Properties

Label 33.6.e.b.25.4
Level $33$
Weight $6$
Character 33.25
Analytic conductor $5.293$
Analytic rank $0$
Dimension $20$
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] = [33,6,Mod(4,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("33.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.e (of order \(5\), 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: \(5.29266605383\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} - 1581925 x^{13} + 89291182 x^{12} - 100741271 x^{11} + 2277268901 x^{10} + \cdots + 25599187870096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4}\cdot 11^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 25.4
Root \(4.70404 + 3.41769i\) of defining polynomial
Character \(\chi\) \(=\) 33.25
Dual form 33.6.e.b.4.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.51306 - 4.00547i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.46148 - 13.7310i) q^{4} +(-62.5986 - 45.4806i) q^{5} +(-49.6176 - 36.0493i) q^{6} +(59.3828 - 182.761i) q^{7} +(36.9828 + 113.821i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\) \(q+(5.51306 - 4.00547i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.46148 - 13.7310i) q^{4} +(-62.5986 - 45.4806i) q^{5} +(-49.6176 - 36.0493i) q^{6} +(59.3828 - 182.761i) q^{7} +(36.9828 + 113.821i) q^{8} +(-65.5304 + 47.6106i) q^{9} -527.281 q^{10} +(385.600 - 111.193i) q^{11} -129.939 q^{12} +(-216.388 + 157.215i) q^{13} +(-404.665 - 1245.43i) q^{14} +(-215.195 + 662.302i) q^{15} +(1033.57 + 750.930i) q^{16} +(1189.63 + 864.319i) q^{17} +(-170.570 + 524.960i) q^{18} +(-727.309 - 2238.43i) q^{19} +(-903.778 + 656.633i) q^{20} -1729.50 q^{21} +(1680.45 - 2157.53i) q^{22} +2228.76 q^{23} +(871.400 - 633.109i) q^{24} +(884.428 + 2721.99i) q^{25} +(-563.240 + 1733.48i) q^{26} +(589.773 + 428.495i) q^{27} +(-2244.57 - 1630.77i) q^{28} +(-2118.06 + 6518.72i) q^{29} +(1466.45 + 4513.27i) q^{30} +(4802.37 - 3489.12i) q^{31} +4876.23 q^{32} +(-2024.17 - 2991.30i) q^{33} +10020.5 q^{34} +(-12029.4 + 8739.85i) q^{35} +(361.380 + 1112.21i) q^{36} +(165.708 - 509.998i) q^{37} +(-12975.7 - 9427.36i) q^{38} +(1947.49 + 1414.94i) q^{39} +(2861.59 - 8807.06i) q^{40} +(-3609.97 - 11110.3i) q^{41} +(-9534.84 + 6927.47i) q^{42} -12622.3 q^{43} +(193.544 - 5790.77i) q^{44} +6267.47 q^{45} +(12287.3 - 8927.23i) q^{46} +(143.345 + 441.170i) q^{47} +(3553.09 - 10935.3i) q^{48} +(-16278.3 - 11826.9i) q^{49} +(15778.8 + 11463.9i) q^{50} +(4089.59 - 12586.5i) q^{51} +(1193.32 + 3672.65i) q^{52} +(-5396.90 + 3921.08i) q^{53} +4967.78 q^{54} +(-29195.1 - 10576.7i) q^{55} +22998.3 q^{56} +(-17137.1 + 12450.8i) q^{57} +(14433.6 + 44421.9i) q^{58} +(-11445.3 + 35225.0i) q^{59} +(8134.00 + 5909.70i) q^{60} +(17177.1 + 12479.9i) q^{61} +(12500.2 - 38471.5i) q^{62} +(4810.01 + 14803.7i) q^{63} +(-6191.20 + 4498.17i) q^{64} +20695.9 q^{65} +(-23140.9 - 8383.43i) q^{66} +23334.8 q^{67} +(17175.5 - 12478.7i) q^{68} +(-6198.52 - 19077.1i) q^{69} +(-31311.4 + 96366.7i) q^{70} +(35440.5 + 25749.0i) q^{71} +(-7842.60 - 5697.98i) q^{72} +(-8749.89 + 26929.4i) q^{73} +(-1129.22 - 3475.39i) q^{74} +(20839.2 - 15140.5i) q^{75} -33980.8 q^{76} +(2576.09 - 77075.7i) q^{77} +16404.2 q^{78} +(39968.3 - 29038.6i) q^{79} +(-30547.1 - 94014.4i) q^{80} +(2027.46 - 6239.88i) q^{81} +(-64404.2 - 46792.4i) q^{82} +(34157.4 + 24816.8i) q^{83} +(-7716.14 + 23747.8i) q^{84} +(-35159.7 - 108210. i) q^{85} +(-69587.7 + 50558.4i) q^{86} +61687.7 q^{87} +(26916.7 + 39777.2i) q^{88} +8883.59 q^{89} +(34552.9 - 25104.2i) q^{90} +(15883.2 + 48883.3i) q^{91} +(9943.57 - 30603.2i) q^{92} +(-43221.3 - 31402.1i) q^{93} +(2557.36 + 1858.03i) q^{94} +(-56276.3 + 173201. i) q^{95} +(-13561.5 - 41738.1i) q^{96} +(-93072.1 + 67620.8i) q^{97} -137115. q^{98} +(-19974.5 + 25645.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.51306 4.00547i 0.974581 0.708074i 0.0180898 0.999836i \(-0.494242\pi\)
0.956491 + 0.291762i \(0.0942415\pi\)
\(3\) −2.78115 8.55951i −0.178411 0.549093i
\(4\) 4.46148 13.7310i 0.139421 0.429095i
\(5\) −62.5986 45.4806i −1.11980 0.813581i −0.135620 0.990761i \(-0.543303\pi\)
−0.984178 + 0.177180i \(0.943303\pi\)
\(6\) −49.6176 36.0493i −0.562674 0.408807i
\(7\) 59.3828 182.761i 0.458053 1.40974i −0.409461 0.912328i \(-0.634283\pi\)
0.867513 0.497414i \(-0.165717\pi\)
\(8\) 36.9828 + 113.821i 0.204303 + 0.628780i
\(9\) −65.5304 + 47.6106i −0.269672 + 0.195928i
\(10\) −527.281 −1.66741
\(11\) 385.600 111.193i 0.960848 0.277075i
\(12\) −129.939 −0.260487
\(13\) −216.388 + 157.215i −0.355120 + 0.258010i −0.751014 0.660286i \(-0.770435\pi\)
0.395894 + 0.918296i \(0.370435\pi\)
\(14\) −404.665 1245.43i −0.551792 1.69824i
\(15\) −215.195 + 662.302i −0.246947 + 0.760025i
\(16\) 1033.57 + 750.930i 1.00934 + 0.733330i
\(17\) 1189.63 + 864.319i 0.998368 + 0.725357i 0.961738 0.273972i \(-0.0883376\pi\)
0.0366302 + 0.999329i \(0.488338\pi\)
\(18\) −170.570 + 524.960i −0.124086 + 0.381896i
\(19\) −727.309 2238.43i −0.462205 1.42252i −0.862464 0.506119i \(-0.831080\pi\)
0.400259 0.916402i \(-0.368920\pi\)
\(20\) −903.778 + 656.633i −0.505227 + 0.367069i
\(21\) −1729.50 −0.855800
\(22\) 1680.45 2157.53i 0.740234 0.950384i
\(23\) 2228.76 0.878503 0.439251 0.898364i \(-0.355244\pi\)
0.439251 + 0.898364i \(0.355244\pi\)
\(24\) 871.400 633.109i 0.308809 0.224363i
\(25\) 884.428 + 2721.99i 0.283017 + 0.871037i
\(26\) −563.240 + 1733.48i −0.163403 + 0.502903i
\(27\) 589.773 + 428.495i 0.155695 + 0.113119i
\(28\) −2244.57 1630.77i −0.541051 0.393096i
\(29\) −2118.06 + 6518.72i −0.467674 + 1.43935i 0.387915 + 0.921695i \(0.373196\pi\)
−0.855588 + 0.517657i \(0.826804\pi\)
\(30\) 1466.45 + 4513.27i 0.297484 + 0.915563i
\(31\) 4802.37 3489.12i 0.897534 0.652097i −0.0402971 0.999188i \(-0.512830\pi\)
0.937832 + 0.347091i \(0.112830\pi\)
\(32\) 4876.23 0.841800
\(33\) −2024.17 2991.30i −0.323566 0.478162i
\(34\) 10020.5 1.48660
\(35\) −12029.4 + 8739.85i −1.65987 + 1.20596i
\(36\) 361.380 + 1112.21i 0.0464738 + 0.143032i
\(37\) 165.708 509.998i 0.0198994 0.0612441i −0.940614 0.339479i \(-0.889749\pi\)
0.960513 + 0.278235i \(0.0897493\pi\)
\(38\) −12975.7 9427.36i −1.45771 1.05909i
\(39\) 1947.49 + 1414.94i 0.205029 + 0.148962i
\(40\) 2861.59 8807.06i 0.282785 0.870324i
\(41\) −3609.97 11110.3i −0.335385 1.03221i −0.966532 0.256546i \(-0.917415\pi\)
0.631147 0.775664i \(-0.282585\pi\)
\(42\) −9534.84 + 6927.47i −0.834047 + 0.605970i
\(43\) −12622.3 −1.04104 −0.520521 0.853849i \(-0.674262\pi\)
−0.520521 + 0.853849i \(0.674262\pi\)
\(44\) 193.544 5790.77i 0.0150712 0.450925i
\(45\) 6267.47 0.461382
\(46\) 12287.3 8927.23i 0.856172 0.622045i
\(47\) 143.345 + 441.170i 0.00946536 + 0.0291314i 0.955678 0.294415i \(-0.0951248\pi\)
−0.946212 + 0.323546i \(0.895125\pi\)
\(48\) 3553.09 10935.3i 0.222589 0.685057i
\(49\) −16278.3 11826.9i −0.968542 0.703687i
\(50\) 15778.8 + 11463.9i 0.892582 + 0.648499i
\(51\) 4089.59 12586.5i 0.220168 0.677608i
\(52\) 1193.32 + 3672.65i 0.0611994 + 0.188352i
\(53\) −5396.90 + 3921.08i −0.263909 + 0.191741i −0.711869 0.702313i \(-0.752151\pi\)
0.447959 + 0.894054i \(0.352151\pi\)
\(54\) 4967.78 0.231835
\(55\) −29195.1 10576.7i −1.30138 0.471460i
\(56\) 22998.3 0.979999
\(57\) −17137.1 + 12450.8i −0.698633 + 0.507587i
\(58\) 14433.6 + 44421.9i 0.563382 + 1.73391i
\(59\) −11445.3 + 35225.0i −0.428053 + 1.31741i 0.471988 + 0.881605i \(0.343537\pi\)
−0.900040 + 0.435806i \(0.856463\pi\)
\(60\) 8134.00 + 5909.70i 0.291693 + 0.211927i
\(61\) 17177.1 + 12479.9i 0.591051 + 0.429424i 0.842691 0.538397i \(-0.180970\pi\)
−0.251640 + 0.967821i \(0.580970\pi\)
\(62\) 12500.2 38471.5i 0.412987 1.27104i
\(63\) 4810.01 + 14803.7i 0.152684 + 0.469914i
\(64\) −6191.20 + 4498.17i −0.188941 + 0.137273i
\(65\) 20695.9 0.607575
\(66\) −23140.9 8383.43i −0.653915 0.236898i
\(67\) 23334.8 0.635064 0.317532 0.948248i \(-0.397146\pi\)
0.317532 + 0.948248i \(0.397146\pi\)
\(68\) 17175.5 12478.7i 0.450441 0.327264i
\(69\) −6198.52 19077.1i −0.156735 0.482380i
\(70\) −31311.4 + 96366.7i −0.763762 + 2.35062i
\(71\) 35440.5 + 25749.0i 0.834361 + 0.606199i 0.920790 0.390059i \(-0.127546\pi\)
−0.0864289 + 0.996258i \(0.527546\pi\)
\(72\) −7842.60 5697.98i −0.178291 0.129536i
\(73\) −8749.89 + 26929.4i −0.192174 + 0.591452i 0.807824 + 0.589424i \(0.200645\pi\)
−0.999998 + 0.00202736i \(0.999355\pi\)
\(74\) −1129.22 3475.39i −0.0239718 0.0737776i
\(75\) 20839.2 15140.5i 0.427787 0.310805i
\(76\) −33980.8 −0.674838
\(77\) 2576.09 77075.7i 0.0495148 1.48146i
\(78\) 16404.2 0.305293
\(79\) 39968.3 29038.6i 0.720522 0.523490i −0.166029 0.986121i \(-0.553094\pi\)
0.886551 + 0.462631i \(0.153094\pi\)
\(80\) −30547.1 94014.4i −0.533637 1.64236i
\(81\) 2027.46 6239.88i 0.0343352 0.105673i
\(82\) −64404.2 46792.4i −1.05774 0.768494i
\(83\) 34157.4 + 24816.8i 0.544238 + 0.395412i 0.825657 0.564173i \(-0.190805\pi\)
−0.281418 + 0.959585i \(0.590805\pi\)
\(84\) −7716.14 + 23747.8i −0.119317 + 0.367220i
\(85\) −35159.7 108210.i −0.527834 1.62451i
\(86\) −69587.7 + 50558.4i −1.01458 + 0.737136i
\(87\) 61687.7 0.873776
\(88\) 26916.7 + 39777.2i 0.370524 + 0.547555i
\(89\) 8883.59 0.118881 0.0594406 0.998232i \(-0.481068\pi\)
0.0594406 + 0.998232i \(0.481068\pi\)
\(90\) 34552.9 25104.2i 0.449654 0.326693i
\(91\) 15883.2 + 48883.3i 0.201064 + 0.618810i
\(92\) 9943.57 30603.2i 0.122482 0.376961i
\(93\) −43221.3 31402.1i −0.518192 0.376488i
\(94\) 2557.36 + 1858.03i 0.0298520 + 0.0216887i
\(95\) −56276.3 + 173201.i −0.639760 + 1.96898i
\(96\) −13561.5 41738.1i −0.150186 0.462226i
\(97\) −93072.1 + 67620.8i −1.00436 + 0.729712i −0.963019 0.269434i \(-0.913164\pi\)
−0.0413427 + 0.999145i \(0.513164\pi\)
\(98\) −137115. −1.44218
\(99\) −19974.5 + 25645.2i −0.204827 + 0.262977i
\(100\) 41321.6 0.413216
\(101\) 83571.5 60718.2i 0.815182 0.592264i −0.100146 0.994973i \(-0.531931\pi\)
0.915328 + 0.402708i \(0.131931\pi\)
\(102\) −27868.6 85770.8i −0.265225 0.816279i
\(103\) 31889.8 98146.6i 0.296182 0.911554i −0.686640 0.726997i \(-0.740915\pi\)
0.982822 0.184556i \(-0.0590848\pi\)
\(104\) −25897.1 18815.3i −0.234784 0.170580i
\(105\) 108264. + 78658.7i 0.958324 + 0.696263i
\(106\) −14047.7 + 43234.3i −0.121434 + 0.373735i
\(107\) 24538.7 + 75522.3i 0.207201 + 0.637699i 0.999616 + 0.0277167i \(0.00882363\pi\)
−0.792415 + 0.609983i \(0.791176\pi\)
\(108\) 8514.95 6186.47i 0.0702462 0.0510368i
\(109\) 117979. 0.951130 0.475565 0.879681i \(-0.342244\pi\)
0.475565 + 0.879681i \(0.342244\pi\)
\(110\) −203319. + 58630.2i −1.60213 + 0.461998i
\(111\) −4826.19 −0.0371789
\(112\) 198617. 144304.i 1.49614 1.08701i
\(113\) −31241.0 96150.0i −0.230160 0.708358i −0.997727 0.0673898i \(-0.978533\pi\)
0.767567 0.640969i \(-0.221467\pi\)
\(114\) −44606.3 + 137284.i −0.321465 + 0.989369i
\(115\) −139517. 101365.i −0.983746 0.714733i
\(116\) 80059.0 + 58166.3i 0.552415 + 0.401353i
\(117\) 6694.89 20604.8i 0.0452146 0.139156i
\(118\) 77994.3 + 240042.i 0.515653 + 1.58702i
\(119\) 228608. 166093.i 1.47987 1.07519i
\(120\) −83342.6 −0.528341
\(121\) 136323. 85752.3i 0.846459 0.532454i
\(122\) 144686. 0.880091
\(123\) −85059.2 + 61799.2i −0.506942 + 0.368315i
\(124\) −26483.6 81508.2i −0.154676 0.476044i
\(125\) −6286.82 + 19348.8i −0.0359879 + 0.110759i
\(126\) 85813.6 + 62347.2i 0.481537 + 0.349857i
\(127\) −38337.5 27853.8i −0.210918 0.153241i 0.477311 0.878735i \(-0.341612\pi\)
−0.688229 + 0.725493i \(0.741612\pi\)
\(128\) −64334.0 + 198000.i −0.347069 + 1.06817i
\(129\) 35104.7 + 108041.i 0.185734 + 0.571629i
\(130\) 114098. 82896.7i 0.592131 0.430208i
\(131\) −137084. −0.697922 −0.348961 0.937137i \(-0.613465\pi\)
−0.348961 + 0.937137i \(0.613465\pi\)
\(132\) −50104.4 + 14448.4i −0.250289 + 0.0721745i
\(133\) −452288. −2.21710
\(134\) 128646. 93467.0i 0.618921 0.449672i
\(135\) −17430.8 53646.5i −0.0823157 0.253342i
\(136\) −54382.0 + 167371.i −0.252120 + 0.775946i
\(137\) −29590.6 21498.8i −0.134695 0.0978617i 0.518398 0.855140i \(-0.326529\pi\)
−0.653093 + 0.757278i \(0.726529\pi\)
\(138\) −110585. 80345.1i −0.494311 0.359138i
\(139\) −42191.2 + 129851.i −0.185219 + 0.570045i −0.999952 0.00979098i \(-0.996883\pi\)
0.814733 + 0.579836i \(0.196883\pi\)
\(140\) 66338.4 + 204169.i 0.286052 + 0.880377i
\(141\) 3377.53 2453.92i 0.0143071 0.0103947i
\(142\) 298523. 1.24239
\(143\) −65957.9 + 84683.1i −0.269729 + 0.346303i
\(144\) −103482. −0.415872
\(145\) 429062. 311732.i 1.69473 1.23129i
\(146\) 59626.3 + 183511.i 0.231502 + 0.712491i
\(147\) −55959.7 + 172226.i −0.213591 + 0.657365i
\(148\) −6263.49 4550.70i −0.0235051 0.0170775i
\(149\) 207706. + 150907.i 0.766448 + 0.556857i 0.900881 0.434065i \(-0.142921\pi\)
−0.134433 + 0.990923i \(0.542921\pi\)
\(150\) 54242.6 166941.i 0.196839 0.605809i
\(151\) 55074.5 + 169502.i 0.196566 + 0.604968i 0.999955 + 0.00951312i \(0.00302817\pi\)
−0.803389 + 0.595455i \(0.796972\pi\)
\(152\) 227883. 165566.i 0.800023 0.581251i
\(153\) −119108. −0.411350
\(154\) −294523. 435242.i −1.00073 1.47887i
\(155\) −459309. −1.53559
\(156\) 28117.3 20428.4i 0.0925043 0.0672083i
\(157\) −102721. 316141.i −0.332589 1.02360i −0.967897 0.251346i \(-0.919127\pi\)
0.635308 0.772259i \(-0.280873\pi\)
\(158\) 104034. 320184.i 0.331537 1.02037i
\(159\) 48572.1 + 35289.7i 0.152368 + 0.110702i
\(160\) −305245. 221774.i −0.942646 0.684873i
\(161\) 132350. 407331.i 0.402401 1.23846i
\(162\) −13816.2 42521.8i −0.0413619 0.127299i
\(163\) −533588. + 387675.i −1.57303 + 1.14287i −0.648853 + 0.760914i \(0.724751\pi\)
−0.924179 + 0.381961i \(0.875249\pi\)
\(164\) −168662. −0.489676
\(165\) −9335.41 + 279312.i −0.0266946 + 0.798692i
\(166\) 287715. 0.810386
\(167\) −242426. + 176133.i −0.672647 + 0.488707i −0.870910 0.491442i \(-0.836470\pi\)
0.198263 + 0.980149i \(0.436470\pi\)
\(168\) −63961.8 196854.i −0.174843 0.538110i
\(169\) −92628.6 + 285082.i −0.249476 + 0.767807i
\(170\) −627271. 455739.i −1.66469 1.20947i
\(171\) 154234. + 112057.i 0.403356 + 0.293055i
\(172\) −56314.4 + 173318.i −0.145144 + 0.446706i
\(173\) 1394.21 + 4290.94i 0.00354172 + 0.0109003i 0.952812 0.303562i \(-0.0981759\pi\)
−0.949270 + 0.314462i \(0.898176\pi\)
\(174\) 340088. 247088.i 0.851565 0.618698i
\(175\) 549995. 1.35757
\(176\) 482042. + 174632.i 1.17301 + 0.424955i
\(177\) 333340. 0.799750
\(178\) 48975.8 35583.0i 0.115859 0.0841768i
\(179\) −193676. 596073.i −0.451796 1.39049i −0.874855 0.484384i \(-0.839044\pi\)
0.423059 0.906102i \(-0.360956\pi\)
\(180\) 27962.2 86058.8i 0.0643266 0.197977i
\(181\) −288678. 209737.i −0.654964 0.475859i 0.209994 0.977703i \(-0.432655\pi\)
−0.864959 + 0.501843i \(0.832655\pi\)
\(182\) 283366. + 205877.i 0.634116 + 0.460712i
\(183\) 59049.6 181736.i 0.130343 0.401156i
\(184\) 82425.7 + 253680.i 0.179481 + 0.552385i
\(185\) −33568.1 + 24388.7i −0.0721103 + 0.0523912i
\(186\) −364062. −0.771602
\(187\) 554828. + 201001.i 1.16026 + 0.420335i
\(188\) 6697.25 0.0138198
\(189\) 113335. 82342.6i 0.230786 0.167676i
\(190\) 383496. + 1.18028e6i 0.770685 + 2.37193i
\(191\) −247988. + 763227.i −0.491866 + 1.51381i 0.329919 + 0.944009i \(0.392979\pi\)
−0.821785 + 0.569798i \(0.807021\pi\)
\(192\) 55720.8 + 40483.5i 0.109085 + 0.0792548i
\(193\) −616717. 448071.i −1.19177 0.865872i −0.198321 0.980137i \(-0.563549\pi\)
−0.993450 + 0.114265i \(0.963549\pi\)
\(194\) −242259. + 745596.i −0.462142 + 1.42233i
\(195\) −57558.3 177146.i −0.108398 0.333615i
\(196\) −235020. + 170752.i −0.436984 + 0.317487i
\(197\) 269860. 0.495419 0.247710 0.968834i \(-0.420322\pi\)
0.247710 + 0.968834i \(0.420322\pi\)
\(198\) −7399.52 + 221391.i −0.0134135 + 0.401325i
\(199\) 840009. 1.50366 0.751832 0.659354i \(-0.229170\pi\)
0.751832 + 0.659354i \(0.229170\pi\)
\(200\) −277112. + 201334.i −0.489869 + 0.355911i
\(201\) −64897.7 199735.i −0.113302 0.348709i
\(202\) 217529. 669487.i 0.375093 1.15442i
\(203\) 1.06559e6 + 774199.i 1.81490 + 1.31860i
\(204\) −154580. 112309.i −0.260062 0.188946i
\(205\) −279326. + 859676.i −0.464222 + 1.42873i
\(206\) −217313. 668822.i −0.356795 1.09810i
\(207\) −146051. + 106112.i −0.236908 + 0.172124i
\(208\) −341710. −0.547645
\(209\) −529348. 782264.i −0.838254 1.23876i
\(210\) 911933. 1.42697
\(211\) −881117. + 640169.i −1.36247 + 0.989893i −0.364188 + 0.931326i \(0.618653\pi\)
−0.998283 + 0.0585678i \(0.981347\pi\)
\(212\) 29762.3 + 91598.8i 0.0454806 + 0.139975i
\(213\) 121834. 374965.i 0.184000 0.566294i
\(214\) 437786. + 318070.i 0.653473 + 0.474776i
\(215\) 790141. + 574071.i 1.16576 + 0.846973i
\(216\) −26960.5 + 82975.8i −0.0393181 + 0.121009i
\(217\) −352499. 1.08488e6i −0.508170 1.56399i
\(218\) 650428. 472563.i 0.926953 0.673471i
\(219\) 254837. 0.359048
\(220\) −275483. + 353692.i −0.383741 + 0.492684i
\(221\) −393307. −0.541690
\(222\) −26607.1 + 19331.2i −0.0362339 + 0.0263255i
\(223\) 9773.06 + 30078.4i 0.0131604 + 0.0405035i 0.957421 0.288695i \(-0.0932214\pi\)
−0.944261 + 0.329199i \(0.893221\pi\)
\(224\) 289564. 891186.i 0.385589 1.18672i
\(225\) −187552. 136265.i −0.246983 0.179443i
\(226\) −557360. 404946.i −0.725879 0.527382i
\(227\) 455496. 1.40187e6i 0.586705 1.80569i −0.00561005 0.999984i \(-0.501786\pi\)
0.592315 0.805707i \(-0.298214\pi\)
\(228\) 94505.8 + 290859.i 0.120399 + 0.370549i
\(229\) −491177. + 356861.i −0.618942 + 0.449687i −0.852552 0.522643i \(-0.824946\pi\)
0.233610 + 0.972330i \(0.424946\pi\)
\(230\) −1.17518e6 −1.46482
\(231\) −666895. + 192309.i −0.822294 + 0.237121i
\(232\) −820301. −1.00058
\(233\) −200287. + 145517.i −0.241693 + 0.175600i −0.702037 0.712140i \(-0.747726\pi\)
0.460344 + 0.887740i \(0.347726\pi\)
\(234\) −45622.5 140412.i −0.0544677 0.167634i
\(235\) 11091.5 34136.0i 0.0131015 0.0403221i
\(236\) 432613. + 314312.i 0.505615 + 0.367351i
\(237\) −359714. 261348.i −0.415994 0.302237i
\(238\) 595047. 1.83137e6i 0.680940 2.09572i
\(239\) −331240. 1.01945e6i −0.375101 1.15444i −0.943411 0.331627i \(-0.892403\pi\)
0.568310 0.822814i \(-0.307597\pi\)
\(240\) −719761. + 522937.i −0.806604 + 0.586032i
\(241\) 319090. 0.353892 0.176946 0.984221i \(-0.443378\pi\)
0.176946 + 0.984221i \(0.443378\pi\)
\(242\) 408079. 1.01880e6i 0.447925 1.11828i
\(243\) −59049.0 −0.0641500
\(244\) 247997. 180181.i 0.266669 0.193746i
\(245\) 481106. + 1.48069e6i 0.512065 + 1.57597i
\(246\) −221402. + 681405.i −0.233262 + 0.717906i
\(247\) 509296. + 370025.i 0.531163 + 0.385912i
\(248\) 574742. + 417574.i 0.593395 + 0.431126i
\(249\) 117423. 361390.i 0.120020 0.369383i
\(250\) 42841.6 + 131853.i 0.0433527 + 0.133426i
\(251\) −427872. + 310867.i −0.428677 + 0.311452i −0.781120 0.624381i \(-0.785351\pi\)
0.352443 + 0.935833i \(0.385351\pi\)
\(252\) 224730. 0.222925
\(253\) 859408. 247823.i 0.844108 0.243411i
\(254\) −322925. −0.314063
\(255\) −828443. + 601899.i −0.797833 + 0.579660i
\(256\) 362730. + 1.11637e6i 0.345927 + 1.06465i
\(257\) 93964.3 289192.i 0.0887422 0.273120i −0.896830 0.442375i \(-0.854136\pi\)
0.985572 + 0.169255i \(0.0541360\pi\)
\(258\) 626290. + 455026.i 0.585768 + 0.425586i
\(259\) −83367.7 60570.2i −0.0772233 0.0561060i
\(260\) 92334.2 284176.i 0.0847090 0.260707i
\(261\) −171563. 528016.i −0.155891 0.479784i
\(262\) −755750. + 549084.i −0.680182 + 0.494181i
\(263\) 252001. 0.224654 0.112327 0.993671i \(-0.464170\pi\)
0.112327 + 0.993671i \(0.464170\pi\)
\(264\) 265614. 341021.i 0.234553 0.301142i
\(265\) 516171. 0.451522
\(266\) −2.49349e6 + 1.81163e6i −2.16074 + 1.56987i
\(267\) −24706.6 76039.2i −0.0212097 0.0652768i
\(268\) 104108. 320411.i 0.0885415 0.272503i
\(269\) −589368. 428201.i −0.496599 0.360801i 0.311117 0.950372i \(-0.399297\pi\)
−0.807717 + 0.589571i \(0.799297\pi\)
\(270\) −310976. 225938.i −0.259608 0.188616i
\(271\) 280308. 862698.i 0.231852 0.713568i −0.765671 0.643232i \(-0.777593\pi\)
0.997523 0.0703359i \(-0.0224071\pi\)
\(272\) 580522. + 1.78666e6i 0.475769 + 1.46427i
\(273\) 374244. 271904.i 0.303912 0.220805i
\(274\) −249247. −0.200565
\(275\) 643703. + 951255.i 0.513279 + 0.758517i
\(276\) −289603. −0.228839
\(277\) 1.57757e6 1.14617e6i 1.23534 0.897531i 0.238066 0.971249i \(-0.423487\pi\)
0.997279 + 0.0737183i \(0.0234866\pi\)
\(278\) 287513. + 884874.i 0.223124 + 0.686704i
\(279\) −148582. + 457287.i −0.114276 + 0.351705i
\(280\) −1.43966e6 1.04598e6i −1.09740 0.797308i
\(281\) 750932. + 545584.i 0.567329 + 0.412189i 0.834134 0.551562i \(-0.185968\pi\)
−0.266805 + 0.963751i \(0.585968\pi\)
\(282\) 8791.43 27057.3i 0.00658320 0.0202610i
\(283\) −461590. 1.42063e6i −0.342603 1.05442i −0.962855 0.270020i \(-0.912970\pi\)
0.620252 0.784402i \(-0.287030\pi\)
\(284\) 511678. 371756.i 0.376445 0.273503i
\(285\) 1.63903e6 1.19529
\(286\) −24434.0 + 731056.i −0.0176636 + 0.528489i
\(287\) −2.24491e6 −1.60877
\(288\) −319541. + 232160.i −0.227010 + 0.164933i
\(289\) 229419. + 706079.i 0.161579 + 0.497289i
\(290\) 1.11681e6 3.43720e6i 0.779804 2.39999i
\(291\) 837649. + 608588.i 0.579869 + 0.421299i
\(292\) 330731. + 240290.i 0.226996 + 0.164922i
\(293\) −721702. + 2.22117e6i −0.491121 + 1.51152i 0.331794 + 0.943352i \(0.392346\pi\)
−0.822915 + 0.568164i \(0.807654\pi\)
\(294\) 381339. + 1.17364e6i 0.257302 + 0.791893i
\(295\) 2.31852e6 1.68450e6i 1.55115 1.12698i
\(296\) 64177.0 0.0425746
\(297\) 275062. + 99648.7i 0.180942 + 0.0655512i
\(298\) 1.74955e6 1.14126
\(299\) −482277. + 350395.i −0.311974 + 0.226663i
\(300\) −114922. 353693.i −0.0737223 0.226894i
\(301\) −749550. + 2.30688e6i −0.476853 + 1.46760i
\(302\) 982565. + 713875.i 0.619932 + 0.450407i
\(303\) −752143. 546464.i −0.470646 0.341944i
\(304\) 929180. 2.85972e6i 0.576655 1.77476i
\(305\) −507670. 1.56245e6i −0.312487 0.961736i
\(306\) −656649. + 477083.i −0.400894 + 0.291267i
\(307\) 577116. 0.349476 0.174738 0.984615i \(-0.444092\pi\)
0.174738 + 0.984615i \(0.444092\pi\)
\(308\) −1.04684e6 379245.i −0.628785 0.227794i
\(309\) −928777. −0.553369
\(310\) −2.53220e6 + 1.83975e6i −1.49656 + 1.08731i
\(311\) 371561. + 1.14355e6i 0.217835 + 0.670429i 0.998940 + 0.0460285i \(0.0146565\pi\)
−0.781105 + 0.624400i \(0.785343\pi\)
\(312\) −89026.3 + 273995.i −0.0517764 + 0.159351i
\(313\) 1.65573e6 + 1.20296e6i 0.955276 + 0.694049i 0.952049 0.305946i \(-0.0989727\pi\)
0.00322738 + 0.999995i \(0.498973\pi\)
\(314\) −1.83260e6 1.33146e6i −1.04892 0.762088i
\(315\) 372180. 1.14545e6i 0.211337 0.650430i
\(316\) −220413. 678361.i −0.124171 0.382158i
\(317\) −358841. + 260713.i −0.200565 + 0.145719i −0.683534 0.729918i \(-0.739558\pi\)
0.482970 + 0.875637i \(0.339558\pi\)
\(318\) 409133. 0.226880
\(319\) −91883.9 + 2.74913e6i −0.0505548 + 1.51258i
\(320\) 592140. 0.323258
\(321\) 578188. 420078.i 0.313189 0.227545i
\(322\) −901900. 2.77576e6i −0.484751 1.49191i
\(323\) 1.06948e6 3.29153e6i 0.570384 1.75546i
\(324\) −76634.6 55678.3i −0.0405567 0.0294661i
\(325\) −619318. 449961.i −0.325241 0.236302i
\(326\) −1.38889e6 + 4.27455e6i −0.723806 + 2.22765i
\(327\) −328119. 1.00985e6i −0.169692 0.522259i
\(328\) 1.13109e6 821783.i 0.580513 0.421767i
\(329\) 89141.1 0.0454034
\(330\) 1.06731e6 + 1.57725e6i 0.539517 + 0.797291i
\(331\) −2.20922e6 −1.10833 −0.554164 0.832407i \(-0.686962\pi\)
−0.554164 + 0.832407i \(0.686962\pi\)
\(332\) 493153. 358296.i 0.245548 0.178401i
\(333\) 13422.4 + 41309.8i 0.00663313 + 0.0204147i
\(334\) −631013. + 1.94206e6i −0.309508 + 0.952569i
\(335\) −1.46073e6 1.06128e6i −0.711143 0.516676i
\(336\) −1.78755e6 1.29873e6i −0.863796 0.627585i
\(337\) −575323. + 1.77066e6i −0.275954 + 0.849300i 0.713011 + 0.701153i \(0.247331\pi\)
−0.988965 + 0.148147i \(0.952669\pi\)
\(338\) 631219. + 1.94269e6i 0.300530 + 0.924938i
\(339\) −736110. + 534815.i −0.347891 + 0.252758i
\(340\) −1.64270e6 −0.770659
\(341\) 1.46382e6 1.87940e6i 0.681715 0.875251i
\(342\) 1.29914e6 0.600608
\(343\) −515224. + 374332.i −0.236462 + 0.171800i
\(344\) −466809. 1.43669e6i −0.212688 0.654587i
\(345\) −479617. + 1.47611e6i −0.216944 + 0.667684i
\(346\) 24873.6 + 18071.8i 0.0111699 + 0.00811541i
\(347\) 78065.2 + 56717.7i 0.0348044 + 0.0252869i 0.605051 0.796186i \(-0.293153\pi\)
−0.570247 + 0.821473i \(0.693153\pi\)
\(348\) 275219. 847035.i 0.121823 0.374933i
\(349\) 829112. + 2.55174e6i 0.364376 + 1.12143i 0.950371 + 0.311119i \(0.100704\pi\)
−0.585995 + 0.810315i \(0.699296\pi\)
\(350\) 3.03215e6 2.20299e6i 1.32306 0.961263i
\(351\) −194986. −0.0844765
\(352\) 1.88027e6 542205.i 0.808842 0.233242i
\(353\) 1.32459e6 0.565774 0.282887 0.959153i \(-0.408708\pi\)
0.282887 + 0.959153i \(0.408708\pi\)
\(354\) 1.83772e6 1.33519e6i 0.779421 0.566283i
\(355\) −1.04745e6 3.22371e6i −0.441124 1.35764i
\(356\) 39634.0 121981.i 0.0165746 0.0510114i
\(357\) −2.05747e6 1.49484e6i −0.854404 0.620761i
\(358\) −3.45530e6 2.51042e6i −1.42488 1.03524i
\(359\) 129004. 397034.i 0.0528285 0.162589i −0.921161 0.389181i \(-0.872758\pi\)
0.973990 + 0.226591i \(0.0727582\pi\)
\(360\) 231789. + 713372.i 0.0942618 + 0.290108i
\(361\) −2.47837e6 + 1.80064e6i −1.00092 + 0.727208i
\(362\) −2.43160e6 −0.975260
\(363\) −1.11313e6 928368.i −0.443384 0.369789i
\(364\) 742081. 0.293561
\(365\) 1.77249e6 1.28779e6i 0.696390 0.505957i
\(366\) −402395. 1.23844e6i −0.157018 0.483252i
\(367\) 1.23515e6 3.80140e6i 0.478690 1.47326i −0.362225 0.932091i \(-0.617983\pi\)
0.840915 0.541167i \(-0.182017\pi\)
\(368\) 2.30357e6 + 1.67364e6i 0.886711 + 0.644233i
\(369\) 765533. + 556192.i 0.292683 + 0.212647i
\(370\) −87374.9 + 268912.i −0.0331805 + 0.102119i
\(371\) 396139. + 1.21919e6i 0.149421 + 0.459871i
\(372\) −624015. + 453373.i −0.233796 + 0.169863i
\(373\) −3.35472e6 −1.24849 −0.624243 0.781230i \(-0.714593\pi\)
−0.624243 + 0.781230i \(0.714593\pi\)
\(374\) 3.86391e6 1.11422e6i 1.42839 0.411899i
\(375\) 183101. 0.0672377
\(376\) −44913.3 + 32631.4i −0.0163834 + 0.0119033i
\(377\) −566519. 1.74357e6i −0.205287 0.631808i
\(378\) 295001. 907919.i 0.106192 0.326827i
\(379\) 3.78617e6 + 2.75081e6i 1.35395 + 0.983700i 0.998804 + 0.0488875i \(0.0155676\pi\)
0.355142 + 0.934812i \(0.384432\pi\)
\(380\) 2.12715e6 + 1.54547e6i 0.755682 + 0.549035i
\(381\) −131793. + 405616.i −0.0465135 + 0.143154i
\(382\) 1.68992e6 + 5.20103e6i 0.592525 + 1.82360i
\(383\) −819026. + 595057.i −0.285299 + 0.207282i −0.721226 0.692700i \(-0.756421\pi\)
0.435926 + 0.899982i \(0.356421\pi\)
\(384\) 1.87370e6 0.648444
\(385\) −3.66671e6 + 4.70767e6i −1.26074 + 1.61865i
\(386\) −5.19474e6 −1.77458
\(387\) 827147. 600957.i 0.280740 0.203970i
\(388\) 513265. + 1.57967e6i 0.173086 + 0.532704i
\(389\) 8553.91 26326.2i 0.00286610 0.00882094i −0.949613 0.313424i \(-0.898524\pi\)
0.952479 + 0.304603i \(0.0985239\pi\)
\(390\) −1.02688e6 746070.i −0.341867 0.248381i
\(391\) 2.65140e6 + 1.92636e6i 0.877069 + 0.637228i
\(392\) 744133. 2.29021e6i 0.244588 0.752765i
\(393\) 381250. + 1.17337e6i 0.124517 + 0.383224i
\(394\) 1.48775e6 1.08092e6i 0.482826 0.350794i
\(395\) −3.82265e6 −1.23274
\(396\) 263019. + 388686.i 0.0842848 + 0.124555i
\(397\) −3.17728e6 −1.01176 −0.505882 0.862603i \(-0.668833\pi\)
−0.505882 + 0.862603i \(0.668833\pi\)
\(398\) 4.63102e6 3.36463e6i 1.46544 1.06471i
\(399\) 1.25788e6 + 3.87136e6i 0.395555 + 1.21739i
\(400\) −1.12991e6 + 3.47750e6i −0.353097 + 1.08672i
\(401\) −973809. 707514.i −0.302422 0.219722i 0.426216 0.904621i \(-0.359846\pi\)
−0.728638 + 0.684899i \(0.759846\pi\)
\(402\) −1.15782e6 841203.i −0.357334 0.259618i
\(403\) −490632. + 1.51001e6i −0.150485 + 0.463146i
\(404\) −460871. 1.41842e6i −0.140484 0.432365i
\(405\) −410710. + 298398.i −0.124422 + 0.0903979i
\(406\) 8.97572e6 2.70243
\(407\) 7188.62 215081.i 0.00215109 0.0643599i
\(408\) 1.58385e6 0.471048
\(409\) −321955. + 233914.i −0.0951672 + 0.0691430i −0.634351 0.773045i \(-0.718733\pi\)
0.539184 + 0.842188i \(0.318733\pi\)
\(410\) 1.90347e6 + 5.85828e6i 0.559225 + 1.72112i
\(411\) −101723. + 313072.i −0.0297041 + 0.0914197i
\(412\) −1.20538e6 875759.i −0.349849 0.254180i
\(413\) 5.75812e6 + 4.18352e6i 1.66114 + 1.20689i
\(414\) −380159. + 1.17001e6i −0.109010 + 0.335497i
\(415\) −1.00952e6 3.10699e6i −0.287737 0.885564i
\(416\) −1.05516e6 + 766618.i −0.298940 + 0.217193i
\(417\) 1.22880e6 0.346053
\(418\) −6.05167e6 2.19238e6i −1.69408 0.613727i
\(419\) −6.67580e6 −1.85767 −0.928834 0.370496i \(-0.879188\pi\)
−0.928834 + 0.370496i \(0.879188\pi\)
\(420\) 1.56308e6 1.13565e6i 0.432374 0.314138i
\(421\) −1.83427e6 5.64529e6i −0.504379 1.55232i −0.801811 0.597577i \(-0.796130\pi\)
0.297432 0.954743i \(-0.403870\pi\)
\(422\) −2.29347e6 + 7.05858e6i −0.626920 + 1.92946i
\(423\) −30397.8 22085.3i −0.00826022 0.00600140i
\(424\) −645895. 469270.i −0.174481 0.126768i
\(425\) −1.30052e6 + 4.00260e6i −0.349257 + 1.07490i
\(426\) −830237. 2.55521e6i −0.221655 0.682185i
\(427\) 3.30087e6 2.39822e6i 0.876109 0.636531i
\(428\) 1.14648e6 0.302522
\(429\) 908285. + 329051.i 0.238275 + 0.0863216i
\(430\) 6.65552e6 1.73585
\(431\) 505652. 367378.i 0.131117 0.0952620i −0.520294 0.853987i \(-0.674178\pi\)
0.651411 + 0.758725i \(0.274178\pi\)
\(432\) 287800. + 885758.i 0.0741962 + 0.228352i
\(433\) 443894. 1.36617e6i 0.113778 0.350174i −0.877912 0.478822i \(-0.841064\pi\)
0.991690 + 0.128648i \(0.0410639\pi\)
\(434\) −6.28881e6 4.56909e6i −1.60267 1.16441i
\(435\) −3.86156e6 2.80559e6i −0.978453 0.710888i
\(436\) 526363. 1.61998e6i 0.132608 0.408125i
\(437\) −1.62099e6 4.98891e6i −0.406049 1.24969i
\(438\) 1.40493e6 1.02074e6i 0.349921 0.254233i
\(439\) 2.77153e6 0.686369 0.343185 0.939268i \(-0.388494\pi\)
0.343185 + 0.939268i \(0.388494\pi\)
\(440\) 124139. 3.71419e6i 0.0305687 0.914602i
\(441\) 1.62981e6 0.399061
\(442\) −2.16832e6 + 1.57538e6i −0.527921 + 0.383557i
\(443\) 310579. + 955863.i 0.0751904 + 0.231412i 0.981587 0.191015i \(-0.0611780\pi\)
−0.906397 + 0.422428i \(0.861178\pi\)
\(444\) −21532.0 + 66268.6i −0.00518354 + 0.0159533i
\(445\) −556100. 404031.i −0.133123 0.0967196i
\(446\) 174358. + 126678.i 0.0415053 + 0.0301554i
\(447\) 714029. 2.19756e6i 0.169023 0.520201i
\(448\) 454441. + 1.39863e6i 0.106975 + 0.329236i
\(449\) 1.52703e6 1.10946e6i 0.357465 0.259713i −0.394529 0.918883i \(-0.629092\pi\)
0.751994 + 0.659170i \(0.229092\pi\)
\(450\) −1.57979e6 −0.367764
\(451\) −2.62740e6 3.88274e6i −0.608254 0.898870i
\(452\) −1.45962e6 −0.336042
\(453\) 1.29768e6 942822.i 0.297114 0.215866i
\(454\) −3.10398e6 9.55308e6i −0.706773 2.17522i
\(455\) 1.22898e6 3.78240e6i 0.278301 0.856524i
\(456\) −2.05094e6 1.49010e6i −0.461893 0.335585i
\(457\) 5.60368e6 + 4.07132e6i 1.25511 + 0.911894i 0.998507 0.0546221i \(-0.0173954\pi\)
0.256607 + 0.966516i \(0.417395\pi\)
\(458\) −1.27849e6 + 3.93480e6i −0.284796 + 0.876513i
\(459\) 331257. + 1.01950e6i 0.0733894 + 0.225869i
\(460\) −2.01430e6 + 1.46348e6i −0.443844 + 0.322471i
\(461\) 152368. 0.0333919 0.0166960 0.999861i \(-0.494685\pi\)
0.0166960 + 0.999861i \(0.494685\pi\)
\(462\) −2.90634e6 + 3.73144e6i −0.633493 + 0.813339i
\(463\) 4.34477e6 0.941920 0.470960 0.882155i \(-0.343908\pi\)
0.470960 + 0.882155i \(0.343908\pi\)
\(464\) −7.08426e6 + 5.14701e6i −1.52756 + 1.10984i
\(465\) 1.27741e6 + 3.93146e6i 0.273966 + 0.843182i
\(466\) −521331. + 1.60449e6i −0.111211 + 0.342273i
\(467\) −1.31894e6 958269.i −0.279856 0.203327i 0.438999 0.898488i \(-0.355333\pi\)
−0.718854 + 0.695161i \(0.755333\pi\)
\(468\) −253056. 183856.i −0.0534074 0.0388027i
\(469\) 1.38569e6 4.26470e6i 0.290893 0.895276i
\(470\) −75583.0 232621.i −0.0157826 0.0485740i
\(471\) −2.42033e6 + 1.75848e6i −0.502716 + 0.365245i
\(472\) −4.43264e6 −0.915815
\(473\) −4.86717e6 + 1.40352e6i −1.00028 + 0.288447i
\(474\) −3.02995e6 −0.619426
\(475\) 5.44972e6 3.95945e6i 1.10826 0.805195i
\(476\) −1.26070e6 3.88005e6i −0.255032 0.784909i
\(477\) 166976. 513899.i 0.0336014 0.103415i
\(478\) −5.90953e6 4.29353e6i −1.18300 0.859497i
\(479\) 3.60467e6 + 2.61894e6i 0.717838 + 0.521540i 0.885693 0.464272i \(-0.153684\pi\)
−0.167855 + 0.985812i \(0.553684\pi\)
\(480\) −1.04934e6 + 3.22953e6i −0.207880 + 0.639789i
\(481\) 44322.1 + 136409.i 0.00873490 + 0.0268833i
\(482\) 1.75916e6 1.27811e6i 0.344896 0.250582i
\(483\) −3.85464e6 −0.751823
\(484\) −569265. 2.25444e6i −0.110459 0.437447i
\(485\) 8.90162e6 1.71836
\(486\) −325541. + 236519.i −0.0625194 + 0.0454230i
\(487\) 983705. + 3.02753e6i 0.187950 + 0.578451i 0.999987 0.00515554i \(-0.00164107\pi\)
−0.812037 + 0.583607i \(0.801641\pi\)
\(488\) −785221. + 2.41666e6i −0.149260 + 0.459374i
\(489\) 4.80230e6 + 3.48907e6i 0.908190 + 0.659839i
\(490\) 8.58323e6 + 6.23608e6i 1.61496 + 1.17333i
\(491\) 430802. 1.32587e6i 0.0806443 0.248198i −0.902603 0.430474i \(-0.858347\pi\)
0.983247 + 0.182276i \(0.0583465\pi\)
\(492\) 469076. + 1.44367e6i 0.0873636 + 0.268877i
\(493\) −8.15396e6 + 5.92420e6i −1.51095 + 1.09777i
\(494\) 4.28991e6 0.790916
\(495\) 2.41673e6 696902.i 0.443318 0.127838i
\(496\) 7.58366e6 1.38412
\(497\) 6.81048e6 4.94811e6i 1.23676 0.898562i
\(498\) −800178. 2.46270e6i −0.144582 0.444977i
\(499\) 241076. 741955.i 0.0433413 0.133391i −0.927044 0.374952i \(-0.877659\pi\)
0.970386 + 0.241561i \(0.0776593\pi\)
\(500\) 237631. + 172649.i 0.0425087 + 0.0308844i
\(501\) 2.18183e6 + 1.58519e6i 0.388353 + 0.282155i
\(502\) −1.11372e6 + 3.42766e6i −0.197249 + 0.607070i
\(503\) −174786. 537936.i −0.0308025 0.0948005i 0.934473 0.356033i \(-0.115871\pi\)
−0.965276 + 0.261233i \(0.915871\pi\)
\(504\) −1.50709e6 + 1.09496e6i −0.264279 + 0.192010i
\(505\) −7.99296e6 −1.39469
\(506\) 3.74532e6 4.80860e6i 0.650298 0.834915i
\(507\) 2.69777e6 0.466107
\(508\) −553504. + 402144.i −0.0951616 + 0.0691389i
\(509\) 3.39259e6 + 1.04413e7i 0.580413 + 1.78633i 0.616958 + 0.786996i \(0.288365\pi\)
−0.0365447 + 0.999332i \(0.511635\pi\)
\(510\) −2.15637e6 + 6.63661e6i −0.367111 + 1.12985i
\(511\) 4.40206e6 + 3.19828e6i 0.745768 + 0.541832i
\(512\) 1.08163e6 + 785852.i 0.182350 + 0.132485i
\(513\) 530208. 1.63181e6i 0.0889514 0.273764i
\(514\) −640321. 1.97071e6i −0.106903 0.329014i
\(515\) −6.46002e6 + 4.69348e6i −1.07329 + 0.779788i
\(516\) 1.64013e6 0.271178
\(517\) 104329. + 154176.i 0.0171664 + 0.0253682i
\(518\) −702224. −0.114988
\(519\) 32850.9 23867.5i 0.00535338 0.00388946i
\(520\) 765391. + 2.35563e6i 0.124129 + 0.382031i
\(521\) −1.19497e6 + 3.67775e6i −0.192870 + 0.593592i 0.807125 + 0.590380i \(0.201022\pi\)
−0.999995 + 0.00321157i \(0.998978\pi\)
\(522\) −3.06079e6 2.22379e6i −0.491651 0.357206i
\(523\) −8.23074e6 5.97998e6i −1.31578 0.955973i −0.999974 0.00715069i \(-0.997724\pi\)
−0.315810 0.948823i \(-0.602276\pi\)
\(524\) −611596. + 1.88230e6i −0.0973053 + 0.299475i
\(525\) −1.52962e6 4.70768e6i −0.242206 0.745434i
\(526\) 1.38930e6 1.00938e6i 0.218943 0.159071i
\(527\) 8.72877e6 1.36907
\(528\) 154137. 4.61172e6i 0.0240615 0.719910i
\(529\) −1.46898e6 −0.228233
\(530\) 2.84568e6 2.06751e6i 0.440045 0.319711i
\(531\) −927070. 2.85323e6i −0.142684 0.439137i
\(532\) −2.01787e6 + 6.21038e6i −0.309111 + 0.951347i
\(533\) 2.52787e6 + 1.83661e6i 0.385423 + 0.280026i
\(534\) −440782. 320247.i −0.0668915 0.0485995i
\(535\) 1.89871e6 5.84363e6i 0.286797 0.882670i
\(536\) 862987. + 2.65600e6i 0.129745 + 0.399315i
\(537\) −4.56345e6 + 3.31554e6i −0.682901 + 0.496156i
\(538\) −4.96437e6 −0.739450
\(539\) −7.59197e6 2.75039e6i −1.12560 0.407777i
\(540\) −814389. −0.120184
\(541\) 5.30778e6 3.85633e6i 0.779686 0.566475i −0.125199 0.992132i \(-0.539957\pi\)
0.904885 + 0.425656i \(0.139957\pi\)
\(542\) −1.91016e6 5.87887e6i −0.279301 0.859599i
\(543\) −992388. + 3.05426e6i −0.144438 + 0.444535i
\(544\) 5.80092e6 + 4.21461e6i 0.840426 + 0.610605i
\(545\) −7.38535e6 5.36577e6i −1.06507 0.773821i
\(546\) 974125. 2.99805e6i 0.139840 0.430385i
\(547\) 90701.7 + 279151.i 0.0129613 + 0.0398906i 0.957328 0.289004i \(-0.0933240\pi\)
−0.944367 + 0.328894i \(0.893324\pi\)
\(548\) −427219. + 310393.i −0.0607713 + 0.0441530i
\(549\) −1.71980e6 −0.243527
\(550\) 7.35900e6 + 2.66600e6i 1.03732 + 0.375796i
\(551\) 1.61321e7 2.26367
\(552\) 1.94214e6 1.41105e6i 0.271289 0.197103i
\(553\) −2.93372e6 9.02905e6i −0.407949 1.25554i
\(554\) 4.10627e6 1.26378e7i 0.568425 1.74943i
\(555\) 302113. + 219498.i 0.0416329 + 0.0302481i
\(556\) 1.59476e6 + 1.15866e6i 0.218780 + 0.158953i
\(557\) −2.87381e6 + 8.84466e6i −0.392482 + 1.20793i 0.538424 + 0.842674i \(0.319020\pi\)
−0.930905 + 0.365260i \(0.880980\pi\)
\(558\) 1.01251e6 + 3.11619e6i 0.137662 + 0.423681i
\(559\) 2.73133e6 1.98442e6i 0.369695 0.268599i
\(560\) −1.89962e7 −2.55974
\(561\) 177411. 5.30807e6i 0.0237998 0.712082i
\(562\) 6.32526e6 0.844768
\(563\) −6.15292e6 + 4.47035e6i −0.818107 + 0.594389i −0.916170 0.400791i \(-0.868735\pi\)
0.0980629 + 0.995180i \(0.468735\pi\)
\(564\) −18626.1 57325.2i −0.00246561 0.00758836i
\(565\) −2.41731e6 + 7.43971e6i −0.318575 + 0.980472i
\(566\) −8.23507e6 5.98313e6i −1.08050 0.785032i
\(567\) −1.02001e6 741083.i −0.133244 0.0968076i
\(568\) −1.62010e6 + 4.98616e6i −0.210703 + 0.648478i
\(569\) −828349. 2.54940e6i −0.107259 0.330108i 0.882995 0.469382i \(-0.155523\pi\)
−0.990254 + 0.139274i \(0.955523\pi\)
\(570\) 9.03605e6 6.56508e6i 1.16491 0.846355i
\(571\) 6.43823e6 0.826373 0.413186 0.910646i \(-0.364416\pi\)
0.413186 + 0.910646i \(0.364416\pi\)
\(572\) 868517. + 1.28348e6i 0.110991 + 0.164021i
\(573\) 7.22254e6 0.918975
\(574\) −1.23763e7 + 8.99194e6i −1.56788 + 1.13913i
\(575\) 1.97118e6 + 6.06665e6i 0.248631 + 0.765208i
\(576\) 191551. 589534.i 0.0240563 0.0740376i
\(577\) −4.41609e6 3.20848e6i −0.552203 0.401199i 0.276394 0.961044i \(-0.410860\pi\)
−0.828597 + 0.559845i \(0.810860\pi\)
\(578\) 4.09298e6 + 2.97373e6i 0.509589 + 0.370238i
\(579\) −2.12009e6 + 6.52495e6i −0.262819 + 0.808874i
\(580\) −2.36615e6 7.28226e6i −0.292060 0.898869i
\(581\) 6.56391e6 4.76896e6i 0.806719 0.586116i
\(582\) 7.05569e6 0.863440
\(583\) −1.64504e6 + 2.11207e6i −0.200450 + 0.257357i
\(584\) −3.38873e6 −0.411155
\(585\) −1.35621e6 + 985342.i −0.163846 + 0.119041i
\(586\) 4.91805e6 + 1.51362e7i 0.591628 + 1.82085i
\(587\) −1.33028e6 + 4.09417e6i −0.159348 + 0.490423i −0.998575 0.0533575i \(-0.983008\pi\)
0.839227 + 0.543781i \(0.183008\pi\)
\(588\) 2.11518e6 + 1.53677e6i 0.252293 + 0.183301i
\(589\) −1.13029e7 8.21207e6i −1.34247 0.975359i
\(590\) 6.03490e6 1.85735e7i 0.713740 2.19666i
\(591\) −750522. 2.30987e6i −0.0883883 0.272031i
\(592\) 554244. 402682.i 0.0649975 0.0472234i
\(593\) −3.50412e6 −0.409206 −0.204603 0.978845i \(-0.565590\pi\)
−0.204603 + 0.978845i \(0.565590\pi\)
\(594\) 1.91558e6 552385.i 0.222758 0.0642356i
\(595\) −2.18646e7 −2.53191
\(596\) 2.99879e6 2.17875e6i 0.345804 0.251241i
\(597\) −2.33619e6 7.19006e6i −0.268270 0.825651i
\(598\) −1.25533e6 + 3.86350e6i −0.143550 + 0.441802i
\(599\) −2.76497e6 2.00887e6i −0.314864 0.228762i 0.419117 0.907932i \(-0.362340\pi\)
−0.733981 + 0.679170i \(0.762340\pi\)
\(600\) 2.49401e6 + 1.81200e6i 0.282826 + 0.205485i
\(601\) −734129. + 2.25942e6i −0.0829060 + 0.255158i −0.983914 0.178645i \(-0.942829\pi\)
0.901008 + 0.433803i \(0.142829\pi\)
\(602\) 5.10782e6 + 1.57203e7i 0.574440 + 1.76794i
\(603\) −1.52914e6 + 1.11098e6i −0.171259 + 0.124427i
\(604\) 2.57315e6 0.286994
\(605\) −1.24337e7 832070.i −1.38106 0.0924212i
\(606\) −6.33546e6 −0.700804
\(607\) 1.11027e6 806658.i 0.122309 0.0888624i −0.524949 0.851134i \(-0.675916\pi\)
0.647258 + 0.762271i \(0.275916\pi\)
\(608\) −3.54652e6 1.09151e7i −0.389084 1.19748i
\(609\) 3.66318e6 1.12741e7i 0.400236 1.23180i
\(610\) −9.05716e6 6.58041e6i −0.985525 0.716026i
\(611\) −100377. 72928.0i −0.0108775 0.00790299i
\(612\) −531398. + 1.63547e6i −0.0573510 + 0.176508i
\(613\) 3.10849e6 + 9.56696e6i 0.334117 + 1.02831i 0.967155 + 0.254186i \(0.0818076\pi\)
−0.633038 + 0.774121i \(0.718192\pi\)
\(614\) 3.18168e6 2.31162e6i 0.340592 0.247455i
\(615\) 8.13525e6 0.867328
\(616\) 8.86813e6 2.55726e6i 0.941630 0.271533i
\(617\) −8.10507e6 −0.857124 −0.428562 0.903512i \(-0.640980\pi\)
−0.428562 + 0.903512i \(0.640980\pi\)
\(618\) −5.12040e6 + 3.72019e6i −0.539303 + 0.391827i
\(619\) 4.06093e6 + 1.24983e7i 0.425989 + 1.31106i 0.902044 + 0.431645i \(0.142067\pi\)
−0.476054 + 0.879416i \(0.657933\pi\)
\(620\) −2.04920e6 + 6.30679e6i −0.214094 + 0.658914i
\(621\) 1.31446e6 + 955012.i 0.136779 + 0.0993757i
\(622\) 6.62888e6 + 4.81616e6i 0.687012 + 0.499143i
\(623\) 527532. 1.62358e6i 0.0544539 0.167592i
\(624\) 950347. + 2.92487e6i 0.0977059 + 0.300708i
\(625\) 8.50936e6 6.18241e6i 0.871359 0.633079i
\(626\) 1.39466e7 1.42243
\(627\) −5.22360e6 + 6.70656e6i −0.530641 + 0.681288i
\(628\) −4.79924e6 −0.485594
\(629\) 637933. 463485.i 0.0642907 0.0467099i
\(630\) −2.53623e6 7.80570e6i −0.254587 0.783539i
\(631\) 4.95667e6 1.52551e7i 0.495583 1.52525i −0.320463 0.947261i \(-0.603839\pi\)
0.816046 0.577987i \(-0.196161\pi\)
\(632\) 4.78336e6 + 3.47531e6i 0.476365 + 0.346100i
\(633\) 7.93005e6 + 5.76152e6i 0.786623 + 0.571515i
\(634\) −934033. + 2.87466e6i −0.0922867 + 0.284029i
\(635\) 1.13307e6 + 3.48722e6i 0.111512 + 0.343198i
\(636\) 701268. 509501.i 0.0687450 0.0499462i
\(637\) 5.38179e6 0.525507
\(638\) 1.05050e7 + 1.55242e7i 1.02175 + 1.50993i
\(639\) −3.54836e6 −0.343776
\(640\) 1.30323e7 9.46856e6i 1.25769 0.913764i
\(641\) −4.35978e6 1.34180e7i −0.419101 1.28986i −0.908531 0.417818i \(-0.862795\pi\)
0.489429 0.872043i \(-0.337205\pi\)
\(642\) 1.50497e6 4.63184e6i 0.144109 0.443522i
\(643\) −8.43426e6 6.12785e6i −0.804488 0.584495i 0.107739 0.994179i \(-0.465639\pi\)
−0.912227 + 0.409684i \(0.865639\pi\)
\(644\) −5.00260e6 3.63460e6i −0.475314 0.345336i
\(645\) 2.71626e6 8.35980e6i 0.257083 0.791219i
\(646\) −7.28801e6 2.24302e7i −0.687112 2.11471i
\(647\) −1.53016e7 + 1.11173e7i −1.43706 + 1.04409i −0.448419 + 0.893824i \(0.648013\pi\)
−0.988646 + 0.150265i \(0.951987\pi\)
\(648\) 785213. 0.0734598
\(649\) −496511. + 1.48554e7i −0.0462719 + 1.38444i
\(650\) −5.21665e6 −0.484293
\(651\) −8.30570e6 + 6.03444e6i −0.768110 + 0.558065i
\(652\) 2.94258e6 + 9.05633e6i 0.271087 + 0.834321i
\(653\) 4.71284e6 1.45046e7i 0.432514 1.33114i −0.463099 0.886307i \(-0.653263\pi\)
0.895613 0.444834i \(-0.146737\pi\)
\(654\) −5.85385e6 4.25307e6i −0.535177 0.388829i
\(655\) 8.58124e6 + 6.23464e6i 0.781532 + 0.567816i
\(656\) 4.61195e6 1.41941e7i 0.418432 1.28780i
\(657\) −708741. 2.18128e6i −0.0640581 0.197151i
\(658\) 491440. 357052.i 0.0442493 0.0321490i
\(659\) 1.05651e7 0.947678 0.473839 0.880612i \(-0.342868\pi\)
0.473839 + 0.880612i \(0.342868\pi\)
\(660\) 3.79359e6 + 1.37433e6i 0.338993 + 0.122809i
\(661\) 815709. 0.0726159 0.0363080 0.999341i \(-0.488440\pi\)
0.0363080 + 0.999341i \(0.488440\pi\)
\(662\) −1.21796e7 + 8.84896e6i −1.08016 + 0.784779i
\(663\) 1.09385e6 + 3.36651e6i 0.0966435 + 0.297438i
\(664\) −1.56144e6 + 4.80563e6i −0.137438 + 0.422990i
\(665\) 2.83126e7 + 2.05703e7i 2.48271 + 1.80379i
\(666\) 239464. + 173981.i 0.0209196 + 0.0151990i
\(667\) −4.72064e6 + 1.45286e7i −0.410853 + 1.26448i
\(668\) 1.33690e6 + 4.11457e6i 0.115920 + 0.356766i
\(669\) 230276. 167305.i 0.0198922 0.0144525i
\(670\) −1.23040e7 −1.05891
\(671\) 8.01116e6 + 2.90226e6i 0.686893 + 0.248846i
\(672\) −8.43344e6 −0.720413
\(673\) −3.58379e6 + 2.60377e6i −0.305003 + 0.221598i −0.729749 0.683715i \(-0.760363\pi\)
0.424746 + 0.905312i \(0.360363\pi\)
\(674\) 3.92055e6 + 1.20662e7i 0.332428 + 1.02311i
\(675\) −644748. + 1.98433e6i −0.0544666 + 0.167631i
\(676\) 3.50120e6 + 2.54377e6i 0.294680 + 0.214098i
\(677\) −6.78268e6 4.92790e6i −0.568760 0.413229i 0.265894 0.964002i \(-0.414333\pi\)
−0.834655 + 0.550774i \(0.814333\pi\)
\(678\) −1.91603e6 + 5.89694e6i −0.160077 + 0.492666i
\(679\) 6.83160e6 + 2.10255e7i 0.568654 + 1.75014i
\(680\) 1.10163e7 8.00384e6i 0.913619 0.663783i
\(681\) −1.32661e7 −1.09617
\(682\) 542271. 1.62245e7i 0.0446432 1.33571i
\(683\) −8.50981e6 −0.698020 −0.349010 0.937119i \(-0.613482\pi\)
−0.349010 + 0.937119i \(0.613482\pi\)
\(684\) 2.22677e6 1.61785e6i 0.181985 0.132220i
\(685\) 874551. + 2.69159e6i 0.0712129 + 0.219171i
\(686\) −1.34108e6 + 4.12743e6i −0.108804 + 0.334865i
\(687\) 4.42060e6 + 3.21175e6i 0.357346 + 0.259627i
\(688\) −1.30460e7 9.47850e6i −1.05077 0.763429i
\(689\) 551373. 1.69695e6i 0.0442483 0.136182i
\(690\) 3.26836e6 + 1.00590e7i 0.261341 + 0.804324i
\(691\) 235039. 170765.i 0.0187260 0.0136052i −0.578383 0.815765i \(-0.696316\pi\)
0.597109 + 0.802160i \(0.296316\pi\)
\(692\) 65139.4 0.00517105
\(693\) 3.50081e6 + 5.17345e6i 0.276908 + 0.409211i
\(694\) 657559. 0.0518246
\(695\) 8.54682e6 6.20963e6i 0.671186 0.487645i
\(696\) 2.28138e6 + 7.02137e6i 0.178515 + 0.549413i
\(697\) 5.30834e6 1.63374e7i 0.413882 1.27380i
\(698\) 1.47919e7 + 1.07469e7i 1.14917 + 0.834922i
\(699\) 1.80259e6 + 1.30966e6i 0.139541 + 0.101383i
\(700\) 2.45379e6 7.55200e6i 0.189275 0.582528i
\(701\) −647725. 1.99349e6i −0.0497847 0.153222i 0.923074 0.384624i \(-0.125669\pi\)
−0.972858 + 0.231402i \(0.925669\pi\)
\(702\) −1.07497e6 + 781012.i −0.0823292 + 0.0598156i
\(703\) −1.26211e6 −0.0963186
\(704\) −1.88716e6 + 2.42291e6i −0.143508 + 0.184250i
\(705\) −323035. −0.0244780
\(706\) 7.30252e6 5.30559e6i 0.551393 0.400610i
\(707\) −6.13424e6 1.88793e7i −0.461543 1.42048i
\(708\) 1.48719e6 4.57711e6i 0.111502 0.343169i
\(709\) 6.56649e6 + 4.77084e6i 0.490589 + 0.356434i 0.805411 0.592717i \(-0.201945\pi\)
−0.314822 + 0.949151i \(0.601945\pi\)
\(710\) −1.86871e7 1.35770e7i −1.39122 1.01078i
\(711\) −1.23659e6 + 3.80583e6i −0.0917384 + 0.282342i
\(712\) 328540. + 1.01114e6i 0.0242878 + 0.0747502i
\(713\) 1.07033e7 7.77641e6i 0.788487 0.572869i
\(714\) −1.73305e7 −1.27223
\(715\) 7.98031e6 2.30124e6i 0.583787 0.168344i
\(716\) −9.04878e6 −0.659641
\(717\) −7.80477e6 + 5.67050e6i −0.566973 + 0.411930i
\(718\) −879102. 2.70560e6i −0.0636397 0.195863i
\(719\) −4.68489e6 + 1.44186e7i −0.337969 + 1.04016i 0.627272 + 0.778801i \(0.284172\pi\)
−0.965241 + 0.261362i \(0.915828\pi\)
\(720\) 6.47785e6 + 4.70643e6i 0.465693 + 0.338346i
\(721\) −1.60437e7 1.16564e7i −1.14939 0.835079i
\(722\) −6.45097e6 + 1.98541e7i −0.460556 + 1.41745i
\(723\) −887438. 2.73125e6i −0.0631382 0.194320i
\(724\) −4.16784e6 + 3.02811e6i −0.295505 + 0.214697i
\(725\) −1.96171e7 −1.38609
\(726\) −9.85532e6 659524.i −0.693952 0.0464397i
\(727\) −1.65253e7 −1.15962 −0.579809 0.814753i \(-0.696873\pi\)
−0.579809 + 0.814753i \(0.696873\pi\)
\(728\) −4.97656e6 + 3.61568e6i −0.348017 + 0.252849i
\(729\) 164224. + 505430.i 0.0114451 + 0.0352243i
\(730\) 4.61365e6 1.41994e7i 0.320433 0.986192i
\(731\) −1.50159e7 1.09097e7i −1.03934 0.755127i
\(732\) −2.23197e6 1.62162e6i −0.153961 0.111859i
\(733\) 1.98608e6 6.11253e6i 0.136533 0.420205i −0.859292 0.511485i \(-0.829096\pi\)
0.995825 + 0.0912798i \(0.0290958\pi\)
\(734\) −8.41696e6 2.59047e7i −0.576654 1.77476i
\(735\) 1.13360e7 8.23605e6i 0.773998 0.562342i
\(736\) 1.08679e7 0.739524
\(737\) 8.99789e6 2.59468e6i 0.610200 0.175960i
\(738\) 6.44825e6 0.435813
\(739\) 1.91705e7 1.39282e7i 1.29129 0.938176i 0.291457 0.956584i \(-0.405860\pi\)
0.999831 + 0.0184081i \(0.00585982\pi\)
\(740\) 185118. + 569735.i 0.0124271 + 0.0382466i
\(741\) 1.75080e6 5.38842e6i 0.117136 0.360509i
\(742\) 7.06737e6 + 5.13474e6i 0.471246 + 0.342380i
\(743\) 2.26845e6 + 1.64812e6i 0.150750 + 0.109526i 0.660603 0.750735i \(-0.270300\pi\)
−0.509854 + 0.860261i \(0.670300\pi\)
\(744\) 1.97579e6 6.08085e6i 0.130860 0.402746i
\(745\) −6.13876e6 1.88932e7i −0.405219 1.24714i
\(746\) −1.84948e7 + 1.34372e7i −1.21675 + 0.884022i
\(747\) −3.41989e6 −0.224239
\(748\) 5.23532e6 6.72160e6i 0.342128 0.439257i
\(749\) 1.52597e7 0.993900
\(750\) 1.00945e6 733407.i 0.0655286 0.0476093i
\(751\) 7.71942e6 + 2.37579e7i 0.499442 + 1.53712i 0.809918 + 0.586543i \(0.199511\pi\)
−0.310477 + 0.950581i \(0.600489\pi\)
\(752\) −183131. + 563621.i −0.0118091 + 0.0363448i
\(753\) 3.85085e6 + 2.79781e6i 0.247497 + 0.179817i
\(754\) −1.01071e7 7.34321e6i −0.647435 0.470389i
\(755\) 4.26146e6 1.31154e7i 0.272076 0.837365i
\(756\) −625007. 1.92358e6i −0.0397723 0.122407i
\(757\) −849837. + 617443.i −0.0539009 + 0.0391613i −0.614409 0.788987i \(-0.710606\pi\)
0.560509 + 0.828149i \(0.310606\pi\)
\(758\) 3.18917e7 2.01606
\(759\) −4.51139e6 6.66687e6i −0.284254 0.420066i
\(760\) −2.17952e7 −1.36876
\(761\) −1.23020e7 + 8.93795e6i −0.770043 + 0.559469i −0.901974 0.431790i \(-0.857882\pi\)
0.131931 + 0.991259i \(0.457882\pi\)
\(762\) 898103. + 2.76408e6i 0.0560324 + 0.172450i
\(763\) 7.00594e6 2.15621e7i 0.435668 1.34085i
\(764\) 9.37351e6 + 6.81025e6i 0.580990 + 0.422114i
\(765\) 7.45599e6 + 5.41709e6i 0.460629 + 0.334667i
\(766\) −2.13186e6 + 6.56118e6i −0.131276 + 0.404026i
\(767\) −3.06128e6 9.42166e6i −0.187895 0.578281i
\(768\) 8.54677e6 6.20959e6i 0.522876 0.379892i
\(769\) 1.95512e7 1.19222 0.596111 0.802902i \(-0.296712\pi\)
0.596111 + 0.802902i \(0.296712\pi\)
\(770\) −1.35833e6 + 4.06406e7i −0.0825615 + 2.47021i
\(771\) −2.73667e6 −0.165801
\(772\) −8.90396e6 + 6.46910e6i −0.537700 + 0.390662i
\(773\) −6.39660e6 1.96867e7i −0.385035 1.18502i −0.936455 0.350789i \(-0.885913\pi\)
0.551419 0.834228i \(-0.314087\pi\)
\(774\) 2.15299e6 6.62623e6i 0.129178 0.397570i
\(775\) 1.37447e7 + 9.98611e6i 0.822018 + 0.597231i
\(776\) −1.11388e7 8.09278e6i −0.664022 0.482440i
\(777\) −286593. + 882042.i −0.0170299 + 0.0524127i
\(778\) −58290.8 179401.i −0.00345264 0.0106261i
\(779\) −2.22441e7 + 1.61613e7i −1.31332 + 0.954185i
\(780\) −2.68920e6 −0.158266
\(781\) 1.65290e7 + 5.98806e6i 0.969657 + 0.351284i
\(782\) 2.23333e7 1.30598
\(783\) −4.04241e6 + 2.93699e6i −0.235633 + 0.171198i
\(784\) −7.94354e6 2.44477e7i −0.461556 1.42052i
\(785\) −7.94812e6 + 2.44618e7i −0.460353 + 1.41682i
\(786\) 6.80175e6 + 4.94176e6i 0.392703 + 0.285315i
\(787\) 7.36518e6 + 5.35111e6i 0.423883 + 0.307969i 0.779198 0.626777i \(-0.215626\pi\)
−0.355315 + 0.934747i \(0.615626\pi\)
\(788\) 1.20398e6 3.70546e6i 0.0690720 0.212582i
\(789\) −700854. 2.15701e6i −0.0400807 0.123356i
\(790\) −2.10745e7 + 1.53115e7i −1.20141 + 0.872873i
\(791\) −1.94277e7 −1.10403
\(792\) −3.65768e6 1.32509e6i −0.207202 0.0750643i
\(793\) −5.67895e6 −0.320690
\(794\) −1.75165e7 + 1.27265e7i −0.986045 + 0.716404i
\(795\) −1.43555e6 4.41817e6i −0.0805565 0.247928i
\(796\) 3.74769e6 1.15342e7i 0.209643 0.645215i
\(797\) −2.32862e7 1.69184e7i −1.29853 0.943440i −0.298593 0.954381i \(-0.596517\pi\)
−0.999940 + 0.0109409i \(0.996517\pi\)
\(798\) 2.24414e7 + 1.63046e7i 1.24751 + 0.906366i
\(799\) −210784. + 648726.i −0.0116807 + 0.0359496i
\(800\) 4.31267e6 + 1.32730e7i 0.238244 + 0.733239i
\(801\) −582145. + 422953.i −0.0320590 + 0.0232922i
\(802\) −8.20260e6 −0.450314
\(803\) −379580. + 1.13569e7i −0.0207737 + 0.621542i
\(804\) −3.03210e6 −0.165426
\(805\) −2.68106e7 + 1.94790e7i −1.45820 + 1.05944i
\(806\) 3.34342e6 + 1.02900e7i 0.181282 + 0.557928i
\(807\) −2.02607e6 + 6.23560e6i −0.109514 + 0.337050i
\(808\) 1.00017e7 + 7.26669e6i 0.538948 + 0.391569i
\(809\) 2.24164e7 + 1.62864e7i 1.20419 + 0.874893i 0.994690 0.102916i \(-0.0328174\pi\)
0.209497 + 0.977809i \(0.432817\pi\)
\(810\) −1.06904e6 + 3.29017e6i −0.0572509 + 0.176200i
\(811\) 7.99370e6 + 2.46021e7i 0.426772 + 1.31347i 0.901287 + 0.433222i \(0.142623\pi\)
−0.474515 + 0.880247i \(0.657377\pi\)
\(812\) 1.53847e7 1.11776e7i 0.818839 0.594921i
\(813\) −8.16385e6 −0.433180
\(814\) −821869. 1.21455e6i −0.0434752 0.0642470i
\(815\) 5.10336e7 2.69130
\(816\) 1.36784e7 9.93796e6i 0.719136 0.522483i
\(817\) 9.18033e6 + 2.82542e7i 0.481175 + 1.48091i
\(818\) −838022. + 2.57917e6i −0.0437897 + 0.134771i
\(819\) −3.36819e6 2.44714e6i −0.175464 0.127482i
\(820\) 1.05580e7 + 7.67086e6i 0.548338 + 0.398391i
\(821\) 4.92930e6 1.51708e7i 0.255227 0.785509i −0.738557 0.674191i \(-0.764493\pi\)
0.993785 0.111318i \(-0.0355073\pi\)
\(822\) 693195. + 2.13344e6i 0.0357829 + 0.110129i
\(823\) −2.62015e6 + 1.90365e6i −0.134843 + 0.0979689i −0.653162 0.757218i \(-0.726558\pi\)
0.518319 + 0.855187i \(0.326558\pi\)
\(824\) 1.23506e7 0.633677
\(825\) 6.35204e6 8.15536e6i 0.324922 0.417166i
\(826\) 4.85019e7 2.47348
\(827\) 1.19832e7 8.70630e6i 0.609268 0.442659i −0.239888 0.970801i \(-0.577111\pi\)
0.849157 + 0.528141i \(0.177111\pi\)
\(828\) 805429. + 2.47886e6i 0.0408274 + 0.125654i
\(829\) −1.18012e6 + 3.63203e6i −0.0596403 + 0.183554i −0.976438 0.215798i \(-0.930765\pi\)
0.916798 + 0.399352i \(0.130765\pi\)
\(830\) −1.80105e7 1.30854e7i −0.907468 0.659314i
\(831\) −1.41981e7 1.03155e7i −0.713227 0.518190i
\(832\) 632522. 1.94670e6i 0.0316787 0.0974971i
\(833\) −9.14299e6 2.81392e7i −0.456537 1.40508i
\(834\) 6.77447e6 4.92194e6i 0.337256 0.245031i
\(835\) 2.31861e7 1.15083
\(836\) −1.31030e7 + 3.77844e6i −0.648417 + 0.186981i
\(837\) 4.32738e6 0.213507
\(838\) −3.68041e7 + 2.67397e7i −1.81045 + 1.31537i
\(839\) 624863. + 1.92313e6i 0.0306464 + 0.0943200i 0.965210 0.261477i \(-0.0842095\pi\)
−0.934563 + 0.355797i \(0.884210\pi\)
\(840\) −4.94912e6 + 1.52318e7i −0.242008 + 0.744824i
\(841\) −2.14136e7 1.55579e7i −1.04400 0.758509i
\(842\) −3.27245e7 2.37757e7i −1.59072 1.15572i
\(843\) 2.58147e6 7.94496e6i 0.125112 0.385055i
\(844\) 4.85909e6 + 1.49548e7i 0.234801 + 0.722642i
\(845\) 1.87641e7 1.36329e7i 0.904036 0.656821i
\(846\) −256047. −0.0122997
\(847\) −7.57698e6 3.00068e7i −0.362900 1.43718i
\(848\) −8.52251e6 −0.406985
\(849\) −1.08761e7 + 7.90197e6i −0.517852 + 0.376241i
\(850\) 8.86243e6 + 2.72758e7i 0.420732 + 1.29488i
\(851\) 369324. 1.13666e6i 0.0174817 0.0538031i
\(852\) −4.60510e6 3.34580e6i −0.217340 0.157907i
\(853\) 9.18761e6 + 6.67519e6i 0.432344 + 0.314117i 0.782586 0.622543i \(-0.213900\pi\)
−0.350241 + 0.936660i \(0.613900\pi\)
\(854\) 8.59187e6 2.64431e7i 0.403128 1.24070i
\(855\) −4.55838e6 1.40293e7i −0.213253 0.656326i
\(856\) −7.68855e6 + 5.58606e6i −0.358641 + 0.260568i
\(857\) 1.67737e7 0.780148 0.390074 0.920784i \(-0.372449\pi\)
0.390074 + 0.920784i \(0.372449\pi\)
\(858\) 6.32543e6 1.82404e6i 0.293341 0.0845892i
\(859\) −3.57379e7 −1.65252 −0.826259 0.563290i \(-0.809535\pi\)
−0.826259 + 0.563290i \(0.809535\pi\)
\(860\) 1.14078e7 8.28825e6i 0.525963 0.382135i
\(861\) 6.24345e6 + 1.92154e7i 0.287023 + 0.883366i
\(862\) 1.31617e6 4.05075e6i 0.0603314 0.185681i
\(863\) 1.46356e7 + 1.06334e7i 0.668934 + 0.486009i 0.869668 0.493637i \(-0.164333\pi\)
−0.200734 + 0.979646i \(0.564333\pi\)
\(864\) 2.87587e6 + 2.08944e6i 0.131064 + 0.0952239i
\(865\) 107879. 332017.i 0.00490225 0.0150876i
\(866\) −3.02492e6 9.30976e6i −0.137063 0.421836i
\(867\) 5.40564e6 3.92743e6i 0.244230 0.177444i
\(868\) −1.64692e7 −0.741948
\(869\) 1.21828e7 1.56415e7i 0.547267 0.702634i
\(870\) −3.25267e7 −1.45694
\(871\) −5.04938e6 + 3.66859e6i −0.225524 + 0.163853i
\(872\) 4.36321e6 + 1.34286e7i 0.194319 + 0.598052i
\(873\) 2.87958e6 8.86244e6i 0.127877 0.393566i
\(874\) −2.89196e7 2.10113e7i −1.28060 0.930410i
\(875\) 3.16289e6 + 2.29798e6i 0.139658 + 0.101467i
\(876\) 1.13695e6 3.49918e6i 0.0500589 0.154066i
\(877\) −1.76442e6 5.43034e6i −0.0774647 0.238412i 0.904824 0.425786i \(-0.140002\pi\)
−0.982289 + 0.187374i \(0.940002\pi\)
\(878\) 1.52796e7 1.11013e7i 0.668922 0.486001i
\(879\) 2.10193e7 0.917584
\(880\) −2.22328e7 3.28553e7i −0.967802 1.43021i
\(881\) −2.55476e7 −1.10895 −0.554473 0.832201i \(-0.687080\pi\)
−0.554473 + 0.832201i \(0.687080\pi\)
\(882\) 8.98522e6 6.52814e6i 0.388917 0.282565i
\(883\) −1.03305e7 3.17939e7i −0.445880 1.37228i −0.881516 0.472154i \(-0.843477\pi\)
0.435636 0.900123i \(-0.356523\pi\)
\(884\) −1.75473e6 + 5.40051e6i −0.0755232 + 0.232436i
\(885\) −2.08666e7 1.51605e7i −0.895559 0.650662i
\(886\) 5.54093e6 + 4.02572e6i 0.237136 + 0.172290i
\(887\) 1.22500e6 3.77016e6i 0.0522790 0.160898i −0.921508 0.388359i \(-0.873042\pi\)
0.973787 + 0.227460i \(0.0730422\pi\)
\(888\) −178486. 549324.i −0.00759577 0.0233774i
\(889\) −7.36719e6 + 5.35258e6i −0.312642 + 0.227148i
\(890\) −4.68415e6 −0.198224
\(891\) 87953.6 2.63154e6i 0.00371158 0.111049i
\(892\) 456610. 0.0192147
\(893\) 883270. 641733.i 0.0370651 0.0269294i
\(894\) −4.86576e6 1.49753e7i −0.203614 0.626659i
\(895\) −1.49859e7 + 4.61218e7i −0.625353 + 1.92464i
\(896\) 3.23664e7 + 2.35155e7i 1.34686 + 0.978554i
\(897\) 4.34049e6 + 3.15355e6i 0.180118 + 0.130864i
\(898\) 3.97474e6 1.22330e7i 0.164482 0.506223i
\(899\) 1.25729e7 + 3.86954e7i 0.518844 + 1.59684i
\(900\) −2.70782e6 + 1.96735e6i −0.111433 + 0.0809608i
\(901\) −9.80939e6 −0.402559
\(902\) −3.00372e7 1.08818e7i −1.22926 0.445332i
\(903\) 2.18303e7 0.890925
\(904\) 9.78854e6 7.11179e6i 0.398379 0.289439i
\(905\) 8.53190e6 + 2.62585e7i 0.346278 + 1.06573i
\(906\) 3.37776e6 1.03957e7i 0.136712 0.420758i
\(907\) −4.52502e6 3.28762e6i −0.182643 0.132698i 0.492707 0.870195i \(-0.336007\pi\)
−0.675350 + 0.737497i \(0.736007\pi\)
\(908\) −1.72170e7 1.25089e7i −0.693014 0.503504i
\(909\) −2.58564e6 + 7.95778e6i −0.103791 + 0.319435i
\(910\) −8.37489e6 2.57753e7i −0.335255 1.03181i
\(911\) −2.06057e7 + 1.49709e7i −0.822603 + 0.597656i −0.917457 0.397835i \(-0.869762\pi\)
0.0948537 + 0.995491i \(0.469762\pi\)
\(912\) −2.70620e7 −1.07739
\(913\) 1.59305e7 + 5.77126e6i 0.632489 + 0.229136i
\(914\) 4.72010e7 1.86890
\(915\) −1.19619e7 + 8.69081e6i −0.472331 + 0.343169i
\(916\) 2.70869e6 + 8.33651e6i 0.106665 + 0.328281i
\(917\) −8.14040e6 + 2.50536e7i −0.319685 + 0.983890i
\(918\) 5.90984e6 + 4.29375e6i 0.231456 + 0.168163i
\(919\) 2.50747e7 + 1.82179e7i 0.979372 + 0.711555i 0.957568 0.288207i \(-0.0930591\pi\)
0.0218036 + 0.999762i \(0.493059\pi\)
\(920\) 6.37778e6 1.96288e7i 0.248428 0.764582i
\(921\) −1.60505e6 4.93983e6i −0.0623504 0.191895i
\(922\) 840014. 610306.i 0.0325431 0.0236440i
\(923\) −1.17171e7 −0.452704
\(924\) −334735. + 1.00151e7i −0.0128980 + 0.385902i
\(925\) 1.53477e6 0.0589777
\(926\) 2.39530e7 1.74028e7i 0.917977 0.666949i
\(927\) 2.58307e6 + 7.94987e6i 0.0987272 + 0.303851i
\(928\) −1.03281e7 + 3.17867e7i −0.393688 + 1.21165i
\(929\) 3.97472e6 + 2.88780e6i 0.151101 + 0.109781i 0.660767 0.750591i \(-0.270231\pi\)
−0.509666 + 0.860372i \(0.670231\pi\)
\(930\) 2.27898e7 + 1.65577e7i 0.864038 + 0.627760i
\(931\) −1.46342e7 + 4.50395e7i −0.553344 + 1.70302i
\(932\) 1.10452e6 + 3.39938e6i 0.0416520 + 0.128192i
\(933\) 8.75482e6 6.36075e6i 0.329263 0.239224i
\(934\) −1.11097e7 −0.416713
\(935\) −2.55898e7 3.78163e7i −0.957279 1.41465i
\(936\) 2.59286e6 0.0967362
\(937\) 3.05244e7 2.21773e7i 1.13579 0.825200i 0.149263 0.988798i \(-0.452310\pi\)
0.986527 + 0.163598i \(0.0523100\pi\)
\(938\) −9.44279e6 2.90619e7i −0.350423 1.07849i
\(939\) 5.69190e6 1.75179e7i 0.210665 0.648361i
\(940\) −419239. 304595.i −0.0154754 0.0112435i
\(941\) −3.20407e7 2.32789e7i −1.17958 0.857017i −0.187458 0.982273i \(-0.560025\pi\)
−0.992124 + 0.125256i \(0.960025\pi\)
\(942\) −6.29992e6 + 1.93892e7i −0.231317 + 0.711921i
\(943\) −8.04575e6 2.47623e7i −0.294637 0.906799i
\(944\) −3.82810e7 + 2.78128e7i −1.39815 + 1.01582i
\(945\) −1.08396e7 −0.394851
\(946\) −2.12112e7 + 2.72330e7i −0.770616 + 0.989391i
\(947\) 3.28138e6 0.118900 0.0594499 0.998231i \(-0.481065\pi\)
0.0594499 + 0.998231i \(0.481065\pi\)
\(948\) −5.19344e6 + 3.77325e6i −0.187687 + 0.136363i
\(949\) −2.34034e6 7.20282e6i −0.0843554 0.259619i
\(950\) 1.41852e7 4.36574e7i 0.509947 1.56946i
\(951\) 3.22957e6 + 2.34642e6i 0.115796 + 0.0841307i
\(952\) 2.73595e7 + 1.98779e7i 0.978399 + 0.710849i
\(953\) 2.58932e6 7.96911e6i 0.0923535 0.284235i −0.894201 0.447665i \(-0.852256\pi\)
0.986555 + 0.163430i \(0.0522558\pi\)
\(954\) −1.13786e6 3.50198e6i −0.0404779 0.124578i
\(955\) 5.02357e7 3.64984e7i 1.78240 1.29499i
\(956\) −1.54759e7 −0.547662
\(957\) 2.37867e7 6.85927e6i 0.839566 0.242102i
\(958\) 3.03629e7 1.06888
\(959\) −5.68632e6 + 4.13135e6i −0.199657 + 0.145059i
\(960\) −1.64683e6 5.06843e6i −0.0576728 0.177499i
\(961\) 2.04185e6 6.28417e6i 0.0713207 0.219502i
\(962\) 790735. + 574503.i 0.0275482 + 0.0200149i
\(963\) −5.20369e6 3.78071e6i −0.180820 0.131373i
\(964\) 1.42362e6 4.38144e6i 0.0493401 0.151853i
\(965\) 1.82271e7 + 5.60973e7i 0.630086 + 1.93920i
\(966\) −2.12509e7 + 1.54396e7i −0.732712 + 0.532347i
\(967\) −1.77337e7 −0.609864 −0.304932 0.952374i \(-0.598634\pi\)
−0.304932 + 0.952374i \(0.598634\pi\)
\(968\) 1.48021e7 + 1.23451e7i 0.507731 + 0.423454i
\(969\) −3.11483e7 −1.06567
\(970\) 4.90752e7 3.56552e7i 1.67468 1.21673i
\(971\) −6.53942e6 2.01263e7i −0.222583 0.685039i −0.998528 0.0542387i \(-0.982727\pi\)
0.775945 0.630800i \(-0.217273\pi\)
\(972\) −263446. + 810804.i −0.00894389 + 0.0275265i
\(973\) 2.12264e7 + 1.54219e7i 0.718776 + 0.522221i
\(974\) 1.75499e7 + 1.27508e7i 0.592759 + 0.430665i
\(975\) −2.12903e6 + 6.55247e6i −0.0717248 + 0.220746i
\(976\) 8.38215e6 + 2.57976e7i 0.281664 + 0.866872i
\(977\) −2.29593e7 + 1.66809e7i −0.769524 + 0.559092i −0.901817 0.432119i \(-0.857766\pi\)
0.132293 + 0.991211i \(0.457766\pi\)
\(978\) 4.04507e7 1.35232
\(979\) 3.42551e6 987797.i 0.114227 0.0329391i
\(980\) 2.24779e7 0.747635
\(981\) −7.73123e6 + 5.61707e6i −0.256493 + 0.186353i
\(982\) −2.93571e6 9.03517e6i −0.0971480 0.298991i
\(983\) −1.39346e7 + 4.28863e7i −0.459950 + 1.41558i 0.405275 + 0.914195i \(0.367176\pi\)
−0.865224 + 0.501385i \(0.832824\pi\)
\(984\) −1.01798e7 7.39605e6i −0.335159 0.243507i
\(985\) −1.68929e7 1.22734e7i −0.554770 0.403064i
\(986\) −2.12241e7 + 6.53209e7i −0.695242 + 2.13974i
\(987\) −247915. 763004.i −0.00810046 0.0249307i
\(988\) 7.35304e6 5.34230e6i 0.239649 0.174115i
\(989\) −2.81321e7 −0.914559
\(990\) 1.05322e7 1.35222e7i 0.341531 0.438490i
\(991\) 2.76456e7 0.894216 0.447108 0.894480i \(-0.352454\pi\)
0.447108 + 0.894480i \(0.352454\pi\)
\(992\) 2.34174e7 1.70138e7i 0.755545 0.548935i
\(993\) 6.14417e6 + 1.89098e7i 0.197738 + 0.608575i
\(994\) 1.77271e7 5.45584e7i 0.569078 1.75144i
\(995\) −5.25834e7 3.82041e7i −1.68380 1.22335i
\(996\) −4.43837e6 3.22467e6i −0.141767 0.103000i
\(997\) 824018. 2.53607e6i 0.0262542 0.0808021i −0.937071 0.349139i \(-0.886474\pi\)
0.963325 + 0.268337i \(0.0864741\pi\)
\(998\) −1.64281e6 5.05606e6i −0.0522110 0.160689i
\(999\) 316262. 229778.i 0.0100261 0.00728441i
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 33.6.e.b.25.4 yes 20
3.2 odd 2 99.6.f.b.91.2 20
11.2 odd 10 363.6.a.t.1.8 10
11.4 even 5 inner 33.6.e.b.4.4 20
11.9 even 5 363.6.a.r.1.3 10
33.2 even 10 1089.6.a.bi.1.3 10
33.20 odd 10 1089.6.a.bk.1.8 10
33.26 odd 10 99.6.f.b.37.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.e.b.4.4 20 11.4 even 5 inner
33.6.e.b.25.4 yes 20 1.1 even 1 trivial
99.6.f.b.37.2 20 33.26 odd 10
99.6.f.b.91.2 20 3.2 odd 2
363.6.a.r.1.3 10 11.9 even 5
363.6.a.t.1.8 10 11.2 odd 10
1089.6.a.bi.1.3 10 33.2 even 10
1089.6.a.bk.1.8 10 33.20 odd 10