Properties

Label 74.5.g.a.23.7
Level $74$
Weight $5$
Character 74.23
Analytic conductor $7.649$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,5,Mod(23,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.23");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 74.g (of order \(12\), degree \(4\), 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: \(7.64937726820\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 23.7
Character \(\chi\) \(=\) 74.23
Dual form 74.5.g.a.29.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.732051 + 2.73205i) q^{2} +(13.7481 - 7.93744i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(5.58720 - 20.8517i) q^{5} +(31.7498 + 31.7498i) q^{6} +(10.7825 + 18.6759i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(85.5060 - 148.101i) q^{9} +O(q^{10})\) \(q+(0.732051 + 2.73205i) q^{2} +(13.7481 - 7.93744i) q^{3} +(-6.92820 + 4.00000i) q^{4} +(5.58720 - 20.8517i) q^{5} +(31.7498 + 31.7498i) q^{6} +(10.7825 + 18.6759i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(85.5060 - 148.101i) q^{9} +61.0580 q^{10} +84.9630i q^{11} +(-63.4995 + 109.984i) q^{12} +(66.1127 - 246.736i) q^{13} +(-43.1300 + 43.1300i) q^{14} +(-88.6961 - 331.019i) q^{15} +(32.0000 - 55.4256i) q^{16} +(-68.7695 + 18.4267i) q^{17} +(467.213 + 125.189i) q^{18} +(-122.946 + 458.841i) q^{19} +(44.6976 + 166.814i) q^{20} +(296.477 + 171.171i) q^{21} +(-232.123 + 62.1972i) q^{22} +(340.952 + 340.952i) q^{23} +(-346.968 - 92.9698i) q^{24} +(137.689 + 79.4947i) q^{25} +722.494 q^{26} -1428.93i q^{27} +(-149.407 - 86.2601i) q^{28} +(302.089 - 302.089i) q^{29} +(839.429 - 484.645i) q^{30} +(-941.814 + 941.814i) q^{31} +(174.851 + 46.8513i) q^{32} +(674.389 + 1168.08i) q^{33} +(-100.686 - 174.392i) q^{34} +(449.668 - 120.488i) q^{35} +1368.10i q^{36} +(-615.430 + 1222.87i) q^{37} -1343.58 q^{38} +(-1049.53 - 3916.91i) q^{39} +(-423.023 + 244.232i) q^{40} +(-2613.28 + 1508.78i) q^{41} +(-250.612 + 935.296i) q^{42} +(-1783.94 - 1783.94i) q^{43} +(-339.852 - 588.641i) q^{44} +(-2610.41 - 2610.41i) q^{45} +(-681.903 + 1181.09i) q^{46} -42.3456 q^{47} -1015.99i q^{48} +(967.975 - 1676.58i) q^{49} +(-116.388 + 434.367i) q^{50} +(-799.186 + 799.186i) q^{51} +(528.902 + 1973.89i) q^{52} +(457.121 - 791.757i) q^{53} +(3903.91 - 1046.05i) q^{54} +(1771.62 + 474.705i) q^{55} +(126.294 - 471.334i) q^{56} +(1951.75 + 7284.04i) q^{57} +(1046.47 + 604.179i) q^{58} +(-3272.46 + 876.854i) q^{59} +(1938.58 + 1938.58i) q^{60} +(2614.07 + 700.438i) q^{61} +(-3262.54 - 1883.63i) q^{62} +3687.88 q^{63} +512.000i q^{64} +(-4775.49 - 2757.13i) q^{65} +(-2697.56 + 2697.56i) q^{66} +(4396.29 - 2538.20i) q^{67} +(402.742 - 402.742i) q^{68} +(7393.71 + 1981.14i) q^{69} +(658.359 + 1140.31i) q^{70} +(3192.16 + 5528.98i) q^{71} +(-3737.71 + 1001.52i) q^{72} -6020.79i q^{73} +(-3791.46 - 786.185i) q^{74} +2523.94 q^{75} +(-983.568 - 3670.73i) q^{76} +(-1586.76 + 916.114i) q^{77} +(9932.88 - 5734.75i) q^{78} +(-1307.86 + 4880.99i) q^{79} +(-976.929 - 976.929i) q^{80} +(-4416.06 - 7648.85i) q^{81} +(-6035.12 - 6035.12i) q^{82} +(-3998.24 + 6925.16i) q^{83} -2738.74 q^{84} +1536.92i q^{85} +(3567.87 - 6179.74i) q^{86} +(1755.32 - 6550.96i) q^{87} +(1359.41 - 1359.41i) q^{88} +(-1321.79 - 4932.98i) q^{89} +(5220.83 - 9042.74i) q^{90} +(5320.87 - 1425.72i) q^{91} +(-3725.99 - 998.376i) q^{92} +(-5472.52 + 20423.7i) q^{93} +(-30.9991 - 115.690i) q^{94} +(8880.69 + 5127.27i) q^{95} +(2775.74 - 743.758i) q^{96} +(-6689.12 - 6689.12i) q^{97} +(5289.11 + 1417.21i) q^{98} +(12583.1 + 7264.85i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9} - 72 q^{10} + 80 q^{12} + 248 q^{13} - 192 q^{14} - 852 q^{15} + 896 q^{16} + 1092 q^{17} + 1112 q^{18} - 320 q^{19} + 336 q^{20} - 858 q^{21} - 112 q^{22} + 2348 q^{23} + 160 q^{24} - 162 q^{25} - 184 q^{26} + 1584 q^{28} - 1308 q^{29} + 2652 q^{30} - 3444 q^{31} + 1792 q^{32} + 1052 q^{33} + 1428 q^{34} - 580 q^{35} - 5694 q^{37} - 824 q^{38} - 6514 q^{39} - 1056 q^{40} - 12186 q^{41} - 1276 q^{42} - 6220 q^{43} + 1280 q^{44} + 12804 q^{45} - 4696 q^{46} + 15928 q^{47} - 4892 q^{49} - 10792 q^{50} - 6218 q^{51} + 1984 q^{52} - 9662 q^{53} - 9836 q^{54} + 1744 q^{55} - 3936 q^{56} + 16046 q^{57} + 13800 q^{58} - 9356 q^{59} - 3024 q^{60} - 6682 q^{61} + 16128 q^{62} + 60268 q^{63} - 28086 q^{65} - 4208 q^{66} + 28086 q^{67} - 5712 q^{68} + 19878 q^{69} - 6028 q^{70} + 680 q^{71} - 8896 q^{72} - 2420 q^{74} + 11076 q^{75} - 2560 q^{76} - 32208 q^{77} + 23436 q^{78} - 15136 q^{79} + 1152 q^{80} - 21274 q^{81} - 2608 q^{82} - 19732 q^{83} + 23936 q^{84} + 12440 q^{86} - 31624 q^{87} - 5120 q^{88} + 45940 q^{89} - 25608 q^{90} - 13106 q^{91} - 6944 q^{92} - 37734 q^{93} - 16960 q^{94} - 37458 q^{95} - 1280 q^{96} + 31792 q^{97} + 5216 q^{98} + 141456 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.732051 + 2.73205i 0.183013 + 0.683013i
\(3\) 13.7481 7.93744i 1.52756 0.881938i 0.528098 0.849183i \(-0.322905\pi\)
0.999463 0.0327547i \(-0.0104280\pi\)
\(4\) −6.92820 + 4.00000i −0.433013 + 0.250000i
\(5\) 5.58720 20.8517i 0.223488 0.834068i −0.759517 0.650488i \(-0.774564\pi\)
0.983005 0.183581i \(-0.0587688\pi\)
\(6\) 31.7498 + 31.7498i 0.881938 + 0.881938i
\(7\) 10.7825 + 18.6759i 0.220051 + 0.381140i 0.954823 0.297174i \(-0.0960442\pi\)
−0.734772 + 0.678314i \(0.762711\pi\)
\(8\) −16.0000 16.0000i −0.250000 0.250000i
\(9\) 85.5060 148.101i 1.05563 1.82840i
\(10\) 61.0580 0.610580
\(11\) 84.9630i 0.702174i 0.936343 + 0.351087i \(0.114188\pi\)
−0.936343 + 0.351087i \(0.885812\pi\)
\(12\) −63.4995 + 109.984i −0.440969 + 0.763781i
\(13\) 66.1127 246.736i 0.391200 1.45998i −0.436958 0.899482i \(-0.643944\pi\)
0.828158 0.560495i \(-0.189389\pi\)
\(14\) −43.1300 + 43.1300i −0.220051 + 0.220051i
\(15\) −88.6961 331.019i −0.394205 1.47119i
\(16\) 32.0000 55.4256i 0.125000 0.216506i
\(17\) −68.7695 + 18.4267i −0.237957 + 0.0637603i −0.375826 0.926690i \(-0.622641\pi\)
0.137870 + 0.990450i \(0.455974\pi\)
\(18\) 467.213 + 125.189i 1.44202 + 0.386387i
\(19\) −122.946 + 458.841i −0.340571 + 1.27103i 0.557132 + 0.830424i \(0.311902\pi\)
−0.897702 + 0.440603i \(0.854765\pi\)
\(20\) 44.6976 + 166.814i 0.111744 + 0.417034i
\(21\) 296.477 + 171.171i 0.672283 + 0.388143i
\(22\) −232.123 + 62.1972i −0.479594 + 0.128507i
\(23\) 340.952 + 340.952i 0.644521 + 0.644521i 0.951664 0.307143i \(-0.0993728\pi\)
−0.307143 + 0.951664i \(0.599373\pi\)
\(24\) −346.968 92.9698i −0.602375 0.161406i
\(25\) 137.689 + 79.4947i 0.220302 + 0.127191i
\(26\) 722.494 1.06878
\(27\) 1428.93i 1.96012i
\(28\) −149.407 86.2601i −0.190570 0.110026i
\(29\) 302.089 302.089i 0.359203 0.359203i −0.504316 0.863519i \(-0.668255\pi\)
0.863519 + 0.504316i \(0.168255\pi\)
\(30\) 839.429 484.645i 0.932699 0.538494i
\(31\) −941.814 + 941.814i −0.980036 + 0.980036i −0.999805 0.0197687i \(-0.993707\pi\)
0.0197687 + 0.999805i \(0.493707\pi\)
\(32\) 174.851 + 46.8513i 0.170753 + 0.0457532i
\(33\) 674.389 + 1168.08i 0.619274 + 1.07261i
\(34\) −100.686 174.392i −0.0870982 0.150859i
\(35\) 449.668 120.488i 0.367076 0.0983576i
\(36\) 1368.10i 1.05563i
\(37\) −615.430 + 1222.87i −0.449547 + 0.893257i
\(38\) −1343.58 −0.930456
\(39\) −1049.53 3916.91i −0.690028 2.57522i
\(40\) −423.023 + 244.232i −0.264389 + 0.152645i
\(41\) −2613.28 + 1508.78i −1.55460 + 0.897549i −0.556843 + 0.830618i \(0.687987\pi\)
−0.997758 + 0.0669312i \(0.978679\pi\)
\(42\) −250.612 + 935.296i −0.142070 + 0.530213i
\(43\) −1783.94 1783.94i −0.964812 0.964812i 0.0345899 0.999402i \(-0.488987\pi\)
−0.999402 + 0.0345899i \(0.988987\pi\)
\(44\) −339.852 588.641i −0.175543 0.304050i
\(45\) −2610.41 2610.41i −1.28909 1.28909i
\(46\) −681.903 + 1181.09i −0.322260 + 0.558172i
\(47\) −42.3456 −0.0191696 −0.00958479 0.999954i \(-0.503051\pi\)
−0.00958479 + 0.999954i \(0.503051\pi\)
\(48\) 1015.99i 0.440969i
\(49\) 967.975 1676.58i 0.403155 0.698285i
\(50\) −116.388 + 434.367i −0.0465553 + 0.173747i
\(51\) −799.186 + 799.186i −0.307261 + 0.307261i
\(52\) 528.902 + 1973.89i 0.195600 + 0.729989i
\(53\) 457.121 791.757i 0.162734 0.281864i −0.773114 0.634267i \(-0.781302\pi\)
0.935848 + 0.352403i \(0.114635\pi\)
\(54\) 3903.91 1046.05i 1.33879 0.358728i
\(55\) 1771.62 + 474.705i 0.585661 + 0.156927i
\(56\) 126.294 471.334i 0.0402722 0.150298i
\(57\) 1951.75 + 7284.04i 0.600724 + 2.24193i
\(58\) 1046.47 + 604.179i 0.311079 + 0.179601i
\(59\) −3272.46 + 876.854i −0.940093 + 0.251897i −0.696153 0.717893i \(-0.745107\pi\)
−0.243940 + 0.969790i \(0.578440\pi\)
\(60\) 1938.58 + 1938.58i 0.538494 + 0.538494i
\(61\) 2614.07 + 700.438i 0.702518 + 0.188239i 0.592358 0.805675i \(-0.298197\pi\)
0.110160 + 0.993914i \(0.464864\pi\)
\(62\) −3262.54 1883.63i −0.848736 0.490018i
\(63\) 3687.88 0.929170
\(64\) 512.000i 0.125000i
\(65\) −4775.49 2757.13i −1.13029 0.652575i
\(66\) −2697.56 + 2697.56i −0.619274 + 0.619274i
\(67\) 4396.29 2538.20i 0.979348 0.565427i 0.0772749 0.997010i \(-0.475378\pi\)
0.902073 + 0.431583i \(0.142045\pi\)
\(68\) 402.742 402.742i 0.0870982 0.0870982i
\(69\) 7393.71 + 1981.14i 1.55297 + 0.416118i
\(70\) 658.359 + 1140.31i 0.134359 + 0.232717i
\(71\) 3192.16 + 5528.98i 0.633239 + 1.09680i 0.986885 + 0.161423i \(0.0516082\pi\)
−0.353647 + 0.935379i \(0.615058\pi\)
\(72\) −3737.71 + 1001.52i −0.721008 + 0.193194i
\(73\) 6020.79i 1.12982i −0.825154 0.564908i \(-0.808912\pi\)
0.825154 0.564908i \(-0.191088\pi\)
\(74\) −3791.46 786.185i −0.692378 0.143569i
\(75\) 2523.94 0.448700
\(76\) −983.568 3670.73i −0.170285 0.635513i
\(77\) −1586.76 + 916.114i −0.267626 + 0.154514i
\(78\) 9932.88 5734.75i 1.63262 0.942595i
\(79\) −1307.86 + 4880.99i −0.209559 + 0.782084i 0.778453 + 0.627703i \(0.216005\pi\)
−0.988011 + 0.154381i \(0.950662\pi\)
\(80\) −976.929 976.929i −0.152645 0.152645i
\(81\) −4416.06 7648.85i −0.673078 1.16581i
\(82\) −6035.12 6035.12i −0.897549 0.897549i
\(83\) −3998.24 + 6925.16i −0.580381 + 1.00525i 0.415053 + 0.909797i \(0.363763\pi\)
−0.995434 + 0.0954516i \(0.969570\pi\)
\(84\) −2738.74 −0.388143
\(85\) 1536.92i 0.212722i
\(86\) 3567.87 6179.74i 0.482406 0.835551i
\(87\) 1755.32 6550.96i 0.231910 0.865498i
\(88\) 1359.41 1359.41i 0.175543 0.175543i
\(89\) −1321.79 4932.98i −0.166871 0.622772i −0.997794 0.0663846i \(-0.978854\pi\)
0.830923 0.556388i \(-0.187813\pi\)
\(90\) 5220.83 9042.74i 0.644547 1.11639i
\(91\) 5320.87 1425.72i 0.642539 0.172168i
\(92\) −3725.99 998.376i −0.440216 0.117956i
\(93\) −5472.52 + 20423.7i −0.632734 + 2.36140i
\(94\) −30.9991 115.690i −0.00350828 0.0130931i
\(95\) 8880.69 + 5127.27i 0.984010 + 0.568118i
\(96\) 2775.74 743.758i 0.301187 0.0807029i
\(97\) −6689.12 6689.12i −0.710928 0.710928i 0.255801 0.966729i \(-0.417661\pi\)
−0.966729 + 0.255801i \(0.917661\pi\)
\(98\) 5289.11 + 1417.21i 0.550720 + 0.147565i
\(99\) 12583.1 + 7264.85i 1.28386 + 0.741235i
\(100\) −1271.91 −0.127191
\(101\) 17485.0i 1.71405i 0.515273 + 0.857026i \(0.327690\pi\)
−0.515273 + 0.857026i \(0.672310\pi\)
\(102\) −2768.46 1598.37i −0.266096 0.153630i
\(103\) 7350.34 7350.34i 0.692840 0.692840i −0.270016 0.962856i \(-0.587029\pi\)
0.962856 + 0.270016i \(0.0870289\pi\)
\(104\) −5005.58 + 2889.97i −0.462794 + 0.267194i
\(105\) 5225.69 5225.69i 0.473985 0.473985i
\(106\) 2497.76 + 669.271i 0.222299 + 0.0595649i
\(107\) −4548.65 7878.50i −0.397297 0.688138i 0.596095 0.802914i \(-0.296718\pi\)
−0.993391 + 0.114776i \(0.963385\pi\)
\(108\) 5715.72 + 9899.92i 0.490031 + 0.848758i
\(109\) 12377.3 3316.48i 1.04177 0.279142i 0.302924 0.953015i \(-0.402037\pi\)
0.738847 + 0.673873i \(0.235371\pi\)
\(110\) 5187.68i 0.428734i
\(111\) 1245.48 + 21697.0i 0.101086 + 1.76098i
\(112\) 1380.16 0.110026
\(113\) −4789.48 17874.6i −0.375086 1.39984i −0.853218 0.521554i \(-0.825353\pi\)
0.478132 0.878288i \(-0.341314\pi\)
\(114\) −18471.6 + 10664.6i −1.42133 + 0.820605i
\(115\) 9014.39 5204.46i 0.681617 0.393532i
\(116\) −884.579 + 3301.29i −0.0657386 + 0.245340i
\(117\) −30888.8 30888.8i −2.25647 2.25647i
\(118\) −4791.22 8298.64i −0.344098 0.595995i
\(119\) −1085.64 1085.64i −0.0766643 0.0766643i
\(120\) −3877.16 + 6715.44i −0.269247 + 0.466350i
\(121\) 7422.29 0.506952
\(122\) 7654.53i 0.514279i
\(123\) −23951.7 + 41485.6i −1.58317 + 2.74212i
\(124\) 2757.82 10292.3i 0.179359 0.669377i
\(125\) 11967.2 11967.2i 0.765902 0.765902i
\(126\) 2699.71 + 10075.5i 0.170050 + 0.634635i
\(127\) −1514.51 + 2623.21i −0.0939000 + 0.162640i −0.909149 0.416471i \(-0.863267\pi\)
0.815249 + 0.579111i \(0.196600\pi\)
\(128\) −1398.81 + 374.810i −0.0853766 + 0.0228766i
\(129\) −38685.6 10365.8i −2.32471 0.622905i
\(130\) 4036.72 15065.2i 0.238859 0.891434i
\(131\) 1069.14 + 3990.08i 0.0623004 + 0.232508i 0.990055 0.140683i \(-0.0449300\pi\)
−0.927754 + 0.373192i \(0.878263\pi\)
\(132\) −9344.61 5395.11i −0.536307 0.309637i
\(133\) −9894.91 + 2651.33i −0.559382 + 0.149886i
\(134\) 10152.8 + 10152.8i 0.565427 + 0.565427i
\(135\) −29795.6 7983.72i −1.63488 0.438064i
\(136\) 1395.14 + 805.484i 0.0754293 + 0.0435491i
\(137\) −20039.9 −1.06771 −0.533856 0.845576i \(-0.679257\pi\)
−0.533856 + 0.845576i \(0.679257\pi\)
\(138\) 21650.3i 1.13686i
\(139\) 32083.3 + 18523.3i 1.66054 + 0.958713i 0.972458 + 0.233080i \(0.0748803\pi\)
0.688082 + 0.725633i \(0.258453\pi\)
\(140\) −2633.44 + 2633.44i −0.134359 + 0.134359i
\(141\) −582.170 + 336.116i −0.0292827 + 0.0169064i
\(142\) −12768.6 + 12768.6i −0.633239 + 0.633239i
\(143\) 20963.4 + 5617.14i 1.02516 + 0.274690i
\(144\) −5472.38 9478.45i −0.263907 0.457101i
\(145\) −4611.25 7986.91i −0.219322 0.379877i
\(146\) 16449.1 4407.52i 0.771679 0.206771i
\(147\) 30733.0i 1.42223i
\(148\) −627.647 10934.0i −0.0286545 0.499178i
\(149\) 2615.82 0.117825 0.0589123 0.998263i \(-0.481237\pi\)
0.0589123 + 0.998263i \(0.481237\pi\)
\(150\) 1847.65 + 6895.52i 0.0821178 + 0.306468i
\(151\) −1581.52 + 913.093i −0.0693620 + 0.0400462i −0.534280 0.845308i \(-0.679417\pi\)
0.464918 + 0.885354i \(0.346084\pi\)
\(152\) 9308.59 5374.32i 0.402899 0.232614i
\(153\) −3151.19 + 11760.4i −0.134615 + 0.502388i
\(154\) −3664.46 3664.46i −0.154514 0.154514i
\(155\) 14376.3 + 24900.5i 0.598391 + 1.03644i
\(156\) 22939.0 + 22939.0i 0.942595 + 0.942595i
\(157\) 20857.0 36125.3i 0.846158 1.46559i −0.0384530 0.999260i \(-0.512243\pi\)
0.884611 0.466329i \(-0.154424\pi\)
\(158\) −14292.5 −0.572525
\(159\) 14513.5i 0.574087i
\(160\) 1953.86 3384.18i 0.0763226 0.132195i
\(161\) −2691.25 + 10043.9i −0.103825 + 0.387480i
\(162\) 17664.3 17664.3i 0.673078 0.673078i
\(163\) −7201.89 26877.8i −0.271064 1.01162i −0.958433 0.285316i \(-0.907901\pi\)
0.687370 0.726308i \(-0.258765\pi\)
\(164\) 12070.2 20906.3i 0.448775 0.777300i
\(165\) 28124.3 7535.89i 1.03303 0.276800i
\(166\) −21846.8 5853.83i −0.792815 0.212434i
\(167\) 7812.95 29158.3i 0.280144 1.04551i −0.672170 0.740396i \(-0.734638\pi\)
0.952315 0.305117i \(-0.0986956\pi\)
\(168\) −2004.89 7482.37i −0.0710351 0.265107i
\(169\) −31773.3 18344.3i −1.11247 0.642285i
\(170\) −4198.93 + 1125.10i −0.145292 + 0.0389308i
\(171\) 57442.0 + 57442.0i 1.96443 + 1.96443i
\(172\) 19495.2 + 5223.73i 0.658979 + 0.176573i
\(173\) 19521.5 + 11270.7i 0.652259 + 0.376582i 0.789321 0.613980i \(-0.210433\pi\)
−0.137062 + 0.990562i \(0.543766\pi\)
\(174\) 19182.5 0.633589
\(175\) 3428.61i 0.111955i
\(176\) 4709.13 + 2718.82i 0.152025 + 0.0877717i
\(177\) −38030.0 + 38030.0i −1.21389 + 1.21389i
\(178\) 12509.5 7222.38i 0.394822 0.227951i
\(179\) −21254.5 + 21254.5i −0.663352 + 0.663352i −0.956169 0.292816i \(-0.905408\pi\)
0.292816 + 0.956169i \(0.405408\pi\)
\(180\) 28527.1 + 7643.82i 0.880467 + 0.235921i
\(181\) −1788.15 3097.17i −0.0545817 0.0945383i 0.837444 0.546524i \(-0.184049\pi\)
−0.892025 + 0.451985i \(0.850716\pi\)
\(182\) 7790.29 + 13493.2i 0.235186 + 0.407354i
\(183\) 41498.1 11119.4i 1.23916 0.332031i
\(184\) 10910.5i 0.322260i
\(185\) 22060.4 + 19665.2i 0.644569 + 0.574585i
\(186\) −59804.8 −1.72866
\(187\) −1565.59 5842.86i −0.0447708 0.167087i
\(188\) 293.379 169.382i 0.00830067 0.00479239i
\(189\) 26686.5 15407.5i 0.747081 0.431328i
\(190\) −7506.84 + 28015.9i −0.207946 + 0.776064i
\(191\) −45087.3 45087.3i −1.23591 1.23591i −0.961657 0.274256i \(-0.911568\pi\)
−0.274256 0.961657i \(-0.588432\pi\)
\(192\) 4063.97 + 7039.00i 0.110242 + 0.190945i
\(193\) −30365.9 30365.9i −0.815213 0.815213i 0.170197 0.985410i \(-0.445560\pi\)
−0.985410 + 0.170197i \(0.945560\pi\)
\(194\) 13378.2 23171.8i 0.355464 0.615682i
\(195\) −87538.2 −2.30212
\(196\) 15487.6i 0.403155i
\(197\) −27055.7 + 46861.9i −0.697151 + 1.20750i 0.272300 + 0.962212i \(0.412216\pi\)
−0.969450 + 0.245288i \(0.921118\pi\)
\(198\) −10636.5 + 39695.9i −0.271311 + 1.01255i
\(199\) 43561.1 43561.1i 1.10000 1.10000i 0.105591 0.994410i \(-0.466327\pi\)
0.994410 0.105591i \(-0.0336733\pi\)
\(200\) −931.106 3474.94i −0.0232777 0.0868734i
\(201\) 40293.7 69790.7i 0.997343 1.72745i
\(202\) −47770.0 + 12799.9i −1.17072 + 0.313693i
\(203\) 8899.06 + 2384.50i 0.215949 + 0.0578635i
\(204\) 2340.18 8733.66i 0.0562327 0.209863i
\(205\) 16859.7 + 62921.3i 0.401183 + 1.49723i
\(206\) 25462.3 + 14700.7i 0.600017 + 0.346420i
\(207\) 79648.6 21341.8i 1.85882 0.498069i
\(208\) −11559.9 11559.9i −0.267194 0.267194i
\(209\) −38984.5 10445.9i −0.892482 0.239140i
\(210\) 18102.3 + 10451.4i 0.410483 + 0.236993i
\(211\) 22233.1 0.499384 0.249692 0.968325i \(-0.419671\pi\)
0.249692 + 0.968325i \(0.419671\pi\)
\(212\) 7313.93i 0.162734i
\(213\) 87771.9 + 50675.1i 1.93462 + 1.11695i
\(214\) 18194.6 18194.6i 0.397297 0.397297i
\(215\) −47165.3 + 27230.9i −1.02034 + 0.589095i
\(216\) −22862.9 + 22862.9i −0.490031 + 0.490031i
\(217\) −27744.3 7434.07i −0.589189 0.157873i
\(218\) 18121.6 + 31387.5i 0.381315 + 0.660456i
\(219\) −47789.7 82774.1i −0.996428 1.72586i
\(220\) −14173.0 + 3797.64i −0.292830 + 0.0784637i
\(221\) 18186.2i 0.372354i
\(222\) −58365.6 + 19286.0i −1.18427 + 0.391324i
\(223\) −71074.0 −1.42923 −0.714614 0.699519i \(-0.753397\pi\)
−0.714614 + 0.699519i \(0.753397\pi\)
\(224\) 1010.35 + 3770.67i 0.0201361 + 0.0751489i
\(225\) 23546.4 13594.5i 0.465115 0.268534i
\(226\) 45328.1 26170.2i 0.887464 0.512378i
\(227\) 11464.9 42787.5i 0.222494 0.830358i −0.760899 0.648870i \(-0.775242\pi\)
0.983393 0.181488i \(-0.0580914\pi\)
\(228\) −42658.3 42658.3i −0.820605 0.820605i
\(229\) 1278.25 + 2213.99i 0.0243750 + 0.0422187i 0.877956 0.478742i \(-0.158907\pi\)
−0.853581 + 0.520961i \(0.825574\pi\)
\(230\) 20817.8 + 20817.8i 0.393532 + 0.393532i
\(231\) −14543.2 + 25189.6i −0.272544 + 0.472060i
\(232\) −9666.86 −0.179601
\(233\) 61126.3i 1.12594i 0.826476 + 0.562972i \(0.190342\pi\)
−0.826476 + 0.562972i \(0.809658\pi\)
\(234\) 61777.5 107002.i 1.12823 1.95416i
\(235\) −236.593 + 882.978i −0.00428417 + 0.0159887i
\(236\) 19164.9 19164.9i 0.344098 0.344098i
\(237\) 20762.1 + 77485.1i 0.369636 + 1.37950i
\(238\) 2171.29 3760.78i 0.0383321 0.0663932i
\(239\) −46714.3 + 12517.1i −0.817813 + 0.219132i −0.643390 0.765538i \(-0.722473\pi\)
−0.174423 + 0.984671i \(0.555806\pi\)
\(240\) −21185.2 5676.55i −0.367798 0.0985513i
\(241\) 2438.25 9099.69i 0.0419802 0.156672i −0.941754 0.336303i \(-0.890823\pi\)
0.983734 + 0.179630i \(0.0574901\pi\)
\(242\) 5433.49 + 20278.1i 0.0927787 + 0.346255i
\(243\) −21187.9 12232.9i −0.358819 0.207165i
\(244\) −20912.6 + 5603.51i −0.351259 + 0.0941196i
\(245\) −29551.3 29551.3i −0.492317 0.492317i
\(246\) −130875. 35067.7i −2.16264 0.579479i
\(247\) 105084. + 60670.4i 1.72244 + 0.994451i
\(248\) 30138.1 0.490018
\(249\) 126943.i 2.04744i
\(250\) 41455.6 + 23934.4i 0.663290 + 0.382951i
\(251\) −6373.78 + 6373.78i −0.101169 + 0.101169i −0.755880 0.654710i \(-0.772791\pi\)
0.654710 + 0.755880i \(0.272791\pi\)
\(252\) −25550.4 + 14751.5i −0.402342 + 0.232293i
\(253\) −28968.3 + 28968.3i −0.452566 + 0.452566i
\(254\) −8275.45 2217.40i −0.128270 0.0343698i
\(255\) 12199.2 + 21129.6i 0.187608 + 0.324946i
\(256\) −2048.00 3547.24i −0.0312500 0.0541266i
\(257\) 32125.3 8607.94i 0.486386 0.130327i −0.00728881 0.999973i \(-0.502320\pi\)
0.493674 + 0.869647i \(0.335653\pi\)
\(258\) 113279.i 1.70181i
\(259\) −29474.0 + 1691.90i −0.439379 + 0.0252218i
\(260\) 44114.0 0.652575
\(261\) −18909.2 70570.1i −0.277583 1.03595i
\(262\) −10118.4 + 5841.88i −0.147404 + 0.0851040i
\(263\) 2089.26 1206.24i 0.0302052 0.0174390i −0.484821 0.874613i \(-0.661115\pi\)
0.515027 + 0.857174i \(0.327782\pi\)
\(264\) 7898.99 29479.4i 0.113335 0.422972i
\(265\) −13955.5 13955.5i −0.198725 0.198725i
\(266\) −14487.2 25092.5i −0.204748 0.354634i
\(267\) −57327.3 57327.3i −0.804153 0.804153i
\(268\) −20305.6 + 35170.4i −0.282713 + 0.489674i
\(269\) −58633.5 −0.810291 −0.405145 0.914252i \(-0.632779\pi\)
−0.405145 + 0.914252i \(0.632779\pi\)
\(270\) 87247.7i 1.19681i
\(271\) 41087.1 71164.9i 0.559457 0.969008i −0.438085 0.898934i \(-0.644343\pi\)
0.997542 0.0700744i \(-0.0223237\pi\)
\(272\) −1179.31 + 4401.25i −0.0159401 + 0.0594892i
\(273\) 61835.0 61835.0i 0.829677 0.829677i
\(274\) −14670.2 54750.0i −0.195405 0.729260i
\(275\) −6754.11 + 11698.5i −0.0893105 + 0.154690i
\(276\) −59149.6 + 15849.1i −0.776487 + 0.208059i
\(277\) −41044.1 10997.7i −0.534923 0.143332i −0.0187621 0.999824i \(-0.505973\pi\)
−0.516160 + 0.856492i \(0.672639\pi\)
\(278\) −27120.0 + 101213.i −0.350913 + 1.30963i
\(279\) 58952.6 + 220014.i 0.757347 + 2.82646i
\(280\) −9122.49 5266.87i −0.116358 0.0671795i
\(281\) −125058. + 33509.2i −1.58379 + 0.424376i −0.940098 0.340905i \(-0.889266\pi\)
−0.643696 + 0.765282i \(0.722600\pi\)
\(282\) −1344.46 1344.46i −0.0169064 0.0169064i
\(283\) −35615.7 9543.21i −0.444702 0.119158i 0.0295174 0.999564i \(-0.490603\pi\)
−0.474219 + 0.880407i \(0.657270\pi\)
\(284\) −44231.8 25537.3i −0.548401 0.316619i
\(285\) 162790. 2.00418
\(286\) 61385.2i 0.750467i
\(287\) −56355.5 32536.9i −0.684183 0.395013i
\(288\) 21889.5 21889.5i 0.263907 0.263907i
\(289\) −67941.6 + 39226.1i −0.813467 + 0.469656i
\(290\) 18445.0 18445.0i 0.219322 0.219322i
\(291\) −145057. 38867.9i −1.71298 0.458992i
\(292\) 24083.2 + 41713.2i 0.282454 + 0.489225i
\(293\) −5063.08 8769.50i −0.0589765 0.102150i 0.835030 0.550205i \(-0.185450\pi\)
−0.894006 + 0.448055i \(0.852117\pi\)
\(294\) 83964.1 22498.1i 0.971402 0.260286i
\(295\) 73135.6i 0.840398i
\(296\) 29412.8 9719.01i 0.335701 0.110927i
\(297\) 121406. 1.37635
\(298\) 1914.91 + 7146.56i 0.0215634 + 0.0804757i
\(299\) 106666. 61583.8i 1.19312 0.688849i
\(300\) −17486.4 + 10095.7i −0.194293 + 0.112175i
\(301\) 14081.2 52551.9i 0.155420 0.580036i
\(302\) −3652.37 3652.37i −0.0400462 0.0400462i
\(303\) 138787. + 240385.i 1.51169 + 2.61832i
\(304\) 21497.3 + 21497.3i 0.232614 + 0.232614i
\(305\) 29210.7 50594.4i 0.314009 0.543879i
\(306\) −34436.9 −0.367774
\(307\) 53438.5i 0.566993i 0.958973 + 0.283497i \(0.0914944\pi\)
−0.958973 + 0.283497i \(0.908506\pi\)
\(308\) 7328.92 12694.1i 0.0772571 0.133813i
\(309\) 42710.0 159396.i 0.447314 1.66940i
\(310\) −57505.4 + 57505.4i −0.598391 + 0.598391i
\(311\) 30150.9 + 112525.i 0.311730 + 1.16339i 0.926995 + 0.375073i \(0.122382\pi\)
−0.615265 + 0.788320i \(0.710951\pi\)
\(312\) −45878.0 + 79463.0i −0.471298 + 0.816312i
\(313\) 185526. 49711.5i 1.89372 0.507421i 0.895691 0.444677i \(-0.146681\pi\)
0.998030 0.0627444i \(-0.0199853\pi\)
\(314\) 113965. + 30536.7i 1.15587 + 0.309715i
\(315\) 20604.9 76898.5i 0.207658 0.774992i
\(316\) −10462.9 39047.9i −0.104779 0.391042i
\(317\) 14447.4 + 8341.22i 0.143771 + 0.0830063i 0.570160 0.821534i \(-0.306881\pi\)
−0.426389 + 0.904540i \(0.640215\pi\)
\(318\) 39651.6 10624.6i 0.392108 0.105065i
\(319\) 25666.4 + 25666.4i 0.252223 + 0.252223i
\(320\) 10676.1 + 2860.65i 0.104259 + 0.0279360i
\(321\) −125070. 72209.3i −1.21379 0.700782i
\(322\) −29410.5 −0.283655
\(323\) 33819.7i 0.324164i
\(324\) 61190.8 + 35328.5i 0.582903 + 0.336539i
\(325\) 28717.2 28717.2i 0.271879 0.271879i
\(326\) 68159.5 39351.9i 0.641344 0.370280i
\(327\) 143839. 143839.i 1.34518 1.34518i
\(328\) 65953.0 + 17672.1i 0.613037 + 0.164263i
\(329\) −456.592 790.840i −0.00421829 0.00730629i
\(330\) 41176.9 + 71320.5i 0.378116 + 0.654917i
\(331\) −187861. + 50337.3i −1.71467 + 0.459445i −0.976563 0.215233i \(-0.930949\pi\)
−0.738111 + 0.674679i \(0.764282\pi\)
\(332\) 63971.9i 0.580381i
\(333\) 128485. + 195708.i 1.15868 + 1.76490i
\(334\) 85381.5 0.765369
\(335\) −28362.9 105852.i −0.252732 0.943210i
\(336\) 18974.5 10954.9i 0.168071 0.0970358i
\(337\) 67112.4 38747.4i 0.590939 0.341179i −0.174529 0.984652i \(-0.555840\pi\)
0.765469 + 0.643473i \(0.222507\pi\)
\(338\) 26857.9 100235.i 0.235093 0.877378i
\(339\) −207724. 207724.i −1.80754 1.80754i
\(340\) −6147.66 10648.1i −0.0531805 0.0921113i
\(341\) −80019.4 80019.4i −0.688155 0.688155i
\(342\) −114884. + 198985.i −0.982217 + 1.70125i
\(343\) 93526.4 0.794961
\(344\) 57086.0i 0.482406i
\(345\) 82620.2 143102.i 0.694142 1.20229i
\(346\) −16501.5 + 61584.4i −0.137839 + 0.514421i
\(347\) −37720.2 + 37720.2i −0.313267 + 0.313267i −0.846174 0.532907i \(-0.821100\pi\)
0.532907 + 0.846174i \(0.321100\pi\)
\(348\) 14042.6 + 52407.7i 0.115955 + 0.432749i
\(349\) −33282.1 + 57646.4i −0.273250 + 0.473283i −0.969692 0.244330i \(-0.921432\pi\)
0.696442 + 0.717613i \(0.254765\pi\)
\(350\) −9367.13 + 2509.91i −0.0764664 + 0.0204891i
\(351\) −352569. 94470.5i −2.86174 0.766800i
\(352\) −3980.62 + 14855.9i −0.0321267 + 0.119898i
\(353\) −19606.3 73171.7i −0.157343 0.587210i −0.998893 0.0470324i \(-0.985024\pi\)
0.841551 0.540178i \(-0.181643\pi\)
\(354\) −131740. 76060.1i −1.05126 0.606946i
\(355\) 133124. 35670.4i 1.05633 0.283043i
\(356\) 28889.5 + 28889.5i 0.227951 + 0.227951i
\(357\) −23542.7 6308.25i −0.184723 0.0494963i
\(358\) −73627.7 42509.0i −0.574480 0.331676i
\(359\) 121559. 0.943190 0.471595 0.881815i \(-0.343678\pi\)
0.471595 + 0.881815i \(0.343678\pi\)
\(360\) 83533.3i 0.644547i
\(361\) −82557.8 47664.8i −0.633496 0.365749i
\(362\) 7152.61 7152.61i 0.0545817 0.0545817i
\(363\) 102042. 58914.0i 0.774401 0.447100i
\(364\) −31161.2 + 31161.2i −0.235186 + 0.235186i
\(365\) −125544. 33639.3i −0.942344 0.252500i
\(366\) 60757.4 + 105235.i 0.453562 + 0.785593i
\(367\) 14675.0 + 25417.8i 0.108955 + 0.188715i 0.915347 0.402666i \(-0.131916\pi\)
−0.806392 + 0.591381i \(0.798583\pi\)
\(368\) 29807.9 7987.00i 0.220108 0.0589778i
\(369\) 516039.i 3.78992i
\(370\) −37577.0 + 74665.9i −0.274485 + 0.545405i
\(371\) 19715.6 0.143240
\(372\) −43780.1 163390.i −0.316367 1.18070i
\(373\) −221805. + 128059.i −1.59424 + 0.920436i −0.601675 + 0.798741i \(0.705500\pi\)
−0.992568 + 0.121695i \(0.961167\pi\)
\(374\) 14816.9 8554.55i 0.105929 0.0611581i
\(375\) 69536.8 259515.i 0.494484 1.84544i
\(376\) 677.530 + 677.530i 0.00479239 + 0.00479239i
\(377\) −54564.4 94508.3i −0.383908 0.664947i
\(378\) 61629.8 + 61629.8i 0.431328 + 0.431328i
\(379\) 29127.1 50449.7i 0.202777 0.351220i −0.746645 0.665223i \(-0.768337\pi\)
0.949422 + 0.314002i \(0.101670\pi\)
\(380\) −82036.3 −0.568118
\(381\) 48085.4i 0.331256i
\(382\) 90174.7 156187.i 0.617957 1.07033i
\(383\) 39260.9 146524.i 0.267647 0.998873i −0.692963 0.720973i \(-0.743695\pi\)
0.960610 0.277900i \(-0.0896382\pi\)
\(384\) −16255.9 + 16255.9i −0.110242 + 0.110242i
\(385\) 10237.0 + 38205.1i 0.0690641 + 0.257751i
\(386\) 60731.8 105190.i 0.407607 0.705995i
\(387\) −416740. + 111665.i −2.78255 + 0.745582i
\(388\) 73100.1 + 19587.1i 0.485573 + 0.130109i
\(389\) 30291.7 113050.i 0.200181 0.747087i −0.790683 0.612226i \(-0.790274\pi\)
0.990864 0.134861i \(-0.0430589\pi\)
\(390\) −64082.4 239159.i −0.421318 1.57238i
\(391\) −29729.7 17164.4i −0.194463 0.112273i
\(392\) −42312.9 + 11337.7i −0.275360 + 0.0737825i
\(393\) 46369.6 + 46369.6i 0.300226 + 0.300226i
\(394\) −147835. 39612.3i −0.952325 0.255175i
\(395\) 94469.7 + 54542.1i 0.605478 + 0.349573i
\(396\) −116238. −0.741235
\(397\) 43050.6i 0.273148i 0.990630 + 0.136574i \(0.0436092\pi\)
−0.990630 + 0.136574i \(0.956391\pi\)
\(398\) 150900. + 87122.2i 0.952628 + 0.550000i
\(399\) −114991. + 114991.i −0.722300 + 0.722300i
\(400\) 8812.08 5087.66i 0.0550755 0.0317979i
\(401\) 21173.2 21173.2i 0.131674 0.131674i −0.638198 0.769872i \(-0.720320\pi\)
0.769872 + 0.638198i \(0.220320\pi\)
\(402\) 220169. + 58994.0i 1.36240 + 0.365053i
\(403\) 170114. + 294646.i 1.04744 + 1.81422i
\(404\) −69940.2 121140.i −0.428513 0.742206i
\(405\) −184165. + 49346.9i −1.12279 + 0.300850i
\(406\) 26058.2i 0.158086i
\(407\) −103899. 52288.8i −0.627221 0.315660i
\(408\) 25573.9 0.153630
\(409\) 45786.1 + 170876.i 0.273708 + 1.02149i 0.956702 + 0.291068i \(0.0940105\pi\)
−0.682995 + 0.730423i \(0.739323\pi\)
\(410\) −159562. + 92123.2i −0.949209 + 0.548026i
\(411\) −275509. + 159065.i −1.63100 + 0.941655i
\(412\) −21523.3 + 80326.0i −0.126799 + 0.473219i
\(413\) −51661.4 51661.4i −0.302877 0.302877i
\(414\) 116614. + 201981.i 0.680375 + 1.17844i
\(415\) 122062. + 122062.i 0.708738 + 0.708738i
\(416\) 23119.8 40044.7i 0.133597 0.231397i
\(417\) 588110. 3.38210
\(418\) 114155.i 0.653342i
\(419\) −66013.7 + 114339.i −0.376015 + 0.651278i −0.990478 0.137668i \(-0.956039\pi\)
0.614463 + 0.788946i \(0.289373\pi\)
\(420\) −15301.9 + 57107.4i −0.0867453 + 0.323738i
\(421\) 186639. 186639.i 1.05302 1.05302i 0.0545078 0.998513i \(-0.482641\pi\)
0.998513 0.0545078i \(-0.0173590\pi\)
\(422\) 16275.7 + 60741.8i 0.0913936 + 0.341085i
\(423\) −3620.80 + 6271.41i −0.0202360 + 0.0350497i
\(424\) −19982.0 + 5354.17i −0.111150 + 0.0297825i
\(425\) −10933.6 2929.65i −0.0605321 0.0162195i
\(426\) −74193.5 + 276894.i −0.408834 + 1.52579i
\(427\) 15105.0 + 56372.5i 0.0828445 + 0.309180i
\(428\) 63028.0 + 36389.2i 0.344069 + 0.198648i
\(429\) 332792. 89171.4i 1.80825 0.484519i
\(430\) −108924. 108924.i −0.589095 0.589095i
\(431\) 111290. + 29820.1i 0.599103 + 0.160529i 0.545610 0.838039i \(-0.316298\pi\)
0.0534927 + 0.998568i \(0.482965\pi\)
\(432\) −79199.3 45725.8i −0.424379 0.245015i
\(433\) −179261. −0.956114 −0.478057 0.878329i \(-0.658659\pi\)
−0.478057 + 0.878329i \(0.658659\pi\)
\(434\) 81241.0i 0.431316i
\(435\) −126791. 73203.0i −0.670056 0.386857i
\(436\) −72486.4 + 72486.4i −0.381315 + 0.381315i
\(437\) −198361. + 114524.i −1.03871 + 0.599699i
\(438\) 191159. 191159.i 0.996428 0.996428i
\(439\) −125960. 33750.9i −0.653589 0.175129i −0.0832378 0.996530i \(-0.526526\pi\)
−0.570351 + 0.821401i \(0.693193\pi\)
\(440\) −20750.7 35941.3i −0.107183 0.185647i
\(441\) −165535. 286716.i −0.851165 1.47426i
\(442\) −49685.5 + 13313.2i −0.254323 + 0.0681456i
\(443\) 181957.i 0.927174i −0.886052 0.463587i \(-0.846562\pi\)
0.886052 0.463587i \(-0.153438\pi\)
\(444\) −95416.9 145339.i −0.484016 0.737254i
\(445\) −110246. −0.556729
\(446\) −52029.8 194178.i −0.261567 0.976180i
\(447\) 35962.5 20762.9i 0.179984 0.103914i
\(448\) −9562.04 + 5520.64i −0.0476425 + 0.0275064i
\(449\) −24501.6 + 91441.2i −0.121535 + 0.453575i −0.999693 0.0247967i \(-0.992106\pi\)
0.878157 + 0.478372i \(0.158773\pi\)
\(450\) 54378.2 + 54378.2i 0.268534 + 0.268534i
\(451\) −128190. 222032.i −0.630235 1.09160i
\(452\) 104681. + 104681.i 0.512378 + 0.512378i
\(453\) −14495.2 + 25106.5i −0.0706365 + 0.122346i
\(454\) 125291. 0.607864
\(455\) 118915.i 0.574399i
\(456\) 85316.6 147773.i 0.410302 0.710665i
\(457\) −79075.8 + 295115.i −0.378627 + 1.41305i 0.469346 + 0.883015i \(0.344490\pi\)
−0.847973 + 0.530040i \(0.822177\pi\)
\(458\) −5113.00 + 5113.00i −0.0243750 + 0.0243750i
\(459\) 26330.5 + 98266.8i 0.124978 + 0.466425i
\(460\) −41635.7 + 72115.1i −0.196766 + 0.340809i
\(461\) −99739.3 + 26725.1i −0.469315 + 0.125753i −0.485723 0.874113i \(-0.661444\pi\)
0.0164081 + 0.999865i \(0.494777\pi\)
\(462\) −79465.6 21292.7i −0.372302 0.0997580i
\(463\) 38820.7 144881.i 0.181093 0.675848i −0.814340 0.580388i \(-0.802901\pi\)
0.995433 0.0954604i \(-0.0304323\pi\)
\(464\) −7076.63 26410.3i −0.0328693 0.122670i
\(465\) 395293. + 228223.i 1.82816 + 1.05549i
\(466\) −167000. + 44747.6i −0.769034 + 0.206062i
\(467\) 117038. + 117038.i 0.536651 + 0.536651i 0.922544 0.385892i \(-0.126106\pi\)
−0.385892 + 0.922544i \(0.626106\pi\)
\(468\) 337559. + 90448.6i 1.54119 + 0.412962i
\(469\) 94806.2 + 54736.4i 0.431013 + 0.248846i
\(470\) −2585.54 −0.0117046
\(471\) 662204.i 2.98504i
\(472\) 66389.1 + 38329.8i 0.297998 + 0.172049i
\(473\) 151569. 151569.i 0.677465 0.677465i
\(474\) −196494. + 113446.i −0.874568 + 0.504932i
\(475\) −53403.7 + 53403.7i −0.236692 + 0.236692i
\(476\) 11864.1 + 3178.98i 0.0523627 + 0.0140305i
\(477\) −78173.2 135400.i −0.343574 0.595088i
\(478\) −68394.5 118463.i −0.299340 0.518473i
\(479\) −185004. + 49571.8i −0.806327 + 0.216055i −0.638360 0.769738i \(-0.720387\pi\)
−0.167967 + 0.985793i \(0.553720\pi\)
\(480\) 62034.5i 0.269247i
\(481\) 261038. + 232696.i 1.12827 + 1.00577i
\(482\) 26645.7 0.114692
\(483\) 42723.3 + 159445.i 0.183134 + 0.683467i
\(484\) −51423.1 + 29689.1i −0.219517 + 0.126738i
\(485\) −176853. + 102106.i −0.751847 + 0.434079i
\(486\) 17910.1 66841.6i 0.0758275 0.282992i
\(487\) 172222. + 172222.i 0.726159 + 0.726159i 0.969852 0.243694i \(-0.0783592\pi\)
−0.243694 + 0.969852i \(0.578359\pi\)
\(488\) −30618.1 53032.2i −0.128570 0.222689i
\(489\) −312353. 312353.i −1.30626 1.30626i
\(490\) 59102.7 102369.i 0.246159 0.426359i
\(491\) 396124. 1.64312 0.821559 0.570124i \(-0.193105\pi\)
0.821559 + 0.570124i \(0.193105\pi\)
\(492\) 383227.i 1.58317i
\(493\) −15208.0 + 26341.1i −0.0625718 + 0.108378i
\(494\) −88827.7 + 331509.i −0.363994 + 1.35844i
\(495\) 221789. 221789.i 0.905168 0.905168i
\(496\) 22062.6 + 82338.7i 0.0896795 + 0.334688i
\(497\) −68838.9 + 119232.i −0.278690 + 0.482705i
\(498\) −346815. + 92928.9i −1.39843 + 0.374707i
\(499\) 169361. + 45380.1i 0.680161 + 0.182249i 0.582327 0.812954i \(-0.302142\pi\)
0.0978333 + 0.995203i \(0.468809\pi\)
\(500\) −35042.4 + 130780.i −0.140170 + 0.523121i
\(501\) −124030. 462885.i −0.494140 1.84416i
\(502\) −22079.4 12747.6i −0.0876153 0.0505847i
\(503\) 241274. 64649.2i 0.953618 0.255521i 0.251721 0.967800i \(-0.419003\pi\)
0.701897 + 0.712279i \(0.252337\pi\)
\(504\) −59006.0 59006.0i −0.232293 0.232293i
\(505\) 364593. + 97692.4i 1.42964 + 0.383070i
\(506\) −100349. 57936.6i −0.391933 0.226283i
\(507\) −582427. −2.26582
\(508\) 24232.2i 0.0939000i
\(509\) 152742. + 88185.6i 0.589553 + 0.340379i 0.764921 0.644124i \(-0.222778\pi\)
−0.175368 + 0.984503i \(0.556111\pi\)
\(510\) −48796.7 + 48796.7i −0.187608 + 0.187608i
\(511\) 112443. 64919.2i 0.430618 0.248617i
\(512\) 8192.00 8192.00i 0.0312500 0.0312500i
\(513\) 655651. + 175681.i 2.49137 + 0.667561i
\(514\) 47034.7 + 81466.5i 0.178029 + 0.308356i
\(515\) −112199. 194335.i −0.423035 0.732718i
\(516\) 309484. 82926.1i 1.16236 0.311453i
\(517\) 3597.81i 0.0134604i
\(518\) −26198.8 79285.9i −0.0976388 0.295486i
\(519\) 357843. 1.32849
\(520\) 32293.7 + 120522.i 0.119429 + 0.445717i
\(521\) −78718.8 + 45448.3i −0.290003 + 0.167434i −0.637943 0.770083i \(-0.720215\pi\)
0.347940 + 0.937517i \(0.386881\pi\)
\(522\) 178959. 103322.i 0.656767 0.379185i
\(523\) −21173.3 + 79020.0i −0.0774080 + 0.288891i −0.993769 0.111463i \(-0.964446\pi\)
0.916361 + 0.400354i \(0.131113\pi\)
\(524\) −23367.5 23367.5i −0.0851040 0.0851040i
\(525\) 27214.4 + 47136.7i 0.0987370 + 0.171017i
\(526\) 4824.95 + 4824.95i 0.0174390 + 0.0174390i
\(527\) 47413.5 82122.7i 0.170719 0.295694i
\(528\) 86321.8 0.309637
\(529\) 47345.0i 0.169185i
\(530\) 27910.9 48343.1i 0.0993624 0.172101i
\(531\) −149953. + 559631.i −0.531820 + 1.98478i
\(532\) 57948.6 57948.6i 0.204748 0.204748i
\(533\) 199499. + 744541.i 0.702242 + 2.62080i
\(534\) 114655. 198587.i 0.402076 0.696417i
\(535\) −189694. + 50828.4i −0.662746 + 0.177582i
\(536\) −110952. 29729.5i −0.386194 0.103480i
\(537\) −123501. + 460914.i −0.428276 + 1.59835i
\(538\) −42922.7 160190.i −0.148294 0.553439i
\(539\) 142447. + 82242.1i 0.490317 + 0.283085i
\(540\) 238365. 63869.7i 0.817439 0.219032i
\(541\) −133198. 133198.i −0.455098 0.455098i 0.441945 0.897042i \(-0.354289\pi\)
−0.897042 + 0.441945i \(0.854289\pi\)
\(542\) 224504. + 60155.7i 0.764233 + 0.204776i
\(543\) −49167.2 28386.7i −0.166754 0.0962754i
\(544\) −12887.7 −0.0435491
\(545\) 276617.i 0.931293i
\(546\) 214203. + 123670.i 0.718521 + 0.414839i
\(547\) −109219. + 109219.i −0.365025 + 0.365025i −0.865659 0.500634i \(-0.833100\pi\)
0.500634 + 0.865659i \(0.333100\pi\)
\(548\) 138840. 80159.5i 0.462333 0.266928i
\(549\) 327254. 327254.i 1.08578 1.08578i
\(550\) −36905.1 9888.70i −0.122000 0.0326899i
\(551\) 101470. + 175752.i 0.334222 + 0.578890i
\(552\) −86601.1 149997.i −0.284214 0.492273i
\(553\) −105259. + 28203.9i −0.344197 + 0.0922273i
\(554\) 120185.i 0.391590i
\(555\) 459378. + 95255.1i 1.49137 + 0.309245i
\(556\) −296373. −0.958713
\(557\) 100899. + 376560.i 0.325219 + 1.21373i 0.914091 + 0.405508i \(0.132905\pi\)
−0.588872 + 0.808226i \(0.700428\pi\)
\(558\) −557934. + 322123.i −1.79190 + 1.03455i
\(559\) −558103. + 322221.i −1.78604 + 1.03117i
\(560\) 7711.24 28778.7i 0.0245894 0.0917689i
\(561\) −67901.2 67901.2i −0.215751 0.215751i
\(562\) −183097. 317134.i −0.579709 1.00408i
\(563\) −342627. 342627.i −1.08095 1.08095i −0.996421 0.0845268i \(-0.973062\pi\)
−0.0845268 0.996421i \(-0.526938\pi\)
\(564\) 2688.93 4657.36i 0.00845319 0.0146414i
\(565\) −399475. −1.25139
\(566\) 104290.i 0.325544i
\(567\) 95232.5 164948.i 0.296223 0.513074i
\(568\) 37389.1 139538.i 0.115891 0.432510i
\(569\) −135904. + 135904.i −0.419767 + 0.419767i −0.885123 0.465356i \(-0.845926\pi\)
0.465356 + 0.885123i \(0.345926\pi\)
\(570\) 119170. + 444750.i 0.366791 + 1.36888i
\(571\) −4479.51 + 7758.74i −0.0137391 + 0.0237968i −0.872813 0.488054i \(-0.837707\pi\)
0.859074 + 0.511851i \(0.171040\pi\)
\(572\) −167708. + 44937.1i −0.512579 + 0.137345i
\(573\) −977741. 261985.i −2.97793 0.797934i
\(574\) 47637.3 177785.i 0.144585 0.539598i
\(575\) 19841.4 + 74049.0i 0.0600117 + 0.223967i
\(576\) 75827.6 + 43779.1i 0.228551 + 0.131954i
\(577\) −143413. + 38427.3i −0.430760 + 0.115422i −0.467683 0.883896i \(-0.654911\pi\)
0.0369227 + 0.999318i \(0.488244\pi\)
\(578\) −156904. 156904.i −0.469656 0.469656i
\(579\) −658499. 176444.i −1.96426 0.526321i
\(580\) 63895.3 + 36890.0i 0.189938 + 0.109661i
\(581\) −172444. −0.510854
\(582\) 424756.i 1.25399i
\(583\) 67270.0 + 38838.4i 0.197918 + 0.114268i
\(584\) −96332.6 + 96332.6i −0.282454 + 0.282454i
\(585\) −816665. + 471502.i −2.38634 + 1.37775i
\(586\) 20252.3 20252.3i 0.0589765 0.0589765i
\(587\) 305670. + 81904.1i 0.887109 + 0.237700i 0.673472 0.739213i \(-0.264802\pi\)
0.213637 + 0.976913i \(0.431469\pi\)
\(588\) 122932. + 212924.i 0.355558 + 0.615844i
\(589\) −316350. 547935.i −0.911880 1.57942i
\(590\) −199810. + 53539.0i −0.574003 + 0.153804i
\(591\) 859013.i 2.45937i
\(592\) 48084.5 + 73242.4i 0.137202 + 0.208987i
\(593\) 174574. 0.496444 0.248222 0.968703i \(-0.420154\pi\)
0.248222 + 0.968703i \(0.420154\pi\)
\(594\) 88875.5 + 331688.i 0.251889 + 0.940063i
\(595\) −28703.2 + 16571.8i −0.0810768 + 0.0468097i
\(596\) −18122.9 + 10463.3i −0.0510195 + 0.0294561i
\(597\) 253117. 944644.i 0.710186 2.65045i
\(598\) 246335. + 246335.i 0.688849 + 0.688849i
\(599\) 192009. + 332569.i 0.535141 + 0.926891i 0.999157 + 0.0410642i \(0.0130748\pi\)
−0.464016 + 0.885827i \(0.653592\pi\)
\(600\) −40383.0 40383.0i −0.112175 0.112175i
\(601\) 307764. 533062.i 0.852056 1.47580i −0.0272929 0.999627i \(-0.508689\pi\)
0.879349 0.476177i \(-0.157978\pi\)
\(602\) 153883. 0.424616
\(603\) 868126.i 2.38753i
\(604\) 7304.74 12652.2i 0.0200231 0.0346810i
\(605\) 41469.8 154767.i 0.113298 0.422833i
\(606\) −555146. + 555146.i −1.51169 + 1.51169i
\(607\) −90260.7 336857.i −0.244975 0.914258i −0.973396 0.229129i \(-0.926412\pi\)
0.728422 0.685129i \(-0.240254\pi\)
\(608\) −42994.5 + 74468.7i −0.116307 + 0.201450i
\(609\) 141272. 37853.6i 0.380908 0.102064i
\(610\) 159610. + 42767.4i 0.428944 + 0.114935i
\(611\) −2799.58 + 10448.2i −0.00749913 + 0.0279871i
\(612\) −25209.5 94083.3i −0.0673073 0.251194i
\(613\) 79666.5 + 45995.5i 0.212009 + 0.122404i 0.602245 0.798311i \(-0.294273\pi\)
−0.390236 + 0.920715i \(0.627606\pi\)
\(614\) −145997. + 39119.7i −0.387263 + 0.103767i
\(615\) 731222. + 731222.i 1.93330 + 1.93330i
\(616\) 40045.9 + 10730.3i 0.105535 + 0.0282781i
\(617\) −526542. 303999.i −1.38313 0.798550i −0.390601 0.920560i \(-0.627733\pi\)
−0.992529 + 0.122010i \(0.961066\pi\)
\(618\) 466743. 1.22208
\(619\) 268422.i 0.700546i −0.936648 0.350273i \(-0.886089\pi\)
0.936648 0.350273i \(-0.113911\pi\)
\(620\) −199204. 115011.i −0.518222 0.299195i
\(621\) 487196. 487196.i 1.26334 1.26334i
\(622\) −285351. + 164747.i −0.737562 + 0.425832i
\(623\) 77875.4 77875.4i 0.200643 0.200643i
\(624\) −250682. 67170.1i −0.643805 0.172507i
\(625\) −132990. 230345.i −0.340453 0.589682i
\(626\) 271629. + 470475.i 0.693150 + 1.20057i
\(627\) −618874. + 165827.i −1.57423 + 0.421813i
\(628\) 333711.i 0.846158i
\(629\) 19789.4 95436.4i 0.0500185 0.241220i
\(630\) 225175. 0.567333
\(631\) 3298.13 + 12308.8i 0.00828340 + 0.0309141i 0.969944 0.243329i \(-0.0782394\pi\)
−0.961660 + 0.274243i \(0.911573\pi\)
\(632\) 99021.5 57170.1i 0.247911 0.143131i
\(633\) 305661. 176474.i 0.762839 0.440425i
\(634\) −12212.4 + 45577.3i −0.0303824 + 0.113389i
\(635\) 46236.6 + 46236.6i 0.114667 + 0.114667i
\(636\) 58053.9 + 100552.i 0.143522 + 0.248587i
\(637\) −349678. 349678.i −0.861766 0.861766i
\(638\) −51332.8 + 88911.1i −0.126111 + 0.218431i
\(639\) 1.09179e6 2.67386
\(640\) 31261.7i 0.0763226i
\(641\) 37672.0 65249.8i 0.0916860 0.158805i −0.816535 0.577296i \(-0.804108\pi\)
0.908221 + 0.418492i \(0.137441\pi\)
\(642\) 105722. 394559.i 0.256504 0.957287i
\(643\) 397860. 397860.i 0.962295 0.962295i −0.0370200 0.999315i \(-0.511787\pi\)
0.999315 + 0.0370200i \(0.0117865\pi\)
\(644\) −21530.0 80351.0i −0.0519125 0.193740i
\(645\) −432288. + 748744.i −1.03909 + 1.79976i
\(646\) 92397.2 24757.8i 0.221408 0.0593262i
\(647\) 693730. + 185884.i 1.65723 + 0.444052i 0.961623 0.274374i \(-0.0884707\pi\)
0.695603 + 0.718426i \(0.255137\pi\)
\(648\) −51724.5 + 193039.i −0.123182 + 0.459721i
\(649\) −74500.2 278038.i −0.176876 0.660109i
\(650\) 99479.3 + 57434.4i 0.235454 + 0.135939i
\(651\) −440438. + 118015.i −1.03926 + 0.278468i
\(652\) 157408. + 157408.i 0.370280 + 0.370280i
\(653\) 327415. + 87730.6i 0.767843 + 0.205743i 0.621418 0.783479i \(-0.286557\pi\)
0.146425 + 0.989222i \(0.453223\pi\)
\(654\) 498273. + 287678.i 1.16496 + 0.672592i
\(655\) 89173.4 0.207851
\(656\) 193124.i 0.448775i
\(657\) −891683. 514814.i −2.06576 1.19267i
\(658\) 1826.37 1826.37i 0.00421829 0.00421829i
\(659\) −494696. + 285613.i −1.13912 + 0.657669i −0.946212 0.323549i \(-0.895124\pi\)
−0.192904 + 0.981218i \(0.561791\pi\)
\(660\) −164708. + 164708.i −0.378116 + 0.378116i
\(661\) 689050. + 184630.i 1.57706 + 0.422572i 0.938014 0.346597i \(-0.112663\pi\)
0.639045 + 0.769169i \(0.279330\pi\)
\(662\) −275048. 476397.i −0.627614 1.08706i
\(663\) 144352. + 250024.i 0.328394 + 0.568794i
\(664\) 174774. 46830.7i 0.396407 0.106217i
\(665\) 221139.i 0.500061i
\(666\) −440627. + 494295.i −0.993398 + 1.11439i
\(667\) 205996. 0.463027
\(668\) 62503.6 + 233267.i 0.140072 + 0.522757i
\(669\) −977130. + 564146.i −2.18323 + 1.26049i
\(670\) 268429. 154978.i 0.597971 0.345239i
\(671\) −59511.4 + 222099.i −0.132177 + 0.493290i
\(672\) 43819.8 + 43819.8i 0.0970358 + 0.0970358i
\(673\) 325418. + 563640.i 0.718474 + 1.24443i 0.961604 + 0.274440i \(0.0884926\pi\)
−0.243130 + 0.969994i \(0.578174\pi\)
\(674\) 154989. + 154989.i 0.341179 + 0.341179i
\(675\) 113592. 196748.i 0.249311 0.431819i
\(676\) 293509. 0.642285
\(677\) 580336.i 1.26620i −0.774070 0.633100i \(-0.781782\pi\)
0.774070 0.633100i \(-0.218218\pi\)
\(678\) 415449. 719579.i 0.903771 1.56538i
\(679\) 52799.6 197051.i 0.114522 0.427404i
\(680\) 24590.7 24590.7i 0.0531805 0.0531805i
\(681\) −182004. 679247.i −0.392451 1.46465i
\(682\) 160039. 277195.i 0.344078 0.595960i
\(683\) 93149.4 24959.3i 0.199682 0.0535046i −0.157592 0.987504i \(-0.550373\pi\)
0.357274 + 0.934000i \(0.383706\pi\)
\(684\) −627738. 168202.i −1.34173 0.359516i
\(685\) −111967. + 417866.i −0.238621 + 0.890544i
\(686\) 68466.1 + 255519.i 0.145488 + 0.542969i
\(687\) 35146.9 + 20292.1i 0.0744686 + 0.0429945i
\(688\) −155962. + 41789.8i −0.329489 + 0.0882864i
\(689\) −165133. 165133.i −0.347854 0.347854i
\(690\) 451445. + 120964.i 0.948215 + 0.254073i
\(691\) −375694. 216907.i −0.786826 0.454274i 0.0520182 0.998646i \(-0.483435\pi\)
−0.838844 + 0.544372i \(0.816768\pi\)
\(692\) −180332. −0.376582
\(693\) 313333.i 0.652439i
\(694\) −130667. 75440.3i −0.271297 0.156634i
\(695\) 565498. 565498.i 1.17074 1.17074i
\(696\) −132901. + 76730.1i −0.274352 + 0.158397i
\(697\) 151912. 151912.i 0.312700 0.312700i
\(698\) −181857. 48728.4i −0.373267 0.100017i
\(699\) 485187. + 840368.i 0.993012 + 1.71995i
\(700\) −13714.4 23754.1i −0.0279886 0.0484777i
\(701\) −63539.8 + 17025.4i −0.129303 + 0.0346467i −0.322890 0.946436i \(-0.604654\pi\)
0.193587 + 0.981083i \(0.437988\pi\)
\(702\) 1.03239e6i 2.09494i
\(703\) −485437. 432731.i −0.982250 0.875604i
\(704\) −43501.1 −0.0877717
\(705\) 3755.89 + 14017.2i 0.00755675 + 0.0282022i
\(706\) 185556. 107131.i 0.372276 0.214934i
\(707\) −326548. + 188533.i −0.653294 + 0.377179i
\(708\) 111360. 415600.i 0.222158 0.829104i
\(709\) −323873. 323873.i −0.644292 0.644292i 0.307316 0.951608i \(-0.400569\pi\)
−0.951608 + 0.307316i \(0.900569\pi\)
\(710\) 194907. + 337589.i 0.386643 + 0.669686i
\(711\) 611048. + 611048.i 1.20875 + 1.20875i
\(712\) −57779.1 + 100076.i −0.113975 + 0.197411i
\(713\) −642226. −1.26331
\(714\) 68937.8i 0.135226i
\(715\) 234254. 405740.i 0.458221 0.793662i
\(716\) 62237.4 232273.i 0.121402 0.453078i
\(717\) −542877. + 542877.i −1.05600 + 1.05600i
\(718\) 88987.5 + 332106.i 0.172616 + 0.644211i
\(719\) 58296.8 100973.i 0.112768 0.195320i −0.804117 0.594471i \(-0.797362\pi\)
0.916885 + 0.399150i \(0.130695\pi\)
\(720\) −228217. + 61150.6i −0.440234 + 0.117960i
\(721\) 216529. + 58018.8i 0.416529 + 0.111609i
\(722\) 69786.0 260445.i 0.133873 0.499622i
\(723\) −38707.0 144457.i −0.0740479 0.276351i
\(724\) 24777.4 + 14305.2i 0.0472692 + 0.0272909i
\(725\) 65608.8 17579.8i 0.124821 0.0334456i
\(726\) 235656. + 235656.i 0.447100 + 0.447100i
\(727\) −268499. 71944.2i −0.508012 0.136121i −0.00429628 0.999991i \(-0.501368\pi\)
−0.503716 + 0.863869i \(0.668034\pi\)
\(728\) −107945. 62322.3i −0.203677 0.117593i
\(729\) 327012. 0.615331
\(730\) 367618.i 0.689844i
\(731\) 155553. + 89808.3i 0.291100 + 0.168067i
\(732\) −243030. + 243030.i −0.453562 + 0.453562i
\(733\) 745442. 430381.i 1.38741 0.801023i 0.394390 0.918943i \(-0.370956\pi\)
0.993023 + 0.117920i \(0.0376225\pi\)
\(734\) −58699.9 + 58699.9i −0.108955 + 0.108955i
\(735\) −640835. 171711.i −1.18624 0.317851i
\(736\) 43641.8 + 75589.8i 0.0805651 + 0.139543i
\(737\) 215653. + 373522.i 0.397028 + 0.687673i
\(738\) −1.40984e6 + 377767.i −2.58856 + 0.693603i
\(739\) 249552.i 0.456953i 0.973549 + 0.228477i \(0.0733744\pi\)
−0.973549 + 0.228477i \(0.926626\pi\)
\(740\) −231499. 48002.9i −0.422753 0.0876606i
\(741\) 1.92627e6 3.50818
\(742\) 14432.9 + 53864.1i 0.0262147 + 0.0978345i
\(743\) 436633. 252090.i 0.790931 0.456644i −0.0493593 0.998781i \(-0.515718\pi\)
0.840290 + 0.542137i \(0.182385\pi\)
\(744\) 414340. 239219.i 0.748533 0.432165i
\(745\) 14615.1 54544.4i 0.0263324 0.0982737i
\(746\) −512237. 512237.i −0.920436 0.920436i
\(747\) 683747. + 1.18429e6i 1.22533 + 2.12234i
\(748\) 34218.2 + 34218.2i 0.0611581 + 0.0611581i
\(749\) 98091.7 169900.i 0.174851 0.302851i
\(750\) 759913. 1.35096
\(751\) 125536.i 0.222581i 0.993788 + 0.111291i \(0.0354984\pi\)
−0.993788 + 0.111291i \(0.964502\pi\)
\(752\) −1355.06 + 2347.03i −0.00239620 + 0.00415034i
\(753\) −37035.5 + 138219.i −0.0653174 + 0.243768i
\(754\) 218258. 218258.i 0.383908 0.383908i
\(755\) 10203.3 + 38079.1i 0.0178997 + 0.0668025i
\(756\) −123260. + 213492.i −0.215664 + 0.373541i
\(757\) −192951. + 51701.2i −0.336710 + 0.0902212i −0.423213 0.906030i \(-0.639098\pi\)
0.0865024 + 0.996252i \(0.472431\pi\)
\(758\) 159154. + 42645.1i 0.276999 + 0.0742216i
\(759\) −168323. + 628191.i −0.292187 + 1.09046i
\(760\) −60054.7 224127.i −0.103973 0.388032i
\(761\) −119653. 69081.7i −0.206612 0.119287i 0.393124 0.919485i \(-0.371394\pi\)
−0.599736 + 0.800198i \(0.704728\pi\)
\(762\) −131372. + 35201.0i −0.226252 + 0.0606240i
\(763\) 195396. + 195396.i 0.335635 + 0.335635i
\(764\) 492724. + 132025.i 0.844144 + 0.226188i
\(765\) 227618. + 131416.i 0.388942 + 0.224556i
\(766\) 429051. 0.731226
\(767\) 865406.i 1.47106i
\(768\) −56312.0 32511.8i −0.0954726 0.0551211i
\(769\) −334643. + 334643.i −0.565886 + 0.565886i −0.930973 0.365087i \(-0.881039\pi\)
0.365087 + 0.930973i \(0.381039\pi\)
\(770\) −96884.3 + 55936.2i −0.163407 + 0.0943433i
\(771\) 373335. 373335.i 0.628044 0.628044i
\(772\) 331844. + 88917.5i 0.556801 + 0.149194i
\(773\) 340586. + 589912.i 0.569990 + 0.987252i 0.996566 + 0.0828003i \(0.0263863\pi\)
−0.426576 + 0.904452i \(0.640280\pi\)
\(774\) −610149. 1.05681e6i −1.01848 1.76407i
\(775\) −204547. + 54808.1i −0.340556 + 0.0912517i
\(776\) 214052.i 0.355464i
\(777\) −391781. + 257208.i −0.648935 + 0.426033i
\(778\) 331033. 0.546906
\(779\) −370997. 1.38458e6i −0.611358 2.28162i
\(780\) 606482. 350153.i 0.996848 0.575530i
\(781\) −469759. + 271215.i −0.770145 + 0.444644i
\(782\) 25130.5 93788.3i 0.0410949 0.153368i
\(783\) −431665. 431665.i −0.704081 0.704081i
\(784\) −61950.4 107301.i −0.100789 0.174571i
\(785\) −636743. 636743.i −1.03330 1.03330i
\(786\) −92739.1 + 160629.i −0.150113 + 0.260003i
\(787\) −401631. −0.648452 −0.324226 0.945980i \(-0.605104\pi\)
−0.324226 + 0.945980i \(0.605104\pi\)
\(788\) 432891.i 0.697151i
\(789\) 19148.9 33166.8i 0.0307602 0.0532782i
\(790\) −79855.2 + 298024.i −0.127953 + 0.477525i
\(791\) 282180. 282180.i 0.450997 0.450997i
\(792\) −85091.8 317567.i −0.135655 0.506273i
\(793\) 345647. 598678.i 0.549650 0.952022i
\(794\) −117616. + 31515.2i −0.186564 + 0.0499896i
\(795\) −302631. 81089.7i −0.478828 0.128301i
\(796\) −127556. + 476045.i −0.201314 + 0.751314i
\(797\) 230523. + 860324.i 0.362909 + 1.35440i 0.870233 + 0.492640i \(0.163968\pi\)
−0.507324 + 0.861756i \(0.669365\pi\)
\(798\) −398340. 229982.i −0.625530 0.361150i
\(799\) 2912.09 780.291i 0.00456153 0.00122226i
\(800\) 20350.6 + 20350.6i 0.0317979 + 0.0317979i
\(801\) −843599. 226042.i −1.31483 0.352309i
\(802\) 73346.3 + 42346.5i 0.114033 + 0.0658368i
\(803\) 511544. 0.793327
\(804\) 644699.i 0.997343i
\(805\) 194395. + 112234.i 0.299981 + 0.173194i
\(806\) −680455. + 680455.i −1.04744 + 1.04744i
\(807\) −806096. + 465400.i −1.23777 + 0.714626i
\(808\) 279761. 279761.i 0.428513 0.428513i
\(809\) 161720. + 43332.6i 0.247096 + 0.0662092i 0.380241 0.924887i \(-0.375841\pi\)
−0.133145 + 0.991097i \(0.542508\pi\)
\(810\) −269636. 467024.i −0.410968 0.711818i
\(811\) −5559.95 9630.12i −0.00845336 0.0146416i 0.861768 0.507303i \(-0.169357\pi\)
−0.870221 + 0.492661i \(0.836024\pi\)
\(812\) −71192.5 + 19076.0i −0.107975 + 0.0289317i
\(813\) 1.30451e6i 1.97363i
\(814\) 66796.6 322134.i 0.100811 0.486170i
\(815\) −600687. −0.904343
\(816\) 18721.4 + 69869.3i 0.0281163 + 0.104932i
\(817\) 1.03787e6 599215.i 1.55489 0.897715i
\(818\) −433324. + 250180.i −0.647599 + 0.373892i
\(819\) 243816. 909932.i 0.363491 1.35657i
\(820\) −368493. 368493.i −0.548026 0.548026i
\(821\) −492837. 853618.i −0.731167 1.26642i −0.956385 0.292110i \(-0.905643\pi\)
0.225218 0.974308i \(-0.427691\pi\)
\(822\) −636261. 636261.i −0.941655 0.941655i
\(823\) 265830. 460431.i 0.392468 0.679775i −0.600306 0.799770i \(-0.704955\pi\)
0.992774 + 0.119995i \(0.0382879\pi\)
\(824\) −235211. −0.346420
\(825\) 214441.i 0.315065i
\(826\) 103323. 178960.i 0.151438 0.262299i
\(827\) −68128.9 + 254261.i −0.0996140 + 0.371765i −0.997679 0.0680991i \(-0.978307\pi\)
0.898065 + 0.439864i \(0.144973\pi\)
\(828\) −466455. + 466455.i −0.680375 + 0.680375i
\(829\) 1081.36 + 4035.70i 0.00157348 + 0.00587232i 0.966708 0.255882i \(-0.0823658\pi\)
−0.965135 + 0.261754i \(0.915699\pi\)
\(830\) −244125. + 422837.i −0.354369 + 0.613785i
\(831\) −651570. + 174588.i −0.943537 + 0.252820i
\(832\) 126329. + 33849.7i 0.182497 + 0.0489000i
\(833\) −35673.2 + 133134.i −0.0514106 + 0.191867i
\(834\) 430527. + 1.60675e6i 0.618968 + 2.31002i
\(835\) −564348. 325827.i −0.809421 0.467319i
\(836\) 311876. 83566.9i 0.446241 0.119570i
\(837\) 1.34579e6 + 1.34579e6i 1.92099 + 1.92099i
\(838\) −360705. 96650.7i −0.513647 0.137631i
\(839\) −56804.5 32796.1i −0.0806973 0.0465906i 0.459108 0.888380i \(-0.348169\pi\)
−0.539806 + 0.841790i \(0.681502\pi\)
\(840\) −167222. −0.236993
\(841\) 524765.i 0.741947i
\(842\) 646535. + 373277.i 0.911943 + 0.526511i
\(843\) −1.45333e6 + 1.45333e6i −2.04507 + 2.04507i
\(844\) −154035. + 88932.2i −0.216239 + 0.124846i
\(845\) −560034. + 560034.i −0.784333 + 0.784333i
\(846\) −19784.4 5301.22i −0.0276429 0.00740688i
\(847\) 80030.9 + 138618.i 0.111555 + 0.193220i
\(848\) −29255.7 50672.4i −0.0406836 0.0704661i
\(849\) −565396. + 151497.i −0.784399 + 0.210179i
\(850\) 32015.9i 0.0443126i
\(851\) −626771. + 207107.i −0.865465 + 0.285980i
\(852\) −810802. −1.11695
\(853\) 186231. + 695023.i 0.255949 + 0.955215i 0.967560 + 0.252641i \(0.0812992\pi\)
−0.711611 + 0.702574i \(0.752034\pi\)
\(854\) −142955. + 82535.1i −0.196012 + 0.113168i
\(855\) 1.51870e6 876824.i 2.07750 1.19945i
\(856\) −53277.5 + 198834.i −0.0727104 + 0.271359i
\(857\) 695178. + 695178.i 0.946529 + 0.946529i 0.998641 0.0521119i \(-0.0165952\pi\)
−0.0521119 + 0.998641i \(0.516595\pi\)
\(858\) 487242. + 843927.i 0.661866 + 1.14639i
\(859\) −57024.4 57024.4i −0.0772813 0.0772813i 0.667410 0.744691i \(-0.267403\pi\)
−0.744691 + 0.667410i \(0.767403\pi\)
\(860\) 217847. 377323.i 0.294548 0.510171i
\(861\) −1.03304e6 −1.39351
\(862\) 325880.i 0.438574i
\(863\) 334819. 579923.i 0.449561 0.778662i −0.548797 0.835956i \(-0.684914\pi\)
0.998357 + 0.0572941i \(0.0182473\pi\)
\(864\) 66947.2 249850.i 0.0896819 0.334697i
\(865\) 344084. 344084.i 0.459867 0.459867i
\(866\) −131228. 489750.i −0.174981 0.653038i
\(867\) −622710. + 1.07857e6i −0.828414 + 1.43486i
\(868\) 221954. 59472.5i 0.294594 0.0789363i
\(869\) −414703. 111119.i −0.549159 0.147147i
\(870\) 107177. 399989.i 0.141599 0.528456i
\(871\) −335615. 1.25253e6i −0.442390 1.65102i
\(872\) −251100. 144973.i −0.330228 0.190657i
\(873\) −1.56262e6 + 418704.i −2.05034 + 0.549387i
\(874\) −458095. 458095.i −0.599699 0.599699i
\(875\) 352535. + 94461.3i 0.460453 + 0.123378i
\(876\) 662193. + 382317.i 0.862932 + 0.498214i
\(877\) 339432. 0.441320 0.220660 0.975351i \(-0.429179\pi\)
0.220660 + 0.975351i \(0.429179\pi\)
\(878\) 368837.i 0.478460i
\(879\) −139215. 80375.8i −0.180181 0.104027i
\(880\) 83002.8 83002.8i 0.107183 0.107183i
\(881\) −385361. + 222488.i −0.496496 + 0.286652i −0.727265 0.686357i \(-0.759209\pi\)
0.230770 + 0.973008i \(0.425876\pi\)
\(882\) 662141. 662141.i 0.851165 0.851165i
\(883\) −414151. 110971.i −0.531174 0.142328i −0.0167437 0.999860i \(-0.505330\pi\)
−0.514430 + 0.857532i \(0.671997\pi\)
\(884\) −72744.6 125997.i −0.0930886 0.161234i
\(885\) 580510. + 1.00547e6i 0.741179 + 1.28376i
\(886\) 497115. 133202.i 0.633271 0.169685i
\(887\) 329892.i 0.419300i 0.977776 + 0.209650i \(0.0672325\pi\)
−0.977776 + 0.209650i \(0.932768\pi\)
\(888\) 327224. 367080.i 0.414973 0.465516i
\(889\) −65321.0 −0.0826512
\(890\) −80705.8 301198.i −0.101888 0.380253i
\(891\) 649869. 375202.i 0.818598 0.472618i
\(892\) 492415. 284296.i 0.618873 0.357307i
\(893\) 5206.22 19429.9i 0.00652859 0.0243650i
\(894\) 83051.8 + 83051.8i 0.103914 + 0.103914i
\(895\) 324439. + 561945.i 0.405030 + 0.701533i
\(896\) −22082.6 22082.6i −0.0275064 0.0275064i
\(897\) 977636. 1.69332e6i 1.21505 2.10452i
\(898\) −267758. −0.332040
\(899\) 569024.i 0.704063i
\(900\) −108756. + 188371.i −0.134267 + 0.232557i
\(901\) −16846.5 + 62872.0i −0.0207520 + 0.0774475i
\(902\) 512762. 512762.i 0.630235 0.630235i
\(903\) −223538. 834255.i −0.274142 1.02311i
\(904\) −209362. + 362625.i −0.256189 + 0.443732i
\(905\) −74572.1 + 19981.5i −0.0910498 + 0.0243967i
\(906\) −79203.5 21222.5i −0.0964912 0.0258548i
\(907\) −88886.5 + 331729.i −0.108049 + 0.403245i −0.998673 0.0514954i \(-0.983601\pi\)
0.890624 + 0.454740i \(0.150268\pi\)
\(908\) 91719.0 + 342300.i 0.111247 + 0.415179i
\(909\) 2.58955e6 + 1.49508e6i 3.13398 + 1.80940i
\(910\) 324882. 87051.8i 0.392322 0.105122i
\(911\) 350788. + 350788.i 0.422676 + 0.422676i 0.886124 0.463448i \(-0.153388\pi\)
−0.463448 + 0.886124i \(0.653388\pi\)
\(912\) 466179. + 124912.i 0.560484 + 0.150181i
\(913\) −588382. 339703.i −0.705859 0.407528i
\(914\) −864157. −1.03443
\(915\) 927432.i 1.10775i
\(916\) −17711.9 10226.0i −0.0211094 0.0121875i
\(917\) −62990.1 + 62990.1i −0.0749089 + 0.0749089i
\(918\) −249195. + 143873.i −0.295701 + 0.170723i
\(919\) −486669. + 486669.i −0.576239 + 0.576239i −0.933865 0.357626i \(-0.883586\pi\)
0.357626 + 0.933865i \(0.383586\pi\)
\(920\) −227502. 60958.9i −0.268787 0.0720213i
\(921\) 424165. + 734676.i 0.500053 + 0.866117i
\(922\) −146028. 252929.i −0.171781 0.297534i
\(923\) 1.57524e6 422084.i 1.84903 0.495446i
\(924\) 232691.i 0.272544i
\(925\) −181949. + 119452.i −0.212651 + 0.139608i
\(926\) 424241. 0.494755
\(927\) −460093. 1.71709e6i −0.535409 1.99817i
\(928\) 66974.0 38667.4i 0.0777696 0.0449003i
\(929\) 1.46827e6 847708.i 1.70128 0.982234i 0.756808 0.653637i \(-0.226758\pi\)
0.944470 0.328597i \(-0.106576\pi\)
\(930\) −334141. + 1.24703e6i −0.386335 + 1.44182i
\(931\) 650275. + 650275.i 0.750236 + 0.750236i
\(932\) −244505. 423496.i −0.281486 0.487548i
\(933\) 1.30767e6 + 1.30767e6i 1.50223 + 1.50223i
\(934\) −234076. + 405431.i −0.268326 + 0.464754i
\(935\) −130581. −0.149368
\(936\) 988440.i 1.12823i
\(937\) −53304.5 + 92326.2i −0.0607135 + 0.105159i −0.894785 0.446498i \(-0.852671\pi\)
0.834071 + 0.551657i \(0.186004\pi\)
\(938\) −80139.6 + 299085.i −0.0910839 + 0.339930i
\(939\) 2.15604e6 2.15604e6i 2.44526 2.44526i
\(940\) −1892.75 7063.83i −0.00214208 0.00799437i
\(941\) 429045. 743127.i 0.484533 0.839235i −0.515309 0.857004i \(-0.672323\pi\)
0.999842 + 0.0177689i \(0.00565633\pi\)
\(942\) 1.80917e6 484767.i 2.03882 0.546300i
\(943\) −1.40542e6 376582.i −1.58046 0.423483i
\(944\) −56118.7 + 209438.i −0.0629743 + 0.235023i
\(945\) −172169. 642543.i −0.192793 0.719513i
\(946\) 525049. + 303137.i 0.586702 + 0.338733i
\(947\) −1.37739e6 + 369072.i −1.53588 + 0.411539i −0.924933 0.380130i \(-0.875879\pi\)
−0.610950 + 0.791669i \(0.709212\pi\)
\(948\) −453784. 453784.i −0.504932 0.504932i
\(949\) −1.48555e6 398051.i −1.64951 0.441984i
\(950\) −184996. 106807.i −0.204981 0.118346i
\(951\) 264832. 0.292826
\(952\) 34740.6i 0.0383321i
\(953\) 699088. + 403619.i 0.769744 + 0.444412i 0.832783 0.553599i \(-0.186746\pi\)
−0.0630396 + 0.998011i \(0.520079\pi\)
\(954\) 312693. 312693.i 0.343574 0.343574i
\(955\) −1.19206e6 + 688236.i −1.30705 + 0.754624i
\(956\) 273578. 273578.i 0.299340 0.299340i
\(957\) 556589. + 149138.i 0.607730 + 0.162841i
\(958\) −270865. 469153.i −0.295136 0.511191i
\(959\) −216080. 374262.i −0.234951 0.406947i
\(960\) 169481. 45412.4i 0.183899 0.0492756i
\(961\) 850508.i 0.920941i
\(962\) −444644. + 883514.i −0.480466 + 0.954692i
\(963\) −1.55575e6 −1.67759
\(964\) 19506.0 + 72797.5i 0.0209901 + 0.0783362i
\(965\) −802841. + 463520.i −0.862134 + 0.497753i
\(966\) −404337. + 233444.i −0.433301 + 0.250166i
\(967\) −332629. + 1.24139e6i −0.355719 + 1.32756i 0.523858 + 0.851806i \(0.324492\pi\)
−0.879577 + 0.475756i \(0.842174\pi\)
\(968\) −118757. 118757.i −0.126738 0.126738i
\(969\) −268442. 464956.i −0.285893 0.495181i
\(970\) −408425. 408425.i −0.434079 0.434079i
\(971\) 450019. 779456.i 0.477301 0.826710i −0.522361 0.852725i \(-0.674948\pi\)
0.999662 + 0.0260152i \(0.00828181\pi\)
\(972\) 195726. 0.207165
\(973\) 798910.i 0.843864i
\(974\) −344445. + 596596.i −0.363079 + 0.628872i
\(975\) 166864. 622746.i 0.175531 0.655092i
\(976\) 122473. 122473.i 0.128570 0.128570i
\(977\) 240414. + 897238.i 0.251867 + 0.939980i 0.969807 + 0.243875i \(0.0784186\pi\)
−0.717940 + 0.696105i \(0.754915\pi\)
\(978\) 624707. 1.08202e6i 0.653128 1.13125i
\(979\) 419121. 112303.i 0.437294 0.117173i
\(980\) 322943. + 86532.3i 0.336259 + 0.0901003i
\(981\) 567158. 2.11666e6i 0.589340 2.19945i
\(982\) 289983. + 1.08223e6i 0.300711 + 1.12227i
\(983\) −564812. 326094.i −0.584517 0.337471i 0.178410 0.983956i \(-0.442905\pi\)
−0.762926 + 0.646485i \(0.776238\pi\)
\(984\) 1.04700e6 280542.i 1.08132 0.289739i
\(985\) 825985. + 825985.i 0.851333 + 0.851333i
\(986\) −83098.1 22266.1i −0.0854747 0.0229029i
\(987\) −12554.5 7248.34i −0.0128874 0.00744054i
\(988\) −970727. −0.994451
\(989\) 1.21647e6i 1.24368i
\(990\) 768299. + 443577.i 0.783898 + 0.452584i
\(991\) −93432.8 + 93432.8i −0.0951376 + 0.0951376i −0.753074 0.657936i \(-0.771430\pi\)
0.657936 + 0.753074i \(0.271430\pi\)
\(992\) −208803. + 120552.i −0.212184 + 0.122504i
\(993\) −2.18318e6 + 2.18318e6i −2.21407 + 2.21407i
\(994\) −376143. 100787.i −0.380697 0.102008i
\(995\) −664939. 1.15171e6i −0.671639 1.16331i
\(996\) −507773. 879489.i −0.511860 0.886567i
\(997\) 1.42946e6 383023.i 1.43808 0.385331i 0.546217 0.837644i \(-0.316067\pi\)
0.891860 + 0.452312i \(0.149401\pi\)
\(998\) 495923.i 0.497912i
\(999\) 1.74739e6 + 879407.i 1.75089 + 0.881168i
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 74.5.g.a.23.7 28
37.29 odd 12 inner 74.5.g.a.29.7 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.5.g.a.23.7 28 1.1 even 1 trivial
74.5.g.a.29.7 yes 28 37.29 odd 12 inner