00874942 + 0.00410505i
\(445\) 3.03596e6i 0.726767i
\(446\) 1.34233e6 + 852936.i 0.319537 + 0.203039i
\(447\) 245186. 0.0580398
\(448\) −1.37424e6 + 5.27768e6i −0.323496 + 1.24236i
\(449\) 5.85475e6i 1.37054i 0.728288 + 0.685271i \(0.240316\pi\)
−0.728288 + 0.685271i \(0.759684\pi\)
\(450\) −1.12266e7 7.13358e6i −2.61348 1.66064i
\(451\) 575914. 0.133326
\(452\) −1.13942e6 + 534591.i −0.262323 + 0.123077i
\(453\) 2.40045e6 0.549600
\(454\) −2.58566e6 1.64297e6i −0.588752 0.374102i
\(455\) −6.74299e6 −1.52695
\(456\) 2.30756e6 + 6.90667e6i 0.519685 + 1.55545i
\(457\) 5.23690e6 1.17296 0.586481 0.809963i \(-0.300513\pi\)
0.586481 + 0.809963i \(0.300513\pi\)
\(458\) −3.75447e6 2.38565e6i −0.836344 0.531426i
\(459\) −2.32020e6 −0.514035
\(460\) 25095.9 11774.5i 0.00552978 0.00259446i
\(461\) 778640. 0.170641 0.0853207 0.996354i \(-0.472809\pi\)
0.0853207 + 0.996354i \(0.472809\pi\)
\(462\) −1.46598e7 9.31505e6i −3.19538 2.03039i
\(463\) 6.79131e6i 1.47232i −0.676809 0.736158i \(-0.736638\pi\)
0.676809 0.736158i \(-0.263362\pi\)
\(464\) 2.93942e6 + 2.44296e6i 0.633821 + 0.526770i
\(465\) −7.65447e6 −1.64166
\(466\) −1.69725e6 1.07846e6i −0.362060 0.230059i
\(467\) 1.18854e6i 0.252187i −0.992018 0.126094i \(-0.959756\pi\)
0.992018 0.126094i \(-0.0402440\pi\)
\(468\) 5.12151e6 2.40291e6i 1.08089 0.507133i
\(469\) 4.23719e6i 0.889500i
\(470\) −4.56521e6 + 7.18460e6i −0.953270 + 1.50023i
\(471\) 1.27661e7 2.65160
\(472\) −273514. + 2.13585e6i −0.0565099 + 0.441281i
\(473\) −6.30798e6 −1.29640
\(474\) 1.17718e7 + 7.47996e6i 2.40655 + 1.52916i
\(475\) −8.11589e6 + 3.91853e6i −1.65045 + 0.796872i
\(476\) −2.61172e6 + 1.22536e6i −0.528334 + 0.247884i
\(477\) 1.16289e7i 2.34014i
\(478\) 316221. 497660.i 0.0633025 0.0996238i
\(479\) 3.09162e6i 0.615669i −0.951440 0.307834i \(-0.900396\pi\)
0.951440 0.307834i \(-0.0996042\pi\)
\(480\) 1.32632e7 4.26792e6i 2.62752 0.845499i
\(481\) 21131.7 0.00416459
\(482\) 928891. 1.46186e6i 0.182116 0.286609i
\(483\) −39174.5 −0.00764075
\(484\) −4.88922e6 1.04208e7i −0.948695 2.02203i
\(485\) 567528.i 0.109555i
\(486\) 3.78089e6 + 2.40244e6i 0.726112 + 0.461383i
\(487\) −3.59773e6 −0.687394 −0.343697 0.939081i \(-0.611679\pi\)
−0.343697 + 0.939081i \(0.611679\pi\)
\(488\) 449936. 3.51351e6i 0.0855267 0.667870i
\(489\) 5.76668e6i 1.09057i
\(490\) 4.89327e6 + 3.10926e6i 0.920681 + 0.585015i
\(491\) 6.96091e6i 1.30305i 0.758626 + 0.651527i \(0.225871\pi\)
−0.758626 + 0.651527i \(0.774129\pi\)
\(492\) 591050. 277309.i 0.110081 0.0516476i
\(493\) 2.02181e6i 0.374647i
\(494\) 444563. 3.80718e6i 0.0819626 0.701917i
\(495\) 2.78750e7i 5.11331i
\(496\) 2.08288e6 2.50616e6i 0.380154 0.457409i
\(497\) 5.92970e6i 1.07682i
\(498\) −2.69127e6 + 4.23546e6i −0.486278 + 0.765292i
\(499\) 3.09077e6i 0.555668i −0.960629 0.277834i \(-0.910384\pi\)
0.960629 0.277834i \(-0.0896165\pi\)
\(500\) 3.32799e6 + 7.09321e6i 0.595328 + 1.26887i
\(501\) 9.01375e6 1.60439
\(502\) 753819. 1.18634e6i 0.133508 0.210112i
\(503\) 8.48635e6i 1.49555i 0.663952 + 0.747775i \(0.268878\pi\)
−0.663952 + 0.747775i \(0.731122\pi\)
\(504\) −1.22687e7 1.57111e6i −2.15140 0.275506i
\(505\) −1.01993e7 −1.77968
\(506\) −31723.1 20157.3i −0.00550806 0.00349991i
\(507\) 4.75163e6 0.820961
\(508\) −2.23326e6 4.75993e6i −0.383955 0.818354i
\(509\) 5.87480e6i 1.00507i −0.864555 0.502537i \(-0.832400\pi\)
0.864555 0.502537i \(-0.167600\pi\)
\(510\) 6.22070e6 + 3.95273e6i 1.05904 + 0.672932i
\(511\) 3.02175e6i 0.511925i
\(512\) −2.21171e6 + 5.50388e6i −0.372867 + 0.927885i
\(513\) −6.06968e6 + 2.93057e6i −1.01829 + 0.491653i
\(514\) −2.66418e6 + 4.19282e6i −0.444791 + 0.700000i
\(515\) −7.33196e6 −1.21815
\(516\) −6.47377e6 + 3.03736e6i −1.07037 + 0.502194i
\(517\) 1.15415e7 1.89905
\(518\) −38995.8 24778.6i −0.00638549 0.00405744i
\(519\) 1.38746e7i 2.26101i
\(520\) −7.27457e6 931572.i −1.17977 0.151080i
\(521\) 1.13055e7i 1.82471i −0.409397 0.912357i \(-0.634261\pi\)
0.409397 0.912357i \(-0.365739\pi\)
\(522\) −4.64892e6 + 7.31635e6i −0.746751 + 1.17522i
\(523\) 9.51562e6 1.52119 0.760594 0.649228i \(-0.224908\pi\)
0.760594 + 0.649228i \(0.224908\pi\)
\(524\) 1.00044e7 4.69387e6i 1.59171 0.746797i
\(525\) 2.43687e7i 3.85863i
\(526\) −3.88779e6 + 6.11851e6i −0.612687 + 0.964231i
\(527\) 1.72380e6 0.270371
\(528\) −1.45285e7 1.20747e7i −2.26797 1.88491i
\(529\) 6.43626e6 0.999987
\(530\) 8.08514e6 1.27242e7i 1.25025 1.96762i
\(531\) −4.88363e6 −0.751635
\(532\) −5.28459e6 + 6.50436e6i −0.809528 + 0.996382i
\(533\) −343655. −0.0523968
\(534\) 2.50261e6 3.93854e6i 0.379787 0.597698i
\(535\) 8.91948e6 1.34727
\(536\) 585386. 4.57122e6i 0.0880096 0.687259i
\(537\) −1.09873e7 −1.64420
\(538\) −5.72178e6 + 9.00478e6i −0.852266 + 1.34127i
\(539\) 7.86068e6i 1.16544i
\(540\) 5.47771e6 + 1.16751e7i 0.808378 + 1.72296i
\(541\) −1.63250e6 −0.239806 −0.119903 0.992786i \(-0.538258\pi\)
−0.119903 + 0.992786i \(0.538258\pi\)
\(542\) −4.17949e6 + 6.57757e6i −0.611118 + 0.961761i
\(543\) 4.49729e6i 0.654563i
\(544\) −2.98690e6 + 961144.i −0.432736 + 0.139249i
\(545\) 2.13433e7i 3.07801i
\(546\) 8.74767e6 + 5.55841e6i 1.25577 + 0.797937i
\(547\) 6.46710e6 0.924148 0.462074 0.886841i \(-0.347106\pi\)
0.462074 + 0.886841i \(0.347106\pi\)
\(548\) −3.65756e6 7.79565e6i −0.520283 1.10892i
\(549\) 8.03369e6 1.13759
\(550\) 1.25389e7 1.97335e7i 1.76748 2.78161i
\(551\) 2.55369e6 + 5.28909e6i 0.358334 + 0.742167i
\(552\) −42262.8 5412.12i −0.00590351 0.000755996i
\(553\) 1.60513e7i 2.23202i
\(554\) −6.44042e6 4.09234e6i −0.891537 0.566496i
\(555\) 118037.i 0.0162662i
\(556\) −3.04900e6 + 1.43053e6i −0.418283 + 0.196250i
\(557\) −5.16001e6 −0.704714 −0.352357 0.935866i \(-0.614620\pi\)
−0.352357 + 0.935866i \(0.614620\pi\)
\(558\) 6.23795e6 + 3.96369e6i 0.848119 + 0.538908i
\(559\) 3.76405e6 0.509479
\(560\) 1.23319e7 + 1.02491e7i 1.66173 + 1.38107i
\(561\) 9.99309e6i 1.34058i
\(562\) −1.37980e6 + 2.17149e6i −0.184279 + 0.290013i
\(563\) −5.95975e6 −0.792423 −0.396211 0.918159i \(-0.629675\pi\)
−0.396211 + 0.918159i \(0.629675\pi\)
\(564\) 1.18449e7 5.55736e6i 1.56795 0.735650i
\(565\) 3.70054e6i 0.487690i
\(566\) 3.50494e6 5.51599e6i 0.459875 0.723740i
\(567\) 1.62083e6i 0.211729i
\(568\) 819212. 6.39715e6i 0.106543 0.831986i
\(569\) 1.04555e7i 1.35383i −0.736063 0.676914i \(-0.763317\pi\)
0.736063 0.676914i \(-0.236683\pi\)
\(570\) 2.12661e7 + 2.48323e6i 2.74157 + 0.320133i
\(571\) 4.60322e6i 0.590842i −0.955367 0.295421i \(-0.904540\pi\)
0.955367 0.295421i \(-0.0954599\pi\)
\(572\) 4.22367e6 + 9.00226e6i 0.539760 + 1.15043i
\(573\) 2.43756e6i 0.310148i
\(574\) 634171. + 402962.i 0.0803390 + 0.0510486i
\(575\) 52732.7i 0.00665135i
\(576\) −1.30188e7 3.38993e6i −1.63499 0.425731i
\(577\) 1.29728e7 1.62216 0.811080 0.584936i \(-0.198880\pi\)
0.811080 + 0.584936i \(0.198880\pi\)
\(578\) 5.37822e6 + 3.41741e6i 0.669606 + 0.425478i
\(579\) 2.33206e7i 2.89097i
\(580\) 1.01736e7 4.77325e6i 1.25576 0.589175i
\(581\) −5.77524e6 −0.709789
\(582\) −467827. + 736253.i −0.0572503 + 0.0900989i
\(583\) −2.04405e7 −2.49069
\(584\) −417467. + 3.25997e6i −0.0506513 + 0.395531i
\(585\) 1.66334e7i 2.00951i
\(586\) 6.69825e6 1.05415e7i 0.805782 1.26812i
\(587\) 9.89340e6i 1.18509i −0.805538 0.592544i \(-0.798124\pi\)
0.805538 0.592544i \(-0.201876\pi\)
\(588\) −3.78500e6 8.06728e6i −0.451463 0.962241i
\(589\) 4.50950e6 2.17728e6i 0.535599 0.258599i
\(590\) 5.34363e6 + 3.39542e6i 0.631984 + 0.401572i
\(591\) 3.68808e6 0.434342
\(592\) −38646.8 32119.4i −0.00453220 0.00376671i
\(593\) −9.91998e6 −1.15844 −0.579220 0.815171i \(-0.696643\pi\)
−0.579220 + 0.815171i \(0.696643\pi\)
\(594\) 9.37758e6 1.47582e7i 1.09050 1.71620i
\(595\) 8.48220e6i 0.982237i
\(596\) 130359. + 277845.i 0.0150323 + 0.0320396i
\(597\) 1.55396e7i 1.78445i
\(598\) 18929.5 + 12028.1i 0.00216465 + 0.00137545i
\(599\) −3.56054e6 −0.405460 −0.202730 0.979235i \(-0.564981\pi\)
−0.202730 + 0.979235i \(0.564981\pi\)
\(600\) 3.36663e6 2.62897e7i 0.381784 2.98132i
\(601\) 1.35986e7i 1.53571i −0.640624 0.767855i \(-0.721324\pi\)
0.640624 0.767855i \(-0.278676\pi\)
\(602\) −6.94607e6 4.41364e6i −0.781174 0.496370i
\(603\) 1.04522e7 1.17061
\(604\) 1.27626e6 + 2.72020e6i 0.142346 + 0.303395i
\(605\) −3.38441e7 −3.75920
\(606\) 1.32315e7 + 8.40750e6i 1.46362 + 0.930006i
\(607\) −1.54890e7 −1.70629 −0.853145 0.521675i \(-0.825308\pi\)
−0.853145 + 0.521675i \(0.825308\pi\)
\(608\) −6.59979e6 + 6.28704e6i −0.724055 + 0.689743i
\(609\) −1.58810e7 −1.73514
\(610\) −8.79039e6 5.58555e6i −0.956497 0.607773i
\(611\) −6.88698e6 −0.746321
\(612\) −3.02268e6 6.44249e6i −0.326223 0.695305i
\(613\) −521655. −0.0560703 −0.0280351 0.999607i \(-0.508925\pi\)
−0.0280351 + 0.999607i \(0.508925\pi\)
\(614\) 1.30343e7 + 8.28220e6i 1.39530 + 0.886594i
\(615\) 1.91958e6i 0.204653i
\(616\) 2.76160e6 2.15651e7i 0.293230 2.28981i
\(617\) −6.54779e6 −0.692440 −0.346220 0.938153i \(-0.612535\pi\)
−0.346220 + 0.938153i \(0.612535\pi\)
\(618\) 9.51173e6 + 6.04390e6i 1.00182 + 0.636570i
\(619\) 8.13536e6i 0.853395i 0.904394 + 0.426697i \(0.140323\pi\)
−0.904394 + 0.426697i \(0.859677\pi\)
\(620\) −4.06969e6 8.67407e6i −0.425189 0.906241i
\(621\) 39437.5i 0.00410375i
\(622\) −312420. + 491679.i −0.0323790 + 0.0509572i
\(623\) 5.37038e6 0.554351
\(624\) 8.66936e6 + 7.20512e6i 0.891304 + 0.740764i
\(625\) 5.13897e6 0.526231
\(626\) 7.34936e6 + 4.66990e6i 0.749573 + 0.476290i
\(627\) −1.26220e7 2.61421e7i −1.28221 2.65566i
\(628\) 6.78745e6 + 1.44666e7i 0.686764 + 1.46376i
\(629\) 26582.2i 0.00267895i
\(630\) −1.95039e7 + 3.06947e7i −1.95781 + 3.08115i
\(631\) 7.55707e6i 0.755580i 0.925891 + 0.377790i \(0.123316\pi\)
−0.925891 + 0.377790i \(0.876684\pi\)
\(632\) −2.21756e6 + 1.73167e7i −0.220842 + 1.72454i
\(633\) 1.99021e7 1.97419
\(634\) −4.61508e6 + 7.26309e6i −0.455991 + 0.717626i
\(635\) −1.54591e7 −1.52142
\(636\) −2.09777e7 + 9.84229e6i −2.05643 + 0.964836i
\(637\) 4.69057e6i 0.458012i
\(638\) −1.28602e7 8.17158e6i −1.25082 0.794793i
\(639\) 1.46272e7 1.41712
\(640\) 1.18881e7 + 1.27608e7i 1.14727 + 1.23148i
\(641\) 1.35581e7i 1.30333i 0.758507 + 0.651665i \(0.225929\pi\)
−0.758507 + 0.651665i \(0.774071\pi\)
\(642\) −1.15712e7 7.35254e6i −1.10801 0.704044i
\(643\) 3.16596e6i 0.301979i 0.988535 + 0.150990i \(0.0482460\pi\)
−0.988535 + 0.150990i \(0.951754\pi\)
\(644\) −20828.1 44392.7i −0.00197895 0.00421790i
\(645\) 2.10252e7i 1.98994i
\(646\) −4.78915e6 559228.i −0.451521 0.0527239i
\(647\) 2.06733e6i 0.194156i −0.995277 0.0970778i \(-0.969050\pi\)
0.995277 0.0970778i \(-0.0309496\pi\)
\(648\) 223924. 1.74860e6i 0.0209490 0.163589i
\(649\) 8.58414e6i 0.799991i
\(650\) −7.48215e6 + 1.17752e7i −0.694613 + 1.09316i
\(651\) 1.35402e7i 1.25219i
\(652\) 6.53481e6 3.06600e6i 0.602025 0.282457i
\(653\) 1.70976e7 1.56911 0.784555 0.620059i \(-0.212891\pi\)
0.784555 + 0.620059i \(0.212891\pi\)
\(654\) 1.75937e7 2.76886e7i 1.60847 2.53137i
\(655\) 3.24919e7i 2.95918i
\(656\) 628494. + 522342.i 0.0570219 + 0.0473909i
\(657\) −7.45395e6 −0.673710
\(658\) 1.27090e7 + 8.07550e6i 1.14432 + 0.727118i
\(659\) −948534. −0.0850823 −0.0425412 0.999095i \(-0.513545\pi\)
−0.0425412 + 0.999095i \(0.513545\pi\)
\(660\) −5.02847e7 + 2.35925e7i −4.49341 + 2.10821i
\(661\) 6.92093e6i 0.616113i −0.951368 0.308057i \(-0.900321\pi\)
0.951368 0.308057i \(-0.0996787\pi\)
\(662\) −6.43670e6 4.08998e6i −0.570845 0.362724i
\(663\) 5.96300e6i 0.526843i
\(664\) −6.23052e6 797873.i −0.548408 0.0702285i
\(665\) 1.07136e7 + 2.21896e7i 0.939469 + 1.94579i
\(666\) 61122.9 96193.5i 0.00533971 0.00840350i
\(667\) −34365.6 −0.00299096
\(668\) 4.79239e6 + 1.02144e7i 0.415538 + 0.885670i
\(669\) −7.18735e6 −0.620874
\(670\) −1.14366e7 7.26702e6i −0.984264 0.625417i
\(671\) 1.41211e7i 1.21077i
\(672\) −7.54963e6 2.34616e7i −0.644915 2.00417i
\(673\) 7.01210e6i 0.596775i −0.954445 0.298388i \(-0.903551\pi\)
0.954445 0.298388i \(-0.0964488\pi\)
\(674\) −9.18338e6 + 1.44526e7i −0.778669 + 1.22545i
\(675\) 2.45323e7 2.07242
\(676\) 2.52632e6 + 5.38456e6i 0.212629 + 0.453193i
\(677\) 1.41401e7i 1.18572i 0.805307 + 0.592858i \(0.202001\pi\)
−0.805307 + 0.592858i \(0.797999\pi\)
\(678\) 3.05044e6 4.80070e6i 0.254852 0.401080i
\(679\) −1.00391e6 −0.0835646
\(680\) −1.17185e6 + 9.15088e6i −0.0971852 + 0.758911i
\(681\) 1.38446e7 1.14397
\(682\) −6.96712e6 + 1.09647e7i −0.573578 + 0.902682i
\(683\) 7.13798e6 0.585495 0.292748 0.956190i \(-0.405430\pi\)
0.292748 + 0.956190i \(0.405430\pi\)
\(684\) −1.60447e7 1.30358e7i −1.31127 1.06536i
\(685\) −2.53183e7 −2.06162
\(686\) −2.98621e6 + 4.69962e6i −0.242276 + 0.381287i
\(687\) 2.01029e7 1.62505
\(688\) −6.88388e6 5.72121e6i −0.554450 0.460804i
\(689\) 1.21971e7 0.978831
\(690\) −67186.5 + 105736.i −0.00537229 + 0.00845476i
\(691\) 2.28937e7i 1.82399i −0.410206 0.911993i \(-0.634543\pi\)
0.410206 0.911993i \(-0.365457\pi\)
\(692\) 1.57228e7 7.37679e6i 1.24814 0.585601i
\(693\) 4.93088e7 3.90024
\(694\) −3.47104e6 + 5.46263e6i −0.273565 + 0.430530i
\(695\) 9.90237e6i 0.777638i
\(696\) −1.71329e7 2.19402e6i −1.34063 0.171679i
\(697\) 432294.i 0.0337052i
\(698\) 8.30520e6 + 5.27725e6i 0.645225 + 0.409986i
\(699\) 9.08773e6 0.703497
\(700\) 2.76147e7 1.29562e7i 2.13007 0.999386i
\(701\) 1.65026e7 1.26841 0.634203 0.773167i \(-0.281329\pi\)
0.634203 + 0.773167i \(0.281329\pi\)
\(702\) −5.59572e6 + 8.80640e6i −0.428562 + 0.674459i
\(703\) −33575.2 69539.6i −0.00256230 0.00530693i
\(704\) 5.95861e6 2.28836e7i 0.453120 1.74017i
\(705\) 3.84691e7i 2.91501i
\(706\) −1.65310e7 1.05040e7i −1.24821 0.793129i
\(707\) 1.80418e7i 1.35747i
\(708\) −4.13335e6 8.80975e6i −0.309898 0.660512i
\(709\) −1.71958e7 −1.28472 −0.642359 0.766404i \(-0.722044\pi\)
−0.642359 + 0.766404i \(0.722044\pi\)
\(710\) −1.60049e7 1.01698e7i −1.19154 0.757120i
\(711\) −3.95948e7 −2.93741
\(712\) 5.79374e6 + 741939.i 0.428311 + 0.0548490i
\(713\) 29300.3i 0.00215848i
\(714\) 6.99207e6 1.10039e7i 0.513287 0.807798i
\(715\) 2.92371e7 2.13879
\(716\) −5.84166e6 1.24508e7i −0.425847 0.907642i
\(717\) 2.66467e6i 0.193573i
\(718\) 3.49925e6 5.50703e6i 0.253317 0.398663i
\(719\) 1.09124e7i 0.787227i −0.919276 0.393613i \(-0.871225\pi\)
0.919276 0.393613i \(-0.128775\pi\)
\(720\) −2.52821e7 + 3.04199e7i −1.81753 + 2.18689i
\(721\) 1.29697e7i 0.929161i
\(722\) −1.32349e7 + 4.58609e6i −0.944880 + 0.327416i
\(723\) 7.82738e6i 0.556892i
\(724\) 5.09634e6 2.39110e6i 0.361337 0.169532i
\(725\) 2.13773e7i 1.51045i
\(726\) 4.39059e7 + 2.78985e7i 3.09159 + 1.96444i
\(727\) 2.03681e7i 1.42927i −0.699497 0.714636i \(-0.746593\pi\)
0.699497 0.714636i \(-0.253407\pi\)
\(728\) −1.64788e6 + 1.28682e7i −0.115238 + 0.899887i
\(729\) −2.26109e7 −1.57579
\(730\) 8.15604e6 + 5.18247e6i 0.566464 + 0.359940i
\(731\) 4.73491e6i 0.327731i
\(732\) 6.79946e6 + 1.44922e7i 0.469025 + 0.999672i
\(733\) 5.38904e6 0.370468 0.185234 0.982694i \(-0.440696\pi\)
0.185234 + 0.982694i \(0.440696\pi\)
\(734\) 6.17920e6 9.72466e6i 0.423343 0.666246i
\(735\) −2.62005e7 −1.78892
\(736\) −16337.0 50769.8i −0.00111168 0.00345470i
\(737\) 1.83721e7i 1.24592i
\(738\) −994012. + 1.56435e6i −0.0671816 + 0.105729i
\(739\) 1.79505e7i 1.20911i 0.796563 + 0.604555i \(0.206649\pi\)
−0.796563 + 0.604555i \(0.793351\pi\)
\(740\) −133760. + 62757.5i −0.00897940 + 0.00421295i
\(741\) 7.53170e6 + 1.55993e7i 0.503904 + 1.04366i
\(742\) −2.25081e7 1.43020e7i −1.50082 0.953646i
\(743\) −235415. −0.0156445 −0.00782225 0.999969i \(-0.502490\pi\)
−0.00782225 + 0.999969i \(0.502490\pi\)
\(744\) −1.87063e6 + 1.46076e7i −0.123896 + 0.967490i
\(745\) 902370. 0.0595654
\(746\) 2.66459e6 4.19346e6i 0.175300 0.275883i
\(747\) 1.42461e7i 0.934105i
\(748\) 1.13242e7 5.31308e6i 0.740037 0.347210i
\(749\) 1.57779e7i 1.02765i
\(750\) −2.98858e7 1.89899e7i −1.94004 1.23273i
\(751\) −4.45310e6 −0.288113 −0.144056 0.989569i \(-0.546015\pi\)
−0.144056 + 0.989569i \(0.546015\pi\)
\(752\) 1.25952e7 + 1.04679e7i 0.812198 + 0.675019i
\(753\) 6.35212e6i 0.408255i
\(754\) 7.67385e6 + 4.87608e6i 0.491570 + 0.312351i
\(755\) 8.83451e6 0.564047
\(756\) 2.06523e7 9.68965e6i 1.31421 0.616600i
\(757\) −2.02606e7 −1.28503 −0.642516 0.766273i \(-0.722109\pi\)
−0.642516 + 0.766273i \(0.722109\pi\)
\(758\) −1.63232e7 1.03720e7i −1.03189 0.655676i
\(759\) 169858. 0.0107024
\(760\) 8.49263e6 + 2.54190e7i 0.533345 + 1.59634i
\(761\) 1.48612e7 0.930236 0.465118 0.885249i \(-0.346012\pi\)
0.465118 + 0.885249i \(0.346012\pi\)
\(762\) 2.00550e7 + 1.27433e7i 1.25122 + 0.795047i
\(763\) 3.77546e7 2.34779
\(764\) −2.76225e6 + 1.29599e6i −0.171210 + 0.0803283i
\(765\) −2.09236e7 −1.29265
\(766\) −5.44723e6 3.46126e6i −0.335432 0.213138i
\(767\) 5.12226e6i 0.314393i
\(768\) −4.90347e6 2.63542e7i −0.299986 1.61230i
\(769\) 6.53060e6 0.398233 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(770\) −5.39532e7 3.42827e7i −3.27937 2.08376i
\(771\) 2.24500e7i 1.36013i
\(772\) −2.64269e7 + 1.23990e7i −1.59589 + 0.748760i
\(773\) 6.08632e6i 0.366358i −0.983080 0.183179i \(-0.941361\pi\)
0.983080 0.183179i \(-0.0586389\pi\)
\(774\) 1.08874e7 1.71343e7i 0.653238 1.02805i
\(775\) −1.82264e7 −1.09005
\(776\) −1.08306e6 138695.i −0.0645649 0.00826811i
\(777\) 208799. 0.0124072
\(778\) −1.39321e7 8.85270e6i −0.825218 0.524356i
\(779\) 546018. + 1.13089e6i 0.0322376 + 0.0667692i
\(780\) 3.00055e7 1.40780e7i 1.76589 0.828520i
\(781\) 2.57107e7i 1.50829i
\(782\) 15130.5 23812.0i 0.000884783 0.00139245i
\(783\) 1.59876e7i 0.931919i
\(784\) 7.12947e6 8.57834e6i 0.414255 0.498440i
\(785\) 4.69840e7 2.72130
\(786\) −2.67838e7 + 4.21516e7i −1.54638 + 2.43365i
\(787\) −9.74658e6 −0.560939 −0.280469 0.959863i \(-0.590490\pi\)
−0.280469 + 0.959863i \(0.590490\pi\)
\(788\) 1.96086e6 + 4.17934e6i 0.112494 + 0.239769i
\(789\) 3.27608e7i 1.87354i
\(790\) 4.33243e7 + 2.75289e7i 2.46981 + 1.56936i
\(791\) 6.54597e6 0.371992
\(792\) 5.31960e7 + 6.81221e6i 3.01346 + 0.385900i
\(793\) 8.42624e6i 0.475829i
\(794\) 7.18302e6 + 4.56420e6i 0.404348 + 0.256929i
\(795\) 6.81302e7i 3.82316i
\(796\) −1.76096e7 + 8.26204e6i −0.985067 + 0.462173i
\(797\) 2.43081e7i 1.35552i −0.735284 0.677759i \(-0.762951\pi\)
0.735284 0.677759i \(-0.237049\pi\)
\(798\) 4.39264e6 3.76180e7i 0.244185 2.09117i
\(799\) 8.66332e6i 0.480084i
\(800\) 3.15816e7 1.01625e7i 1.74465 0.561405i
\(801\) 1.32474e7i 0.729543i
\(802\) 1.85848e7 2.92483e7i 1.02029 1.60570i
\(803\) 1.31021e7i 0.717053i
\(804\) 8.84637e6 + 1.88550e7i 0.482642 + 1.02869i
\(805\) −144176. −0.00784159
\(806\) 4.15737e6 6.54276e6i 0.225414 0.354751i
\(807\) 4.82151e7i 2.60615i
\(808\) −2.49254e6 + 1.94640e7i −0.134312 + 1.04883i
\(809\) −1.34685e7 −0.723513 −0.361757 0.932273i \(-0.617823\pi\)
−0.361757 + 0.932273i \(0.617823\pi\)
\(810\) −4.37480e6 2.77981e6i −0.234285 0.148869i
\(811\) −3.56801e7 −1.90491 −0.952454 0.304681i \(-0.901450\pi\)
−0.952454 + 0.304681i \(0.901450\pi\)
\(812\) −8.44351e6 1.79963e7i −0.449400 0.957843i
\(813\) 3.52188e7i 1.86874i
\(814\) 169083. + 107438.i 0.00894414 + 0.00568324i
\(815\) 2.12234e7i 1.11924i
\(816\) 9.06352e6 1.09054e7i 0.476510 0.573347i
\(817\) −5.98052e6 1.23866e7i −0.313461 0.649228i
\(818\) 8.64638e6 1.36074e7i 0.451805 0.711039i
\(819\) −2.94232e7 −1.53278
\(820\) 2.17528e6 1.02059e6i 0.112974 0.0530052i
\(821\) 4.06465e6 0.210458 0.105229 0.994448i \(-0.466442\pi\)
0.105229 + 0.994448i \(0.466442\pi\)
\(822\) 3.28454e7 + 2.08705e7i 1.69549 + 1.07734i
\(823\) 1.59194e7i 0.819272i −0.912249 0.409636i \(-0.865656\pi\)
0.912249 0.409636i \(-0.134344\pi\)
\(824\) −1.79181e6 + 1.39921e7i −0.0919337 + 0.717902i
\(825\) 1.05661e8i 5.40478i
\(826\) 6.00624e6 9.45247e6i 0.306304 0.482053i
\(827\) 3.72616e7 1.89452 0.947258 0.320472i \(-0.103842\pi\)
0.947258 + 0.320472i \(0.103842\pi\)
\(828\) 109506. 51378.0i 0.00555089 0.00260436i
\(829\) 1.08401e7i 0.547829i 0.961754 + 0.273915i \(0.0883186\pi\)
−0.961754 + 0.273915i \(0.911681\pi\)
\(830\) −9.90485e6 + 1.55880e7i −0.499060 + 0.785408i
\(831\) 3.44845e7 1.73229
\(832\) −3.55558e6 + 1.36549e7i −0.178074 + 0.683882i
\(833\) 5.90040e6 0.294624
\(834\) 8.16275e6 1.28463e7i 0.406370 0.639534i
\(835\) 3.31738e7 1.64657
\(836\) 2.29135e7 2.82024e7i 1.13390 1.39563i
\(837\) −1.36311e7 −0.672538
\(838\) −1.52833e7 + 2.40525e7i −0.751811 + 1.18318i
\(839\) −3.51785e7 −1.72533 −0.862666 0.505774i \(-0.831207\pi\)
−0.862666 + 0.505774i \(0.831207\pi\)
\(840\) −7.18787e7 9.20470e6i −3.51481 0.450102i
\(841\) 6.57966e6 0.320785
\(842\) 6.80622e6 1.07115e7i 0.330846 0.520677i
\(843\) 1.16270e7i 0.563507i
\(844\) 1.05815e7 + 2.25531e7i 0.511316 + 1.08981i
\(845\) 1.74877e7 0.842540
\(846\) −1.99204e7 + 3.13501e7i −0.956910 + 1.50596i
\(847\) 5.98677e7i 2.86737i
\(848\) −2.23066e7 1.85391e7i −1.06523 0.885316i
\(849\) 2.95347e7i 1.40625i
\(850\) 1.48124e7 + 9.41200e6i 0.703197 + 0.446822i
\(851\) 451.831 2.13871e−5
\(852\) 1.23800e7 + 2.63864e7i 0.584279 + 1.24532i
\(853\) −3.24795e7 −1.52840 −0.764199 0.644980i \(-0.776866\pi\)
−0.764199 + 0.644980i \(0.776866\pi\)
\(854\) −9.88041e6 + 1.55495e7i −0.463586 + 0.729579i
\(855\) −5.47365e7 + 2.64280e7i −2.56072 + 1.23637i
\(856\) 2.17978e6 1.70217e7i 0.101678 0.793997i
\(857\) 9.87730e6i 0.459395i −0.973262 0.229697i \(-0.926226\pi\)
0.973262 0.229697i \(-0.0737737\pi\)
\(858\) −3.79292e7 2.41008e7i −1.75896 1.11767i
\(859\) 1.03156e7i 0.476994i 0.971143 + 0.238497i \(0.0766547\pi\)
−0.971143 + 0.238497i \(0.923345\pi\)
\(860\) −2.38258e7 + 1.11786e7i −1.09850 + 0.515394i
\(861\) −3.39560e6 −0.156102
\(862\) −2.56614e7 1.63057e7i −1.17629 0.747430i
\(863\) 2.29287e7 1.04798 0.523988 0.851725i \(-0.324444\pi\)
0.523988 + 0.851725i \(0.324444\pi\)
\(864\) 2.36191e7 7.60031e6i 1.07641 0.346375i
\(865\) 5.10635e7i 2.32044i
\(866\) 3.61395e6 5.68755e6i 0.163752 0.257709i
\(867\) −2.87971e7 −1.30107
\(868\) −1.53438e7 + 7.19898e6i −0.691246 + 0.324318i
\(869\) 6.95973e7i 3.12639i
\(870\) −2.72367e7 + 4.28645e7i −1.21999 + 1.91999i
\(871\) 1.09629e7i 0.489643i
\(872\) 4.07309e7 + 5.21596e6i 1.81398 + 0.232296i
\(873\) 2.47642e6i 0.109974i
\(874\) 9505.48 81403.6i 0.000420916 0.00360467i
\(875\) 4.07506e7i 1.79934i
\(876\) −6.30878e6 1.34464e7i −0.277770 0.592034i
\(877\) 1.21889e7i 0.535138i 0.963539 + 0.267569i \(0.0862204\pi\)
−0.963539 + 0.267569i \(0.913780\pi\)
\(878\) −957685. 608528.i −0.0419263 0.0266406i
\(879\) 5.64435e7i 2.46400i
\(880\) −5.34702e7 4.44392e7i −2.32758 1.93446i
\(881\) 2.02657e7 0.879675 0.439837 0.898077i \(-0.355036\pi\)
0.439837 + 0.898077i \(0.355036\pi\)
\(882\) 2.13519e7 + 1.35673e7i 0.924198 + 0.587249i
\(883\) 2.17676e7i 0.939525i 0.882793 + 0.469762i \(0.155660\pi\)
−0.882793 + 0.469762i \(0.844340\pi\)
\(884\) −6.75729e6 + 3.17038e6i −0.290832 + 0.136452i
\(885\) −2.86118e7 −1.22797
\(886\) −262533. + 413168.i −0.0112357 + 0.0176824i
\(887\) 4.67578e7 1.99547 0.997734 0.0672753i \(-0.0214306\pi\)
0.997734 + 0.0672753i \(0.0214306\pi\)
\(888\) 225259. + 28846.4i 0.00958628 + 0.00122761i
\(889\) 2.73459e7i 1.16048i
\(890\) 9.21049e6 1.44952e7i 0.389770 0.613409i
\(891\) 7.02778e6i 0.296568i
\(892\) −3.82133e6 8.14472e6i −0.160806 0.342739i
\(893\) 1.09424e7 + 2.26634e7i 0.459181 + 0.951036i
\(894\) −1.17064e6 743845.i −0.0489870 0.0311271i
\(895\) −4.04371e7 −1.68742
\(896\) 2.25728e7 2.10292e7i 0.939324 0.875090i
\(897\) −101356. −0.00420600
\(898\) 1.77622e7 2.79536e7i 0.735029 1.15677i
\(899\) 1.18781e7i 0.490169i
\(900\) 3.19599e7 + 6.81188e7i 1.31522 + 2.80324i
\(901\) 1.53431e7i 0.629651i
\(902\) −2.74971e6 1.74721e6i −0.112531 0.0715038i
\(903\) 3.71919e7 1.51785
\(904\) 7.06201e6 + 904353.i 0.287414 + 0.0368059i
\(905\) 1.65516e7i 0.671768i
\(906\) −1.14610e7 7.28249e6i −0.463876 0.294754i
\(907\) −1.19607e7 −0.482768 −0.241384 0.970430i \(-0.577601\pi\)
−0.241384 + 0.970430i \(0.577601\pi\)
\(908\) 7.36085e6 + 1.56888e7i 0.296287 + 0.631502i
\(909\) −4.45047e7 −1.78647
\(910\) 3.21946e7 + 2.04569e7i 1.28878 + 0.818911i
\(911\) 3.75316e6 0.149831 0.0749154 0.997190i \(-0.476131\pi\)
0.0749154 + 0.997190i \(0.476131\pi\)
\(912\) 9.93602e6 3.99767e7i 0.395572 1.59155i
\(913\) 2.50410e7 0.994201
\(914\) −2.50037e7 1.58877e7i −0.990008 0.629066i
\(915\) 4.70671e7 1.85851
\(916\) 1.06882e7 + 2.27807e7i 0.420888 + 0.897073i
\(917\) −5.74756e7 −2.25715
\(918\) 1.10778e7 + 7.03902e6i 0.433858 + 0.275680i
\(919\) 2.96847e7i 1.15943i 0.814820 + 0.579713i \(0.196835\pi\)
−0.814820 + 0.579713i \(0.803165\pi\)
\(920\) −155542. 19918.5i −0.00605868 0.000775868i
\(921\) −6.97907e7 −2.71112
\(922\) −3.71763e6 2.36224e6i −0.144025 0.0915159i
\(923\) 1.53419e7i 0.592754i
\(924\) 4.17334e7 + 8.89497e7i 1.60806 + 3.42740i
\(925\) 281063.i 0.0108006i
\(926\) −2.06035e7 + 3.24253e7i −0.789612 + 1.24267i
\(927\) −3.19931e7 −1.22280
\(928\) −6.62287e6 2.05816e7i −0.252451 0.784528i
\(929\) −3.17744e7 −1.20792 −0.603960 0.797015i \(-0.706411\pi\)
−0.603960 + 0.797015i \(0.706411\pi\)
\(930\) 3.65464e7 + 2.32222e7i 1.38560 + 0.880431i
\(931\) 1.54356e7 7.45262e6i 0.583644 0.281796i
\(932\) 4.83172e6 + 1.02982e7i 0.182206 + 0.388350i
\(933\) 2.63264e6i 0.0990118i
\(934\) −3.60581e6 + 5.67473e6i −0.135250 + 0.212852i
\(935\) 3.67781e7i 1.37582i
\(936\) −3.17427e7 4.06493e6i −1.18428 0.151657i
\(937\) −1.15538e7 −0.429909 −0.214954 0.976624i \(-0.568960\pi\)
−0.214954 + 0.976624i \(0.568960\pi\)
\(938\) −1.28548e7 + 2.02306e7i −0.477044 + 0.750760i
\(939\) −3.93513e7 −1.45645
\(940\) 4.35933e7 2.04531e7i 1.60916 0.754987i
\(941\) 1.49823e7i 0.551574i 0.961219 + 0.275787i \(0.0889384\pi\)
−0.961219 + 0.275787i \(0.911062\pi\)
\(942\) −6.09522e7 3.87300e7i −2.23801 1.42207i
\(943\) −7347.91 −0.000269082
\(944\) 7.78563e6 9.36785e6i 0.284357 0.342145i
\(945\) 6.70736e7i 2.44327i
\(946\) 3.01176e7 + 1.91372e7i 1.09419 + 0.695264i
\(947\) 6.25833e6i 0.226769i 0.993551 + 0.113384i \(0.0361692\pi\)
−0.993551 + 0.113384i \(0.963831\pi\)
\(948\) −3.35118e7 7.14264e7i −1.21109 2.58130i
\(949\) 7.81817e6i 0.281799i
\(950\) 5.06375e7 + 5.91292e6i 1.82038 + 0.212566i
\(951\) 3.88894e7i 1.39438i
\(952\) 1.61872e7 + 2.07291e6i 0.578868 + 0.0741292i
\(953\) 2.60023e7i 0.927426i −0.885985 0.463713i \(-0.846517\pi\)
0.885985 0.463713i \(-0.153483\pi\)
\(954\) 3.52797e7 5.55222e7i 1.25503 1.97513i
\(955\) 8.97110e6i 0.318300i
\(956\) −3.01961e6 + 1.41674e6i −0.106858 + 0.0501354i
\(957\) 6.88586e7 2.43040
\(958\) −9.37936e6 + 1.47610e7i −0.330187 + 0.519639i
\(959\) 4.47862e7i 1.57252i
\(960\) −7.62735e7 1.98607e7i −2.67113 0.695530i
\(961\) −1.85019e7 −0.646260
\(962\) −100894. 64109.5i −0.00351501 0.00223349i
\(963\) 3.89203e7 1.35242
\(964\) −8.87001e6 + 4.16163e6i −0.307420 + 0.144235i
\(965\) 8.58280e7i 2.96695i
\(966\) 187039. + 118848.i 0.00644897 + 0.00409778i
\(967\) 1.89582e6i 0.0651973i 0.999469 + 0.0325987i \(0.0103783\pi\)
−0.999469 + 0.0325987i \(0.989622\pi\)
\(968\) −8.27097e6 + 6.45873e7i −0.283706 + 2.21543i
\(969\) 1.96228e7 9.47434e6i 0.671356 0.324145i
\(970\) −1.72177e6 + 2.70967e6i −0.0587551 + 0.0924672i
\(971\) −1.71402e7 −0.583401 −0.291700 0.956510i \(-0.594221\pi\)
−0.291700 + 0.956510i \(0.594221\pi\)
\(972\) −1.07634e7 2.29410e7i −0.365414 0.778836i
\(973\) 1.75165e7 0.593152
\(974\) 1.71774e7 + 1.09148e7i 0.580177 + 0.368654i
\(975\) 6.30490e7i 2.12406i
\(976\) −1.28075e7 + 1.54103e7i −0.430369 + 0.517830i
\(977\) 1.93553e6i 0.0648729i −0.999474 0.0324365i \(-0.989673\pi\)
0.999474 0.0324365i \(-0.0103267\pi\)
\(978\) −1.74950e7 + 2.75331e7i −0.584879 + 0.920467i
\(979\) −2.32855e7 −0.776478
\(980\) −1.39301e7 2.96905e7i −0.463330 0.987533i
\(981\) 9.31317e7i 3.08976i
\(982\) 2.11180e7 3.32350e7i 0.698835 1.09981i
\(983\) 9.93053e6 0.327785 0.163892 0.986478i \(-0.447595\pi\)
0.163892 + 0.986478i \(0.447595\pi\)
\(984\) −3.66328e6 469115.i −0.120610 0.0154451i
\(985\) 1.35734e7 0.445758
\(986\) 6.13376e6 9.65315e6i 0.200925 0.316211i
\(987\) −6.80490e7 −2.22346
\(988\) −1.36728e7 + 1.68287e7i −0.445620 + 0.548478i
\(989\) 80481.5 0.00261641
\(990\) 8.45673e7 1.33090e8i 2.74230 4.31576i
\(991\) 4.04697e7 1.30902 0.654510 0.756054i \(-0.272875\pi\)
0.654510 + 0.756054i \(0.272875\pi\)
\(992\) −1.75479e7 + 5.64669e6i −0.566170 + 0.182186i
\(993\) 3.44646e7 1.10917
\(994\) −1.79895e7 + 2.83114e7i −0.577502 + 0.908858i
\(995\) 5.71914e7i 1.83136i
\(996\) 2.56991e7 1.20575e7i 0.820861 0.385131i
\(997\) 2.76211e7 0.880041 0.440020 0.897988i \(-0.354971\pi\)
0.440020 + 0.897988i \(0.354971\pi\)
\(998\) −9.37679e6 + 1.47569e7i −0.298008 + 0.468997i
\(999\) 210201.i 0.00666377i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 76.6.d.a.75.9 48
4.3 odd 2 inner 76.6.d.a.75.39 yes 48
19.18 odd 2 inner 76.6.d.a.75.40 yes 48
76.75 even 2 inner 76.6.d.a.75.10 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.6.d.a.75.9 48 1.1 even 1 trivial
76.6.d.a.75.10 yes 48 76.75 even 2 inner
76.6.d.a.75.39 yes 48 4.3 odd 2 inner
76.6.d.a.75.40 yes 48 19.18 odd 2 inner