Properties

Label 76.5.b.a.39.17
Level $76$
Weight $5$
Character 76.39
Analytic conductor $7.856$
Analytic rank $0$
Dimension $36$
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] = [76,5,Mod(39,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.39");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.17
Character \(\chi\) \(=\) 76.39
Dual form 76.5.b.a.39.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.591318 - 3.95605i) q^{2} +4.43430i q^{3} +(-15.3007 + 4.67857i) q^{4} +13.1035 q^{5} +(17.5423 - 2.62208i) q^{6} -8.96798i q^{7} +(27.5562 + 57.7638i) q^{8} +61.3370 q^{9} +O(q^{10})\) \(q+(-0.591318 - 3.95605i) q^{2} +4.43430i q^{3} +(-15.3007 + 4.67857i) q^{4} +13.1035 q^{5} +(17.5423 - 2.62208i) q^{6} -8.96798i q^{7} +(27.5562 + 57.7638i) q^{8} +61.3370 q^{9} +(-7.74835 - 51.8382i) q^{10} -193.669i q^{11} +(-20.7462 - 67.8478i) q^{12} +173.528 q^{13} +(-35.4778 + 5.30293i) q^{14} +58.1049i q^{15} +(212.222 - 143.171i) q^{16} +83.2927 q^{17} +(-36.2697 - 242.652i) q^{18} -82.8191i q^{19} +(-200.493 + 61.3057i) q^{20} +39.7667 q^{21} +(-766.166 + 114.520i) q^{22} -684.081i q^{23} +(-256.142 + 122.193i) q^{24} -453.298 q^{25} +(-102.610 - 686.485i) q^{26} +631.165i q^{27} +(41.9573 + 137.216i) q^{28} +1433.18 q^{29} +(229.866 - 34.3585i) q^{30} +750.769i q^{31} +(-691.881 - 754.902i) q^{32} +858.787 q^{33} +(-49.2525 - 329.510i) q^{34} -117.512i q^{35} +(-938.498 + 286.969i) q^{36} +437.540 q^{37} +(-327.637 + 48.9724i) q^{38} +769.474i q^{39} +(361.084 + 756.909i) q^{40} +895.241 q^{41} +(-23.5147 - 157.319i) q^{42} +928.943i q^{43} +(906.096 + 2963.27i) q^{44} +803.731 q^{45} +(-2706.26 + 404.510i) q^{46} +2116.78i q^{47} +(634.861 + 941.055i) q^{48} +2320.58 q^{49} +(268.043 + 1793.27i) q^{50} +369.344i q^{51} +(-2655.09 + 811.862i) q^{52} -3581.37 q^{53} +(2496.92 - 373.219i) q^{54} -2537.75i q^{55} +(518.024 - 247.124i) q^{56} +367.244 q^{57} +(-847.467 - 5669.75i) q^{58} +306.954i q^{59} +(-271.848 - 889.045i) q^{60} -7090.53 q^{61} +(2970.08 - 443.943i) q^{62} -550.069i q^{63} +(-2577.31 + 3183.50i) q^{64} +2273.83 q^{65} +(-507.817 - 3397.41i) q^{66} -4562.45i q^{67} +(-1274.43 + 389.691i) q^{68} +3033.42 q^{69} +(-464.884 + 69.4870i) q^{70} +149.139i q^{71} +(1690.22 + 3543.06i) q^{72} -2829.51 q^{73} +(-258.725 - 1730.93i) q^{74} -2010.06i q^{75} +(387.475 + 1267.19i) q^{76} -1736.82 q^{77} +(3044.08 - 455.004i) q^{78} -6895.61i q^{79} +(2780.86 - 1876.04i) q^{80} +2169.53 q^{81} +(-529.372 - 3541.62i) q^{82} +7842.11i q^{83} +(-608.457 + 186.051i) q^{84} +1091.43 q^{85} +(3674.95 - 549.301i) q^{86} +6355.16i q^{87} +(11187.1 - 5336.80i) q^{88} -8713.81 q^{89} +(-475.261 - 3179.60i) q^{90} -1556.19i q^{91} +(3200.52 + 10466.9i) q^{92} -3329.13 q^{93} +(8374.09 - 1251.69i) q^{94} -1085.22i q^{95} +(3347.46 - 3068.01i) q^{96} -2174.99 q^{97} +(-1372.20 - 9180.32i) q^{98} -11879.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.591318 3.95605i −0.147830 0.989013i
\(3\) 4.43430i 0.492700i 0.969181 + 0.246350i \(0.0792312\pi\)
−0.969181 + 0.246350i \(0.920769\pi\)
\(4\) −15.3007 + 4.67857i −0.956293 + 0.292411i
\(5\) 13.1035 0.524141 0.262070 0.965049i \(-0.415595\pi\)
0.262070 + 0.965049i \(0.415595\pi\)
\(6\) 17.5423 2.62208i 0.487286 0.0728356i
\(7\) 8.96798i 0.183020i −0.995804 0.0915100i \(-0.970831\pi\)
0.995804 0.0915100i \(-0.0291693\pi\)
\(8\) 27.5562 + 57.7638i 0.430566 + 0.902559i
\(9\) 61.3370 0.757247
\(10\) −7.74835 51.8382i −0.0774835 0.518382i
\(11\) 193.669i 1.60057i −0.599618 0.800287i \(-0.704681\pi\)
0.599618 0.800287i \(-0.295319\pi\)
\(12\) −20.7462 67.8478i −0.144071 0.471165i
\(13\) 173.528 1.02679 0.513396 0.858152i \(-0.328387\pi\)
0.513396 + 0.858152i \(0.328387\pi\)
\(14\) −35.4778 + 5.30293i −0.181009 + 0.0270557i
\(15\) 58.1049i 0.258244i
\(16\) 212.222 143.171i 0.828992 0.559260i
\(17\) 83.2927 0.288210 0.144105 0.989562i \(-0.453970\pi\)
0.144105 + 0.989562i \(0.453970\pi\)
\(18\) −36.2697 242.652i −0.111943 0.748927i
\(19\) 82.8191i 0.229416i
\(20\) −200.493 + 61.3057i −0.501232 + 0.153264i
\(21\) 39.7667 0.0901738
\(22\) −766.166 + 114.520i −1.58299 + 0.236612i
\(23\) 684.081i 1.29316i −0.762846 0.646580i \(-0.776199\pi\)
0.762846 0.646580i \(-0.223801\pi\)
\(24\) −256.142 + 122.193i −0.444691 + 0.212140i
\(25\) −453.298 −0.725276
\(26\) −102.610 686.485i −0.151790 1.01551i
\(27\) 631.165i 0.865795i
\(28\) 41.9573 + 137.216i 0.0535170 + 0.175021i
\(29\) 1433.18 1.70414 0.852071 0.523426i \(-0.175346\pi\)
0.852071 + 0.523426i \(0.175346\pi\)
\(30\) 229.866 34.3585i 0.255407 0.0381761i
\(31\) 750.769i 0.781237i 0.920553 + 0.390619i \(0.127739\pi\)
−0.920553 + 0.390619i \(0.872261\pi\)
\(32\) −691.881 754.902i −0.675665 0.737209i
\(33\) 858.787 0.788602
\(34\) −49.2525 329.510i −0.0426059 0.285043i
\(35\) 117.512i 0.0959282i
\(36\) −938.498 + 286.969i −0.724150 + 0.221427i
\(37\) 437.540 0.319606 0.159803 0.987149i \(-0.448914\pi\)
0.159803 + 0.987149i \(0.448914\pi\)
\(38\) −327.637 + 48.9724i −0.226895 + 0.0339144i
\(39\) 769.474i 0.505900i
\(40\) 361.084 + 756.909i 0.225677 + 0.473068i
\(41\) 895.241 0.532565 0.266282 0.963895i \(-0.414205\pi\)
0.266282 + 0.963895i \(0.414205\pi\)
\(42\) −23.5147 157.319i −0.0133304 0.0891831i
\(43\) 928.943i 0.502403i 0.967935 + 0.251202i \(0.0808257\pi\)
−0.967935 + 0.251202i \(0.919174\pi\)
\(44\) 906.096 + 2963.27i 0.468025 + 1.53062i
\(45\) 803.731 0.396904
\(46\) −2706.26 + 404.510i −1.27895 + 0.191167i
\(47\) 2116.78i 0.958252i 0.877746 + 0.479126i \(0.159046\pi\)
−0.877746 + 0.479126i \(0.840954\pi\)
\(48\) 634.861 + 941.055i 0.275547 + 0.408444i
\(49\) 2320.58 0.966504
\(50\) 268.043 + 1793.27i 0.107217 + 0.717308i
\(51\) 369.344i 0.142001i
\(52\) −2655.09 + 811.862i −0.981914 + 0.300245i
\(53\) −3581.37 −1.27496 −0.637481 0.770466i \(-0.720024\pi\)
−0.637481 + 0.770466i \(0.720024\pi\)
\(54\) 2496.92 373.219i 0.856282 0.127990i
\(55\) 2537.75i 0.838926i
\(56\) 518.024 247.124i 0.165186 0.0788022i
\(57\) 367.244 0.113033
\(58\) −847.467 5669.75i −0.251922 1.68542i
\(59\) 306.954i 0.0881797i 0.999028 + 0.0440899i \(0.0140388\pi\)
−0.999028 + 0.0440899i \(0.985961\pi\)
\(60\) −271.848 889.045i −0.0755133 0.246957i
\(61\) −7090.53 −1.90554 −0.952772 0.303687i \(-0.901782\pi\)
−0.952772 + 0.303687i \(0.901782\pi\)
\(62\) 2970.08 443.943i 0.772654 0.115490i
\(63\) 550.069i 0.138591i
\(64\) −2577.31 + 3183.50i −0.629226 + 0.777223i
\(65\) 2273.83 0.538184
\(66\) −507.817 3397.41i −0.116579 0.779937i
\(67\) 4562.45i 1.01636i −0.861250 0.508181i \(-0.830318\pi\)
0.861250 0.508181i \(-0.169682\pi\)
\(68\) −1274.43 + 389.691i −0.275613 + 0.0842756i
\(69\) 3033.42 0.637139
\(70\) −464.884 + 69.4870i −0.0948742 + 0.0141810i
\(71\) 149.139i 0.0295853i 0.999891 + 0.0147926i \(0.00470882\pi\)
−0.999891 + 0.0147926i \(0.995291\pi\)
\(72\) 1690.22 + 3543.06i 0.326045 + 0.683460i
\(73\) −2829.51 −0.530964 −0.265482 0.964116i \(-0.585531\pi\)
−0.265482 + 0.964116i \(0.585531\pi\)
\(74\) −258.725 1730.93i −0.0472471 0.316094i
\(75\) 2010.06i 0.357343i
\(76\) 387.475 + 1267.19i 0.0670836 + 0.219389i
\(77\) −1736.82 −0.292937
\(78\) 3044.08 455.004i 0.500342 0.0747870i
\(79\) 6895.61i 1.10489i −0.833550 0.552444i \(-0.813695\pi\)
0.833550 0.552444i \(-0.186305\pi\)
\(80\) 2780.86 1876.04i 0.434509 0.293131i
\(81\) 2169.53 0.330670
\(82\) −529.372 3541.62i −0.0787288 0.526713i
\(83\) 7842.11i 1.13835i 0.822216 + 0.569176i \(0.192738\pi\)
−0.822216 + 0.569176i \(0.807262\pi\)
\(84\) −608.457 + 186.051i −0.0862326 + 0.0263678i
\(85\) 1091.43 0.151063
\(86\) 3674.95 549.301i 0.496883 0.0742700i
\(87\) 6355.16i 0.839630i
\(88\) 11187.1 5336.80i 1.44461 0.689153i
\(89\) −8713.81 −1.10009 −0.550045 0.835135i \(-0.685389\pi\)
−0.550045 + 0.835135i \(0.685389\pi\)
\(90\) −475.261 3179.60i −0.0586742 0.392543i
\(91\) 1556.19i 0.187923i
\(92\) 3200.52 + 10466.9i 0.378134 + 1.23664i
\(93\) −3329.13 −0.384915
\(94\) 8374.09 1251.69i 0.947724 0.141658i
\(95\) 1085.22i 0.120246i
\(96\) 3347.46 3068.01i 0.363222 0.332900i
\(97\) −2174.99 −0.231161 −0.115580 0.993298i \(-0.536873\pi\)
−0.115580 + 0.993298i \(0.536873\pi\)
\(98\) −1372.20 9180.32i −0.142878 0.955885i
\(99\) 11879.1i 1.21203i
\(100\) 6935.77 2120.78i 0.693577 0.212078i
\(101\) −4516.78 −0.442778 −0.221389 0.975186i \(-0.571059\pi\)
−0.221389 + 0.975186i \(0.571059\pi\)
\(102\) 1461.15 218.400i 0.140441 0.0209919i
\(103\) 2460.95i 0.231968i −0.993251 0.115984i \(-0.962998\pi\)
0.993251 0.115984i \(-0.0370021\pi\)
\(104\) 4781.77 + 10023.6i 0.442102 + 0.926740i
\(105\) 521.083 0.0472638
\(106\) 2117.73 + 14168.1i 0.188477 + 1.26095i
\(107\) 8505.12i 0.742870i 0.928459 + 0.371435i \(0.121134\pi\)
−0.928459 + 0.371435i \(0.878866\pi\)
\(108\) −2952.95 9657.25i −0.253168 0.827954i
\(109\) −2706.22 −0.227777 −0.113888 0.993494i \(-0.536331\pi\)
−0.113888 + 0.993494i \(0.536331\pi\)
\(110\) −10039.5 + 1500.62i −0.829709 + 0.124018i
\(111\) 1940.18i 0.157470i
\(112\) −1283.95 1903.20i −0.102356 0.151722i
\(113\) 6191.77 0.484907 0.242453 0.970163i \(-0.422048\pi\)
0.242453 + 0.970163i \(0.422048\pi\)
\(114\) −217.158 1452.84i −0.0167096 0.111791i
\(115\) 8963.88i 0.677798i
\(116\) −21928.7 + 6705.25i −1.62966 + 0.498309i
\(117\) 10643.7 0.777535
\(118\) 1214.32 181.507i 0.0872109 0.0130356i
\(119\) 746.967i 0.0527482i
\(120\) −3356.36 + 1601.15i −0.233081 + 0.111191i
\(121\) −22866.8 −1.56184
\(122\) 4192.76 + 28050.5i 0.281696 + 1.88461i
\(123\) 3969.77i 0.262394i
\(124\) −3512.53 11487.3i −0.228442 0.747092i
\(125\) −14129.5 −0.904288
\(126\) −2176.10 + 325.266i −0.137069 + 0.0204879i
\(127\) 2796.70i 0.173396i −0.996235 0.0866979i \(-0.972369\pi\)
0.996235 0.0866979i \(-0.0276315\pi\)
\(128\) 14118.1 + 8313.50i 0.861701 + 0.507416i
\(129\) −4119.21 −0.247534
\(130\) −1344.55 8995.37i −0.0795594 0.532271i
\(131\) 24318.3i 1.41707i 0.705676 + 0.708535i \(0.250644\pi\)
−0.705676 + 0.708535i \(0.749356\pi\)
\(132\) −13140.0 + 4017.90i −0.754134 + 0.230596i
\(133\) −742.719 −0.0419876
\(134\) −18049.3 + 2697.86i −1.00520 + 0.150248i
\(135\) 8270.48i 0.453799i
\(136\) 2295.23 + 4811.30i 0.124093 + 0.260126i
\(137\) 24493.0 1.30497 0.652485 0.757801i \(-0.273726\pi\)
0.652485 + 0.757801i \(0.273726\pi\)
\(138\) −1793.72 12000.4i −0.0941880 0.630139i
\(139\) 30575.5i 1.58250i 0.611493 + 0.791250i \(0.290569\pi\)
−0.611493 + 0.791250i \(0.709431\pi\)
\(140\) 549.788 + 1798.02i 0.0280504 + 0.0917355i
\(141\) −9386.43 −0.472131
\(142\) 590.003 88.1889i 0.0292602 0.00437358i
\(143\) 33607.0i 1.64346i
\(144\) 13017.1 8781.66i 0.627752 0.423498i
\(145\) 18779.8 0.893211
\(146\) 1673.14 + 11193.7i 0.0784922 + 0.525131i
\(147\) 10290.1i 0.476196i
\(148\) −6694.66 + 2047.06i −0.305637 + 0.0934561i
\(149\) 42569.0 1.91744 0.958718 0.284357i \(-0.0917802\pi\)
0.958718 + 0.284357i \(0.0917802\pi\)
\(150\) −7951.89 + 1188.58i −0.353417 + 0.0528259i
\(151\) 32464.1i 1.42380i −0.702280 0.711901i \(-0.747834\pi\)
0.702280 0.711901i \(-0.252166\pi\)
\(152\) 4783.94 2282.18i 0.207061 0.0987786i
\(153\) 5108.92 0.218246
\(154\) 1027.01 + 6870.96i 0.0433047 + 0.289718i
\(155\) 9837.72i 0.409479i
\(156\) −3600.04 11773.5i −0.147931 0.483789i
\(157\) 195.182 0.00791845 0.00395923 0.999992i \(-0.498740\pi\)
0.00395923 + 0.999992i \(0.498740\pi\)
\(158\) −27279.4 + 4077.50i −1.09275 + 0.163335i
\(159\) 15880.8i 0.628173i
\(160\) −9066.08 9891.87i −0.354144 0.386401i
\(161\) −6134.82 −0.236674
\(162\) −1282.88 8582.76i −0.0488828 0.327037i
\(163\) 21326.3i 0.802678i 0.915930 + 0.401339i \(0.131455\pi\)
−0.915930 + 0.401339i \(0.868545\pi\)
\(164\) −13697.8 + 4188.45i −0.509288 + 0.155728i
\(165\) 11253.1 0.413339
\(166\) 31023.8 4637.18i 1.12585 0.168282i
\(167\) 20994.1i 0.752774i 0.926462 + 0.376387i \(0.122834\pi\)
−0.926462 + 0.376387i \(0.877166\pi\)
\(168\) 1095.82 + 2297.07i 0.0388258 + 0.0813872i
\(169\) 1550.90 0.0543015
\(170\) −645.381 4317.74i −0.0223315 0.149403i
\(171\) 5079.87i 0.173724i
\(172\) −4346.13 14213.5i −0.146908 0.480445i
\(173\) 34458.3 1.15134 0.575668 0.817684i \(-0.304742\pi\)
0.575668 + 0.817684i \(0.304742\pi\)
\(174\) 25141.3 3757.92i 0.830405 0.124122i
\(175\) 4065.16i 0.132740i
\(176\) −27727.8 41100.9i −0.895137 1.32686i
\(177\) −1361.12 −0.0434461
\(178\) 5152.63 + 34472.3i 0.162626 + 1.08800i
\(179\) 26297.9i 0.820756i 0.911915 + 0.410378i \(0.134603\pi\)
−0.911915 + 0.410378i \(0.865397\pi\)
\(180\) −12297.6 + 3760.31i −0.379557 + 0.116059i
\(181\) −24396.4 −0.744677 −0.372339 0.928097i \(-0.621444\pi\)
−0.372339 + 0.928097i \(0.621444\pi\)
\(182\) −6156.38 + 920.205i −0.185859 + 0.0277806i
\(183\) 31441.5i 0.938861i
\(184\) 39515.1 18850.7i 1.16715 0.556791i
\(185\) 5733.32 0.167518
\(186\) 1968.58 + 13170.2i 0.0569019 + 0.380686i
\(187\) 16131.2i 0.461301i
\(188\) −9903.50 32388.2i −0.280203 0.916370i
\(189\) 5660.27 0.158458
\(190\) −4293.19 + 641.711i −0.118925 + 0.0177759i
\(191\) 20922.9i 0.573527i −0.958001 0.286764i \(-0.907421\pi\)
0.958001 0.286764i \(-0.0925795\pi\)
\(192\) −14116.6 11428.5i −0.382937 0.310019i
\(193\) 55571.2 1.49188 0.745942 0.666011i \(-0.232000\pi\)
0.745942 + 0.666011i \(0.232000\pi\)
\(194\) 1286.11 + 8604.37i 0.0341723 + 0.228621i
\(195\) 10082.8i 0.265163i
\(196\) −35506.4 + 10857.0i −0.924261 + 0.282616i
\(197\) −50210.5 −1.29378 −0.646892 0.762582i \(-0.723932\pi\)
−0.646892 + 0.762582i \(0.723932\pi\)
\(198\) −46994.3 + 7024.33i −1.19871 + 0.179174i
\(199\) 4943.87i 0.124842i −0.998050 0.0624211i \(-0.980118\pi\)
0.998050 0.0624211i \(-0.0198822\pi\)
\(200\) −12491.2 26184.2i −0.312279 0.654605i
\(201\) 20231.3 0.500761
\(202\) 2670.86 + 17868.6i 0.0654557 + 0.437914i
\(203\) 12852.8i 0.311892i
\(204\) −1728.00 5651.22i −0.0415226 0.135794i
\(205\) 11730.8 0.279139
\(206\) −9735.63 + 1455.20i −0.229419 + 0.0342917i
\(207\) 41959.5i 0.979241i
\(208\) 36826.4 24844.1i 0.851202 0.574244i
\(209\) −16039.5 −0.367197
\(210\) −308.126 2061.43i −0.00698699 0.0467445i
\(211\) 67805.4i 1.52300i −0.648166 0.761499i \(-0.724464\pi\)
0.648166 0.761499i \(-0.275536\pi\)
\(212\) 54797.4 16755.7i 1.21924 0.372812i
\(213\) −661.329 −0.0145767
\(214\) 33646.7 5029.23i 0.734708 0.109818i
\(215\) 12172.4i 0.263330i
\(216\) −36458.4 + 17392.5i −0.781431 + 0.372782i
\(217\) 6732.88 0.142982
\(218\) 1600.24 + 10705.9i 0.0336721 + 0.225274i
\(219\) 12546.9i 0.261606i
\(220\) 11873.0 + 38829.3i 0.245311 + 0.802259i
\(221\) 14453.6 0.295932
\(222\) 7675.46 1147.26i 0.155739 0.0232786i
\(223\) 35884.4i 0.721598i 0.932644 + 0.360799i \(0.117496\pi\)
−0.932644 + 0.360799i \(0.882504\pi\)
\(224\) −6769.94 + 6204.77i −0.134924 + 0.123660i
\(225\) −27803.9 −0.549213
\(226\) −3661.31 24495.0i −0.0716835 0.479579i
\(227\) 79862.5i 1.54985i 0.632050 + 0.774927i \(0.282214\pi\)
−0.632050 + 0.774927i \(0.717786\pi\)
\(228\) −5619.09 + 1718.18i −0.108093 + 0.0330521i
\(229\) −56160.1 −1.07092 −0.535460 0.844561i \(-0.679862\pi\)
−0.535460 + 0.844561i \(0.679862\pi\)
\(230\) −35461.6 + 5300.50i −0.670351 + 0.100199i
\(231\) 7701.58i 0.144330i
\(232\) 39493.1 + 82786.1i 0.733746 + 1.53809i
\(233\) −71608.6 −1.31903 −0.659513 0.751694i \(-0.729237\pi\)
−0.659513 + 0.751694i \(0.729237\pi\)
\(234\) −6293.80 42106.9i −0.114943 0.768992i
\(235\) 27737.3i 0.502259i
\(236\) −1436.10 4696.60i −0.0257847 0.0843256i
\(237\) 30577.2 0.544378
\(238\) −2955.04 + 441.695i −0.0521686 + 0.00779773i
\(239\) 11359.8i 0.198873i 0.995044 + 0.0994366i \(0.0317040\pi\)
−0.995044 + 0.0994366i \(0.968296\pi\)
\(240\) 8318.92 + 12331.1i 0.144426 + 0.214082i
\(241\) −42161.8 −0.725914 −0.362957 0.931806i \(-0.618233\pi\)
−0.362957 + 0.931806i \(0.618233\pi\)
\(242\) 13521.6 + 90462.3i 0.230885 + 1.54467i
\(243\) 60744.7i 1.02872i
\(244\) 108490. 33173.5i 1.82226 0.557201i
\(245\) 30407.7 0.506584
\(246\) 15704.6 2347.39i 0.259511 0.0387896i
\(247\) 14371.4i 0.235562i
\(248\) −43367.3 + 20688.4i −0.705113 + 0.336374i
\(249\) −34774.2 −0.560866
\(250\) 8355.03 + 55897.0i 0.133680 + 0.894352i
\(251\) 7549.02i 0.119824i −0.998204 0.0599119i \(-0.980918\pi\)
0.998204 0.0599119i \(-0.0190820\pi\)
\(252\) 2573.54 + 8416.43i 0.0405256 + 0.132534i
\(253\) −132486. −2.06980
\(254\) −11063.9 + 1653.74i −0.171491 + 0.0256330i
\(255\) 4839.71i 0.0744285i
\(256\) 24540.3 60767.9i 0.374456 0.927245i
\(257\) −24834.0 −0.375994 −0.187997 0.982170i \(-0.560200\pi\)
−0.187997 + 0.982170i \(0.560200\pi\)
\(258\) 2435.76 + 16295.8i 0.0365928 + 0.244814i
\(259\) 3923.85i 0.0584942i
\(260\) −34791.1 + 10638.3i −0.514661 + 0.157371i
\(261\) 87907.2 1.29046
\(262\) 96204.6 14379.9i 1.40150 0.209485i
\(263\) 10991.3i 0.158905i −0.996839 0.0794527i \(-0.974683\pi\)
0.996839 0.0794527i \(-0.0253173\pi\)
\(264\) 23664.9 + 49606.8i 0.339545 + 0.711760i
\(265\) −46928.5 −0.668260
\(266\) 439.183 + 2938.24i 0.00620701 + 0.0415263i
\(267\) 38639.6i 0.542014i
\(268\) 21345.7 + 69808.6i 0.297195 + 0.971940i
\(269\) 123859. 1.71168 0.855839 0.517242i \(-0.173041\pi\)
0.855839 + 0.517242i \(0.173041\pi\)
\(270\) 32718.4 4890.48i 0.448813 0.0670848i
\(271\) 38457.3i 0.523649i −0.965116 0.261824i \(-0.915676\pi\)
0.965116 0.261824i \(-0.0843241\pi\)
\(272\) 17676.5 11925.1i 0.238924 0.161184i
\(273\) 6900.62 0.0925898
\(274\) −14483.2 96895.6i −0.192913 1.29063i
\(275\) 87789.9i 1.16086i
\(276\) −46413.4 + 14192.1i −0.609292 + 0.186306i
\(277\) −63456.0 −0.827015 −0.413508 0.910501i \(-0.635696\pi\)
−0.413508 + 0.910501i \(0.635696\pi\)
\(278\) 120958. 18079.8i 1.56511 0.233940i
\(279\) 46049.9i 0.591590i
\(280\) 6787.94 3238.19i 0.0865809 0.0413034i
\(281\) −49117.0 −0.622041 −0.311020 0.950403i \(-0.600671\pi\)
−0.311020 + 0.950403i \(0.600671\pi\)
\(282\) 5550.37 + 37133.2i 0.0697948 + 0.466943i
\(283\) 71155.9i 0.888460i 0.895913 + 0.444230i \(0.146523\pi\)
−0.895913 + 0.444230i \(0.853477\pi\)
\(284\) −697.759 2281.94i −0.00865105 0.0282922i
\(285\) 4812.20 0.0592453
\(286\) −132951. + 19872.4i −1.62540 + 0.242951i
\(287\) 8028.50i 0.0974699i
\(288\) −42437.9 46303.4i −0.511645 0.558249i
\(289\) −76583.3 −0.916935
\(290\) −11104.8 74293.7i −0.132043 0.883397i
\(291\) 9644.55i 0.113893i
\(292\) 43293.4 13238.1i 0.507758 0.155260i
\(293\) 2819.70 0.0328448 0.0164224 0.999865i \(-0.494772\pi\)
0.0164224 + 0.999865i \(0.494772\pi\)
\(294\) 40708.2 6084.73i 0.470964 0.0703958i
\(295\) 4022.17i 0.0462186i
\(296\) 12057.0 + 25274.0i 0.137611 + 0.288463i
\(297\) 122237. 1.38577
\(298\) −25171.8 168405.i −0.283454 1.89637i
\(299\) 118707.i 1.32781i
\(300\) 9404.19 + 30755.2i 0.104491 + 0.341725i
\(301\) 8330.74 0.0919498
\(302\) −128430. + 19196.6i −1.40816 + 0.210480i
\(303\) 20028.8i 0.218157i
\(304\) −11857.3 17576.0i −0.128303 0.190184i
\(305\) −92910.9 −0.998774
\(306\) −3021.00 20211.2i −0.0322632 0.215848i
\(307\) 161051.i 1.70878i 0.519631 + 0.854391i \(0.326069\pi\)
−0.519631 + 0.854391i \(0.673931\pi\)
\(308\) 26574.6 8125.84i 0.280133 0.0856578i
\(309\) 10912.6 0.114290
\(310\) 38918.5 5817.22i 0.404980 0.0605330i
\(311\) 138439.i 1.43133i −0.698446 0.715663i \(-0.746125\pi\)
0.698446 0.715663i \(-0.253875\pi\)
\(312\) −44447.7 + 21203.8i −0.456605 + 0.217823i
\(313\) 26633.8 0.271860 0.135930 0.990718i \(-0.456598\pi\)
0.135930 + 0.990718i \(0.456598\pi\)
\(314\) −115.415 772.150i −0.00117058 0.00783145i
\(315\) 7207.84i 0.0726414i
\(316\) 32261.6 + 105508.i 0.323081 + 1.05660i
\(317\) −45290.4 −0.450700 −0.225350 0.974278i \(-0.572353\pi\)
−0.225350 + 0.974278i \(0.572353\pi\)
\(318\) −62825.4 + 9390.63i −0.621271 + 0.0928625i
\(319\) 277564.i 2.72760i
\(320\) −33771.8 + 41715.1i −0.329803 + 0.407374i
\(321\) −37714.2 −0.366012
\(322\) 3627.63 + 24269.7i 0.0349874 + 0.234074i
\(323\) 6898.22i 0.0661199i
\(324\) −33195.3 + 10150.3i −0.316218 + 0.0966915i
\(325\) −78659.8 −0.744708
\(326\) 84368.1 12610.7i 0.793859 0.118659i
\(327\) 12000.2i 0.112226i
\(328\) 24669.5 + 51712.5i 0.229304 + 0.480671i
\(329\) 18983.2 0.175379
\(330\) −6654.19 44518.0i −0.0611036 0.408797i
\(331\) 1136.55i 0.0103737i 0.999987 + 0.00518685i \(0.00165103\pi\)
−0.999987 + 0.00518685i \(0.998349\pi\)
\(332\) −36689.9 119990.i −0.332866 1.08860i
\(333\) 26837.4 0.242020
\(334\) 83053.8 12414.2i 0.744504 0.111282i
\(335\) 59784.2i 0.532717i
\(336\) 8439.36 5693.42i 0.0747534 0.0504307i
\(337\) 126361. 1.11263 0.556317 0.830970i \(-0.312214\pi\)
0.556317 + 0.830970i \(0.312214\pi\)
\(338\) −917.078 6135.46i −0.00802736 0.0537049i
\(339\) 27456.2i 0.238913i
\(340\) −16699.6 + 5106.32i −0.144460 + 0.0441723i
\(341\) 145401. 1.25043
\(342\) −20096.2 + 3003.82i −0.171816 + 0.0256816i
\(343\) 42343.0i 0.359909i
\(344\) −53659.3 + 25598.2i −0.453449 + 0.216318i
\(345\) 39748.5 0.333951
\(346\) −20375.8 136319.i −0.170201 1.13869i
\(347\) 164302.i 1.36453i 0.731103 + 0.682267i \(0.239006\pi\)
−0.731103 + 0.682267i \(0.760994\pi\)
\(348\) −29733.1 97238.3i −0.245517 0.802932i
\(349\) −57342.3 −0.470787 −0.235394 0.971900i \(-0.575638\pi\)
−0.235394 + 0.971900i \(0.575638\pi\)
\(350\) 16082.0 2403.80i 0.131282 0.0196229i
\(351\) 109525.i 0.888991i
\(352\) −146201. + 133996.i −1.17996 + 1.08145i
\(353\) 229162. 1.83905 0.919524 0.393034i \(-0.128575\pi\)
0.919524 + 0.393034i \(0.128575\pi\)
\(354\) 804.857 + 5384.67i 0.00642262 + 0.0429688i
\(355\) 1954.25i 0.0155069i
\(356\) 133327. 40768.2i 1.05201 0.321678i
\(357\) 3312.27 0.0259890
\(358\) 104036. 15550.4i 0.811739 0.121332i
\(359\) 140525.i 1.09035i −0.838322 0.545175i \(-0.816463\pi\)
0.838322 0.545175i \(-0.183537\pi\)
\(360\) 22147.8 + 46426.5i 0.170894 + 0.358229i
\(361\) −6859.00 −0.0526316
\(362\) 14426.0 + 96513.3i 0.110085 + 0.736495i
\(363\) 101398.i 0.769516i
\(364\) 7280.76 + 23810.8i 0.0549508 + 0.179710i
\(365\) −37076.5 −0.278300
\(366\) −124384. + 18591.9i −0.928545 + 0.138791i
\(367\) 181307.i 1.34612i 0.739589 + 0.673059i \(0.235020\pi\)
−0.739589 + 0.673059i \(0.764980\pi\)
\(368\) −97940.4 145177.i −0.723213 1.07202i
\(369\) 54911.4 0.403283
\(370\) −3390.21 22681.3i −0.0247642 0.165678i
\(371\) 32117.6i 0.233343i
\(372\) 50938.0 15575.6i 0.368092 0.112553i
\(373\) 181780. 1.30656 0.653280 0.757117i \(-0.273393\pi\)
0.653280 + 0.757117i \(0.273393\pi\)
\(374\) −63816.0 + 9538.69i −0.456233 + 0.0681939i
\(375\) 62654.4i 0.445542i
\(376\) −122273. + 58330.5i −0.864879 + 0.412591i
\(377\) 248697. 1.74980
\(378\) −3347.02 22392.3i −0.0234247 0.156717i
\(379\) 151291.i 1.05326i 0.850095 + 0.526629i \(0.176544\pi\)
−0.850095 + 0.526629i \(0.823456\pi\)
\(380\) 5077.29 + 16604.6i 0.0351613 + 0.114991i
\(381\) 12401.4 0.0854320
\(382\) −82771.9 + 12372.1i −0.567226 + 0.0847843i
\(383\) 150881.i 1.02858i 0.857616 + 0.514290i \(0.171945\pi\)
−0.857616 + 0.514290i \(0.828055\pi\)
\(384\) −36864.5 + 62603.9i −0.250004 + 0.424560i
\(385\) −22758.5 −0.153540
\(386\) −32860.2 219842.i −0.220544 1.47549i
\(387\) 56978.6i 0.380443i
\(388\) 33278.8 10175.8i 0.221057 0.0675938i
\(389\) −1428.09 −0.00943750 −0.00471875 0.999989i \(-0.501502\pi\)
−0.00471875 + 0.999989i \(0.501502\pi\)
\(390\) 39888.2 5962.15i 0.262250 0.0391989i
\(391\) 56979.0i 0.372701i
\(392\) 63946.3 + 134045.i 0.416144 + 0.872327i
\(393\) −107835. −0.698190
\(394\) 29690.4 + 198635.i 0.191259 + 1.27957i
\(395\) 90356.8i 0.579117i
\(396\) 55577.2 + 181758.i 0.354410 + 1.15906i
\(397\) −208771. −1.32461 −0.662307 0.749233i \(-0.730423\pi\)
−0.662307 + 0.749233i \(0.730423\pi\)
\(398\) −19558.2 + 2923.40i −0.123471 + 0.0184554i
\(399\) 3293.44i 0.0206873i
\(400\) −96199.7 + 64898.9i −0.601248 + 0.405618i
\(401\) 237252. 1.47544 0.737719 0.675108i \(-0.235903\pi\)
0.737719 + 0.675108i \(0.235903\pi\)
\(402\) −11963.1 80035.9i −0.0740273 0.495259i
\(403\) 130279.i 0.802168i
\(404\) 69109.9 21132.1i 0.423426 0.129473i
\(405\) 28428.4 0.173318
\(406\) −50846.2 + 7600.07i −0.308465 + 0.0461068i
\(407\) 84738.1i 0.511552i
\(408\) −21334.7 + 10177.7i −0.128164 + 0.0611408i
\(409\) −315975. −1.88889 −0.944443 0.328676i \(-0.893397\pi\)
−0.944443 + 0.328676i \(0.893397\pi\)
\(410\) −6936.64 46407.7i −0.0412650 0.276072i
\(411\) 108609.i 0.642959i
\(412\) 11513.7 + 37654.2i 0.0678298 + 0.221829i
\(413\) 2752.75 0.0161386
\(414\) −165994. + 24811.4i −0.968482 + 0.144761i
\(415\) 102759.i 0.596657i
\(416\) −120061. 130996.i −0.693767 0.756960i
\(417\) −135581. −0.779697
\(418\) 9484.46 + 63453.2i 0.0542825 + 0.363162i
\(419\) 233329.i 1.32905i −0.747266 0.664525i \(-0.768634\pi\)
0.747266 0.664525i \(-0.231366\pi\)
\(420\) −7972.93 + 2437.92i −0.0451980 + 0.0138204i
\(421\) −162883. −0.918992 −0.459496 0.888180i \(-0.651970\pi\)
−0.459496 + 0.888180i \(0.651970\pi\)
\(422\) −268242. + 40094.6i −1.50626 + 0.225144i
\(423\) 129837.i 0.725634i
\(424\) −98689.0 206873.i −0.548955 1.15073i
\(425\) −37756.4 −0.209032
\(426\) 391.056 + 2616.25i 0.00215486 + 0.0144165i
\(427\) 63587.7i 0.348752i
\(428\) −39791.8 130134.i −0.217223 0.710401i
\(429\) 149024. 0.809730
\(430\) 48154.8 7197.78i 0.260437 0.0389280i
\(431\) 353158.i 1.90114i 0.310512 + 0.950570i \(0.399500\pi\)
−0.310512 + 0.950570i \(0.600500\pi\)
\(432\) 90364.2 + 133947.i 0.484205 + 0.717737i
\(433\) 107507. 0.573406 0.286703 0.958020i \(-0.407441\pi\)
0.286703 + 0.958020i \(0.407441\pi\)
\(434\) −3981.27 26635.6i −0.0211370 0.141411i
\(435\) 83275.0i 0.440085i
\(436\) 41407.0 12661.2i 0.217821 0.0666044i
\(437\) −56655.0 −0.296671
\(438\) −49636.1 + 7419.20i −0.258732 + 0.0386731i
\(439\) 365722.i 1.89767i −0.315766 0.948837i \(-0.602261\pi\)
0.315766 0.948837i \(-0.397739\pi\)
\(440\) 146590. 69930.9i 0.757180 0.361213i
\(441\) 142337. 0.731882
\(442\) −8546.67 57179.2i −0.0437474 0.292680i
\(443\) 11929.3i 0.0607867i 0.999538 + 0.0303934i \(0.00967600\pi\)
−0.999538 + 0.0303934i \(0.990324\pi\)
\(444\) −9077.28 29686.1i −0.0460458 0.150587i
\(445\) −114182. −0.576602
\(446\) 141960. 21219.1i 0.713670 0.106674i
\(447\) 188764.i 0.944720i
\(448\) 28549.6 + 23113.2i 0.142247 + 0.115161i
\(449\) −85864.7 −0.425914 −0.212957 0.977062i \(-0.568309\pi\)
−0.212957 + 0.977062i \(0.568309\pi\)
\(450\) 16441.0 + 109994.i 0.0811899 + 0.543179i
\(451\) 173381.i 0.852409i
\(452\) −94738.4 + 28968.6i −0.463713 + 0.141792i
\(453\) 143955. 0.701507
\(454\) 315940. 47224.1i 1.53283 0.229114i
\(455\) 20391.6i 0.0984983i
\(456\) 10119.9 + 21213.4i 0.0486682 + 0.102019i
\(457\) −281117. −1.34603 −0.673015 0.739629i \(-0.735001\pi\)
−0.673015 + 0.739629i \(0.735001\pi\)
\(458\) 33208.5 + 222172.i 0.158313 + 1.05915i
\(459\) 52571.4i 0.249531i
\(460\) 41938.1 + 137153.i 0.198195 + 0.648173i
\(461\) −7044.46 −0.0331471 −0.0165736 0.999863i \(-0.505276\pi\)
−0.0165736 + 0.999863i \(0.505276\pi\)
\(462\) −30467.9 + 4554.09i −0.142744 + 0.0213362i
\(463\) 216166.i 1.00838i −0.863592 0.504192i \(-0.831791\pi\)
0.863592 0.504192i \(-0.168209\pi\)
\(464\) 304153. 205190.i 1.41272 0.953059i
\(465\) −43623.4 −0.201750
\(466\) 42343.4 + 283287.i 0.194991 + 1.30453i
\(467\) 211192.i 0.968373i −0.874965 0.484187i \(-0.839116\pi\)
0.874965 0.484187i \(-0.160884\pi\)
\(468\) −162856. + 49797.2i −0.743551 + 0.227360i
\(469\) −40915.9 −0.186014
\(470\) 109730. 16401.6i 0.496741 0.0742488i
\(471\) 865.495i 0.00390142i
\(472\) −17730.8 + 8458.49i −0.0795874 + 0.0379672i
\(473\) 179908. 0.804133
\(474\) −18080.8 120965.i −0.0804752 0.538397i
\(475\) 37541.7i 0.166390i
\(476\) 3494.73 + 11429.1i 0.0154241 + 0.0504427i
\(477\) −219670. −0.965461
\(478\) 44940.1 6717.28i 0.196688 0.0293993i
\(479\) 318333.i 1.38743i −0.720251 0.693714i \(-0.755973\pi\)
0.720251 0.693714i \(-0.244027\pi\)
\(480\) 43863.5 40201.7i 0.190380 0.174487i
\(481\) 75925.4 0.328168
\(482\) 24931.1 + 166794.i 0.107312 + 0.717939i
\(483\) 27203.6i 0.116609i
\(484\) 349878. 106984.i 1.49357 0.456697i
\(485\) −28500.0 −0.121161
\(486\) 240309. 35919.4i 1.01741 0.152075i
\(487\) 158377.i 0.667780i −0.942612 0.333890i \(-0.891639\pi\)
0.942612 0.333890i \(-0.108361\pi\)
\(488\) −195388. 409576.i −0.820463 1.71987i
\(489\) −94567.3 −0.395479
\(490\) −17980.6 120294.i −0.0748881 0.501018i
\(491\) 38055.1i 0.157852i −0.996880 0.0789260i \(-0.974851\pi\)
0.996880 0.0789260i \(-0.0251491\pi\)
\(492\) −18572.8 60740.1i −0.0767269 0.250926i
\(493\) 119374. 0.491151
\(494\) −56854.1 + 8498.08i −0.232974 + 0.0348230i
\(495\) 155658.i 0.635274i
\(496\) 107488. + 159330.i 0.436915 + 0.647640i
\(497\) 1337.48 0.00541470
\(498\) 20562.6 + 137569.i 0.0829125 + 0.554704i
\(499\) 477988.i 1.91962i 0.280644 + 0.959812i \(0.409452\pi\)
−0.280644 + 0.959812i \(0.590548\pi\)
\(500\) 216191. 66105.8i 0.864764 0.264423i
\(501\) −93094.2 −0.370892
\(502\) −29864.3 + 4463.87i −0.118507 + 0.0177135i
\(503\) 157454.i 0.622327i 0.950356 + 0.311163i \(0.100719\pi\)
−0.950356 + 0.311163i \(0.899281\pi\)
\(504\) 31774.1 15157.8i 0.125087 0.0596727i
\(505\) −59185.8 −0.232078
\(506\) 78341.1 + 524120.i 0.305977 + 2.04706i
\(507\) 6877.17i 0.0267543i
\(508\) 13084.6 + 42791.4i 0.0507028 + 0.165817i
\(509\) −85407.2 −0.329654 −0.164827 0.986322i \(-0.552707\pi\)
−0.164827 + 0.986322i \(0.552707\pi\)
\(510\) 19146.2 2861.81i 0.0736107 0.0110027i
\(511\) 25375.0i 0.0971771i
\(512\) −254912. 61149.7i −0.972413 0.233267i
\(513\) 52272.5 0.198627
\(514\) 14684.8 + 98244.7i 0.0555830 + 0.371863i
\(515\) 32247.1i 0.121584i
\(516\) 63026.8 19272.0i 0.236715 0.0723815i
\(517\) 409955. 1.53375
\(518\) −15522.9 + 2320.24i −0.0578515 + 0.00864717i
\(519\) 152798.i 0.567263i
\(520\) 62658.1 + 131345.i 0.231724 + 0.485743i
\(521\) −181842. −0.669915 −0.334957 0.942233i \(-0.608722\pi\)
−0.334957 + 0.942233i \(0.608722\pi\)
\(522\) −51981.1 347765.i −0.190768 1.27628i
\(523\) 479579.i 1.75330i −0.481128 0.876651i \(-0.659773\pi\)
0.481128 0.876651i \(-0.340227\pi\)
\(524\) −113775. 372087.i −0.414366 1.35513i
\(525\) −18026.1 −0.0654009
\(526\) −43482.2 + 6499.37i −0.157159 + 0.0234909i
\(527\) 62533.6i 0.225160i
\(528\) 182254. 122953.i 0.653745 0.441034i
\(529\) −188126. −0.672262
\(530\) 27749.7 + 185652.i 0.0987885 + 0.660917i
\(531\) 18827.6i 0.0667738i
\(532\) 11364.1 3474.86i 0.0401525 0.0122776i
\(533\) 155349. 0.546833
\(534\) −152860. + 22848.3i −0.536058 + 0.0801256i
\(535\) 111447.i 0.389368i
\(536\) 263544. 125724.i 0.917327 0.437611i
\(537\) −116612. −0.404386
\(538\) −73239.9 489992.i −0.253037 1.69287i
\(539\) 449424.i 1.54696i
\(540\) −38694.0 126544.i −0.132696 0.433964i
\(541\) −90387.3 −0.308825 −0.154413 0.988006i \(-0.549349\pi\)
−0.154413 + 0.988006i \(0.549349\pi\)
\(542\) −152139. + 22740.5i −0.517895 + 0.0774107i
\(543\) 108181.i 0.366902i
\(544\) −57628.6 62877.8i −0.194733 0.212471i
\(545\) −35461.0 −0.119387
\(546\) −4080.46 27299.2i −0.0136875 0.0915725i
\(547\) 106106.i 0.354622i 0.984155 + 0.177311i \(0.0567398\pi\)
−0.984155 + 0.177311i \(0.943260\pi\)
\(548\) −374760. + 114592.i −1.24793 + 0.381587i
\(549\) −434912. −1.44297
\(550\) 347301. 51911.7i 1.14810 0.171609i
\(551\) 118695.i 0.390957i
\(552\) 83589.6 + 175222.i 0.274331 + 0.575056i
\(553\) −61839.7 −0.202217
\(554\) 37522.7 + 251035.i 0.122257 + 0.817929i
\(555\) 25423.2i 0.0825362i
\(556\) −143049. 467826.i −0.462740 1.51333i
\(557\) −566621. −1.82634 −0.913171 0.407576i \(-0.866374\pi\)
−0.913171 + 0.407576i \(0.866374\pi\)
\(558\) 182176. 27230.2i 0.585090 0.0874544i
\(559\) 161198.i 0.515863i
\(560\) −16824.3 24938.6i −0.0536489 0.0795237i
\(561\) 71530.7 0.227283
\(562\) 29043.7 + 194309.i 0.0919560 + 0.615206i
\(563\) 568120.i 1.79235i −0.443698 0.896176i \(-0.646334\pi\)
0.443698 0.896176i \(-0.353666\pi\)
\(564\) 143619. 43915.1i 0.451495 0.138056i
\(565\) 81134.0 0.254159
\(566\) 281496. 42075.8i 0.878699 0.131341i
\(567\) 19456.3i 0.0605192i
\(568\) −8614.86 + 4109.72i −0.0267025 + 0.0127384i
\(569\) −86245.2 −0.266386 −0.133193 0.991090i \(-0.542523\pi\)
−0.133193 + 0.991090i \(0.542523\pi\)
\(570\) −2845.54 19037.3i −0.00875820 0.0585943i
\(571\) 75126.1i 0.230419i −0.993341 0.115210i \(-0.963246\pi\)
0.993341 0.115210i \(-0.0367540\pi\)
\(572\) 157233. + 514211.i 0.480564 + 1.57162i
\(573\) 92778.2 0.282577
\(574\) −31761.2 + 4747.40i −0.0963990 + 0.0144089i
\(575\) 310092.i 0.937898i
\(576\) −158084. + 195267.i −0.476479 + 0.588550i
\(577\) 489075. 1.46901 0.734504 0.678604i \(-0.237415\pi\)
0.734504 + 0.678604i \(0.237415\pi\)
\(578\) 45285.1 + 302968.i 0.135550 + 0.906861i
\(579\) 246419.i 0.735050i
\(580\) −287343. + 87862.4i −0.854171 + 0.261184i
\(581\) 70327.9 0.208341
\(582\) −38154.3 + 5703.00i −0.112641 + 0.0168367i
\(583\) 693601.i 2.04067i
\(584\) −77970.6 163443.i −0.228615 0.479227i
\(585\) 139470. 0.407538
\(586\) −1667.34 11154.9i −0.00485544 0.0324840i
\(587\) 562634.i 1.63286i 0.577442 + 0.816432i \(0.304051\pi\)
−0.577442 + 0.816432i \(0.695949\pi\)
\(588\) −48143.0 157446.i −0.139245 0.455383i
\(589\) 62178.0 0.179228
\(590\) 15911.9 2378.38i 0.0457108 0.00683247i
\(591\) 222648.i 0.637447i
\(592\) 92855.6 62642.9i 0.264951 0.178743i
\(593\) −354885. −1.00920 −0.504602 0.863352i \(-0.668361\pi\)
−0.504602 + 0.863352i \(0.668361\pi\)
\(594\) −72281.1 483577.i −0.204857 1.37054i
\(595\) 9787.89i 0.0276475i
\(596\) −651335. + 199162.i −1.83363 + 0.560679i
\(597\) 21922.6 0.0615097
\(598\) −469612. + 70193.7i −1.31322 + 0.196289i
\(599\) 214683.i 0.598333i 0.954201 + 0.299167i \(0.0967087\pi\)
−0.954201 + 0.299167i \(0.903291\pi\)
\(600\) 116108. 55389.6i 0.322523 0.153860i
\(601\) 79153.3 0.219139 0.109570 0.993979i \(-0.465053\pi\)
0.109570 + 0.993979i \(0.465053\pi\)
\(602\) −4926.12 32956.8i −0.0135929 0.0909395i
\(603\) 279847.i 0.769637i
\(604\) 151886. + 496723.i 0.416335 + 1.36157i
\(605\) −299636. −0.818622
\(606\) −79234.8 + 11843.4i −0.215760 + 0.0322500i
\(607\) 483102.i 1.31118i 0.755118 + 0.655589i \(0.227580\pi\)
−0.755118 + 0.655589i \(0.772420\pi\)
\(608\) −62520.3 + 57301.0i −0.169127 + 0.155008i
\(609\) 56992.9 0.153669
\(610\) 54939.9 + 367560.i 0.147648 + 0.987800i
\(611\) 367320.i 0.983926i
\(612\) −78170.0 + 23902.5i −0.208707 + 0.0638175i
\(613\) 199537. 0.531010 0.265505 0.964109i \(-0.414461\pi\)
0.265505 + 0.964109i \(0.414461\pi\)
\(614\) 637126. 95232.3i 1.69001 0.252608i
\(615\) 52017.9i 0.137532i
\(616\) −47860.3 100325.i −0.126129 0.264393i
\(617\) 121881. 0.320159 0.160079 0.987104i \(-0.448825\pi\)
0.160079 + 0.987104i \(0.448825\pi\)
\(618\) −6452.80 43170.7i −0.0168955 0.113035i
\(619\) 133551.i 0.348550i 0.984697 + 0.174275i \(0.0557582\pi\)
−0.984697 + 0.174275i \(0.944242\pi\)
\(620\) −46026.5 150524.i −0.119736 0.391581i
\(621\) 431768. 1.11961
\(622\) −547673. + 81861.7i −1.41560 + 0.211592i
\(623\) 78145.2i 0.201338i
\(624\) 110166. + 163299.i 0.282930 + 0.419387i
\(625\) 98164.8 0.251302
\(626\) −15749.1 105365.i −0.0401889 0.268873i
\(627\) 71124.0i 0.180918i
\(628\) −2986.42 + 913.172i −0.00757236 + 0.00231544i
\(629\) 36443.9 0.0921135
\(630\) −28514.6 + 4262.13i −0.0718432 + 0.0107385i
\(631\) 559153.i 1.40434i −0.712010 0.702169i \(-0.752215\pi\)
0.712010 0.702169i \(-0.247785\pi\)
\(632\) 398316. 190017.i 0.997227 0.475728i
\(633\) 300669. 0.750380
\(634\) 26781.0 + 179171.i 0.0666267 + 0.445748i
\(635\) 36646.6i 0.0908838i
\(636\) 74299.6 + 242988.i 0.183685 + 0.600718i
\(637\) 402684. 0.992398
\(638\) −1.09806e6 + 164128.i −2.69764 + 0.403220i
\(639\) 9147.77i 0.0224034i
\(640\) 184997. + 108936.i 0.451653 + 0.265957i
\(641\) 523535. 1.27418 0.637089 0.770791i \(-0.280139\pi\)
0.637089 + 0.770791i \(0.280139\pi\)
\(642\) 22301.1 + 149199.i 0.0541073 + 0.361990i
\(643\) 508744.i 1.23049i −0.788337 0.615244i \(-0.789057\pi\)
0.788337 0.615244i \(-0.210943\pi\)
\(644\) 93867.0 28702.2i 0.226330 0.0692060i
\(645\) −53976.2 −0.129743
\(646\) −27289.7 + 4079.04i −0.0653934 + 0.00977447i
\(647\) 303404.i 0.724792i −0.932024 0.362396i \(-0.881959\pi\)
0.932024 0.362396i \(-0.118041\pi\)
\(648\) 59784.0 + 125320.i 0.142375 + 0.298449i
\(649\) 59447.5 0.141138
\(650\) 46512.9 + 311182.i 0.110090 + 0.736526i
\(651\) 29855.6i 0.0704472i
\(652\) −99776.8 326308.i −0.234711 0.767595i
\(653\) 479003. 1.12334 0.561671 0.827361i \(-0.310159\pi\)
0.561671 + 0.827361i \(0.310159\pi\)
\(654\) −47473.3 + 7095.92i −0.110993 + 0.0165903i
\(655\) 318656.i 0.742745i
\(656\) 189990. 128172.i 0.441492 0.297842i
\(657\) −173554. −0.402071
\(658\) −11225.1 75098.6i −0.0259262 0.173452i
\(659\) 28254.6i 0.0650606i −0.999471 0.0325303i \(-0.989643\pi\)
0.999471 0.0325303i \(-0.0103565\pi\)
\(660\) −172181. + 52648.6i −0.395273 + 0.120865i
\(661\) 546615. 1.25106 0.625530 0.780200i \(-0.284883\pi\)
0.625530 + 0.780200i \(0.284883\pi\)
\(662\) 4496.26 672.065i 0.0102597 0.00153354i
\(663\) 64091.5i 0.145805i
\(664\) −452990. + 216099.i −1.02743 + 0.490136i
\(665\) −9732.24 −0.0220074
\(666\) −15869.4 106170.i −0.0357778 0.239361i
\(667\) 980414.i 2.20373i
\(668\) −98222.5 321225.i −0.220119 0.719873i
\(669\) −159122. −0.355531
\(670\) −236509. + 35351.5i −0.526864 + 0.0787513i
\(671\) 1.37322e6i 3.04996i
\(672\) −27513.8 30019.9i −0.0609273 0.0664769i
\(673\) 146970. 0.324489 0.162244 0.986751i \(-0.448127\pi\)
0.162244 + 0.986751i \(0.448127\pi\)
\(674\) −74719.3 499889.i −0.164480 1.10041i
\(675\) 286105.i 0.627941i
\(676\) −23729.9 + 7256.02i −0.0519281 + 0.0158783i
\(677\) −636186. −1.38806 −0.694028 0.719948i \(-0.744166\pi\)
−0.694028 + 0.719948i \(0.744166\pi\)
\(678\) 108618. 16235.3i 0.236288 0.0353184i
\(679\) 19505.2i 0.0423070i
\(680\) 30075.6 + 63045.0i 0.0650425 + 0.136343i
\(681\) −354134. −0.763613
\(682\) −85978.2 575214.i −0.184850 1.23669i
\(683\) 471150.i 1.00999i −0.863122 0.504996i \(-0.831494\pi\)
0.863122 0.504996i \(-0.168506\pi\)
\(684\) 23766.5 + 77725.6i 0.0507989 + 0.166131i
\(685\) 320945. 0.683989
\(686\) −167511. + 25038.2i −0.355955 + 0.0532052i
\(687\) 249030.i 0.527641i
\(688\) 132997. + 197142.i 0.280974 + 0.416488i
\(689\) −621467. −1.30912
\(690\) −23504.0 157247.i −0.0493678 0.330282i
\(691\) 727652.i 1.52394i 0.647613 + 0.761970i \(0.275767\pi\)
−0.647613 + 0.761970i \(0.724233\pi\)
\(692\) −527236. + 161216.i −1.10101 + 0.336663i
\(693\) −106531. −0.221826
\(694\) 649988. 97154.8i 1.34954 0.201718i
\(695\) 400646.i 0.829453i
\(696\) −367098. + 175124.i −0.757816 + 0.361516i
\(697\) 74567.0 0.153490
\(698\) 33907.6 + 226849.i 0.0695962 + 0.465614i
\(699\) 317534.i 0.649883i
\(700\) −19019.1 62199.8i −0.0388146 0.126938i
\(701\) 610269. 1.24190 0.620948 0.783852i \(-0.286748\pi\)
0.620948 + 0.783852i \(0.286748\pi\)
\(702\) 433285. 64763.9i 0.879224 0.131419i
\(703\) 36236.7i 0.0733226i
\(704\) 616547. + 499146.i 1.24400 + 1.00712i
\(705\) −122995. −0.247463
\(706\) −135508. 906576.i −0.271866 1.81884i
\(707\) 40506.4i 0.0810373i
\(708\) 20826.1 6368.11i 0.0415472 0.0127041i
\(709\) 31766.6 0.0631943 0.0315972 0.999501i \(-0.489941\pi\)
0.0315972 + 0.999501i \(0.489941\pi\)
\(710\) 7731.12 1155.58i 0.0153365 0.00229237i
\(711\) 422956.i 0.836674i
\(712\) −240120. 503342.i −0.473661 0.992896i
\(713\) 513587. 1.01026
\(714\) −1958.61 13103.5i −0.00384194 0.0257035i
\(715\) 440370.i 0.861402i
\(716\) −123036. 402375.i −0.239998 0.784883i
\(717\) −50372.9 −0.0979848
\(718\) −555926. + 83095.2i −1.07837 + 0.161186i
\(719\) 63172.8i 0.122200i −0.998132 0.0611001i \(-0.980539\pi\)
0.998132 0.0611001i \(-0.0194609\pi\)
\(720\) 170569. 115071.i 0.329030 0.221973i
\(721\) −22069.7 −0.0424547
\(722\) 4055.85 + 27134.6i 0.00778050 + 0.0520533i
\(723\) 186958.i 0.357658i
\(724\) 373281. 114140.i 0.712130 0.217752i
\(725\) −649659. −1.23597
\(726\) −401137. + 59958.6i −0.761061 + 0.113757i
\(727\) 259499.i 0.490984i 0.969399 + 0.245492i \(0.0789496\pi\)
−0.969399 + 0.245492i \(0.921050\pi\)
\(728\) 89891.6 42882.8i 0.169612 0.0809134i
\(729\) −93628.2 −0.176178
\(730\) 21924.0 + 146677.i 0.0411410 + 0.275242i
\(731\) 77374.2i 0.144798i
\(732\) 147101. + 481077.i 0.274533 + 0.897826i
\(733\) −176670. −0.328817 −0.164409 0.986392i \(-0.552572\pi\)
−0.164409 + 0.986392i \(0.552572\pi\)
\(734\) 717261. 107210.i 1.33133 0.198996i
\(735\) 134837.i 0.249594i
\(736\) −516414. + 473303.i −0.953328 + 0.873743i
\(737\) −883607. −1.62676
\(738\) −32470.1 217232.i −0.0596171 0.398852i
\(739\) 309358.i 0.566465i −0.959051 0.283232i \(-0.908593\pi\)
0.959051 0.283232i \(-0.0914068\pi\)
\(740\) −87723.7 + 26823.7i −0.160197 + 0.0489841i
\(741\) 63727.1 0.116061
\(742\) 127059. 18991.7i 0.230780 0.0344950i
\(743\) 173374.i 0.314055i −0.987594 0.157028i \(-0.949809\pi\)
0.987594 0.157028i \(-0.0501911\pi\)
\(744\) −91738.4 192303.i −0.165732 0.347409i
\(745\) 557804. 1.00501
\(746\) −107490. 719132.i −0.193148 1.29220i
\(747\) 481012.i 0.862014i
\(748\) 75471.1 + 246819.i 0.134889 + 0.441139i
\(749\) 76273.7 0.135960
\(750\) −247864. + 37048.7i −0.440647 + 0.0658643i
\(751\) 357686.i 0.634194i −0.948393 0.317097i \(-0.897292\pi\)
0.948393 0.317097i \(-0.102708\pi\)
\(752\) 303061. + 449227.i 0.535913 + 0.794384i
\(753\) 33474.6 0.0590372
\(754\) −147059. 983859.i −0.258672 1.73057i
\(755\) 425394.i 0.746273i
\(756\) −86606.0 + 26482.0i −0.151532 + 0.0463347i
\(757\) 423414. 0.738880 0.369440 0.929255i \(-0.379550\pi\)
0.369440 + 0.929255i \(0.379550\pi\)
\(758\) 598515. 89461.1i 1.04169 0.155703i
\(759\) 587481.i 1.01979i
\(760\) 62686.5 29904.6i 0.108529 0.0517739i
\(761\) 660959. 1.14131 0.570657 0.821189i \(-0.306689\pi\)
0.570657 + 0.821189i \(0.306689\pi\)
\(762\) −7333.17 49060.6i −0.0126294 0.0844934i
\(763\) 24269.3i 0.0416877i
\(764\) 97889.0 + 320134.i 0.167706 + 0.548460i
\(765\) 66944.9 0.114392
\(766\) 596895. 89218.9i 1.01728 0.152055i
\(767\) 53265.0i 0.0905422i
\(768\) 269463. + 108819.i 0.456853 + 0.184494i
\(769\) −557564. −0.942849 −0.471424 0.881906i \(-0.656260\pi\)
−0.471424 + 0.881906i \(0.656260\pi\)
\(770\) 13457.5 + 90033.8i 0.0226978 + 0.151853i
\(771\) 110121.i 0.185252i
\(772\) −850277. + 259993.i −1.42668 + 0.436242i
\(773\) 159973. 0.267725 0.133862 0.991000i \(-0.457262\pi\)
0.133862 + 0.991000i \(0.457262\pi\)
\(774\) 225410. 33692.5i 0.376263 0.0562408i
\(775\) 340322.i 0.566613i
\(776\) −59934.5 125636.i −0.0995299 0.208636i
\(777\) 17399.5 0.0288201
\(778\) 844.457 + 5649.61i 0.00139514 + 0.00933381i
\(779\) 74143.1i 0.122179i
\(780\) −47173.2 154274.i −0.0775364 0.253573i
\(781\) 28883.7 0.0473534
\(782\) −225412. + 33692.7i −0.368606 + 0.0550963i
\(783\) 904575.i 1.47544i
\(784\) 492477. 332238.i 0.801224 0.540527i
\(785\) 2557.57 0.00415038
\(786\) 63764.6 + 426600.i 0.103213 + 0.690519i
\(787\) 536068.i 0.865506i 0.901512 + 0.432753i \(0.142458\pi\)
−0.901512 + 0.432753i \(0.857542\pi\)
\(788\) 768254. 234913.i 1.23724 0.378316i
\(789\) 48738.8 0.0782926
\(790\) −357456. + 53429.6i −0.572755 + 0.0856106i
\(791\) 55527.7i 0.0887476i
\(792\) 686182. 327343.i 1.09393 0.521859i
\(793\) −1.23040e6 −1.95660
\(794\) 123450. + 825909.i 0.195817 + 1.31006i
\(795\) 208095.i 0.329251i
\(796\) 23130.3 + 75644.7i 0.0365052 + 0.119386i
\(797\) 169520. 0.266873 0.133437 0.991057i \(-0.457399\pi\)
0.133437 + 0.991057i \(0.457399\pi\)
\(798\) −13029.0 + 1947.47i −0.0204600 + 0.00305819i
\(799\) 176312.i 0.276178i
\(800\) 313628. + 342195.i 0.490044 + 0.534680i
\(801\) −534479. −0.833039
\(802\) −140291. 938581.i −0.218113 1.45923i
\(803\) 547989.i 0.849848i
\(804\) −309552. + 94653.3i −0.478874 + 0.146428i
\(805\) −80387.8 −0.124050
\(806\) 515392. 77036.5i 0.793355 0.118584i
\(807\) 549226.i 0.843343i
\(808\) −124466. 260906.i −0.190645 0.399634i
\(809\) −951147. −1.45328 −0.726642 0.687016i \(-0.758920\pi\)
−0.726642 + 0.687016i \(0.758920\pi\)
\(810\) −16810.3 112464.i −0.0256215 0.171414i
\(811\) 418188.i 0.635814i 0.948122 + 0.317907i \(0.102980\pi\)
−0.948122 + 0.317907i \(0.897020\pi\)
\(812\) 60132.5 + 196656.i 0.0912005 + 0.298260i
\(813\) 170531. 0.258002
\(814\) −335228. + 50107.2i −0.505932 + 0.0756225i
\(815\) 279450.i 0.420716i
\(816\) 52879.3 + 78383.0i 0.0794155 + 0.117718i
\(817\) 76934.2 0.115259
\(818\) 186842. + 1.25001e6i 0.279233 + 1.86813i
\(819\) 95452.2i 0.142304i
\(820\) −179490. + 54883.4i −0.266939 + 0.0816232i
\(821\) −754344. −1.11914 −0.559568 0.828784i \(-0.689033\pi\)
−0.559568 + 0.828784i \(0.689033\pi\)
\(822\) 429664. 64222.6i 0.635894 0.0950483i
\(823\) 520834.i 0.768953i 0.923135 + 0.384477i \(0.125618\pi\)
−0.923135 + 0.384477i \(0.874382\pi\)
\(824\) 142154. 67814.4i 0.209365 0.0998774i
\(825\) −389286. −0.571954
\(826\) −1627.75 10890.0i −0.00238577 0.0159613i
\(827\) 633719.i 0.926585i −0.886205 0.463293i \(-0.846668\pi\)
0.886205 0.463293i \(-0.153332\pi\)
\(828\) 196310. + 642009.i 0.286341 + 0.936441i
\(829\) 68381.2 0.0995011 0.0497505 0.998762i \(-0.484157\pi\)
0.0497505 + 0.998762i \(0.484157\pi\)
\(830\) 406521. 60763.4i 0.590102 0.0882035i
\(831\) 281383.i 0.407470i
\(832\) −447235. + 552427.i −0.646084 + 0.798046i
\(833\) 193287. 0.278556
\(834\) 80171.3 + 536364.i 0.115262 + 0.771130i
\(835\) 275097.i 0.394560i
\(836\) 245416. 75042.0i 0.351148 0.107372i
\(837\) −473859. −0.676391
\(838\) −923062. + 137972.i −1.31445 + 0.196473i
\(839\) 57238.5i 0.0813139i 0.999173 + 0.0406569i \(0.0129451\pi\)
−0.999173 + 0.0406569i \(0.987055\pi\)
\(840\) 14359.1 + 30099.7i 0.0203502 + 0.0426584i
\(841\) 1.34673e6 1.90410
\(842\) 96315.7 + 644373.i 0.135854 + 0.908895i
\(843\) 217799.i 0.306479i
\(844\) 317232. + 1.03747e6i 0.445341 + 1.45643i
\(845\) 20322.3 0.0284616
\(846\) 513642. 76774.9i 0.717661 0.107270i
\(847\) 205069.i 0.285847i
\(848\) −760045. + 512747.i −1.05693 + 0.713036i
\(849\) −315526. −0.437744
\(850\) 22326.0 + 149366.i 0.0309011 + 0.206735i
\(851\) 299313.i 0.413301i
\(852\) 10118.8 3094.07i 0.0139396 0.00426237i
\(853\) −158388. −0.217684 −0.108842 0.994059i \(-0.534714\pi\)
−0.108842 + 0.994059i \(0.534714\pi\)
\(854\) 251556. 37600.5i 0.344921 0.0515559i
\(855\) 66564.3i 0.0910561i
\(856\) −491288. + 234369.i −0.670484 + 0.319855i
\(857\) 958773. 1.30543 0.652716 0.757603i \(-0.273630\pi\)
0.652716 + 0.757603i \(0.273630\pi\)
\(858\) −88120.3 589545.i −0.119702 0.800833i
\(859\) 1.28765e6i 1.74507i −0.488555 0.872533i \(-0.662476\pi\)
0.488555 0.872533i \(-0.337524\pi\)
\(860\) −56949.6 186247.i −0.0770005 0.251821i
\(861\) 35600.8 0.0480234
\(862\) 1.39711e6 208828.i 1.88025 0.281044i
\(863\) 1.04487e6i 1.40295i 0.712696 + 0.701473i \(0.247474\pi\)
−0.712696 + 0.701473i \(0.752526\pi\)
\(864\) 476467. 436691.i 0.638272 0.584988i
\(865\) 451526. 0.603462
\(866\) −63571.0 425304.i −0.0847663 0.567106i
\(867\) 339593.i 0.451774i
\(868\) −103018. + 31500.2i −0.136733 + 0.0418094i
\(869\) −1.33547e6 −1.76846
\(870\) 329440. 49242.0i 0.435249 0.0650575i
\(871\) 791712.i 1.04359i
\(872\) −74573.1 156321.i −0.0980730 0.205582i
\(873\) −133407. −0.175046
\(874\) 33501.1 + 224130.i 0.0438568 + 0.293412i
\(875\) 126713.i 0.165503i
\(876\) 58701.5 + 191976.i 0.0764964 + 0.250172i
\(877\) −1.30314e6 −1.69431 −0.847156 0.531344i \(-0.821687\pi\)
−0.847156 + 0.531344i \(0.821687\pi\)
\(878\) −1.44681e6 + 216258.i −1.87682 + 0.280532i
\(879\) 12503.4i 0.0161826i
\(880\) −363331. 538567.i −0.469178 0.695463i
\(881\) −1.09260e6 −1.40769 −0.703846 0.710353i \(-0.748535\pi\)
−0.703846 + 0.710353i \(0.748535\pi\)
\(882\) −84166.5 563093.i −0.108194 0.723841i
\(883\) 941564.i 1.20761i 0.797130 + 0.603807i \(0.206350\pi\)
−0.797130 + 0.603807i \(0.793650\pi\)
\(884\) −221150. + 67622.1i −0.282997 + 0.0865335i
\(885\) −17835.5 −0.0227719
\(886\) 47193.0 7054.03i 0.0601188 0.00898607i
\(887\) 1.09323e6i 1.38952i −0.719242 0.694759i \(-0.755511\pi\)
0.719242 0.694759i \(-0.244489\pi\)
\(888\) −112072. + 53464.1i −0.142126 + 0.0678011i
\(889\) −25080.7 −0.0317349
\(890\) 67517.6 + 451708.i 0.0852388 + 0.570267i
\(891\) 420171.i 0.529262i
\(892\) −167888. 549055.i −0.211003 0.690059i
\(893\) 175310. 0.219838
\(894\) 746759. 111619.i 0.934341 0.139658i
\(895\) 344595.i 0.430192i
\(896\) 74555.3 126611.i 0.0928672 0.157709i
\(897\) 526383. 0.654209
\(898\) 50773.4 + 339685.i 0.0629627 + 0.421235i
\(899\) 1.07599e6i 1.33134i
\(900\) 425419. 130083.i 0.525209 0.160596i
\(901\) −298302. −0.367457
\(902\) −685903. + 102523.i −0.843043 + 0.126011i
\(903\) 36941.0i 0.0453036i
\(904\) 170622. + 357660.i 0.208784 + 0.437657i
\(905\) −319678. −0.390316
\(906\) −85123.5 569495.i −0.103703 0.693799i
\(907\) 543026.i 0.660095i −0.943964 0.330047i \(-0.892935\pi\)
0.943964 0.330047i \(-0.107065\pi\)
\(908\) −373642. 1.22195e6i −0.453194 1.48211i
\(909\) −277046. −0.335293
\(910\) −80670.3 + 12057.9i −0.0974161 + 0.0145610i
\(911\) 1.63167e6i 1.96606i 0.183454 + 0.983028i \(0.441272\pi\)
−0.183454 + 0.983028i \(0.558728\pi\)
\(912\) 77937.3 52578.6i 0.0937035 0.0632149i
\(913\) 1.51878e6 1.82202
\(914\) 166229. + 1.11211e6i 0.198983 + 1.33124i
\(915\) 411995.i 0.492095i
\(916\) 859287. 262749.i 1.02411 0.313148i
\(917\) 218086. 0.259352
\(918\) 207975. 31086.4i 0.246789 0.0368880i
\(919\) 327137.i 0.387346i −0.981066 0.193673i \(-0.937960\pi\)
0.981066 0.193673i \(-0.0620401\pi\)
\(920\) 517787. 247011.i 0.611753 0.291837i
\(921\) −714148. −0.841916
\(922\) 4165.52 + 27868.3i 0.00490013 + 0.0327829i
\(923\) 25879.8i 0.0303779i
\(924\) 36032.4 + 117840.i 0.0422036 + 0.138022i
\(925\) −198336. −0.231802
\(926\) −855164. + 127823.i −0.997304 + 0.149069i
\(927\) 150947.i 0.175657i
\(928\) −991593. 1.08191e6i −1.15143 1.25631i
\(929\) −16017.8 −0.0185598 −0.00927988 0.999957i \(-0.502954\pi\)
−0.00927988 + 0.999957i \(0.502954\pi\)
\(930\) 25795.3 + 172576.i 0.0298246 + 0.199533i
\(931\) 192188.i 0.221731i
\(932\) 1.09566e6 335026.i 1.26137 0.385697i
\(933\) 613881. 0.705214
\(934\) −835485. + 124881.i −0.957733 + 0.143154i
\(935\) 211376.i 0.241787i
\(936\) 293300. + 614819.i 0.334780 + 0.701771i
\(937\) 753326. 0.858032 0.429016 0.903297i \(-0.358860\pi\)
0.429016 + 0.903297i \(0.358860\pi\)
\(938\) 24194.3 + 161866.i 0.0274984 + 0.183971i
\(939\) 118102.i 0.133945i
\(940\) −129771. 424399.i −0.146866 0.480307i
\(941\) −433839. −0.489947 −0.244974 0.969530i \(-0.578779\pi\)
−0.244974 + 0.969530i \(0.578779\pi\)
\(942\) 3423.94 511.783i 0.00385855 0.000576745i
\(943\) 612418.i 0.688691i
\(944\) 43946.7 + 65142.3i 0.0493154 + 0.0731003i
\(945\) 74169.5 0.0830542
\(946\) −106383. 711725.i −0.118875 0.795298i
\(947\) 495248.i 0.552233i 0.961124 + 0.276117i \(0.0890476\pi\)
−0.961124 + 0.276117i \(0.910952\pi\)
\(948\) −467852. + 143057.i −0.520585 + 0.159182i
\(949\) −490999. −0.545190
\(950\) 148517. 22199.1i 0.164562 0.0245973i
\(951\) 200831.i 0.222060i
\(952\) 43147.6 20583.6i 0.0476083 0.0227116i
\(953\) 655146. 0.721360 0.360680 0.932690i \(-0.382545\pi\)
0.360680 + 0.932690i \(0.382545\pi\)
\(954\) 129895. + 869027.i 0.142724 + 0.954853i
\(955\) 274163.i 0.300609i
\(956\) −53147.8 173813.i −0.0581526 0.190181i
\(957\) 1.23080e6 1.34389
\(958\) −1.25934e6 + 188236.i −1.37218 + 0.205103i
\(959\) 219653.i 0.238836i
\(960\) −184977. 149754.i −0.200713 0.162494i
\(961\) 359867. 0.389668
\(962\) −44896.0 300365.i −0.0485130 0.324563i
\(963\) 521678.i 0.562536i
\(964\) 645105. 197257.i 0.694187 0.212265i
\(965\) 728178. 0.781957
\(966\) −107619. + 16086.0i −0.115328 + 0.0172383i
\(967\) 300375.i 0.321226i 0.987017 + 0.160613i \(0.0513471\pi\)
−0.987017 + 0.160613i \(0.948653\pi\)
\(968\) −630124. 1.32087e6i −0.672473 1.40965i
\(969\) 30588.8 0.0325772
\(970\) 16852.6 + 112748.i 0.0179111 + 0.119829i
\(971\) 994951.i 1.05527i −0.849471 0.527635i \(-0.823079\pi\)
0.849471 0.527635i \(-0.176921\pi\)
\(972\) −284198. 929435.i −0.300807 0.983754i
\(973\) 274200. 0.289629
\(974\) −626547. + 93651.1i −0.660443 + 0.0987177i
\(975\) 348801.i 0.366917i
\(976\) −1.50477e6 + 1.01516e6i −1.57968 + 1.06570i
\(977\) 1.39627e6 1.46278 0.731391 0.681959i \(-0.238872\pi\)
0.731391 + 0.681959i \(0.238872\pi\)
\(978\) 55919.4 + 374113.i 0.0584635 + 0.391134i
\(979\) 1.68760e6i 1.76077i
\(980\) −465259. + 142265.i −0.484443 + 0.148131i
\(981\) −165991. −0.172483
\(982\) −150548. + 22502.7i −0.156118 + 0.0233352i
\(983\) 1.17073e6i 1.21157i −0.795629 0.605784i \(-0.792859\pi\)
0.795629 0.605784i \(-0.207141\pi\)
\(984\) −229309. + 109392.i −0.236826 + 0.112978i
\(985\) −657934. −0.678125
\(986\) −70587.8 472248.i −0.0726066 0.485754i
\(987\) 84177.3i 0.0864093i
\(988\) 67237.7 + 219892.i 0.0688809 + 0.225266i
\(989\) 635473. 0.649687
\(990\) −615791. + 92043.4i −0.628294 + 0.0939123i
\(991\) 28788.9i 0.0293142i 0.999893 + 0.0146571i \(0.00466567\pi\)
−0.999893 + 0.0146571i \(0.995334\pi\)
\(992\) 566757. 519443.i 0.575935 0.527855i
\(993\) −5039.82 −0.00511112
\(994\) −790.876 5291.14i −0.000800452 0.00535521i
\(995\) 64782.2i 0.0654349i
\(996\) 532070. 162694.i 0.536352 0.164003i
\(997\) 954503. 0.960256 0.480128 0.877198i \(-0.340590\pi\)
0.480128 + 0.877198i \(0.340590\pi\)
\(998\) 1.89095e6 282643.i 1.89853 0.283777i
\(999\) 276160.i 0.276713i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 76.5.b.a.39.17 36
4.3 odd 2 inner 76.5.b.a.39.18 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.5.b.a.39.17 36 1.1 even 1 trivial
76.5.b.a.39.18 yes 36 4.3 odd 2 inner