Properties

Label 60.4.j.b.7.6
Level $60$
Weight $4$
Character 60.7
Analytic conductor $3.540$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,4,Mod(7,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 60.j (of order \(4\), 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: \(3.54011460034\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.6
Character \(\chi\) \(=\) 60.7
Dual form 60.4.j.b.43.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.949450 + 2.66431i) q^{2} +(2.12132 + 2.12132i) q^{3} +(-6.19709 - 5.05926i) q^{4} +(-10.6252 - 3.47923i) q^{5} +(-7.66594 + 3.63776i) q^{6} +(-24.7270 + 24.7270i) q^{7} +(19.3633 - 11.7074i) q^{8} +9.00000i q^{9} +O(q^{10})\) \(q+(-0.949450 + 2.66431i) q^{2} +(2.12132 + 2.12132i) q^{3} +(-6.19709 - 5.05926i) q^{4} +(-10.6252 - 3.47923i) q^{5} +(-7.66594 + 3.63776i) q^{6} +(-24.7270 + 24.7270i) q^{7} +(19.3633 - 11.7074i) q^{8} +9.00000i q^{9} +(19.3578 - 25.0055i) q^{10} -35.1552i q^{11} +(-2.41370 - 23.8783i) q^{12} +(-28.9954 + 28.9954i) q^{13} +(-42.4033 - 89.3575i) q^{14} +(-15.1589 - 29.9200i) q^{15} +(12.8078 + 62.7053i) q^{16} +(54.2483 + 54.2483i) q^{17} +(-23.9788 - 8.54505i) q^{18} -20.8686 q^{19} +(48.2430 + 75.3167i) q^{20} -104.908 q^{21} +(93.6644 + 33.3782i) q^{22} +(-14.3469 - 14.3469i) q^{23} +(65.9109 + 16.2404i) q^{24} +(100.790 + 73.9350i) q^{25} +(-49.7231 - 104.783i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(278.336 - 28.1351i) q^{28} +120.702i q^{29} +(94.1088 - 11.9805i) q^{30} +183.498i q^{31} +(-179.227 - 25.4117i) q^{32} +(74.5755 - 74.5755i) q^{33} +(-196.040 + 93.0282i) q^{34} +(348.760 - 176.699i) q^{35} +(45.5333 - 55.7738i) q^{36} +(96.2550 + 96.2550i) q^{37} +(19.8137 - 55.6005i) q^{38} -123.017 q^{39} +(-246.471 + 57.0248i) q^{40} -363.161 q^{41} +(99.6048 - 279.507i) q^{42} +(-159.934 - 159.934i) q^{43} +(-177.859 + 217.860i) q^{44} +(31.3130 - 95.6268i) q^{45} +(51.8464 - 24.6030i) q^{46} +(24.6756 - 24.6756i) q^{47} +(-105.849 + 160.188i) q^{48} -879.851i q^{49} +(-292.681 + 198.338i) q^{50} +230.156i q^{51} +(326.383 - 32.9918i) q^{52} +(270.152 - 270.152i) q^{53} +(-32.7399 - 68.9935i) q^{54} +(-122.313 + 373.532i) q^{55} +(-189.305 + 768.286i) q^{56} +(-44.2691 - 44.2691i) q^{57} +(-321.587 - 114.600i) q^{58} +417.707 q^{59} +(-57.4320 + 262.110i) q^{60} -110.271 q^{61} +(-488.897 - 174.223i) q^{62} +(-222.543 - 222.543i) q^{63} +(237.872 - 453.388i) q^{64} +(408.964 - 207.201i) q^{65} +(127.886 + 269.498i) q^{66} +(51.4010 - 51.4010i) q^{67} +(-61.7253 - 610.638i) q^{68} -60.8689i q^{69} +(139.649 + 1096.97i) q^{70} -291.518i q^{71} +(105.367 + 174.269i) q^{72} +(-752.831 + 752.831i) q^{73} +(-347.843 + 165.064i) q^{74} +(56.9681 + 370.648i) q^{75} +(129.325 + 105.580i) q^{76} +(869.284 + 869.284i) q^{77} +(116.799 - 327.756i) q^{78} +127.922 q^{79} +(82.0806 - 710.818i) q^{80} -81.0000 q^{81} +(344.804 - 967.574i) q^{82} +(187.015 + 187.015i) q^{83} +(650.123 + 530.756i) q^{84} +(-387.657 - 765.142i) q^{85} +(577.963 - 274.264i) q^{86} +(-256.047 + 256.047i) q^{87} +(-411.578 - 680.720i) q^{88} +51.0463i q^{89} +(225.049 + 174.221i) q^{90} -1433.94i q^{91} +(16.3244 + 161.494i) q^{92} +(-389.259 + 389.259i) q^{93} +(42.3152 + 89.1717i) q^{94} +(221.734 + 72.6067i) q^{95} +(-326.291 - 434.104i) q^{96} +(676.202 + 676.202i) q^{97} +(2344.19 + 835.375i) q^{98} +316.397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 24 q^{5} - 36 q^{6} + 84 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 24 q^{5} - 36 q^{6} + 84 q^{8} + 128 q^{10} + 24 q^{12} - 412 q^{13} - 180 q^{16} + 20 q^{17} + 52 q^{20} + 144 q^{21} - 436 q^{22} + 132 q^{25} + 704 q^{26} + 508 q^{28} + 480 q^{30} + 340 q^{32} - 96 q^{33} + 324 q^{36} + 508 q^{37} - 1792 q^{38} - 2696 q^{40} - 1696 q^{41} - 1500 q^{42} + 612 q^{45} + 2584 q^{46} + 528 q^{48} + 832 q^{50} + 504 q^{52} + 1772 q^{53} - 512 q^{56} + 720 q^{57} - 1060 q^{58} - 84 q^{60} + 2096 q^{61} - 472 q^{62} + 28 q^{65} - 648 q^{66} + 5872 q^{68} + 2956 q^{70} + 756 q^{72} - 3348 q^{73} - 3480 q^{76} - 384 q^{77} - 1032 q^{78} - 4828 q^{80} - 2268 q^{81} - 928 q^{82} - 476 q^{85} - 3616 q^{86} + 380 q^{88} - 1116 q^{90} + 472 q^{92} - 2688 q^{93} + 396 q^{96} + 8300 q^{97} + 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.949450 + 2.66431i −0.335681 + 0.941976i
\(3\) 2.12132 + 2.12132i 0.408248 + 0.408248i
\(4\) −6.19709 5.05926i −0.774636 0.632407i
\(5\) −10.6252 3.47923i −0.950347 0.311191i
\(6\) −7.66594 + 3.63776i −0.521601 + 0.247519i
\(7\) −24.7270 + 24.7270i −1.33513 + 1.33513i −0.434426 + 0.900708i \(0.643049\pi\)
−0.900708 + 0.434426i \(0.856951\pi\)
\(8\) 19.3633 11.7074i 0.855743 0.517401i
\(9\) 9.00000i 0.333333i
\(10\) 19.3578 25.0055i 0.612149 0.790743i
\(11\) 35.1552i 0.963609i −0.876279 0.481805i \(-0.839981\pi\)
0.876279 0.481805i \(-0.160019\pi\)
\(12\) −2.41370 23.8783i −0.0580646 0.574423i
\(13\) −28.9954 + 28.9954i −0.618607 + 0.618607i −0.945174 0.326567i \(-0.894108\pi\)
0.326567 + 0.945174i \(0.394108\pi\)
\(14\) −42.4033 89.3575i −0.809484 1.70584i
\(15\) −15.1589 29.9200i −0.260934 0.515021i
\(16\) 12.8078 + 62.7053i 0.200122 + 0.979771i
\(17\) 54.2483 + 54.2483i 0.773950 + 0.773950i 0.978795 0.204844i \(-0.0656689\pi\)
−0.204844 + 0.978795i \(0.565669\pi\)
\(18\) −23.9788 8.54505i −0.313992 0.111894i
\(19\) −20.8686 −0.251979 −0.125989 0.992032i \(-0.540211\pi\)
−0.125989 + 0.992032i \(0.540211\pi\)
\(20\) 48.2430 + 75.3167i 0.539373 + 0.842067i
\(21\) −104.908 −1.09013
\(22\) 93.6644 + 33.3782i 0.907696 + 0.323466i
\(23\) −14.3469 14.3469i −0.130067 0.130067i 0.639076 0.769143i \(-0.279317\pi\)
−0.769143 + 0.639076i \(0.779317\pi\)
\(24\) 65.9109 + 16.2404i 0.560584 + 0.138128i
\(25\) 100.790 + 73.9350i 0.806320 + 0.591480i
\(26\) −49.7231 104.783i −0.375058 0.790367i
\(27\) −19.0919 + 19.0919i −0.136083 + 0.136083i
\(28\) 278.336 28.1351i 1.87859 0.189894i
\(29\) 120.702i 0.772888i 0.922313 + 0.386444i \(0.126297\pi\)
−0.922313 + 0.386444i \(0.873703\pi\)
\(30\) 94.1088 11.9805i 0.572728 0.0729107i
\(31\) 183.498i 1.06314i 0.847015 + 0.531569i \(0.178398\pi\)
−0.847015 + 0.531569i \(0.821602\pi\)
\(32\) −179.227 25.4117i −0.990098 0.140381i
\(33\) 74.5755 74.5755i 0.393392 0.393392i
\(34\) −196.040 + 93.0282i −0.988843 + 0.469241i
\(35\) 348.760 176.699i 1.68432 0.853358i
\(36\) 45.5333 55.7738i 0.210802 0.258212i
\(37\) 96.2550 + 96.2550i 0.427682 + 0.427682i 0.887838 0.460156i \(-0.152207\pi\)
−0.460156 + 0.887838i \(0.652207\pi\)
\(38\) 19.8137 55.6005i 0.0845846 0.237358i
\(39\) −123.017 −0.505090
\(40\) −246.471 + 57.0248i −0.974264 + 0.225410i
\(41\) −363.161 −1.38332 −0.691661 0.722222i \(-0.743121\pi\)
−0.691661 + 0.722222i \(0.743121\pi\)
\(42\) 99.6048 279.507i 0.365937 1.02688i
\(43\) −159.934 159.934i −0.567202 0.567202i 0.364142 0.931344i \(-0.381362\pi\)
−0.931344 + 0.364142i \(0.881362\pi\)
\(44\) −177.859 + 217.860i −0.609394 + 0.746446i
\(45\) 31.3130 95.6268i 0.103730 0.316782i
\(46\) 51.8464 24.6030i 0.166181 0.0788589i
\(47\) 24.6756 24.6756i 0.0765810 0.0765810i −0.667779 0.744360i \(-0.732755\pi\)
0.744360 + 0.667779i \(0.232755\pi\)
\(48\) −105.849 + 160.188i −0.318290 + 0.481689i
\(49\) 879.851i 2.56516i
\(50\) −292.681 + 198.338i −0.827826 + 0.560985i
\(51\) 230.156i 0.631928i
\(52\) 326.383 32.9918i 0.870406 0.0879835i
\(53\) 270.152 270.152i 0.700155 0.700155i −0.264289 0.964444i \(-0.585137\pi\)
0.964444 + 0.264289i \(0.0851372\pi\)
\(54\) −32.7399 68.9935i −0.0825062 0.173867i
\(55\) −122.313 + 373.532i −0.299867 + 0.915763i
\(56\) −189.305 + 768.286i −0.451732 + 1.83333i
\(57\) −44.2691 44.2691i −0.102870 0.102870i
\(58\) −321.587 114.600i −0.728041 0.259444i
\(59\) 417.707 0.921709 0.460854 0.887476i \(-0.347543\pi\)
0.460854 + 0.887476i \(0.347543\pi\)
\(60\) −57.4320 + 262.110i −0.123574 + 0.563971i
\(61\) −110.271 −0.231455 −0.115727 0.993281i \(-0.536920\pi\)
−0.115727 + 0.993281i \(0.536920\pi\)
\(62\) −488.897 174.223i −1.00145 0.356876i
\(63\) −222.543 222.543i −0.445044 0.445044i
\(64\) 237.872 453.388i 0.464593 0.885524i
\(65\) 408.964 207.201i 0.780396 0.395386i
\(66\) 127.886 + 269.498i 0.238511 + 0.502620i
\(67\) 51.4010 51.4010i 0.0937259 0.0937259i −0.658689 0.752415i \(-0.728889\pi\)
0.752415 + 0.658689i \(0.228889\pi\)
\(68\) −61.7253 610.638i −0.110078 1.08898i
\(69\) 60.8689i 0.106199i
\(70\) 139.649 + 1096.97i 0.238447 + 1.87305i
\(71\) 291.518i 0.487279i −0.969866 0.243640i \(-0.921659\pi\)
0.969866 0.243640i \(-0.0783414\pi\)
\(72\) 105.367 + 174.269i 0.172467 + 0.285248i
\(73\) −752.831 + 752.831i −1.20702 + 1.20702i −0.235028 + 0.971988i \(0.575518\pi\)
−0.971988 + 0.235028i \(0.924482\pi\)
\(74\) −347.843 + 165.064i −0.546431 + 0.259301i
\(75\) 56.9681 + 370.648i 0.0877081 + 0.570649i
\(76\) 129.325 + 105.580i 0.195192 + 0.159353i
\(77\) 869.284 + 869.284i 1.28655 + 1.28655i
\(78\) 116.799 327.756i 0.169549 0.475783i
\(79\) 127.922 0.182182 0.0910911 0.995843i \(-0.470965\pi\)
0.0910911 + 0.995843i \(0.470965\pi\)
\(80\) 82.0806 710.818i 0.114711 0.993399i
\(81\) −81.0000 −0.111111
\(82\) 344.804 967.574i 0.464356 1.30306i
\(83\) 187.015 + 187.015i 0.247320 + 0.247320i 0.819870 0.572550i \(-0.194046\pi\)
−0.572550 + 0.819870i \(0.694046\pi\)
\(84\) 650.123 + 530.756i 0.844455 + 0.689407i
\(85\) −387.657 765.142i −0.494675 0.976368i
\(86\) 577.963 274.264i 0.724690 0.343891i
\(87\) −256.047 + 256.047i −0.315530 + 0.315530i
\(88\) −411.578 680.720i −0.498572 0.824602i
\(89\) 51.0463i 0.0607966i 0.999538 + 0.0303983i \(0.00967757\pi\)
−0.999538 + 0.0303983i \(0.990322\pi\)
\(90\) 225.049 + 174.221i 0.263581 + 0.204050i
\(91\) 1433.94i 1.65184i
\(92\) 16.3244 + 161.494i 0.0184993 + 0.183010i
\(93\) −389.259 + 389.259i −0.434025 + 0.434025i
\(94\) 42.3152 + 89.1717i 0.0464306 + 0.0978442i
\(95\) 221.734 + 72.6067i 0.239467 + 0.0784136i
\(96\) −326.291 434.104i −0.346895 0.461516i
\(97\) 676.202 + 676.202i 0.707813 + 0.707813i 0.966075 0.258262i \(-0.0831497\pi\)
−0.258262 + 0.966075i \(0.583150\pi\)
\(98\) 2344.19 + 835.375i 2.41632 + 0.861077i
\(99\) 316.397 0.321203
\(100\) −250.548 968.104i −0.250548 0.968104i
\(101\) −772.225 −0.760785 −0.380392 0.924825i \(-0.624211\pi\)
−0.380392 + 0.924825i \(0.624211\pi\)
\(102\) −613.207 218.522i −0.595260 0.212126i
\(103\) −68.3141 68.3141i −0.0653514 0.0653514i 0.673676 0.739027i \(-0.264714\pi\)
−0.739027 + 0.673676i \(0.764714\pi\)
\(104\) −221.984 + 900.908i −0.209301 + 0.849436i
\(105\) 1114.67 + 364.998i 1.03600 + 0.339240i
\(106\) 463.272 + 976.264i 0.424500 + 0.894558i
\(107\) −213.988 + 213.988i −0.193336 + 0.193336i −0.797136 0.603800i \(-0.793653\pi\)
0.603800 + 0.797136i \(0.293653\pi\)
\(108\) 214.905 21.7233i 0.191474 0.0193549i
\(109\) 1178.72i 1.03579i 0.855445 + 0.517893i \(0.173284\pi\)
−0.855445 + 0.517893i \(0.826716\pi\)
\(110\) −879.074 680.529i −0.761967 0.589872i
\(111\) 408.375i 0.349201i
\(112\) −1867.21 1233.82i −1.57531 1.04094i
\(113\) −888.386 + 888.386i −0.739578 + 0.739578i −0.972496 0.232918i \(-0.925173\pi\)
0.232918 + 0.972496i \(0.425173\pi\)
\(114\) 159.978 75.9152i 0.131432 0.0623694i
\(115\) 102.523 + 202.355i 0.0831332 + 0.164085i
\(116\) 610.661 747.999i 0.488780 0.598707i
\(117\) −260.959 260.959i −0.206202 0.206202i
\(118\) −396.592 + 1112.90i −0.309401 + 0.868227i
\(119\) −2682.80 −2.06665
\(120\) −643.813 401.877i −0.489765 0.305718i
\(121\) 95.1094 0.0714571
\(122\) 104.697 293.796i 0.0776951 0.218025i
\(123\) −770.381 770.381i −0.564739 0.564739i
\(124\) 928.366 1137.16i 0.672337 0.823546i
\(125\) −813.678 1136.25i −0.582220 0.813031i
\(126\) 804.217 381.630i 0.568614 0.269828i
\(127\) −1452.14 + 1452.14i −1.01462 + 1.01462i −0.0147282 + 0.999892i \(0.504688\pi\)
−0.999892 + 0.0147282i \(0.995312\pi\)
\(128\) 982.120 + 1064.23i 0.678187 + 0.734889i
\(129\) 678.542i 0.463118i
\(130\) 163.756 + 1286.33i 0.110479 + 0.867838i
\(131\) 306.809i 0.204626i 0.994752 + 0.102313i \(0.0326244\pi\)
−0.994752 + 0.102313i \(0.967376\pi\)
\(132\) −839.448 + 84.8542i −0.553519 + 0.0559516i
\(133\) 516.019 516.019i 0.336425 0.336425i
\(134\) 88.1455 + 185.751i 0.0568254 + 0.119749i
\(135\) 269.280 136.430i 0.171674 0.0869781i
\(136\) 1685.53 + 415.315i 1.06274 + 0.261860i
\(137\) −212.111 212.111i −0.132276 0.132276i 0.637869 0.770145i \(-0.279816\pi\)
−0.770145 + 0.637869i \(0.779816\pi\)
\(138\) 162.174 + 57.7920i 0.100037 + 0.0356492i
\(139\) 1953.77 1.19220 0.596102 0.802909i \(-0.296715\pi\)
0.596102 + 0.802909i \(0.296715\pi\)
\(140\) −3055.26 669.452i −1.84441 0.404136i
\(141\) 104.690 0.0625281
\(142\) 776.694 + 276.782i 0.459005 + 0.163571i
\(143\) 1019.34 + 1019.34i 0.596095 + 0.596095i
\(144\) −564.348 + 115.270i −0.326590 + 0.0667073i
\(145\) 419.948 1282.48i 0.240516 0.734512i
\(146\) −1291.00 2720.55i −0.731807 1.54215i
\(147\) 1866.45 1866.45i 1.04722 1.04722i
\(148\) −109.522 1083.48i −0.0608286 0.601767i
\(149\) 398.340i 0.219015i −0.993986 0.109508i \(-0.965073\pi\)
0.993986 0.109508i \(-0.0349274\pi\)
\(150\) −1041.61 200.131i −0.566980 0.108938i
\(151\) 1429.31i 0.770302i −0.922854 0.385151i \(-0.874149\pi\)
0.922854 0.385151i \(-0.125851\pi\)
\(152\) −404.085 + 244.319i −0.215629 + 0.130374i
\(153\) −488.235 + 488.235i −0.257983 + 0.257983i
\(154\) −3141.38 + 1490.70i −1.64377 + 0.780026i
\(155\) 638.433 1949.71i 0.330840 1.01035i
\(156\) 762.348 + 622.376i 0.391261 + 0.319423i
\(157\) −253.872 253.872i −0.129052 0.129052i 0.639630 0.768683i \(-0.279087\pi\)
−0.768683 + 0.639630i \(0.779087\pi\)
\(158\) −121.456 + 340.825i −0.0611552 + 0.171611i
\(159\) 1146.16 0.571674
\(160\) 1815.91 + 893.575i 0.897251 + 0.441521i
\(161\) 709.514 0.347314
\(162\) 76.9055 215.809i 0.0372979 0.104664i
\(163\) 2598.96 + 2598.96i 1.24887 + 1.24887i 0.956218 + 0.292657i \(0.0945394\pi\)
0.292657 + 0.956218i \(0.405461\pi\)
\(164\) 2250.54 + 1837.33i 1.07157 + 0.874824i
\(165\) −1051.85 + 532.915i −0.496279 + 0.251439i
\(166\) −675.828 + 320.705i −0.315991 + 0.149949i
\(167\) −2551.77 + 2551.77i −1.18241 + 1.18241i −0.203286 + 0.979119i \(0.565162\pi\)
−0.979119 + 0.203286i \(0.934838\pi\)
\(168\) −2031.36 + 1228.20i −0.932873 + 0.564035i
\(169\) 515.530i 0.234652i
\(170\) 2406.64 306.375i 1.08577 0.138223i
\(171\) 187.818i 0.0839929i
\(172\) 181.977 + 1800.27i 0.0806723 + 0.798078i
\(173\) 2002.13 2002.13i 0.879878 0.879878i −0.113644 0.993522i \(-0.536252\pi\)
0.993522 + 0.113644i \(0.0362523\pi\)
\(174\) −439.084 925.292i −0.191304 0.403139i
\(175\) −4320.43 + 664.044i −1.86625 + 0.286840i
\(176\) 2204.42 450.261i 0.944117 0.192839i
\(177\) 886.091 + 886.091i 0.376286 + 0.376286i
\(178\) −136.003 48.4659i −0.0572689 0.0204083i
\(179\) 1233.94 0.515245 0.257622 0.966246i \(-0.417061\pi\)
0.257622 + 0.966246i \(0.417061\pi\)
\(180\) −677.851 + 434.187i −0.280689 + 0.179791i
\(181\) 3372.19 1.38482 0.692412 0.721502i \(-0.256548\pi\)
0.692412 + 0.721502i \(0.256548\pi\)
\(182\) 3820.46 + 1361.46i 1.55600 + 0.554493i
\(183\) −233.920 233.920i −0.0944910 0.0944910i
\(184\) −445.770 109.838i −0.178601 0.0440072i
\(185\) −687.836 1357.62i −0.273355 0.539537i
\(186\) −667.524 1406.69i −0.263147 0.554535i
\(187\) 1907.11 1907.11i 0.745785 0.745785i
\(188\) −277.757 + 28.0766i −0.107753 + 0.0108920i
\(189\) 944.171i 0.363377i
\(190\) −403.972 + 521.831i −0.154248 + 0.199250i
\(191\) 238.122i 0.0902091i 0.998982 + 0.0451045i \(0.0143621\pi\)
−0.998982 + 0.0451045i \(0.985638\pi\)
\(192\) 1466.38 457.180i 0.551183 0.171845i
\(193\) −1990.01 + 1990.01i −0.742196 + 0.742196i −0.973000 0.230804i \(-0.925864\pi\)
0.230804 + 0.973000i \(0.425864\pi\)
\(194\) −2443.63 + 1159.59i −0.904343 + 0.429143i
\(195\) 1307.08 + 428.005i 0.480011 + 0.157180i
\(196\) −4451.39 + 5452.51i −1.62223 + 1.98707i
\(197\) −1671.87 1671.87i −0.604650 0.604650i 0.336893 0.941543i \(-0.390624\pi\)
−0.941543 + 0.336893i \(0.890624\pi\)
\(198\) −300.403 + 842.980i −0.107822 + 0.302565i
\(199\) 4536.41 1.61597 0.807984 0.589204i \(-0.200559\pi\)
0.807984 + 0.589204i \(0.200559\pi\)
\(200\) 2817.21 + 251.629i 0.996035 + 0.0889643i
\(201\) 218.076 0.0765268
\(202\) 733.189 2057.45i 0.255381 0.716641i
\(203\) −2984.59 2984.59i −1.03191 1.03191i
\(204\) 1164.42 1426.30i 0.399636 0.489514i
\(205\) 3858.66 + 1263.52i 1.31464 + 0.430478i
\(206\) 246.871 117.149i 0.0834966 0.0396221i
\(207\) 129.122 129.122i 0.0433557 0.0433557i
\(208\) −2189.54 1446.80i −0.729889 0.482296i
\(209\) 733.642i 0.242809i
\(210\) −2030.79 + 2623.27i −0.667323 + 0.862014i
\(211\) 61.2230i 0.0199752i 0.999950 + 0.00998760i \(0.00317920\pi\)
−0.999950 + 0.00998760i \(0.996821\pi\)
\(212\) −3040.92 + 307.386i −0.985148 + 0.0995820i
\(213\) 618.403 618.403i 0.198931 0.198931i
\(214\) −366.959 773.300i −0.117219 0.247017i
\(215\) 1142.88 + 2255.78i 0.362530 + 0.715547i
\(216\) −146.164 + 593.198i −0.0460426 + 0.186861i
\(217\) −4537.37 4537.37i −1.41943 1.41943i
\(218\) −3140.47 1119.13i −0.975686 0.347694i
\(219\) −3193.99 −0.985525
\(220\) 2647.78 1695.99i 0.811423 0.519745i
\(221\) −3145.91 −0.957541
\(222\) −1088.04 387.732i −0.328939 0.117220i
\(223\) −2752.79 2752.79i −0.826639 0.826639i 0.160411 0.987050i \(-0.448718\pi\)
−0.987050 + 0.160411i \(0.948718\pi\)
\(224\) 5060.10 3803.39i 1.50934 1.13448i
\(225\) −665.415 + 907.110i −0.197160 + 0.268773i
\(226\) −1523.46 3210.41i −0.448402 0.944928i
\(227\) 1077.03 1077.03i 0.314912 0.314912i −0.531897 0.846809i \(-0.678521\pi\)
0.846809 + 0.531897i \(0.178521\pi\)
\(228\) 50.3706 + 498.308i 0.0146310 + 0.144742i
\(229\) 2189.64i 0.631859i 0.948783 + 0.315929i \(0.102316\pi\)
−0.948783 + 0.315929i \(0.897684\pi\)
\(230\) −636.478 + 81.0264i −0.182470 + 0.0232292i
\(231\) 3688.06i 1.05046i
\(232\) 1413.11 + 2337.18i 0.399893 + 0.661393i
\(233\) 3410.98 3410.98i 0.959060 0.959060i −0.0401343 0.999194i \(-0.512779\pi\)
0.999194 + 0.0401343i \(0.0127786\pi\)
\(234\) 943.043 447.508i 0.263456 0.125019i
\(235\) −348.035 + 176.331i −0.0966098 + 0.0489472i
\(236\) −2588.57 2113.29i −0.713989 0.582896i
\(237\) 271.364 + 271.364i 0.0743756 + 0.0743756i
\(238\) 2547.18 7147.80i 0.693737 1.94674i
\(239\) −5713.06 −1.54622 −0.773111 0.634271i \(-0.781300\pi\)
−0.773111 + 0.634271i \(0.781300\pi\)
\(240\) 1681.99 1333.75i 0.452384 0.358723i
\(241\) −2598.16 −0.694448 −0.347224 0.937782i \(-0.612876\pi\)
−0.347224 + 0.937782i \(0.612876\pi\)
\(242\) −90.3016 + 253.401i −0.0239868 + 0.0673108i
\(243\) −171.827 171.827i −0.0453609 0.0453609i
\(244\) 683.358 + 557.889i 0.179293 + 0.146374i
\(245\) −3061.20 + 9348.59i −0.798256 + 2.43779i
\(246\) 2783.97 1321.09i 0.721543 0.342398i
\(247\) 605.095 605.095i 0.155876 0.155876i
\(248\) 2148.30 + 3553.13i 0.550069 + 0.909774i
\(249\) 793.438i 0.201936i
\(250\) 3799.86 1089.08i 0.961296 0.275518i
\(251\) 6357.14i 1.59864i 0.600904 + 0.799321i \(0.294807\pi\)
−0.600904 + 0.799321i \(0.705193\pi\)
\(252\) 253.216 + 2505.02i 0.0632980 + 0.626197i
\(253\) −504.370 + 504.370i −0.125334 + 0.125334i
\(254\) −2490.22 5247.69i −0.615158 1.29634i
\(255\) 800.765 2445.46i 0.196650 0.600551i
\(256\) −3767.92 + 1606.23i −0.919903 + 0.392147i
\(257\) 5632.26 + 5632.26i 1.36705 + 1.36705i 0.864620 + 0.502426i \(0.167559\pi\)
0.502426 + 0.864620i \(0.332441\pi\)
\(258\) 1807.85 + 644.242i 0.436246 + 0.155460i
\(259\) −4760.20 −1.14202
\(260\) −3582.67 785.014i −0.854568 0.187248i
\(261\) −1086.32 −0.257629
\(262\) −817.435 291.300i −0.192753 0.0686893i
\(263\) 2996.95 + 2996.95i 0.702661 + 0.702661i 0.964981 0.262320i \(-0.0844875\pi\)
−0.262320 + 0.964981i \(0.584487\pi\)
\(264\) 570.936 2317.11i 0.133101 0.540184i
\(265\) −3810.34 + 1930.50i −0.883272 + 0.447508i
\(266\) 884.900 + 1864.77i 0.203973 + 0.429836i
\(267\) −108.286 + 108.286i −0.0248201 + 0.0248201i
\(268\) −578.588 + 58.4855i −0.131876 + 0.0133305i
\(269\) 1623.82i 0.368051i −0.982921 0.184026i \(-0.941087\pi\)
0.982921 0.184026i \(-0.0589130\pi\)
\(270\) 107.824 + 846.979i 0.0243036 + 0.190909i
\(271\) 1754.44i 0.393264i −0.980477 0.196632i \(-0.937000\pi\)
0.980477 0.196632i \(-0.0630004\pi\)
\(272\) −2706.86 + 4096.46i −0.603410 + 0.913178i
\(273\) 3041.85 3041.85i 0.674363 0.674363i
\(274\) 766.517 363.740i 0.169004 0.0801983i
\(275\) 2599.20 3543.30i 0.569955 0.776977i
\(276\) −307.952 + 377.210i −0.0671613 + 0.0822659i
\(277\) −1806.98 1806.98i −0.391953 0.391953i 0.483430 0.875383i \(-0.339391\pi\)
−0.875383 + 0.483430i \(0.839391\pi\)
\(278\) −1855.00 + 5205.44i −0.400201 + 1.12303i
\(279\) −1651.49 −0.354380
\(280\) 4684.45 7504.56i 0.999819 1.60173i
\(281\) 3208.09 0.681062 0.340531 0.940233i \(-0.389393\pi\)
0.340531 + 0.940233i \(0.389393\pi\)
\(282\) −99.3977 + 278.926i −0.0209895 + 0.0588999i
\(283\) 1659.92 + 1659.92i 0.348664 + 0.348664i 0.859612 0.510948i \(-0.170705\pi\)
−0.510948 + 0.859612i \(0.670705\pi\)
\(284\) −1474.87 + 1806.56i −0.308159 + 0.377464i
\(285\) 316.346 + 624.390i 0.0657499 + 0.129774i
\(286\) −3683.65 + 1748.03i −0.761605 + 0.361409i
\(287\) 8979.89 8979.89i 1.84692 1.84692i
\(288\) 228.705 1613.04i 0.0467937 0.330033i
\(289\) 972.761i 0.197997i
\(290\) 3018.20 + 2336.52i 0.611155 + 0.473122i
\(291\) 2868.88i 0.577927i
\(292\) 8474.13 856.593i 1.69833 0.171672i
\(293\) −3662.88 + 3662.88i −0.730334 + 0.730334i −0.970686 0.240352i \(-0.922737\pi\)
0.240352 + 0.970686i \(0.422737\pi\)
\(294\) 3200.69 + 6744.88i 0.634925 + 1.33799i
\(295\) −4438.22 1453.30i −0.875944 0.286828i
\(296\) 2990.71 + 736.911i 0.587269 + 0.144703i
\(297\) 671.180 + 671.180i 0.131131 + 0.131131i
\(298\) 1061.30 + 378.204i 0.206307 + 0.0735194i
\(299\) 831.991 0.160921
\(300\) 1522.17 2585.15i 0.292941 0.497513i
\(301\) 7909.37 1.51458
\(302\) 3808.12 + 1357.06i 0.725605 + 0.258576i
\(303\) −1638.14 1638.14i −0.310589 0.310589i
\(304\) −267.281 1308.58i −0.0504264 0.246881i
\(305\) 1171.65 + 383.657i 0.219962 + 0.0720267i
\(306\) −837.254 1764.36i −0.156414 0.329614i
\(307\) −4150.58 + 4150.58i −0.771615 + 0.771615i −0.978389 0.206774i \(-0.933704\pi\)
0.206774 + 0.978389i \(0.433704\pi\)
\(308\) −989.096 9784.96i −0.182984 1.81023i
\(309\) 289.832i 0.0533592i
\(310\) 4588.47 + 3552.13i 0.840669 + 0.650799i
\(311\) 4316.72i 0.787070i −0.919310 0.393535i \(-0.871252\pi\)
0.919310 0.393535i \(-0.128748\pi\)
\(312\) −2382.01 + 1440.22i −0.432227 + 0.261334i
\(313\) 4399.27 4399.27i 0.794445 0.794445i −0.187768 0.982213i \(-0.560125\pi\)
0.982213 + 0.187768i \(0.0601254\pi\)
\(314\) 917.433 435.355i 0.164884 0.0782436i
\(315\) 1590.29 + 3138.84i 0.284453 + 0.561441i
\(316\) −792.746 647.192i −0.141125 0.115213i
\(317\) −7436.77 7436.77i −1.31764 1.31764i −0.915643 0.401993i \(-0.868318\pi\)
−0.401993 0.915643i \(-0.631682\pi\)
\(318\) −1088.22 + 3053.72i −0.191900 + 0.538503i
\(319\) 4243.30 0.744762
\(320\) −4104.88 + 3989.74i −0.717092 + 0.696978i
\(321\) −907.873 −0.157858
\(322\) −673.649 + 1890.37i −0.116587 + 0.327161i
\(323\) −1132.09 1132.09i −0.195019 0.195019i
\(324\) 501.964 + 409.800i 0.0860707 + 0.0702675i
\(325\) −5066.22 + 778.672i −0.864688 + 0.132901i
\(326\) −9392.03 + 4456.86i −1.59563 + 0.757185i
\(327\) −2500.44 + 2500.44i −0.422858 + 0.422858i
\(328\) −7031.98 + 4251.69i −1.18377 + 0.715732i
\(329\) 1220.31i 0.204492i
\(330\) −421.176 3308.42i −0.0702575 0.551886i
\(331\) 9421.59i 1.56452i −0.622949 0.782262i \(-0.714066\pi\)
0.622949 0.782262i \(-0.285934\pi\)
\(332\) −212.791 2105.11i −0.0351760 0.347990i
\(333\) −866.295 + 866.295i −0.142561 + 0.142561i
\(334\) −4375.92 9221.47i −0.716885 1.51071i
\(335\) −724.982 + 367.311i −0.118239 + 0.0599054i
\(336\) −1343.64 6578.28i −0.218159 1.06808i
\(337\) 310.592 + 310.592i 0.0502048 + 0.0502048i 0.731763 0.681559i \(-0.238698\pi\)
−0.681559 + 0.731763i \(0.738698\pi\)
\(338\) −1373.53 489.471i −0.221036 0.0787683i
\(339\) −3769.10 −0.603863
\(340\) −1468.70 + 6702.91i −0.234269 + 1.06917i
\(341\) 6450.93 1.02445
\(342\) 500.405 + 178.324i 0.0791193 + 0.0281949i
\(343\) 13274.7 + 13274.7i 2.08970 + 2.08970i
\(344\) −4969.26 1224.42i −0.778850 0.191909i
\(345\) −211.777 + 646.745i −0.0330483 + 0.100926i
\(346\) 3433.36 + 7235.20i 0.533465 + 1.12418i
\(347\) 831.727 831.727i 0.128673 0.128673i −0.639837 0.768510i \(-0.720998\pi\)
0.768510 + 0.639837i \(0.220998\pi\)
\(348\) 2882.15 291.338i 0.443965 0.0448774i
\(349\) 1646.43i 0.252525i −0.991997 0.126263i \(-0.959702\pi\)
0.991997 0.126263i \(-0.0402982\pi\)
\(350\) 2332.81 12141.4i 0.356269 1.85425i
\(351\) 1107.15i 0.168363i
\(352\) −893.354 + 6300.76i −0.135273 + 0.954067i
\(353\) 3573.21 3573.21i 0.538761 0.538761i −0.384404 0.923165i \(-0.625593\pi\)
0.923165 + 0.384404i \(0.125593\pi\)
\(354\) −3202.12 + 1519.52i −0.480765 + 0.228140i
\(355\) −1014.26 + 3097.44i −0.151637 + 0.463085i
\(356\) 258.256 316.338i 0.0384482 0.0470952i
\(357\) −5691.07 5691.07i −0.843708 0.843708i
\(358\) −1171.56 + 3287.59i −0.172958 + 0.485348i
\(359\) 8383.39 1.23247 0.616237 0.787561i \(-0.288656\pi\)
0.616237 + 0.787561i \(0.288656\pi\)
\(360\) −513.224 2218.24i −0.0751368 0.324755i
\(361\) −6423.50 −0.936507
\(362\) −3201.73 + 8984.56i −0.464860 + 1.30447i
\(363\) 201.757 + 201.757i 0.0291722 + 0.0291722i
\(364\) −7254.68 + 8886.26i −1.04464 + 1.27958i
\(365\) 10618.3 5379.72i 1.52270 0.771472i
\(366\) 845.330 401.140i 0.120727 0.0572894i
\(367\) −6243.28 + 6243.28i −0.888002 + 0.888002i −0.994331 0.106329i \(-0.966090\pi\)
0.106329 + 0.994331i \(0.466090\pi\)
\(368\) 715.877 1083.38i 0.101407 0.153465i
\(369\) 3268.45i 0.461108i
\(370\) 4270.19 543.614i 0.599991 0.0763815i
\(371\) 13360.1i 1.86960i
\(372\) 4381.64 442.910i 0.610691 0.0617307i
\(373\) 5265.16 5265.16i 0.730884 0.730884i −0.239911 0.970795i \(-0.577118\pi\)
0.970795 + 0.239911i \(0.0771183\pi\)
\(374\) 3270.43 + 6891.85i 0.452165 + 0.952858i
\(375\) 684.269 4136.41i 0.0942280 0.569609i
\(376\) 188.912 766.688i 0.0259106 0.105157i
\(377\) −3499.80 3499.80i −0.478113 0.478113i
\(378\) 2515.56 + 896.443i 0.342293 + 0.121979i
\(379\) −8343.55 −1.13082 −0.565408 0.824811i \(-0.691281\pi\)
−0.565408 + 0.824811i \(0.691281\pi\)
\(380\) −1006.77 1571.76i −0.135911 0.212183i
\(381\) −6160.91 −0.828434
\(382\) −634.432 226.085i −0.0849747 0.0302815i
\(383\) −5925.06 5925.06i −0.790486 0.790486i 0.191087 0.981573i \(-0.438799\pi\)
−0.981573 + 0.191087i \(0.938799\pi\)
\(384\) −174.189 + 4340.97i −0.0231486 + 0.576886i
\(385\) −6211.89 12260.8i −0.822304 1.62303i
\(386\) −3412.58 7191.41i −0.449989 0.948272i
\(387\) 1439.40 1439.40i 0.189067 0.189067i
\(388\) −769.402 7611.56i −0.100671 0.995924i
\(389\) 81.4316i 0.0106137i −0.999986 0.00530687i \(-0.998311\pi\)
0.999986 0.00530687i \(-0.00168924\pi\)
\(390\) −2381.35 + 3076.10i −0.309190 + 0.399396i
\(391\) 1556.60i 0.201331i
\(392\) −10300.8 17036.8i −1.32722 2.19512i
\(393\) −650.841 + 650.841i −0.0835384 + 0.0835384i
\(394\) 6041.75 2867.03i 0.772536 0.366596i
\(395\) −1359.20 445.071i −0.173136 0.0566935i
\(396\) −1960.74 1600.74i −0.248815 0.203131i
\(397\) 10554.8 + 10554.8i 1.33433 + 1.33433i 0.901454 + 0.432876i \(0.142501\pi\)
0.432876 + 0.901454i \(0.357499\pi\)
\(398\) −4307.10 + 12086.4i −0.542451 + 1.52220i
\(399\) 2189.28 0.274690
\(400\) −3345.22 + 7267.01i −0.418153 + 0.908377i
\(401\) −6515.71 −0.811419 −0.405710 0.914002i \(-0.632976\pi\)
−0.405710 + 0.914002i \(0.632976\pi\)
\(402\) −207.052 + 581.022i −0.0256886 + 0.0720864i
\(403\) −5320.62 5320.62i −0.657665 0.657665i
\(404\) 4785.55 + 3906.89i 0.589331 + 0.481126i
\(405\) 860.642 + 281.817i 0.105594 + 0.0345768i
\(406\) 10785.6 5118.16i 1.31842 0.625640i
\(407\) 3383.87 3383.87i 0.412118 0.412118i
\(408\) 2694.54 + 4456.57i 0.326960 + 0.540768i
\(409\) 4656.50i 0.562956i 0.959568 + 0.281478i \(0.0908247\pi\)
−0.959568 + 0.281478i \(0.909175\pi\)
\(410\) −7030.01 + 9081.02i −0.846799 + 1.09385i
\(411\) 899.909i 0.108003i
\(412\) 77.7298 + 768.967i 0.00929483 + 0.0919522i
\(413\) −10328.6 + 10328.6i −1.23060 + 1.23060i
\(414\) 221.427 + 466.618i 0.0262863 + 0.0553937i
\(415\) −1336.41 2637.74i −0.158076 0.312004i
\(416\) 5933.58 4459.93i 0.699321 0.525640i
\(417\) 4144.57 + 4144.57i 0.486715 + 0.486715i
\(418\) −1954.65 696.557i −0.228720 0.0815065i
\(419\) 8824.96 1.02894 0.514472 0.857507i \(-0.327988\pi\)
0.514472 + 0.857507i \(0.327988\pi\)
\(420\) −5061.07 7901.32i −0.587988 0.917964i
\(421\) 15889.0 1.83939 0.919696 0.392632i \(-0.128435\pi\)
0.919696 + 0.392632i \(0.128435\pi\)
\(422\) −163.117 58.1282i −0.0188161 0.00670530i
\(423\) 222.080 + 222.080i 0.0255270 + 0.0255270i
\(424\) 2068.23 8393.81i 0.236892 0.961413i
\(425\) 1456.84 + 9478.54i 0.166275 + 1.08183i
\(426\) 1060.47 + 2234.76i 0.120611 + 0.254166i
\(427\) 2726.67 2726.67i 0.309023 0.309023i
\(428\) 2408.72 243.481i 0.272032 0.0274979i
\(429\) 4324.70i 0.486710i
\(430\) −7095.20 + 903.249i −0.795723 + 0.101299i
\(431\) 12016.0i 1.34290i −0.741048 0.671452i \(-0.765671\pi\)
0.741048 0.671452i \(-0.234329\pi\)
\(432\) −1441.69 952.638i −0.160563 0.106097i
\(433\) −11629.7 + 11629.7i −1.29073 + 1.29073i −0.356396 + 0.934335i \(0.615995\pi\)
−0.934335 + 0.356396i \(0.884005\pi\)
\(434\) 16397.0 7780.95i 1.81355 0.860593i
\(435\) 3611.40 1829.71i 0.398053 0.201673i
\(436\) 5963.44 7304.62i 0.655039 0.802358i
\(437\) 299.401 + 299.401i 0.0327742 + 0.0327742i
\(438\) 3032.54 8509.78i 0.330823 0.928341i
\(439\) 9052.02 0.984121 0.492061 0.870561i \(-0.336244\pi\)
0.492061 + 0.870561i \(0.336244\pi\)
\(440\) 2004.72 + 8664.76i 0.217208 + 0.938810i
\(441\) 7918.66 0.855054
\(442\) 2986.88 8381.67i 0.321429 0.901980i
\(443\) −12202.6 12202.6i −1.30873 1.30873i −0.922336 0.386389i \(-0.873722\pi\)
−0.386389 0.922336i \(-0.626278\pi\)
\(444\) 2066.08 2530.74i 0.220837 0.270503i
\(445\) 177.602 542.377i 0.0189194 0.0577779i
\(446\) 9947.93 4720.65i 1.05616 0.501187i
\(447\) 845.007 845.007i 0.0894127 0.0894127i
\(448\) 5329.09 + 17092.8i 0.562000 + 1.80259i
\(449\) 287.237i 0.0301906i −0.999886 0.0150953i \(-0.995195\pi\)
0.999886 0.0150953i \(-0.00480516\pi\)
\(450\) −1785.04 2634.13i −0.186995 0.275942i
\(451\) 12767.0i 1.33298i
\(452\) 9999.99 1010.83i 1.04062 0.105189i
\(453\) 3032.02 3032.02i 0.314474 0.314474i
\(454\) 1846.96 + 3892.13i 0.190929 + 0.402350i
\(455\) −4989.00 + 15235.9i −0.514040 + 1.56983i
\(456\) −1375.47 338.916i −0.141255 0.0348053i
\(457\) −1239.27 1239.27i −0.126851 0.126851i 0.640831 0.767682i \(-0.278590\pi\)
−0.767682 + 0.640831i \(0.778590\pi\)
\(458\) −5833.88 2078.96i −0.595195 0.212103i
\(459\) −2071.41 −0.210643
\(460\) 388.425 1772.70i 0.0393704 0.179680i
\(461\) −6295.73 −0.636055 −0.318027 0.948082i \(-0.603020\pi\)
−0.318027 + 0.948082i \(0.603020\pi\)
\(462\) −9826.13 3501.63i −0.989509 0.352620i
\(463\) 2108.18 + 2108.18i 0.211610 + 0.211610i 0.804951 0.593341i \(-0.202192\pi\)
−0.593341 + 0.804951i \(0.702192\pi\)
\(464\) −7568.64 + 1545.92i −0.757253 + 0.154672i
\(465\) 5490.28 2781.64i 0.547539 0.277409i
\(466\) 5849.36 + 12326.5i 0.581472 + 1.22535i
\(467\) −13383.7 + 13383.7i −1.32617 + 1.32617i −0.417491 + 0.908681i \(0.637091\pi\)
−0.908681 + 0.417491i \(0.862909\pi\)
\(468\) 296.926 + 2937.44i 0.0293278 + 0.290135i
\(469\) 2541.99i 0.250273i
\(470\) −139.359 1094.69i −0.0136769 0.107435i
\(471\) 1077.09i 0.105371i
\(472\) 8088.17 4890.28i 0.788746 0.476893i
\(473\) −5622.51 + 5622.51i −0.546561 + 0.546561i
\(474\) −980.645 + 465.352i −0.0950265 + 0.0450935i
\(475\) −2103.35 1542.92i −0.203175 0.149040i
\(476\) 16625.5 + 13573.0i 1.60090 + 1.30697i
\(477\) 2431.37 + 2431.37i 0.233385 + 0.233385i
\(478\) 5424.26 15221.4i 0.519038 1.45650i
\(479\) −966.896 −0.0922309 −0.0461154 0.998936i \(-0.514684\pi\)
−0.0461154 + 0.998936i \(0.514684\pi\)
\(480\) 1956.56 + 5747.68i 0.186051 + 0.546551i
\(481\) −5581.91 −0.529134
\(482\) 2466.82 6922.29i 0.233113 0.654153i
\(483\) 1505.11 + 1505.11i 0.141790 + 0.141790i
\(484\) −589.401 481.183i −0.0553532 0.0451900i
\(485\) −4832.12 9537.44i −0.452403 0.892934i
\(486\) 620.941 294.659i 0.0579557 0.0275021i
\(487\) 2440.48 2440.48i 0.227082 0.227082i −0.584391 0.811472i \(-0.698666\pi\)
0.811472 + 0.584391i \(0.198666\pi\)
\(488\) −2135.20 + 1290.99i −0.198066 + 0.119755i
\(489\) 11026.5i 1.01970i
\(490\) −22001.1 17032.0i −2.02838 1.57026i
\(491\) 4478.81i 0.411661i 0.978588 + 0.205831i \(0.0659896\pi\)
−0.978588 + 0.205831i \(0.934010\pi\)
\(492\) 876.562 + 8671.68i 0.0803221 + 0.794613i
\(493\) −6547.86 + 6547.86i −0.598176 + 0.598176i
\(494\) 1037.65 + 2186.67i 0.0945065 + 0.199156i
\(495\) −3361.78 1100.82i −0.305254 0.0999556i
\(496\) −11506.3 + 2350.21i −1.04163 + 0.212757i
\(497\) 7208.37 + 7208.37i 0.650583 + 0.650583i
\(498\) −2113.97 753.330i −0.190219 0.0677862i
\(499\) 3918.32 0.351519 0.175759 0.984433i \(-0.443762\pi\)
0.175759 + 0.984433i \(0.443762\pi\)
\(500\) −706.127 + 11158.0i −0.0631579 + 0.998004i
\(501\) −10826.2 −0.965430
\(502\) −16937.4 6035.79i −1.50588 0.536635i
\(503\) 9403.59 + 9403.59i 0.833569 + 0.833569i 0.988003 0.154434i \(-0.0493554\pi\)
−0.154434 + 0.988003i \(0.549355\pi\)
\(504\) −6914.57 1703.75i −0.611110 0.150577i
\(505\) 8205.05 + 2686.75i 0.723010 + 0.236750i
\(506\) −864.924 1822.67i −0.0759892 0.160134i
\(507\) −1093.61 + 1093.61i −0.0957963 + 0.0957963i
\(508\) 16345.8 1652.29i 1.42761 0.144308i
\(509\) 8533.02i 0.743063i −0.928420 0.371532i \(-0.878833\pi\)
0.928420 0.371532i \(-0.121167\pi\)
\(510\) 5755.16 + 4455.33i 0.499692 + 0.386834i
\(511\) 37230.5i 3.22306i
\(512\) −702.051 11563.9i −0.0605987 0.998162i
\(513\) 398.422 398.422i 0.0342900 0.0342900i
\(514\) −20353.6 + 9658.53i −1.74662 + 0.828832i
\(515\) 488.171 + 963.532i 0.0417697 + 0.0824433i
\(516\) −3432.92 + 4204.98i −0.292880 + 0.358748i
\(517\) −867.476 867.476i −0.0737941 0.0737941i
\(518\) 4519.57 12682.6i 0.383356 1.07576i
\(519\) 8494.30 0.718417
\(520\) 5493.09 8800.00i 0.463246 0.742126i
\(521\) 9514.75 0.800094 0.400047 0.916495i \(-0.368994\pi\)
0.400047 + 0.916495i \(0.368994\pi\)
\(522\) 1031.40 2894.28i 0.0864813 0.242680i
\(523\) −2837.39 2837.39i −0.237228 0.237228i 0.578473 0.815701i \(-0.303649\pi\)
−0.815701 + 0.578473i \(0.803649\pi\)
\(524\) 1552.23 1901.32i 0.129407 0.158511i
\(525\) −10573.7 7756.36i −0.878995 0.644791i
\(526\) −10830.3 + 5139.35i −0.897760 + 0.426019i
\(527\) −9954.49 + 9954.49i −0.822816 + 0.822816i
\(528\) 5631.43 + 3721.14i 0.464160 + 0.306708i
\(529\) 11755.3i 0.966165i
\(530\) −1525.72 11984.8i −0.125044 0.982241i
\(531\) 3759.36i 0.307236i
\(532\) −5808.49 + 587.142i −0.473365 + 0.0478493i
\(533\) 10530.0 10530.0i 0.855733 0.855733i
\(534\) −185.694 391.318i −0.0150483 0.0317116i
\(535\) 3018.17 1529.15i 0.243901 0.123572i
\(536\) 393.517 1597.07i 0.0317114 0.128699i
\(537\) 2617.58 + 2617.58i 0.210348 + 0.210348i
\(538\) 4326.35 + 1541.73i 0.346696 + 0.123548i
\(539\) −30931.4 −2.47181
\(540\) −2358.99 516.888i −0.187990 0.0411913i
\(541\) −21064.4 −1.67399 −0.836996 0.547210i \(-0.815690\pi\)
−0.836996 + 0.547210i \(0.815690\pi\)
\(542\) 4674.36 + 1665.75i 0.370445 + 0.132011i
\(543\) 7153.50 + 7153.50i 0.565352 + 0.565352i
\(544\) −8344.21 11101.3i −0.657638 0.874934i
\(545\) 4101.03 12524.1i 0.322328 0.984357i
\(546\) 5216.34 + 10992.5i 0.408862 + 0.861604i
\(547\) 1757.20 1757.20i 0.137354 0.137354i −0.635087 0.772441i \(-0.719036\pi\)
0.772441 + 0.635087i \(0.219036\pi\)
\(548\) 241.346 + 2387.59i 0.0188134 + 0.186118i
\(549\) 992.438i 0.0771516i
\(550\) 6972.62 + 10289.3i 0.540570 + 0.797701i
\(551\) 2518.88i 0.194751i
\(552\) −712.619 1178.62i −0.0549476 0.0908794i
\(553\) −3163.14 + 3163.14i −0.243237 + 0.243237i
\(554\) 6530.00 3098.72i 0.500782 0.237639i
\(555\) 1420.83 4339.07i 0.108668 0.331862i
\(556\) −12107.7 9884.61i −0.923524 0.753959i
\(557\) 4185.97 + 4185.97i 0.318430 + 0.318430i 0.848164 0.529734i \(-0.177708\pi\)
−0.529734 + 0.848164i \(0.677708\pi\)
\(558\) 1568.00 4400.07i 0.118959 0.333817i
\(559\) 9274.70 0.701750
\(560\) 15546.8 + 19606.0i 1.17317 + 1.47947i
\(561\) 8091.19 0.608931
\(562\) −3045.92 + 8547.33i −0.228620 + 0.641543i
\(563\) 4751.36 + 4751.36i 0.355677 + 0.355677i 0.862216 0.506540i \(-0.169076\pi\)
−0.506540 + 0.862216i \(0.669076\pi\)
\(564\) −648.771 529.652i −0.0484365 0.0395432i
\(565\) 12530.2 6348.39i 0.933007 0.472706i
\(566\) −5998.55 + 2846.53i −0.445473 + 0.211393i
\(567\) 2002.89 2002.89i 0.148348 0.148348i
\(568\) −3412.93 5644.74i −0.252119 0.416986i
\(569\) 15307.4i 1.12781i −0.825841 0.563903i \(-0.809299\pi\)
0.825841 0.563903i \(-0.190701\pi\)
\(570\) −1963.92 + 250.016i −0.144315 + 0.0183720i
\(571\) 18367.1i 1.34613i 0.739585 + 0.673063i \(0.235022\pi\)
−0.739585 + 0.673063i \(0.764978\pi\)
\(572\) −1159.84 11474.1i −0.0847817 0.838732i
\(573\) −505.134 + 505.134i −0.0368277 + 0.0368277i
\(574\) 15399.2 + 32451.2i 1.11978 + 2.35973i
\(575\) −385.287 2506.77i −0.0279436 0.181808i
\(576\) 4080.50 + 2140.84i 0.295175 + 0.154864i
\(577\) −6309.83 6309.83i −0.455254 0.455254i 0.441840 0.897094i \(-0.354326\pi\)
−0.897094 + 0.441840i \(0.854326\pi\)
\(578\) −2591.74 923.588i −0.186509 0.0664640i
\(579\) −8442.89 −0.606001
\(580\) −9090.86 + 5823.02i −0.650823 + 0.416875i
\(581\) −9248.66 −0.660411
\(582\) −7643.59 2723.86i −0.544393 0.193999i
\(583\) −9497.25 9497.25i −0.674676 0.674676i
\(584\) −5763.54 + 23391.0i −0.408385 + 1.65741i
\(585\) 1864.81 + 3680.68i 0.131795 + 0.260132i
\(586\) −6281.33 13236.8i −0.442797 0.933116i
\(587\) 6395.12 6395.12i 0.449667 0.449667i −0.445577 0.895244i \(-0.647001\pi\)
0.895244 + 0.445577i \(0.147001\pi\)
\(588\) −21009.4 + 2123.69i −1.47349 + 0.148945i
\(589\) 3829.37i 0.267888i
\(590\) 8085.91 10445.0i 0.564223 0.728835i
\(591\) 7093.16i 0.493695i
\(592\) −4802.89 + 7268.52i −0.333442 + 0.504619i
\(593\) −924.317 + 924.317i −0.0640087 + 0.0640087i −0.738386 0.674378i \(-0.764412\pi\)
0.674378 + 0.738386i \(0.264412\pi\)
\(594\) −2425.48 + 1150.98i −0.167540 + 0.0795037i
\(595\) 28505.3 + 9334.06i 1.96404 + 0.643125i
\(596\) −2015.31 + 2468.55i −0.138507 + 0.169657i
\(597\) 9623.18 + 9623.18i 0.659716 + 0.659716i
\(598\) −789.935 + 2216.68i −0.0540181 + 0.151583i
\(599\) 16688.6 1.13836 0.569181 0.822212i \(-0.307260\pi\)
0.569181 + 0.822212i \(0.307260\pi\)
\(600\) 5442.42 + 6509.99i 0.370310 + 0.442949i
\(601\) −224.497 −0.0152370 −0.00761848 0.999971i \(-0.502425\pi\)
−0.00761848 + 0.999971i \(0.502425\pi\)
\(602\) −7509.56 + 21073.0i −0.508417 + 1.42670i
\(603\) 462.609 + 462.609i 0.0312420 + 0.0312420i
\(604\) −7231.25 + 8857.56i −0.487144 + 0.596703i
\(605\) −1010.56 330.907i −0.0679090 0.0222368i
\(606\) 5919.83 2809.17i 0.396826 0.188308i
\(607\) 2845.34 2845.34i 0.190262 0.190262i −0.605547 0.795809i \(-0.707046\pi\)
0.795809 + 0.605547i \(0.207046\pi\)
\(608\) 3740.22 + 530.308i 0.249484 + 0.0353731i
\(609\) 12662.6i 0.842549i
\(610\) −2134.61 + 2757.38i −0.141685 + 0.183021i
\(611\) 1430.96i 0.0947470i
\(612\) 5495.74 555.528i 0.362994 0.0366926i
\(613\) 16137.6 16137.6i 1.06328 1.06328i 0.0654249 0.997857i \(-0.479160\pi\)
0.997857 0.0654249i \(-0.0208403\pi\)
\(614\) −7117.65 14999.2i −0.467826 0.985859i
\(615\) 5505.13 + 10865.8i 0.360956 + 0.712440i
\(616\) 27009.3 + 6655.08i 1.76661 + 0.435293i
\(617\) −187.494 187.494i −0.0122338 0.0122338i 0.700963 0.713197i \(-0.252754\pi\)
−0.713197 + 0.700963i \(0.752754\pi\)
\(618\) 772.203 + 275.181i 0.0502630 + 0.0179117i
\(619\) −14428.3 −0.936867 −0.468434 0.883499i \(-0.655181\pi\)
−0.468434 + 0.883499i \(0.655181\pi\)
\(620\) −13820.5 + 8852.52i −0.895234 + 0.573429i
\(621\) 547.820 0.0353998
\(622\) 11501.1 + 4098.51i 0.741401 + 0.264205i
\(623\) −1262.22 1262.22i −0.0811715 0.0811715i
\(624\) −1575.58 7713.83i −0.101080 0.494873i
\(625\) 4692.24 + 14903.8i 0.300303 + 0.953844i
\(626\) 7544.12 + 15897.9i 0.481667 + 1.01503i
\(627\) −1556.29 + 1556.29i −0.0991264 + 0.0991264i
\(628\) 288.863 + 2857.67i 0.0183549 + 0.181582i
\(629\) 10443.3i 0.662009i
\(630\) −9872.75 + 1256.84i −0.624349 + 0.0794823i
\(631\) 23046.4i 1.45398i 0.686648 + 0.726990i \(0.259081\pi\)
−0.686648 + 0.726990i \(0.740919\pi\)
\(632\) 2476.99 1497.64i 0.155901 0.0942612i
\(633\) −129.874 + 129.874i −0.00815484 + 0.00815484i
\(634\) 26874.7 12753.0i 1.68349 0.798875i
\(635\) 20481.6 10377.0i 1.27998 0.648500i
\(636\) −7102.84 5798.71i −0.442839 0.361531i
\(637\) 25511.6 + 25511.6i 1.58683 + 1.58683i
\(638\) −4028.80 + 11305.5i −0.250003 + 0.701547i
\(639\) 2623.66 0.162426
\(640\) −6732.52 14724.7i −0.415822 0.909446i
\(641\) −19800.3 −1.22007 −0.610036 0.792374i \(-0.708845\pi\)
−0.610036 + 0.792374i \(0.708845\pi\)
\(642\) 861.980 2418.85i 0.0529901 0.148699i
\(643\) −2880.22 2880.22i −0.176648 0.176648i 0.613245 0.789893i \(-0.289864\pi\)
−0.789893 + 0.613245i \(0.789864\pi\)
\(644\) −4396.92 3589.62i −0.269042 0.219644i
\(645\) −2360.80 + 7209.65i −0.144118 + 0.440123i
\(646\) 4091.10 1941.37i 0.249167 0.118239i
\(647\) −304.839 + 304.839i −0.0185231 + 0.0185231i −0.716308 0.697785i \(-0.754169\pi\)
0.697785 + 0.716308i \(0.254169\pi\)
\(648\) −1568.42 + 948.303i −0.0950826 + 0.0574890i
\(649\) 14684.6i 0.888167i
\(650\) 2735.51 14237.3i 0.165070 0.859127i
\(651\) 19250.4i 1.15896i
\(652\) −2957.17 29254.8i −0.177626 1.75722i
\(653\) −2622.41 + 2622.41i −0.157156 + 0.157156i −0.781305 0.624149i \(-0.785446\pi\)
0.624149 + 0.781305i \(0.285446\pi\)
\(654\) −4287.90 9035.99i −0.256376 0.540268i
\(655\) 1067.46 3259.91i 0.0636780 0.194466i
\(656\) −4651.29 22772.1i −0.276833 1.35534i
\(657\) −6775.48 6775.48i −0.402339 0.402339i
\(658\) −3251.28 1158.62i −0.192626 0.0686440i
\(659\) 4095.69 0.242102 0.121051 0.992646i \(-0.461373\pi\)
0.121051 + 0.992646i \(0.461373\pi\)
\(660\) 9214.53 + 2019.04i 0.543447 + 0.119077i
\(661\) −13157.5 −0.774232 −0.387116 0.922031i \(-0.626529\pi\)
−0.387116 + 0.922031i \(0.626529\pi\)
\(662\) 25102.0 + 8945.33i 1.47374 + 0.525182i
\(663\) −6673.48 6673.48i −0.390915 0.390915i
\(664\) 5810.69 + 1431.75i 0.339606 + 0.0836790i
\(665\) −7278.16 + 3687.46i −0.424413 + 0.215028i
\(666\) −1485.57 3130.58i −0.0864337 0.182144i
\(667\) 1731.70 1731.70i 0.100527 0.100527i
\(668\) 28723.6 2903.47i 1.66370 0.168172i
\(669\) 11679.1i 0.674948i
\(670\) −290.294 2280.32i −0.0167389 0.131487i
\(671\) 3876.60i 0.223032i
\(672\) 18802.3 + 2665.89i 1.07934 + 0.153034i
\(673\) −1199.59 + 1199.59i −0.0687087 + 0.0687087i −0.740626 0.671917i \(-0.765471\pi\)
0.671917 + 0.740626i \(0.265471\pi\)
\(674\) −1122.40 + 532.621i −0.0641445 + 0.0304389i
\(675\) −3335.83 + 512.713i −0.190216 + 0.0292360i
\(676\) 2608.20 3194.79i 0.148396 0.181770i
\(677\) 9185.47 + 9185.47i 0.521457 + 0.521457i 0.918011 0.396554i \(-0.129794\pi\)
−0.396554 + 0.918011i \(0.629794\pi\)
\(678\) 3578.58 10042.1i 0.202706 0.568824i
\(679\) −33440.9 −1.89005
\(680\) −16464.2 10277.2i −0.928488 0.579575i
\(681\) 4569.46 0.257125
\(682\) −6124.84 + 17187.3i −0.343889 + 0.965007i
\(683\) −7460.74 7460.74i −0.417975 0.417975i 0.466530 0.884505i \(-0.345504\pi\)
−0.884505 + 0.466530i \(0.845504\pi\)
\(684\) −950.219 + 1163.92i −0.0531177 + 0.0650639i
\(685\) 1515.74 + 2991.70i 0.0845451 + 0.166871i
\(686\) −47971.6 + 22764.3i −2.66992 + 1.26697i
\(687\) −4644.93 + 4644.93i −0.257955 + 0.257955i
\(688\) 7980.31 12077.1i 0.442219 0.669238i
\(689\) 15666.3i 0.866241i
\(690\) −1522.06 1178.29i −0.0839764 0.0650098i
\(691\) 24513.0i 1.34952i 0.738036 + 0.674761i \(0.235753\pi\)
−0.738036 + 0.674761i \(0.764247\pi\)
\(692\) −22536.6 + 2278.08i −1.23803 + 0.125144i
\(693\) −7823.56 + 7823.56i −0.428849 + 0.428849i
\(694\) 1426.29 + 3005.66i 0.0780136 + 0.164400i
\(695\) −20759.2 6797.60i −1.13301 0.371004i
\(696\) −1960.25 + 7955.56i −0.106757 + 0.433268i
\(697\) −19700.9 19700.9i −1.07062 1.07062i
\(698\) 4386.59 + 1563.20i 0.237873 + 0.0847680i
\(699\) 14471.6 0.783069
\(700\) 30133.6 + 17743.0i 1.62706 + 0.958033i
\(701\) 11328.2 0.610355 0.305178 0.952295i \(-0.401284\pi\)
0.305178 + 0.952295i \(0.401284\pi\)
\(702\) 2949.80 + 1051.19i 0.158594 + 0.0565165i
\(703\) −2008.71 2008.71i −0.107767 0.107767i
\(704\) −15939.0 8362.43i −0.853300 0.447686i
\(705\) −1112.35 364.239i −0.0594234 0.0194582i
\(706\) 6127.55 + 12912.7i 0.326648 + 0.688352i
\(707\) 19094.8 19094.8i 1.01575 1.01575i
\(708\) −1008.22 9974.14i −0.0535186 0.529451i
\(709\) 21881.0i 1.15904i 0.814958 + 0.579520i \(0.196760\pi\)
−0.814958 + 0.579520i \(0.803240\pi\)
\(710\) −7289.55 5643.16i −0.385313 0.298287i
\(711\) 1151.30i 0.0607274i
\(712\) 597.621 + 988.422i 0.0314562 + 0.0520263i
\(713\) 2632.64 2632.64i 0.138279 0.138279i
\(714\) 20566.2 9759.39i 1.07797 0.511535i
\(715\) −7284.19 14377.2i −0.380998 0.751997i
\(716\) −7646.82 6242.81i −0.399127 0.325844i
\(717\) −12119.2 12119.2i −0.631242 0.631242i
\(718\) −7959.61 + 22335.9i −0.413719 + 1.16096i
\(719\) 1377.95 0.0714728 0.0357364 0.999361i \(-0.488622\pi\)
0.0357364 + 0.999361i \(0.488622\pi\)
\(720\) 6397.37 + 738.726i 0.331133 + 0.0382370i
\(721\) 3378.41 0.174506
\(722\) 6098.79 17114.2i 0.314368 0.882166i
\(723\) −5511.52 5511.52i −0.283507 0.283507i
\(724\) −20897.8 17060.8i −1.07273 0.875773i
\(725\) −8924.08 + 12165.5i −0.457147 + 0.623195i
\(726\) −729.103 + 345.986i −0.0372721 + 0.0176870i
\(727\) −14563.5 + 14563.5i −0.742957 + 0.742957i −0.973146 0.230189i \(-0.926066\pi\)
0.230189 + 0.973146i \(0.426066\pi\)
\(728\) −16787.8 27765.8i −0.854666 1.41355i
\(729\) 729.000i 0.0370370i
\(730\) 4251.72 + 33398.1i 0.215566 + 1.69331i
\(731\) 17352.3i 0.877972i
\(732\) 266.161 + 2633.08i 0.0134393 + 0.132953i
\(733\) 14095.0 14095.0i 0.710247 0.710247i −0.256340 0.966587i \(-0.582517\pi\)
0.966587 + 0.256340i \(0.0825167\pi\)
\(734\) −10706.3 22561.7i −0.538390 1.13456i
\(735\) −26325.1 + 13337.6i −1.32111 + 0.669339i
\(736\) 2206.78 + 2935.94i 0.110520 + 0.147038i
\(737\) −1807.01 1807.01i −0.0903151 0.0903151i
\(738\) 8708.16 + 3103.23i 0.434352 + 0.154785i
\(739\) 21280.1 1.05927 0.529635 0.848225i \(-0.322329\pi\)
0.529635 + 0.848225i \(0.322329\pi\)
\(740\) −2605.98 + 11893.2i −0.129456 + 0.590817i
\(741\) 2567.20 0.127272
\(742\) −35595.4 12684.8i −1.76112 0.627590i
\(743\) 21284.9 + 21284.9i 1.05096 + 1.05096i 0.998630 + 0.0523340i \(0.0166661\pi\)
0.0523340 + 0.998630i \(0.483334\pi\)
\(744\) −2980.10 + 12094.6i −0.146849 + 0.595978i
\(745\) −1385.92 + 4232.45i −0.0681557 + 0.208141i
\(746\) 9029.01 + 19027.0i 0.443131 + 0.933819i
\(747\) −1683.14 + 1683.14i −0.0824401 + 0.0824401i
\(748\) −21467.1 + 2169.97i −1.04935 + 0.106072i
\(749\) 10582.6i 0.516259i
\(750\) 10371.0 + 5750.42i 0.504927 + 0.279968i
\(751\) 15103.2i 0.733855i 0.930250 + 0.366927i \(0.119590\pi\)
−0.930250 + 0.366927i \(0.880410\pi\)
\(752\) 1863.33 + 1231.25i 0.0903573 + 0.0597063i
\(753\) −13485.5 + 13485.5i −0.652643 + 0.652643i
\(754\) 12647.4 6001.66i 0.610865 0.289877i
\(755\) −4972.89 + 15186.7i −0.239711 + 0.732054i
\(756\) −4776.80 + 5851.11i −0.229802 + 0.281485i
\(757\) −3670.42 3670.42i −0.176227 0.176227i 0.613482 0.789709i \(-0.289768\pi\)
−0.789709 + 0.613482i \(0.789768\pi\)
\(758\) 7921.78 22229.8i 0.379594 1.06520i
\(759\) −2139.86 −0.102335
\(760\) 5143.53 1190.03i 0.245494 0.0567986i
\(761\) 37834.8 1.80225 0.901123 0.433564i \(-0.142744\pi\)
0.901123 + 0.433564i \(0.142744\pi\)
\(762\) 5849.48 16414.6i 0.278090 0.780364i
\(763\) −29146.2 29146.2i −1.38291 1.38291i
\(764\) 1204.72 1475.67i 0.0570489 0.0698792i
\(765\) 6886.28 3488.92i 0.325456 0.164892i
\(766\) 21411.7 10160.6i 1.00997 0.479267i
\(767\) −12111.6 + 12111.6i −0.570175 + 0.570175i
\(768\) −11400.3 4585.63i −0.535642 0.215455i
\(769\) 30282.3i 1.42004i 0.704183 + 0.710019i \(0.251314\pi\)
−0.704183 + 0.710019i \(0.748686\pi\)
\(770\) 38564.3 4909.41i 1.80489 0.229770i
\(771\) 23895.7i 1.11619i
\(772\) 22400.2 2264.29i 1.04430 0.105562i
\(773\) −23218.3 + 23218.3i −1.08034 + 1.08034i −0.0838641 + 0.996477i \(0.526726\pi\)
−0.996477 + 0.0838641i \(0.973274\pi\)
\(774\) 2468.38 + 5201.66i 0.114630 + 0.241563i
\(775\) −13567.0 + 18494.8i −0.628825 + 0.857230i
\(776\) 21010.1 + 5176.88i 0.971929 + 0.239483i
\(777\) −10097.9 10097.9i −0.466230 0.466230i
\(778\) 216.959 + 77.3152i 0.00999788 + 0.00356284i
\(779\) 7578.68 0.348568
\(780\) −5934.72 9265.25i −0.272432 0.425320i
\(781\) −10248.4 −0.469547
\(782\) 4147.25 + 1477.91i 0.189649 + 0.0675831i
\(783\) −2304.42 2304.42i −0.105177 0.105177i
\(784\) 55171.3 11268.9i 2.51327 0.513345i
\(785\) 1814.16 + 3580.72i 0.0824845 + 0.162804i
\(786\) −1116.10 2351.98i −0.0506488 0.106733i
\(787\) 19881.2 19881.2i 0.900492 0.900492i −0.0949865 0.995479i \(-0.530281\pi\)
0.995479 + 0.0949865i \(0.0302808\pi\)
\(788\) 1902.31 + 18819.2i 0.0859985 + 0.850769i
\(789\) 12715.0i 0.573721i
\(790\) 2476.30 3198.76i 0.111523 0.144059i
\(791\) 43934.3i 1.97487i
\(792\) 6126.48 3704.20i 0.274867 0.166191i
\(793\) 3197.35 3197.35i 0.143179 0.143179i
\(794\) −38142.4 + 18099.9i −1.70482 + 0.808996i
\(795\) −12178.2 3987.74i −0.543289 0.177900i
\(796\) −28112.5 22950.9i −1.25179 1.02195i
\(797\) −17974.6 17974.6i −0.798862 0.798862i 0.184054 0.982916i \(-0.441078\pi\)
−0.982916 + 0.184054i \(0.941078\pi\)
\(798\) −2078.62 + 5832.93i −0.0922083 + 0.258751i
\(799\) 2677.22 0.118540
\(800\) −16185.5 15812.4i −0.715303 0.698815i
\(801\) −459.417 −0.0202655
\(802\) 6186.35 17359.9i 0.272378 0.764337i
\(803\) 26466.0 + 26466.0i 1.16309 + 1.16309i
\(804\) −1351.44 1103.30i −0.0592804 0.0483961i
\(805\) −7538.73 2468.56i −0.330069 0.108081i
\(806\) 19227.4 9124.11i 0.840270 0.398738i
\(807\) 3444.64 3444.64i 0.150256 0.150256i
\(808\) −14952.8 + 9040.78i −0.651036 + 0.393631i
\(809\) 33951.7i 1.47550i 0.675075 + 0.737749i \(0.264111\pi\)
−0.675075 + 0.737749i \(0.735889\pi\)
\(810\) −1567.98 + 2025.44i −0.0680165 + 0.0878603i
\(811\) 5751.71i 0.249038i 0.992217 + 0.124519i \(0.0397388\pi\)
−0.992217 + 0.124519i \(0.960261\pi\)
\(812\) 3395.95 + 33595.6i 0.146767 + 1.45194i
\(813\) 3721.72 3721.72i 0.160549 0.160549i
\(814\) 5802.86 + 12228.5i 0.249865 + 0.526546i
\(815\) −18572.1 36656.9i −0.798225 1.57550i
\(816\) −14432.0 + 2947.79i −0.619144 + 0.126462i
\(817\) 3337.60 + 3337.60i 0.142923 + 0.142923i
\(818\) −12406.4 4421.12i −0.530291 0.188974i
\(819\) 12905.5 0.550615
\(820\) −17520.0 27352.1i −0.746128 1.16485i
\(821\) −4301.92 −0.182872 −0.0914361 0.995811i \(-0.529146\pi\)
−0.0914361 + 0.995811i \(0.529146\pi\)
\(822\) 2397.64 + 854.419i 0.101736 + 0.0362546i
\(823\) 25444.1 + 25444.1i 1.07767 + 1.07767i 0.996718 + 0.0809559i \(0.0257973\pi\)
0.0809559 + 0.996718i \(0.474203\pi\)
\(824\) −2122.57 523.000i −0.0897368 0.0221111i
\(825\) 13030.2 2002.73i 0.549883 0.0845163i
\(826\) −17712.2 37325.3i −0.746108 1.57229i
\(827\) 14358.8 14358.8i 0.603756 0.603756i −0.337551 0.941307i \(-0.609599\pi\)
0.941307 + 0.337551i \(0.109599\pi\)
\(828\) −1453.45 + 146.919i −0.0610034 + 0.00616642i
\(829\) 1655.91i 0.0693753i 0.999398 + 0.0346877i \(0.0110436\pi\)
−0.999398 + 0.0346877i \(0.988956\pi\)
\(830\) 8296.62 1056.19i 0.346964 0.0441700i
\(831\) 7666.37i 0.320028i
\(832\) 6249.00 + 20043.4i 0.260391 + 0.835191i
\(833\) 47730.4 47730.4i 1.98531 1.98531i
\(834\) −14977.5 + 7107.34i −0.621855 + 0.295093i
\(835\) 35991.2 18234.9i 1.49165 0.755741i
\(836\) 3711.69 4546.45i 0.153554 0.188089i
\(837\) −3503.33 3503.33i −0.144675 0.144675i
\(838\) −8378.86 + 23512.4i −0.345397 + 0.969240i
\(839\) 21952.9 0.903337 0.451669 0.892186i \(-0.350829\pi\)
0.451669 + 0.892186i \(0.350829\pi\)
\(840\) 25856.8 5982.35i 1.06208 0.245727i
\(841\) 9820.10 0.402645
\(842\) −15085.8 + 42333.3i −0.617450 + 1.73266i
\(843\) 6805.38 + 6805.38i 0.278042 + 0.278042i
\(844\) 309.743 379.404i 0.0126325 0.0154735i
\(845\) 1793.65 5477.62i 0.0730217 0.223001i
\(846\) −802.545 + 380.836i −0.0326147 + 0.0154769i
\(847\) −2351.77 + 2351.77i −0.0954047 + 0.0954047i
\(848\) 20400.0 + 13479.9i 0.826108 + 0.545875i
\(849\) 7042.44i 0.284683i
\(850\) −26636.9 5117.93i −1.07487 0.206522i
\(851\) 2761.93i 0.111255i
\(852\) −6960.96 + 703.637i −0.279905 + 0.0282937i
\(853\) 2701.54 2701.54i 0.108440 0.108440i −0.650805 0.759245i \(-0.725569\pi\)
0.759245 + 0.650805i \(0.225569\pi\)
\(854\) 4675.86 + 9853.53i 0.187359 + 0.394825i
\(855\) −653.461 + 1995.60i −0.0261379 + 0.0798224i
\(856\) −1638.25 + 6648.75i −0.0654138 + 0.265478i
\(857\) 9284.02 + 9284.02i 0.370054 + 0.370054i 0.867497 0.497443i \(-0.165728\pi\)
−0.497443 + 0.867497i \(0.665728\pi\)
\(858\) −11522.3 4106.09i −0.458468 0.163379i
\(859\) −27094.0 −1.07618 −0.538089 0.842888i \(-0.680854\pi\)
−0.538089 + 0.842888i \(0.680854\pi\)
\(860\) 4330.00 19761.4i 0.171688 0.783556i
\(861\) 38098.5 1.50800
\(862\) 32014.4 + 11408.6i 1.26498 + 0.450788i
\(863\) −500.709 500.709i −0.0197501 0.0197501i 0.697163 0.716913i \(-0.254445\pi\)
−0.716913 + 0.697163i \(0.754445\pi\)
\(864\) 3906.93 2936.62i 0.153839 0.115632i
\(865\) −28238.8 + 14307.2i −1.11000 + 0.562379i
\(866\) −19943.3 42026.9i −0.782563 1.64911i
\(867\) −2063.54 + 2063.54i −0.0808321 + 0.0808321i
\(868\) 5162.75 + 51074.2i 0.201884 + 1.99720i
\(869\) 4497.14i 0.175552i
\(870\) 1446.06 + 11359.1i 0.0563518 + 0.442654i
\(871\) 2980.79i 0.115959i
\(872\) 13799.8 + 22823.8i 0.535917 + 0.886368i
\(873\) −6085.82 + 6085.82i −0.235938 + 0.235938i
\(874\) −1081.96 + 513.431i −0.0418741 + 0.0198708i
\(875\) 48215.8 + 7976.13i 1.86285 + 0.308163i
\(876\) 19793.5 + 16159.2i 0.763423 + 0.623253i
\(877\) −35402.9 35402.9i −1.36314 1.36314i −0.869887 0.493252i \(-0.835808\pi\)
−0.493252 0.869887i \(-0.664192\pi\)
\(878\) −8594.44 + 24117.4i −0.330351 + 0.927018i
\(879\) −15540.3 −0.596315
\(880\) −24989.0 2885.56i −0.957248 0.110537i
\(881\) 12786.2 0.488966 0.244483 0.969654i \(-0.421382\pi\)
0.244483 + 0.969654i \(0.421382\pi\)
\(882\) −7518.37 + 21097.7i −0.287026 + 0.805440i
\(883\) −24669.9 24669.9i −0.940212 0.940212i 0.0580988 0.998311i \(-0.481496\pi\)
−0.998311 + 0.0580988i \(0.981496\pi\)
\(884\) 19495.5 + 15916.0i 0.741746 + 0.605556i
\(885\) −6331.98 12497.8i −0.240505 0.474699i
\(886\) 44097.4 20925.8i 1.67210 0.793472i
\(887\) −36047.5 + 36047.5i −1.36455 + 1.36455i −0.496535 + 0.868017i \(0.665395\pi\)
−0.868017 + 0.496535i \(0.834605\pi\)
\(888\) 4781.03 + 7907.48i 0.180677 + 0.298826i
\(889\) 71814.2i 2.70931i
\(890\) 1276.44 + 988.146i 0.0480745 + 0.0372165i
\(891\) 2847.57i 0.107068i
\(892\) 3132.21 + 30986.4i 0.117572 + 1.16312i
\(893\) −514.946 + 514.946i −0.0192968 + 0.0192968i
\(894\) 1449.07 + 3053.65i 0.0542104 + 0.114239i
\(895\) −13110.8 4293.15i −0.489661 0.160340i
\(896\) −50600.2 2030.42i −1.88665 0.0757049i
\(897\) 1764.92 + 1764.92i 0.0656956 + 0.0656956i
\(898\) 765.289 + 272.718i 0.0284388 + 0.0101344i
\(899\) −22148.6 −0.821687
\(900\) 8712.94 2254.93i 0.322701 0.0835160i
\(901\) 29310.6 1.08377
\(902\) −34015.3 12121.6i −1.25564 0.447458i
\(903\) 16778.3 + 16778.3i 0.618325 + 0.618325i
\(904\) −6801.32 + 27602.8i −0.250231 + 1.01555i
\(905\) −35830.2 11732.6i −1.31606 0.430945i
\(906\) 5199.49 + 10957.0i 0.190664 + 0.401790i
\(907\) 21947.1 21947.1i 0.803465 0.803465i −0.180170 0.983635i \(-0.557665\pi\)
0.983635 + 0.180170i \(0.0576649\pi\)
\(908\) −12123.4 + 1225.48i −0.443095 + 0.0447895i
\(909\) 6950.03i 0.253595i
\(910\) −35856.4 27758.0i −1.30618 1.01117i
\(911\) 23974.7i 0.871919i 0.899966 + 0.435960i \(0.143591\pi\)
−0.899966 + 0.435960i \(0.856409\pi\)
\(912\) 2208.92 3342.90i 0.0802024 0.121375i
\(913\) 6574.56 6574.56i 0.238320 0.238320i
\(914\) 4478.44 2125.18i 0.162072 0.0769088i
\(915\) 1671.59 + 3299.31i 0.0603945 + 0.119204i
\(916\) 11078.0 13569.4i 0.399592 0.489460i
\(917\) −7586.48 7586.48i −0.273204 0.273204i
\(918\) 1966.70 5518.86i 0.0707088 0.198420i
\(919\) −12744.3 −0.457448 −0.228724 0.973491i \(-0.573455\pi\)
−0.228724 + 0.973491i \(0.573455\pi\)
\(920\) 4354.24 + 2717.98i 0.156038 + 0.0974012i
\(921\) −17609.4 −0.630021
\(922\) 5977.48 16773.8i 0.213512 0.599148i
\(923\) 8452.69 + 8452.69i 0.301434 + 0.301434i
\(924\) 18658.9 22855.2i 0.664319 0.813725i
\(925\) 2584.93 + 16818.2i 0.0918832 + 0.597814i
\(926\) −7618.44 + 3615.23i −0.270365 + 0.128298i
\(927\) 614.827 614.827i 0.0217838 0.0217838i
\(928\) 3067.23 21633.0i 0.108499 0.765234i
\(929\) 39451.0i 1.39327i 0.717427 + 0.696634i \(0.245320\pi\)
−0.717427 + 0.696634i \(0.754680\pi\)
\(930\) 2198.40 + 17268.8i 0.0775142 + 0.608889i
\(931\) 18361.3i 0.646366i
\(932\) −38395.2 + 3881.11i −1.34944 + 0.136406i
\(933\) 9157.15 9157.15i 0.321320 0.321320i
\(934\) −22951.1 48365.4i −0.804051 1.69439i
\(935\) −26898.7 + 13628.2i −0.940837 + 0.476673i
\(936\) −8108.17 1997.85i −0.283145 0.0697670i
\(937\) 13496.0 + 13496.0i 0.470539 + 0.470539i 0.902089 0.431550i \(-0.142033\pi\)
−0.431550 + 0.902089i \(0.642033\pi\)
\(938\) −6772.64 2413.49i −0.235751 0.0840120i
\(939\) 18664.5 0.648662
\(940\) 3048.91 + 668.060i 0.105792 + 0.0231805i
\(941\) 19991.7 0.692574 0.346287 0.938129i \(-0.387442\pi\)
0.346287 + 0.938129i \(0.387442\pi\)
\(942\) 2869.70 + 1022.64i 0.0992566 + 0.0353710i
\(943\) 5210.25 + 5210.25i 0.179925 + 0.179925i
\(944\) 5349.91 + 26192.5i 0.184454 + 0.903064i
\(945\) −3284.98 + 10032.0i −0.113080 + 0.345335i
\(946\) −9641.82 20318.4i −0.331377 0.698318i
\(947\) −11191.3 + 11191.3i −0.384023 + 0.384023i −0.872549 0.488526i \(-0.837535\pi\)
0.488526 + 0.872549i \(0.337535\pi\)
\(948\) −308.766 3054.57i −0.0105783 0.104650i
\(949\) 43657.3i 1.49334i
\(950\) 6107.85 4139.05i 0.208595 0.141356i
\(951\) 31551.5i 1.07585i
\(952\) −51947.7 + 31408.7i −1.76852 + 1.06929i
\(953\) 2419.80 2419.80i 0.0822506 0.0822506i −0.664785 0.747035i \(-0.731477\pi\)
0.747035 + 0.664785i \(0.231477\pi\)
\(954\) −8786.37 + 4169.45i −0.298186 + 0.141500i
\(955\) 828.482 2530.10i 0.0280723 0.0857299i
\(956\) 35404.3 + 28903.8i 1.19776 + 0.977842i
\(957\) 9001.39 + 9001.39i 0.304048 + 0.304048i
\(958\) 918.020 2576.11i 0.0309602 0.0868792i
\(959\) 10489.7 0.353213
\(960\) −17171.3 244.246i −0.577292 0.00821145i
\(961\) −3880.70 −0.130264
\(962\) 5299.75 14871.9i 0.177620 0.498431i
\(963\) −1925.89 1925.89i −0.0644454 0.0644454i
\(964\) 16101.0 + 13144.8i 0.537945 + 0.439174i
\(965\) 28067.9 14220.6i 0.936309 0.474379i
\(966\) −5439.09 + 2581.05i −0.181159 + 0.0859666i
\(967\) 34223.1 34223.1i 1.13810 1.13810i 0.149308 0.988791i \(-0.452295\pi\)
0.988791 0.149308i \(-0.0477046\pi\)
\(968\) 1841.63 1113.49i 0.0611489 0.0369719i
\(969\) 4803.05i 0.159232i
\(970\) 29998.6 3818.95i 0.992985 0.126411i
\(971\) 6050.87i 0.199981i −0.994988 0.0999906i \(-0.968119\pi\)
0.994988 0.0999906i \(-0.0318813\pi\)
\(972\) 195.510 + 1934.14i 0.00645162 + 0.0638248i
\(973\) −48310.8 + 48310.8i −1.59175 + 1.59175i
\(974\) 4185.08 + 8819.31i 0.137678 + 0.290132i
\(975\) −12398.9 9095.27i −0.407264 0.298751i
\(976\) −1412.33 6914.58i −0.0463191 0.226773i
\(977\) −37140.0 37140.0i −1.21619 1.21619i −0.968957 0.247230i \(-0.920480\pi\)
−0.247230 0.968957i \(-0.579520\pi\)
\(978\) −29377.9 10469.1i −0.960534 0.342295i
\(979\) 1794.54 0.0585842
\(980\) 66267.5 42446.7i 2.16004 1.38358i
\(981\) −10608.5 −0.345262
\(982\) −11932.9 4252.41i −0.387775 0.138187i
\(983\) 1908.75 + 1908.75i 0.0619325 + 0.0619325i 0.737395 0.675462i \(-0.236056\pi\)
−0.675462 + 0.737395i \(0.736056\pi\)
\(984\) −23936.3 5897.90i −0.775468 0.191075i
\(985\) 11947.2 + 23580.8i 0.386466 + 0.762790i
\(986\) −11228.7 23662.4i −0.362671 0.764264i
\(987\) −2588.66 + 2588.66i −0.0834833 + 0.0834833i
\(988\) −6811.16 + 688.495i −0.219324 + 0.0221700i
\(989\) 4589.12i 0.147549i
\(990\) 6124.76 7911.66i 0.196624 0.253989i
\(991\) 33844.2i 1.08486i −0.840101 0.542430i \(-0.817505\pi\)
0.840101 0.542430i \(-0.182495\pi\)
\(992\) 4663.01 32887.8i 0.149245 1.05261i
\(993\) 19986.2 19986.2i 0.638714 0.638714i
\(994\) −26049.3 + 12361.3i −0.831222 + 0.394445i
\(995\) −48200.3 15783.2i −1.53573 0.502876i
\(996\) 4014.21 4917.01i 0.127706 0.156427i
\(997\) 1241.05 + 1241.05i 0.0394227 + 0.0394227i 0.726543 0.687121i \(-0.241126\pi\)
−0.687121 + 0.726543i \(0.741126\pi\)
\(998\) −3720.25 + 10439.6i −0.117998 + 0.331122i
\(999\) −3675.38 −0.116400
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 60.4.j.b.7.6 28
3.2 odd 2 180.4.k.f.127.9 28
4.3 odd 2 inner 60.4.j.b.7.13 yes 28
5.3 odd 4 inner 60.4.j.b.43.13 yes 28
12.11 even 2 180.4.k.f.127.2 28
15.8 even 4 180.4.k.f.163.2 28
20.3 even 4 inner 60.4.j.b.43.6 yes 28
60.23 odd 4 180.4.k.f.163.9 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.4.j.b.7.6 28 1.1 even 1 trivial
60.4.j.b.7.13 yes 28 4.3 odd 2 inner
60.4.j.b.43.6 yes 28 20.3 even 4 inner
60.4.j.b.43.13 yes 28 5.3 odd 4 inner
180.4.k.f.127.2 28 12.11 even 2
180.4.k.f.127.9 28 3.2 odd 2
180.4.k.f.163.2 28 15.8 even 4
180.4.k.f.163.9 28 60.23 odd 4