Properties

Label 32.6.g.a.5.17
Level $32$
Weight $6$
Character 32.5
Analytic conductor $5.132$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [32,6,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.13228223402\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(19\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 5.17
Character \(\chi\) \(=\) 32.5
Dual form 32.6.g.a.13.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.94686 + 2.74382i) q^{2} +(6.19399 + 14.9536i) q^{3} +(16.9429 + 27.1466i) q^{4} +(-2.09949 - 0.869637i) q^{5} +(-10.3893 + 90.9686i) q^{6} +(-63.4847 - 63.4847i) q^{7} +(9.32842 + 180.779i) q^{8} +(-13.4180 + 13.4180i) q^{9} +O(q^{10})\) \(q+(4.94686 + 2.74382i) q^{2} +(6.19399 + 14.9536i) q^{3} +(16.9429 + 27.1466i) q^{4} +(-2.09949 - 0.869637i) q^{5} +(-10.3893 + 90.9686i) q^{6} +(-63.4847 - 63.4847i) q^{7} +(9.32842 + 180.779i) q^{8} +(-13.4180 + 13.4180i) q^{9} +(-7.99975 - 10.0626i) q^{10} +(-89.6819 + 216.511i) q^{11} +(-300.996 + 421.503i) q^{12} +(825.073 - 341.756i) q^{13} +(-139.859 - 488.241i) q^{14} -36.7815i q^{15} +(-449.879 + 919.883i) q^{16} -309.045i q^{17} +(-103.193 + 29.5603i) q^{18} +(383.892 - 159.013i) q^{19} +(-11.9636 - 71.7282i) q^{20} +(556.102 - 1342.55i) q^{21} +(-1037.71 + 824.980i) q^{22} +(1577.64 - 1577.64i) q^{23} +(-2645.52 + 1259.24i) q^{24} +(-2206.06 - 2206.06i) q^{25} +(5019.24 + 573.233i) q^{26} +(3349.97 + 1387.60i) q^{27} +(647.783 - 2799.01i) q^{28} +(-2629.22 - 6347.50i) q^{29} +(100.922 - 181.953i) q^{30} -1318.74 q^{31} +(-4749.49 + 3316.15i) q^{32} -3793.11 q^{33} +(847.964 - 1528.80i) q^{34} +(78.0768 + 188.494i) q^{35} +(-591.591 - 136.914i) q^{36} +(4027.50 + 1668.25i) q^{37} +(2335.37 + 266.716i) q^{38} +(10221.0 + 10221.0i) q^{39} +(137.627 - 387.656i) q^{40} +(-10736.0 + 10736.0i) q^{41} +(6434.68 - 5115.56i) q^{42} +(-5996.71 + 14477.3i) q^{43} +(-7397.02 + 1233.76i) q^{44} +(39.8396 - 16.5021i) q^{45} +(12133.1 - 3475.60i) q^{46} +19463.4i q^{47} +(-16542.1 - 1029.57i) q^{48} -8746.38i q^{49} +(-4860.03 - 16966.1i) q^{50} +(4621.33 - 1914.22i) q^{51} +(23256.6 + 16607.6i) q^{52} +(712.472 - 1720.06i) q^{53} +(12764.5 + 16056.0i) q^{54} +(376.572 - 376.572i) q^{55} +(10884.5 - 12068.9i) q^{56} +(4755.65 + 4755.65i) q^{57} +(4410.03 - 38614.3i) q^{58} +(-37126.5 - 15378.3i) q^{59} +(998.493 - 623.183i) q^{60} +(-15872.5 - 38319.5i) q^{61} +(-6523.63 - 3618.40i) q^{62} +1703.67 q^{63} +(-32594.0 + 3372.76i) q^{64} -2029.43 q^{65} +(-18764.0 - 10407.6i) q^{66} +(-18692.3 - 45127.3i) q^{67} +(8389.52 - 5236.10i) q^{68} +(33363.3 + 13819.5i) q^{69} +(-130.959 + 1146.68i) q^{70} +(42991.5 + 42991.5i) q^{71} +(-2550.85 - 2300.52i) q^{72} +(-3477.70 + 3477.70i) q^{73} +(15346.1 + 19303.3i) q^{74} +(19324.2 - 46652.8i) q^{75} +(10820.9 + 7727.24i) q^{76} +(19438.6 - 8051.73i) q^{77} +(22517.2 + 78606.3i) q^{78} +33851.2i q^{79} +(1744.48 - 1540.05i) q^{80} +63300.1i q^{81} +(-82566.9 + 23651.7i) q^{82} +(7972.53 - 3302.33i) q^{83} +(45867.6 - 7650.33i) q^{84} +(-268.757 + 648.836i) q^{85} +(-69388.2 + 55163.5i) q^{86} +(78632.7 - 78632.7i) q^{87} +(-39977.2 - 14192.9i) q^{88} +(25746.4 + 25746.4i) q^{89} +(242.360 + 27.6793i) q^{90} +(-74075.8 - 30683.2i) q^{91} +(69557.3 + 16097.9i) q^{92} +(-8168.27 - 19720.0i) q^{93} +(-53404.2 + 96282.8i) q^{94} -944.262 q^{95} +(-79006.6 - 50481.8i) q^{96} -123688. q^{97} +(23998.5 - 43267.1i) q^{98} +(-1701.79 - 4108.49i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 204 q^{10} - 4 q^{11} - 1588 q^{12} - 4 q^{13} + 2476 q^{14} + 4176 q^{16} - 1624 q^{18} - 4 q^{19} - 7604 q^{20} - 4 q^{21} - 12384 q^{22} + 1668 q^{23} + 21456 q^{24} - 4 q^{25} + 12976 q^{26} - 7468 q^{27} - 2184 q^{28} - 4 q^{29} - 32316 q^{30} + 23056 q^{31} - 18584 q^{32} - 8 q^{33} - 6256 q^{34} - 4780 q^{35} + 65584 q^{36} - 4 q^{37} + 404 q^{38} - 44908 q^{39} - 28952 q^{40} - 4 q^{41} - 53624 q^{42} + 32068 q^{43} + 3716 q^{44} + 968 q^{45} + 63324 q^{46} + 112368 q^{48} - 4524 q^{50} - 19912 q^{51} + 18468 q^{52} - 49460 q^{53} + 1312 q^{54} + 110044 q^{55} - 80984 q^{56} - 4 q^{57} - 84576 q^{58} - 28964 q^{59} - 46088 q^{60} + 96156 q^{61} + 63480 q^{62} - 158768 q^{63} - 49192 q^{64} - 8 q^{65} - 145012 q^{66} - 61164 q^{67} - 151216 q^{68} - 44644 q^{69} - 56296 q^{70} + 143836 q^{71} + 27092 q^{72} - 4 q^{73} + 213100 q^{74} + 205744 q^{75} + 255996 q^{76} - 14900 q^{77} + 83508 q^{78} - 97096 q^{80} + 435196 q^{82} - 329244 q^{83} + 597472 q^{84} + 12496 q^{85} + 269888 q^{86} - 282188 q^{87} - 199840 q^{88} - 4 q^{89} - 706840 q^{90} + 200108 q^{91} - 650328 q^{92} - 976 q^{93} - 261592 q^{94} + 577592 q^{95} - 501376 q^{96} - 8 q^{97} - 395624 q^{98} + 338544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.94686 + 2.74382i 0.874490 + 0.485044i
\(3\) 6.19399 + 14.9536i 0.397344 + 0.959274i 0.988293 + 0.152565i \(0.0487535\pi\)
−0.590949 + 0.806709i \(0.701247\pi\)
\(4\) 16.9429 + 27.1466i 0.529464 + 0.848332i
\(5\) −2.09949 0.869637i −0.0375568 0.0155565i 0.363826 0.931467i \(-0.381470\pi\)
−0.401383 + 0.915910i \(0.631470\pi\)
\(6\) −10.3893 + 90.9686i −0.117817 + 1.03161i
\(7\) −63.4847 63.4847i −0.489693 0.489693i 0.418516 0.908209i \(-0.362550\pi\)
−0.908209 + 0.418516i \(0.862550\pi\)
\(8\) 9.32842 + 180.779i 0.0515327 + 0.998671i
\(9\) −13.4180 + 13.4180i −0.0552180 + 0.0552180i
\(10\) −7.99975 10.0626i −0.0252974 0.0318207i
\(11\) −89.6819 + 216.511i −0.223472 + 0.539509i −0.995357 0.0962531i \(-0.969314\pi\)
0.771885 + 0.635762i \(0.219314\pi\)
\(12\) −300.996 + 421.503i −0.603404 + 0.844982i
\(13\) 825.073 341.756i 1.35405 0.560865i 0.416631 0.909076i \(-0.363211\pi\)
0.937416 + 0.348211i \(0.113211\pi\)
\(14\) −139.859 488.241i −0.190709 0.665754i
\(15\) 36.7815i 0.0422086i
\(16\) −449.879 + 919.883i −0.439335 + 0.898323i
\(17\) 309.045i 0.259358i −0.991556 0.129679i \(-0.958605\pi\)
0.991556 0.129679i \(-0.0413946\pi\)
\(18\) −103.193 + 29.5603i −0.0750707 + 0.0215044i
\(19\) 383.892 159.013i 0.243964 0.101053i −0.257351 0.966318i \(-0.582850\pi\)
0.501315 + 0.865265i \(0.332850\pi\)
\(20\) −11.9636 71.7282i −0.00668788 0.0400973i
\(21\) 556.102 1342.55i 0.275173 0.664327i
\(22\) −1037.71 + 824.980i −0.457110 + 0.363401i
\(23\) 1577.64 1577.64i 0.621853 0.621853i −0.324152 0.946005i \(-0.605079\pi\)
0.946005 + 0.324152i \(0.105079\pi\)
\(24\) −2645.52 + 1259.24i −0.937524 + 0.446251i
\(25\) −2206.06 2206.06i −0.705938 0.705938i
\(26\) 5019.24 + 573.233i 1.45614 + 0.166302i
\(27\) 3349.97 + 1387.60i 0.884365 + 0.366316i
\(28\) 647.783 2799.01i 0.156147 0.674698i
\(29\) −2629.22 6347.50i −0.580540 1.40155i −0.892324 0.451395i \(-0.850927\pi\)
0.311784 0.950153i \(-0.399073\pi\)
\(30\) 100.922 181.953i 0.0204730 0.0369110i
\(31\) −1318.74 −0.246465 −0.123233 0.992378i \(-0.539326\pi\)
−0.123233 + 0.992378i \(0.539326\pi\)
\(32\) −4749.49 + 3316.15i −0.819920 + 0.572478i
\(33\) −3793.11 −0.606333
\(34\) 847.964 1528.80i 0.125800 0.226806i
\(35\) 78.0768 + 188.494i 0.0107734 + 0.0260092i
\(36\) −591.591 136.914i −0.0760791 0.0176072i
\(37\) 4027.50 + 1668.25i 0.483650 + 0.200335i 0.611167 0.791502i \(-0.290701\pi\)
−0.127516 + 0.991836i \(0.540701\pi\)
\(38\) 2335.37 + 266.716i 0.262359 + 0.0299633i
\(39\) 10221.0 + 10221.0i 1.07605 + 1.07605i
\(40\) 137.627 387.656i 0.0136005 0.0383086i
\(41\) −10736.0 + 10736.0i −0.997427 + 0.997427i −0.999997 0.00256976i \(-0.999182\pi\)
0.00256976 + 0.999997i \(0.499182\pi\)
\(42\) 6434.68 5115.56i 0.562864 0.447476i
\(43\) −5996.71 + 14477.3i −0.494586 + 1.19404i 0.457776 + 0.889068i \(0.348646\pi\)
−0.952362 + 0.304969i \(0.901354\pi\)
\(44\) −7397.02 + 1233.76i −0.576003 + 0.0960725i
\(45\) 39.8396 16.5021i 0.00293281 0.00121481i
\(46\) 12133.1 3475.60i 0.845431 0.242178i
\(47\) 19463.4i 1.28521i 0.766197 + 0.642605i \(0.222147\pi\)
−0.766197 + 0.642605i \(0.777853\pi\)
\(48\) −16542.1 1029.57i −1.03631 0.0644987i
\(49\) 8746.38i 0.520401i
\(50\) −4860.03 16966.1i −0.274925 0.959747i
\(51\) 4621.33 1914.22i 0.248795 0.103054i
\(52\) 23256.6 + 16607.6i 1.19272 + 0.851724i
\(53\) 712.472 1720.06i 0.0348400 0.0841111i −0.905502 0.424342i \(-0.860505\pi\)
0.940342 + 0.340231i \(0.110505\pi\)
\(54\) 12764.5 + 16056.0i 0.595688 + 0.749295i
\(55\) 376.572 376.572i 0.0167858 0.0167858i
\(56\) 10884.5 12068.9i 0.463807 0.514278i
\(57\) 4755.65 + 4755.65i 0.193875 + 0.193875i
\(58\) 4410.03 38614.3i 0.172136 1.50723i
\(59\) −37126.5 15378.3i −1.38852 0.575145i −0.441777 0.897125i \(-0.645652\pi\)
−0.946747 + 0.321979i \(0.895652\pi\)
\(60\) 998.493 623.183i 0.0358069 0.0223479i
\(61\) −15872.5 38319.5i −0.546160 1.31855i −0.920314 0.391180i \(-0.872067\pi\)
0.374155 0.927366i \(-0.377933\pi\)
\(62\) −6523.63 3618.40i −0.215531 0.119547i
\(63\) 1703.67 0.0540797
\(64\) −32594.0 + 3372.76i −0.994689 + 0.102929i
\(65\) −2029.43 −0.0595788
\(66\) −18764.0 10407.6i −0.530232 0.294098i
\(67\) −18692.3 45127.3i −0.508717 1.22815i −0.944622 0.328159i \(-0.893572\pi\)
0.435905 0.899993i \(-0.356428\pi\)
\(68\) 8389.52 5236.10i 0.220021 0.137321i
\(69\) 33363.3 + 13819.5i 0.843618 + 0.349438i
\(70\) −130.959 + 1146.68i −0.00319442 + 0.0279704i
\(71\) 42991.5 + 42991.5i 1.01213 + 1.01213i 0.999926 + 0.0122058i \(0.00388531\pi\)
0.0122058 + 0.999926i \(0.496115\pi\)
\(72\) −2550.85 2300.52i −0.0579901 0.0522991i
\(73\) −3477.70 + 3477.70i −0.0763809 + 0.0763809i −0.744265 0.667884i \(-0.767200\pi\)
0.667884 + 0.744265i \(0.267200\pi\)
\(74\) 15346.1 + 19303.3i 0.325776 + 0.409782i
\(75\) 19324.2 46652.8i 0.396688 0.957689i
\(76\) 10820.9 + 7727.24i 0.214897 + 0.153458i
\(77\) 19438.6 8051.73i 0.373627 0.154761i
\(78\) 22517.2 + 78606.3i 0.419061 + 1.46292i
\(79\) 33851.2i 0.610248i 0.952313 + 0.305124i \(0.0986979\pi\)
−0.952313 + 0.305124i \(0.901302\pi\)
\(80\) 1744.48 1540.05i 0.0304748 0.0269036i
\(81\) 63300.1i 1.07199i
\(82\) −82566.9 + 23651.7i −1.35604 + 0.388444i
\(83\) 7972.53 3302.33i 0.127028 0.0526169i −0.318264 0.948002i \(-0.603100\pi\)
0.445292 + 0.895385i \(0.353100\pi\)
\(84\) 45867.6 7650.33i 0.709264 0.118299i
\(85\) −268.757 + 648.836i −0.00403471 + 0.00974064i
\(86\) −69388.2 + 55163.5i −1.01167 + 0.804277i
\(87\) 78632.7 78632.7i 1.11379 1.11379i
\(88\) −39977.2 14192.9i −0.550308 0.195373i
\(89\) 25746.4 + 25746.4i 0.344542 + 0.344542i 0.858072 0.513530i \(-0.171662\pi\)
−0.513530 + 0.858072i \(0.671662\pi\)
\(90\) 242.360 + 27.6793i 0.00315395 + 0.000360204i
\(91\) −74075.8 30683.2i −0.937719 0.388416i
\(92\) 69557.3 + 16097.9i 0.856787 + 0.198289i
\(93\) −8168.27 19720.0i −0.0979316 0.236428i
\(94\) −53404.2 + 96282.8i −0.623384 + 1.12390i
\(95\) −944.262 −0.0107345
\(96\) −79006.6 50481.8i −0.874954 0.559058i
\(97\) −123688. −1.33475 −0.667373 0.744724i \(-0.732581\pi\)
−0.667373 + 0.744724i \(0.732581\pi\)
\(98\) 23998.5 43267.1i 0.252417 0.455085i
\(99\) −1701.79 4108.49i −0.0174509 0.0421303i
\(100\) 22510.1 97263.9i 0.225101 0.972639i
\(101\) 81180.1 + 33625.9i 0.791856 + 0.327997i 0.741689 0.670744i \(-0.234025\pi\)
0.0501663 + 0.998741i \(0.484025\pi\)
\(102\) 28113.4 + 3210.75i 0.267555 + 0.0305567i
\(103\) −121909. 121909.i −1.13225 1.13225i −0.989802 0.142453i \(-0.954501\pi\)
−0.142453 0.989802i \(-0.545499\pi\)
\(104\) 69478.9 + 145968.i 0.629897 + 1.32334i
\(105\) −2335.06 + 2335.06i −0.0206693 + 0.0206693i
\(106\) 8244.03 6553.99i 0.0712648 0.0566554i
\(107\) 3602.26 8696.61i 0.0304169 0.0734329i −0.907941 0.419098i \(-0.862347\pi\)
0.938358 + 0.345665i \(0.112347\pi\)
\(108\) 19089.3 + 114450.i 0.157482 + 0.944186i
\(109\) 193505. 80152.4i 1.56000 0.646175i 0.574914 0.818214i \(-0.305035\pi\)
0.985090 + 0.172039i \(0.0550354\pi\)
\(110\) 2896.10 829.603i 0.0228208 0.00653715i
\(111\) 70558.8i 0.543555i
\(112\) 86959.0 29838.1i 0.655042 0.224764i
\(113\) 163787.i 1.20665i 0.797495 + 0.603326i \(0.206158\pi\)
−0.797495 + 0.603326i \(0.793842\pi\)
\(114\) 10476.9 + 36574.2i 0.0755039 + 0.263580i
\(115\) −4684.21 + 1940.26i −0.0330287 + 0.0136809i
\(116\) 127767. 178919.i 0.881603 1.23456i
\(117\) −6485.12 + 15656.5i −0.0437979 + 0.105738i
\(118\) −141464. 177943.i −0.935279 1.17645i
\(119\) −19619.6 + 19619.6i −0.127006 + 0.127006i
\(120\) 6649.31 343.113i 0.0421525 0.00217512i
\(121\) 75046.0 + 75046.0i 0.465976 + 0.465976i
\(122\) 26623.1 233112.i 0.161942 1.41797i
\(123\) −227040. 94042.9i −1.35313 0.560484i
\(124\) −22343.3 35799.4i −0.130495 0.209084i
\(125\) 5430.74 + 13111.0i 0.0310874 + 0.0750515i
\(126\) 8427.82 + 4674.57i 0.0472922 + 0.0262310i
\(127\) −4644.48 −0.0255522 −0.0127761 0.999918i \(-0.504067\pi\)
−0.0127761 + 0.999918i \(0.504067\pi\)
\(128\) −170492. 72747.5i −0.919770 0.392458i
\(129\) −253632. −1.34193
\(130\) −10039.3 5568.41i −0.0521010 0.0288983i
\(131\) 148058. + 357445.i 0.753798 + 1.81983i 0.536928 + 0.843628i \(0.319585\pi\)
0.216869 + 0.976201i \(0.430415\pi\)
\(132\) −64266.2 102970.i −0.321032 0.514372i
\(133\) −34466.2 14276.4i −0.168952 0.0699824i
\(134\) 31352.9 274527.i 0.150840 1.32076i
\(135\) −5826.51 5826.51i −0.0275153 0.0275153i
\(136\) 55868.7 2882.90i 0.259013 0.0133654i
\(137\) 273192. 273192.i 1.24356 1.24356i 0.285048 0.958513i \(-0.407990\pi\)
0.958513 0.285048i \(-0.0920095\pi\)
\(138\) 127125. + 159906.i 0.568242 + 0.714772i
\(139\) 43113.0 104084.i 0.189265 0.456927i −0.800553 0.599262i \(-0.795461\pi\)
0.989819 + 0.142335i \(0.0454610\pi\)
\(140\) −3794.13 + 5313.15i −0.0163604 + 0.0229104i
\(141\) −291048. + 120556.i −1.23287 + 0.510671i
\(142\) 94711.9 + 330634.i 0.394170 + 1.37603i
\(143\) 209287.i 0.855858i
\(144\) −6306.50 18379.4i −0.0253444 0.0738628i
\(145\) 15613.0i 0.0616688i
\(146\) −26745.9 + 7661.50i −0.103842 + 0.0297462i
\(147\) 130790. 54175.0i 0.499207 0.206778i
\(148\) 22950.2 + 137598.i 0.0861255 + 0.516366i
\(149\) −100614. + 242903.i −0.371272 + 0.896329i 0.622264 + 0.782807i \(0.286213\pi\)
−0.993536 + 0.113521i \(0.963787\pi\)
\(150\) 223601. 177763.i 0.811421 0.645078i
\(151\) 58568.5 58568.5i 0.209036 0.209036i −0.594822 0.803858i \(-0.702777\pi\)
0.803858 + 0.594822i \(0.202777\pi\)
\(152\) 32327.4 + 67916.3i 0.113491 + 0.238432i
\(153\) 4146.75 + 4146.75i 0.0143212 + 0.0143212i
\(154\) 118253. + 13505.3i 0.401799 + 0.0458883i
\(155\) 2768.68 + 1146.83i 0.00925645 + 0.00383415i
\(156\) −104292. + 450638.i −0.343116 + 1.48257i
\(157\) −160884. 388409.i −0.520912 1.25759i −0.937337 0.348423i \(-0.886717\pi\)
0.416425 0.909170i \(-0.363283\pi\)
\(158\) −92881.7 + 167457.i −0.295997 + 0.533655i
\(159\) 30134.1 0.0945291
\(160\) 12855.3 2831.88i 0.0396994 0.00874532i
\(161\) −200312. −0.609035
\(162\) −173684. + 313137.i −0.519963 + 0.937446i
\(163\) 137299. + 331469.i 0.404761 + 0.977180i 0.986494 + 0.163800i \(0.0523751\pi\)
−0.581732 + 0.813380i \(0.697625\pi\)
\(164\) −473343. 109547.i −1.37425 0.318047i
\(165\) 7963.60 + 3298.63i 0.0227719 + 0.00943244i
\(166\) 48500.0 + 5539.05i 0.136607 + 0.0156015i
\(167\) 27962.6 + 27962.6i 0.0775866 + 0.0775866i 0.744835 0.667249i \(-0.232528\pi\)
−0.667249 + 0.744835i \(0.732528\pi\)
\(168\) 247892. + 88007.6i 0.677625 + 0.240573i
\(169\) 301404. 301404.i 0.811767 0.811767i
\(170\) −3109.79 + 2472.28i −0.00825295 + 0.00656108i
\(171\) −3017.42 + 7284.69i −0.00789124 + 0.0190511i
\(172\) −494613. + 82497.1i −1.27481 + 0.212627i
\(173\) −98041.0 + 40609.9i −0.249053 + 0.103161i −0.503718 0.863868i \(-0.668035\pi\)
0.254665 + 0.967029i \(0.418035\pi\)
\(174\) 604739. 173231.i 1.51424 0.433762i
\(175\) 280102.i 0.691386i
\(176\) −158819. 179901.i −0.386475 0.437775i
\(177\) 650427.i 1.56051i
\(178\) 56720.4 + 198008.i 0.134180 + 0.468417i
\(179\) 530697. 219822.i 1.23798 0.512788i 0.334898 0.942254i \(-0.391298\pi\)
0.903083 + 0.429466i \(0.141298\pi\)
\(180\) 1122.97 + 801.918i 0.00258338 + 0.00184480i
\(181\) −91277.3 + 220363.i −0.207094 + 0.499968i −0.992963 0.118424i \(-0.962216\pi\)
0.785870 + 0.618392i \(0.212216\pi\)
\(182\) −282253. 355036.i −0.631627 0.794501i
\(183\) 474701. 474701.i 1.04783 1.04783i
\(184\) 299921. + 270487.i 0.653073 + 0.588981i
\(185\) −7004.93 7004.93i −0.0150479 0.0150479i
\(186\) 13700.8 119964.i 0.0290377 0.254255i
\(187\) 66911.7 + 27715.7i 0.139926 + 0.0579592i
\(188\) −528366. + 329766.i −1.09029 + 0.680473i
\(189\) −124580. 300763.i −0.253685 0.612450i
\(190\) −4671.13 2590.89i −0.00938724 0.00520672i
\(191\) −497895. −0.987539 −0.493770 0.869593i \(-0.664381\pi\)
−0.493770 + 0.869593i \(0.664381\pi\)
\(192\) −252322. 466506.i −0.493971 0.913281i
\(193\) 369971. 0.714949 0.357474 0.933923i \(-0.383638\pi\)
0.357474 + 0.933923i \(0.383638\pi\)
\(194\) −611868. 339378.i −1.16722 0.647411i
\(195\) −12570.3 30347.4i −0.0236733 0.0571524i
\(196\) 237435. 148189.i 0.441473 0.275534i
\(197\) −66408.2 27507.2i −0.121915 0.0504987i 0.320892 0.947116i \(-0.396017\pi\)
−0.442807 + 0.896617i \(0.646017\pi\)
\(198\) 2854.44 24993.5i 0.00517438 0.0453070i
\(199\) −455988. 455988.i −0.816245 0.816245i 0.169317 0.985562i \(-0.445844\pi\)
−0.985562 + 0.169317i \(0.945844\pi\)
\(200\) 378229. 419387.i 0.668621 0.741379i
\(201\) 559035. 559035.i 0.975999 0.975999i
\(202\) 309323. + 389086.i 0.533376 + 0.670915i
\(203\) −236054. + 569885.i −0.402042 + 0.970615i
\(204\) 130263. + 93021.3i 0.219152 + 0.156497i
\(205\) 31876.4 13203.6i 0.0529767 0.0219437i
\(206\) −268571. 937567.i −0.440952 1.53934i
\(207\) 42337.4i 0.0686749i
\(208\) −56806.8 + 912719.i −0.0910421 + 1.46278i
\(209\) 97377.7i 0.154203i
\(210\) −17958.2 + 5144.22i −0.0281006 + 0.00804955i
\(211\) 43305.2 17937.6i 0.0669628 0.0277369i −0.348951 0.937141i \(-0.613462\pi\)
0.415913 + 0.909404i \(0.363462\pi\)
\(212\) 58765.1 9801.51i 0.0898007 0.0149780i
\(213\) −376589. + 909167.i −0.568747 + 1.37308i
\(214\) 41681.8 33137.0i 0.0622175 0.0494628i
\(215\) 25180.1 25180.1i 0.0371502 0.0371502i
\(216\) −219599. + 618548.i −0.320255 + 0.902067i
\(217\) 83720.0 + 83720.0i 0.120692 + 0.120692i
\(218\) 1.17717e6 + 134441.i 1.67763 + 0.191598i
\(219\) −73545.0 30463.3i −0.103620 0.0429207i
\(220\) 16602.9 + 3842.46i 0.0231274 + 0.00535245i
\(221\) −105618. 254984.i −0.145465 0.351182i
\(222\) −193601. + 349045.i −0.263648 + 0.475334i
\(223\) −1.13612e6 −1.52989 −0.764945 0.644096i \(-0.777234\pi\)
−0.764945 + 0.644096i \(0.777234\pi\)
\(224\) 512044. + 90995.1i 0.681848 + 0.121171i
\(225\) 59201.6 0.0779609
\(226\) −449401. + 810229.i −0.585279 + 1.05520i
\(227\) 202769. + 489528.i 0.261179 + 0.630541i 0.999012 0.0444421i \(-0.0141510\pi\)
−0.737833 + 0.674983i \(0.764151\pi\)
\(228\) −48525.5 + 209674.i −0.0618206 + 0.267121i
\(229\) 1.12919e6 + 467728.i 1.42292 + 0.589392i 0.955592 0.294693i \(-0.0952172\pi\)
0.467327 + 0.884085i \(0.345217\pi\)
\(230\) −28495.9 3254.43i −0.0355191 0.00405654i
\(231\) 240805. + 240805.i 0.296917 + 0.296917i
\(232\) 1.12297e6 534520.i 1.36977 0.651994i
\(233\) −969887. + 969887.i −1.17039 + 1.17039i −0.188276 + 0.982116i \(0.560290\pi\)
−0.982116 + 0.188276i \(0.939710\pi\)
\(234\) −75039.6 + 59656.3i −0.0895882 + 0.0712224i
\(235\) 16926.1 40863.2i 0.0199934 0.0482684i
\(236\) −211560. 1.26841e6i −0.247260 1.48245i
\(237\) −506197. + 209674.i −0.585395 + 0.242479i
\(238\) −150888. + 43222.7i −0.172668 + 0.0494618i
\(239\) 529355.i 0.599449i −0.954026 0.299724i \(-0.903105\pi\)
0.954026 0.299724i \(-0.0968947\pi\)
\(240\) 33834.6 + 16547.2i 0.0379170 + 0.0185437i
\(241\) 1.07740e6i 1.19491i 0.801904 + 0.597453i \(0.203820\pi\)
−0.801904 + 0.597453i \(0.796180\pi\)
\(242\) 165329. + 577155.i 0.181472 + 0.633511i
\(243\) −132522. + 54892.3i −0.143970 + 0.0596342i
\(244\) 771320. 1.08013e6i 0.829393 1.16145i
\(245\) −7606.18 + 18362.9i −0.00809564 + 0.0195446i
\(246\) −865096. 1.08817e6i −0.911437 1.14646i
\(247\) 262395. 262395.i 0.273661 0.273661i
\(248\) −12301.8 238401.i −0.0127010 0.246138i
\(249\) 98763.5 + 98763.5i 0.100948 + 0.100948i
\(250\) −9109.06 + 79759.1i −0.00921773 + 0.0807105i
\(251\) 522122. + 216270.i 0.523104 + 0.216677i 0.628580 0.777745i \(-0.283637\pi\)
−0.105476 + 0.994422i \(0.533637\pi\)
\(252\) 28865.1 + 46248.9i 0.0286333 + 0.0458776i
\(253\) 200091. + 483062.i 0.196529 + 0.474462i
\(254\) −22975.6 12743.6i −0.0223451 0.0123939i
\(255\) −11367.1 −0.0109471
\(256\) −643794. 827672.i −0.613970 0.789329i
\(257\) −747289. −0.705758 −0.352879 0.935669i \(-0.614797\pi\)
−0.352879 + 0.935669i \(0.614797\pi\)
\(258\) −1.25468e6 695922.i −1.17350 0.650895i
\(259\) −149777. 361593.i −0.138738 0.334943i
\(260\) −34384.4 55092.3i −0.0315449 0.0505426i
\(261\) 120449. + 49891.8i 0.109447 + 0.0453344i
\(262\) −248341. + 2.17447e6i −0.223509 + 1.95705i
\(263\) −444344. 444344.i −0.396123 0.396123i 0.480740 0.876863i \(-0.340368\pi\)
−0.876863 + 0.480740i \(0.840368\pi\)
\(264\) −35383.8 685715.i −0.0312460 0.605527i
\(265\) −2991.65 + 2991.65i −0.00261696 + 0.00261696i
\(266\) −131328. 165192.i −0.113803 0.143148i
\(267\) −225529. + 544475.i −0.193608 + 0.467412i
\(268\) 908352. 1.27202e6i 0.772533 1.08182i
\(269\) 243603. 100904.i 0.205259 0.0850212i −0.277685 0.960672i \(-0.589567\pi\)
0.482945 + 0.875651i \(0.339567\pi\)
\(270\) −12836.0 44809.9i −0.0107157 0.0374080i
\(271\) 882745.i 0.730150i −0.930978 0.365075i \(-0.881043\pi\)
0.930978 0.365075i \(-0.118957\pi\)
\(272\) 284285. + 139033.i 0.232987 + 0.113945i
\(273\) 1.29775e6i 1.05387i
\(274\) 2.10104e6 601853.i 1.69066 0.484299i
\(275\) 675480. 279793.i 0.538618 0.223103i
\(276\) 190116. + 1.13984e6i 0.150226 + 0.900683i
\(277\) 114671. 276841.i 0.0897957 0.216786i −0.872601 0.488433i \(-0.837569\pi\)
0.962397 + 0.271648i \(0.0875685\pi\)
\(278\) 498862. 396594.i 0.387140 0.307776i
\(279\) 17694.8 17694.8i 0.0136093 0.0136093i
\(280\) −33347.4 + 15873.0i −0.0254195 + 0.0120994i
\(281\) 736095. + 736095.i 0.556119 + 0.556119i 0.928200 0.372081i \(-0.121356\pi\)
−0.372081 + 0.928200i \(0.621356\pi\)
\(282\) −1.77056e6 202211.i −1.32583 0.151419i
\(283\) −1.62792e6 674307.i −1.20828 0.500485i −0.314614 0.949220i \(-0.601875\pi\)
−0.893665 + 0.448734i \(0.851875\pi\)
\(284\) −438675. + 1.89547e6i −0.322736 + 1.39451i
\(285\) −5848.74 14120.1i −0.00426531 0.0102974i
\(286\) −574246. + 1.03531e6i −0.415129 + 0.748439i
\(287\) 1.36314e6 0.976866
\(288\) 19232.5 108224.i 0.0136633 0.0768854i
\(289\) 1.32435e6 0.932734
\(290\) −42839.3 + 77235.2i −0.0299121 + 0.0539288i
\(291\) −766123. 1.84958e6i −0.530354 1.28039i
\(292\) −153330. 35485.6i −0.105237 0.0243554i
\(293\) −301964. 125078.i −0.205488 0.0851160i 0.277566 0.960707i \(-0.410472\pi\)
−0.483054 + 0.875591i \(0.660472\pi\)
\(294\) 795646. + 90868.5i 0.536848 + 0.0613120i
\(295\) 64573.1 + 64573.1i 0.0432013 + 0.0432013i
\(296\) −264013. + 743649.i −0.175145 + 0.493332i
\(297\) −600863. + 600863.i −0.395262 + 0.395262i
\(298\) −1.16421e6 + 925541.i −0.759432 + 0.603747i
\(299\) 762498. 1.84083e6i 0.493243 1.19079i
\(300\) 1.59387e6 265845.i 1.02247 0.170539i
\(301\) 1.29979e6 538391.i 0.826907 0.342516i
\(302\) 450432. 129029.i 0.284192 0.0814083i
\(303\) 1.42221e6i 0.889935i
\(304\) −26431.3 + 424673.i −0.0164034 + 0.263555i
\(305\) 94254.6i 0.0580167i
\(306\) 9135.45 + 31891.4i 0.00557733 + 0.0194702i
\(307\) −1.42227e6 + 589122.i −0.861262 + 0.356746i −0.769201 0.639007i \(-0.779346\pi\)
−0.0920611 + 0.995753i \(0.529346\pi\)
\(308\) 547923. + 391273.i 0.329111 + 0.235019i
\(309\) 1.06788e6 2.57809e6i 0.636248 1.53604i
\(310\) 10549.6 + 13270.0i 0.00623494 + 0.00784271i
\(311\) −1.31601e6 + 1.31601e6i −0.771541 + 0.771541i −0.978376 0.206835i \(-0.933684\pi\)
0.206835 + 0.978376i \(0.433684\pi\)
\(312\) −1.75239e6 + 1.94308e6i −1.01916 + 1.13007i
\(313\) −1.06193e6 1.06193e6i −0.612681 0.612681i 0.330963 0.943644i \(-0.392626\pi\)
−0.943644 + 0.330963i \(0.892626\pi\)
\(314\) 269854. 2.36284e6i 0.154456 1.35242i
\(315\) −3576.84 1481.58i −0.00203106 0.000841293i
\(316\) −918946. + 573536.i −0.517693 + 0.323105i
\(317\) 424579. + 1.02502e6i 0.237307 + 0.572909i 0.997002 0.0773696i \(-0.0246522\pi\)
−0.759696 + 0.650279i \(0.774652\pi\)
\(318\) 149069. + 82682.7i 0.0826648 + 0.0458508i
\(319\) 1.61010e6 0.885882
\(320\) 71363.7 + 21263.8i 0.0389585 + 0.0116082i
\(321\) 152358. 0.0825283
\(322\) −990915. 549620.i −0.532595 0.295409i
\(323\) −49142.2 118640.i −0.0262089 0.0632739i
\(324\) −1.71838e6 + 1.07248e6i −0.909405 + 0.567582i
\(325\) −2.57409e6 1.06622e6i −1.35181 0.559938i
\(326\) −230294. + 2.01646e6i −0.120016 + 1.05086i
\(327\) 2.39713e6 + 2.39713e6i 1.23972 + 1.23972i
\(328\) −2.04098e6 1.84068e6i −1.04750 0.944702i
\(329\) 1.23563e6 1.23563e6i 0.629359 0.629359i
\(330\) 30344.0 + 38168.6i 0.0153387 + 0.0192940i
\(331\) 550897. 1.32998e6i 0.276376 0.667231i −0.723354 0.690478i \(-0.757400\pi\)
0.999730 + 0.0232470i \(0.00740041\pi\)
\(332\) 224725. + 160476.i 0.111894 + 0.0799035i
\(333\) −76425.4 + 31656.4i −0.0377683 + 0.0156441i
\(334\) 61602.7 + 215052.i 0.0302158 + 0.105482i
\(335\) 111000.i 0.0540393i
\(336\) 984810. + 1.11553e6i 0.475887 + 0.539057i
\(337\) 2.57502e6i 1.23511i 0.786528 + 0.617554i \(0.211876\pi\)
−0.786528 + 0.617554i \(0.788124\pi\)
\(338\) 2.31800e6 664003.i 1.10363 0.316139i
\(339\) −2.44920e6 + 1.01449e6i −1.15751 + 0.479457i
\(340\) −22167.2 + 3697.30i −0.0103995 + 0.00173455i
\(341\) 118267. 285523.i 0.0550781 0.132970i
\(342\) −34914.6 + 27757.1i −0.0161414 + 0.0128324i
\(343\) −1.62225e6 + 1.62225e6i −0.744530 + 0.744530i
\(344\) −2.67314e6 949028.i −1.21794 0.432397i
\(345\) −58027.8 58027.8i −0.0262475 0.0262475i
\(346\) −596421. 68115.6i −0.267832 0.0305884i
\(347\) 2.97957e6 + 1.23418e6i 1.32840 + 0.550243i 0.930200 0.367054i \(-0.119634\pi\)
0.398204 + 0.917297i \(0.369634\pi\)
\(348\) 3.46688e6 + 802350.i 1.53458 + 0.355153i
\(349\) 503983. + 1.21672e6i 0.221489 + 0.534722i 0.995093 0.0989482i \(-0.0315478\pi\)
−0.773604 + 0.633670i \(0.781548\pi\)
\(350\) −768550. + 1.38562e6i −0.335353 + 0.604610i
\(351\) 3.23819e6 1.40292
\(352\) −292040. 1.32572e6i −0.125628 0.570287i
\(353\) −1.55824e6 −0.665574 −0.332787 0.943002i \(-0.607989\pi\)
−0.332787 + 0.943002i \(0.607989\pi\)
\(354\) 1.78466e6 3.21757e6i 0.756914 1.36465i
\(355\) −52873.2 127647.i −0.0222672 0.0537577i
\(356\) −262711. + 1.13515e6i −0.109863 + 0.474709i
\(357\) −414908. 171860.i −0.172298 0.0713683i
\(358\) 3.22844e6 + 368711.i 1.33133 + 0.152047i
\(359\) 390154. + 390154.i 0.159772 + 0.159772i 0.782466 0.622694i \(-0.213962\pi\)
−0.622694 + 0.782466i \(0.713962\pi\)
\(360\) 3354.87 + 7048.22i 0.00136433 + 0.00286631i
\(361\) −1.62878e6 + 1.62878e6i −0.657800 + 0.657800i
\(362\) −1.05617e6 + 839656.i −0.423608 + 0.336767i
\(363\) −657374. + 1.58704e6i −0.261846 + 0.632152i
\(364\) −422111. 2.53077e6i −0.166983 1.00115i
\(365\) 10325.7 4277.06i 0.00405685 0.00168040i
\(366\) 3.65078e6 1.04578e6i 1.42457 0.408074i
\(367\) 387740.i 0.150271i −0.997173 0.0751356i \(-0.976061\pi\)
0.997173 0.0751356i \(-0.0239390\pi\)
\(368\) 741497. + 2.16099e6i 0.285424 + 0.831827i
\(369\) 288109.i 0.110152i
\(370\) −15432.1 53872.7i −0.00586032 0.0204581i
\(371\) −154428. + 63966.4i −0.0582496 + 0.0241278i
\(372\) 396936. 555854.i 0.148718 0.208259i
\(373\) 1.53471e6 3.70512e6i 0.571156 1.37889i −0.329415 0.944185i \(-0.606851\pi\)
0.900571 0.434708i \(-0.143149\pi\)
\(374\) 254956. + 320700.i 0.0942509 + 0.118555i
\(375\) −162418. + 162418.i −0.0596426 + 0.0596426i
\(376\) −3.51857e6 + 181563.i −1.28350 + 0.0662304i
\(377\) −4.33860e6 4.33860e6i −1.57216 1.57216i
\(378\) 208960. 1.82966e6i 0.0752202 0.658629i
\(379\) −1.47772e6 612093.i −0.528439 0.218887i 0.102480 0.994735i \(-0.467322\pi\)
−0.630919 + 0.775848i \(0.717322\pi\)
\(380\) −15998.5 25633.5i −0.00568356 0.00910645i
\(381\) −28767.9 69451.7i −0.0101530 0.0245115i
\(382\) −2.46302e6 1.36614e6i −0.863593 0.479000i
\(383\) 142494. 0.0496362 0.0248181 0.999692i \(-0.492099\pi\)
0.0248181 + 0.999692i \(0.492099\pi\)
\(384\) 31812.0 3.00007e6i 0.0110094 1.03825i
\(385\) −47813.2 −0.0164398
\(386\) 1.83020e6 + 1.01514e6i 0.625215 + 0.346782i
\(387\) −113793. 274720.i −0.0386222 0.0932423i
\(388\) −2.09563e6 3.35771e6i −0.706701 1.13231i
\(389\) −3.77507e6 1.56369e6i −1.26489 0.523933i −0.353480 0.935442i \(-0.615002\pi\)
−0.911406 + 0.411509i \(0.865002\pi\)
\(390\) 21084.3 184615.i 0.00701938 0.0614618i
\(391\) −487561. 487561.i −0.161282 0.161282i
\(392\) 1.58116e6 81589.9i 0.519710 0.0268177i
\(393\) −4.42801e6 + 4.42801e6i −1.44620 + 1.44620i
\(394\) −253037. 318287.i −0.0821191 0.103295i
\(395\) 29438.2 71070.2i 0.00949334 0.0229190i
\(396\) 82698.4 115807.i 0.0265008 0.0371107i
\(397\) 2.76926e6 1.14706e6i 0.881834 0.365268i 0.104626 0.994512i \(-0.466635\pi\)
0.777208 + 0.629244i \(0.216635\pi\)
\(398\) −1.00456e6 3.50686e6i −0.317883 1.10971i
\(399\) 603822.i 0.189879i
\(400\) 3.02177e6 1.03686e6i 0.944304 0.324018i
\(401\) 2.58223e6i 0.801925i −0.916095 0.400962i \(-0.868676\pi\)
0.916095 0.400962i \(-0.131324\pi\)
\(402\) 4.29936e6 1.23158e6i 1.32690 0.380098i
\(403\) −1.08806e6 + 450688.i −0.333725 + 0.138234i
\(404\) 462593. + 2.77348e6i 0.141009 + 0.845419i
\(405\) 55048.1 132898.i 0.0166765 0.0402606i
\(406\) −2.73139e6 + 2.17145e6i −0.822373 + 0.653785i
\(407\) −722388. + 722388.i −0.216165 + 0.216165i
\(408\) 389160. + 817583.i 0.115738 + 0.243154i
\(409\) 4.19686e6 + 4.19686e6i 1.24056 + 1.24056i 0.959771 + 0.280785i \(0.0905947\pi\)
0.280785 + 0.959771i \(0.409405\pi\)
\(410\) 193917. + 22146.7i 0.0569712 + 0.00650652i
\(411\) 5.77736e6 + 2.39306e6i 1.68704 + 0.698794i
\(412\) 1.24394e6 5.37492e6i 0.361039 1.56002i
\(413\) 1.38068e6 + 3.33325e6i 0.398306 + 0.961596i
\(414\) −116166. + 209437.i −0.0333104 + 0.0600555i
\(415\) −19610.1 −0.00558932
\(416\) −2.78536e6 + 4.35923e6i −0.789128 + 1.23503i
\(417\) 1.82347e6 0.513522
\(418\) −267187. + 481714.i −0.0747954 + 0.134849i
\(419\) −162163. 391497.i −0.0451250 0.108941i 0.899710 0.436488i \(-0.143778\pi\)
−0.944835 + 0.327547i \(0.893778\pi\)
\(420\) −102952. 23826.4i −0.0284780 0.00659076i
\(421\) 4.56770e6 + 1.89200e6i 1.25601 + 0.520255i 0.908682 0.417489i \(-0.137090\pi\)
0.347326 + 0.937745i \(0.387090\pi\)
\(422\) 263442. + 30087.0i 0.0720119 + 0.00822428i
\(423\) −261159. 261159.i −0.0709667 0.0709667i
\(424\) 317596. + 112754.i 0.0857948 + 0.0304592i
\(425\) −681770. + 681770.i −0.183090 + 0.183090i
\(426\) −4.35753e6 + 3.46423e6i −1.16337 + 0.924874i
\(427\) −1.42504e6 + 3.44036e6i −0.378232 + 0.913134i
\(428\) 297116. 49556.5i 0.0784002 0.0130765i
\(429\) −3.12959e6 + 1.29632e6i −0.821003 + 0.340071i
\(430\) 193652. 55472.6i 0.0505069 0.0144680i
\(431\) 4.31266e6i 1.11829i −0.829072 0.559143i \(-0.811130\pi\)
0.829072 0.559143i \(-0.188870\pi\)
\(432\) −2.78351e6 + 2.45733e6i −0.717602 + 0.633510i
\(433\) 754344.i 0.193352i −0.995316 0.0966762i \(-0.969179\pi\)
0.995316 0.0966762i \(-0.0308211\pi\)
\(434\) 184438. + 643864.i 0.0470031 + 0.164085i
\(435\) −233470. + 96706.6i −0.0591573 + 0.0245038i
\(436\) 5.45439e6 + 3.89500e6i 1.37414 + 0.981275i
\(437\) 354778. 856509.i 0.0888695 0.214550i
\(438\) −280231. 352492.i −0.0697960 0.0877939i
\(439\) −3.32741e6 + 3.32741e6i −0.824034 + 0.824034i −0.986684 0.162650i \(-0.947996\pi\)
0.162650 + 0.986684i \(0.447996\pi\)
\(440\) 71589.1 + 64563.5i 0.0176285 + 0.0158985i
\(441\) 117359. + 117359.i 0.0287355 + 0.0287355i
\(442\) 177155. 1.55117e6i 0.0431317 0.377662i
\(443\) −1.40682e6 582722.i −0.340587 0.141076i 0.205833 0.978587i \(-0.434010\pi\)
−0.546420 + 0.837511i \(0.684010\pi\)
\(444\) −1.91543e6 + 1.19547e6i −0.461115 + 0.287793i
\(445\) −31664.3 76444.4i −0.00758002 0.0182998i
\(446\) −5.62020e6 3.11730e6i −1.33787 0.742064i
\(447\) −4.25548e6 −1.00735
\(448\) 2.28334e6 + 1.85510e6i 0.537496 + 0.436689i
\(449\) 7.02116e6 1.64359 0.821794 0.569784i \(-0.192973\pi\)
0.821794 + 0.569784i \(0.192973\pi\)
\(450\) 292862. + 162439.i 0.0681760 + 0.0378145i
\(451\) −1.36163e6 3.28728e6i −0.315224 0.761018i
\(452\) −4.44625e6 + 2.77501e6i −1.02364 + 0.638879i
\(453\) 1.23858e6 + 513038.i 0.283583 + 0.117464i
\(454\) −340108. + 2.97799e6i −0.0774421 + 0.678085i
\(455\) 128838. + 128838.i 0.0291753 + 0.0291753i
\(456\) −815358. + 904083.i −0.183627 + 0.203609i
\(457\) 4.15830e6 4.15830e6i 0.931377 0.931377i −0.0664154 0.997792i \(-0.521156\pi\)
0.997792 + 0.0664154i \(0.0211562\pi\)
\(458\) 4.30261e6 + 5.41209e6i 0.958447 + 1.20560i
\(459\) 428831. 1.03529e6i 0.0950068 0.229367i
\(460\) −132035. 94286.8i −0.0290935 0.0207757i
\(461\) −1.58159e6 + 655116.i −0.346610 + 0.143571i −0.549195 0.835694i \(-0.685066\pi\)
0.202585 + 0.979265i \(0.435066\pi\)
\(462\) 530502. + 1.85195e6i 0.115633 + 0.403669i
\(463\) 6.44663e6i 1.39759i −0.715321 0.698796i \(-0.753720\pi\)
0.715321 0.698796i \(-0.246280\pi\)
\(464\) 7.02179e6 + 437030.i 1.51409 + 0.0942359i
\(465\) 48505.3i 0.0104029i
\(466\) −7.45910e6 + 2.13670e6i −1.59119 + 0.455804i
\(467\) 2.11968e6 878001.i 0.449758 0.186296i −0.146295 0.989241i \(-0.546735\pi\)
0.596053 + 0.802945i \(0.296735\pi\)
\(468\) −534897. + 89216.2i −0.112890 + 0.0188291i
\(469\) −1.67821e6 + 4.05157e6i −0.352302 + 0.850533i
\(470\) 195853. 155702.i 0.0408964 0.0325125i
\(471\) 4.81160e6 4.81160e6i 0.999395 0.999395i
\(472\) 2.43374e6 6.85513e6i 0.502827 1.41632i
\(473\) −2.59671e6 2.59671e6i −0.533668 0.533668i
\(474\) −3.07940e6 351689.i −0.629535 0.0718974i
\(475\) −1.19768e6 496096.i −0.243561 0.100886i
\(476\) −865019. 200194.i −0.174988 0.0404980i
\(477\) 13519.8 + 32639.6i 0.00272065 + 0.00656824i
\(478\) 1.45246e6 2.61864e6i 0.290759 0.524212i
\(479\) −2.32912e6 −0.463823 −0.231912 0.972737i \(-0.574498\pi\)
−0.231912 + 0.972737i \(0.574498\pi\)
\(480\) 121973. + 174693.i 0.0241635 + 0.0346077i
\(481\) 3.89312e6 0.767246
\(482\) −2.95619e6 + 5.32974e6i −0.579582 + 1.04493i
\(483\) −1.24073e6 2.99539e6i −0.241997 0.584231i
\(484\) −765751. + 3.30874e6i −0.148585 + 0.642021i
\(485\) 259682. + 107564.i 0.0501288 + 0.0207640i
\(486\) −806181. 92071.7i −0.154825 0.0176822i
\(487\) −1.19139e6 1.19139e6i −0.227631 0.227631i 0.584071 0.811702i \(-0.301459\pi\)
−0.811702 + 0.584071i \(0.801459\pi\)
\(488\) 6.77929e6 3.22686e6i 1.28865 0.613382i
\(489\) −4.10623e6 + 4.10623e6i −0.776554 + 0.776554i
\(490\) −88011.3 + 69968.9i −0.0165595 + 0.0131648i
\(491\) 2.41981e6 5.84194e6i 0.452979 1.09359i −0.518205 0.855256i \(-0.673400\pi\)
0.971184 0.238331i \(-0.0766003\pi\)
\(492\) −1.29375e6 7.75672e6i −0.240957 1.44466i
\(493\) −1.96166e6 + 812547.i −0.363502 + 0.150567i
\(494\) 2.01800e6 578066.i 0.372052 0.106576i
\(495\) 10105.7i 0.00185375i
\(496\) 593274. 1.21309e6i 0.108281 0.221405i
\(497\) 5.45861e6i 0.991268i
\(498\) 217580. + 759559.i 0.0393138 + 0.137242i
\(499\) 1.65121e6 683953.i 0.296859 0.122963i −0.229283 0.973360i \(-0.573638\pi\)
0.526142 + 0.850397i \(0.323638\pi\)
\(500\) −263906. + 369564.i −0.0472090 + 0.0661095i
\(501\) −244942. + 591342.i −0.0435983 + 0.105255i
\(502\) 1.98946e6 + 2.50247e6i 0.352351 + 0.443210i
\(503\) −296902. + 296902.i −0.0523231 + 0.0523231i −0.732784 0.680461i \(-0.761780\pi\)
0.680461 + 0.732784i \(0.261780\pi\)
\(504\) 15892.6 + 307988.i 0.00278688 + 0.0540079i
\(505\) −141194. 141194.i −0.0246371 0.0246371i
\(506\) −335616. + 2.93866e6i −0.0582728 + 0.510238i
\(507\) 6.37396e6 + 2.64018e6i 1.10126 + 0.456156i
\(508\) −78690.8 126082.i −0.0135290 0.0216767i
\(509\) −9842.30 23761.4i −0.00168384 0.00406516i 0.923035 0.384715i \(-0.125700\pi\)
−0.924719 + 0.380650i \(0.875700\pi\)
\(510\) −56231.5 31189.4i −0.00957314 0.00530983i
\(511\) 441561. 0.0748064
\(512\) −913774. 5.86084e6i −0.154051 0.988063i
\(513\) 1.50667e6 0.252770
\(514\) −3.69673e6 2.05043e6i −0.617178 0.342324i
\(515\) 149931. + 361964.i 0.0249099 + 0.0601378i
\(516\) −4.29725e6 6.88526e6i −0.710504 1.13840i
\(517\) −4.21405e6 1.74552e6i −0.693383 0.287209i
\(518\) 251223. 2.19971e6i 0.0411372 0.360198i
\(519\) −1.21453e6 1.21453e6i −0.197920 0.197920i
\(520\) −18931.4 366879.i −0.00307026 0.0594996i
\(521\) 4.68273e6 4.68273e6i 0.755797 0.755797i −0.219758 0.975554i \(-0.570527\pi\)
0.975554 + 0.219758i \(0.0705267\pi\)
\(522\) 458952. + 577299.i 0.0737210 + 0.0927310i
\(523\) −4.15033e6 + 1.00198e7i −0.663480 + 1.60178i 0.128831 + 0.991667i \(0.458877\pi\)
−0.792312 + 0.610117i \(0.791123\pi\)
\(524\) −7.19488e6 + 1.00754e7i −1.14471 + 1.60301i
\(525\) −4.18853e6 + 1.73495e6i −0.663229 + 0.274719i
\(526\) −978907. 3.41731e6i −0.154268 0.538543i
\(527\) 407550.i 0.0639226i
\(528\) 1.70644e6 3.48922e6i 0.266383 0.544683i
\(529\) 1.45846e6i 0.226597i
\(530\) −23007.9 + 6590.72i −0.00355784 + 0.00101916i
\(531\) 704507. 291816.i 0.108430 0.0449131i
\(532\) −196401. 1.17752e6i −0.0300860 0.180381i
\(533\) −5.18886e6 + 1.25270e7i −0.791141 + 1.90998i
\(534\) −2.60961e6 + 2.07463e6i −0.396024 + 0.314839i
\(535\) −15125.8 + 15125.8i −0.00228472 + 0.00228472i
\(536\) 7.98368e6 3.80014e6i 1.20030 0.571331i
\(537\) 6.57426e6 + 6.57426e6i 0.983810 + 0.983810i
\(538\) 1.48193e6 + 169248.i 0.220736 + 0.0252097i
\(539\) 1.89369e6 + 784392.i 0.280761 + 0.116295i
\(540\) 59452.4 256888.i 0.00877374 0.0379105i
\(541\) 1.43835e6 + 3.47249e6i 0.211287 + 0.510091i 0.993621 0.112767i \(-0.0359714\pi\)
−0.782335 + 0.622858i \(0.785971\pi\)
\(542\) 2.42210e6 4.36682e6i 0.354155 0.638509i
\(543\) −3.86059e6 −0.561894
\(544\) 1.02484e6 + 1.46780e6i 0.148476 + 0.212653i
\(545\) −475965. −0.0686410
\(546\) 3.56080e6 6.41980e6i 0.511171 0.921594i
\(547\) 1.62541e6 + 3.92408e6i 0.232270 + 0.560750i 0.996444 0.0842605i \(-0.0268528\pi\)
−0.764173 + 0.645011i \(0.776853\pi\)
\(548\) 1.20449e7 + 2.78759e6i 1.71337 + 0.396531i
\(549\) 727146. + 301194.i 0.102965 + 0.0426496i
\(550\) 4.10921e6 + 469301.i 0.579230 + 0.0661523i
\(551\) −2.01868e6 2.01868e6i −0.283262 0.283262i
\(552\) −2.18705e6 + 6.16029e6i −0.305500 + 0.860504i
\(553\) 2.14903e6 2.14903e6i 0.298834 0.298834i
\(554\) 1.32687e6 1.05486e6i 0.183676 0.146022i
\(555\) 61360.5 148137.i 0.00845584 0.0204142i
\(556\) 3.55598e6 593108.i 0.487835 0.0813667i
\(557\) 616764. 255472.i 0.0842328 0.0348904i −0.340169 0.940364i \(-0.610484\pi\)
0.424402 + 0.905474i \(0.360484\pi\)
\(558\) 136085. 38982.4i 0.0185023 0.00530008i
\(559\) 1.39943e7i 1.89418i
\(560\) −208518. 12978.0i −0.0280978 0.00174878i
\(561\) 1.17224e6i 0.157257i
\(562\) 1.62164e6 + 5.66107e6i 0.216578 + 0.756063i
\(563\) 66963.1 27737.0i 0.00890358 0.00368798i −0.378227 0.925713i \(-0.623466\pi\)
0.387131 + 0.922025i \(0.373466\pi\)
\(564\) −8.20388e6 5.85841e6i −1.08598 0.775501i
\(565\) 142435. 343868.i 0.0187713 0.0453180i
\(566\) −6.20292e6 7.80243e6i −0.813870 1.02374i
\(567\) 4.01859e6 4.01859e6i 0.524947 0.524947i
\(568\) −7.37091e6 + 8.17300e6i −0.958629 + 1.06294i
\(569\) −5.05653e6 5.05653e6i −0.654745 0.654745i 0.299387 0.954132i \(-0.403218\pi\)
−0.954132 + 0.299387i \(0.903218\pi\)
\(570\) 9810.19 85898.2i 0.00126471 0.0110738i
\(571\) −8.89824e6 3.68577e6i −1.14213 0.473084i −0.270240 0.962793i \(-0.587103\pi\)
−0.871886 + 0.489709i \(0.837103\pi\)
\(572\) −5.68143e6 + 3.54592e6i −0.726052 + 0.453147i
\(573\) −3.08396e6 7.44533e6i −0.392393 0.947321i
\(574\) 6.74326e6 + 3.74021e6i 0.854260 + 0.473823i
\(575\) −6.96072e6 −0.877980
\(576\) 392089. 482600.i 0.0492412 0.0606082i
\(577\) −6.35911e6 −0.795164 −0.397582 0.917567i \(-0.630151\pi\)
−0.397582 + 0.917567i \(0.630151\pi\)
\(578\) 6.55137e6 + 3.63378e6i 0.815666 + 0.452417i
\(579\) 2.29160e6 + 5.53241e6i 0.284081 + 0.685832i
\(580\) −423840. + 264529.i −0.0523157 + 0.0326515i
\(581\) −715781. 296486.i −0.0879711 0.0364388i
\(582\) 1.28503e6 1.12517e7i 0.157255 1.37693i
\(583\) 308516. + 308516.i 0.0375930 + 0.0375930i
\(584\) −661136. 596253.i −0.0802155 0.0723433i
\(585\) 27230.9 27230.9i 0.00328982 0.00328982i
\(586\) −1.15058e6 1.44728e6i −0.138412 0.174104i
\(587\) −835435. + 2.01692e6i −0.100073 + 0.241598i −0.965985 0.258599i \(-0.916739\pi\)
0.865912 + 0.500197i \(0.166739\pi\)
\(588\) 3.68662e6 + 2.63263e6i 0.439729 + 0.314012i
\(589\) −506255. + 209698.i −0.0601286 + 0.0249061i
\(590\) 142257. + 496611.i 0.0168245 + 0.0587336i
\(591\) 1.16342e6i 0.137015i
\(592\) −3.34648e6 + 2.95432e6i −0.392450 + 0.346461i
\(593\) 2.07838e6i 0.242710i −0.992609 0.121355i \(-0.961276\pi\)
0.992609 0.121355i \(-0.0387239\pi\)
\(594\) −4.62105e6 + 1.32372e6i −0.537371 + 0.153933i
\(595\) 58253.1 24129.2i 0.00674570 0.00279416i
\(596\) −8.29869e6 + 1.38415e6i −0.956960 + 0.159613i
\(597\) 3.99428e6 9.64304e6i 0.458672 1.10733i
\(598\) 8.82290e6 7.01419e6i 1.00892 0.802093i
\(599\) −9.69064e6 + 9.69064e6i −1.10353 + 1.10353i −0.109553 + 0.993981i \(0.534942\pi\)
−0.993981 + 0.109553i \(0.965058\pi\)
\(600\) 8.61410e6 + 3.05821e6i 0.976859 + 0.346808i
\(601\) −358495. 358495.i −0.0404852 0.0404852i 0.686574 0.727060i \(-0.259114\pi\)
−0.727060 + 0.686574i \(0.759114\pi\)
\(602\) 7.90713e6 + 903051.i 0.889258 + 0.101560i
\(603\) 856329. + 354703.i 0.0959063 + 0.0397257i
\(604\) 2.58225e6 + 597619.i 0.288009 + 0.0666549i
\(605\) −92295.4 222821.i −0.0102516 0.0247496i
\(606\) −3.90230e6 + 7.03549e6i −0.431658 + 0.778239i
\(607\) 1.31076e7 1.44394 0.721972 0.691923i \(-0.243236\pi\)
0.721972 + 0.691923i \(0.243236\pi\)
\(608\) −1.29598e6 + 2.02827e6i −0.142180 + 0.222519i
\(609\) −9.98395e6 −1.09084
\(610\) −258618. + 466265.i −0.0281407 + 0.0507350i
\(611\) 6.65174e6 + 1.60587e7i 0.720829 + 1.74024i
\(612\) −42312.5 + 182828.i −0.00456657 + 0.0197317i
\(613\) 4.88906e6 + 2.02511e6i 0.525501 + 0.217670i 0.629632 0.776894i \(-0.283206\pi\)
−0.104130 + 0.994564i \(0.533206\pi\)
\(614\) −8.65221e6 988144.i −0.926203 0.105779i
\(615\) 394884. + 394884.i 0.0421000 + 0.0421000i
\(616\) 1.63691e6 + 3.43898e6i 0.173810 + 0.365155i
\(617\) 7.98865e6 7.98865e6i 0.844812 0.844812i −0.144668 0.989480i \(-0.546211\pi\)
0.989480 + 0.144668i \(0.0462114\pi\)
\(618\) 1.23565e7 9.82338e6i 1.30144 1.03464i
\(619\) 4.92433e6 1.18884e7i 0.516559 1.24708i −0.423445 0.905922i \(-0.639179\pi\)
0.940004 0.341162i \(-0.110821\pi\)
\(620\) 15777.0 + 94591.0i 0.00164833 + 0.00988258i
\(621\) 7.47418e6 3.09590e6i 0.777740 0.322150i
\(622\) −1.01210e7 + 2.89922e6i −1.04894 + 0.300473i
\(623\) 3.26901e6i 0.337440i
\(624\) −1.40003e7 + 4.80390e6i −1.43938 + 0.493893i
\(625\) 9.71724e6i 0.995045i
\(626\) −2.33947e6 8.16695e6i −0.238606 0.832960i
\(627\) −1.45615e6 + 603156.i −0.147923 + 0.0612718i
\(628\) 7.81815e6 1.09482e7i 0.791052 1.10776i
\(629\) 515563. 1.24468e6i 0.0519583 0.125438i
\(630\) −13628.9 17143.4i −0.00136808 0.00172086i
\(631\) 1.20522e7 1.20522e7i 1.20501 1.20501i 0.232389 0.972623i \(-0.425346\pi\)
0.972623 0.232389i \(-0.0746544\pi\)
\(632\) −6.11958e6 + 315778.i −0.609437 + 0.0314477i
\(633\) 536464. + 536464.i 0.0532146 + 0.0532146i
\(634\) −712152. + 6.23562e6i −0.0703639 + 0.616107i
\(635\) 9751.04 + 4039.01i 0.000959658 + 0.000397503i
\(636\) 510558. + 818040.i 0.0500498 + 0.0801921i
\(637\) −2.98913e6 7.21640e6i −0.291875 0.704648i
\(638\) 7.96494e6 + 4.41783e6i 0.774695 + 0.429692i
\(639\) −1.15372e6 −0.111776
\(640\) 294682. + 300999.i 0.0284383 + 0.0290479i
\(641\) −1.53916e7 −1.47958 −0.739788 0.672840i \(-0.765074\pi\)
−0.739788 + 0.672840i \(0.765074\pi\)
\(642\) 753694. + 418044.i 0.0721702 + 0.0400299i
\(643\) 4.37786e6 + 1.05691e7i 0.417575 + 1.00811i 0.983048 + 0.183348i \(0.0586934\pi\)
−0.565474 + 0.824766i \(0.691307\pi\)
\(644\) −3.39386e6 5.43779e6i −0.322462 0.516664i
\(645\) 532498. + 220568.i 0.0503986 + 0.0208758i
\(646\) 82427.1 721733.i 0.00777121 0.0680448i
\(647\) −6.52550e6 6.52550e6i −0.612849 0.612849i 0.330839 0.943687i \(-0.392668\pi\)
−0.943687 + 0.330839i \(0.892668\pi\)
\(648\) −1.14433e7 + 590490.i −1.07057 + 0.0552427i
\(649\) 6.65914e6 6.65914e6i 0.620593 0.620593i
\(650\) −9.80814e6 1.23373e7i −0.910549 1.14535i
\(651\) −733355. + 1.77048e6i −0.0678206 + 0.163734i
\(652\) −6.67204e6 + 9.34325e6i −0.614666 + 0.860754i
\(653\) 6.41840e6 2.65859e6i 0.589039 0.243988i −0.0681982 0.997672i \(-0.521725\pi\)
0.657237 + 0.753684i \(0.271725\pi\)
\(654\) 5.28098e6 + 1.84356e7i 0.482803 + 1.68544i
\(655\) 879208.i 0.0800734i
\(656\) −5.04595e6 1.47057e7i −0.457808 1.33422i
\(657\) 93327.3i 0.00843520i
\(658\) 9.50284e6 2.72214e6i 0.855635 0.245101i
\(659\) 1.22358e7 5.06822e6i 1.09753 0.454613i 0.240906 0.970549i \(-0.422556\pi\)
0.856627 + 0.515935i \(0.172556\pi\)
\(660\) 45379.5 + 272073.i 0.00405508 + 0.0243123i
\(661\) 2.22223e6 5.36495e6i 0.197827 0.477597i −0.793571 0.608478i \(-0.791780\pi\)
0.991398 + 0.130881i \(0.0417805\pi\)
\(662\) 6.37445e6 5.06767e6i 0.565324 0.449432i
\(663\) 3.15874e6 3.15874e6i 0.279081 0.279081i
\(664\) 671363. + 1.41046e6i 0.0590931 + 0.124148i
\(665\) 59946.2 + 59946.2i 0.00525663 + 0.00525663i
\(666\) −464925. 53097.8i −0.0406160 0.00463864i
\(667\) −1.41620e7 5.86610e6i −1.23257 0.510546i
\(668\) −285324. + 1.23286e6i −0.0247399 + 0.106899i
\(669\) −7.03708e6 1.69890e7i −0.607893 1.46758i
\(670\) −304564. + 549100.i −0.0262115 + 0.0472568i
\(671\) 9.72008e6 0.833419
\(672\) 1.81089e6 + 8.22053e6i 0.154692 + 0.702226i
\(673\) −1.23747e7 −1.05317 −0.526583 0.850124i \(-0.676527\pi\)
−0.526583 + 0.850124i \(0.676527\pi\)
\(674\) −7.06539e6 + 1.27382e7i −0.599082 + 1.08009i
\(675\) −4.32909e6 1.04514e7i −0.365710 0.882903i
\(676\) 1.32887e7 + 3.07545e6i 1.11845 + 0.258846i
\(677\) −281503. 116602.i −0.0236054 0.00977768i 0.370850 0.928693i \(-0.379067\pi\)
−0.394455 + 0.918915i \(0.629067\pi\)
\(678\) −1.48994e7 1.70162e6i −1.24479 0.142164i
\(679\) 7.85230e6 + 7.85230e6i 0.653616 + 0.653616i
\(680\) −119803. 42532.9i −0.00993562 0.00352738i
\(681\) −6.06426e6 + 6.06426e6i −0.501084 + 0.501084i
\(682\) 1.36848e6 1.08794e6i 0.112662 0.0895658i
\(683\) 3.15725e6 7.62228e6i 0.258975 0.625220i −0.739896 0.672721i \(-0.765126\pi\)
0.998871 + 0.0475004i \(0.0151255\pi\)
\(684\) −248878. + 41510.8i −0.0203398 + 0.00339251i
\(685\) −811143. + 335986.i −0.0660497 + 0.0273587i
\(686\) −1.24762e7 + 3.57388e6i −1.01221 + 0.289954i
\(687\) 1.97826e7i 1.59916i
\(688\) −1.06197e7 1.20293e7i −0.855342 0.968880i
\(689\) 1.66266e6i 0.133431i
\(690\) −127837. 446274.i −0.0102220 0.0356844i
\(691\) 5.83716e6 2.41783e6i 0.465058 0.192633i −0.137836 0.990455i \(-0.544015\pi\)
0.602893 + 0.797822i \(0.294015\pi\)
\(692\) −2.76352e6 1.97343e6i −0.219380 0.156660i
\(693\) −152789. + 368864.i −0.0120853 + 0.0291765i
\(694\) 1.13532e7 + 1.42807e7i 0.894783 + 1.12552i
\(695\) −181030. + 181030.i −0.0142164 + 0.0142164i
\(696\) 1.49486e7 + 1.34816e7i 1.16971 + 1.05492i
\(697\) 3.31789e6 + 3.31789e6i 0.258690 + 0.258690i
\(698\) −845338. + 7.40179e6i −0.0656738 + 0.575040i
\(699\) −2.05108e7 8.49585e6i −1.58778 0.657679i
\(700\) −7.60382e6 + 4.74573e6i −0.586525 + 0.366065i
\(701\) 9.43551e6 + 2.27793e7i 0.725221 + 1.75084i 0.657897 + 0.753108i \(0.271446\pi\)
0.0673239 + 0.997731i \(0.478554\pi\)
\(702\) 1.60189e7 + 8.88502e6i 1.22684 + 0.680480i
\(703\) 1.81140e6 0.138238
\(704\) 2.19285e6 7.35944e6i 0.166754 0.559645i
\(705\) 715893. 0.0542469
\(706\) −7.70838e6 4.27553e6i −0.582038 0.322833i
\(707\) −3.01896e6 7.28842e6i −0.227148 0.548384i
\(708\) 1.76569e7 1.10201e7i 1.32383 0.826233i
\(709\) 1.92972e6 + 799317.i 0.144171 + 0.0597178i 0.453603 0.891204i \(-0.350139\pi\)
−0.309431 + 0.950922i \(0.600139\pi\)
\(710\) 88685.1 776528.i 0.00660244 0.0578111i
\(711\) −454214. 454214.i −0.0336966 0.0336966i
\(712\) −4.41424e6 + 4.89458e6i −0.326329 + 0.361839i
\(713\) −2.08050e6 + 2.08050e6i −0.153265 + 0.153265i
\(714\) −1.58094e6 1.98860e6i −0.116056 0.145983i
\(715\) 182004. 439396.i 0.0133142 0.0321433i
\(716\) 1.49589e7 + 1.06822e7i 1.09048 + 0.778716i
\(717\) 7.91576e6 3.27882e6i 0.575036 0.238188i
\(718\) 859524. + 3.00055e6i 0.0622224 + 0.217215i
\(719\) 1.73078e7i 1.24859i 0.781190 + 0.624293i \(0.214613\pi\)
−0.781190 + 0.624293i \(0.785387\pi\)
\(720\) −2742.99 + 44071.8i −0.000197193 + 0.00316832i
\(721\) 1.54788e7i 1.10892i
\(722\) −1.25264e7 + 3.58826e6i −0.894302 + 0.256177i
\(723\) −1.61110e7 + 6.67339e6i −1.14624 + 0.474789i
\(724\) −7.52861e6 + 1.25571e6i −0.533788 + 0.0890312i
\(725\) −8.20274e6 + 1.98032e7i −0.579581 + 1.39923i
\(726\) −7.60650e6 + 6.04715e6i −0.535603 + 0.425804i
\(727\) 8.01518e6 8.01518e6i 0.562442 0.562442i −0.367559 0.930000i \(-0.619806\pi\)
0.930000 + 0.367559i \(0.119806\pi\)
\(728\) 4.85586e6 1.36776e7i 0.339577 0.956489i
\(729\) 9.23498e6 + 9.23498e6i 0.643602 + 0.643602i
\(730\) 62815.4 + 7173.97i 0.00436274 + 0.000498256i
\(731\) 4.47415e6 + 1.85325e6i 0.309683 + 0.128275i
\(732\) 2.09293e7 + 4.84374e6i 1.44370 + 0.334120i
\(733\) −9.51812e6 2.29788e7i −0.654321 1.57967i −0.806444 0.591310i \(-0.798611\pi\)
0.152123 0.988362i \(-0.451389\pi\)
\(734\) 1.06389e6 1.91810e6i 0.0728882 0.131411i
\(735\) −321705. −0.0219654
\(736\) −2.26129e6 + 1.27247e7i −0.153873 + 0.865867i
\(737\) 1.14469e7 0.776283
\(738\) 790521. 1.42524e6i 0.0534285 0.0963266i
\(739\) −4.57465e6 1.10442e7i −0.308139 0.743914i −0.999765 0.0216584i \(-0.993105\pi\)
0.691626 0.722256i \(-0.256895\pi\)
\(740\) 71476.7 308844.i 0.00479827 0.0207329i
\(741\) 5.54903e6 + 2.29848e6i 0.371254 + 0.153779i
\(742\) −939449. 107292.i −0.0626417 0.00715413i
\(743\) 2.29256e6 + 2.29256e6i 0.152352 + 0.152352i 0.779168 0.626816i \(-0.215642\pi\)
−0.626816 + 0.779168i \(0.715642\pi\)
\(744\) 3.48875e6 1.66061e6i 0.231067 0.109985i
\(745\) 422475. 422475.i 0.0278875 0.0278875i
\(746\) 1.77582e7 1.41178e7i 1.16829 0.928792i
\(747\) −62664.6 + 151286.i −0.00410885 + 0.00991965i
\(748\) 381287. + 2.28601e6i 0.0249171 + 0.149391i
\(749\) −780790. + 323414.i −0.0508546 + 0.0210646i
\(750\) −1.24911e6 + 357814.i −0.0810862 + 0.0232276i
\(751\) 1.28174e7i 0.829276i 0.909987 + 0.414638i \(0.136092\pi\)
−0.909987 + 0.414638i \(0.863908\pi\)
\(752\) −1.79041e7 8.75618e6i −1.15453 0.564638i
\(753\) 9.14719e6i 0.587896i
\(754\) −9.55809e6 3.33668e7i −0.612270 2.13740i
\(755\) −173897. + 72030.6i −0.0111026 + 0.00459885i
\(756\) 6.05397e6 8.47773e6i 0.385244 0.539480i
\(757\) −2.29625e6 + 5.54365e6i −0.145640 + 0.351606i −0.979819 0.199888i \(-0.935942\pi\)
0.834179 + 0.551494i \(0.185942\pi\)
\(758\) −5.63062e6 7.08255e6i −0.355945 0.447731i
\(759\) −5.98416e6 + 5.98416e6i −0.377050 + 0.377050i
\(760\) −8808.47 170703.i −0.000553180 0.0107203i
\(761\) 1.56002e7 + 1.56002e7i 0.976492 + 0.976492i 0.999730 0.0232379i \(-0.00739751\pi\)
−0.0232379 + 0.999730i \(0.507398\pi\)
\(762\) 48252.8 422502.i 0.00301047 0.0263598i
\(763\) −1.73731e7 7.19616e6i −1.08035 0.447496i
\(764\) −8.43577e6 1.35162e7i −0.522867 0.837761i
\(765\) −5099.89 12312.2i −0.000315070 0.000760647i
\(766\) 704896. + 390978.i 0.0434064 + 0.0240758i
\(767\) −3.58876e7 −2.20271
\(768\) 8.38903e6 1.47536e7i 0.513226 0.902601i
\(769\) −902297. −0.0550216 −0.0275108 0.999622i \(-0.508758\pi\)
−0.0275108 + 0.999622i \(0.508758\pi\)
\(770\) −236525. 131191.i −0.0143764 0.00797402i
\(771\) −4.62870e6 1.11747e7i −0.280429 0.677015i
\(772\) 6.26837e6 + 1.00435e7i 0.378540 + 0.606514i
\(773\) 2.40926e7 + 9.97950e6i 1.45023 + 0.600703i 0.962253 0.272156i \(-0.0877367\pi\)
0.487972 + 0.872859i \(0.337737\pi\)
\(774\) 190866. 1.67123e6i 0.0114519 0.100273i
\(775\) 2.90922e6 + 2.90922e6i 0.173989 + 0.173989i
\(776\) −1.15381e6 2.23602e7i −0.0687831 1.33297i
\(777\) 4.47941e6 4.47941e6i 0.266175 0.266175i
\(778\) −1.43843e7 1.80935e7i −0.851999 1.07170i
\(779\) −2.41429e6 + 5.82861e6i −0.142543 + 0.344129i
\(780\) 610852. 855412.i 0.0359500 0.0503430i
\(781\) −1.31637e7 + 5.45259e6i −0.772237 + 0.319871i
\(782\) −1.07411e6 3.74968e6i −0.0628107 0.219269i
\(783\) 2.49123e7i 1.45214i
\(784\) 8.04565e6 + 3.93481e6i 0.467488 + 0.228630i
\(785\) 955371.i 0.0553348i
\(786\) −3.40545e7 + 9.75508e6i −1.96615 + 0.563215i
\(787\) 1.98015e6 820205.i 0.113962 0.0472047i −0.324974 0.945723i \(-0.605355\pi\)
0.438936 + 0.898518i \(0.355355\pi\)
\(788\) −378418. 2.26881e6i −0.0217098 0.130161i
\(789\) 3.89229e6 9.39682e6i 0.222594 0.537388i
\(790\) 340631. 270801.i 0.0194185 0.0154377i
\(791\) 1.03979e7 1.03979e7i 0.590889 0.590889i
\(792\) 726853. 345974.i 0.0411750 0.0195988i
\(793\) −2.61919e7 2.61919e7i −1.47905 1.47905i
\(794\) 1.68465e7 + 1.92399e6i 0.948326 + 0.108306i
\(795\) −63266.3 26205.7i −0.00355021 0.00147055i
\(796\) 4.65279e6 2.01043e7i 0.260274 1.12462i
\(797\) 3.63608e6 + 8.77827e6i 0.202762 + 0.489512i 0.992250 0.124254i \(-0.0396538\pi\)
−0.789488 + 0.613766i \(0.789654\pi\)
\(798\) 1.65678e6 2.98702e6i 0.0920996 0.166047i
\(799\) 6.01506e6 0.333329
\(800\) 1.77932e7 + 3.16203e6i 0.982947 + 0.174679i
\(801\) −690930. −0.0380498
\(802\) 7.08518e6 1.27739e7i 0.388969 0.701275i
\(803\) −441074. 1.06485e6i −0.0241392 0.0582772i
\(804\) 2.46476e7 + 5.70427e6i 1.34473 + 0.311214i
\(805\) 420553. + 174199.i 0.0228734 + 0.00947447i
\(806\) −6.61908e6 755947.i −0.358889 0.0409877i
\(807\) 3.01775e6 + 3.01775e6i 0.163117 + 0.163117i
\(808\) −5.32157e6 + 1.49893e7i −0.286755 + 0.807706i
\(809\) −7.81387e6 + 7.81387e6i −0.419754 + 0.419754i −0.885119 0.465365i \(-0.845923\pi\)
0.465365 + 0.885119i \(0.345923\pi\)
\(810\) 636963. 506385.i 0.0341116 0.0271186i
\(811\) 2.72035e6 6.56751e6i 0.145235 0.350629i −0.834475 0.551045i \(-0.814229\pi\)
0.979711 + 0.200416i \(0.0642292\pi\)
\(812\) −1.94699e7 + 3.24741e6i −1.03627 + 0.172841i
\(813\) 1.32002e7 5.46771e6i 0.700414 0.290121i
\(814\) −5.55566e6 + 1.59145e6i −0.293883 + 0.0841844i
\(815\) 815317.i 0.0429964i
\(816\) −318182. + 5.11225e6i −0.0167282 + 0.268774i
\(817\) 6.51130e6i 0.341281i
\(818\) 9.24584e6 + 3.22767e7i 0.483129 + 1.68658i
\(819\) 1.40565e6 582240.i 0.0732265 0.0303314i
\(820\) 898512. + 641629.i 0.0466648 + 0.0333234i
\(821\) −4.33547e6 + 1.04667e7i −0.224480 + 0.541943i −0.995489 0.0948818i \(-0.969753\pi\)
0.771008 + 0.636825i \(0.219753\pi\)
\(822\) 2.20137e7 + 2.76902e7i 1.13635 + 1.42938i
\(823\) 4.64730e6 4.64730e6i 0.239167 0.239167i −0.577338 0.816505i \(-0.695909\pi\)
0.816505 + 0.577338i \(0.195909\pi\)
\(824\) 2.09014e7 2.31759e7i 1.07240 1.18910i
\(825\) 8.36783e6 + 8.36783e6i 0.428033 + 0.428033i
\(826\) −2.31583e6 + 2.02774e7i −0.118102 + 1.03410i
\(827\) 3.07509e6 + 1.27374e6i 0.156349 + 0.0647618i 0.459485 0.888185i \(-0.348034\pi\)
−0.303137 + 0.952947i \(0.598034\pi\)
\(828\) −1.14932e6 + 717317.i −0.0582592 + 0.0363609i
\(829\) −1.12391e7 2.71337e7i −0.567998 1.37127i −0.903240 0.429136i \(-0.858818\pi\)
0.335242 0.942132i \(-0.391182\pi\)
\(830\) −97008.3 53806.6i −0.00488780 0.00271107i
\(831\) 4.85004e6 0.243637
\(832\) −2.57397e7 + 1.39220e7i −1.28913 + 0.697256i
\(833\) −2.70302e6 −0.134970
\(834\) 9.02046e6 + 5.00328e6i 0.449069 + 0.249081i
\(835\) −34389.9 83024.6i −0.00170693 0.00412089i
\(836\) −2.64347e6 + 1.64986e6i −0.130816 + 0.0816452i
\(837\) −4.41775e6 1.82989e6i −0.217965 0.0902841i
\(838\) 271999. 2.38163e6i 0.0133800 0.117156i
\(839\) 9.64715e6 + 9.64715e6i 0.473145 + 0.473145i 0.902931 0.429786i \(-0.141411\pi\)
−0.429786 + 0.902931i \(0.641411\pi\)
\(840\) −443912. 400347.i −0.0217069 0.0195767i
\(841\) −1.88744e7 + 1.88744e7i −0.920202 + 0.920202i
\(842\) 1.74044e7 + 2.18924e7i 0.846019 + 1.06418i
\(843\) −6.44791e6 + 1.55666e7i −0.312500 + 0.754442i
\(844\) 1.22066e6 + 871676.i 0.0589846 + 0.0421210i
\(845\) −894905. + 370682.i −0.0431157 + 0.0178591i
\(846\) −575344. 2.00849e6i −0.0276377 0.0964817i
\(847\) 9.52854e6i 0.456371i
\(848\) 1.26173e6 + 1.42921e6i 0.0602526 + 0.0682505i
\(849\) 2.85199e7i 1.35794i
\(850\) −5.24328e6 + 1.50197e6i −0.248918 + 0.0713038i
\(851\) 8.98583e6 3.72205e6i 0.425338 0.176181i
\(852\) −3.10613e7 + 5.18076e6i −1.46596 + 0.244509i
\(853\) 3.33293e6 8.04640e6i 0.156839 0.378642i −0.825854 0.563884i \(-0.809307\pi\)
0.982693 + 0.185241i \(0.0593067\pi\)
\(854\) −1.64892e7 + 1.31089e7i −0.773670 + 0.615067i
\(855\) 12670.1 12670.1i 0.000592739 0.000592739i
\(856\) 1.60577e6 + 570086.i 0.0749028 + 0.0265923i
\(857\) 128369. + 128369.i 0.00597046 + 0.00597046i 0.710086 0.704115i \(-0.248656\pi\)
−0.704115 + 0.710086i \(0.748656\pi\)
\(858\) −1.90385e7 2.17434e6i −0.882908 0.100834i
\(859\) 3.82676e7 + 1.58510e7i 1.76949 + 0.732947i 0.994944 + 0.100431i \(0.0320221\pi\)
0.774547 + 0.632516i \(0.217978\pi\)
\(860\) 1.11018e6 + 256931.i 0.0511854 + 0.0118460i
\(861\) 8.44326e6 + 2.03838e7i 0.388152 + 0.937083i
\(862\) 1.18332e7 2.13342e7i 0.542418 0.977929i
\(863\) 6.35352e6 0.290394 0.145197 0.989403i \(-0.453618\pi\)
0.145197 + 0.989403i \(0.453618\pi\)
\(864\) −2.05121e7 + 4.51859e6i −0.934816 + 0.205929i
\(865\) 241152. 0.0109585
\(866\) 2.06979e6 3.73163e6i 0.0937844 0.169085i
\(867\) 8.20300e6 + 1.98038e7i 0.370617 + 0.894747i
\(868\) −854259. + 3.69117e6i −0.0384849 + 0.166290i
\(869\) −7.32916e6 3.03584e6i −0.329234 0.136373i
\(870\) −1.42029e6 162207.i −0.0636179 0.00726562i
\(871\) −3.08450e7 3.08450e7i −1.37765 1.37765i
\(872\) 1.62949e7 + 3.42339e7i 0.725708 + 1.52463i
\(873\) 1.65964e6 1.65964e6i 0.0737019 0.0737019i
\(874\) 4.10515e6 3.26358e6i 0.181782 0.144516i
\(875\) 487577. 1.17711e6i 0.0215290 0.0519755i
\(876\) −419086. 2.51263e6i −0.0184520 0.110629i
\(877\) −9.38709e6 + 3.88826e6i −0.412128 + 0.170709i −0.579107 0.815251i \(-0.696599\pi\)
0.166979 + 0.985960i \(0.446599\pi\)
\(878\) −2.55901e7 + 7.33041e6i −1.12030 + 0.320916i
\(879\) 5.29019e6i 0.230940i
\(880\) 176991. + 515815.i 0.00770449 + 0.0224537i
\(881\) 3.02284e7i 1.31212i −0.754707 0.656062i \(-0.772221\pi\)
0.754707 0.656062i \(-0.227779\pi\)
\(882\) 258545. + 902568.i 0.0111909 + 0.0390669i
\(883\) 2.33973e7 9.69146e6i 1.00986 0.418300i 0.184459 0.982840i \(-0.440947\pi\)
0.825405 + 0.564541i \(0.190947\pi\)
\(884\) 5.13249e6 7.18733e6i 0.220901 0.309341i
\(885\) −565636. + 1.36556e6i −0.0242761 + 0.0586076i
\(886\) −5.36044e6 6.74270e6i −0.229412 0.288569i
\(887\) −1.94775e7 + 1.94775e7i −0.831235 + 0.831235i −0.987686 0.156451i \(-0.949995\pi\)
0.156451 + 0.987686i \(0.449995\pi\)
\(888\) −1.27555e7 + 658202.i −0.542833 + 0.0280109i
\(889\) 294854. + 294854.i 0.0125127 + 0.0125127i
\(890\) 53111.1 465041.i 0.00224755 0.0196796i
\(891\) −1.37052e7 5.67687e6i −0.578350 0.239560i
\(892\) −1.92490e7 3.08417e7i −0.810022 1.29785i
\(893\) 3.09494e6 + 7.47186e6i 0.129875 + 0.313545i
\(894\) −2.10513e7 1.16763e7i −0.880916 0.488608i
\(895\) −1.30536e6 −0.0544718
\(896\) 6.20529e6 + 1.54420e7i 0.258221 + 0.642589i
\(897\) 3.22500e7 1.33829
\(898\) 3.47327e7 + 1.92648e7i 1.43730 + 0.797213i
\(899\) 3.46727e6 + 8.37072e6i 0.143083 + 0.345433i
\(900\) 1.00304e6 + 1.60712e6i 0.0412775 + 0.0661368i
\(901\) −531575. 220186.i −0.0218149 0.00903601i
\(902\) 2.28389e6 1.99978e7i 0.0934672 0.818400i
\(903\) 1.61018e7 + 1.61018e7i 0.657134 + 0.657134i
\(904\) −2.96091e7 + 1.52787e6i −1.20505 + 0.0621821i
\(905\) 383272. 383272.i 0.0155555 0.0155555i
\(906\) 4.71941e6 + 5.93638e6i 0.191015 + 0.240271i
\(907\) −1.50394e7 + 3.63084e7i −0.607035 + 1.46551i 0.259175 + 0.965830i \(0.416549\pi\)
−0.866210 + 0.499681i \(0.833451\pi\)
\(908\) −9.85355e6 + 1.37985e7i −0.396623 + 0.555415i
\(909\) −1.54046e6 + 638080.i −0.0618360 + 0.0256133i
\(910\) 283835. + 990853.i 0.0113622 + 0.0396648i
\(911\) 3.45052e7i 1.37749i −0.725004 0.688745i \(-0.758162\pi\)
0.725004 0.688745i \(-0.241838\pi\)
\(912\) −6.51411e6 + 2.23518e6i −0.259339 + 0.0889866i
\(913\) 2.02230e6i 0.0802914i
\(914\) 3.19802e7 9.16089e6i 1.26624 0.362721i
\(915\) −1.40945e6 + 583812.i −0.0556539 + 0.0230526i
\(916\) 6.43456e6 + 3.85785e7i 0.253385 + 1.51917i
\(917\) 1.32928e7 3.20917e7i 0.522028 1.26029i
\(918\) 4.96202e6 3.94480e6i 0.194335 0.154496i
\(919\) 9.14468e6 9.14468e6i 0.357174 0.357174i −0.505596 0.862770i \(-0.668727\pi\)
0.862770 + 0.505596i \(0.168727\pi\)
\(920\) −394455. 828706.i −0.0153648 0.0322798i
\(921\) −1.76190e7 1.76190e7i −0.684435 0.684435i
\(922\) −9.62143e6 1.09884e6i −0.372745 0.0425702i
\(923\) 5.01637e7 + 2.07785e7i 1.93814 + 0.802805i
\(924\) −2.45712e6 + 1.06170e7i −0.0946772 + 0.409091i
\(925\) −5.20465e6 1.25651e7i −0.200004 0.482851i
\(926\) 1.76884e7 3.18906e7i 0.677894 1.22218i
\(927\) 3.27155e6 0.125042
\(928\) 3.35367e7 + 2.14285e7i 1.27835 + 0.816811i
\(929\) 1.69632e7 0.644863 0.322431 0.946593i \(-0.395500\pi\)
0.322431 + 0.946593i \(0.395500\pi\)
\(930\) −133090. + 239949.i −0.00504589 + 0.00909727i
\(931\) −1.39079e6 3.35767e6i −0.0525882 0.126959i
\(932\) −4.27618e7 9.89650e6i −1.61256 0.373200i
\(933\) −2.78305e7 1.15278e7i −1.04669 0.433552i
\(934\) 1.28949e7 + 1.47268e6i 0.483670 + 0.0552386i
\(935\) −116378. 116378.i −0.00435352 0.00435352i
\(936\) −2.89085e6 1.02632e6i −0.107854 0.0382908i
\(937\) 2.39347e7 2.39347e7i 0.890594 0.890594i −0.103985 0.994579i \(-0.533159\pi\)
0.994579 + 0.103985i \(0.0331594\pi\)
\(938\) −1.94187e7 + 1.54378e7i −0.720631 + 0.572900i
\(939\) 9.30209e6 2.24572e7i 0.344284 0.831174i
\(940\) 1.39608e6 232853.i 0.0515335 0.00859534i
\(941\) −1.71763e7 + 7.11466e6i −0.632348 + 0.261927i −0.675750 0.737131i \(-0.736180\pi\)
0.0434026 + 0.999058i \(0.486180\pi\)
\(942\) 3.70045e7 1.06001e7i 1.35871 0.389210i
\(943\) 3.38749e7i 1.24051i
\(944\) 3.08486e7 2.72336e7i 1.12669 0.994662i
\(945\) 739789.i 0.0269481i
\(946\) −5.72065e6 1.99705e7i −0.207835 0.725539i
\(947\) −4.37514e7 + 1.81224e7i −1.58532 + 0.656661i −0.989245 0.146269i \(-0.953273\pi\)
−0.596074 + 0.802930i \(0.703273\pi\)
\(948\) −1.42684e7 1.01891e7i −0.515648 0.368226i
\(949\) −1.68083e6 + 4.05788e6i −0.0605840 + 0.146263i
\(950\) −4.56356e6 5.74034e6i −0.164057 0.206362i
\(951\) −1.26980e7 + 1.26980e7i −0.455284 + 0.455284i
\(952\) −3.72983e6 3.36379e6i −0.133382 0.120292i
\(953\) −1.10556e7 1.10556e7i −0.394320 0.394320i 0.481904 0.876224i \(-0.339945\pi\)
−0.876224 + 0.481904i \(0.839945\pi\)
\(954\) −22676.9 + 198559.i −0.000806702 + 0.00706349i
\(955\) 1.04533e6 + 432988.i 0.0370888 + 0.0153627i
\(956\) 1.43702e7 8.96878e6i 0.508532 0.317387i
\(957\) 9.97294e6 + 2.40768e7i 0.352000 + 0.849804i
\(958\) −1.15218e7 6.39068e6i −0.405609 0.224975i
\(959\) −3.46871e7 −1.21793
\(960\) 124055. + 1.19885e6i 0.00434447 + 0.0419844i
\(961\) −2.68901e7 −0.939255
\(962\) 1.92587e7 + 1.06820e7i 0.670949 + 0.372148i
\(963\) 68355.9 + 165026.i 0.00237526 + 0.00573438i
\(964\) −2.92477e7 + 1.82542e7i −1.01368 + 0.632660i
\(965\) −776751. 321741.i −0.0268512 0.0111221i
\(966\) 2.08109e6 1.82221e7i 0.0717545 0.628283i
\(967\) −7.90354e6 7.90354e6i −0.271804 0.271804i 0.558022 0.829826i \(-0.311560\pi\)
−0.829826 + 0.558022i \(0.811560\pi\)
\(968\) −1.28667e7 + 1.42668e7i −0.441344 + 0.489370i
\(969\) 1.46971e6 1.46971e6i 0.0502830 0.0502830i
\(970\) 989474. + 1.24462e6i 0.0337656 + 0.0424726i
\(971\) 8.44568e6 2.03897e7i 0.287466 0.694005i −0.712504 0.701668i \(-0.752439\pi\)
0.999971 + 0.00766285i \(0.00243919\pi\)
\(972\) −3.73544e6 2.66748e6i −0.126816 0.0905600i
\(973\) −9.34475e6 + 3.87072e6i −0.316436 + 0.131072i
\(974\) −2.62468e6 9.16261e6i −0.0886500 0.309472i
\(975\) 4.50961e7i 1.51924i
\(976\) 4.23901e7 + 2.63832e6i 1.42443 + 0.0886551i
\(977\) 2.34272e7i 0.785207i −0.919708 0.392604i \(-0.871574\pi\)
0.919708 0.392604i \(-0.128426\pi\)
\(978\) −3.15798e7 + 9.04619e6i −1.05575 + 0.302426i
\(979\) −7.88339e6 + 3.26541e6i −0.262879 + 0.108888i
\(980\) −627362. + 104639.i −0.0208667 + 0.00348038i
\(981\) −1.52096e6 + 3.67192e6i −0.0504598 + 0.121821i
\(982\) 2.79997e7 2.22597e7i 0.926563 0.736616i
\(983\) −3.98753e7 + 3.98753e7i −1.31619 + 1.31619i −0.399430 + 0.916764i \(0.630792\pi\)
−0.916764 + 0.399430i \(0.869208\pi\)
\(984\) 1.48830e7 4.19212e7i 0.490009 1.38021i
\(985\) 115502. + 115502.i 0.00379314 + 0.00379314i
\(986\) −1.19336e7 1.36290e6i −0.390911 0.0446448i
\(987\) 2.61306e7 + 1.08236e7i 0.853800 + 0.353656i
\(988\) 1.15689e7 + 2.67742e6i 0.377050 + 0.0872618i
\(989\) 1.33794e7 + 3.23007e7i 0.434956 + 1.05008i
\(990\) −27728.2 + 49991.3i −0.000899152 + 0.00162109i
\(991\) 5.90335e7 1.90948 0.954739 0.297446i \(-0.0961347\pi\)
0.954739 + 0.297446i \(0.0961347\pi\)
\(992\) 6.26335e6 4.37314e6i 0.202082 0.141096i
\(993\) 2.33003e7 0.749874
\(994\) 1.49775e7 2.70030e7i 0.480809 0.866853i
\(995\) 560797. + 1.35388e6i 0.0179576 + 0.0433535i
\(996\) −1.00776e6 + 4.35443e6i −0.0321891 + 0.139086i
\(997\) −3.58931e7 1.48674e7i −1.14360 0.473693i −0.271215 0.962519i \(-0.587425\pi\)
−0.872381 + 0.488826i \(0.837425\pi\)
\(998\) 1.00449e7 + 1.14720e6i 0.319243 + 0.0364598i
\(999\) 1.11771e7 + 1.11771e7i 0.354338 + 0.354338i
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 32.6.g.a.5.17 76
4.3 odd 2 128.6.g.a.113.5 76
32.13 even 8 inner 32.6.g.a.13.17 yes 76
32.19 odd 8 128.6.g.a.17.5 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.6.g.a.5.17 76 1.1 even 1 trivial
32.6.g.a.13.17 yes 76 32.13 even 8 inner
128.6.g.a.17.5 76 32.19 odd 8
128.6.g.a.113.5 76 4.3 odd 2