Properties

Label 22.4.c.a.9.1
Level $22$
Weight $4$
Character 22.9
Analytic conductor $1.298$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [22,4,Mod(3,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\), degree \(4\), 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: \(1.29804202013\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 9.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 22.9
Dual form 22.4.c.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.618034 - 1.90211i) q^{2} +(2.54508 - 1.84911i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(0.190983 + 0.587785i) q^{5} +(-1.94427 - 5.98385i) q^{6} +(7.92705 + 5.75934i) q^{7} +(-6.47214 + 4.70228i) q^{8} +(-5.28522 + 16.2662i) q^{9} +O(q^{10})\) \(q+(0.618034 - 1.90211i) q^{2} +(2.54508 - 1.84911i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(0.190983 + 0.587785i) q^{5} +(-1.94427 - 5.98385i) q^{6} +(7.92705 + 5.75934i) q^{7} +(-6.47214 + 4.70228i) q^{8} +(-5.28522 + 16.2662i) q^{9} +1.23607 q^{10} +(-13.5967 + 33.8545i) q^{11} -12.5836 q^{12} +(4.30244 - 13.2415i) q^{13} +(15.8541 - 11.5187i) q^{14} +(1.57295 + 1.14281i) q^{15} +(4.94427 + 15.2169i) q^{16} +(-37.2943 - 114.780i) q^{17} +(27.6738 + 20.1062i) q^{18} +(37.6697 - 27.3686i) q^{19} +(0.763932 - 2.35114i) q^{20} +30.8247 q^{21} +(55.9919 + 46.7858i) q^{22} -82.8328 q^{23} +(-7.77709 + 23.9354i) q^{24} +(100.818 - 73.2486i) q^{25} +(-22.5279 - 16.3675i) q^{26} +(42.8744 + 131.954i) q^{27} +(-12.1115 - 37.2752i) q^{28} +(-166.065 - 120.653i) q^{29} +(3.14590 - 2.28563i) q^{30} +(-89.7320 + 276.167i) q^{31} +32.0000 q^{32} +(27.9959 + 111.305i) q^{33} -241.374 q^{34} +(-1.87132 + 5.75934i) q^{35} +(55.3475 - 40.2123i) q^{36} +(38.9746 + 28.3167i) q^{37} +(-28.7771 - 88.5668i) q^{38} +(-13.5350 - 41.6566i) q^{39} +(-4.00000 - 2.90617i) q^{40} +(136.503 - 99.1749i) q^{41} +(19.0507 - 58.6320i) q^{42} +366.026 q^{43} +(123.597 - 77.5877i) q^{44} -10.5704 q^{45} +(-51.1935 + 157.557i) q^{46} +(179.585 - 130.476i) q^{47} +(40.7214 + 29.5858i) q^{48} +(-76.3247 - 234.903i) q^{49} +(-77.0182 - 237.038i) q^{50} +(-307.158 - 223.164i) q^{51} +(-45.0557 + 32.7349i) q^{52} +(-173.612 + 534.324i) q^{53} +277.489 q^{54} +(-22.4959 - 1.52633i) q^{55} -78.3870 q^{56} +(45.2649 - 139.311i) q^{57} +(-332.130 + 241.306i) q^{58} +(-332.529 - 241.596i) q^{59} +(-2.40325 - 7.39645i) q^{60} +(93.9317 + 289.092i) q^{61} +(469.843 + 341.361i) q^{62} +(-135.579 + 98.5039i) q^{63} +(19.7771 - 60.8676i) q^{64} +8.60488 q^{65} +(229.016 + 15.5386i) q^{66} +107.692 q^{67} +(-149.177 + 459.120i) q^{68} +(-210.817 + 153.167i) q^{69} +(9.79837 + 7.11894i) q^{70} +(21.4603 + 66.0480i) q^{71} +(-42.2817 - 130.130i) q^{72} +(-66.7599 - 48.5039i) q^{73} +(77.9493 - 56.6335i) q^{74} +(121.146 - 372.848i) q^{75} -186.249 q^{76} +(-302.762 + 190.058i) q^{77} -87.6006 q^{78} +(391.180 - 1203.93i) q^{79} +(-8.00000 + 5.81234i) q^{80} +(-20.4791 - 14.8789i) q^{81} +(-104.279 - 320.937i) q^{82} +(256.968 + 790.866i) q^{83} +(-99.7508 - 72.4732i) q^{84} +(60.3435 - 43.8421i) q^{85} +(226.217 - 696.223i) q^{86} -645.750 q^{87} +(-71.1935 - 283.047i) q^{88} +1482.95 q^{89} +(-6.53289 + 20.1062i) q^{90} +(110.368 - 80.1872i) q^{91} +(268.053 + 194.752i) q^{92} +(282.288 + 868.792i) q^{93} +(-137.190 - 422.229i) q^{94} +(23.2812 + 16.9147i) q^{95} +(81.4427 - 59.1716i) q^{96} +(119.587 - 368.052i) q^{97} -493.984 q^{98} +(-478.824 - 400.096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} + 28 q^{6} + 25 q^{7} - 8 q^{8} - 124 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} + 28 q^{6} + 25 q^{7} - 8 q^{8} - 124 q^{9} - 4 q^{10} + 44 q^{11} - 104 q^{12} + 91 q^{13} + 50 q^{14} + 13 q^{15} - 16 q^{16} + 23 q^{17} + 142 q^{18} + 59 q^{19} + 12 q^{20} - 230 q^{21} - 22 q^{22} - 224 q^{23} + 112 q^{24} + 126 q^{25} - 108 q^{26} + 773 q^{27} - 120 q^{28} - 425 q^{29} + 26 q^{30} - 227 q^{31} + 128 q^{32} - 11 q^{33} - 724 q^{34} + 35 q^{35} + 284 q^{36} - 61 q^{37} + 28 q^{38} - 839 q^{39} - 16 q^{40} + 347 q^{41} + 510 q^{42} + 1160 q^{43} + 396 q^{44} - 248 q^{45} - 8 q^{46} + 251 q^{47} - 16 q^{48} + 48 q^{49} + 242 q^{50} - 247 q^{51} - 216 q^{52} - 245 q^{53} - 1144 q^{54} + 33 q^{55} + 80 q^{56} - 331 q^{57} - 850 q^{58} - 827 q^{59} - 108 q^{60} + 1335 q^{61} + 976 q^{62} + 370 q^{63} - 64 q^{64} + 182 q^{65} + 1408 q^{66} - 88 q^{67} + 92 q^{68} - 244 q^{69} - 10 q^{70} - 1665 q^{71} - 992 q^{72} - 153 q^{73} - 122 q^{74} - 1709 q^{75} - 584 q^{76} - 55 q^{77} + 1832 q^{78} + 677 q^{79} - 32 q^{80} + 1376 q^{81} - 596 q^{82} + 887 q^{83} - 560 q^{84} + 181 q^{85} - 240 q^{86} + 1670 q^{87} - 88 q^{88} + 1728 q^{89} + 354 q^{90} - 245 q^{91} + 464 q^{92} + 1033 q^{93} + 292 q^{94} + 73 q^{95} - 32 q^{96} + 2019 q^{97} - 1484 q^{98} - 5654 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034 1.90211i 0.218508 0.672499i
\(3\) 2.54508 1.84911i 0.489802 0.355862i −0.315306 0.948990i \(-0.602107\pi\)
0.805108 + 0.593128i \(0.202107\pi\)
\(4\) −3.23607 2.35114i −0.404508 0.293893i
\(5\) 0.190983 + 0.587785i 0.0170820 + 0.0525731i 0.959234 0.282612i \(-0.0912010\pi\)
−0.942152 + 0.335185i \(0.891201\pi\)
\(6\) −1.94427 5.98385i −0.132291 0.407150i
\(7\) 7.92705 + 5.75934i 0.428021 + 0.310975i 0.780857 0.624710i \(-0.214783\pi\)
−0.352836 + 0.935685i \(0.614783\pi\)
\(8\) −6.47214 + 4.70228i −0.286031 + 0.207813i
\(9\) −5.28522 + 16.2662i −0.195749 + 0.602453i
\(10\) 1.23607 0.0390879
\(11\) −13.5967 + 33.8545i −0.372689 + 0.927957i
\(12\) −12.5836 −0.302714
\(13\) 4.30244 13.2415i 0.0917909 0.282503i −0.894613 0.446841i \(-0.852549\pi\)
0.986404 + 0.164338i \(0.0525488\pi\)
\(14\) 15.8541 11.5187i 0.302656 0.219893i
\(15\) 1.57295 + 1.14281i 0.0270756 + 0.0196716i
\(16\) 4.94427 + 15.2169i 0.0772542 + 0.237764i
\(17\) −37.2943 114.780i −0.532070 1.63754i −0.749895 0.661557i \(-0.769896\pi\)
0.217825 0.975988i \(-0.430104\pi\)
\(18\) 27.6738 + 20.1062i 0.362376 + 0.263282i
\(19\) 37.6697 27.3686i 0.454843 0.330463i −0.336662 0.941626i \(-0.609298\pi\)
0.791505 + 0.611163i \(0.209298\pi\)
\(20\) 0.763932 2.35114i 0.00854102 0.0262866i
\(21\) 30.8247 0.320309
\(22\) 55.9919 + 46.7858i 0.542614 + 0.453398i
\(23\) −82.8328 −0.750949 −0.375475 0.926833i \(-0.622520\pi\)
−0.375475 + 0.926833i \(0.622520\pi\)
\(24\) −7.77709 + 23.9354i −0.0661455 + 0.203575i
\(25\) 100.818 73.2486i 0.806545 0.585989i
\(26\) −22.5279 16.3675i −0.169926 0.123459i
\(27\) 42.8744 + 131.954i 0.305600 + 0.940539i
\(28\) −12.1115 37.2752i −0.0817446 0.251584i
\(29\) −166.065 120.653i −1.06336 0.772577i −0.0886536 0.996063i \(-0.528256\pi\)
−0.974707 + 0.223486i \(0.928256\pi\)
\(30\) 3.14590 2.28563i 0.0191453 0.0139099i
\(31\) −89.7320 + 276.167i −0.519882 + 1.60003i 0.254338 + 0.967115i \(0.418143\pi\)
−0.774220 + 0.632917i \(0.781857\pi\)
\(32\) 32.0000 0.176777
\(33\) 27.9959 + 111.305i 0.147681 + 0.587140i
\(34\) −241.374 −1.21751
\(35\) −1.87132 + 5.75934i −0.00903747 + 0.0278145i
\(36\) 55.3475 40.2123i 0.256239 0.186168i
\(37\) 38.9746 + 28.3167i 0.173173 + 0.125817i 0.670995 0.741461i \(-0.265867\pi\)
−0.497823 + 0.867279i \(0.665867\pi\)
\(38\) −28.7771 88.5668i −0.122849 0.378090i
\(39\) −13.5350 41.6566i −0.0555728 0.171036i
\(40\) −4.00000 2.90617i −0.0158114 0.0114876i
\(41\) 136.503 99.1749i 0.519954 0.377769i −0.296633 0.954992i \(-0.595864\pi\)
0.816587 + 0.577223i \(0.195864\pi\)
\(42\) 19.0507 58.6320i 0.0699902 0.215408i
\(43\) 366.026 1.29810 0.649052 0.760744i \(-0.275166\pi\)
0.649052 + 0.760744i \(0.275166\pi\)
\(44\) 123.597 77.5877i 0.423475 0.265836i
\(45\) −10.5704 −0.0350166
\(46\) −51.1935 + 157.557i −0.164088 + 0.505012i
\(47\) 179.585 130.476i 0.557343 0.404933i −0.273143 0.961973i \(-0.588063\pi\)
0.830485 + 0.557040i \(0.188063\pi\)
\(48\) 40.7214 + 29.5858i 0.122450 + 0.0889655i
\(49\) −76.3247 234.903i −0.222521 0.684849i
\(50\) −77.0182 237.038i −0.217840 0.670444i
\(51\) −307.158 223.164i −0.843349 0.612729i
\(52\) −45.0557 + 32.7349i −0.120156 + 0.0872984i
\(53\) −173.612 + 534.324i −0.449953 + 1.38481i 0.427007 + 0.904248i \(0.359568\pi\)
−0.876960 + 0.480564i \(0.840432\pi\)
\(54\) 277.489 0.699287
\(55\) −22.4959 1.52633i −0.0551518 0.00374201i
\(56\) −78.3870 −0.187052
\(57\) 45.2649 139.311i 0.105184 0.323723i
\(58\) −332.130 + 241.306i −0.751910 + 0.546294i
\(59\) −332.529 241.596i −0.733755 0.533104i 0.156994 0.987600i \(-0.449820\pi\)
−0.890749 + 0.454495i \(0.849820\pi\)
\(60\) −2.40325 7.39645i −0.00517098 0.0159146i
\(61\) 93.9317 + 289.092i 0.197159 + 0.606794i 0.999945 + 0.0105259i \(0.00335056\pi\)
−0.802785 + 0.596268i \(0.796649\pi\)
\(62\) 469.843 + 341.361i 0.962421 + 0.699240i
\(63\) −135.579 + 98.5039i −0.271132 + 0.196989i
\(64\) 19.7771 60.8676i 0.0386271 0.118882i
\(65\) 8.60488 0.0164201
\(66\) 229.016 + 15.5386i 0.427121 + 0.0289798i
\(67\) 107.692 0.196368 0.0981841 0.995168i \(-0.468697\pi\)
0.0981841 + 0.995168i \(0.468697\pi\)
\(68\) −149.177 + 459.120i −0.266035 + 0.818772i
\(69\) −210.817 + 153.167i −0.367816 + 0.267234i
\(70\) 9.79837 + 7.11894i 0.0167304 + 0.0121554i
\(71\) 21.4603 + 66.0480i 0.0358714 + 0.110401i 0.967389 0.253296i \(-0.0815145\pi\)
−0.931518 + 0.363696i \(0.881515\pi\)
\(72\) −42.2817 130.130i −0.0692077 0.212999i
\(73\) −66.7599 48.5039i −0.107036 0.0777664i 0.532980 0.846128i \(-0.321072\pi\)
−0.640016 + 0.768362i \(0.721072\pi\)
\(74\) 77.9493 56.6335i 0.122452 0.0889663i
\(75\) 121.146 372.848i 0.186516 0.574037i
\(76\) −186.249 −0.281109
\(77\) −302.762 + 190.058i −0.448090 + 0.281288i
\(78\) −87.6006 −0.127164
\(79\) 391.180 1203.93i 0.557103 1.71459i −0.133220 0.991087i \(-0.542532\pi\)
0.690323 0.723501i \(-0.257468\pi\)
\(80\) −8.00000 + 5.81234i −0.0111803 + 0.00812299i
\(81\) −20.4791 14.8789i −0.0280920 0.0204100i
\(82\) −104.279 320.937i −0.140435 0.432214i
\(83\) 256.968 + 790.866i 0.339830 + 1.04589i 0.964294 + 0.264836i \(0.0853178\pi\)
−0.624463 + 0.781054i \(0.714682\pi\)
\(84\) −99.7508 72.4732i −0.129568 0.0941366i
\(85\) 60.3435 43.8421i 0.0770020 0.0559452i
\(86\) 226.217 696.223i 0.283646 0.872973i
\(87\) −645.750 −0.795767
\(88\) −71.1935 283.047i −0.0862415 0.342874i
\(89\) 1482.95 1.76621 0.883104 0.469176i \(-0.155449\pi\)
0.883104 + 0.469176i \(0.155449\pi\)
\(90\) −6.53289 + 20.1062i −0.00765141 + 0.0235486i
\(91\) 110.368 80.1872i 0.127140 0.0923726i
\(92\) 268.053 + 194.752i 0.303765 + 0.220698i
\(93\) 282.288 + 868.792i 0.314751 + 0.968705i
\(94\) −137.190 422.229i −0.150533 0.463293i
\(95\) 23.2812 + 16.9147i 0.0251431 + 0.0182675i
\(96\) 81.4427 59.1716i 0.0865855 0.0629081i
\(97\) 119.587 368.052i 0.125178 0.385258i −0.868756 0.495241i \(-0.835080\pi\)
0.993933 + 0.109983i \(0.0350797\pi\)
\(98\) −493.984 −0.509183
\(99\) −478.824 400.096i −0.486097 0.406174i
\(100\) −498.472 −0.498472
\(101\) −336.914 + 1036.91i −0.331922 + 1.02155i 0.636296 + 0.771445i \(0.280466\pi\)
−0.968218 + 0.250107i \(0.919534\pi\)
\(102\) −614.317 + 446.327i −0.596338 + 0.433265i
\(103\) 707.305 + 513.887i 0.676629 + 0.491600i 0.872238 0.489082i \(-0.162668\pi\)
−0.195609 + 0.980682i \(0.562668\pi\)
\(104\) 34.4195 + 105.932i 0.0324530 + 0.0998800i
\(105\) 5.88699 + 18.1183i 0.00547154 + 0.0168397i
\(106\) 909.046 + 660.461i 0.832966 + 0.605185i
\(107\) −699.953 + 508.546i −0.632402 + 0.459467i −0.857232 0.514931i \(-0.827818\pi\)
0.224829 + 0.974398i \(0.427818\pi\)
\(108\) 171.498 527.816i 0.152800 0.470269i
\(109\) −1852.09 −1.62750 −0.813751 0.581214i \(-0.802578\pi\)
−0.813751 + 0.581214i \(0.802578\pi\)
\(110\) −16.8065 + 41.8465i −0.0145676 + 0.0362719i
\(111\) 151.555 0.129594
\(112\) −48.4458 + 149.101i −0.0408723 + 0.125792i
\(113\) 255.807 185.855i 0.212959 0.154724i −0.476193 0.879341i \(-0.657983\pi\)
0.689151 + 0.724617i \(0.257983\pi\)
\(114\) −237.010 172.198i −0.194720 0.141472i
\(115\) −15.8197 48.6879i −0.0128277 0.0394797i
\(116\) 253.724 + 780.884i 0.203084 + 0.625028i
\(117\) 192.651 + 139.969i 0.152227 + 0.110599i
\(118\) −665.058 + 483.193i −0.518843 + 0.376962i
\(119\) 365.424 1124.66i 0.281499 0.866363i
\(120\) −15.5542 −0.0118325
\(121\) −961.257 920.623i −0.722207 0.691677i
\(122\) 607.939 0.451149
\(123\) 164.025 504.817i 0.120241 0.370064i
\(124\) 939.686 682.722i 0.680534 0.494437i
\(125\) 124.809 + 90.6791i 0.0893061 + 0.0648847i
\(126\) 103.573 + 318.765i 0.0732304 + 0.225380i
\(127\) 254.435 + 783.070i 0.177775 + 0.547135i 0.999749 0.0223893i \(-0.00712732\pi\)
−0.821974 + 0.569525i \(0.807127\pi\)
\(128\) −103.554 75.2365i −0.0715077 0.0519534i
\(129\) 931.568 676.824i 0.635814 0.461946i
\(130\) 5.31811 16.3675i 0.00358791 0.0110425i
\(131\) −313.483 −0.209077 −0.104539 0.994521i \(-0.533337\pi\)
−0.104539 + 0.994521i \(0.533337\pi\)
\(132\) 171.096 426.011i 0.112818 0.280906i
\(133\) 456.235 0.297448
\(134\) 66.5573 204.842i 0.0429080 0.132057i
\(135\) −69.3723 + 50.4019i −0.0442268 + 0.0321326i
\(136\) 781.102 + 567.504i 0.492492 + 0.357817i
\(137\) −579.760 1784.32i −0.361549 1.11273i −0.952114 0.305744i \(-0.901095\pi\)
0.590564 0.806990i \(-0.298905\pi\)
\(138\) 161.050 + 495.659i 0.0993438 + 0.305749i
\(139\) 688.754 + 500.409i 0.420283 + 0.305353i 0.777752 0.628572i \(-0.216360\pi\)
−0.357469 + 0.933925i \(0.616360\pi\)
\(140\) 19.5967 14.2379i 0.0118302 0.00859514i
\(141\) 215.793 664.144i 0.128887 0.396674i
\(142\) 138.894 0.0820826
\(143\) 389.787 + 325.699i 0.227941 + 0.190464i
\(144\) −273.653 −0.158364
\(145\) 39.2026 120.653i 0.0224524 0.0691014i
\(146\) −133.520 + 97.0078i −0.0756861 + 0.0549892i
\(147\) −628.615 456.716i −0.352703 0.256254i
\(148\) −59.5480 183.270i −0.0330731 0.101788i
\(149\) −267.551 823.438i −0.147105 0.452743i 0.850171 0.526507i \(-0.176499\pi\)
−0.997276 + 0.0737645i \(0.976499\pi\)
\(150\) −634.327 460.866i −0.345284 0.250863i
\(151\) −1300.48 + 944.851i −0.700869 + 0.509211i −0.880215 0.474575i \(-0.842602\pi\)
0.179346 + 0.983786i \(0.442602\pi\)
\(152\) −115.108 + 354.267i −0.0614245 + 0.189045i
\(153\) 2064.15 1.09070
\(154\) 174.395 + 693.350i 0.0912543 + 0.362803i
\(155\) −179.464 −0.0929993
\(156\) −54.1401 + 166.626i −0.0277864 + 0.0855178i
\(157\) −2393.91 + 1739.28i −1.21691 + 0.884138i −0.995840 0.0911192i \(-0.970956\pi\)
−0.221072 + 0.975257i \(0.570956\pi\)
\(158\) −2048.24 1488.14i −1.03133 0.749302i
\(159\) 546.167 + 1680.93i 0.272414 + 0.838405i
\(160\) 6.11146 + 18.8091i 0.00301971 + 0.00929370i
\(161\) −656.620 477.062i −0.321422 0.233527i
\(162\) −40.9582 + 29.7578i −0.0198641 + 0.0144321i
\(163\) −750.919 + 2311.09i −0.360838 + 1.11054i 0.591709 + 0.806152i \(0.298453\pi\)
−0.952547 + 0.304393i \(0.901547\pi\)
\(164\) −674.906 −0.321349
\(165\) −60.0764 + 37.7129i −0.0283451 + 0.0177936i
\(166\) 1663.13 0.777615
\(167\) −348.515 + 1072.62i −0.161490 + 0.497016i −0.998761 0.0497734i \(-0.984150\pi\)
0.837270 + 0.546789i \(0.184150\pi\)
\(168\) −199.502 + 144.946i −0.0916183 + 0.0665646i
\(169\) 1620.58 + 1177.42i 0.737634 + 0.535923i
\(170\) −46.0983 141.876i −0.0207975 0.0640082i
\(171\) 246.092 + 757.393i 0.110053 + 0.338709i
\(172\) −1184.49 860.579i −0.525094 0.381503i
\(173\) 2157.38 1567.43i 0.948105 0.688839i −0.00225265 0.999997i \(-0.500717\pi\)
0.950358 + 0.311159i \(0.100717\pi\)
\(174\) −399.096 + 1228.29i −0.173881 + 0.535152i
\(175\) 1221.05 0.527446
\(176\) −582.387 39.5145i −0.249427 0.0169234i
\(177\) −1293.05 −0.549106
\(178\) 916.515 2820.74i 0.385931 1.18777i
\(179\) 237.941 172.875i 0.0993552 0.0721858i −0.536998 0.843583i \(-0.680442\pi\)
0.636354 + 0.771397i \(0.280442\pi\)
\(180\) 34.2067 + 24.8526i 0.0141645 + 0.0102911i
\(181\) −382.326 1176.68i −0.157006 0.483215i 0.841353 0.540487i \(-0.181760\pi\)
−0.998359 + 0.0572719i \(0.981760\pi\)
\(182\) −84.3138 259.491i −0.0343393 0.105686i
\(183\) 773.628 + 562.074i 0.312504 + 0.227047i
\(184\) 536.105 389.503i 0.214795 0.156057i
\(185\) −9.20067 + 28.3167i −0.00365647 + 0.0112534i
\(186\) 1827.00 0.720228
\(187\) 4392.91 + 298.055i 1.71787 + 0.116556i
\(188\) −887.915 −0.344457
\(189\) −420.100 + 1292.93i −0.161681 + 0.497604i
\(190\) 46.5623 33.8295i 0.0177789 0.0129171i
\(191\) −3086.91 2242.77i −1.16943 0.849639i −0.178488 0.983942i \(-0.557120\pi\)
−0.990940 + 0.134303i \(0.957120\pi\)
\(192\) −62.2167 191.483i −0.0233860 0.0719746i
\(193\) −1454.46 4476.38i −0.542459 1.66952i −0.726956 0.686684i \(-0.759066\pi\)
0.184497 0.982833i \(-0.440934\pi\)
\(194\) −626.167 454.937i −0.231733 0.168364i
\(195\) 21.9001 15.9114i 0.00804257 0.00584327i
\(196\) −305.299 + 939.613i −0.111260 + 0.342425i
\(197\) 2794.25 1.01057 0.505284 0.862953i \(-0.331388\pi\)
0.505284 + 0.862953i \(0.331388\pi\)
\(198\) −1056.96 + 663.503i −0.379367 + 0.238147i
\(199\) −4188.70 −1.49211 −0.746053 0.665886i \(-0.768054\pi\)
−0.746053 + 0.665886i \(0.768054\pi\)
\(200\) −308.073 + 948.150i −0.108920 + 0.335222i
\(201\) 274.085 199.135i 0.0961815 0.0698799i
\(202\) 1764.10 + 1281.70i 0.614464 + 0.446434i
\(203\) −621.522 1912.85i −0.214888 0.661357i
\(204\) 469.296 + 1444.35i 0.161065 + 0.495708i
\(205\) 84.3632 + 61.2934i 0.0287423 + 0.0208825i
\(206\) 1414.61 1027.77i 0.478449 0.347614i
\(207\) 437.790 1347.38i 0.146997 0.452412i
\(208\) 222.768 0.0742604
\(209\) 414.367 + 1647.41i 0.137140 + 0.545234i
\(210\) 38.1014 0.0125202
\(211\) 259.707 799.296i 0.0847344 0.260786i −0.899708 0.436492i \(-0.856221\pi\)
0.984443 + 0.175706i \(0.0562208\pi\)
\(212\) 1818.09 1320.92i 0.588996 0.427931i
\(213\) 176.749 + 128.415i 0.0568573 + 0.0413093i
\(214\) 534.717 + 1645.69i 0.170806 + 0.525687i
\(215\) 69.9048 + 215.145i 0.0221743 + 0.0682454i
\(216\) −897.974 652.416i −0.282867 0.205515i
\(217\) −2301.85 + 1672.39i −0.720090 + 0.523176i
\(218\) −1144.65 + 3522.88i −0.355622 + 1.09449i
\(219\) −259.599 −0.0801007
\(220\) 69.2098 + 57.8304i 0.0212096 + 0.0177224i
\(221\) −1680.32 −0.511451
\(222\) 93.6659 288.274i 0.0283173 0.0871517i
\(223\) 4212.12 3060.28i 1.26486 0.918977i 0.265877 0.964007i \(-0.414338\pi\)
0.998986 + 0.0450300i \(0.0143383\pi\)
\(224\) 253.666 + 184.299i 0.0756641 + 0.0549732i
\(225\) 658.634 + 2027.07i 0.195151 + 0.600612i
\(226\) −195.420 601.439i −0.0575182 0.177023i
\(227\) −741.975 539.077i −0.216946 0.157620i 0.474005 0.880522i \(-0.342808\pi\)
−0.690951 + 0.722902i \(0.742808\pi\)
\(228\) −474.020 + 344.396i −0.137687 + 0.100036i
\(229\) −1563.39 + 4811.63i −0.451144 + 1.38848i 0.424458 + 0.905447i \(0.360464\pi\)
−0.875603 + 0.483032i \(0.839536\pi\)
\(230\) −102.387 −0.0293530
\(231\) −419.115 + 1043.55i −0.119376 + 0.297233i
\(232\) 1642.14 0.464706
\(233\) −1528.11 + 4703.03i −0.429655 + 1.32234i 0.468811 + 0.883299i \(0.344683\pi\)
−0.898466 + 0.439044i \(0.855317\pi\)
\(234\) 385.301 279.938i 0.107641 0.0782056i
\(235\) 110.989 + 80.6385i 0.0308091 + 0.0223841i
\(236\) 508.059 + 1563.64i 0.140135 + 0.431291i
\(237\) −1230.61 3787.43i −0.337286 1.03806i
\(238\) −1913.38 1390.15i −0.521118 0.378615i
\(239\) −237.104 + 172.266i −0.0641716 + 0.0466234i −0.619409 0.785069i \(-0.712628\pi\)
0.555237 + 0.831692i \(0.312628\pi\)
\(240\) −9.61301 + 29.5858i −0.00258549 + 0.00795731i
\(241\) −1254.72 −0.335369 −0.167684 0.985841i \(-0.553629\pi\)
−0.167684 + 0.985841i \(0.553629\pi\)
\(242\) −2345.22 + 1259.44i −0.622960 + 0.334546i
\(243\) −3825.74 −1.00996
\(244\) 375.727 1156.37i 0.0985797 0.303397i
\(245\) 123.496 89.7250i 0.0322035 0.0233972i
\(246\) −858.846 623.988i −0.222594 0.161724i
\(247\) −200.331 616.557i −0.0516064 0.158828i
\(248\) −717.856 2209.33i −0.183806 0.565697i
\(249\) 2116.41 + 1537.66i 0.538642 + 0.391346i
\(250\) 249.618 181.358i 0.0631489 0.0458804i
\(251\) 1559.79 4800.55i 0.392244 1.20720i −0.538842 0.842407i \(-0.681138\pi\)
0.931087 0.364798i \(-0.118862\pi\)
\(252\) 670.339 0.167569
\(253\) 1126.26 2804.27i 0.279870 0.696848i
\(254\) 1646.74 0.406793
\(255\) 72.5103 223.164i 0.0178069 0.0548041i
\(256\) −207.108 + 150.473i −0.0505636 + 0.0367366i
\(257\) 4315.54 + 3135.43i 1.04746 + 0.761021i 0.971727 0.236107i \(-0.0758716\pi\)
0.0757290 + 0.997128i \(0.475872\pi\)
\(258\) −711.655 2190.25i −0.171727 0.528523i
\(259\) 145.868 + 448.936i 0.0349954 + 0.107705i
\(260\) −27.8460 20.2313i −0.00664205 0.00482573i
\(261\) 2840.26 2063.57i 0.673593 0.489394i
\(262\) −193.743 + 596.280i −0.0456851 + 0.140604i
\(263\) 724.100 0.169772 0.0848858 0.996391i \(-0.472947\pi\)
0.0848858 + 0.996391i \(0.472947\pi\)
\(264\) −704.579 588.733i −0.164257 0.137250i
\(265\) −347.225 −0.0804900
\(266\) 281.969 867.810i 0.0649948 0.200033i
\(267\) 3774.24 2742.14i 0.865092 0.628526i
\(268\) −348.498 253.199i −0.0794326 0.0577111i
\(269\) 1248.11 + 3841.28i 0.282894 + 0.870658i 0.987022 + 0.160585i \(0.0513380\pi\)
−0.704128 + 0.710073i \(0.748662\pi\)
\(270\) 52.9957 + 163.104i 0.0119452 + 0.0367637i
\(271\) 1959.43 + 1423.61i 0.439215 + 0.319108i 0.785323 0.619087i \(-0.212497\pi\)
−0.346108 + 0.938195i \(0.612497\pi\)
\(272\) 1562.20 1135.01i 0.348245 0.253015i
\(273\) 132.621 408.166i 0.0294015 0.0904885i
\(274\) −3752.29 −0.827314
\(275\) 1109.00 + 4409.09i 0.243182 + 0.966830i
\(276\) 1042.33 0.227323
\(277\) 1355.90 4173.02i 0.294108 0.905171i −0.689412 0.724370i \(-0.742131\pi\)
0.983520 0.180801i \(-0.0578692\pi\)
\(278\) 1377.51 1000.82i 0.297185 0.215917i
\(279\) −4017.94 2919.20i −0.862178 0.626409i
\(280\) −14.9706 46.0747i −0.00319523 0.00983390i
\(281\) 13.4137 + 41.2832i 0.00284767 + 0.00876423i 0.952470 0.304632i \(-0.0985333\pi\)
−0.949623 + 0.313396i \(0.898533\pi\)
\(282\) −1129.91 820.927i −0.238600 0.173353i
\(283\) −1434.70 + 1042.37i −0.301356 + 0.218948i −0.728179 0.685387i \(-0.759633\pi\)
0.426822 + 0.904335i \(0.359633\pi\)
\(284\) 85.8412 264.192i 0.0179357 0.0552004i
\(285\) 90.5298 0.0188159
\(286\) 860.418 540.126i 0.177894 0.111672i
\(287\) 1653.24 0.340028
\(288\) −169.127 + 520.519i −0.0346038 + 0.106500i
\(289\) −7808.90 + 5673.50i −1.58944 + 1.15479i
\(290\) −205.267 149.135i −0.0415645 0.0301984i
\(291\) −376.209 1157.85i −0.0757862 0.233246i
\(292\) 102.000 + 313.924i 0.0204421 + 0.0629144i
\(293\) 1702.90 + 1237.23i 0.339537 + 0.246688i 0.744467 0.667660i \(-0.232704\pi\)
−0.404929 + 0.914348i \(0.632704\pi\)
\(294\) −1257.23 + 913.431i −0.249399 + 0.181199i
\(295\) 78.4994 241.596i 0.0154929 0.0476823i
\(296\) −385.403 −0.0756793
\(297\) −5050.19 342.651i −0.986672 0.0669449i
\(298\) −1731.63 −0.336612
\(299\) −356.383 + 1096.83i −0.0689303 + 0.212146i
\(300\) −1268.65 + 921.731i −0.244153 + 0.177387i
\(301\) 2901.51 + 2108.07i 0.555615 + 0.403678i
\(302\) 993.475 + 3057.60i 0.189298 + 0.582600i
\(303\) 1059.90 + 3262.02i 0.200955 + 0.618476i
\(304\) 602.715 + 437.898i 0.113711 + 0.0826157i
\(305\) −151.985 + 110.423i −0.0285332 + 0.0207306i
\(306\) 1275.71 3926.24i 0.238326 0.733491i
\(307\) −7670.26 −1.42594 −0.712972 0.701193i \(-0.752651\pi\)
−0.712972 + 0.701193i \(0.752651\pi\)
\(308\) 1426.61 + 96.7944i 0.263924 + 0.0179070i
\(309\) 2750.39 0.506356
\(310\) −110.915 + 341.361i −0.0203211 + 0.0625419i
\(311\) −3874.53 + 2815.01i −0.706446 + 0.513263i −0.882025 0.471203i \(-0.843820\pi\)
0.175579 + 0.984465i \(0.443820\pi\)
\(312\) 283.481 + 205.961i 0.0514390 + 0.0373726i
\(313\) −1235.36 3802.04i −0.223088 0.686593i −0.998480 0.0551136i \(-0.982448\pi\)
0.775392 0.631480i \(-0.217552\pi\)
\(314\) 1828.79 + 5628.43i 0.328677 + 1.01156i
\(315\) −83.7924 60.8787i −0.0149878 0.0108893i
\(316\) −4096.49 + 2976.27i −0.729258 + 0.529837i
\(317\) 2056.15 6328.19i 0.364306 1.12122i −0.586108 0.810233i \(-0.699341\pi\)
0.950414 0.310986i \(-0.100659\pi\)
\(318\) 3534.87 0.623351
\(319\) 6342.60 3981.55i 1.11322 0.698822i
\(320\) 39.5542 0.00690983
\(321\) −841.082 + 2588.58i −0.146245 + 0.450096i
\(322\) −1313.24 + 954.125i −0.227279 + 0.165128i
\(323\) −4546.24 3303.04i −0.783156 0.568996i
\(324\) 31.2893 + 96.2984i 0.00536510 + 0.0165121i
\(325\) −536.162 1650.14i −0.0915104 0.281640i
\(326\) 3931.86 + 2856.67i 0.667993 + 0.485326i
\(327\) −4713.72 + 3424.72i −0.797153 + 0.579166i
\(328\) −417.115 + 1283.75i −0.0702174 + 0.216107i
\(329\) 2175.03 0.364478
\(330\) 34.6049 + 137.580i 0.00577253 + 0.0229501i
\(331\) 10258.7 1.70352 0.851762 0.523929i \(-0.175534\pi\)
0.851762 + 0.523929i \(0.175534\pi\)
\(332\) 1027.87 3163.47i 0.169915 0.522945i
\(333\) −666.596 + 484.310i −0.109697 + 0.0796998i
\(334\) 1824.85 + 1325.83i 0.298955 + 0.217204i
\(335\) 20.5673 + 63.2997i 0.00335437 + 0.0103237i
\(336\) 152.406 + 469.056i 0.0247453 + 0.0761581i
\(337\) −3067.44 2228.63i −0.495829 0.360241i 0.311593 0.950216i \(-0.399138\pi\)
−0.807421 + 0.589975i \(0.799138\pi\)
\(338\) 3241.17 2354.84i 0.521586 0.378955i
\(339\) 307.385 946.034i 0.0492474 0.151568i
\(340\) −298.354 −0.0475898
\(341\) −8129.43 6792.80i −1.29101 1.07874i
\(342\) 1592.74 0.251829
\(343\) 1786.42 5498.02i 0.281217 0.865496i
\(344\) −2368.97 + 1721.16i −0.371298 + 0.269764i
\(345\) −130.292 94.6625i −0.0203324 0.0147723i
\(346\) −1648.09 5072.29i −0.256074 0.788116i
\(347\) 2975.13 + 9156.50i 0.460269 + 1.41656i 0.864837 + 0.502053i \(0.167422\pi\)
−0.404568 + 0.914508i \(0.632578\pi\)
\(348\) 2089.69 + 1518.25i 0.321894 + 0.233870i
\(349\) 8002.14 5813.90i 1.22735 0.891721i 0.230660 0.973034i \(-0.425911\pi\)
0.996689 + 0.0813131i \(0.0259114\pi\)
\(350\) 754.653 2322.58i 0.115251 0.354707i
\(351\) 1931.74 0.293757
\(352\) −435.096 + 1083.34i −0.0658826 + 0.164041i
\(353\) 4714.45 0.710836 0.355418 0.934708i \(-0.384339\pi\)
0.355418 + 0.934708i \(0.384339\pi\)
\(354\) −799.151 + 2459.53i −0.119984 + 0.369273i
\(355\) −34.7235 + 25.2281i −0.00519136 + 0.00377174i
\(356\) −4798.93 3486.63i −0.714447 0.519076i
\(357\) −1149.59 3538.06i −0.170427 0.524521i
\(358\) −181.771 559.434i −0.0268349 0.0825894i
\(359\) −3481.89 2529.74i −0.511887 0.371907i 0.301652 0.953418i \(-0.402462\pi\)
−0.813539 + 0.581511i \(0.802462\pi\)
\(360\) 68.4133 49.7052i 0.0100158 0.00727692i
\(361\) −1449.58 + 4461.36i −0.211340 + 0.650439i
\(362\) −2474.47 −0.359268
\(363\) −4148.82 565.591i −0.599880 0.0817791i
\(364\) −545.690 −0.0785768
\(365\) 15.7599 48.5039i 0.00226003 0.00695564i
\(366\) 1547.26 1124.15i 0.220974 0.160547i
\(367\) 7592.84 + 5516.52i 1.07995 + 0.784632i 0.977675 0.210123i \(-0.0673865\pi\)
0.102279 + 0.994756i \(0.467387\pi\)
\(368\) −409.548 1260.46i −0.0580140 0.178549i
\(369\) 891.756 + 2744.54i 0.125807 + 0.387196i
\(370\) 48.1753 + 35.0014i 0.00676896 + 0.00491794i
\(371\) −4453.59 + 3235.72i −0.623231 + 0.452804i
\(372\) 1129.15 3475.17i 0.157376 0.484352i
\(373\) −4540.37 −0.630272 −0.315136 0.949047i \(-0.602050\pi\)
−0.315136 + 0.949047i \(0.602050\pi\)
\(374\) 3281.90 8171.60i 0.453751 1.12979i
\(375\) 485.325 0.0668322
\(376\) −548.762 + 1688.91i −0.0752665 + 0.231647i
\(377\) −2312.12 + 1679.85i −0.315862 + 0.229487i
\(378\) 2199.67 + 1598.15i 0.299309 + 0.217461i
\(379\) 128.538 + 395.598i 0.0174209 + 0.0536161i 0.959389 0.282086i \(-0.0910264\pi\)
−0.941968 + 0.335702i \(0.891026\pi\)
\(380\) −35.5704 109.475i −0.00480191 0.0147788i
\(381\) 2095.54 + 1522.50i 0.281779 + 0.204725i
\(382\) −6173.81 + 4485.54i −0.826911 + 0.600786i
\(383\) −201.720 + 620.829i −0.0269122 + 0.0828274i −0.963611 0.267310i \(-0.913865\pi\)
0.936698 + 0.350138i \(0.113865\pi\)
\(384\) −402.675 −0.0535128
\(385\) −169.536 141.661i −0.0224424 0.0187525i
\(386\) −9413.49 −1.24128
\(387\) −1934.53 + 5953.87i −0.254102 + 0.782047i
\(388\) −1252.33 + 909.874i −0.163860 + 0.119051i
\(389\) 358.300 + 260.320i 0.0467006 + 0.0339299i 0.610891 0.791715i \(-0.290811\pi\)
−0.564190 + 0.825645i \(0.690811\pi\)
\(390\) −16.7302 51.4903i −0.00217223 0.00668542i
\(391\) 3089.19 + 9507.56i 0.399558 + 1.22971i
\(392\) 1598.56 + 1161.43i 0.205969 + 0.149645i
\(393\) −797.841 + 579.665i −0.102406 + 0.0744026i
\(394\) 1726.94 5314.97i 0.220817 0.679605i
\(395\) 782.359 0.0996577
\(396\) 608.823 + 2420.52i 0.0772588 + 0.307161i
\(397\) 3516.62 0.444570 0.222285 0.974982i \(-0.428649\pi\)
0.222285 + 0.974982i \(0.428649\pi\)
\(398\) −2588.76 + 7967.38i −0.326037 + 1.00344i
\(399\) 1161.16 843.630i 0.145691 0.105850i
\(400\) 1613.09 + 1171.98i 0.201636 + 0.146497i
\(401\) 1379.82 + 4246.65i 0.171833 + 0.528847i 0.999475 0.0324095i \(-0.0103181\pi\)
−0.827642 + 0.561257i \(0.810318\pi\)
\(402\) −209.382 644.413i −0.0259777 0.0799512i
\(403\) 3270.81 + 2376.38i 0.404294 + 0.293737i
\(404\) 3528.20 2563.39i 0.434492 0.315677i
\(405\) 4.83446 14.8789i 0.000593151 0.00182553i
\(406\) −4022.57 −0.491717
\(407\) −1488.58 + 934.452i −0.181293 + 0.113806i
\(408\) 3037.35 0.368557
\(409\) 1695.47 5218.11i 0.204976 0.630853i −0.794738 0.606953i \(-0.792392\pi\)
0.999714 0.0239000i \(-0.00760832\pi\)
\(410\) 168.726 122.587i 0.0203239 0.0147662i
\(411\) −4774.94 3469.20i −0.573067 0.416358i
\(412\) −1080.67 3325.95i −0.129225 0.397713i
\(413\) −1244.54 3830.29i −0.148280 0.456359i
\(414\) −2292.30 1665.45i −0.272126 0.197711i
\(415\) −415.783 + 302.084i −0.0491807 + 0.0357319i
\(416\) 137.678 423.729i 0.0162265 0.0499400i
\(417\) 2678.25 0.314519
\(418\) 3389.66 + 229.986i 0.396636 + 0.0269114i
\(419\) −5133.78 −0.598571 −0.299286 0.954164i \(-0.596748\pi\)
−0.299286 + 0.954164i \(0.596748\pi\)
\(420\) 23.5480 72.4732i 0.00273577 0.00841983i
\(421\) 4869.80 3538.12i 0.563752 0.409590i −0.269078 0.963118i \(-0.586719\pi\)
0.832830 + 0.553528i \(0.186719\pi\)
\(422\) −1359.84 987.984i −0.156863 0.113968i
\(423\) 1173.21 + 3610.76i 0.134854 + 0.415038i
\(424\) −1388.90 4274.59i −0.159082 0.489605i
\(425\) −12167.4 8840.15i −1.38872 1.00897i
\(426\) 353.497 256.831i 0.0402042 0.0292101i
\(427\) −920.378 + 2832.63i −0.104310 + 0.321032i
\(428\) 3460.76 0.390846
\(429\) 1594.30 + 108.172i 0.179425 + 0.0121738i
\(430\) 452.433 0.0507402
\(431\) 4073.52 12537.0i 0.455254 1.40113i −0.415583 0.909555i \(-0.636422\pi\)
0.870837 0.491572i \(-0.163578\pi\)
\(432\) −1795.95 + 1304.83i −0.200017 + 0.145321i
\(433\) 2983.11 + 2167.36i 0.331084 + 0.240546i 0.740890 0.671626i \(-0.234404\pi\)
−0.409807 + 0.912172i \(0.634404\pi\)
\(434\) 1758.46 + 5411.97i 0.194490 + 0.598578i
\(435\) −123.327 379.563i −0.0135933 0.0418359i
\(436\) 5993.48 + 4354.52i 0.658338 + 0.478311i
\(437\) −3120.29 + 2267.02i −0.341564 + 0.248161i
\(438\) −160.441 + 493.786i −0.0175026 + 0.0538676i
\(439\) −10680.8 −1.16120 −0.580600 0.814189i \(-0.697182\pi\)
−0.580600 + 0.814189i \(0.697182\pi\)
\(440\) 152.774 95.9036i 0.0165528 0.0103910i
\(441\) 4224.38 0.456148
\(442\) −1038.50 + 3196.16i −0.111756 + 0.343950i
\(443\) 9746.78 7081.45i 1.04534 0.759481i 0.0740158 0.997257i \(-0.476418\pi\)
0.971320 + 0.237776i \(0.0764185\pi\)
\(444\) −490.441 356.326i −0.0524219 0.0380867i
\(445\) 283.219 + 871.657i 0.0301704 + 0.0928551i
\(446\) −3217.77 9903.29i −0.341628 1.05142i
\(447\) −2203.57 1600.99i −0.233166 0.169405i
\(448\) 507.331 368.598i 0.0535026 0.0388719i
\(449\) 1940.68 5972.81i 0.203979 0.627782i −0.795775 0.605592i \(-0.792936\pi\)
0.999754 0.0221898i \(-0.00706381\pi\)
\(450\) 4262.77 0.446553
\(451\) 1501.53 + 5969.68i 0.156772 + 0.623285i
\(452\) −1264.78 −0.131616
\(453\) −1562.69 + 4809.45i −0.162078 + 0.498825i
\(454\) −1483.95 + 1078.15i −0.153404 + 0.111454i
\(455\) 68.2113 + 49.5584i 0.00702812 + 0.00510623i
\(456\) 362.119 + 1114.49i 0.0371881 + 0.114453i
\(457\) −2396.54 7375.81i −0.245308 0.754980i −0.995586 0.0938571i \(-0.970080\pi\)
0.750278 0.661123i \(-0.229920\pi\)
\(458\) 8186.04 + 5947.51i 0.835172 + 0.606788i
\(459\) 13546.7 9842.26i 1.37757 1.00087i
\(460\) −63.2786 + 194.752i −0.00641387 + 0.0197399i
\(461\) 5774.66 0.583411 0.291706 0.956508i \(-0.405777\pi\)
0.291706 + 0.956508i \(0.405777\pi\)
\(462\) 1725.93 + 1442.16i 0.173804 + 0.145228i
\(463\) −10005.7 −1.00433 −0.502164 0.864773i \(-0.667462\pi\)
−0.502164 + 0.864773i \(0.667462\pi\)
\(464\) 1014.90 3123.53i 0.101542 0.312514i
\(465\) −456.751 + 331.849i −0.0455512 + 0.0330949i
\(466\) 8001.27 + 5813.26i 0.795390 + 0.577885i
\(467\) 375.196 + 1154.73i 0.0371777 + 0.114421i 0.967923 0.251247i \(-0.0808406\pi\)
−0.930745 + 0.365668i \(0.880841\pi\)
\(468\) −294.344 905.898i −0.0290728 0.0894768i
\(469\) 853.680 + 620.234i 0.0840496 + 0.0610656i
\(470\) 221.979 161.277i 0.0217854 0.0158280i
\(471\) −2876.59 + 8853.23i −0.281415 + 0.866105i
\(472\) 3288.23 0.320663
\(473\) −4976.77 + 12391.6i −0.483789 + 1.20458i
\(474\) −7964.69 −0.771794
\(475\) 1793.07 5518.51i 0.173204 0.533066i
\(476\) −3826.77 + 2780.31i −0.368486 + 0.267721i
\(477\) −7773.86 5648.04i −0.746207 0.542151i
\(478\) 181.132 + 557.466i 0.0173321 + 0.0533429i
\(479\) −2826.91 8700.32i −0.269655 0.829912i −0.990584 0.136904i \(-0.956285\pi\)
0.720929 0.693008i \(-0.243715\pi\)
\(480\) 50.3344 + 36.5701i 0.00478633 + 0.00347747i
\(481\) 542.643 394.254i 0.0514395 0.0373730i
\(482\) −775.462 + 2386.63i −0.0732808 + 0.225535i
\(483\) −2553.30 −0.240536
\(484\) 946.179 + 5239.25i 0.0888598 + 0.492041i
\(485\) 239.175 0.0223925
\(486\) −2364.44 + 7276.98i −0.220685 + 0.679199i
\(487\) 2671.20 1940.74i 0.248550 0.180582i −0.456534 0.889706i \(-0.650909\pi\)
0.705084 + 0.709124i \(0.250909\pi\)
\(488\) −1967.33 1429.35i −0.182494 0.132589i
\(489\) 2362.32 + 7270.46i 0.218461 + 0.672355i
\(490\) −94.3425 290.356i −0.00869788 0.0267693i
\(491\) −3192.31 2319.35i −0.293416 0.213179i 0.431332 0.902193i \(-0.358044\pi\)
−0.724748 + 0.689014i \(0.758044\pi\)
\(492\) −1717.69 + 1247.98i −0.157397 + 0.114356i
\(493\) −7655.31 + 23560.6i −0.699346 + 2.15237i
\(494\) −1296.57 −0.118088
\(495\) 143.724 357.857i 0.0130503 0.0324939i
\(496\) −4646.06 −0.420593
\(497\) −210.276 + 647.163i −0.0189782 + 0.0584089i
\(498\) 4232.81 3075.32i 0.380877 0.276724i
\(499\) −8426.88 6122.48i −0.755990 0.549259i 0.141688 0.989911i \(-0.454747\pi\)
−0.897678 + 0.440653i \(0.854747\pi\)
\(500\) −190.691 586.887i −0.0170559 0.0524928i
\(501\) 1096.39 + 3374.35i 0.0977708 + 0.300907i
\(502\) −8167.19 5933.81i −0.726134 0.527568i
\(503\) −11332.3 + 8233.41i −1.00454 + 0.729840i −0.963057 0.269299i \(-0.913208\pi\)
−0.0414821 + 0.999139i \(0.513208\pi\)
\(504\) 414.292 1275.06i 0.0366152 0.112690i
\(505\) −673.827 −0.0593761
\(506\) −4637.96 3875.40i −0.407476 0.340479i
\(507\) 6301.71 0.552009
\(508\) 1017.74 3132.28i 0.0888875 0.273568i
\(509\) −472.527 + 343.311i −0.0411481 + 0.0298959i −0.608169 0.793807i \(-0.708096\pi\)
0.567021 + 0.823703i \(0.308096\pi\)
\(510\) −379.669 275.845i −0.0329647 0.0239503i
\(511\) −249.859 768.985i −0.0216303 0.0665713i
\(512\) 158.217 + 486.941i 0.0136568 + 0.0420312i
\(513\) 5226.47 + 3797.25i 0.449813 + 0.326808i
\(514\) 8631.09 6270.85i 0.740663 0.538123i
\(515\) −166.972 + 513.887i −0.0142867 + 0.0439700i
\(516\) −4605.93 −0.392955
\(517\) 1975.43 + 7853.80i 0.168045 + 0.668104i
\(518\) 944.079 0.0800781
\(519\) 2592.36 7978.46i 0.219252 0.674789i
\(520\) −55.6919 + 40.4626i −0.00469664 + 0.00341231i
\(521\) 8627.69 + 6268.38i 0.725500 + 0.527107i 0.888137 0.459579i \(-0.152000\pi\)
−0.162636 + 0.986686i \(0.552000\pi\)
\(522\) −2169.77 6677.85i −0.181931 0.559927i
\(523\) −3403.11 10473.7i −0.284527 0.875683i −0.986540 0.163519i \(-0.947715\pi\)
0.702013 0.712164i \(-0.252285\pi\)
\(524\) 1014.45 + 737.043i 0.0845736 + 0.0614463i
\(525\) 3107.69 2257.87i 0.258344 0.187698i
\(526\) 447.519 1377.32i 0.0370965 0.114171i
\(527\) 35044.9 2.89674
\(528\) −1555.29 + 976.331i −0.128192 + 0.0804723i
\(529\) −5305.72 −0.436075
\(530\) −214.597 + 660.461i −0.0175877 + 0.0541294i
\(531\) 5687.35 4132.10i 0.464802 0.337698i
\(532\) −1476.41 1072.67i −0.120320 0.0874178i
\(533\) −725.935 2234.20i −0.0589939 0.181564i
\(534\) −2883.26 8873.77i −0.233653 0.719111i
\(535\) −432.595 314.299i −0.0349583 0.0253987i
\(536\) −696.997 + 506.398i −0.0561673 + 0.0408079i
\(537\) 285.917 879.961i 0.0229762 0.0707134i
\(538\) 8077.92 0.647331
\(539\) 8990.30 + 609.984i 0.718441 + 0.0487456i
\(540\) 342.995 0.0273337
\(541\) −2854.45 + 8785.09i −0.226843 + 0.698152i 0.771256 + 0.636525i \(0.219629\pi\)
−0.998099 + 0.0616270i \(0.980371\pi\)
\(542\) 3918.87 2847.22i 0.310572 0.225643i
\(543\) −3148.86 2287.78i −0.248859 0.180807i
\(544\) −1193.42 3672.96i −0.0940577 0.289480i
\(545\) −353.717 1088.63i −0.0278011 0.0855628i
\(546\) −694.414 504.522i −0.0544289 0.0395449i
\(547\) −2628.40 + 1909.65i −0.205452 + 0.149270i −0.685754 0.727834i \(-0.740527\pi\)
0.480301 + 0.877104i \(0.340527\pi\)
\(548\) −2319.04 + 7137.27i −0.180775 + 0.556367i
\(549\) −5198.89 −0.404159
\(550\) 9071.99 + 615.527i 0.703329 + 0.0477203i
\(551\) −9557.72 −0.738970
\(552\) 644.198 1982.64i 0.0496719 0.152874i
\(553\) 10034.7 7290.66i 0.771646 0.560633i
\(554\) −7099.56 5158.14i −0.544461 0.395574i
\(555\) 28.9444 + 89.0816i 0.00221373 + 0.00681316i
\(556\) −1052.32 3238.71i −0.0802669 0.247036i
\(557\) −673.700 489.472i −0.0512488 0.0372345i 0.561866 0.827228i \(-0.310084\pi\)
−0.613115 + 0.789994i \(0.710084\pi\)
\(558\) −8035.88 + 5838.41i −0.609652 + 0.442938i
\(559\) 1574.81 4846.75i 0.119154 0.366719i
\(560\) −96.8916 −0.00731146
\(561\) 11731.5 7364.40i 0.882892 0.554234i
\(562\) 86.8154 0.00651617
\(563\) −3629.80 + 11171.4i −0.271719 + 0.836266i 0.718350 + 0.695682i \(0.244898\pi\)
−0.990069 + 0.140583i \(0.955102\pi\)
\(564\) −2259.82 + 1641.85i −0.168715 + 0.122579i
\(565\) 158.098 + 114.865i 0.0117721 + 0.00855291i
\(566\) 1096.01 + 3373.17i 0.0813936 + 0.250504i
\(567\) −76.6459 235.892i −0.00567694 0.0174718i
\(568\) −449.470 326.559i −0.0332031 0.0241235i
\(569\) 5406.32 3927.92i 0.398321 0.289397i −0.370536 0.928818i \(-0.620826\pi\)
0.768857 + 0.639421i \(0.220826\pi\)
\(570\) 55.9505 172.198i 0.00411142 0.0126536i
\(571\) −2066.18 −0.151431 −0.0757153 0.997129i \(-0.524124\pi\)
−0.0757153 + 0.997129i \(0.524124\pi\)
\(572\) −495.613 1970.43i −0.0362284 0.144035i
\(573\) −12003.6 −0.875142
\(574\) 1021.76 3144.66i 0.0742988 0.228668i
\(575\) −8351.05 + 6067.39i −0.605674 + 0.440048i
\(576\) 885.560 + 643.397i 0.0640596 + 0.0465420i
\(577\) −5411.80 16655.8i −0.390461 1.20172i −0.932440 0.361325i \(-0.882325\pi\)
0.541979 0.840392i \(-0.317675\pi\)
\(578\) 5965.47 + 18359.8i 0.429292 + 1.32123i
\(579\) −11979.1 8703.30i −0.859815 0.624692i
\(580\) −410.535 + 298.271i −0.0293906 + 0.0213535i
\(581\) −2517.87 + 7749.20i −0.179791 + 0.553341i
\(582\) −2434.88 −0.173417
\(583\) −15728.7 13142.6i −1.11735 0.933640i
\(584\) 660.158 0.0467766
\(585\) −45.4787 + 139.969i −0.00321421 + 0.00989231i
\(586\) 3405.80 2474.46i 0.240089 0.174435i
\(587\) 12737.4 + 9254.24i 0.895618 + 0.650704i 0.937337 0.348425i \(-0.113283\pi\)
−0.0417190 + 0.999129i \(0.513283\pi\)
\(588\) 960.439 + 2955.93i 0.0673602 + 0.207314i
\(589\) 4178.13 + 12859.0i 0.292287 + 0.899566i
\(590\) −411.028 298.629i −0.0286810 0.0208379i
\(591\) 7111.59 5166.88i 0.494978 0.359622i
\(592\) −238.192 + 733.079i −0.0165365 + 0.0508942i
\(593\) −714.295 −0.0494647 −0.0247324 0.999694i \(-0.507873\pi\)
−0.0247324 + 0.999694i \(0.507873\pi\)
\(594\) −3772.95 + 9394.26i −0.260616 + 0.648908i
\(595\) 730.847 0.0503560
\(596\) −1070.20 + 3293.75i −0.0735525 + 0.226371i
\(597\) −10660.6 + 7745.38i −0.730836 + 0.530984i
\(598\) 1866.05 + 1355.76i 0.127606 + 0.0927111i
\(599\) 4457.78 + 13719.6i 0.304073 + 0.935842i 0.980021 + 0.198892i \(0.0637344\pi\)
−0.675948 + 0.736949i \(0.736266\pi\)
\(600\) 969.165 + 2982.78i 0.0659434 + 0.202953i
\(601\) −2337.55 1698.33i −0.158653 0.115268i 0.505626 0.862753i \(-0.331262\pi\)
−0.664279 + 0.747484i \(0.731262\pi\)
\(602\) 5803.02 4216.14i 0.392879 0.285444i
\(603\) −569.175 + 1751.74i −0.0384388 + 0.118303i
\(604\) 6429.91 0.433161
\(605\) 357.545 740.836i 0.0240269 0.0497839i
\(606\) 6859.79 0.459835
\(607\) −2828.28 + 8704.55i −0.189121 + 0.582054i −0.999995 0.00316656i \(-0.998992\pi\)
0.810874 + 0.585221i \(0.198992\pi\)
\(608\) 1205.43 875.796i 0.0804057 0.0584181i
\(609\) −5118.90 3719.10i −0.340604 0.247464i
\(610\) 116.106 + 357.337i 0.00770655 + 0.0237183i
\(611\) −955.050 2939.34i −0.0632360 0.194620i
\(612\) −6679.72 4853.10i −0.441196 0.320547i
\(613\) −1026.19 + 745.573i −0.0676143 + 0.0491247i −0.621079 0.783748i \(-0.713305\pi\)
0.553465 + 0.832873i \(0.313305\pi\)
\(614\) −4740.48 + 14589.7i −0.311580 + 0.958945i
\(615\) 328.050 0.0215094
\(616\) 1065.81 2653.75i 0.0697121 0.173576i
\(617\) 2961.74 0.193250 0.0966250 0.995321i \(-0.469195\pi\)
0.0966250 + 0.995321i \(0.469195\pi\)
\(618\) 1699.83 5231.54i 0.110643 0.340524i
\(619\) −19572.8 + 14220.5i −1.27092 + 0.923374i −0.999239 0.0390142i \(-0.987578\pi\)
−0.271677 + 0.962388i \(0.587578\pi\)
\(620\) 580.758 + 421.945i 0.0376190 + 0.0273318i
\(621\) −3551.41 10930.1i −0.229490 0.706297i
\(622\) 2959.88 + 9109.57i 0.190804 + 0.587236i
\(623\) 11755.4 + 8540.82i 0.755974 + 0.549247i
\(624\) 566.963 411.923i 0.0363729 0.0264264i
\(625\) 4784.17 14724.2i 0.306187 0.942347i
\(626\) −7995.39 −0.510479
\(627\) 4100.85 + 3426.60i 0.261200 + 0.218254i
\(628\) 11836.2 0.752093
\(629\) 1796.67 5529.57i 0.113891 0.350522i
\(630\) −167.585 + 121.757i −0.0105980 + 0.00769989i
\(631\) 2127.22 + 1545.51i 0.134205 + 0.0975055i 0.652862 0.757477i \(-0.273568\pi\)
−0.518658 + 0.854982i \(0.673568\pi\)
\(632\) 3129.44 + 9631.42i 0.196966 + 0.606198i
\(633\) −817.011 2514.50i −0.0513006 0.157887i
\(634\) −10766.2 7822.07i −0.674414 0.489991i
\(635\) −411.684 + 299.106i −0.0257278 + 0.0186924i
\(636\) 2184.67 6723.72i 0.136207 0.419202i
\(637\) −3438.86 −0.213898
\(638\) −3653.43 14525.1i −0.226709 0.901337i
\(639\) −1187.77 −0.0735331
\(640\) 24.4458 75.2365i 0.00150985 0.00464685i
\(641\) 6812.72 4949.73i 0.419791 0.304996i −0.357763 0.933813i \(-0.616460\pi\)
0.777554 + 0.628816i \(0.216460\pi\)
\(642\) 4403.96 + 3199.67i 0.270733 + 0.196699i
\(643\) −4706.41 14484.8i −0.288651 0.888377i −0.985280 0.170946i \(-0.945318\pi\)
0.696629 0.717431i \(-0.254682\pi\)
\(644\) 1003.23 + 3087.61i 0.0613861 + 0.188927i
\(645\) 575.741 + 418.300i 0.0351469 + 0.0255357i
\(646\) −9092.48 + 6606.07i −0.553775 + 0.402341i
\(647\) 6370.80 19607.3i 0.387113 1.19141i −0.547823 0.836594i \(-0.684543\pi\)
0.934936 0.354816i \(-0.115457\pi\)
\(648\) 202.508 0.0122767
\(649\) 12700.4 7972.68i 0.768160 0.482211i
\(650\) −3470.11 −0.209398
\(651\) −2765.96 + 8512.75i −0.166523 + 0.512505i
\(652\) 7863.73 5713.33i 0.472343 0.343177i
\(653\) −4692.68 3409.43i −0.281223 0.204321i 0.438227 0.898864i \(-0.355606\pi\)
−0.719451 + 0.694543i \(0.755606\pi\)
\(654\) 3600.96 + 11082.6i 0.215304 + 0.662637i
\(655\) −59.8699 184.261i −0.00357147 0.0109918i
\(656\) 2184.04 + 1586.80i 0.129988 + 0.0944422i
\(657\) 1141.82 829.578i 0.0678029 0.0492617i
\(658\) 1344.24 4137.15i 0.0796414 0.245111i
\(659\) −14795.0 −0.874552 −0.437276 0.899327i \(-0.644057\pi\)
−0.437276 + 0.899327i \(0.644057\pi\)
\(660\) 283.080 + 19.2067i 0.0166952 + 0.00113276i
\(661\) 12343.7 0.726344 0.363172 0.931722i \(-0.381694\pi\)
0.363172 + 0.931722i \(0.381694\pi\)
\(662\) 6340.20 19513.1i 0.372234 1.14562i
\(663\) −4276.56 + 3107.10i −0.250510 + 0.182006i
\(664\) −5382.01 3910.26i −0.314552 0.228535i
\(665\) 87.1331 + 268.168i 0.00508102 + 0.0156378i
\(666\) 509.234 + 1567.26i 0.0296283 + 0.0911864i
\(667\) 13755.6 + 9994.04i 0.798530 + 0.580166i
\(668\) 3649.69 2651.66i 0.211393 0.153586i
\(669\) 5061.39 15577.4i 0.292503 0.900233i
\(670\) 133.115 0.00767562
\(671\) −11064.2 750.699i −0.636558 0.0431899i
\(672\) 986.390 0.0566232
\(673\) −295.599 + 909.760i −0.0169309 + 0.0521080i −0.959165 0.282847i \(-0.908721\pi\)
0.942234 + 0.334955i \(0.108721\pi\)
\(674\) −6134.88 + 4457.25i −0.350604 + 0.254729i
\(675\) 13988.0 + 10162.9i 0.797625 + 0.579509i
\(676\) −2476.03 7620.44i −0.140876 0.433571i
\(677\) −1280.10 3939.73i −0.0726707 0.223657i 0.908124 0.418702i \(-0.137515\pi\)
−0.980794 + 0.195045i \(0.937515\pi\)
\(678\) −1609.49 1169.36i −0.0911682 0.0662376i
\(679\) 3067.71 2228.82i 0.173384 0.125971i
\(680\) −184.393 + 567.504i −0.0103988 + 0.0320041i
\(681\) −2885.20 −0.162351
\(682\) −17944.9 + 11264.9i −1.00755 + 0.632486i
\(683\) 18776.7 1.05193 0.525967 0.850505i \(-0.323704\pi\)
0.525967 + 0.850505i \(0.323704\pi\)
\(684\) 984.368 3029.57i 0.0550267 0.169355i
\(685\) 938.072 681.549i 0.0523239 0.0380155i
\(686\) −9353.79 6795.93i −0.520597 0.378236i
\(687\) 4918.28 + 15136.9i 0.273136 + 0.840625i
\(688\) 1809.73 + 5569.79i 0.100284 + 0.308643i
\(689\) 6328.32 + 4597.79i 0.349913 + 0.254226i
\(690\) −260.584 + 189.325i −0.0143772 + 0.0104456i
\(691\) −1074.88 + 3308.14i −0.0591757 + 0.182124i −0.976275 0.216535i \(-0.930524\pi\)
0.917099 + 0.398659i \(0.130524\pi\)
\(692\) −10666.7 −0.585961
\(693\) −1491.37 5929.29i −0.0817495 0.325015i
\(694\) 19255.4 1.05321
\(695\) −162.593 + 500.409i −0.00887409 + 0.0273116i
\(696\) 4179.38 3036.50i 0.227614 0.165371i
\(697\) −16474.1 11969.1i −0.895265 0.650448i
\(698\) −6113.09 18814.2i −0.331496 1.02024i
\(699\) 4807.27 + 14795.3i 0.260125 + 0.800583i
\(700\) −3951.41 2870.87i −0.213356 0.155012i
\(701\) −29002.2 + 21071.3i −1.56262 + 1.13531i −0.628802 + 0.777566i \(0.716454\pi\)
−0.933819 + 0.357745i \(0.883546\pi\)
\(702\) 1193.88 3674.39i 0.0641882 0.197551i
\(703\) 2243.15 0.120344
\(704\) 1791.74 + 1497.15i 0.0959215 + 0.0801503i
\(705\) 431.587 0.0230560
\(706\) 2913.69 8967.42i 0.155323 0.478036i
\(707\) −8642.67 + 6279.26i −0.459747 + 0.334026i
\(708\) 4184.41 + 3040.15i 0.222118 + 0.161378i
\(709\) 10717.5 + 32985.1i 0.567707 + 1.74722i 0.659769 + 0.751468i \(0.270654\pi\)
−0.0920627 + 0.995753i \(0.529346\pi\)
\(710\) 26.5264 + 81.6399i 0.00140214 + 0.00431534i
\(711\) 17515.9 + 12726.0i 0.923906 + 0.671257i
\(712\) −9597.87 + 6973.26i −0.505190 + 0.367042i
\(713\) 7432.75 22875.7i 0.390405 1.20154i
\(714\) −7440.27 −0.389979
\(715\) −116.998 + 291.314i −0.00611957 + 0.0152371i
\(716\) −1176.45 −0.0614049
\(717\) −284.911 + 876.865i −0.0148399 + 0.0456724i
\(718\) −6963.79 + 5059.49i −0.361959 + 0.262978i
\(719\) 18179.4 + 13208.1i 0.942946 + 0.685091i 0.949128 0.314890i \(-0.101968\pi\)
−0.00618169 + 0.999981i \(0.501968\pi\)
\(720\) −52.2631 160.849i −0.00270518 0.00832569i
\(721\) 2647.19 + 8147.22i 0.136736 + 0.420830i
\(722\) 7590.12 + 5514.54i 0.391240 + 0.284252i
\(723\) −3193.38 + 2320.13i −0.164264 + 0.119345i
\(724\) −1529.30 + 4706.71i −0.0785030 + 0.241607i
\(725\) −25580.0 −1.31037
\(726\) −3639.93 + 7541.96i −0.186075 + 0.385549i
\(727\) −16477.2 −0.840585 −0.420293 0.907389i \(-0.638073\pi\)
−0.420293 + 0.907389i \(0.638073\pi\)
\(728\) −337.255 + 1037.96i −0.0171697 + 0.0528428i
\(729\) −9183.89 + 6672.49i −0.466590 + 0.338997i
\(730\) −82.5197 59.9541i −0.00418383 0.00303973i
\(731\) −13650.7 42012.5i −0.690683 2.12570i
\(732\) −1182.00 3637.82i −0.0596829 0.183685i
\(733\) 30799.8 + 22377.4i 1.55200 + 1.12759i 0.942206 + 0.335034i \(0.108748\pi\)
0.609794 + 0.792560i \(0.291252\pi\)
\(734\) 15185.7 11033.0i 0.763643 0.554819i
\(735\) 148.396 456.716i 0.00744717 0.0229200i
\(736\) −2650.65 −0.132750
\(737\) −1464.26 + 3645.86i −0.0731841 + 0.182221i
\(738\) 5771.56 0.287878
\(739\) −6023.10 + 18537.2i −0.299815 + 0.922735i 0.681747 + 0.731588i \(0.261221\pi\)
−0.981561 + 0.191147i \(0.938779\pi\)
\(740\) 96.3506 70.0028i 0.00478638 0.00347751i
\(741\) −1649.94 1198.75i −0.0817978 0.0594296i
\(742\) 3402.24 + 10471.0i 0.168329 + 0.518063i
\(743\) −5296.66 16301.5i −0.261529 0.804902i −0.992473 0.122465i \(-0.960920\pi\)
0.730944 0.682437i \(-0.239080\pi\)
\(744\) −5912.31 4295.55i −0.291338 0.211670i
\(745\) 432.907 314.525i 0.0212892 0.0154675i
\(746\) −2806.10 + 8636.30i −0.137719 + 0.423857i
\(747\) −14222.5 −0.696621
\(748\) −13515.0 11292.9i −0.660637 0.552016i
\(749\) −8477.45 −0.413564
\(750\) 299.948 923.144i 0.0146034 0.0449446i
\(751\) −980.769 + 712.570i −0.0476548 + 0.0346233i −0.611358 0.791354i \(-0.709376\pi\)
0.563703 + 0.825978i \(0.309376\pi\)
\(752\) 2873.35 + 2087.61i 0.139336 + 0.101233i
\(753\) −4906.95 15102.1i −0.237476 0.730876i
\(754\) 1766.30 + 5436.12i 0.0853115 + 0.262562i
\(755\) −803.738 583.950i −0.0387431 0.0281485i
\(756\) 4399.34 3196.31i 0.211643 0.153768i
\(757\) 8417.09 25905.1i 0.404127 1.24378i −0.517495 0.855686i \(-0.673135\pi\)
0.921622 0.388089i \(-0.126865\pi\)
\(758\) 831.913 0.0398634
\(759\) −2318.98 9219.67i −0.110901 0.440913i
\(760\) −230.217 −0.0109879
\(761\) 4973.21 15306.0i 0.236897 0.729095i −0.759967 0.649962i \(-0.774785\pi\)
0.996864 0.0791328i \(-0.0252151\pi\)
\(762\) 4191.08 3045.00i 0.199248 0.144762i
\(763\) −14681.6 10666.8i −0.696604 0.506113i
\(764\) 4716.37 + 14515.5i 0.223341 + 0.687373i
\(765\) 394.217 + 1213.28i 0.0186313 + 0.0573413i
\(766\) 1056.22 + 767.387i 0.0498207 + 0.0361969i
\(767\) −4629.79 + 3363.74i −0.217956 + 0.158354i
\(768\) −248.867 + 765.933i −0.0116930 + 0.0359873i
\(769\) 4026.65 0.188823 0.0944113 0.995533i \(-0.469903\pi\)
0.0944113 + 0.995533i \(0.469903\pi\)
\(770\) −374.234 + 234.925i −0.0175149 + 0.0109949i
\(771\) 16781.2 0.783864
\(772\) −5817.86 + 17905.5i −0.271230 + 0.834759i
\(773\) 16588.2 12052.0i 0.771845 0.560778i −0.130675 0.991425i \(-0.541715\pi\)
0.902520 + 0.430647i \(0.141715\pi\)
\(774\) 10129.3 + 7359.39i 0.470402 + 0.341767i
\(775\) 11182.2 + 34415.4i 0.518293 + 1.59514i
\(776\) 956.698 + 2944.41i 0.0442570 + 0.136209i
\(777\) 1201.38 + 872.855i 0.0554689 + 0.0403005i
\(778\) 716.599 520.640i 0.0330223 0.0239921i
\(779\) 2427.73 7471.78i 0.111659 0.343651i
\(780\) −108.280 −0.00497058
\(781\) −2527.81 171.510i −0.115816 0.00785802i
\(782\) 19993.7 0.914287
\(783\) 8800.72 27085.8i 0.401676 1.23623i
\(784\) 3197.13 2322.85i 0.145642 0.105815i
\(785\) −1479.52 1074.93i −0.0672692 0.0488740i
\(786\) 609.496 + 1875.84i 0.0276590 + 0.0851258i
\(787\) −7419.80 22835.8i −0.336070 1.03432i −0.966192 0.257822i \(-0.916995\pi\)
0.630122 0.776496i \(-0.283005\pi\)
\(788\) −9042.37 6569.67i −0.408783 0.296998i
\(789\) 1842.90 1338.94i 0.0831545 0.0604153i
\(790\) 483.525 1488.14i 0.0217760 0.0670196i
\(791\) 3098.20 0.139266
\(792\) 4980.38 + 337.914i 0.223447 + 0.0151607i
\(793\) 4232.16 0.189519
\(794\) 2173.39 6689.01i 0.0971420 0.298972i
\(795\) −883.717 + 642.058i −0.0394242 + 0.0286433i
\(796\) 13554.9 + 9848.23i 0.603570 + 0.438519i
\(797\) −4679.60 14402.3i −0.207980 0.640097i −0.999578 0.0290543i \(-0.990750\pi\)
0.791598 0.611043i \(-0.209250\pi\)
\(798\) −887.045 2730.04i −0.0393497 0.121106i
\(799\) −21673.5 15746.7i −0.959641 0.697220i
\(800\) 3226.18 2343.96i 0.142578 0.103589i
\(801\) −7837.72 + 24122.0i −0.345733 + 1.06406i
\(802\) 8930.39 0.393196
\(803\) 2549.79 1600.63i 0.112055 0.0703424i
\(804\) −1355.15 −0.0594434
\(805\) 155.007 477.062i 0.00678668 0.0208873i
\(806\) 6541.62 4752.76i 0.285879 0.207703i
\(807\) 10279.5 + 7468.49i 0.448396 + 0.325779i
\(808\) −2695.31 8295.31i −0.117352 0.361173i
\(809\) 8952.81 + 27553.9i 0.389078 + 1.19746i 0.933478 + 0.358634i \(0.116757\pi\)
−0.544400 + 0.838825i \(0.683243\pi\)
\(810\) −25.3135 18.3914i −0.00109806 0.000797786i
\(811\) 27000.7 19617.2i 1.16908 0.849385i 0.178180 0.983998i \(-0.442979\pi\)
0.990898 + 0.134612i \(0.0429789\pi\)
\(812\) −2486.09 + 7651.39i −0.107444 + 0.330679i
\(813\) 7619.34 0.328686
\(814\) 857.442 + 3408.97i 0.0369206 + 0.146787i
\(815\) −1501.84 −0.0645486
\(816\) 1877.19 5777.38i 0.0805326 0.247854i
\(817\) 13788.1 10017.6i 0.590434 0.428975i
\(818\) −8877.57 6449.94i −0.379459 0.275693i
\(819\) 721.023 + 2219.08i 0.0307626 + 0.0946776i
\(820\) −128.895 396.700i −0.00548930 0.0168943i
\(821\) −25870.7 18796.1i −1.09975 0.799014i −0.118729 0.992927i \(-0.537882\pi\)
−0.981019 + 0.193913i \(0.937882\pi\)
\(822\) −9549.89 + 6938.40i −0.405220 + 0.294409i
\(823\) 821.815 2529.29i 0.0348076 0.107127i −0.932143 0.362090i \(-0.882063\pi\)
0.966951 + 0.254963i \(0.0820633\pi\)
\(824\) −6994.21 −0.295698
\(825\) 10975.4 + 9170.85i 0.463169 + 0.387016i
\(826\) −8054.82 −0.339301
\(827\) −12358.8 + 38036.6i −0.519660 + 1.59935i 0.254981 + 0.966946i \(0.417931\pi\)
−0.774641 + 0.632402i \(0.782069\pi\)
\(828\) −4584.59 + 3330.90i −0.192422 + 0.139803i
\(829\) −749.222 544.342i −0.0313891 0.0228055i 0.571980 0.820268i \(-0.306175\pi\)
−0.603369 + 0.797462i \(0.706175\pi\)
\(830\) 317.630 + 977.565i 0.0132833 + 0.0408816i
\(831\) −4265.51 13127.9i −0.178061 0.548016i
\(832\) −720.892 523.758i −0.0300390 0.0218246i
\(833\) −24115.7 + 17521.1i −1.00307 + 0.728776i
\(834\) 1655.25 5094.33i 0.0687249 0.211514i
\(835\) −697.029 −0.0288882
\(836\) 2532.38 6305.38i 0.104766 0.260857i
\(837\) −40288.5 −1.66377
\(838\) −3172.85 + 9765.02i −0.130793 + 0.402538i
\(839\) −16532.6 + 12011.6i −0.680295 + 0.494263i −0.873455 0.486904i \(-0.838126\pi\)
0.193161 + 0.981167i \(0.438126\pi\)
\(840\) −123.299 89.5818i −0.00506454 0.00367960i
\(841\) 5483.73 + 16877.2i 0.224844 + 0.691999i
\(842\) −3720.20 11449.6i −0.152264 0.468621i
\(843\) 110.476 + 80.2658i 0.00451365 + 0.00327936i
\(844\) −2719.69 + 1975.97i −0.110919 + 0.0805872i
\(845\) −382.568 + 1177.42i −0.0155748 + 0.0479344i
\(846\) 7593.15 0.308579
\(847\) −2317.75 12834.0i −0.0940247 0.520640i
\(848\) −8989.15 −0.364019
\(849\) −1723.97 + 5305.83i −0.0696896 + 0.214482i
\(850\) −24334.9 + 17680.3i −0.981975 + 0.713446i
\(851\) −3228.38 2345.56i −0.130044 0.0944825i
\(852\) −270.048 831.121i −0.0108588 0.0334199i
\(853\) 12290.0 + 37824.8i 0.493320 + 1.51828i 0.819558 + 0.572996i \(0.194219\pi\)
−0.326238 + 0.945288i \(0.605781\pi\)
\(854\) 4819.16 + 3501.33i 0.193101 + 0.140296i
\(855\) −398.185 + 289.298i −0.0159271 + 0.0115717i
\(856\) 2138.87 6582.76i 0.0854030 0.262843i
\(857\) 3490.30 0.139121 0.0695604 0.997578i \(-0.477840\pi\)
0.0695604 + 0.997578i \(0.477840\pi\)
\(858\) 1191.08 2965.68i 0.0473927 0.118003i
\(859\) 2730.16 0.108442 0.0542210 0.998529i \(-0.482732\pi\)
0.0542210 + 0.998529i \(0.482732\pi\)
\(860\) 279.619 860.579i 0.0110871 0.0341227i
\(861\) 4207.65 3057.03i 0.166546 0.121003i
\(862\) −21329.2 15496.6i −0.842780 0.612315i
\(863\) −6176.75 19010.1i −0.243637 0.749838i −0.995858 0.0909265i \(-0.971017\pi\)
0.752220 0.658912i \(-0.228983\pi\)
\(864\) 1371.98 + 4222.53i 0.0540229 + 0.166265i
\(865\) 1333.33 + 968.722i 0.0524100 + 0.0380781i
\(866\) 5966.23 4334.72i 0.234112 0.170092i
\(867\) −9383.38 + 28879.1i −0.367562 + 1.13124i
\(868\) 11381.0 0.445040
\(869\) 35439.6 + 29612.7i 1.38344 + 1.15597i
\(870\) −798.191 −0.0311048
\(871\) 463.338 1426.01i 0.0180248 0.0554747i
\(872\) 11987.0 8709.03i 0.465516 0.338217i
\(873\) 5354.77 + 3890.47i 0.207596 + 0.150828i
\(874\) 2383.69 + 7336.23i 0.0922533 + 0.283927i
\(875\) 467.116 + 1437.64i 0.0180473 + 0.0555439i
\(876\) 840.079 + 610.353i 0.0324014 + 0.0235410i
\(877\) 5058.17 3674.97i 0.194757 0.141499i −0.486133 0.873885i \(-0.661593\pi\)
0.680890 + 0.732385i \(0.261593\pi\)
\(878\) −6601.10 + 20316.1i −0.253732 + 0.780906i
\(879\) 6621.80 0.254093
\(880\) −88.0000 349.865i −0.00337100 0.0134022i
\(881\) −22948.7 −0.877595 −0.438797 0.898586i \(-0.644595\pi\)
−0.438797 + 0.898586i \(0.644595\pi\)
\(882\) 2610.81 8035.25i 0.0996719 0.306759i
\(883\) 23437.3 17028.2i 0.893238 0.648975i −0.0434821 0.999054i \(-0.513845\pi\)
0.936720 + 0.350079i \(0.113845\pi\)
\(884\) 5437.64 + 3950.67i 0.206886 + 0.150312i
\(885\) −246.951 760.037i −0.00937985 0.0288682i
\(886\) −7445.88 22916.1i −0.282336 0.868939i
\(887\) −6849.58 4976.51i −0.259286 0.188382i 0.450546 0.892753i \(-0.351229\pi\)
−0.709832 + 0.704371i \(0.751229\pi\)
\(888\) −980.882 + 712.653i −0.0370678 + 0.0269314i
\(889\) −2493.05 + 7672.81i −0.0940541 + 0.289469i
\(890\) 1833.03 0.0690374
\(891\) 782.168 491.004i 0.0294092 0.0184616i
\(892\) −20825.9 −0.781728
\(893\) 3193.95 9829.97i 0.119688 0.368362i
\(894\) −4407.14 + 3201.97i −0.164873 + 0.119788i
\(895\) 147.056 + 106.842i 0.00549222 + 0.00399033i
\(896\) −387.567 1192.81i −0.0144505 0.0444742i
\(897\) 1121.15 + 3450.53i 0.0417324 + 0.128439i
\(898\) −10161.5 7382.80i −0.377612 0.274351i
\(899\) 48221.7 35035.1i 1.78897 1.29976i
\(900\) 2634.53 8108.26i 0.0975753 0.300306i
\(901\) 67804.5 2.50710
\(902\) 12283.0 + 833.392i 0.453414 + 0.0307638i
\(903\) 11282.6 0.415795
\(904\) −781.678 + 2405.76i −0.0287591 + 0.0885114i
\(905\) 618.617 449.451i 0.0227221 0.0165086i
\(906\) 8182.33 + 5944.81i 0.300044 + 0.217995i
\(907\) −5947.88 18305.7i −0.217746 0.670155i −0.998947 0.0458748i \(-0.985392\pi\)
0.781201 0.624280i \(-0.214608\pi\)
\(908\) 1133.64 + 3488.98i 0.0414329 + 0.127517i
\(909\) −15086.0 10960.6i −0.550463 0.399935i
\(910\) 136.423 99.1168i 0.00496963 0.00361065i
\(911\) −14273.8 + 43930.1i −0.519112 + 1.59766i 0.256562 + 0.966528i \(0.417410\pi\)
−0.775674 + 0.631134i \(0.782590\pi\)
\(912\) 2343.68 0.0850955
\(913\) −30268.3 2053.68i −1.09719 0.0744435i
\(914\) −15510.8 −0.561324
\(915\) −182.629 + 562.074i −0.00659838 + 0.0203077i
\(916\) 16372.1 11895.0i 0.590556 0.429064i
\(917\) −2485.00 1805.45i −0.0894894 0.0650178i
\(918\) −10348.8 31850.2i −0.372070 1.14511i
\(919\) −15399.0 47393.1i −0.552736 1.70115i −0.701848 0.712327i \(-0.747641\pi\)
0.149111 0.988820i \(-0.452359\pi\)
\(920\) 331.331 + 240.726i 0.0118736 + 0.00862664i
\(921\) −19521.5 + 14183.2i −0.698430 + 0.507439i
\(922\) 3568.93 10984.1i 0.127480 0.392343i
\(923\) 966.910 0.0344813
\(924\) 3809.83 2391.61i 0.135643 0.0851497i
\(925\) 6003.51 0.213399
\(926\) −6183.85 + 19031.9i −0.219454 + 0.675409i
\(927\) −12097.3 + 8789.18i −0.428615 + 0.311407i
\(928\) −5314.07 3860.90i −0.187977 0.136574i
\(929\) 9988.82 + 30742.4i 0.352769 + 1.08571i 0.957292 + 0.289124i \(0.0933638\pi\)
−0.604523 + 0.796588i \(0.706636\pi\)
\(930\) 348.927 + 1073.89i 0.0123030 + 0.0378646i
\(931\) −9304.11 6759.83i −0.327529 0.237964i
\(932\) 16002.5 11626.5i 0.562426 0.408626i
\(933\) −4655.74 + 14328.9i −0.163368 + 0.502794i
\(934\) 2428.32 0.0850717
\(935\) 663.778 + 2639.01i 0.0232170 + 0.0923046i
\(936\) −1905.03 −0.0665257
\(937\) 3858.70 11875.9i 0.134534 0.414053i −0.860983 0.508633i \(-0.830151\pi\)
0.995517 + 0.0945803i \(0.0301509\pi\)
\(938\) 1707.36 1240.47i 0.0594320 0.0431799i
\(939\) −10174.5 7392.19i −0.353601 0.256906i
\(940\) −169.577 521.903i −0.00588402 0.0181092i
\(941\) −9013.72 27741.4i −0.312263 0.961045i −0.976867 0.213850i \(-0.931400\pi\)
0.664604 0.747196i \(-0.268600\pi\)
\(942\) 15062.0 + 10943.2i 0.520963 + 0.378502i
\(943\) −11306.9 + 8214.93i −0.390459 + 0.283685i
\(944\) 2032.24 6254.58i 0.0700674 0.215645i
\(945\) −840.199 −0.0289224
\(946\) 20494.5 + 17124.8i 0.704370 + 0.588558i
\(947\) 41085.7 1.40983 0.704913 0.709294i \(-0.250986\pi\)
0.704913 + 0.709294i \(0.250986\pi\)
\(948\) −4922.45 + 15149.7i −0.168643 + 0.519030i
\(949\) −929.497 + 675.319i −0.0317942 + 0.0230999i
\(950\) −9388.65 6821.25i −0.320640 0.232959i
\(951\) −6468.45 19907.8i −0.220561 0.678818i
\(952\) 2923.39 + 8997.27i 0.0995248 + 0.306306i
\(953\) 14095.2 + 10240.7i 0.479105 + 0.348090i 0.800979 0.598692i \(-0.204313\pi\)
−0.321874 + 0.946782i \(0.604313\pi\)
\(954\) −15547.7 + 11296.1i −0.527648 + 0.383359i
\(955\) 728.720 2242.77i 0.0246920 0.0759940i
\(956\) 1172.31 0.0396602
\(957\) 8780.10 21861.6i 0.296573 0.738437i
\(958\) −18296.1 −0.617037
\(959\) 5680.71 17483.4i 0.191282 0.588706i
\(960\) 100.669 73.1401i 0.00338445 0.00245894i
\(961\) −44114.8 32051.3i −1.48081 1.07587i
\(962\) −414.543 1275.83i −0.0138933 0.0427593i
\(963\) −4572.72 14073.4i −0.153015 0.470933i
\(964\) 4060.37 + 2950.03i 0.135660 + 0.0985624i
\(965\) 2353.37 1709.82i 0.0785054 0.0570375i
\(966\) −1578.02 + 4856.66i −0.0525591 + 0.161760i
\(967\) 39352.0 1.30866 0.654330 0.756209i \(-0.272951\pi\)
0.654330 + 0.756209i \(0.272951\pi\)
\(968\) 10550.4 + 1438.29i 0.350313 + 0.0477567i
\(969\) −17678.3 −0.586076
\(970\) 147.818 454.937i 0.00489294 0.0150589i
\(971\) −12674.3 + 9208.40i −0.418885 + 0.304338i −0.777189 0.629267i \(-0.783355\pi\)
0.358304 + 0.933605i \(0.383355\pi\)
\(972\) 12380.3 + 8994.85i 0.408539 + 0.296821i
\(973\) 2577.76 + 7933.53i 0.0849324 + 0.261395i
\(974\) −2040.62 6280.37i −0.0671310 0.206608i
\(975\) −4415.86 3208.31i −0.145047 0.105383i
\(976\) −3934.66 + 2858.70i −0.129042 + 0.0937549i
\(977\) −15281.8 + 47032.4i −0.500417 + 1.54012i 0.307925 + 0.951411i \(0.400365\pi\)
−0.808342 + 0.588714i \(0.799635\pi\)
\(978\) 15289.2 0.499893
\(979\) −20163.3 + 50204.6i −0.658246 + 1.63897i
\(980\) −610.597 −0.0199029
\(981\) 9788.68 30126.5i 0.318582 0.980493i
\(982\) −6384.63 + 4638.70i −0.207476 + 0.150740i
\(983\) 40813.4 + 29652.7i 1.32426 + 0.962130i 0.999869 + 0.0162067i \(0.00515899\pi\)
0.324390 + 0.945923i \(0.394841\pi\)
\(984\) 1312.20 + 4038.54i 0.0425116 + 0.130837i
\(985\) 533.653 + 1642.42i 0.0172626 + 0.0531287i
\(986\) 40083.7 + 29122.5i 1.29465 + 0.940618i
\(987\) 5535.64 4021.88i 0.178522 0.129704i
\(988\) −801.326 + 2466.23i −0.0258032 + 0.0794141i
\(989\) −30319.0 −0.974811
\(990\) −591.859 494.546i −0.0190005 0.0158765i
\(991\) −37174.1 −1.19160 −0.595799 0.803134i \(-0.703164\pi\)
−0.595799 + 0.803134i \(0.703164\pi\)
\(992\) −2871.42 + 8837.33i −0.0919030 + 0.282848i
\(993\) 26109.1 18969.4i 0.834389 0.606219i
\(994\) 1101.02 + 799.938i 0.0351330 + 0.0255256i
\(995\) −799.971 2462.06i −0.0254882 0.0784447i
\(996\) −3233.58 9951.94i −0.102871 0.316606i
\(997\) −31032.6 22546.5i −0.985770 0.716204i −0.0267790 0.999641i \(-0.508525\pi\)
−0.958991 + 0.283438i \(0.908525\pi\)
\(998\) −16853.8 + 12245.0i −0.534565 + 0.388385i
\(999\) −2065.49 + 6356.92i −0.0654146 + 0.201325i
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 22.4.c.a.9.1 yes 4
3.2 odd 2 198.4.f.b.163.1 4
4.3 odd 2 176.4.m.a.97.1 4
11.2 odd 10 242.4.c.m.3.1 4
11.3 even 5 242.4.c.f.81.1 4
11.4 even 5 242.4.a.k.1.2 2
11.5 even 5 inner 22.4.c.a.5.1 4
11.6 odd 10 242.4.c.j.27.1 4
11.7 odd 10 242.4.a.h.1.2 2
11.8 odd 10 242.4.c.m.81.1 4
11.9 even 5 242.4.c.f.3.1 4
11.10 odd 2 242.4.c.j.9.1 4
33.5 odd 10 198.4.f.b.181.1 4
33.26 odd 10 2178.4.a.z.1.1 2
33.29 even 10 2178.4.a.bi.1.1 2
44.7 even 10 1936.4.a.bc.1.1 2
44.15 odd 10 1936.4.a.bb.1.1 2
44.27 odd 10 176.4.m.a.49.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.4.c.a.5.1 4 11.5 even 5 inner
22.4.c.a.9.1 yes 4 1.1 even 1 trivial
176.4.m.a.49.1 4 44.27 odd 10
176.4.m.a.97.1 4 4.3 odd 2
198.4.f.b.163.1 4 3.2 odd 2
198.4.f.b.181.1 4 33.5 odd 10
242.4.a.h.1.2 2 11.7 odd 10
242.4.a.k.1.2 2 11.4 even 5
242.4.c.f.3.1 4 11.9 even 5
242.4.c.f.81.1 4 11.3 even 5
242.4.c.j.9.1 4 11.10 odd 2
242.4.c.j.27.1 4 11.6 odd 10
242.4.c.m.3.1 4 11.2 odd 10
242.4.c.m.81.1 4 11.8 odd 10
1936.4.a.bb.1.1 2 44.15 odd 10
1936.4.a.bc.1.1 2 44.7 even 10
2178.4.a.z.1.1 2 33.26 odd 10
2178.4.a.bi.1.1 2 33.29 even 10