Properties

Label 117.4.t.a.103.31
Level $117$
Weight $4$
Character 117.103
Analytic conductor $6.903$
Analytic rank $0$
Dimension $80$
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] = [117,4,Mod(25,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.25");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.t (of order \(6\), 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: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 103.31
Character \(\chi\) \(=\) 117.103
Dual form 117.4.t.a.25.31

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.81478 - 1.62512i) q^{2} +(-5.02430 - 1.32530i) q^{3} +(1.28200 - 2.22049i) q^{4} +(-8.08964 - 4.67056i) q^{5} +(-16.2961 + 4.43465i) q^{6} +(-5.60310 + 3.23495i) q^{7} +17.6683i q^{8} +(23.4872 + 13.3174i) q^{9} +O(q^{10})\) \(q+(2.81478 - 1.62512i) q^{2} +(-5.02430 - 1.32530i) q^{3} +(1.28200 - 2.22049i) q^{4} +(-8.08964 - 4.67056i) q^{5} +(-16.2961 + 4.43465i) q^{6} +(-5.60310 + 3.23495i) q^{7} +17.6683i q^{8} +(23.4872 + 13.3174i) q^{9} -30.3608 q^{10} +(-28.4864 + 16.4466i) q^{11} +(-9.38396 + 9.45738i) q^{12} +(-28.5009 + 37.2115i) q^{13} +(-10.5143 + 18.2114i) q^{14} +(34.4549 + 34.1875i) q^{15} +(38.9690 + 67.4962i) q^{16} -99.5008 q^{17} +(87.7536 - 0.683865i) q^{18} -136.315i q^{19} +(-20.7419 + 11.9753i) q^{20} +(32.4389 - 8.82760i) q^{21} +(-53.4553 + 92.5874i) q^{22} +(-7.91924 + 13.7165i) q^{23} +(23.4157 - 88.7706i) q^{24} +(-18.8718 - 32.6869i) q^{25} +(-19.7508 + 151.060i) q^{26} +(-100.357 - 98.0380i) q^{27} +16.5888i q^{28} +(29.1948 + 50.5668i) q^{29} +(152.542 + 40.2370i) q^{30} +(80.0415 + 46.2120i) q^{31} +(96.9690 + 55.9851i) q^{32} +(164.921 - 44.8799i) q^{33} +(-280.073 + 161.700i) q^{34} +60.4361 q^{35} +(59.6817 - 35.0802i) q^{36} -384.369i q^{37} +(-221.528 - 383.697i) q^{38} +(192.513 - 149.190i) q^{39} +(82.5206 - 142.930i) q^{40} +(33.4192 + 19.2946i) q^{41} +(76.9627 - 77.5648i) q^{42} +(240.935 + 417.312i) q^{43} +84.3383i q^{44} +(-127.803 - 217.431i) q^{45} +51.4787i q^{46} +(-232.759 + 134.383i) q^{47} +(-106.339 - 390.767i) q^{48} +(-150.570 + 260.795i) q^{49} +(-106.240 - 61.3377i) q^{50} +(499.922 + 131.868i) q^{51} +(46.0897 + 110.991i) q^{52} -475.493 q^{53} +(-441.807 - 112.864i) q^{54} +307.260 q^{55} +(-57.1560 - 98.9970i) q^{56} +(-180.658 + 684.887i) q^{57} +(164.354 + 94.8898i) q^{58} +(-347.780 - 200.791i) q^{59} +(120.084 - 32.6785i) q^{60} +(-119.890 - 207.655i) q^{61} +300.399 q^{62} +(-174.682 + 1.36130i) q^{63} -259.574 q^{64} +(404.361 - 167.913i) q^{65} +(391.281 - 394.342i) q^{66} +(671.583 + 387.739i) q^{67} +(-127.560 + 220.940i) q^{68} +(57.9671 - 58.4206i) q^{69} +(170.115 - 98.2157i) q^{70} -769.570i q^{71} +(-235.295 + 414.977i) q^{72} +501.277i q^{73} +(-624.643 - 1081.91i) q^{74} +(51.4977 + 189.240i) q^{75} +(-302.686 - 174.756i) q^{76} +(106.408 - 184.304i) q^{77} +(299.433 - 732.793i) q^{78} +(418.818 + 725.413i) q^{79} -728.027i q^{80} +(374.295 + 625.575i) q^{81} +125.424 q^{82} +(19.4098 - 11.2062i) q^{83} +(21.9851 - 83.3473i) q^{84} +(804.926 + 464.724i) q^{85} +(1356.36 + 783.095i) q^{86} +(-79.6673 - 292.755i) q^{87} +(-290.583 - 503.305i) q^{88} -126.567i q^{89} +(-713.089 - 404.326i) q^{90} +(39.3159 - 300.699i) q^{91} +(20.3049 + 35.1692i) q^{92} +(-340.908 - 338.261i) q^{93} +(-436.777 + 756.520i) q^{94} +(-636.667 + 1102.74i) q^{95} +(-413.005 - 409.799i) q^{96} +(72.1507 - 41.6562i) q^{97} +978.776i q^{98} +(-888.091 + 6.92091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{3} + 150 q^{4} - 68 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{3} + 150 q^{4} - 68 q^{9} - 40 q^{10} + 190 q^{12} - 13 q^{13} + 78 q^{14} - 530 q^{16} + 264 q^{17} - 34 q^{22} - 174 q^{23} + 798 q^{25} - 1032 q^{26} + 302 q^{27} + 642 q^{29} + 198 q^{30} - 2136 q^{35} - 802 q^{36} - 708 q^{38} + 211 q^{39} + 88 q^{40} - 1212 q^{42} + 166 q^{43} + 4334 q^{48} + 1610 q^{49} + 150 q^{51} + 786 q^{52} + 1296 q^{53} - 508 q^{55} - 888 q^{56} + 838 q^{61} + 3540 q^{62} - 3652 q^{64} - 201 q^{65} - 2418 q^{66} + 612 q^{68} - 1890 q^{69} + 4458 q^{74} - 632 q^{75} - 2166 q^{77} - 2280 q^{78} + 514 q^{79} - 4076 q^{81} - 5188 q^{82} - 4458 q^{87} + 2338 q^{88} - 2226 q^{90} - 1086 q^{91} + 516 q^{92} + 488 q^{94} + 2136 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.81478 1.62512i 0.995176 0.574565i 0.0883585 0.996089i \(-0.471838\pi\)
0.906817 + 0.421524i \(0.138505\pi\)
\(3\) −5.02430 1.32530i −0.966927 0.255053i
\(4\) 1.28200 2.22049i 0.160250 0.277561i
\(5\) −8.08964 4.67056i −0.723560 0.417747i 0.0925018 0.995713i \(-0.470514\pi\)
−0.816061 + 0.577965i \(0.803847\pi\)
\(6\) −16.2961 + 4.43465i −1.10881 + 0.301739i
\(7\) −5.60310 + 3.23495i −0.302539 + 0.174671i −0.643583 0.765376i \(-0.722553\pi\)
0.341044 + 0.940047i \(0.389220\pi\)
\(8\) 17.6683i 0.780834i
\(9\) 23.4872 + 13.3174i 0.869895 + 0.493236i
\(10\) −30.3608 −0.960092
\(11\) −28.4864 + 16.4466i −0.780816 + 0.450804i −0.836719 0.547632i \(-0.815529\pi\)
0.0559037 + 0.998436i \(0.482196\pi\)
\(12\) −9.38396 + 9.45738i −0.225743 + 0.227509i
\(13\) −28.5009 + 37.2115i −0.608056 + 0.793894i
\(14\) −10.5143 + 18.2114i −0.200720 + 0.347657i
\(15\) 34.4549 + 34.1875i 0.593081 + 0.588478i
\(16\) 38.9690 + 67.4962i 0.608890 + 1.05463i
\(17\) −99.5008 −1.41956 −0.709779 0.704425i \(-0.751205\pi\)
−0.709779 + 0.704425i \(0.751205\pi\)
\(18\) 87.7536 0.683865i 1.14910 0.00895492i
\(19\) 136.315i 1.64594i −0.568087 0.822968i \(-0.692316\pi\)
0.568087 0.822968i \(-0.307684\pi\)
\(20\) −20.7419 + 11.9753i −0.231901 + 0.133888i
\(21\) 32.4389 8.82760i 0.337084 0.0917305i
\(22\) −53.4553 + 92.5874i −0.518033 + 0.897259i
\(23\) −7.91924 + 13.7165i −0.0717946 + 0.124352i −0.899688 0.436534i \(-0.856206\pi\)
0.827893 + 0.560886i \(0.189539\pi\)
\(24\) 23.4157 88.7706i 0.199154 0.755009i
\(25\) −18.8718 32.6869i −0.150974 0.261495i
\(26\) −19.7508 + 151.060i −0.148979 + 1.13943i
\(27\) −100.357 98.0380i −0.715324 0.698793i
\(28\) 16.5888i 0.111964i
\(29\) 29.1948 + 50.5668i 0.186943 + 0.323794i 0.944229 0.329288i \(-0.106809\pi\)
−0.757287 + 0.653082i \(0.773476\pi\)
\(30\) 152.542 + 40.2370i 0.928339 + 0.244875i
\(31\) 80.0415 + 46.2120i 0.463738 + 0.267739i 0.713615 0.700539i \(-0.247057\pi\)
−0.249877 + 0.968278i \(0.580390\pi\)
\(32\) 96.9690 + 55.9851i 0.535683 + 0.309277i
\(33\) 164.921 44.8799i 0.869971 0.236745i
\(34\) −280.073 + 161.700i −1.41271 + 0.815628i
\(35\) 60.4361 0.291873
\(36\) 59.6817 35.0802i 0.276304 0.162408i
\(37\) 384.369i 1.70783i −0.520410 0.853916i \(-0.674221\pi\)
0.520410 0.853916i \(-0.325779\pi\)
\(38\) −221.528 383.697i −0.945698 1.63800i
\(39\) 192.513 149.190i 0.790431 0.612551i
\(40\) 82.5206 142.930i 0.326191 0.564980i
\(41\) 33.4192 + 19.2946i 0.127298 + 0.0734953i 0.562297 0.826936i \(-0.309918\pi\)
−0.434999 + 0.900431i \(0.643251\pi\)
\(42\) 76.9627 77.5648i 0.282752 0.284964i
\(43\) 240.935 + 417.312i 0.854472 + 1.47999i 0.877134 + 0.480245i \(0.159452\pi\)
−0.0226626 + 0.999743i \(0.507214\pi\)
\(44\) 84.3383i 0.288966i
\(45\) −127.803 217.431i −0.423373 0.720282i
\(46\) 51.4787i 0.165003i
\(47\) −232.759 + 134.383i −0.722369 + 0.417060i −0.815624 0.578582i \(-0.803606\pi\)
0.0932547 + 0.995642i \(0.470273\pi\)
\(48\) −106.339 390.767i −0.319766 1.17505i
\(49\) −150.570 + 260.795i −0.438980 + 0.760336i
\(50\) −106.240 61.3377i −0.300492 0.173489i
\(51\) 499.922 + 131.868i 1.37261 + 0.362063i
\(52\) 46.0897 + 110.991i 0.122913 + 0.295994i
\(53\) −475.493 −1.23234 −0.616170 0.787613i \(-0.711316\pi\)
−0.616170 + 0.787613i \(0.711316\pi\)
\(54\) −441.807 112.864i −1.11338 0.284422i
\(55\) 307.260 0.753289
\(56\) −57.1560 98.9970i −0.136389 0.236233i
\(57\) −180.658 + 684.887i −0.419802 + 1.59150i
\(58\) 164.354 + 94.8898i 0.372081 + 0.214821i
\(59\) −347.780 200.791i −0.767408 0.443063i 0.0645411 0.997915i \(-0.479442\pi\)
−0.831949 + 0.554852i \(0.812775\pi\)
\(60\) 120.084 32.6785i 0.258380 0.0703129i
\(61\) −119.890 207.655i −0.251645 0.435861i 0.712334 0.701840i \(-0.247638\pi\)
−0.963979 + 0.265979i \(0.914305\pi\)
\(62\) 300.399 0.615334
\(63\) −174.682 + 1.36130i −0.349331 + 0.00272235i
\(64\) −259.574 −0.506981
\(65\) 404.361 167.913i 0.771612 0.320416i
\(66\) 391.281 394.342i 0.729749 0.735458i
\(67\) 671.583 + 387.739i 1.22458 + 0.707012i 0.965891 0.258948i \(-0.0833758\pi\)
0.258690 + 0.965960i \(0.416709\pi\)
\(68\) −127.560 + 220.940i −0.227484 + 0.394014i
\(69\) 57.9671 58.4206i 0.101136 0.101928i
\(70\) 170.115 98.2157i 0.290465 0.167700i
\(71\) 769.570i 1.28635i −0.765717 0.643177i \(-0.777616\pi\)
0.765717 0.643177i \(-0.222384\pi\)
\(72\) −235.295 + 414.977i −0.385135 + 0.679244i
\(73\) 501.277i 0.803699i 0.915706 + 0.401850i \(0.131633\pi\)
−0.915706 + 0.401850i \(0.868367\pi\)
\(74\) −624.643 1081.91i −0.981261 1.69959i
\(75\) 51.4977 + 189.240i 0.0792859 + 0.291353i
\(76\) −302.686 174.756i −0.456848 0.263761i
\(77\) 106.408 184.304i 0.157485 0.272772i
\(78\) 299.433 732.793i 0.434668 1.06375i
\(79\) 418.818 + 725.413i 0.596464 + 1.03311i 0.993338 + 0.115233i \(0.0367615\pi\)
−0.396875 + 0.917873i \(0.629905\pi\)
\(80\) 728.027i 1.01745i
\(81\) 374.295 + 625.575i 0.513436 + 0.858128i
\(82\) 125.424 0.168911
\(83\) 19.4098 11.2062i 0.0256687 0.0148198i −0.487111 0.873340i \(-0.661949\pi\)
0.512779 + 0.858520i \(0.328616\pi\)
\(84\) 21.9851 83.3473i 0.0285569 0.108261i
\(85\) 804.926 + 464.724i 1.02713 + 0.593016i
\(86\) 1356.36 + 783.095i 1.70070 + 0.981899i
\(87\) −79.6673 292.755i −0.0981750 0.360765i
\(88\) −290.583 503.305i −0.352003 0.609687i
\(89\) 126.567i 0.150742i −0.997156 0.0753710i \(-0.975986\pi\)
0.997156 0.0753710i \(-0.0240141\pi\)
\(90\) −713.089 404.326i −0.835180 0.473552i
\(91\) 39.3159 300.699i 0.0452904 0.346394i
\(92\) 20.3049 + 35.1692i 0.0230102 + 0.0398548i
\(93\) −340.908 338.261i −0.380113 0.377162i
\(94\) −436.777 + 756.520i −0.479256 + 0.830096i
\(95\) −636.667 + 1102.74i −0.687586 + 1.19093i
\(96\) −413.005 409.799i −0.439084 0.435676i
\(97\) 72.1507 41.6562i 0.0755237 0.0436036i −0.461763 0.887004i \(-0.652783\pi\)
0.537286 + 0.843400i \(0.319449\pi\)
\(98\) 978.776i 1.00889i
\(99\) −888.091 + 6.92091i −0.901581 + 0.00702604i
\(100\) −96.7746 −0.0967746
\(101\) 23.5768 + 40.8362i 0.0232275 + 0.0402313i 0.877406 0.479749i \(-0.159272\pi\)
−0.854178 + 0.519981i \(0.825939\pi\)
\(102\) 1621.47 441.251i 1.57402 0.428336i
\(103\) −46.2842 + 80.1666i −0.0442769 + 0.0766898i −0.887315 0.461165i \(-0.847432\pi\)
0.843038 + 0.537855i \(0.180765\pi\)
\(104\) −657.463 503.561i −0.619899 0.474791i
\(105\) −303.649 80.0958i −0.282220 0.0744433i
\(106\) −1338.41 + 772.731i −1.22639 + 0.708059i
\(107\) 647.225 0.584763 0.292381 0.956302i \(-0.405552\pi\)
0.292381 + 0.956302i \(0.405552\pi\)
\(108\) −346.350 + 97.1574i −0.308589 + 0.0865646i
\(109\) 68.6751i 0.0603476i 0.999545 + 0.0301738i \(0.00960607\pi\)
−0.999545 + 0.0301738i \(0.990394\pi\)
\(110\) 864.869 499.332i 0.749655 0.432813i
\(111\) −509.402 + 1931.18i −0.435589 + 1.65135i
\(112\) −436.694 252.125i −0.368426 0.212711i
\(113\) −849.291 + 1471.02i −0.707032 + 1.22461i 0.258922 + 0.965898i \(0.416633\pi\)
−0.965953 + 0.258716i \(0.916700\pi\)
\(114\) 604.509 + 2221.40i 0.496644 + 1.82503i
\(115\) 128.128 73.9745i 0.103895 0.0599840i
\(116\) 149.711 0.119830
\(117\) −1164.97 + 494.437i −0.920522 + 0.390690i
\(118\) −1305.23 −1.01827
\(119\) 557.513 321.880i 0.429472 0.247956i
\(120\) −604.033 + 608.758i −0.459503 + 0.463098i
\(121\) −124.517 + 215.670i −0.0935514 + 0.162036i
\(122\) −674.927 389.670i −0.500861 0.289172i
\(123\) −142.337 141.232i −0.104342 0.103532i
\(124\) 205.226 118.488i 0.148628 0.0858104i
\(125\) 1520.21i 1.08777i
\(126\) −489.480 + 287.710i −0.346082 + 0.203423i
\(127\) 483.018 0.337487 0.168744 0.985660i \(-0.446029\pi\)
0.168744 + 0.985660i \(0.446029\pi\)
\(128\) −1506.40 + 869.719i −1.04022 + 0.600570i
\(129\) −657.469 2416.01i −0.448736 1.64898i
\(130\) 865.310 1129.77i 0.583790 0.762212i
\(131\) 75.0145 129.929i 0.0500309 0.0866560i −0.839925 0.542702i \(-0.817401\pi\)
0.889956 + 0.456046i \(0.150735\pi\)
\(132\) 111.773 423.741i 0.0737017 0.279409i
\(133\) 440.972 + 763.787i 0.287497 + 0.497960i
\(134\) 2520.48 1.62490
\(135\) 353.962 + 1261.82i 0.225661 + 0.804443i
\(136\) 1758.00i 1.10844i
\(137\) −1536.64 + 887.178i −0.958275 + 0.553261i −0.895642 0.444776i \(-0.853283\pi\)
−0.0626336 + 0.998037i \(0.519950\pi\)
\(138\) 68.2245 258.644i 0.0420845 0.159545i
\(139\) 1462.43 2533.00i 0.892384 1.54565i 0.0553745 0.998466i \(-0.482365\pi\)
0.837009 0.547189i \(-0.184302\pi\)
\(140\) 77.4792 134.198i 0.0467727 0.0810128i
\(141\) 1347.55 366.708i 0.804851 0.219024i
\(142\) −1250.64 2166.17i −0.739095 1.28015i
\(143\) 199.884 1528.77i 0.116889 0.893999i
\(144\) 16.3985 + 2104.26i 0.00948989 + 1.21774i
\(145\) 545.423i 0.312379i
\(146\) 814.633 + 1410.99i 0.461778 + 0.799822i
\(147\) 1102.14 1110.76i 0.618388 0.623226i
\(148\) −853.487 492.761i −0.474028 0.273680i
\(149\) −1934.38 1116.82i −1.06356 0.614049i −0.137148 0.990551i \(-0.543793\pi\)
−0.926416 + 0.376502i \(0.877127\pi\)
\(150\) 452.491 + 448.978i 0.246305 + 0.244393i
\(151\) −1227.17 + 708.505i −0.661361 + 0.381837i −0.792795 0.609488i \(-0.791375\pi\)
0.131435 + 0.991325i \(0.458042\pi\)
\(152\) 2408.45 1.28520
\(153\) −2336.99 1325.09i −1.23487 0.700177i
\(154\) 691.702i 0.361941i
\(155\) −431.671 747.676i −0.223695 0.387450i
\(156\) −84.4722 618.736i −0.0433538 0.317554i
\(157\) −7.80661 + 13.5215i −0.00396838 + 0.00687344i −0.868003 0.496559i \(-0.834597\pi\)
0.864034 + 0.503433i \(0.167930\pi\)
\(158\) 2357.76 + 1361.25i 1.18717 + 0.685415i
\(159\) 2389.02 + 630.169i 1.19158 + 0.314312i
\(160\) −522.963 905.799i −0.258399 0.447561i
\(161\) 102.473i 0.0501617i
\(162\) 2070.19 + 1152.59i 1.00401 + 0.558985i
\(163\) 841.823i 0.404519i −0.979332 0.202260i \(-0.935171\pi\)
0.979332 0.202260i \(-0.0648285\pi\)
\(164\) 85.6868 49.4713i 0.0407989 0.0235552i
\(165\) −1543.76 407.210i −0.728375 0.192129i
\(166\) 36.4229 63.0862i 0.0170299 0.0294966i
\(167\) 3327.99 + 1921.41i 1.54208 + 0.890320i 0.998707 + 0.0508286i \(0.0161862\pi\)
0.543373 + 0.839492i \(0.317147\pi\)
\(168\) 155.968 + 573.139i 0.0716263 + 0.263206i
\(169\) −572.397 2121.12i −0.260536 0.965464i
\(170\) 3020.92 1.36291
\(171\) 1815.36 3201.65i 0.811835 1.43179i
\(172\) 1235.52 0.547717
\(173\) −1876.45 3250.11i −0.824647 1.42833i −0.902188 0.431342i \(-0.858040\pi\)
0.0775409 0.996989i \(-0.475293\pi\)
\(174\) −700.006 694.572i −0.304985 0.302617i
\(175\) 211.481 + 122.099i 0.0913513 + 0.0527417i
\(176\) −2220.17 1281.82i −0.950861 0.548980i
\(177\) 1481.24 + 1469.74i 0.629023 + 0.624140i
\(178\) −205.685 356.258i −0.0866111 0.150015i
\(179\) 2418.17 1.00973 0.504867 0.863197i \(-0.331541\pi\)
0.504867 + 0.863197i \(0.331541\pi\)
\(180\) −646.647 + 5.03934i −0.267768 + 0.00208672i
\(181\) 1764.27 0.724516 0.362258 0.932078i \(-0.382006\pi\)
0.362258 + 0.932078i \(0.382006\pi\)
\(182\) −378.005 910.296i −0.153954 0.370745i
\(183\) 327.158 + 1202.21i 0.132154 + 0.485629i
\(184\) −242.347 139.919i −0.0970981 0.0560596i
\(185\) −1795.22 + 3109.40i −0.713443 + 1.23572i
\(186\) −1509.29 398.118i −0.594983 0.156943i
\(187\) 2834.42 1636.45i 1.10841 0.639942i
\(188\) 689.118i 0.267336i
\(189\) 879.460 + 224.666i 0.338472 + 0.0864659i
\(190\) 4138.63i 1.58025i
\(191\) −88.0254 152.465i −0.0333471 0.0577589i 0.848870 0.528601i \(-0.177283\pi\)
−0.882217 + 0.470842i \(0.843950\pi\)
\(192\) 1304.18 + 344.013i 0.490214 + 0.129307i
\(193\) −3675.27 2121.92i −1.37074 0.791394i −0.379715 0.925104i \(-0.623978\pi\)
−0.991021 + 0.133709i \(0.957311\pi\)
\(194\) 135.392 234.507i 0.0501062 0.0867865i
\(195\) −2254.16 + 307.747i −0.827816 + 0.113017i
\(196\) 386.062 + 668.679i 0.140693 + 0.243688i
\(197\) 2439.54i 0.882285i 0.897437 + 0.441143i \(0.145427\pi\)
−0.897437 + 0.441143i \(0.854573\pi\)
\(198\) −2488.54 + 1462.73i −0.893195 + 0.525009i
\(199\) −365.385 −0.130158 −0.0650791 0.997880i \(-0.520730\pi\)
−0.0650791 + 0.997880i \(0.520730\pi\)
\(200\) 577.520 333.432i 0.204184 0.117886i
\(201\) −2860.37 2838.16i −1.00375 0.995963i
\(202\) 132.727 + 76.6301i 0.0462310 + 0.0266915i
\(203\) −327.163 188.887i −0.113115 0.0653069i
\(204\) 933.711 941.016i 0.320455 0.322962i
\(205\) −180.233 312.172i −0.0614049 0.106356i
\(206\) 300.869i 0.101760i
\(207\) −368.669 + 216.699i −0.123789 + 0.0727614i
\(208\) −3622.29 473.608i −1.20750 0.157879i
\(209\) 2241.92 + 3883.12i 0.741995 + 1.28517i
\(210\) −984.871 + 268.013i −0.323631 + 0.0880697i
\(211\) −372.285 + 644.817i −0.121465 + 0.210384i −0.920346 0.391106i \(-0.872093\pi\)
0.798880 + 0.601490i \(0.205426\pi\)
\(212\) −609.582 + 1055.83i −0.197482 + 0.342050i
\(213\) −1019.91 + 3866.55i −0.328089 + 1.24381i
\(214\) 1821.80 1051.82i 0.581942 0.335984i
\(215\) 4501.21i 1.42781i
\(216\) 1732.16 1773.14i 0.545641 0.558549i
\(217\) −597.974 −0.187065
\(218\) 111.605 + 193.306i 0.0346736 + 0.0600564i
\(219\) 664.341 2518.57i 0.204986 0.777119i
\(220\) 393.907 682.267i 0.120715 0.209084i
\(221\) 2835.86 3702.58i 0.863170 1.12698i
\(222\) 1704.54 + 6263.70i 0.515321 + 1.89366i
\(223\) −3735.03 + 2156.42i −1.12160 + 0.647555i −0.941808 0.336150i \(-0.890875\pi\)
−0.179790 + 0.983705i \(0.557542\pi\)
\(224\) −724.437 −0.216087
\(225\) −7.94144 1019.05i −0.00235302 0.301940i
\(226\) 5520.78i 1.62494i
\(227\) −956.541 + 552.259i −0.279682 + 0.161475i −0.633279 0.773923i \(-0.718292\pi\)
0.353597 + 0.935398i \(0.384958\pi\)
\(228\) 1289.18 + 1279.17i 0.374466 + 0.371559i
\(229\) −3114.84 1798.35i −0.898840 0.518945i −0.0220160 0.999758i \(-0.507008\pi\)
−0.876824 + 0.480812i \(0.840342\pi\)
\(230\) 240.434 416.444i 0.0689294 0.119389i
\(231\) −778.884 + 784.978i −0.221848 + 0.223583i
\(232\) −893.427 + 515.821i −0.252829 + 0.145971i
\(233\) −3144.44 −0.884116 −0.442058 0.896987i \(-0.645751\pi\)
−0.442058 + 0.896987i \(0.645751\pi\)
\(234\) −2475.61 + 3284.94i −0.691605 + 0.917705i
\(235\) 2510.58 0.696903
\(236\) −891.708 + 514.828i −0.245954 + 0.142002i
\(237\) −1142.88 4199.75i −0.313240 1.15107i
\(238\) 1046.19 1812.05i 0.284933 0.493519i
\(239\) −2680.85 1547.79i −0.725563 0.418904i 0.0912338 0.995830i \(-0.470919\pi\)
−0.816797 + 0.576926i \(0.804252\pi\)
\(240\) −964.851 + 3657.83i −0.259504 + 0.983798i
\(241\) 4175.25 2410.58i 1.11598 0.644312i 0.175609 0.984460i \(-0.443811\pi\)
0.940372 + 0.340148i \(0.110477\pi\)
\(242\) 809.418i 0.215005i
\(243\) −1051.50 3639.13i −0.277587 0.960700i
\(244\) −614.795 −0.161304
\(245\) 2436.12 1406.49i 0.635256 0.366765i
\(246\) −630.166 166.224i −0.163325 0.0430814i
\(247\) 5072.49 + 3885.10i 1.30670 + 1.00082i
\(248\) −816.484 + 1414.19i −0.209060 + 0.362102i
\(249\) −112.372 + 30.5798i −0.0285996 + 0.00778279i
\(250\) 2470.51 + 4279.05i 0.624995 + 1.08252i
\(251\) −3992.23 −1.00393 −0.501967 0.864887i \(-0.667390\pi\)
−0.501967 + 0.864887i \(0.667390\pi\)
\(252\) −220.920 + 389.625i −0.0552248 + 0.0973971i
\(253\) 520.979i 0.129461i
\(254\) 1359.59 784.959i 0.335859 0.193908i
\(255\) −3428.29 3401.68i −0.841913 0.835378i
\(256\) −1788.49 + 3097.76i −0.436643 + 0.756288i
\(257\) −2587.41 + 4481.53i −0.628009 + 1.08774i 0.359942 + 0.932975i \(0.382797\pi\)
−0.987951 + 0.154769i \(0.950537\pi\)
\(258\) −5776.93 5732.09i −1.39402 1.38319i
\(259\) 1243.41 + 2153.66i 0.298309 + 0.516686i
\(260\) 145.542 1113.14i 0.0347158 0.265516i
\(261\) 12.2855 + 1576.47i 0.00291361 + 0.373874i
\(262\) 487.629i 0.114984i
\(263\) 599.129 + 1037.72i 0.140471 + 0.243303i 0.927674 0.373391i \(-0.121805\pi\)
−0.787203 + 0.616694i \(0.788472\pi\)
\(264\) 792.949 + 2913.86i 0.184858 + 0.679302i
\(265\) 3846.57 + 2220.82i 0.891671 + 0.514806i
\(266\) 2482.48 + 1433.26i 0.572221 + 0.330372i
\(267\) −167.738 + 635.909i −0.0384473 + 0.145757i
\(268\) 1721.94 994.163i 0.392479 0.226598i
\(269\) −6299.35 −1.42780 −0.713900 0.700248i \(-0.753073\pi\)
−0.713900 + 0.700248i \(0.753073\pi\)
\(270\) 3046.92 + 2976.51i 0.686777 + 0.670906i
\(271\) 6375.25i 1.42904i 0.699617 + 0.714518i \(0.253354\pi\)
−0.699617 + 0.714518i \(0.746646\pi\)
\(272\) −3877.44 6715.92i −0.864354 1.49711i
\(273\) −596.050 + 1458.70i −0.132141 + 0.323386i
\(274\) −2883.53 + 4994.42i −0.635768 + 1.10118i
\(275\) 1075.18 + 620.755i 0.235766 + 0.136120i
\(276\) −55.4085 203.611i −0.0120841 0.0444055i
\(277\) 0.0249887 + 0.0432816i 5.42030e−6 + 9.38823e-6i 0.866028 0.499995i \(-0.166665\pi\)
−0.866023 + 0.500005i \(0.833332\pi\)
\(278\) 9506.44i 2.05093i
\(279\) 1264.53 + 2151.33i 0.271345 + 0.461637i
\(280\) 1067.80i 0.227905i
\(281\) 4135.13 2387.42i 0.877870 0.506838i 0.00791441 0.999969i \(-0.497481\pi\)
0.869955 + 0.493130i \(0.164147\pi\)
\(282\) 3197.11 3222.12i 0.675125 0.680407i
\(283\) −1231.99 + 2133.88i −0.258779 + 0.448218i −0.965915 0.258859i \(-0.916653\pi\)
0.707136 + 0.707077i \(0.249987\pi\)
\(284\) −1708.82 986.590i −0.357042 0.206138i
\(285\) 4660.26 4696.72i 0.968597 0.976174i
\(286\) −1921.79 4627.98i −0.397336 0.956847i
\(287\) −249.668 −0.0513500
\(288\) 1531.95 + 2606.30i 0.313442 + 0.533257i
\(289\) 4987.40 1.01514
\(290\) −886.376 1535.25i −0.179482 0.310872i
\(291\) −417.714 + 113.672i −0.0841471 + 0.0228989i
\(292\) 1113.08 + 642.638i 0.223076 + 0.128793i
\(293\) 1072.10 + 618.974i 0.213763 + 0.123416i 0.603059 0.797697i \(-0.293948\pi\)
−0.389296 + 0.921113i \(0.627282\pi\)
\(294\) 1297.17 4917.66i 0.257321 0.975523i
\(295\) 1875.61 + 3248.65i 0.370177 + 0.641165i
\(296\) 6791.12 1.33353
\(297\) 4471.21 + 1142.21i 0.873555 + 0.223158i
\(298\) −7259.83 −1.41124
\(299\) −284.707 685.620i −0.0550671 0.132610i
\(300\) 486.225 + 128.255i 0.0935740 + 0.0246827i
\(301\) −2699.97 1558.83i −0.517022 0.298503i
\(302\) −2302.81 + 3988.58i −0.438780 + 0.759989i
\(303\) −64.3369 236.420i −0.0121982 0.0448250i
\(304\) 9200.74 5312.05i 1.73585 1.00219i
\(305\) 2239.81i 0.420495i
\(306\) −8731.55 + 68.0451i −1.63121 + 0.0127120i
\(307\) 4673.94i 0.868912i −0.900693 0.434456i \(-0.856941\pi\)
0.900693 0.434456i \(-0.143059\pi\)
\(308\) −272.831 472.556i −0.0504739 0.0874234i
\(309\) 338.790 341.441i 0.0623725 0.0628605i
\(310\) −2430.12 1403.03i −0.445231 0.257054i
\(311\) 2442.04 4229.73i 0.445258 0.771209i −0.552812 0.833306i \(-0.686445\pi\)
0.998070 + 0.0620967i \(0.0197787\pi\)
\(312\) 2635.92 + 3401.38i 0.478300 + 0.617195i
\(313\) 1417.14 + 2454.57i 0.255916 + 0.443260i 0.965144 0.261720i \(-0.0842896\pi\)
−0.709228 + 0.704979i \(0.750956\pi\)
\(314\) 50.7466i 0.00912037i
\(315\) 1419.47 + 804.850i 0.253899 + 0.143962i
\(316\) 2147.70 0.382334
\(317\) −4881.15 + 2818.14i −0.864836 + 0.499313i −0.865629 0.500686i \(-0.833081\pi\)
0.000792843 1.00000i \(0.499748\pi\)
\(318\) 7748.67 2108.64i 1.36643 0.371845i
\(319\) −1663.31 960.311i −0.291935 0.168549i
\(320\) 2099.86 + 1212.36i 0.366831 + 0.211790i
\(321\) −3251.85 857.765i −0.565423 0.149146i
\(322\) −166.531 288.440i −0.0288212 0.0499197i
\(323\) 13563.4i 2.33650i
\(324\) 1868.93 29.1310i 0.320461 0.00499503i
\(325\) 1754.19 + 229.358i 0.299400 + 0.0391461i
\(326\) −1368.06 2369.55i −0.232423 0.402568i
\(327\) 91.0149 345.044i 0.0153919 0.0583517i
\(328\) −340.901 + 590.459i −0.0573876 + 0.0993982i
\(329\) 869.448 1505.93i 0.145697 0.252354i
\(330\) −5007.13 + 1362.59i −0.835252 + 0.227297i
\(331\) −7545.23 + 4356.24i −1.25294 + 0.723385i −0.971692 0.236250i \(-0.924082\pi\)
−0.281248 + 0.959635i \(0.590748\pi\)
\(332\) 57.4656i 0.00949950i
\(333\) 5118.78 9027.73i 0.842365 1.48564i
\(334\) 12490.1 2.04619
\(335\) −3621.91 6273.34i −0.590705 1.02313i
\(336\) 1859.94 + 1845.50i 0.301988 + 0.299644i
\(337\) 2635.03 4564.00i 0.425932 0.737735i −0.570575 0.821245i \(-0.693280\pi\)
0.996507 + 0.0835100i \(0.0266130\pi\)
\(338\) −5058.25 5040.29i −0.814001 0.811112i
\(339\) 6216.62 6265.26i 0.995990 1.00378i
\(340\) 2063.83 1191.55i 0.329197 0.190062i
\(341\) −3040.12 −0.482791
\(342\) −93.2211 11962.1i −0.0147392 1.89134i
\(343\) 4167.53i 0.656050i
\(344\) −7373.18 + 4256.90i −1.15562 + 0.667200i
\(345\) −741.790 + 201.863i −0.115758 + 0.0315013i
\(346\) −10563.6 6098.90i −1.64134 0.947627i
\(347\) −918.399 + 1590.71i −0.142081 + 0.246092i −0.928280 0.371881i \(-0.878713\pi\)
0.786199 + 0.617974i \(0.212046\pi\)
\(348\) −752.192 198.411i −0.115867 0.0305631i
\(349\) −11253.3 + 6497.08i −1.72600 + 0.996507i −0.821246 + 0.570574i \(0.806721\pi\)
−0.904754 + 0.425933i \(0.859946\pi\)
\(350\) 793.698 0.121214
\(351\) 6508.41 940.274i 0.989725 0.142986i
\(352\) −3683.06 −0.557693
\(353\) −3831.40 + 2212.06i −0.577691 + 0.333530i −0.760215 0.649671i \(-0.774907\pi\)
0.182524 + 0.983201i \(0.441573\pi\)
\(354\) 6557.88 + 1729.82i 0.984597 + 0.259714i
\(355\) −3594.32 + 6225.55i −0.537371 + 0.930754i
\(356\) −281.040 162.259i −0.0418402 0.0241564i
\(357\) −3227.70 + 878.353i −0.478510 + 0.130217i
\(358\) 6806.62 3929.80i 1.00486 0.580158i
\(359\) 8186.11i 1.20347i 0.798695 + 0.601736i \(0.205524\pi\)
−0.798695 + 0.601736i \(0.794476\pi\)
\(360\) 3841.63 2258.06i 0.562421 0.330584i
\(361\) −11722.8 −1.70911
\(362\) 4966.05 2867.15i 0.721021 0.416282i
\(363\) 911.437 918.567i 0.131785 0.132816i
\(364\) −617.297 472.797i −0.0888877 0.0680805i
\(365\) 2341.24 4055.15i 0.335743 0.581524i
\(366\) 2874.61 + 2852.30i 0.410542 + 0.407355i
\(367\) 4429.04 + 7671.32i 0.629957 + 1.09112i 0.987560 + 0.157243i \(0.0502607\pi\)
−0.357603 + 0.933874i \(0.616406\pi\)
\(368\) −1234.42 −0.174860
\(369\) 527.969 + 898.231i 0.0744850 + 0.126721i
\(370\) 11669.7i 1.63968i
\(371\) 2664.24 1538.20i 0.372831 0.215254i
\(372\) −1188.15 + 323.331i −0.165599 + 0.0450643i
\(373\) 1129.84 1956.93i 0.156838 0.271652i −0.776889 0.629638i \(-0.783203\pi\)
0.933727 + 0.357986i \(0.116537\pi\)
\(374\) 5318.85 9212.51i 0.735377 1.27371i
\(375\) 2014.72 7637.97i 0.277440 1.05180i
\(376\) −2374.32 4112.44i −0.325655 0.564050i
\(377\) −2713.75 354.818i −0.370730 0.0484723i
\(378\) 2840.60 796.837i 0.386520 0.108426i
\(379\) 14184.3i 1.92242i −0.275817 0.961210i \(-0.588948\pi\)
0.275817 0.961210i \(-0.411052\pi\)
\(380\) 1632.41 + 2827.42i 0.220371 + 0.381694i
\(381\) −2426.83 640.141i −0.326325 0.0860773i
\(382\) −495.545 286.103i −0.0663725 0.0383202i
\(383\) −708.447 409.022i −0.0945169 0.0545693i 0.451997 0.892020i \(-0.350712\pi\)
−0.546513 + 0.837450i \(0.684045\pi\)
\(384\) 8721.23 2373.31i 1.15899 0.315396i
\(385\) −1721.61 + 993.970i −0.227899 + 0.131578i
\(386\) −13793.5 −1.81883
\(387\) 101.388 + 13010.1i 0.0133174 + 1.70889i
\(388\) 213.613i 0.0279499i
\(389\) 6371.85 + 11036.4i 0.830502 + 1.43847i 0.897640 + 0.440729i \(0.145280\pi\)
−0.0671380 + 0.997744i \(0.521387\pi\)
\(390\) −5844.86 + 4529.52i −0.758887 + 0.588105i
\(391\) 787.970 1364.80i 0.101917 0.176525i
\(392\) −4607.79 2660.31i −0.593696 0.342770i
\(393\) −549.090 + 553.385i −0.0704781 + 0.0710295i
\(394\) 3964.54 + 6866.78i 0.506930 + 0.878029i
\(395\) 7824.44i 0.996685i
\(396\) −1123.17 + 1980.87i −0.142528 + 0.251370i
\(397\) 1970.75i 0.249141i 0.992211 + 0.124570i \(0.0397553\pi\)
−0.992211 + 0.124570i \(0.960245\pi\)
\(398\) −1028.48 + 593.793i −0.129530 + 0.0747843i
\(399\) −1203.33 4421.91i −0.150983 0.554818i
\(400\) 1470.83 2547.55i 0.183854 0.318444i
\(401\) 12106.5 + 6989.68i 1.50765 + 0.870444i 0.999960 + 0.00890549i \(0.00283474\pi\)
0.507693 + 0.861538i \(0.330499\pi\)
\(402\) −12663.7 3340.38i −1.57116 0.414436i
\(403\) −4000.87 + 1661.38i −0.494535 + 0.205358i
\(404\) 120.902 0.0148889
\(405\) −106.129 6808.85i −0.0130213 0.835393i
\(406\) −1227.86 −0.150092
\(407\) 6321.57 + 10949.3i 0.769898 + 1.33350i
\(408\) −2329.88 + 8832.74i −0.282711 + 1.07178i
\(409\) 2278.10 + 1315.26i 0.275415 + 0.159011i 0.631346 0.775501i \(-0.282503\pi\)
−0.355931 + 0.934512i \(0.615836\pi\)
\(410\) −1014.63 585.798i −0.122217 0.0705622i
\(411\) 8896.30 2420.95i 1.06769 0.290551i
\(412\) 118.673 + 205.547i 0.0141908 + 0.0245791i
\(413\) 2598.20 0.309561
\(414\) −685.561 + 1209.09i −0.0813852 + 0.143535i
\(415\) −209.357 −0.0247637
\(416\) −4847.00 + 2012.74i −0.571259 + 0.237218i
\(417\) −10704.6 + 10788.4i −1.25709 + 1.26693i
\(418\) 12621.0 + 7286.76i 1.47683 + 0.852649i
\(419\) 2188.35 3790.34i 0.255150 0.441933i −0.709786 0.704417i \(-0.751208\pi\)
0.964936 + 0.262484i \(0.0845417\pi\)
\(420\) −567.130 + 571.567i −0.0658884 + 0.0664039i
\(421\) 7355.20 4246.53i 0.851474 0.491599i −0.00967417 0.999953i \(-0.503079\pi\)
0.861148 + 0.508355i \(0.169746\pi\)
\(422\) 2420.03i 0.279159i
\(423\) −7256.48 + 56.5499i −0.834095 + 0.00650012i
\(424\) 8401.13i 0.962252i
\(425\) 1877.76 + 3252.37i 0.214317 + 0.371208i
\(426\) 3412.77 + 12541.0i 0.388144 + 1.42632i
\(427\) 1343.51 + 775.676i 0.152265 + 0.0879100i
\(428\) 829.743 1437.16i 0.0937083 0.162308i
\(429\) −3030.34 + 7416.07i −0.341040 + 0.834619i
\(430\) −7314.98 12669.9i −0.820372 1.42093i
\(431\) 851.101i 0.0951185i 0.998868 + 0.0475593i \(0.0151443\pi\)
−0.998868 + 0.0475593i \(0.984856\pi\)
\(432\) 2706.38 10594.2i 0.301413 1.17989i
\(433\) 6389.28 0.709121 0.354560 0.935033i \(-0.384631\pi\)
0.354560 + 0.935033i \(0.384631\pi\)
\(434\) −1683.17 + 971.777i −0.186163 + 0.107481i
\(435\) −722.848 + 2740.37i −0.0796733 + 0.302048i
\(436\) 152.492 + 88.0416i 0.0167501 + 0.00967070i
\(437\) 1869.77 + 1079.51i 0.204675 + 0.118169i
\(438\) −2222.99 8168.85i −0.242508 0.891148i
\(439\) −3417.48 5919.24i −0.371543 0.643531i 0.618260 0.785973i \(-0.287838\pi\)
−0.989803 + 0.142442i \(0.954504\pi\)
\(440\) 5428.74i 0.588193i
\(441\) −7009.58 + 4120.14i −0.756892 + 0.444892i
\(442\) 1965.22 15030.5i 0.211484 1.61749i
\(443\) 2452.39 + 4247.66i 0.263017 + 0.455559i 0.967042 0.254616i \(-0.0819491\pi\)
−0.704025 + 0.710175i \(0.748616\pi\)
\(444\) 3635.12 + 3606.90i 0.388548 + 0.385531i
\(445\) −591.137 + 1023.88i −0.0629721 + 0.109071i
\(446\) −7008.87 + 12139.7i −0.744125 + 1.28886i
\(447\) 8238.81 + 8174.86i 0.871773 + 0.865006i
\(448\) 1454.42 839.711i 0.153382 0.0885549i
\(449\) 14662.5i 1.54112i −0.637366 0.770561i \(-0.719976\pi\)
0.637366 0.770561i \(-0.280024\pi\)
\(450\) −1678.42 2855.49i −0.175826 0.299131i
\(451\) −1269.32 −0.132528
\(452\) 2177.58 + 3771.69i 0.226604 + 0.392489i
\(453\) 7104.64 1933.38i 0.736876 0.200526i
\(454\) −1794.97 + 3108.98i −0.185555 + 0.321391i
\(455\) −1722.48 + 2248.92i −0.177475 + 0.231717i
\(456\) −12100.8 3191.91i −1.24270 0.327795i
\(457\) −9706.10 + 5603.82i −0.993506 + 0.573601i −0.906320 0.422591i \(-0.861121\pi\)
−0.0871856 + 0.996192i \(0.527787\pi\)
\(458\) −11690.1 −1.19267
\(459\) 9985.61 + 9754.85i 1.01544 + 0.991977i
\(460\) 379.341i 0.0384498i
\(461\) 12830.5 7407.70i 1.29626 0.748397i 0.316506 0.948591i \(-0.397490\pi\)
0.979756 + 0.200193i \(0.0641570\pi\)
\(462\) −916.710 + 3475.32i −0.0923143 + 0.349971i
\(463\) 8387.03 + 4842.25i 0.841853 + 0.486044i 0.857894 0.513827i \(-0.171773\pi\)
−0.0160404 + 0.999871i \(0.505106\pi\)
\(464\) −2275.38 + 3941.07i −0.227655 + 0.394310i
\(465\) 1177.95 + 4328.64i 0.117476 + 0.431690i
\(466\) −8850.91 + 5110.07i −0.879851 + 0.507982i
\(467\) 9860.98 0.977112 0.488556 0.872532i \(-0.337524\pi\)
0.488556 + 0.872532i \(0.337524\pi\)
\(468\) −395.595 + 3220.66i −0.0390734 + 0.318109i
\(469\) −5017.27 −0.493978
\(470\) 7066.74 4079.98i 0.693541 0.400416i
\(471\) 57.1427 57.5898i 0.00559023 0.00563396i
\(472\) 3547.62 6144.66i 0.345959 0.599218i
\(473\) −13726.8 7925.14i −1.33437 0.770399i
\(474\) −10042.0 9964.08i −0.973092 0.965539i
\(475\) −4455.71 + 2572.51i −0.430405 + 0.248494i
\(476\) 1650.60i 0.158940i
\(477\) −11168.0 6332.32i −1.07201 0.607834i
\(478\) −10061.3 −0.962750
\(479\) −4811.72 + 2778.05i −0.458983 + 0.264994i −0.711617 0.702568i \(-0.752037\pi\)
0.252633 + 0.967562i \(0.418703\pi\)
\(480\) 1427.07 + 5244.09i 0.135701 + 0.498664i
\(481\) 14302.9 + 10954.9i 1.35584 + 1.03846i
\(482\) 7834.95 13570.5i 0.740398 1.28241i
\(483\) −135.808 + 514.857i −0.0127939 + 0.0485027i
\(484\) 319.262 + 552.977i 0.0299832 + 0.0519325i
\(485\) −778.231 −0.0728612
\(486\) −8873.74 8534.55i −0.828233 0.796574i
\(487\) 12548.5i 1.16761i −0.811894 0.583805i \(-0.801563\pi\)
0.811894 0.583805i \(-0.198437\pi\)
\(488\) 3668.90 2118.24i 0.340335 0.196493i
\(489\) −1115.66 + 4229.57i −0.103174 + 0.391141i
\(490\) 4571.43 7917.94i 0.421461 0.729992i
\(491\) 6630.65 11484.6i 0.609444 1.05559i −0.381888 0.924208i \(-0.624726\pi\)
0.991332 0.131379i \(-0.0419405\pi\)
\(492\) −496.081 + 134.998i −0.0454574 + 0.0123703i
\(493\) −2904.90 5031.44i −0.265376 0.459644i
\(494\) 20591.7 + 2692.33i 1.87543 + 0.245210i
\(495\) 7216.66 + 4091.89i 0.655282 + 0.371549i
\(496\) 7203.33i 0.652095i
\(497\) 2489.52 + 4311.98i 0.224689 + 0.389173i
\(498\) −266.607 + 268.693i −0.0239899 + 0.0241776i
\(499\) 7410.77 + 4278.61i 0.664833 + 0.383842i 0.794116 0.607766i \(-0.207934\pi\)
−0.129283 + 0.991608i \(0.541268\pi\)
\(500\) 3375.60 + 1948.91i 0.301923 + 0.174315i
\(501\) −14174.4 14064.3i −1.26400 1.25419i
\(502\) −11237.3 + 6487.84i −0.999092 + 0.576826i
\(503\) −14538.3 −1.28873 −0.644364 0.764719i \(-0.722878\pi\)
−0.644364 + 0.764719i \(0.722878\pi\)
\(504\) −24.0518 3086.33i −0.00212570 0.272770i
\(505\) 440.467i 0.0388130i
\(506\) −846.651 1466.44i −0.0743839 0.128837i
\(507\) 64.7760 + 11415.8i 0.00567416 + 0.999984i
\(508\) 619.229 1072.54i 0.0540824 0.0936734i
\(509\) 3743.30 + 2161.20i 0.325970 + 0.188199i 0.654051 0.756451i \(-0.273068\pi\)
−0.328080 + 0.944650i \(0.606402\pi\)
\(510\) −15178.0 4003.62i −1.31783 0.347614i
\(511\) −1621.61 2808.71i −0.140383 0.243150i
\(512\) 2289.49i 0.197621i
\(513\) −13364.0 + 13680.2i −1.15017 + 1.17738i
\(514\) 16819.4i 1.44333i
\(515\) 748.846 432.346i 0.0640740 0.0369931i
\(516\) −6207.61 1637.43i −0.529602 0.139697i
\(517\) 4420.31 7656.19i 0.376025 0.651294i
\(518\) 6999.88 + 4041.38i 0.593740 + 0.342796i
\(519\) 5120.50 + 18816.4i 0.433073 + 1.59142i
\(520\) 2966.73 + 7144.35i 0.250192 + 0.602501i
\(521\) −3712.85 −0.312213 −0.156106 0.987740i \(-0.549894\pi\)
−0.156106 + 0.987740i \(0.549894\pi\)
\(522\) 2596.53 + 4417.45i 0.217714 + 0.370396i
\(523\) 9455.23 0.790532 0.395266 0.918567i \(-0.370652\pi\)
0.395266 + 0.918567i \(0.370652\pi\)
\(524\) −192.337 333.138i −0.0160349 0.0277733i
\(525\) −900.728 893.736i −0.0748781 0.0742968i
\(526\) 3372.84 + 1947.31i 0.279587 + 0.161419i
\(527\) −7964.19 4598.12i −0.658302 0.380071i
\(528\) 9456.01 + 9382.61i 0.779394 + 0.773344i
\(529\) 5958.07 + 10319.7i 0.489691 + 0.848170i
\(530\) 14436.3 1.18316
\(531\) −5494.36 9347.52i −0.449030 0.763932i
\(532\) 2261.31 0.184286
\(533\) −1670.46 + 693.666i −0.135752 + 0.0563715i
\(534\) 561.278 + 2062.54i 0.0454848 + 0.167144i
\(535\) −5235.82 3022.90i −0.423111 0.244283i
\(536\) −6850.67 + 11865.7i −0.552059 + 0.956195i
\(537\) −12149.6 3204.79i −0.976340 0.257536i
\(538\) −17731.3 + 10237.2i −1.42091 + 0.820364i
\(539\) 9905.49i 0.791576i
\(540\) 3255.63 + 831.680i 0.259444 + 0.0662775i
\(541\) 15468.2i 1.22926i 0.788814 + 0.614632i \(0.210695\pi\)
−0.788814 + 0.614632i \(0.789305\pi\)
\(542\) 10360.5 + 17944.9i 0.821074 + 1.42214i
\(543\) −8864.24 2338.19i −0.700555 0.184790i
\(544\) −9648.49 5570.56i −0.760433 0.439036i
\(545\) 320.751 555.557i 0.0252100 0.0436651i
\(546\) 692.799 + 5074.57i 0.0543023 + 0.397750i
\(547\) −10339.7 17908.9i −0.808218 1.39987i −0.914097 0.405495i \(-0.867099\pi\)
0.105879 0.994379i \(-0.466234\pi\)
\(548\) 4549.45i 0.354640i
\(549\) −50.4509 6473.85i −0.00392202 0.503274i
\(550\) 4035.19 0.312838
\(551\) 6893.01 3979.68i 0.532944 0.307696i
\(552\) 1032.19 + 1024.18i 0.0795886 + 0.0789708i
\(553\) −4693.36 2709.71i −0.360907 0.208370i
\(554\) 0.140675 + 0.0812189i 1.07883e−5 + 6.22863e-6i
\(555\) 13140.6 13243.4i 1.00502 1.01288i
\(556\) −3749.66 6494.61i −0.286009 0.495382i
\(557\) 8377.79i 0.637304i −0.947872 0.318652i \(-0.896770\pi\)
0.947872 0.318652i \(-0.103230\pi\)
\(558\) 7055.53 + 4000.53i 0.535276 + 0.303505i
\(559\) −22395.7 2928.20i −1.69452 0.221556i
\(560\) 2355.13 + 4079.21i 0.177719 + 0.307818i
\(561\) −16409.7 + 4465.58i −1.23497 + 0.336073i
\(562\) 7759.67 13440.1i 0.582423 1.00879i
\(563\) 11893.7 20600.4i 0.890334 1.54210i 0.0508578 0.998706i \(-0.483804\pi\)
0.839476 0.543397i \(-0.182862\pi\)
\(564\) 913.286 3462.34i 0.0681849 0.258494i
\(565\) 13740.9 7933.32i 1.02316 0.590721i
\(566\) 8008.53i 0.594741i
\(567\) −4120.92 2294.33i −0.305225 0.169935i
\(568\) 13597.0 1.00443
\(569\) 3737.01 + 6472.69i 0.275331 + 0.476888i 0.970219 0.242231i \(-0.0778791\pi\)
−0.694887 + 0.719119i \(0.744546\pi\)
\(570\) 5484.91 20793.7i 0.403048 1.52799i
\(571\) 3413.95 5913.13i 0.250209 0.433374i −0.713374 0.700783i \(-0.752834\pi\)
0.963583 + 0.267409i \(0.0861674\pi\)
\(572\) −3138.36 2403.72i −0.229408 0.175707i
\(573\) 240.205 + 882.687i 0.0175126 + 0.0643539i
\(574\) −702.762 + 405.740i −0.0511023 + 0.0295039i
\(575\) 597.801 0.0433566
\(576\) −6096.67 3456.85i −0.441020 0.250061i
\(577\) 14789.6i 1.06707i −0.845777 0.533536i \(-0.820863\pi\)
0.845777 0.533536i \(-0.179137\pi\)
\(578\) 14038.4 8105.10i 1.01025 0.583266i
\(579\) 15653.5 + 15532.0i 1.12355 + 1.11483i
\(580\) −1211.11 699.233i −0.0867043 0.0500588i
\(581\) −72.5033 + 125.579i −0.00517718 + 0.00896714i
\(582\) −991.043 + 998.796i −0.0705843 + 0.0711365i
\(583\) 13545.1 7820.26i 0.962230 0.555544i
\(584\) −8856.69 −0.627556
\(585\) 11733.5 + 1441.22i 0.829262 + 0.101858i
\(586\) 4023.62 0.283642
\(587\) −12025.7 + 6943.02i −0.845575 + 0.488193i −0.859155 0.511715i \(-0.829010\pi\)
0.0135805 + 0.999908i \(0.495677\pi\)
\(588\) −1053.49 3871.29i −0.0738866 0.271513i
\(589\) 6299.38 10910.8i 0.440682 0.763283i
\(590\) 10558.9 + 6096.17i 0.736783 + 0.425382i
\(591\) 3233.12 12257.0i 0.225030 0.853106i
\(592\) 25943.4 14978.4i 1.80113 1.03988i
\(593\) 4297.30i 0.297587i −0.988868 0.148794i \(-0.952461\pi\)
0.988868 0.148794i \(-0.0475390\pi\)
\(594\) 14441.7 4051.15i 0.997559 0.279833i
\(595\) −6013.44 −0.414331
\(596\) −4959.76 + 2863.52i −0.340872 + 0.196803i
\(597\) 1835.81 + 484.244i 0.125853 + 0.0331973i
\(598\) −1915.60 1467.19i −0.130995 0.100331i
\(599\) 14570.0 25236.1i 0.993850 1.72140i 0.401023 0.916068i \(-0.368655\pi\)
0.592827 0.805330i \(-0.298012\pi\)
\(600\) −3343.53 + 909.874i −0.227499 + 0.0619091i
\(601\) −5202.61 9011.18i −0.353110 0.611604i 0.633683 0.773593i \(-0.281542\pi\)
−0.986793 + 0.161989i \(0.948209\pi\)
\(602\) −10133.1 −0.686037
\(603\) 10609.9 + 18050.6i 0.716534 + 1.21903i
\(604\) 3633.22i 0.244757i
\(605\) 2014.59 1163.13i 0.135380 0.0781617i
\(606\) −565.304 560.915i −0.0378942 0.0376001i
\(607\) −12713.2 + 22019.9i −0.850104 + 1.47242i 0.0310091 + 0.999519i \(0.490128\pi\)
−0.881113 + 0.472905i \(0.843205\pi\)
\(608\) 7631.61 13218.3i 0.509050 0.881701i
\(609\) 1393.43 + 1382.61i 0.0927170 + 0.0919973i
\(610\) 3639.95 + 6304.57i 0.241602 + 0.418467i
\(611\) 1633.22 12491.4i 0.108139 0.827081i
\(612\) −5938.37 + 3490.50i −0.392230 + 0.230548i
\(613\) 977.352i 0.0643962i 0.999482 + 0.0321981i \(0.0102507\pi\)
−0.999482 + 0.0321981i \(0.989749\pi\)
\(614\) −7595.69 13156.1i −0.499246 0.864720i
\(615\) 491.823 + 1807.31i 0.0322475 + 0.118500i
\(616\) 3256.33 + 1880.05i 0.212989 + 0.122969i
\(617\) −23369.0 13492.1i −1.52480 0.880343i −0.999568 0.0293838i \(-0.990645\pi\)
−0.525231 0.850960i \(-0.676021\pi\)
\(618\) 398.740 1511.66i 0.0259542 0.0983943i
\(619\) 6587.41 3803.25i 0.427739 0.246955i −0.270644 0.962680i \(-0.587237\pi\)
0.698383 + 0.715724i \(0.253903\pi\)
\(620\) −2213.61 −0.143388
\(621\) 2139.49 600.165i 0.138253 0.0387823i
\(622\) 15874.4i 1.02332i
\(623\) 409.437 + 709.166i 0.0263303 + 0.0456054i
\(624\) 17571.8 + 7180.15i 1.12730 + 0.460635i
\(625\) 4741.24 8212.06i 0.303439 0.525572i
\(626\) 7977.91 + 4606.05i 0.509363 + 0.294081i
\(627\) −6117.80 22481.2i −0.389667 1.43192i
\(628\) 20.0162 + 34.6690i 0.00127187 + 0.00220294i
\(629\) 38245.0i 2.42437i
\(630\) 5303.49 41.3302i 0.335390 0.00261370i
\(631\) 29518.2i 1.86228i 0.364656 + 0.931142i \(0.381187\pi\)
−0.364656 + 0.931142i \(0.618813\pi\)
\(632\) −12816.8 + 7399.77i −0.806684 + 0.465739i
\(633\) 2725.05 2746.37i 0.171107 0.172446i
\(634\) −9159.59 + 15864.9i −0.573776 + 0.993809i
\(635\) −3907.44 2255.96i −0.244192 0.140984i
\(636\) 4462.01 4496.92i 0.278192 0.280368i
\(637\) −5413.20 13035.8i −0.336702 0.810830i
\(638\) −6242.47 −0.387369
\(639\) 10248.7 18075.0i 0.634477 1.11899i
\(640\) 16248.3 1.00355
\(641\) 8343.82 + 14451.9i 0.514136 + 0.890509i 0.999866 + 0.0164002i \(0.00522059\pi\)
−0.485730 + 0.874109i \(0.661446\pi\)
\(642\) −10547.2 + 2870.22i −0.648389 + 0.176446i
\(643\) −7105.56 4102.40i −0.435794 0.251606i 0.266018 0.963968i \(-0.414292\pi\)
−0.701812 + 0.712362i \(0.747625\pi\)
\(644\) −227.541 131.371i −0.0139230 0.00803842i
\(645\) −5965.43 + 22615.4i −0.364169 + 1.38059i
\(646\) 22042.2 + 38178.1i 1.34247 + 2.32523i
\(647\) −11773.5 −0.715401 −0.357700 0.933836i \(-0.616439\pi\)
−0.357700 + 0.933836i \(0.616439\pi\)
\(648\) −11052.8 + 6613.14i −0.670055 + 0.400908i
\(649\) 13209.3 0.798939
\(650\) 5310.41 2205.17i 0.320448 0.133068i
\(651\) 3004.40 + 792.493i 0.180878 + 0.0477116i
\(652\) −1869.26 1079.22i −0.112279 0.0648243i
\(653\) −10049.8 + 17406.8i −0.602265 + 1.04315i 0.390212 + 0.920725i \(0.372402\pi\)
−0.992477 + 0.122429i \(0.960932\pi\)
\(654\) −304.550 1119.13i −0.0182092 0.0669138i
\(655\) −1213.68 + 700.719i −0.0724007 + 0.0418005i
\(656\) 3007.56i 0.179002i
\(657\) −6675.70 + 11773.6i −0.396414 + 0.699134i
\(658\) 5651.81i 0.334849i
\(659\) −3970.48 6877.07i −0.234701 0.406514i 0.724485 0.689291i \(-0.242078\pi\)
−0.959186 + 0.282777i \(0.908744\pi\)
\(660\) −2883.31 + 2905.87i −0.170050 + 0.171380i
\(661\) −18533.3 10700.2i −1.09056 0.629638i −0.156838 0.987624i \(-0.550130\pi\)
−0.933727 + 0.357986i \(0.883463\pi\)
\(662\) −14158.8 + 24523.7i −0.831264 + 1.43979i
\(663\) −19155.2 + 14844.5i −1.12206 + 0.869551i
\(664\) 197.995 + 342.937i 0.0115718 + 0.0200430i
\(665\) 8238.35i 0.480405i
\(666\) −262.856 33729.7i −0.0152935 1.96246i
\(667\) −924.801 −0.0536858
\(668\) 8532.96 4926.51i 0.494237 0.285348i
\(669\) 21623.8 5884.49i 1.24966 0.340071i
\(670\) −20389.8 11772.1i −1.17571 0.678797i
\(671\) 6830.46 + 3943.57i 0.392976 + 0.226885i
\(672\) 3639.79 + 960.093i 0.208940 + 0.0551137i
\(673\) −13143.1 22764.5i −0.752791 1.30387i −0.946465 0.322806i \(-0.895374\pi\)
0.193674 0.981066i \(-0.437960\pi\)
\(674\) 17128.9i 0.978902i
\(675\) −1310.64 + 5130.52i −0.0747355 + 0.292554i
\(676\) −5443.75 1448.28i −0.309726 0.0824011i
\(677\) 1702.82 + 2949.36i 0.0966684 + 0.167435i 0.910304 0.413941i \(-0.135848\pi\)
−0.813635 + 0.581376i \(0.802515\pi\)
\(678\) 7316.68 27738.1i 0.414447 1.57120i
\(679\) −269.512 + 466.808i −0.0152326 + 0.0263836i
\(680\) −8210.86 + 14221.6i −0.463047 + 0.802021i
\(681\) 5537.85 1507.02i 0.311617 0.0848002i
\(682\) −8557.29 + 4940.55i −0.480462 + 0.277395i
\(683\) 30610.8i 1.71492i 0.514549 + 0.857461i \(0.327959\pi\)
−0.514549 + 0.857461i \(0.672041\pi\)
\(684\) −4781.95 8135.50i −0.267314 0.454779i
\(685\) 16574.5 0.924492
\(686\) −6772.71 11730.7i −0.376944 0.652886i
\(687\) 13266.5 + 13163.5i 0.736753 + 0.731034i
\(688\) −18778.0 + 32524.4i −1.04056 + 1.80230i
\(689\) 13552.0 17693.8i 0.749331 0.978347i
\(690\) −1759.93 + 1773.69i −0.0971003 + 0.0978600i
\(691\) −5645.65 + 3259.51i −0.310811 + 0.179447i −0.647289 0.762244i \(-0.724097\pi\)
0.336478 + 0.941691i \(0.390764\pi\)
\(692\) −9622.45 −0.528599
\(693\) 4953.68 2911.71i 0.271536 0.159606i
\(694\) 5970.02i 0.326540i
\(695\) −23661.0 + 13660.7i −1.29139 + 0.745582i
\(696\) 5172.46 1407.58i 0.281698 0.0766584i
\(697\) −3325.23 1919.82i −0.180706 0.104331i
\(698\) −21117.0 + 36575.8i −1.14512 + 1.98340i
\(699\) 15798.6 + 4167.31i 0.854875 + 0.225497i
\(700\) 542.238 313.061i 0.0292781 0.0169037i
\(701\) 21446.2 1.15551 0.577755 0.816210i \(-0.303929\pi\)
0.577755 + 0.816210i \(0.303929\pi\)
\(702\) 16791.7 13223.6i 0.902795 0.710958i
\(703\) −52395.2 −2.81098
\(704\) 7394.33 4269.12i 0.395859 0.228549i
\(705\) −12613.9 3327.26i −0.673854 0.177748i
\(706\) −7189.71 + 12452.9i −0.383269 + 0.663842i
\(707\) −264.207 152.540i −0.0140545 0.00811435i
\(708\) 5162.51 1404.87i 0.274038 0.0745739i
\(709\) 9187.32 5304.30i 0.486653 0.280969i −0.236532 0.971624i \(-0.576011\pi\)
0.723185 + 0.690654i \(0.242677\pi\)
\(710\) 23364.8i 1.23502i
\(711\) 176.243 + 22615.5i 0.00929623 + 1.19289i
\(712\) 2236.21 0.117704
\(713\) −1267.73 + 731.927i −0.0665877 + 0.0384444i
\(714\) −7657.85 + 7717.76i −0.401383 + 0.404523i
\(715\) −8757.18 + 11433.6i −0.458042 + 0.598032i
\(716\) 3100.10 5369.52i 0.161810 0.280263i
\(717\) 11418.1 + 11329.5i 0.594724 + 0.590107i
\(718\) 13303.4 + 23042.1i 0.691473 + 1.19767i
\(719\) −6348.37 −0.329283 −0.164641 0.986354i \(-0.552647\pi\)
−0.164641 + 0.986354i \(0.552647\pi\)
\(720\) 9695.41 17099.3i 0.501842 0.885074i
\(721\) 598.909i 0.0309356i
\(722\) −32997.0 + 19050.8i −1.70086 + 0.981993i
\(723\) −24172.4 + 6578.04i −1.24341 + 0.338368i
\(724\) 2261.80 3917.55i 0.116104 0.201098i
\(725\) 1101.92 1908.57i 0.0564470 0.0977692i
\(726\) 1072.72 4066.76i 0.0548379 0.207895i
\(727\) 12477.9 + 21612.4i 0.636562 + 1.10256i 0.986182 + 0.165666i \(0.0529773\pi\)
−0.349620 + 0.936891i \(0.613689\pi\)
\(728\) 5312.83 + 694.643i 0.270476 + 0.0353643i
\(729\) 460.119 + 19677.6i 0.0233765 + 0.999727i
\(730\) 15219.2i 0.771625i
\(731\) −23973.2 41522.9i −1.21297 2.10093i
\(732\) 3088.92 + 814.786i 0.155969 + 0.0411412i
\(733\) −5325.44 3074.64i −0.268349 0.154931i 0.359788 0.933034i \(-0.382849\pi\)
−0.628137 + 0.778103i \(0.716182\pi\)
\(734\) 24933.6 + 14395.4i 1.25384 + 0.723902i
\(735\) −14103.8 + 3838.07i −0.707791 + 0.192611i
\(736\) −1535.84 + 886.719i −0.0769183 + 0.0444088i
\(737\) −25508.0 −1.27490
\(738\) 2945.85 + 1670.31i 0.146935 + 0.0833131i
\(739\) 27560.7i 1.37190i 0.727648 + 0.685951i \(0.240614\pi\)
−0.727648 + 0.685951i \(0.759386\pi\)
\(740\) 4602.94 + 7972.52i 0.228658 + 0.396048i
\(741\) −20336.8 26242.5i −1.00822 1.30100i
\(742\) 4999.50 8659.38i 0.247355 0.428431i
\(743\) −6964.89 4021.18i −0.343899 0.198550i 0.318096 0.948059i \(-0.396957\pi\)
−0.661995 + 0.749508i \(0.730290\pi\)
\(744\) 5976.49 6023.24i 0.294501 0.296805i
\(745\) 10432.3 + 18069.3i 0.513034 + 0.888602i
\(746\) 7344.46i 0.360455i
\(747\) 605.118 4.71570i 0.0296387 0.000230975i
\(748\) 8391.73i 0.410203i
\(749\) −3626.47 + 2093.74i −0.176914 + 0.102141i
\(750\) −6741.58 24773.4i −0.328223 1.20613i
\(751\) −3530.34 + 6114.73i −0.171536 + 0.297110i −0.938957 0.344034i \(-0.888206\pi\)
0.767421 + 0.641144i \(0.221540\pi\)
\(752\) −18140.7 10473.6i −0.879687 0.507887i
\(753\) 20058.2 + 5290.89i 0.970731 + 0.256057i
\(754\) −8215.23 + 3411.42i −0.396792 + 0.164770i
\(755\) 13236.5 0.638045
\(756\) 1626.34 1664.81i 0.0782398 0.0800907i
\(757\) 1001.86 0.0481019 0.0240509 0.999711i \(-0.492344\pi\)
0.0240509 + 0.999711i \(0.492344\pi\)
\(758\) −23051.1 39925.6i −1.10456 1.91315i
\(759\) −690.452 + 2617.55i −0.0330195 + 0.125179i
\(760\) −19483.5 11248.8i −0.929921 0.536890i
\(761\) 19643.7 + 11341.3i 0.935719 + 0.540238i 0.888616 0.458652i \(-0.151668\pi\)
0.0471033 + 0.998890i \(0.485001\pi\)
\(762\) −7871.29 + 2142.01i −0.374208 + 0.101833i
\(763\) −222.161 384.794i −0.0105410 0.0182575i
\(764\) −451.395 −0.0213755
\(765\) 12716.5 + 21634.5i 0.601003 + 1.02248i
\(766\) −2658.83 −0.125415
\(767\) 17383.8 7218.71i 0.818373 0.339834i
\(768\) 13091.4 13193.8i 0.615096 0.619908i
\(769\) 13432.6 + 7755.34i 0.629900 + 0.363673i 0.780714 0.624889i \(-0.214856\pi\)
−0.150813 + 0.988562i \(0.548189\pi\)
\(770\) −3230.63 + 5595.62i −0.151200 + 0.261886i
\(771\) 18939.3 19087.5i 0.884672 0.891593i
\(772\) −9423.40 + 5440.60i −0.439321 + 0.253642i
\(773\) 19202.7i 0.893499i −0.894659 0.446750i \(-0.852581\pi\)
0.894659 0.446750i \(-0.147419\pi\)
\(774\) 21428.3 + 36455.9i 0.995123 + 1.69300i
\(775\) 3488.41i 0.161687i
\(776\) 735.993 + 1274.78i 0.0340472 + 0.0589714i
\(777\) −3393.05 12468.5i −0.156660 0.575683i
\(778\) 35870.7 + 20710.0i 1.65299 + 0.954355i
\(779\) 2630.14 4555.53i 0.120969 0.209524i
\(780\) −2206.49 + 5399.88i −0.101288 + 0.247880i
\(781\) 12656.8 + 21922.3i 0.579894 + 1.00441i
\(782\) 5122.17i 0.234231i
\(783\) 2027.56 7936.94i 0.0925405 0.362252i
\(784\) −23470.2 −1.06916
\(785\) 126.305 72.9225i 0.00574272 0.00331556i
\(786\) −646.253 + 2449.99i −0.0293271 + 0.111181i
\(787\) −17403.0 10047.6i −0.788245 0.455093i 0.0510996 0.998694i \(-0.483727\pi\)
−0.839344 + 0.543600i \(0.817061\pi\)
\(788\) 5416.98 + 3127.50i 0.244888 + 0.141386i
\(789\) −1634.91 6007.85i −0.0737700 0.271084i
\(790\) −12715.6 22024.1i −0.572660 0.991877i
\(791\) 10989.7i 0.493992i
\(792\) −122.280 15691.0i −0.00548617 0.703985i
\(793\) 11144.1 + 1457.08i 0.499042 + 0.0652488i
\(794\) 3202.69 + 5547.22i 0.143148 + 0.247939i
\(795\) −16383.1 16255.9i −0.730877 0.725204i
\(796\) −468.424 + 811.334i −0.0208579 + 0.0361269i
\(797\) −12012.0 + 20805.3i −0.533859 + 0.924671i 0.465359 + 0.885122i \(0.345925\pi\)
−0.999218 + 0.0395485i \(0.987408\pi\)
\(798\) −10573.2 10491.2i −0.469033 0.465392i
\(799\) 23159.7 13371.2i 1.02544 0.592041i
\(800\) 4226.16i 0.186772i
\(801\) 1685.54 2972.69i 0.0743514 0.131130i
\(802\) 45436.1 2.00051
\(803\) −8244.32 14279.6i −0.362311 0.627541i
\(804\) −9969.11 + 2712.89i −0.437293 + 0.119000i
\(805\) −478.608 + 828.973i −0.0209549 + 0.0362950i
\(806\) −8561.64 + 11178.3i −0.374158 + 0.488510i
\(807\) 31649.8 + 8348.51i 1.38058 + 0.364165i
\(808\) −721.505 + 416.561i −0.0314139 + 0.0181368i
\(809\) −9049.70 −0.393289 −0.196644 0.980475i \(-0.563004\pi\)
−0.196644 + 0.980475i \(0.563004\pi\)
\(810\) −11363.9 18992.9i −0.492946 0.823882i
\(811\) 12498.2i 0.541150i 0.962699 + 0.270575i \(0.0872138\pi\)
−0.962699 + 0.270575i \(0.912786\pi\)
\(812\) −838.845 + 484.308i −0.0362533 + 0.0209309i
\(813\) 8449.10 32031.2i 0.364481 1.38177i
\(814\) 35587.7 + 20546.6i 1.53237 + 0.884713i
\(815\) −3931.78 + 6810.05i −0.168987 + 0.292694i
\(816\) 10580.8 + 38881.6i 0.453926 + 1.66805i
\(817\) 56885.9 32843.1i 2.43597 1.40641i
\(818\) 8549.80 0.365448
\(819\) 4927.94 6538.99i 0.210252 0.278988i
\(820\) −924.234 −0.0393606
\(821\) 20787.0 12001.4i 0.883645 0.510173i 0.0117864 0.999931i \(-0.496248\pi\)
0.871858 + 0.489758i \(0.162915\pi\)
\(822\) 21106.8 21271.9i 0.895602 0.902609i
\(823\) −2440.79 + 4227.58i −0.103379 + 0.179057i −0.913075 0.407792i \(-0.866299\pi\)
0.809696 + 0.586850i \(0.199632\pi\)
\(824\) −1416.40 817.761i −0.0598820 0.0345729i
\(825\) −4579.34 4543.79i −0.193251 0.191751i
\(826\) 7313.35 4222.37i 0.308068 0.177863i
\(827\) 36016.1i 1.51439i −0.653187 0.757197i \(-0.726568\pi\)
0.653187 0.757197i \(-0.273432\pi\)
\(828\) 8.54453 + 1096.43i 0.000358627 + 0.0460190i
\(829\) −4377.50 −0.183398 −0.0916990 0.995787i \(-0.529230\pi\)
−0.0916990 + 0.995787i \(0.529230\pi\)
\(830\) −589.296 + 340.230i −0.0246443 + 0.0142284i
\(831\) −0.0681895 0.250577i −2.84653e−6 1.04602e-5i
\(832\) 7398.10 9659.16i 0.308273 0.402489i
\(833\) 14981.8 25949.3i 0.623157 1.07934i
\(834\) −12598.9 + 47763.2i −0.523097 + 1.98310i
\(835\) −17948.1 31087.1i −0.743858 1.28840i
\(836\) 11496.6 0.475619
\(837\) −3502.21 12484.8i −0.144628 0.515577i
\(838\) 14225.3i 0.586402i
\(839\) 20711.7 11957.9i 0.852263 0.492054i −0.00915102 0.999958i \(-0.502913\pi\)
0.861414 + 0.507904i \(0.169580\pi\)
\(840\) 1415.15 5364.95i 0.0581279 0.220367i
\(841\) 10489.8 18168.9i 0.430105 0.744964i
\(842\) 13802.2 23906.1i 0.564911 0.978454i
\(843\) −23940.2 + 6514.84i −0.978107 + 0.266172i
\(844\) 954.540 + 1653.31i 0.0389297 + 0.0674281i
\(845\) −5276.35 + 19832.6i −0.214807 + 0.807409i
\(846\) −20333.5 + 11951.8i −0.826337 + 0.485711i
\(847\) 1611.23i 0.0653629i
\(848\) −18529.5 32094.0i −0.750359 1.29966i
\(849\) 9017.92 9088.47i 0.364540 0.367392i
\(850\) 10571.0 + 6103.15i 0.426566 + 0.246278i
\(851\) 5272.20 + 3043.91i 0.212372 + 0.122613i
\(852\) 7278.12 + 7221.62i 0.292658 + 0.290386i
\(853\) −28289.4 + 16332.9i −1.13553 + 0.655601i −0.945321 0.326142i \(-0.894251\pi\)
−0.190214 + 0.981743i \(0.560918\pi\)
\(854\) 5042.25 0.202040
\(855\) −29639.1 + 17421.5i −1.18554 + 0.696845i
\(856\) 11435.3i 0.456603i
\(857\) 15973.8 + 27667.4i 0.636703 + 1.10280i 0.986152 + 0.165846i \(0.0530355\pi\)
−0.349449 + 0.936955i \(0.613631\pi\)
\(858\) 3522.22 + 25799.3i 0.140148 + 1.02654i
\(859\) −6996.89 + 12119.0i −0.277917 + 0.481366i −0.970867 0.239619i \(-0.922977\pi\)
0.692950 + 0.720986i \(0.256311\pi\)
\(860\) −9994.89 5770.55i −0.396306 0.228807i
\(861\) 1254.41 + 330.884i 0.0496517 + 0.0130970i
\(862\) 1383.14 + 2395.66i 0.0546518 + 0.0946597i
\(863\) 10612.0i 0.418583i −0.977853 0.209292i \(-0.932884\pi\)
0.977853 0.209292i \(-0.0671158\pi\)
\(864\) −4242.87 15125.2i −0.167066 0.595565i
\(865\) 35056.3i 1.37798i
\(866\) 17984.4 10383.3i 0.705700 0.407436i
\(867\) −25058.2 6609.78i −0.981570 0.258916i
\(868\) −766.603 + 1327.80i −0.0299772 + 0.0519220i
\(869\) −23861.2 13776.3i −0.931457 0.537777i
\(870\) 2418.76 + 8888.26i 0.0942571 + 0.346368i
\(871\) −33569.1 + 13939.7i −1.30591 + 0.542285i
\(872\) −1213.37 −0.0471214
\(873\) 2249.37 17.5294i 0.0872046 0.000679587i
\(874\) 7017.32 0.271584
\(875\) −4917.80 8517.87i −0.190002 0.329093i
\(876\) −4740.77 4703.97i −0.182849 0.181430i
\(877\) −2998.55 1731.21i −0.115455 0.0666578i 0.441161 0.897428i \(-0.354567\pi\)
−0.556615 + 0.830770i \(0.687900\pi\)
\(878\) −19238.9 11107.6i −0.739501 0.426951i
\(879\) −4566.20 4530.76i −0.175215 0.173855i
\(880\) 11973.6 + 20738.9i 0.458670 + 0.794440i
\(881\) 46965.4 1.79603 0.898016 0.439963i \(-0.145008\pi\)
0.898016 + 0.439963i \(0.145008\pi\)
\(882\) −13034.7 + 22988.7i −0.497621 + 0.877629i
\(883\) −2872.66 −0.109482 −0.0547410 0.998501i \(-0.517433\pi\)
−0.0547410 + 0.998501i \(0.517433\pi\)
\(884\) −4585.96 11043.7i −0.174482 0.420181i
\(885\) −5118.20 18807.9i −0.194403 0.714375i
\(886\) 13805.9 + 7970.83i 0.523497 + 0.302241i
\(887\) −13523.1 + 23422.7i −0.511907 + 0.886648i 0.487998 + 0.872845i \(0.337727\pi\)
−0.999905 + 0.0138036i \(0.995606\pi\)
\(888\) −34120.6 9000.25i −1.28943 0.340122i
\(889\) −2706.40 + 1562.54i −0.102103 + 0.0589492i
\(890\) 3842.66i 0.144726i
\(891\) −20950.9 11664.5i −0.787747 0.438580i
\(892\) 11058.1i 0.415083i
\(893\) 18318.5 + 31728.5i 0.686455 + 1.18897i
\(894\) 36475.6 + 9621.43i 1.36457 + 0.359943i
\(895\) −19562.1 11294.2i −0.730603 0.421814i
\(896\) 5627.00 9746.25i 0.209805 0.363392i
\(897\) 521.806 + 3822.08i 0.0194232 + 0.142269i
\(898\) −23828.2 41271.6i −0.885475 1.53369i
\(899\) 5396.59i 0.200207i
\(900\) −2272.96 1288.78i −0.0841838 0.0477327i
\(901\) 47311.9 1.74938
\(902\) −3572.87 + 2062.80i −0.131889 + 0.0761459i
\(903\) 11499.5 + 11410.3i 0.423789 + 0.420499i
\(904\) −25990.3 15005.5i −0.956221 0.552074i
\(905\) −14272.3 8240.14i −0.524231 0.302665i
\(906\) 16856.0 16987.9i 0.618106 0.622942i
\(907\) 5016.16 + 8688.24i 0.183637 + 0.318069i 0.943116 0.332463i \(-0.107880\pi\)
−0.759479 + 0.650531i \(0.774546\pi\)
\(908\) 2831.99i 0.103505i
\(909\) 9.92137 + 1273.11i 0.000362014 + 0.0464536i
\(910\) −1193.66 + 9129.46i −0.0434830 + 0.332570i
\(911\) −16542.3 28652.2i −0.601616 1.04203i −0.992576 0.121622i \(-0.961190\pi\)
0.390960 0.920408i \(-0.372143\pi\)
\(912\) −53267.3 + 14495.6i −1.93405 + 0.526314i
\(913\) −368.610 + 638.450i −0.0133617 + 0.0231431i
\(914\) −18213.7 + 31547.1i −0.659142 + 1.14167i
\(915\) 2968.41 11253.5i 0.107249 0.406588i
\(916\) −7986.45 + 4610.98i −0.288078 + 0.166322i
\(917\) 970.673i 0.0349558i
\(918\) 43960.1 + 11230.0i 1.58050 + 0.403753i
\(919\) −25742.6 −0.924014 −0.462007 0.886876i \(-0.652870\pi\)
−0.462007 + 0.886876i \(0.652870\pi\)
\(920\) 1307.00 + 2263.79i 0.0468375 + 0.0811250i
\(921\) −6194.36 + 23483.3i −0.221619 + 0.840174i
\(922\) 24076.7 41702.1i 0.860006 1.48957i
\(923\) 28636.9 + 21933.4i 1.02123 + 0.782176i
\(924\) 744.505 + 2735.85i 0.0265070 + 0.0974056i
\(925\) −12563.8 + 7253.73i −0.446590 + 0.257839i
\(926\) 31476.9 1.11706
\(927\) −2154.70 + 1266.50i −0.0763425 + 0.0448732i
\(928\) 6537.89i 0.231268i
\(929\) −24645.6 + 14229.2i −0.870395 + 0.502523i −0.867480 0.497473i \(-0.834261\pi\)
−0.00291574 + 0.999996i \(0.500928\pi\)
\(930\) 10350.2 + 10269.9i 0.364943 + 0.362110i
\(931\) 35550.3 + 20525.0i 1.25146 + 0.722533i
\(932\) −4031.17 + 6982.19i −0.141680 + 0.245396i
\(933\) −17875.2 + 18015.0i −0.627231 + 0.632138i
\(934\) 27756.5 16025.2i 0.972399 0.561415i
\(935\) −30572.6 −1.06934
\(936\) −8735.84 20582.9i −0.305064 0.718775i
\(937\) 30105.7 1.04964 0.524818 0.851214i \(-0.324133\pi\)
0.524818 + 0.851214i \(0.324133\pi\)
\(938\) −14122.5 + 8153.64i −0.491595 + 0.283823i
\(939\) −3867.13 14210.6i −0.134397 0.493872i
\(940\) 3218.57 5574.72i 0.111679 0.193433i
\(941\) 23544.6 + 13593.5i 0.815655 + 0.470918i 0.848916 0.528528i \(-0.177256\pi\)
−0.0332611 + 0.999447i \(0.510589\pi\)
\(942\) 67.2543 254.966i 0.00232618 0.00881873i
\(943\) −529.309 + 305.597i −0.0182785 + 0.0105531i
\(944\) 31298.4i 1.07911i
\(945\) −6065.20 5925.03i −0.208784 0.203959i
\(946\) −51517.1 −1.77058
\(947\) 23808.5 13745.9i 0.816973 0.471680i −0.0323984 0.999475i \(-0.510315\pi\)
0.849372 + 0.527795i \(0.176981\pi\)
\(948\) −10790.7 2846.34i −0.369689 0.0975155i
\(949\) −18653.3 14286.9i −0.638052 0.488694i
\(950\) −8361.24 + 14482.1i −0.285552 + 0.494591i
\(951\) 28259.3 7690.18i 0.963585 0.262220i
\(952\) 5687.06 + 9850.28i 0.193612 + 0.335346i
\(953\) 40303.9 1.36996 0.684980 0.728562i \(-0.259811\pi\)
0.684980 + 0.728562i \(0.259811\pi\)
\(954\) −41726.2 + 325.173i −1.41608 + 0.0110355i
\(955\) 1644.51i 0.0557227i
\(956\) −6873.69 + 3968.53i −0.232543 + 0.134259i
\(957\) 7084.26 + 7029.27i 0.239291 + 0.237434i
\(958\) −9029.29 + 15639.2i −0.304513 + 0.527432i
\(959\) 5739.95 9941.89i 0.193277 0.334766i
\(960\) −8943.61 8874.18i −0.300681 0.298347i
\(961\) −10624.4 18402.0i −0.356632 0.617704i
\(962\) 58062.6 + 7591.59i 1.94596 + 0.254431i
\(963\) 15201.5 + 8619.34i 0.508683 + 0.288426i
\(964\) 12361.5i 0.413004i
\(965\) 19821.1 + 34331.1i 0.661206 + 1.14524i
\(966\) 454.433 + 1669.91i 0.0151358 + 0.0556197i
\(967\) −36272.8 20942.1i −1.20626 0.696435i −0.244321 0.969694i \(-0.578565\pi\)
−0.961940 + 0.273259i \(0.911898\pi\)
\(968\) −3810.51 2200.00i −0.126523 0.0730481i
\(969\) 17975.6 68146.8i 0.595933 2.25923i
\(970\) −2190.55 + 1264.72i −0.0725097 + 0.0418635i
\(971\) −34348.3 −1.13521 −0.567605 0.823301i \(-0.692130\pi\)
−0.567605 + 0.823301i \(0.692130\pi\)
\(972\) −9428.67 2330.52i −0.311137 0.0769049i
\(973\) 18923.5i 0.623494i
\(974\) −20392.7 35321.2i −0.670867 1.16198i
\(975\) −8509.63 3477.19i −0.279514 0.114215i
\(976\) 9343.96 16184.2i 0.306448 0.530783i
\(977\) 17184.0 + 9921.18i 0.562707 + 0.324879i 0.754231 0.656609i \(-0.228010\pi\)
−0.191524 + 0.981488i \(0.561343\pi\)
\(978\) 3733.19 + 13718.4i 0.122059 + 0.448534i
\(979\) 2081.60 + 3605.43i 0.0679551 + 0.117702i
\(980\) 7212.50i 0.235097i
\(981\) −914.572 + 1612.98i −0.0297656 + 0.0524961i
\(982\) 43102.3i 1.40066i
\(983\) −7289.05 + 4208.33i −0.236505 + 0.136546i −0.613569 0.789641i \(-0.710267\pi\)
0.377064 + 0.926187i \(0.376934\pi\)
\(984\) 2495.32 2514.85i 0.0808415 0.0814739i
\(985\) 11394.0 19735.0i 0.368572 0.638386i
\(986\) −16353.3 9441.60i −0.528191 0.304951i
\(987\) −6364.17 + 6413.96i −0.205242 + 0.206847i
\(988\) 15129.8 6282.71i 0.487188 0.202307i
\(989\) −7632.09 −0.245386
\(990\) 26963.1 210.124i 0.865601 0.00674564i
\(991\) 13346.4 0.427814 0.213907 0.976854i \(-0.431381\pi\)
0.213907 + 0.976854i \(0.431381\pi\)
\(992\) 5174.36 + 8962.26i 0.165611 + 0.286847i
\(993\) 43682.8 11887.4i 1.39600 0.379894i
\(994\) 14014.9 + 8091.53i 0.447210 + 0.258197i
\(995\) 2955.84 + 1706.55i 0.0941772 + 0.0543732i
\(996\) −76.1590 + 288.724i −0.00242288 + 0.00918533i
\(997\) −7909.96 13700.4i −0.251265 0.435203i 0.712610 0.701561i \(-0.247513\pi\)
−0.963874 + 0.266358i \(0.914180\pi\)
\(998\) 27813.0 0.882168
\(999\) −37682.7 + 38574.1i −1.19342 + 1.22165i
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 117.4.t.a.103.31 yes 80
3.2 odd 2 351.4.t.a.64.10 80
9.2 odd 6 351.4.t.a.181.31 80
9.7 even 3 inner 117.4.t.a.25.10 80
13.12 even 2 inner 117.4.t.a.103.10 yes 80
39.38 odd 2 351.4.t.a.64.31 80
117.25 even 6 inner 117.4.t.a.25.31 yes 80
117.38 odd 6 351.4.t.a.181.10 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.t.a.25.10 80 9.7 even 3 inner
117.4.t.a.25.31 yes 80 117.25 even 6 inner
117.4.t.a.103.10 yes 80 13.12 even 2 inner
117.4.t.a.103.31 yes 80 1.1 even 1 trivial
351.4.t.a.64.10 80 3.2 odd 2
351.4.t.a.64.31 80 39.38 odd 2
351.4.t.a.181.10 80 117.38 odd 6
351.4.t.a.181.31 80 9.2 odd 6