Properties

Label 42.4.e.c.37.2
Level $42$
Weight $4$
Character 42.37
Analytic conductor $2.478$
Analytic rank $0$
Dimension $4$
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] = [42,4,Mod(25,42)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("42.25");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 42.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: \(2.47808022024\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 337x^{2} + 336x + 112896 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.2
Root \(9.41856 - 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 42.37
Dual form 42.4.e.c.25.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.91856 - 13.7153i) q^{5} +6.00000 q^{6} +(18.3371 + 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.91856 - 13.7153i) q^{5} +6.00000 q^{6} +(18.3371 + 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(15.8371 + 27.4307i) q^{10} +(-25.9186 - 44.8923i) q^{11} +(-6.00000 + 10.3923i) q^{12} +38.8371 q^{13} +(-22.8371 + 29.1627i) q^{14} -47.5114 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-13.6742 - 23.6845i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(-38.2557 + 66.2608i) q^{19} -63.3485 q^{20} +(-20.7557 - 51.5384i) q^{21} +103.674 q^{22} +(-73.6742 + 127.608i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-62.9072 - 108.958i) q^{25} +(-38.8371 + 67.2679i) q^{26} +27.0000 q^{27} +(-27.6742 - 68.7178i) q^{28} +240.208 q^{29} +(47.5114 - 82.2921i) q^{30} +(148.337 + 256.927i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-77.7557 + 134.677i) q^{33} +54.6970 q^{34} +(180.837 - 230.927i) q^{35} +36.0000 q^{36} +(80.7670 - 139.893i) q^{37} +(-76.5114 - 132.522i) q^{38} +(-58.2557 - 100.902i) q^{39} +(63.3485 - 109.723i) q^{40} -102.977 q^{41} +(110.023 + 15.5885i) q^{42} -328.557 q^{43} +(-103.674 + 179.569i) q^{44} +(71.2670 + 123.438i) q^{45} +(-147.348 - 255.215i) q^{46} +(-33.9773 + 58.8504i) q^{47} +48.0000 q^{48} +(329.500 + 95.2825i) q^{49} +251.629 q^{50} +(-41.0227 + 71.0534i) q^{51} +(-77.6742 - 134.536i) q^{52} +(33.2443 + 57.5808i) q^{53} +(-27.0000 + 46.7654i) q^{54} -820.951 q^{55} +(146.697 + 20.7846i) q^{56} +229.534 q^{57} +(-240.208 + 416.053i) q^{58} +(230.964 + 400.041i) q^{59} +(95.0227 + 164.584i) q^{60} +(-92.6742 + 160.516i) q^{61} -593.348 q^{62} +(-102.767 + 131.232i) q^{63} +64.0000 q^{64} +(307.534 - 532.665i) q^{65} +(-155.511 - 269.354i) q^{66} +(-272.604 - 472.164i) q^{67} +(-54.6970 + 94.7379i) q^{68} +442.045 q^{69} +(219.140 + 544.146i) q^{70} -130.742 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-90.6496 - 157.010i) q^{73} +(161.534 + 279.785i) q^{74} +(-188.722 + 326.875i) q^{75} +306.045 q^{76} +(-358.638 - 890.533i) q^{77} +233.023 q^{78} +(204.848 - 354.808i) q^{79} +(126.697 + 219.446i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(102.977 - 178.362i) q^{82} +347.928 q^{83} +(-137.023 + 174.976i) q^{84} -433.121 q^{85} +(328.557 - 569.077i) q^{86} +(-360.312 - 624.080i) q^{87} +(-207.348 - 359.138i) q^{88} +(-578.580 + 1002.13i) q^{89} -285.068 q^{90} +(712.161 + 100.902i) q^{91} +589.394 q^{92} +(445.011 - 770.782i) q^{93} +(-67.9546 - 117.701i) q^{94} +(605.860 + 1049.38i) q^{95} +(-48.0000 + 83.1384i) q^{96} +1618.30 q^{97} +(-494.534 + 475.428i) q^{98} +466.534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 5 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 5 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} - 10 q^{10} - 67 q^{11} - 24 q^{12} + 82 q^{13} - 18 q^{14} + 30 q^{15} - 32 q^{16} + 92 q^{17} - 36 q^{18} - 43 q^{19} + 40 q^{20} + 27 q^{21} + 268 q^{22} - 148 q^{23} - 48 q^{24} - 435 q^{25} - 82 q^{26} + 108 q^{27} + 36 q^{28} + 154 q^{29} - 30 q^{30} + 520 q^{31} - 64 q^{32} - 201 q^{33} - 368 q^{34} + 650 q^{35} + 144 q^{36} - 7 q^{37} - 86 q^{38} - 123 q^{39} - 40 q^{40} - 852 q^{41} - 214 q^{43} - 268 q^{44} - 45 q^{45} - 296 q^{46} - 576 q^{47} + 192 q^{48} + 1318 q^{49} + 1740 q^{50} + 276 q^{51} - 164 q^{52} + 243 q^{53} - 108 q^{54} - 1010 q^{55} + 258 q^{57} - 154 q^{58} + 7 q^{59} - 60 q^{60} - 224 q^{61} - 2080 q^{62} - 81 q^{63} + 256 q^{64} + 570 q^{65} - 402 q^{66} - 687 q^{67} + 368 q^{68} + 888 q^{69} + 1390 q^{70} + 944 q^{71} - 144 q^{72} + 921 q^{73} - 14 q^{74} - 1305 q^{75} + 344 q^{76} - 371 q^{77} + 492 q^{78} + 526 q^{79} - 80 q^{80} - 162 q^{81} + 852 q^{82} - 442 q^{83} - 108 q^{84} - 5840 q^{85} + 214 q^{86} - 231 q^{87} - 536 q^{88} - 774 q^{89} + 180 q^{90} + 1345 q^{91} + 1184 q^{92} + 1560 q^{93} - 1152 q^{94} + 1910 q^{95} - 192 q^{96} + 3906 q^{97} - 1318 q^{98} + 1206 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 7.91856 13.7153i 0.708258 1.22674i −0.257245 0.966346i \(-0.582815\pi\)
0.965503 0.260392i \(-0.0838518\pi\)
\(6\) 6.00000 0.408248
\(7\) 18.3371 + 2.59808i 0.990111 + 0.140283i
\(8\) 8.00000 0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 15.8371 + 27.4307i 0.500814 + 0.867435i
\(11\) −25.9186 44.8923i −0.710431 1.23050i −0.964696 0.263368i \(-0.915167\pi\)
0.254265 0.967135i \(-0.418167\pi\)
\(12\) −6.00000 + 10.3923i −0.144338 + 0.250000i
\(13\) 38.8371 0.828575 0.414288 0.910146i \(-0.364031\pi\)
0.414288 + 0.910146i \(0.364031\pi\)
\(14\) −22.8371 + 29.1627i −0.435963 + 0.556719i
\(15\) −47.5114 −0.817825
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −13.6742 23.6845i −0.195088 0.337902i 0.751842 0.659344i \(-0.229166\pi\)
−0.946929 + 0.321442i \(0.895832\pi\)
\(18\) −9.00000 15.5885i −0.117851 0.204124i
\(19\) −38.2557 + 66.2608i −0.461919 + 0.800067i −0.999057 0.0434278i \(-0.986172\pi\)
0.537138 + 0.843494i \(0.319505\pi\)
\(20\) −63.3485 −0.708258
\(21\) −20.7557 51.5384i −0.215679 0.535552i
\(22\) 103.674 1.00470
\(23\) −73.6742 + 127.608i −0.667919 + 1.15687i 0.310566 + 0.950552i \(0.399481\pi\)
−0.978485 + 0.206318i \(0.933852\pi\)
\(24\) −12.0000 20.7846i −0.102062 0.176777i
\(25\) −62.9072 108.958i −0.503258 0.871668i
\(26\) −38.8371 + 67.2679i −0.292946 + 0.507397i
\(27\) 27.0000 0.192450
\(28\) −27.6742 68.7178i −0.186784 0.463802i
\(29\) 240.208 1.53812 0.769061 0.639175i \(-0.220724\pi\)
0.769061 + 0.639175i \(0.220724\pi\)
\(30\) 47.5114 82.2921i 0.289145 0.500814i
\(31\) 148.337 + 256.927i 0.859424 + 1.48857i 0.872480 + 0.488651i \(0.162511\pi\)
−0.0130559 + 0.999915i \(0.504156\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) −77.7557 + 134.677i −0.410167 + 0.710431i
\(34\) 54.6970 0.275896
\(35\) 180.837 230.927i 0.873344 1.11525i
\(36\) 36.0000 0.166667
\(37\) 80.7670 139.893i 0.358865 0.621573i −0.628906 0.777481i \(-0.716497\pi\)
0.987772 + 0.155908i \(0.0498304\pi\)
\(38\) −76.5114 132.522i −0.326626 0.565733i
\(39\) −58.2557 100.902i −0.239189 0.414288i
\(40\) 63.3485 109.723i 0.250407 0.433717i
\(41\) −102.977 −0.392252 −0.196126 0.980579i \(-0.562836\pi\)
−0.196126 + 0.980579i \(0.562836\pi\)
\(42\) 110.023 + 15.5885i 0.404211 + 0.0572703i
\(43\) −328.557 −1.16522 −0.582610 0.812752i \(-0.697968\pi\)
−0.582610 + 0.812752i \(0.697968\pi\)
\(44\) −103.674 + 179.569i −0.355215 + 0.615251i
\(45\) 71.2670 + 123.438i 0.236086 + 0.408913i
\(46\) −147.348 255.215i −0.472290 0.818031i
\(47\) −33.9773 + 58.8504i −0.105449 + 0.182643i −0.913921 0.405891i \(-0.866961\pi\)
0.808473 + 0.588534i \(0.200295\pi\)
\(48\) 48.0000 0.144338
\(49\) 329.500 + 95.2825i 0.960641 + 0.277791i
\(50\) 251.629 0.711714
\(51\) −41.0227 + 71.0534i −0.112634 + 0.195088i
\(52\) −77.6742 134.536i −0.207144 0.358784i
\(53\) 33.2443 + 57.5808i 0.0861596 + 0.149233i 0.905885 0.423524i \(-0.139207\pi\)
−0.819725 + 0.572757i \(0.805874\pi\)
\(54\) −27.0000 + 46.7654i −0.0680414 + 0.117851i
\(55\) −820.951 −2.01267
\(56\) 146.697 + 20.7846i 0.350057 + 0.0495975i
\(57\) 229.534 0.533378
\(58\) −240.208 + 416.053i −0.543809 + 0.941904i
\(59\) 230.964 + 400.041i 0.509643 + 0.882728i 0.999938 + 0.0111711i \(0.00355595\pi\)
−0.490294 + 0.871557i \(0.663111\pi\)
\(60\) 95.0227 + 164.584i 0.204456 + 0.354129i
\(61\) −92.6742 + 160.516i −0.194520 + 0.336919i −0.946743 0.321990i \(-0.895648\pi\)
0.752223 + 0.658909i \(0.228982\pi\)
\(62\) −593.348 −1.21541
\(63\) −102.767 + 131.232i −0.205515 + 0.262440i
\(64\) 64.0000 0.125000
\(65\) 307.534 532.665i 0.586845 1.01644i
\(66\) −155.511 269.354i −0.290032 0.502351i
\(67\) −272.604 472.164i −0.497073 0.860956i 0.502921 0.864332i \(-0.332259\pi\)
−0.999994 + 0.00337637i \(0.998925\pi\)
\(68\) −54.6970 + 94.7379i −0.0975438 + 0.168951i
\(69\) 442.045 0.771247
\(70\) 219.140 + 544.146i 0.374175 + 0.929113i
\(71\) −130.742 −0.218539 −0.109270 0.994012i \(-0.534851\pi\)
−0.109270 + 0.994012i \(0.534851\pi\)
\(72\) −36.0000 + 62.3538i −0.0589256 + 0.102062i
\(73\) −90.6496 157.010i −0.145339 0.251734i 0.784160 0.620558i \(-0.213094\pi\)
−0.929499 + 0.368824i \(0.879761\pi\)
\(74\) 161.534 + 279.785i 0.253756 + 0.439519i
\(75\) −188.722 + 326.875i −0.290556 + 0.503258i
\(76\) 306.045 0.461919
\(77\) −358.638 890.533i −0.530787 1.31800i
\(78\) 233.023 0.338264
\(79\) 204.848 354.808i 0.291737 0.505304i −0.682483 0.730901i \(-0.739100\pi\)
0.974221 + 0.225597i \(0.0724333\pi\)
\(80\) 126.697 + 219.446i 0.177064 + 0.306685i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 102.977 178.362i 0.138682 0.240205i
\(83\) 347.928 0.460121 0.230061 0.973176i \(-0.426108\pi\)
0.230061 + 0.973176i \(0.426108\pi\)
\(84\) −137.023 + 174.976i −0.177981 + 0.227280i
\(85\) −433.121 −0.552689
\(86\) 328.557 569.077i 0.411967 0.713548i
\(87\) −360.312 624.080i −0.444018 0.769061i
\(88\) −207.348 359.138i −0.251175 0.435048i
\(89\) −578.580 + 1002.13i −0.689093 + 1.19354i 0.283038 + 0.959109i \(0.408658\pi\)
−0.972132 + 0.234436i \(0.924676\pi\)
\(90\) −285.068 −0.333876
\(91\) 712.161 + 100.902i 0.820382 + 0.116235i
\(92\) 589.394 0.667919
\(93\) 445.011 770.782i 0.496188 0.859424i
\(94\) −67.9546 117.701i −0.0745636 0.129148i
\(95\) 605.860 + 1049.38i 0.654315 + 1.13331i
\(96\) −48.0000 + 83.1384i −0.0510310 + 0.0883883i
\(97\) 1618.30 1.69395 0.846976 0.531631i \(-0.178421\pi\)
0.846976 + 0.531631i \(0.178421\pi\)
\(98\) −494.534 + 475.428i −0.509750 + 0.490056i
\(99\) 466.534 0.473621
\(100\) −251.629 + 435.834i −0.251629 + 0.435834i
\(101\) −359.371 622.449i −0.354047 0.613228i 0.632907 0.774228i \(-0.281861\pi\)
−0.986954 + 0.161000i \(0.948528\pi\)
\(102\) −82.0454 142.107i −0.0796442 0.137948i
\(103\) 805.790 1395.67i 0.770843 1.33514i −0.166259 0.986082i \(-0.553169\pi\)
0.937102 0.349057i \(-0.113498\pi\)
\(104\) 310.697 0.292946
\(105\) −871.222 123.438i −0.809738 0.114727i
\(106\) −132.977 −0.121848
\(107\) −467.335 + 809.448i −0.422234 + 0.731330i −0.996158 0.0875784i \(-0.972087\pi\)
0.573924 + 0.818909i \(0.305420\pi\)
\(108\) −54.0000 93.5307i −0.0481125 0.0833333i
\(109\) 598.509 + 1036.65i 0.525934 + 0.910944i 0.999544 + 0.0302095i \(0.00961746\pi\)
−0.473610 + 0.880735i \(0.657049\pi\)
\(110\) 820.951 1421.93i 0.711587 1.23251i
\(111\) −484.602 −0.414382
\(112\) −182.697 + 233.302i −0.154136 + 0.196830i
\(113\) −2384.64 −1.98521 −0.992604 0.121400i \(-0.961262\pi\)
−0.992604 + 0.121400i \(0.961262\pi\)
\(114\) −229.534 + 397.565i −0.188578 + 0.326626i
\(115\) 1166.79 + 2020.94i 0.946118 + 1.63872i
\(116\) −480.417 832.106i −0.384531 0.666027i
\(117\) −174.767 + 302.705i −0.138096 + 0.239189i
\(118\) −923.856 −0.720744
\(119\) −189.212 469.832i −0.145757 0.361928i
\(120\) −380.091 −0.289145
\(121\) −678.044 + 1174.41i −0.509424 + 0.882349i
\(122\) −185.348 321.033i −0.137546 0.238237i
\(123\) 154.466 + 267.543i 0.113234 + 0.196126i
\(124\) 593.348 1027.71i 0.429712 0.744283i
\(125\) −12.8977 −0.00922883
\(126\) −124.534 309.230i −0.0880506 0.218638i
\(127\) −2673.92 −1.86829 −0.934143 0.356898i \(-0.883834\pi\)
−0.934143 + 0.356898i \(0.883834\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 492.835 + 853.616i 0.336370 + 0.582610i
\(130\) 615.068 + 1065.33i 0.414962 + 0.718735i
\(131\) 19.4299 33.6536i 0.0129588 0.0224453i −0.859473 0.511181i \(-0.829208\pi\)
0.872432 + 0.488735i \(0.162542\pi\)
\(132\) 622.045 0.410167
\(133\) −873.650 + 1115.64i −0.569587 + 0.727356i
\(134\) 1090.42 0.702968
\(135\) 213.801 370.314i 0.136304 0.236086i
\(136\) −109.394 189.476i −0.0689739 0.119466i
\(137\) 384.072 + 665.232i 0.239514 + 0.414851i 0.960575 0.278021i \(-0.0896784\pi\)
−0.721061 + 0.692872i \(0.756345\pi\)
\(138\) −442.045 + 765.645i −0.272677 + 0.472290i
\(139\) 1052.55 0.642274 0.321137 0.947033i \(-0.395935\pi\)
0.321137 + 0.947033i \(0.395935\pi\)
\(140\) −1161.63 164.584i −0.701254 0.0993564i
\(141\) 203.864 0.121762
\(142\) 130.742 226.453i 0.0772652 0.133827i
\(143\) −1006.60 1743.49i −0.588646 1.01956i
\(144\) −72.0000 124.708i −0.0416667 0.0721688i
\(145\) 1902.10 3294.54i 1.08939 1.88687i
\(146\) 362.598 0.205540
\(147\) −246.699 998.990i −0.138418 0.560512i
\(148\) −646.136 −0.358865
\(149\) −180.489 + 312.615i −0.0992363 + 0.171882i −0.911369 0.411591i \(-0.864973\pi\)
0.812132 + 0.583473i \(0.198307\pi\)
\(150\) −377.443 653.751i −0.205454 0.355857i
\(151\) −774.195 1340.95i −0.417239 0.722679i 0.578422 0.815738i \(-0.303669\pi\)
−0.995661 + 0.0930587i \(0.970336\pi\)
\(152\) −306.045 + 530.086i −0.163313 + 0.282866i
\(153\) 246.136 0.130058
\(154\) 1901.09 + 269.354i 0.994766 + 0.140942i
\(155\) 4698.47 2.43477
\(156\) −233.023 + 403.607i −0.119595 + 0.207144i
\(157\) 483.534 + 837.506i 0.245798 + 0.425734i 0.962356 0.271794i \(-0.0876168\pi\)
−0.716558 + 0.697528i \(0.754283\pi\)
\(158\) 409.697 + 709.616i 0.206289 + 0.357304i
\(159\) 99.7330 172.743i 0.0497443 0.0861596i
\(160\) −506.788 −0.250407
\(161\) −1682.51 + 2148.54i −0.823604 + 1.05173i
\(162\) 162.000 0.0785674
\(163\) 663.250 1148.78i 0.318710 0.552022i −0.661509 0.749937i \(-0.730084\pi\)
0.980219 + 0.197915i \(0.0634170\pi\)
\(164\) 205.955 + 356.724i 0.0980631 + 0.169850i
\(165\) 1231.43 + 2132.89i 0.581008 + 1.00634i
\(166\) −347.928 + 602.629i −0.162677 + 0.281766i
\(167\) 1416.70 0.656451 0.328225 0.944599i \(-0.393549\pi\)
0.328225 + 0.944599i \(0.393549\pi\)
\(168\) −166.045 412.307i −0.0762541 0.189346i
\(169\) −688.678 −0.313463
\(170\) 433.121 750.188i 0.195405 0.338452i
\(171\) −344.301 596.347i −0.153973 0.266689i
\(172\) 657.114 + 1138.15i 0.291305 + 0.504555i
\(173\) 518.299 897.721i 0.227778 0.394523i −0.729371 0.684118i \(-0.760187\pi\)
0.957149 + 0.289595i \(0.0935207\pi\)
\(174\) 1441.25 0.627936
\(175\) −870.454 2161.42i −0.376001 0.933647i
\(176\) 829.394 0.355215
\(177\) 692.892 1200.12i 0.294243 0.509643i
\(178\) −1157.16 2004.26i −0.487263 0.843964i
\(179\) 383.716 + 664.615i 0.160225 + 0.277518i 0.934949 0.354781i \(-0.115445\pi\)
−0.774724 + 0.632299i \(0.782111\pi\)
\(180\) 285.068 493.753i 0.118043 0.204456i
\(181\) −3957.71 −1.62527 −0.812636 0.582772i \(-0.801968\pi\)
−0.812636 + 0.582772i \(0.801968\pi\)
\(182\) −886.928 + 1132.60i −0.361228 + 0.461284i
\(183\) 556.045 0.224612
\(184\) −589.394 + 1020.86i −0.236145 + 0.409015i
\(185\) −1279.12 2215.50i −0.508338 0.880468i
\(186\) 890.023 + 1541.56i 0.350858 + 0.607704i
\(187\) −708.833 + 1227.74i −0.277193 + 0.480112i
\(188\) 271.818 0.105449
\(189\) 495.102 + 70.1481i 0.190547 + 0.0269975i
\(190\) −2423.44 −0.925341
\(191\) 902.648 1563.43i 0.341954 0.592282i −0.642841 0.765999i \(-0.722244\pi\)
0.984796 + 0.173717i \(0.0555778\pi\)
\(192\) −96.0000 166.277i −0.0360844 0.0625000i
\(193\) −1685.42 2919.23i −0.628597 1.08876i −0.987833 0.155515i \(-0.950296\pi\)
0.359237 0.933247i \(-0.383037\pi\)
\(194\) −1618.30 + 2802.98i −0.598903 + 1.03733i
\(195\) −1845.20 −0.677630
\(196\) −328.932 1331.99i −0.119873 0.485418i
\(197\) −4612.31 −1.66809 −0.834044 0.551697i \(-0.813980\pi\)
−0.834044 + 0.551697i \(0.813980\pi\)
\(198\) −466.534 + 808.061i −0.167450 + 0.290032i
\(199\) 1114.93 + 1931.12i 0.397163 + 0.687906i 0.993375 0.114921i \(-0.0366615\pi\)
−0.596212 + 0.802827i \(0.703328\pi\)
\(200\) −503.258 871.668i −0.177928 0.308181i
\(201\) −817.812 + 1416.49i −0.286985 + 0.497073i
\(202\) 1437.48 0.500698
\(203\) 4404.73 + 624.080i 1.52291 + 0.215772i
\(204\) 328.182 0.112634
\(205\) −815.432 + 1412.37i −0.277816 + 0.481191i
\(206\) 1611.58 + 2791.34i 0.545068 + 0.944086i
\(207\) −663.068 1148.47i −0.222640 0.385623i
\(208\) −310.697 + 538.143i −0.103572 + 0.179392i
\(209\) 3966.13 1.31265
\(210\) 1085.02 1385.56i 0.356541 0.455299i
\(211\) 912.614 0.297758 0.148879 0.988855i \(-0.452434\pi\)
0.148879 + 0.988855i \(0.452434\pi\)
\(212\) 132.977 230.323i 0.0430798 0.0746164i
\(213\) 196.114 + 339.679i 0.0630868 + 0.109270i
\(214\) −934.670 1618.90i −0.298564 0.517129i
\(215\) −2601.70 + 4506.27i −0.825276 + 1.42942i
\(216\) 216.000 0.0680414
\(217\) 2052.56 + 5096.70i 0.642105 + 1.59441i
\(218\) −2394.04 −0.743783
\(219\) −271.949 + 471.029i −0.0839114 + 0.145339i
\(220\) 1641.90 + 2843.86i 0.503168 + 0.871513i
\(221\) −531.068 919.837i −0.161645 0.279977i
\(222\) 484.602 839.356i 0.146506 0.253756i
\(223\) −4319.47 −1.29710 −0.648549 0.761173i \(-0.724624\pi\)
−0.648549 + 0.761173i \(0.724624\pi\)
\(224\) −221.394 549.742i −0.0660380 0.163979i
\(225\) 1132.33 0.335505
\(226\) 2384.64 4130.32i 0.701877 1.21569i
\(227\) −1030.64 1785.12i −0.301349 0.521951i 0.675093 0.737733i \(-0.264103\pi\)
−0.976442 + 0.215782i \(0.930770\pi\)
\(228\) −459.068 795.129i −0.133344 0.230959i
\(229\) 1737.32 3009.12i 0.501332 0.868333i −0.498667 0.866794i \(-0.666177\pi\)
0.999999 0.00153905i \(-0.000489896\pi\)
\(230\) −4667.15 −1.33801
\(231\) −1775.72 + 2267.57i −0.505773 + 0.645866i
\(232\) 1921.67 0.543809
\(233\) −388.049 + 672.121i −0.109107 + 0.188979i −0.915409 0.402525i \(-0.868132\pi\)
0.806302 + 0.591505i \(0.201466\pi\)
\(234\) −349.534 605.411i −0.0976485 0.169132i
\(235\) 538.102 + 932.020i 0.149370 + 0.258716i
\(236\) 923.856 1600.17i 0.254822 0.441364i
\(237\) −1229.09 −0.336869
\(238\) 1002.98 + 142.107i 0.273167 + 0.0387035i
\(239\) 2006.80 0.543133 0.271567 0.962420i \(-0.412458\pi\)
0.271567 + 0.962420i \(0.412458\pi\)
\(240\) 380.091 658.337i 0.102228 0.177064i
\(241\) −402.824 697.711i −0.107669 0.186488i 0.807157 0.590337i \(-0.201005\pi\)
−0.914825 + 0.403850i \(0.867672\pi\)
\(242\) −1356.09 2348.81i −0.360217 0.623915i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 741.394 0.194520
\(245\) 3916.00 3764.71i 1.02116 0.981707i
\(246\) −617.864 −0.160136
\(247\) −1485.74 + 2573.38i −0.382734 + 0.662915i
\(248\) 1186.70 + 2055.42i 0.303852 + 0.526287i
\(249\) −521.892 903.944i −0.132826 0.230061i
\(250\) 12.8977 22.3394i 0.00326289 0.00565148i
\(251\) 1421.78 0.357539 0.178769 0.983891i \(-0.442788\pi\)
0.178769 + 0.983891i \(0.442788\pi\)
\(252\) 660.136 + 93.5307i 0.165019 + 0.0233805i
\(253\) 7638.12 1.89804
\(254\) 2673.92 4631.37i 0.660539 1.14409i
\(255\) 649.682 + 1125.28i 0.159548 + 0.276345i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 732.909 1269.44i 0.177890 0.308114i −0.763268 0.646082i \(-0.776406\pi\)
0.941157 + 0.337968i \(0.109740\pi\)
\(258\) −1971.34 −0.475699
\(259\) 1844.49 2355.39i 0.442513 0.565084i
\(260\) −2460.27 −0.586845
\(261\) −1080.94 + 1872.24i −0.256354 + 0.444018i
\(262\) 38.8598 + 67.3072i 0.00916324 + 0.0158712i
\(263\) −3495.69 6054.72i −0.819596 1.41958i −0.905980 0.423320i \(-0.860865\pi\)
0.0863847 0.996262i \(-0.472469\pi\)
\(264\) −622.045 + 1077.41i −0.145016 + 0.251175i
\(265\) 1052.99 0.244093
\(266\) −1058.70 2628.85i −0.244033 0.605958i
\(267\) 3471.48 0.795696
\(268\) −1090.42 + 1888.66i −0.248537 + 0.430478i
\(269\) −404.479 700.578i −0.0916786 0.158792i 0.816539 0.577290i \(-0.195890\pi\)
−0.908218 + 0.418498i \(0.862557\pi\)
\(270\) 427.602 + 740.629i 0.0963816 + 0.166938i
\(271\) −3330.88 + 5769.26i −0.746630 + 1.29320i 0.202799 + 0.979220i \(0.434996\pi\)
−0.949429 + 0.313981i \(0.898337\pi\)
\(272\) 437.576 0.0975438
\(273\) −806.091 2001.60i −0.178706 0.443745i
\(274\) −1536.29 −0.338725
\(275\) −3260.93 + 5648.09i −0.715059 + 1.23852i
\(276\) −884.091 1531.29i −0.192812 0.333960i
\(277\) 3765.73 + 6522.44i 0.816827 + 1.41479i 0.908009 + 0.418951i \(0.137602\pi\)
−0.0911823 + 0.995834i \(0.529065\pi\)
\(278\) −1052.55 + 1823.07i −0.227078 + 0.393311i
\(279\) −2670.07 −0.572949
\(280\) 1446.70 1847.42i 0.308774 0.394301i
\(281\) 1690.19 0.358819 0.179410 0.983774i \(-0.442581\pi\)
0.179410 + 0.983774i \(0.442581\pi\)
\(282\) −203.864 + 353.102i −0.0430493 + 0.0745636i
\(283\) −1589.12 2752.43i −0.333792 0.578145i 0.649460 0.760396i \(-0.274995\pi\)
−0.983252 + 0.182251i \(0.941662\pi\)
\(284\) 261.485 + 452.905i 0.0546348 + 0.0946302i
\(285\) 1817.58 3148.14i 0.377769 0.654315i
\(286\) 4026.41 0.832470
\(287\) −1888.31 267.543i −0.388374 0.0550263i
\(288\) 288.000 0.0589256
\(289\) 2082.53 3607.05i 0.423882 0.734184i
\(290\) 3804.21 + 6589.08i 0.770313 + 1.33422i
\(291\) −2427.45 4204.46i −0.489002 0.846976i
\(292\) −362.598 + 628.039i −0.0726694 + 0.125867i
\(293\) −2176.53 −0.433974 −0.216987 0.976174i \(-0.569623\pi\)
−0.216987 + 0.976174i \(0.569623\pi\)
\(294\) 1977.00 + 571.695i 0.392180 + 0.113408i
\(295\) 7315.61 1.44383
\(296\) 646.136 1119.14i 0.126878 0.219759i
\(297\) −699.801 1212.09i −0.136722 0.236810i
\(298\) −360.977 625.231i −0.0701706 0.121539i
\(299\) −2861.30 + 4955.91i −0.553421 + 0.958554i
\(300\) 1509.77 0.290556
\(301\) −6024.79 853.616i −1.15370 0.163460i
\(302\) 3096.78 0.590065
\(303\) −1078.11 + 1867.35i −0.204409 + 0.354047i
\(304\) −612.091 1060.17i −0.115480 0.200017i
\(305\) 1467.69 + 2542.12i 0.275541 + 0.477250i
\(306\) −246.136 + 426.321i −0.0459826 + 0.0796442i
\(307\) 623.504 0.115913 0.0579564 0.998319i \(-0.481542\pi\)
0.0579564 + 0.998319i \(0.481542\pi\)
\(308\) −2367.62 + 3023.43i −0.438012 + 0.559337i
\(309\) −4834.74 −0.890093
\(310\) −4698.47 + 8137.98i −0.860822 + 1.49099i
\(311\) −233.996 405.293i −0.0426647 0.0738973i 0.843905 0.536493i \(-0.180251\pi\)
−0.886569 + 0.462596i \(0.846918\pi\)
\(312\) −466.045 807.214i −0.0845661 0.146473i
\(313\) −1806.41 + 3128.79i −0.326211 + 0.565014i −0.981757 0.190141i \(-0.939105\pi\)
0.655546 + 0.755156i \(0.272439\pi\)
\(314\) −1934.14 −0.347610
\(315\) 986.131 + 2448.66i 0.176388 + 0.437988i
\(316\) −1638.79 −0.291737
\(317\) −2265.87 + 3924.60i −0.401463 + 0.695355i −0.993903 0.110260i \(-0.964832\pi\)
0.592439 + 0.805615i \(0.298165\pi\)
\(318\) 199.466 + 345.485i 0.0351745 + 0.0609240i
\(319\) −6225.85 10783.5i −1.09273 1.89266i
\(320\) 506.788 877.782i 0.0885322 0.153342i
\(321\) 2804.01 0.487553
\(322\) −2038.88 5062.73i −0.352864 0.876196i
\(323\) 2092.47 0.360459
\(324\) −162.000 + 280.592i −0.0277778 + 0.0481125i
\(325\) −2443.13 4231.63i −0.416987 0.722242i
\(326\) 1326.50 + 2297.57i 0.225362 + 0.390339i
\(327\) 1795.53 3109.95i 0.303648 0.525934i
\(328\) −823.818 −0.138682
\(329\) −775.943 + 990.871i −0.130028 + 0.166044i
\(330\) −4925.70 −0.821670
\(331\) 618.528 1071.32i 0.102711 0.177901i −0.810090 0.586306i \(-0.800582\pi\)
0.912801 + 0.408405i \(0.133915\pi\)
\(332\) −695.856 1205.26i −0.115030 0.199238i
\(333\) 726.903 + 1259.03i 0.119622 + 0.207191i
\(334\) −1416.70 + 2453.79i −0.232090 + 0.401992i
\(335\) −8634.53 −1.40822
\(336\) 880.182 + 124.708i 0.142910 + 0.0202481i
\(337\) −1867.83 −0.301921 −0.150960 0.988540i \(-0.548237\pi\)
−0.150960 + 0.988540i \(0.548237\pi\)
\(338\) 688.678 1192.83i 0.110826 0.191956i
\(339\) 3576.97 + 6195.49i 0.573080 + 0.992604i
\(340\) 866.242 + 1500.38i 0.138172 + 0.239322i
\(341\) 7689.37 13318.4i 1.22112 2.11505i
\(342\) 1377.20 0.217751
\(343\) 5794.53 + 2603.27i 0.912173 + 0.409806i
\(344\) −2628.45 −0.411967
\(345\) 3500.36 6062.81i 0.546241 0.946118i
\(346\) 1036.60 + 1795.44i 0.161063 + 0.278970i
\(347\) 31.6819 + 54.8746i 0.00490136 + 0.00848940i 0.868466 0.495749i \(-0.165107\pi\)
−0.863564 + 0.504239i \(0.831773\pi\)
\(348\) −1441.25 + 2496.32i −0.222009 + 0.384531i
\(349\) 1223.79 0.187702 0.0938508 0.995586i \(-0.470082\pi\)
0.0938508 + 0.995586i \(0.470082\pi\)
\(350\) 4614.15 + 653.751i 0.704676 + 0.0998413i
\(351\) 1048.60 0.159459
\(352\) −829.394 + 1436.55i −0.125588 + 0.217524i
\(353\) 2257.81 + 3910.64i 0.340428 + 0.589638i 0.984512 0.175316i \(-0.0560949\pi\)
−0.644085 + 0.764954i \(0.722762\pi\)
\(354\) 1385.78 + 2400.25i 0.208061 + 0.360372i
\(355\) −1035.29 + 1793.18i −0.154782 + 0.268090i
\(356\) 4628.64 0.689093
\(357\) −936.841 + 1196.34i −0.138888 + 0.177358i
\(358\) −1534.86 −0.226592
\(359\) −1114.25 + 1929.93i −0.163810 + 0.283727i −0.936232 0.351383i \(-0.885712\pi\)
0.772422 + 0.635109i \(0.219045\pi\)
\(360\) 570.136 + 987.505i 0.0834690 + 0.144572i
\(361\) 502.506 + 870.365i 0.0732622 + 0.126894i
\(362\) 3957.71 6854.95i 0.574620 0.995271i
\(363\) 4068.26 0.588232
\(364\) −1074.79 2668.80i −0.154764 0.384295i
\(365\) −2871.26 −0.411749
\(366\) −556.045 + 963.099i −0.0794125 + 0.137546i
\(367\) 718.670 + 1244.77i 0.102219 + 0.177048i 0.912598 0.408857i \(-0.134072\pi\)
−0.810380 + 0.585905i \(0.800739\pi\)
\(368\) −1178.79 2041.72i −0.166980 0.289217i
\(369\) 463.398 802.628i 0.0653754 0.113234i
\(370\) 5116.47 0.718899
\(371\) 460.006 + 1142.24i 0.0643728 + 0.159844i
\(372\) −3560.09 −0.496188
\(373\) 6118.71 10597.9i 0.849370 1.47115i −0.0324014 0.999475i \(-0.510315\pi\)
0.881771 0.471677i \(-0.156351\pi\)
\(374\) −1417.67 2455.47i −0.196005 0.339490i
\(375\) 19.3465 + 33.5092i 0.00266413 + 0.00461442i
\(376\) −271.818 + 470.803i −0.0372818 + 0.0645740i
\(377\) 9329.00 1.27445
\(378\) −616.602 + 787.394i −0.0839011 + 0.107141i
\(379\) −10647.0 −1.44301 −0.721503 0.692411i \(-0.756549\pi\)
−0.721503 + 0.692411i \(0.756549\pi\)
\(380\) 2423.44 4197.52i 0.327157 0.566653i
\(381\) 4010.89 + 6947.06i 0.539328 + 0.934143i
\(382\) 1805.30 + 3126.86i 0.241798 + 0.418807i
\(383\) 3357.41 5815.20i 0.447925 0.775829i −0.550326 0.834950i \(-0.685496\pi\)
0.998251 + 0.0591208i \(0.0188297\pi\)
\(384\) 384.000 0.0510310
\(385\) −15053.9 2132.89i −1.99277 0.282344i
\(386\) 6741.68 0.888970
\(387\) 1478.51 2560.85i 0.194203 0.336370i
\(388\) −3236.60 5605.95i −0.423488 0.733503i
\(389\) 5326.54 + 9225.83i 0.694258 + 1.20249i 0.970430 + 0.241381i \(0.0776005\pi\)
−0.276173 + 0.961108i \(0.589066\pi\)
\(390\) 1845.20 3195.99i 0.239578 0.414962i
\(391\) 4029.76 0.521211
\(392\) 2636.00 + 762.260i 0.339638 + 0.0982141i
\(393\) −116.580 −0.0149635
\(394\) 4612.31 7988.76i 0.589758 1.02149i
\(395\) −3244.21 5619.14i −0.413250 0.715771i
\(396\) −933.068 1616.12i −0.118405 0.205084i
\(397\) −1610.52 + 2789.50i −0.203601 + 0.352648i −0.949686 0.313203i \(-0.898598\pi\)
0.746085 + 0.665851i \(0.231931\pi\)
\(398\) −4459.73 −0.561673
\(399\) 4208.99 + 596.347i 0.528103 + 0.0748238i
\(400\) 2013.03 0.251629
\(401\) −6242.50 + 10812.3i −0.777395 + 1.34649i 0.156043 + 0.987750i \(0.450126\pi\)
−0.933438 + 0.358738i \(0.883207\pi\)
\(402\) −1635.62 2832.99i −0.202929 0.351484i
\(403\) 5760.99 + 9978.32i 0.712097 + 1.23339i
\(404\) −1437.48 + 2489.80i −0.177024 + 0.306614i
\(405\) −1282.81 −0.157391
\(406\) −5485.67 + 7005.14i −0.670564 + 0.856303i
\(407\) −8373.46 −1.01980
\(408\) −328.182 + 568.428i −0.0398221 + 0.0689739i
\(409\) −3518.69 6094.56i −0.425399 0.736813i 0.571059 0.820909i \(-0.306533\pi\)
−0.996458 + 0.0840967i \(0.973200\pi\)
\(410\) −1630.86 2824.74i −0.196445 0.340253i
\(411\) 1152.22 1995.70i 0.138284 0.239514i
\(412\) −6446.32 −0.770843
\(413\) 3195.88 + 7935.67i 0.380772 + 0.945493i
\(414\) 2652.27 0.314860
\(415\) 2755.09 4771.95i 0.325884 0.564448i
\(416\) −621.394 1076.29i −0.0732364 0.126849i
\(417\) −1578.82 2734.60i −0.185408 0.321137i
\(418\) −3966.13 + 6869.54i −0.464090 + 0.803828i
\(419\) −1549.66 −0.180682 −0.0903410 0.995911i \(-0.528796\pi\)
−0.0903410 + 0.995911i \(0.528796\pi\)
\(420\) 1314.84 + 3264.88i 0.152756 + 0.379309i
\(421\) 5531.63 0.640369 0.320184 0.947355i \(-0.396255\pi\)
0.320184 + 0.947355i \(0.396255\pi\)
\(422\) −912.614 + 1580.69i −0.105273 + 0.182339i
\(423\) −305.795 529.653i −0.0351496 0.0608809i
\(424\) 265.955 + 460.647i 0.0304620 + 0.0527618i
\(425\) −1720.42 + 2979.85i −0.196359 + 0.340103i
\(426\) −784.454 −0.0892182
\(427\) −2116.41 + 2702.64i −0.239860 + 0.306299i
\(428\) 3738.68 0.422234
\(429\) −3019.81 + 5230.46i −0.339855 + 0.588646i
\(430\) −5203.39 9012.54i −0.583558 1.01075i
\(431\) 1014.97 + 1757.97i 0.113432 + 0.196470i 0.917152 0.398538i \(-0.130482\pi\)
−0.803720 + 0.595008i \(0.797149\pi\)
\(432\) −216.000 + 374.123i −0.0240563 + 0.0416667i
\(433\) −327.739 −0.0363744 −0.0181872 0.999835i \(-0.505789\pi\)
−0.0181872 + 0.999835i \(0.505789\pi\)
\(434\) −10880.3 1541.56i −1.20339 0.170501i
\(435\) −11412.6 −1.25792
\(436\) 2394.04 4146.60i 0.262967 0.455472i
\(437\) −5636.92 9763.43i −0.617049 1.06876i
\(438\) −543.898 942.058i −0.0593343 0.102770i
\(439\) −3954.34 + 6849.12i −0.429910 + 0.744625i −0.996865 0.0791234i \(-0.974788\pi\)
0.566955 + 0.823749i \(0.308121\pi\)
\(440\) −6567.61 −0.711587
\(441\) −2225.40 + 2139.43i −0.240298 + 0.231015i
\(442\) 2124.27 0.228600
\(443\) 1460.41 2529.51i 0.156628 0.271288i −0.777023 0.629473i \(-0.783271\pi\)
0.933651 + 0.358185i \(0.116604\pi\)
\(444\) 969.205 + 1678.71i 0.103596 + 0.179433i
\(445\) 9163.03 + 15870.8i 0.976111 + 1.69067i
\(446\) 4319.47 7481.53i 0.458593 0.794307i
\(447\) 1082.93 0.114588
\(448\) 1173.58 + 166.277i 0.123764 + 0.0175354i
\(449\) −10240.2 −1.07631 −0.538156 0.842845i \(-0.680879\pi\)
−0.538156 + 0.842845i \(0.680879\pi\)
\(450\) −1132.33 + 1961.25i −0.118619 + 0.205454i
\(451\) 2669.02 + 4622.88i 0.278668 + 0.482668i
\(452\) 4769.29 + 8260.65i 0.496302 + 0.859620i
\(453\) −2322.59 + 4022.84i −0.240893 + 0.417239i
\(454\) 4122.57 0.426171
\(455\) 7023.19 8968.54i 0.723632 0.924069i
\(456\) 1836.27 0.188578
\(457\) −2946.31 + 5103.17i −0.301582 + 0.522355i −0.976494 0.215543i \(-0.930848\pi\)
0.674913 + 0.737897i \(0.264181\pi\)
\(458\) 3474.63 + 6018.24i 0.354495 + 0.614004i
\(459\) −369.205 639.481i −0.0375446 0.0650292i
\(460\) 4667.15 8083.74i 0.473059 0.819362i
\(461\) −12643.4 −1.27735 −0.638677 0.769475i \(-0.720518\pi\)
−0.638677 + 0.769475i \(0.720518\pi\)
\(462\) −2151.83 5343.20i −0.216693 0.538070i
\(463\) 15093.2 1.51499 0.757494 0.652842i \(-0.226423\pi\)
0.757494 + 0.652842i \(0.226423\pi\)
\(464\) −1921.67 + 3328.42i −0.192265 + 0.333013i
\(465\) −7047.70 12207.0i −0.702858 1.21739i
\(466\) −776.099 1344.24i −0.0771504 0.133628i
\(467\) 1410.12 2442.39i 0.139727 0.242014i −0.787666 0.616102i \(-0.788711\pi\)
0.927393 + 0.374088i \(0.122044\pi\)
\(468\) 1398.14 0.138096
\(469\) −3772.06 9366.38i −0.371380 0.922173i
\(470\) −2152.41 −0.211241
\(471\) 1450.60 2512.52i 0.141911 0.245798i
\(472\) 1847.71 + 3200.33i 0.180186 + 0.312091i
\(473\) 8515.72 + 14749.7i 0.827808 + 1.43381i
\(474\) 1229.09 2128.85i 0.119101 0.206289i
\(475\) 9626.23 0.929856
\(476\) −1249.12 + 1595.11i −0.120280 + 0.153596i
\(477\) −598.398 −0.0574397
\(478\) −2006.80 + 3475.87i −0.192027 + 0.332600i
\(479\) 8224.25 + 14244.8i 0.784500 + 1.35879i 0.929297 + 0.369332i \(0.120414\pi\)
−0.144798 + 0.989461i \(0.546253\pi\)
\(480\) 760.182 + 1316.67i 0.0722862 + 0.125203i
\(481\) 3136.76 5433.03i 0.297347 0.515020i
\(482\) 1611.30 0.152267
\(483\) 8105.84 + 1148.47i 0.763620 + 0.108193i
\(484\) 5424.35 0.509424
\(485\) 12814.6 22195.5i 1.19975 2.07804i
\(486\) −243.000 420.888i −0.0226805 0.0392837i
\(487\) −3165.53 5482.87i −0.294546 0.510169i 0.680333 0.732903i \(-0.261835\pi\)
−0.974879 + 0.222734i \(0.928502\pi\)
\(488\) −741.394 + 1284.13i −0.0687732 + 0.119119i
\(489\) −3979.50 −0.368015
\(490\) 2604.67 + 10547.4i 0.240136 + 0.972416i
\(491\) −9286.90 −0.853588 −0.426794 0.904349i \(-0.640357\pi\)
−0.426794 + 0.904349i \(0.640357\pi\)
\(492\) 617.864 1070.17i 0.0566168 0.0980631i
\(493\) −3284.67 5689.21i −0.300069 0.519735i
\(494\) −2971.48 5146.76i −0.270634 0.468752i
\(495\) 3694.28 6398.68i 0.335445 0.581008i
\(496\) −4746.79 −0.429712
\(497\) −2397.44 339.679i −0.216378 0.0306573i
\(498\) 2087.57 0.187844
\(499\) 121.725 210.835i 0.0109202 0.0189143i −0.860514 0.509427i \(-0.829857\pi\)
0.871434 + 0.490513i \(0.163191\pi\)
\(500\) 25.7954 + 44.6789i 0.00230721 + 0.00399620i
\(501\) −2125.05 3680.69i −0.189501 0.328225i
\(502\) −1421.78 + 2462.60i −0.126409 + 0.218947i
\(503\) 8499.30 0.753409 0.376705 0.926333i \(-0.377057\pi\)
0.376705 + 0.926333i \(0.377057\pi\)
\(504\) −822.136 + 1049.86i −0.0726604 + 0.0927866i
\(505\) −11382.8 −1.00303
\(506\) −7638.12 + 13229.6i −0.671059 + 1.16231i
\(507\) 1033.02 + 1789.24i 0.0904890 + 0.156731i
\(508\) 5347.85 + 9262.75i 0.467072 + 0.808992i
\(509\) 3841.55 6653.76i 0.334526 0.579416i −0.648868 0.760901i \(-0.724757\pi\)
0.983394 + 0.181485i \(0.0580904\pi\)
\(510\) −2598.73 −0.225634
\(511\) −1254.33 3114.62i −0.108588 0.269634i
\(512\) 512.000 0.0441942
\(513\) −1032.90 + 1789.04i −0.0888963 + 0.153973i
\(514\) 1465.82 + 2538.87i 0.125787 + 0.217869i
\(515\) −12761.4 22103.4i −1.09191 1.89124i
\(516\) 1971.34 3414.46i 0.168185 0.291305i
\(517\) 3522.57 0.299656
\(518\) 2235.17 + 5550.13i 0.189590 + 0.470770i
\(519\) −3109.80 −0.263015
\(520\) 2460.27 4261.32i 0.207481 0.359368i
\(521\) 10765.3 + 18646.1i 0.905253 + 1.56794i 0.820578 + 0.571535i \(0.193652\pi\)
0.0846750 + 0.996409i \(0.473015\pi\)
\(522\) −2161.87 3744.48i −0.181270 0.313968i
\(523\) 8423.53 14590.0i 0.704274 1.21984i −0.262679 0.964883i \(-0.584606\pi\)
0.966953 0.254955i \(-0.0820606\pi\)
\(524\) −155.439 −0.0129588
\(525\) −4309.86 + 5503.64i −0.358281 + 0.457521i
\(526\) 13982.8 1.15908
\(527\) 4056.80 7026.58i 0.335326 0.580802i
\(528\) −1244.09 2154.83i −0.102542 0.177608i
\(529\) −4772.29 8265.84i −0.392232 0.679366i
\(530\) −1052.99 + 1823.83i −0.0862998 + 0.149476i
\(531\) −4157.35 −0.339762
\(532\) 5611.99 + 795.129i 0.457351 + 0.0647993i
\(533\) −3999.34 −0.325011
\(534\) −3471.48 + 6012.77i −0.281321 + 0.487263i
\(535\) 7401.24 + 12819.3i 0.598100 + 1.03594i
\(536\) −2180.83 3777.31i −0.175742 0.304394i
\(537\) 1151.15 1993.85i 0.0925059 0.160225i
\(538\) 1617.92 0.129653
\(539\) −4262.72 17261.6i −0.340646 1.37942i
\(540\) −1710.41 −0.136304
\(541\) −8720.02 + 15103.5i −0.692981 + 1.20028i 0.277875 + 0.960617i \(0.410370\pi\)
−0.970856 + 0.239662i \(0.922963\pi\)
\(542\) −6661.77 11538.5i −0.527947 0.914432i
\(543\) 5936.56 + 10282.4i 0.469175 + 0.812636i
\(544\) −437.576 + 757.903i −0.0344870 + 0.0597332i
\(545\) 18957.3 1.48999
\(546\) 4272.97 + 605.411i 0.334920 + 0.0474527i
\(547\) 11520.7 0.900530 0.450265 0.892895i \(-0.351329\pi\)
0.450265 + 0.892895i \(0.351329\pi\)
\(548\) 1536.29 2660.93i 0.119757 0.207426i
\(549\) −834.068 1444.65i −0.0648400 0.112306i
\(550\) −6521.86 11296.2i −0.505623 0.875765i
\(551\) −9189.33 + 15916.4i −0.710488 + 1.23060i
\(552\) 3536.36 0.272677
\(553\) 4678.15 5973.94i 0.359738 0.459382i
\(554\) −15062.9 −1.15517
\(555\) −3837.35 + 6646.49i −0.293489 + 0.508338i
\(556\) −2105.10 3646.14i −0.160568 0.278113i
\(557\) −5746.51 9953.25i −0.437141 0.757151i 0.560327 0.828272i \(-0.310676\pi\)
−0.997468 + 0.0711212i \(0.977342\pi\)
\(558\) 2670.07 4624.69i 0.202568 0.350858i
\(559\) −12760.2 −0.965472
\(560\) 1753.12 + 4353.17i 0.132291 + 0.328491i
\(561\) 4253.00 0.320075
\(562\) −1690.19 + 2927.49i −0.126862 + 0.219731i
\(563\) −9055.65 15684.8i −0.677886 1.17413i −0.975616 0.219483i \(-0.929563\pi\)
0.297730 0.954650i \(-0.403770\pi\)
\(564\) −407.727 706.204i −0.0304405 0.0527244i
\(565\) −18882.9 + 32706.2i −1.40604 + 2.43533i
\(566\) 6356.46 0.472053
\(567\) −560.403 1391.54i −0.0415075 0.103067i
\(568\) −1045.94 −0.0772652
\(569\) −2208.81 + 3825.77i −0.162738 + 0.281871i −0.935850 0.352399i \(-0.885366\pi\)
0.773112 + 0.634270i \(0.218699\pi\)
\(570\) 3635.16 + 6296.28i 0.267123 + 0.462670i
\(571\) −6609.87 11448.6i −0.484439 0.839073i 0.515401 0.856949i \(-0.327643\pi\)
−0.999840 + 0.0178762i \(0.994310\pi\)
\(572\) −4026.41 + 6973.95i −0.294323 + 0.509782i
\(573\) −5415.89 −0.394855
\(574\) 2351.70 3003.10i 0.171007 0.218375i
\(575\) 18538.6 1.34454
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) 8748.20 + 15152.3i 0.631182 + 1.09324i 0.987310 + 0.158803i \(0.0507634\pi\)
−0.356128 + 0.934437i \(0.615903\pi\)
\(578\) 4165.06 + 7214.10i 0.299730 + 0.519147i
\(579\) −5056.26 + 8757.70i −0.362921 + 0.628597i
\(580\) −15216.8 −1.08939
\(581\) 6380.00 + 903.944i 0.455571 + 0.0645472i
\(582\) 9709.80 0.691553
\(583\) 1723.29 2984.83i 0.122421 0.212039i
\(584\) −725.197 1256.08i −0.0513850 0.0890015i
\(585\) 2767.81 + 4793.98i 0.195615 + 0.338815i
\(586\) 2176.53 3769.87i 0.153433 0.265754i
\(587\) −4280.53 −0.300982 −0.150491 0.988611i \(-0.548085\pi\)
−0.150491 + 0.988611i \(0.548085\pi\)
\(588\) −2967.20 + 2852.57i −0.208105 + 0.200065i
\(589\) −22699.0 −1.58794
\(590\) −7315.61 + 12671.0i −0.510473 + 0.884165i
\(591\) 6918.47 + 11983.1i 0.481536 + 0.834044i
\(592\) 1292.27 + 2238.28i 0.0897164 + 0.155393i
\(593\) 795.466 1377.79i 0.0550858 0.0954114i −0.837168 0.546946i \(-0.815790\pi\)
0.892253 + 0.451535i \(0.149123\pi\)
\(594\) 2799.20 0.193355
\(595\) −7942.20 1125.28i −0.547224 0.0775329i
\(596\) 1443.91 0.0992363
\(597\) 3344.80 5793.36i 0.229302 0.397163i
\(598\) −5722.59 9911.82i −0.391328 0.677800i
\(599\) 6961.42 + 12057.5i 0.474851 + 0.822467i 0.999585 0.0287997i \(-0.00916851\pi\)
−0.524734 + 0.851266i \(0.675835\pi\)
\(600\) −1509.77 + 2615.00i −0.102727 + 0.177928i
\(601\) 12559.7 0.852446 0.426223 0.904618i \(-0.359844\pi\)
0.426223 + 0.904618i \(0.359844\pi\)
\(602\) 7503.29 9581.62i 0.507992 0.648700i
\(603\) 4906.87 0.331382
\(604\) −3096.78 + 5363.78i −0.208620 + 0.361340i
\(605\) 10738.3 + 18599.2i 0.721607 + 1.24986i
\(606\) −2156.23 3734.70i −0.144539 0.250349i
\(607\) −3839.19 + 6649.66i −0.256718 + 0.444648i −0.965361 0.260919i \(-0.915974\pi\)
0.708643 + 0.705567i \(0.249308\pi\)
\(608\) 2448.36 0.163313
\(609\) −4985.69 12379.9i −0.331741 0.823745i
\(610\) −5870.77 −0.389673
\(611\) −1319.58 + 2285.58i −0.0873723 + 0.151333i
\(612\) −492.273 852.641i −0.0325146 0.0563170i
\(613\) −3079.19 5333.31i −0.202883 0.351403i 0.746573 0.665303i \(-0.231698\pi\)
−0.949456 + 0.313900i \(0.898364\pi\)
\(614\) −623.504 + 1079.94i −0.0409814 + 0.0709818i
\(615\) 4892.59 0.320794
\(616\) −2869.11 7124.27i −0.187662 0.465982i
\(617\) 8813.12 0.575045 0.287523 0.957774i \(-0.407168\pi\)
0.287523 + 0.957774i \(0.407168\pi\)
\(618\) 4834.74 8374.01i 0.314695 0.545068i
\(619\) −11595.0 20083.1i −0.752894 1.30405i −0.946415 0.322954i \(-0.895324\pi\)
0.193521 0.981096i \(-0.438009\pi\)
\(620\) −9396.93 16276.0i −0.608693 1.05429i
\(621\) −1989.20 + 3445.40i −0.128541 + 0.222640i
\(622\) 935.985 0.0603369
\(623\) −13213.1 + 16873.0i −0.849713 + 1.08507i
\(624\) 1864.18 0.119595
\(625\) 7761.27 13442.9i 0.496721 0.860346i
\(626\) −3612.81 6257.57i −0.230666 0.399525i
\(627\) −5949.19 10304.3i −0.378928 0.656323i
\(628\) 1934.14 3350.02i 0.122899 0.212867i
\(629\) −4417.71 −0.280041
\(630\) −5227.33 740.629i −0.330574 0.0468371i
\(631\) 7936.94 0.500736 0.250368 0.968151i \(-0.419448\pi\)
0.250368 + 0.968151i \(0.419448\pi\)
\(632\) 1638.79 2838.46i 0.103145 0.178652i
\(633\) −1368.92 2371.04i −0.0859553 0.148879i
\(634\) −4531.74 7849.20i −0.283877 0.491690i
\(635\) −21173.6 + 36673.8i −1.32323 + 2.29190i
\(636\) −797.864 −0.0497443
\(637\) 12796.8 + 3700.50i 0.795964 + 0.230171i
\(638\) 24903.4 1.54535
\(639\) 588.341 1019.04i 0.0364232 0.0630868i
\(640\) 1013.58 + 1755.56i 0.0626017 + 0.108429i
\(641\) −16057.3 27812.1i −0.989432 1.71375i −0.620286 0.784376i \(-0.712984\pi\)
−0.369146 0.929371i \(-0.620350\pi\)
\(642\) −2804.01 + 4856.69i −0.172376 + 0.298564i
\(643\) −24786.7 −1.52021 −0.760104 0.649802i \(-0.774852\pi\)
−0.760104 + 0.649802i \(0.774852\pi\)
\(644\) 10807.8 + 1531.29i 0.661314 + 0.0936977i
\(645\) 15610.2 0.952946
\(646\) −2092.47 + 3624.26i −0.127441 + 0.220735i
\(647\) −3772.80 6534.67i −0.229249 0.397070i 0.728337 0.685219i \(-0.240294\pi\)
−0.957586 + 0.288149i \(0.906960\pi\)
\(648\) −324.000 561.184i −0.0196419 0.0340207i
\(649\) 11972.5 20737.0i 0.724133 1.25423i
\(650\) 9772.54 0.589708
\(651\) 10162.8 12977.8i 0.611844 0.781318i
\(652\) −5306.00 −0.318710
\(653\) 2444.49 4233.99i 0.146494 0.253735i −0.783435 0.621473i \(-0.786534\pi\)
0.929929 + 0.367738i \(0.119868\pi\)
\(654\) 3591.06 + 6219.89i 0.214712 + 0.371892i
\(655\) −307.714 532.976i −0.0183563 0.0317941i
\(656\) 823.818 1426.89i 0.0490316 0.0849251i
\(657\) 1631.69 0.0968926
\(658\) −940.295 2334.84i −0.0557090 0.138331i
\(659\) 25895.9 1.53075 0.765374 0.643586i \(-0.222554\pi\)
0.765374 + 0.643586i \(0.222554\pi\)
\(660\) 4925.70 8531.57i 0.290504 0.503168i
\(661\) −4091.68 7087.00i −0.240769 0.417023i 0.720165 0.693803i \(-0.244066\pi\)
−0.960933 + 0.276780i \(0.910733\pi\)
\(662\) 1237.06 + 2142.65i 0.0726278 + 0.125795i
\(663\) −1593.20 + 2759.51i −0.0933257 + 0.161645i
\(664\) 2783.42 0.162677
\(665\) 8383.36 + 20816.7i 0.488861 + 1.21389i
\(666\) −2907.61 −0.169171
\(667\) −17697.2 + 30652.4i −1.02734 + 1.77941i
\(668\) −2833.39 4907.58i −0.164113 0.284252i
\(669\) 6479.20 + 11222.3i 0.374440 + 0.648549i
\(670\) 8634.53 14955.4i 0.497882 0.862357i
\(671\) 9607.93 0.552772
\(672\) −1096.18 + 1399.81i −0.0629258 + 0.0803555i
\(673\) −4635.02 −0.265478 −0.132739 0.991151i \(-0.542377\pi\)
−0.132739 + 0.991151i \(0.542377\pi\)
\(674\) 1867.83 3235.18i 0.106745 0.184888i
\(675\) −1698.49 2941.88i −0.0968520 0.167753i
\(676\) 1377.36 + 2385.65i 0.0783657 + 0.135733i
\(677\) 12192.9 21118.7i 0.692187 1.19890i −0.278932 0.960311i \(-0.589980\pi\)
0.971120 0.238593i \(-0.0766862\pi\)
\(678\) −14307.9 −0.810458
\(679\) 29674.9 + 4204.46i 1.67720 + 0.237633i
\(680\) −3464.97 −0.195405
\(681\) −3091.93 + 5355.37i −0.173984 + 0.301349i
\(682\) 15378.7 + 26636.8i 0.863464 + 1.49556i
\(683\) 9196.71 + 15929.2i 0.515230 + 0.892405i 0.999844 + 0.0176767i \(0.00562697\pi\)
−0.484613 + 0.874728i \(0.661040\pi\)
\(684\) −1377.20 + 2385.39i −0.0769864 + 0.133344i
\(685\) 12165.2 0.678552
\(686\) −10303.5 + 7433.15i −0.573456 + 0.413701i
\(687\) −10423.9 −0.578889
\(688\) 2628.45 4552.62i 0.145652 0.252277i
\(689\) 1291.11 + 2236.27i 0.0713897 + 0.123651i
\(690\) 7000.73 + 12125.6i 0.386251 + 0.669006i
\(691\) 7449.44 12902.8i 0.410116 0.710341i −0.584786 0.811187i \(-0.698822\pi\)
0.994902 + 0.100846i \(0.0321550\pi\)
\(692\) −4146.39 −0.227778
\(693\) 8554.89 + 1212.09i 0.468937 + 0.0664409i
\(694\) −126.727 −0.00693157
\(695\) 8334.67 14436.1i 0.454895 0.787902i
\(696\) −2882.50 4992.64i −0.156984 0.271904i
\(697\) 1408.14 + 2438.96i 0.0765236 + 0.132543i
\(698\) −1223.79 + 2119.66i −0.0663625 + 0.114943i
\(699\) 2328.30 0.125986
\(700\) −5746.48 + 7338.19i −0.310281 + 0.396225i
\(701\) −5725.70 −0.308497 −0.154249 0.988032i \(-0.549296\pi\)
−0.154249 + 0.988032i \(0.549296\pi\)
\(702\) −1048.60 + 1816.23i −0.0563774 + 0.0976485i
\(703\) 6179.60 + 10703.4i 0.331533 + 0.574232i
\(704\) −1658.79 2873.10i −0.0888039 0.153813i
\(705\) 1614.31 2796.06i 0.0862387 0.149370i
\(706\) −9031.23 −0.481437
\(707\) −4972.66 12347.6i −0.264521 0.656831i
\(708\) −5543.14 −0.294243
\(709\) 11728.4 20314.2i 0.621255 1.07604i −0.367998 0.929827i \(-0.619957\pi\)
0.989252 0.146218i \(-0.0467101\pi\)
\(710\) −2070.58 3586.36i −0.109447 0.189568i
\(711\) 1843.64 + 3193.27i 0.0972458 + 0.168435i
\(712\) −4628.64 + 8017.03i −0.243631 + 0.421982i
\(713\) −43714.5 −2.29610
\(714\) −1135.27 2818.99i −0.0595049 0.147756i
\(715\) −31883.4 −1.66765
\(716\) 1534.86 2658.46i 0.0801125 0.138759i
\(717\) −3010.19 5213.81i −0.156789 0.271567i
\(718\) −2228.49 3859.86i −0.115831 0.200625i
\(719\) 4229.50 7325.71i 0.219379 0.379976i −0.735239 0.677808i \(-0.762930\pi\)
0.954618 + 0.297832i \(0.0962634\pi\)
\(720\) −2280.55 −0.118043
\(721\) 18401.9 23499.0i 0.950518 1.21380i
\(722\) −2010.02 −0.103608
\(723\) −1208.47 + 2093.13i −0.0621626 + 0.107669i
\(724\) 7915.42 + 13709.9i 0.406318 + 0.703763i
\(725\) −15110.8 26172.7i −0.774072 1.34073i
\(726\) −4068.26 + 7046.44i −0.207972 + 0.360217i
\(727\) −11822.2 −0.603111 −0.301555 0.953449i \(-0.597506\pi\)
−0.301555 + 0.953449i \(0.597506\pi\)
\(728\) 5697.29 + 807.214i 0.290049 + 0.0410953i
\(729\) 729.000 0.0370370
\(730\) 2871.26 4973.16i 0.145575 0.252144i
\(731\) 4492.77 + 7781.70i 0.227320 + 0.393730i
\(732\) −1112.09 1926.20i −0.0561531 0.0972600i
\(733\) −2514.48 + 4355.20i −0.126704 + 0.219458i −0.922398 0.386241i \(-0.873773\pi\)
0.795694 + 0.605699i \(0.207107\pi\)
\(734\) −2874.68 −0.144559
\(735\) −15655.0 4527.00i −0.785637 0.227185i
\(736\) 4715.15 0.236145
\(737\) −14131.0 + 24475.6i −0.706272 + 1.22330i
\(738\) 926.795 + 1605.26i 0.0462274 + 0.0800682i
\(739\) 8871.95 + 15366.7i 0.441624 + 0.764914i 0.997810 0.0661431i \(-0.0210694\pi\)
−0.556187 + 0.831057i \(0.687736\pi\)
\(740\) −5116.47 + 8861.99i −0.254169 + 0.440234i
\(741\) 8914.44 0.441944
\(742\) −2438.42 345.485i −0.120643 0.0170932i
\(743\) −13202.3 −0.651877 −0.325938 0.945391i \(-0.605680\pi\)
−0.325938 + 0.945391i \(0.605680\pi\)
\(744\) 3560.09 6166.26i 0.175429 0.303852i
\(745\) 2858.42 + 4950.93i 0.140570 + 0.243474i
\(746\) 12237.4 + 21195.8i 0.600595 + 1.04026i
\(747\) −1565.68 + 2711.83i −0.0766869 + 0.132826i
\(748\) 5670.67 0.277193
\(749\) −10672.6 + 13628.8i −0.520652 + 0.664866i
\(750\) −77.3861 −0.00376766
\(751\) −7800.49 + 13510.8i −0.379020 + 0.656482i −0.990920 0.134453i \(-0.957072\pi\)
0.611900 + 0.790935i \(0.290406\pi\)
\(752\) −543.636 941.606i −0.0263622 0.0456607i
\(753\) −2132.68 3693.90i −0.103213 0.178769i
\(754\) −9329.00 + 16158.3i −0.450586 + 0.780439i
\(755\) −24522.0 −1.18205
\(756\) −747.205 1855.38i −0.0359465 0.0892587i
\(757\) 2948.08 0.141545 0.0707725 0.997492i \(-0.477454\pi\)
0.0707725 + 0.997492i \(0.477454\pi\)
\(758\) 10647.0 18441.1i 0.510180 0.883657i
\(759\) −11457.2 19844.4i −0.547917 0.949021i
\(760\) 4846.88 + 8395.04i 0.231335 + 0.400684i
\(761\) −848.515 + 1469.67i −0.0404187 + 0.0700073i −0.885527 0.464588i \(-0.846203\pi\)
0.845108 + 0.534595i \(0.179536\pi\)
\(762\) −16043.5 −0.762725
\(763\) 8281.65 + 20564.1i 0.392943 + 0.975716i
\(764\) −7221.18 −0.341954
\(765\) 1949.05 3375.85i 0.0921149 0.159548i
\(766\) 6714.81 + 11630.4i 0.316731 + 0.548594i
\(767\) 8969.98 + 15536.5i 0.422278 + 0.731407i
\(768\) −384.000 + 665.108i −0.0180422 + 0.0312500i
\(769\) −96.7799 −0.00453833 −0.00226916 0.999997i \(-0.500722\pi\)
−0.00226916 + 0.999997i \(0.500722\pi\)
\(770\) 18748.2 23941.2i 0.877450 1.12049i
\(771\) −4397.45 −0.205409
\(772\) −6741.68 + 11676.9i −0.314298 + 0.544381i
\(773\) −18163.4 31459.9i −0.845138 1.46382i −0.885501 0.464637i \(-0.846185\pi\)
0.0403629 0.999185i \(-0.487149\pi\)
\(774\) 2957.01 + 5121.69i 0.137322 + 0.237849i
\(775\) 18662.9 32325.2i 0.865023 1.49826i
\(776\) 12946.4 0.598903
\(777\) −8886.21 1259.03i −0.410284 0.0581307i
\(778\) −21306.2 −0.981828
\(779\) 3939.47 6823.35i 0.181189 0.313828i
\(780\) 3690.41 + 6391.98i 0.169407 + 0.293422i
\(781\) 3388.66 + 5869.32i 0.155257 + 0.268913i
\(782\) −4029.76 + 6979.74i −0.184276 + 0.319175i
\(783\) 6485.62 0.296012
\(784\) −3956.27 + 3803.43i −0.180224 + 0.173261i
\(785\) 15315.6 0.696352
\(786\) 116.580 201.922i 0.00529040 0.00916324i
\(787\) −3548.23 6145.72i −0.160713 0.278362i 0.774412 0.632682i \(-0.218046\pi\)
−0.935124 + 0.354319i \(0.884713\pi\)
\(788\) 9224.62 + 15977.5i 0.417022 + 0.722304i
\(789\) −10487.1 + 18164.2i −0.473194 + 0.819596i
\(790\) 12976.8 0.584424
\(791\) −43727.5 6195.49i −1.96558 0.278491i
\(792\) 3732.27 0.167450
\(793\) −3599.20 + 6234.00i −0.161174 + 0.279162i
\(794\) −3221.04 5579.01i −0.143968 0.249360i
\(795\) −1579.48 2735.74i −0.0704635 0.122046i
\(796\) 4459.73 7724.47i 0.198581 0.343953i
\(797\) 40289.6 1.79063 0.895314 0.445436i \(-0.146951\pi\)
0.895314 + 0.445436i \(0.146951\pi\)
\(798\) −5241.90 + 6693.84i −0.232533 + 0.296942i
\(799\) 1858.45 0.0822871
\(800\) −2013.03 + 3486.67i −0.0889642 + 0.154091i
\(801\) −5207.22 9019.16i −0.229698 0.397848i
\(802\) −12485.0 21624.7i −0.549702 0.952111i
\(803\) −4699.02 + 8138.93i −0.206506 + 0.357680i
\(804\) 6542.50 0.286985
\(805\) 16145.0 + 40089.5i 0.706877 + 1.75524i
\(806\) −23043.9 −1.00706
\(807\) −1213.44 + 2101.74i −0.0529306 + 0.0916786i
\(808\) −2874.97 4979.59i −0.125175 0.216809i
\(809\) 5782.98 + 10016.4i 0.251321 + 0.435301i 0.963890 0.266301i \(-0.0858017\pi\)
−0.712569 + 0.701602i \(0.752468\pi\)
\(810\) 1282.81 2221.89i 0.0556460 0.0963816i
\(811\) 18014.2 0.779981 0.389991 0.920819i \(-0.372478\pi\)
0.389991 + 0.920819i \(0.372478\pi\)
\(812\) −6647.58 16506.6i −0.287296 0.713384i
\(813\) 19985.3 0.862134
\(814\) 8373.46 14503.3i 0.360552 0.624495i
\(815\) −10504.0 18193.4i −0.451458 0.781948i
\(816\) −656.364 1136.86i −0.0281585 0.0487719i
\(817\) 12569.2 21770.4i 0.538237 0.932253i
\(818\) 14074.8 0.601605
\(819\) −3991.18 + 5096.69i −0.170284 + 0.217451i
\(820\) 6523.45 0.277816
\(821\) 8396.22 14542.7i 0.356918 0.618201i −0.630526 0.776168i \(-0.717161\pi\)
0.987444 + 0.157967i \(0.0504941\pi\)
\(822\) 2304.43 + 3991.39i 0.0977814 + 0.169362i
\(823\) 4409.52 + 7637.50i 0.186763 + 0.323483i 0.944169 0.329461i \(-0.106867\pi\)
−0.757406 + 0.652944i \(0.773534\pi\)
\(824\) 6446.32 11165.4i 0.272534 0.472043i
\(825\) 19565.6 0.825680
\(826\) −16940.9 2400.25i −0.713617 0.101108i
\(827\) 8250.13 0.346898 0.173449 0.984843i \(-0.444509\pi\)
0.173449 + 0.984843i \(0.444509\pi\)
\(828\) −2652.27 + 4593.87i −0.111320 + 0.192812i
\(829\) 10775.2 + 18663.3i 0.451435 + 0.781909i 0.998475 0.0551975i \(-0.0175789\pi\)
−0.547040 + 0.837106i \(0.684246\pi\)
\(830\) 5510.18 + 9543.91i 0.230435 + 0.399125i
\(831\) 11297.2 19567.3i 0.471595 0.816827i
\(832\) 2485.58 0.103572
\(833\) −2248.95 9106.95i −0.0935431 0.378796i
\(834\) 6315.30 0.262207
\(835\) 11218.2 19430.5i 0.464936 0.805293i
\(836\) −7932.26 13739.1i −0.328161 0.568392i
\(837\) 4005.10 + 6937.04i 0.165396 + 0.286475i
\(838\) 1549.66 2684.09i 0.0638808 0.110645i
\(839\) 30130.4 1.23983 0.619916 0.784669i \(-0.287167\pi\)
0.619916 + 0.784669i \(0.287167\pi\)
\(840\) −6969.77 987.505i −0.286286 0.0405621i
\(841\) 33311.0 1.36582
\(842\) −5531.63 + 9581.07i −0.226405 + 0.392144i
\(843\) −2535.28 4391.24i −0.103582 0.179410i
\(844\) −1825.23 3161.39i −0.0744395 0.128933i
\(845\) −5453.34 + 9445.46i −0.222012 + 0.384537i
\(846\) 1223.18 0.0497091
\(847\) −15484.6 + 19773.6i −0.628165 + 0.802160i
\(848\) −1063.82 −0.0430798
\(849\) −4767.35 + 8257.29i −0.192715 + 0.333792i
\(850\) −3440.83 5959.70i −0.138847 0.240489i
\(851\) 11900.9 + 20613.0i 0.479386 + 0.830321i
\(852\) 784.454 1358.72i 0.0315434 0.0546348i
\(853\) −40738.6 −1.63525 −0.817623 0.575754i \(-0.804709\pi\)
−0.817623 + 0.575754i \(0.804709\pi\)
\(854\) −2564.69 6368.37i −0.102766 0.255177i
\(855\) −10905.5 −0.436210
\(856\) −3738.68 + 6475.59i −0.149282 + 0.258564i
\(857\) 18254.1 + 31617.0i 0.727594 + 1.26023i 0.957897 + 0.287111i \(0.0926949\pi\)
−0.230303 + 0.973119i \(0.573972\pi\)
\(858\) −6039.61 10460.9i −0.240314 0.416235i
\(859\) 10990.4 19036.0i 0.436541 0.756110i −0.560879 0.827897i \(-0.689537\pi\)
0.997420 + 0.0717871i \(0.0228702\pi\)
\(860\) 20813.6 0.825276
\(861\) 2137.36 + 5307.28i 0.0846006 + 0.210072i
\(862\) −4059.86 −0.160417
\(863\) 11713.0 20287.6i 0.462012 0.800228i −0.537049 0.843551i \(-0.680461\pi\)
0.999061 + 0.0433226i \(0.0137943\pi\)
\(864\) −432.000 748.246i −0.0170103 0.0294628i
\(865\) −8208.37 14217.3i −0.322651 0.558847i
\(866\) 327.739 567.660i 0.0128603 0.0222747i
\(867\) −12495.2 −0.489456
\(868\) 13550.4 17303.7i 0.529873 0.676642i
\(869\) −21237.5 −0.829037
\(870\) 11412.6 19767.2i 0.444740 0.770313i
\(871\) −10587.2 18337.5i −0.411863 0.713367i
\(872\) 4788.08 + 8293.19i 0.185946 + 0.322068i
\(873\) −7282.35 + 12613.4i −0.282325 + 0.489002i
\(874\) 22547.7 0.872639
\(875\) −236.506 33.5092i −0.00913757 0.00129465i
\(876\) 2175.59 0.0839114
\(877\) −153.701 + 266.217i −0.00591802 + 0.0102503i −0.868969 0.494866i \(-0.835217\pi\)
0.863051 + 0.505116i \(0.168550\pi\)
\(878\) −7908.68 13698.2i −0.303992 0.526530i
\(879\) 3264.80 + 5654.80i 0.125278 + 0.216987i
\(880\) 6567.61 11375.4i 0.251584 0.435756i
\(881\) −19941.7 −0.762605 −0.381302 0.924450i \(-0.624524\pi\)
−0.381302 + 0.924450i \(0.624524\pi\)
\(882\) −1480.19 5993.94i −0.0565087 0.228828i
\(883\) −37524.1 −1.43011 −0.715056 0.699068i \(-0.753599\pi\)
−0.715056 + 0.699068i \(0.753599\pi\)
\(884\) −2124.27 + 3679.35i −0.0808224 + 0.139989i
\(885\) −10973.4 19006.5i −0.416799 0.721917i
\(886\) 2920.82 + 5059.01i 0.110753 + 0.191829i
\(887\) 1440.10 2494.33i 0.0545140 0.0944210i −0.837481 0.546467i \(-0.815972\pi\)
0.891995 + 0.452046i \(0.149306\pi\)
\(888\) −3876.82 −0.146506
\(889\) −49032.1 6947.06i −1.84981 0.262089i
\(890\) −36652.1 −1.38043
\(891\) −2099.40 + 3636.27i −0.0789368 + 0.136722i
\(892\) 8638.93 + 14963.1i 0.324274 + 0.561660i
\(893\) −2599.65 4502.72i −0.0974176 0.168732i
\(894\) −1082.93 + 1875.69i −0.0405130 + 0.0701706i
\(895\) 12153.9 0.453922
\(896\) −1461.58 + 1866.42i −0.0544953 + 0.0695899i
\(897\) 17167.8 0.639036
\(898\) 10240.2 17736.5i 0.380534 0.659104i
\(899\) 35631.8 + 61716.1i 1.32190 + 2.28960i
\(900\) −2264.66 3922.50i −0.0838763 0.145278i
\(901\) 909.182 1574.75i 0.0336174 0.0582270i
\(902\) −10676.1 −0.394096
\(903\) 6819.42 + 16933.3i 0.251314 + 0.624036i
\(904\) −19077.2 −0.701877
\(905\) −31339.4 + 54281.4i −1.15111 + 1.99378i
\(906\) −4645.17 8045.67i −0.170337 0.295033i
\(907\) −9159.62 15864.9i −0.335326 0.580801i 0.648222 0.761452i \(-0.275513\pi\)
−0.983547 + 0.180651i \(0.942180\pi\)
\(908\) −4122.57 + 7140.50i −0.150674 + 0.260975i
\(909\) 6468.68 0.236031
\(910\) 8510.77 + 21133.1i 0.310032 + 0.769840i
\(911\) 46150.7 1.67842 0.839210 0.543807i \(-0.183018\pi\)
0.839210 + 0.543807i \(0.183018\pi\)
\(912\) −1836.27 + 3180.52i −0.0666722 + 0.115480i
\(913\) −9017.79 15619.3i −0.326884 0.566180i
\(914\) −5892.63 10206.3i −0.213250 0.369360i
\(915\) 4403.08 7626.36i 0.159083 0.275541i
\(916\) −13898.5 −0.501332
\(917\) 443.723 566.630i 0.0159793 0.0204054i
\(918\) 1476.82 0.0530961
\(919\) −23632.1 + 40932.1i −0.848261 + 1.46923i 0.0344969 + 0.999405i \(0.489017\pi\)
−0.882758 + 0.469827i \(0.844316\pi\)
\(920\) 9334.30 + 16167.5i 0.334503 + 0.579376i
\(921\) −935.256 1619.91i −0.0334612 0.0579564i
\(922\) 12643.4 21899.0i 0.451613 0.782217i
\(923\) −5077.66 −0.181076
\(924\) 11406.5 + 1616.12i 0.406112 + 0.0575395i
\(925\) −20323.3 −0.722407
\(926\) −15093.2 + 26142.2i −0.535629 + 0.927737i
\(927\) 7252.11 + 12561.0i 0.256948 + 0.445046i
\(928\) −3843.33 6656.85i −0.135952 0.235476i
\(929\) 26635.7 46134.4i 0.940678 1.62930i 0.176496 0.984301i \(-0.443524\pi\)
0.764182 0.645001i \(-0.223143\pi\)
\(930\) 28190.8 0.993992
\(931\) −18918.7 + 18187.8i −0.665990 + 0.640260i
\(932\) 3104.39 0.109107
\(933\) −701.989 + 1215.88i −0.0246324 + 0.0426647i
\(934\) 2820.23 + 4884.79i 0.0988018 + 0.171130i
\(935\) 11225.9 + 19443.8i 0.392648 + 0.680086i
\(936\) −1398.14 + 2421.64i −0.0488243 + 0.0845661i
\(937\) 17197.8 0.599602 0.299801 0.954002i \(-0.403080\pi\)
0.299801 + 0.954002i \(0.403080\pi\)
\(938\) 19995.1 + 2832.99i 0.696016 + 0.0986143i
\(939\) 10838.4 0.376676
\(940\) 2152.41 3728.08i 0.0746849 0.129358i
\(941\) −14417.4 24971.7i −0.499463 0.865096i 0.500537 0.865715i \(-0.333136\pi\)
−1.00000 0.000619696i \(0.999803\pi\)
\(942\) 2901.20 + 5025.03i 0.100346 + 0.173805i
\(943\) 7586.77 13140.7i 0.261993 0.453785i
\(944\) −7390.85 −0.254822
\(945\) 4882.60 6235.03i 0.168075 0.214630i
\(946\) −34062.9 −1.17070
\(947\) 25920.6 44895.8i 0.889448 1.54057i 0.0489180 0.998803i \(-0.484423\pi\)
0.840530 0.541766i \(-0.182244\pi\)
\(948\) 2458.18 + 4257.70i 0.0842173 + 0.145869i
\(949\) −3520.57 6097.81i −0.120424 0.208581i
\(950\) −9626.23 + 16673.1i −0.328754 + 0.569418i
\(951\) 13595.2 0.463570
\(952\) −1513.70 3758.66i −0.0515328 0.127961i
\(953\) −5887.31 −0.200114 −0.100057 0.994982i \(-0.531903\pi\)
−0.100057 + 0.994982i \(0.531903\pi\)
\(954\) 598.398 1036.46i 0.0203080 0.0351745i
\(955\) −14295.3 24760.3i −0.484384 0.838977i
\(956\) −4013.59 6951.74i −0.135783 0.235184i
\(957\) −18677.6 + 32350.5i −0.630888 + 1.09273i
\(958\) −32897.0 −1.10945
\(959\) 5314.45 + 13196.3i 0.178949 + 0.444349i
\(960\) −3040.73 −0.102228
\(961\) −29112.3 + 50424.0i −0.977218 + 1.69259i
\(962\) 6273.52 + 10866.1i 0.210256 + 0.364174i
\(963\) −4206.02 7285.04i −0.140745 0.243777i
\(964\) −1611.30 + 2790.85i −0.0538344 + 0.0932439i
\(965\) −53384.4 −1.78083
\(966\) −10095.0 + 12891.3i −0.336235 + 0.429368i
\(967\) −36620.0 −1.21781 −0.608904 0.793244i \(-0.708391\pi\)
−0.608904 + 0.793244i \(0.708391\pi\)
\(968\) −5424.35 + 9395.25i −0.180109 + 0.311957i
\(969\) −3138.70 5436.40i −0.104055 0.180229i
\(970\) 25629.2 + 44391.1i 0.848355 + 1.46939i
\(971\) 21182.4 36689.1i 0.700079 1.21257i −0.268359 0.963319i \(-0.586481\pi\)
0.968438 0.249254i \(-0.0801853\pi\)
\(972\) 972.000 0.0320750
\(973\) 19300.7 + 2734.60i 0.635923 + 0.0901001i
\(974\) 12662.1 0.416551
\(975\) −7329.40 + 12694.9i −0.240747 + 0.416987i
\(976\) −1482.79 2568.26i −0.0486300 0.0842296i
\(977\) −2511.16 4349.46i −0.0822304 0.142427i 0.821977 0.569520i \(-0.192871\pi\)
−0.904208 + 0.427093i \(0.859538\pi\)
\(978\) 3979.50 6892.70i 0.130113 0.225362i
\(979\) 59983.8 1.95821
\(980\) −20873.3 6036.00i −0.680382 0.196748i
\(981\) −10773.2 −0.350623
\(982\) 9286.90 16085.4i 0.301789 0.522714i
\(983\) −14146.4 24502.3i −0.459003 0.795016i 0.539906 0.841725i \(-0.318460\pi\)
−0.998909 + 0.0467095i \(0.985127\pi\)
\(984\) 1235.73 + 2140.34i 0.0400341 + 0.0693411i
\(985\) −36522.9 + 63259.4i −1.18144 + 2.04631i
\(986\) 13138.7 0.424361
\(987\) 3738.27 + 529.653i 0.120558 + 0.0170811i
\(988\) 11885.9 0.382734
\(989\) 24206.2 41926.3i 0.778273 1.34801i
\(990\) 7388.56 + 12797.4i 0.237196 + 0.410835i
\(991\) −18200.5 31524.2i −0.583410 1.01050i −0.995072 0.0991586i \(-0.968385\pi\)
0.411662 0.911337i \(-0.364948\pi\)
\(992\) 4746.79 8221.68i 0.151926 0.263144i
\(993\) −3711.17 −0.118601
\(994\) 2985.78 3812.81i 0.0952749 0.121665i
\(995\) 35314.6 1.12517
\(996\) −2087.57 + 3615.77i −0.0664128 + 0.115030i
\(997\) 1178.60 + 2041.39i 0.0374389 + 0.0648460i 0.884138 0.467226i \(-0.154747\pi\)
−0.846699 + 0.532072i \(0.821413\pi\)
\(998\) 243.451 + 421.669i 0.00772174 + 0.0133745i
\(999\) 2180.71 3777.10i 0.0690637 0.119622i
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 42.4.e.c.37.2 yes 4
3.2 odd 2 126.4.g.g.37.1 4
4.3 odd 2 336.4.q.j.289.2 4
7.2 even 3 294.4.a.n.1.1 2
7.3 odd 6 294.4.e.l.67.1 4
7.4 even 3 inner 42.4.e.c.25.2 4
7.5 odd 6 294.4.a.m.1.2 2
7.6 odd 2 294.4.e.l.79.1 4
21.2 odd 6 882.4.a.v.1.2 2
21.5 even 6 882.4.a.z.1.1 2
21.11 odd 6 126.4.g.g.109.1 4
21.17 even 6 882.4.g.bf.361.2 4
21.20 even 2 882.4.g.bf.667.2 4
28.11 odd 6 336.4.q.j.193.2 4
28.19 even 6 2352.4.a.ca.1.2 2
28.23 odd 6 2352.4.a.bq.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.e.c.25.2 4 7.4 even 3 inner
42.4.e.c.37.2 yes 4 1.1 even 1 trivial
126.4.g.g.37.1 4 3.2 odd 2
126.4.g.g.109.1 4 21.11 odd 6
294.4.a.m.1.2 2 7.5 odd 6
294.4.a.n.1.1 2 7.2 even 3
294.4.e.l.67.1 4 7.3 odd 6
294.4.e.l.79.1 4 7.6 odd 2
336.4.q.j.193.2 4 28.11 odd 6
336.4.q.j.289.2 4 4.3 odd 2
882.4.a.v.1.2 2 21.2 odd 6
882.4.a.z.1.1 2 21.5 even 6
882.4.g.bf.361.2 4 21.17 even 6
882.4.g.bf.667.2 4 21.20 even 2
2352.4.a.bq.1.1 2 28.23 odd 6
2352.4.a.ca.1.2 2 28.19 even 6