Properties

Label 150.6.g.d.31.5
Level $150$
Weight $6$
Character 150.31
Analytic conductor $24.058$
Analytic rank $0$
Dimension $28$
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] = [150,6,Mod(31,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.31");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 150.g (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: \(24.0575729719\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 31.5
Character \(\chi\) \(=\) 150.31
Dual form 150.6.g.d.121.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(31.6852 - 46.0549i) q^{5} +(29.1246 + 21.1603i) q^{6} +113.911 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\) \(q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(31.6852 - 46.0549i) q^{5} +(29.1246 + 21.1603i) q^{6} +113.911 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(214.368 + 63.6106i) q^{10} +(-165.042 - 507.948i) q^{11} +(-44.4984 + 136.952i) q^{12} +(-89.1312 + 274.318i) q^{13} +(140.801 + 433.342i) q^{14} +(-12.9288 - 502.949i) q^{15} +(79.1084 - 243.470i) q^{16} +(-1188.89 - 863.782i) q^{17} +324.000 q^{18} +(381.884 + 277.455i) q^{19} +(22.9845 + 894.132i) q^{20} +(829.401 - 602.595i) q^{21} +(1728.34 - 1255.72i) q^{22} +(-366.911 - 1129.24i) q^{23} -576.000 q^{24} +(-1117.10 - 2918.51i) q^{25} -1153.74 q^{26} +(-225.273 - 693.320i) q^{27} +(-1474.49 + 1071.28i) q^{28} +(4172.74 - 3031.68i) q^{29} +(1897.35 - 670.863i) q^{30} +(621.850 + 451.801i) q^{31} +1024.00 q^{32} +(-3888.77 - 2825.36i) q^{33} +(1816.47 - 5590.51i) q^{34} +(3609.28 - 5246.14i) q^{35} +(400.486 + 1232.57i) q^{36} +(3313.56 - 10198.1i) q^{37} +(-583.467 + 1795.73i) q^{38} +(802.181 + 2468.86i) q^{39} +(-3373.07 + 1192.65i) q^{40} +(-5024.56 + 15464.0i) q^{41} +(3317.61 + 2410.38i) q^{42} +17150.2 q^{43} +(6913.38 + 5022.86i) q^{44} +(-2754.77 - 3593.66i) q^{45} +(3842.35 - 2791.63i) q^{46} +(-605.222 + 439.720i) q^{47} +(-711.975 - 2191.23i) q^{48} -3831.35 q^{49} +(9721.87 - 7857.18i) q^{50} -13226.0 q^{51} +(-1426.10 - 4389.08i) q^{52} +(20557.4 - 14935.8i) q^{53} +(2359.09 - 1713.98i) q^{54} +(-28622.8 - 8493.41i) q^{55} +(-5897.96 - 4285.12i) q^{56} +4248.31 q^{57} +(16691.0 + 12126.7i) q^{58} +(3020.05 - 9294.77i) q^{59} +(4897.37 + 6388.72i) q^{60} +(8601.29 + 26472.1i) q^{61} +(-950.103 + 2924.12i) q^{62} +(2851.23 - 8775.18i) q^{63} +(1265.73 + 3895.53i) q^{64} +(9809.52 + 12796.7i) q^{65} +(5941.52 - 18286.1i) q^{66} +(-8231.16 - 5980.29i) q^{67} +23512.9 q^{68} +(-8645.28 - 6281.16i) q^{69} +(24418.8 + 7245.93i) q^{70} +(58572.2 - 42555.2i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(11841.2 + 36443.3i) q^{73} +42891.6 q^{74} +(-23572.9 - 15340.6i) q^{75} -7552.56 q^{76} +(-18800.1 - 57860.7i) q^{77} +(-8400.55 + 6103.35i) q^{78} +(1780.20 - 1293.39i) q^{79} +(-8706.44 - 11357.7i) q^{80} +(-5307.96 - 3856.46i) q^{81} -65039.3 q^{82} +(1627.79 + 1182.66i) q^{83} +(-5068.85 + 15600.3i) q^{84} +(-77451.6 + 27385.3i) q^{85} +(21198.9 + 65243.4i) q^{86} +(14344.6 - 44148.2i) q^{87} +(-10562.7 + 32508.6i) q^{88} +(15541.7 + 47832.4i) q^{89} +(10266.0 - 14921.8i) q^{90} +(-10153.0 + 31247.7i) q^{91} +(15369.4 + 11166.5i) q^{92} +6917.84 q^{93} +(-2420.89 - 1758.88i) q^{94} +(24878.2 - 8796.41i) q^{95} +(7455.90 - 5417.03i) q^{96} +(-55938.1 + 40641.4i) q^{97} +(-4735.81 - 14575.3i) q^{98} -43261.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9} + 44 q^{10} - 135 q^{11} + 1008 q^{12} + 616 q^{13} - 48 q^{14} + 531 q^{15} - 1792 q^{16} - 3372 q^{17} + 9072 q^{18} + 488 q^{19} - 944 q^{20} - 387 q^{21} - 1920 q^{22} - 620 q^{23} - 16128 q^{24} + 6659 q^{25} - 1616 q^{26} + 5103 q^{27} + 688 q^{28} + 5682 q^{29} + 2844 q^{30} + 3339 q^{31} + 28672 q^{32} + 4320 q^{33} + 14032 q^{34} - 23984 q^{35} - 9072 q^{36} + 4506 q^{37} - 1528 q^{38} - 5544 q^{39} - 5056 q^{40} + 44962 q^{41} - 1548 q^{42} + 38028 q^{43} - 7680 q^{44} + 9396 q^{45} + 7480 q^{46} - 58300 q^{47} + 16128 q^{48} + 114402 q^{49} + 7476 q^{50} + 2448 q^{51} + 9856 q^{52} - 138 q^{53} + 20412 q^{54} + 96850 q^{55} + 2752 q^{56} + 1908 q^{57} + 22728 q^{58} + 40245 q^{59} - 16704 q^{60} + 79380 q^{61} - 54504 q^{62} - 972 q^{63} - 28672 q^{64} + 3532 q^{65} + 4860 q^{66} - 34352 q^{67} - 4352 q^{68} - 16830 q^{69} - 69476 q^{70} + 115860 q^{71} - 36288 q^{72} - 121214 q^{73} - 37856 q^{74} + 21969 q^{75} - 3392 q^{76} + 195005 q^{77} + 14904 q^{78} + 36224 q^{79} + 29696 q^{80} - 45927 q^{81} + 34608 q^{82} + 85051 q^{83} + 1728 q^{84} + 137496 q^{85} - 18568 q^{86} + 127062 q^{87} - 8640 q^{88} - 53826 q^{89} + 3564 q^{90} - 408104 q^{91} + 29920 q^{92} - 185166 q^{93} - 233200 q^{94} - 482004 q^{95} + 64512 q^{96} - 244169 q^{97} - 395952 q^{98} + 99630 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.23607 + 3.80423i 0.218508 + 0.672499i
\(3\) 7.28115 5.29007i 0.467086 0.339358i
\(4\) −12.9443 + 9.40456i −0.404508 + 0.293893i
\(5\) 31.6852 46.0549i 0.566801 0.823854i
\(6\) 29.1246 + 21.1603i 0.330280 + 0.239962i
\(7\) 113.911 0.878657 0.439329 0.898326i \(-0.355216\pi\)
0.439329 + 0.898326i \(0.355216\pi\)
\(8\) −51.7771 37.6183i −0.286031 0.207813i
\(9\) 25.0304 77.0356i 0.103006 0.317019i
\(10\) 214.368 + 63.6106i 0.677892 + 0.201154i
\(11\) −165.042 507.948i −0.411257 1.26572i −0.915556 0.402190i \(-0.868249\pi\)
0.504299 0.863529i \(-0.331751\pi\)
\(12\) −44.4984 + 136.952i −0.0892055 + 0.274546i
\(13\) −89.1312 + 274.318i −0.146275 + 0.450189i −0.997173 0.0751425i \(-0.976059\pi\)
0.850897 + 0.525332i \(0.176059\pi\)
\(14\) 140.801 + 433.342i 0.191994 + 0.590896i
\(15\) −12.9288 502.949i −0.0148364 0.577160i
\(16\) 79.1084 243.470i 0.0772542 0.237764i
\(17\) −1188.89 863.782i −0.997748 0.724906i −0.0361435 0.999347i \(-0.511507\pi\)
−0.961604 + 0.274441i \(0.911507\pi\)
\(18\) 324.000 0.235702
\(19\) 381.884 + 277.455i 0.242688 + 0.176323i 0.702480 0.711704i \(-0.252076\pi\)
−0.459792 + 0.888027i \(0.652076\pi\)
\(20\) 22.9845 + 894.132i 0.0128487 + 0.499835i
\(21\) 829.401 602.595i 0.410409 0.298179i
\(22\) 1728.34 1255.72i 0.761331 0.553139i
\(23\) −366.911 1129.24i −0.144624 0.445108i 0.852338 0.522991i \(-0.175184\pi\)
−0.996963 + 0.0778830i \(0.975184\pi\)
\(24\) −576.000 −0.204124
\(25\) −1117.10 2918.51i −0.357472 0.933924i
\(26\) −1153.74 −0.334714
\(27\) −225.273 693.320i −0.0594703 0.183031i
\(28\) −1474.49 + 1071.28i −0.355424 + 0.258231i
\(29\) 4172.74 3031.68i 0.921354 0.669403i −0.0225063 0.999747i \(-0.507165\pi\)
0.943861 + 0.330343i \(0.107165\pi\)
\(30\) 1897.35 670.863i 0.384897 0.136091i
\(31\) 621.850 + 451.801i 0.116220 + 0.0844389i 0.644377 0.764708i \(-0.277117\pi\)
−0.528157 + 0.849147i \(0.677117\pi\)
\(32\) 1024.00 0.176777
\(33\) −3888.77 2825.36i −0.621624 0.451636i
\(34\) 1816.47 5590.51i 0.269482 0.829382i
\(35\) 3609.28 5246.14i 0.498024 0.723886i
\(36\) 400.486 + 1232.57i 0.0515028 + 0.158509i
\(37\) 3313.56 10198.1i 0.397915 1.22466i −0.528754 0.848775i \(-0.677341\pi\)
0.926668 0.375880i \(-0.122659\pi\)
\(38\) −583.467 + 1795.73i −0.0655477 + 0.201735i
\(39\) 802.181 + 2468.86i 0.0844522 + 0.259917i
\(40\) −3373.07 + 1192.65i −0.333331 + 0.117859i
\(41\) −5024.56 + 15464.0i −0.466808 + 1.43669i 0.389886 + 0.920863i \(0.372514\pi\)
−0.856694 + 0.515825i \(0.827486\pi\)
\(42\) 3317.61 + 2410.38i 0.290203 + 0.210845i
\(43\) 17150.2 1.41449 0.707244 0.706970i \(-0.249938\pi\)
0.707244 + 0.706970i \(0.249938\pi\)
\(44\) 6913.38 + 5022.86i 0.538342 + 0.391129i
\(45\) −2754.77 3593.66i −0.202794 0.264548i
\(46\) 3842.35 2791.63i 0.267733 0.194519i
\(47\) −605.222 + 439.720i −0.0399641 + 0.0290356i −0.607588 0.794252i \(-0.707863\pi\)
0.567624 + 0.823288i \(0.307863\pi\)
\(48\) −711.975 2191.23i −0.0446028 0.137273i
\(49\) −3831.35 −0.227962
\(50\) 9721.87 7857.18i 0.549952 0.444469i
\(51\) −13226.0 −0.712037
\(52\) −1426.10 4389.08i −0.0731377 0.225095i
\(53\) 20557.4 14935.8i 1.00526 0.730363i 0.0420490 0.999116i \(-0.486611\pi\)
0.963209 + 0.268753i \(0.0866114\pi\)
\(54\) 2359.09 1713.98i 0.110093 0.0799874i
\(55\) −28622.8 8493.41i −1.27587 0.378595i
\(56\) −5897.96 4285.12i −0.251323 0.182597i
\(57\) 4248.31 0.173193
\(58\) 16691.0 + 12126.7i 0.651496 + 0.473340i
\(59\) 3020.05 9294.77i 0.112950 0.347623i −0.878564 0.477624i \(-0.841498\pi\)
0.991514 + 0.130001i \(0.0414981\pi\)
\(60\) 4897.37 + 6388.72i 0.175624 + 0.229106i
\(61\) 8601.29 + 26472.1i 0.295964 + 0.910884i 0.982896 + 0.184162i \(0.0589572\pi\)
−0.686932 + 0.726722i \(0.741043\pi\)
\(62\) −950.103 + 2924.12i −0.0313900 + 0.0966085i
\(63\) 2851.23 8775.18i 0.0905067 0.278551i
\(64\) 1265.73 + 3895.53i 0.0386271 + 0.118882i
\(65\) 9809.52 + 12796.7i 0.287981 + 0.375678i
\(66\) 5941.52 18286.1i 0.167895 0.516728i
\(67\) −8231.16 5980.29i −0.224014 0.162755i 0.470118 0.882604i \(-0.344211\pi\)
−0.694131 + 0.719848i \(0.744211\pi\)
\(68\) 23512.9 0.616642
\(69\) −8645.28 6281.16i −0.218603 0.158824i
\(70\) 24418.8 + 7245.93i 0.595634 + 0.176746i
\(71\) 58572.2 42555.2i 1.37894 1.00186i 0.381962 0.924178i \(-0.375248\pi\)
0.996978 0.0776808i \(-0.0247515\pi\)
\(72\) −4193.94 + 3047.08i −0.0953436 + 0.0692712i
\(73\) 11841.2 + 36443.3i 0.260068 + 0.800407i 0.992789 + 0.119877i \(0.0382502\pi\)
−0.732721 + 0.680529i \(0.761750\pi\)
\(74\) 42891.6 0.910526
\(75\) −23572.9 15340.6i −0.483905 0.314912i
\(76\) −7552.56 −0.149989
\(77\) −18800.1 57860.7i −0.361354 1.11213i
\(78\) −8400.55 + 6103.35i −0.156340 + 0.113588i
\(79\) 1780.20 1293.39i 0.0320923 0.0233165i −0.571623 0.820516i \(-0.693686\pi\)
0.603716 + 0.797200i \(0.293686\pi\)
\(80\) −8706.44 11357.7i −0.152095 0.198411i
\(81\) −5307.96 3856.46i −0.0898908 0.0653095i
\(82\) −65039.3 −1.06817
\(83\) 1627.79 + 1182.66i 0.0259361 + 0.0188437i 0.600678 0.799491i \(-0.294897\pi\)
−0.574742 + 0.818335i \(0.694897\pi\)
\(84\) −5068.85 + 15600.3i −0.0783811 + 0.241232i
\(85\) −77451.6 + 27385.3i −1.16274 + 0.411121i
\(86\) 21198.9 + 65243.4i 0.309077 + 0.951241i
\(87\) 14344.6 44148.2i 0.203185 0.625338i
\(88\) −10562.7 + 32508.6i −0.145401 + 0.447499i
\(89\) 15541.7 + 47832.4i 0.207981 + 0.640099i 0.999578 + 0.0290554i \(0.00924993\pi\)
−0.791597 + 0.611043i \(0.790750\pi\)
\(90\) 10266.0 14921.8i 0.133596 0.194184i
\(91\) −10153.0 + 31247.7i −0.128526 + 0.395562i
\(92\) 15369.4 + 11166.5i 0.189316 + 0.137546i
\(93\) 6917.84 0.0829399
\(94\) −2420.89 1758.88i −0.0282589 0.0205313i
\(95\) 24878.2 8796.41i 0.282820 0.0999992i
\(96\) 7455.90 5417.03i 0.0825700 0.0599906i
\(97\) −55938.1 + 40641.4i −0.603641 + 0.438571i −0.847169 0.531323i \(-0.821695\pi\)
0.243528 + 0.969894i \(0.421695\pi\)
\(98\) −4735.81 14575.3i −0.0498114 0.153304i
\(99\) −43261.1 −0.443618
\(100\) 41907.4 + 27272.2i 0.419074 + 0.272722i
\(101\) −142547. −1.39044 −0.695222 0.718795i \(-0.744694\pi\)
−0.695222 + 0.718795i \(0.744694\pi\)
\(102\) −16348.2 50314.6i −0.155586 0.478844i
\(103\) −159295. + 115735.i −1.47948 + 1.07491i −0.501762 + 0.865006i \(0.667315\pi\)
−0.977722 + 0.209903i \(0.932685\pi\)
\(104\) 14934.3 10850.4i 0.135395 0.0983700i
\(105\) −1472.73 57291.3i −0.0130361 0.507125i
\(106\) 82229.4 + 59743.2i 0.710825 + 0.516445i
\(107\) −172030. −1.45260 −0.726299 0.687379i \(-0.758761\pi\)
−0.726299 + 0.687379i \(0.758761\pi\)
\(108\) 9436.37 + 6855.93i 0.0778477 + 0.0565597i
\(109\) 32350.9 99565.7i 0.260807 0.802682i −0.731822 0.681495i \(-0.761330\pi\)
0.992630 0.121187i \(-0.0386700\pi\)
\(110\) −3068.93 119386.i −0.0241828 0.940746i
\(111\) −29822.0 91782.7i −0.229736 0.707055i
\(112\) 9011.29 27733.9i 0.0678800 0.208913i
\(113\) −20190.0 + 62138.3i −0.148744 + 0.457787i −0.997473 0.0710405i \(-0.977368\pi\)
0.848730 + 0.528827i \(0.177368\pi\)
\(114\) 5251.20 + 16161.5i 0.0378440 + 0.116472i
\(115\) −63632.5 18882.0i −0.448678 0.133139i
\(116\) −25501.5 + 78485.7i −0.175963 + 0.541559i
\(117\) 18901.2 + 13732.5i 0.127651 + 0.0927441i
\(118\) 39092.4 0.258456
\(119\) −135428. 98394.0i −0.876678 0.636944i
\(120\) −18250.7 + 26527.6i −0.115698 + 0.168169i
\(121\) −100479. + 73002.2i −0.623895 + 0.453286i
\(122\) −90073.9 + 65442.5i −0.547898 + 0.398071i
\(123\) 45221.0 + 139176.i 0.269512 + 0.829472i
\(124\) −12298.4 −0.0718280
\(125\) −169807. 41025.6i −0.972033 0.234844i
\(126\) 36907.1 0.207101
\(127\) 94969.4 + 292286.i 0.522486 + 1.60805i 0.769235 + 0.638966i \(0.220637\pi\)
−0.246750 + 0.969079i \(0.579363\pi\)
\(128\) −13254.9 + 9630.27i −0.0715077 + 0.0519534i
\(129\) 124874. 90725.9i 0.660687 0.480017i
\(130\) −36556.4 + 53135.3i −0.189716 + 0.275756i
\(131\) 171584. + 124663.i 0.873571 + 0.634686i 0.931543 0.363632i \(-0.118463\pi\)
−0.0579720 + 0.998318i \(0.518463\pi\)
\(132\) 76908.6 0.384185
\(133\) 43500.7 + 31605.1i 0.213239 + 0.154927i
\(134\) 12576.1 38705.3i 0.0605040 0.186212i
\(135\) −39068.6 11593.0i −0.184499 0.0547473i
\(136\) 29063.5 + 89448.2i 0.134741 + 0.414691i
\(137\) 44177.9 135966.i 0.201096 0.618910i −0.798755 0.601656i \(-0.794508\pi\)
0.999851 0.0172539i \(-0.00549235\pi\)
\(138\) 13208.8 40652.5i 0.0590427 0.181715i
\(139\) 67333.9 + 207232.i 0.295595 + 0.909747i 0.983021 + 0.183493i \(0.0587405\pi\)
−0.687426 + 0.726254i \(0.741260\pi\)
\(140\) 2618.18 + 101851.i 0.0112896 + 0.439184i
\(141\) −2080.57 + 6403.33i −0.00881321 + 0.0271243i
\(142\) 234289. + 170221.i 0.975058 + 0.708421i
\(143\) 154049. 0.629970
\(144\) −16775.8 12188.3i −0.0674181 0.0489821i
\(145\) −7409.33 288234.i −0.0292657 1.13848i
\(146\) −124002. + 90092.8i −0.481445 + 0.349791i
\(147\) −27896.6 + 20268.1i −0.106478 + 0.0773606i
\(148\) 53016.9 + 163169.i 0.198957 + 0.612328i
\(149\) 497873. 1.83719 0.918593 0.395205i \(-0.129326\pi\)
0.918593 + 0.395205i \(0.129326\pi\)
\(150\) 29221.4 108639.i 0.106041 0.394236i
\(151\) −296256. −1.05737 −0.528683 0.848820i \(-0.677314\pi\)
−0.528683 + 0.848820i \(0.677314\pi\)
\(152\) −9335.47 28731.6i −0.0327738 0.100868i
\(153\) −96300.4 + 69966.3i −0.332583 + 0.241635i
\(154\) 196877. 143039.i 0.668949 0.486020i
\(155\) 40511.1 14323.9i 0.135439 0.0478884i
\(156\) −33602.2 24413.4i −0.110549 0.0803188i
\(157\) 186019. 0.602292 0.301146 0.953578i \(-0.402631\pi\)
0.301146 + 0.953578i \(0.402631\pi\)
\(158\) 7120.81 + 5173.57i 0.0226927 + 0.0164872i
\(159\) 70669.9 217500.i 0.221688 0.682285i
\(160\) 32445.6 47160.2i 0.100197 0.145638i
\(161\) −41795.1 128632.i −0.127075 0.391098i
\(162\) 8109.84 24959.5i 0.0242787 0.0747221i
\(163\) −61380.6 + 188910.i −0.180951 + 0.556911i −0.999855 0.0170197i \(-0.994582\pi\)
0.818904 + 0.573931i \(0.194582\pi\)
\(164\) −80393.0 247424.i −0.233404 0.718344i
\(165\) −253338. + 89575.0i −0.724420 + 0.256140i
\(166\) −2487.05 + 7654.35i −0.00700510 + 0.0215595i
\(167\) −2134.10 1550.52i −0.00592139 0.00430214i 0.584821 0.811163i \(-0.301165\pi\)
−0.590742 + 0.806861i \(0.701165\pi\)
\(168\) −65612.6 −0.179355
\(169\) 233077. + 169340.i 0.627743 + 0.456082i
\(170\) −199915. 260794.i −0.530547 0.692109i
\(171\) 30932.6 22473.9i 0.0808959 0.0587743i
\(172\) −221997. + 161291.i −0.572172 + 0.415707i
\(173\) 31968.8 + 98389.9i 0.0812103 + 0.249940i 0.983415 0.181368i \(-0.0580524\pi\)
−0.902205 + 0.431307i \(0.858052\pi\)
\(174\) 185681. 0.464936
\(175\) −127250. 332450.i −0.314095 0.820599i
\(176\) −136726. −0.332714
\(177\) −27180.5 83652.9i −0.0652115 0.200700i
\(178\) −162755. + 118248.i −0.385020 + 0.279733i
\(179\) 188118. 136676.i 0.438831 0.318830i −0.346339 0.938109i \(-0.612575\pi\)
0.785170 + 0.619280i \(0.212575\pi\)
\(180\) 69455.3 + 20609.8i 0.159781 + 0.0474125i
\(181\) −6126.57 4451.21i −0.0139002 0.0100991i 0.580813 0.814037i \(-0.302735\pi\)
−0.594714 + 0.803938i \(0.702735\pi\)
\(182\) −131423. −0.294099
\(183\) 202666. + 147246.i 0.447357 + 0.325024i
\(184\) −23482.3 + 72271.2i −0.0511325 + 0.157370i
\(185\) −364680. 475733.i −0.783399 1.02196i
\(186\) 8550.93 + 26317.0i 0.0181230 + 0.0557769i
\(187\) −242538. + 746456.i −0.507197 + 1.56099i
\(188\) 3698.79 11383.7i 0.00763247 0.0234903i
\(189\) −25661.1 78976.6i −0.0522540 0.160821i
\(190\) 64214.7 + 83769.4i 0.129048 + 0.168345i
\(191\) 251349. 773574.i 0.498534 1.53433i −0.312843 0.949805i \(-0.601281\pi\)
0.811377 0.584524i \(-0.198719\pi\)
\(192\) 29823.6 + 21668.1i 0.0583858 + 0.0424197i
\(193\) 140786. 0.272060 0.136030 0.990705i \(-0.456566\pi\)
0.136030 + 0.990705i \(0.456566\pi\)
\(194\) −223753. 162566.i −0.426839 0.310116i
\(195\) 139120. + 41281.9i 0.262001 + 0.0777451i
\(196\) 49594.0 36032.2i 0.0922124 0.0669962i
\(197\) −205998. + 149666.i −0.378179 + 0.274763i −0.760594 0.649227i \(-0.775092\pi\)
0.382415 + 0.923991i \(0.375092\pi\)
\(198\) −53473.7 164575.i −0.0969342 0.298333i
\(199\) 132678. 0.237502 0.118751 0.992924i \(-0.462111\pi\)
0.118751 + 0.992924i \(0.462111\pi\)
\(200\) −51949.1 + 193135.i −0.0918339 + 0.341418i
\(201\) −91568.5 −0.159866
\(202\) −176197. 542280.i −0.303823 0.935072i
\(203\) 475320. 345340.i 0.809555 0.588176i
\(204\) 171201. 124385.i 0.288025 0.209262i
\(205\) 552989. + 721385.i 0.919034 + 1.19890i
\(206\) −637182. 462940.i −1.04615 0.760075i
\(207\) −96175.4 −0.156005
\(208\) 59737.2 + 43401.6i 0.0957385 + 0.0695581i
\(209\) 77905.7 239769.i 0.123368 0.379688i
\(210\) 216129. 76418.5i 0.338193 0.119578i
\(211\) −198525. 610996.i −0.306979 0.944783i −0.978931 0.204189i \(-0.934544\pi\)
0.671953 0.740594i \(-0.265456\pi\)
\(212\) −125635. + 386666.i −0.191987 + 0.590876i
\(213\) 201353. 619702.i 0.304095 0.935909i
\(214\) −212641. 654442.i −0.317404 0.976869i
\(215\) 543408. 789852.i 0.801733 1.16533i
\(216\) −14417.5 + 44372.5i −0.0210259 + 0.0647112i
\(217\) 70835.4 + 51464.9i 0.102118 + 0.0741929i
\(218\) 418758. 0.596791
\(219\) 279005. + 202709.i 0.393099 + 0.285603i
\(220\) 450379. 159244.i 0.627366 0.221823i
\(221\) 342918. 249145.i 0.472291 0.343140i
\(222\) 312300. 226899.i 0.425294 0.308994i
\(223\) 116926. + 359863.i 0.157453 + 0.484590i 0.998401 0.0565253i \(-0.0180022\pi\)
−0.840948 + 0.541116i \(0.818002\pi\)
\(224\) 116645. 0.155326
\(225\) −252791. + 13005.0i −0.332893 + 0.0171260i
\(226\) −261344. −0.340363
\(227\) 381492. + 1.17411e6i 0.491383 + 1.51232i 0.822518 + 0.568739i \(0.192569\pi\)
−0.331135 + 0.943584i \(0.607431\pi\)
\(228\) −54991.3 + 39953.5i −0.0700579 + 0.0509000i
\(229\) 1.00471e6 729962.i 1.26605 0.919838i 0.267010 0.963694i \(-0.413964\pi\)
0.999038 + 0.0438558i \(0.0139642\pi\)
\(230\) −6822.66 265412.i −0.00850421 0.330827i
\(231\) −442973. 321839.i −0.546195 0.396834i
\(232\) −330099. −0.402647
\(233\) 1.13082e6 + 821586.i 1.36459 + 0.991432i 0.998138 + 0.0609950i \(0.0194274\pi\)
0.366451 + 0.930437i \(0.380573\pi\)
\(234\) −28878.5 + 88878.9i −0.0344774 + 0.106111i
\(235\) 1074.66 + 41806.0i 0.00126941 + 0.0493820i
\(236\) 48320.9 + 148716.i 0.0564748 + 0.173812i
\(237\) 6119.79 18834.8i 0.00707727 0.0217816i
\(238\) 206915. 636819.i 0.236783 0.728742i
\(239\) 245992. + 757084.i 0.278564 + 0.857333i 0.988254 + 0.152819i \(0.0488351\pi\)
−0.709690 + 0.704514i \(0.751165\pi\)
\(240\) −123476. 36639.7i −0.138374 0.0410605i
\(241\) −321400. + 989167.i −0.356454 + 1.09705i 0.598708 + 0.800967i \(0.295681\pi\)
−0.955162 + 0.296085i \(0.904319\pi\)
\(242\) −401916. 292009.i −0.441160 0.320522i
\(243\) −59049.0 −0.0641500
\(244\) −360296. 261770.i −0.387422 0.281479i
\(245\) −121397. + 176452.i −0.129209 + 0.187807i
\(246\) −473561. + 344062.i −0.498928 + 0.362493i
\(247\) −110149. + 80027.7i −0.114878 + 0.0834637i
\(248\) −15201.6 46785.9i −0.0156950 0.0483043i
\(249\) 18108.6 0.0185091
\(250\) −53822.5 696695.i −0.0544645 0.705006i
\(251\) −1.32104e6 −1.32352 −0.661761 0.749715i \(-0.730191\pi\)
−0.661761 + 0.749715i \(0.730191\pi\)
\(252\) 45619.6 + 140403.i 0.0452533 + 0.139275i
\(253\) −513038. + 372744.i −0.503904 + 0.366108i
\(254\) −994532. + 722570.i −0.967241 + 0.702741i
\(255\) −419067. + 609121.i −0.403583 + 0.586615i
\(256\) −53019.7 38521.1i −0.0505636 0.0367366i
\(257\) 1.15312e6 1.08903 0.544516 0.838750i \(-0.316713\pi\)
0.544516 + 0.838750i \(0.316713\pi\)
\(258\) 499494. + 362904.i 0.467177 + 0.339424i
\(259\) 377449. 1.16167e6i 0.349631 1.07605i
\(260\) −247325. 73390.0i −0.226900 0.0673292i
\(261\) −129102. 397334.i −0.117309 0.361039i
\(262\) −262157. + 806835.i −0.235943 + 0.726159i
\(263\) 100180. 308322.i 0.0893080 0.274862i −0.896421 0.443205i \(-0.853842\pi\)
0.985729 + 0.168343i \(0.0538415\pi\)
\(264\) 95064.3 + 292578.i 0.0839475 + 0.258364i
\(265\) −36502.7 1.42001e6i −0.0319308 1.24216i
\(266\) −66463.2 + 204553.i −0.0575940 + 0.177256i
\(267\) 366198. + 266058.i 0.314368 + 0.228401i
\(268\) 162788. 0.138448
\(269\) 351944. + 255702.i 0.296546 + 0.215454i 0.726102 0.687587i \(-0.241330\pi\)
−0.429556 + 0.903040i \(0.641330\pi\)
\(270\) −4188.92 162956.i −0.00349698 0.136038i
\(271\) −650876. + 472889.i −0.538363 + 0.391144i −0.823477 0.567350i \(-0.807969\pi\)
0.285114 + 0.958494i \(0.407969\pi\)
\(272\) −304357. + 221128.i −0.249437 + 0.181227i
\(273\) 91377.0 + 281229.i 0.0742045 + 0.228378i
\(274\) 571851. 0.460157
\(275\) −1.29808e6 + 1.04911e6i −1.03507 + 0.836542i
\(276\) 170978. 0.135104
\(277\) 363599. + 1.11904e6i 0.284723 + 0.876288i 0.986481 + 0.163873i \(0.0523986\pi\)
−0.701758 + 0.712415i \(0.747601\pi\)
\(278\) −705130. + 512307.i −0.547214 + 0.397574i
\(279\) 50369.9 36595.9i 0.0387401 0.0281463i
\(280\) −384229. + 135855.i −0.292883 + 0.103557i
\(281\) −2.08582e6 1.51544e6i −1.57584 1.14491i −0.921278 0.388904i \(-0.872854\pi\)
−0.654560 0.756010i \(-0.727146\pi\)
\(282\) −26931.4 −0.0201668
\(283\) −1.21273e6 881102.i −0.900117 0.653973i 0.0383792 0.999263i \(-0.487781\pi\)
−0.938496 + 0.345290i \(0.887781\pi\)
\(284\) −357961. + 1.10169e6i −0.263354 + 0.810521i
\(285\) 134609. 195655.i 0.0981658 0.142686i
\(286\) 190416. + 586039.i 0.137654 + 0.423654i
\(287\) −572351. + 1.76152e6i −0.410164 + 1.26236i
\(288\) 25631.1 78884.4i 0.0182090 0.0560415i
\(289\) 228589. + 703525.i 0.160994 + 0.495490i
\(290\) 1.08735e6 384464.i 0.759232 0.268448i
\(291\) −192298. + 591833.i −0.133120 + 0.409701i
\(292\) −496009. 360371.i −0.340433 0.247339i
\(293\) 2.31456e6 1.57507 0.787535 0.616270i \(-0.211357\pi\)
0.787535 + 0.616270i \(0.211357\pi\)
\(294\) −111587. 81072.4i −0.0752911 0.0547022i
\(295\) −332378. 433595.i −0.222371 0.290087i
\(296\) −555200. + 403376.i −0.368316 + 0.267597i
\(297\) −314991. + 228854.i −0.207208 + 0.150545i
\(298\) 615405. + 1.89402e6i 0.401440 + 1.23550i
\(299\) 342473. 0.221538
\(300\) 449406. 23120.1i 0.288294 0.0148315i
\(301\) 1.95360e6 1.24285
\(302\) −366193. 1.12703e6i −0.231043 0.711077i
\(303\) −1.03790e6 + 754081.i −0.649457 + 0.471858i
\(304\) 97762.4 71028.5i 0.0606719 0.0440807i
\(305\) 1.49170e6 + 442640.i 0.918189 + 0.272459i
\(306\) −385202. 279865.i −0.235171 0.170862i
\(307\) −2.63378e6 −1.59490 −0.797449 0.603386i \(-0.793818\pi\)
−0.797449 + 0.603386i \(0.793818\pi\)
\(308\) 787508. + 572158.i 0.473018 + 0.343668i
\(309\) −547609. + 1.68537e6i −0.326268 + 1.00415i
\(310\) 104566. + 136408.i 0.0617994 + 0.0806186i
\(311\) 455620. + 1.40225e6i 0.267117 + 0.822102i 0.991198 + 0.132387i \(0.0422641\pi\)
−0.724081 + 0.689715i \(0.757736\pi\)
\(312\) 51339.6 158007.i 0.0298583 0.0918945i
\(313\) 383322. 1.17974e6i 0.221158 0.680655i −0.777501 0.628882i \(-0.783513\pi\)
0.998659 0.0517727i \(-0.0164871\pi\)
\(314\) 229932. + 707657.i 0.131606 + 0.405041i
\(315\) −313798. 409356.i −0.178186 0.232447i
\(316\) −10879.6 + 33484.0i −0.00612909 + 0.0188634i
\(317\) 1.55057e6 + 1.12655e6i 0.866648 + 0.629657i 0.929685 0.368354i \(-0.120079\pi\)
−0.0630372 + 0.998011i \(0.520079\pi\)
\(318\) 914771. 0.507276
\(319\) −2.22861e6 1.61918e6i −1.22619 0.890879i
\(320\) 219513. + 65137.2i 0.119835 + 0.0355594i
\(321\) −1.25258e6 + 910051.i −0.678488 + 0.492950i
\(322\) 437684. 317996.i 0.235246 0.170916i
\(323\) −214359. 659729.i −0.114323 0.351852i
\(324\) 104976. 0.0555556
\(325\) 900168. 46309.9i 0.472732 0.0243201i
\(326\) −794527. −0.414061
\(327\) −291158. 896092.i −0.150577 0.463429i
\(328\) 841886. 611666.i 0.432085 0.313928i
\(329\) −68941.3 + 50088.8i −0.0351147 + 0.0255124i
\(330\) −653906. 853034.i −0.330545 0.431203i
\(331\) −1.17108e6 850838.i −0.587511 0.426852i 0.253913 0.967227i \(-0.418282\pi\)
−0.841424 + 0.540375i \(0.818282\pi\)
\(332\) −32193.0 −0.0160294
\(333\) −702675. 510523.i −0.347251 0.252293i
\(334\) 3260.62 10035.1i 0.00159931 0.00492218i
\(335\) −536227. + 189599.i −0.261058 + 0.0923046i
\(336\) −81101.6 249605.i −0.0391905 0.120616i
\(337\) −462184. + 1.42245e6i −0.221687 + 0.682282i 0.776924 + 0.629594i \(0.216779\pi\)
−0.998611 + 0.0526877i \(0.983221\pi\)
\(338\) −356109. + 1.09599e6i −0.169548 + 0.521814i
\(339\) 181710. + 559245.i 0.0858773 + 0.264303i
\(340\) 745009. 1.08288e6i 0.349514 0.508023i
\(341\) 126860. 390434.i 0.0590796 0.181828i
\(342\) 123730. + 89895.5i 0.0572020 + 0.0415597i
\(343\) −2.35093e6 −1.07896
\(344\) −887989. 645162.i −0.404587 0.293949i
\(345\) −563205. + 199137.i −0.254753 + 0.0900752i
\(346\) −334782. + 243233.i −0.150339 + 0.109228i
\(347\) −1.55289e6 + 1.12824e6i −0.692335 + 0.503011i −0.877427 0.479710i \(-0.840742\pi\)
0.185092 + 0.982721i \(0.440742\pi\)
\(348\) 229514. + 706371.i 0.101592 + 0.312669i
\(349\) 1.75842e6 0.772785 0.386393 0.922334i \(-0.373721\pi\)
0.386393 + 0.922334i \(0.373721\pi\)
\(350\) 1.10742e6 895017.i 0.483219 0.390536i
\(351\) 210269. 0.0910976
\(352\) −169003. 520138.i −0.0727006 0.223750i
\(353\) 1.70701e6 1.24022e6i 0.729122 0.529738i −0.160164 0.987090i \(-0.551202\pi\)
0.889286 + 0.457352i \(0.151202\pi\)
\(354\) 284638. 206801.i 0.120721 0.0877092i
\(355\) −104004. 4.04590e6i −0.0438004 1.70390i
\(356\) −651019. 472993.i −0.272250 0.197801i
\(357\) −1.50658e6 −0.625636
\(358\) 752472. + 546703.i 0.310301 + 0.225447i
\(359\) 22543.0 69380.1i 0.00923156 0.0284118i −0.946335 0.323188i \(-0.895245\pi\)
0.955566 + 0.294777i \(0.0952452\pi\)
\(360\) 7446.97 + 289699.i 0.00302847 + 0.117812i
\(361\) −696302. 2.14300e6i −0.281209 0.865474i
\(362\) 9360.56 28808.8i 0.00375431 0.0115546i
\(363\) −345416. + 1.06308e6i −0.137586 + 0.423447i
\(364\) −162448. 499963.i −0.0642630 0.197781i
\(365\) 2.05358e6 + 609370.i 0.806826 + 0.239414i
\(366\) −309647. + 952994.i −0.120827 + 0.371867i
\(367\) 696475. + 506019.i 0.269923 + 0.196111i 0.714510 0.699625i \(-0.246650\pi\)
−0.444587 + 0.895736i \(0.646650\pi\)
\(368\) −303962. −0.117004
\(369\) 1.06551e6 + 774140.i 0.407373 + 0.295974i
\(370\) 1.35903e6 1.97536e6i 0.516088 0.750141i
\(371\) 2.34170e6 1.70135e6i 0.883277 0.641739i
\(372\) −89546.5 + 65059.3i −0.0335499 + 0.0243754i
\(373\) −429980. 1.32334e6i −0.160021 0.492493i 0.838614 0.544726i \(-0.183366\pi\)
−0.998635 + 0.0522329i \(0.983366\pi\)
\(374\) −3.13948e6 −1.16059
\(375\) −1.45342e6 + 599578.i −0.533719 + 0.220175i
\(376\) 47878.1 0.0174650
\(377\) 459720. + 1.41487e6i 0.166587 + 0.512701i
\(378\) 268726. 195241.i 0.0967342 0.0702815i
\(379\) 113073. 82152.5i 0.0404354 0.0293780i −0.567384 0.823453i \(-0.692044\pi\)
0.607819 + 0.794075i \(0.292044\pi\)
\(380\) −239304. + 347832.i −0.0850141 + 0.123569i
\(381\) 2.23770e6 + 1.62578e6i 0.789749 + 0.573786i
\(382\) 3.25353e6 1.14077
\(383\) 412257. + 299522.i 0.143606 + 0.104336i 0.657268 0.753657i \(-0.271712\pi\)
−0.513663 + 0.857992i \(0.671712\pi\)
\(384\) −45566.4 + 140239.i −0.0157695 + 0.0485334i
\(385\) −3.26045e6 967490.i −1.12105 0.332656i
\(386\) 174021. + 535581.i 0.0594474 + 0.182960i
\(387\) 429277. 1.32118e6i 0.145700 0.448419i
\(388\) 341863. 1.05215e6i 0.115285 0.354811i
\(389\) −901260. 2.77379e6i −0.301979 0.929394i −0.980787 0.195079i \(-0.937504\pi\)
0.678809 0.734315i \(-0.262496\pi\)
\(390\) 14916.4 + 580272.i 0.00496596 + 0.193183i
\(391\) −539196. + 1.65947e6i −0.178363 + 0.548945i
\(392\) 198376. + 144129.i 0.0652040 + 0.0473735i
\(393\) 1.90880e6 0.623419
\(394\) −823992. 598665.i −0.267413 0.194287i
\(395\) −3161.01 122968.i −0.00101937 0.0396552i
\(396\) 559984. 406852.i 0.179447 0.130376i
\(397\) 1.77605e6 1.29038e6i 0.565561 0.410904i −0.267929 0.963439i \(-0.586339\pi\)
0.833490 + 0.552535i \(0.186339\pi\)
\(398\) 164000. + 504739.i 0.0518961 + 0.159720i
\(399\) 483928. 0.152177
\(400\) −798943. + 41102.3i −0.249670 + 0.0128445i
\(401\) 2.81838e6 0.875263 0.437631 0.899154i \(-0.355817\pi\)
0.437631 + 0.899154i \(0.355817\pi\)
\(402\) −113185. 348347.i −0.0349320 0.107510i
\(403\) −179363. + 130315.i −0.0550137 + 0.0399698i
\(404\) 1.84516e6 1.34059e6i 0.562447 0.408641i
\(405\) −345792. + 122265.i −0.104756 + 0.0370394i
\(406\) 1.90128e6 + 1.38136e6i 0.572442 + 0.415903i
\(407\) −5.72696e6 −1.71371
\(408\) 684803. + 497538.i 0.203664 + 0.147971i
\(409\) 1.30964e6 4.03067e6i 0.387119 1.19143i −0.547812 0.836601i \(-0.684539\pi\)
0.934931 0.354829i \(-0.115461\pi\)
\(410\) −2.06078e6 + 2.99538e6i −0.605441 + 0.880018i
\(411\) −397601. 1.22369e6i −0.116103 0.357328i
\(412\) 973527. 2.99621e6i 0.282556 0.869619i
\(413\) 344017. 1.05877e6i 0.0992440 0.305442i
\(414\) −118879. 365873.i −0.0340883 0.104913i
\(415\) 106044. 37495.0i 0.0302250 0.0106869i
\(416\) −91270.3 + 280901.i −0.0258581 + 0.0795830i
\(417\) 1.58654e6 + 1.15269e6i 0.446798 + 0.324618i
\(418\) 1.00843e6 0.282297
\(419\) −1.21471e6 882538.i −0.338016 0.245583i 0.405808 0.913958i \(-0.366990\pi\)
−0.743824 + 0.668375i \(0.766990\pi\)
\(420\) 557863. + 727744.i 0.154314 + 0.201305i
\(421\) 1.51719e6 1.10230e6i 0.417189 0.303106i −0.359317 0.933216i \(-0.616990\pi\)
0.776506 + 0.630110i \(0.216990\pi\)
\(422\) 2.07898e6 1.51046e6i 0.568288 0.412885i
\(423\) 18725.1 + 57630.0i 0.00508831 + 0.0156602i
\(424\) −1.62626e6 −0.439314
\(425\) −1.19284e6 + 4.43473e6i −0.320340 + 1.19095i
\(426\) 2.60637e6 0.695845
\(427\) 979780. + 3.01545e6i 0.260051 + 0.800355i
\(428\) 2.22681e6 1.61787e6i 0.587588 0.426908i
\(429\) 1.12166e6 814932.i 0.294250 0.213785i
\(430\) 3.67646e6 + 1.09094e6i 0.958869 + 0.284530i
\(431\) −4.50346e6 3.27195e6i −1.16776 0.848426i −0.177019 0.984207i \(-0.556645\pi\)
−0.990739 + 0.135782i \(0.956645\pi\)
\(432\) −186624. −0.0481125
\(433\) −2.79471e6 2.03048e6i −0.716337 0.520449i 0.168875 0.985637i \(-0.445987\pi\)
−0.885212 + 0.465188i \(0.845987\pi\)
\(434\) −108227. + 333088.i −0.0275811 + 0.0848858i
\(435\) −1.57873e6 2.05948e6i −0.400022 0.521837i
\(436\) 517614. + 1.59305e6i 0.130404 + 0.401341i
\(437\) 173195. 533039.i 0.0433842 0.133523i
\(438\) −426282. + 1.31196e6i −0.106172 + 0.326765i
\(439\) 1.17266e6 + 3.60908e6i 0.290410 + 0.893790i 0.984725 + 0.174119i \(0.0557076\pi\)
−0.694315 + 0.719672i \(0.744292\pi\)
\(440\) 1.16250e6 + 1.51651e6i 0.286260 + 0.373433i
\(441\) −95900.1 + 295150.i −0.0234813 + 0.0722681i
\(442\) 1.37167e6 + 996578.i 0.333960 + 0.242636i
\(443\) −5.05153e6 −1.22296 −0.611482 0.791258i \(-0.709426\pi\)
−0.611482 + 0.791258i \(0.709426\pi\)
\(444\) 1.24920e6 + 907597.i 0.300728 + 0.218492i
\(445\) 2.69535e6 + 799807.i 0.645232 + 0.191463i
\(446\) −1.22447e6 + 889629.i −0.291481 + 0.211774i
\(447\) 3.62509e6 2.63378e6i 0.858124 0.623464i
\(448\) 144181. + 443742.i 0.0339400 + 0.104457i
\(449\) 2.58164e6 0.604338 0.302169 0.953254i \(-0.402289\pi\)
0.302169 + 0.953254i \(0.402289\pi\)
\(450\) −361941. 945598.i −0.0842570 0.220128i
\(451\) 8.68417e6 2.01042
\(452\) −323039. 994213.i −0.0743720 0.228893i
\(453\) −2.15709e6 + 1.56722e6i −0.493881 + 0.358825i
\(454\) −3.99503e6 + 2.90256e6i −0.909664 + 0.660909i
\(455\) 1.11741e6 + 1.45768e6i 0.253037 + 0.330092i
\(456\) −219965. 159814.i −0.0495384 0.0359918i
\(457\) −5.15690e6 −1.15504 −0.577522 0.816375i \(-0.695980\pi\)
−0.577522 + 0.816375i \(0.695980\pi\)
\(458\) 4.01882e6 + 2.91985e6i 0.895231 + 0.650424i
\(459\) −331051. + 1.01887e6i −0.0733438 + 0.225729i
\(460\) 1.00125e6 354022.i 0.220622 0.0780074i
\(461\) −2.06380e6 6.35172e6i −0.452288 1.39200i −0.874290 0.485404i \(-0.838672\pi\)
0.422002 0.906595i \(-0.361328\pi\)
\(462\) 676803. 2.08298e6i 0.147522 0.454026i
\(463\) −818846. + 2.52015e6i −0.177521 + 0.546353i −0.999740 0.0228184i \(-0.992736\pi\)
0.822219 + 0.569172i \(0.192736\pi\)
\(464\) −408025. 1.25577e6i −0.0879815 0.270779i
\(465\) 219193. 318600.i 0.0470104 0.0683304i
\(466\) −1.72773e6 + 5.31741e6i −0.368563 + 1.13432i
\(467\) 1.46568e6 + 1.06488e6i 0.310990 + 0.225947i 0.732321 0.680960i \(-0.238437\pi\)
−0.421331 + 0.906907i \(0.638437\pi\)
\(468\) −373811. −0.0788929
\(469\) −937618. 681219.i −0.196831 0.143006i
\(470\) −157711. + 55763.3i −0.0329320 + 0.0116440i
\(471\) 1.35443e6 984051.i 0.281322 0.204393i
\(472\) −506023. + 367647.i −0.104548 + 0.0759584i
\(473\) −2.83051e6 8.71142e6i −0.581718 1.79034i
\(474\) 79216.2 0.0161945
\(475\) 383153. 1.42448e6i 0.0779181 0.289682i
\(476\) 2.67837e6 0.541817
\(477\) −636029. 1.95750e6i −0.127991 0.393917i
\(478\) −2.57606e6 + 1.87162e6i −0.515687 + 0.374668i
\(479\) 2.71956e6 1.97587e6i 0.541576 0.393478i −0.283094 0.959092i \(-0.591361\pi\)
0.824670 + 0.565614i \(0.191361\pi\)
\(480\) −13239.1 515020.i −0.00262273 0.102028i
\(481\) 2.50217e6 + 1.81793e6i 0.493122 + 0.358274i
\(482\) −4.16029e6 −0.815654
\(483\) −984790. 715492.i −0.192077 0.139552i
\(484\) 614072. 1.88992e6i 0.119153 0.366716i
\(485\) 99326.5 + 3.86395e6i 0.0191739 + 0.745895i
\(486\) −72988.6 224636.i −0.0140173 0.0431408i
\(487\) 2.48098e6 7.63567e6i 0.474025 1.45890i −0.373244 0.927733i \(-0.621755\pi\)
0.847269 0.531165i \(-0.178245\pi\)
\(488\) 550483. 1.69421e6i 0.104639 0.322046i
\(489\) 552425. + 1.70019e6i 0.104472 + 0.321533i
\(490\) −821319. 243714.i −0.154533 0.0458555i
\(491\) 204401. 629081.i 0.0382630 0.117761i −0.930101 0.367305i \(-0.880281\pi\)
0.968364 + 0.249544i \(0.0802806\pi\)
\(492\) −1.89424e6 1.37625e6i −0.352796 0.256321i
\(493\) −7.57966e6 −1.40453
\(494\) −440595. 320111.i −0.0812310 0.0590178i
\(495\) −1.37074e6 + 1.99238e6i −0.251444 + 0.365477i
\(496\) 159194. 115661.i 0.0290551 0.0211097i
\(497\) 6.67200e6 4.84749e6i 1.21162 0.880290i
\(498\) 22383.4 + 68889.1i 0.00404439 + 0.0124474i
\(499\) 7.25334e6 1.30403 0.652014 0.758207i \(-0.273924\pi\)
0.652014 + 0.758207i \(0.273924\pi\)
\(500\) 2.58386e6 1.06592e6i 0.462215 0.190677i
\(501\) −23741.0 −0.00422577
\(502\) −1.63289e6 5.02553e6i −0.289200 0.890067i
\(503\) −7.68482e6 + 5.58335e6i −1.35430 + 0.983954i −0.355512 + 0.934672i \(0.615694\pi\)
−0.998785 + 0.0492827i \(0.984306\pi\)
\(504\) −477735. + 347095.i −0.0837743 + 0.0608656i
\(505\) −4.51661e6 + 6.56497e6i −0.788106 + 1.14552i
\(506\) −2.05215e6 1.49097e6i −0.356314 0.258877i
\(507\) 2.59289e6 0.447985
\(508\) −3.97813e6 2.89028e6i −0.683942 0.496913i
\(509\) −3.48764e6 + 1.07339e7i −0.596674 + 1.83638i −0.0504661 + 0.998726i \(0.516071\pi\)
−0.546208 + 0.837649i \(0.683929\pi\)
\(510\) −2.83523e6 841312.i −0.482684 0.143229i
\(511\) 1.34883e6 + 4.15128e6i 0.228511 + 0.703283i
\(512\) 81007.0 249314.i 0.0136568 0.0420312i
\(513\) 106337. 327271.i 0.0178398 0.0549053i
\(514\) 1.42533e6 + 4.38672e6i 0.237962 + 0.732373i
\(515\) 282853. + 1.10034e7i 0.0469940 + 1.82814i
\(516\) −763159. + 2.34876e6i −0.126180 + 0.388342i
\(517\) 323242. + 234849.i 0.0531865 + 0.0386422i
\(518\) 4.88581e6 0.800041
\(519\) 753259. + 547275.i 0.122751 + 0.0891840i
\(520\) −26518.1 1.03159e6i −0.00430065 0.167302i
\(521\) 3.31849e6 2.41102e6i 0.535607 0.389141i −0.286844 0.957977i \(-0.592606\pi\)
0.822451 + 0.568836i \(0.192606\pi\)
\(522\) 1.35197e6 982263.i 0.217165 0.157780i
\(523\) 2.21046e6 + 6.80309e6i 0.353369 + 1.08756i 0.956949 + 0.290255i \(0.0937401\pi\)
−0.603581 + 0.797302i \(0.706260\pi\)
\(524\) −3.39343e6 −0.539896
\(525\) −2.68521e6 1.74746e6i −0.425186 0.276700i
\(526\) 1.29675e6 0.204359
\(527\) −349057. 1.07429e6i −0.0547481 0.168497i
\(528\) −995526. + 723292.i −0.155406 + 0.112909i
\(529\) 4.06656e6 2.95453e6i 0.631812 0.459038i
\(530\) 5.35692e6 1.89409e6i 0.828372 0.292895i
\(531\) −640435. 465303.i −0.0985686 0.0716143i
\(532\) −860317. −0.131789
\(533\) −3.79421e6 2.75665e6i −0.578499 0.420304i
\(534\) −559501. + 1.72197e6i −0.0849078 + 0.261319i
\(535\) −5.45081e6 + 7.92283e6i −0.823334 + 1.19673i
\(536\) 201218. + 619284.i 0.0302520 + 0.0931061i
\(537\) 646692. 1.99031e6i 0.0967747 0.297842i
\(538\) −537722. + 1.65494e6i −0.0800944 + 0.246505i
\(539\) 632334. + 1.94613e6i 0.0937508 + 0.288535i
\(540\) 614742. 217360.i 0.0907211 0.0320771i
\(541\) −975940. + 3.00363e6i −0.143361 + 0.441219i −0.996797 0.0799791i \(-0.974515\pi\)
0.853436 + 0.521198i \(0.174515\pi\)
\(542\) −2.60351e6 1.89156e6i −0.380680 0.276580i
\(543\) −68155.7 −0.00991979
\(544\) −1.21743e6 884513.i −0.176379 0.128146i
\(545\) −3.56044e6 4.64467e6i −0.513467 0.669829i
\(546\) −956912. + 695237.i −0.137370 + 0.0998048i
\(547\) −487636. + 354288.i −0.0696831 + 0.0506277i −0.622081 0.782953i \(-0.713713\pi\)
0.552398 + 0.833580i \(0.313713\pi\)
\(548\) 706847. + 2.17545e6i 0.100548 + 0.309455i
\(549\) 2.25458e6 0.319253
\(550\) −5.59556e6 3.64143e6i −0.788745 0.513293i
\(551\) 2.43466e6 0.341632
\(552\) 211341. + 650441.i 0.0295213 + 0.0908573i
\(553\) 202784. 147331.i 0.0281982 0.0204872i
\(554\) −3.80765e6 + 2.76642e6i −0.527088 + 0.382952i
\(555\) −5.17195e6 1.53470e6i −0.712725 0.211491i
\(556\) −2.82052e6 2.04923e6i −0.386939 0.281127i
\(557\) 4.81121e6 0.657077 0.328539 0.944490i \(-0.393444\pi\)
0.328539 + 0.944490i \(0.393444\pi\)
\(558\) 201480. + 146383.i 0.0273934 + 0.0199024i
\(559\) −1.52862e6 + 4.70461e6i −0.206905 + 0.636787i
\(560\) −991756. 1.29377e6i −0.133640 0.174336i
\(561\) 2.18284e6 + 6.71811e6i 0.292830 + 0.901238i
\(562\) 3.18685e6 9.80813e6i 0.425619 1.30992i
\(563\) 4.56462e6 1.40485e7i 0.606923 1.86792i 0.123934 0.992290i \(-0.460449\pi\)
0.482989 0.875627i \(-0.339551\pi\)
\(564\) −33289.1 102453.i −0.00440661 0.0135621i
\(565\) 2.22205e6 + 2.89871e6i 0.292841 + 0.382018i
\(566\) 1.85289e6 5.70261e6i 0.243113 0.748226i
\(567\) −604634. 439292.i −0.0789832 0.0573846i
\(568\) −4.63355e6 −0.602619
\(569\) −8.32929e6 6.05158e6i −1.07852 0.783589i −0.101094 0.994877i \(-0.532234\pi\)
−0.977424 + 0.211288i \(0.932234\pi\)
\(570\) 910703. + 270238.i 0.117406 + 0.0348385i
\(571\) 3.90035e6 2.83377e6i 0.500626 0.363726i −0.308630 0.951182i \(-0.599870\pi\)
0.809256 + 0.587456i \(0.199870\pi\)
\(572\) −1.99406e6 + 1.44877e6i −0.254828 + 0.185144i
\(573\) −2.26214e6 6.96217e6i −0.287829 0.885845i
\(574\) −7.40867e6 −0.938557
\(575\) −2.88582e6 + 2.33231e6i −0.363998 + 0.294182i
\(576\) 331776. 0.0416667
\(577\) 2.42161e6 + 7.45296e6i 0.302806 + 0.931942i 0.980487 + 0.196586i \(0.0629854\pi\)
−0.677680 + 0.735357i \(0.737015\pi\)
\(578\) −2.39382e6 + 1.73921e6i −0.298038 + 0.216537i
\(579\) 1.02508e6 744766.i 0.127076 0.0923259i
\(580\) 2.80663e6 + 3.66130e6i 0.346429 + 0.451924i
\(581\) 185423. + 134718.i 0.0227889 + 0.0165571i
\(582\) −2.48916e6 −0.304611
\(583\) −1.09794e7 7.97703e6i −1.33785 0.972007i
\(584\) 757834. 2.33237e6i 0.0919479 0.282987i
\(585\) 1.23134e6 435375.i 0.148761 0.0525986i
\(586\) 2.86096e6 + 8.80512e6i 0.344165 + 1.05923i
\(587\) −2.03769e6 + 6.27136e6i −0.244086 + 0.751219i 0.751700 + 0.659506i \(0.229234\pi\)
−0.995785 + 0.0917134i \(0.970766\pi\)
\(588\) 170489. 524712.i 0.0203354 0.0625860i
\(589\) 112120. + 345071.i 0.0133167 + 0.0409846i
\(590\) 1.23865e6 1.80040e6i 0.146493 0.212930i
\(591\) −708158. + 2.17949e6i −0.0833991 + 0.256676i
\(592\) −2.22080e6 1.61351e6i −0.260438 0.189220i
\(593\) 1.45348e7 1.69735 0.848676 0.528913i \(-0.177400\pi\)
0.848676 + 0.528913i \(0.177400\pi\)
\(594\) −1.25996e6 915417.i −0.146518 0.106452i
\(595\) −8.82257e6 + 3.11947e6i −1.02165 + 0.361234i
\(596\) −6.44461e6 + 4.68228e6i −0.743157 + 0.539935i
\(597\) 966052. 701878.i 0.110934 0.0805982i
\(598\) 423320. + 1.30284e6i 0.0484078 + 0.148984i
\(599\) −1.32683e7 −1.51094 −0.755471 0.655182i \(-0.772592\pi\)
−0.755471 + 0.655182i \(0.772592\pi\)
\(600\) 643450. + 1.68106e6i 0.0729687 + 0.190636i
\(601\) 1.01059e7 1.14128 0.570638 0.821202i \(-0.306696\pi\)
0.570638 + 0.821202i \(0.306696\pi\)
\(602\) 2.41478e6 + 7.43192e6i 0.271573 + 0.835814i
\(603\) −666724. + 484404.i −0.0746712 + 0.0542518i
\(604\) 3.83482e6 2.78616e6i 0.427713 0.310752i
\(605\) 178415. + 6.94063e6i 0.0198173 + 0.770922i
\(606\) −4.15162e6 3.01633e6i −0.459236 0.333654i
\(607\) −1.43062e6 −0.157599 −0.0787994 0.996890i \(-0.525109\pi\)
−0.0787994 + 0.996890i \(0.525109\pi\)
\(608\) 391049. + 284114.i 0.0429015 + 0.0311698i
\(609\) 1.63401e6 5.02895e6i 0.178530 0.549458i
\(610\) 159940. + 6.22190e6i 0.0174033 + 0.677015i
\(611\) −66678.7 205216.i −0.00722576 0.0222386i
\(612\) 588536. 1.81133e6i 0.0635176 0.195487i
\(613\) −3.60392e6 + 1.10917e7i −0.387368 + 1.19220i 0.547380 + 0.836884i \(0.315625\pi\)
−0.934748 + 0.355312i \(0.884375\pi\)
\(614\) −3.25553e6 1.00195e7i −0.348498 1.07257i
\(615\) 7.84257e6 + 2.32717e6i 0.836124 + 0.248108i
\(616\) −1.20320e6 + 3.70308e6i −0.127758 + 0.393198i
\(617\) 5.06271e6 + 3.67828e6i 0.535390 + 0.388984i 0.822370 0.568953i \(-0.192651\pi\)
−0.286980 + 0.957937i \(0.592651\pi\)
\(618\) −7.08840e6 −0.746581
\(619\) 1.11034e7 + 8.06706e6i 1.16474 + 0.846230i 0.990369 0.138451i \(-0.0442122\pi\)
0.174367 + 0.984681i \(0.444212\pi\)
\(620\) −389677. + 566401.i −0.0407122 + 0.0591758i
\(621\) −700268. + 508774.i −0.0728677 + 0.0529415i
\(622\) −4.77131e6 + 3.46656e6i −0.494495 + 0.359272i
\(623\) 1.77036e6 + 5.44862e6i 0.182744 + 0.562427i
\(624\) 664553. 0.0683232
\(625\) −7.26980e6 + 6.52054e6i −0.744427 + 0.667704i
\(626\) 4.96182e6 0.506064
\(627\) −701151. 2.15792e6i −0.0712267 0.219213i
\(628\) −2.40788e6 + 1.74942e6i −0.243632 + 0.177009i
\(629\) −1.27484e7 + 9.26224e6i −1.28478 + 0.933446i
\(630\) 1.16941e6 1.69975e6i 0.117385 0.170621i
\(631\) −9.68036e6 7.03319e6i −0.967872 0.703200i −0.0129066 0.999917i \(-0.504108\pi\)
−0.954966 + 0.296716i \(0.904108\pi\)
\(632\) −140829. −0.0140249
\(633\) −4.67770e6 3.39855e6i −0.464005 0.337119i
\(634\) −2.36906e6 + 7.29121e6i −0.234074 + 0.720405i
\(635\) 1.64703e7 + 4.88732e6i 1.62094 + 0.480990i
\(636\) 1.13072e6 + 3.47999e6i 0.110844 + 0.341142i
\(637\) 341493. 1.05101e6i 0.0333452 0.102626i
\(638\) 3.40502e6 1.04796e7i 0.331183 1.01927i
\(639\) −1.81218e6 5.57731e6i −0.175569 0.540347i
\(640\) 23536.1 + 915591.i 0.00227135 + 0.0883592i
\(641\) 3.33003e6 1.02488e7i 0.320113 0.985206i −0.653485 0.756939i \(-0.726694\pi\)
0.973598 0.228267i \(-0.0733060\pi\)
\(642\) −5.01031e6 3.64021e6i −0.479764 0.348569i
\(643\) 1.47695e7 1.40877 0.704383 0.709820i \(-0.251224\pi\)
0.704383 + 0.709820i \(0.251224\pi\)
\(644\) 1.75074e6 + 1.27199e6i 0.166344 + 0.120856i
\(645\) −221732. 8.62570e6i −0.0209859 0.816385i
\(646\) 2.24480e6 1.63094e6i 0.211639 0.153765i
\(647\) −4.32513e6 + 3.14239e6i −0.406199 + 0.295121i −0.772061 0.635548i \(-0.780774\pi\)
0.365862 + 0.930669i \(0.380774\pi\)
\(648\) 129757. + 399352.i 0.0121393 + 0.0373610i
\(649\) −5.21969e6 −0.486444
\(650\) 1.28884e6 + 3.36720e6i 0.119651 + 0.312597i
\(651\) 788017. 0.0728757
\(652\) −982089. 3.02256e6i −0.0904757 0.278456i
\(653\) 6.07870e6 4.41643e6i 0.557863 0.405311i −0.272813 0.962067i \(-0.587954\pi\)
0.830676 + 0.556756i \(0.187954\pi\)
\(654\) 3.04904e6 2.21526e6i 0.278753 0.202526i
\(655\) 1.11780e7 3.95230e6i 1.01803 0.359954i
\(656\) 3.36754e6 + 2.44666e6i 0.305530 + 0.221980i
\(657\) 3.10382e6 0.280533
\(658\) −275765. 200355.i −0.0248299 0.0180400i
\(659\) −1.13437e6 + 3.49122e6i −0.101751 + 0.313158i −0.988954 0.148221i \(-0.952645\pi\)
0.887203 + 0.461379i \(0.152645\pi\)
\(660\) 2.43686e6 3.54202e6i 0.217757 0.316512i
\(661\) 5.42876e6 + 1.67080e7i 0.483278 + 1.48738i 0.834459 + 0.551070i \(0.185780\pi\)
−0.351181 + 0.936307i \(0.614220\pi\)
\(662\) 1.78925e6 5.50674e6i 0.158681 0.488371i
\(663\) 1.17885e6 3.62812e6i 0.104153 0.320551i
\(664\) −39792.8 122470.i −0.00350255 0.0107797i
\(665\) 2.83390e6 1.00201e6i 0.248502 0.0878650i
\(666\) 1.07359e6 3.30418e6i 0.0937894 0.288654i
\(667\) −4.95451e6 3.59966e6i −0.431207 0.313290i
\(668\) 42206.3 0.00365962
\(669\) 2.75506e6 + 2.00167e6i 0.237994 + 0.172912i
\(670\) −1.38409e6 1.80557e6i −0.119118 0.155392i
\(671\) 1.20268e7 8.73801e6i 1.03121 0.749215i
\(672\) 849307. 617058.i 0.0725507 0.0527112i
\(673\) 3.37332e6 + 1.03820e7i 0.287091 + 0.883575i 0.985764 + 0.168134i \(0.0537742\pi\)
−0.698673 + 0.715441i \(0.746226\pi\)
\(674\) −5.98263e6 −0.507274
\(675\) −1.77181e6 + 1.43197e6i −0.149678 + 0.120969i
\(676\) −4.60958e6 −0.387966
\(677\) 2.20052e6 + 6.77250e6i 0.184524 + 0.567908i 0.999940 0.0109686i \(-0.00349147\pi\)
−0.815415 + 0.578876i \(0.803491\pi\)
\(678\) −1.90289e6 + 1.38253e6i −0.158979 + 0.115505i
\(679\) −6.37195e6 + 4.62949e6i −0.530393 + 0.385353i
\(680\) 5.04041e6 + 1.49567e6i 0.418016 + 0.124040i
\(681\) 8.98883e6 + 6.53076e6i 0.742737 + 0.539630i
\(682\) 1.64210e6 0.135189
\(683\) −1.10355e7 8.01778e6i −0.905193 0.657661i 0.0346017 0.999401i \(-0.488984\pi\)
−0.939794 + 0.341740i \(0.888984\pi\)
\(684\) −189043. + 581816.i −0.0154497 + 0.0475494i
\(685\) −4.86209e6 6.34270e6i −0.395910 0.516473i
\(686\) −2.90591e6 8.94347e6i −0.235761 0.725597i
\(687\) 3.45387e6 1.06299e7i 0.279199 0.859287i
\(688\) 1.35673e6 4.17558e6i 0.109275 0.336314i
\(689\) 2.26485e6 + 6.97049e6i 0.181757 + 0.559391i
\(690\) −1.45372e6 1.89641e6i −0.116241 0.151639i
\(691\) 5.55753e6 1.71043e7i 0.442778 1.36273i −0.442124 0.896954i \(-0.645775\pi\)
0.884902 0.465777i \(-0.154225\pi\)
\(692\) −1.33913e6 972933.i −0.106306 0.0772356i
\(693\) −4.92790e6 −0.389789
\(694\) −6.21155e6 4.51296e6i −0.489555 0.355682i
\(695\) 1.16775e7 + 3.46514e6i 0.917043 + 0.272119i
\(696\) −2.40350e6 + 1.74625e6i −0.188071 + 0.136641i
\(697\) 1.93312e7 1.40449e7i 1.50722 1.09506i
\(698\) 2.17352e6 + 6.68942e6i 0.168860 + 0.519697i
\(699\) 1.25799e7 0.973831
\(700\) 4.77370e6 + 3.10659e6i 0.368222 + 0.239629i
\(701\) 2.40582e7 1.84913 0.924567 0.381021i \(-0.124427\pi\)
0.924567 + 0.381021i \(0.124427\pi\)
\(702\) 259907. + 799910.i 0.0199056 + 0.0612630i
\(703\) 4.09490e6 2.97512e6i 0.312504 0.227047i
\(704\) 1.76982e6 1.28585e6i 0.134586 0.0977822i
\(705\) 228981. + 298711.i 0.0173511 + 0.0226349i
\(706\) 6.82805e6 + 4.96087e6i 0.515567 + 0.374581i
\(707\) −1.62376e7 −1.22172
\(708\) 1.13855e6 + 827206.i 0.0853629 + 0.0620198i
\(709\) 314725. 968625.i 0.0235134 0.0723669i −0.938611 0.344977i \(-0.887887\pi\)
0.962125 + 0.272610i \(0.0878868\pi\)
\(710\) 1.52630e7 5.39666e6i 1.13630 0.401772i
\(711\) −55078.1 169513.i −0.00408606 0.0125756i
\(712\) 994668. 3.06127e6i 0.0735323 0.226309i
\(713\) 282026. 867988.i 0.0207762 0.0639425i
\(714\) −1.86224e6 5.73137e6i −0.136707 0.420739i
\(715\) 4.88108e6 7.09472e6i 0.357068 0.519004i
\(716\) −1.14967e6 + 3.53834e6i −0.0838093 + 0.257939i
\(717\) 5.79613e6 + 4.21113e6i 0.421056 + 0.305915i
\(718\) 291802. 0.0211241
\(719\) −1.65953e7 1.20572e7i −1.19719 0.869809i −0.203184 0.979141i \(-0.565129\pi\)
−0.994005 + 0.109332i \(0.965129\pi\)
\(720\) −1.09287e6 + 386417.i −0.0785668 + 0.0277796i
\(721\) −1.81455e7 + 1.31835e7i −1.29996 + 0.944476i
\(722\) 7.29177e6 5.29778e6i 0.520583 0.378226i
\(723\) 2.89260e6 + 8.90251e6i 0.205799 + 0.633383i
\(724\) 121166. 0.00859079
\(725\) −1.35094e7 8.79152e6i −0.954530 0.621182i
\(726\) −4.47115e6 −0.314831
\(727\) −1.96619e6 6.05131e6i −0.137971 0.424632i 0.858069 0.513535i \(-0.171664\pi\)
−0.996040 + 0.0889021i \(0.971664\pi\)
\(728\) 1.70118e6 1.23598e6i 0.118966 0.0864335i
\(729\) −429945. + 312373.i −0.0299636 + 0.0217698i
\(730\) 220184. + 8.56551e6i 0.0152925 + 0.594903i
\(731\) −2.03898e7 1.48141e7i −1.41130 1.02537i
\(732\) −4.00815e6 −0.276482
\(733\) −1.68896e7 1.22710e7i −1.16107 0.843567i −0.171158 0.985244i \(-0.554751\pi\)
−0.989913 + 0.141676i \(0.954751\pi\)
\(734\) −1.06412e6 + 3.27502e6i −0.0729038 + 0.224375i
\(735\) 49534.7 + 1.92697e6i 0.00338213 + 0.131570i
\(736\) −375717. 1.15634e6i −0.0255662 0.0786848i
\(737\) −1.67919e6 + 5.16800e6i −0.113875 + 0.350472i
\(738\) −1.62796e6 + 5.01034e6i −0.110028 + 0.338631i
\(739\) 4.54508e6 + 1.39883e7i 0.306147 + 0.942224i 0.979247 + 0.202672i \(0.0649625\pi\)
−0.673100 + 0.739552i \(0.735037\pi\)
\(740\) 9.19458e6 + 2.72836e6i 0.617238 + 0.183156i
\(741\) −378657. + 1.16539e6i −0.0253338 + 0.0779695i
\(742\) 9.36681e6 + 6.80539e6i 0.624571 + 0.453778i
\(743\) 2.12839e7 1.41442 0.707210 0.707003i \(-0.249953\pi\)
0.707210 + 0.707003i \(0.249953\pi\)
\(744\) −358186. 260237.i −0.0237234 0.0172360i
\(745\) 1.57752e7 2.29295e7i 1.04132 1.51357i
\(746\) 4.50281e6 3.27148e6i 0.296235 0.215227i
\(747\) 131851. 95795.6i 0.00864536 0.00628122i
\(748\) −3.88061e6 1.19433e7i −0.253598 0.780495i
\(749\) −1.95961e7 −1.27633
\(750\) −4.07745e6 4.78802e6i −0.264689 0.310816i
\(751\) −2.82716e6 −0.182916 −0.0914579 0.995809i \(-0.529153\pi\)
−0.0914579 + 0.995809i \(0.529153\pi\)
\(752\) 59180.6 + 182139.i 0.00381623 + 0.0117452i
\(753\) −9.61868e6 + 6.98838e6i −0.618199 + 0.449148i
\(754\) −4.81426e6 + 3.49776e6i −0.308390 + 0.224059i
\(755\) −9.38693e6 + 1.36440e7i −0.599316 + 0.871115i
\(756\) 1.07490e6 + 780964.i 0.0684014 + 0.0496966i
\(757\) 1.17188e7 0.743262 0.371631 0.928381i \(-0.378799\pi\)
0.371631 + 0.928381i \(0.378799\pi\)
\(758\) 452293. + 328610.i 0.0285921 + 0.0207734i
\(759\) −1.76367e6 + 5.42801e6i −0.111125 + 0.342008i
\(760\) −1.61903e6 480423.i −0.101676 0.0301710i
\(761\) −3.55678e6 1.09466e7i −0.222636 0.685202i −0.998523 0.0543308i \(-0.982697\pi\)
0.775887 0.630872i \(-0.217303\pi\)
\(762\) −3.41890e6 + 1.05223e7i −0.213304 + 0.656482i
\(763\) 3.68511e6 1.13416e7i 0.229160 0.705283i
\(764\) 4.02159e6 + 1.23772e7i 0.249267 + 0.767164i
\(765\) 170996. + 6.65200e6i 0.0105641 + 0.410959i
\(766\) −629873. + 1.93855e6i −0.0387865 + 0.119373i
\(767\) 2.28054e6 + 1.65691e6i 0.139975 + 0.101697i
\(768\) −589824. −0.0360844
\(769\) 1.08256e7 + 7.86525e6i 0.660139 + 0.479619i 0.866710 0.498812i \(-0.166230\pi\)
−0.206571 + 0.978432i \(0.566230\pi\)
\(770\) −349584. 1.35994e7i −0.0212483 0.826593i
\(771\) 8.39603e6 6.10007e6i 0.508672 0.369572i
\(772\) −1.82237e6 + 1.32403e6i −0.110051 + 0.0799566i
\(773\) −6.80324e6 2.09382e7i −0.409512 1.26035i −0.917068 0.398730i \(-0.869451\pi\)
0.507556 0.861619i \(-0.330549\pi\)
\(774\) 5.55668e6 0.333398
\(775\) 623916. 2.31958e6i 0.0373140 0.138725i
\(776\) 4.42517e6 0.263801
\(777\) −3.39704e6 1.04550e7i −0.201859 0.621259i
\(778\) 9.43812e6 6.85719e6i 0.559032 0.406160i
\(779\) −6.20937e6 + 4.51137e6i −0.366610 + 0.266357i
\(780\) −2.18905e6 + 774001.i −0.128830 + 0.0455517i
\(781\) −3.12827e7 2.27282e7i −1.83517 1.33333i
\(782\) −6.97950e6 −0.408138
\(783\) −3.04193e6 2.21009e6i −0.177315 0.128827i
\(784\) −303092. + 932821.i −0.0176110 + 0.0542011i
\(785\) 5.89403e6 8.56706e6i 0.341380 0.496201i
\(786\) 2.35941e6 + 7.26152e6i 0.136222 + 0.419248i
\(787\) 4.41610e6 1.35914e7i 0.254157 0.782215i −0.739837 0.672786i \(-0.765098\pi\)
0.993995 0.109430i \(-0.0349024\pi\)
\(788\) 1.25895e6 3.87464e6i 0.0722258 0.222288i
\(789\) −901618. 2.77489e6i −0.0515620 0.158692i
\(790\) 463892. 164022.i 0.0264453 0.00935051i
\(791\) −2.29985e6 + 7.07822e6i −0.130695 + 0.402238i
\(792\) 2.23993e6 + 1.62741e6i 0.126889 + 0.0921899i
\(793\) −8.02840e6 −0.453363
\(794\) 7.10421e6 + 5.16151e6i 0.399912 + 0.290553i
\(795\) −7.77773e6 1.01462e7i −0.436450 0.569358i
\(796\) −1.71743e6 + 1.24778e6i −0.0960716 + 0.0698001i
\(797\) −2.57094e7 + 1.86789e7i −1.43366 + 1.04161i −0.444337 + 0.895860i \(0.646561\pi\)
−0.989321 + 0.145754i \(0.953439\pi\)
\(798\) 598168. + 1.84097e6i 0.0332519 + 0.102339i
\(799\) 1.09937e6 0.0609222
\(800\) −1.14391e6 2.98856e6i −0.0631927 0.165096i
\(801\) 4.07381e6 0.224347
\(802\) 3.48371e6 + 1.07218e7i 0.191252 + 0.588613i
\(803\) 1.65570e7 1.20294e7i 0.906135 0.658346i
\(804\) 1.18529e6 861162.i 0.0646671 0.0469834i
\(805\) −7.24843e6 2.15086e6i −0.394234 0.116983i
\(806\) −717453. 521260.i −0.0389005 0.0282629i
\(807\) 3.91524e6 0.211629
\(808\) 7.38065e6 + 5.36236e6i 0.397710 + 0.288953i
\(809\) 6.70151e6 2.06251e7i 0.359999 1.10796i −0.593055 0.805162i \(-0.702078\pi\)
0.953054 0.302801i \(-0.0979216\pi\)
\(810\) −892546. 1.16434e6i −0.0477989 0.0623547i
\(811\) 3.16074e6 + 9.72774e6i 0.168747 + 0.519350i 0.999293 0.0376004i \(-0.0119714\pi\)
−0.830546 + 0.556950i \(0.811971\pi\)
\(812\) −2.90490e6 + 8.94036e6i −0.154611 + 0.475844i
\(813\) −2.23751e6 + 6.88636e6i −0.118724 + 0.365396i
\(814\) −7.07892e6 2.17867e7i −0.374460 1.15247i
\(815\) 6.75537e6 + 8.81252e6i 0.356250 + 0.464736i
\(816\) −1.04629e6 + 3.22014e6i −0.0550079 + 0.169297i
\(817\) 6.54941e6 + 4.75842e6i 0.343279 + 0.249406i
\(818\) 1.69524e7 0.885824
\(819\) 2.15305e6 + 1.56428e6i 0.112162 + 0.0814903i
\(820\) −1.39423e7 4.13719e6i −0.724105 0.214867i
\(821\) −2.80940e7 + 2.04115e7i −1.45464 + 1.05686i −0.469924 + 0.882707i \(0.655719\pi\)
−0.984719 + 0.174152i \(0.944281\pi\)
\(822\) 4.16373e6 3.02513e6i 0.214933 0.156158i
\(823\) 3.77929e6 + 1.16315e7i 0.194496 + 0.598598i 0.999982 + 0.00598272i \(0.00190437\pi\)
−0.805486 + 0.592615i \(0.798096\pi\)
\(824\) 1.26016e7 0.646558
\(825\) −3.90169e6 + 1.45056e7i −0.199581 + 0.741997i
\(826\) 4.45304e6 0.227095
\(827\) 9.18753e6 + 2.82763e7i 0.467127 + 1.43767i 0.856287 + 0.516500i \(0.172765\pi\)
−0.389160 + 0.921170i \(0.627235\pi\)
\(828\) 1.24492e6 904488.i 0.0631053 0.0458487i
\(829\) 1.19313e7 8.66857e6i 0.602976 0.438088i −0.243958 0.969786i \(-0.578446\pi\)
0.846934 + 0.531698i \(0.178446\pi\)
\(830\) 273717. + 357070.i 0.0137914 + 0.0179911i
\(831\) 8.56722e6 + 6.22445e6i 0.430366 + 0.312679i
\(832\) −1.18143e6 −0.0591697
\(833\) 4.55507e6 + 3.30945e6i 0.227448 + 0.165251i
\(834\) −2.42402e6 + 7.46037e6i −0.120676 + 0.371403i
\(835\) −139028. + 49157.4i −0.00690059 + 0.00243990i
\(836\) 1.24649e6 + 3.83630e6i 0.0616841 + 0.189844i
\(837\) 173156. 532920.i 0.00854328 0.0262935i
\(838\) 1.85591e6 5.71191e6i 0.0912951 0.280977i
\(839\) −3.94301e6 1.21353e7i −0.193385 0.595178i −0.999992 0.00408925i \(-0.998698\pi\)
0.806607 0.591089i \(-0.201302\pi\)
\(840\) −2.07895e6 + 3.02178e6i −0.101659 + 0.147763i
\(841\) 1.88244e6 5.79355e6i 0.0917764 0.282459i
\(842\) 6.06874e6 + 4.40920e6i 0.294998 + 0.214328i
\(843\) −2.32040e7 −1.12459
\(844\) 8.31591e6 + 6.04186e6i 0.401840 + 0.291954i
\(845\) 1.51840e7 5.36874e6i 0.731551 0.258661i
\(846\) −196092. + 142469.i −0.00941963 + 0.00684376i
\(847\) −1.14456e7 + 8.31573e6i −0.548190 + 0.398283i
\(848\) −2.01017e6 6.18666e6i −0.0959936 0.295438i
\(849\) −1.34912e7 −0.642363
\(850\) −1.83452e7 + 943782.i −0.870912 + 0.0448048i
\(851\) −1.27318e7 −0.602652
\(852\) 3.22165e6 + 9.91522e6i 0.152048 + 0.467954i
\(853\) −8.42379e6 + 6.12024e6i −0.396401 + 0.288002i −0.768074 0.640362i \(-0.778785\pi\)
0.371672 + 0.928364i \(0.378785\pi\)
\(854\) −1.02604e7 + 7.45461e6i −0.481414 + 0.349768i
\(855\) −54925.5 2.13669e6i −0.00256956 0.0999598i
\(856\) 8.90722e6 + 6.47148e6i 0.415487 + 0.301869i
\(857\) −4.04202e7 −1.87995 −0.939976 0.341240i \(-0.889153\pi\)
−0.939976 + 0.341240i \(0.889153\pi\)
\(858\) 4.48663e6 + 3.25973e6i 0.208066 + 0.151169i
\(859\) 1.02872e7 3.16607e7i 0.475679 1.46399i −0.369361 0.929286i \(-0.620423\pi\)
0.845040 0.534703i \(-0.179577\pi\)
\(860\) 394189. + 1.53346e7i 0.0181743 + 0.707010i
\(861\) 5.15116e6 + 1.58536e7i 0.236809 + 0.728822i
\(862\) 6.88067e6 2.11765e7i 0.315401 0.970703i
\(863\) −1.03986e7 + 3.20036e7i −0.475278 + 1.46276i 0.370304 + 0.928910i \(0.379253\pi\)
−0.845582 + 0.533845i \(0.820747\pi\)
\(864\) −230680. 709960.i −0.0105130 0.0323556i
\(865\) 5.54427e6 + 1.64518e6i 0.251944 + 0.0747607i
\(866\) 4.26994e6 1.31415e7i 0.193476 0.595458i
\(867\) 5.38609e6 + 3.91322e6i 0.243347 + 0.176802i
\(868\) −1.40092e6 −0.0631122
\(869\) −950784. 690785.i −0.0427103 0.0310308i
\(870\) 5.88332e6 8.55150e6i 0.263527 0.383040i
\(871\) 2.37415e6 1.72492e6i 0.106038 0.0770414i
\(872\) −5.42052e6 + 3.93824e6i −0.241407 + 0.175393i
\(873\) 1.73068e6 + 5.32650e6i 0.0768568 + 0.236541i
\(874\) 2.24188e6 0.0992737
\(875\) −1.93429e7 4.67326e6i −0.854084 0.206348i
\(876\) −5.51790e6 −0.242948
\(877\) 4.45361e6 + 1.37068e7i 0.195530 + 0.601779i 0.999970 + 0.00774555i \(0.00246551\pi\)
−0.804440 + 0.594034i \(0.797534\pi\)
\(878\) −1.22803e7 + 8.92214e6i −0.537616 + 0.390601i
\(879\) 1.68527e7 1.22442e7i 0.735693 0.534512i
\(880\) −4.33220e6 + 6.29692e6i −0.188583 + 0.274108i
\(881\) −1.42662e7 1.03650e7i −0.619255 0.449915i 0.233406 0.972379i \(-0.425013\pi\)
−0.852661 + 0.522464i \(0.825013\pi\)
\(882\) −1.24136e6 −0.0537311
\(883\) 3.25924e7 + 2.36797e7i 1.40674 + 1.02206i 0.993786 + 0.111305i \(0.0355032\pi\)
0.412955 + 0.910752i \(0.364497\pi\)
\(884\) −2.09573e6 + 6.44999e6i −0.0901996 + 0.277606i
\(885\) −4.71384e6 1.39876e6i −0.202310 0.0600325i
\(886\) −6.24403e6 1.92172e7i −0.267227 0.822441i
\(887\) 4.22852e6 1.30140e7i 0.180459 0.555397i −0.819381 0.573249i \(-0.805683\pi\)
0.999841 + 0.0178521i \(0.00568281\pi\)
\(888\) −1.90861e6 + 5.87409e6i −0.0812240 + 0.249982i
\(889\) 1.08180e7 + 3.32945e7i 0.459086 + 1.41292i
\(890\) 288995. + 1.12424e7i 0.0122297 + 0.475754i
\(891\) −1.08284e6 + 3.33264e6i −0.0456952 + 0.140635i
\(892\) −4.89788e6 3.55852e6i −0.206109 0.149747i
\(893\) −353127. −0.0148184
\(894\) 1.45004e7 + 1.05351e7i 0.606785 + 0.440855i
\(895\) −334032. 1.29943e7i −0.0139389 0.542246i
\(896\) −1.50988e6 + 1.09699e6i −0.0628307 + 0.0456492i
\(897\) 2.49360e6 1.81171e6i 0.103477 0.0751807i
\(898\) 3.19108e6 + 9.82114e6i 0.132053 + 0.406416i
\(899\) 3.96454e6 0.163604
\(900\) 3.14988e6 2.54573e6i 0.129625 0.104762i
\(901\) −3.73418e7 −1.53244
\(902\) 1.07342e7 + 3.30366e7i 0.439293 + 1.35201i
\(903\) 1.42244e7 1.03347e7i 0.580518 0.421771i
\(904\) 3.38291e6 2.45783e6i 0.137680 0.100030i
\(905\) −399121. + 141121.i −0.0161988 + 0.00572756i
\(906\) −8.62835e6 6.26886e6i −0.349226 0.253728i
\(907\) −3.66340e7 −1.47865 −0.739326 0.673347i \(-0.764856\pi\)
−0.739326 + 0.673347i \(0.764856\pi\)
\(908\) −1.59801e7 1.16102e7i −0.643229 0.467333i
\(909\) −3.56800e6 + 1.09812e7i −0.143224 + 0.440797i
\(910\) −4.16417e6 + 6.05268e6i −0.166696 + 0.242295i
\(911\) −1.05572e6 3.24917e6i −0.0421457 0.129711i 0.927770 0.373153i \(-0.121723\pi\)
−0.969915 + 0.243442i \(0.921723\pi\)
\(912\) 336077. 1.03434e6i 0.0133799 0.0411790i
\(913\) 332076. 1.02202e6i 0.0131844 0.0405774i
\(914\) −6.37428e6 1.96180e7i −0.252386 0.776765i
\(915\) 1.32029e7 4.66827e6i 0.521335 0.184333i
\(916\) −6.14022e6 + 1.88976e7i −0.241794 + 0.744164i
\(917\) 1.95452e7 + 1.42004e7i 0.767569 + 0.557672i
\(918\) −4.28522e6 −0.167829
\(919\) 2.96804e7 + 2.15641e7i 1.15926 + 0.842251i 0.989684 0.143266i \(-0.0457604\pi\)
0.169575 + 0.985517i \(0.445760\pi\)
\(920\) 2.58440e6 + 3.37140e6i 0.100668 + 0.131323i
\(921\) −1.91769e7 + 1.39329e7i −0.744955 + 0.541241i
\(922\) 2.16124e7 1.57023e7i 0.837289 0.608326i
\(923\) 6.45303e6 + 1.98604e7i 0.249321 + 0.767332i
\(924\) 8.76072e6 0.337567
\(925\) −3.34648e7 + 1.72162e6i −1.28598 + 0.0661582i
\(926\) −1.05994e7 −0.406212
\(927\) 4.92848e6 + 1.51683e7i 0.188371 + 0.579746i
\(928\) 4.27289e6 3.10444e6i 0.162874 0.118335i
\(929\) −1.42676e7 + 1.03661e7i −0.542392 + 0.394071i −0.824972 0.565173i \(-0.808809\pi\)
0.282581 + 0.959243i \(0.408809\pi\)
\(930\) 1.48297e6 + 440048.i 0.0562242 + 0.0166837i
\(931\) −1.46313e6 1.06303e6i −0.0553235 0.0401948i
\(932\) −2.23642e7 −0.843363
\(933\) 1.07355e7 + 7.79976e6i 0.403753 + 0.293344i
\(934\) −2.23935e6 + 6.89202e6i −0.0839954 + 0.258511i
\(935\) 2.66931e7 + 3.48217e7i 0.998549 + 1.30263i
\(936\) −462056. 1.42206e6i −0.0172387 0.0530553i
\(937\) 1.42157e7 4.37515e7i 0.528957 1.62796i −0.227398 0.973802i \(-0.573022\pi\)
0.756355 0.654161i \(-0.226978\pi\)
\(938\) 1.43255e6 4.40894e6i 0.0531623 0.163617i
\(939\) −3.44990e6 1.06177e7i −0.127686 0.392976i
\(940\) −407078. 531042.i −0.0150265 0.0196024i
\(941\) −6.02744e6 + 1.85506e7i −0.221901 + 0.682940i 0.776691 + 0.629882i \(0.216897\pi\)
−0.998591 + 0.0530582i \(0.983103\pi\)
\(942\) 5.41772e6 + 3.93620e6i 0.198925 + 0.144527i
\(943\) 1.93061e7 0.706994
\(944\) −2.02409e6 1.47059e6i −0.0739265 0.0537107i
\(945\) −4.45033e6 1.32057e6i −0.162111 0.0481041i
\(946\) 2.96415e7 2.15358e7i 1.07689 0.782409i
\(947\) −3.17911e7 + 2.30976e7i −1.15194 + 0.836935i −0.988738 0.149657i \(-0.952183\pi\)
−0.163205 + 0.986592i \(0.552183\pi\)
\(948\) 97916.6 + 301356.i 0.00353863 + 0.0108908i
\(949\) −1.10525e7 −0.398376
\(950\) 5.89264e6 303152.i 0.211837 0.0108981i
\(951\) 1.72495e7 0.618479
\(952\) 3.31064e6 + 1.01891e7i 0.118391 + 0.364371i
\(953\) 1.37148e7 9.96436e6i 0.489166 0.355400i −0.315698 0.948860i \(-0.602239\pi\)
0.804863 + 0.593460i \(0.202239\pi\)
\(954\) 6.66058e6 4.83920e6i 0.236942 0.172148i
\(955\) −2.76628e7 3.60867e7i −0.981494 1.28038i
\(956\) −1.03042e7 7.48646e6i −0.364645 0.264930i
\(957\) −2.47924e7 −0.875063
\(958\) 1.08782e7 + 7.90350e6i 0.382952 + 0.278231i
\(959\) 5.03234e6 1.54879e7i 0.176695 0.543810i
\(960\) 1.94289e6 686964.i 0.0680408 0.0240578i
\(961\) −8.66432e6 2.66660e7i −0.302640 0.931429i
\(962\) −3.82298e6 + 1.17659e7i −0.133188 + 0.409909i
\(963\) −4.30598e6 + 1.32524e7i −0.149626 + 0.460501i
\(964\) −5.14240e6 1.58267e7i −0.178227 0.548526i
\(965\) 4.46082e6 6.48387e6i 0.154204 0.224138i
\(966\) 1.50463e6 4.63076e6i 0.0518783 0.159665i
\(967\) 1.01661e6 + 738612.i 0.0349614 + 0.0254010i 0.605129 0.796128i \(-0.293122\pi\)
−0.570167 + 0.821529i \(0.693122\pi\)
\(968\) 7.94872e6 0.272652
\(969\) −5.05079e6 3.66962e6i −0.172803 0.125548i
\(970\) −1.45766e7 + 5.15397e6i −0.497423 + 0.175878i
\(971\) −1.02165e7 + 7.42271e6i −0.347739 + 0.252647i −0.747920 0.663789i \(-0.768947\pi\)
0.400181 + 0.916436i \(0.368947\pi\)
\(972\) 764346. 555330.i 0.0259492 0.0188532i
\(973\) 7.67005e6 + 2.36060e7i 0.259727 + 0.799356i
\(974\) 3.21145e7 1.08468
\(975\) 6.30928e6 5.09914e6i 0.212553 0.171785i
\(976\) 7.12560e6 0.239440
\(977\) 2.87851e6 + 8.85915e6i 0.0964788 + 0.296931i 0.987636 0.156763i \(-0.0501059\pi\)
−0.891157 + 0.453694i \(0.850106\pi\)
\(978\) −5.78507e6 + 4.20310e6i −0.193402 + 0.140515i
\(979\) 2.17313e7 1.57887e7i 0.724652 0.526490i
\(980\) −88061.6 3.42573e6i −0.00292901 0.113943i
\(981\) −6.86035e6 4.98434e6i −0.227601 0.165362i
\(982\) 2.64582e6 0.0875551
\(983\) −1.24753e7 9.06383e6i −0.411781 0.299177i 0.362541 0.931968i \(-0.381909\pi\)
−0.774323 + 0.632791i \(0.781909\pi\)
\(984\) 2.89415e6 8.90727e6i 0.0952868 0.293263i
\(985\) 365780. + 1.42294e7i 0.0120124 + 0.467301i
\(986\) −9.36897e6 2.88347e7i −0.306902 0.944547i
\(987\) −236999. + 729408.i −0.00774379 + 0.0238329i
\(988\) 673169. 2.07180e6i 0.0219397 0.0675236i
\(989\) −6.29262e6 1.93667e7i −0.204569 0.629600i
\(990\) −9.27380e6 2.75186e6i −0.300725 0.0892358i
\(991\) 8.60026e6 2.64689e7i 0.278181 0.856153i −0.710179 0.704021i \(-0.751386\pi\)
0.988360 0.152132i \(-0.0486138\pi\)
\(992\) 636775. + 462644.i 0.0205450 + 0.0149268i
\(993\) −1.30278e7 −0.419274
\(994\) 2.66880e7 + 1.93900e7i 0.856742 + 0.622459i
\(995\) 4.20394e6 6.11048e6i 0.134617 0.195667i
\(996\) −234402. + 170303.i −0.00748710 + 0.00543970i
\(997\) −2.66287e7 + 1.93469e7i −0.848421 + 0.616414i −0.924710 0.380672i \(-0.875693\pi\)
0.0762893 + 0.997086i \(0.475693\pi\)
\(998\) 8.96562e6 + 2.75933e7i 0.284940 + 0.876956i
\(999\) −7.81699e6 −0.247814
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 150.6.g.d.31.5 28
25.21 even 5 inner 150.6.g.d.121.5 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.6.g.d.31.5 28 1.1 even 1 trivial
150.6.g.d.121.5 yes 28 25.21 even 5 inner