Properties

Label 22.4.c.a.5.1
Level $22$
Weight $4$
Character 22.5
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 5.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 22.5
Dual form 22.4.c.a.9.1

$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\)

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 0.805108 0.593128i \(-0.202107\pi\)
−0.315306 + 0.948990i \(0.602107\pi\)
\(4\) −3.23607 + 2.35114i −0.404508 + 0.293893i
\(5\) 0.190983 0.587785i 0.0170820 0.0525731i −0.942152 0.335185i \(-0.891201\pi\)
0.959234 + 0.282612i \(0.0912010\pi\)
\(6\) −1.94427 + 5.98385i −0.132291 + 0.407150i
\(7\) 7.92705 5.75934i 0.428021 0.310975i −0.352836 0.935685i \(-0.614783\pi\)
0.780857 + 0.624710i \(0.214783\pi\)
\(8\) −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 0.986404 0.164338i \(-0.0525488\pi\)
−0.894613 + 0.446841i \(0.852549\pi\)
\(14\) 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 0.217825 + 0.975988i \(0.430104\pi\)
−0.749895 + 0.661557i \(0.769896\pi\)
\(18\) 27.6738 20.1062i 0.362376 0.263282i
\(19\) 37.6697 + 27.3686i 0.454843 + 0.330463i 0.791505 0.611163i \(-0.209298\pi\)
−0.336662 + 0.941626i \(0.609298\pi\)
\(20\) 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 −0.974707 0.223486i \(-0.928256\pi\)
−0.0886536 + 0.996063i \(0.528256\pi\)
\(30\) 3.14590 + 2.28563i 0.0191453 + 0.0139099i
\(31\) −89.7320 276.167i −0.519882 1.60003i −0.774220 0.632917i \(-0.781857\pi\)
0.254338 0.967115i \(-0.418143\pi\)
\(32\) 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 −0.497823 0.867279i \(-0.665867\pi\)
0.670995 + 0.741461i \(0.265867\pi\)
\(38\) −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 0.816587 0.577223i \(-0.195864\pi\)
−0.296633 + 0.954992i \(0.595864\pi\)
\(42\) 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 0.830485 0.557040i \(-0.188063\pi\)
−0.273143 + 0.961973i \(0.588063\pi\)
\(48\) 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 −0.876960 0.480564i \(-0.840432\pi\)
0.427007 0.904248i \(-0.359568\pi\)
\(54\) 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 −0.890749 0.454495i \(-0.849820\pi\)
0.156994 + 0.987600i \(0.449820\pi\)
\(60\) −2.40325 + 7.39645i −0.00517098 + 0.0159146i
\(61\) 93.9317 289.092i 0.197159 0.606794i −0.802785 0.596268i \(-0.796649\pi\)
0.999945 0.0105259i \(-0.00335056\pi\)
\(62\) 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 −0.931518 0.363696i \(-0.881515\pi\)
0.967389 + 0.253296i \(0.0815145\pi\)
\(72\) −42.2817 + 130.130i −0.0692077 + 0.212999i
\(73\) −66.7599 + 48.5039i −0.107036 + 0.0777664i −0.640016 0.768362i \(-0.721072\pi\)
0.532980 + 0.846128i \(0.321072\pi\)
\(74\) 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 0.690323 + 0.723501i \(0.257468\pi\)
−0.133220 + 0.991087i \(0.542532\pi\)
\(80\) −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 −0.624463 0.781054i \(-0.714682\pi\)
0.964294 0.264836i \(-0.0853178\pi\)
\(84\) −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 0.993933 0.109983i \(-0.0350797\pi\)
−0.868756 + 0.495241i \(0.835080\pi\)
\(98\) −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 −0.968218 0.250107i \(-0.919534\pi\)
0.636296 0.771445i \(-0.280466\pi\)
\(102\) −614.317 446.327i −0.596338 0.433265i
\(103\) 707.305 513.887i 0.676629 0.491600i −0.195609 0.980682i \(-0.562668\pi\)
0.872238 + 0.489082i \(0.162668\pi\)
\(104\) 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 0.224829 0.974398i \(-0.427818\pi\)
−0.857232 + 0.514931i \(0.827818\pi\)
\(108\) 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 0.689151 0.724617i \(-0.257983\pi\)
−0.476193 + 0.879341i \(0.657983\pi\)
\(114\) −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 −0.821974 0.569525i \(-0.807127\pi\)
0.999749 + 0.0223893i \(0.00712732\pi\)
\(128\) −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 0.590564 + 0.806990i \(0.298905\pi\)
−0.952114 + 0.305744i \(0.901095\pi\)
\(138\) 161.050 495.659i 0.0993438 0.305749i
\(139\) 688.754 500.409i 0.420283 0.305353i −0.357469 0.933925i \(-0.616360\pi\)
0.777752 + 0.628572i \(0.216360\pi\)
\(140\) 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 −0.997276 0.0737645i \(-0.976499\pi\)
0.850171 + 0.526507i \(0.176499\pi\)
\(150\) −634.327 + 460.866i −0.345284 + 0.250863i
\(151\) −1300.48 944.851i −0.700869 0.509211i 0.179346 0.983786i \(-0.442602\pi\)
−0.880215 + 0.474575i \(0.842602\pi\)
\(152\) −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 −0.221072 0.975257i \(-0.570956\pi\)
−0.995840 + 0.0911192i \(0.970956\pi\)
\(158\) −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 −0.952547 0.304393i \(-0.901547\pi\)
0.591709 0.806152i \(-0.298453\pi\)
\(164\) −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 0.837270 0.546789i \(-0.184150\pi\)
−0.998761 + 0.0497734i \(0.984150\pi\)
\(168\) −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 0.950358 0.311159i \(-0.100717\pi\)
−0.00225265 + 0.999997i \(0.500717\pi\)
\(174\) −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 0.636354 0.771397i \(-0.280442\pi\)
−0.536998 + 0.843583i \(0.680442\pi\)
\(180\) 34.2067 24.8526i 0.0141645 0.0102911i
\(181\) −382.326 + 1176.68i −0.157006 + 0.483215i −0.998359 0.0572719i \(-0.981760\pi\)
0.841353 + 0.540487i \(0.181760\pi\)
\(182\) −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 −0.990940 0.134303i \(-0.957120\pi\)
−0.178488 + 0.983942i \(0.557120\pi\)
\(192\) −62.2167 + 191.483i −0.0233860 + 0.0719746i
\(193\) −1454.46 + 4476.38i −0.542459 + 1.66952i 0.184497 + 0.982833i \(0.440934\pi\)
−0.726956 + 0.686684i \(0.759066\pi\)
\(194\) −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 0.984443 0.175706i \(-0.0562208\pi\)
−0.899708 + 0.436492i \(0.856221\pi\)
\(212\) 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 0.998986 0.0450300i \(-0.0143383\pi\)
0.265877 + 0.964007i \(0.414338\pi\)
\(224\) 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 −0.690951 0.722902i \(-0.742808\pi\)
0.474005 + 0.880522i \(0.342808\pi\)
\(228\) −474.020 344.396i −0.137687 0.100036i
\(229\) −1563.39 4811.63i −0.451144 1.38848i −0.875603 0.483032i \(-0.839536\pi\)
0.424458 0.905447i \(-0.360464\pi\)
\(230\) −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 −0.898466 0.439044i \(-0.855317\pi\)
0.468811 0.883299i \(-0.344683\pi\)
\(234\) 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 0.555237 0.831692i \(-0.312628\pi\)
−0.619409 + 0.785069i \(0.712628\pi\)
\(240\) −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 0.931087 + 0.364798i \(0.118862\pi\)
−0.538842 + 0.842407i \(0.681138\pi\)
\(252\) 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 0.0757290 0.997128i \(-0.475872\pi\)
0.971727 + 0.236107i \(0.0758716\pi\)
\(258\) −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 −0.704128 0.710073i \(-0.748662\pi\)
0.987022 0.160585i \(-0.0513380\pi\)
\(270\) 52.9957 163.104i 0.0119452 0.0367637i
\(271\) 1959.43 1423.61i 0.439215 0.319108i −0.346108 0.938195i \(-0.612497\pi\)
0.785323 + 0.619087i \(0.212497\pi\)
\(272\) 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 0.983520 + 0.180801i \(0.0578692\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(278\) 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 −0.949623 0.313396i \(-0.898533\pi\)
0.952470 + 0.304632i \(0.0985333\pi\)
\(282\) −1129.91 + 820.927i −0.238600 + 0.173353i
\(283\) −1434.70 1042.37i −0.301356 0.218948i 0.426822 0.904335i \(-0.359633\pi\)
−0.728179 + 0.685387i \(0.759633\pi\)
\(284\) 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 −0.404929 0.914348i \(-0.632704\pi\)
0.744467 + 0.667660i \(0.232704\pi\)
\(294\) −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 0.175579 0.984465i \(-0.443820\pi\)
−0.882025 + 0.471203i \(0.843820\pi\)
\(312\) 283.481 205.961i 0.0514390 0.0373726i
\(313\) −1235.36 + 3802.04i −0.223088 + 0.686593i 0.775392 + 0.631480i \(0.217552\pi\)
−0.998480 + 0.0551136i \(0.982448\pi\)
\(314\) 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 0.950414 + 0.310986i \(0.100659\pi\)
−0.586108 + 0.810233i \(0.699341\pi\)
\(318\) 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 −0.807421 0.589975i \(-0.799138\pi\)
0.311593 + 0.950216i \(0.399138\pi\)
\(338\) 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 −0.404568 0.914508i \(-0.632578\pi\)
0.864837 0.502053i \(-0.167422\pi\)
\(348\) 2089.69 1518.25i 0.321894 0.233870i
\(349\) 8002.14 + 5813.90i 1.22735 + 0.891721i 0.996689 0.0813131i \(-0.0259114\pi\)
0.230660 + 0.973034i \(0.425911\pi\)
\(350\) 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 −0.813539 0.581511i \(-0.802462\pi\)
0.301652 + 0.953418i \(0.402462\pi\)
\(360\) 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 0.102279 0.994756i \(-0.467387\pi\)
0.977675 + 0.210123i \(0.0673865\pi\)
\(368\) −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 −0.941968 0.335702i \(-0.891026\pi\)
0.959389 + 0.282086i \(0.0910264\pi\)
\(380\) −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 0.936698 0.350138i \(-0.113865\pi\)
−0.963611 + 0.267310i \(0.913865\pi\)
\(384\) −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 −0.564190 0.825645i \(-0.690811\pi\)
0.610891 + 0.791715i \(0.290811\pi\)
\(390\) −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 −0.827642 0.561257i \(-0.810318\pi\)
0.999475 + 0.0324095i \(0.0103181\pi\)
\(402\) −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 0.999714 + 0.0239000i \(0.00760832\pi\)
−0.794738 + 0.606953i \(0.792392\pi\)
\(410\) 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 0.832830 0.553528i \(-0.186719\pi\)
−0.269078 + 0.963118i \(0.586719\pi\)
\(422\) −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 0.870837 + 0.491572i \(0.163578\pi\)
−0.415583 + 0.909555i \(0.636422\pi\)
\(432\) −1795.95 1304.83i −0.200017 0.145321i
\(433\) 2983.11 2167.36i 0.331084 0.240546i −0.409807 0.912172i \(-0.634404\pi\)
0.740890 + 0.671626i \(0.234404\pi\)
\(434\) 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 0.971320 0.237776i \(-0.0764185\pi\)
0.0740158 + 0.997257i \(0.476418\pi\)
\(444\) −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 0.999754 + 0.0221898i \(0.00706381\pi\)
−0.795775 + 0.605592i \(0.792936\pi\)
\(450\) 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 0.750278 + 0.661123i \(0.229920\pi\)
−0.995586 + 0.0938571i \(0.970080\pi\)
\(458\) 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 −0.930745 0.365668i \(-0.880841\pi\)
0.967923 + 0.251247i \(0.0808406\pi\)
\(468\) −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 0.720929 + 0.693008i \(0.243715\pi\)
−0.990584 + 0.136904i \(0.956285\pi\)
\(480\) 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 0.705084 0.709124i \(-0.250909\pi\)
−0.456534 + 0.889706i \(0.650909\pi\)
\(488\) −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 −0.724748 0.689014i \(-0.758044\pi\)
0.431332 + 0.902193i \(0.358044\pi\)
\(492\) −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 −0.897678 0.440653i \(-0.854747\pi\)
0.141688 + 0.989911i \(0.454747\pi\)
\(500\) −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 −0.0414821 0.999139i \(-0.513208\pi\)
−0.963057 + 0.269299i \(0.913208\pi\)
\(504\) 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 0.567021 0.823703i \(-0.308096\pi\)
−0.608169 + 0.793807i \(0.708096\pi\)
\(510\) −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 −0.162636 0.986686i \(-0.552000\pi\)
0.888137 + 0.459579i \(0.152000\pi\)
\(522\) −2169.77 + 6677.85i −0.181931 + 0.559927i
\(523\) −3403.11 + 10473.7i −0.284527 + 0.875683i 0.702013 + 0.712164i \(0.252285\pi\)
−0.986540 + 0.163519i \(0.947715\pi\)
\(524\) 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 −0.998099 0.0616270i \(-0.980371\pi\)
0.771256 0.636525i \(-0.219629\pi\)
\(542\) 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 0.480301 0.877104i \(-0.340527\pi\)
−0.685754 + 0.727834i \(0.740527\pi\)
\(548\) −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 −0.613115 0.789994i \(-0.710084\pi\)
0.561866 + 0.827228i \(0.310084\pi\)
\(558\) −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 −0.990069 0.140583i \(-0.955102\pi\)
0.718350 0.695682i \(-0.244898\pi\)
\(564\) −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 0.768857 0.639421i \(-0.220826\pi\)
−0.370536 + 0.928818i \(0.620826\pi\)
\(570\) 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 0.541979 + 0.840392i \(0.317675\pi\)
−0.932440 + 0.361325i \(0.882325\pi\)
\(578\) 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 −0.0417190 0.999129i \(-0.513283\pi\)
0.937337 + 0.348425i \(0.113283\pi\)
\(588\) 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 −0.675948 0.736949i \(-0.736266\pi\)
0.980021 0.198892i \(-0.0637344\pi\)
\(600\) 969.165 2982.78i 0.0659434 0.202953i
\(601\) −2337.55 + 1698.33i −0.158653 + 0.115268i −0.664279 0.747484i \(-0.731262\pi\)
0.505626 + 0.862753i \(0.331262\pi\)
\(602\) 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 0.810874 0.585221i \(-0.198992\pi\)
−0.999995 + 0.00316656i \(0.998992\pi\)
\(608\) 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 0.553465 0.832873i \(-0.313305\pi\)
−0.621079 + 0.783748i \(0.713305\pi\)
\(614\) −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 −0.271677 0.962388i \(-0.587578\pi\)
−0.999239 + 0.0390142i \(0.987578\pi\)
\(620\) 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 −0.518658 0.854982i \(-0.673568\pi\)
0.652862 + 0.757477i \(0.273568\pi\)
\(632\) 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 0.777554 0.628816i \(-0.216460\pi\)
−0.357763 + 0.933813i \(0.616460\pi\)
\(642\) 4403.96 3199.67i 0.270733 0.196699i
\(643\) −4706.41 + 14484.8i −0.288651 + 0.888377i 0.696629 + 0.717431i \(0.254682\pi\)
−0.985280 + 0.170946i \(0.945318\pi\)
\(644\) 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 0.934936 + 0.354816i \(0.115457\pi\)
−0.547823 + 0.836594i \(0.684543\pi\)
\(648\) 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 −0.719451 0.694543i \(-0.755606\pi\)
0.438227 + 0.898864i \(0.355606\pi\)
\(654\) 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 0.942234 0.334955i \(-0.108721\pi\)
−0.959165 + 0.282847i \(0.908721\pi\)
\(674\) −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 −0.980794 0.195045i \(-0.937515\pi\)
0.908124 + 0.418702i \(0.137515\pi\)
\(678\) −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 0.917099 0.398659i \(-0.130524\pi\)
−0.976275 + 0.216535i \(0.930524\pi\)
\(692\) −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 −0.933819 0.357745i \(-0.883546\pi\)
−0.628802 0.777566i \(-0.716454\pi\)
\(702\) 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 −0.0920627 0.995753i \(-0.529346\pi\)
0.659769 0.751468i \(-0.270654\pi\)
\(710\) 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 −0.00618169 0.999981i \(-0.501968\pi\)
0.949128 + 0.314890i \(0.101968\pi\)
\(720\) −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 0.609794 0.792560i \(-0.291252\pi\)
0.942206 0.335034i \(-0.108748\pi\)
\(734\) 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 −0.981561 0.191147i \(-0.938779\pi\)
0.681747 0.731588i \(-0.261221\pi\)
\(740\) 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 0.730944 + 0.682437i \(0.239080\pi\)
−0.992473 + 0.122465i \(0.960920\pi\)
\(744\) −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 0.563703 0.825978i \(-0.309376\pi\)
−0.611358 + 0.791354i \(0.709376\pi\)
\(752\) 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 0.921622 + 0.388089i \(0.126865\pi\)
−0.517495 + 0.855686i \(0.673135\pi\)
\(758\) 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 0.996864 + 0.0791328i \(0.0252151\pi\)
−0.759967 + 0.649962i \(0.774785\pi\)
\(762\) 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 0.902520 0.430647i \(-0.141715\pi\)
−0.130675 + 0.991425i \(0.541715\pi\)
\(774\) 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 0.630122 + 0.776496i \(0.283005\pi\)
−0.966192 + 0.257822i \(0.916995\pi\)
\(788\) −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 0.791598 + 0.611043i \(0.209250\pi\)
−0.999578 + 0.0290543i \(0.990750\pi\)
\(798\) −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 −0.544400 0.838825i \(-0.683243\pi\)
0.933478 0.358634i \(-0.116757\pi\)
\(810\) −25.3135 + 18.3914i −0.00109806 + 0.000797786i
\(811\) 27000.7 + 19617.2i 1.16908 + 0.849385i 0.990898 0.134612i \(-0.0429789\pi\)
0.178180 + 0.983998i \(0.442979\pi\)
\(812\) −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 −0.981019 0.193913i \(-0.937882\pi\)
−0.118729 + 0.992927i \(0.537882\pi\)
\(822\) −9549.89 6938.40i −0.405220 0.294409i
\(823\) 821.815 + 2529.29i 0.0348076 + 0.107127i 0.966951 0.254963i \(-0.0820633\pi\)
−0.932143 + 0.362090i \(0.882063\pi\)
\(824\) −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 −0.774641 0.632402i \(-0.782069\pi\)
0.254981 0.966946i \(-0.417931\pi\)
\(828\) −4584.59 3330.90i −0.192422 0.139803i
\(829\) −749.222 + 544.342i −0.0313891 + 0.0228055i −0.603369 0.797462i \(-0.706175\pi\)
0.571980 + 0.820268i \(0.306175\pi\)
\(830\) 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 0.193161 0.981167i \(-0.438126\pi\)
−0.873455 + 0.486904i \(0.838126\pi\)
\(840\) −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 −0.326238 0.945288i \(-0.605781\pi\)
0.819558 0.572996i \(-0.194219\pi\)
\(854\) 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 0.752220 + 0.658912i \(0.228983\pi\)
−0.995858 + 0.0909265i \(0.971017\pi\)
\(864\) 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 0.680890 0.732385i \(-0.261593\pi\)
−0.486133 + 0.873885i \(0.661593\pi\)
\(878\) −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 0.936720 0.350079i \(-0.113845\pi\)
−0.0434821 + 0.999054i \(0.513845\pi\)
\(884\) 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 −0.709832 0.704371i \(-0.751229\pi\)
0.450546 + 0.892753i \(0.351229\pi\)
\(888\) −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 0.781201 + 0.624280i \(0.214608\pi\)
−0.998947 + 0.0458748i \(0.985392\pi\)
\(908\) 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 −0.775674 0.631134i \(-0.782590\pi\)
0.256562 0.966528i \(-0.417410\pi\)
\(912\) 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 0.149111 + 0.988820i \(0.452359\pi\)
−0.701848 + 0.712327i \(0.747641\pi\)
\(920\) 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 −0.604523 0.796588i \(-0.706636\pi\)
0.957292 0.289124i \(-0.0933638\pi\)
\(930\) 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 0.995517 0.0945803i \(-0.0301509\pi\)
−0.860983 + 0.508633i \(0.830151\pi\)
\(938\) 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 0.664604 + 0.747196i \(0.268600\pi\)
−0.976867 + 0.213850i \(0.931400\pi\)
\(942\) 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 −0.321874 0.946782i \(-0.604313\pi\)
0.800979 + 0.598692i \(0.204313\pi\)
\(954\) −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 0.358304 0.933605i \(-0.383355\pi\)
−0.777189 + 0.629267i \(0.783355\pi\)
\(972\) 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 −0.808342 0.588714i \(-0.799635\pi\)
0.307925 0.951411i \(-0.400365\pi\)
\(978\) 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 0.324390 0.945923i \(-0.394841\pi\)
0.999869 0.0162067i \(-0.00515899\pi\)
\(984\) 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 −0.958991 0.283438i \(-0.908525\pi\)
−0.0267790 + 0.999641i \(0.508525\pi\)
\(998\) −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.5.1 4
3.2 odd 2 198.4.f.b.181.1 4
4.3 odd 2 176.4.m.a.49.1 4
11.2 odd 10 242.4.c.j.9.1 4
11.3 even 5 242.4.a.k.1.2 2
11.4 even 5 242.4.c.f.3.1 4
11.5 even 5 242.4.c.f.81.1 4
11.6 odd 10 242.4.c.m.81.1 4
11.7 odd 10 242.4.c.m.3.1 4
11.8 odd 10 242.4.a.h.1.2 2
11.9 even 5 inner 22.4.c.a.9.1 yes 4
11.10 odd 2 242.4.c.j.27.1 4
33.8 even 10 2178.4.a.bi.1.1 2
33.14 odd 10 2178.4.a.z.1.1 2
33.20 odd 10 198.4.f.b.163.1 4
44.3 odd 10 1936.4.a.bb.1.1 2
44.19 even 10 1936.4.a.bc.1.1 2
44.31 odd 10 176.4.m.a.97.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.4.c.a.5.1 4 1.1 even 1 trivial
22.4.c.a.9.1 yes 4 11.9 even 5 inner
176.4.m.a.49.1 4 4.3 odd 2
176.4.m.a.97.1 4 44.31 odd 10
198.4.f.b.163.1 4 33.20 odd 10
198.4.f.b.181.1 4 3.2 odd 2
242.4.a.h.1.2 2 11.8 odd 10
242.4.a.k.1.2 2 11.3 even 5
242.4.c.f.3.1 4 11.4 even 5
242.4.c.f.81.1 4 11.5 even 5
242.4.c.j.9.1 4 11.2 odd 10
242.4.c.j.27.1 4 11.10 odd 2
242.4.c.m.3.1 4 11.7 odd 10
242.4.c.m.81.1 4 11.6 odd 10
1936.4.a.bb.1.1 2 44.3 odd 10
1936.4.a.bc.1.1 2 44.19 even 10
2178.4.a.z.1.1 2 33.14 odd 10
2178.4.a.bi.1.1 2 33.8 even 10