Properties

Label 392.3.j.e.117.6
Level $392$
Weight $3$
Character 392.117
Analytic conductor $10.681$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,3,Mod(117,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.117");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.j (of order \(6\), degree \(2\), not 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: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 117.6
Character \(\chi\) \(=\) 392.117
Dual form 392.3.j.e.325.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.215431 + 1.98836i) q^{2} +(-0.455431 - 0.788830i) q^{3} +(-3.90718 - 0.856711i) q^{4} +(3.17251 - 5.49495i) q^{5} +(1.66660 - 0.735624i) q^{6} +(2.54518 - 7.58433i) q^{8} +(4.08516 - 7.07571i) q^{9} +O(q^{10})\) \(q+(-0.215431 + 1.98836i) q^{2} +(-0.455431 - 0.788830i) q^{3} +(-3.90718 - 0.856711i) q^{4} +(3.17251 - 5.49495i) q^{5} +(1.66660 - 0.735624i) q^{6} +(2.54518 - 7.58433i) q^{8} +(4.08516 - 7.07571i) q^{9} +(10.2425 + 7.49189i) q^{10} +(-11.4442 + 6.60732i) q^{11} +(1.10365 + 3.47227i) q^{12} -19.4243 q^{13} -5.77945 q^{15} +(14.5321 + 6.69465i) q^{16} +(-13.7930 + 7.96338i) q^{17} +(13.1890 + 9.64712i) q^{18} +(-8.22725 + 14.2500i) q^{19} +(-17.1032 + 18.7518i) q^{20} +(-10.6723 - 24.1787i) q^{22} +(-11.9607 + 20.7166i) q^{23} +(-7.14190 + 1.44643i) q^{24} +(-7.62967 - 13.2150i) q^{25} +(4.18461 - 38.6227i) q^{26} -15.6398 q^{27} -16.6618i q^{29} +(1.24507 - 11.4916i) q^{30} +(11.1360 - 6.42939i) q^{31} +(-16.4421 + 27.4528i) q^{32} +(10.4241 + 6.01837i) q^{33} +(-12.8627 - 29.1410i) q^{34} +(-22.0233 + 24.1463i) q^{36} +(-41.1844 - 23.7778i) q^{37} +(-26.5618 - 19.4287i) q^{38} +(8.84646 + 15.3225i) q^{39} +(-33.6009 - 38.0470i) q^{40} +6.49499i q^{41} -33.2928i q^{43} +(50.3752 - 16.0116i) q^{44} +(-25.9205 - 44.8956i) q^{45} +(-38.6154 - 28.2453i) q^{46} +(18.9713 + 10.9531i) q^{47} +(-1.33743 - 14.5123i) q^{48} +(27.9198 - 12.3236i) q^{50} +(12.5635 + 7.25355i) q^{51} +(75.8944 + 16.6411i) q^{52} +(32.2028 - 18.5923i) q^{53} +(3.36930 - 31.0976i) q^{54} +83.8473i q^{55} +14.9878 q^{57} +(33.1296 + 3.58946i) q^{58} +(-27.3428 - 47.3591i) q^{59} +(22.5813 + 4.95132i) q^{60} +(-5.12340 + 8.87399i) q^{61} +(10.3849 + 23.5276i) q^{62} +(-51.0441 - 38.6070i) q^{64} +(-61.6240 + 106.736i) q^{65} +(-14.2124 + 19.4304i) q^{66} +(14.8386 - 8.56706i) q^{67} +(60.7140 - 19.2978i) q^{68} +21.7892 q^{69} +32.0568 q^{71} +(-43.2670 - 48.9922i) q^{72} +(-92.8082 + 53.5828i) q^{73} +(56.1514 - 76.7671i) q^{74} +(-6.94958 + 12.0370i) q^{75} +(44.3535 - 48.6290i) q^{76} +(-32.3725 + 14.2890i) q^{78} +(29.1542 - 50.4965i) q^{79} +(82.8900 - 58.6143i) q^{80} +(-29.6436 - 51.3443i) q^{81} +(-12.9144 - 1.39922i) q^{82} -36.3441 q^{83} +101.056i q^{85} +(66.1983 + 7.17232i) q^{86} +(-13.1433 + 7.58829i) q^{87} +(20.9845 + 103.614i) q^{88} +(-0.929882 - 0.536867i) q^{89} +(94.8528 - 41.8674i) q^{90} +(64.4808 - 70.6965i) q^{92} +(-10.1434 - 5.85629i) q^{93} +(-25.8657 + 35.3622i) q^{94} +(52.2021 + 90.4167i) q^{95} +(29.1439 + 0.467106i) q^{96} -169.517i q^{97} +107.968i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 28 q^{15} + 16 q^{16} + 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} + 30 q^{24} - 32 q^{25} + 30 q^{26} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 136 q^{71} + 96 q^{72} - 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} - 276 q^{80} - 18 q^{81} + 642 q^{82} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.215431 + 1.98836i −0.107716 + 0.994182i
\(3\) −0.455431 0.788830i −0.151810 0.262943i 0.780083 0.625677i \(-0.215177\pi\)
−0.931893 + 0.362733i \(0.881844\pi\)
\(4\) −3.90718 0.856711i −0.976795 0.214178i
\(5\) 3.17251 5.49495i 0.634503 1.09899i −0.352118 0.935956i \(-0.614538\pi\)
0.986620 0.163035i \(-0.0521283\pi\)
\(6\) 1.66660 0.735624i 0.277766 0.122604i
\(7\) 0 0
\(8\) 2.54518 7.58433i 0.318148 0.948041i
\(9\) 4.08516 7.07571i 0.453907 0.786190i
\(10\) 10.2425 + 7.49189i 1.02425 + 0.749189i
\(11\) −11.4442 + 6.60732i −1.04038 + 0.600666i −0.919942 0.392054i \(-0.871764\pi\)
−0.120442 + 0.992720i \(0.538431\pi\)
\(12\) 1.10365 + 3.47227i 0.0919710 + 0.289356i
\(13\) −19.4243 −1.49418 −0.747090 0.664723i \(-0.768550\pi\)
−0.747090 + 0.664723i \(0.768550\pi\)
\(14\) 0 0
\(15\) −5.77945 −0.385296
\(16\) 14.5321 + 6.69465i 0.908256 + 0.418415i
\(17\) −13.7930 + 7.96338i −0.811352 + 0.468434i −0.847425 0.530915i \(-0.821848\pi\)
0.0360732 + 0.999349i \(0.488515\pi\)
\(18\) 13.1890 + 9.64712i 0.732723 + 0.535951i
\(19\) −8.22725 + 14.2500i −0.433013 + 0.750001i −0.997131 0.0756934i \(-0.975883\pi\)
0.564118 + 0.825694i \(0.309216\pi\)
\(20\) −17.1032 + 18.7518i −0.855158 + 0.937592i
\(21\) 0 0
\(22\) −10.6723 24.1787i −0.485105 1.09903i
\(23\) −11.9607 + 20.7166i −0.520032 + 0.900721i 0.479697 + 0.877434i \(0.340746\pi\)
−0.999729 + 0.0232870i \(0.992587\pi\)
\(24\) −7.14190 + 1.44643i −0.297579 + 0.0602677i
\(25\) −7.62967 13.2150i −0.305187 0.528599i
\(26\) 4.18461 38.6227i 0.160947 1.48549i
\(27\) −15.6398 −0.579252
\(28\) 0 0
\(29\) 16.6618i 0.574544i −0.957849 0.287272i \(-0.907252\pi\)
0.957849 0.287272i \(-0.0927483\pi\)
\(30\) 1.24507 11.4916i 0.0415024 0.383055i
\(31\) 11.1360 6.42939i 0.359227 0.207400i −0.309515 0.950895i \(-0.600167\pi\)
0.668741 + 0.743495i \(0.266833\pi\)
\(32\) −16.4421 + 27.4528i −0.513814 + 0.857901i
\(33\) 10.4241 + 6.01837i 0.315882 + 0.182375i
\(34\) −12.8627 29.1410i −0.378314 0.857089i
\(35\) 0 0
\(36\) −22.0233 + 24.1463i −0.611759 + 0.670730i
\(37\) −41.1844 23.7778i −1.11309 0.642644i −0.173463 0.984840i \(-0.555496\pi\)
−0.939628 + 0.342196i \(0.888829\pi\)
\(38\) −26.5618 19.4287i −0.698995 0.511281i
\(39\) 8.84646 + 15.3225i 0.226832 + 0.392885i
\(40\) −33.6009 38.0470i −0.840023 0.951176i
\(41\) 6.49499i 0.158415i 0.996858 + 0.0792073i \(0.0252389\pi\)
−0.996858 + 0.0792073i \(0.974761\pi\)
\(42\) 0 0
\(43\) 33.2928i 0.774252i −0.922027 0.387126i \(-0.873468\pi\)
0.922027 0.387126i \(-0.126532\pi\)
\(44\) 50.3752 16.0116i 1.14489 0.363900i
\(45\) −25.9205 44.8956i −0.576010 0.997679i
\(46\) −38.6154 28.2453i −0.839465 0.614028i
\(47\) 18.9713 + 10.9531i 0.403645 + 0.233045i 0.688056 0.725658i \(-0.258465\pi\)
−0.284411 + 0.958703i \(0.591798\pi\)
\(48\) −1.33743 14.5123i −0.0278631 0.302340i
\(49\) 0 0
\(50\) 27.9198 12.3236i 0.558397 0.246473i
\(51\) 12.5635 + 7.25355i 0.246343 + 0.142226i
\(52\) 75.8944 + 16.6411i 1.45951 + 0.320020i
\(53\) 32.2028 18.5923i 0.607601 0.350798i −0.164425 0.986390i \(-0.552577\pi\)
0.772026 + 0.635591i \(0.219244\pi\)
\(54\) 3.36930 31.0976i 0.0623945 0.575882i
\(55\) 83.8473i 1.52450i
\(56\) 0 0
\(57\) 14.9878 0.262944
\(58\) 33.1296 + 3.58946i 0.571201 + 0.0618873i
\(59\) −27.3428 47.3591i −0.463437 0.802696i 0.535693 0.844413i \(-0.320051\pi\)
−0.999129 + 0.0417169i \(0.986717\pi\)
\(60\) 22.5813 + 4.95132i 0.376356 + 0.0825219i
\(61\) −5.12340 + 8.87399i −0.0839902 + 0.145475i −0.904960 0.425496i \(-0.860100\pi\)
0.820970 + 0.570971i \(0.193433\pi\)
\(62\) 10.3849 + 23.5276i 0.167499 + 0.379477i
\(63\) 0 0
\(64\) −51.0441 38.6070i −0.797564 0.603234i
\(65\) −61.6240 + 106.736i −0.948061 + 1.64209i
\(66\) −14.2124 + 19.4304i −0.215339 + 0.294400i
\(67\) 14.8386 8.56706i 0.221471 0.127867i −0.385160 0.922850i \(-0.625854\pi\)
0.606631 + 0.794983i \(0.292520\pi\)
\(68\) 60.7140 19.2978i 0.892853 0.283791i
\(69\) 21.7892 0.315785
\(70\) 0 0
\(71\) 32.0568 0.451505 0.225752 0.974185i \(-0.427516\pi\)
0.225752 + 0.974185i \(0.427516\pi\)
\(72\) −43.2670 48.9922i −0.600931 0.680447i
\(73\) −92.8082 + 53.5828i −1.27135 + 0.734011i −0.975241 0.221144i \(-0.929021\pi\)
−0.296104 + 0.955156i \(0.595687\pi\)
\(74\) 56.1514 76.7671i 0.758802 1.03739i
\(75\) −6.94958 + 12.0370i −0.0926611 + 0.160494i
\(76\) 44.3535 48.6290i 0.583598 0.639855i
\(77\) 0 0
\(78\) −32.3725 + 14.2890i −0.415032 + 0.183193i
\(79\) 29.1542 50.4965i 0.369040 0.639196i −0.620376 0.784305i \(-0.713020\pi\)
0.989416 + 0.145109i \(0.0463532\pi\)
\(80\) 82.8900 58.6143i 1.03613 0.732679i
\(81\) −29.6436 51.3443i −0.365971 0.633880i
\(82\) −12.9144 1.39922i −0.157493 0.0170637i
\(83\) −36.3441 −0.437880 −0.218940 0.975738i \(-0.570260\pi\)
−0.218940 + 0.975738i \(0.570260\pi\)
\(84\) 0 0
\(85\) 101.056i 1.18889i
\(86\) 66.1983 + 7.17232i 0.769747 + 0.0833990i
\(87\) −13.1433 + 7.58829i −0.151072 + 0.0872217i
\(88\) 20.9845 + 103.614i 0.238460 + 1.17743i
\(89\) −0.929882 0.536867i −0.0104481 0.00603222i 0.494767 0.869026i \(-0.335253\pi\)
−0.505215 + 0.862994i \(0.668587\pi\)
\(90\) 94.8528 41.8674i 1.05392 0.465193i
\(91\) 0 0
\(92\) 64.4808 70.6965i 0.700878 0.768440i
\(93\) −10.1434 5.85629i −0.109069 0.0629709i
\(94\) −25.8657 + 35.3622i −0.275167 + 0.376194i
\(95\) 52.2021 + 90.4167i 0.549496 + 0.951755i
\(96\) 29.1439 + 0.467106i 0.303582 + 0.00486569i
\(97\) 169.517i 1.74760i −0.486286 0.873799i \(-0.661649\pi\)
0.486286 0.873799i \(-0.338351\pi\)
\(98\) 0 0
\(99\) 107.968i 1.09059i
\(100\) 18.4891 + 58.1697i 0.184891 + 0.581697i
\(101\) −14.0630 24.3579i −0.139238 0.241167i 0.787971 0.615713i \(-0.211132\pi\)
−0.927208 + 0.374546i \(0.877799\pi\)
\(102\) −17.1293 + 23.4182i −0.167934 + 0.229590i
\(103\) 144.029 + 83.1551i 1.39834 + 0.807331i 0.994219 0.107374i \(-0.0342444\pi\)
0.404120 + 0.914706i \(0.367578\pi\)
\(104\) −49.4385 + 147.321i −0.475370 + 1.41654i
\(105\) 0 0
\(106\) 30.0308 + 68.0363i 0.283309 + 0.641852i
\(107\) −171.112 98.7918i −1.59918 0.923288i −0.991645 0.128996i \(-0.958825\pi\)
−0.607536 0.794292i \(-0.707842\pi\)
\(108\) 61.1075 + 13.3988i 0.565811 + 0.124063i
\(109\) −9.97643 + 5.75990i −0.0915269 + 0.0528431i −0.545065 0.838394i \(-0.683495\pi\)
0.453538 + 0.891237i \(0.350162\pi\)
\(110\) −166.719 18.0633i −1.51563 0.164212i
\(111\) 43.3167i 0.390240i
\(112\) 0 0
\(113\) −14.7908 −0.130892 −0.0654460 0.997856i \(-0.520847\pi\)
−0.0654460 + 0.997856i \(0.520847\pi\)
\(114\) −3.22884 + 29.8012i −0.0283231 + 0.261414i
\(115\) 75.8911 + 131.447i 0.659923 + 1.14302i
\(116\) −14.2743 + 65.1005i −0.123054 + 0.561211i
\(117\) −79.3516 + 137.441i −0.678219 + 1.17471i
\(118\) 100.058 44.1648i 0.847945 0.374278i
\(119\) 0 0
\(120\) −14.7097 + 43.8332i −0.122581 + 0.365277i
\(121\) 26.8135 46.4423i 0.221599 0.383821i
\(122\) −16.5410 12.0989i −0.135582 0.0991715i
\(123\) 5.12345 2.95802i 0.0416541 0.0240490i
\(124\) −49.0186 + 15.5804i −0.395311 + 0.125648i
\(125\) 61.8047 0.494438
\(126\) 0 0
\(127\) −70.2656 −0.553272 −0.276636 0.960975i \(-0.589220\pi\)
−0.276636 + 0.960975i \(0.589220\pi\)
\(128\) 87.7612 93.1771i 0.685635 0.727946i
\(129\) −26.2624 + 15.1626i −0.203584 + 0.117540i
\(130\) −198.954 145.525i −1.53041 1.11942i
\(131\) −71.0646 + 123.088i −0.542478 + 0.939600i 0.456283 + 0.889835i \(0.349181\pi\)
−0.998761 + 0.0497649i \(0.984153\pi\)
\(132\) −35.5729 32.4453i −0.269492 0.245798i
\(133\) 0 0
\(134\) 13.8377 + 31.3501i 0.103267 + 0.233956i
\(135\) −49.6175 + 85.9400i −0.367537 + 0.636593i
\(136\) 25.2913 + 124.879i 0.185965 + 0.918226i
\(137\) −126.537 219.168i −0.923626 1.59977i −0.793756 0.608236i \(-0.791877\pi\)
−0.129870 0.991531i \(-0.541456\pi\)
\(138\) −4.69407 + 43.3248i −0.0340150 + 0.313948i
\(139\) −49.1909 −0.353892 −0.176946 0.984221i \(-0.556622\pi\)
−0.176946 + 0.984221i \(0.556622\pi\)
\(140\) 0 0
\(141\) 19.9535i 0.141514i
\(142\) −6.90605 + 63.7407i −0.0486341 + 0.448878i
\(143\) 222.296 128.343i 1.55452 0.897503i
\(144\) 106.735 75.4762i 0.741218 0.524140i
\(145\) −91.5556 52.8597i −0.631418 0.364549i
\(146\) −86.5484 196.080i −0.592797 1.34301i
\(147\) 0 0
\(148\) 140.544 + 128.187i 0.949622 + 0.866131i
\(149\) 36.1077 + 20.8468i 0.242334 + 0.139911i 0.616249 0.787551i \(-0.288652\pi\)
−0.373915 + 0.927463i \(0.621985\pi\)
\(150\) −22.4368 16.4115i −0.149579 0.109410i
\(151\) 48.8145 + 84.5492i 0.323275 + 0.559928i 0.981162 0.193188i \(-0.0618829\pi\)
−0.657887 + 0.753117i \(0.728550\pi\)
\(152\) 87.1370 + 98.6670i 0.573269 + 0.649125i
\(153\) 130.127i 0.850503i
\(154\) 0 0
\(155\) 81.5892i 0.526382i
\(156\) −21.4377 67.4466i −0.137421 0.432350i
\(157\) −14.0827 24.3919i −0.0896986 0.155363i 0.817685 0.575666i \(-0.195257\pi\)
−0.907384 + 0.420303i \(0.861924\pi\)
\(158\) 94.1246 + 68.8476i 0.595726 + 0.435744i
\(159\) −29.3324 16.9350i −0.184480 0.106510i
\(160\) 98.6895 + 177.443i 0.616809 + 1.10902i
\(161\) 0 0
\(162\) 108.477 47.8811i 0.669612 0.295563i
\(163\) 209.952 + 121.216i 1.28805 + 0.743655i 0.978306 0.207165i \(-0.0664237\pi\)
0.309743 + 0.950820i \(0.399757\pi\)
\(164\) 5.56433 25.3771i 0.0339289 0.154738i
\(165\) 66.1413 38.1867i 0.400856 0.231434i
\(166\) 7.82965 72.2652i 0.0471665 0.435333i
\(167\) 60.1108i 0.359945i −0.983672 0.179972i \(-0.942399\pi\)
0.983672 0.179972i \(-0.0576008\pi\)
\(168\) 0 0
\(169\) 208.305 1.23257
\(170\) −200.936 21.7706i −1.18197 0.128062i
\(171\) 67.2193 + 116.427i 0.393096 + 0.680861i
\(172\) −28.5223 + 130.081i −0.165828 + 0.756285i
\(173\) 69.6820 120.693i 0.402786 0.697646i −0.591275 0.806470i \(-0.701375\pi\)
0.994061 + 0.108824i \(0.0347085\pi\)
\(174\) −12.2568 27.7684i −0.0704414 0.159589i
\(175\) 0 0
\(176\) −210.542 + 19.4032i −1.19626 + 0.110246i
\(177\) −24.9055 + 43.1376i −0.140709 + 0.243715i
\(178\) 1.26781 1.73328i 0.00712255 0.00973755i
\(179\) −252.643 + 145.863i −1.41141 + 0.814879i −0.995522 0.0945354i \(-0.969863\pi\)
−0.415891 + 0.909415i \(0.636530\pi\)
\(180\) 62.8134 + 197.621i 0.348963 + 1.09790i
\(181\) 166.844 0.921791 0.460895 0.887455i \(-0.347528\pi\)
0.460895 + 0.887455i \(0.347528\pi\)
\(182\) 0 0
\(183\) 9.33343 0.0510024
\(184\) 126.679 + 143.442i 0.688474 + 0.779574i
\(185\) −261.316 + 150.871i −1.41252 + 0.815518i
\(186\) 13.8296 18.9071i 0.0743529 0.101651i
\(187\) 105.233 182.269i 0.562745 0.974703i
\(188\) −64.7407 59.0486i −0.344365 0.314088i
\(189\) 0 0
\(190\) −191.027 + 84.3182i −1.00541 + 0.443780i
\(191\) 65.6781 113.758i 0.343864 0.595590i −0.641283 0.767305i \(-0.721597\pi\)
0.985147 + 0.171715i \(0.0549307\pi\)
\(192\) −7.20727 + 57.8480i −0.0375379 + 0.301292i
\(193\) 40.7196 + 70.5284i 0.210982 + 0.365432i 0.952022 0.306029i \(-0.0990004\pi\)
−0.741040 + 0.671461i \(0.765667\pi\)
\(194\) 337.062 + 36.5193i 1.73743 + 0.188244i
\(195\) 112.262 0.575702
\(196\) 0 0
\(197\) 2.09549i 0.0106370i −0.999986 0.00531851i \(-0.998307\pi\)
0.999986 0.00531851i \(-0.00169294\pi\)
\(198\) −214.680 23.2597i −1.08424 0.117473i
\(199\) 109.937 63.4721i 0.552447 0.318955i −0.197662 0.980270i \(-0.563335\pi\)
0.750108 + 0.661315i \(0.230001\pi\)
\(200\) −119.646 + 24.2314i −0.598228 + 0.121157i
\(201\) −13.5159 7.80341i −0.0672433 0.0388230i
\(202\) 51.4619 22.7149i 0.254762 0.112450i
\(203\) 0 0
\(204\) −42.8737 39.1042i −0.210165 0.191687i
\(205\) 35.6897 + 20.6055i 0.174096 + 0.100514i
\(206\) −196.371 + 268.468i −0.953257 + 1.30324i
\(207\) 97.7231 + 169.261i 0.472092 + 0.817687i
\(208\) −282.276 130.039i −1.35710 0.625188i
\(209\) 217.440i 1.04038i
\(210\) 0 0
\(211\) 7.16822i 0.0339726i 0.999856 + 0.0169863i \(0.00540717\pi\)
−0.999856 + 0.0169863i \(0.994593\pi\)
\(212\) −141.750 + 45.0550i −0.668634 + 0.212523i
\(213\) −14.5997 25.2874i −0.0685432 0.118720i
\(214\) 233.297 318.951i 1.09017 1.49042i
\(215\) −182.943 105.622i −0.850896 0.491265i
\(216\) −39.8062 + 118.617i −0.184288 + 0.549155i
\(217\) 0 0
\(218\) −9.30353 21.0776i −0.0426768 0.0966864i
\(219\) 84.5355 + 48.8066i 0.386007 + 0.222861i
\(220\) 71.8329 327.606i 0.326513 1.48912i
\(221\) 267.920 154.683i 1.21231 0.699925i
\(222\) −86.1293 9.33176i −0.387970 0.0420350i
\(223\) 279.720i 1.25435i 0.778878 + 0.627175i \(0.215789\pi\)
−0.778878 + 0.627175i \(0.784211\pi\)
\(224\) 0 0
\(225\) −124.674 −0.554106
\(226\) 3.18640 29.4095i 0.0140991 0.130130i
\(227\) −152.392 263.950i −0.671330 1.16278i −0.977527 0.210809i \(-0.932390\pi\)
0.306198 0.951968i \(-0.400943\pi\)
\(228\) −58.5600 12.8402i −0.256842 0.0563167i
\(229\) 207.344 359.130i 0.905433 1.56826i 0.0850971 0.996373i \(-0.472880\pi\)
0.820335 0.571883i \(-0.193787\pi\)
\(230\) −277.714 + 122.581i −1.20745 + 0.532962i
\(231\) 0 0
\(232\) −126.368 42.4072i −0.544691 0.182790i
\(233\) 82.4628 142.830i 0.353918 0.613004i −0.633014 0.774140i \(-0.718183\pi\)
0.986932 + 0.161136i \(0.0515159\pi\)
\(234\) −256.188 187.389i −1.09482 0.800808i
\(235\) 120.373 69.4976i 0.512227 0.295735i
\(236\) 66.2601 + 208.465i 0.280763 + 0.883327i
\(237\) −53.1109 −0.224097
\(238\) 0 0
\(239\) −19.1182 −0.0799926 −0.0399963 0.999200i \(-0.512735\pi\)
−0.0399963 + 0.999200i \(0.512735\pi\)
\(240\) −83.9875 38.6914i −0.349948 0.161214i
\(241\) 303.376 175.154i 1.25882 0.726780i 0.285975 0.958237i \(-0.407683\pi\)
0.972845 + 0.231457i \(0.0743492\pi\)
\(242\) 86.5677 + 63.3201i 0.357718 + 0.261653i
\(243\) −97.3804 + 168.668i −0.400743 + 0.694106i
\(244\) 27.6205 30.2830i 0.113199 0.124111i
\(245\) 0 0
\(246\) 4.77788 + 10.8245i 0.0194223 + 0.0440022i
\(247\) 159.809 276.797i 0.647000 1.12064i
\(248\) −20.4194 100.823i −0.0823362 0.406545i
\(249\) 16.5522 + 28.6693i 0.0664748 + 0.115138i
\(250\) −13.3147 + 122.890i −0.0532587 + 0.491561i
\(251\) −88.3204 −0.351874 −0.175937 0.984401i \(-0.556296\pi\)
−0.175937 + 0.984401i \(0.556296\pi\)
\(252\) 0 0
\(253\) 316.114i 1.24946i
\(254\) 15.1374 139.714i 0.0595961 0.550053i
\(255\) 79.7158 46.0240i 0.312611 0.180486i
\(256\) 166.363 + 194.574i 0.649857 + 0.760056i
\(257\) −74.5499 43.0414i −0.290077 0.167476i 0.347899 0.937532i \(-0.386895\pi\)
−0.637977 + 0.770056i \(0.720228\pi\)
\(258\) −24.4910 55.4857i −0.0949265 0.215061i
\(259\) 0 0
\(260\) 332.218 364.242i 1.27776 1.40093i
\(261\) −117.894 68.0661i −0.451701 0.260789i
\(262\) −229.433 167.819i −0.875699 0.640531i
\(263\) −159.605 276.444i −0.606863 1.05112i −0.991754 0.128156i \(-0.959094\pi\)
0.384891 0.922962i \(-0.374239\pi\)
\(264\) 72.1765 63.7421i 0.273396 0.241447i
\(265\) 235.937i 0.890330i
\(266\) 0 0
\(267\) 0.978025i 0.00366302i
\(268\) −65.3165 + 20.7607i −0.243718 + 0.0774651i
\(269\) 28.7340 + 49.7687i 0.106818 + 0.185014i 0.914479 0.404632i \(-0.132601\pi\)
−0.807662 + 0.589646i \(0.799267\pi\)
\(270\) −160.191 117.172i −0.593300 0.433970i
\(271\) −26.7398 15.4382i −0.0986709 0.0569677i 0.449853 0.893103i \(-0.351477\pi\)
−0.548523 + 0.836135i \(0.684810\pi\)
\(272\) −253.753 + 23.3855i −0.932915 + 0.0859759i
\(273\) 0 0
\(274\) 463.046 204.385i 1.68995 0.745932i
\(275\) 174.631 + 100.823i 0.635023 + 0.366631i
\(276\) −85.1341 18.6670i −0.308457 0.0676341i
\(277\) −308.465 + 178.092i −1.11359 + 0.642933i −0.939757 0.341842i \(-0.888949\pi\)
−0.173834 + 0.984775i \(0.555616\pi\)
\(278\) 10.5973 97.8095i 0.0381197 0.351833i
\(279\) 105.060i 0.376561i
\(280\) 0 0
\(281\) −294.160 −1.04683 −0.523416 0.852077i \(-0.675343\pi\)
−0.523416 + 0.852077i \(0.675343\pi\)
\(282\) 39.6749 + 4.29861i 0.140691 + 0.0152433i
\(283\) 207.501 + 359.402i 0.733219 + 1.26997i 0.955501 + 0.294989i \(0.0953161\pi\)
−0.222282 + 0.974982i \(0.571351\pi\)
\(284\) −125.252 27.4635i −0.441028 0.0967023i
\(285\) 47.5490 82.3572i 0.166838 0.288973i
\(286\) 207.303 + 469.655i 0.724835 + 1.64215i
\(287\) 0 0
\(288\) 127.080 + 228.489i 0.441250 + 0.793363i
\(289\) −17.6691 + 30.6037i −0.0611386 + 0.105895i
\(290\) 124.828 170.658i 0.430442 0.588477i
\(291\) −133.720 + 77.2034i −0.459520 + 0.265304i
\(292\) 408.523 129.848i 1.39905 0.444685i
\(293\) −370.564 −1.26472 −0.632362 0.774673i \(-0.717915\pi\)
−0.632362 + 0.774673i \(0.717915\pi\)
\(294\) 0 0
\(295\) −346.981 −1.17621
\(296\) −285.161 + 251.837i −0.963380 + 0.850801i
\(297\) 178.986 103.337i 0.602645 0.347937i
\(298\) −49.2298 + 67.3042i −0.165201 + 0.225853i
\(299\) 232.329 402.406i 0.777021 1.34584i
\(300\) 37.4655 41.0770i 0.124885 0.136923i
\(301\) 0 0
\(302\) −178.631 + 78.8464i −0.591492 + 0.261081i
\(303\) −12.8095 + 22.1867i −0.0422755 + 0.0732233i
\(304\) −214.958 + 152.004i −0.707099 + 0.500013i
\(305\) 32.5081 + 56.3057i 0.106584 + 0.184609i
\(306\) −258.740 28.0334i −0.845554 0.0916124i
\(307\) −160.327 −0.522239 −0.261120 0.965306i \(-0.584092\pi\)
−0.261120 + 0.965306i \(0.584092\pi\)
\(308\) 0 0
\(309\) 151.486i 0.490245i
\(310\) 162.229 + 17.5769i 0.523320 + 0.0566996i
\(311\) −409.490 + 236.419i −1.31669 + 0.760191i −0.983195 0.182561i \(-0.941561\pi\)
−0.333495 + 0.942752i \(0.608228\pi\)
\(312\) 138.727 28.0959i 0.444637 0.0900508i
\(313\) −200.063 115.506i −0.639179 0.369030i 0.145119 0.989414i \(-0.453643\pi\)
−0.784298 + 0.620384i \(0.786977\pi\)
\(314\) 51.5339 22.7467i 0.164121 0.0724418i
\(315\) 0 0
\(316\) −157.171 + 172.322i −0.497378 + 0.545323i
\(317\) 195.132 + 112.659i 0.615557 + 0.355392i 0.775137 0.631793i \(-0.217681\pi\)
−0.159580 + 0.987185i \(0.551014\pi\)
\(318\) 39.9921 54.6751i 0.125761 0.171934i
\(319\) 110.090 + 190.681i 0.345109 + 0.597746i
\(320\) −374.082 + 158.004i −1.16901 + 0.493762i
\(321\) 179.972i 0.560659i
\(322\) 0 0
\(323\) 262.067i 0.811353i
\(324\) 71.8357 + 226.007i 0.221715 + 0.697553i
\(325\) 148.201 + 256.692i 0.456004 + 0.789822i
\(326\) −286.251 + 391.347i −0.878072 + 1.20045i
\(327\) 9.08716 + 5.24648i 0.0277895 + 0.0160443i
\(328\) 49.2602 + 16.5309i 0.150183 + 0.0503992i
\(329\) 0 0
\(330\) 61.6801 + 139.740i 0.186909 + 0.423453i
\(331\) −17.9257 10.3494i −0.0541561 0.0312671i 0.472677 0.881236i \(-0.343288\pi\)
−0.526834 + 0.849968i \(0.676621\pi\)
\(332\) 142.003 + 31.1364i 0.427719 + 0.0937842i
\(333\) −336.490 + 194.273i −1.01048 + 0.583401i
\(334\) 119.522 + 12.9497i 0.357851 + 0.0387717i
\(335\) 108.716i 0.324527i
\(336\) 0 0
\(337\) 34.9645 0.103752 0.0518762 0.998654i \(-0.483480\pi\)
0.0518762 + 0.998654i \(0.483480\pi\)
\(338\) −44.8754 + 414.186i −0.132768 + 1.22540i
\(339\) 6.73619 + 11.6674i 0.0198708 + 0.0344172i
\(340\) 86.5756 394.843i 0.254634 1.16130i
\(341\) −84.9621 + 147.159i −0.249156 + 0.431550i
\(342\) −245.981 + 108.574i −0.719243 + 0.317469i
\(343\) 0 0
\(344\) −252.504 84.7363i −0.734023 0.246326i
\(345\) 69.1264 119.730i 0.200366 0.347045i
\(346\) 224.969 + 164.554i 0.650201 + 0.475590i
\(347\) 379.958 219.369i 1.09498 0.632188i 0.160083 0.987104i \(-0.448824\pi\)
0.934898 + 0.354916i \(0.115491\pi\)
\(348\) 57.8542 18.3888i 0.166248 0.0528414i
\(349\) 435.121 1.24677 0.623383 0.781917i \(-0.285758\pi\)
0.623383 + 0.781917i \(0.285758\pi\)
\(350\) 0 0
\(351\) 303.793 0.865507
\(352\) 6.77670 422.814i 0.0192520 1.20118i
\(353\) −243.447 + 140.554i −0.689653 + 0.398171i −0.803482 0.595329i \(-0.797022\pi\)
0.113829 + 0.993500i \(0.463688\pi\)
\(354\) −80.4078 58.8144i −0.227141 0.166142i
\(355\) 101.701 176.151i 0.286481 0.496200i
\(356\) 3.17327 + 2.89428i 0.00891369 + 0.00812999i
\(357\) 0 0
\(358\) −235.602 533.769i −0.658107 1.49098i
\(359\) −131.965 + 228.570i −0.367590 + 0.636685i −0.989188 0.146652i \(-0.953150\pi\)
0.621598 + 0.783336i \(0.286484\pi\)
\(360\) −406.475 + 82.3220i −1.12910 + 0.228672i
\(361\) 45.1247 + 78.1583i 0.124999 + 0.216505i
\(362\) −35.9434 + 331.747i −0.0992912 + 0.916427i
\(363\) −48.8468 −0.134564
\(364\) 0 0
\(365\) 679.969i 1.86293i
\(366\) −2.01071 + 18.5583i −0.00549375 + 0.0507056i
\(367\) 134.181 77.4694i 0.365615 0.211088i −0.305926 0.952055i \(-0.598966\pi\)
0.671541 + 0.740967i \(0.265633\pi\)
\(368\) −312.505 + 220.982i −0.849197 + 0.600496i
\(369\) 45.9567 + 26.5331i 0.124544 + 0.0719055i
\(370\) −243.691 552.094i −0.658623 1.49214i
\(371\) 0 0
\(372\) 34.6149 + 31.5715i 0.0930508 + 0.0848697i
\(373\) 506.505 + 292.431i 1.35792 + 0.783997i 0.989344 0.145600i \(-0.0465112\pi\)
0.368579 + 0.929597i \(0.379845\pi\)
\(374\) 339.747 + 248.509i 0.908415 + 0.664462i
\(375\) −28.1478 48.7534i −0.0750608 0.130009i
\(376\) 131.357 116.007i 0.349355 0.308529i
\(377\) 323.644i 0.858472i
\(378\) 0 0
\(379\) 128.176i 0.338195i −0.985599 0.169098i \(-0.945915\pi\)
0.985599 0.169098i \(-0.0540853\pi\)
\(380\) −126.502 397.996i −0.332900 1.04736i
\(381\) 32.0011 + 55.4276i 0.0839925 + 0.145479i
\(382\) 212.043 + 155.099i 0.555085 + 0.406018i
\(383\) 216.437 + 124.960i 0.565110 + 0.326266i 0.755194 0.655502i \(-0.227543\pi\)
−0.190084 + 0.981768i \(0.560876\pi\)
\(384\) −113.470 26.7929i −0.295495 0.0697733i
\(385\) 0 0
\(386\) −149.008 + 65.7713i −0.386032 + 0.170392i
\(387\) −235.571 136.007i −0.608709 0.351439i
\(388\) −145.227 + 662.334i −0.374297 + 1.70705i
\(389\) 187.428 108.212i 0.481821 0.278179i −0.239354 0.970932i \(-0.576936\pi\)
0.721175 + 0.692753i \(0.243602\pi\)
\(390\) −24.1847 + 223.218i −0.0620121 + 0.572353i
\(391\) 380.991i 0.974402i
\(392\) 0 0
\(393\) 129.460 0.329415
\(394\) 4.16660 + 0.451434i 0.0105751 + 0.00114577i
\(395\) −184.984 320.401i −0.468314 0.811143i
\(396\) 92.4974 421.850i 0.233579 1.06528i
\(397\) −349.941 + 606.116i −0.881463 + 1.52674i −0.0317493 + 0.999496i \(0.510108\pi\)
−0.849714 + 0.527244i \(0.823226\pi\)
\(398\) 102.522 + 232.268i 0.257592 + 0.583589i
\(399\) 0 0
\(400\) −22.4055 243.119i −0.0560137 0.607798i
\(401\) 90.4903 156.734i 0.225662 0.390858i −0.730856 0.682532i \(-0.760879\pi\)
0.956518 + 0.291674i \(0.0942123\pi\)
\(402\) 18.4278 25.1934i 0.0458402 0.0626703i
\(403\) −216.310 + 124.887i −0.536749 + 0.309892i
\(404\) 34.0791 + 107.218i 0.0843541 + 0.265392i
\(405\) −376.179 −0.928837
\(406\) 0 0
\(407\) 628.431 1.54406
\(408\) 86.9897 76.8242i 0.213210 0.188295i
\(409\) 310.767 179.421i 0.759821 0.438683i −0.0694104 0.997588i \(-0.522112\pi\)
0.829232 + 0.558905i \(0.188778\pi\)
\(410\) −48.6598 + 66.5250i −0.118682 + 0.162256i
\(411\) −115.258 + 199.632i −0.280432 + 0.485723i
\(412\) −491.507 448.293i −1.19298 1.08809i
\(413\) 0 0
\(414\) −357.606 + 157.845i −0.863782 + 0.381268i
\(415\) −115.302 + 199.709i −0.277836 + 0.481226i
\(416\) 319.376 533.253i 0.767731 1.28186i
\(417\) 22.4031 + 38.8033i 0.0537245 + 0.0930535i
\(418\) 432.351 + 46.8435i 1.03433 + 0.112066i
\(419\) 780.890 1.86370 0.931849 0.362846i \(-0.118195\pi\)
0.931849 + 0.362846i \(0.118195\pi\)
\(420\) 0 0
\(421\) 114.961i 0.273068i 0.990635 + 0.136534i \(0.0435962\pi\)
−0.990635 + 0.136534i \(0.956404\pi\)
\(422\) −14.2530 1.54426i −0.0337749 0.00365938i
\(423\) 155.002 89.4904i 0.366435 0.211561i
\(424\) −59.0482 291.558i −0.139265 0.687636i
\(425\) 210.472 + 121.516i 0.495228 + 0.285920i
\(426\) 53.4258 23.5818i 0.125413 0.0553563i
\(427\) 0 0
\(428\) 583.931 + 532.591i 1.36432 + 1.24437i
\(429\) −202.482 116.903i −0.471985 0.272501i
\(430\) 249.426 341.002i 0.580061 0.793028i
\(431\) −154.856 268.219i −0.359295 0.622317i 0.628548 0.777771i \(-0.283649\pi\)
−0.987843 + 0.155453i \(0.950316\pi\)
\(432\) −227.279 104.703i −0.526109 0.242368i
\(433\) 595.775i 1.37592i 0.725747 + 0.687962i \(0.241494\pi\)
−0.725747 + 0.687962i \(0.758506\pi\)
\(434\) 0 0
\(435\) 96.2958i 0.221370i
\(436\) 43.9143 13.9580i 0.100721 0.0320138i
\(437\) −196.808 340.881i −0.450361 0.780048i
\(438\) −115.257 + 157.573i −0.263144 + 0.359755i
\(439\) −698.796 403.450i −1.59179 0.919020i −0.993000 0.118113i \(-0.962315\pi\)
−0.598789 0.800907i \(-0.704351\pi\)
\(440\) 635.925 + 213.407i 1.44529 + 0.485015i
\(441\) 0 0
\(442\) 249.849 + 566.045i 0.565269 + 1.28065i
\(443\) −385.214 222.403i −0.869557 0.502039i −0.00235617 0.999997i \(-0.500750\pi\)
−0.867201 + 0.497958i \(0.834083\pi\)
\(444\) 37.1099 169.246i 0.0835808 0.381185i
\(445\) −5.90012 + 3.40644i −0.0132587 + 0.00765491i
\(446\) −556.185 60.2605i −1.24705 0.135113i
\(447\) 37.9772i 0.0849601i
\(448\) 0 0
\(449\) 262.420 0.584455 0.292228 0.956349i \(-0.405604\pi\)
0.292228 + 0.956349i \(0.405604\pi\)
\(450\) 26.8586 247.897i 0.0596859 0.550882i
\(451\) −42.9145 74.3302i −0.0951542 0.164812i
\(452\) 57.7903 + 12.6714i 0.127855 + 0.0280342i
\(453\) 44.4633 77.0127i 0.0981530 0.170006i
\(454\) 557.659 246.147i 1.22832 0.542174i
\(455\) 0 0
\(456\) 38.1466 113.672i 0.0836549 0.249281i
\(457\) −194.738 + 337.296i −0.426122 + 0.738065i −0.996524 0.0833004i \(-0.973454\pi\)
0.570403 + 0.821365i \(0.306787\pi\)
\(458\) 669.413 + 489.643i 1.46160 + 1.06909i
\(459\) 215.720 124.546i 0.469978 0.271342i
\(460\) −183.908 578.605i −0.399800 1.25784i
\(461\) 158.714 0.344283 0.172141 0.985072i \(-0.444931\pi\)
0.172141 + 0.985072i \(0.444931\pi\)
\(462\) 0 0
\(463\) −528.844 −1.14221 −0.571106 0.820877i \(-0.693485\pi\)
−0.571106 + 0.820877i \(0.693485\pi\)
\(464\) 111.545 242.130i 0.240398 0.521833i
\(465\) −64.3601 + 37.1583i −0.138409 + 0.0799103i
\(466\) 266.233 + 194.736i 0.571314 + 0.417889i
\(467\) −218.449 + 378.365i −0.467771 + 0.810203i −0.999322 0.0368236i \(-0.988276\pi\)
0.531551 + 0.847026i \(0.321609\pi\)
\(468\) 427.788 469.025i 0.914078 1.00219i
\(469\) 0 0
\(470\) 112.254 + 254.318i 0.238839 + 0.541102i
\(471\) −12.8274 + 22.2177i −0.0272344 + 0.0471713i
\(472\) −428.779 + 86.8392i −0.908430 + 0.183981i
\(473\) 219.977 + 381.011i 0.465067 + 0.805519i
\(474\) 11.4417 105.604i 0.0241387 0.222793i
\(475\) 251.085 0.528600
\(476\) 0 0
\(477\) 303.811i 0.636920i
\(478\) 4.11866 38.0140i 0.00861645 0.0795272i
\(479\) −472.737 + 272.935i −0.986925 + 0.569802i −0.904354 0.426783i \(-0.859647\pi\)
−0.0825716 + 0.996585i \(0.526313\pi\)
\(480\) 95.0260 158.662i 0.197971 0.330546i
\(481\) 799.980 + 461.869i 1.66316 + 0.960226i
\(482\) 282.913 + 640.955i 0.586957 + 1.32978i
\(483\) 0 0
\(484\) −144.553 + 158.487i −0.298663 + 0.327453i
\(485\) −931.488 537.795i −1.92059 1.10886i
\(486\) −314.394 229.964i −0.646902 0.473177i
\(487\) −324.115 561.384i −0.665534 1.15274i −0.979140 0.203185i \(-0.934871\pi\)
0.313606 0.949553i \(-0.398463\pi\)
\(488\) 54.2633 + 61.4435i 0.111195 + 0.125909i
\(489\) 220.822i 0.451579i
\(490\) 0 0
\(491\) 732.074i 1.49098i 0.666514 + 0.745492i \(0.267786\pi\)
−0.666514 + 0.745492i \(0.732214\pi\)
\(492\) −22.5524 + 7.16822i −0.0458382 + 0.0145695i
\(493\) 132.684 + 229.815i 0.269136 + 0.466157i
\(494\) 515.946 + 377.389i 1.04442 + 0.763945i
\(495\) 593.279 + 342.530i 1.19854 + 0.691980i
\(496\) 204.872 18.8807i 0.413049 0.0380659i
\(497\) 0 0
\(498\) −60.5709 + 26.7356i −0.121628 + 0.0536859i
\(499\) −23.1264 13.3520i −0.0463454 0.0267575i 0.476648 0.879094i \(-0.341852\pi\)
−0.522994 + 0.852337i \(0.675185\pi\)
\(500\) −241.482 52.9488i −0.482964 0.105898i
\(501\) −47.4172 + 27.3763i −0.0946451 + 0.0546434i
\(502\) 19.0270 175.613i 0.0379023 0.349827i
\(503\) 616.414i 1.22548i −0.790286 0.612738i \(-0.790068\pi\)
0.790286 0.612738i \(-0.209932\pi\)
\(504\) 0 0
\(505\) −178.460 −0.353387
\(506\) 628.549 + 68.1007i 1.24219 + 0.134586i
\(507\) −94.8687 164.317i −0.187118 0.324097i
\(508\) 274.540 + 60.1973i 0.540433 + 0.118499i
\(509\) −66.3763 + 114.967i −0.130405 + 0.225869i −0.923833 0.382796i \(-0.874961\pi\)
0.793428 + 0.608665i \(0.208295\pi\)
\(510\) 74.3391 + 168.419i 0.145763 + 0.330233i
\(511\) 0 0
\(512\) −422.725 + 288.874i −0.825634 + 0.564206i
\(513\) 128.673 222.868i 0.250824 0.434440i
\(514\) 101.642 138.960i 0.197748 0.270350i
\(515\) 913.867 527.621i 1.77450 1.02451i
\(516\) 115.602 36.7437i 0.224035 0.0712087i
\(517\) −289.483 −0.559928
\(518\) 0 0
\(519\) −126.942 −0.244589
\(520\) 652.676 + 739.039i 1.25515 + 1.42123i
\(521\) 585.480 338.027i 1.12376 0.648804i 0.181403 0.983409i \(-0.441936\pi\)
0.942359 + 0.334605i \(0.108603\pi\)
\(522\) 160.738 219.752i 0.307927 0.420981i
\(523\) −186.224 + 322.550i −0.356069 + 0.616730i −0.987300 0.158865i \(-0.949217\pi\)
0.631231 + 0.775595i \(0.282550\pi\)
\(524\) 383.113 420.043i 0.731131 0.801609i
\(525\) 0 0
\(526\) 584.055 257.798i 1.11037 0.490110i
\(527\) −102.399 + 177.361i −0.194306 + 0.336548i
\(528\) 111.193 + 157.245i 0.210594 + 0.297813i
\(529\) −21.6179 37.4433i −0.0408656 0.0707813i
\(530\) 469.129 + 50.8283i 0.885150 + 0.0959024i
\(531\) −446.799 −0.841429
\(532\) 0 0
\(533\) 126.161i 0.236700i
\(534\) −1.94467 0.210697i −0.00364170 0.000394564i
\(535\) −1085.71 + 626.836i −2.02937 + 1.17166i
\(536\) −27.2085 134.345i −0.0507622 0.250644i
\(537\) 230.123 + 132.862i 0.428534 + 0.247414i
\(538\) −105.148 + 46.4119i −0.195443 + 0.0862674i
\(539\) 0 0
\(540\) 267.490 293.275i 0.495352 0.543102i
\(541\) 60.3373 + 34.8357i 0.111529 + 0.0643914i 0.554727 0.832032i \(-0.312823\pi\)
−0.443198 + 0.896424i \(0.646156\pi\)
\(542\) 36.4574 49.8426i 0.0672646 0.0919605i
\(543\) −75.9860 131.612i −0.139937 0.242379i
\(544\) 8.16752 509.591i 0.0150138 0.936748i
\(545\) 73.0934i 0.134116i
\(546\) 0 0
\(547\) 466.463i 0.852765i 0.904543 + 0.426383i \(0.140212\pi\)
−0.904543 + 0.426383i \(0.859788\pi\)
\(548\) 306.638 + 964.734i 0.559558 + 1.76046i
\(549\) 41.8599 + 72.5034i 0.0762475 + 0.132065i
\(550\) −238.095 + 325.510i −0.432899 + 0.591836i
\(551\) 237.430 + 137.081i 0.430908 + 0.248785i
\(552\) 55.4574 165.256i 0.100466 0.299377i
\(553\) 0 0
\(554\) −287.659 651.707i −0.519241 1.17637i
\(555\) 238.023 + 137.423i 0.428870 + 0.247608i
\(556\) 192.198 + 42.1424i 0.345679 + 0.0757957i
\(557\) 118.835 68.6094i 0.213348 0.123177i −0.389518 0.921019i \(-0.627358\pi\)
0.602866 + 0.797842i \(0.294025\pi\)
\(558\) 208.898 + 22.6333i 0.374370 + 0.0405615i
\(559\) 646.692i 1.15687i
\(560\) 0 0
\(561\) −191.706 −0.341722
\(562\) 63.3712 584.897i 0.112760 1.04074i
\(563\) −84.5632 146.468i −0.150201 0.260156i 0.781100 0.624406i \(-0.214659\pi\)
−0.931301 + 0.364250i \(0.881325\pi\)
\(564\) −17.0944 + 77.9620i −0.0303092 + 0.138231i
\(565\) −46.9240 + 81.2747i −0.0830513 + 0.143849i
\(566\) −759.324 + 335.161i −1.34156 + 0.592157i
\(567\) 0 0
\(568\) 81.5905 243.130i 0.143645 0.428045i
\(569\) −372.466 + 645.129i −0.654597 + 1.13379i 0.327398 + 0.944887i \(0.393828\pi\)
−0.981995 + 0.188908i \(0.939505\pi\)
\(570\) 153.513 + 112.287i 0.269320 + 0.196995i
\(571\) −767.828 + 443.306i −1.34471 + 0.776367i −0.987494 0.157655i \(-0.949606\pi\)
−0.357213 + 0.934023i \(0.616273\pi\)
\(572\) −978.505 + 311.015i −1.71067 + 0.543732i
\(573\) −119.647 −0.208809
\(574\) 0 0
\(575\) 365.026 0.634827
\(576\) −481.696 + 203.458i −0.836277 + 0.353225i
\(577\) 207.900 120.031i 0.360311 0.208026i −0.308906 0.951093i \(-0.599963\pi\)
0.669217 + 0.743067i \(0.266630\pi\)
\(578\) −57.0448 41.7255i −0.0986935 0.0721894i
\(579\) 37.0900 64.2417i 0.0640586 0.110953i
\(580\) 312.439 + 284.969i 0.538687 + 0.491326i
\(581\) 0 0
\(582\) −124.701 282.516i −0.214263 0.485423i
\(583\) −245.691 + 425.549i −0.421425 + 0.729930i
\(584\) 170.176 + 840.266i 0.291398 + 1.43881i
\(585\) 503.488 + 872.067i 0.860663 + 1.49071i
\(586\) 79.8311 736.817i 0.136231 1.25737i
\(587\) 190.873 0.325168 0.162584 0.986695i \(-0.448017\pi\)
0.162584 + 0.986695i \(0.448017\pi\)
\(588\) 0 0
\(589\) 211.585i 0.359227i
\(590\) 74.7506 689.925i 0.126696 1.16936i
\(591\) −1.65299 + 0.954353i −0.00279693 + 0.00161481i
\(592\) −439.311 621.256i −0.742080 1.04942i
\(593\) −637.548 368.089i −1.07512 0.620723i −0.145547 0.989351i \(-0.546494\pi\)
−0.929577 + 0.368629i \(0.879827\pi\)
\(594\) 166.913 + 378.150i 0.280998 + 0.636617i
\(595\) 0 0
\(596\) −123.220 112.386i −0.206744 0.188567i
\(597\) −100.137 57.8144i −0.167734 0.0968415i
\(598\) 750.078 + 548.646i 1.25431 + 0.917468i
\(599\) −558.330 967.057i −0.932104 1.61445i −0.779718 0.626131i \(-0.784638\pi\)
−0.152386 0.988321i \(-0.548696\pi\)
\(600\) 73.6049 + 83.3444i 0.122675 + 0.138907i
\(601\) 183.100i 0.304659i −0.988330 0.152329i \(-0.951323\pi\)
0.988330 0.152329i \(-0.0486774\pi\)
\(602\) 0 0
\(603\) 139.991i 0.232158i
\(604\) −118.293 372.169i −0.195849 0.616173i
\(605\) −170.132 294.678i −0.281210 0.487071i
\(606\) −41.3556 30.2496i −0.0682436 0.0499168i
\(607\) −394.026 227.491i −0.649136 0.374779i 0.138989 0.990294i \(-0.455615\pi\)
−0.788125 + 0.615515i \(0.788948\pi\)
\(608\) −255.931 460.161i −0.420938 0.756844i
\(609\) 0 0
\(610\) −118.959 + 52.5079i −0.195015 + 0.0860786i
\(611\) −368.505 212.757i −0.603118 0.348211i
\(612\) 111.481 508.429i 0.182159 0.830767i
\(613\) −232.853 + 134.438i −0.379859 + 0.219312i −0.677757 0.735286i \(-0.737048\pi\)
0.297898 + 0.954598i \(0.403714\pi\)
\(614\) 34.5395 318.789i 0.0562533 0.519201i
\(615\) 37.5375i 0.0610366i
\(616\) 0 0
\(617\) −184.934 −0.299731 −0.149866 0.988706i \(-0.547884\pi\)
−0.149866 + 0.988706i \(0.547884\pi\)
\(618\) 301.209 + 32.6348i 0.487393 + 0.0528071i
\(619\) −496.809 860.498i −0.802599 1.39014i −0.917900 0.396812i \(-0.870116\pi\)
0.115301 0.993331i \(-0.463217\pi\)
\(620\) −69.8984 + 318.784i −0.112739 + 0.514167i
\(621\) 187.064 324.004i 0.301229 0.521745i
\(622\) −381.871 865.148i −0.613940 1.39091i
\(623\) 0 0
\(624\) 25.9787 + 281.892i 0.0416325 + 0.451750i
\(625\) 386.818 669.988i 0.618909 1.07198i
\(626\) 272.769 372.914i 0.435732 0.595710i
\(627\) −171.524 + 99.0292i −0.273562 + 0.157941i
\(628\) 34.1267 + 107.368i 0.0543419 + 0.170969i
\(629\) 757.408 1.20415
\(630\) 0 0
\(631\) 805.857 1.27711 0.638555 0.769576i \(-0.279532\pi\)
0.638555 + 0.769576i \(0.279532\pi\)
\(632\) −308.779 349.637i −0.488575 0.553224i
\(633\) 5.65451 3.26463i 0.00893287 0.00515740i
\(634\) −266.045 + 363.722i −0.419629 + 0.573694i
\(635\) −222.918 + 386.106i −0.351053 + 0.608041i
\(636\) 100.098 + 91.2976i 0.157387 + 0.143550i
\(637\) 0 0
\(638\) −402.860 + 177.820i −0.631442 + 0.278714i
\(639\) 130.957 226.825i 0.204941 0.354969i
\(640\) −233.580 777.849i −0.364969 1.21539i
\(641\) −2.75221 4.76696i −0.00429361 0.00743676i 0.863871 0.503714i \(-0.168033\pi\)
−0.868164 + 0.496277i \(0.834700\pi\)
\(642\) −357.849 38.7715i −0.557397 0.0603917i
\(643\) −1024.08 −1.59266 −0.796331 0.604861i \(-0.793229\pi\)
−0.796331 + 0.604861i \(0.793229\pi\)
\(644\) 0 0
\(645\) 192.414i 0.298317i
\(646\) 521.084 + 56.4574i 0.806632 + 0.0873954i
\(647\) −395.404 + 228.287i −0.611134 + 0.352839i −0.773409 0.633907i \(-0.781450\pi\)
0.162275 + 0.986746i \(0.448117\pi\)
\(648\) −464.860 + 94.1465i −0.717377 + 0.145288i
\(649\) 625.834 + 361.325i 0.964304 + 0.556741i
\(650\) −542.325 + 239.379i −0.834346 + 0.368275i
\(651\) 0 0
\(652\) −716.473 653.480i −1.09888 1.00227i
\(653\) 24.4603 + 14.1222i 0.0374584 + 0.0216266i 0.518612 0.855010i \(-0.326449\pi\)
−0.481154 + 0.876636i \(0.659782\pi\)
\(654\) −12.3896 + 16.9383i −0.0189443 + 0.0258996i
\(655\) 450.907 + 780.994i 0.688407 + 1.19236i
\(656\) −43.4817 + 94.3859i −0.0662831 + 0.143881i
\(657\) 875.579i 1.33269i
\(658\) 0 0
\(659\) 132.188i 0.200589i −0.994958 0.100295i \(-0.968021\pi\)
0.994958 0.100295i \(-0.0319785\pi\)
\(660\) −291.141 + 92.5382i −0.441122 + 0.140209i
\(661\) 346.924 + 600.889i 0.524847 + 0.909061i 0.999581 + 0.0289321i \(0.00921065\pi\)
−0.474735 + 0.880129i \(0.657456\pi\)
\(662\) 24.4401 33.4132i 0.0369186 0.0504731i
\(663\) −244.038 140.895i −0.368082 0.212512i
\(664\) −92.5022 + 275.645i −0.139311 + 0.415129i
\(665\) 0 0
\(666\) −313.794 710.917i −0.471162 1.06744i
\(667\) 345.175 + 199.287i 0.517504 + 0.298781i
\(668\) −51.4976 + 234.864i −0.0770922 + 0.351592i
\(669\) 220.652 127.393i 0.329823 0.190424i
\(670\) 216.168 + 23.4209i 0.322638 + 0.0349566i
\(671\) 135.408i 0.201800i
\(672\) 0 0
\(673\) 532.137 0.790694 0.395347 0.918532i \(-0.370624\pi\)
0.395347 + 0.918532i \(0.370624\pi\)
\(674\) −7.53246 + 69.5222i −0.0111757 + 0.103149i
\(675\) 119.327 + 206.680i 0.176780 + 0.306192i
\(676\) −813.885 178.457i −1.20397 0.263990i
\(677\) −143.115 + 247.883i −0.211396 + 0.366149i −0.952152 0.305626i \(-0.901134\pi\)
0.740756 + 0.671775i \(0.234468\pi\)
\(678\) −24.6503 + 10.8805i −0.0363573 + 0.0160479i
\(679\) 0 0
\(680\) 766.440 + 257.205i 1.12712 + 0.378243i
\(681\) −138.808 + 240.423i −0.203830 + 0.353043i
\(682\) −274.301 200.638i −0.402202 0.294191i
\(683\) −387.838 + 223.918i −0.567844 + 0.327845i −0.756288 0.654239i \(-0.772989\pi\)
0.188443 + 0.982084i \(0.439656\pi\)
\(684\) −162.893 512.490i −0.238148 0.749254i
\(685\) −1605.76 −2.34417
\(686\) 0 0
\(687\) −377.724 −0.549817
\(688\) 222.884 483.815i 0.323959 0.703219i
\(689\) −625.519 + 361.143i −0.907865 + 0.524156i
\(690\) 223.176 + 163.242i 0.323443 + 0.236583i
\(691\) 510.366 883.980i 0.738591 1.27928i −0.214539 0.976715i \(-0.568825\pi\)
0.953130 0.302561i \(-0.0978417\pi\)
\(692\) −375.659 + 411.871i −0.542860 + 0.595189i
\(693\) 0 0
\(694\) 354.331 + 802.754i 0.510563 + 1.15671i
\(695\) −156.059 + 270.302i −0.224545 + 0.388924i
\(696\) 24.1000 + 118.997i 0.0346264 + 0.170972i
\(697\) −51.7221 89.5854i −0.0742068 0.128530i
\(698\) −93.7387 + 865.180i −0.134296 + 1.23951i
\(699\) −150.225 −0.214914
\(700\) 0 0
\(701\) 1311.02i 1.87021i −0.354369 0.935106i \(-0.615304\pi\)
0.354369 0.935106i \(-0.384696\pi\)
\(702\) −65.4465 + 604.051i −0.0932287 + 0.860472i
\(703\) 677.669 391.252i 0.963967 0.556546i
\(704\) 839.249 + 104.562i 1.19212 + 0.148526i
\(705\) −109.644 63.3028i −0.155523 0.0897912i
\(706\) −227.027 514.342i −0.321568 0.728530i
\(707\) 0 0
\(708\) 134.267 147.210i 0.189642 0.207923i
\(709\) 465.495 + 268.754i 0.656552 + 0.379061i 0.790962 0.611865i \(-0.209581\pi\)
−0.134410 + 0.990926i \(0.542914\pi\)
\(710\) 328.342 + 240.166i 0.462454 + 0.338263i
\(711\) −238.199 412.573i −0.335020 0.580271i
\(712\) −6.43850 + 5.68610i −0.00904283 + 0.00798610i
\(713\) 307.601i 0.431417i
\(714\) 0 0
\(715\) 1628.68i 2.27787i
\(716\) 1112.08 353.472i 1.55319 0.493677i
\(717\) 8.70704 + 15.0810i 0.0121437 + 0.0210335i
\(718\) −426.050 311.635i −0.593385 0.434032i
\(719\) 233.275 + 134.681i 0.324443 + 0.187318i 0.653371 0.757037i \(-0.273354\pi\)
−0.328928 + 0.944355i \(0.606687\pi\)
\(720\) −76.1187 825.955i −0.105720 1.14716i
\(721\) 0 0
\(722\) −165.128 + 72.8866i −0.228710 + 0.100951i
\(723\) −276.334 159.541i −0.382204 0.220666i
\(724\) −651.890 142.937i −0.900400 0.197427i
\(725\) −220.185 + 127.124i −0.303703 + 0.175343i
\(726\) 10.5231 97.1252i 0.0144947 0.133781i
\(727\) 460.316i 0.633172i −0.948564 0.316586i \(-0.897463\pi\)
0.948564 0.316586i \(-0.102537\pi\)
\(728\) 0 0
\(729\) −356.185 −0.488594
\(730\) −1352.03 146.487i −1.85209 0.200666i
\(731\) 265.124 + 459.208i 0.362686 + 0.628191i
\(732\) −36.4674 7.99605i −0.0498188 0.0109236i
\(733\) −33.3410 + 57.7484i −0.0454857 + 0.0787836i −0.887872 0.460091i \(-0.847817\pi\)
0.842386 + 0.538874i \(0.181150\pi\)
\(734\) 125.130 + 283.490i 0.170478 + 0.386226i
\(735\) 0 0
\(736\) −372.070 668.979i −0.505530 0.908939i
\(737\) −113.211 + 196.087i −0.153610 + 0.266061i
\(738\) −62.6580 + 85.6626i −0.0849024 + 0.116074i
\(739\) 808.772 466.944i 1.09441 0.631860i 0.159665 0.987171i \(-0.448958\pi\)
0.934748 + 0.355311i \(0.115625\pi\)
\(740\) 1150.26 365.607i 1.55441 0.494064i
\(741\) −291.128 −0.392885
\(742\) 0 0
\(743\) −1198.23 −1.61269 −0.806345 0.591446i \(-0.798557\pi\)
−0.806345 + 0.591446i \(0.798557\pi\)
\(744\) −70.2328 + 62.0255i −0.0943989 + 0.0833676i
\(745\) 229.104 132.273i 0.307523 0.177548i
\(746\) −690.576 + 944.117i −0.925705 + 1.26557i
\(747\) −148.471 + 257.160i −0.198757 + 0.344257i
\(748\) −567.318 + 622.005i −0.758446 + 0.831557i
\(749\) 0 0
\(750\) 103.003 45.4651i 0.137338 0.0606201i
\(751\) 84.2993 146.011i 0.112249 0.194422i −0.804427 0.594051i \(-0.797528\pi\)
0.916677 + 0.399629i \(0.130861\pi\)
\(752\) 202.366 + 286.178i 0.269103 + 0.380555i
\(753\) 40.2239 + 69.6698i 0.0534182 + 0.0925230i
\(754\) −643.522 69.7230i −0.853477 0.0924708i
\(755\) 619.458 0.820474
\(756\) 0 0
\(757\) 209.207i 0.276364i 0.990407 + 0.138182i \(0.0441259\pi\)
−0.990407 + 0.138182i \(0.955874\pi\)
\(758\) 254.860 + 27.6131i 0.336227 + 0.0364289i
\(759\) −249.360 + 143.968i −0.328538 + 0.189681i
\(760\) 818.614 165.791i 1.07712 0.218146i
\(761\) −479.127 276.624i −0.629602 0.363501i 0.150996 0.988534i \(-0.451752\pi\)
−0.780598 + 0.625033i \(0.785085\pi\)
\(762\) −117.104 + 51.6891i −0.153680 + 0.0678334i
\(763\) 0 0
\(764\) −354.073 + 388.205i −0.463447 + 0.508121i
\(765\) 715.041 + 412.829i 0.934695 + 0.539646i
\(766\) −295.093 + 403.435i −0.385239 + 0.526678i
\(767\) 531.115 + 919.919i 0.692458 + 1.19937i
\(768\) 77.7191 219.848i 0.101197 0.286260i
\(769\) 219.524i 0.285467i 0.989761 + 0.142734i \(0.0455892\pi\)
−0.989761 + 0.142734i \(0.954411\pi\)
\(770\) 0 0
\(771\) 78.4096i 0.101699i
\(772\) −98.6763 310.452i −0.127819 0.402140i
\(773\) −333.337 577.357i −0.431225 0.746904i 0.565754 0.824574i \(-0.308585\pi\)
−0.996979 + 0.0776701i \(0.975252\pi\)
\(774\) 321.180 439.100i 0.414961 0.567312i
\(775\) −169.928 98.1082i −0.219262 0.126591i
\(776\) −1285.67 431.452i −1.65680 0.555995i
\(777\) 0 0
\(778\) 174.786 + 395.988i 0.224661 + 0.508981i
\(779\) −92.5538 53.4359i −0.118811 0.0685956i
\(780\) −438.628 96.1761i −0.562343 0.123303i
\(781\) −366.866 + 211.810i −0.469738 + 0.271204i
\(782\) 757.549 + 82.0774i 0.968733 + 0.104958i
\(783\) 260.587i 0.332806i
\(784\) 0 0
\(785\) −178.710 −0.227656
\(786\) −27.8898 + 257.414i −0.0354832 + 0.327499i
\(787\) 459.932 + 796.626i 0.584412 + 1.01223i 0.994948 + 0.100387i \(0.0320081\pi\)
−0.410536 + 0.911844i \(0.634659\pi\)
\(788\) −1.79523 + 8.18746i −0.00227821 + 0.0103902i
\(789\) −145.378 + 251.803i −0.184256 + 0.319141i
\(790\) 676.926 298.791i 0.856868 0.378216i
\(791\) 0 0
\(792\) 818.865 + 274.798i 1.03392 + 0.346967i
\(793\) 99.5187 172.371i 0.125496 0.217366i
\(794\) −1129.79 826.386i −1.42291 1.04079i
\(795\) −186.115 + 107.453i −0.234106 + 0.135161i
\(796\) −483.920 + 153.813i −0.607940 + 0.193232i
\(797\) 1016.13 1.27494 0.637470 0.770476i \(-0.279981\pi\)
0.637470 + 0.770476i \(0.279981\pi\)
\(798\) 0 0
\(799\) −348.895 −0.436664
\(800\) 488.236 + 7.82525i 0.610295 + 0.00978156i
\(801\) −7.59744 + 4.38638i −0.00948494 + 0.00547613i
\(802\) 292.149 + 213.693i 0.364276 + 0.266450i
\(803\) 708.078 1226.43i 0.881791 1.52731i
\(804\) 46.1238 + 42.0686i 0.0573679 + 0.0523241i
\(805\) 0 0
\(806\) −201.720 457.007i −0.250273 0.567007i
\(807\) 26.1727 45.3325i 0.0324321 0.0561741i
\(808\) −220.531 + 44.6634i −0.272934 + 0.0552765i
\(809\) −565.950 980.254i −0.699567 1.21169i −0.968617 0.248560i \(-0.920043\pi\)
0.269049 0.963126i \(-0.413291\pi\)
\(810\) 81.0407 747.981i 0.100050 0.923433i
\(811\) 481.066 0.593176 0.296588 0.955006i \(-0.404151\pi\)
0.296588 + 0.955006i \(0.404151\pi\)
\(812\) 0 0
\(813\) 28.1242i 0.0345931i
\(814\) −135.384 + 1249.55i −0.166319 + 1.53507i
\(815\) 1332.15 769.117i 1.63454 0.943702i
\(816\) 134.014 + 189.518i 0.164233 + 0.232252i
\(817\) 474.423 + 273.908i 0.580690 + 0.335261i
\(818\) 289.806 + 656.570i 0.354286 + 0.802653i
\(819\) 0 0
\(820\) −121.793 111.085i −0.148528 0.135469i
\(821\) 630.185 + 363.838i 0.767582 + 0.443164i 0.832011 0.554758i \(-0.187189\pi\)
−0.0644292 + 0.997922i \(0.520523\pi\)
\(822\) −372.111 272.181i −0.452690 0.331120i
\(823\) 313.323 + 542.692i 0.380709 + 0.659407i 0.991164 0.132644i \(-0.0423468\pi\)
−0.610455 + 0.792051i \(0.709013\pi\)
\(824\) 997.256 880.718i 1.21026 1.06883i
\(825\) 183.673i 0.222633i
\(826\) 0 0
\(827\) 1468.52i 1.77572i 0.460116 + 0.887859i \(0.347808\pi\)
−0.460116 + 0.887859i \(0.652192\pi\)
\(828\) −236.813 745.055i −0.286007 0.899824i
\(829\) −409.352 709.019i −0.493790 0.855270i 0.506184 0.862425i \(-0.331056\pi\)
−0.999974 + 0.00715566i \(0.997722\pi\)
\(830\) −372.254 272.286i −0.448499 0.328055i
\(831\) 280.969 + 162.218i 0.338110 + 0.195208i
\(832\) 991.498 + 749.915i 1.19170 + 0.901341i
\(833\) 0 0
\(834\) −81.9814 + 36.1861i −0.0982990 + 0.0433886i
\(835\) −330.306 190.702i −0.395576 0.228386i
\(836\) −186.284 + 849.579i −0.222827 + 1.01624i
\(837\) −174.165 + 100.554i −0.208083 + 0.120137i
\(838\) −168.228 + 1552.69i −0.200749 + 1.85285i
\(839\) 1108.84i 1.32162i −0.750555 0.660808i \(-0.770214\pi\)
0.750555 0.660808i \(-0.229786\pi\)
\(840\) 0 0
\(841\) 563.386 0.669900
\(842\) −228.585 24.7663i −0.271479 0.0294136i
\(843\) 133.970 + 232.042i 0.158920 + 0.275258i
\(844\) 6.14109 28.0075i 0.00727618 0.0331843i
\(845\) 660.850 1144.63i 0.782072 1.35459i
\(846\) 144.547 + 327.479i 0.170860 + 0.387091i
\(847\) 0 0
\(848\) 592.443 54.5986i 0.698636 0.0643852i
\(849\) 189.005 327.366i 0.222621 0.385590i
\(850\) −286.960 + 392.316i −0.337600 + 0.461549i
\(851\) 985.191 568.800i 1.15769 0.668390i
\(852\) 35.3796 + 111.310i 0.0415254 + 0.130646i
\(853\) 610.400 0.715592 0.357796 0.933800i \(-0.383528\pi\)
0.357796 + 0.933800i \(0.383528\pi\)
\(854\) 0 0
\(855\) 853.017 0.997680
\(856\) −1184.78 + 1046.33i −1.38409 + 1.22235i
\(857\) −384.614 + 222.057i −0.448791 + 0.259110i −0.707319 0.706894i \(-0.750096\pi\)
0.258529 + 0.966004i \(0.416762\pi\)
\(858\) 276.066 377.423i 0.321755 0.439886i
\(859\) 40.7547 70.5892i 0.0474443 0.0821760i −0.841328 0.540525i \(-0.818226\pi\)
0.888772 + 0.458349i \(0.151559\pi\)
\(860\) 624.302 + 569.413i 0.725932 + 0.662108i
\(861\) 0 0
\(862\) 566.677 250.128i 0.657398 0.290171i
\(863\) 525.730 910.592i 0.609189 1.05515i −0.382185 0.924086i \(-0.624828\pi\)
0.991374 0.131061i \(-0.0418384\pi\)
\(864\) 257.151 429.357i 0.297628 0.496941i
\(865\) −442.134 765.799i −0.511138 0.885317i
\(866\) −1184.62 128.349i −1.36792 0.148208i
\(867\) 32.1882 0.0371259
\(868\) 0 0
\(869\) 770.524i 0.886679i
\(870\) −191.471 20.7451i −0.220082 0.0238450i
\(871\) −288.230 + 166.409i −0.330918 + 0.191056i
\(872\) 18.2931 + 90.3245i 0.0209784 + 0.103583i
\(873\) −1199.45 692.505i −1.37395 0.793248i
\(874\) 720.194 317.889i 0.824020 0.363717i
\(875\) 0 0
\(876\) −288.482 263.119i −0.329318 0.300364i
\(877\) −1350.68 779.814i −1.54011 0.889183i −0.998831 0.0483410i \(-0.984607\pi\)
−0.541280 0.840842i \(-0.682060\pi\)
\(878\) 952.747 1302.54i 1.08513 1.48354i
\(879\) 168.767 + 292.312i 0.191998 + 0.332551i
\(880\) −561.328 + 1218.48i −0.637873 + 1.38463i
\(881\) 1515.22i 1.71989i −0.510389 0.859944i \(-0.670499\pi\)
0.510389 0.859944i \(-0.329501\pi\)
\(882\) 0 0
\(883\) 763.828i 0.865037i −0.901625 0.432519i \(-0.857625\pi\)
0.901625 0.432519i \(-0.142375\pi\)
\(884\) −1179.33 + 374.846i −1.33408 + 0.424034i
\(885\) 158.026 + 273.709i 0.178561 + 0.309276i
\(886\) 525.206 718.033i 0.592783 0.810421i
\(887\) −496.554 286.686i −0.559813 0.323208i 0.193258 0.981148i \(-0.438095\pi\)
−0.753070 + 0.657940i \(0.771428\pi\)
\(888\) 328.528 + 110.249i 0.369964 + 0.124154i
\(889\) 0 0
\(890\) −5.50216 12.4654i −0.00618221 0.0140061i
\(891\) 678.496 + 391.730i 0.761500 + 0.439652i
\(892\) 239.639 1092.92i 0.268654 1.22524i
\(893\) −312.163 + 180.228i −0.349567 + 0.201823i
\(894\) 75.5124 + 8.18146i 0.0844658 + 0.00915153i
\(895\) 1851.01i 2.06817i
\(896\) 0 0
\(897\) −423.240 −0.471840
\(898\) −56.5335 + 521.787i −0.0629549 + 0.581055i
\(899\) −107.125 185.546i −0.119160 0.206391i
\(900\) 487.123 + 106.809i 0.541248 + 0.118677i
\(901\) −296.115 + 512.887i −0.328652 + 0.569242i
\(902\) 157.041 69.3167i 0.174103 0.0768477i
\(903\) 0 0
\(904\) −37.6452 + 112.178i −0.0416430 + 0.124091i
\(905\) 529.315 916.800i 0.584878 1.01304i
\(906\) 143.550 + 105.000i 0.158444 + 0.115894i
\(907\) −885.036 + 510.976i −0.975784 + 0.563369i −0.900995 0.433830i \(-0.857162\pi\)
−0.0747894 + 0.997199i \(0.523828\pi\)
\(908\) 369.293 + 1161.86i 0.406710 + 1.27958i
\(909\) −229.799 −0.252804
\(910\) 0 0
\(911\) 630.111 0.691669 0.345835 0.938295i \(-0.387596\pi\)
0.345835 + 0.938295i \(0.387596\pi\)
\(912\) 217.804 + 100.338i 0.238820 + 0.110020i
\(913\) 415.930 240.137i 0.455564 0.263020i
\(914\) −628.714 459.873i −0.687871 0.503144i
\(915\) 29.6104 51.2868i 0.0323611 0.0560511i
\(916\) −1117.80 + 1225.55i −1.22031 + 1.33794i
\(917\) 0 0
\(918\) 201.170 + 455.760i 0.219139 + 0.496471i
\(919\) 421.489 730.041i 0.458639 0.794386i −0.540250 0.841504i \(-0.681670\pi\)
0.998889 + 0.0471182i \(0.0150038\pi\)
\(920\) 1190.10 241.026i 1.29358 0.261985i
\(921\) 73.0182 + 126.471i 0.0792814 + 0.137319i
\(922\) −34.1920 + 315.582i −0.0370846 + 0.342280i
\(923\) −622.683 −0.674630
\(924\) 0 0
\(925\) 725.668i 0.784506i
\(926\) 113.929 1051.53i 0.123034 1.13557i
\(927\) 1176.76 679.405i 1.26943 0.732907i
\(928\) 457.413 + 273.954i 0.492902 + 0.295209i
\(929\) −670.867 387.325i −0.722139 0.416927i 0.0934003 0.995629i \(-0.470226\pi\)
−0.815540 + 0.578701i \(0.803560\pi\)
\(930\) −60.0190 135.976i −0.0645366 0.146211i
\(931\) 0 0
\(932\) −444.561 + 487.415i −0.476997 + 0.522977i
\(933\) 372.990 + 215.346i 0.399774 + 0.230810i
\(934\) −705.266 515.867i −0.755103 0.552321i
\(935\) −667.708 1156.50i −0.714126 1.23690i
\(936\) 840.434 + 951.641i 0.897900 + 1.01671i
\(937\) 1586.27i 1.69293i −0.532447 0.846463i \(-0.678727\pi\)
0.532447 0.846463i \(-0.321273\pi\)
\(938\) 0 0
\(939\) 210.421i 0.224090i
\(940\) −529.860 + 168.414i −0.563681 + 0.179164i
\(941\) 410.023 + 710.181i 0.435731 + 0.754708i 0.997355 0.0726842i \(-0.0231565\pi\)
−0.561624 + 0.827393i \(0.689823\pi\)
\(942\) −41.4134 30.2919i −0.0439633 0.0321570i
\(943\) −134.554 77.6849i −0.142687 0.0823805i
\(944\) −80.2954 871.277i −0.0850587 0.922963i
\(945\) 0 0
\(946\) −804.977 + 355.312i −0.850928 + 0.375594i
\(947\) 551.949 + 318.668i 0.582839 + 0.336502i 0.762261 0.647270i \(-0.224089\pi\)
−0.179422 + 0.983772i \(0.557423\pi\)
\(948\) 207.514 + 45.5007i 0.218896 + 0.0479965i
\(949\) 1802.74 1040.81i 1.89962 1.09675i
\(950\) −54.0915 + 499.248i −0.0569384 + 0.525524i
\(951\) 205.234i 0.215809i
\(952\) 0 0
\(953\) −350.626 −0.367918 −0.183959 0.982934i \(-0.558891\pi\)
−0.183959 + 0.982934i \(0.558891\pi\)
\(954\) 604.086 + 65.4503i 0.633214 + 0.0686062i
\(955\) −416.729 721.796i −0.436365 0.755807i
\(956\) 74.6983 + 16.3788i 0.0781363 + 0.0171326i
\(957\) 100.277 173.684i 0.104782 0.181488i
\(958\) −440.852 998.772i −0.460179 1.04256i
\(959\) 0 0
\(960\) 295.007 + 223.127i 0.307299 + 0.232424i
\(961\) −397.826 + 689.055i −0.413971 + 0.717019i
\(962\) −1090.70 + 1491.15i −1.13379 + 1.55005i
\(963\) −1398.04 + 807.161i −1.45176 + 0.838174i
\(964\) −1335.40 + 424.453i −1.38527 + 0.440304i
\(965\) 516.734 0.535475
\(966\) 0 0
\(967\) −649.816 −0.671992 −0.335996 0.941863i \(-0.609073\pi\)
−0.335996 + 0.941863i \(0.609073\pi\)
\(968\) −283.989 321.566i −0.293377 0.332197i
\(969\) −206.726 + 119.354i −0.213340 + 0.123172i
\(970\) 1270.00 1736.28i 1.30928 1.78998i
\(971\) −485.305 + 840.573i −0.499799 + 0.865677i −1.00000 0.000232071i \(-0.999926\pi\)
0.500201 + 0.865909i \(0.333259\pi\)
\(972\) 524.982 575.589i 0.540105 0.592169i
\(973\) 0 0
\(974\) 1186.06 523.519i 1.21772 0.537494i
\(975\) 134.991 233.811i 0.138452 0.239807i
\(976\) −133.862 + 94.6583i −0.137154 + 0.0969860i
\(977\) 300.437 + 520.373i 0.307510 + 0.532623i 0.977817 0.209461i \(-0.0671709\pi\)
−0.670307 + 0.742084i \(0.733838\pi\)
\(978\) 439.074 + 47.5719i 0.448951 + 0.0486421i
\(979\) 14.1890 0.0144934
\(980\) 0 0
\(981\) 94.1205i 0.0959434i
\(982\) −1455.63 157.712i −1.48231 0.160602i
\(983\) −1098.66 + 634.311i −1.11766 + 0.645281i −0.940802 0.338955i \(-0.889926\pi\)
−0.176857 + 0.984236i \(0.556593\pi\)
\(984\) −9.39453 46.3866i −0.00954728 0.0471409i
\(985\) −11.5146 6.64797i −0.0116900 0.00674921i
\(986\) −485.541 + 214.315i −0.492435 + 0.217358i
\(987\) 0 0
\(988\) −861.537 + 944.586i −0.872001 + 0.956059i
\(989\) 689.714 + 398.207i 0.697385 + 0.402636i
\(990\) −808.885 + 1105.86i −0.817055 + 1.11703i
\(991\) 774.555 + 1341.57i 0.781590 + 1.35375i 0.931015 + 0.364980i \(0.118924\pi\)
−0.149426 + 0.988773i \(0.547742\pi\)
\(992\) −6.59420 + 411.428i −0.00664738 + 0.414746i
\(993\) 18.8538i 0.0189867i
\(994\) 0 0
\(995\) 805.464i 0.809512i
\(996\) −40.1112 126.197i −0.0402723 0.126703i
\(997\) 470.469 + 814.876i 0.471885 + 0.817328i 0.999483 0.0321661i \(-0.0102406\pi\)
−0.527598 + 0.849494i \(0.676907\pi\)
\(998\) 31.5308 43.1072i 0.0315940 0.0431936i
\(999\) 644.116 + 371.881i 0.644761 + 0.372253i
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 392.3.j.e.117.6 28
7.2 even 3 392.3.h.a.293.26 28
7.3 odd 6 inner 392.3.j.e.325.4 28
7.4 even 3 56.3.j.a.45.4 yes 28
7.5 odd 6 392.3.h.a.293.25 28
7.6 odd 2 56.3.j.a.5.6 yes 28
8.5 even 2 inner 392.3.j.e.117.4 28
28.11 odd 6 224.3.n.a.17.9 28
28.19 even 6 1568.3.h.a.881.17 28
28.23 odd 6 1568.3.h.a.881.11 28
28.27 even 2 224.3.n.a.145.6 28
56.5 odd 6 392.3.h.a.293.28 28
56.11 odd 6 224.3.n.a.17.6 28
56.13 odd 2 56.3.j.a.5.4 28
56.19 even 6 1568.3.h.a.881.12 28
56.27 even 2 224.3.n.a.145.9 28
56.37 even 6 392.3.h.a.293.27 28
56.45 odd 6 inner 392.3.j.e.325.6 28
56.51 odd 6 1568.3.h.a.881.18 28
56.53 even 6 56.3.j.a.45.6 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.3.j.a.5.4 28 56.13 odd 2
56.3.j.a.5.6 yes 28 7.6 odd 2
56.3.j.a.45.4 yes 28 7.4 even 3
56.3.j.a.45.6 yes 28 56.53 even 6
224.3.n.a.17.6 28 56.11 odd 6
224.3.n.a.17.9 28 28.11 odd 6
224.3.n.a.145.6 28 28.27 even 2
224.3.n.a.145.9 28 56.27 even 2
392.3.h.a.293.25 28 7.5 odd 6
392.3.h.a.293.26 28 7.2 even 3
392.3.h.a.293.27 28 56.37 even 6
392.3.h.a.293.28 28 56.5 odd 6
392.3.j.e.117.4 28 8.5 even 2 inner
392.3.j.e.117.6 28 1.1 even 1 trivial
392.3.j.e.325.4 28 7.3 odd 6 inner
392.3.j.e.325.6 28 56.45 odd 6 inner
1568.3.h.a.881.11 28 28.23 odd 6
1568.3.h.a.881.12 28 56.19 even 6
1568.3.h.a.881.17 28 28.19 even 6
1568.3.h.a.881.18 28 56.51 odd 6