Properties

Label 17.4.c.a.4.4
Level $17$
Weight $4$
Character 17.4
Analytic conductor $1.003$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [17,4,Mod(4,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 17.c (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: \(1.00303247010\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 46x^{6} + 561x^{4} + 836x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 4.4
Root \(4.46767i\) of defining polynomial
Character \(\chi\) \(=\) 17.4
Dual form 17.4.c.a.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.46767i q^{2} +(3.94546 - 3.94546i) q^{3} -21.8954 q^{4} +(4.79064 - 4.79064i) q^{5} +(21.5725 + 21.5725i) q^{6} +(3.33761 + 3.33761i) q^{7} -75.9757i q^{8} -4.13329i q^{9} +O(q^{10})\) \(q+5.46767i q^{2} +(3.94546 - 3.94546i) q^{3} -21.8954 q^{4} +(4.79064 - 4.79064i) q^{5} +(21.5725 + 21.5725i) q^{6} +(3.33761 + 3.33761i) q^{7} -75.9757i q^{8} -4.13329i q^{9} +(26.1937 + 26.1937i) q^{10} +(-6.70048 - 6.70048i) q^{11} +(-86.3876 + 86.3876i) q^{12} -33.7223 q^{13} +(-18.2490 + 18.2490i) q^{14} -37.8026i q^{15} +240.247 q^{16} +(-56.0931 - 42.0305i) q^{17} +22.5994 q^{18} +27.4317i q^{19} +(-104.893 + 104.893i) q^{20} +26.3368 q^{21} +(36.6360 - 36.6360i) q^{22} +(58.6134 + 58.6134i) q^{23} +(-299.759 - 299.759i) q^{24} +79.0995i q^{25} -184.382i q^{26} +(90.2197 + 90.2197i) q^{27} +(-73.0784 - 73.0784i) q^{28} +(147.098 - 147.098i) q^{29} +206.692 q^{30} +(-158.115 + 158.115i) q^{31} +705.786i q^{32} -52.8729 q^{33} +(229.809 - 306.699i) q^{34} +31.9786 q^{35} +90.5001i q^{36} +(122.947 - 122.947i) q^{37} -149.988 q^{38} +(-133.050 + 133.050i) q^{39} +(-363.973 - 363.973i) q^{40} +(-60.9335 - 60.9335i) q^{41} +144.001i q^{42} +258.362i q^{43} +(146.710 + 146.710i) q^{44} +(-19.8011 - 19.8011i) q^{45} +(-320.479 + 320.479i) q^{46} +88.9429 q^{47} +(947.884 - 947.884i) q^{48} -320.721i q^{49} -432.490 q^{50} +(-387.143 + 55.4832i) q^{51} +738.364 q^{52} -541.310i q^{53} +(-493.292 + 493.292i) q^{54} -64.1992 q^{55} +(253.577 - 253.577i) q^{56} +(108.231 + 108.231i) q^{57} +(804.282 + 804.282i) q^{58} +13.5759i q^{59} +827.704i q^{60} +(-112.176 - 112.176i) q^{61} +(-864.520 - 864.520i) q^{62} +(13.7953 - 13.7953i) q^{63} -1937.03 q^{64} +(-161.551 + 161.551i) q^{65} -289.092i q^{66} +357.758 q^{67} +(1228.18 + 920.277i) q^{68} +462.513 q^{69} +174.848i q^{70} +(679.278 - 679.278i) q^{71} -314.029 q^{72} +(-635.175 + 635.175i) q^{73} +(672.233 + 672.233i) q^{74} +(312.084 + 312.084i) q^{75} -600.630i q^{76} -44.7272i q^{77} +(-727.473 - 727.473i) q^{78} +(-319.090 - 319.090i) q^{79} +(1150.94 - 1150.94i) q^{80} +823.515 q^{81} +(333.164 - 333.164i) q^{82} +559.916i q^{83} -576.656 q^{84} +(-470.075 + 67.3686i) q^{85} -1412.64 q^{86} -1160.74i q^{87} +(-509.074 + 509.074i) q^{88} -602.266 q^{89} +(108.266 - 108.266i) q^{90} +(-112.552 - 112.552i) q^{91} +(-1283.37 - 1283.37i) q^{92} +1247.67i q^{93} +486.311i q^{94} +(131.416 + 131.416i) q^{95} +(2784.65 + 2784.65i) q^{96} +(-580.502 + 580.502i) q^{97} +1753.60 q^{98} +(-27.6950 + 27.6950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7} + 78 q^{10} - 108 q^{11} - 174 q^{12} - 88 q^{13} + 108 q^{14} + 420 q^{16} - 10 q^{17} + 428 q^{18} - 306 q^{20} - 260 q^{21} + 30 q^{22} - 22 q^{23} - 862 q^{24} + 540 q^{27} - 764 q^{28} + 46 q^{29} - 120 q^{30} + 610 q^{31} + 816 q^{33} + 1002 q^{34} + 1172 q^{35} - 574 q^{37} - 768 q^{38} - 844 q^{39} - 342 q^{40} - 968 q^{41} + 550 q^{44} - 1154 q^{45} - 944 q^{46} - 368 q^{47} + 2494 q^{48} + 468 q^{50} + 296 q^{51} + 2564 q^{52} - 1592 q^{54} - 1996 q^{55} + 684 q^{56} - 300 q^{57} + 266 q^{58} + 1258 q^{61} - 2516 q^{62} + 122 q^{63} - 3044 q^{64} + 628 q^{65} + 764 q^{67} + 1914 q^{68} + 1812 q^{69} + 1266 q^{71} + 1404 q^{72} - 1732 q^{73} + 1538 q^{74} + 1292 q^{75} - 2836 q^{78} + 914 q^{79} + 498 q^{80} + 280 q^{81} - 280 q^{82} - 2952 q^{84} - 2498 q^{85} - 4244 q^{86} + 442 q^{88} - 2156 q^{89} + 2478 q^{90} - 1632 q^{91} - 1768 q^{92} + 1484 q^{95} + 3998 q^{96} + 1836 q^{97} + 6728 q^{98} - 2088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.46767i 1.93311i 0.256451 + 0.966557i \(0.417447\pi\)
−0.256451 + 0.966557i \(0.582553\pi\)
\(3\) 3.94546 3.94546i 0.759304 0.759304i −0.216892 0.976196i \(-0.569592\pi\)
0.976196 + 0.216892i \(0.0695919\pi\)
\(4\) −21.8954 −2.73693
\(5\) 4.79064 4.79064i 0.428488 0.428488i −0.459625 0.888113i \(-0.652016\pi\)
0.888113 + 0.459625i \(0.152016\pi\)
\(6\) 21.5725 + 21.5725i 1.46782 + 1.46782i
\(7\) 3.33761 + 3.33761i 0.180214 + 0.180214i 0.791449 0.611235i \(-0.209327\pi\)
−0.611235 + 0.791449i \(0.709327\pi\)
\(8\) 75.9757i 3.35769i
\(9\) 4.13329i 0.153085i
\(10\) 26.1937 + 26.1937i 0.828316 + 0.828316i
\(11\) −6.70048 6.70048i −0.183661 0.183661i 0.609288 0.792949i \(-0.291455\pi\)
−0.792949 + 0.609288i \(0.791455\pi\)
\(12\) −86.3876 + 86.3876i −2.07816 + 2.07816i
\(13\) −33.7223 −0.719452 −0.359726 0.933058i \(-0.617130\pi\)
−0.359726 + 0.933058i \(0.617130\pi\)
\(14\) −18.2490 + 18.2490i −0.348374 + 0.348374i
\(15\) 37.8026i 0.650705i
\(16\) 240.247 3.75386
\(17\) −56.0931 42.0305i −0.800269 0.599641i
\(18\) 22.5994 0.295930
\(19\) 27.4317i 0.331225i 0.986191 + 0.165612i \(0.0529601\pi\)
−0.986191 + 0.165612i \(0.947040\pi\)
\(20\) −104.893 + 104.893i −1.17274 + 1.17274i
\(21\) 26.3368 0.273674
\(22\) 36.6360 36.6360i 0.355038 0.355038i
\(23\) 58.6134 + 58.6134i 0.531380 + 0.531380i 0.920983 0.389603i \(-0.127388\pi\)
−0.389603 + 0.920983i \(0.627388\pi\)
\(24\) −299.759 299.759i −2.54950 2.54950i
\(25\) 79.0995i 0.632796i
\(26\) 184.382i 1.39078i
\(27\) 90.2197 + 90.2197i 0.643066 + 0.643066i
\(28\) −73.0784 73.0784i −0.493233 0.493233i
\(29\) 147.098 147.098i 0.941908 0.941908i −0.0564944 0.998403i \(-0.517992\pi\)
0.998403 + 0.0564944i \(0.0179923\pi\)
\(30\) 206.692 1.25789
\(31\) −158.115 + 158.115i −0.916072 + 0.916072i −0.996741 0.0806685i \(-0.974294\pi\)
0.0806685 + 0.996741i \(0.474294\pi\)
\(32\) 705.786i 3.89895i
\(33\) −52.8729 −0.278909
\(34\) 229.809 306.699i 1.15918 1.54701i
\(35\) 31.9786 0.154439
\(36\) 90.5001i 0.418982i
\(37\) 122.947 122.947i 0.546279 0.546279i −0.379083 0.925363i \(-0.623761\pi\)
0.925363 + 0.379083i \(0.123761\pi\)
\(38\) −149.988 −0.640296
\(39\) −133.050 + 133.050i −0.546282 + 0.546282i
\(40\) −363.973 363.973i −1.43873 1.43873i
\(41\) −60.9335 60.9335i −0.232103 0.232103i 0.581467 0.813570i \(-0.302479\pi\)
−0.813570 + 0.581467i \(0.802479\pi\)
\(42\) 144.001i 0.529044i
\(43\) 258.362i 0.916274i 0.888882 + 0.458137i \(0.151483\pi\)
−0.888882 + 0.458137i \(0.848517\pi\)
\(44\) 146.710 + 146.710i 0.502667 + 0.502667i
\(45\) −19.8011 19.8011i −0.0655949 0.0655949i
\(46\) −320.479 + 320.479i −1.02722 + 1.02722i
\(47\) 88.9429 0.276035 0.138018 0.990430i \(-0.455927\pi\)
0.138018 + 0.990430i \(0.455927\pi\)
\(48\) 947.884 947.884i 2.85032 2.85032i
\(49\) 320.721i 0.935046i
\(50\) −432.490 −1.22327
\(51\) −387.143 + 55.4832i −1.06296 + 0.152337i
\(52\) 738.364 1.96909
\(53\) 541.310i 1.40292i −0.712710 0.701458i \(-0.752533\pi\)
0.712710 0.701458i \(-0.247467\pi\)
\(54\) −493.292 + 493.292i −1.24312 + 1.24312i
\(55\) −64.1992 −0.157393
\(56\) 253.577 253.577i 0.605102 0.605102i
\(57\) 108.231 + 108.231i 0.251500 + 0.251500i
\(58\) 804.282 + 804.282i 1.82082 + 1.82082i
\(59\) 13.5759i 0.0299564i 0.999888 + 0.0149782i \(0.00476789\pi\)
−0.999888 + 0.0149782i \(0.995232\pi\)
\(60\) 827.704i 1.78093i
\(61\) −112.176 112.176i −0.235453 0.235453i 0.579511 0.814964i \(-0.303243\pi\)
−0.814964 + 0.579511i \(0.803243\pi\)
\(62\) −864.520 864.520i −1.77087 1.77087i
\(63\) 13.7953 13.7953i 0.0275880 0.0275880i
\(64\) −1937.03 −3.78326
\(65\) −161.551 + 161.551i −0.308276 + 0.308276i
\(66\) 289.092i 0.539163i
\(67\) 357.758 0.652345 0.326172 0.945310i \(-0.394241\pi\)
0.326172 + 0.945310i \(0.394241\pi\)
\(68\) 1228.18 + 920.277i 2.19028 + 1.64118i
\(69\) 462.513 0.806957
\(70\) 174.848i 0.298548i
\(71\) 679.278 679.278i 1.13543 1.13543i 0.146170 0.989259i \(-0.453305\pi\)
0.989259 0.146170i \(-0.0466948\pi\)
\(72\) −314.029 −0.514010
\(73\) −635.175 + 635.175i −1.01838 + 1.01838i −0.0185509 + 0.999828i \(0.505905\pi\)
−0.999828 + 0.0185509i \(0.994095\pi\)
\(74\) 672.233 + 672.233i 1.05602 + 1.05602i
\(75\) 312.084 + 312.084i 0.480484 + 0.480484i
\(76\) 600.630i 0.906540i
\(77\) 44.7272i 0.0661965i
\(78\) −727.473 727.473i −1.05603 1.05603i
\(79\) −319.090 319.090i −0.454436 0.454436i 0.442388 0.896824i \(-0.354132\pi\)
−0.896824 + 0.442388i \(0.854132\pi\)
\(80\) 1150.94 1150.94i 1.60848 1.60848i
\(81\) 823.515 1.12965
\(82\) 333.164 333.164i 0.448681 0.448681i
\(83\) 559.916i 0.740467i 0.928939 + 0.370234i \(0.120722\pi\)
−0.928939 + 0.370234i \(0.879278\pi\)
\(84\) −576.656 −0.749028
\(85\) −470.075 + 67.3686i −0.599845 + 0.0859664i
\(86\) −1412.64 −1.77126
\(87\) 1160.74i 1.43039i
\(88\) −509.074 + 509.074i −0.616676 + 0.616676i
\(89\) −602.266 −0.717304 −0.358652 0.933471i \(-0.616763\pi\)
−0.358652 + 0.933471i \(0.616763\pi\)
\(90\) 108.266 108.266i 0.126802 0.126802i
\(91\) −112.552 112.552i −0.129655 0.129655i
\(92\) −1283.37 1283.37i −1.45435 1.45435i
\(93\) 1247.67i 1.39115i
\(94\) 486.311i 0.533608i
\(95\) 131.416 + 131.416i 0.141926 + 0.141926i
\(96\) 2784.65 + 2784.65i 2.96049 + 2.96049i
\(97\) −580.502 + 580.502i −0.607640 + 0.607640i −0.942329 0.334689i \(-0.891369\pi\)
0.334689 + 0.942329i \(0.391369\pi\)
\(98\) 1753.60 1.80755
\(99\) −27.6950 + 27.6950i −0.0281157 + 0.0281157i
\(100\) 1731.92i 1.73192i
\(101\) 246.217 0.242570 0.121285 0.992618i \(-0.461299\pi\)
0.121285 + 0.992618i \(0.461299\pi\)
\(102\) −303.364 2116.77i −0.294485 2.05482i
\(103\) −102.854 −0.0983931 −0.0491965 0.998789i \(-0.515666\pi\)
−0.0491965 + 0.998789i \(0.515666\pi\)
\(104\) 2562.07i 2.41569i
\(105\) 126.170 126.170i 0.117266 0.117266i
\(106\) 2959.70 2.71200
\(107\) −1445.44 + 1445.44i −1.30594 + 1.30594i −0.381625 + 0.924317i \(0.624635\pi\)
−0.924317 + 0.381625i \(0.875365\pi\)
\(108\) −1975.40 1975.40i −1.76003 1.76003i
\(109\) −185.564 185.564i −0.163063 0.163063i 0.620859 0.783922i \(-0.286784\pi\)
−0.783922 + 0.620859i \(0.786784\pi\)
\(110\) 351.020i 0.304259i
\(111\) 970.163i 0.829584i
\(112\) 801.850 + 801.850i 0.676498 + 0.676498i
\(113\) 211.740 + 211.740i 0.176273 + 0.176273i 0.789729 0.613456i \(-0.210221\pi\)
−0.613456 + 0.789729i \(0.710221\pi\)
\(114\) −591.771 + 591.771i −0.486179 + 0.486179i
\(115\) 561.591 0.455380
\(116\) −3220.77 + 3220.77i −2.57794 + 2.57794i
\(117\) 139.384i 0.110137i
\(118\) −74.2284 −0.0579092
\(119\) −46.9353 327.498i −0.0361559 0.252283i
\(120\) −2872.08 −2.18486
\(121\) 1241.21i 0.932537i
\(122\) 613.340 613.340i 0.455157 0.455157i
\(123\) −480.821 −0.352473
\(124\) 3461.99 3461.99i 2.50723 2.50723i
\(125\) 977.768 + 977.768i 0.699634 + 0.699634i
\(126\) 75.4281 + 75.4281i 0.0533307 + 0.0533307i
\(127\) 761.059i 0.531757i −0.964007 0.265878i \(-0.914338\pi\)
0.964007 0.265878i \(-0.0856619\pi\)
\(128\) 4944.76i 3.41452i
\(129\) 1019.35 + 1019.35i 0.695730 + 0.695730i
\(130\) −883.309 883.309i −0.595933 0.595933i
\(131\) 1024.15 1024.15i 0.683054 0.683054i −0.277633 0.960687i \(-0.589550\pi\)
0.960687 + 0.277633i \(0.0895500\pi\)
\(132\) 1157.68 0.763354
\(133\) −91.5565 + 91.5565i −0.0596914 + 0.0596914i
\(134\) 1956.10i 1.26106i
\(135\) 864.420 0.551092
\(136\) −3193.30 + 4261.71i −2.01341 + 2.68705i
\(137\) 1902.77 1.18660 0.593301 0.804981i \(-0.297824\pi\)
0.593301 + 0.804981i \(0.297824\pi\)
\(138\) 2528.87i 1.55994i
\(139\) −437.312 + 437.312i −0.266851 + 0.266851i −0.827830 0.560979i \(-0.810425\pi\)
0.560979 + 0.827830i \(0.310425\pi\)
\(140\) −700.185 −0.422689
\(141\) 350.920 350.920i 0.209595 0.209595i
\(142\) 3714.07 + 3714.07i 2.19492 + 2.19492i
\(143\) 225.955 + 225.955i 0.132135 + 0.132135i
\(144\) 993.009i 0.574658i
\(145\) 1409.38i 0.807193i
\(146\) −3472.93 3472.93i −1.96864 1.96864i
\(147\) −1265.39 1265.39i −0.709984 0.709984i
\(148\) −2691.97 + 2691.97i −1.49513 + 1.49513i
\(149\) −1398.00 −0.768647 −0.384323 0.923199i \(-0.625565\pi\)
−0.384323 + 0.923199i \(0.625565\pi\)
\(150\) −1706.37 + 1706.37i −0.928831 + 0.928831i
\(151\) 2503.54i 1.34924i −0.738166 0.674619i \(-0.764308\pi\)
0.738166 0.674619i \(-0.235692\pi\)
\(152\) 2084.15 1.11215
\(153\) −173.724 + 231.849i −0.0917959 + 0.122509i
\(154\) 244.553 0.127965
\(155\) 1514.94i 0.785052i
\(156\) 2913.18 2913.18i 1.49514 1.49514i
\(157\) −2715.22 −1.38024 −0.690121 0.723694i \(-0.742443\pi\)
−0.690121 + 0.723694i \(0.742443\pi\)
\(158\) 1744.68 1744.68i 0.878478 0.878478i
\(159\) −2135.71 2135.71i −1.06524 1.06524i
\(160\) 3381.17 + 3381.17i 1.67065 + 1.67065i
\(161\) 391.257i 0.191524i
\(162\) 4502.71i 2.18374i
\(163\) 2340.59 + 2340.59i 1.12472 + 1.12472i 0.991022 + 0.133697i \(0.0426850\pi\)
0.133697 + 0.991022i \(0.457315\pi\)
\(164\) 1334.17 + 1334.17i 0.635249 + 0.635249i
\(165\) −253.295 + 253.295i −0.119509 + 0.119509i
\(166\) −3061.44 −1.43141
\(167\) 247.639 247.639i 0.114748 0.114748i −0.647401 0.762149i \(-0.724144\pi\)
0.762149 + 0.647401i \(0.224144\pi\)
\(168\) 2000.96i 0.918912i
\(169\) −1059.81 −0.482389
\(170\) −368.349 2570.22i −0.166183 1.15957i
\(171\) 113.383 0.0507055
\(172\) 5656.94i 2.50778i
\(173\) −1478.19 + 1478.19i −0.649622 + 0.649622i −0.952902 0.303279i \(-0.901919\pi\)
0.303279 + 0.952902i \(0.401919\pi\)
\(174\) 6346.52 2.76511
\(175\) −264.003 + 264.003i −0.114039 + 0.114039i
\(176\) −1609.77 1609.77i −0.689437 0.689437i
\(177\) 53.5630 + 53.5630i 0.0227460 + 0.0227460i
\(178\) 3292.99i 1.38663i
\(179\) 739.046i 0.308597i 0.988024 + 0.154299i \(0.0493118\pi\)
−0.988024 + 0.154299i \(0.950688\pi\)
\(180\) 433.554 + 433.554i 0.179529 + 0.179529i
\(181\) 2306.67 + 2306.67i 0.947258 + 0.947258i 0.998677 0.0514191i \(-0.0163744\pi\)
−0.0514191 + 0.998677i \(0.516374\pi\)
\(182\) 615.396 615.396i 0.250638 0.250638i
\(183\) −885.169 −0.357560
\(184\) 4453.19 4453.19i 1.78421 1.78421i
\(185\) 1177.99i 0.468148i
\(186\) −6821.85 −2.68926
\(187\) 94.2257 + 657.475i 0.0368474 + 0.257109i
\(188\) −1947.44 −0.755489
\(189\) 602.236i 0.231779i
\(190\) −718.538 + 718.538i −0.274359 + 0.274359i
\(191\) −265.840 −0.100710 −0.0503548 0.998731i \(-0.516035\pi\)
−0.0503548 + 0.998731i \(0.516035\pi\)
\(192\) −7642.47 + 7642.47i −2.87264 + 2.87264i
\(193\) 25.1722 + 25.1722i 0.00938825 + 0.00938825i 0.711785 0.702397i \(-0.247887\pi\)
−0.702397 + 0.711785i \(0.747887\pi\)
\(194\) −3174.00 3174.00i −1.17464 1.17464i
\(195\) 1274.79i 0.468151i
\(196\) 7022.32i 2.55916i
\(197\) 446.683 + 446.683i 0.161547 + 0.161547i 0.783252 0.621704i \(-0.213559\pi\)
−0.621704 + 0.783252i \(0.713559\pi\)
\(198\) −151.427 151.427i −0.0543508 0.0543508i
\(199\) 2696.51 2696.51i 0.960554 0.960554i −0.0386973 0.999251i \(-0.512321\pi\)
0.999251 + 0.0386973i \(0.0123208\pi\)
\(200\) 6009.64 2.12473
\(201\) 1411.52 1411.52i 0.495328 0.495328i
\(202\) 1346.24i 0.468915i
\(203\) 981.909 0.339490
\(204\) 8476.66 1214.83i 2.90924 0.416936i
\(205\) −583.821 −0.198906
\(206\) 562.371i 0.190205i
\(207\) 242.266 242.266i 0.0813461 0.0813461i
\(208\) −8101.67 −2.70072
\(209\) 183.806 183.806i 0.0608331 0.0608331i
\(210\) 689.857 + 689.857i 0.226689 + 0.226689i
\(211\) 1667.04 + 1667.04i 0.543903 + 0.543903i 0.924671 0.380768i \(-0.124340\pi\)
−0.380768 + 0.924671i \(0.624340\pi\)
\(212\) 11852.2i 3.83969i
\(213\) 5360.13i 1.72427i
\(214\) −7903.18 7903.18i −2.52454 2.52454i
\(215\) 1237.72 + 1237.72i 0.392612 + 0.392612i
\(216\) 6854.51 6854.51i 2.15921 2.15921i
\(217\) −1055.45 −0.330178
\(218\) 1014.61 1014.61i 0.315219 0.315219i
\(219\) 5012.12i 1.54652i
\(220\) 1405.67 0.430774
\(221\) 1891.59 + 1417.36i 0.575755 + 0.431413i
\(222\) 5304.53 1.60368
\(223\) 5273.08i 1.58346i 0.610871 + 0.791730i \(0.290819\pi\)
−0.610871 + 0.791730i \(0.709181\pi\)
\(224\) −2355.64 + 2355.64i −0.702645 + 0.702645i
\(225\) 326.941 0.0968714
\(226\) −1157.72 + 1157.72i −0.340755 + 0.340755i
\(227\) −2472.24 2472.24i −0.722857 0.722857i 0.246329 0.969186i \(-0.420776\pi\)
−0.969186 + 0.246329i \(0.920776\pi\)
\(228\) −2369.76 2369.76i −0.688339 0.688339i
\(229\) 1982.99i 0.572226i −0.958196 0.286113i \(-0.907637\pi\)
0.958196 0.286113i \(-0.0923633\pi\)
\(230\) 3070.60i 0.880301i
\(231\) −176.469 176.469i −0.0502633 0.0502633i
\(232\) −11175.9 11175.9i −3.16263 3.16263i
\(233\) −10.2611 + 10.2611i −0.00288509 + 0.00288509i −0.708548 0.705663i \(-0.750649\pi\)
0.705663 + 0.708548i \(0.250649\pi\)
\(234\) −762.104 −0.212907
\(235\) 426.094 426.094i 0.118278 0.118278i
\(236\) 297.250i 0.0819886i
\(237\) −2517.92 −0.690111
\(238\) 1790.65 256.627i 0.487693 0.0698934i
\(239\) −5365.31 −1.45210 −0.726052 0.687640i \(-0.758647\pi\)
−0.726052 + 0.687640i \(0.758647\pi\)
\(240\) 9081.95i 2.44265i
\(241\) −119.928 + 119.928i −0.0320551 + 0.0320551i −0.722953 0.690898i \(-0.757216\pi\)
0.690898 + 0.722953i \(0.257216\pi\)
\(242\) 6786.51 1.80270
\(243\) 813.212 813.212i 0.214681 0.214681i
\(244\) 2456.14 + 2456.14i 0.644418 + 0.644418i
\(245\) −1536.46 1536.46i −0.400656 0.400656i
\(246\) 2628.97i 0.681371i
\(247\) 925.060i 0.238300i
\(248\) 12012.9 + 12012.9i 3.07588 + 3.07588i
\(249\) 2209.13 + 2209.13i 0.562239 + 0.562239i
\(250\) −5346.11 + 5346.11i −1.35247 + 1.35247i
\(251\) −4824.87 −1.21332 −0.606659 0.794962i \(-0.707491\pi\)
−0.606659 + 0.794962i \(0.707491\pi\)
\(252\) −302.054 + 302.054i −0.0755064 + 0.0755064i
\(253\) 785.475i 0.195187i
\(254\) 4161.22 1.02795
\(255\) −1588.86 + 2120.46i −0.390190 + 0.520739i
\(256\) 11540.1 2.81740
\(257\) 5583.38i 1.35518i −0.735439 0.677591i \(-0.763024\pi\)
0.735439 0.677591i \(-0.236976\pi\)
\(258\) −5573.50 + 5573.50i −1.34493 + 1.34493i
\(259\) 820.697 0.196894
\(260\) 3537.24 3537.24i 0.843731 0.843731i
\(261\) −607.996 607.996i −0.144192 0.144192i
\(262\) 5599.69 + 5599.69i 1.32042 + 1.32042i
\(263\) 4116.11i 0.965059i −0.875880 0.482529i \(-0.839718\pi\)
0.875880 0.482529i \(-0.160282\pi\)
\(264\) 4017.06i 0.936488i
\(265\) −2593.22 2593.22i −0.601133 0.601133i
\(266\) −500.601 500.601i −0.115390 0.115390i
\(267\) −2376.21 + 2376.21i −0.544652 + 0.544652i
\(268\) −7833.27 −1.78542
\(269\) 4277.93 4277.93i 0.969629 0.969629i −0.0299232 0.999552i \(-0.509526\pi\)
0.999552 + 0.0299232i \(0.00952628\pi\)
\(270\) 4726.37i 1.06532i
\(271\) 6555.61 1.46947 0.734733 0.678357i \(-0.237308\pi\)
0.734733 + 0.678357i \(0.237308\pi\)
\(272\) −13476.2 10097.7i −3.00410 2.25097i
\(273\) −888.136 −0.196895
\(274\) 10403.7i 2.29384i
\(275\) 530.005 530.005i 0.116220 0.116220i
\(276\) −10126.9 −2.20859
\(277\) 1725.33 1725.33i 0.374241 0.374241i −0.494778 0.869019i \(-0.664751\pi\)
0.869019 + 0.494778i \(0.164751\pi\)
\(278\) −2391.08 2391.08i −0.515854 0.515854i
\(279\) 653.533 + 653.533i 0.140237 + 0.140237i
\(280\) 2429.60i 0.518558i
\(281\) 519.764i 0.110343i −0.998477 0.0551717i \(-0.982429\pi\)
0.998477 0.0551717i \(-0.0175706\pi\)
\(282\) 1918.72 + 1918.72i 0.405170 + 0.405170i
\(283\) 3290.24 + 3290.24i 0.691112 + 0.691112i 0.962477 0.271365i \(-0.0874749\pi\)
−0.271365 + 0.962477i \(0.587475\pi\)
\(284\) −14873.1 + 14873.1i −3.10759 + 3.10759i
\(285\) 1036.99 0.215530
\(286\) −1235.45 + 1235.45i −0.255432 + 0.255432i
\(287\) 406.744i 0.0836563i
\(288\) 2917.21 0.596870
\(289\) 1379.87 + 4715.25i 0.280860 + 0.959749i
\(290\) 7706.05 1.56040
\(291\) 4580.69i 0.922766i
\(292\) 13907.4 13907.4i 2.78723 2.78723i
\(293\) 1856.79 0.370220 0.185110 0.982718i \(-0.440736\pi\)
0.185110 + 0.982718i \(0.440736\pi\)
\(294\) 6918.74 6918.74i 1.37248 1.37248i
\(295\) 65.0371 + 65.0371i 0.0128360 + 0.0128360i
\(296\) −9340.97 9340.97i −1.83423 1.83423i
\(297\) 1209.03i 0.236212i
\(298\) 7643.79i 1.48588i
\(299\) −1976.58 1976.58i −0.382302 0.382302i
\(300\) −6833.21 6833.21i −1.31505 1.31505i
\(301\) −862.310 + 862.310i −0.165125 + 0.165125i
\(302\) 13688.5 2.60823
\(303\) 971.440 971.440i 0.184184 0.184184i
\(304\) 6590.39i 1.24337i
\(305\) −1074.79 −0.201777
\(306\) −1267.67 949.867i −0.236824 0.177452i
\(307\) 759.641 0.141221 0.0706107 0.997504i \(-0.477505\pi\)
0.0706107 + 0.997504i \(0.477505\pi\)
\(308\) 979.321i 0.181175i
\(309\) −405.805 + 405.805i −0.0747102 + 0.0747102i
\(310\) −8283.21 −1.51760
\(311\) −722.960 + 722.960i −0.131818 + 0.131818i −0.769937 0.638120i \(-0.779713\pi\)
0.638120 + 0.769937i \(0.279713\pi\)
\(312\) 10108.6 + 10108.6i 1.83424 + 1.83424i
\(313\) −2786.70 2786.70i −0.503238 0.503238i 0.409205 0.912443i \(-0.365806\pi\)
−0.912443 + 0.409205i \(0.865806\pi\)
\(314\) 14845.9i 2.66817i
\(315\) 132.177i 0.0236422i
\(316\) 6986.63 + 6986.63i 1.24376 + 1.24376i
\(317\) 3806.81 + 3806.81i 0.674485 + 0.674485i 0.958747 0.284262i \(-0.0917485\pi\)
−0.284262 + 0.958747i \(0.591748\pi\)
\(318\) 11677.4 11677.4i 2.05923 2.05923i
\(319\) −1971.25 −0.345984
\(320\) −9279.61 + 9279.61i −1.62108 + 1.62108i
\(321\) 11405.8i 1.98321i
\(322\) −2139.27 −0.370238
\(323\) 1152.97 1538.73i 0.198616 0.265069i
\(324\) −18031.2 −3.09177
\(325\) 2667.41i 0.455266i
\(326\) −12797.6 + 12797.6i −2.17421 + 2.17421i
\(327\) −1464.27 −0.247628
\(328\) −4629.47 + 4629.47i −0.779328 + 0.779328i
\(329\) 296.857 + 296.857i 0.0497454 + 0.0497454i
\(330\) −1384.94 1384.94i −0.231025 0.231025i
\(331\) 1697.70i 0.281915i 0.990016 + 0.140958i \(0.0450181\pi\)
−0.990016 + 0.140958i \(0.954982\pi\)
\(332\) 12259.6i 2.02661i
\(333\) −508.174 508.174i −0.0836269 0.0836269i
\(334\) 1354.01 + 1354.01i 0.221820 + 0.221820i
\(335\) 1713.89 1713.89i 0.279522 0.279522i
\(336\) 6327.33 1.02733
\(337\) −7987.91 + 7987.91i −1.29119 + 1.29119i −0.357131 + 0.934054i \(0.616245\pi\)
−0.934054 + 0.357131i \(0.883755\pi\)
\(338\) 5794.69i 0.932514i
\(339\) 1670.82 0.267689
\(340\) 10292.5 1475.06i 1.64173 0.235284i
\(341\) 2118.89 0.336493
\(342\) 619.942i 0.0980194i
\(343\) 2215.24 2215.24i 0.348722 0.348722i
\(344\) 19629.2 3.07656
\(345\) 2215.74 2215.74i 0.345772 0.345772i
\(346\) −8082.26 8082.26i −1.25579 1.25579i
\(347\) −2544.06 2544.06i −0.393580 0.393580i 0.482381 0.875961i \(-0.339772\pi\)
−0.875961 + 0.482381i \(0.839772\pi\)
\(348\) 25414.8i 3.91488i
\(349\) 3741.37i 0.573842i 0.957954 + 0.286921i \(0.0926318\pi\)
−0.957954 + 0.286921i \(0.907368\pi\)
\(350\) −1443.48 1443.48i −0.220450 0.220450i
\(351\) −3042.41 3042.41i −0.462655 0.462655i
\(352\) 4729.10 4729.10i 0.716085 0.716085i
\(353\) −5726.82 −0.863478 −0.431739 0.901999i \(-0.642100\pi\)
−0.431739 + 0.901999i \(0.642100\pi\)
\(354\) −292.865 + 292.865i −0.0439706 + 0.0439706i
\(355\) 6508.36i 0.973036i
\(356\) 13186.9 1.96321
\(357\) −1477.31 1106.95i −0.219013 0.164106i
\(358\) −4040.86 −0.596554
\(359\) 6048.82i 0.889260i 0.895714 + 0.444630i \(0.146665\pi\)
−0.895714 + 0.444630i \(0.853335\pi\)
\(360\) −1504.40 + 1504.40i −0.220247 + 0.220247i
\(361\) 6106.50 0.890290
\(362\) −12612.1 + 12612.1i −1.83116 + 1.83116i
\(363\) −4897.13 4897.13i −0.708079 0.708079i
\(364\) 2464.37 + 2464.37i 0.354857 + 0.354857i
\(365\) 6085.79i 0.872726i
\(366\) 4839.81i 0.691205i
\(367\) −2432.09 2432.09i −0.345924 0.345924i 0.512665 0.858589i \(-0.328658\pi\)
−0.858589 + 0.512665i \(0.828658\pi\)
\(368\) 14081.7 + 14081.7i 1.99472 + 1.99472i
\(369\) −251.855 + 251.855i −0.0355314 + 0.0355314i
\(370\) 6440.85 0.904984
\(371\) 1806.68 1806.68i 0.252825 0.252825i
\(372\) 27318.3i 3.80749i
\(373\) −6816.14 −0.946184 −0.473092 0.881013i \(-0.656862\pi\)
−0.473092 + 0.881013i \(0.656862\pi\)
\(374\) −3594.86 + 515.195i −0.497021 + 0.0712303i
\(375\) 7715.48 1.06247
\(376\) 6757.50i 0.926839i
\(377\) −4960.46 + 4960.46i −0.677658 + 0.677658i
\(378\) −3292.83 −0.448055
\(379\) 4184.48 4184.48i 0.567130 0.567130i −0.364193 0.931323i \(-0.618655\pi\)
0.931323 + 0.364193i \(0.118655\pi\)
\(380\) −2877.40 2877.40i −0.388441 0.388441i
\(381\) −3002.73 3002.73i −0.403765 0.403765i
\(382\) 1453.53i 0.194683i
\(383\) 7584.88i 1.01193i 0.862554 + 0.505965i \(0.168863\pi\)
−0.862554 + 0.505965i \(0.831137\pi\)
\(384\) −19509.3 19509.3i −2.59266 2.59266i
\(385\) −214.272 214.272i −0.0283644 0.0283644i
\(386\) −137.633 + 137.633i −0.0181486 + 0.0181486i
\(387\) 1067.88 0.140267
\(388\) 12710.3 12710.3i 1.66307 1.66307i
\(389\) 1389.74i 0.181137i −0.995890 0.0905687i \(-0.971132\pi\)
0.995890 0.0905687i \(-0.0288685\pi\)
\(390\) −6970.12 −0.904989
\(391\) −824.253 5751.36i −0.106609 0.743884i
\(392\) −24367.0 −3.13959
\(393\) 8081.45i 1.03729i
\(394\) −2442.32 + 2442.32i −0.312290 + 0.312290i
\(395\) −3057.30 −0.389441
\(396\) 606.394 606.394i 0.0769506 0.0769506i
\(397\) 9672.31 + 9672.31i 1.22277 + 1.22277i 0.966643 + 0.256126i \(0.0824461\pi\)
0.256126 + 0.966643i \(0.417554\pi\)
\(398\) 14743.6 + 14743.6i 1.85686 + 1.85686i
\(399\) 722.464i 0.0906478i
\(400\) 19003.4i 2.37543i
\(401\) 9399.33 + 9399.33i 1.17052 + 1.17052i 0.982085 + 0.188439i \(0.0603427\pi\)
0.188439 + 0.982085i \(0.439657\pi\)
\(402\) 7717.73 + 7717.73i 0.957525 + 0.957525i
\(403\) 5331.99 5331.99i 0.659070 0.659070i
\(404\) −5391.04 −0.663897
\(405\) 3945.16 3945.16i 0.484041 0.484041i
\(406\) 5368.76i 0.656273i
\(407\) −1647.60 −0.200660
\(408\) 4215.37 + 29413.5i 0.511500 + 3.56908i
\(409\) −6570.02 −0.794295 −0.397147 0.917755i \(-0.630000\pi\)
−0.397147 + 0.917755i \(0.630000\pi\)
\(410\) 3192.14i 0.384509i
\(411\) 7507.29 7507.29i 0.900991 0.900991i
\(412\) 2252.03 0.269295
\(413\) −45.3110 + 45.3110i −0.00539856 + 0.00539856i
\(414\) 1324.63 + 1324.63i 0.157251 + 0.157251i
\(415\) 2682.36 + 2682.36i 0.317281 + 0.317281i
\(416\) 23800.7i 2.80511i
\(417\) 3450.80i 0.405243i
\(418\) 1004.99 + 1004.99i 0.117597 + 0.117597i
\(419\) −9830.40 9830.40i −1.14617 1.14617i −0.987299 0.158874i \(-0.949214\pi\)
−0.158874 0.987299i \(-0.550786\pi\)
\(420\) −2762.55 + 2762.55i −0.320949 + 0.320949i
\(421\) 3041.18 0.352062 0.176031 0.984385i \(-0.443674\pi\)
0.176031 + 0.984385i \(0.443674\pi\)
\(422\) −9114.80 + 9114.80i −1.05143 + 1.05143i
\(423\) 367.626i 0.0422567i
\(424\) −41126.4 −4.71055
\(425\) 3324.60 4436.93i 0.379451 0.506407i
\(426\) 29307.4 3.33322
\(427\) 748.797i 0.0848638i
\(428\) 31648.5 31648.5i 3.57427 3.57427i
\(429\) 1782.99 0.200661
\(430\) −6767.43 + 6767.43i −0.758964 + 0.758964i
\(431\) 4422.43 + 4422.43i 0.494248 + 0.494248i 0.909642 0.415394i \(-0.136356\pi\)
−0.415394 + 0.909642i \(0.636356\pi\)
\(432\) 21675.0 + 21675.0i 2.41398 + 2.41398i
\(433\) 10180.7i 1.12992i −0.825119 0.564959i \(-0.808892\pi\)
0.825119 0.564959i \(-0.191108\pi\)
\(434\) 5770.86i 0.638272i
\(435\) −5560.67 5560.67i −0.612905 0.612905i
\(436\) 4063.01 + 4063.01i 0.446292 + 0.446292i
\(437\) −1607.87 + 1607.87i −0.176006 + 0.176006i
\(438\) −27404.6 −2.98960
\(439\) −7042.71 + 7042.71i −0.765672 + 0.765672i −0.977341 0.211669i \(-0.932110\pi\)
0.211669 + 0.977341i \(0.432110\pi\)
\(440\) 4877.58i 0.528476i
\(441\) −1325.63 −0.143141
\(442\) −7749.69 + 10342.6i −0.833971 + 1.11300i
\(443\) 6833.02 0.732836 0.366418 0.930450i \(-0.380584\pi\)
0.366418 + 0.930450i \(0.380584\pi\)
\(444\) 21242.1i 2.27051i
\(445\) −2885.24 + 2885.24i −0.307356 + 0.307356i
\(446\) −28831.5 −3.06101
\(447\) −5515.74 + 5515.74i −0.583636 + 0.583636i
\(448\) −6465.05 6465.05i −0.681796 0.681796i
\(449\) 4645.28 + 4645.28i 0.488251 + 0.488251i 0.907754 0.419503i \(-0.137796\pi\)
−0.419503 + 0.907754i \(0.637796\pi\)
\(450\) 1787.61i 0.187263i
\(451\) 816.567i 0.0852564i
\(452\) −4636.14 4636.14i −0.482446 0.482446i
\(453\) −9877.60 9877.60i −1.02448 1.02448i
\(454\) 13517.4 13517.4i 1.39737 1.39737i
\(455\) −1078.39 −0.111111
\(456\) 8222.92 8222.92i 0.844459 0.844459i
\(457\) 10031.6i 1.02682i −0.858144 0.513410i \(-0.828382\pi\)
0.858144 0.513410i \(-0.171618\pi\)
\(458\) 10842.4 1.10618
\(459\) −1268.72 8852.68i −0.129017 0.900235i
\(460\) −12296.3 −1.24634
\(461\) 1359.04i 0.137304i 0.997641 + 0.0686518i \(0.0218698\pi\)
−0.997641 + 0.0686518i \(0.978130\pi\)
\(462\) 964.876 964.876i 0.0971647 0.0971647i
\(463\) 81.1156 0.00814203 0.00407102 0.999992i \(-0.498704\pi\)
0.00407102 + 0.999992i \(0.498704\pi\)
\(464\) 35339.8 35339.8i 3.53579 3.53579i
\(465\) 5977.14 + 5977.14i 0.596093 + 0.596093i
\(466\) −56.1043 56.1043i −0.00557721 0.00557721i
\(467\) 10790.7i 1.06924i 0.845094 + 0.534618i \(0.179545\pi\)
−0.845094 + 0.534618i \(0.820455\pi\)
\(468\) 3051.87i 0.301437i
\(469\) 1194.06 + 1194.06i 0.117562 + 0.117562i
\(470\) 2329.74 + 2329.74i 0.228644 + 0.228644i
\(471\) −10712.8 + 10712.8i −1.04802 + 1.04802i
\(472\) 1031.44 0.100584
\(473\) 1731.15 1731.15i 0.168284 0.168284i
\(474\) 13767.1i 1.33406i
\(475\) −2169.84 −0.209598
\(476\) 1027.67 + 7170.72i 0.0989561 + 0.690482i
\(477\) −2237.39 −0.214765
\(478\) 29335.7i 2.80708i
\(479\) −1974.01 + 1974.01i −0.188298 + 0.188298i −0.794960 0.606662i \(-0.792508\pi\)
0.606662 + 0.794960i \(0.292508\pi\)
\(480\) 26680.5 2.53707
\(481\) −4146.04 + 4146.04i −0.393021 + 0.393021i
\(482\) −655.729 655.729i −0.0619661 0.0619661i
\(483\) 1543.69 + 1543.69i 0.145425 + 0.145425i
\(484\) 27176.8i 2.55229i
\(485\) 5561.95i 0.520733i
\(486\) 4446.38 + 4446.38i 0.415003 + 0.415003i
\(487\) 4575.10 + 4575.10i 0.425703 + 0.425703i 0.887162 0.461459i \(-0.152674\pi\)
−0.461459 + 0.887162i \(0.652674\pi\)
\(488\) −8522.63 + 8522.63i −0.790576 + 0.790576i
\(489\) 18469.4 1.70801
\(490\) 8400.85 8400.85i 0.774514 0.774514i
\(491\) 221.719i 0.0203789i 0.999948 + 0.0101895i \(0.00324346\pi\)
−0.999948 + 0.0101895i \(0.996757\pi\)
\(492\) 10527.8 0.964694
\(493\) −14433.8 + 2068.57i −1.31859 + 0.188973i
\(494\) 5057.93 0.460662
\(495\) 265.354i 0.0240945i
\(496\) −37986.6 + 37986.6i −3.43881 + 3.43881i
\(497\) 4534.33 0.409241
\(498\) −12078.8 + 12078.8i −1.08687 + 1.08687i
\(499\) −5125.17 5125.17i −0.459788 0.459788i 0.438798 0.898586i \(-0.355404\pi\)
−0.898586 + 0.438798i \(0.855404\pi\)
\(500\) −21408.7 21408.7i −1.91485 1.91485i
\(501\) 1954.10i 0.174257i
\(502\) 26380.8i 2.34548i
\(503\) −5194.90 5194.90i −0.460495 0.460495i 0.438323 0.898818i \(-0.355573\pi\)
−0.898818 + 0.438323i \(0.855573\pi\)
\(504\) −1048.11 1048.11i −0.0926318 0.0926318i
\(505\) 1179.54 1179.54i 0.103938 0.103938i
\(506\) 4294.72 0.377320
\(507\) −4181.43 + 4181.43i −0.366280 + 0.366280i
\(508\) 16663.7i 1.45538i
\(509\) −1656.30 −0.144232 −0.0721162 0.997396i \(-0.522975\pi\)
−0.0721162 + 0.997396i \(0.522975\pi\)
\(510\) −11594.0 8687.38i −1.00665 0.754281i
\(511\) −4239.93 −0.367052
\(512\) 23539.3i 2.03184i
\(513\) −2474.88 + 2474.88i −0.213000 + 0.213000i
\(514\) 30528.1 2.61972
\(515\) −492.736 + 492.736i −0.0421602 + 0.0421602i
\(516\) −22319.2 22319.2i −1.90416 1.90416i
\(517\) −595.960 595.960i −0.0506969 0.0506969i
\(518\) 4487.30i 0.380619i
\(519\) 11664.3i 0.986522i
\(520\) 12274.0 + 12274.0i 1.03510 + 1.03510i
\(521\) −12169.0 12169.0i −1.02329 1.02329i −0.999722 0.0235669i \(-0.992498\pi\)
−0.0235669 0.999722i \(-0.507502\pi\)
\(522\) 3324.33 3324.33i 0.278739 0.278739i
\(523\) 22280.9 1.86286 0.931429 0.363922i \(-0.118563\pi\)
0.931429 + 0.363922i \(0.118563\pi\)
\(524\) −22424.1 + 22424.1i −1.86947 + 1.86947i
\(525\) 2083.23i 0.173180i
\(526\) 22505.6 1.86557
\(527\) 15514.8 2223.49i 1.28242 0.183789i
\(528\) −12702.6 −1.04698
\(529\) 5295.94i 0.435271i
\(530\) 14178.9 14178.9i 1.16206 1.16206i
\(531\) 56.1130 0.00458587
\(532\) 2004.67 2004.67i 0.163371 0.163371i
\(533\) 2054.81 + 2054.81i 0.166987 + 0.166987i
\(534\) −12992.4 12992.4i −1.05287 1.05287i
\(535\) 13849.2i 1.11916i
\(536\) 27180.9i 2.19037i
\(537\) 2915.88 + 2915.88i 0.234319 + 0.234319i
\(538\) 23390.3 + 23390.3i 1.87440 + 1.87440i
\(539\) −2148.98 + 2148.98i −0.171731 + 0.171731i
\(540\) −18926.9 −1.50830
\(541\) −6005.23 + 6005.23i −0.477237 + 0.477237i −0.904247 0.427010i \(-0.859567\pi\)
0.427010 + 0.904247i \(0.359567\pi\)
\(542\) 35843.9i 2.84064i
\(543\) 18201.8 1.43851
\(544\) 29664.6 39589.7i 2.33797 3.12021i
\(545\) −1777.94 −0.139741
\(546\) 4856.04i 0.380621i
\(547\) 8851.45 8851.45i 0.691885 0.691885i −0.270762 0.962646i \(-0.587276\pi\)
0.962646 + 0.270762i \(0.0872756\pi\)
\(548\) −41662.0 −3.24765
\(549\) −463.654 + 463.654i −0.0360442 + 0.0360442i
\(550\) 2897.89 + 2897.89i 0.224666 + 0.224666i
\(551\) 4035.15 + 4035.15i 0.311984 + 0.311984i
\(552\) 35139.8i 2.70951i
\(553\) 2130.00i 0.163792i
\(554\) 9433.52 + 9433.52i 0.723451 + 0.723451i
\(555\) −4647.70 4647.70i −0.355467 0.355467i
\(556\) 9575.15 9575.15i 0.730354 0.730354i
\(557\) 21449.2 1.63165 0.815827 0.578295i \(-0.196282\pi\)
0.815827 + 0.578295i \(0.196282\pi\)
\(558\) −3573.31 + 3573.31i −0.271093 + 0.271093i
\(559\) 8712.53i 0.659215i
\(560\) 7682.76 0.579742
\(561\) 2965.81 + 2222.28i 0.223202 + 0.167245i
\(562\) 2841.90 0.213306
\(563\) 9661.93i 0.723271i 0.932319 + 0.361636i \(0.117782\pi\)
−0.932319 + 0.361636i \(0.882218\pi\)
\(564\) −7683.56 + 7683.56i −0.573646 + 0.573646i
\(565\) 2028.74 0.151061
\(566\) −17990.0 + 17990.0i −1.33600 + 1.33600i
\(567\) 2748.57 + 2748.57i 0.203579 + 0.203579i
\(568\) −51608.7 51608.7i −3.81242 3.81242i
\(569\) 22571.3i 1.66298i −0.555537 0.831492i \(-0.687487\pi\)
0.555537 0.831492i \(-0.312513\pi\)
\(570\) 5669.92i 0.416644i
\(571\) −12344.5 12344.5i −0.904732 0.904732i 0.0911089 0.995841i \(-0.470959\pi\)
−0.995841 + 0.0911089i \(0.970959\pi\)
\(572\) −4947.39 4947.39i −0.361645 0.361645i
\(573\) −1048.86 + 1048.86i −0.0764692 + 0.0764692i
\(574\) 2223.94 0.161717
\(575\) −4636.29 + 4636.29i −0.336255 + 0.336255i
\(576\) 8006.29i 0.579159i
\(577\) −22153.0 −1.59834 −0.799168 0.601108i \(-0.794726\pi\)
−0.799168 + 0.601108i \(0.794726\pi\)
\(578\) −25781.4 + 7544.66i −1.85530 + 0.542935i
\(579\) 198.631 0.0142571
\(580\) 30859.1i 2.20923i
\(581\) −1868.78 + 1868.78i −0.133443 + 0.133443i
\(582\) −25045.7 −1.78381
\(583\) −3627.03 + 3627.03i −0.257661 + 0.257661i
\(584\) 48257.9 + 48257.9i 3.41940 + 3.41940i
\(585\) 667.737 + 667.737i 0.0471924 + 0.0471924i
\(586\) 10152.3i 0.715678i
\(587\) 16152.5i 1.13575i −0.823116 0.567873i \(-0.807766\pi\)
0.823116 0.567873i \(-0.192234\pi\)
\(588\) 27706.3 + 27706.3i 1.94318 + 1.94318i
\(589\) −4337.36 4337.36i −0.303426 0.303426i
\(590\) −355.602 + 355.602i −0.0248134 + 0.0248134i
\(591\) 3524.74 0.245327
\(592\) 29537.6 29537.6i 2.05065 2.05065i
\(593\) 8336.26i 0.577284i 0.957437 + 0.288642i \(0.0932037\pi\)
−0.957437 + 0.288642i \(0.906796\pi\)
\(594\) 6610.58 0.456625
\(595\) −1793.78 1344.08i −0.123593 0.0926080i
\(596\) 30609.8 2.10373
\(597\) 21277.9i 1.45870i
\(598\) 10807.3 10807.3i 0.739033 0.739033i
\(599\) −9798.73 −0.668390 −0.334195 0.942504i \(-0.608464\pi\)
−0.334195 + 0.942504i \(0.608464\pi\)
\(600\) 23710.8 23710.8i 1.61332 1.61332i
\(601\) −5458.38 5458.38i −0.370469 0.370469i 0.497179 0.867648i \(-0.334369\pi\)
−0.867648 + 0.497179i \(0.834369\pi\)
\(602\) −4714.83 4714.83i −0.319206 0.319206i
\(603\) 1478.72i 0.0998640i
\(604\) 54816.1i 3.69277i
\(605\) −5946.18 5946.18i −0.399581 0.399581i
\(606\) 5311.52 + 5311.52i 0.356049 + 0.356049i
\(607\) −17165.0 + 17165.0i −1.14779 + 1.14779i −0.160799 + 0.986987i \(0.551407\pi\)
−0.986987 + 0.160799i \(0.948593\pi\)
\(608\) −19360.9 −1.29143
\(609\) 3874.08 3874.08i 0.257776 0.257776i
\(610\) 5876.58i 0.390059i
\(611\) −2999.36 −0.198594
\(612\) 3803.77 5076.43i 0.251239 0.335298i
\(613\) −12662.6 −0.834318 −0.417159 0.908833i \(-0.636974\pi\)
−0.417159 + 0.908833i \(0.636974\pi\)
\(614\) 4153.47i 0.272997i
\(615\) −2303.44 + 2303.44i −0.151030 + 0.151030i
\(616\) −3398.18 −0.222267
\(617\) 13203.5 13203.5i 0.861514 0.861514i −0.130000 0.991514i \(-0.541498\pi\)
0.991514 + 0.130000i \(0.0414978\pi\)
\(618\) −2218.81 2218.81i −0.144423 0.144423i
\(619\) 13686.4 + 13686.4i 0.888697 + 0.888697i 0.994398 0.105701i \(-0.0337087\pi\)
−0.105701 + 0.994398i \(0.533709\pi\)
\(620\) 33170.3i 2.14863i
\(621\) 10576.2i 0.683425i
\(622\) −3952.91 3952.91i −0.254819 0.254819i
\(623\) −2010.13 2010.13i −0.129268 0.129268i
\(624\) −31964.8 + 31964.8i −2.05067 + 2.05067i
\(625\) −519.171 −0.0332269
\(626\) 15236.8 15236.8i 0.972816 0.972816i
\(627\) 1450.40i 0.0923816i
\(628\) 59450.9 3.77763
\(629\) −12064.0 + 1728.94i −0.764742 + 0.109599i
\(630\) 722.698 0.0457032
\(631\) 6088.34i 0.384109i 0.981384 + 0.192055i \(0.0615151\pi\)
−0.981384 + 0.192055i \(0.938485\pi\)
\(632\) −24243.1 + 24243.1i −1.52585 + 1.52585i
\(633\) 13154.4 0.825975
\(634\) −20814.4 + 20814.4i −1.30386 + 1.30386i
\(635\) −3645.96 3645.96i −0.227851 0.227851i
\(636\) 46762.4 + 46762.4i 2.91549 + 2.91549i
\(637\) 10815.4i 0.672720i
\(638\) 10778.1i 0.668826i
\(639\) −2807.65 2807.65i −0.173817 0.173817i
\(640\) −23688.6 23688.6i −1.46308 1.46308i
\(641\) 6462.87 6462.87i 0.398234 0.398234i −0.479376 0.877610i \(-0.659137\pi\)
0.877610 + 0.479376i \(0.159137\pi\)
\(642\) −62363.4 −3.83378
\(643\) −17003.8 + 17003.8i −1.04287 + 1.04287i −0.0438299 + 0.999039i \(0.513956\pi\)
−0.999039 + 0.0438299i \(0.986044\pi\)
\(644\) 8566.75i 0.524188i
\(645\) 9766.73 0.596224
\(646\) 8413.28 + 6304.07i 0.512409 + 0.383948i
\(647\) 22785.1 1.38451 0.692253 0.721655i \(-0.256618\pi\)
0.692253 + 0.721655i \(0.256618\pi\)
\(648\) 62567.1i 3.79301i
\(649\) 90.9649 90.9649i 0.00550182 0.00550182i
\(650\) 14584.5 0.880082
\(651\) −4164.24 + 4164.24i −0.250705 + 0.250705i
\(652\) −51248.3 51248.3i −3.07828 3.07828i
\(653\) −5235.78 5235.78i −0.313770 0.313770i 0.532598 0.846368i \(-0.321216\pi\)
−0.846368 + 0.532598i \(0.821216\pi\)
\(654\) 8006.17i 0.478694i
\(655\) 9812.63i 0.585361i
\(656\) −14639.1 14639.1i −0.871281 0.871281i
\(657\) 2625.36 + 2625.36i 0.155898 + 0.155898i
\(658\) −1623.11 + 1623.11i −0.0961635 + 0.0961635i
\(659\) −18416.5 −1.08863 −0.544314 0.838882i \(-0.683210\pi\)
−0.544314 + 0.838882i \(0.683210\pi\)
\(660\) 5546.01 5546.01i 0.327088 0.327088i
\(661\) 23526.7i 1.38439i −0.721709 0.692197i \(-0.756643\pi\)
0.721709 0.692197i \(-0.243357\pi\)
\(662\) −9282.45 −0.544974
\(663\) 13055.3 1871.02i 0.764746 0.109599i
\(664\) 42540.0 2.48626
\(665\) 877.228i 0.0511541i
\(666\) 2778.53 2778.53i 0.161660 0.161660i
\(667\) 17243.8 1.00102
\(668\) −5422.16 + 5422.16i −0.314057 + 0.314057i
\(669\) 20804.7 + 20804.7i 1.20233 + 1.20233i
\(670\) 9370.99 + 9370.99i 0.540348 + 0.540348i
\(671\) 1503.26i 0.0864870i
\(672\) 18588.1i 1.06704i
\(673\) 14333.6 + 14333.6i 0.820979 + 0.820979i 0.986248 0.165269i \(-0.0528493\pi\)
−0.165269 + 0.986248i \(0.552849\pi\)
\(674\) −43675.3 43675.3i −2.49601 2.49601i
\(675\) −7136.33 + 7136.33i −0.406930 + 0.406930i
\(676\) 23205.0 1.32027
\(677\) 23854.8 23854.8i 1.35423 1.35423i 0.473366 0.880866i \(-0.343039\pi\)
0.880866 0.473366i \(-0.156961\pi\)
\(678\) 9135.51i 0.517474i
\(679\) −3874.98 −0.219010
\(680\) 5118.38 + 35714.3i 0.288648 + 2.01409i
\(681\) −19508.3 −1.09774
\(682\) 11585.4i 0.650480i
\(683\) 466.809 466.809i 0.0261522 0.0261522i −0.693910 0.720062i \(-0.744113\pi\)
0.720062 + 0.693910i \(0.244113\pi\)
\(684\) −2482.58 −0.138777
\(685\) 9115.48 9115.48i 0.508445 0.508445i
\(686\) 12112.2 + 12112.2i 0.674120 + 0.674120i
\(687\) −7823.81 7823.81i −0.434494 0.434494i
\(688\) 62070.6i 3.43956i
\(689\) 18254.2i 1.00933i
\(690\) 12114.9 + 12114.9i 0.668416 + 0.668416i
\(691\) 15237.1 + 15237.1i 0.838850 + 0.838850i 0.988708 0.149858i \(-0.0478815\pi\)
−0.149858 + 0.988708i \(0.547882\pi\)
\(692\) 32365.6 32365.6i 1.77797 1.77797i
\(693\) −184.870 −0.0101337
\(694\) 13910.1 13910.1i 0.760836 0.760836i
\(695\) 4190.01i 0.228685i
\(696\) −88187.7 −4.80280
\(697\) 856.879 + 5979.01i 0.0465662 + 0.324923i
\(698\) −20456.6 −1.10930
\(699\) 80.9694i 0.00438132i
\(700\) 5780.47 5780.47i 0.312116 0.312116i
\(701\) −13156.7 −0.708878 −0.354439 0.935079i \(-0.615328\pi\)
−0.354439 + 0.935079i \(0.615328\pi\)
\(702\) 16634.9 16634.9i 0.894365 0.894365i
\(703\) 3372.65 + 3372.65i 0.180941 + 0.180941i
\(704\) 12979.0 + 12979.0i 0.694837 + 0.694837i
\(705\) 3362.27i 0.179618i
\(706\) 31312.4i 1.66920i
\(707\) 821.777 + 821.777i 0.0437145 + 0.0437145i
\(708\) −1172.79 1172.79i −0.0622543 0.0622543i
\(709\) 23107.7 23107.7i 1.22402 1.22402i 0.257828 0.966191i \(-0.416993\pi\)
0.966191 0.257828i \(-0.0830069\pi\)
\(710\) 35585.6 1.88099
\(711\) −1318.89 + 1318.89i −0.0695672 + 0.0695672i
\(712\) 45757.6i 2.40848i
\(713\) −18535.3 −0.973565
\(714\) 6052.44 8077.46i 0.317236 0.423377i
\(715\) 2164.94 0.113237
\(716\) 16181.7i 0.844609i
\(717\) −21168.6 + 21168.6i −1.10259 + 1.10259i
\(718\) −33073.0 −1.71904
\(719\) 9521.59 9521.59i 0.493874 0.493874i −0.415650 0.909524i \(-0.636446\pi\)
0.909524 + 0.415650i \(0.136446\pi\)
\(720\) −4757.15 4757.15i −0.246234 0.246234i
\(721\) −343.286 343.286i −0.0177318 0.0177318i
\(722\) 33388.3i 1.72103i
\(723\) 946.345i 0.0486791i
\(724\) −50505.6 50505.6i −2.59258 2.59258i
\(725\) 11635.4 + 11635.4i 0.596036 + 0.596036i
\(726\) 26775.9 26775.9i 1.36880 1.36880i
\(727\) −32562.8 −1.66119 −0.830596 0.556875i \(-0.812000\pi\)
−0.830596 + 0.556875i \(0.812000\pi\)
\(728\) −8551.20 + 8551.20i −0.435341 + 0.435341i
\(729\) 15817.9i 0.803633i
\(730\) −33275.1 −1.68708
\(731\) 10859.1 14492.3i 0.549436 0.733265i
\(732\) 19381.2 0.978618
\(733\) 36291.9i 1.82875i 0.404869 + 0.914375i \(0.367317\pi\)
−0.404869 + 0.914375i \(0.632683\pi\)
\(734\) 13297.9 13297.9i 0.668710 0.668710i
\(735\) −12124.1 −0.608439
\(736\) −41368.5 + 41368.5i −2.07182 + 2.07182i
\(737\) −2397.15 2397.15i −0.119810 0.119810i
\(738\) −1377.06 1377.06i −0.0686862 0.0686862i
\(739\) 13314.8i 0.662776i 0.943495 + 0.331388i \(0.107517\pi\)
−0.943495 + 0.331388i \(0.892483\pi\)
\(740\) 25792.6i 1.28129i
\(741\) −3649.79 3649.79i −0.180942 0.180942i
\(742\) 9878.34 + 9878.34i 0.488740 + 0.488740i
\(743\) 2986.28 2986.28i 0.147451 0.147451i −0.629527 0.776978i \(-0.716751\pi\)
0.776978 + 0.629527i \(0.216751\pi\)
\(744\) 94792.7 4.67106
\(745\) −6697.30 + 6697.30i −0.329356 + 0.329356i
\(746\) 37268.4i 1.82908i
\(747\) 2314.29 0.113354
\(748\) −2063.11 14395.7i −0.100849 0.703689i
\(749\) −9648.62 −0.470698
\(750\) 42185.7i 2.05387i
\(751\) 25948.6 25948.6i 1.26082 1.26082i 0.310129 0.950695i \(-0.399628\pi\)
0.950695 0.310129i \(-0.100372\pi\)
\(752\) 21368.3 1.03620
\(753\) −19036.3 + 19036.3i −0.921277 + 0.921277i
\(754\) −27122.2 27122.2i −1.30999 1.30999i
\(755\) −11993.5 11993.5i −0.578132 0.578132i
\(756\) 13186.2i 0.634363i
\(757\) 8664.38i 0.416000i −0.978129 0.208000i \(-0.933305\pi\)
0.978129 0.208000i \(-0.0666955\pi\)
\(758\) 22879.4 + 22879.4i 1.09633 + 1.09633i
\(759\) −3099.06 3099.06i −0.148207 0.148207i
\(760\) 9984.40 9984.40i 0.476543 0.476543i
\(761\) −30593.6 −1.45731 −0.728657 0.684879i \(-0.759855\pi\)
−0.728657 + 0.684879i \(0.759855\pi\)
\(762\) 16417.9 16417.9i 0.780524 0.780524i
\(763\) 1238.68i 0.0587724i
\(764\) 5820.69 0.275635
\(765\) 278.454 + 1942.95i 0.0131601 + 0.0918270i
\(766\) −41471.6 −1.95618
\(767\) 457.809i 0.0215522i
\(768\) 45530.9 45530.9i 2.13926 2.13926i
\(769\) 24560.3 1.15171 0.575857 0.817550i \(-0.304668\pi\)
0.575857 + 0.817550i \(0.304668\pi\)
\(770\) 1171.57 1171.57i 0.0548317 0.0548317i
\(771\) −22029.0 22029.0i −1.02900 1.02900i
\(772\) −551.156 551.156i −0.0256950 0.0256950i
\(773\) 4421.49i 0.205731i 0.994695 + 0.102865i \(0.0328011\pi\)
−0.994695 + 0.102865i \(0.967199\pi\)
\(774\) 5838.83i 0.271153i
\(775\) −12506.8 12506.8i −0.579687 0.579687i
\(776\) 44104.1 + 44104.1i 2.04026 + 2.04026i
\(777\) 3238.02 3238.02i 0.149503 0.149503i
\(778\) 7598.63 0.350159
\(779\) 1671.51 1671.51i 0.0768782 0.0768782i
\(780\) 27912.0i 1.28130i
\(781\) −9102.98 −0.417068
\(782\) 31446.5 4506.74i 1.43801 0.206088i
\(783\) 26542.2 1.21142
\(784\) 77052.2i 3.51003i
\(785\) −13007.6 + 13007.6i −0.591417 + 0.591417i
\(786\) 44186.7 2.00520
\(787\) 18102.6 18102.6i 0.819932 0.819932i −0.166166 0.986098i \(-0.553139\pi\)
0.986098 + 0.166166i \(0.0531387\pi\)
\(788\) −9780.33 9780.33i −0.442144 0.442144i
\(789\) −16240.0 16240.0i −0.732773 0.732773i
\(790\) 16716.3i 0.752834i
\(791\) 1413.41i 0.0635336i
\(792\) 2104.15 + 2104.15i 0.0944036 + 0.0944036i
\(793\) 3782.82 + 3782.82i 0.169397 + 0.169397i
\(794\) −52885.0 + 52885.0i −2.36375 + 2.36375i
\(795\) −20462.9 −0.912885
\(796\) −59041.2 + 59041.2i −2.62897 + 2.62897i
\(797\) 29252.2i 1.30008i 0.759899 + 0.650042i \(0.225249\pi\)
−0.759899 + 0.650042i \(0.774751\pi\)
\(798\) −3950.20 −0.175232
\(799\) −4989.08 3738.32i −0.220902 0.165522i
\(800\) −55827.3 −2.46724
\(801\) 2489.34i 0.109808i
\(802\) −51392.4 + 51392.4i −2.26276 + 2.26276i
\(803\) 8511.96 0.374073
\(804\) −30905.8 + 30905.8i −1.35568 + 1.35568i
\(805\) 1874.37 + 1874.37i 0.0820658 + 0.0820658i
\(806\) 29153.6 + 29153.6i 1.27406 + 1.27406i
\(807\) 33756.8i 1.47249i
\(808\) 18706.5i 0.814473i
\(809\) 21127.9 + 21127.9i 0.918191 + 0.918191i 0.996898 0.0787072i \(-0.0250792\pi\)
−0.0787072 + 0.996898i \(0.525079\pi\)
\(810\) 21570.9 + 21570.9i 0.935707 + 0.935707i
\(811\) 5743.99 5743.99i 0.248704 0.248704i −0.571735 0.820439i \(-0.693729\pi\)
0.820439 + 0.571735i \(0.193729\pi\)
\(812\) −21499.3 −0.929161
\(813\) 25864.9 25864.9i 1.11577 1.11577i
\(814\) 9008.56i 0.387899i
\(815\) 22425.9 0.963858
\(816\) −93009.8 + 13329.7i −3.99019 + 0.571852i
\(817\) −7087.31 −0.303493
\(818\) 35922.7i 1.53546i
\(819\) −465.208 + 465.208i −0.0198482 + 0.0198482i
\(820\) 12783.0 0.544393
\(821\) 19490.2 19490.2i 0.828518 0.828518i −0.158794 0.987312i \(-0.550760\pi\)
0.987312 + 0.158794i \(0.0507605\pi\)
\(822\) 41047.4 + 41047.4i 1.74172 + 1.74172i
\(823\) 13917.8 + 13917.8i 0.589483 + 0.589483i 0.937491 0.348008i \(-0.113142\pi\)
−0.348008 + 0.937491i \(0.613142\pi\)
\(824\) 7814.39i 0.330373i
\(825\) 4182.22i 0.176492i
\(826\) −247.745 247.745i −0.0104360 0.0104360i
\(827\) 21762.7 + 21762.7i 0.915071 + 0.915071i 0.996666 0.0815942i \(-0.0260012\pi\)
−0.0815942 + 0.996666i \(0.526001\pi\)
\(828\) −5304.52 + 5304.52i −0.222639 + 0.222639i
\(829\) 29861.7 1.25108 0.625538 0.780194i \(-0.284880\pi\)
0.625538 + 0.780194i \(0.284880\pi\)
\(830\) −14666.2 + 14666.2i −0.613341 + 0.613341i
\(831\) 13614.4i 0.568326i
\(832\) 65321.0 2.72187
\(833\) −13480.1 + 17990.2i −0.560692 + 0.748288i
\(834\) −18867.8 −0.783380
\(835\) 2372.70i 0.0983361i
\(836\) −4024.51 + 4024.51i −0.166496 + 0.166496i
\(837\) −28530.1 −1.17819
\(838\) 53749.4 53749.4i 2.21568 2.21568i
\(839\) −20354.4 20354.4i −0.837558 0.837558i 0.150979 0.988537i \(-0.451758\pi\)
−0.988537 + 0.150979i \(0.951758\pi\)
\(840\) −9585.87 9585.87i −0.393743 0.393743i
\(841\) 18886.4i 0.774383i
\(842\) 16628.2i 0.680576i
\(843\) −2050.71 2050.71i −0.0837842 0.0837842i
\(844\) −36500.5 36500.5i −1.48862 1.48862i
\(845\) −5077.17 + 5077.17i −0.206698 + 0.206698i
\(846\) 2010.06 0.0816871
\(847\) 4142.66 4142.66i 0.168056 0.168056i
\(848\) 130048.i 5.26635i
\(849\) 25963.0 1.04953
\(850\) 24259.7 + 18177.8i 0.978942 + 0.733522i
\(851\) 14412.7 0.580563
\(852\) 117362.i 4.71921i
\(853\) 1527.89 1527.89i 0.0613293 0.0613293i −0.675777 0.737106i \(-0.736192\pi\)
0.737106 + 0.675777i \(0.236192\pi\)
\(854\) 4094.18 0.164051
\(855\) 543.178 543.178i 0.0217267 0.0217267i
\(856\) 109818. + 109818.i 4.38494 + 4.38494i
\(857\) −17938.8 17938.8i −0.715025 0.715025i 0.252557 0.967582i \(-0.418729\pi\)
−0.967582 + 0.252557i \(0.918729\pi\)
\(858\) 9748.83i 0.387902i
\(859\) 4878.89i 0.193790i −0.995295 0.0968951i \(-0.969109\pi\)
0.995295 0.0968951i \(-0.0308911\pi\)
\(860\) −27100.4 27100.4i −1.07455 1.07455i
\(861\) −1604.79 1604.79i −0.0635206 0.0635206i
\(862\) −24180.4 + 24180.4i −0.955438 + 0.955438i
\(863\) −39426.2 −1.55514 −0.777569 0.628797i \(-0.783548\pi\)
−0.777569 + 0.628797i \(0.783548\pi\)
\(864\) −63675.7 + 63675.7i −2.50728 + 2.50728i
\(865\) 14163.0i 0.556711i
\(866\) 55664.9 2.18426
\(867\) 24048.0 + 13159.6i 0.941999 + 0.515482i
\(868\) 23109.6 0.903674
\(869\) 4276.12i 0.166924i
\(870\) 30403.9 30403.9i 1.18481 1.18481i
\(871\) −12064.4 −0.469330
\(872\) −14098.4 + 14098.4i −0.547514 + 0.547514i
\(873\) 2399.38 + 2399.38i 0.0930203 + 0.0930203i
\(874\) −8791.29 8791.29i −0.340240 0.340240i
\(875\) 6526.81i 0.252167i
\(876\) 109743.i 4.23271i
\(877\) 1781.74 + 1781.74i 0.0686034 + 0.0686034i 0.740576 0.671973i \(-0.234553\pi\)
−0.671973 + 0.740576i \(0.734553\pi\)
\(878\) −38507.2 38507.2i −1.48013 1.48013i
\(879\) 7325.87 7325.87i 0.281110 0.281110i
\(880\) −15423.7 −0.590831
\(881\) −2784.04 + 2784.04i −0.106466 + 0.106466i −0.758333 0.651867i \(-0.773986\pi\)
0.651867 + 0.758333i \(0.273986\pi\)
\(882\) 7248.11i 0.276708i
\(883\) −8794.76 −0.335184 −0.167592 0.985856i \(-0.553599\pi\)
−0.167592 + 0.985856i \(0.553599\pi\)
\(884\) −41417.1 31033.8i −1.57580 1.18075i
\(885\) 513.203 0.0194928
\(886\) 37360.7i 1.41666i
\(887\) −385.409 + 385.409i −0.0145894 + 0.0145894i −0.714364 0.699774i \(-0.753284\pi\)
0.699774 + 0.714364i \(0.253284\pi\)
\(888\) −73708.8 −2.78548
\(889\) 2540.12 2540.12i 0.0958300 0.0958300i
\(890\) −15775.5 15775.5i −0.594154 0.594154i
\(891\) −5517.94 5517.94i −0.207473 0.207473i
\(892\) 115456.i 4.33382i
\(893\) 2439.86i 0.0914298i
\(894\) −30158.2 30158.2i −1.12824 1.12824i
\(895\) 3540.51 + 3540.51i 0.132230 + 0.132230i
\(896\) 16503.7 16503.7i 0.615345 0.615345i
\(897\) −15597.0 −0.580567
\(898\) −25398.9 + 25398.9i −0.943844 + 0.943844i
\(899\) 46516.6i 1.72571i
\(900\) −7158.51 −0.265130
\(901\) −22751.5 + 30363.7i −0.841247 + 1.12271i
\(902\) −4464.72 −0.164810
\(903\) 6804.42i 0.250761i
\(904\) 16087.1 16087.1i 0.591868 0.591868i
\(905\) 22100.9 0.811777
\(906\) 54007.5 54007.5i 1.98044 1.98044i
\(907\) 1870.27 + 1870.27i 0.0684688 + 0.0684688i 0.740512 0.672043i \(-0.234583\pi\)
−0.672043 + 0.740512i \(0.734583\pi\)
\(908\) 54130.9 + 54130.9i 1.97841 + 1.97841i
\(909\) 1017.69i 0.0371337i
\(910\) 5896.28i 0.214791i
\(911\) −576.131 576.131i −0.0209529 0.0209529i 0.696553 0.717506i \(-0.254716\pi\)
−0.717506 + 0.696553i \(0.754716\pi\)
\(912\) 26002.1 + 26002.1i 0.944097 + 0.944097i
\(913\) 3751.71 3751.71i 0.135995 0.135995i
\(914\) 54849.3 1.98496
\(915\) −4240.53 + 4240.53i −0.153210 + 0.153210i
\(916\) 43418.5i 1.56614i
\(917\) 6836.40 0.246192
\(918\) 48403.6 6936.93i 1.74026 0.249404i
\(919\) −44667.9 −1.60333 −0.801664 0.597774i \(-0.796052\pi\)
−0.801664 + 0.597774i \(0.796052\pi\)
\(920\) 42667.3i 1.52902i
\(921\) 2997.13 2997.13i 0.107230 0.107230i
\(922\) −7430.81 −0.265424
\(923\) −22906.8 + 22906.8i −0.816887 + 0.816887i
\(924\) 3863.87 + 3863.87i 0.137567 + 0.137567i
\(925\) 9725.03 + 9725.03i 0.345683 + 0.345683i
\(926\) 443.514i 0.0157395i
\(927\) 425.124i 0.0150625i
\(928\) 103819. + 103819.i 3.67246 + 3.67246i
\(929\) 4929.53 + 4929.53i 0.174093 + 0.174093i 0.788775 0.614682i \(-0.210716\pi\)
−0.614682 + 0.788775i \(0.710716\pi\)
\(930\) −32681.1 + 32681.1i −1.15232 + 1.15232i
\(931\) 8797.93 0.309711
\(932\) 224.671 224.671i 0.00789629 0.00789629i
\(933\) 5704.82i 0.200179i
\(934\) −59000.0 −2.06696
\(935\) 3601.13 + 2698.33i 0.125957 + 0.0943794i
\(936\) 10589.8 0.369805
\(937\) 46241.3i 1.61221i −0.591776 0.806103i \(-0.701573\pi\)
0.591776 0.806103i \(-0.298427\pi\)
\(938\) −6528.71 + 6528.71i −0.227260 + 0.227260i
\(939\) −21989.6 −0.764221
\(940\) −9329.51 + 9329.51i −0.323718 + 0.323718i
\(941\) −21810.5 21810.5i −0.755582 0.755582i 0.219933 0.975515i \(-0.429416\pi\)
−0.975515 + 0.219933i \(0.929416\pi\)
\(942\) −58574.0 58574.0i −2.02595 2.02595i
\(943\) 7143.03i 0.246669i
\(944\) 3261.56i 0.112452i
\(945\) 2885.10 + 2885.10i 0.0993145 + 0.0993145i
\(946\) 9465.34 + 9465.34i 0.325312 + 0.325312i
\(947\) −17699.8 + 17699.8i −0.607355 + 0.607355i −0.942254 0.334899i \(-0.891298\pi\)
0.334899 + 0.942254i \(0.391298\pi\)
\(948\) 55130.9 1.88879
\(949\) 21419.5 21419.5i 0.732674 0.732674i
\(950\) 11864.0i 0.405177i
\(951\) 30039.2 1.02428
\(952\) −24881.9 + 3565.94i −0.847088 + 0.121400i
\(953\) −8104.79 −0.275488 −0.137744 0.990468i \(-0.543985\pi\)
−0.137744 + 0.990468i \(0.543985\pi\)
\(954\) 12233.3i 0.415165i
\(955\) −1273.55 + 1273.55i −0.0431528 + 0.0431528i
\(956\) 117476. 3.97431
\(957\) −7777.48 + 7777.48i −0.262707 + 0.262707i
\(958\) −10793.2 10793.2i −0.364001 0.364001i
\(959\) 6350.70 + 6350.70i 0.213842 + 0.213842i
\(960\) 73224.7i 2.46179i
\(961\) 20209.5i 0.678377i
\(962\) −22669.2 22669.2i −0.759755 0.759755i
\(963\) 5974.41 + 5974.41i 0.199920 + 0.199920i
\(964\) 2625.89 2625.89i 0.0877325 0.0877325i
\(965\) 241.182 0.00804550
\(966\) −8440.38 + 8440.38i −0.281123 + 0.281123i
\(967\) 12592.3i 0.418759i −0.977834 0.209379i \(-0.932856\pi\)
0.977834 0.209379i \(-0.0671443\pi\)
\(968\) −94301.6 −3.13117
\(969\) −1522.00 10620.0i −0.0504579 0.352078i
\(970\) −30410.9 −1.00664
\(971\) 43998.8i 1.45416i 0.686553 + 0.727080i \(0.259123\pi\)
−0.686553 + 0.727080i \(0.740877\pi\)
\(972\) −17805.6 + 17805.6i −0.587568 + 0.587568i
\(973\) −2919.16 −0.0961807
\(974\) −25015.1 + 25015.1i −0.822933 + 0.822933i
\(975\) −10524.2 10524.2i −0.345685 0.345685i
\(976\) −26949.9 26949.9i −0.883856 0.883856i
\(977\) 8709.69i 0.285207i −0.989780 0.142604i \(-0.954453\pi\)
0.989780 0.142604i \(-0.0455474\pi\)
\(978\) 100985.i 3.30177i
\(979\) 4035.47 + 4035.47i 0.131741 + 0.131741i
\(980\) 33641.4 + 33641.4i 1.09657 + 1.09657i
\(981\) −766.991 + 766.991i −0.0249624 + 0.0249624i
\(982\) −1212.29 −0.0393948
\(983\) 24475.0 24475.0i 0.794132 0.794132i −0.188031 0.982163i \(-0.560211\pi\)
0.982163 + 0.188031i \(0.0602107\pi\)
\(984\) 36530.7i 1.18349i
\(985\) 4279.80 0.138442
\(986\) −11310.2 78919.0i −0.365306 2.54898i
\(987\) 2342.47 0.0755437
\(988\) 20254.6i 0.652212i
\(989\) −15143.4 + 15143.4i −0.486889 + 0.486889i
\(990\) −1450.87 −0.0465773
\(991\) −20930.6 + 20930.6i −0.670919 + 0.670919i −0.957928 0.287009i \(-0.907339\pi\)
0.287009 + 0.957928i \(0.407339\pi\)
\(992\) −111595. 111595.i −3.57172 3.57172i
\(993\) 6698.19 + 6698.19i 0.214059 + 0.214059i
\(994\) 24792.2i 0.791109i
\(995\) 25836.0i 0.823171i
\(996\) −48369.8 48369.8i −1.53881 1.53881i
\(997\) 25813.9 + 25813.9i 0.819993 + 0.819993i 0.986107 0.166114i \(-0.0531219\pi\)
−0.166114 + 0.986107i \(0.553122\pi\)
\(998\) 28022.7 28022.7i 0.888822 0.888822i
\(999\) 22184.4 0.702587
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 17.4.c.a.4.4 8
3.2 odd 2 153.4.f.a.55.1 8
4.3 odd 2 272.4.o.e.225.1 8
17.2 even 8 289.4.b.c.288.1 8
17.8 even 8 289.4.a.f.1.7 8
17.9 even 8 289.4.a.f.1.8 8
17.13 even 4 inner 17.4.c.a.13.1 yes 8
17.15 even 8 289.4.b.c.288.2 8
51.47 odd 4 153.4.f.a.64.4 8
68.47 odd 4 272.4.o.e.81.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.c.a.4.4 8 1.1 even 1 trivial
17.4.c.a.13.1 yes 8 17.13 even 4 inner
153.4.f.a.55.1 8 3.2 odd 2
153.4.f.a.64.4 8 51.47 odd 4
272.4.o.e.81.1 8 68.47 odd 4
272.4.o.e.225.1 8 4.3 odd 2
289.4.a.f.1.7 8 17.8 even 8
289.4.a.f.1.8 8 17.9 even 8
289.4.b.c.288.1 8 17.2 even 8
289.4.b.c.288.2 8 17.15 even 8