Properties

Label 63.4.f.c.43.5
Level $63$
Weight $4$
Character 63.43
Analytic conductor $3.717$
Analytic rank $0$
Dimension $18$
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] = [63,4,Mod(22,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, 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("63.22");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.f (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: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + 5832 x^{10} - 32373 x^{9} + 52488 x^{8} - 6561 x^{7} - 40824 x^{6} + 1673055 x^{5} + \cdots + 387420489 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 43.5
Root \(2.85089 + 0.934028i\) of defining polynomial
Character \(\chi\) \(=\) 63.43
Dual form 63.4.f.c.22.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.377604 - 0.654029i) q^{2} +(3.46745 - 3.86999i) q^{3} +(3.71483 + 6.43428i) q^{4} +(6.62462 + 11.4742i) q^{5} +(-1.22176 - 3.72913i) q^{6} +(-3.50000 + 6.06218i) q^{7} +11.6526 q^{8} +(-2.95361 - 26.8380i) q^{9} +O(q^{10})\) \(q+(0.377604 - 0.654029i) q^{2} +(3.46745 - 3.86999i) q^{3} +(3.71483 + 6.43428i) q^{4} +(6.62462 + 11.4742i) q^{5} +(-1.22176 - 3.72913i) q^{6} +(-3.50000 + 6.06218i) q^{7} +11.6526 q^{8} +(-2.95361 - 26.8380i) q^{9} +10.0059 q^{10} +(6.82672 - 11.8242i) q^{11} +(37.7816 + 7.93417i) q^{12} +(-31.6370 - 54.7969i) q^{13} +(2.64322 + 4.57820i) q^{14} +(67.3755 + 14.1489i) q^{15} +(-25.3186 + 43.8531i) q^{16} +46.8779 q^{17} +(-18.6681 - 8.20236i) q^{18} -71.2778 q^{19} +(-49.2187 + 85.2493i) q^{20} +(11.3245 + 34.5652i) q^{21} +(-5.15559 - 8.92974i) q^{22} +(-7.54915 - 13.0755i) q^{23} +(40.4047 - 45.0954i) q^{24} +(-25.2712 + 43.7710i) q^{25} -47.7850 q^{26} +(-114.104 - 81.6288i) q^{27} -52.0076 q^{28} +(-50.9271 + 88.2083i) q^{29} +(34.6950 - 38.7228i) q^{30} +(-113.589 - 196.742i) q^{31} +(65.7311 + 113.850i) q^{32} +(-22.0883 - 67.4192i) q^{33} +(17.7013 - 30.6595i) q^{34} -92.7447 q^{35} +(161.711 - 118.703i) q^{36} -112.457 q^{37} +(-26.9147 + 46.6177i) q^{38} +(-321.763 - 67.5706i) q^{39} +(77.1940 + 133.704i) q^{40} +(255.235 + 442.080i) q^{41} +(26.8828 + 5.64542i) q^{42} +(-175.214 + 303.479i) q^{43} +101.440 q^{44} +(288.377 - 211.682i) q^{45} -11.4023 q^{46} +(274.505 - 475.457i) q^{47} +(81.9200 + 250.041i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(19.0850 + 33.0561i) q^{50} +(162.547 - 181.417i) q^{51} +(235.052 - 407.123i) q^{52} -43.0044 q^{53} +(-96.4737 + 43.8040i) q^{54} +180.898 q^{55} +(-40.7841 + 70.6401i) q^{56} +(-247.152 + 275.844i) q^{57} +(38.4605 + 66.6155i) q^{58} +(-166.527 - 288.433i) q^{59} +(159.250 + 486.073i) q^{60} +(214.028 - 370.708i) q^{61} -171.567 q^{62} +(173.034 + 76.0275i) q^{63} -305.816 q^{64} +(419.166 - 726.018i) q^{65} +(-52.4347 - 11.0113i) q^{66} +(363.134 + 628.966i) q^{67} +(174.143 + 301.625i) q^{68} +(-76.7784 - 16.1235i) q^{69} +(-35.0207 + 60.6577i) q^{70} -775.662 q^{71} +(-34.4172 - 312.732i) q^{72} +768.941 q^{73} +(-42.4643 + 73.5503i) q^{74} +(81.7666 + 249.573i) q^{75} +(-264.785 - 458.621i) q^{76} +(47.7871 + 82.7696i) q^{77} +(-165.692 + 184.927i) q^{78} +(-24.4554 + 42.3580i) q^{79} -670.904 q^{80} +(-711.552 + 158.538i) q^{81} +385.511 q^{82} +(238.505 - 413.103i) q^{83} +(-180.334 + 201.269i) q^{84} +(310.548 + 537.885i) q^{85} +(132.323 + 229.190i) q^{86} +(164.778 + 502.945i) q^{87} +(79.5490 - 137.783i) q^{88} -1255.64 q^{89} +(-29.5536 - 268.538i) q^{90} +442.918 q^{91} +(56.0877 - 97.1467i) q^{92} +(-1155.25 - 242.605i) q^{93} +(-207.308 - 359.069i) q^{94} +(-472.188 - 817.854i) q^{95} +(668.516 + 140.389i) q^{96} +(-842.449 + 1459.16i) q^{97} -37.0051 q^{98} +(-337.502 - 148.291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.377604 0.654029i 0.133503 0.231234i −0.791522 0.611141i \(-0.790711\pi\)
0.925025 + 0.379907i \(0.124044\pi\)
\(3\) 3.46745 3.86999i 0.667311 0.744780i
\(4\) 3.71483 + 6.43428i 0.464354 + 0.804285i
\(5\) 6.62462 + 11.4742i 0.592524 + 1.02628i 0.993891 + 0.110364i \(0.0352018\pi\)
−0.401367 + 0.915917i \(0.631465\pi\)
\(6\) −1.22176 3.72913i −0.0831304 0.253735i
\(7\) −3.50000 + 6.06218i −0.188982 + 0.327327i
\(8\) 11.6526 0.514977
\(9\) −2.95361 26.8380i −0.109393 0.993999i
\(10\) 10.0059 0.316415
\(11\) 6.82672 11.8242i 0.187121 0.324104i −0.757168 0.653220i \(-0.773418\pi\)
0.944289 + 0.329117i \(0.106751\pi\)
\(12\) 37.7816 + 7.93417i 0.908883 + 0.190866i
\(13\) −31.6370 54.7969i −0.674964 1.16907i −0.976479 0.215610i \(-0.930826\pi\)
0.301516 0.953461i \(-0.402507\pi\)
\(14\) 2.64322 + 4.57820i 0.0504594 + 0.0873982i
\(15\) 67.3755 + 14.1489i 1.15975 + 0.243549i
\(16\) −25.3186 + 43.8531i −0.395603 + 0.685204i
\(17\) 46.8779 0.668797 0.334399 0.942432i \(-0.391467\pi\)
0.334399 + 0.942432i \(0.391467\pi\)
\(18\) −18.6681 8.20236i −0.244451 0.107406i
\(19\) −71.2778 −0.860644 −0.430322 0.902675i \(-0.641600\pi\)
−0.430322 + 0.902675i \(0.641600\pi\)
\(20\) −49.2187 + 85.2493i −0.550282 + 0.953116i
\(21\) 11.3245 + 34.5652i 0.117676 + 0.359179i
\(22\) −5.15559 8.92974i −0.0499625 0.0865376i
\(23\) −7.54915 13.0755i −0.0684395 0.118541i 0.829775 0.558098i \(-0.188469\pi\)
−0.898215 + 0.439557i \(0.855135\pi\)
\(24\) 40.4047 45.0954i 0.343649 0.383544i
\(25\) −25.2712 + 43.7710i −0.202169 + 0.350168i
\(26\) −47.7850 −0.360439
\(27\) −114.104 81.6288i −0.813309 0.581832i
\(28\) −52.0076 −0.351019
\(29\) −50.9271 + 88.2083i −0.326101 + 0.564823i −0.981735 0.190256i \(-0.939068\pi\)
0.655634 + 0.755079i \(0.272402\pi\)
\(30\) 34.6950 38.7228i 0.211147 0.235659i
\(31\) −113.589 196.742i −0.658104 1.13987i −0.981106 0.193471i \(-0.938025\pi\)
0.323002 0.946398i \(-0.395308\pi\)
\(32\) 65.7311 + 113.850i 0.363117 + 0.628937i
\(33\) −22.0883 67.4192i −0.116518 0.355642i
\(34\) 17.7013 30.6595i 0.0892865 0.154649i
\(35\) −92.7447 −0.447906
\(36\) 161.711 118.703i 0.748661 0.549550i
\(37\) −112.457 −0.499672 −0.249836 0.968288i \(-0.580377\pi\)
−0.249836 + 0.968288i \(0.580377\pi\)
\(38\) −26.9147 + 46.6177i −0.114899 + 0.199010i
\(39\) −321.763 67.5706i −1.32111 0.277435i
\(40\) 77.1940 + 133.704i 0.305136 + 0.528511i
\(41\) 255.235 + 442.080i 0.972220 + 1.68393i 0.688820 + 0.724933i \(0.258129\pi\)
0.283400 + 0.959002i \(0.408538\pi\)
\(42\) 26.8828 + 5.64542i 0.0987645 + 0.0207407i
\(43\) −175.214 + 303.479i −0.621392 + 1.07628i 0.367835 + 0.929891i \(0.380099\pi\)
−0.989227 + 0.146391i \(0.953234\pi\)
\(44\) 101.440 0.347562
\(45\) 288.377 211.682i 0.955305 0.701236i
\(46\) −11.4023 −0.0365475
\(47\) 274.505 475.457i 0.851931 1.47559i −0.0275329 0.999621i \(-0.508765\pi\)
0.879464 0.475966i \(-0.157902\pi\)
\(48\) 81.9200 + 250.041i 0.246336 + 0.751881i
\(49\) −24.5000 42.4352i −0.0714286 0.123718i
\(50\) 19.0850 + 33.0561i 0.0539805 + 0.0934969i
\(51\) 162.547 181.417i 0.446296 0.498107i
\(52\) 235.052 407.123i 0.626844 1.08573i
\(53\) −43.0044 −0.111455 −0.0557275 0.998446i \(-0.517748\pi\)
−0.0557275 + 0.998446i \(0.517748\pi\)
\(54\) −96.4737 + 43.8040i −0.243119 + 0.110388i
\(55\) 180.898 0.443496
\(56\) −40.7841 + 70.6401i −0.0973214 + 0.168566i
\(57\) −247.152 + 275.844i −0.574317 + 0.640990i
\(58\) 38.4605 + 66.6155i 0.0870709 + 0.150811i
\(59\) −166.527 288.433i −0.367456 0.636453i 0.621711 0.783247i \(-0.286438\pi\)
−0.989167 + 0.146794i \(0.953105\pi\)
\(60\) 159.250 + 486.073i 0.342652 + 1.04586i
\(61\) 214.028 370.708i 0.449238 0.778103i −0.549099 0.835757i \(-0.685029\pi\)
0.998337 + 0.0576548i \(0.0183623\pi\)
\(62\) −171.567 −0.351435
\(63\) 173.034 + 76.0275i 0.346036 + 0.152041i
\(64\) −305.816 −0.597297
\(65\) 419.166 726.018i 0.799865 1.38541i
\(66\) −52.4347 11.0113i −0.0977920 0.0205364i
\(67\) 363.134 + 628.966i 0.662147 + 1.14687i 0.980050 + 0.198749i \(0.0636880\pi\)
−0.317903 + 0.948123i \(0.602979\pi\)
\(68\) 174.143 + 301.625i 0.310559 + 0.537903i
\(69\) −76.7784 16.1235i −0.133957 0.0281311i
\(70\) −35.0207 + 60.6577i −0.0597968 + 0.103571i
\(71\) −775.662 −1.29654 −0.648269 0.761412i \(-0.724507\pi\)
−0.648269 + 0.761412i \(0.724507\pi\)
\(72\) −34.4172 312.732i −0.0563348 0.511886i
\(73\) 768.941 1.23285 0.616423 0.787416i \(-0.288581\pi\)
0.616423 + 0.787416i \(0.288581\pi\)
\(74\) −42.4643 + 73.5503i −0.0667078 + 0.115541i
\(75\) 81.7666 + 249.573i 0.125888 + 0.384242i
\(76\) −264.785 458.621i −0.399643 0.692203i
\(77\) 47.7871 + 82.7696i 0.0707252 + 0.122500i
\(78\) −165.692 + 184.927i −0.240525 + 0.268447i
\(79\) −24.4554 + 42.3580i −0.0348285 + 0.0603247i −0.882914 0.469534i \(-0.844422\pi\)
0.848086 + 0.529859i \(0.177755\pi\)
\(80\) −670.904 −0.937617
\(81\) −711.552 + 158.538i −0.976066 + 0.217473i
\(82\) 385.511 0.519177
\(83\) 238.505 413.103i 0.315414 0.546313i −0.664111 0.747634i \(-0.731190\pi\)
0.979525 + 0.201321i \(0.0645233\pi\)
\(84\) −180.334 + 201.269i −0.234238 + 0.261431i
\(85\) 310.548 + 537.885i 0.396279 + 0.686375i
\(86\) 132.323 + 229.190i 0.165915 + 0.287374i
\(87\) 164.778 + 502.945i 0.203058 + 0.619786i
\(88\) 79.5490 137.783i 0.0963631 0.166906i
\(89\) −1255.64 −1.49548 −0.747740 0.663992i \(-0.768861\pi\)
−0.747740 + 0.663992i \(0.768861\pi\)
\(90\) −29.5536 268.538i −0.0346136 0.314516i
\(91\) 442.918 0.510225
\(92\) 56.0877 97.1467i 0.0635603 0.110090i
\(93\) −1155.25 242.605i −1.28811 0.270505i
\(94\) −207.308 359.069i −0.227471 0.393991i
\(95\) −472.188 817.854i −0.509952 0.883263i
\(96\) 668.516 + 140.389i 0.710731 + 0.149254i
\(97\) −842.449 + 1459.16i −0.881832 + 1.52738i −0.0325300 + 0.999471i \(0.510356\pi\)
−0.849302 + 0.527907i \(0.822977\pi\)
\(98\) −37.0051 −0.0381437
\(99\) −337.502 148.291i −0.342628 0.150544i
\(100\) −375.513 −0.375513
\(101\) 675.564 1170.11i 0.665556 1.15278i −0.313579 0.949562i \(-0.601528\pi\)
0.979134 0.203214i \(-0.0651387\pi\)
\(102\) −57.2736 174.814i −0.0555974 0.169697i
\(103\) −210.779 365.080i −0.201638 0.349247i 0.747419 0.664353i \(-0.231293\pi\)
−0.949056 + 0.315107i \(0.897960\pi\)
\(104\) −368.653 638.526i −0.347591 0.602045i
\(105\) −321.587 + 358.921i −0.298892 + 0.333591i
\(106\) −16.2386 + 28.1261i −0.0148796 + 0.0257722i
\(107\) 1882.83 1.70112 0.850560 0.525878i \(-0.176263\pi\)
0.850560 + 0.525878i \(0.176263\pi\)
\(108\) 101.345 1037.41i 0.0902955 0.924308i
\(109\) −217.462 −0.191093 −0.0955464 0.995425i \(-0.530460\pi\)
−0.0955464 + 0.995425i \(0.530460\pi\)
\(110\) 68.3076 118.312i 0.0592080 0.102551i
\(111\) −389.940 + 435.209i −0.333437 + 0.372146i
\(112\) −177.230 306.972i −0.149524 0.258983i
\(113\) 744.858 + 1290.13i 0.620091 + 1.07403i 0.989468 + 0.144750i \(0.0462378\pi\)
−0.369377 + 0.929280i \(0.620429\pi\)
\(114\) 87.0844 + 265.804i 0.0715457 + 0.218376i
\(115\) 100.021 173.241i 0.0811040 0.140476i
\(116\) −756.742 −0.605705
\(117\) −1377.19 + 1010.92i −1.08822 + 0.798801i
\(118\) −251.524 −0.196226
\(119\) −164.073 + 284.182i −0.126391 + 0.218915i
\(120\) 785.099 + 164.872i 0.597245 + 0.125422i
\(121\) 572.292 + 991.238i 0.429971 + 0.744732i
\(122\) −161.636 279.961i −0.119949 0.207758i
\(123\) 2595.86 + 545.133i 1.90293 + 0.399618i
\(124\) 843.930 1461.73i 0.611186 1.05861i
\(125\) 986.507 0.705887
\(126\) 115.062 84.4610i 0.0813538 0.0597173i
\(127\) 1340.67 0.936733 0.468366 0.883534i \(-0.344843\pi\)
0.468366 + 0.883534i \(0.344843\pi\)
\(128\) −641.326 + 1110.81i −0.442858 + 0.767052i
\(129\) 566.916 + 1730.37i 0.386931 + 1.18101i
\(130\) −316.557 548.294i −0.213569 0.369912i
\(131\) 162.310 + 281.129i 0.108253 + 0.187499i 0.915062 0.403312i \(-0.132141\pi\)
−0.806810 + 0.590811i \(0.798808\pi\)
\(132\) 351.740 392.573i 0.231932 0.258857i
\(133\) 249.472 432.098i 0.162646 0.281712i
\(134\) 548.483 0.353595
\(135\) 180.727 1850.01i 0.115219 1.17943i
\(136\) 546.249 0.344415
\(137\) −817.305 + 1415.61i −0.509687 + 0.882803i 0.490250 + 0.871582i \(0.336905\pi\)
−0.999937 + 0.0112217i \(0.996428\pi\)
\(138\) −39.5371 + 44.1270i −0.0243885 + 0.0272198i
\(139\) 563.815 + 976.556i 0.344044 + 0.595902i 0.985180 0.171526i \(-0.0548696\pi\)
−0.641135 + 0.767428i \(0.721536\pi\)
\(140\) −344.531 596.745i −0.207987 0.360244i
\(141\) −888.181 2710.96i −0.530485 1.61918i
\(142\) −292.893 + 507.305i −0.173092 + 0.299803i
\(143\) −863.909 −0.505201
\(144\) 1251.71 + 549.974i 0.724368 + 0.318272i
\(145\) −1349.49 −0.772890
\(146\) 290.355 502.909i 0.164589 0.285076i
\(147\) −249.176 52.3273i −0.139808 0.0293597i
\(148\) −417.760 723.582i −0.232025 0.401879i
\(149\) 1524.86 + 2641.14i 0.838401 + 1.45215i 0.891231 + 0.453550i \(0.149843\pi\)
−0.0528301 + 0.998604i \(0.516824\pi\)
\(150\) 194.103 + 40.7618i 0.105656 + 0.0221879i
\(151\) 1601.59 2774.04i 0.863150 1.49502i −0.00572215 0.999984i \(-0.501821\pi\)
0.868872 0.495036i \(-0.164845\pi\)
\(152\) −830.571 −0.443212
\(153\) −138.459 1258.11i −0.0731618 0.664784i
\(154\) 72.1783 0.0377681
\(155\) 1504.97 2606.69i 0.779885 1.35080i
\(156\) −760.528 2321.33i −0.390327 1.19138i
\(157\) 234.152 + 405.564i 0.119028 + 0.206163i 0.919383 0.393364i \(-0.128689\pi\)
−0.800355 + 0.599527i \(0.795355\pi\)
\(158\) 18.4689 + 31.9891i 0.00929942 + 0.0161071i
\(159\) −149.116 + 166.427i −0.0743751 + 0.0830094i
\(160\) −870.888 + 1508.42i −0.430311 + 0.745320i
\(161\) 105.688 0.0517354
\(162\) −164.996 + 525.240i −0.0800206 + 0.254733i
\(163\) −3912.57 −1.88010 −0.940049 0.341039i \(-0.889221\pi\)
−0.940049 + 0.341039i \(0.889221\pi\)
\(164\) −1896.31 + 3284.51i −0.902908 + 1.56388i
\(165\) 627.254 700.072i 0.295949 0.330306i
\(166\) −180.121 311.979i −0.0842174 0.145869i
\(167\) 376.475 + 652.074i 0.174446 + 0.302150i 0.939969 0.341259i \(-0.110853\pi\)
−0.765523 + 0.643408i \(0.777520\pi\)
\(168\) 131.960 + 402.775i 0.0606006 + 0.184969i
\(169\) −903.302 + 1564.56i −0.411152 + 0.712137i
\(170\) 469.056 0.211618
\(171\) 210.527 + 1912.95i 0.0941485 + 0.855479i
\(172\) −2603.56 −1.15418
\(173\) −585.162 + 1013.53i −0.257162 + 0.445418i −0.965481 0.260475i \(-0.916121\pi\)
0.708318 + 0.705893i \(0.249454\pi\)
\(174\) 391.161 + 82.1442i 0.170424 + 0.0357893i
\(175\) −176.898 306.397i −0.0764129 0.132351i
\(176\) 345.686 + 598.746i 0.148051 + 0.256433i
\(177\) −1693.65 355.669i −0.719224 0.151038i
\(178\) −474.135 + 821.225i −0.199651 + 0.345806i
\(179\) 456.552 0.190638 0.0953192 0.995447i \(-0.469613\pi\)
0.0953192 + 0.995447i \(0.469613\pi\)
\(180\) 2433.29 + 1069.14i 1.00759 + 0.442715i
\(181\) −969.577 −0.398166 −0.199083 0.979983i \(-0.563796\pi\)
−0.199083 + 0.979983i \(0.563796\pi\)
\(182\) 167.248 289.681i 0.0681165 0.117981i
\(183\) −692.503 2113.70i −0.279734 0.853819i
\(184\) −87.9672 152.364i −0.0352447 0.0610456i
\(185\) −744.987 1290.36i −0.296068 0.512805i
\(186\) −594.899 + 663.961i −0.234517 + 0.261742i
\(187\) 320.022 554.295i 0.125146 0.216760i
\(188\) 4078.97 1.58239
\(189\) 894.213 406.018i 0.344150 0.156262i
\(190\) −713.200 −0.272321
\(191\) 1104.66 1913.33i 0.418484 0.724835i −0.577303 0.816530i \(-0.695895\pi\)
0.995787 + 0.0916946i \(0.0292283\pi\)
\(192\) −1060.40 + 1183.50i −0.398583 + 0.444855i
\(193\) −334.133 578.736i −0.124619 0.215846i 0.796965 0.604025i \(-0.206437\pi\)
−0.921584 + 0.388179i \(0.873104\pi\)
\(194\) 636.223 + 1101.97i 0.235454 + 0.407819i
\(195\) −1356.24 4139.60i −0.498064 1.52022i
\(196\) 182.027 315.280i 0.0663363 0.114898i
\(197\) −1668.64 −0.603480 −0.301740 0.953390i \(-0.597567\pi\)
−0.301740 + 0.953390i \(0.597567\pi\)
\(198\) −224.429 + 164.741i −0.0805527 + 0.0591293i
\(199\) −1022.53 −0.364248 −0.182124 0.983276i \(-0.558297\pi\)
−0.182124 + 0.983276i \(0.558297\pi\)
\(200\) −294.475 + 510.045i −0.104113 + 0.180328i
\(201\) 3693.24 + 775.584i 1.29603 + 0.272167i
\(202\) −510.191 883.676i −0.177707 0.307798i
\(203\) −356.490 617.458i −0.123254 0.213483i
\(204\) 1771.12 + 371.937i 0.607859 + 0.127651i
\(205\) −3381.67 + 5857.23i −1.15213 + 1.99554i
\(206\) −318.364 −0.107677
\(207\) −328.623 + 241.224i −0.110342 + 0.0809962i
\(208\) 3204.02 1.06807
\(209\) −486.594 + 842.805i −0.161045 + 0.278938i
\(210\) 113.312 + 345.857i 0.0372346 + 0.113650i
\(211\) −926.172 1604.18i −0.302182 0.523394i 0.674448 0.738322i \(-0.264382\pi\)
−0.976630 + 0.214928i \(0.931048\pi\)
\(212\) −159.754 276.702i −0.0517545 0.0896415i
\(213\) −2689.57 + 3001.80i −0.865193 + 0.965634i
\(214\) 710.962 1231.42i 0.227105 0.393357i
\(215\) −4642.90 −1.47276
\(216\) −1329.61 951.187i −0.418835 0.299630i
\(217\) 1590.25 0.497480
\(218\) −82.1146 + 142.227i −0.0255115 + 0.0441872i
\(219\) 2666.26 2975.79i 0.822691 0.918198i
\(220\) 672.005 + 1163.95i 0.205939 + 0.356697i
\(221\) −1483.08 2568.76i −0.451414 0.781872i
\(222\) 137.396 + 419.368i 0.0415379 + 0.126784i
\(223\) 1821.92 3155.65i 0.547106 0.947615i −0.451365 0.892339i \(-0.649063\pi\)
0.998471 0.0552757i \(-0.0176038\pi\)
\(224\) −920.236 −0.274490
\(225\) 1249.36 + 548.945i 0.370182 + 0.162650i
\(226\) 1125.04 0.331136
\(227\) −2313.26 + 4006.69i −0.676373 + 1.17151i 0.299692 + 0.954036i \(0.403116\pi\)
−0.976065 + 0.217477i \(0.930217\pi\)
\(228\) −2692.98 565.530i −0.782225 0.164268i
\(229\) −369.370 639.768i −0.106588 0.184616i 0.807798 0.589460i \(-0.200659\pi\)
−0.914386 + 0.404844i \(0.867326\pi\)
\(230\) −75.5362 130.833i −0.0216553 0.0375080i
\(231\) 486.017 + 102.064i 0.138431 + 0.0290706i
\(232\) −593.432 + 1027.86i −0.167934 + 0.290871i
\(233\) 5281.44 1.48497 0.742486 0.669861i \(-0.233646\pi\)
0.742486 + 0.669861i \(0.233646\pi\)
\(234\) 141.138 + 1282.45i 0.0394295 + 0.358276i
\(235\) 7273.98 2.01916
\(236\) 1237.24 2142.96i 0.341259 0.591079i
\(237\) 79.1272 + 241.517i 0.0216872 + 0.0661949i
\(238\) 123.909 + 214.616i 0.0337471 + 0.0584517i
\(239\) −735.318 1273.61i −0.199012 0.344698i 0.749197 0.662348i \(-0.230440\pi\)
−0.948208 + 0.317650i \(0.897106\pi\)
\(240\) −2326.33 + 2596.39i −0.625682 + 0.698318i
\(241\) 2497.89 4326.48i 0.667650 1.15640i −0.310910 0.950439i \(-0.600634\pi\)
0.978560 0.205964i \(-0.0660329\pi\)
\(242\) 864.397 0.229610
\(243\) −1853.73 + 3303.42i −0.489370 + 0.872076i
\(244\) 3180.31 0.834421
\(245\) 324.606 562.235i 0.0846463 0.146612i
\(246\) 1336.74 1491.92i 0.346452 0.386673i
\(247\) 2255.02 + 3905.80i 0.580904 + 1.00615i
\(248\) −1323.61 2292.56i −0.338908 0.587006i
\(249\) −771.700 2355.43i −0.196404 0.599474i
\(250\) 372.509 645.204i 0.0942380 0.163225i
\(251\) 1656.71 0.416617 0.208308 0.978063i \(-0.433204\pi\)
0.208308 + 0.978063i \(0.433204\pi\)
\(252\) 153.610 + 1395.78i 0.0383990 + 0.348912i
\(253\) −206.144 −0.0512259
\(254\) 506.241 876.835i 0.125057 0.216604i
\(255\) 3158.42 + 663.271i 0.775639 + 0.162885i
\(256\) −738.931 1279.87i −0.180403 0.312467i
\(257\) −1881.10 3258.16i −0.456575 0.790811i 0.542202 0.840248i \(-0.317591\pi\)
−0.998777 + 0.0494368i \(0.984257\pi\)
\(258\) 1345.78 + 282.616i 0.324747 + 0.0681972i
\(259\) 393.601 681.736i 0.0944292 0.163556i
\(260\) 6228.53 1.48568
\(261\) 2517.75 + 1106.25i 0.597106 + 0.262356i
\(262\) 245.155 0.0578082
\(263\) −212.838 + 368.646i −0.0499017 + 0.0864322i −0.889897 0.456161i \(-0.849224\pi\)
0.839996 + 0.542593i \(0.182557\pi\)
\(264\) −257.386 785.609i −0.0600039 0.183147i
\(265\) −284.888 493.441i −0.0660397 0.114384i
\(266\) −188.403 326.324i −0.0434276 0.0752188i
\(267\) −4353.87 + 4859.32i −0.997950 + 1.11380i
\(268\) −2697.96 + 4673.01i −0.614941 + 1.06511i
\(269\) −1371.63 −0.310891 −0.155446 0.987844i \(-0.549681\pi\)
−0.155446 + 0.987844i \(0.549681\pi\)
\(270\) −1141.72 816.771i −0.257343 0.184100i
\(271\) 944.084 0.211620 0.105810 0.994386i \(-0.466256\pi\)
0.105810 + 0.994386i \(0.466256\pi\)
\(272\) −1186.88 + 2055.74i −0.264578 + 0.458263i
\(273\) 1535.80 1714.09i 0.340478 0.380005i
\(274\) 617.235 + 1069.08i 0.136089 + 0.235714i
\(275\) 345.039 + 597.625i 0.0756604 + 0.131048i
\(276\) −181.475 553.910i −0.0395780 0.120802i
\(277\) −1138.54 + 1972.01i −0.246961 + 0.427750i −0.962681 0.270638i \(-0.912765\pi\)
0.715720 + 0.698388i \(0.246099\pi\)
\(278\) 851.594 0.183724
\(279\) −4944.66 + 3629.60i −1.06104 + 0.778848i
\(280\) −1080.72 −0.230661
\(281\) 509.924 883.214i 0.108254 0.187502i −0.806809 0.590813i \(-0.798807\pi\)
0.915063 + 0.403311i \(0.132141\pi\)
\(282\) −2108.42 442.771i −0.445230 0.0934987i
\(283\) −1172.93 2031.58i −0.246374 0.426731i 0.716143 0.697953i \(-0.245906\pi\)
−0.962517 + 0.271222i \(0.912572\pi\)
\(284\) −2881.45 4990.82i −0.602052 1.04278i
\(285\) −4802.37 1008.50i −0.998133 0.209609i
\(286\) −326.215 + 565.021i −0.0674458 + 0.116820i
\(287\) −3573.29 −0.734929
\(288\) 2861.35 2100.36i 0.585440 0.429739i
\(289\) −2715.46 −0.552710
\(290\) −509.572 + 882.605i −0.103183 + 0.178718i
\(291\) 2725.80 + 8319.84i 0.549104 + 1.67601i
\(292\) 2856.48 + 4947.58i 0.572476 + 0.991558i
\(293\) −824.163 1427.49i −0.164328 0.284625i 0.772088 0.635515i \(-0.219212\pi\)
−0.936416 + 0.350891i \(0.885879\pi\)
\(294\) −128.313 + 143.209i −0.0254537 + 0.0284087i
\(295\) 2206.35 3821.51i 0.435453 0.754227i
\(296\) −1310.42 −0.257320
\(297\) −1744.15 + 791.936i −0.340761 + 0.154723i
\(298\) 2303.18 0.447716
\(299\) −477.665 + 827.341i −0.0923883 + 0.160021i
\(300\) −1302.07 + 1453.23i −0.250584 + 0.279674i
\(301\) −1226.50 2124.35i −0.234864 0.406796i
\(302\) −1209.53 2094.97i −0.230466 0.399179i
\(303\) −2185.83 6671.72i −0.414432 1.26495i
\(304\) 1804.65 3125.75i 0.340473 0.589717i
\(305\) 5671.42 1.06474
\(306\) −875.120 384.509i −0.163488 0.0718331i
\(307\) −6918.79 −1.28624 −0.643121 0.765765i \(-0.722361\pi\)
−0.643121 + 0.765765i \(0.722361\pi\)
\(308\) −355.042 + 614.950i −0.0656831 + 0.113766i
\(309\) −2143.72 450.184i −0.394667 0.0828804i
\(310\) −1136.56 1968.59i −0.208234 0.360672i
\(311\) −242.477 419.983i −0.0442110 0.0765757i 0.843073 0.537799i \(-0.180744\pi\)
−0.887284 + 0.461223i \(0.847411\pi\)
\(312\) −3749.37 787.372i −0.680341 0.142872i
\(313\) −2147.26 + 3719.17i −0.387765 + 0.671628i −0.992149 0.125065i \(-0.960086\pi\)
0.604384 + 0.796693i \(0.293419\pi\)
\(314\) 353.667 0.0635624
\(315\) 273.932 + 2489.08i 0.0489978 + 0.445218i
\(316\) −363.391 −0.0646910
\(317\) 912.824 1581.06i 0.161733 0.280130i −0.773757 0.633482i \(-0.781625\pi\)
0.935490 + 0.353353i \(0.114958\pi\)
\(318\) 52.5412 + 160.369i 0.00926529 + 0.0282800i
\(319\) 695.330 + 1204.35i 0.122041 + 0.211381i
\(320\) −2025.92 3508.99i −0.353913 0.612995i
\(321\) 6528.61 7286.52i 1.13518 1.26696i
\(322\) 39.9082 69.1231i 0.00690683 0.0119630i
\(323\) −3341.35 −0.575597
\(324\) −3663.37 3989.38i −0.628150 0.684051i
\(325\) 3198.02 0.545828
\(326\) −1477.40 + 2558.93i −0.250999 + 0.434743i
\(327\) −754.039 + 841.577i −0.127518 + 0.142322i
\(328\) 2974.15 + 5151.38i 0.500671 + 0.867187i
\(329\) 1921.54 + 3328.20i 0.322000 + 0.557720i
\(330\) −221.014 674.592i −0.0368679 0.112530i
\(331\) 4978.50 8623.02i 0.826717 1.43192i −0.0738835 0.997267i \(-0.523539\pi\)
0.900600 0.434648i \(-0.143127\pi\)
\(332\) 3544.03 0.585855
\(333\) 332.155 + 3018.13i 0.0546607 + 0.496674i
\(334\) 568.633 0.0931563
\(335\) −4811.25 + 8333.33i −0.784676 + 1.35910i
\(336\) −1802.51 378.530i −0.292664 0.0614598i
\(337\) 609.417 + 1055.54i 0.0985076 + 0.170620i 0.911067 0.412258i \(-0.135260\pi\)
−0.812560 + 0.582878i \(0.801926\pi\)
\(338\) 682.180 + 1181.57i 0.109780 + 0.190145i
\(339\) 7575.55 + 1590.87i 1.21371 + 0.254880i
\(340\) −2307.27 + 3996.31i −0.368027 + 0.637441i
\(341\) −3101.77 −0.492581
\(342\) 1330.62 + 584.646i 0.210385 + 0.0924387i
\(343\) 343.000 0.0539949
\(344\) −2041.69 + 3536.32i −0.320002 + 0.554260i
\(345\) −323.623 987.781i −0.0505023 0.154146i
\(346\) 441.919 + 765.426i 0.0686639 + 0.118929i
\(347\) 1130.99 + 1958.93i 0.174970 + 0.303057i 0.940151 0.340758i \(-0.110684\pi\)
−0.765181 + 0.643815i \(0.777350\pi\)
\(348\) −2623.96 + 2928.58i −0.404193 + 0.451116i
\(349\) −3540.17 + 6131.75i −0.542983 + 0.940473i 0.455748 + 0.890109i \(0.349372\pi\)
−0.998731 + 0.0503647i \(0.983962\pi\)
\(350\) −267.190 −0.0408054
\(351\) −863.094 + 8835.04i −0.131249 + 1.34353i
\(352\) 1794.91 0.271787
\(353\) 3848.28 6665.41i 0.580235 1.00500i −0.415216 0.909723i \(-0.636294\pi\)
0.995451 0.0952740i \(-0.0303727\pi\)
\(354\) −872.147 + 973.395i −0.130944 + 0.146145i
\(355\) −5138.47 8900.08i −0.768229 1.33061i
\(356\) −4664.50 8079.14i −0.694432 1.20279i
\(357\) 530.868 + 1620.35i 0.0787017 + 0.240218i
\(358\) 172.396 298.598i 0.0254508 0.0440821i
\(359\) −5452.32 −0.801567 −0.400784 0.916173i \(-0.631262\pi\)
−0.400784 + 0.916173i \(0.631262\pi\)
\(360\) 3360.34 2466.64i 0.491960 0.361120i
\(361\) −1778.48 −0.259292
\(362\) −366.116 + 634.131i −0.0531564 + 0.0920696i
\(363\) 5820.47 + 1222.31i 0.841586 + 0.176734i
\(364\) 1645.37 + 2849.86i 0.236925 + 0.410366i
\(365\) 5093.94 + 8822.96i 0.730490 + 1.26525i
\(366\) −1643.91 345.223i −0.234777 0.0493035i
\(367\) 2855.40 4945.69i 0.406132 0.703441i −0.588320 0.808628i \(-0.700211\pi\)
0.994453 + 0.105187i \(0.0335440\pi\)
\(368\) 764.536 0.108299
\(369\) 11110.7 8155.72i 1.56747 1.15060i
\(370\) −1125.24 −0.158104
\(371\) 150.516 260.701i 0.0210630 0.0364822i
\(372\) −2730.59 8334.47i −0.380577 1.16162i
\(373\) −139.606 241.805i −0.0193795 0.0335662i 0.856173 0.516689i \(-0.172836\pi\)
−0.875552 + 0.483123i \(0.839502\pi\)
\(374\) −241.683 418.607i −0.0334148 0.0578761i
\(375\) 3420.66 3817.77i 0.471046 0.525730i
\(376\) 3198.70 5540.31i 0.438724 0.759893i
\(377\) 6444.72 0.880425
\(378\) 72.1102 738.154i 0.00981203 0.100441i
\(379\) −4973.85 −0.674115 −0.337058 0.941484i \(-0.609432\pi\)
−0.337058 + 0.941484i \(0.609432\pi\)
\(380\) 3508.20 6076.38i 0.473597 0.820294i
\(381\) 4648.70 5188.37i 0.625092 0.697659i
\(382\) −834.247 1444.96i −0.111738 0.193535i
\(383\) 4909.92 + 8504.23i 0.655053 + 1.13458i 0.981881 + 0.189501i \(0.0606869\pi\)
−0.326828 + 0.945084i \(0.605980\pi\)
\(384\) 2075.05 + 6333.60i 0.275761 + 0.841693i
\(385\) −633.142 + 1096.63i −0.0838128 + 0.145168i
\(386\) −504.680 −0.0665480
\(387\) 8662.27 + 3806.02i 1.13780 + 0.499925i
\(388\) −12518.2 −1.63793
\(389\) 2206.60 3821.95i 0.287607 0.498150i −0.685631 0.727949i \(-0.740474\pi\)
0.973238 + 0.229799i \(0.0738070\pi\)
\(390\) −3219.54 676.106i −0.418019 0.0877845i
\(391\) −353.888 612.953i −0.0457721 0.0792797i
\(392\) −285.488 494.481i −0.0367840 0.0637118i
\(393\) 1650.77 + 346.663i 0.211884 + 0.0444958i
\(394\) −630.084 + 1091.34i −0.0805664 + 0.139545i
\(395\) −648.032 −0.0825469
\(396\) −299.616 2722.46i −0.0380209 0.345476i
\(397\) −977.573 −0.123584 −0.0617922 0.998089i \(-0.519682\pi\)
−0.0617922 + 0.998089i \(0.519682\pi\)
\(398\) −386.112 + 668.765i −0.0486282 + 0.0842265i
\(399\) −807.184 2463.73i −0.101278 0.309125i
\(400\) −1279.66 2216.44i −0.159958 0.277055i
\(401\) 7542.21 + 13063.5i 0.939251 + 1.62683i 0.766871 + 0.641801i \(0.221812\pi\)
0.172380 + 0.985031i \(0.444854\pi\)
\(402\) 1901.83 2122.62i 0.235957 0.263350i
\(403\) −7187.25 + 12448.7i −0.888393 + 1.53874i
\(404\) 10038.4 1.23621
\(405\) −6532.86 7114.23i −0.801531 0.872861i
\(406\) −538.447 −0.0658194
\(407\) −767.715 + 1329.72i −0.0934993 + 0.161946i
\(408\) 1894.09 2113.98i 0.229832 0.256513i
\(409\) 553.615 + 958.890i 0.0669304 + 0.115927i 0.897549 0.440915i \(-0.145346\pi\)
−0.830618 + 0.556842i \(0.812013\pi\)
\(410\) 2553.86 + 4423.42i 0.307625 + 0.532822i
\(411\) 2644.45 + 8071.53i 0.317374 + 0.968708i
\(412\) 1566.02 2712.42i 0.187263 0.324348i
\(413\) 2331.37 0.277771
\(414\) 33.6781 + 306.016i 0.00399804 + 0.0363282i
\(415\) 6320.03 0.747562
\(416\) 4159.07 7203.73i 0.490181 0.849019i
\(417\) 5734.26 + 1204.20i 0.673400 + 0.141415i
\(418\) 367.479 + 636.492i 0.0430000 + 0.0744781i
\(419\) −3879.30 6719.15i −0.452306 0.783417i 0.546223 0.837640i \(-0.316065\pi\)
−0.998529 + 0.0542226i \(0.982732\pi\)
\(420\) −3504.04 735.852i −0.407094 0.0854902i
\(421\) −2420.37 + 4192.20i −0.280194 + 0.485309i −0.971432 0.237317i \(-0.923732\pi\)
0.691239 + 0.722626i \(0.257065\pi\)
\(422\) −1398.90 −0.161369
\(423\) −13571.1 5962.85i −1.55993 0.685399i
\(424\) −501.113 −0.0573967
\(425\) −1184.66 + 2051.89i −0.135210 + 0.234191i
\(426\) 947.674 + 2892.54i 0.107782 + 0.328977i
\(427\) 1498.20 + 2594.95i 0.169796 + 0.294095i
\(428\) 6994.39 + 12114.6i 0.789922 + 1.36818i
\(429\) −2995.56 + 3343.32i −0.337126 + 0.376263i
\(430\) −1753.17 + 3036.59i −0.196618 + 0.340552i
\(431\) −14945.3 −1.67027 −0.835136 0.550043i \(-0.814611\pi\)
−0.835136 + 0.550043i \(0.814611\pi\)
\(432\) 6468.63 2937.09i 0.720421 0.327108i
\(433\) −4492.90 −0.498649 −0.249325 0.968420i \(-0.580209\pi\)
−0.249325 + 0.968420i \(0.580209\pi\)
\(434\) 600.484 1040.07i 0.0664151 0.115034i
\(435\) −4679.29 + 5222.51i −0.515758 + 0.575633i
\(436\) −807.836 1399.21i −0.0887347 0.153693i
\(437\) 538.087 + 931.994i 0.0589020 + 0.102021i
\(438\) −939.462 2867.48i −0.102487 0.312816i
\(439\) −1421.09 + 2461.40i −0.154499 + 0.267600i −0.932876 0.360197i \(-0.882710\pi\)
0.778378 + 0.627796i \(0.216043\pi\)
\(440\) 2107.93 0.228390
\(441\) −1066.51 + 782.867i −0.115162 + 0.0845338i
\(442\) −2240.06 −0.241061
\(443\) 530.564 918.964i 0.0569026 0.0985582i −0.836171 0.548469i \(-0.815211\pi\)
0.893074 + 0.449911i \(0.148544\pi\)
\(444\) −4248.81 892.255i −0.454144 0.0953706i
\(445\) −8318.15 14407.5i −0.886108 1.53478i
\(446\) −1375.92 2383.17i −0.146081 0.253019i
\(447\) 15508.6 + 3256.82i 1.64101 + 0.344613i
\(448\) 1070.36 1853.91i 0.112879 0.195511i
\(449\) −11131.1 −1.16995 −0.584977 0.811050i \(-0.698897\pi\)
−0.584977 + 0.811050i \(0.698897\pi\)
\(450\) 830.790 609.837i 0.0870307 0.0638844i
\(451\) 6969.68 0.727692
\(452\) −5534.04 + 9585.24i −0.575884 + 0.997460i
\(453\) −5182.06 15817.0i −0.537471 1.64050i
\(454\) 1746.99 + 3025.88i 0.180596 + 0.312801i
\(455\) 2934.17 + 5082.12i 0.302320 + 0.523634i
\(456\) −2879.96 + 3214.30i −0.295760 + 0.330095i
\(457\) 5168.70 8952.45i 0.529063 0.916363i −0.470363 0.882473i \(-0.655877\pi\)
0.999426 0.0338903i \(-0.0107897\pi\)
\(458\) −557.902 −0.0569193
\(459\) −5348.96 3826.58i −0.543939 0.389128i
\(460\) 1486.24 0.150644
\(461\) −2445.94 + 4236.49i −0.247112 + 0.428011i −0.962723 0.270488i \(-0.912815\pi\)
0.715611 + 0.698499i \(0.246148\pi\)
\(462\) 250.274 279.329i 0.0252031 0.0281289i
\(463\) 1886.10 + 3266.82i 0.189318 + 0.327909i 0.945023 0.327003i \(-0.106039\pi\)
−0.755705 + 0.654912i \(0.772705\pi\)
\(464\) −2578.80 4466.62i −0.258013 0.446891i
\(465\) −4869.44 14862.8i −0.485623 1.48225i
\(466\) 1994.29 3454.21i 0.198248 0.343376i
\(467\) −1446.52 −0.143334 −0.0716669 0.997429i \(-0.522832\pi\)
−0.0716669 + 0.997429i \(0.522832\pi\)
\(468\) −11620.6 5105.84i −1.14778 0.504311i
\(469\) −5083.87 −0.500536
\(470\) 2746.68 4757.39i 0.269564 0.466898i
\(471\) 2381.44 + 500.105i 0.232974 + 0.0489249i
\(472\) −1940.47 3360.99i −0.189231 0.327758i
\(473\) 2392.27 + 4143.54i 0.232551 + 0.402791i
\(474\) 187.837 + 39.4461i 0.0182018 + 0.00382240i
\(475\) 1801.27 3119.90i 0.173996 0.301370i
\(476\) −2438.01 −0.234760
\(477\) 127.018 + 1154.15i 0.0121924 + 0.110786i
\(478\) −1110.63 −0.106275
\(479\) −550.722 + 953.878i −0.0525326 + 0.0909892i −0.891096 0.453815i \(-0.850063\pi\)
0.838563 + 0.544804i \(0.183396\pi\)
\(480\) 2817.82 + 8600.70i 0.267948 + 0.817847i
\(481\) 3557.82 + 6162.32i 0.337261 + 0.584153i
\(482\) −1886.43 3267.39i −0.178266 0.308767i
\(483\) 366.468 409.012i 0.0345236 0.0385314i
\(484\) −4251.93 + 7364.57i −0.399318 + 0.691638i
\(485\) −22323.6 −2.09003
\(486\) 1460.56 + 2459.78i 0.136321 + 0.229584i
\(487\) −1543.15 −0.143587 −0.0717933 0.997420i \(-0.522872\pi\)
−0.0717933 + 0.997420i \(0.522872\pi\)
\(488\) 2493.98 4319.70i 0.231347 0.400705i
\(489\) −13566.6 + 15141.6i −1.25461 + 1.40026i
\(490\) −245.145 424.604i −0.0226011 0.0391462i
\(491\) −8031.45 13910.9i −0.738196 1.27859i −0.953307 0.302003i \(-0.902345\pi\)
0.215111 0.976590i \(-0.430989\pi\)
\(492\) 6135.64 + 18727.5i 0.562228 + 1.71606i
\(493\) −2387.35 + 4135.02i −0.218095 + 0.377752i
\(494\) 3406.01 0.310210
\(495\) −534.302 4854.93i −0.0485153 0.440834i
\(496\) 11503.7 1.04139
\(497\) 2714.82 4702.20i 0.245022 0.424391i
\(498\) −1831.91 384.704i −0.164839 0.0346164i
\(499\) −5280.99 9146.94i −0.473767 0.820588i 0.525782 0.850619i \(-0.323773\pi\)
−0.999549 + 0.0300313i \(0.990439\pi\)
\(500\) 3664.71 + 6347.46i 0.327781 + 0.567734i
\(501\) 3828.92 + 804.078i 0.341445 + 0.0717037i
\(502\) 625.581 1083.54i 0.0556196 0.0963360i
\(503\) 11032.3 0.977943 0.488971 0.872300i \(-0.337372\pi\)
0.488971 + 0.872300i \(0.337372\pi\)
\(504\) 2016.30 + 885.918i 0.178200 + 0.0782975i
\(505\) 17901.4 1.57743
\(506\) −77.8407 + 134.824i −0.00683882 + 0.0118452i
\(507\) 2922.69 + 8920.81i 0.256019 + 0.781434i
\(508\) 4980.35 + 8626.23i 0.434975 + 0.753399i
\(509\) 3107.83 + 5382.92i 0.270633 + 0.468750i 0.969024 0.246967i \(-0.0794338\pi\)
−0.698391 + 0.715716i \(0.746100\pi\)
\(510\) 1626.43 1815.24i 0.141215 0.157608i
\(511\) −2691.29 + 4661.46i −0.232986 + 0.403543i
\(512\) −11377.3 −0.982053
\(513\) 8133.08 + 5818.32i 0.699970 + 0.500750i
\(514\) −2841.24 −0.243817
\(515\) 2792.66 4837.03i 0.238950 0.413874i
\(516\) −9027.70 + 10075.7i −0.770198 + 0.859612i
\(517\) −3747.95 6491.63i −0.318829 0.552228i
\(518\) −297.250 514.852i −0.0252132 0.0436705i
\(519\) 1893.33 + 5778.94i 0.160131 + 0.488761i
\(520\) 4884.37 8459.99i 0.411912 0.713452i
\(521\) 11890.3 0.999855 0.499928 0.866067i \(-0.333360\pi\)
0.499928 + 0.866067i \(0.333360\pi\)
\(522\) 1674.23 1228.96i 0.140381 0.103046i
\(523\) −9534.37 −0.797149 −0.398574 0.917136i \(-0.630495\pi\)
−0.398574 + 0.917136i \(0.630495\pi\)
\(524\) −1205.91 + 2088.70i −0.100535 + 0.174132i
\(525\) −1799.14 377.821i −0.149563 0.0314085i
\(526\) 160.737 + 278.404i 0.0133240 + 0.0230779i
\(527\) −5324.82 9222.86i −0.440138 0.762342i
\(528\) 3515.79 + 738.319i 0.289782 + 0.0608546i
\(529\) 5969.52 10339.5i 0.490632 0.849800i
\(530\) −430.299 −0.0352660
\(531\) −7249.09 + 5321.15i −0.592436 + 0.434874i
\(532\) 3706.99 0.302102
\(533\) 16149.8 27972.2i 1.31243 2.27319i
\(534\) 1534.09 + 4682.45i 0.124320 + 0.379456i
\(535\) 12473.0 + 21603.9i 1.00795 + 1.74583i
\(536\) 4231.45 + 7329.09i 0.340990 + 0.590613i
\(537\) 1583.07 1766.85i 0.127215 0.141984i
\(538\) −517.932 + 897.085i −0.0415049 + 0.0718886i
\(539\) −669.019 −0.0534632
\(540\) 12574.8 5709.63i 1.00210 0.455006i
\(541\) −6195.53 −0.492360 −0.246180 0.969224i \(-0.579175\pi\)
−0.246180 + 0.969224i \(0.579175\pi\)
\(542\) 356.489 617.458i 0.0282519 0.0489337i
\(543\) −3361.96 + 3752.25i −0.265701 + 0.296546i
\(544\) 3081.34 + 5337.03i 0.242851 + 0.420631i
\(545\) −1440.61 2495.20i −0.113227 0.196115i
\(546\) −541.141 1651.70i −0.0424152 0.129462i
\(547\) 10611.2 18379.2i 0.829439 1.43663i −0.0690400 0.997614i \(-0.521994\pi\)
0.898479 0.439017i \(-0.144673\pi\)
\(548\) −12144.6 −0.946700
\(549\) −10581.2 4649.15i −0.822576 0.361423i
\(550\) 521.151 0.0404036
\(551\) 3629.97 6287.29i 0.280657 0.486112i
\(552\) −894.667 187.881i −0.0689847 0.0144869i
\(553\) −171.188 296.506i −0.0131639 0.0228006i
\(554\) 859.835 + 1489.28i 0.0659402 + 0.114212i
\(555\) −7576.86 1591.15i −0.579495 0.121695i
\(556\) −4188.95 + 7255.48i −0.319517 + 0.553419i
\(557\) 8798.79 0.669330 0.334665 0.942337i \(-0.391377\pi\)
0.334665 + 0.942337i \(0.391377\pi\)
\(558\) 506.742 + 4604.50i 0.0384446 + 0.349326i
\(559\) 22173.0 1.67767
\(560\) 2348.16 4067.14i 0.177193 0.306907i
\(561\) −1035.45 3160.47i −0.0779267 0.237852i
\(562\) −385.098 667.009i −0.0289046 0.0500642i
\(563\) −699.467 1211.51i −0.0523606 0.0906912i 0.838657 0.544660i \(-0.183341\pi\)
−0.891018 + 0.453969i \(0.850008\pi\)
\(564\) 14143.6 15785.5i 1.05595 1.17853i
\(565\) −9868.80 + 17093.3i −0.734838 + 1.27278i
\(566\) −1771.62 −0.131566
\(567\) 1529.35 4868.44i 0.113274 0.360591i
\(568\) −9038.47 −0.667686
\(569\) 7119.00 12330.5i 0.524506 0.908471i −0.475087 0.879939i \(-0.657583\pi\)
0.999593 0.0285321i \(-0.00908329\pi\)
\(570\) −2472.98 + 2760.07i −0.181723 + 0.202819i
\(571\) 6280.19 + 10877.6i 0.460276 + 0.797221i 0.998974 0.0452773i \(-0.0144171\pi\)
−0.538698 + 0.842499i \(0.681084\pi\)
\(572\) −3209.27 5558.63i −0.234592 0.406325i
\(573\) −3574.20 10909.4i −0.260584 0.795368i
\(574\) −1349.29 + 2337.03i −0.0981153 + 0.169941i
\(575\) 763.104 0.0553455
\(576\) 903.262 + 8207.48i 0.0653401 + 0.593713i
\(577\) 1067.68 0.0770330 0.0385165 0.999258i \(-0.487737\pi\)
0.0385165 + 0.999258i \(0.487737\pi\)
\(578\) −1025.37 + 1775.99i −0.0737884 + 0.127805i
\(579\) −3398.29 713.645i −0.243917 0.0512229i
\(580\) −5013.13 8682.99i −0.358895 0.621624i
\(581\) 1669.54 + 2891.72i 0.119215 + 0.206487i
\(582\) 6470.69 + 1358.85i 0.460857 + 0.0967804i
\(583\) −293.579 + 508.494i −0.0208556 + 0.0361230i
\(584\) 8960.15 0.634886
\(585\) −20722.9 9105.20i −1.46459 0.643511i
\(586\) −1244.83 −0.0877532
\(587\) −9690.25 + 16784.0i −0.681362 + 1.18015i 0.293203 + 0.956050i \(0.405279\pi\)
−0.974565 + 0.224103i \(0.928055\pi\)
\(588\) −588.960 1797.66i −0.0413066 0.126078i
\(589\) 8096.39 + 14023.4i 0.566393 + 0.981022i
\(590\) −1666.25 2886.03i −0.116269 0.201383i
\(591\) −5785.92 + 6457.61i −0.402709 + 0.449460i
\(592\) 2847.26 4931.60i 0.197672 0.342378i
\(593\) 14325.4 0.992030 0.496015 0.868314i \(-0.334796\pi\)
0.496015 + 0.868314i \(0.334796\pi\)
\(594\) −140.650 + 1439.76i −0.00971541 + 0.0994516i
\(595\) −4347.67 −0.299558
\(596\) −11329.2 + 19622.8i −0.778630 + 1.34863i
\(597\) −3545.57 + 3957.18i −0.243067 + 0.271284i
\(598\) 360.736 + 624.814i 0.0246682 + 0.0427266i
\(599\) −10008.6 17335.4i −0.682703 1.18248i −0.974153 0.225890i \(-0.927471\pi\)
0.291450 0.956586i \(-0.405862\pi\)
\(600\) 952.793 + 2908.17i 0.0648293 + 0.197876i
\(601\) 11674.9 20221.6i 0.792396 1.37247i −0.132083 0.991239i \(-0.542167\pi\)
0.924479 0.381232i \(-0.124500\pi\)
\(602\) −1852.52 −0.125420
\(603\) 15807.6 11603.5i 1.06756 0.783633i
\(604\) 23798.6 1.60323
\(605\) −7582.43 + 13133.2i −0.509537 + 0.882543i
\(606\) −5188.88 1089.67i −0.347828 0.0730442i
\(607\) −9244.78 16012.4i −0.618178 1.07072i −0.989818 0.142338i \(-0.954538\pi\)
0.371640 0.928377i \(-0.378795\pi\)
\(608\) −4685.17 8114.95i −0.312514 0.541291i
\(609\) −3625.66 761.393i −0.241247 0.0506621i
\(610\) 2141.55 3709.27i 0.142146 0.246203i
\(611\) −34738.1 −2.30009
\(612\) 7580.65 5564.54i 0.500702 0.367538i
\(613\) −2325.71 −0.153238 −0.0766189 0.997060i \(-0.524412\pi\)
−0.0766189 + 0.997060i \(0.524412\pi\)
\(614\) −2612.56 + 4525.08i −0.171717 + 0.297423i
\(615\) 10941.6 + 33396.6i 0.717413 + 2.18973i
\(616\) 556.843 + 964.480i 0.0364218 + 0.0630845i
\(617\) −4537.18 7858.63i −0.296045 0.512766i 0.679182 0.733970i \(-0.262335\pi\)
−0.975228 + 0.221204i \(0.929001\pi\)
\(618\) −1103.91 + 1232.06i −0.0718540 + 0.0801956i
\(619\) −11155.4 + 19321.7i −0.724349 + 1.25461i 0.234893 + 0.972021i \(0.424526\pi\)
−0.959241 + 0.282588i \(0.908807\pi\)
\(620\) 22362.9 1.44857
\(621\) −205.950 + 2108.20i −0.0133083 + 0.136230i
\(622\) −366.241 −0.0236092
\(623\) 4394.74 7611.92i 0.282619 0.489511i
\(624\) 11109.8 12399.5i 0.712735 0.795477i
\(625\) 9694.13 + 16790.7i 0.620424 + 1.07461i
\(626\) 1621.63 + 2808.74i 0.103536 + 0.179329i
\(627\) 1574.41 + 4805.49i 0.100280 + 0.306081i
\(628\) −1739.67 + 3013.20i −0.110542 + 0.191465i
\(629\) −5271.76 −0.334180
\(630\) 1731.37 + 760.726i 0.109491 + 0.0481080i
\(631\) 6407.05 0.404217 0.202108 0.979363i \(-0.435221\pi\)
0.202108 + 0.979363i \(0.435221\pi\)
\(632\) −284.969 + 493.581i −0.0179359 + 0.0310658i
\(633\) −9419.60 1978.13i −0.591462 0.124208i
\(634\) −689.371 1194.03i −0.0431837 0.0747963i
\(635\) 8881.41 + 15383.1i 0.555037 + 0.961351i
\(636\) −1624.77 341.204i −0.101300 0.0212730i
\(637\) −1550.21 + 2685.05i −0.0964234 + 0.167010i
\(638\) 1050.24 0.0651713
\(639\) 2291.00 + 20817.2i 0.141832 + 1.28876i
\(640\) −16994.2 −1.04962
\(641\) 6985.22 12098.8i 0.430420 0.745510i −0.566489 0.824069i \(-0.691699\pi\)
0.996909 + 0.0785592i \(0.0250320\pi\)
\(642\) −2300.37 7021.31i −0.141415 0.431634i
\(643\) −3948.21 6838.51i −0.242150 0.419416i 0.719177 0.694827i \(-0.244519\pi\)
−0.961326 + 0.275411i \(0.911186\pi\)
\(644\) 392.614 + 680.027i 0.0240235 + 0.0416100i
\(645\) −16099.0 + 17968.0i −0.982787 + 1.09688i
\(646\) −1261.71 + 2185.34i −0.0768439 + 0.133098i
\(647\) −4339.84 −0.263704 −0.131852 0.991269i \(-0.542092\pi\)
−0.131852 + 0.991269i \(0.542092\pi\)
\(648\) −8291.43 + 1847.38i −0.502651 + 0.111993i
\(649\) −4547.32 −0.275036
\(650\) 1207.58 2091.60i 0.0728697 0.126214i
\(651\) 5514.11 6154.24i 0.331974 0.370513i
\(652\) −14534.5 25174.5i −0.873031 1.51213i
\(653\) 14916.5 + 25836.1i 0.893917 + 1.54831i 0.835139 + 0.550038i \(0.185387\pi\)
0.0587774 + 0.998271i \(0.481280\pi\)
\(654\) 265.687 + 810.946i 0.0158856 + 0.0484870i
\(655\) −2150.48 + 3724.75i −0.128285 + 0.222195i
\(656\) −25848.8 −1.53845
\(657\) −2271.15 20636.8i −0.134865 1.22545i
\(658\) 2902.32 0.171952
\(659\) 1546.96 2679.41i 0.0914429 0.158384i −0.816676 0.577097i \(-0.804185\pi\)
0.908118 + 0.418713i \(0.137519\pi\)
\(660\) 6834.60 + 1435.27i 0.403086 + 0.0846484i
\(661\) −10745.5 18611.7i −0.632300 1.09518i −0.987080 0.160226i \(-0.948778\pi\)
0.354781 0.934950i \(-0.384556\pi\)
\(662\) −3759.80 6512.16i −0.220738 0.382330i
\(663\) −15083.6 3167.57i −0.883556 0.185548i
\(664\) 2779.21 4813.72i 0.162431 0.281338i
\(665\) 6610.63 0.385488
\(666\) 2099.36 + 922.416i 0.122145 + 0.0536680i
\(667\) 1537.83 0.0892726
\(668\) −2797.08 + 4844.69i −0.162009 + 0.280609i
\(669\) −5894.94 17992.9i −0.340675 1.03983i
\(670\) 3633.49 + 6293.39i 0.209513 + 0.362888i
\(671\) −2922.22 5061.44i −0.168124 0.291199i
\(672\) −3190.87 + 3561.30i −0.183170 + 0.204435i
\(673\) −8644.89 + 14973.4i −0.495150 + 0.857625i −0.999984 0.00559099i \(-0.998220\pi\)
0.504834 + 0.863216i \(0.331554\pi\)
\(674\) 920.472 0.0526042
\(675\) 6456.52 2931.59i 0.368165 0.167166i
\(676\) −13422.5 −0.763681
\(677\) 8127.32 14076.9i 0.461386 0.799144i −0.537644 0.843172i \(-0.680686\pi\)
0.999030 + 0.0440278i \(0.0140190\pi\)
\(678\) 3901.03 4353.90i 0.220971 0.246623i
\(679\) −5897.14 10214.1i −0.333301 0.577295i
\(680\) 3618.69 + 6267.76i 0.204074 + 0.353467i
\(681\) 7484.72 + 22845.3i 0.421168 + 1.28551i
\(682\) −1171.24 + 2028.65i −0.0657611 + 0.113902i
\(683\) 19985.7 1.11967 0.559833 0.828605i \(-0.310865\pi\)
0.559833 + 0.828605i \(0.310865\pi\)
\(684\) −11526.4 + 8460.87i −0.644330 + 0.472967i
\(685\) −21657.3 −1.20801
\(686\) 129.518 224.332i 0.00720849 0.0124855i
\(687\) −3756.67 788.904i −0.208626 0.0438116i
\(688\) −8872.33 15367.3i −0.491649 0.851561i
\(689\) 1360.53 + 2356.51i 0.0752281 + 0.130299i
\(690\) −768.239 161.331i −0.0423860 0.00890110i
\(691\) −2469.99 + 4278.15i −0.135981 + 0.235526i −0.925972 0.377593i \(-0.876752\pi\)
0.789991 + 0.613119i \(0.210085\pi\)
\(692\) −8695.12 −0.477657
\(693\) 2080.22 1526.98i 0.114028 0.0837014i
\(694\) 1708.26 0.0934362
\(695\) −7470.12 + 12938.6i −0.407709 + 0.706173i
\(696\) 1920.09 + 5860.61i 0.104570 + 0.319175i
\(697\) 11964.9 + 20723.8i 0.650218 + 1.12621i
\(698\) 2673.56 + 4630.74i 0.144980 + 0.251112i
\(699\) 18313.1 20439.1i 0.990938 1.10598i
\(700\) 1314.29 2276.42i 0.0709652 0.122915i
\(701\) −22730.8 −1.22472 −0.612361 0.790578i \(-0.709780\pi\)
−0.612361 + 0.790578i \(0.709780\pi\)
\(702\) 5452.46 + 3900.63i 0.293148 + 0.209715i
\(703\) 8015.71 0.430040
\(704\) −2087.72 + 3616.04i −0.111767 + 0.193586i
\(705\) 25222.1 28150.2i 1.34741 1.50383i
\(706\) −2906.25 5033.76i −0.154926 0.268340i
\(707\) 4728.95 + 8190.78i 0.251556 + 0.435709i
\(708\) −4003.16 12218.7i −0.212497 0.648596i
\(709\) 14275.0 24725.0i 0.756147 1.30969i −0.188655 0.982043i \(-0.560413\pi\)
0.944802 0.327642i \(-0.106254\pi\)
\(710\) −7761.21 −0.410244
\(711\) 1209.04 + 531.225i 0.0637727 + 0.0280204i
\(712\) −14631.5 −0.770137
\(713\) −1715.01 + 2970.48i −0.0900806 + 0.156024i
\(714\) 1260.21 + 264.645i 0.0660534 + 0.0138713i
\(715\) −5723.07 9912.64i −0.299343 0.518478i
\(716\) 1696.01 + 2937.58i 0.0885237 + 0.153328i
\(717\) −7478.52 1570.50i −0.389527 0.0818010i
\(718\) −2058.82 + 3565.98i −0.107012 + 0.185350i
\(719\) 27985.7 1.45158 0.725792 0.687914i \(-0.241474\pi\)
0.725792 + 0.687914i \(0.241474\pi\)
\(720\) 1981.59 + 18005.7i 0.102569 + 0.931990i
\(721\) 2950.91 0.152424
\(722\) −671.561 + 1163.18i −0.0346162 + 0.0599570i
\(723\) −8082.11 24668.7i −0.415736 1.26893i
\(724\) −3601.81 6238.53i −0.184890 0.320239i
\(725\) −2573.98 4458.26i −0.131855 0.228380i
\(726\) 2997.25 3345.21i 0.153221 0.171009i
\(727\) −4156.09 + 7198.55i −0.212023 + 0.367235i −0.952348 0.305015i \(-0.901339\pi\)
0.740325 + 0.672250i \(0.234672\pi\)
\(728\) 5161.14 0.262754
\(729\) 6356.48 + 18628.4i 0.322943 + 0.946419i
\(730\) 7693.96 0.390091
\(731\) −8213.65 + 14226.5i −0.415585 + 0.719815i
\(732\) 11027.6 12307.8i 0.556818 0.621460i
\(733\) 18731.5 + 32443.9i 0.943880 + 1.63485i 0.757979 + 0.652279i \(0.226187\pi\)
0.185901 + 0.982568i \(0.440480\pi\)
\(734\) −2156.42 3735.02i −0.108440 0.187823i
\(735\) −1050.29 3205.74i −0.0527080 0.160878i
\(736\) 992.429 1718.94i 0.0497030 0.0860881i
\(737\) 9916.06 0.495607
\(738\) −1138.65 10346.3i −0.0567944 0.516061i
\(739\) −16040.4 −0.798452 −0.399226 0.916853i \(-0.630721\pi\)
−0.399226 + 0.916853i \(0.630721\pi\)
\(740\) 5535.00 9586.91i 0.274960 0.476246i
\(741\) 22934.6 + 4816.28i 1.13701 + 0.238773i
\(742\) −113.670 196.883i −0.00562395 0.00974097i
\(743\) 4372.63 + 7573.62i 0.215903 + 0.373956i 0.953552 0.301230i \(-0.0973971\pi\)
−0.737648 + 0.675185i \(0.764064\pi\)
\(744\) −13461.7 2826.97i −0.663347 0.139304i
\(745\) −20203.3 + 34993.1i −0.993545 + 1.72087i
\(746\) −210.863 −0.0103489
\(747\) −11791.3 5180.85i −0.577539 0.253758i
\(748\) 4755.32 0.232449
\(749\) −6589.90 + 11414.0i −0.321481 + 0.556822i
\(750\) −1205.28 3678.81i −0.0586806 0.179108i
\(751\) −4637.53 8032.44i −0.225334 0.390290i 0.731085 0.682286i \(-0.239014\pi\)
−0.956420 + 0.291996i \(0.905681\pi\)
\(752\) 13900.2 + 24075.8i 0.674053 + 1.16749i
\(753\) 5744.57 6411.46i 0.278013 0.310288i
\(754\) 2433.55 4215.03i 0.117539 0.203584i
\(755\) 42439.7 2.04575
\(756\) 5934.28 + 4245.32i 0.285487 + 0.204234i
\(757\) 26200.4 1.25795 0.628975 0.777425i \(-0.283475\pi\)
0.628975 + 0.777425i \(0.283475\pi\)
\(758\) −1878.14 + 3253.04i −0.0899964 + 0.155878i
\(759\) −714.793 + 797.775i −0.0341836 + 0.0381520i
\(760\) −5502.21 9530.11i −0.262614 0.454860i
\(761\) 18128.8 + 31400.1i 0.863560 + 1.49573i 0.868470 + 0.495743i \(0.165104\pi\)
−0.00490907 + 0.999988i \(0.501563\pi\)
\(762\) −1637.98 4999.53i −0.0778709 0.237682i
\(763\) 761.118 1318.30i 0.0361132 0.0625498i
\(764\) 16414.5 0.777298
\(765\) 13518.5 9923.18i 0.638905 0.468985i
\(766\) 7416.01 0.349806
\(767\) −10536.8 + 18250.3i −0.496039 + 0.859165i
\(768\) −7515.27 1578.21i −0.353104 0.0741522i
\(769\) 2312.94 + 4006.14i 0.108462 + 0.187861i 0.915147 0.403120i \(-0.132074\pi\)
−0.806686 + 0.590981i \(0.798741\pi\)
\(770\) 478.154 + 828.186i 0.0223785 + 0.0387607i
\(771\) −19131.7 4017.67i −0.893657 0.187669i
\(772\) 2482.50 4299.81i 0.115735 0.200458i
\(773\) 33492.2 1.55838 0.779192 0.626785i \(-0.215630\pi\)
0.779192 + 0.626785i \(0.215630\pi\)
\(774\) 5760.15 4228.21i 0.267499 0.196356i
\(775\) 11482.1 0.532194
\(776\) −9816.71 + 17003.0i −0.454123 + 0.786564i
\(777\) −1273.52 3887.12i −0.0587997 0.179472i
\(778\) −1666.44 2886.36i −0.0767928 0.133009i
\(779\) −18192.6 31510.5i −0.836735 1.44927i
\(780\) 21597.1 24104.3i 0.991411 1.10650i
\(781\) −5295.23 + 9171.61i −0.242610 + 0.420212i
\(782\) −534.518 −0.0244429
\(783\) 13011.3 5907.81i 0.593853 0.269640i
\(784\) 2481.22 0.113029
\(785\) −3102.34 + 5373.41i −0.141054 + 0.244313i
\(786\) 850.063 948.748i 0.0385760 0.0430544i
\(787\) 197.498 + 342.077i 0.00894542 + 0.0154939i 0.870463 0.492233i \(-0.163819\pi\)
−0.861518 + 0.507727i \(0.830486\pi\)
\(788\) −6198.71 10736.5i −0.280228 0.485370i
\(789\) 688.651 + 2101.94i 0.0310730 + 0.0948429i
\(790\) −244.699 + 423.831i −0.0110203 + 0.0190876i
\(791\) −10428.0 −0.468745
\(792\) −3932.77 1727.98i −0.176446 0.0775265i
\(793\) −27084.9 −1.21288
\(794\) −369.135 + 639.361i −0.0164989 + 0.0285769i
\(795\) −2897.44 608.466i −0.129260 0.0271447i
\(796\) −3798.53 6579.25i −0.169140 0.292959i
\(797\) −21709.0 37601.0i −0.964831 1.67114i −0.710068 0.704133i \(-0.751336\pi\)
−0.254763 0.967003i \(-0.581998\pi\)
\(798\) −1916.15 402.393i −0.0850011 0.0178503i
\(799\) 12868.2 22288.4i 0.569769 0.986869i
\(800\) −6644.41 −0.293644
\(801\) 3708.68 + 33698.9i 0.163595 + 1.48650i
\(802\) 11391.9 0.501572
\(803\) 5249.35 9092.13i 0.230692 0.399570i
\(804\) 8729.44 + 26644.5i 0.382915 + 1.16875i
\(805\) 700.144 + 1212.68i 0.0306544 + 0.0530951i
\(806\) 5427.86 + 9401.33i 0.237206 + 0.410853i
\(807\) −4756.05 + 5308.19i −0.207461 + 0.231545i
\(808\) 7872.07 13634.8i 0.342746 0.593653i
\(809\) 934.793 0.0406249 0.0203125 0.999794i \(-0.493534\pi\)
0.0203125 + 0.999794i \(0.493534\pi\)
\(810\) −7119.74 + 1586.32i −0.308842 + 0.0688117i
\(811\) −8844.71 −0.382959 −0.191480 0.981497i \(-0.561329\pi\)
−0.191480 + 0.981497i \(0.561329\pi\)
\(812\) 2648.60 4587.50i 0.114467 0.198263i
\(813\) 3273.56 3653.59i 0.141216 0.157610i
\(814\) 579.784 + 1004.22i 0.0249649 + 0.0432404i
\(815\) −25919.3 44893.5i −1.11400 1.92951i
\(816\) 3840.24 + 11721.4i 0.164749 + 0.502856i
\(817\) 12488.8 21631.3i 0.534797 0.926296i
\(818\) 836.189 0.0357416
\(819\) −1308.21 11887.0i −0.0558150 0.507163i
\(820\) −50249.3 −2.13998
\(821\) −5033.13 + 8717.64i −0.213956 + 0.370582i −0.952949 0.303131i \(-0.901968\pi\)
0.738993 + 0.673713i \(0.235301\pi\)
\(822\) 6277.56 + 1318.29i 0.266369 + 0.0559377i
\(823\) 14839.3 + 25702.5i 0.628513 + 1.08862i 0.987850 + 0.155409i \(0.0496695\pi\)
−0.359337 + 0.933208i \(0.616997\pi\)
\(824\) −2456.12 4254.13i −0.103839 0.179854i
\(825\) 3509.20 + 736.936i 0.148091 + 0.0310992i
\(826\) 880.334 1524.78i 0.0370832 0.0642300i
\(827\) −2344.57 −0.0985837 −0.0492919 0.998784i \(-0.515696\pi\)
−0.0492919 + 0.998784i \(0.515696\pi\)
\(828\) −2772.88 1218.35i −0.116382 0.0511358i
\(829\) −15019.6 −0.629255 −0.314627 0.949215i \(-0.601880\pi\)
−0.314627 + 0.949215i \(0.601880\pi\)
\(830\) 2386.47 4133.48i 0.0998017 0.172862i
\(831\) 3683.83 + 11244.0i 0.153779 + 0.469374i
\(832\) 9675.11 + 16757.8i 0.403154 + 0.698283i
\(833\) −1148.51 1989.27i −0.0477712 0.0827422i
\(834\) 2952.86 3295.66i 0.122601 0.136834i
\(835\) −4988.01 + 8639.48i −0.206727 + 0.358062i
\(836\) −7230.45 −0.299127
\(837\) −3098.84 + 31721.2i −0.127971 + 1.30997i
\(838\) −5859.35 −0.241537
\(839\) −13994.2 + 24238.7i −0.575845 + 0.997392i 0.420105 + 0.907476i \(0.361993\pi\)
−0.995949 + 0.0899166i \(0.971340\pi\)
\(840\) −3747.33 + 4182.36i −0.153923 + 0.171792i
\(841\) 7007.36 + 12137.1i 0.287317 + 0.497647i
\(842\) 1827.88 + 3165.98i 0.0748134 + 0.129581i
\(843\) −1649.89 5035.90i −0.0674084 0.205748i
\(844\) 6881.15 11918.5i 0.280638 0.486080i
\(845\) −23936.1 −0.974471
\(846\) −9024.37 + 6624.29i −0.366742 + 0.269205i
\(847\) −8012.08 −0.325028
\(848\) 1088.81 1885.88i 0.0440919 0.0763694i
\(849\) −11929.3 2505.16i −0.482229 0.101269i
\(850\) 894.663 + 1549.60i 0.0361020 + 0.0625305i
\(851\) 848.958 + 1470.44i 0.0341973 + 0.0592315i
\(852\) −29305.7 6154.23i −1.17840 0.247465i
\(853\) −14095.8 + 24414.6i −0.565804 + 0.980001i 0.431171 + 0.902270i \(0.358101\pi\)
−0.996974 + 0.0777305i \(0.975233\pi\)
\(854\) 2262.90 0.0906731
\(855\) −20554.9 + 15088.2i −0.822177 + 0.603515i
\(856\) 21939.8 0.876037
\(857\) 9885.20 17121.7i 0.394016 0.682457i −0.598959 0.800780i \(-0.704419\pi\)
0.992975 + 0.118323i \(0.0377520\pi\)
\(858\) 1055.49 + 3221.63i 0.0419975 + 0.128187i
\(859\) −9981.80 17289.0i −0.396478 0.686720i 0.596811 0.802382i \(-0.296434\pi\)
−0.993289 + 0.115662i \(0.963101\pi\)
\(860\) −17247.6 29873.7i −0.683881 1.18452i
\(861\) −12390.2 + 13828.6i −0.490426 + 0.547360i
\(862\) −5643.38 + 9774.62i −0.222986 + 0.386224i
\(863\) 31276.4 1.23368 0.616838 0.787090i \(-0.288413\pi\)
0.616838 + 0.787090i \(0.288413\pi\)
\(864\) 1793.22 18356.3i 0.0706095 0.722793i
\(865\) −15505.9 −0.609499
\(866\) −1696.54 + 2938.49i −0.0665712 + 0.115305i
\(867\) −9415.73 + 10508.8i −0.368829 + 0.411647i
\(868\) 5907.51 + 10232.1i 0.231007 + 0.400115i
\(869\) 333.901 + 578.333i 0.0130343 + 0.0225761i
\(870\) 1648.76 + 5032.43i 0.0642506 + 0.196109i
\(871\) 22976.9 39797.2i 0.893851 1.54820i
\(872\) −2534.00 −0.0984083
\(873\) 41649.3 + 18299.8i 1.61468 + 0.709455i
\(874\) 812.734 0.0314544
\(875\) −3452.77 + 5980.38i −0.133400 + 0.231056i
\(876\) 29051.8 + 6100.90i 1.12051 + 0.235309i
\(877\) −10282.8 17810.4i −0.395925 0.685762i 0.597294 0.802023i \(-0.296243\pi\)
−0.993219 + 0.116260i \(0.962909\pi\)
\(878\) 1073.22 + 1858.87i 0.0412521 + 0.0714507i
\(879\) −8382.12 1760.25i −0.321640 0.0675448i
\(880\) −4580.08 + 7932.93i −0.175448 + 0.303885i
\(881\) −10408.7 −0.398045 −0.199022 0.979995i \(-0.563777\pi\)
−0.199022 + 0.979995i \(0.563777\pi\)
\(882\) 109.299 + 993.143i 0.00417266 + 0.0379148i
\(883\) 23371.7 0.890737 0.445369 0.895347i \(-0.353073\pi\)
0.445369 + 0.895347i \(0.353073\pi\)
\(884\) 11018.8 19085.0i 0.419232 0.726131i
\(885\) −7138.80 21789.4i −0.271150 0.827620i
\(886\) −400.686 694.008i −0.0151933 0.0263156i
\(887\) −18388.0 31849.0i −0.696065 1.20562i −0.969820 0.243820i \(-0.921599\pi\)
0.273755 0.961799i \(-0.411734\pi\)
\(888\) −4543.81 + 5071.31i −0.171712 + 0.191646i
\(889\) −4692.34 + 8127.37i −0.177026 + 0.306618i
\(890\) −12563.8 −0.473192
\(891\) −2982.98 + 9495.85i −0.112159 + 0.357040i
\(892\) 27072.5 1.01620
\(893\) −19566.1 + 33889.5i −0.733209 + 1.26996i
\(894\) 7986.14 8913.27i 0.298766 0.333450i
\(895\) 3024.48 + 5238.56i 0.112958 + 0.195649i
\(896\) −4489.28 7775.67i −0.167384 0.289918i
\(897\) 1545.52 + 4717.32i 0.0575288 + 0.175593i
\(898\) −4203.15 + 7280.06i −0.156192 + 0.270533i
\(899\) 23139.1 0.858433
\(900\) 1109.12 + 10078.0i 0.0410785 + 0.373259i
\(901\) −2015.96 −0.0745408
\(902\) 2631.77 4558.37i 0.0971491 0.168267i
\(903\) −12474.0 2619.56i −0.459701 0.0965377i
\(904\) 8679.52 + 15033.4i 0.319332 + 0.553100i
\(905\) −6423.08 11125.1i −0.235923 0.408631i
\(906\) −12301.5 2583.33i −0.451093 0.0947300i
\(907\) 8993.19 15576.7i 0.329233 0.570248i −0.653127 0.757248i \(-0.726543\pi\)
0.982360 + 0.187001i \(0.0598766\pi\)
\(908\) −34373.5 −1.25631
\(909\) −33398.8 14674.7i −1.21867 0.535456i
\(910\) 4431.80 0.161443
\(911\) 19270.2 33377.0i 0.700823 1.21386i −0.267354 0.963598i \(-0.586149\pi\)
0.968178 0.250263i \(-0.0805172\pi\)
\(912\) −5839.07 17822.4i −0.212008 0.647102i
\(913\) −3256.42 5640.29i −0.118041 0.204454i
\(914\) −3903.44 6760.96i −0.141263 0.244675i
\(915\) 19665.4 21948.3i 0.710510 0.792994i
\(916\) 2744.30 4753.26i 0.0989892 0.171454i
\(917\) −2272.34 −0.0818313
\(918\) −4522.48 + 2053.44i −0.162597 + 0.0738274i
\(919\) 10755.6 0.386066 0.193033 0.981192i \(-0.438168\pi\)
0.193033 + 0.981192i \(0.438168\pi\)
\(920\) 1165.50 2018.70i 0.0417667 0.0723420i
\(921\) −23990.5 + 26775.6i −0.858322 + 0.957966i
\(922\) 1847.19 + 3199.43i 0.0659804 + 0.114281i
\(923\) 24539.6 + 42503.9i 0.875116 + 1.51574i
\(924\) 1148.76 + 3506.32i 0.0408999 + 0.124837i
\(925\) 2841.93 4922.37i 0.101018 0.174969i
\(926\) 2848.79 0.101098
\(927\) −9175.45 + 6735.19i −0.325093 + 0.238633i
\(928\) −13390.0 −0.473650
\(929\) −19864.7 + 34406.6i −0.701549 + 1.21512i 0.266374 + 0.963870i \(0.414174\pi\)
−0.967923 + 0.251248i \(0.919159\pi\)
\(930\) −11559.4 2427.48i −0.407578 0.0855918i
\(931\) 1746.31 + 3024.69i 0.0614746 + 0.106477i
\(932\) 19619.7 + 33982.2i 0.689553 + 1.19434i
\(933\) −2466.11 517.885i −0.0865345 0.0181723i
\(934\) −546.210 + 946.064i −0.0191355 + 0.0331436i
\(935\) 8480.11 0.296609
\(936\) −16047.9 + 11779.9i −0.560407 + 0.411364i
\(937\) 20261.6 0.706422 0.353211 0.935544i \(-0.385090\pi\)
0.353211 + 0.935544i \(0.385090\pi\)
\(938\) −1919.69 + 3325.00i −0.0668231 + 0.115741i
\(939\) 6947.61 + 21205.9i 0.241455 + 0.736984i
\(940\) 27021.6 + 46802.8i 0.937604 + 1.62398i
\(941\) −25892.5 44847.1i −0.896993 1.55364i −0.831319 0.555796i \(-0.812413\pi\)
−0.0656744 0.997841i \(-0.520920\pi\)
\(942\) 1226.32 1368.69i 0.0424159 0.0473400i
\(943\) 3853.62 6674.66i 0.133076 0.230495i
\(944\) 16864.9 0.581467
\(945\) 10582.5 + 7570.64i 0.364286 + 0.260606i
\(946\) 3613.32 0.124185
\(947\) −4413.81 + 7644.94i −0.151457 + 0.262331i −0.931763 0.363067i \(-0.881730\pi\)
0.780306 + 0.625397i \(0.215063\pi\)
\(948\) −1260.04 + 1406.32i −0.0431690 + 0.0481805i
\(949\) −24327.0 42135.6i −0.832126 1.44128i
\(950\) −1360.33 2356.17i −0.0464580 0.0804676i
\(951\) −2953.50 9014.86i −0.100709 0.307389i
\(952\) −1911.87 + 3311.46i −0.0650883 + 0.112736i
\(953\) −6211.21 −0.211123 −0.105562 0.994413i \(-0.533664\pi\)
−0.105562 + 0.994413i \(0.533664\pi\)
\(954\) 802.810 + 352.738i 0.0272452 + 0.0119710i
\(955\) 29271.8 0.991847
\(956\) 5463.16 9462.48i 0.184824 0.320124i
\(957\) 7071.83 + 1485.09i 0.238871 + 0.0501632i
\(958\) 415.909 + 720.376i 0.0140265 + 0.0242947i
\(959\) −5721.14 9909.30i −0.192643 0.333668i
\(960\) −20604.5 4326.97i −0.692716 0.145471i
\(961\) −10909.5 + 18895.8i −0.366202 + 0.634280i
\(962\) 5373.77 0.180101
\(963\) −5561.14 50531.3i −0.186091 1.69091i
\(964\) 37117.0 1.24010
\(965\) 4427.01 7667.81i 0.147679 0.255788i
\(966\) −129.126 394.125i −0.00430078 0.0131271i
\(967\) 9791.42 + 16959.2i 0.325616 + 0.563984i 0.981637 0.190759i \(-0.0610949\pi\)
−0.656021 + 0.754743i \(0.727762\pi\)
\(968\) 6668.68 + 11550.5i 0.221425 + 0.383520i
\(969\) −11586.0 + 12931.0i −0.384102 + 0.428693i
\(970\) −8429.47 + 14600.3i −0.279025 + 0.483285i
\(971\) 20509.6 0.677842 0.338921 0.940815i \(-0.389938\pi\)
0.338921 + 0.940815i \(0.389938\pi\)
\(972\) −28141.4 + 344.230i −0.928638 + 0.0113592i
\(973\) −7893.41 −0.260073
\(974\) −582.698 + 1009.26i −0.0191693 + 0.0332021i
\(975\) 11089.0 12376.3i 0.364237 0.406522i
\(976\) 10837.8 + 18771.6i 0.355440 + 0.615639i
\(977\) −6343.27 10986.9i −0.207717 0.359776i 0.743278 0.668982i \(-0.233270\pi\)
−0.950995 + 0.309207i \(0.899937\pi\)
\(978\) 4780.23 + 14590.5i 0.156293 + 0.477047i
\(979\) −8571.92 + 14847.0i −0.279836 + 0.484690i
\(980\) 4823.43 0.157223
\(981\) 642.299 + 5836.25i 0.0209042 + 0.189946i
\(982\) −12130.8 −0.394205
\(983\) 16788.1 29077.8i 0.544716 0.943476i −0.453909 0.891048i \(-0.649971\pi\)
0.998625 0.0524278i \(-0.0166959\pi\)
\(984\) 30248.5 + 6352.21i 0.979966 + 0.205794i
\(985\) −11054.1 19146.3i −0.357576 0.619341i
\(986\) 1802.95 + 3122.79i 0.0582328 + 0.100862i
\(987\) 19542.9 + 4104.04i 0.630252 + 0.132354i
\(988\) −16754.0 + 29018.8i −0.539490 + 0.934424i
\(989\) 5290.86 0.170111
\(990\) −3377.02 1483.79i −0.108413 0.0476343i
\(991\) 47127.7 1.51066 0.755329 0.655346i \(-0.227477\pi\)
0.755329 + 0.655346i \(0.227477\pi\)
\(992\) 14932.7 25864.2i 0.477937 0.827811i
\(993\) −16108.3 49166.6i −0.514784 1.57125i
\(994\) −2050.25 3551.14i −0.0654225 0.113315i
\(995\) −6773.88 11732.7i −0.215826 0.373821i
\(996\) 12288.7 13715.3i 0.390947 0.436333i
\(997\) 19952.6 34559.0i 0.633808 1.09779i −0.352958 0.935639i \(-0.614824\pi\)
0.986766 0.162148i \(-0.0518424\pi\)
\(998\) −7976.48 −0.252997
\(999\) 12831.8 + 9179.76i 0.406388 + 0.290725i
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 63.4.f.c.43.5 yes 18
3.2 odd 2 189.4.f.c.127.5 18
9.2 odd 6 567.4.a.k.1.5 9
9.4 even 3 inner 63.4.f.c.22.5 18
9.5 odd 6 189.4.f.c.64.5 18
9.7 even 3 567.4.a.j.1.5 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.f.c.22.5 18 9.4 even 3 inner
63.4.f.c.43.5 yes 18 1.1 even 1 trivial
189.4.f.c.64.5 18 9.5 odd 6
189.4.f.c.127.5 18 3.2 odd 2
567.4.a.j.1.5 9 9.7 even 3
567.4.a.k.1.5 9 9.2 odd 6