Properties

Label 42.5.g.a.31.1
Level $42$
Weight $5$
Character 42.31
Analytic conductor $4.342$
Analytic rank $0$
Dimension $4$
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] = [42,5,Mod(19,42)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("42.19");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 42.g (of order \(6\), degree \(2\), 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: \(4.34153844952\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 42.31
Dual form 42.5.g.a.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41421 - 2.44949i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-12.2574 + 7.07679i) q^{5} +14.6969i q^{6} +(12.1985 + 47.4573i) q^{7} +22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +O(q^{10})\) \(q+(-1.41421 - 2.44949i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-12.2574 + 7.07679i) q^{5} +14.6969i q^{6} +(12.1985 + 47.4573i) q^{7} +22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +(34.6690 + 20.0162i) q^{10} +(-32.0147 + 55.4511i) q^{11} +(36.0000 - 20.7846i) q^{12} +228.919i q^{13} +(98.9949 - 96.9948i) q^{14} +73.5442 q^{15} +(-32.0000 - 55.4256i) q^{16} +(-195.250 - 112.728i) q^{17} +(38.1838 - 66.1362i) q^{18} +(-255.250 + 147.369i) q^{19} -113.229i q^{20} +(68.4045 - 245.251i) q^{21} +181.103 q^{22} +(-354.749 - 614.444i) q^{23} +(-101.823 - 58.7878i) q^{24} +(-212.338 + 367.780i) q^{25} +(560.735 - 323.741i) q^{26} -140.296i q^{27} +(-377.588 - 105.316i) q^{28} +740.397 q^{29} +(-104.007 - 180.146i) q^{30} +(-577.390 - 333.356i) q^{31} +(-90.5097 + 156.767i) q^{32} +(288.132 - 166.353i) q^{33} +637.683i q^{34} +(-485.367 - 495.375i) q^{35} -216.000 q^{36} +(416.882 + 722.061i) q^{37} +(721.955 + 416.821i) q^{38} +(594.749 - 1030.14i) q^{39} +(-277.352 + 160.129i) q^{40} +2817.60i q^{41} +(-697.477 + 179.280i) q^{42} +3066.41 q^{43} +(-256.118 - 443.609i) q^{44} +(-330.949 - 191.073i) q^{45} +(-1003.38 + 1737.91i) q^{46} +(-531.502 + 306.863i) q^{47} +332.554i q^{48} +(-2103.39 + 1157.81i) q^{49} +1201.17 q^{50} +(585.749 + 1014.55i) q^{51} +(-1586.00 - 915.677i) q^{52} +(576.300 - 998.181i) q^{53} +(-343.654 + 198.409i) q^{54} -906.246i q^{55} +(276.020 + 1073.84i) q^{56} +1531.50 q^{57} +(-1047.08 - 1813.59i) q^{58} +(-3024.67 - 1746.30i) q^{59} +(-294.177 + 509.529i) q^{60} +(1967.79 - 1136.11i) q^{61} +1885.75i q^{62} +(-945.000 + 925.907i) q^{63} +512.000 q^{64} +(-1620.01 - 2805.94i) q^{65} +(-814.962 - 470.518i) q^{66} +(4337.31 - 7512.44i) q^{67} +(1562.00 - 901.820i) q^{68} +3686.66i q^{69} +(-527.005 + 1889.47i) q^{70} -353.591 q^{71} +(305.470 + 529.090i) q^{72} +(3524.68 + 2034.97i) q^{73} +(1179.12 - 2042.30i) q^{74} +(1911.04 - 1103.34i) q^{75} -2357.90i q^{76} +(-3022.09 - 842.913i) q^{77} -3364.41 q^{78} +(-3236.41 - 5605.63i) q^{79} +(784.471 + 452.915i) q^{80} +(-364.500 + 631.333i) q^{81} +(6901.69 - 3984.69i) q^{82} +8225.83i q^{83} +(1425.53 + 1454.92i) q^{84} +3191.00 q^{85} +(-4336.55 - 7511.13i) q^{86} +(-3331.79 - 1923.61i) q^{87} +(-724.410 + 1254.72i) q^{88} +(-13456.5 + 7769.13i) q^{89} +1080.87i q^{90} +(-10863.9 + 2792.47i) q^{91} +5675.99 q^{92} +(1732.17 + 3000.21i) q^{93} +(1503.32 + 867.939i) q^{94} +(2085.79 - 3612.70i) q^{95} +(814.587 - 470.302i) q^{96} -1558.61i q^{97} +(5810.70 + 3514.84i) q^{98} -1728.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{3} - 16 q^{4} - 66 q^{5} - 70 q^{7} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{3} - 16 q^{4} - 66 q^{5} - 70 q^{7} + 54 q^{9} - 48 q^{10} - 162 q^{11} + 144 q^{12} + 396 q^{15} - 128 q^{16} - 204 q^{17} - 444 q^{19} + 630 q^{21} - 192 q^{22} + 312 q^{23} - 476 q^{25} + 1632 q^{26} - 560 q^{28} + 2724 q^{29} + 144 q^{30} - 3786 q^{31} + 1458 q^{33} + 672 q^{35} - 864 q^{36} + 1396 q^{37} + 1632 q^{38} + 648 q^{39} + 384 q^{40} - 1008 q^{42} - 632 q^{43} - 1296 q^{44} - 1782 q^{45} - 4896 q^{46} - 7896 q^{47} - 98 q^{49} + 2112 q^{50} + 612 q^{51} - 1728 q^{52} - 1038 q^{53} + 2688 q^{56} + 2664 q^{57} - 336 q^{58} - 966 q^{59} - 1584 q^{60} + 5088 q^{61} - 3780 q^{63} + 2048 q^{64} - 744 q^{65} + 864 q^{66} + 14600 q^{67} + 1632 q^{68} + 5376 q^{70} - 9696 q^{71} + 22584 q^{73} + 768 q^{74} + 4284 q^{75} - 3654 q^{77} - 9792 q^{78} + 3974 q^{79} + 4224 q^{80} - 1458 q^{81} + 18816 q^{82} + 1224 q^{85} - 18240 q^{86} - 12258 q^{87} + 768 q^{88} - 33156 q^{89} - 18984 q^{91} - 4992 q^{92} + 11358 q^{93} - 16320 q^{94} + 3252 q^{95} + 23520 q^{98} - 8748 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 2.44949i −0.353553 0.612372i
\(3\) −4.50000 2.59808i −0.500000 0.288675i
\(4\) −4.00000 + 6.92820i −0.250000 + 0.433013i
\(5\) −12.2574 + 7.07679i −0.490294 + 0.283072i −0.724697 0.689068i \(-0.758020\pi\)
0.234402 + 0.972140i \(0.424687\pi\)
\(6\) 14.6969i 0.408248i
\(7\) 12.1985 + 47.4573i 0.248949 + 0.968517i
\(8\) 22.6274 0.353553
\(9\) 13.5000 + 23.3827i 0.166667 + 0.288675i
\(10\) 34.6690 + 20.0162i 0.346690 + 0.200162i
\(11\) −32.0147 + 55.4511i −0.264584 + 0.458274i −0.967455 0.253044i \(-0.918568\pi\)
0.702870 + 0.711318i \(0.251901\pi\)
\(12\) 36.0000 20.7846i 0.250000 0.144338i
\(13\) 228.919i 1.35455i 0.735729 + 0.677276i \(0.236839\pi\)
−0.735729 + 0.677276i \(0.763161\pi\)
\(14\) 98.9949 96.9948i 0.505076 0.494872i
\(15\) 73.5442 0.326863
\(16\) −32.0000 55.4256i −0.125000 0.216506i
\(17\) −195.250 112.728i −0.675605 0.390061i 0.122592 0.992457i \(-0.460879\pi\)
−0.798197 + 0.602397i \(0.794213\pi\)
\(18\) 38.1838 66.1362i 0.117851 0.204124i
\(19\) −255.250 + 147.369i −0.707063 + 0.408223i −0.809973 0.586468i \(-0.800518\pi\)
0.102910 + 0.994691i \(0.467185\pi\)
\(20\) 113.229i 0.283072i
\(21\) 68.4045 245.251i 0.155112 0.556124i
\(22\) 181.103 0.374179
\(23\) −354.749 614.444i −0.670604 1.16152i −0.977733 0.209852i \(-0.932702\pi\)
0.307129 0.951668i \(-0.400632\pi\)
\(24\) −101.823 58.7878i −0.176777 0.102062i
\(25\) −212.338 + 367.780i −0.339741 + 0.588449i
\(26\) 560.735 323.741i 0.829490 0.478906i
\(27\) 140.296i 0.192450i
\(28\) −377.588 105.316i −0.481617 0.134331i
\(29\) 740.397 0.880377 0.440188 0.897905i \(-0.354912\pi\)
0.440188 + 0.897905i \(0.354912\pi\)
\(30\) −104.007 180.146i −0.115563 0.200162i
\(31\) −577.390 333.356i −0.600822 0.346885i 0.168543 0.985694i \(-0.446094\pi\)
−0.769365 + 0.638809i \(0.779427\pi\)
\(32\) −90.5097 + 156.767i −0.0883883 + 0.153093i
\(33\) 288.132 166.353i 0.264584 0.152758i
\(34\) 637.683i 0.551629i
\(35\) −485.367 495.375i −0.396218 0.404388i
\(36\) −216.000 −0.166667
\(37\) 416.882 + 722.061i 0.304516 + 0.527437i 0.977153 0.212535i \(-0.0681720\pi\)
−0.672638 + 0.739972i \(0.734839\pi\)
\(38\) 721.955 + 416.821i 0.499969 + 0.288657i
\(39\) 594.749 1030.14i 0.391025 0.677276i
\(40\) −277.352 + 160.129i −0.173345 + 0.100081i
\(41\) 2817.60i 1.67615i 0.545558 + 0.838073i \(0.316318\pi\)
−0.545558 + 0.838073i \(0.683682\pi\)
\(42\) −697.477 + 179.280i −0.395395 + 0.101633i
\(43\) 3066.41 1.65841 0.829207 0.558942i \(-0.188793\pi\)
0.829207 + 0.558942i \(0.188793\pi\)
\(44\) −256.118 443.609i −0.132292 0.229137i
\(45\) −330.949 191.073i −0.163431 0.0943572i
\(46\) −1003.38 + 1737.91i −0.474188 + 0.821318i
\(47\) −531.502 + 306.863i −0.240608 + 0.138915i −0.615456 0.788171i \(-0.711028\pi\)
0.374848 + 0.927086i \(0.377695\pi\)
\(48\) 332.554i 0.144338i
\(49\) −2103.39 + 1157.81i −0.876049 + 0.482222i
\(50\) 1201.17 0.480466
\(51\) 585.749 + 1014.55i 0.225202 + 0.390061i
\(52\) −1586.00 915.677i −0.586538 0.338638i
\(53\) 576.300 998.181i 0.205162 0.355351i −0.745022 0.667040i \(-0.767561\pi\)
0.950184 + 0.311688i \(0.100895\pi\)
\(54\) −343.654 + 198.409i −0.117851 + 0.0680414i
\(55\) 906.246i 0.299585i
\(56\) 276.020 + 1073.84i 0.0880166 + 0.342422i
\(57\) 1531.50 0.471375
\(58\) −1047.08 1813.59i −0.311260 0.539119i
\(59\) −3024.67 1746.30i −0.868909 0.501665i −0.00192348 0.999998i \(-0.500612\pi\)
−0.866986 + 0.498333i \(0.833946\pi\)
\(60\) −294.177 + 509.529i −0.0817157 + 0.141536i
\(61\) 1967.79 1136.11i 0.528834 0.305323i −0.211707 0.977333i \(-0.567902\pi\)
0.740542 + 0.672010i \(0.234569\pi\)
\(62\) 1885.75i 0.490569i
\(63\) −945.000 + 925.907i −0.238095 + 0.233285i
\(64\) 512.000 0.125000
\(65\) −1620.01 2805.94i −0.383435 0.664129i
\(66\) −814.962 470.518i −0.187089 0.108016i
\(67\) 4337.31 7512.44i 0.966208 1.67352i 0.259874 0.965642i \(-0.416319\pi\)
0.706334 0.707879i \(-0.250348\pi\)
\(68\) 1562.00 901.820i 0.337802 0.195030i
\(69\) 3686.66i 0.774346i
\(70\) −527.005 + 1889.47i −0.107552 + 0.385606i
\(71\) −353.591 −0.0701431 −0.0350715 0.999385i \(-0.511166\pi\)
−0.0350715 + 0.999385i \(0.511166\pi\)
\(72\) 305.470 + 529.090i 0.0589256 + 0.102062i
\(73\) 3524.68 + 2034.97i 0.661415 + 0.381868i 0.792816 0.609461i \(-0.208614\pi\)
−0.131401 + 0.991329i \(0.541948\pi\)
\(74\) 1179.12 2042.30i 0.215325 0.372954i
\(75\) 1911.04 1103.34i 0.339741 0.196150i
\(76\) 2357.90i 0.408223i
\(77\) −3022.09 842.913i −0.509714 0.142168i
\(78\) −3364.41 −0.552993
\(79\) −3236.41 5605.63i −0.518573 0.898194i −0.999767 0.0215805i \(-0.993130\pi\)
0.481194 0.876614i \(-0.340203\pi\)
\(80\) 784.471 + 452.915i 0.122574 + 0.0707679i
\(81\) −364.500 + 631.333i −0.0555556 + 0.0962250i
\(82\) 6901.69 3984.69i 1.02643 0.592607i
\(83\) 8225.83i 1.19405i 0.802222 + 0.597026i \(0.203651\pi\)
−0.802222 + 0.597026i \(0.796349\pi\)
\(84\) 1425.53 + 1454.92i 0.202031 + 0.206197i
\(85\) 3191.00 0.441660
\(86\) −4336.55 7511.13i −0.586338 1.01557i
\(87\) −3331.79 1923.61i −0.440188 0.254143i
\(88\) −724.410 + 1254.72i −0.0935447 + 0.162024i
\(89\) −13456.5 + 7769.13i −1.69884 + 0.980828i −0.751983 + 0.659183i \(0.770902\pi\)
−0.946860 + 0.321645i \(0.895764\pi\)
\(90\) 1080.87i 0.133441i
\(91\) −10863.9 + 2792.47i −1.31191 + 0.337214i
\(92\) 5675.99 0.670604
\(93\) 1732.17 + 3000.21i 0.200274 + 0.346885i
\(94\) 1503.32 + 867.939i 0.170135 + 0.0982276i
\(95\) 2085.79 3612.70i 0.231113 0.400299i
\(96\) 814.587 470.302i 0.0883883 0.0510310i
\(97\) 1558.61i 0.165651i −0.996564 0.0828254i \(-0.973606\pi\)
0.996564 0.0828254i \(-0.0263944\pi\)
\(98\) 5810.70 + 3514.84i 0.605030 + 0.365977i
\(99\) −1728.79 −0.176390
\(100\) −1698.70 2942.24i −0.169870 0.294224i
\(101\) 13627.2 + 7867.66i 1.33587 + 0.771264i 0.986192 0.165607i \(-0.0529583\pi\)
0.349676 + 0.936871i \(0.386292\pi\)
\(102\) 1656.75 2869.57i 0.159242 0.275814i
\(103\) 29.2099 16.8644i 0.00275332 0.00158963i −0.498623 0.866819i \(-0.666161\pi\)
0.501376 + 0.865229i \(0.332827\pi\)
\(104\) 5179.85i 0.478906i
\(105\) 897.127 + 3490.21i 0.0813721 + 0.316572i
\(106\) −3260.05 −0.290143
\(107\) 2723.23 + 4716.78i 0.237858 + 0.411981i 0.960099 0.279659i \(-0.0902215\pi\)
−0.722242 + 0.691641i \(0.756888\pi\)
\(108\) 972.000 + 561.184i 0.0833333 + 0.0481125i
\(109\) −8348.89 + 14460.7i −0.702709 + 1.21713i 0.264803 + 0.964303i \(0.414693\pi\)
−0.967512 + 0.252825i \(0.918640\pi\)
\(110\) −2219.84 + 1281.62i −0.183458 + 0.105919i
\(111\) 4332.37i 0.351625i
\(112\) 2240.00 2194.74i 0.178571 0.174964i
\(113\) 9455.64 0.740515 0.370258 0.928929i \(-0.379269\pi\)
0.370258 + 0.928929i \(0.379269\pi\)
\(114\) −2165.87 3751.39i −0.166656 0.288657i
\(115\) 8696.58 + 5020.97i 0.657586 + 0.379658i
\(116\) −2961.59 + 5129.62i −0.220094 + 0.381214i
\(117\) −5352.74 + 3090.41i −0.391025 + 0.225759i
\(118\) 9878.54i 0.709461i
\(119\) 2967.99 10641.1i 0.209589 0.751440i
\(120\) 1664.11 0.115563
\(121\) 5270.62 + 9128.97i 0.359990 + 0.623521i
\(122\) −5565.76 3213.39i −0.373942 0.215896i
\(123\) 7320.35 12679.2i 0.483862 0.838073i
\(124\) 4619.12 2666.85i 0.300411 0.173442i
\(125\) 14856.7i 0.950827i
\(126\) 3604.43 + 1005.34i 0.227037 + 0.0633244i
\(127\) −2380.07 −0.147564 −0.0737822 0.997274i \(-0.523507\pi\)
−0.0737822 + 0.997274i \(0.523507\pi\)
\(128\) −724.077 1254.14i −0.0441942 0.0765466i
\(129\) −13798.8 7966.76i −0.829207 0.478743i
\(130\) −4582.09 + 7936.41i −0.271129 + 0.469610i
\(131\) −3758.37 + 2169.90i −0.219006 + 0.126443i −0.605490 0.795853i \(-0.707023\pi\)
0.386484 + 0.922296i \(0.373690\pi\)
\(132\) 2661.65i 0.152758i
\(133\) −10107.4 10315.8i −0.571393 0.583176i
\(134\) −24535.5 −1.36642
\(135\) 992.846 + 1719.66i 0.0544772 + 0.0943572i
\(136\) −4418.00 2550.73i −0.238862 0.137907i
\(137\) 15379.6 26638.2i 0.819414 1.41927i −0.0867001 0.996234i \(-0.527632\pi\)
0.906114 0.423033i \(-0.139034\pi\)
\(138\) 9030.44 5213.73i 0.474188 0.273773i
\(139\) 27186.6i 1.40710i −0.710644 0.703551i \(-0.751596\pi\)
0.710644 0.703551i \(-0.248404\pi\)
\(140\) 5373.53 1381.22i 0.274160 0.0704703i
\(141\) 3189.01 0.160405
\(142\) 500.054 + 866.118i 0.0247993 + 0.0429537i
\(143\) −12693.8 7328.78i −0.620755 0.358393i
\(144\) 864.000 1496.49i 0.0416667 0.0721688i
\(145\) −9075.31 + 5239.63i −0.431644 + 0.249210i
\(146\) 11511.6i 0.540043i
\(147\) 12473.4 + 254.611i 0.577230 + 0.0117827i
\(148\) −6670.12 −0.304516
\(149\) 2913.46 + 5046.26i 0.131231 + 0.227299i 0.924151 0.382027i \(-0.124774\pi\)
−0.792920 + 0.609325i \(0.791440\pi\)
\(150\) −5405.25 3120.72i −0.240233 0.138699i
\(151\) −12593.4 + 21812.4i −0.552317 + 0.956642i 0.445789 + 0.895138i \(0.352923\pi\)
−0.998107 + 0.0615039i \(0.980410\pi\)
\(152\) −5775.64 + 3334.57i −0.249985 + 0.144329i
\(153\) 6087.29i 0.260040i
\(154\) 2209.18 + 8594.64i 0.0931513 + 0.362399i
\(155\) 9436.37 0.392773
\(156\) 4757.99 + 8241.09i 0.195513 + 0.338638i
\(157\) 20694.6 + 11948.0i 0.839571 + 0.484726i 0.857118 0.515120i \(-0.172253\pi\)
−0.0175475 + 0.999846i \(0.505586\pi\)
\(158\) −9153.96 + 15855.1i −0.366686 + 0.635119i
\(159\) −5186.70 + 2994.54i −0.205162 + 0.118450i
\(160\) 2562.07i 0.100081i
\(161\) 24832.5 24330.7i 0.958005 0.938650i
\(162\) 2061.92 0.0785674
\(163\) 21293.0 + 36880.5i 0.801422 + 1.38810i 0.918680 + 0.395001i \(0.129256\pi\)
−0.117259 + 0.993101i \(0.537411\pi\)
\(164\) −19520.9 11270.4i −0.725793 0.419037i
\(165\) −2354.50 + 4078.11i −0.0864828 + 0.149793i
\(166\) 20149.1 11633.1i 0.731205 0.422161i
\(167\) 26356.3i 0.945043i 0.881319 + 0.472521i \(0.156656\pi\)
−0.881319 + 0.472521i \(0.843344\pi\)
\(168\) 1547.82 5549.39i 0.0548405 0.196619i
\(169\) −23843.0 −0.834809
\(170\) −4512.75 7816.31i −0.156150 0.270461i
\(171\) −6891.74 3978.95i −0.235688 0.136074i
\(172\) −12265.6 + 21244.7i −0.414603 + 0.718114i
\(173\) 24265.3 14009.6i 0.810763 0.468094i −0.0364578 0.999335i \(-0.511607\pi\)
0.847221 + 0.531241i \(0.178274\pi\)
\(174\) 10881.6i 0.359412i
\(175\) −20044.1 5590.63i −0.654500 0.182551i
\(176\) 4097.88 0.132292
\(177\) 9074.02 + 15716.7i 0.289636 + 0.501665i
\(178\) 38060.8 + 21974.4i 1.20126 + 0.693550i
\(179\) −12699.2 + 21995.7i −0.396343 + 0.686487i −0.993272 0.115808i \(-0.963054\pi\)
0.596928 + 0.802295i \(0.296388\pi\)
\(180\) 2647.59 1528.59i 0.0817157 0.0471786i
\(181\) 44097.2i 1.34603i −0.739630 0.673014i \(-0.764999\pi\)
0.739630 0.673014i \(-0.235001\pi\)
\(182\) 22204.0 + 22661.8i 0.670329 + 0.684152i
\(183\) −11806.8 −0.352556
\(184\) −8027.06 13903.3i −0.237094 0.410659i
\(185\) −10219.8 5900.38i −0.298605 0.172400i
\(186\) 4899.32 8485.87i 0.141615 0.245285i
\(187\) 12501.7 7217.88i 0.357509 0.206408i
\(188\) 4909.81i 0.138915i
\(189\) 6658.08 1711.40i 0.186391 0.0479102i
\(190\) −11799.0 −0.326843
\(191\) 32279.6 + 55909.8i 0.884832 + 1.53257i 0.845906 + 0.533332i \(0.179060\pi\)
0.0389256 + 0.999242i \(0.487606\pi\)
\(192\) −2304.00 1330.22i −0.0625000 0.0360844i
\(193\) −18337.3 + 31761.1i −0.492290 + 0.852670i −0.999961 0.00888055i \(-0.997173\pi\)
0.507671 + 0.861551i \(0.330507\pi\)
\(194\) −3817.80 + 2204.20i −0.101440 + 0.0585664i
\(195\) 16835.7i 0.442753i
\(196\) 392.000 19204.0i 0.0102041 0.499896i
\(197\) −73147.0 −1.88480 −0.942398 0.334494i \(-0.891434\pi\)
−0.942398 + 0.334494i \(0.891434\pi\)
\(198\) 2444.89 + 4234.67i 0.0623632 + 0.108016i
\(199\) −1213.33 700.514i −0.0306387 0.0176893i 0.484602 0.874735i \(-0.338964\pi\)
−0.515241 + 0.857045i \(0.672298\pi\)
\(200\) −4804.66 + 8321.92i −0.120117 + 0.208048i
\(201\) −39035.8 + 22537.3i −0.966208 + 0.557840i
\(202\) 44506.2i 1.09073i
\(203\) 9031.72 + 35137.3i 0.219169 + 0.852660i
\(204\) −9371.99 −0.225202
\(205\) −19939.6 34536.4i −0.474469 0.821805i
\(206\) −82.6182 47.6996i −0.00194689 0.00112404i
\(207\) 9578.23 16590.0i 0.223535 0.387173i
\(208\) 12688.0 7325.41i 0.293269 0.169319i
\(209\) 18871.8i 0.432038i
\(210\) 7280.50 7133.40i 0.165091 0.161755i
\(211\) 58231.7 1.30796 0.653980 0.756512i \(-0.273098\pi\)
0.653980 + 0.756512i \(0.273098\pi\)
\(212\) 4610.40 + 7985.45i 0.102581 + 0.177676i
\(213\) 1591.16 + 918.657i 0.0350715 + 0.0202486i
\(214\) 7702.46 13341.1i 0.168191 0.291315i
\(215\) −37586.1 + 21700.3i −0.813111 + 0.469450i
\(216\) 3174.54i 0.0680414i
\(217\) 8776.92 31467.8i 0.186390 0.668263i
\(218\) 47228.4 0.993781
\(219\) −10574.0 18314.8i −0.220472 0.381868i
\(220\) 6278.65 + 3624.98i 0.129724 + 0.0748963i
\(221\) 25805.5 44696.4i 0.528357 0.915141i
\(222\) −10612.1 + 6126.89i −0.215325 + 0.124318i
\(223\) 61050.9i 1.22767i −0.789434 0.613836i \(-0.789626\pi\)
0.789434 0.613836i \(-0.210374\pi\)
\(224\) −8543.84 2383.02i −0.170277 0.0474933i
\(225\) −11466.3 −0.226494
\(226\) −13372.3 23161.5i −0.261812 0.453471i
\(227\) 21645.2 + 12496.8i 0.420058 + 0.242520i 0.695102 0.718911i \(-0.255359\pi\)
−0.275044 + 0.961432i \(0.588693\pi\)
\(228\) −6125.99 + 10610.5i −0.117844 + 0.204112i
\(229\) −16392.9 + 9464.44i −0.312597 + 0.180478i −0.648088 0.761565i \(-0.724431\pi\)
0.335491 + 0.942043i \(0.391098\pi\)
\(230\) 28402.9i 0.536917i
\(231\) 11409.5 + 11644.7i 0.213817 + 0.218226i
\(232\) 16753.3 0.311260
\(233\) −3342.37 5789.15i −0.0615662 0.106636i 0.833599 0.552369i \(-0.186276\pi\)
−0.895166 + 0.445734i \(0.852943\pi\)
\(234\) 15139.8 + 8740.99i 0.276497 + 0.159635i
\(235\) 4343.21 7522.66i 0.0786457 0.136218i
\(236\) 24197.4 13970.4i 0.434455 0.250832i
\(237\) 33633.8i 0.598796i
\(238\) −30262.7 + 7778.77i −0.534262 + 0.137327i
\(239\) −96461.0 −1.68871 −0.844356 0.535782i \(-0.820017\pi\)
−0.844356 + 0.535782i \(0.820017\pi\)
\(240\) −2353.41 4076.23i −0.0408579 0.0707679i
\(241\) 47371.8 + 27350.1i 0.815616 + 0.470896i 0.848902 0.528550i \(-0.177264\pi\)
−0.0332863 + 0.999446i \(0.510597\pi\)
\(242\) 14907.6 25820.6i 0.254551 0.440896i
\(243\) 3280.50 1894.00i 0.0555556 0.0320750i
\(244\) 18177.7i 0.305323i
\(245\) 17588.4 29077.0i 0.293019 0.484415i
\(246\) −41410.1 −0.684284
\(247\) −33735.5 58431.6i −0.552959 0.957753i
\(248\) −13064.9 7542.99i −0.212423 0.122642i
\(249\) 21371.3 37016.2i 0.344693 0.597026i
\(250\) −36391.3 + 21010.5i −0.582260 + 0.336168i
\(251\) 108137.i 1.71643i 0.513286 + 0.858217i \(0.328428\pi\)
−0.513286 + 0.858217i \(0.671572\pi\)
\(252\) −2634.87 10250.8i −0.0414914 0.161419i
\(253\) 45428.8 0.709725
\(254\) 3365.92 + 5829.95i 0.0521719 + 0.0903643i
\(255\) −14359.5 8290.45i −0.220830 0.127496i
\(256\) −2048.00 + 3547.24i −0.0312500 + 0.0541266i
\(257\) 31078.3 17943.0i 0.470533 0.271663i −0.245930 0.969288i \(-0.579093\pi\)
0.716463 + 0.697625i \(0.245760\pi\)
\(258\) 45066.8i 0.677045i
\(259\) −29181.8 + 28592.2i −0.435023 + 0.426233i
\(260\) 25920.2 0.383435
\(261\) 9995.36 + 17312.5i 0.146729 + 0.254143i
\(262\) 10630.3 + 6137.39i 0.154861 + 0.0894090i
\(263\) 32715.8 56665.4i 0.472984 0.819232i −0.526538 0.850151i \(-0.676510\pi\)
0.999522 + 0.0309199i \(0.00984367\pi\)
\(264\) 6519.69 3764.15i 0.0935447 0.0540081i
\(265\) 16313.4i 0.232302i
\(266\) −10974.5 + 39346.7i −0.155103 + 0.556089i
\(267\) 80739.2 1.13256
\(268\) 34698.5 + 60099.5i 0.483104 + 0.836761i
\(269\) −59938.7 34605.6i −0.828329 0.478236i 0.0249511 0.999689i \(-0.492057\pi\)
−0.853280 + 0.521453i \(0.825390\pi\)
\(270\) 2808.19 4863.93i 0.0385212 0.0667206i
\(271\) 5672.94 3275.27i 0.0772449 0.0445973i −0.460880 0.887462i \(-0.652466\pi\)
0.538125 + 0.842865i \(0.319133\pi\)
\(272\) 14429.1i 0.195030i
\(273\) 56142.5 + 15659.1i 0.753298 + 0.210108i
\(274\) −87000.1 −1.15883
\(275\) −13595.9 23548.8i −0.179780 0.311389i
\(276\) −25542.0 14746.7i −0.335302 0.193587i
\(277\) −39551.6 + 68505.4i −0.515471 + 0.892823i 0.484367 + 0.874865i \(0.339050\pi\)
−0.999839 + 0.0179578i \(0.994284\pi\)
\(278\) −66593.4 + 38447.7i −0.861671 + 0.497486i
\(279\) 18001.2i 0.231257i
\(280\) −10982.6 11209.1i −0.140084 0.142973i
\(281\) 34363.1 0.435191 0.217596 0.976039i \(-0.430179\pi\)
0.217596 + 0.976039i \(0.430179\pi\)
\(282\) −4509.95 7811.45i −0.0567118 0.0982276i
\(283\) 79598.4 + 45956.1i 0.993874 + 0.573813i 0.906430 0.422356i \(-0.138797\pi\)
0.0874439 + 0.996169i \(0.472130\pi\)
\(284\) 1414.37 2449.75i 0.0175358 0.0303729i
\(285\) −18772.1 + 10838.1i −0.231113 + 0.133433i
\(286\) 41457.8i 0.506844i
\(287\) −133716. + 34370.5i −1.62338 + 0.417274i
\(288\) −4887.52 −0.0589256
\(289\) −16345.5 28311.3i −0.195705 0.338972i
\(290\) 25668.9 + 14819.9i 0.305218 + 0.176218i
\(291\) −4049.38 + 7013.74i −0.0478193 + 0.0828254i
\(292\) −28197.4 + 16279.8i −0.330707 + 0.190934i
\(293\) 23218.2i 0.270453i −0.990815 0.135227i \(-0.956824\pi\)
0.990815 0.135227i \(-0.0431763\pi\)
\(294\) −17016.3 30913.5i −0.196866 0.357646i
\(295\) 49432.7 0.568028
\(296\) 9432.97 + 16338.4i 0.107663 + 0.186477i
\(297\) 7779.58 + 4491.54i 0.0881948 + 0.0509193i
\(298\) 8240.51 14273.0i 0.0927943 0.160724i
\(299\) 140658. 81208.9i 1.57334 0.908367i
\(300\) 17653.5i 0.196150i
\(301\) 37405.5 + 145523.i 0.412860 + 1.60620i
\(302\) 71239.0 0.781095
\(303\) −40881.6 70808.9i −0.445289 0.771264i
\(304\) 16336.0 + 9431.59i 0.176766 + 0.102056i
\(305\) −16080.0 + 27851.3i −0.172856 + 0.299396i
\(306\) −14910.7 + 8608.72i −0.159242 + 0.0919382i
\(307\) 66385.9i 0.704367i 0.935931 + 0.352183i \(0.114561\pi\)
−0.935931 + 0.352183i \(0.885439\pi\)
\(308\) 17928.2 17566.0i 0.188989 0.185171i
\(309\) −175.260 −0.00183555
\(310\) −13345.0 23114.3i −0.138866 0.240523i
\(311\) −82879.0 47850.2i −0.856888 0.494724i 0.00608108 0.999982i \(-0.498064\pi\)
−0.862969 + 0.505257i \(0.831398\pi\)
\(312\) 13457.6 23309.3i 0.138248 0.239453i
\(313\) 41486.1 23952.0i 0.423461 0.244486i −0.273096 0.961987i \(-0.588048\pi\)
0.696557 + 0.717501i \(0.254714\pi\)
\(314\) 67588.2i 0.685507i
\(315\) 5030.75 18036.7i 0.0507005 0.181776i
\(316\) 51782.6 0.518573
\(317\) 17064.1 + 29555.9i 0.169811 + 0.294121i 0.938353 0.345678i \(-0.112351\pi\)
−0.768543 + 0.639799i \(0.779018\pi\)
\(318\) 14670.2 + 8469.85i 0.145071 + 0.0837571i
\(319\) −23703.6 + 41055.8i −0.232934 + 0.403454i
\(320\) −6275.77 + 3623.32i −0.0612868 + 0.0353839i
\(321\) 28300.7i 0.274654i
\(322\) −94716.3 26418.0i −0.913509 0.254793i
\(323\) 66450.0 0.636927
\(324\) −2916.00 5050.66i −0.0277778 0.0481125i
\(325\) −84192.0 48608.3i −0.797084 0.460196i
\(326\) 60225.6 104314.i 0.566691 0.981537i
\(327\) 75140.0 43382.1i 0.702709 0.405709i
\(328\) 63755.1i 0.592607i
\(329\) −21046.4 21480.4i −0.194440 0.198450i
\(330\) 13319.0 0.122305
\(331\) −66642.6 115428.i −0.608270 1.05355i −0.991526 0.129912i \(-0.958531\pi\)
0.383256 0.923642i \(-0.374803\pi\)
\(332\) −56990.2 32903.3i −0.517040 0.298513i
\(333\) −11255.8 + 19495.7i −0.101505 + 0.175812i
\(334\) 64559.5 37273.4i 0.578718 0.334123i
\(335\) 122777.i 1.09402i
\(336\) −15782.1 + 4056.65i −0.139793 + 0.0359326i
\(337\) −49734.4 −0.437922 −0.218961 0.975734i \(-0.570267\pi\)
−0.218961 + 0.975734i \(0.570267\pi\)
\(338\) 33719.0 + 58403.1i 0.295149 + 0.511214i
\(339\) −42550.4 24566.5i −0.370258 0.213768i
\(340\) −12764.0 + 22107.9i −0.110415 + 0.191245i
\(341\) 36970.0 21344.6i 0.317936 0.183561i
\(342\) 22508.3i 0.192438i
\(343\) −80605.0 85697.8i −0.685131 0.728420i
\(344\) 69384.9 0.586338
\(345\) −26089.7 45188.8i −0.219195 0.379658i
\(346\) −68632.7 39625.1i −0.573296 0.330993i
\(347\) −9384.77 + 16254.9i −0.0779408 + 0.134997i −0.902361 0.430980i \(-0.858168\pi\)
0.824421 + 0.565978i \(0.191501\pi\)
\(348\) 26654.3 15388.9i 0.220094 0.127071i
\(349\) 4574.17i 0.0375545i 0.999824 + 0.0187772i \(0.00597733\pi\)
−0.999824 + 0.0187772i \(0.994023\pi\)
\(350\) 14652.4 + 57004.1i 0.119611 + 0.465340i
\(351\) 32116.5 0.260683
\(352\) −5795.28 10037.7i −0.0467724 0.0810121i
\(353\) 52734.9 + 30446.5i 0.423203 + 0.244336i 0.696447 0.717608i \(-0.254763\pi\)
−0.273244 + 0.961945i \(0.588097\pi\)
\(354\) 25665.2 44453.4i 0.204804 0.354731i
\(355\) 4334.10 2502.29i 0.0343908 0.0198555i
\(356\) 124306.i 0.980828i
\(357\) −41002.5 + 40174.0i −0.321717 + 0.315217i
\(358\) 71837.7 0.560514
\(359\) −116059. 201020.i −0.900513 1.55973i −0.826830 0.562452i \(-0.809858\pi\)
−0.0736826 0.997282i \(-0.523475\pi\)
\(360\) −7488.51 4323.50i −0.0577817 0.0333603i
\(361\) −21725.5 + 37629.7i −0.166708 + 0.288746i
\(362\) −108016. + 62362.9i −0.824271 + 0.475893i
\(363\) 54773.8i 0.415681i
\(364\) 24108.8 86437.1i 0.181959 0.652375i
\(365\) −57604.4 −0.432384
\(366\) 16697.3 + 28920.5i 0.124647 + 0.215896i
\(367\) −125329. 72358.9i −0.930509 0.537229i −0.0435362 0.999052i \(-0.513862\pi\)
−0.886972 + 0.461822i \(0.847196\pi\)
\(368\) −22704.0 + 39324.4i −0.167651 + 0.290380i
\(369\) −65883.1 + 38037.6i −0.483862 + 0.279358i
\(370\) 33377.6i 0.243810i
\(371\) 54401.0 + 15173.4i 0.395238 + 0.110239i
\(372\) −27714.7 −0.200274
\(373\) 74441.6 + 128937.i 0.535054 + 0.926741i 0.999161 + 0.0409616i \(0.0130421\pi\)
−0.464107 + 0.885779i \(0.653625\pi\)
\(374\) −35360.2 20415.2i −0.252797 0.145952i
\(375\) −38598.8 + 66855.0i −0.274480 + 0.475414i
\(376\) −12026.5 + 6943.52i −0.0850676 + 0.0491138i
\(377\) 169491.i 1.19252i
\(378\) −13608.0 13888.6i −0.0952381 0.0972020i
\(379\) 140667. 0.979299 0.489649 0.871919i \(-0.337125\pi\)
0.489649 + 0.871919i \(0.337125\pi\)
\(380\) 16686.3 + 28901.6i 0.115556 + 0.200149i
\(381\) 10710.3 + 6183.59i 0.0737822 + 0.0425982i
\(382\) 91300.4 158137.i 0.625671 1.08369i
\(383\) 25393.9 14661.2i 0.173114 0.0999473i −0.410939 0.911663i \(-0.634799\pi\)
0.584053 + 0.811715i \(0.301466\pi\)
\(384\) 7524.83i 0.0510310i
\(385\) 43008.0 11054.8i 0.290153 0.0745814i
\(386\) 103731. 0.696202
\(387\) 41396.5 + 71700.8i 0.276402 + 0.478743i
\(388\) 10798.4 + 6234.43i 0.0717289 + 0.0414127i
\(389\) −66209.9 + 114679.i −0.437546 + 0.757852i −0.997500 0.0706723i \(-0.977486\pi\)
0.559954 + 0.828524i \(0.310819\pi\)
\(390\) 41238.8 23809.2i 0.271129 0.156537i
\(391\) 159960.i 1.04630i
\(392\) −47594.4 + 26198.4i −0.309730 + 0.170491i
\(393\) 22550.2 0.146004
\(394\) 103446. + 179173.i 0.666376 + 1.15420i
\(395\) 79339.7 + 45806.8i 0.508507 + 0.293586i
\(396\) 6915.18 11977.4i 0.0440974 0.0763790i
\(397\) 29642.0 17113.8i 0.188073 0.108584i −0.403007 0.915197i \(-0.632035\pi\)
0.591080 + 0.806613i \(0.298702\pi\)
\(398\) 3962.70i 0.0250164i
\(399\) 18682.0 + 72680.8i 0.117348 + 0.456535i
\(400\) 27179.3 0.169870
\(401\) 89540.6 + 155089.i 0.556841 + 0.964477i 0.997758 + 0.0669288i \(0.0213200\pi\)
−0.440917 + 0.897548i \(0.645347\pi\)
\(402\) 110410. + 63745.1i 0.683212 + 0.394453i
\(403\) 76311.7 132176.i 0.469873 0.813845i
\(404\) −109018. + 62941.3i −0.667934 + 0.385632i
\(405\) 10318.0i 0.0629048i
\(406\) 73295.6 71814.7i 0.444657 0.435674i
\(407\) −53385.5 −0.322281
\(408\) 13254.0 + 22956.6i 0.0796208 + 0.137907i
\(409\) 43099.3 + 24883.4i 0.257646 + 0.148752i 0.623260 0.782014i \(-0.285808\pi\)
−0.365614 + 0.930767i \(0.619141\pi\)
\(410\) −56397.6 + 97683.6i −0.335501 + 0.581104i
\(411\) −138416. + 79914.7i −0.819414 + 0.473089i
\(412\) 269.830i 0.00158963i
\(413\) 45978.1 164845.i 0.269557 0.966442i
\(414\) −54182.7 −0.316126
\(415\) −58212.4 100827.i −0.338002 0.585437i
\(416\) −35887.0 20719.4i −0.207372 0.119727i
\(417\) −70633.0 + 122340.i −0.406196 + 0.703551i
\(418\) −46226.4 + 26688.8i −0.264568 + 0.152748i
\(419\) 43951.2i 0.250347i 0.992135 + 0.125174i \(0.0399488\pi\)
−0.992135 + 0.125174i \(0.960051\pi\)
\(420\) −27769.4 7745.35i −0.157423 0.0439079i
\(421\) −218257. −1.23141 −0.615707 0.787975i \(-0.711129\pi\)
−0.615707 + 0.787975i \(0.711129\pi\)
\(422\) −82352.0 142638.i −0.462433 0.800958i
\(423\) −14350.6 8285.30i −0.0802025 0.0463050i
\(424\) 13040.2 22586.3i 0.0725357 0.125636i
\(425\) 82917.9 47872.7i 0.459061 0.265039i
\(426\) 5196.71i 0.0286358i
\(427\) 77920.6 + 79527.4i 0.427363 + 0.436175i
\(428\) −43571.7 −0.237858
\(429\) 38081.5 + 65959.0i 0.206918 + 0.358393i
\(430\) 106309. + 61377.8i 0.574956 + 0.331951i
\(431\) 38369.8 66458.5i 0.206555 0.357763i −0.744072 0.668099i \(-0.767108\pi\)
0.950627 + 0.310336i \(0.100442\pi\)
\(432\) −7776.00 + 4489.48i −0.0416667 + 0.0240563i
\(433\) 216713.i 1.15587i −0.816083 0.577935i \(-0.803859\pi\)
0.816083 0.577935i \(-0.196141\pi\)
\(434\) −89492.6 + 23003.3i −0.475125 + 0.122127i
\(435\) 54451.9 0.287763
\(436\) −66791.1 115686.i −0.351354 0.608564i
\(437\) 181099. + 104558.i 0.948318 + 0.547512i
\(438\) −29907.9 + 51802.0i −0.155897 + 0.270021i
\(439\) 20578.6 11881.0i 0.106779 0.0616489i −0.445659 0.895203i \(-0.647031\pi\)
0.552438 + 0.833554i \(0.313697\pi\)
\(440\) 20506.0i 0.105919i
\(441\) −55468.6 33552.5i −0.285214 0.172523i
\(442\) −145978. −0.747210
\(443\) −87432.4 151437.i −0.445517 0.771659i 0.552571 0.833466i \(-0.313647\pi\)
−0.998088 + 0.0618072i \(0.980314\pi\)
\(444\) 30015.5 + 17329.5i 0.152258 + 0.0879062i
\(445\) 109961. 190458.i 0.555289 0.961788i
\(446\) −149544. + 86339.0i −0.751793 + 0.434048i
\(447\) 30277.6i 0.151532i
\(448\) 6245.62 + 24298.1i 0.0311186 + 0.121065i
\(449\) −195154. −0.968023 −0.484011 0.875062i \(-0.660821\pi\)
−0.484011 + 0.875062i \(0.660821\pi\)
\(450\) 16215.7 + 28086.5i 0.0800777 + 0.138699i
\(451\) −156239. 90204.7i −0.768134 0.443482i
\(452\) −37822.6 + 65510.6i −0.185129 + 0.320653i
\(453\) 113340. 65437.2i 0.552317 0.318881i
\(454\) 70692.8i 0.342976i
\(455\) 113401. 111110.i 0.547764 0.536697i
\(456\) 34653.9 0.166656
\(457\) −29236.1 50638.5i −0.139987 0.242464i 0.787505 0.616309i \(-0.211373\pi\)
−0.927491 + 0.373844i \(0.878039\pi\)
\(458\) 46366.1 + 26769.5i 0.221039 + 0.127617i
\(459\) −15815.2 + 27392.8i −0.0750672 + 0.130020i
\(460\) −69572.6 + 40167.8i −0.328793 + 0.189829i
\(461\) 307243.i 1.44571i −0.691002 0.722853i \(-0.742831\pi\)
0.691002 0.722853i \(-0.257169\pi\)
\(462\) 12388.2 44415.5i 0.0580398 0.208090i
\(463\) −17772.2 −0.0829049 −0.0414524 0.999140i \(-0.513199\pi\)
−0.0414524 + 0.999140i \(0.513199\pi\)
\(464\) −23692.7 41037.0i −0.110047 0.190607i
\(465\) −42463.7 24516.4i −0.196387 0.113384i
\(466\) −9453.65 + 16374.2i −0.0435339 + 0.0754029i
\(467\) 56261.4 32482.5i 0.257974 0.148942i −0.365436 0.930837i \(-0.619080\pi\)
0.623410 + 0.781895i \(0.285747\pi\)
\(468\) 49446.5i 0.225759i
\(469\) 409429. + 114197.i 1.86137 + 0.519168i
\(470\) −24568.9 −0.111222
\(471\) −62083.7 107532.i −0.279857 0.484726i
\(472\) −68440.5 39514.2i −0.307206 0.177365i
\(473\) −98170.2 + 170036.i −0.438790 + 0.760007i
\(474\) 82385.6 47565.4i 0.366686 0.211706i
\(475\) 125168.i 0.554760i
\(476\) 61852.0 + 63127.4i 0.272986 + 0.278615i
\(477\) 31120.2 0.136775
\(478\) 136416. + 236280.i 0.597050 + 1.03412i
\(479\) 182677. + 105468.i 0.796181 + 0.459675i 0.842134 0.539268i \(-0.181299\pi\)
−0.0459530 + 0.998944i \(0.514632\pi\)
\(480\) −6656.46 + 11529.3i −0.0288909 + 0.0500405i
\(481\) −165294. + 95432.3i −0.714440 + 0.412482i
\(482\) 154716.i 0.665948i
\(483\) −174959. + 44971.7i −0.749967 + 0.192773i
\(484\) −84329.8 −0.359990
\(485\) 11029.9 + 19104.4i 0.0468910 + 0.0812177i
\(486\) −9278.66 5357.03i −0.0392837 0.0226805i
\(487\) 114444. 198223.i 0.482542 0.835787i −0.517257 0.855830i \(-0.673047\pi\)
0.999799 + 0.0200431i \(0.00638033\pi\)
\(488\) 44526.1 25707.1i 0.186971 0.107948i
\(489\) 221283.i 0.925402i
\(490\) −96097.7 1961.59i −0.400240 0.00816987i
\(491\) 140350. 0.582169 0.291085 0.956697i \(-0.405984\pi\)
0.291085 + 0.956697i \(0.405984\pi\)
\(492\) 58562.8 + 101434.i 0.241931 + 0.419037i
\(493\) −144562. 83463.1i −0.594787 0.343400i
\(494\) −95418.3 + 165269.i −0.391001 + 0.677234i
\(495\) 21190.5 12234.3i 0.0864828 0.0499309i
\(496\) 42669.6i 0.173442i
\(497\) −4313.28 16780.5i −0.0174620 0.0679348i
\(498\) −120894. −0.487470
\(499\) 172663. + 299062.i 0.693424 + 1.20105i 0.970709 + 0.240258i \(0.0772322\pi\)
−0.277285 + 0.960788i \(0.589434\pi\)
\(500\) 102930. + 59426.7i 0.411720 + 0.237707i
\(501\) 68475.7 118603.i 0.272810 0.472521i
\(502\) 264881. 152929.i 1.05110 0.606851i
\(503\) 58979.0i 0.233110i 0.993184 + 0.116555i \(0.0371851\pi\)
−0.993184 + 0.116555i \(0.962815\pi\)
\(504\) −21382.9 + 20950.9i −0.0841794 + 0.0824786i
\(505\) −222711. −0.873291
\(506\) −64246.0 111277.i −0.250926 0.434616i
\(507\) 107293. + 61945.9i 0.417404 + 0.240988i
\(508\) 9520.26 16489.6i 0.0368911 0.0638972i
\(509\) 20653.6 11924.3i 0.0797186 0.0460255i −0.459611 0.888120i \(-0.652011\pi\)
0.539329 + 0.842095i \(0.318678\pi\)
\(510\) 46897.9i 0.180307i
\(511\) −53578.7 + 192095.i −0.205187 + 0.735657i
\(512\) 11585.2 0.0441942
\(513\) 20675.2 + 35810.6i 0.0785626 + 0.136074i
\(514\) −87902.6 50750.6i −0.332717 0.192094i
\(515\) −238.691 + 413.425i −0.000899957 + 0.00155877i
\(516\) 110391. 63734.1i 0.414603 0.239371i
\(517\) 39296.5i 0.147019i
\(518\) 111305. + 31045.0i 0.414817 + 0.115700i
\(519\) −145592. −0.540509
\(520\) −36656.7 63491.3i −0.135565 0.234805i
\(521\) 417171. + 240854.i 1.53688 + 0.887315i 0.999019 + 0.0442788i \(0.0140990\pi\)
0.537856 + 0.843037i \(0.319234\pi\)
\(522\) 28271.1 48967.1i 0.103753 0.179706i
\(523\) −399593. + 230705.i −1.46088 + 0.843438i −0.999052 0.0435320i \(-0.986139\pi\)
−0.461826 + 0.886970i \(0.652806\pi\)
\(524\) 34718.3i 0.126443i
\(525\) 75673.4 + 77233.9i 0.274552 + 0.280214i
\(526\) −185068. −0.668900
\(527\) 75156.9 + 130176.i 0.270612 + 0.468714i
\(528\) −18440.5 10646.6i −0.0661461 0.0381895i
\(529\) −111774. + 193598.i −0.399419 + 0.691813i
\(530\) 39959.6 23070.7i 0.142255 0.0821312i
\(531\) 94299.9i 0.334443i
\(532\) 111899. 28762.8i 0.395371 0.101627i
\(533\) −645003. −2.27043
\(534\) −114182. 197770.i −0.400421 0.693550i
\(535\) −66759.3 38543.5i −0.233240 0.134661i
\(536\) 98142.1 169987.i 0.341606 0.591679i
\(537\) 114293. 65987.2i 0.396343 0.228829i
\(538\) 195759.i 0.676328i
\(539\) 3137.44 153703.i 0.0107994 0.529059i
\(540\) −15885.5 −0.0544772
\(541\) 254098. + 440111.i 0.868174 + 1.50372i 0.863861 + 0.503731i \(0.168040\pi\)
0.00431302 + 0.999991i \(0.498627\pi\)
\(542\) −16045.5 9263.87i −0.0546204 0.0315351i
\(543\) −114568. + 198438.i −0.388565 + 0.673014i
\(544\) 35344.0 20405.9i 0.119431 0.0689536i
\(545\) 236333.i 0.795668i
\(546\) −41040.7 159666.i −0.137667 0.535583i
\(547\) 40170.8 0.134257 0.0671283 0.997744i \(-0.478616\pi\)
0.0671283 + 0.997744i \(0.478616\pi\)
\(548\) 123037. + 213106.i 0.409707 + 0.709634i
\(549\) 53130.4 + 30674.9i 0.176278 + 0.101774i
\(550\) −38455.0 + 66606.0i −0.127124 + 0.220185i
\(551\) −188986. + 109111.i −0.622482 + 0.359390i
\(552\) 83419.7i 0.273773i
\(553\) 226549. 221972.i 0.740818 0.725851i
\(554\) 223738. 0.728987
\(555\) 30659.3 + 53103.4i 0.0995350 + 0.172400i
\(556\) 188355. + 108747.i 0.609293 + 0.351776i
\(557\) 39230.2 67948.7i 0.126447 0.219013i −0.795850 0.605493i \(-0.792976\pi\)
0.922298 + 0.386480i \(0.126309\pi\)
\(558\) −44093.9 + 25457.6i −0.141615 + 0.0817616i
\(559\) 701959.i 2.24641i
\(560\) −11924.8 + 42753.8i −0.0380254 + 0.136332i
\(561\) −75010.4 −0.238339
\(562\) −48596.8 84172.2i −0.153863 0.266499i
\(563\) −355612. 205312.i −1.12191 0.647737i −0.180024 0.983662i \(-0.557618\pi\)
−0.941889 + 0.335926i \(0.890951\pi\)
\(564\) −12756.1 + 22094.1i −0.0401013 + 0.0694574i
\(565\) −115901. + 66915.6i −0.363071 + 0.209619i
\(566\) 259967.i 0.811495i
\(567\) −34407.7 9596.89i −0.107026 0.0298514i
\(568\) −8000.86 −0.0247993
\(569\) 74404.3 + 128872.i 0.229812 + 0.398047i 0.957752 0.287594i \(-0.0928554\pi\)
−0.727940 + 0.685641i \(0.759522\pi\)
\(570\) 53095.6 + 30654.8i 0.163421 + 0.0943514i
\(571\) −36146.3 + 62607.3i −0.110864 + 0.192023i −0.916119 0.400906i \(-0.868695\pi\)
0.805255 + 0.592929i \(0.202029\pi\)
\(572\) 101551. 58630.3i 0.310378 0.179197i
\(573\) 335459.i 1.02172i
\(574\) 273293. + 278928.i 0.829477 + 0.846582i
\(575\) 301307. 0.911326
\(576\) 6912.00 + 11971.9i 0.0208333 + 0.0360844i
\(577\) −482666. 278667.i −1.44976 0.837018i −0.451290 0.892377i \(-0.649036\pi\)
−0.998466 + 0.0553596i \(0.982369\pi\)
\(578\) −46232.1 + 80076.3i −0.138385 + 0.239689i
\(579\) 165036. 95283.4i 0.492290 0.284223i
\(580\) 83834.1i 0.249210i
\(581\) −390376. + 100343.i −1.15646 + 0.297258i
\(582\) 22906.8 0.0676267
\(583\) 36900.2 + 63913.0i 0.108565 + 0.188041i
\(584\) 79754.4 + 46046.2i 0.233845 + 0.135011i
\(585\) 43740.3 75760.5i 0.127812 0.221376i
\(586\) −56872.6 + 32835.4i −0.165618 + 0.0956197i
\(587\) 308119.i 0.894217i 0.894480 + 0.447109i \(0.147546\pi\)
−0.894480 + 0.447109i \(0.852454\pi\)
\(588\) −51657.5 + 85399.6i −0.149410 + 0.247002i
\(589\) 196505. 0.566426
\(590\) −69908.3 121085.i −0.200828 0.347845i
\(591\) 329162. + 190042.i 0.942398 + 0.544094i
\(592\) 26680.5 46211.9i 0.0761290 0.131859i
\(593\) −200805. + 115935.i −0.571038 + 0.329689i −0.757564 0.652761i \(-0.773611\pi\)
0.186526 + 0.982450i \(0.440277\pi\)
\(594\) 25408.0i 0.0720108i
\(595\) 38925.3 + 151436.i 0.109951 + 0.427755i
\(596\) −46615.3 −0.131231
\(597\) 3639.98 + 6304.62i 0.0102129 + 0.0176893i
\(598\) −397841. 229693.i −1.11252 0.642312i
\(599\) 167042. 289325.i 0.465555 0.806365i −0.533671 0.845692i \(-0.679188\pi\)
0.999226 + 0.0393269i \(0.0125214\pi\)
\(600\) 43242.0 24965.8i 0.120117 0.0693493i
\(601\) 645072.i 1.78591i −0.450147 0.892955i \(-0.648628\pi\)
0.450147 0.892955i \(-0.351372\pi\)
\(602\) 303559. 297426.i 0.837625 0.820702i
\(603\) 234215. 0.644139
\(604\) −100747. 174499.i −0.276159 0.478321i
\(605\) −129208. 74598.1i −0.353002 0.203806i
\(606\) −115631. + 200278.i −0.314867 + 0.545366i
\(607\) 120643. 69653.0i 0.327433 0.189044i −0.327268 0.944932i \(-0.606128\pi\)
0.654701 + 0.755888i \(0.272795\pi\)
\(608\) 53353.1i 0.144329i
\(609\) 50646.5 181583.i 0.136557 0.489598i
\(610\) 90962.0 0.244456
\(611\) −70246.8 121671.i −0.188167 0.325915i
\(612\) 42174.0 + 24349.1i 0.112601 + 0.0650101i
\(613\) 203665. 352759.i 0.541997 0.938765i −0.456793 0.889573i \(-0.651002\pi\)
0.998789 0.0491924i \(-0.0156647\pi\)
\(614\) 162611. 93883.8i 0.431335 0.249031i
\(615\) 207218.i 0.547870i
\(616\) −68382.1 19072.9i −0.180211 0.0502639i
\(617\) 276504. 0.726325 0.363163 0.931726i \(-0.381697\pi\)
0.363163 + 0.931726i \(0.381697\pi\)
\(618\) 247.855 + 429.297i 0.000648963 + 0.00112404i
\(619\) 193904. + 111950.i 0.506064 + 0.292176i 0.731214 0.682148i \(-0.238954\pi\)
−0.225150 + 0.974324i \(0.572287\pi\)
\(620\) −37745.5 + 65377.1i −0.0981933 + 0.170076i
\(621\) −86204.1 + 49770.0i −0.223535 + 0.129058i
\(622\) 270682.i 0.699646i
\(623\) −532852. 543839.i −1.37287 1.40118i
\(624\) −76127.9 −0.195513
\(625\) −27573.7 47759.1i −0.0705888 0.122263i
\(626\) −117340. 67746.5i −0.299432 0.172877i
\(627\) −49030.5 + 84923.3i −0.124719 + 0.216019i
\(628\) −165557. + 95584.2i −0.419785 + 0.242363i
\(629\) 187976.i 0.475119i
\(630\) −51295.4 + 13185.0i −0.129240 + 0.0332200i
\(631\) 299528. 0.752278 0.376139 0.926563i \(-0.377251\pi\)
0.376139 + 0.926563i \(0.377251\pi\)
\(632\) −73231.7 126841.i −0.183343 0.317560i
\(633\) −262042. 151290.i −0.653980 0.377575i
\(634\) 48264.6 83596.7i 0.120074 0.207975i
\(635\) 29173.3 16843.2i 0.0723500 0.0417713i
\(636\) 47912.7i 0.118450i
\(637\) −265046. 481507.i −0.653194 1.18665i
\(638\) 134088. 0.329418
\(639\) −4773.48 8267.92i −0.0116905 0.0202486i
\(640\) 17750.6 + 10248.3i 0.0433363 + 0.0250202i
\(641\) −288942. + 500462.i −0.703226 + 1.21802i 0.264102 + 0.964495i \(0.414924\pi\)
−0.967328 + 0.253528i \(0.918409\pi\)
\(642\) −69322.2 + 40023.2i −0.168191 + 0.0971050i
\(643\) 135320.i 0.327295i 0.986519 + 0.163647i \(0.0523259\pi\)
−0.986519 + 0.163647i \(0.947674\pi\)
\(644\) 69238.5 + 269367.i 0.166946 + 0.649491i
\(645\) 225516. 0.542074
\(646\) −93974.4 162768.i −0.225188 0.390037i
\(647\) 188880. + 109050.i 0.451209 + 0.260506i 0.708341 0.705871i \(-0.249444\pi\)
−0.257132 + 0.966376i \(0.582777\pi\)
\(648\) −8247.69 + 14285.4i −0.0196419 + 0.0340207i
\(649\) 193668. 111814.i 0.459800 0.265465i
\(650\) 274970.i 0.650816i
\(651\) −121252. + 118802.i −0.286106 + 0.280325i
\(652\) −340688. −0.801422
\(653\) −72127.2 124928.i −0.169150 0.292977i 0.768971 0.639284i \(-0.220769\pi\)
−0.938121 + 0.346307i \(0.887436\pi\)
\(654\) −212528. 122703.i −0.496890 0.286880i
\(655\) 30711.8 53194.4i 0.0715851 0.123989i
\(656\) 156167. 90163.3i 0.362896 0.209518i
\(657\) 109889.i 0.254579i
\(658\) −22851.9 + 81930.8i −0.0527802 + 0.189232i
\(659\) −159392. −0.367024 −0.183512 0.983017i \(-0.558747\pi\)
−0.183512 + 0.983017i \(0.558747\pi\)
\(660\) −18836.0 32624.8i −0.0432414 0.0748963i
\(661\) 305674. + 176481.i 0.699609 + 0.403919i 0.807202 0.590276i \(-0.200981\pi\)
−0.107593 + 0.994195i \(0.534314\pi\)
\(662\) −188494. + 326481.i −0.430112 + 0.744975i
\(663\) −232249. + 134089.i −0.528357 + 0.305047i
\(664\) 186129.i 0.422161i
\(665\) 196892. + 54916.7i 0.445231 + 0.124183i
\(666\) 63672.5 0.143550
\(667\) −262655. 454932.i −0.590384 1.02258i
\(668\) −182602. 105425.i −0.409216 0.236261i
\(669\) −158615. + 274729.i −0.354398 + 0.613836i
\(670\) 300741. 173633.i 0.669950 0.386796i
\(671\) 145488.i 0.323135i
\(672\) 32256.0 + 32921.1i 0.0714286 + 0.0729015i
\(673\) 504858. 1.11465 0.557326 0.830294i \(-0.311827\pi\)
0.557326 + 0.830294i \(0.311827\pi\)
\(674\) 70335.1 + 121824.i 0.154829 + 0.268172i
\(675\) 51598.2 + 29790.2i 0.113247 + 0.0653832i
\(676\) 95371.9 165189.i 0.208702 0.361483i
\(677\) −169486. + 97853.0i −0.369792 + 0.213500i −0.673368 0.739308i \(-0.735153\pi\)
0.303576 + 0.952807i \(0.401820\pi\)
\(678\) 138969.i 0.302314i
\(679\) 73967.4 19012.7i 0.160436 0.0412385i
\(680\) 72204.0 0.156150
\(681\) −64935.5 112472.i −0.140019 0.242520i
\(682\) −104567. 60371.7i −0.224815 0.129797i
\(683\) 117221. 203032.i 0.251283 0.435235i −0.712596 0.701574i \(-0.752481\pi\)
0.963879 + 0.266340i \(0.0858142\pi\)
\(684\) 55134.0 31831.6i 0.117844 0.0680372i
\(685\) 435352.i 0.927812i
\(686\) −95923.3 + 318636.i −0.203834 + 0.677091i
\(687\) 98357.4 0.208398
\(688\) −98125.0 169958.i −0.207302 0.359057i
\(689\) 228503. + 131926.i 0.481341 + 0.277902i
\(690\) −73792.9 + 127813.i −0.154995 + 0.268459i
\(691\) −77344.0 + 44654.6i −0.161983 + 0.0935212i −0.578800 0.815469i \(-0.696479\pi\)
0.416817 + 0.908990i \(0.363146\pi\)
\(692\) 224153.i 0.468094i
\(693\) −21088.7 82044.0i −0.0439120 0.170836i
\(694\) 53088.3 0.110225
\(695\) 192394. + 333236.i 0.398311 + 0.689895i
\(696\) −75389.7 43526.3i −0.155630 0.0898531i
\(697\) 317621. 550136.i 0.653799 1.13241i
\(698\) 11204.4 6468.85i 0.0229973 0.0132775i
\(699\) 34734.9i 0.0710905i
\(700\) 118909. 116507.i 0.242672 0.237769i
\(701\) 122213. 0.248704 0.124352 0.992238i \(-0.460315\pi\)
0.124352 + 0.992238i \(0.460315\pi\)
\(702\) −45419.5 78669.0i −0.0921655 0.159635i
\(703\) −212818. 122871.i −0.430624 0.248621i
\(704\) −16391.5 + 28391.0i −0.0330731 + 0.0572842i
\(705\) −39088.9 + 22568.0i −0.0786457 + 0.0454061i
\(706\) 172231.i 0.345544i
\(707\) −207147. + 742683.i −0.414419 + 1.48582i
\(708\) −145184. −0.289636
\(709\) −42009.9 72763.3i −0.0835717 0.144750i 0.821210 0.570626i \(-0.193299\pi\)
−0.904782 + 0.425876i \(0.859966\pi\)
\(710\) −12258.7 7077.55i −0.0243179 0.0140400i
\(711\) 87383.1 151352.i 0.172858 0.299398i
\(712\) −304487. + 175795.i −0.600632 + 0.346775i
\(713\) 473032.i 0.930489i
\(714\) 156392. + 43620.4i 0.306774 + 0.0855645i
\(715\) 207457. 0.405804
\(716\) −101594. 175966.i −0.198172 0.343243i
\(717\) 434074. + 250613.i 0.844356 + 0.487489i
\(718\) −328264. + 568570.i −0.636759 + 1.10290i
\(719\) 657416. 379560.i 1.27169 0.734213i 0.296388 0.955068i \(-0.404218\pi\)
0.975307 + 0.220855i \(0.0708846\pi\)
\(720\) 24457.4i 0.0471786i
\(721\) 1156.65 + 1180.51i 0.00222502 + 0.00227090i
\(722\) 122898. 0.235760
\(723\) −142115. 246151.i −0.271872 0.470896i
\(724\) 305515. + 176389.i 0.582847 + 0.336507i
\(725\) −157214. + 272303.i −0.299100 + 0.518057i
\(726\) −134168. + 77461.9i −0.254551 + 0.146965i
\(727\) 92384.1i 0.174795i −0.996174 0.0873974i \(-0.972145\pi\)
0.996174 0.0873974i \(-0.0278550\pi\)
\(728\) −245822. + 63186.3i −0.463829 + 0.119223i
\(729\) −19683.0 −0.0370370
\(730\) 81464.9 + 141101.i 0.152871 + 0.264780i
\(731\) −598715. 345668.i −1.12043 0.646882i
\(732\) 47227.0 81799.6i 0.0881391 0.152661i
\(733\) 2903.50 1676.34i 0.00540399 0.00312000i −0.497296 0.867581i \(-0.665674\pi\)
0.502700 + 0.864461i \(0.332340\pi\)
\(734\) 409324.i 0.759757i
\(735\) −154692. + 85150.5i −0.286348 + 0.157620i
\(736\) 128433. 0.237094
\(737\) 277715. + 481017.i 0.511287 + 0.885575i
\(738\) 186346. + 107587.i 0.342142 + 0.197536i
\(739\) 13592.8 23543.4i 0.0248897 0.0431103i −0.853312 0.521400i \(-0.825410\pi\)
0.878202 + 0.478290i \(0.158743\pi\)
\(740\) 81758.0 47203.0i 0.149302 0.0861998i
\(741\) 350589.i 0.638502i
\(742\) −39767.6 154713.i −0.0722307 0.281008i
\(743\) 773801. 1.40169 0.700845 0.713314i \(-0.252807\pi\)
0.700845 + 0.713314i \(0.252807\pi\)
\(744\) 39194.6 + 67887.0i 0.0708076 + 0.122642i
\(745\) −71422.6 41235.9i −0.128684 0.0742955i
\(746\) 210553. 364688.i 0.378340 0.655305i
\(747\) −192342. + 111049.i −0.344693 + 0.199009i
\(748\) 115486.i 0.206408i
\(749\) −190626. + 186775.i −0.339797 + 0.332931i
\(750\) 218348. 0.388174
\(751\) −98922.2 171338.i −0.175394 0.303791i 0.764904 0.644145i \(-0.222786\pi\)
−0.940297 + 0.340354i \(0.889453\pi\)
\(752\) 34016.1 + 19639.2i 0.0601519 + 0.0347287i
\(753\) 280948. 486617.i 0.495492 0.858217i
\(754\) 415167. 239697.i 0.730264 0.421618i
\(755\) 356483.i 0.625381i
\(756\) −14775.4 + 52974.1i −0.0258521 + 0.0926873i
\(757\) −770706. −1.34492 −0.672461 0.740132i \(-0.734763\pi\)
−0.672461 + 0.740132i \(0.734763\pi\)
\(758\) −198934. 344564.i −0.346234 0.599696i
\(759\) −204430. 118027.i −0.354863 0.204880i
\(760\) 47196.1 81746.0i 0.0817107 0.141527i
\(761\) −131757. + 76069.9i −0.227512 + 0.131354i −0.609424 0.792845i \(-0.708599\pi\)
0.381912 + 0.924199i \(0.375266\pi\)
\(762\) 34979.7i 0.0602429i
\(763\) −788109. 219817.i −1.35375 0.377583i
\(764\) −516473. −0.884832
\(765\) 43078.4 + 74614.0i 0.0736100 + 0.127496i
\(766\) −71824.8 41468.0i −0.122410 0.0706734i
\(767\) 399760. 692405.i 0.679531 1.17698i
\(768\) 18432.0 10641.7i 0.0312500 0.0180422i
\(769\) 961897.i 1.62658i 0.581857 + 0.813291i \(0.302326\pi\)
−0.581857 + 0.813291i \(0.697674\pi\)
\(770\) −87901.2 89713.7i −0.148256 0.151313i
\(771\) −186470. −0.313689
\(772\) −146698. 254089.i −0.246145 0.426335i
\(773\) −130829. 75534.4i −0.218951 0.126411i 0.386514 0.922284i \(-0.373679\pi\)
−0.605464 + 0.795872i \(0.707013\pi\)
\(774\) 117087. 202801.i 0.195446 0.338522i
\(775\) 245204. 141569.i 0.408248 0.235702i
\(776\) 35267.3i 0.0585664i
\(777\) 205603. 52848.3i 0.340554 0.0875365i
\(778\) 374540. 0.618783
\(779\) −415226. 719192.i −0.684242 1.18514i
\(780\) −116641. 67342.7i −0.191717 0.110688i
\(781\) 11320.1 19607.0i 0.0185588 0.0321447i
\(782\) 391821. 226218.i 0.640728 0.369924i
\(783\) 103875.i 0.169429i
\(784\) 131481. + 79531.9i 0.213910 + 0.129392i
\(785\) −338215. −0.548849
\(786\) −31890.8 55236.5i −0.0516203 0.0894090i
\(787\) −172244. 99445.4i −0.278097 0.160559i 0.354465 0.935069i \(-0.384663\pi\)
−0.632561 + 0.774510i \(0.717996\pi\)
\(788\) 292588. 506777.i 0.471199 0.816140i
\(789\) −294442. + 169996.i −0.472984 + 0.273077i
\(790\) 259123.i 0.415194i
\(791\) 115344. + 448739.i 0.184350 + 0.717202i
\(792\) −39118.2 −0.0623632
\(793\) 260076. + 450465.i 0.413575 + 0.716333i
\(794\) −83840.2 48405.1i −0.132988 0.0767804i
\(795\) 42383.5 73410.4i 0.0670599 0.116151i
\(796\) 9706.60 5604.11i 0.0153194 0.00884465i
\(797\) 990756.i 1.55973i −0.625947 0.779866i \(-0.715287\pi\)
0.625947 0.779866i \(-0.284713\pi\)
\(798\) 151611. 148547.i 0.238081 0.233270i
\(799\) 138368. 0.216741
\(800\) −38437.3 66575.4i −0.0600583 0.104024i
\(801\) −363326. 209767.i −0.566281 0.326943i
\(802\) 253259. 438657.i 0.393746 0.681988i
\(803\) −225683. + 130298.i −0.350000 + 0.202073i
\(804\) 360597.i 0.557840i
\(805\) −132197. + 473965.i −0.204000 + 0.731399i
\(806\) −431684. −0.664501
\(807\) 179816. + 311451.i 0.276110 + 0.478236i
\(808\) 308348. + 178025.i 0.472301 + 0.272683i
\(809\) 46144.3 79924.3i 0.0705052 0.122119i −0.828618 0.559815i \(-0.810872\pi\)
0.899123 + 0.437696i \(0.144206\pi\)
\(810\) −25273.7 + 14591.8i −0.0385212 + 0.0222402i
\(811\) 617125.i 0.938277i −0.883125 0.469139i \(-0.844564\pi\)
0.883125 0.469139i \(-0.155436\pi\)
\(812\) −279565. 77975.4i −0.424005 0.118262i
\(813\) −34037.6 −0.0514966
\(814\) 75498.5 + 130767.i 0.113943 + 0.197356i
\(815\) −521991. 301372.i −0.785865 0.453719i
\(816\) 37488.0 64931.0i 0.0563004 0.0975152i
\(817\) −782700. + 451892.i −1.17260 + 0.677003i
\(818\) 140762.i 0.210367i
\(819\) −211958. 216329.i −0.315996 0.322512i
\(820\) 319033. 0.474469
\(821\) −153533. 265927.i −0.227780 0.394526i 0.729370 0.684119i \(-0.239813\pi\)
−0.957150 + 0.289593i \(0.906480\pi\)
\(822\) 391500. + 226033.i 0.579413 + 0.334524i
\(823\) −423429. + 733401.i −0.625146 + 1.08278i 0.363367 + 0.931646i \(0.381627\pi\)
−0.988513 + 0.151138i \(0.951706\pi\)
\(824\) 660.946 381.597i 0.000973445 0.000562019i
\(825\) 141293.i 0.207592i
\(826\) −468809. + 120503.i −0.687125 + 0.176619i
\(827\) 294059. 0.429956 0.214978 0.976619i \(-0.431032\pi\)
0.214978 + 0.976619i \(0.431032\pi\)
\(828\) 76625.9 + 132720.i 0.111767 + 0.193587i
\(829\) 895803. + 517192.i 1.30348 + 0.752563i 0.980999 0.194013i \(-0.0621506\pi\)
0.322479 + 0.946577i \(0.395484\pi\)
\(830\) −164650. + 285182.i −0.239004 + 0.413967i
\(831\) 355964. 205516.i 0.515471 0.297608i
\(832\) 117207.i 0.169319i
\(833\) 541205. + 11047.3i 0.779959 + 0.0159208i
\(834\) 399560. 0.574447
\(835\) −186518. 323059.i −0.267515 0.463349i
\(836\) 130748. + 75487.4i 0.187078 + 0.108009i
\(837\) −46768.6 + 81005.6i −0.0667580 + 0.115628i
\(838\) 107658. 62156.4i 0.153306 0.0885111i
\(839\) 307258.i 0.436495i 0.975893 + 0.218248i \(0.0700340\pi\)
−0.975893 + 0.218248i \(0.929966\pi\)
\(840\) 20299.7 + 78974.4i 0.0287694 + 0.111925i
\(841\) −159093. −0.224937
\(842\) 308662. + 534618.i 0.435370 + 0.754084i
\(843\) −154634. 89278.1i −0.217596 0.125629i
\(844\) −232927. + 403441.i −0.326990 + 0.566363i
\(845\) 292252. 168732.i 0.409302 0.236311i
\(846\) 46868.7i 0.0654851i
\(847\) −368943. + 361489.i −0.514272 + 0.503881i
\(848\) −73766.4 −0.102581
\(849\) −238795. 413605.i −0.331291 0.573813i
\(850\) −234527. 135404.i −0.324605 0.187411i
\(851\) 295777. 512302.i 0.408419 0.707402i
\(852\) −12729.3 + 7349.26i −0.0175358 + 0.0101243i
\(853\) 70737.4i 0.0972190i 0.998818 + 0.0486095i \(0.0154790\pi\)
−0.998818 + 0.0486095i \(0.984521\pi\)
\(854\) 84605.2 303335.i 0.116006 0.415916i
\(855\) 112633. 0.154075
\(856\) 61619.7 + 106728.i 0.0840954 + 0.145657i
\(857\) 285670. + 164932.i 0.388958 + 0.224565i 0.681709 0.731624i \(-0.261237\pi\)
−0.292751 + 0.956189i \(0.594571\pi\)
\(858\) 107711. 186560.i 0.146313 0.253422i
\(859\) −60589.3 + 34981.2i −0.0821125 + 0.0474077i −0.540494 0.841348i \(-0.681763\pi\)
0.458382 + 0.888756i \(0.348429\pi\)
\(860\) 347205.i 0.469450i
\(861\) 691018. + 192737.i 0.932145 + 0.259991i
\(862\) −217052. −0.292113
\(863\) 386112. + 668765.i 0.518431 + 0.897949i 0.999771 + 0.0214151i \(0.00681715\pi\)
−0.481339 + 0.876534i \(0.659850\pi\)
\(864\) 21993.8 + 12698.2i 0.0294628 + 0.0170103i
\(865\) −198286. + 343441.i −0.265008 + 0.459008i
\(866\) −530836. + 306478.i −0.707823 + 0.408662i
\(867\) 169868.i 0.225981i
\(868\) 182908. + 186680.i 0.242769 + 0.247775i
\(869\) 414451. 0.548825
\(870\) −77006.6 133379.i −0.101739 0.176218i
\(871\) 1.71974e6 + 992893.i 2.26687 + 1.30878i
\(872\) −188914. + 327208.i −0.248445 + 0.430320i
\(873\) 36444.4 21041.2i 0.0478193 0.0276085i
\(874\) 591468.i 0.774299i
\(875\) 705058. 181229.i 0.920892 0.236707i
\(876\) 169185. 0.220472
\(877\) −121260. 210028.i −0.157659 0.273073i 0.776365 0.630283i \(-0.217061\pi\)
−0.934024 + 0.357211i \(0.883728\pi\)
\(878\) −58204.9 33604.6i −0.0755042 0.0435923i
\(879\) −60322.5 + 104482.i −0.0780732 + 0.135227i
\(880\) −50229.2 + 28999.9i −0.0648621 + 0.0374482i
\(881\) 646528.i 0.832982i 0.909140 + 0.416491i \(0.136740\pi\)
−0.909140 + 0.416491i \(0.863260\pi\)
\(882\) −3742.01 + 183320.i −0.00481025 + 0.235653i
\(883\) −461877. −0.592387 −0.296193 0.955128i \(-0.595717\pi\)
−0.296193 + 0.955128i \(0.595717\pi\)
\(884\) 206444. + 357571.i 0.264179 + 0.457571i
\(885\) −222447. 128430.i −0.284014 0.163976i
\(886\) −247296. + 428329.i −0.315028 + 0.545645i
\(887\) −186391. + 107613.i −0.236907 + 0.136778i −0.613754 0.789497i \(-0.710342\pi\)
0.376847 + 0.926275i \(0.377008\pi\)
\(888\) 98030.3i 0.124318i
\(889\) −29033.2 112952.i −0.0367359 0.142919i
\(890\) −622034. −0.785297
\(891\) −23338.7 40423.9i −0.0293983 0.0509193i
\(892\) 422973. + 244204.i 0.531598 + 0.306918i
\(893\) 90443.9 156653.i 0.113417 0.196443i
\(894\) −74164.6 + 42818.9i −0.0927943 + 0.0535748i
\(895\) 359479.i 0.448774i
\(896\) 50685.4 49661.4i 0.0631345 0.0618590i
\(897\) −843948. −1.04889
\(898\) 275990. + 478029.i 0.342248 + 0.592791i
\(899\) −427498. 246816.i −0.528950 0.305389i
\(900\) 45865.0 79440.6i 0.0566235 0.0980748i
\(901\) −225045. + 129930.i −0.277217 + 0.160051i
\(902\) 510275.i 0.627179i
\(903\) 209756. 752038.i 0.257240 0.922283i
\(904\) 213957. 0.261812
\(905\) 312067. + 540516.i 0.381022 + 0.659950i
\(906\) −320575. 185084.i −0.390547 0.225483i
\(907\) −549134. + 951128.i −0.667519 + 1.15618i 0.311076 + 0.950385i \(0.399311\pi\)
−0.978596 + 0.205793i \(0.934023\pi\)
\(908\) −173161. + 99974.7i −0.210029 + 0.121260i
\(909\) 424854.i 0.514176i
\(910\) −432535. 120641.i −0.522322 0.145685i
\(911\) −1.32312e6 −1.59427 −0.797133 0.603803i \(-0.793651\pi\)
−0.797133 + 0.603803i \(0.793651\pi\)
\(912\) −49008.0 84884.3i −0.0589219 0.102056i
\(913\) −456131. 263348.i −0.547203 0.315928i
\(914\) −82692.2 + 143227.i −0.0989857 + 0.171448i
\(915\) 144720. 83553.9i 0.172856 0.0997987i
\(916\) 151431.i 0.180478i
\(917\) −148824. 151893.i −0.176984 0.180633i
\(918\) 89464.5 0.106161
\(919\) −258264. 447326.i −0.305797 0.529656i 0.671642 0.740876i \(-0.265589\pi\)
−0.977438 + 0.211221i \(0.932256\pi\)
\(920\) 196781. + 113612.i 0.232492 + 0.134229i
\(921\) 172476. 298736.i 0.203333 0.352183i
\(922\) −752588. + 434507.i −0.885310 + 0.511134i
\(923\) 80943.8i 0.0950124i
\(924\) −126315. + 32468.1i −0.147949 + 0.0380289i
\(925\) −354080. −0.413826
\(926\) 25133.7 + 43532.9i 0.0293113 + 0.0507687i
\(927\) 788.669 + 455.338i 0.000917773 + 0.000529876i
\(928\) −67013.1 + 116070.i −0.0778151 + 0.134780i
\(929\) 1.07335e6 619697.i 1.24368 0.718039i 0.273838 0.961776i \(-0.411707\pi\)
0.969841 + 0.243737i \(0.0783734\pi\)
\(930\) 138686.i 0.160349i
\(931\) 366265. 605506.i 0.422568 0.698585i
\(932\) 53477.9 0.0615662
\(933\) 248637. + 430652.i 0.285629 + 0.494724i
\(934\) −159131. 91874.5i −0.182415 0.105318i
\(935\) −102159. + 176944.i −0.116856 + 0.202401i
\(936\) −121119. + 69928.0i −0.138248 + 0.0798177i
\(937\) 1.15260e6i 1.31281i −0.754411 0.656403i \(-0.772077\pi\)
0.754411 0.656403i \(-0.227923\pi\)
\(938\) −299296. 1.16439e6i −0.340170 1.32340i
\(939\) −248917. −0.282308
\(940\) 34745.7 + 60181.3i 0.0393228 + 0.0681092i
\(941\) 93104.2 + 53753.7i 0.105145 + 0.0607057i 0.551650 0.834075i \(-0.313998\pi\)
−0.446505 + 0.894781i \(0.647332\pi\)
\(942\) −175599. + 304147.i −0.197889 + 0.342753i
\(943\) 1.73126e6 999543.i 1.94688 1.12403i
\(944\) 223526.i 0.250832i
\(945\) −69499.2 + 68095.1i −0.0778245 + 0.0762521i
\(946\) 555334. 0.620543
\(947\) 206307. + 357335.i 0.230046 + 0.398451i 0.957821 0.287364i \(-0.0927790\pi\)
−0.727775 + 0.685815i \(0.759446\pi\)
\(948\) −233022. 134535.i −0.259286 0.149699i
\(949\) −465845. + 806867.i −0.517260 + 0.895920i
\(950\) −306597. + 177014.i −0.339720 + 0.196137i
\(951\) 177335.i 0.196080i
\(952\) 67158.0 240781.i 0.0741010 0.265674i
\(953\) 1.43052e6 1.57510 0.787550 0.616251i \(-0.211349\pi\)
0.787550 + 0.616251i \(0.211349\pi\)
\(954\) −44010.6 76228.6i −0.0483572 0.0837571i
\(955\) −791324. 456871.i −0.867656 0.500942i
\(956\) 385844. 668301.i 0.422178 0.731234i
\(957\) 213332. 123168.i 0.232934 0.134485i
\(958\) 596619.i 0.650079i
\(959\) 1.45179e6 + 404928.i 1.57858 + 0.440292i
\(960\) 37654.6 0.0408579
\(961\) −239507. 414839.i −0.259342 0.449193i
\(962\) 467521. + 269923.i 0.505186 + 0.291669i
\(963\) −73527.3 + 127353.i −0.0792859 + 0.137327i
\(964\) −378974. + 218801.i −0.407808 + 0.235448i
\(965\) 519077.i 0.557413i
\(966\) 357587. + 364961.i 0.383202 + 0.391104i
\(967\) −344533. −0.368449 −0.184225 0.982884i \(-0.558977\pi\)
−0.184225 + 0.982884i \(0.558977\pi\)
\(968\) 119260. + 206565.i 0.127276 + 0.220448i
\(969\) −299025. 172642.i −0.318463 0.183865i
\(970\) 31197.4 54035.5i 0.0331570 0.0574296i
\(971\) −1.25848e6 + 726581.i −1.33477 + 0.770630i −0.986027 0.166588i \(-0.946725\pi\)
−0.348744 + 0.937218i \(0.613392\pi\)
\(972\) 30304.0i 0.0320750i
\(973\) 1.29020e6 331636.i 1.36280 0.350296i
\(974\) −647393. −0.682417
\(975\) 252576. + 437474.i 0.265695 + 0.460196i
\(976\) −125939. 72710.8i −0.132209 0.0763307i
\(977\) −772853. + 1.33862e6i −0.809669 + 1.40239i 0.103424 + 0.994637i \(0.467020\pi\)
−0.913093 + 0.407751i \(0.866313\pi\)
\(978\) −542031. + 312941.i −0.566691 + 0.327179i
\(979\) 994907.i 1.03805i
\(980\) 131098. + 238164.i 0.136503 + 0.247985i
\(981\) −450840. −0.468473
\(982\) −198485. 343786.i −0.205828 0.356504i
\(983\) 116280. + 67134.0i 0.120336 + 0.0694761i 0.558960 0.829195i \(-0.311201\pi\)
−0.438624 + 0.898671i \(0.644534\pi\)
\(984\) 165641. 286898.i 0.171071 0.296304i
\(985\) 896589. 517646.i 0.924105 0.533532i
\(986\) 472139.i 0.485641i
\(987\) 38901.1 + 151342.i 0.0399326 + 0.155355i
\(988\) 539768. 0.552959
\(989\) −1.08781e6 1.88414e6i −1.11214 1.92628i
\(990\) −59935.7 34603.9i −0.0611526 0.0353065i
\(991\) 395596. 685192.i 0.402814 0.697694i −0.591251 0.806488i \(-0.701366\pi\)
0.994064 + 0.108794i \(0.0346990\pi\)
\(992\) 104519. 60344.0i 0.106211 0.0613212i
\(993\) 692571.i 0.702369i
\(994\) −35003.8 + 34296.5i −0.0354276 + 0.0347118i
\(995\) 19829.5 0.0200293
\(996\) 170971. + 296130.i 0.172347 + 0.298513i
\(997\) 582624. + 336378.i 0.586136 + 0.338406i 0.763568 0.645727i \(-0.223446\pi\)
−0.177432 + 0.984133i \(0.556779\pi\)
\(998\) 488366. 845874.i 0.490325 0.849268i
\(999\) 101302. 58487.0i 0.101505 0.0586041i
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 42.5.g.a.31.1 yes 4
3.2 odd 2 126.5.n.b.73.2 4
4.3 odd 2 336.5.bh.d.241.2 4
7.2 even 3 294.5.g.c.19.1 4
7.3 odd 6 294.5.c.a.97.3 4
7.4 even 3 294.5.c.a.97.4 4
7.5 odd 6 inner 42.5.g.a.19.1 4
7.6 odd 2 294.5.g.c.31.1 4
21.5 even 6 126.5.n.b.19.2 4
21.11 odd 6 882.5.c.a.685.2 4
21.17 even 6 882.5.c.a.685.1 4
28.19 even 6 336.5.bh.d.145.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.5.g.a.19.1 4 7.5 odd 6 inner
42.5.g.a.31.1 yes 4 1.1 even 1 trivial
126.5.n.b.19.2 4 21.5 even 6
126.5.n.b.73.2 4 3.2 odd 2
294.5.c.a.97.3 4 7.3 odd 6
294.5.c.a.97.4 4 7.4 even 3
294.5.g.c.19.1 4 7.2 even 3
294.5.g.c.31.1 4 7.6 odd 2
336.5.bh.d.145.2 4 28.19 even 6
336.5.bh.d.241.2 4 4.3 odd 2
882.5.c.a.685.1 4 21.17 even 6
882.5.c.a.685.2 4 21.11 odd 6