Properties

Label 225.4.e.d.76.6
Level $225$
Weight $4$
Character 225.76
Analytic conductor $13.275$
Analytic rank $0$
Dimension $14$
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] = [225,4,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.76");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), degree \(2\), 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: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + 209529 x^{6} - 55412 x^{5} + 765088 x^{4} + 276096 x^{3} + 1572480 x^{2} + \cdots + 82944 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.6
Root \(-1.52087 + 2.63422i\) of defining polynomial
Character \(\chi\) \(=\) 225.76
Dual form 225.4.e.d.151.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.52087 + 2.63422i) q^{2} +(-4.01867 + 3.29398i) q^{3} +(-0.626094 + 1.08443i) q^{4} +(-14.7890 - 5.57636i) q^{6} +(-6.85611 - 11.8751i) q^{7} +20.5251 q^{8} +(5.29939 - 26.4748i) q^{9} +O(q^{10})\) \(q+(1.52087 + 2.63422i) q^{2} +(-4.01867 + 3.29398i) q^{3} +(-0.626094 + 1.08443i) q^{4} +(-14.7890 - 5.57636i) q^{6} +(-6.85611 - 11.8751i) q^{7} +20.5251 q^{8} +(5.29939 - 26.4748i) q^{9} +(-15.9034 - 27.5455i) q^{11} +(-1.05602 - 6.42029i) q^{12} +(29.1216 - 50.4401i) q^{13} +(20.8545 - 36.1211i) q^{14} +(36.2248 + 62.7431i) q^{16} -109.055 q^{17} +(77.8003 - 26.3050i) q^{18} +129.695 q^{19} +(66.6689 + 25.1383i) q^{21} +(48.3740 - 83.7863i) q^{22} +(39.8342 - 68.9949i) q^{23} +(-82.4836 + 67.6093i) q^{24} +177.161 q^{26} +(65.9111 + 123.850i) q^{27} +17.1703 q^{28} +(-4.51769 - 7.82486i) q^{29} +(16.6904 - 28.9087i) q^{31} +(-28.0860 + 48.6463i) q^{32} +(154.645 + 58.3108i) q^{33} +(-165.858 - 287.275i) q^{34} +(25.3921 + 22.3225i) q^{36} +22.1645 q^{37} +(197.250 + 341.647i) q^{38} +(49.1186 + 298.628i) q^{39} +(-60.8698 + 105.430i) q^{41} +(35.1747 + 213.853i) q^{42} +(5.07086 + 8.78298i) q^{43} +39.8281 q^{44} +242.331 q^{46} +(-220.746 - 382.343i) q^{47} +(-352.250 - 132.820i) q^{48} +(77.4875 - 134.212i) q^{49} +(438.255 - 359.225i) q^{51} +(36.4657 + 63.1604i) q^{52} +593.610 q^{53} +(-226.006 + 361.984i) q^{54} +(-140.722 - 243.738i) q^{56} +(-521.202 + 427.214i) q^{57} +(13.7416 - 23.8012i) q^{58} +(-221.230 + 383.182i) q^{59} +(-72.2881 - 125.207i) q^{61} +101.536 q^{62} +(-350.725 + 118.583i) q^{63} +408.736 q^{64} +(81.5912 + 496.052i) q^{66} +(431.360 - 747.138i) q^{67} +(68.2786 - 118.262i) q^{68} +(67.1873 + 408.481i) q^{69} -818.541 q^{71} +(108.771 - 543.398i) q^{72} -495.052 q^{73} +(33.7093 + 58.3863i) q^{74} +(-81.2014 + 140.645i) q^{76} +(-218.071 + 377.710i) q^{77} +(-711.950 + 583.563i) q^{78} +(-585.263 - 1013.71i) q^{79} +(-672.833 - 280.601i) q^{81} -370.300 q^{82} +(-212.022 - 367.232i) q^{83} +(-69.0017 + 56.5586i) q^{84} +(-15.4242 + 26.7156i) q^{86} +(43.9300 + 16.5644i) q^{87} +(-326.419 - 565.374i) q^{88} +1031.37 q^{89} -798.643 q^{91} +(49.8799 + 86.3945i) q^{92} +(28.1513 + 171.152i) q^{93} +(671.452 - 1162.99i) q^{94} +(-47.3718 - 288.008i) q^{96} +(799.356 + 1384.53i) q^{97} +471.394 q^{98} +(-813.541 + 275.066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52087 + 2.63422i 0.537709 + 0.931339i 0.999027 + 0.0441043i \(0.0140434\pi\)
−0.461318 + 0.887235i \(0.652623\pi\)
\(3\) −4.01867 + 3.29398i −0.773393 + 0.633927i
\(4\) −0.626094 + 1.08443i −0.0782617 + 0.135553i
\(5\) 0 0
\(6\) −14.7890 5.57636i −1.00626 0.379423i
\(7\) −6.85611 11.8751i −0.370195 0.641197i 0.619400 0.785075i \(-0.287376\pi\)
−0.989595 + 0.143879i \(0.954043\pi\)
\(8\) 20.5251 0.907090
\(9\) 5.29939 26.4748i 0.196274 0.980549i
\(10\) 0 0
\(11\) −15.9034 27.5455i −0.435914 0.755026i 0.561455 0.827507i \(-0.310242\pi\)
−0.997370 + 0.0724812i \(0.976908\pi\)
\(12\) −1.05602 6.42029i −0.0254038 0.154448i
\(13\) 29.1216 50.4401i 0.621298 1.07612i −0.367946 0.929847i \(-0.619939\pi\)
0.989244 0.146272i \(-0.0467276\pi\)
\(14\) 20.8545 36.1211i 0.398115 0.689555i
\(15\) 0 0
\(16\) 36.2248 + 62.7431i 0.566012 + 0.980361i
\(17\) −109.055 −1.55586 −0.777932 0.628348i \(-0.783731\pi\)
−0.777932 + 0.628348i \(0.783731\pi\)
\(18\) 77.8003 26.3050i 1.01876 0.344453i
\(19\) 129.695 1.56601 0.783004 0.622017i \(-0.213687\pi\)
0.783004 + 0.622017i \(0.213687\pi\)
\(20\) 0 0
\(21\) 66.6689 + 25.1383i 0.692778 + 0.261221i
\(22\) 48.3740 83.7863i 0.468790 0.811968i
\(23\) 39.8342 68.9949i 0.361131 0.625497i −0.627017 0.779006i \(-0.715724\pi\)
0.988147 + 0.153509i \(0.0490575\pi\)
\(24\) −82.4836 + 67.6093i −0.701537 + 0.575028i
\(25\) 0 0
\(26\) 177.161 1.33631
\(27\) 65.9111 + 123.850i 0.469800 + 0.882773i
\(28\) 17.1703 0.115888
\(29\) −4.51769 7.82486i −0.0289280 0.0501048i 0.851199 0.524843i \(-0.175876\pi\)
−0.880127 + 0.474738i \(0.842543\pi\)
\(30\) 0 0
\(31\) 16.6904 28.9087i 0.0966998 0.167489i −0.813617 0.581401i \(-0.802505\pi\)
0.910317 + 0.413912i \(0.135838\pi\)
\(32\) −28.0860 + 48.6463i −0.155154 + 0.268735i
\(33\) 154.645 + 58.3108i 0.815764 + 0.307594i
\(34\) −165.858 287.275i −0.836602 1.44904i
\(35\) 0 0
\(36\) 25.3921 + 22.3225i 0.117556 + 0.103345i
\(37\) 22.1645 0.0984817 0.0492408 0.998787i \(-0.484320\pi\)
0.0492408 + 0.998787i \(0.484320\pi\)
\(38\) 197.250 + 341.647i 0.842056 + 1.45848i
\(39\) 49.1186 + 298.628i 0.201673 + 1.22612i
\(40\) 0 0
\(41\) −60.8698 + 105.430i −0.231860 + 0.401593i −0.958356 0.285578i \(-0.907814\pi\)
0.726495 + 0.687171i \(0.241148\pi\)
\(42\) 35.1747 + 213.853i 0.129228 + 0.785672i
\(43\) 5.07086 + 8.78298i 0.0179837 + 0.0311487i 0.874877 0.484345i \(-0.160942\pi\)
−0.856894 + 0.515493i \(0.827609\pi\)
\(44\) 39.8281 0.136462
\(45\) 0 0
\(46\) 242.331 0.776733
\(47\) −220.746 382.343i −0.685088 1.18661i −0.973409 0.229073i \(-0.926430\pi\)
0.288321 0.957534i \(-0.406903\pi\)
\(48\) −352.250 132.820i −1.05923 0.399395i
\(49\) 77.4875 134.212i 0.225911 0.391289i
\(50\) 0 0
\(51\) 438.255 359.225i 1.20329 0.986304i
\(52\) 36.4657 + 63.1604i 0.0972477 + 0.168438i
\(53\) 593.610 1.53846 0.769232 0.638969i \(-0.220639\pi\)
0.769232 + 0.638969i \(0.220639\pi\)
\(54\) −226.006 + 361.984i −0.569546 + 0.912218i
\(55\) 0 0
\(56\) −140.722 243.738i −0.335800 0.581623i
\(57\) −521.202 + 427.214i −1.21114 + 0.992734i
\(58\) 13.7416 23.8012i 0.0311097 0.0538836i
\(59\) −221.230 + 383.182i −0.488164 + 0.845525i −0.999907 0.0136133i \(-0.995667\pi\)
0.511743 + 0.859139i \(0.329000\pi\)
\(60\) 0 0
\(61\) −72.2881 125.207i −0.151730 0.262804i 0.780133 0.625613i \(-0.215151\pi\)
−0.931864 + 0.362809i \(0.881818\pi\)
\(62\) 101.536 0.207985
\(63\) −350.725 + 118.583i −0.701385 + 0.237145i
\(64\) 408.736 0.798312
\(65\) 0 0
\(66\) 81.5912 + 496.052i 0.152169 + 0.925149i
\(67\) 431.360 747.138i 0.786553 1.36235i −0.141514 0.989936i \(-0.545197\pi\)
0.928067 0.372414i \(-0.121470\pi\)
\(68\) 68.2786 118.262i 0.121765 0.210902i
\(69\) 67.1873 + 408.481i 0.117223 + 0.712685i
\(70\) 0 0
\(71\) −818.541 −1.36821 −0.684105 0.729384i \(-0.739807\pi\)
−0.684105 + 0.729384i \(0.739807\pi\)
\(72\) 108.771 543.398i 0.178038 0.889446i
\(73\) −495.052 −0.793719 −0.396859 0.917879i \(-0.629900\pi\)
−0.396859 + 0.917879i \(0.629900\pi\)
\(74\) 33.7093 + 58.3863i 0.0529545 + 0.0917198i
\(75\) 0 0
\(76\) −81.2014 + 140.645i −0.122558 + 0.212277i
\(77\) −218.071 + 377.710i −0.322747 + 0.559014i
\(78\) −711.950 + 583.563i −1.03349 + 0.847122i
\(79\) −585.263 1013.71i −0.833510 1.44368i −0.895238 0.445588i \(-0.852995\pi\)
0.0617284 0.998093i \(-0.480339\pi\)
\(80\) 0 0
\(81\) −672.833 280.601i −0.922953 0.384912i
\(82\) −370.300 −0.498693
\(83\) −212.022 367.232i −0.280390 0.485651i 0.691090 0.722768i \(-0.257131\pi\)
−0.971481 + 0.237118i \(0.923797\pi\)
\(84\) −69.0017 + 56.5586i −0.0896273 + 0.0734648i
\(85\) 0 0
\(86\) −15.4242 + 26.7156i −0.0193400 + 0.0334978i
\(87\) 43.9300 + 16.5644i 0.0541355 + 0.0204125i
\(88\) −326.419 565.374i −0.395413 0.684876i
\(89\) 1031.37 1.22837 0.614183 0.789163i \(-0.289486\pi\)
0.614183 + 0.789163i \(0.289486\pi\)
\(90\) 0 0
\(91\) −798.643 −0.920006
\(92\) 49.8799 + 86.3945i 0.0565254 + 0.0979049i
\(93\) 28.1513 + 171.152i 0.0313888 + 0.190835i
\(94\) 671.452 1162.99i 0.736756 1.27610i
\(95\) 0 0
\(96\) −47.3718 288.008i −0.0503632 0.306195i
\(97\) 799.356 + 1384.53i 0.836725 + 1.44925i 0.892618 + 0.450814i \(0.148866\pi\)
−0.0558930 + 0.998437i \(0.517801\pi\)
\(98\) 471.394 0.485897
\(99\) −813.541 + 275.066i −0.825898 + 0.279244i
\(100\) 0 0
\(101\) 107.000 + 185.330i 0.105415 + 0.182584i 0.913908 0.405922i \(-0.133050\pi\)
−0.808493 + 0.588506i \(0.799716\pi\)
\(102\) 1612.81 + 608.129i 1.56561 + 0.590331i
\(103\) 836.160 1448.27i 0.799897 1.38546i −0.119786 0.992800i \(-0.538221\pi\)
0.919683 0.392662i \(-0.128446\pi\)
\(104\) 597.723 1035.29i 0.563573 0.976137i
\(105\) 0 0
\(106\) 902.804 + 1563.70i 0.827246 + 1.43283i
\(107\) 600.699 0.542727 0.271363 0.962477i \(-0.412525\pi\)
0.271363 + 0.962477i \(0.412525\pi\)
\(108\) −175.572 6.06581i −0.156430 0.00540447i
\(109\) −771.570 −0.678009 −0.339005 0.940785i \(-0.610090\pi\)
−0.339005 + 0.940785i \(0.610090\pi\)
\(110\) 0 0
\(111\) −89.0718 + 73.0094i −0.0761650 + 0.0624302i
\(112\) 496.722 860.348i 0.419070 0.725850i
\(113\) −583.338 + 1010.37i −0.485627 + 0.841131i −0.999864 0.0165177i \(-0.994742\pi\)
0.514237 + 0.857648i \(0.328075\pi\)
\(114\) −1918.06 723.228i −1.57581 0.594180i
\(115\) 0 0
\(116\) 11.3140 0.00905583
\(117\) −1181.06 1038.29i −0.933244 0.820427i
\(118\) −1345.85 −1.04996
\(119\) 747.692 + 1295.04i 0.575973 + 0.997615i
\(120\) 0 0
\(121\) 159.663 276.545i 0.119957 0.207772i
\(122\) 219.882 380.846i 0.163173 0.282624i
\(123\) −102.667 624.190i −0.0752618 0.457572i
\(124\) 20.8996 + 36.1991i 0.0151358 + 0.0262159i
\(125\) 0 0
\(126\) −845.783 743.539i −0.598003 0.525712i
\(127\) −1630.10 −1.13896 −0.569479 0.822006i \(-0.692855\pi\)
−0.569479 + 0.822006i \(0.692855\pi\)
\(128\) 846.322 + 1465.87i 0.584414 + 1.01223i
\(129\) −49.3091 18.5926i −0.0336544 0.0126898i
\(130\) 0 0
\(131\) −129.412 + 224.149i −0.0863115 + 0.149496i −0.905949 0.423386i \(-0.860841\pi\)
0.819638 + 0.572882i \(0.194175\pi\)
\(132\) −160.056 + 131.193i −0.105538 + 0.0865067i
\(133\) −889.206 1540.15i −0.579729 1.00412i
\(134\) 2624.17 1.69175
\(135\) 0 0
\(136\) −2238.36 −1.41131
\(137\) 526.385 + 911.726i 0.328264 + 0.568569i 0.982167 0.188009i \(-0.0602033\pi\)
−0.653904 + 0.756578i \(0.726870\pi\)
\(138\) −973.847 + 798.232i −0.600720 + 0.492392i
\(139\) −1192.25 + 2065.03i −0.727519 + 1.26010i 0.230410 + 0.973094i \(0.425993\pi\)
−0.957929 + 0.287006i \(0.907340\pi\)
\(140\) 0 0
\(141\) 2146.54 + 809.378i 1.28206 + 0.483418i
\(142\) −1244.89 2156.22i −0.735699 1.27427i
\(143\) −1852.53 −1.08333
\(144\) 1853.08 626.544i 1.07239 0.362583i
\(145\) 0 0
\(146\) −752.910 1304.08i −0.426790 0.739221i
\(147\) 130.696 + 794.597i 0.0733308 + 0.445831i
\(148\) −13.8771 + 24.0358i −0.00770735 + 0.0133495i
\(149\) −573.144 + 992.715i −0.315126 + 0.545815i −0.979464 0.201617i \(-0.935380\pi\)
0.664338 + 0.747432i \(0.268714\pi\)
\(150\) 0 0
\(151\) 583.058 + 1009.89i 0.314229 + 0.544261i 0.979273 0.202543i \(-0.0649207\pi\)
−0.665044 + 0.746804i \(0.731587\pi\)
\(152\) 2662.01 1.42051
\(153\) −577.924 + 2887.21i −0.305375 + 1.52560i
\(154\) −1326.63 −0.694175
\(155\) 0 0
\(156\) −354.593 133.704i −0.181988 0.0686208i
\(157\) −1737.81 + 3009.97i −0.883390 + 1.53008i −0.0358423 + 0.999357i \(0.511411\pi\)
−0.847548 + 0.530719i \(0.821922\pi\)
\(158\) 1780.22 3083.43i 0.896371 1.55256i
\(159\) −2385.52 + 1955.34i −1.18984 + 0.975274i
\(160\) 0 0
\(161\) −1092.43 −0.534755
\(162\) −284.126 2199.15i −0.137796 1.06655i
\(163\) 2223.32 1.06837 0.534183 0.845369i \(-0.320619\pi\)
0.534183 + 0.845369i \(0.320619\pi\)
\(164\) −76.2204 132.018i −0.0362915 0.0628588i
\(165\) 0 0
\(166\) 644.915 1117.03i 0.301537 0.522277i
\(167\) −793.991 + 1375.23i −0.367909 + 0.637238i −0.989239 0.146312i \(-0.953260\pi\)
0.621329 + 0.783550i \(0.286593\pi\)
\(168\) 1368.39 + 515.967i 0.628412 + 0.236951i
\(169\) −597.632 1035.13i −0.272022 0.471156i
\(170\) 0 0
\(171\) 687.306 3433.66i 0.307366 1.53555i
\(172\) −12.6993 −0.00562974
\(173\) 753.898 + 1305.79i 0.331317 + 0.573857i 0.982770 0.184831i \(-0.0591738\pi\)
−0.651454 + 0.758689i \(0.725840\pi\)
\(174\) 23.1776 + 140.914i 0.0100982 + 0.0613945i
\(175\) 0 0
\(176\) 1152.19 1995.66i 0.493465 0.854707i
\(177\) −373.143 2268.61i −0.158458 0.963384i
\(178\) 1568.58 + 2716.85i 0.660504 + 1.14403i
\(179\) 1572.66 0.656683 0.328341 0.944559i \(-0.393510\pi\)
0.328341 + 0.944559i \(0.393510\pi\)
\(180\) 0 0
\(181\) 1984.41 0.814918 0.407459 0.913223i \(-0.366415\pi\)
0.407459 + 0.913223i \(0.366415\pi\)
\(182\) −1214.63 2103.81i −0.494695 0.856838i
\(183\) 702.930 + 265.048i 0.283946 + 0.107065i
\(184\) 817.601 1416.13i 0.327578 0.567382i
\(185\) 0 0
\(186\) −408.040 + 334.458i −0.160854 + 0.131847i
\(187\) 1734.34 + 3003.97i 0.678223 + 1.17472i
\(188\) 552.831 0.214465
\(189\) 1018.84 1631.83i 0.392114 0.628032i
\(190\) 0 0
\(191\) 1174.18 + 2033.73i 0.444819 + 0.770450i 0.998040 0.0625853i \(-0.0199345\pi\)
−0.553220 + 0.833035i \(0.686601\pi\)
\(192\) −1642.57 + 1346.37i −0.617409 + 0.506071i
\(193\) −117.085 + 202.797i −0.0436681 + 0.0756354i −0.887033 0.461705i \(-0.847238\pi\)
0.843365 + 0.537341i \(0.180571\pi\)
\(194\) −2431.43 + 4211.37i −0.899829 + 1.55855i
\(195\) 0 0
\(196\) 97.0288 + 168.059i 0.0353604 + 0.0612460i
\(197\) 717.846 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(198\) −1961.87 1724.71i −0.704163 0.619040i
\(199\) 1701.45 0.606094 0.303047 0.952976i \(-0.401996\pi\)
0.303047 + 0.952976i \(0.401996\pi\)
\(200\) 0 0
\(201\) 727.564 + 4423.39i 0.255315 + 1.55225i
\(202\) −325.467 + 563.725i −0.113365 + 0.196354i
\(203\) −61.9475 + 107.296i −0.0214180 + 0.0370971i
\(204\) 115.164 + 700.164i 0.0395248 + 0.240300i
\(205\) 0 0
\(206\) 5086.77 1.72045
\(207\) −1615.53 1420.23i −0.542450 0.476875i
\(208\) 4219.69 1.40665
\(209\) −2062.60 3572.52i −0.682645 1.18238i
\(210\) 0 0
\(211\) 2469.33 4277.01i 0.805667 1.39546i −0.110172 0.993912i \(-0.535140\pi\)
0.915840 0.401544i \(-0.131526\pi\)
\(212\) −371.656 + 643.727i −0.120403 + 0.208544i
\(213\) 3289.44 2696.26i 1.05816 0.867345i
\(214\) 913.585 + 1582.38i 0.291829 + 0.505463i
\(215\) 0 0
\(216\) 1352.83 + 2542.03i 0.426150 + 0.800754i
\(217\) −457.726 −0.143191
\(218\) −1173.46 2032.49i −0.364572 0.631456i
\(219\) 1989.45 1630.69i 0.613857 0.503160i
\(220\) 0 0
\(221\) −3175.85 + 5500.73i −0.966655 + 1.67430i
\(222\) −327.790 123.597i −0.0990983 0.0373662i
\(223\) −1526.57 2644.10i −0.458416 0.794001i 0.540461 0.841369i \(-0.318250\pi\)
−0.998877 + 0.0473684i \(0.984917\pi\)
\(224\) 770.242 0.229750
\(225\) 0 0
\(226\) −3548.73 −1.04450
\(227\) −419.976 727.420i −0.122797 0.212690i 0.798073 0.602561i \(-0.205853\pi\)
−0.920869 + 0.389871i \(0.872520\pi\)
\(228\) −136.960 832.682i −0.0397825 0.241867i
\(229\) −700.753 + 1213.74i −0.202214 + 0.350245i −0.949242 0.314548i \(-0.898147\pi\)
0.747027 + 0.664793i \(0.231480\pi\)
\(230\) 0 0
\(231\) −367.814 2236.21i −0.104764 0.636935i
\(232\) −92.7259 160.606i −0.0262403 0.0454496i
\(233\) 2856.99 0.803295 0.401647 0.915794i \(-0.368438\pi\)
0.401647 + 0.915794i \(0.368438\pi\)
\(234\) 938.843 4690.30i 0.262282 1.31032i
\(235\) 0 0
\(236\) −277.021 479.815i −0.0764092 0.132345i
\(237\) 5691.11 + 2145.90i 1.55982 + 0.588149i
\(238\) −2274.29 + 3939.18i −0.619412 + 1.07285i
\(239\) 854.917 1480.76i 0.231381 0.400763i −0.726834 0.686813i \(-0.759009\pi\)
0.958215 + 0.286050i \(0.0923424\pi\)
\(240\) 0 0
\(241\) 2166.23 + 3752.02i 0.579000 + 1.00286i 0.995594 + 0.0937648i \(0.0298902\pi\)
−0.416594 + 0.909092i \(0.636776\pi\)
\(242\) 971.309 0.258009
\(243\) 3628.19 1088.66i 0.957812 0.287396i
\(244\) 181.036 0.0474987
\(245\) 0 0
\(246\) 1488.11 1219.76i 0.385686 0.316135i
\(247\) 3776.93 6541.84i 0.972957 1.68521i
\(248\) 342.573 593.354i 0.0877154 0.151927i
\(249\) 2061.70 + 777.390i 0.524719 + 0.197852i
\(250\) 0 0
\(251\) −1724.73 −0.433722 −0.216861 0.976202i \(-0.569582\pi\)
−0.216861 + 0.976202i \(0.569582\pi\)
\(252\) 90.9920 454.580i 0.0227459 0.113634i
\(253\) −2534.00 −0.629688
\(254\) −2479.16 4294.04i −0.612428 1.06076i
\(255\) 0 0
\(256\) −939.349 + 1627.00i −0.229333 + 0.397217i
\(257\) −2926.63 + 5069.07i −0.710342 + 1.23035i 0.254386 + 0.967103i \(0.418127\pi\)
−0.964729 + 0.263246i \(0.915207\pi\)
\(258\) −26.0156 158.168i −0.00627776 0.0381671i
\(259\) −151.962 263.206i −0.0364574 0.0631462i
\(260\) 0 0
\(261\) −231.103 + 78.1380i −0.0548081 + 0.0185311i
\(262\) −787.277 −0.185642
\(263\) 196.180 + 339.794i 0.0459962 + 0.0796677i 0.888107 0.459637i \(-0.152020\pi\)
−0.842111 + 0.539305i \(0.818687\pi\)
\(264\) 3174.10 + 1196.83i 0.739971 + 0.279015i
\(265\) 0 0
\(266\) 2704.73 4684.73i 0.623450 1.07985i
\(267\) −4144.72 + 3397.30i −0.950010 + 0.778695i
\(268\) 540.144 + 935.557i 0.123114 + 0.213240i
\(269\) −4610.33 −1.04497 −0.522485 0.852648i \(-0.674995\pi\)
−0.522485 + 0.852648i \(0.674995\pi\)
\(270\) 0 0
\(271\) −1155.72 −0.259058 −0.129529 0.991576i \(-0.541347\pi\)
−0.129529 + 0.991576i \(0.541347\pi\)
\(272\) −3950.49 6842.44i −0.880638 1.52531i
\(273\) 3209.48 2630.71i 0.711526 0.583216i
\(274\) −1601.13 + 2773.23i −0.353020 + 0.611449i
\(275\) 0 0
\(276\) −485.033 182.888i −0.105781 0.0398860i
\(277\) −304.205 526.898i −0.0659852 0.114290i 0.831145 0.556055i \(-0.187686\pi\)
−0.897131 + 0.441765i \(0.854352\pi\)
\(278\) −7253.02 −1.56477
\(279\) −676.904 595.075i −0.145251 0.127693i
\(280\) 0 0
\(281\) −1374.62 2380.91i −0.291825 0.505456i 0.682416 0.730964i \(-0.260929\pi\)
−0.974241 + 0.225508i \(0.927596\pi\)
\(282\) 1132.52 + 6885.42i 0.239151 + 1.45397i
\(283\) 510.780 884.697i 0.107289 0.185830i −0.807382 0.590029i \(-0.799116\pi\)
0.914671 + 0.404199i \(0.132450\pi\)
\(284\) 512.483 887.647i 0.107078 0.185465i
\(285\) 0 0
\(286\) −2817.46 4879.98i −0.582516 1.00895i
\(287\) 1669.32 0.343334
\(288\) 1139.06 + 1001.37i 0.233056 + 0.204882i
\(289\) 6979.96 1.42071
\(290\) 0 0
\(291\) −7772.95 2930.89i −1.56584 0.590418i
\(292\) 309.949 536.848i 0.0621178 0.107591i
\(293\) −2616.25 + 4531.47i −0.521648 + 0.903521i 0.478035 + 0.878341i \(0.341349\pi\)
−0.999683 + 0.0251800i \(0.991984\pi\)
\(294\) −1894.37 + 1552.76i −0.375790 + 0.308023i
\(295\) 0 0
\(296\) 454.929 0.0893317
\(297\) 2363.29 3785.18i 0.461724 0.739524i
\(298\) −3486.71 −0.677785
\(299\) −2320.07 4018.48i −0.448739 0.777240i
\(300\) 0 0
\(301\) 69.5327 120.434i 0.0133149 0.0230622i
\(302\) −1773.51 + 3071.81i −0.337927 + 0.585307i
\(303\) −1040.47 392.322i −0.197272 0.0743839i
\(304\) 4698.18 + 8137.49i 0.886379 + 1.53525i
\(305\) 0 0
\(306\) −8484.50 + 2868.69i −1.58506 + 0.535921i
\(307\) 4912.68 0.913296 0.456648 0.889648i \(-0.349050\pi\)
0.456648 + 0.889648i \(0.349050\pi\)
\(308\) −273.066 472.964i −0.0505174 0.0874988i
\(309\) 1410.33 + 8574.42i 0.259647 + 1.57858i
\(310\) 0 0
\(311\) 414.430 717.813i 0.0755632 0.130879i −0.825768 0.564010i \(-0.809258\pi\)
0.901331 + 0.433131i \(0.142591\pi\)
\(312\) 1008.16 + 6129.36i 0.182936 + 1.11220i
\(313\) 4618.60 + 7999.66i 0.834054 + 1.44462i 0.894798 + 0.446471i \(0.147319\pi\)
−0.0607442 + 0.998153i \(0.519347\pi\)
\(314\) −10571.9 −1.90003
\(315\) 0 0
\(316\) 1465.72 0.260928
\(317\) −4549.20 7879.45i −0.806021 1.39607i −0.915599 0.402091i \(-0.868283\pi\)
0.109578 0.993978i \(-0.465050\pi\)
\(318\) −8778.88 3310.18i −1.54810 0.583729i
\(319\) −143.693 + 248.884i −0.0252203 + 0.0436828i
\(320\) 0 0
\(321\) −2414.01 + 1978.69i −0.419741 + 0.344049i
\(322\) −1661.45 2877.71i −0.287543 0.498039i
\(323\) −14143.9 −2.43649
\(324\) 725.548 553.955i 0.124408 0.0949855i
\(325\) 0 0
\(326\) 3381.38 + 5856.72i 0.574470 + 0.995011i
\(327\) 3100.68 2541.54i 0.524368 0.429808i
\(328\) −1249.36 + 2163.95i −0.210318 + 0.364281i
\(329\) −3026.92 + 5242.78i −0.507233 + 0.878553i
\(330\) 0 0
\(331\) −2981.73 5164.50i −0.495137 0.857603i 0.504847 0.863209i \(-0.331549\pi\)
−0.999984 + 0.00560570i \(0.998216\pi\)
\(332\) 530.982 0.0877754
\(333\) 117.458 586.801i 0.0193294 0.0965661i
\(334\) −4830.23 −0.791313
\(335\) 0 0
\(336\) 837.807 + 5093.65i 0.136030 + 0.827027i
\(337\) 298.427 516.890i 0.0482384 0.0835514i −0.840898 0.541194i \(-0.817973\pi\)
0.889136 + 0.457642i \(0.151306\pi\)
\(338\) 1817.84 3148.60i 0.292537 0.506690i
\(339\) −983.901 5981.85i −0.157635 0.958377i
\(340\) 0 0
\(341\) −1061.74 −0.168611
\(342\) 10090.3 3411.63i 1.59539 0.539415i
\(343\) −6828.34 −1.07492
\(344\) 104.080 + 180.272i 0.0163128 + 0.0282546i
\(345\) 0 0
\(346\) −2293.16 + 3971.87i −0.356304 + 0.617137i
\(347\) −2281.05 + 3950.90i −0.352891 + 0.611226i −0.986755 0.162219i \(-0.948135\pi\)
0.633863 + 0.773445i \(0.281468\pi\)
\(348\) −45.4671 + 37.2680i −0.00700372 + 0.00574074i
\(349\) −337.633 584.798i −0.0517854 0.0896949i 0.838971 0.544177i \(-0.183158\pi\)
−0.890756 + 0.454482i \(0.849825\pi\)
\(350\) 0 0
\(351\) 8166.42 + 282.140i 1.24185 + 0.0429046i
\(352\) 1786.65 0.270536
\(353\) −1680.91 2911.43i −0.253445 0.438979i 0.711027 0.703165i \(-0.248230\pi\)
−0.964472 + 0.264185i \(0.914897\pi\)
\(354\) 5408.52 4433.20i 0.812033 0.665598i
\(355\) 0 0
\(356\) −645.732 + 1118.44i −0.0961341 + 0.166509i
\(357\) −7270.57 2741.46i −1.07787 0.406424i
\(358\) 2391.81 + 4142.74i 0.353104 + 0.611594i
\(359\) 7701.61 1.13224 0.566122 0.824322i \(-0.308443\pi\)
0.566122 + 0.824322i \(0.308443\pi\)
\(360\) 0 0
\(361\) 9961.87 1.45238
\(362\) 3018.03 + 5227.39i 0.438189 + 0.758965i
\(363\) 269.300 + 1637.27i 0.0389382 + 0.236734i
\(364\) 500.026 866.070i 0.0720013 0.124710i
\(365\) 0 0
\(366\) 370.868 + 2254.78i 0.0529661 + 0.322020i
\(367\) 2954.75 + 5117.77i 0.420263 + 0.727917i 0.995965 0.0897425i \(-0.0286044\pi\)
−0.575702 + 0.817660i \(0.695271\pi\)
\(368\) 5771.94 0.817617
\(369\) 2468.66 + 2170.23i 0.348274 + 0.306172i
\(370\) 0 0
\(371\) −4069.86 7049.20i −0.569532 0.986459i
\(372\) −203.228 76.6295i −0.0283249 0.0106803i
\(373\) −4212.19 + 7295.73i −0.584716 + 1.01276i 0.410195 + 0.911998i \(0.365461\pi\)
−0.994911 + 0.100760i \(0.967873\pi\)
\(374\) −5275.42 + 9137.30i −0.729374 + 1.26331i
\(375\) 0 0
\(376\) −4530.84 7847.64i −0.621436 1.07636i
\(377\) −526.249 −0.0718917
\(378\) 5848.13 + 202.046i 0.795754 + 0.0274923i
\(379\) −3510.24 −0.475749 −0.237875 0.971296i \(-0.576451\pi\)
−0.237875 + 0.971296i \(0.576451\pi\)
\(380\) 0 0
\(381\) 6550.81 5369.50i 0.880862 0.722016i
\(382\) −3571.54 + 6186.09i −0.478367 + 0.828555i
\(383\) 2866.01 4964.08i 0.382367 0.662279i −0.609033 0.793145i \(-0.708442\pi\)
0.991400 + 0.130866i \(0.0417758\pi\)
\(384\) −8229.64 3103.09i −1.09366 0.412380i
\(385\) 0 0
\(386\) −712.283 −0.0939229
\(387\) 259.400 87.7056i 0.0340725 0.0115202i
\(388\) −2001.89 −0.261934
\(389\) −7183.60 12442.4i −0.936306 1.62173i −0.772288 0.635273i \(-0.780888\pi\)
−0.164019 0.986457i \(-0.552446\pi\)
\(390\) 0 0
\(391\) −4344.11 + 7524.23i −0.561870 + 0.973188i
\(392\) 1590.44 2754.72i 0.204922 0.354934i
\(393\) −218.276 1327.06i −0.0280167 0.170334i
\(394\) 1091.75 + 1890.97i 0.139598 + 0.241791i
\(395\) 0 0
\(396\) 211.065 1054.44i 0.0267838 0.133807i
\(397\) 9014.42 1.13960 0.569800 0.821784i \(-0.307021\pi\)
0.569800 + 0.821784i \(0.307021\pi\)
\(398\) 2587.69 + 4482.01i 0.325902 + 0.564479i
\(399\) 8646.64 + 3260.32i 1.08490 + 0.409073i
\(400\) 0 0
\(401\) −5255.55 + 9102.87i −0.654487 + 1.13361i 0.327535 + 0.944839i \(0.393782\pi\)
−0.982022 + 0.188766i \(0.939551\pi\)
\(402\) −10545.7 + 8643.97i −1.30839 + 1.07244i
\(403\) −972.104 1683.73i −0.120159 0.208121i
\(404\) −267.969 −0.0329998
\(405\) 0 0
\(406\) −376.857 −0.0460667
\(407\) −352.491 610.533i −0.0429296 0.0743562i
\(408\) 8995.23 7373.12i 1.09150 0.894666i
\(409\) −1659.10 + 2873.65i −0.200580 + 0.347415i −0.948715 0.316131i \(-0.897616\pi\)
0.748135 + 0.663546i \(0.230949\pi\)
\(410\) 0 0
\(411\) −5118.57 1930.02i −0.614308 0.231632i
\(412\) 1047.03 + 1813.51i 0.125203 + 0.216857i
\(413\) 6067.11 0.722864
\(414\) 1284.20 6415.66i 0.152452 0.761625i
\(415\) 0 0
\(416\) 1635.81 + 2833.31i 0.192794 + 0.333929i
\(417\) −2010.93 12225.9i −0.236153 1.43575i
\(418\) 6273.89 10866.7i 0.734129 1.27155i
\(419\) 243.069 421.008i 0.0283406 0.0490873i −0.851507 0.524343i \(-0.824311\pi\)
0.879848 + 0.475255i \(0.157644\pi\)
\(420\) 0 0
\(421\) −2525.96 4375.10i −0.292418 0.506482i 0.681963 0.731387i \(-0.261126\pi\)
−0.974381 + 0.224904i \(0.927793\pi\)
\(422\) 15022.1 1.73286
\(423\) −11292.3 + 3818.03i −1.29799 + 0.438863i
\(424\) 12183.9 1.39553
\(425\) 0 0
\(426\) 12105.4 + 4564.48i 1.37678 + 0.519130i
\(427\) −991.230 + 1716.86i −0.112340 + 0.194578i
\(428\) −376.094 + 651.414i −0.0424747 + 0.0735684i
\(429\) 7444.70 6102.19i 0.837840 0.686752i
\(430\) 0 0
\(431\) 6944.24 0.776084 0.388042 0.921642i \(-0.373152\pi\)
0.388042 + 0.921642i \(0.373152\pi\)
\(432\) −5383.10 + 8621.89i −0.599525 + 0.960234i
\(433\) 13738.3 1.52476 0.762378 0.647131i \(-0.224032\pi\)
0.762378 + 0.647131i \(0.224032\pi\)
\(434\) −696.142 1205.75i −0.0769952 0.133360i
\(435\) 0 0
\(436\) 483.075 836.711i 0.0530622 0.0919064i
\(437\) 5166.31 8948.31i 0.565533 0.979533i
\(438\) 7321.31 + 2760.59i 0.798688 + 0.301155i
\(439\) −4240.92 7345.48i −0.461066 0.798589i 0.537949 0.842978i \(-0.319199\pi\)
−0.999014 + 0.0443883i \(0.985866\pi\)
\(440\) 0 0
\(441\) −3142.61 2762.71i −0.339338 0.298317i
\(442\) −19320.2 −2.07912
\(443\) −279.098 483.411i −0.0299330 0.0518455i 0.850671 0.525699i \(-0.176196\pi\)
−0.880604 + 0.473853i \(0.842863\pi\)
\(444\) −23.4061 142.303i −0.00250181 0.0152103i
\(445\) 0 0
\(446\) 4643.44 8042.67i 0.492989 0.853882i
\(447\) −966.707 5877.32i −0.102290 0.621896i
\(448\) −2802.34 4853.79i −0.295531 0.511875i
\(449\) 14775.0 1.55295 0.776476 0.630147i \(-0.217005\pi\)
0.776476 + 0.630147i \(0.217005\pi\)
\(450\) 0 0
\(451\) 3872.15 0.404285
\(452\) −730.449 1265.17i −0.0760120 0.131657i
\(453\) −5669.66 2137.82i −0.588044 0.221729i
\(454\) 1277.46 2212.62i 0.132058 0.228730i
\(455\) 0 0
\(456\) −10697.7 + 8768.60i −1.09861 + 0.900499i
\(457\) −7103.97 12304.4i −0.727154 1.25947i −0.958081 0.286497i \(-0.907509\pi\)
0.230927 0.972971i \(-0.425824\pi\)
\(458\) −4263.02 −0.434930
\(459\) −7187.92 13506.4i −0.730944 1.37347i
\(460\) 0 0
\(461\) 3851.26 + 6670.57i 0.389091 + 0.673925i 0.992328 0.123637i \(-0.0394558\pi\)
−0.603237 + 0.797562i \(0.706123\pi\)
\(462\) 5331.29 4369.90i 0.536870 0.440056i
\(463\) 3954.53 6849.45i 0.396939 0.687518i −0.596408 0.802682i \(-0.703406\pi\)
0.993347 + 0.115163i \(0.0367391\pi\)
\(464\) 327.304 566.908i 0.0327472 0.0567199i
\(465\) 0 0
\(466\) 4345.11 + 7525.96i 0.431939 + 0.748140i
\(467\) −11639.8 −1.15337 −0.576685 0.816967i \(-0.695654\pi\)
−0.576685 + 0.816967i \(0.695654\pi\)
\(468\) 1865.41 630.711i 0.184249 0.0622962i
\(469\) −11829.8 −1.16471
\(470\) 0 0
\(471\) −2931.11 17820.4i −0.286749 1.74336i
\(472\) −4540.77 + 7864.84i −0.442809 + 0.766967i
\(473\) 161.288 279.359i 0.0156787 0.0271563i
\(474\) 3002.65 + 18255.3i 0.290962 + 1.76897i
\(475\) 0 0
\(476\) −1872.50 −0.180307
\(477\) 3145.77 15715.7i 0.301960 1.50854i
\(478\) 5200.87 0.497662
\(479\) 9347.93 + 16191.1i 0.891687 + 1.54445i 0.837853 + 0.545897i \(0.183811\pi\)
0.0538341 + 0.998550i \(0.482856\pi\)
\(480\) 0 0
\(481\) 645.465 1117.98i 0.0611865 0.105978i
\(482\) −6589.10 + 11412.7i −0.622667 + 1.07849i
\(483\) 4390.12 3598.45i 0.413576 0.338996i
\(484\) 199.928 + 346.286i 0.0187761 + 0.0325212i
\(485\) 0 0
\(486\) 8385.77 + 7901.75i 0.782687 + 0.737512i
\(487\) 2249.54 0.209315 0.104658 0.994508i \(-0.466625\pi\)
0.104658 + 0.994508i \(0.466625\pi\)
\(488\) −1483.72 2569.88i −0.137633 0.238387i
\(489\) −8934.78 + 7323.57i −0.826267 + 0.677266i
\(490\) 0 0
\(491\) −994.175 + 1721.96i −0.0913778 + 0.158271i −0.908091 0.418773i \(-0.862460\pi\)
0.816713 + 0.577044i \(0.195794\pi\)
\(492\) 741.168 + 279.466i 0.0679155 + 0.0256084i
\(493\) 492.676 + 853.339i 0.0450081 + 0.0779563i
\(494\) 22976.9 2.09267
\(495\) 0 0
\(496\) 2418.43 0.218933
\(497\) 5612.01 + 9720.28i 0.506505 + 0.877292i
\(498\) 1087.76 + 6613.29i 0.0978790 + 0.595078i
\(499\) −1206.95 + 2090.50i −0.108278 + 0.187543i −0.915073 0.403289i \(-0.867867\pi\)
0.806795 + 0.590832i \(0.201200\pi\)
\(500\) 0 0
\(501\) −1339.20 8142.00i −0.119423 0.726063i
\(502\) −2623.10 4543.34i −0.233216 0.403942i
\(503\) 8758.56 0.776391 0.388196 0.921577i \(-0.373098\pi\)
0.388196 + 0.921577i \(0.373098\pi\)
\(504\) −7198.67 + 2433.94i −0.636219 + 0.215111i
\(505\) 0 0
\(506\) −3853.88 6675.12i −0.338589 0.586453i
\(507\) 5811.38 + 2191.25i 0.509058 + 0.191947i
\(508\) 1020.59 1767.72i 0.0891368 0.154389i
\(509\) 5924.01 10260.7i 0.515869 0.893511i −0.483961 0.875089i \(-0.660802\pi\)
0.999830 0.0184220i \(-0.00586422\pi\)
\(510\) 0 0
\(511\) 3394.13 + 5878.81i 0.293831 + 0.508930i
\(512\) 7826.64 0.675570
\(513\) 8548.36 + 16062.7i 0.735710 + 1.38243i
\(514\) −17804.1 −1.52783
\(515\) 0 0
\(516\) 51.0344 41.8313i 0.00435400 0.00356884i
\(517\) −7021.23 + 12161.1i −0.597279 + 1.03452i
\(518\) 462.230 800.606i 0.0392070 0.0679085i
\(519\) −7330.91 2764.21i −0.620022 0.233787i
\(520\) 0 0
\(521\) 3816.55 0.320933 0.160466 0.987041i \(-0.448700\pi\)
0.160466 + 0.987041i \(0.448700\pi\)
\(522\) −557.310 489.939i −0.0467295 0.0410806i
\(523\) 12158.9 1.01658 0.508288 0.861187i \(-0.330278\pi\)
0.508288 + 0.861187i \(0.330278\pi\)
\(524\) −162.049 280.676i −0.0135098 0.0233996i
\(525\) 0 0
\(526\) −596.729 + 1033.57i −0.0494651 + 0.0856761i
\(527\) −1820.17 + 3152.63i −0.150452 + 0.260590i
\(528\) 1943.37 + 11815.2i 0.160179 + 0.973846i
\(529\) 2909.97 + 5040.22i 0.239169 + 0.414253i
\(530\) 0 0
\(531\) 8972.28 + 7887.65i 0.733265 + 0.644623i
\(532\) 2226.90 0.181482
\(533\) 3545.25 + 6140.55i 0.288108 + 0.499018i
\(534\) −15252.8 5751.27i −1.23606 0.466071i
\(535\) 0 0
\(536\) 8853.71 15335.1i 0.713474 1.23577i
\(537\) −6320.00 + 5180.31i −0.507874 + 0.416289i
\(538\) −7011.72 12144.7i −0.561890 0.973222i
\(539\) −4929.26 −0.393911
\(540\) 0 0
\(541\) 14919.8 1.18568 0.592840 0.805321i \(-0.298007\pi\)
0.592840 + 0.805321i \(0.298007\pi\)
\(542\) −1757.69 3044.42i −0.139298 0.241271i
\(543\) −7974.69 + 6536.61i −0.630252 + 0.516598i
\(544\) 3062.91 5305.12i 0.241399 0.418116i
\(545\) 0 0
\(546\) 11811.1 + 4453.52i 0.925766 + 0.349072i
\(547\) −513.578 889.543i −0.0401444 0.0695322i 0.845255 0.534363i \(-0.179448\pi\)
−0.885400 + 0.464831i \(0.846115\pi\)
\(548\) −1318.27 −0.102762
\(549\) −3697.91 + 1250.30i −0.287473 + 0.0971973i
\(550\) 0 0
\(551\) −585.923 1014.85i −0.0453015 0.0784646i
\(552\) 1379.02 + 8384.10i 0.106332 + 0.646469i
\(553\) −8025.26 + 13900.2i −0.617123 + 1.06889i
\(554\) 925.313 1602.69i 0.0709617 0.122909i
\(555\) 0 0
\(556\) −1492.92 2585.81i −0.113874 0.197235i
\(557\) 10590.8 0.805648 0.402824 0.915277i \(-0.368029\pi\)
0.402824 + 0.915277i \(0.368029\pi\)
\(558\) 538.079 2688.15i 0.0408220 0.203940i
\(559\) 590.685 0.0446929
\(560\) 0 0
\(561\) −16864.8 6359.07i −1.26922 0.478574i
\(562\) 4181.23 7242.11i 0.313834 0.543576i
\(563\) −1096.03 + 1898.38i −0.0820467 + 0.142109i −0.904129 0.427260i \(-0.859479\pi\)
0.822082 + 0.569369i \(0.192812\pi\)
\(564\) −2221.64 + 1821.01i −0.165865 + 0.135955i
\(565\) 0 0
\(566\) 3107.32 0.230761
\(567\) 1280.84 + 9913.81i 0.0948684 + 0.734287i
\(568\) −16800.6 −1.24109
\(569\) 8284.89 + 14349.8i 0.610405 + 1.05725i 0.991172 + 0.132582i \(0.0423267\pi\)
−0.380767 + 0.924671i \(0.624340\pi\)
\(570\) 0 0
\(571\) −3639.66 + 6304.08i −0.266752 + 0.462027i −0.968021 0.250869i \(-0.919284\pi\)
0.701269 + 0.712896i \(0.252617\pi\)
\(572\) 1159.86 2008.93i 0.0847833 0.146849i
\(573\) −11417.7 4305.19i −0.832429 0.313878i
\(574\) 2538.82 + 4397.36i 0.184614 + 0.319760i
\(575\) 0 0
\(576\) 2166.05 10821.2i 0.156688 0.782784i
\(577\) 17938.0 1.29422 0.647112 0.762395i \(-0.275976\pi\)
0.647112 + 0.762395i \(0.275976\pi\)
\(578\) 10615.6 + 18386.8i 0.763930 + 1.32317i
\(579\) −197.484 1200.65i −0.0141747 0.0861782i
\(580\) 0 0
\(581\) −2907.29 + 5035.57i −0.207598 + 0.359571i
\(582\) −4101.03 24933.2i −0.292085 1.77580i
\(583\) −9440.42 16351.3i −0.670639 1.16158i
\(584\) −10161.0 −0.719974
\(585\) 0 0
\(586\) −15915.9 −1.12198
\(587\) 5754.83 + 9967.67i 0.404646 + 0.700868i 0.994280 0.106803i \(-0.0340613\pi\)
−0.589634 + 0.807671i \(0.700728\pi\)
\(588\) −943.509 355.762i −0.0661729 0.0249513i
\(589\) 2164.67 3749.32i 0.151433 0.262289i
\(590\) 0 0
\(591\) −2884.79 + 2364.57i −0.200785 + 0.164578i
\(592\) 802.904 + 1390.67i 0.0557418 + 0.0965476i
\(593\) 9612.80 0.665684 0.332842 0.942983i \(-0.391992\pi\)
0.332842 + 0.942983i \(0.391992\pi\)
\(594\) 13565.3 + 468.664i 0.937021 + 0.0323729i
\(595\) 0 0
\(596\) −717.684 1243.07i −0.0493247 0.0854328i
\(597\) −6837.57 + 5604.55i −0.468749 + 0.384219i
\(598\) 7057.05 12223.2i 0.482582 0.835857i
\(599\) −3686.00 + 6384.33i −0.251429 + 0.435487i −0.963919 0.266194i \(-0.914234\pi\)
0.712491 + 0.701681i \(0.247567\pi\)
\(600\) 0 0
\(601\) 12095.3 + 20949.7i 0.820927 + 1.42189i 0.904993 + 0.425427i \(0.139876\pi\)
−0.0840654 + 0.996460i \(0.526790\pi\)
\(602\) 423.001 0.0286383
\(603\) −17494.4 15379.6i −1.18147 1.03865i
\(604\) −1460.20 −0.0983684
\(605\) 0 0
\(606\) −548.956 3337.50i −0.0367984 0.223724i
\(607\) −658.866 + 1141.19i −0.0440569 + 0.0763088i −0.887213 0.461360i \(-0.847362\pi\)
0.843156 + 0.537669i \(0.180695\pi\)
\(608\) −3642.62 + 6309.20i −0.242973 + 0.420842i
\(609\) −104.485 635.242i −0.00695230 0.0422681i
\(610\) 0 0
\(611\) −25713.9 −1.70257
\(612\) −2769.13 2434.38i −0.182901 0.160791i
\(613\) 4137.52 0.272615 0.136307 0.990667i \(-0.456477\pi\)
0.136307 + 0.990667i \(0.456477\pi\)
\(614\) 7471.56 + 12941.1i 0.491087 + 0.850588i
\(615\) 0 0
\(616\) −4475.93 + 7752.54i −0.292760 + 0.507076i
\(617\) −3895.81 + 6747.74i −0.254197 + 0.440281i −0.964677 0.263436i \(-0.915144\pi\)
0.710480 + 0.703717i \(0.248478\pi\)
\(618\) −20442.0 + 16755.7i −1.33058 + 1.09064i
\(619\) −10978.2 19014.8i −0.712844 1.23468i −0.963785 0.266680i \(-0.914073\pi\)
0.250941 0.968002i \(-0.419260\pi\)
\(620\) 0 0
\(621\) 11170.5 + 385.927i 0.721831 + 0.0249384i
\(622\) 2521.18 0.162524
\(623\) −7071.17 12247.6i −0.454736 0.787625i
\(624\) −16957.5 + 13899.6i −1.08789 + 0.891712i
\(625\) 0 0
\(626\) −14048.6 + 24332.9i −0.896957 + 1.55357i
\(627\) 20056.7 + 7562.63i 1.27749 + 0.481694i
\(628\) −2176.06 3769.05i −0.138271 0.239493i
\(629\) −2417.15 −0.153224
\(630\) 0 0
\(631\) −11152.7 −0.703618 −0.351809 0.936072i \(-0.614433\pi\)
−0.351809 + 0.936072i \(0.614433\pi\)
\(632\) −12012.6 20806.4i −0.756068 1.30955i
\(633\) 4164.95 + 25321.8i 0.261520 + 1.58997i
\(634\) 13837.5 23967.2i 0.866810 1.50136i
\(635\) 0 0
\(636\) −626.861 3811.15i −0.0390828 0.237613i
\(637\) −4513.11 7816.94i −0.280716 0.486214i
\(638\) −874.155 −0.0542447
\(639\) −4337.77 + 21670.7i −0.268544 + 1.34160i
\(640\) 0 0
\(641\) −2404.72 4165.10i −0.148176 0.256648i 0.782377 0.622805i \(-0.214007\pi\)
−0.930553 + 0.366156i \(0.880674\pi\)
\(642\) −8883.71 3349.71i −0.546125 0.205923i
\(643\) −1276.51 + 2210.98i −0.0782904 + 0.135603i −0.902512 0.430664i \(-0.858279\pi\)
0.824222 + 0.566267i \(0.191613\pi\)
\(644\) 683.964 1184.66i 0.0418509 0.0724879i
\(645\) 0 0
\(646\) −21511.0 37258.2i −1.31013 2.26920i
\(647\) −8446.00 −0.513210 −0.256605 0.966516i \(-0.582604\pi\)
−0.256605 + 0.966516i \(0.582604\pi\)
\(648\) −13810.0 5759.36i −0.837201 0.349150i
\(649\) 14073.2 0.851191
\(650\) 0 0
\(651\) 1839.45 1507.74i 0.110743 0.0907727i
\(652\) −1392.01 + 2411.02i −0.0836122 + 0.144821i
\(653\) 4047.44 7010.37i 0.242555 0.420118i −0.718886 0.695128i \(-0.755348\pi\)
0.961441 + 0.275010i \(0.0886812\pi\)
\(654\) 11410.7 + 4302.55i 0.682254 + 0.257252i
\(655\) 0 0
\(656\) −8819.97 −0.524942
\(657\) −2623.47 + 13106.4i −0.155786 + 0.778280i
\(658\) −18414.2 −1.09097
\(659\) −1087.67 1883.89i −0.0642936 0.111360i 0.832087 0.554645i \(-0.187146\pi\)
−0.896380 + 0.443286i \(0.853813\pi\)
\(660\) 0 0
\(661\) 4438.47 7687.66i 0.261175 0.452368i −0.705379 0.708830i \(-0.749223\pi\)
0.966554 + 0.256462i \(0.0825567\pi\)
\(662\) 9069.64 15709.1i 0.532480 0.922282i
\(663\) −5356.62 32566.8i −0.313776 1.90768i
\(664\) −4351.77 7537.48i −0.254339 0.440529i
\(665\) 0 0
\(666\) 1724.41 583.037i 0.100329 0.0339223i
\(667\) −719.834 −0.0417872
\(668\) −994.226 1722.05i −0.0575865 0.0997427i
\(669\) 14844.4 + 5597.27i 0.857874 + 0.323472i
\(670\) 0 0
\(671\) −2299.25 + 3982.42i −0.132283 + 0.229120i
\(672\) −3095.35 + 2537.16i −0.177687 + 0.145645i
\(673\) −4583.96 7939.65i −0.262554 0.454757i 0.704366 0.709837i \(-0.251231\pi\)
−0.966920 + 0.255080i \(0.917898\pi\)
\(674\) 1815.47 0.103753
\(675\) 0 0
\(676\) 1496.70 0.0851557
\(677\) −9438.93 16348.7i −0.535846 0.928112i −0.999122 0.0418983i \(-0.986659\pi\)
0.463276 0.886214i \(-0.346674\pi\)
\(678\) 14261.2 11689.4i 0.807812 0.662139i
\(679\) 10961.0 18984.9i 0.619503 1.07301i
\(680\) 0 0
\(681\) 4083.85 + 1539.87i 0.229800 + 0.0866488i
\(682\) −1614.77 2796.86i −0.0906638 0.157034i
\(683\) 27207.5 1.52426 0.762128 0.647426i \(-0.224155\pi\)
0.762128 + 0.647426i \(0.224155\pi\)
\(684\) 3293.23 + 2895.13i 0.184094 + 0.161839i
\(685\) 0 0
\(686\) −10385.0 17987.4i −0.577991 1.00111i
\(687\) −1181.94 7185.89i −0.0656388 0.399067i
\(688\) −367.381 + 636.323i −0.0203580 + 0.0352610i
\(689\) 17286.9 29941.7i 0.955845 1.65557i
\(690\) 0 0
\(691\) 8703.62 + 15075.1i 0.479162 + 0.829934i 0.999714 0.0238963i \(-0.00760715\pi\)
−0.520552 + 0.853830i \(0.674274\pi\)
\(692\) −1888.04 −0.103718
\(693\) 8844.17 + 7775.03i 0.484794 + 0.426189i
\(694\) −13876.7 −0.759011
\(695\) 0 0
\(696\) 901.668 + 339.985i 0.0491058 + 0.0185159i
\(697\) 6638.15 11497.6i 0.360743 0.624825i
\(698\) 1026.99 1778.80i 0.0556909 0.0964595i
\(699\) −11481.3 + 9410.87i −0.621263 + 0.509230i
\(700\) 0 0
\(701\) 18543.0 0.999086 0.499543 0.866289i \(-0.333501\pi\)
0.499543 + 0.866289i \(0.333501\pi\)
\(702\) 11676.8 + 21941.3i 0.627798 + 1.17966i
\(703\) 2874.63 0.154223
\(704\) −6500.29 11258.8i −0.347996 0.602746i
\(705\) 0 0
\(706\) 5112.91 8855.81i 0.272559 0.472086i
\(707\) 1467.21 2541.28i 0.0780482 0.135184i
\(708\) 2693.76 + 1015.72i 0.142991 + 0.0539165i
\(709\) −13116.9 22719.1i −0.694803 1.20343i −0.970247 0.242117i \(-0.922158\pi\)
0.275444 0.961317i \(-0.411175\pi\)
\(710\) 0 0
\(711\) −29939.2 + 10122.7i −1.57920 + 0.533941i
\(712\) 21168.9 1.11424
\(713\) −1329.70 2303.11i −0.0698425 0.120971i
\(714\) −3835.98 23321.7i −0.201061 1.22240i
\(715\) 0 0
\(716\) −984.633 + 1705.43i −0.0513931 + 0.0890155i
\(717\) 1441.96 + 8766.76i 0.0751062 + 0.456626i
\(718\) 11713.2 + 20287.8i 0.608817 + 1.05450i
\(719\) −3043.06 −0.157840 −0.0789199 0.996881i \(-0.525147\pi\)
−0.0789199 + 0.996881i \(0.525147\pi\)
\(720\) 0 0
\(721\) −22931.2 −1.18447
\(722\) 15150.7 + 26241.8i 0.780958 + 1.35266i
\(723\) −21064.4 7942.60i −1.08353 0.408559i
\(724\) −1242.43 + 2151.95i −0.0637769 + 0.110465i
\(725\) 0 0
\(726\) −3903.37 + 3199.47i −0.199542 + 0.163559i
\(727\) 10971.2 + 19002.7i 0.559698 + 0.969426i 0.997521 + 0.0703647i \(0.0224163\pi\)
−0.437823 + 0.899061i \(0.644250\pi\)
\(728\) −16392.2 −0.834528
\(729\) −10994.5 + 16326.1i −0.558577 + 0.829453i
\(730\) 0 0
\(731\) −553.002 957.827i −0.0279802 0.0484631i
\(732\) −727.525 + 596.330i −0.0367351 + 0.0301107i
\(733\) −13288.4 + 23016.2i −0.669604 + 1.15979i 0.308411 + 0.951253i \(0.400203\pi\)
−0.978015 + 0.208535i \(0.933131\pi\)
\(734\) −8987.58 + 15566.9i −0.451959 + 0.782815i
\(735\) 0 0
\(736\) 2237.56 + 3875.57i 0.112062 + 0.194097i
\(737\) −27440.4 −1.37148
\(738\) −1962.37 + 9803.63i −0.0978803 + 0.488993i
\(739\) 28787.7 1.43298 0.716489 0.697598i \(-0.245748\pi\)
0.716489 + 0.697598i \(0.245748\pi\)
\(740\) 0 0
\(741\) 6370.45 + 38730.6i 0.315822 + 1.92011i
\(742\) 12379.5 21441.8i 0.612485 1.06086i
\(743\) −2251.51 + 3899.73i −0.111171 + 0.192553i −0.916243 0.400624i \(-0.868793\pi\)
0.805072 + 0.593177i \(0.202127\pi\)
\(744\) 577.808 + 3512.92i 0.0284724 + 0.173105i
\(745\) 0 0
\(746\) −25624.8 −1.25763
\(747\) −10846.0 + 3667.13i −0.531238 + 0.179616i
\(748\) −4343.45 −0.212316
\(749\) −4118.46 7133.38i −0.200915 0.347995i
\(750\) 0 0
\(751\) −2852.83 + 4941.24i −0.138617 + 0.240091i −0.926973 0.375128i \(-0.877599\pi\)
0.788357 + 0.615219i \(0.210932\pi\)
\(752\) 15993.0 27700.6i 0.775536 1.34327i
\(753\) 6931.13 5681.24i 0.335438 0.274948i
\(754\) −800.356 1386.26i −0.0386568 0.0669556i
\(755\) 0 0
\(756\) 1131.71 + 2126.53i 0.0544444 + 0.102303i
\(757\) −17397.6 −0.835305 −0.417652 0.908607i \(-0.637147\pi\)
−0.417652 + 0.908607i \(0.637147\pi\)
\(758\) −5338.62 9246.77i −0.255815 0.443084i
\(759\) 10183.3 8346.94i 0.486996 0.399176i
\(760\) 0 0
\(761\) 17757.2 30756.3i 0.845857 1.46507i −0.0390179 0.999239i \(-0.512423\pi\)
0.884875 0.465829i \(-0.154244\pi\)
\(762\) 24107.4 + 9090.00i 1.14609 + 0.432147i
\(763\) 5289.97 + 9162.50i 0.250996 + 0.434737i
\(764\) −2940.58 −0.139249
\(765\) 0 0
\(766\) 17435.3 0.822408
\(767\) 12885.1 + 22317.7i 0.606591 + 1.05065i
\(768\) −1584.37 9632.57i −0.0744416 0.452585i
\(769\) −15631.8 + 27075.1i −0.733027 + 1.26964i 0.222556 + 0.974920i \(0.428560\pi\)
−0.955583 + 0.294721i \(0.904773\pi\)
\(770\) 0 0
\(771\) −4936.26 30011.2i −0.230577 1.40185i
\(772\) −146.612 253.940i −0.00683508 0.0118387i
\(773\) 6676.47 0.310654 0.155327 0.987863i \(-0.450357\pi\)
0.155327 + 0.987863i \(0.450357\pi\)
\(774\) 625.551 + 549.930i 0.0290503 + 0.0255385i
\(775\) 0 0
\(776\) 16406.9 + 28417.5i 0.758985 + 1.31460i
\(777\) 1477.68 + 557.179i 0.0682260 + 0.0257254i
\(778\) 21850.7 37846.5i 1.00692 1.74404i
\(779\) −7894.53 + 13673.7i −0.363095 + 0.628898i
\(780\) 0 0
\(781\) 13017.6 + 22547.1i 0.596422 + 1.03303i
\(782\) −26427.3 −1.20849
\(783\) 671.341 1075.26i 0.0306408 0.0490761i
\(784\) 11227.9 0.511473
\(785\) 0 0
\(786\) 3163.81 2593.28i 0.143574 0.117683i
\(787\) 4716.91 8169.93i 0.213646 0.370047i −0.739207 0.673479i \(-0.764799\pi\)
0.952853 + 0.303432i \(0.0981326\pi\)
\(788\) −449.439 + 778.451i −0.0203180 + 0.0351919i
\(789\) −1907.66 719.306i −0.0860766 0.0324562i
\(790\) 0 0
\(791\) 15997.7 0.719107
\(792\) −16698.0 + 5645.75i −0.749164 + 0.253299i
\(793\) −8420.57 −0.377078
\(794\) 13709.8 + 23746.0i 0.612773 + 1.06135i
\(795\) 0 0
\(796\) −1065.27 + 1845.10i −0.0474340 + 0.0821580i
\(797\) −11738.1 + 20331.1i −0.521689 + 0.903592i 0.477992 + 0.878364i \(0.341365\pi\)
−0.999682 + 0.0252283i \(0.991969\pi\)
\(798\) 4562.00 + 27735.7i 0.202372 + 1.23037i
\(799\) 24073.4 + 41696.4i 1.06590 + 1.84620i
\(800\) 0 0
\(801\) 5465.61 27305.3i 0.241096 1.20447i
\(802\) −31972.0 −1.40769
\(803\) 7873.02 + 13636.5i 0.345993 + 0.599278i
\(804\) −5252.37 1980.47i −0.230394 0.0868729i
\(805\) 0 0
\(806\) 2956.89 5121.48i 0.129221 0.223817i
\(807\) 18527.4 15186.3i 0.808173 0.662435i
\(808\) 2196.19 + 3803.91i 0.0956208 + 0.165620i
\(809\) −33269.8 −1.44586 −0.722932 0.690919i \(-0.757206\pi\)
−0.722932 + 0.690919i \(0.757206\pi\)
\(810\) 0 0
\(811\) 27892.8 1.20771 0.603853 0.797096i \(-0.293631\pi\)
0.603853 + 0.797096i \(0.293631\pi\)
\(812\) −77.5699 134.355i −0.00335243 0.00580657i
\(813\) 4644.44 3806.91i 0.200354 0.164224i
\(814\) 1072.19 1857.08i 0.0461672 0.0799640i
\(815\) 0 0
\(816\) 38414.6 + 14484.7i 1.64801 + 0.621404i
\(817\) 657.666 + 1139.11i 0.0281626 + 0.0487790i
\(818\) −10093.1 −0.431415
\(819\) −4232.32 + 21143.9i −0.180573 + 0.902111i
\(820\) 0 0
\(821\) 1848.66 + 3201.98i 0.0785856 + 0.136114i 0.902640 0.430397i \(-0.141626\pi\)
−0.824054 + 0.566511i \(0.808293\pi\)
\(822\) −2700.58 16418.8i −0.114591 0.696680i
\(823\) 3572.25 6187.32i 0.151301 0.262061i −0.780405 0.625275i \(-0.784987\pi\)
0.931706 + 0.363213i \(0.118320\pi\)
\(824\) 17162.3 29725.9i 0.725578 1.25674i
\(825\) 0 0
\(826\) 9227.29 + 15982.1i 0.388691 + 0.673232i
\(827\) −19866.9 −0.835357 −0.417679 0.908595i \(-0.637156\pi\)
−0.417679 + 0.908595i \(0.637156\pi\)
\(828\) 2551.61 862.723i 0.107095 0.0362098i
\(829\) −36736.5 −1.53910 −0.769548 0.638589i \(-0.779518\pi\)
−0.769548 + 0.638589i \(0.779518\pi\)
\(830\) 0 0
\(831\) 2958.09 + 1115.39i 0.123484 + 0.0465611i
\(832\) 11903.0 20616.7i 0.495990 0.859079i
\(833\) −8450.38 + 14636.5i −0.351487 + 0.608793i
\(834\) 29147.5 23891.3i 1.21018 0.991952i
\(835\) 0 0
\(836\) 5165.52 0.213700
\(837\) 4680.42 + 161.703i 0.193284 + 0.00667773i
\(838\) 1478.71 0.0609560
\(839\) −15006.1 25991.4i −0.617485 1.06951i −0.989943 0.141466i \(-0.954818\pi\)
0.372458 0.928049i \(-0.378515\pi\)
\(840\) 0 0
\(841\) 12153.7 21050.8i 0.498326 0.863127i
\(842\) 7683.32 13307.9i 0.314471 0.544680i
\(843\) 13366.8 + 5040.12i 0.546117 + 0.205920i
\(844\) 3092.07 + 5355.62i 0.126106 + 0.218422i
\(845\) 0 0
\(846\) −27231.7 23939.7i −1.10667 0.972890i
\(847\) −4378.68 −0.177631
\(848\) 21503.4 + 37245.0i 0.870789 + 1.50825i
\(849\) 861.519 + 5237.80i 0.0348260 + 0.211733i
\(850\) 0 0
\(851\) 882.905 1529.24i 0.0355648 0.0616000i
\(852\) 864.391 + 5255.27i 0.0347577 + 0.211318i
\(853\) −2690.51 4660.10i −0.107997 0.187056i 0.806962 0.590604i \(-0.201110\pi\)
−0.914959 + 0.403548i \(0.867777\pi\)
\(854\) −6030.13 −0.241624
\(855\) 0 0
\(856\) 12329.4 0.492302
\(857\) 7319.88 + 12678.4i 0.291765 + 0.505352i 0.974227 0.225569i \(-0.0724242\pi\)
−0.682462 + 0.730921i \(0.739091\pi\)
\(858\) 27397.0 + 10330.4i 1.09011 + 0.411041i
\(859\) −14770.0 + 25582.4i −0.586667 + 1.01614i 0.407999 + 0.912983i \(0.366227\pi\)
−0.994665 + 0.103154i \(0.967107\pi\)
\(860\) 0 0
\(861\) −6708.44 + 5498.71i −0.265532 + 0.217649i
\(862\) 10561.3 + 18292.7i 0.417307 + 0.722797i
\(863\) −3387.63 −0.133622 −0.0668112 0.997766i \(-0.521283\pi\)
−0.0668112 + 0.997766i \(0.521283\pi\)
\(864\) −7876.00 272.106i −0.310124 0.0107144i
\(865\) 0 0
\(866\) 20894.1 + 36189.7i 0.819875 + 1.42007i
\(867\) −28050.2 + 22991.9i −1.09877 + 0.900628i
\(868\) 286.580 496.370i 0.0112064 0.0194100i
\(869\) −18615.4 + 32242.8i −0.726678 + 1.25864i
\(870\) 0 0
\(871\) −25123.8 43515.7i −0.977368 1.69285i
\(872\) −15836.5 −0.615015
\(873\) 40891.2 13825.7i 1.58529 0.536000i
\(874\) 31429.2 1.21637
\(875\) 0 0
\(876\) 522.783 + 3178.38i 0.0201635 + 0.122588i
\(877\) −122.052 + 211.400i −0.00469944 + 0.00813967i −0.868366 0.495925i \(-0.834829\pi\)
0.863666 + 0.504064i \(0.168163\pi\)
\(878\) 12899.8 22343.1i 0.495838 0.858817i
\(879\) −4412.75 26828.4i −0.169327 1.02946i
\(880\) 0 0
\(881\) 13910.2 0.531948 0.265974 0.963980i \(-0.414307\pi\)
0.265974 + 0.963980i \(0.414307\pi\)
\(882\) 2498.10 12480.1i 0.0953689 0.476446i
\(883\) 8805.87 0.335607 0.167803 0.985820i \(-0.446333\pi\)
0.167803 + 0.985820i \(0.446333\pi\)
\(884\) −3976.76 6887.95i −0.151304 0.262067i
\(885\) 0 0
\(886\) 848.943 1470.41i 0.0321905 0.0557556i
\(887\) 6640.41 11501.5i 0.251368 0.435381i −0.712535 0.701637i \(-0.752453\pi\)
0.963903 + 0.266255i \(0.0857864\pi\)
\(888\) −1828.21 + 1498.53i −0.0690885 + 0.0566298i
\(889\) 11176.1 + 19357.6i 0.421637 + 0.730296i
\(890\) 0 0
\(891\) 2971.04 + 22996.0i 0.111710 + 0.864642i
\(892\) 3823.11 0.143506
\(893\) −28629.7 49588.2i −1.07285 1.85824i
\(894\) 14011.9 11485.2i 0.524194 0.429666i
\(895\) 0 0
\(896\) 11605.0 20100.4i 0.432695 0.749449i
\(897\) 22560.4 + 8506.67i 0.839765 + 0.316644i
\(898\) 22470.9 + 38920.7i 0.835036 + 1.44633i
\(899\) −301.609 −0.0111893
\(900\) 0 0
\(901\) −64736.1 −2.39364
\(902\) 5889.04 + 10200.1i 0.217387 + 0.376526i
\(903\) 117.279 + 713.025i 0.00432204 + 0.0262768i
\(904\) −11973.1 + 20738.0i −0.440507 + 0.762981i
\(905\) 0 0
\(906\) −2991.33 18186.5i −0.109691 0.666894i
\(907\) −542.122 938.982i −0.0198466 0.0343753i 0.855932 0.517089i \(-0.172984\pi\)
−0.875778 + 0.482714i \(0.839651\pi\)
\(908\) 1051.78 0.0384411
\(909\) 5473.61 1850.68i 0.199723 0.0675281i
\(910\) 0 0
\(911\) −25094.4 43464.7i −0.912638 1.58073i −0.810324 0.585983i \(-0.800709\pi\)
−0.102314 0.994752i \(-0.532625\pi\)
\(912\) −45685.2 17226.2i −1.65876 0.625455i
\(913\) −6743.74 + 11680.5i −0.244452 + 0.423404i
\(914\) 21608.4 37426.9i 0.781995 1.35445i
\(915\) 0 0
\(916\) −877.475 1519.83i −0.0316513 0.0548216i
\(917\) 3549.06 0.127808
\(918\) 24647.0 39476.1i 0.886136 1.41929i
\(919\) 30376.1 1.09033 0.545166 0.838328i \(-0.316467\pi\)
0.545166 + 0.838328i \(0.316467\pi\)
\(920\) 0 0
\(921\) −19742.5 + 16182.3i −0.706336 + 0.578962i
\(922\) −11714.5 + 20290.2i −0.418435 + 0.724751i
\(923\) −23837.2 + 41287.2i −0.850066 + 1.47236i
\(924\) 2655.30 + 1001.21i 0.0945377 + 0.0356466i
\(925\) 0 0
\(926\) 24057.3 0.853750
\(927\) −33911.6 29812.2i −1.20151 1.05627i
\(928\) 507.534 0.0179533
\(929\) 23098.8 + 40008.3i 0.815766 + 1.41295i 0.908776 + 0.417283i \(0.137018\pi\)
−0.0930102 + 0.995665i \(0.529649\pi\)
\(930\) 0 0
\(931\) 10049.8 17406.7i 0.353778 0.612762i
\(932\) −1788.74 + 3098.20i −0.0628672 + 0.108889i
\(933\) 699.007 + 4249.78i 0.0245278 + 0.149123i
\(934\) −17702.6 30661.7i −0.620177 1.07418i
\(935\) 0 0
\(936\) −24241.5 21311.0i −0.846536 0.744201i
\(937\) −37004.7 −1.29017 −0.645085 0.764111i \(-0.723178\pi\)
−0.645085 + 0.764111i \(0.723178\pi\)
\(938\) −17991.6 31162.4i −0.626277 1.08474i
\(939\) −44911.3 16934.4i −1.56084 0.588533i
\(940\) 0 0
\(941\) −21907.2 + 37944.4i −0.758932 + 1.31451i 0.184464 + 0.982839i \(0.440945\pi\)
−0.943396 + 0.331669i \(0.892388\pi\)
\(942\) 42485.1 34823.7i 1.46947 1.20448i
\(943\) 4849.40 + 8399.41i 0.167464 + 0.290055i
\(944\) −32056.0 −1.10523
\(945\) 0 0
\(946\) 981.191 0.0337223
\(947\) 2304.86 + 3992.14i 0.0790898 + 0.136988i 0.902857 0.429940i \(-0.141465\pi\)
−0.823768 + 0.566928i \(0.808132\pi\)
\(948\) −5890.24 + 4828.05i −0.201800 + 0.165409i
\(949\) −14416.7 + 24970.5i −0.493136 + 0.854136i
\(950\) 0 0
\(951\) 44236.5 + 16679.9i 1.50838 + 0.568752i
\(952\) 15346.5 + 26580.8i 0.522460 + 0.904927i
\(953\) −4281.80 −0.145542 −0.0727708 0.997349i \(-0.523184\pi\)
−0.0727708 + 0.997349i \(0.523184\pi\)
\(954\) 46183.1 15614.9i 1.56733 0.529928i
\(955\) 0 0
\(956\) 1070.52 + 1854.19i 0.0362165 + 0.0627288i
\(957\) −242.363 1473.50i −0.00818651 0.0497718i
\(958\) −28434.0 + 49249.1i −0.958936 + 1.66093i
\(959\) 7217.91 12501.8i 0.243043 0.420963i
\(960\) 0 0
\(961\) 14338.4 + 24834.8i 0.481298 + 0.833633i
\(962\) 3926.68 0.131602
\(963\) 3183.34 15903.4i 0.106523 0.532170i
\(964\) −5425.05 −0.181254
\(965\) 0 0
\(966\) 16155.9 + 6091.79i 0.538104 + 0.202899i
\(967\) −18114.9 + 31375.9i −0.602416 + 1.04341i 0.390038 + 0.920799i \(0.372462\pi\)
−0.992454 + 0.122616i \(0.960872\pi\)
\(968\) 3277.10 5676.11i 0.108812 0.188468i
\(969\) 56839.7 46589.7i 1.88437 1.54456i
\(970\) 0 0
\(971\) 844.928 0.0279249 0.0139624 0.999903i \(-0.495555\pi\)
0.0139624 + 0.999903i \(0.495555\pi\)
\(972\) −1091.02 + 4616.10i −0.0360025 + 0.152327i
\(973\) 32696.7 1.07730
\(974\) 3421.26 + 5925.80i 0.112551 + 0.194943i
\(975\) 0 0
\(976\) 5237.24 9071.16i 0.171762 0.297501i
\(977\) 22922.5 39702.9i 0.750619 1.30011i −0.196904 0.980423i \(-0.563089\pi\)
0.947523 0.319687i \(-0.103578\pi\)
\(978\) −32880.6 12398.0i −1.07506 0.405363i
\(979\) −16402.2 28409.5i −0.535463 0.927449i
\(980\) 0 0
\(981\) −4088.85 + 20427.2i −0.133075 + 0.664821i
\(982\) −6048.05 −0.196539
\(983\) −20101.0 34815.9i −0.652210 1.12966i −0.982586 0.185811i \(-0.940509\pi\)
0.330376 0.943849i \(-0.392824\pi\)
\(984\) −2107.26 12811.6i −0.0682692 0.415059i
\(985\) 0 0
\(986\) −1498.59 + 2595.64i −0.0484025 + 0.0838356i
\(987\) −5105.42 31039.6i −0.164648 1.00101i
\(988\) 4729.43 + 8191.61i 0.152291 + 0.263775i
\(989\) 807.974 0.0259778
\(990\) 0 0
\(991\) 1797.91 0.0576313 0.0288157 0.999585i \(-0.490826\pi\)
0.0288157 + 0.999585i \(0.490826\pi\)
\(992\) 937.534 + 1623.86i 0.0300068 + 0.0519733i
\(993\) 28994.3 + 10932.7i 0.926594 + 0.349384i
\(994\) −17070.3 + 29566.6i −0.544704 + 0.943455i
\(995\) 0 0
\(996\) −2133.84 + 1749.04i −0.0678849 + 0.0556432i
\(997\) 4566.04 + 7908.61i 0.145043 + 0.251222i 0.929389 0.369102i \(-0.120335\pi\)
−0.784346 + 0.620324i \(0.787001\pi\)
\(998\) −7342.47 −0.232888
\(999\) 1460.89 + 2745.07i 0.0462667 + 0.0869370i
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 225.4.e.d.76.6 14
5.2 odd 4 225.4.k.d.49.4 28
5.3 odd 4 225.4.k.d.49.11 28
5.4 even 2 45.4.e.c.31.2 yes 14
9.4 even 3 2025.4.a.bb.1.2 7
9.5 odd 6 2025.4.a.ba.1.6 7
9.7 even 3 inner 225.4.e.d.151.6 14
15.14 odd 2 135.4.e.c.91.6 14
45.4 even 6 405.4.a.m.1.6 7
45.7 odd 12 225.4.k.d.124.11 28
45.14 odd 6 405.4.a.n.1.2 7
45.29 odd 6 135.4.e.c.46.6 14
45.34 even 6 45.4.e.c.16.2 14
45.43 odd 12 225.4.k.d.124.4 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.2 14 45.34 even 6
45.4.e.c.31.2 yes 14 5.4 even 2
135.4.e.c.46.6 14 45.29 odd 6
135.4.e.c.91.6 14 15.14 odd 2
225.4.e.d.76.6 14 1.1 even 1 trivial
225.4.e.d.151.6 14 9.7 even 3 inner
225.4.k.d.49.4 28 5.2 odd 4
225.4.k.d.49.11 28 5.3 odd 4
225.4.k.d.124.4 28 45.43 odd 12
225.4.k.d.124.11 28 45.7 odd 12
405.4.a.m.1.6 7 45.4 even 6
405.4.a.n.1.2 7 45.14 odd 6
2025.4.a.ba.1.6 7 9.5 odd 6
2025.4.a.bb.1.2 7 9.4 even 3