Properties

Label 43.4.g.a.10.4
Level $43$
Weight $4$
Character 43.10
Analytic conductor $2.537$
Analytic rank $0$
Dimension $120$
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] = [43,4,Mod(9,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.9");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), 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: \(2.53708213025\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(10\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 10.4
Character \(\chi\) \(=\) 43.10
Dual form 43.4.g.a.13.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.582989 - 2.55424i) q^{2} +(-4.15286 - 3.85329i) q^{3} +(1.02347 - 0.492879i) q^{4} +(-13.6446 + 2.05660i) q^{5} +(-7.42117 + 12.8538i) q^{6} +(9.34797 + 16.1912i) q^{7} +(-14.9236 - 18.7136i) q^{8} +(0.380687 + 5.07991i) q^{9} +O(q^{10})\) \(q+(-0.582989 - 2.55424i) q^{2} +(-4.15286 - 3.85329i) q^{3} +(1.02347 - 0.492879i) q^{4} +(-13.6446 + 2.05660i) q^{5} +(-7.42117 + 12.8538i) q^{6} +(9.34797 + 16.1912i) q^{7} +(-14.9236 - 18.7136i) q^{8} +(0.380687 + 5.07991i) q^{9} +(13.2077 + 33.6527i) q^{10} +(-41.3369 - 19.9068i) q^{11} +(-6.14956 - 1.89689i) q^{12} +(13.3353 - 33.9779i) q^{13} +(35.9064 - 33.3162i) q^{14} +(64.5889 + 44.0360i) q^{15} +(-33.4326 + 41.9232i) q^{16} +(62.1043 + 9.36072i) q^{17} +(12.7534 - 3.93390i) q^{18} +(11.9608 - 159.606i) q^{19} +(-12.9513 + 8.83002i) q^{20} +(23.5685 - 103.260i) q^{21} +(-26.7478 + 117.190i) q^{22} +(30.1976 - 20.5884i) q^{23} +(-10.1333 + 135.220i) q^{24} +(62.4994 - 19.2785i) q^{25} +(-94.5620 - 14.2529i) q^{26} +(-77.3753 + 97.0255i) q^{27} +(17.5477 + 11.9638i) q^{28} +(-0.0346418 + 0.0321429i) q^{29} +(74.8239 - 190.648i) q^{30} +(142.348 + 43.9085i) q^{31} +(-45.9489 - 22.1278i) q^{32} +(94.9596 + 241.953i) q^{33} +(-12.2966 - 164.087i) q^{34} +(-160.848 - 201.697i) q^{35} +(2.89341 + 5.01153i) q^{36} +(-157.839 + 273.385i) q^{37} +(-414.644 + 62.4976i) q^{38} +(-186.307 + 89.7205i) q^{39} +(242.113 + 224.648i) q^{40} +(-3.55430 - 15.5724i) q^{41} -277.492 q^{42} +(16.1534 - 281.507i) q^{43} -52.1189 q^{44} +(-15.6417 - 68.5306i) q^{45} +(-70.1926 - 65.1292i) q^{46} +(359.524 - 173.138i) q^{47} +(300.384 - 45.2756i) q^{48} +(-3.26909 + 5.66222i) q^{49} +(-85.6784 - 148.399i) q^{50} +(-221.841 - 278.180i) q^{51} +(-3.09862 - 41.3482i) q^{52} +(140.095 + 356.955i) q^{53} +(292.936 + 141.070i) q^{54} +(604.966 + 186.607i) q^{55} +(163.490 - 416.565i) q^{56} +(-664.679 + 616.732i) q^{57} +(0.102296 + 0.0697445i) q^{58} +(326.190 - 409.029i) q^{59} +(87.8095 + 13.2352i) q^{60} +(315.527 - 97.3271i) q^{61} +(29.1657 - 389.189i) q^{62} +(-78.6910 + 53.6506i) q^{63} +(-125.188 + 548.484i) q^{64} +(-112.077 + 491.040i) q^{65} +(562.647 - 383.606i) q^{66} +(-13.4238 + 179.128i) q^{67} +(68.1759 - 21.0295i) q^{68} +(-204.740 - 30.8595i) q^{69} +(-421.411 + 528.432i) q^{70} +(-343.160 - 233.962i) q^{71} +(89.3823 - 82.9346i) q^{72} +(-312.093 + 795.200i) q^{73} +(790.310 + 243.778i) q^{74} +(-333.837 - 160.768i) q^{75} +(-66.4248 - 169.248i) q^{76} +(-64.1018 - 855.380i) q^{77} +(337.783 + 423.566i) q^{78} +(-527.961 - 914.456i) q^{79} +(369.957 - 640.784i) q^{80} +(831.203 - 125.284i) q^{81} +(-37.7036 + 18.1571i) q^{82} +(43.9650 + 40.7936i) q^{83} +(-26.7731 - 117.301i) q^{84} -866.641 q^{85} +(-728.454 + 122.856i) q^{86} +0.267719 q^{87} +(244.367 + 1070.64i) q^{88} +(-1006.40 - 933.801i) q^{89} +(-165.925 + 79.9051i) q^{90} +(674.799 - 101.710i) q^{91} +(20.7589 - 35.9555i) q^{92} +(-421.959 - 730.855i) q^{93} +(-651.835 - 817.375i) q^{94} +(165.044 + 2202.36i) q^{95} +(105.555 + 268.949i) q^{96} +(-712.425 - 343.086i) q^{97} +(16.3685 + 5.04902i) q^{98} +(85.3883 - 217.566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 12 q^{2} - 9 q^{3} - 92 q^{4} + 5 q^{5} - 22 q^{6} - 54 q^{7} + 2 q^{8} + 201 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 12 q^{2} - 9 q^{3} - 92 q^{4} + 5 q^{5} - 22 q^{6} - 54 q^{7} + 2 q^{8} + 201 q^{9} - 41 q^{10} - 68 q^{11} + 114 q^{12} - 167 q^{13} + 254 q^{14} - 163 q^{15} - 344 q^{16} + 68 q^{17} - 72 q^{18} - 407 q^{19} + 621 q^{20} + 193 q^{21} - 520 q^{22} - 219 q^{23} + 1072 q^{24} - 87 q^{25} - 133 q^{26} + 180 q^{27} + 1228 q^{28} - 17 q^{29} - 1796 q^{30} - 953 q^{31} - 2730 q^{32} + 473 q^{33} - 1043 q^{34} - 241 q^{35} - 175 q^{36} - 228 q^{37} + 1512 q^{38} + 1250 q^{39} + 2673 q^{40} - 236 q^{41} + 5286 q^{42} + 1789 q^{43} - 2756 q^{44} + 856 q^{45} + 4331 q^{46} + 962 q^{47} + 5243 q^{48} - 1264 q^{49} - 3273 q^{50} - 4803 q^{51} - 3538 q^{52} - 1375 q^{53} - 2646 q^{54} - 1460 q^{55} - 3305 q^{56} - 719 q^{57} + 142 q^{58} + 1202 q^{59} + 4043 q^{60} + 837 q^{61} - 3959 q^{62} + 3279 q^{63} + 5718 q^{64} + 54 q^{65} - 3457 q^{66} + 1384 q^{67} - 747 q^{68} - 4715 q^{69} - 2553 q^{70} - 1619 q^{71} - 20137 q^{72} - 3630 q^{73} - 5006 q^{74} - 1186 q^{75} + 1092 q^{76} + 3515 q^{77} + 2980 q^{78} + 4422 q^{79} - 1610 q^{80} - 4089 q^{81} + 5292 q^{82} + 10398 q^{83} + 17399 q^{84} + 8666 q^{85} + 1858 q^{86} + 2754 q^{87} + 7290 q^{88} + 11478 q^{89} + 29113 q^{90} + 11920 q^{91} + 3286 q^{92} - 4 q^{93} - 14736 q^{94} - 1741 q^{95} - 6200 q^{96} + 2236 q^{97} - 5254 q^{98} - 7417 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.582989 2.55424i −0.206118 0.903061i −0.967122 0.254314i \(-0.918150\pi\)
0.761004 0.648747i \(-0.224707\pi\)
\(3\) −4.15286 3.85329i −0.799219 0.741567i 0.170614 0.985338i \(-0.445425\pi\)
−0.969833 + 0.243771i \(0.921615\pi\)
\(4\) 1.02347 0.492879i 0.127934 0.0616099i
\(5\) −13.6446 + 2.05660i −1.22041 + 0.183947i −0.727485 0.686123i \(-0.759311\pi\)
−0.492927 + 0.870071i \(0.664073\pi\)
\(6\) −7.42117 + 12.8538i −0.504947 + 0.874594i
\(7\) 9.34797 + 16.1912i 0.504743 + 0.874240i 0.999985 + 0.00548536i \(0.00174605\pi\)
−0.495242 + 0.868755i \(0.664921\pi\)
\(8\) −14.9236 18.7136i −0.659536 0.827032i
\(9\) 0.380687 + 5.07991i 0.0140995 + 0.188145i
\(10\) 13.2077 + 33.6527i 0.417664 + 1.06419i
\(11\) −41.3369 19.9068i −1.13305 0.545647i −0.229148 0.973391i \(-0.573594\pi\)
−0.903900 + 0.427744i \(0.859308\pi\)
\(12\) −6.14956 1.89689i −0.147935 0.0456320i
\(13\) 13.3353 33.9779i 0.284504 0.724905i −0.715159 0.698962i \(-0.753646\pi\)
0.999663 0.0259433i \(-0.00825895\pi\)
\(14\) 35.9064 33.3162i 0.685456 0.636010i
\(15\) 64.5889 + 44.0360i 1.11179 + 0.758003i
\(16\) −33.4326 + 41.9232i −0.522385 + 0.655050i
\(17\) 62.1043 + 9.36072i 0.886030 + 0.133547i 0.576262 0.817265i \(-0.304511\pi\)
0.309768 + 0.950812i \(0.399749\pi\)
\(18\) 12.7534 3.93390i 0.167000 0.0515127i
\(19\) 11.9608 159.606i 0.144421 1.92716i −0.184556 0.982822i \(-0.559085\pi\)
0.328977 0.944338i \(-0.393296\pi\)
\(20\) −12.9513 + 8.83002i −0.144800 + 0.0987227i
\(21\) 23.5685 103.260i 0.244908 1.07301i
\(22\) −26.7478 + 117.190i −0.259211 + 1.13568i
\(23\) 30.1976 20.5884i 0.273767 0.186651i −0.418652 0.908147i \(-0.637497\pi\)
0.692419 + 0.721496i \(0.256545\pi\)
\(24\) −10.1333 + 135.220i −0.0861858 + 1.15007i
\(25\) 62.4994 19.2785i 0.499995 0.154228i
\(26\) −94.5620 14.2529i −0.713275 0.107509i
\(27\) −77.3753 + 97.0255i −0.551514 + 0.691577i
\(28\) 17.5477 + 11.9638i 0.118436 + 0.0807482i
\(29\) −0.0346418 + 0.0321429i −0.000221821 + 0.000205820i −0.680284 0.732949i \(-0.738143\pi\)
0.680062 + 0.733155i \(0.261953\pi\)
\(30\) 74.8239 190.648i 0.455364 1.16025i
\(31\) 142.348 + 43.9085i 0.824724 + 0.254394i 0.678260 0.734822i \(-0.262734\pi\)
0.146464 + 0.989216i \(0.453211\pi\)
\(32\) −45.9489 22.1278i −0.253834 0.122240i
\(33\) 94.9596 + 241.953i 0.500920 + 1.27632i
\(34\) −12.2966 164.087i −0.0620249 0.827665i
\(35\) −160.848 201.697i −0.776808 0.974087i
\(36\) 2.89341 + 5.01153i 0.0133954 + 0.0232015i
\(37\) −157.839 + 273.385i −0.701312 + 1.21471i 0.266694 + 0.963781i \(0.414069\pi\)
−0.968006 + 0.250927i \(0.919265\pi\)
\(38\) −414.644 + 62.4976i −1.77011 + 0.266801i
\(39\) −186.307 + 89.7205i −0.764947 + 0.368379i
\(40\) 242.113 + 224.648i 0.957036 + 0.888000i
\(41\) −3.55430 15.5724i −0.0135388 0.0593172i 0.967707 0.252077i \(-0.0811135\pi\)
−0.981246 + 0.192759i \(0.938256\pi\)
\(42\) −277.492 −1.01947
\(43\) 16.1534 281.507i 0.0572876 0.998358i
\(44\) −52.1189 −0.178573
\(45\) −15.6417 68.5306i −0.0518160 0.227021i
\(46\) −70.1926 65.1292i −0.224986 0.208756i
\(47\) 359.524 173.138i 1.11579 0.537335i 0.217199 0.976127i \(-0.430308\pi\)
0.898589 + 0.438792i \(0.144594\pi\)
\(48\) 300.384 45.2756i 0.903264 0.136145i
\(49\) −3.26909 + 5.66222i −0.00953086 + 0.0165079i
\(50\) −85.6784 148.399i −0.242335 0.419737i
\(51\) −221.841 278.180i −0.609097 0.763784i
\(52\) −3.09862 41.3482i −0.00826348 0.110269i
\(53\) 140.095 + 356.955i 0.363085 + 0.925125i 0.989355 + 0.145519i \(0.0464852\pi\)
−0.626271 + 0.779606i \(0.715420\pi\)
\(54\) 292.936 + 141.070i 0.738213 + 0.355505i
\(55\) 604.966 + 186.607i 1.48316 + 0.457493i
\(56\) 163.490 416.565i 0.390129 0.994032i
\(57\) −664.679 + 616.732i −1.54454 + 1.43313i
\(58\) 0.102296 + 0.0697445i 0.000231589 + 0.000157895i
\(59\) 326.190 409.029i 0.719767 0.902560i −0.278557 0.960420i \(-0.589856\pi\)
0.998325 + 0.0578600i \(0.0184277\pi\)
\(60\) 87.8095 + 13.2352i 0.188936 + 0.0284775i
\(61\) 315.527 97.3271i 0.662280 0.204286i 0.0546487 0.998506i \(-0.482596\pi\)
0.607631 + 0.794219i \(0.292120\pi\)
\(62\) 29.1657 389.189i 0.0597427 0.797211i
\(63\) −78.6910 + 53.6506i −0.157367 + 0.107291i
\(64\) −125.188 + 548.484i −0.244508 + 1.07126i
\(65\) −112.077 + 491.040i −0.213868 + 0.937016i
\(66\) 562.647 383.606i 1.04935 0.715434i
\(67\) −13.4238 + 179.128i −0.0244773 + 0.326626i 0.971501 + 0.237034i \(0.0761754\pi\)
−0.995979 + 0.0895921i \(0.971444\pi\)
\(68\) 68.1759 21.0295i 0.121581 0.0375029i
\(69\) −204.740 30.8595i −0.357214 0.0538413i
\(70\) −421.411 + 528.432i −0.719546 + 0.902282i
\(71\) −343.160 233.962i −0.573600 0.391074i 0.241494 0.970402i \(-0.422362\pi\)
−0.815094 + 0.579328i \(0.803315\pi\)
\(72\) 89.3823 82.9346i 0.146303 0.135749i
\(73\) −312.093 + 795.200i −0.500380 + 1.27495i 0.428157 + 0.903705i \(0.359163\pi\)
−0.928536 + 0.371242i \(0.878932\pi\)
\(74\) 790.310 + 243.778i 1.24151 + 0.382955i
\(75\) −333.837 160.768i −0.513976 0.247518i
\(76\) −66.4248 169.248i −0.100256 0.255448i
\(77\) −64.1018 855.380i −0.0948712 1.26597i
\(78\) 337.783 + 423.566i 0.490338 + 0.614864i
\(79\) −527.961 914.456i −0.751902 1.30233i −0.946900 0.321529i \(-0.895803\pi\)
0.194998 0.980804i \(-0.437530\pi\)
\(80\) 369.957 640.784i 0.517030 0.895522i
\(81\) 831.203 125.284i 1.14020 0.171857i
\(82\) −37.7036 + 18.1571i −0.0507764 + 0.0244526i
\(83\) 43.9650 + 40.7936i 0.0581420 + 0.0539479i 0.708709 0.705501i \(-0.249278\pi\)
−0.650567 + 0.759449i \(0.725469\pi\)
\(84\) −26.7731 117.301i −0.0347760 0.152364i
\(85\) −866.641 −1.10589
\(86\) −728.454 + 122.856i −0.913386 + 0.154045i
\(87\) 0.267719 0.000329913
\(88\) 244.367 + 1070.64i 0.296018 + 1.29694i
\(89\) −1006.40 933.801i −1.19863 1.11216i −0.990987 0.133960i \(-0.957231\pi\)
−0.207642 0.978205i \(-0.566579\pi\)
\(90\) −165.925 + 79.9051i −0.194333 + 0.0935860i
\(91\) 674.799 101.710i 0.777343 0.117166i
\(92\) 20.7589 35.9555i 0.0235246 0.0407458i
\(93\) −421.959 730.855i −0.470485 0.814904i
\(94\) −651.835 817.375i −0.715230 0.896870i
\(95\) 165.044 + 2202.36i 0.178244 + 2.37849i
\(96\) 105.555 + 268.949i 0.112220 + 0.285932i
\(97\) −712.425 343.086i −0.745730 0.359125i 0.0221191 0.999755i \(-0.492959\pi\)
−0.767849 + 0.640631i \(0.778673\pi\)
\(98\) 16.3685 + 5.04902i 0.0168722 + 0.00520437i
\(99\) 85.3883 217.566i 0.0866854 0.220871i
\(100\) 54.4646 50.5357i 0.0544646 0.0505357i
\(101\) 479.849 + 327.155i 0.472740 + 0.322309i 0.776147 0.630553i \(-0.217172\pi\)
−0.303407 + 0.952861i \(0.598124\pi\)
\(102\) −581.208 + 728.812i −0.564198 + 0.707482i
\(103\) 398.973 + 60.1355i 0.381670 + 0.0575275i 0.337075 0.941478i \(-0.390562\pi\)
0.0445945 + 0.999005i \(0.485800\pi\)
\(104\) −834.859 + 257.520i −0.787161 + 0.242807i
\(105\) −109.218 + 1457.42i −0.101511 + 1.35456i
\(106\) 830.077 565.937i 0.760606 0.518572i
\(107\) −255.322 + 1118.64i −0.230682 + 1.01068i 0.718395 + 0.695636i \(0.244877\pi\)
−0.949076 + 0.315046i \(0.897980\pi\)
\(108\) −31.3698 + 137.440i −0.0279496 + 0.122455i
\(109\) −158.547 + 108.096i −0.139322 + 0.0949880i −0.630975 0.775803i \(-0.717345\pi\)
0.491653 + 0.870791i \(0.336393\pi\)
\(110\) 123.952 1654.02i 0.107439 1.43368i
\(111\) 1708.92 527.131i 1.46129 0.450748i
\(112\) −991.313 149.416i −0.836342 0.126058i
\(113\) 384.321 481.924i 0.319946 0.401200i −0.595686 0.803218i \(-0.703120\pi\)
0.915632 + 0.402018i \(0.131691\pi\)
\(114\) 1962.78 + 1338.20i 1.61256 + 1.09942i
\(115\) −369.693 + 343.025i −0.299774 + 0.278150i
\(116\) −0.0196124 + 0.0499716i −1.56980e−5 + 3.99978e-5i
\(117\) 177.681 + 54.8074i 0.140399 + 0.0433072i
\(118\) −1234.92 594.708i −0.963423 0.463960i
\(119\) 428.988 + 1093.04i 0.330465 + 0.842010i
\(120\) −139.827 1865.87i −0.106370 1.41941i
\(121\) 482.591 + 605.150i 0.362578 + 0.454658i
\(122\) −432.546 749.191i −0.320991 0.555972i
\(123\) −45.2446 + 78.3659i −0.0331672 + 0.0574473i
\(124\) 167.331 25.2211i 0.121184 0.0182655i
\(125\) 740.897 356.797i 0.530143 0.255303i
\(126\) 182.913 + 169.718i 0.129327 + 0.119998i
\(127\) −402.538 1763.63i −0.281255 1.23226i −0.896186 0.443679i \(-0.853673\pi\)
0.614930 0.788581i \(-0.289184\pi\)
\(128\) 1065.95 0.736074
\(129\) −1151.81 + 1106.82i −0.786134 + 0.755424i
\(130\) 1319.58 0.890265
\(131\) −576.714 2526.75i −0.384639 1.68521i −0.682726 0.730675i \(-0.739206\pi\)
0.298087 0.954539i \(-0.403652\pi\)
\(132\) 216.443 + 200.829i 0.142719 + 0.132424i
\(133\) 2696.01 1298.33i 1.75770 0.846462i
\(134\) 465.362 70.1421i 0.300009 0.0452191i
\(135\) 856.214 1483.01i 0.545860 0.945458i
\(136\) −751.647 1301.89i −0.473921 0.820855i
\(137\) 1614.92 + 2025.04i 1.00709 + 1.26285i 0.964589 + 0.263758i \(0.0849621\pi\)
0.0425040 + 0.999096i \(0.486466\pi\)
\(138\) 40.5383 + 540.946i 0.0250061 + 0.333684i
\(139\) 341.325 + 869.682i 0.208279 + 0.530687i 0.996395 0.0848408i \(-0.0270382\pi\)
−0.788115 + 0.615528i \(0.788943\pi\)
\(140\) −264.036 127.153i −0.159394 0.0767601i
\(141\) −2160.21 666.336i −1.29023 0.397983i
\(142\) −397.538 + 1012.91i −0.234934 + 0.598603i
\(143\) −1227.63 + 1139.07i −0.717899 + 0.666113i
\(144\) −225.694 153.875i −0.130610 0.0890482i
\(145\) 0.406569 0.509821i 0.000232853 0.000291989i
\(146\) 2213.08 + 333.568i 1.25449 + 0.189084i
\(147\) 35.3943 10.9177i 0.0198590 0.00612568i
\(148\) −26.7983 + 357.598i −0.0148838 + 0.198611i
\(149\) −1833.40 + 1249.99i −1.00804 + 0.687269i −0.950388 0.311068i \(-0.899313\pi\)
−0.0576507 + 0.998337i \(0.518361\pi\)
\(150\) −216.016 + 946.427i −0.117584 + 0.515170i
\(151\) −101.627 + 445.256i −0.0547700 + 0.239963i −0.994902 0.100848i \(-0.967844\pi\)
0.940132 + 0.340811i \(0.110702\pi\)
\(152\) −3165.29 + 2158.06i −1.68907 + 1.15159i
\(153\) −23.9093 + 319.048i −0.0126337 + 0.168585i
\(154\) −2147.48 + 662.409i −1.12369 + 0.346613i
\(155\) −2032.59 306.363i −1.05330 0.158759i
\(156\) −146.459 + 183.653i −0.0751672 + 0.0942566i
\(157\) 2298.66 + 1567.20i 1.16849 + 0.796664i 0.982569 0.185900i \(-0.0595201\pi\)
0.185923 + 0.982564i \(0.440472\pi\)
\(158\) −2027.95 + 1881.66i −1.02111 + 0.947447i
\(159\) 793.660 2022.21i 0.395858 1.00863i
\(160\) 672.464 + 207.428i 0.332268 + 0.102491i
\(161\) 615.636 + 296.475i 0.301360 + 0.145127i
\(162\) −804.587 2050.05i −0.390212 0.994244i
\(163\) −267.627 3571.24i −0.128602 1.71608i −0.572419 0.819961i \(-0.693995\pi\)
0.443817 0.896118i \(-0.353624\pi\)
\(164\) −11.3131 14.1861i −0.00538660 0.00675458i
\(165\) −1793.29 3106.07i −0.846105 1.46550i
\(166\) 78.5655 136.079i 0.0367341 0.0636254i
\(167\) 3309.70 498.857i 1.53361 0.231154i 0.672699 0.739916i \(-0.265135\pi\)
0.860907 + 0.508763i \(0.169897\pi\)
\(168\) −2284.10 + 1099.96i −1.04894 + 0.505143i
\(169\) 633.851 + 588.127i 0.288507 + 0.267696i
\(170\) 505.242 + 2213.61i 0.227943 + 0.998683i
\(171\) 815.336 0.364622
\(172\) −122.216 296.077i −0.0541797 0.131254i
\(173\) 1818.98 0.799390 0.399695 0.916648i \(-0.369116\pi\)
0.399695 + 0.916648i \(0.369116\pi\)
\(174\) −0.156077 0.683818i −6.80009e−5 0.000297932i
\(175\) 896.384 + 831.723i 0.387201 + 0.359270i
\(176\) 2216.56 1067.44i 0.949314 0.457165i
\(177\) −2930.73 + 441.736i −1.24456 + 0.187587i
\(178\) −1798.43 + 3114.98i −0.757294 + 1.31167i
\(179\) 655.446 + 1135.27i 0.273689 + 0.474044i 0.969804 0.243887i \(-0.0784227\pi\)
−0.696114 + 0.717931i \(0.745089\pi\)
\(180\) −49.7861 62.4298i −0.0206158 0.0258514i
\(181\) 63.1899 + 843.210i 0.0259495 + 0.346273i 0.995033 + 0.0995412i \(0.0317375\pi\)
−0.969084 + 0.246731i \(0.920643\pi\)
\(182\) −653.192 1664.31i −0.266032 0.677838i
\(183\) −1685.37 811.631i −0.680799 0.327855i
\(184\) −835.940 257.853i −0.334926 0.103311i
\(185\) 1591.41 4054.84i 0.632447 1.61145i
\(186\) −1620.78 + 1503.87i −0.638933 + 0.592843i
\(187\) −2380.85 1623.24i −0.931045 0.634775i
\(188\) 282.628 354.404i 0.109642 0.137487i
\(189\) −2294.26 345.804i −0.882977 0.133087i
\(190\) 5529.13 1705.51i 2.11119 0.651215i
\(191\) −235.496 + 3142.47i −0.0892140 + 1.19048i 0.755459 + 0.655196i \(0.227414\pi\)
−0.844673 + 0.535282i \(0.820205\pi\)
\(192\) 2633.36 1795.39i 0.989825 0.674851i
\(193\) 493.012 2160.03i 0.183874 0.805606i −0.795888 0.605444i \(-0.792996\pi\)
0.979763 0.200163i \(-0.0641471\pi\)
\(194\) −460.988 + 2019.72i −0.170603 + 0.747462i
\(195\) 2357.56 1607.36i 0.865788 0.590284i
\(196\) −0.555033 + 7.40641i −0.000202272 + 0.00269913i
\(197\) −1507.82 + 465.102i −0.545320 + 0.168209i −0.555161 0.831743i \(-0.687343\pi\)
0.00984164 + 0.999952i \(0.496867\pi\)
\(198\) −605.496 91.2639i −0.217327 0.0327568i
\(199\) −1604.60 + 2012.10i −0.571592 + 0.716753i −0.980653 0.195754i \(-0.937285\pi\)
0.409062 + 0.912507i \(0.365856\pi\)
\(200\) −1293.49 881.884i −0.457316 0.311793i
\(201\) 745.980 692.169i 0.261778 0.242895i
\(202\) 555.887 1416.38i 0.193624 0.493346i
\(203\) −0.844261 0.260420i −0.000291899 9.00389e-5i
\(204\) −364.158 175.369i −0.124981 0.0601878i
\(205\) 80.5233 + 205.170i 0.0274341 + 0.0699009i
\(206\) −78.9963 1054.13i −0.0267181 0.356528i
\(207\) 116.083 + 145.564i 0.0389774 + 0.0488762i
\(208\) 978.626 + 1695.03i 0.326228 + 0.565044i
\(209\) −3671.66 + 6359.49i −1.21519 + 2.10476i
\(210\) 3786.27 570.688i 1.24418 0.187530i
\(211\) 4053.30 1951.96i 1.32247 0.636866i 0.366521 0.930410i \(-0.380549\pi\)
0.955946 + 0.293544i \(0.0948346\pi\)
\(212\) 319.319 + 296.285i 0.103448 + 0.0959856i
\(213\) 523.570 + 2293.91i 0.168425 + 0.737916i
\(214\) 3006.13 0.960255
\(215\) 358.539 + 3874.27i 0.113731 + 1.22895i
\(216\) 2970.42 0.935700
\(217\) 619.734 + 2715.23i 0.193872 + 0.849411i
\(218\) 368.534 + 341.949i 0.114497 + 0.106237i
\(219\) 4360.22 2099.77i 1.34537 0.647897i
\(220\) 711.142 107.187i 0.217933 0.0328481i
\(221\) 1146.24 1985.34i 0.348888 0.604293i
\(222\) −2342.70 4057.67i −0.708251 1.22673i
\(223\) −4072.64 5106.93i −1.22298 1.53357i −0.764143 0.645047i \(-0.776838\pi\)
−0.458837 0.888520i \(-0.651734\pi\)
\(224\) −71.2539 950.817i −0.0212538 0.283612i
\(225\) 121.726 + 310.152i 0.0360669 + 0.0918970i
\(226\) −1455.01 700.694i −0.428254 0.206236i
\(227\) −474.075 146.233i −0.138614 0.0427569i 0.224672 0.974435i \(-0.427869\pi\)
−0.363286 + 0.931678i \(0.618345\pi\)
\(228\) −376.308 + 958.816i −0.109305 + 0.278505i
\(229\) 880.866 817.324i 0.254189 0.235853i −0.542777 0.839877i \(-0.682627\pi\)
0.796966 + 0.604024i \(0.206437\pi\)
\(230\) 1091.70 + 744.306i 0.312975 + 0.213383i
\(231\) −3029.82 + 3799.28i −0.862977 + 1.08214i
\(232\) 1.11849 + 0.168585i 0.000316519 + 4.77076e-5i
\(233\) 1279.95 394.811i 0.359880 0.111008i −0.109542 0.993982i \(-0.534938\pi\)
0.469422 + 0.882974i \(0.344462\pi\)
\(234\) 36.4051 485.793i 0.0101704 0.135715i
\(235\) −4549.50 + 3101.80i −1.26288 + 0.861016i
\(236\) 132.245 579.403i 0.0364763 0.159813i
\(237\) −1331.12 + 5832.00i −0.364832 + 1.59843i
\(238\) 2541.80 1732.97i 0.692272 0.471983i
\(239\) 275.635 3678.09i 0.0745998 0.995465i −0.826805 0.562488i \(-0.809844\pi\)
0.901405 0.432977i \(-0.142537\pi\)
\(240\) −4005.51 + 1235.54i −1.07731 + 0.332306i
\(241\) 1786.71 + 269.303i 0.477561 + 0.0719807i 0.383412 0.923577i \(-0.374749\pi\)
0.0941488 + 0.995558i \(0.469987\pi\)
\(242\) 1264.35 1585.45i 0.335850 0.421143i
\(243\) −1166.14 795.063i −0.307852 0.209890i
\(244\) 274.963 255.129i 0.0721423 0.0669382i
\(245\) 32.9605 83.9820i 0.00859498 0.0218997i
\(246\) 226.543 + 69.8792i 0.0587148 + 0.0181111i
\(247\) −5263.56 2534.80i −1.35592 0.652976i
\(248\) −1302.66 3319.12i −0.333544 0.849855i
\(249\) −25.3911 338.820i −0.00646222 0.0862323i
\(250\) −1343.28 1684.42i −0.339826 0.426129i
\(251\) 2535.56 + 4391.73i 0.637623 + 1.10440i 0.985953 + 0.167024i \(0.0534157\pi\)
−0.348330 + 0.937372i \(0.613251\pi\)
\(252\) −54.0950 + 93.6953i −0.0135225 + 0.0234216i
\(253\) −1658.12 + 249.922i −0.412037 + 0.0621046i
\(254\) −4270.07 + 2056.36i −1.05483 + 0.507981i
\(255\) 3599.04 + 3339.42i 0.883846 + 0.820089i
\(256\) 380.067 + 1665.18i 0.0927898 + 0.406539i
\(257\) 4390.62 1.06568 0.532839 0.846217i \(-0.321125\pi\)
0.532839 + 0.846217i \(0.321125\pi\)
\(258\) 3498.57 + 2296.74i 0.844230 + 0.554221i
\(259\) −5901.89 −1.41593
\(260\) 127.316 + 557.808i 0.0303685 + 0.133053i
\(261\) −0.176471 0.163741i −4.18516e−5 3.88326e-5i
\(262\) −6117.71 + 2946.13i −1.44257 + 0.694705i
\(263\) 5315.86 801.237i 1.24635 0.187857i 0.507455 0.861678i \(-0.330586\pi\)
0.738894 + 0.673821i \(0.235348\pi\)
\(264\) 3110.68 5387.85i 0.725185 1.25606i
\(265\) −2645.65 4582.40i −0.613287 1.06224i
\(266\) −4887.99 6129.35i −1.12670 1.41284i
\(267\) 581.224 + 7755.89i 0.133222 + 1.77773i
\(268\) 74.5496 + 189.949i 0.0169920 + 0.0432948i
\(269\) 598.525 + 288.235i 0.135661 + 0.0653308i 0.500483 0.865747i \(-0.333156\pi\)
−0.364822 + 0.931077i \(0.618870\pi\)
\(270\) −4287.12 1322.40i −0.966318 0.298070i
\(271\) 160.680 409.406i 0.0360170 0.0917698i −0.911734 0.410782i \(-0.865256\pi\)
0.947751 + 0.319012i \(0.103351\pi\)
\(272\) −2468.74 + 2290.66i −0.550329 + 0.510631i
\(273\) −3194.27 2177.81i −0.708153 0.482811i
\(274\) 4230.97 5305.47i 0.932855 1.16976i
\(275\) −2967.30 447.249i −0.650673 0.0980731i
\(276\) −224.756 + 69.3280i −0.0490171 + 0.0151198i
\(277\) 251.668 3358.27i 0.0545894 0.728445i −0.901014 0.433789i \(-0.857176\pi\)
0.955604 0.294655i \(-0.0952048\pi\)
\(278\) 2022.39 1378.84i 0.436312 0.297473i
\(279\) −168.862 + 739.831i −0.0362347 + 0.158755i
\(280\) −1374.05 + 6020.10i −0.293268 + 1.28489i
\(281\) −1039.93 + 709.015i −0.220773 + 0.150521i −0.668657 0.743571i \(-0.733130\pi\)
0.447883 + 0.894092i \(0.352178\pi\)
\(282\) −442.605 + 5906.16i −0.0934637 + 1.24719i
\(283\) −4455.28 + 1374.27i −0.935826 + 0.288664i −0.724913 0.688841i \(-0.758120\pi\)
−0.210913 + 0.977505i \(0.567644\pi\)
\(284\) −466.531 70.3182i −0.0974772 0.0146923i
\(285\) 7800.92 9782.05i 1.62136 2.03312i
\(286\) 3625.17 + 2471.60i 0.749513 + 0.511009i
\(287\) 218.910 203.119i 0.0450239 0.0417761i
\(288\) 94.9154 241.840i 0.0194199 0.0494812i
\(289\) −925.408 285.451i −0.188359 0.0581011i
\(290\) −1.53923 0.741255i −0.000311679 0.000150097i
\(291\) 1636.59 + 4169.97i 0.329687 + 0.840028i
\(292\) 72.5184 + 967.691i 0.0145336 + 0.193938i
\(293\) −4867.39 6103.52i −0.970498 1.21697i −0.976175 0.216983i \(-0.930379\pi\)
0.00567715 0.999984i \(-0.498193\pi\)
\(294\) −48.5209 84.0406i −0.00962516 0.0166713i
\(295\) −3609.53 + 6251.88i −0.712389 + 1.23389i
\(296\) 7471.54 1126.15i 1.46714 0.221136i
\(297\) 5129.92 2470.44i 1.00225 0.482658i
\(298\) 4261.62 + 3954.21i 0.828420 + 0.768662i
\(299\) −296.854 1300.60i −0.0574165 0.251558i
\(300\) −420.913 −0.0810047
\(301\) 4708.92 2369.98i 0.901720 0.453831i
\(302\) 1196.54 0.227990
\(303\) −732.120 3207.63i −0.138809 0.608163i
\(304\) 6291.30 + 5837.47i 1.18694 + 1.10132i
\(305\) −4105.08 + 1976.90i −0.770676 + 0.371138i
\(306\) 828.865 124.931i 0.154847 0.0233394i
\(307\) −4554.97 + 7889.43i −0.846794 + 1.46669i 0.0372608 + 0.999306i \(0.488137\pi\)
−0.884054 + 0.467384i \(0.845197\pi\)
\(308\) −487.206 843.865i −0.0901335 0.156116i
\(309\) −1425.16 1787.10i −0.262377 0.329011i
\(310\) 402.450 + 5370.32i 0.0737343 + 0.983915i
\(311\) 1960.39 + 4995.00i 0.357439 + 0.910740i 0.990609 + 0.136727i \(0.0436584\pi\)
−0.633169 + 0.774013i \(0.718246\pi\)
\(312\) 4459.36 + 2147.51i 0.809171 + 0.389676i
\(313\) 3520.88 + 1086.05i 0.635821 + 0.196125i 0.595875 0.803077i \(-0.296805\pi\)
0.0399457 + 0.999202i \(0.487281\pi\)
\(314\) 2662.92 6785.00i 0.478589 1.21943i
\(315\) 963.372 893.878i 0.172317 0.159887i
\(316\) −991.071 675.701i −0.176431 0.120288i
\(317\) −2821.46 + 3538.00i −0.499902 + 0.626857i −0.966207 0.257767i \(-0.917013\pi\)
0.466305 + 0.884624i \(0.345585\pi\)
\(318\) −5627.92 848.272i −0.992447 0.149587i
\(319\) 2.07184 0.639079i 0.000363639 0.000112168i
\(320\) 580.131 7741.32i 0.101345 1.35235i
\(321\) 5370.76 3661.73i 0.933853 0.636690i
\(322\) 398.359 1745.33i 0.0689431 0.302060i
\(323\) 2236.84 9800.23i 0.385328 1.68823i
\(324\) 788.966 537.908i 0.135282 0.0922338i
\(325\) 178.407 2380.68i 0.0304500 0.406327i
\(326\) −8965.78 + 2765.58i −1.52322 + 0.469850i
\(327\) 1074.95 + 162.023i 0.181789 + 0.0274002i
\(328\) −238.373 + 298.910i −0.0401279 + 0.0503188i
\(329\) 6164.13 + 4202.63i 1.03295 + 0.704251i
\(330\) −6888.18 + 6391.29i −1.14904 + 1.06615i
\(331\) −387.524 + 987.394i −0.0643511 + 0.163964i −0.959432 0.281939i \(-0.909022\pi\)
0.895081 + 0.445903i \(0.147118\pi\)
\(332\) 65.1034 + 20.0817i 0.0107621 + 0.00331966i
\(333\) −1448.86 697.734i −0.238429 0.114822i
\(334\) −3203.72 8162.94i −0.524849 1.33729i
\(335\) −185.231 2471.74i −0.0302098 0.403121i
\(336\) 3541.04 + 4440.33i 0.574939 + 0.720951i
\(337\) −207.430 359.280i −0.0335295 0.0580748i 0.848774 0.528756i \(-0.177341\pi\)
−0.882303 + 0.470681i \(0.844008\pi\)
\(338\) 1132.69 1961.88i 0.182279 0.315717i
\(339\) −3453.03 + 520.460i −0.553224 + 0.0833850i
\(340\) −886.985 + 427.149i −0.141481 + 0.0681336i
\(341\) −5010.14 4648.73i −0.795643 0.738249i
\(342\) −475.332 2082.57i −0.0751550 0.329276i
\(343\) 6290.47 0.990243
\(344\) −5509.07 + 3898.81i −0.863457 + 0.611074i
\(345\) 2857.06 0.445852
\(346\) −1060.44 4646.11i −0.164768 0.721897i
\(347\) 2298.29 + 2132.50i 0.355558 + 0.329910i 0.837646 0.546213i \(-0.183931\pi\)
−0.482088 + 0.876123i \(0.660121\pi\)
\(348\) 0.274003 0.131953i 4.22072e−5 2.03259e-5i
\(349\) 11962.3 1803.03i 1.83475 0.276544i 0.861749 0.507335i \(-0.169369\pi\)
0.973003 + 0.230791i \(0.0741312\pi\)
\(350\) 1601.84 2774.47i 0.244634 0.423719i
\(351\) 2264.90 + 3922.91i 0.344419 + 0.596552i
\(352\) 1458.89 + 1829.39i 0.220907 + 0.277008i
\(353\) 174.802 + 2332.58i 0.0263564 + 0.351701i 0.994754 + 0.102292i \(0.0326175\pi\)
−0.968398 + 0.249410i \(0.919763\pi\)
\(354\) 2836.88 + 7228.26i 0.425929 + 1.08525i
\(355\) 5163.45 + 2486.59i 0.771965 + 0.371759i
\(356\) −1490.27 459.689i −0.221866 0.0684367i
\(357\) 2430.29 6192.28i 0.360293 0.918012i
\(358\) 2517.63 2336.02i 0.371678 0.344867i
\(359\) −1468.73 1001.37i −0.215924 0.147215i 0.450528 0.892762i \(-0.351236\pi\)
−0.666452 + 0.745548i \(0.732188\pi\)
\(360\) −1049.02 + 1315.43i −0.153579 + 0.192582i
\(361\) −18548.5 2795.74i −2.70426 0.407601i
\(362\) 2116.92 652.985i 0.307357 0.0948070i
\(363\) 327.686 4372.67i 0.0473803 0.632247i
\(364\) 640.509 436.692i 0.0922303 0.0628815i
\(365\) 2622.98 11492.0i 0.376146 1.64800i
\(366\) −1090.55 + 4778.02i −0.155749 + 0.682379i
\(367\) 904.163 616.448i 0.128602 0.0876794i −0.497311 0.867573i \(-0.665679\pi\)
0.625913 + 0.779893i \(0.284727\pi\)
\(368\) −146.455 + 1954.31i −0.0207459 + 0.276835i
\(369\) 77.7535 23.9838i 0.0109693 0.00338359i
\(370\) −11284.8 1700.91i −1.58560 0.238990i
\(371\) −4469.92 + 5605.10i −0.625517 + 0.784373i
\(372\) −792.088 540.036i −0.110397 0.0752677i
\(373\) −114.210 + 105.972i −0.0158541 + 0.0147105i −0.688060 0.725654i \(-0.741537\pi\)
0.672206 + 0.740364i \(0.265347\pi\)
\(374\) −2758.13 + 7027.61i −0.381336 + 0.971629i
\(375\) −4451.69 1373.16i −0.613025 0.189093i
\(376\) −8605.43 4144.16i −1.18030 0.568401i
\(377\) 0.630187 + 1.60569i 8.60909e−5 + 0.000219356i
\(378\) 454.261 + 6061.69i 0.0618113 + 0.824814i
\(379\) 5494.38 + 6889.74i 0.744664 + 0.933779i 0.999448 0.0332193i \(-0.0105760\pi\)
−0.254785 + 0.966998i \(0.582005\pi\)
\(380\) 1254.41 + 2172.71i 0.169342 + 0.293310i
\(381\) −5124.11 + 8875.22i −0.689019 + 1.19342i
\(382\) 8163.92 1230.51i 1.09346 0.164813i
\(383\) −5622.35 + 2707.58i −0.750100 + 0.361229i −0.769554 0.638581i \(-0.779522\pi\)
0.0194538 + 0.999811i \(0.493807\pi\)
\(384\) −4426.74 4107.41i −0.588284 0.545848i
\(385\) 2633.81 + 11539.5i 0.348654 + 1.52755i
\(386\) −5804.65 −0.765411
\(387\) 1436.18 25.1082i 0.188644 0.00329799i
\(388\) −898.249 −0.117530
\(389\) −2191.37 9601.01i −0.285622 1.25139i −0.890467 0.455047i \(-0.849622\pi\)
0.604846 0.796343i \(-0.293235\pi\)
\(390\) −5480.02 5084.71i −0.711517 0.660191i
\(391\) 2068.12 995.956i 0.267492 0.128818i
\(392\) 154.747 23.3244i 0.0199385 0.00300525i
\(393\) −7341.29 + 12715.5i −0.942288 + 1.63209i
\(394\) 2067.03 + 3580.20i 0.264303 + 0.457786i
\(395\) 9084.49 + 11391.6i 1.15719 + 1.45107i
\(396\) −19.8410 264.759i −0.00251779 0.0335976i
\(397\) −1187.30 3025.20i −0.150098 0.382444i 0.835972 0.548772i \(-0.184904\pi\)
−0.986071 + 0.166327i \(0.946809\pi\)
\(398\) 6074.85 + 2925.49i 0.765087 + 0.368446i
\(399\) −16199.0 4996.73i −2.03249 0.626941i
\(400\) −1281.30 + 3264.71i −0.160163 + 0.408088i
\(401\) 2745.11 2547.09i 0.341855 0.317195i −0.490496 0.871443i \(-0.663184\pi\)
0.832352 + 0.554248i \(0.186994\pi\)
\(402\) −2202.86 1501.89i −0.273306 0.186337i
\(403\) 3390.18 4251.15i 0.419049 0.525471i
\(404\) 652.361 + 98.3276i 0.0803371 + 0.0121089i
\(405\) −11083.8 + 3418.90i −1.35990 + 0.419472i
\(406\) −0.172981 + 2.30827i −2.11450e−5 + 0.000282161i
\(407\) 11966.8 8158.81i 1.45742 0.993654i
\(408\) −1895.08 + 8302.89i −0.229952 + 1.00749i
\(409\) −441.482 + 1934.26i −0.0533738 + 0.233846i −0.994578 0.103992i \(-0.966838\pi\)
0.941204 + 0.337838i \(0.109696\pi\)
\(410\) 477.110 325.288i 0.0574702 0.0391825i
\(411\) 1096.55 14632.5i 0.131603 1.75612i
\(412\) 437.978 135.098i 0.0523729 0.0161549i
\(413\) 9671.86 + 1457.80i 1.15235 + 0.173689i
\(414\) 304.129 381.366i 0.0361042 0.0452733i
\(415\) −683.781 466.194i −0.0808807 0.0551436i
\(416\) −1364.60 + 1266.16i −0.160829 + 0.149228i
\(417\) 1933.66 4926.90i 0.227079 0.578588i
\(418\) 18384.2 + 5670.78i 2.15120 + 0.663557i
\(419\) −981.240 472.540i −0.114407 0.0550957i 0.375805 0.926699i \(-0.377366\pi\)
−0.490212 + 0.871603i \(0.663081\pi\)
\(420\) 606.548 + 1545.46i 0.0704679 + 0.179549i
\(421\) −669.444 8933.11i −0.0774981 1.03414i −0.891424 0.453171i \(-0.850293\pi\)
0.813926 0.580969i \(-0.197326\pi\)
\(422\) −7348.82 9215.12i −0.847713 1.06300i
\(423\) 1016.39 + 1760.44i 0.116829 + 0.202354i
\(424\) 4589.21 7948.74i 0.525640 0.910436i
\(425\) 4061.94 612.239i 0.463607 0.0698776i
\(426\) 5553.97 2674.65i 0.631668 0.304195i
\(427\) 4525.37 + 4198.93i 0.512876 + 0.475880i
\(428\) 290.039 + 1270.74i 0.0327559 + 0.143513i
\(429\) 9487.37 1.06773
\(430\) 9686.81 3174.45i 1.08637 0.356013i
\(431\) −8840.93 −0.988057 −0.494029 0.869446i \(-0.664476\pi\)
−0.494029 + 0.869446i \(0.664476\pi\)
\(432\) −1480.76 6487.64i −0.164915 0.722539i
\(433\) 1332.77 + 1236.63i 0.147919 + 0.137249i 0.750662 0.660687i \(-0.229735\pi\)
−0.602742 + 0.797936i \(0.705925\pi\)
\(434\) 6574.07 3165.90i 0.727109 0.350157i
\(435\) −3.65292 + 0.550589i −0.000402630 + 6.06867e-5i
\(436\) −108.991 + 188.778i −0.0119718 + 0.0207358i
\(437\) −2924.83 5065.96i −0.320169 0.554549i
\(438\) −7905.28 9912.91i −0.862395 1.08141i
\(439\) −346.914 4629.24i −0.0377159 0.503284i −0.983789 0.179330i \(-0.942607\pi\)
0.946073 0.323953i \(-0.105012\pi\)
\(440\) −5536.17 14105.9i −0.599833 1.52835i
\(441\) −30.0081 14.4511i −0.00324027 0.00156043i
\(442\) −5739.29 1770.34i −0.617625 0.190512i
\(443\) −2460.21 + 6268.52i −0.263856 + 0.672295i −0.999990 0.00454168i \(-0.998554\pi\)
0.736133 + 0.676836i \(0.236650\pi\)
\(444\) 1489.22 1381.79i 0.159179 0.147696i
\(445\) 15652.4 + 10671.6i 1.66740 + 1.13681i
\(446\) −10670.0 + 13379.8i −1.13283 + 1.42052i
\(447\) 12430.4 + 1873.58i 1.31530 + 0.198249i
\(448\) −10050.8 + 3100.28i −1.05995 + 0.326951i
\(449\) −531.528 + 7092.75i −0.0558672 + 0.745495i 0.896985 + 0.442061i \(0.145752\pi\)
−0.952852 + 0.303435i \(0.901867\pi\)
\(450\) 721.240 491.733i 0.0755546 0.0515122i
\(451\) −163.073 + 714.470i −0.0170262 + 0.0745966i
\(452\) 155.813 682.661i 0.0162142 0.0710391i
\(453\) 2137.74 1457.49i 0.221722 0.151167i
\(454\) −97.1334 + 1296.16i −0.0100412 + 0.133990i
\(455\) −8998.20 + 2775.58i −0.927126 + 0.285980i
\(456\) 21460.7 + 3234.68i 2.20392 + 0.332188i
\(457\) −1639.29 + 2055.60i −0.167796 + 0.210409i −0.858619 0.512615i \(-0.828677\pi\)
0.690823 + 0.723024i \(0.257248\pi\)
\(458\) −2601.18 1773.45i −0.265382 0.180935i
\(459\) −5713.57 + 5301.42i −0.581016 + 0.539104i
\(460\) −209.301 + 533.291i −0.0212146 + 0.0540540i
\(461\) −9488.59 2926.84i −0.958628 0.295698i −0.224321 0.974515i \(-0.572016\pi\)
−0.734307 + 0.678818i \(0.762493\pi\)
\(462\) 11470.6 + 5523.96i 1.15511 + 0.556273i
\(463\) 514.552 + 1311.06i 0.0516485 + 0.131598i 0.954370 0.298628i \(-0.0965290\pi\)
−0.902721 + 0.430226i \(0.858434\pi\)
\(464\) −0.189366 2.52692i −1.89463e−5 0.000252821i
\(465\) 7260.54 + 9104.43i 0.724085 + 0.907974i
\(466\) −1754.64 3039.12i −0.174425 0.302113i
\(467\) 2341.40 4055.42i 0.232006 0.401847i −0.726392 0.687280i \(-0.758804\pi\)
0.958398 + 0.285434i \(0.0921377\pi\)
\(468\) 208.866 31.4814i 0.0206300 0.00310947i
\(469\) −3025.78 + 1457.14i −0.297905 + 0.143463i
\(470\) 10575.0 + 9812.21i 1.03785 + 0.962986i
\(471\) −3507.14 15365.8i −0.343101 1.50322i
\(472\) −12522.3 −1.22116
\(473\) −6271.62 + 11315.0i −0.609661 + 1.09993i
\(474\) 15672.4 1.51868
\(475\) −2329.42 10205.8i −0.225013 0.985844i
\(476\) 977.798 + 907.264i 0.0941540 + 0.0873621i
\(477\) −1759.97 + 847.557i −0.168938 + 0.0813564i
\(478\) −9555.43 + 1440.25i −0.914342 + 0.137815i
\(479\) 2861.91 4956.98i 0.272994 0.472840i −0.696633 0.717428i \(-0.745319\pi\)
0.969627 + 0.244588i \(0.0786527\pi\)
\(480\) −1993.37 3452.62i −0.189551 0.328312i
\(481\) 7184.20 + 9008.71i 0.681022 + 0.853974i
\(482\) −353.767 4720.69i −0.0334308 0.446103i
\(483\) −1414.25 3603.45i −0.133231 0.339467i
\(484\) 792.185 + 381.496i 0.0743976 + 0.0358280i
\(485\) 10426.4 + 3216.11i 0.976158 + 0.301105i
\(486\) −1350.93 + 3442.12i −0.126090 + 0.321271i
\(487\) −4518.38 + 4192.44i −0.420426 + 0.390098i −0.861819 0.507216i \(-0.830675\pi\)
0.441393 + 0.897314i \(0.354484\pi\)
\(488\) −6530.14 4452.17i −0.605749 0.412993i
\(489\) −12649.6 + 15862.1i −1.16981 + 1.46689i
\(490\) −233.726 35.2285i −0.0215483 0.00324788i
\(491\) 10068.4 3105.70i 0.925423 0.285455i 0.204817 0.978800i \(-0.434340\pi\)
0.720606 + 0.693345i \(0.243864\pi\)
\(492\) −7.68174 + 102.506i −0.000703902 + 0.00939291i
\(493\) −2.45228 + 1.67194i −0.000224027 + 0.000152739i
\(494\) −3405.88 + 14922.2i −0.310198 + 1.35907i
\(495\) −717.646 + 3144.21i −0.0651632 + 0.285499i
\(496\) −6599.86 + 4499.71i −0.597464 + 0.407344i
\(497\) 580.275 7743.23i 0.0523720 0.698856i
\(498\) −850.626 + 262.383i −0.0765411 + 0.0236098i
\(499\) −1626.90 245.215i −0.145952 0.0219987i 0.0756600 0.997134i \(-0.475894\pi\)
−0.221612 + 0.975135i \(0.571132\pi\)
\(500\) 582.431 730.346i 0.0520942 0.0653241i
\(501\) −15667.0 10681.6i −1.39710 0.952529i
\(502\) 9739.33 9036.78i 0.865911 0.803448i
\(503\) −2058.31 + 5244.49i −0.182456 + 0.464892i −0.992613 0.121322i \(-0.961287\pi\)
0.810157 + 0.586213i \(0.199382\pi\)
\(504\) 2178.35 + 671.932i 0.192523 + 0.0593854i
\(505\) −7220.18 3477.05i −0.636225 0.306390i
\(506\) 1605.03 + 4089.55i 0.141012 + 0.359293i
\(507\) −366.067 4884.83i −0.0320663 0.427895i
\(508\) −1281.25 1606.63i −0.111902 0.140320i
\(509\) −2873.06 4976.29i −0.250189 0.433340i 0.713389 0.700769i \(-0.247159\pi\)
−0.963578 + 0.267428i \(0.913826\pi\)
\(510\) 6431.49 11139.7i 0.558414 0.967201i
\(511\) −15792.6 + 2380.36i −1.36717 + 0.206068i
\(512\) 11714.8 5641.55i 1.01118 0.486960i
\(513\) 14560.4 + 13510.0i 1.25313 + 1.16273i
\(514\) −2559.68 11214.7i −0.219655 0.962372i
\(515\) −5567.51 −0.476376
\(516\) −633.323 + 1700.50i −0.0540320 + 0.145078i
\(517\) −18308.2 −1.55744
\(518\) 3440.74 + 15074.9i 0.291848 + 1.27867i
\(519\) −7553.97 7009.06i −0.638887 0.592801i
\(520\) 10861.7 5230.73i 0.915996 0.441121i
\(521\) −10947.8 + 1650.11i −0.920594 + 0.138757i −0.592207 0.805786i \(-0.701743\pi\)
−0.328387 + 0.944543i \(0.606505\pi\)
\(522\) −0.315353 + 0.546208i −2.64418e−5 + 4.57986e-5i
\(523\) 4907.38 + 8499.83i 0.410296 + 0.710653i 0.994922 0.100650i \(-0.0320921\pi\)
−0.584626 + 0.811303i \(0.698759\pi\)
\(524\) −1835.63 2301.81i −0.153034 0.191899i
\(525\) −517.688 6908.06i −0.0430357 0.574272i
\(526\) −5145.64 13110.9i −0.426541 1.08681i
\(527\) 8429.41 + 4059.39i 0.696756 + 0.335540i
\(528\) −13318.2 4108.12i −1.09773 0.338604i
\(529\) −3957.09 + 10082.5i −0.325231 + 0.828676i
\(530\) −10162.2 + 9429.12i −0.832862 + 0.772783i
\(531\) 2202.01 + 1501.30i 0.179960 + 0.122695i
\(532\) 2119.38 2657.61i 0.172719 0.216583i
\(533\) −576.516 86.8957i −0.0468511 0.00706167i
\(534\) 19471.6 6006.19i 1.57794 0.486729i
\(535\) 1183.18 15788.5i 0.0956141 1.27588i
\(536\) 3552.46 2422.03i 0.286274 0.195178i
\(537\) 1652.54 7240.23i 0.132797 0.581823i
\(538\) 387.287 1696.82i 0.0310356 0.135976i
\(539\) 247.850 168.981i 0.0198064 0.0135038i
\(540\) 145.370 1939.83i 0.0115847 0.154587i
\(541\) −3068.95 + 946.645i −0.243890 + 0.0752301i −0.414290 0.910145i \(-0.635970\pi\)
0.170400 + 0.985375i \(0.445494\pi\)
\(542\) −1139.40 171.736i −0.0902975 0.0136102i
\(543\) 2986.72 3745.23i 0.236045 0.295991i
\(544\) −2646.49 1804.35i −0.208580 0.142207i
\(545\) 1941.01 1800.99i 0.152557 0.141552i
\(546\) −3700.44 + 9428.57i −0.290045 + 0.739021i
\(547\) −9018.92 2781.97i −0.704974 0.217456i −0.0785185 0.996913i \(-0.525019\pi\)
−0.626456 + 0.779457i \(0.715495\pi\)
\(548\) 2650.93 + 1276.62i 0.206646 + 0.0995155i
\(549\) 614.530 + 1565.80i 0.0477733 + 0.121724i
\(550\) 587.523 + 7839.95i 0.0455492 + 0.607812i
\(551\) 4.71584 + 5.91348i 0.000364613 + 0.000457210i
\(552\) 2477.96 + 4291.95i 0.191067 + 0.330938i
\(553\) 9870.73 17096.6i 0.759035 1.31469i
\(554\) −8724.57 + 1315.02i −0.669082 + 0.100848i
\(555\) −22233.4 + 10707.0i −1.70046 + 0.818899i
\(556\) 777.986 + 721.865i 0.0593416 + 0.0550610i
\(557\) 2342.56 + 10263.4i 0.178200 + 0.780746i 0.982461 + 0.186469i \(0.0597045\pi\)
−0.804261 + 0.594277i \(0.797438\pi\)
\(558\) 1988.15 0.150834
\(559\) −9349.59 4302.84i −0.707416 0.325565i
\(560\) 13833.4 1.04387
\(561\) 3632.55 + 15915.2i 0.273380 + 1.19776i
\(562\) 2417.27 + 2242.89i 0.181435 + 0.168347i
\(563\) 7998.55 3851.90i 0.598755 0.288345i −0.109853 0.993948i \(-0.535038\pi\)
0.708608 + 0.705603i \(0.249324\pi\)
\(564\) −2539.34 + 382.744i −0.189584 + 0.0285752i
\(565\) −4252.80 + 7366.06i −0.316666 + 0.548482i
\(566\) 6107.60 + 10578.7i 0.453572 + 0.785609i
\(567\) 9798.55 + 12287.0i 0.725750 + 0.910062i
\(568\) 742.901 + 9913.32i 0.0548793 + 0.732313i
\(569\) 3070.75 + 7824.15i 0.226244 + 0.576460i 0.998249 0.0591569i \(-0.0188412\pi\)
−0.772005 + 0.635617i \(0.780746\pi\)
\(570\) −29533.6 14222.6i −2.17022 1.04512i
\(571\) 17617.9 + 5434.41i 1.29122 + 0.398289i 0.862917 0.505346i \(-0.168635\pi\)
0.428304 + 0.903635i \(0.359111\pi\)
\(572\) −695.022 + 1770.89i −0.0508048 + 0.129449i
\(573\) 13086.9 12142.8i 0.954121 0.885294i
\(574\) −646.437 440.733i −0.0470065 0.0320485i
\(575\) 1490.42 1868.93i 0.108095 0.135547i
\(576\) −2833.91 427.143i −0.204999 0.0308987i
\(577\) 1734.89 535.142i 0.125172 0.0386105i −0.231536 0.972826i \(-0.574375\pi\)
0.356708 + 0.934216i \(0.383899\pi\)
\(578\) −189.607 + 2530.13i −0.0136447 + 0.182075i
\(579\) −10370.6 + 7070.57i −0.744367 + 0.507501i
\(580\) 0.164833 0.722179i 1.18005e−5 5.17014e-5i
\(581\) −249.511 + 1093.18i −0.0178167 + 0.0780599i
\(582\) 9697.00 6611.31i 0.690642 0.470872i
\(583\) 1314.76 17544.3i 0.0933993 1.24633i
\(584\) 19538.6 6026.86i 1.38444 0.427043i
\(585\) −2537.11 382.408i −0.179310 0.0270267i
\(586\) −12752.2 + 15990.8i −0.898958 + 1.12726i
\(587\) 3636.37 + 2479.23i 0.255688 + 0.174325i 0.684380 0.729126i \(-0.260073\pi\)
−0.428692 + 0.903451i \(0.641025\pi\)
\(588\) 30.8440 28.6191i 0.00216324 0.00200720i
\(589\) 8710.64 22194.4i 0.609365 1.55264i
\(590\) 18073.1 + 5574.82i 1.26112 + 0.389003i
\(591\) 8053.96 + 3878.58i 0.560568 + 0.269955i
\(592\) −6184.20 15757.1i −0.429340 1.09394i
\(593\) 1052.62 + 14046.2i 0.0728933 + 0.972694i 0.907011 + 0.421107i \(0.138358\pi\)
−0.834118 + 0.551587i \(0.814023\pi\)
\(594\) −9300.78 11662.8i −0.642451 0.805608i
\(595\) −8101.33 14031.9i −0.558189 0.966811i
\(596\) −1260.34 + 2182.98i −0.0866201 + 0.150030i
\(597\) 14416.9 2172.99i 0.988347 0.148969i
\(598\) −3148.99 + 1516.48i −0.215338 + 0.103701i
\(599\) 10891.7 + 10106.0i 0.742944 + 0.689351i 0.957845 0.287285i \(-0.0927525\pi\)
−0.214901 + 0.976636i \(0.568943\pi\)
\(600\) 1973.51 + 8646.53i 0.134281 + 0.588322i
\(601\) 8545.44 0.579993 0.289997 0.957028i \(-0.406346\pi\)
0.289997 + 0.957028i \(0.406346\pi\)
\(602\) −8798.74 10646.1i −0.595697 0.720766i
\(603\) −915.065 −0.0617982
\(604\) 115.445 + 505.798i 0.00777714 + 0.0340739i
\(605\) −7829.31 7264.54i −0.526127 0.488175i
\(606\) −7766.24 + 3740.03i −0.520598 + 0.250707i
\(607\) 16383.4 2469.40i 1.09552 0.165123i 0.423675 0.905814i \(-0.360740\pi\)
0.671846 + 0.740691i \(0.265502\pi\)
\(608\) −4081.31 + 7069.04i −0.272235 + 0.471525i
\(609\) 2.50262 + 4.33467i 0.000166521 + 0.000288423i
\(610\) 7442.70 + 9332.86i 0.494010 + 0.619469i
\(611\) −1088.48 14524.7i −0.0720705 0.961714i
\(612\) 132.782 + 338.322i 0.00877023 + 0.0223462i
\(613\) 9278.70 + 4468.38i 0.611359 + 0.294415i 0.713828 0.700321i \(-0.246960\pi\)
−0.102469 + 0.994736i \(0.532674\pi\)
\(614\) 22807.0 + 7035.03i 1.49905 + 0.462395i
\(615\) 456.178 1162.32i 0.0299104 0.0762104i
\(616\) −15050.6 + 13964.9i −0.984425 + 0.913413i
\(617\) −20078.6 13689.4i −1.31011 0.893215i −0.311729 0.950171i \(-0.600908\pi\)
−0.998377 + 0.0569561i \(0.981860\pi\)
\(618\) −3733.82 + 4682.06i −0.243036 + 0.304758i
\(619\) 17746.4 + 2674.84i 1.15232 + 0.173685i 0.697289 0.716790i \(-0.254390\pi\)
0.455033 + 0.890475i \(0.349628\pi\)
\(620\) −2231.30 + 688.265i −0.144534 + 0.0445829i
\(621\) −338.950 + 4522.97i −0.0219027 + 0.292272i
\(622\) 11615.5 7919.34i 0.748779 0.510509i
\(623\) 5711.54 25023.9i 0.367300 1.60925i
\(624\) 2467.35 10810.2i 0.158290 0.693514i
\(625\) −16130.5 + 10997.6i −1.03235 + 0.703846i
\(626\) 721.394 9626.34i 0.0460586 0.614610i
\(627\) 39752.9 12262.1i 2.53202 0.781025i
\(628\) 3125.06 + 471.028i 0.198573 + 0.0299300i
\(629\) −12361.6 + 15500.9i −0.783605 + 0.982609i
\(630\) −2844.82 1939.56i −0.179905 0.122657i
\(631\) −10135.5 + 9404.41i −0.639445 + 0.593318i −0.931791 0.362994i \(-0.881754\pi\)
0.292346 + 0.956312i \(0.405564\pi\)
\(632\) −9233.68 + 23527.0i −0.581164 + 1.48078i
\(633\) −24354.3 7512.30i −1.52922 0.471702i
\(634\) 10681.8 + 5144.07i 0.669129 + 0.322235i
\(635\) 9119.55 + 23236.2i 0.569918 + 1.45213i
\(636\) −184.416 2460.86i −0.0114978 0.153427i
\(637\) 148.796 + 186.584i 0.00925511 + 0.0116055i
\(638\) −2.84022 4.91941i −0.000176247 0.000305269i
\(639\) 1057.87 1832.29i 0.0654911 0.113434i
\(640\) −14544.5 + 2192.22i −0.898313 + 0.135399i
\(641\) 13793.4 6642.55i 0.849931 0.409305i 0.0423793 0.999102i \(-0.486506\pi\)
0.807552 + 0.589796i \(0.200792\pi\)
\(642\) −12484.0 11583.5i −0.767454 0.712093i
\(643\) −1313.17 5753.36i −0.0805386 0.352862i 0.918562 0.395278i \(-0.129352\pi\)
−0.999100 + 0.0424156i \(0.986495\pi\)
\(644\) 776.215 0.0474956
\(645\) 13439.8 17470.9i 0.820449 1.06654i
\(646\) −26336.2 −1.60400
\(647\) −1136.65 4979.98i −0.0690669 0.302602i 0.928583 0.371126i \(-0.121028\pi\)
−0.997649 + 0.0685240i \(0.978171\pi\)
\(648\) −14749.1 13685.1i −0.894132 0.829633i
\(649\) −21626.1 + 10414.6i −1.30801 + 0.629904i
\(650\) −6184.85 + 932.216i −0.373215 + 0.0562531i
\(651\) 7888.92 13664.0i 0.474948 0.822634i
\(652\) −2034.10 3523.16i −0.122180 0.211622i
\(653\) −4406.46 5525.52i −0.264070 0.331134i 0.632064 0.774916i \(-0.282208\pi\)
−0.896135 + 0.443782i \(0.853636\pi\)
\(654\) −212.839 2840.14i −0.0127258 0.169814i
\(655\) 13065.5 + 33290.4i 0.779409 + 1.98590i
\(656\) 771.676 + 371.619i 0.0459282 + 0.0221178i
\(657\) −4158.36 1282.68i −0.246930 0.0761678i
\(658\) 7140.92 18194.8i 0.423073 1.07797i
\(659\) 3409.73 3163.77i 0.201554 0.187015i −0.572937 0.819599i \(-0.694196\pi\)
0.774492 + 0.632584i \(0.218006\pi\)
\(660\) −3366.30 2295.10i −0.198535 0.135359i
\(661\) 16603.5 20820.1i 0.977004 1.22512i 0.00267426 0.999996i \(-0.499149\pi\)
0.974329 0.225127i \(-0.0722798\pi\)
\(662\) 2747.97 + 414.189i 0.161333 + 0.0243171i
\(663\) −12410.3 + 3828.07i −0.726962 + 0.224238i
\(664\) 107.278 1431.53i 0.00626989 0.0836659i
\(665\) −34115.9 + 23259.8i −1.98941 + 1.35636i
\(666\) −937.512 + 4107.51i −0.0545463 + 0.238983i
\(667\) −0.384329 + 1.68386i −2.23108e−5 + 9.77499e-5i
\(668\) 3141.52 2141.85i 0.181959 0.124058i
\(669\) −2765.39 + 36901.5i −0.159815 + 2.13258i
\(670\) −6205.44 + 1914.12i −0.357816 + 0.110372i
\(671\) −14980.4 2257.93i −0.861863 0.129905i
\(672\) −3367.87 + 4223.17i −0.193331 + 0.242429i
\(673\) 14580.4 + 9940.72i 0.835114 + 0.569371i 0.903647 0.428278i \(-0.140880\pi\)
−0.0685332 + 0.997649i \(0.521832\pi\)
\(674\) −796.758 + 739.283i −0.0455341 + 0.0422495i
\(675\) −2965.40 + 7555.72i −0.169094 + 0.430844i
\(676\) 938.606 + 289.522i 0.0534027 + 0.0164726i
\(677\) −2195.60 1057.35i −0.124644 0.0600253i 0.370523 0.928823i \(-0.379179\pi\)
−0.495166 + 0.868798i \(0.664893\pi\)
\(678\) 3342.46 + 8516.45i 0.189331 + 0.482407i
\(679\) −1104.77 14742.1i −0.0624407 0.833213i
\(680\) 12933.4 + 16218.0i 0.729372 + 0.914604i
\(681\) 1405.29 + 2434.04i 0.0790762 + 0.136964i
\(682\) −8953.13 + 15507.3i −0.502688 + 0.870680i
\(683\) −30179.3 + 4548.79i −1.69074 + 0.254838i −0.922688 0.385547i \(-0.874013\pi\)
−0.768054 + 0.640385i \(0.778775\pi\)
\(684\) 834.476 401.862i 0.0466476 0.0224643i
\(685\) −26199.6 24309.7i −1.46137 1.35595i
\(686\) −3667.28 16067.4i −0.204107 0.894250i
\(687\) −6807.51 −0.378053
\(688\) 11261.6 + 10088.7i 0.624048 + 0.559053i
\(689\) 13996.8 0.773927
\(690\) −1665.64 7297.62i −0.0918980 0.402632i
\(691\) 2572.22 + 2386.67i 0.141609 + 0.131394i 0.747797 0.663927i \(-0.231112\pi\)
−0.606188 + 0.795321i \(0.707302\pi\)
\(692\) 1861.68 896.537i 0.102269 0.0492503i
\(693\) 4320.85 651.264i 0.236848 0.0356991i
\(694\) 4107.05 7113.62i 0.224642 0.389091i
\(695\) −6445.83 11164.5i −0.351805 0.609344i
\(696\) −3.99532 5.00998i −0.000217590 0.000272849i
\(697\) −74.9685 1000.39i −0.00407408 0.0543648i
\(698\) −11579.3 29503.5i −0.627912 1.59989i
\(699\) −6836.77 3292.41i −0.369943 0.178155i
\(700\) 1327.37 + 409.438i 0.0716710 + 0.0221076i
\(701\) 749.608 1909.97i 0.0403884 0.102908i −0.909256 0.416237i \(-0.863349\pi\)
0.949645 + 0.313328i \(0.101444\pi\)
\(702\) 8699.66 8072.11i 0.467732 0.433992i
\(703\) 41745.9 + 28461.9i 2.23965 + 1.52697i
\(704\) 16093.4 20180.5i 0.861568 1.08037i
\(705\) 30845.6 + 4649.22i 1.64782 + 0.248369i
\(706\) 5856.06 1806.35i 0.312175 0.0962932i
\(707\) −811.412 + 10827.5i −0.0431631 + 0.575971i
\(708\) −2781.80 + 1896.60i −0.147665 + 0.100676i
\(709\) −577.487 + 2530.13i −0.0305895 + 0.134021i −0.987917 0.154984i \(-0.950467\pi\)
0.957327 + 0.289005i \(0.0933246\pi\)
\(710\) 3341.11 14638.4i 0.176605 0.773758i
\(711\) 4444.37 3030.12i 0.234426 0.159829i
\(712\) −2455.70 + 32769.0i −0.129257 + 1.72482i
\(713\) 5202.58 1604.78i 0.273265 0.0842911i
\(714\) −17233.4 2597.52i −0.903284 0.136148i
\(715\) 14407.9 18067.0i 0.753603 0.944988i
\(716\) 1230.38 + 838.860i 0.0642200 + 0.0437845i
\(717\) −15317.5 + 14212.5i −0.797825 + 0.740274i
\(718\) −1701.48 + 4335.29i −0.0884380 + 0.225336i
\(719\) 8586.83 + 2648.69i 0.445389 + 0.137384i 0.509334 0.860569i \(-0.329892\pi\)
−0.0639445 + 0.997953i \(0.520368\pi\)
\(720\) 3395.96 + 1635.41i 0.175778 + 0.0846502i
\(721\) 2755.92 + 7021.98i 0.142352 + 0.362708i
\(722\) 3672.59 + 49007.2i 0.189307 + 2.52612i
\(723\) −6382.26 8003.10i −0.328297 0.411672i
\(724\) 480.274 + 831.860i 0.0246537 + 0.0427014i
\(725\) −1.54542 + 2.67675i −7.91663e−5 + 0.000137120i
\(726\) −11359.9 + 1712.23i −0.580723 + 0.0875299i
\(727\) −24069.8 + 11591.4i −1.22792 + 0.591335i −0.931507 0.363724i \(-0.881505\pi\)
−0.296414 + 0.955060i \(0.595791\pi\)
\(728\) −11973.8 11110.1i −0.609585 0.565613i
\(729\) −3271.11 14331.7i −0.166190 0.728124i
\(730\) −30882.6 −1.56578
\(731\) 3638.30 17331.6i 0.184087 0.876924i
\(732\) −2124.97 −0.107297
\(733\) 6251.79 + 27390.9i 0.315027 + 1.38023i 0.846157 + 0.532934i \(0.178911\pi\)
−0.531129 + 0.847291i \(0.678232\pi\)
\(734\) −2101.67 1950.07i −0.105687 0.0980632i
\(735\) −460.488 + 221.759i −0.0231093 + 0.0111289i
\(736\) −1843.12 + 277.806i −0.0923077 + 0.0139131i
\(737\) 4120.76 7137.37i 0.205957 0.356728i
\(738\) −106.590 184.619i −0.00531657 0.00920856i
\(739\) −16687.3 20925.2i −0.830651 1.04160i −0.998443 0.0557806i \(-0.982235\pi\)
0.167792 0.985822i \(-0.446336\pi\)
\(740\) −369.782 4934.40i −0.0183696 0.245125i
\(741\) 12091.5 + 30808.7i 0.599451 + 1.52738i
\(742\) 16922.7 + 8149.55i 0.837267 + 0.403207i
\(743\) −14800.2 4565.24i −0.730774 0.225414i −0.0930311 0.995663i \(-0.529656\pi\)
−0.637743 + 0.770249i \(0.720132\pi\)
\(744\) −7379.78 + 18803.4i −0.363650 + 0.926565i
\(745\) 22445.3 20826.2i 1.10380 1.02418i
\(746\) 337.261 + 229.941i 0.0165523 + 0.0112852i
\(747\) −190.491 + 238.868i −0.00933025 + 0.0116998i
\(748\) −3236.81 487.870i −0.158221 0.0238480i
\(749\) −20498.8 + 6323.05i −1.00001 + 0.308463i
\(750\) −912.108 + 12171.2i −0.0444073 + 0.592574i
\(751\) 12247.6 8350.28i 0.595102 0.405734i −0.227972 0.973668i \(-0.573209\pi\)
0.823074 + 0.567934i \(0.192257\pi\)
\(752\) −4761.36 + 20860.9i −0.230889 + 1.01159i
\(753\) 6392.76 28008.5i 0.309383 1.35549i
\(754\) 3.73393 2.54575i 0.000180347 0.000122958i
\(755\) 470.947 6284.35i 0.0227013 0.302928i
\(756\) −2518.55 + 776.871i −0.121163 + 0.0373737i
\(757\) −2564.71 386.567i −0.123139 0.0185601i 0.0871838 0.996192i \(-0.472213\pi\)
−0.210322 + 0.977632i \(0.567451\pi\)
\(758\) 14394.9 18050.6i 0.689771 0.864945i
\(759\) 7848.98 + 5351.35i 0.375362 + 0.255918i
\(760\) 38751.0 35955.6i 1.84953 1.71612i
\(761\) 12146.6 30949.1i 0.578601 1.47425i −0.279181 0.960239i \(-0.590063\pi\)
0.857782 0.514013i \(-0.171842\pi\)
\(762\) 25656.8 + 7914.06i 1.21975 + 0.376242i
\(763\) −3232.29 1556.59i −0.153364 0.0738562i
\(764\) 1307.84 + 3332.31i 0.0619317 + 0.157799i
\(765\) −329.919 4402.46i −0.0155925 0.208067i
\(766\) 10193.6 + 12782.3i 0.480821 + 0.602931i
\(767\) −9548.08 16537.8i −0.449493 0.778545i
\(768\) 4838.07 8379.78i 0.227316 0.393723i
\(769\) 19363.8 2918.62i 0.908032 0.136864i 0.321613 0.946871i \(-0.395775\pi\)
0.586420 + 0.810007i \(0.300537\pi\)
\(770\) 27939.2 13454.8i 1.30761 0.629711i
\(771\) −18233.6 16918.3i −0.851710 0.790271i
\(772\) −560.047 2453.73i −0.0261095 0.114393i
\(773\) −11570.7 −0.538380 −0.269190 0.963087i \(-0.586756\pi\)
−0.269190 + 0.963087i \(0.586756\pi\)
\(774\) −901.409 3653.71i −0.0418611 0.169677i
\(775\) 9743.15 0.451593
\(776\) 4211.58 + 18452.1i 0.194828 + 0.853599i
\(777\) 24509.8 + 22741.7i 1.13164 + 1.05001i
\(778\) −23245.8 + 11194.6i −1.07121 + 0.515867i
\(779\) −2527.96 + 381.028i −0.116269 + 0.0175247i
\(780\) 1620.67 2807.09i 0.0743966 0.128859i
\(781\) 9527.71 + 16502.5i 0.436528 + 0.756089i
\(782\) −3749.61 4701.86i −0.171465 0.215010i
\(783\) −0.438262 5.84820i −2.00028e−5 0.000266919i
\(784\) −128.084 326.354i −0.00583475 0.0148667i
\(785\) −34587.5 16656.4i −1.57259 0.757317i
\(786\) 36758.3 + 11338.4i 1.66810 + 0.514540i
\(787\) −1497.98 + 3816.78i −0.0678489 + 0.172876i −0.960776 0.277324i \(-0.910552\pi\)
0.892927 + 0.450201i \(0.148648\pi\)
\(788\) −1313.98 + 1219.20i −0.0594018 + 0.0551168i
\(789\) −25163.4 17156.1i −1.13541 0.774113i
\(790\) 23800.7 29845.2i 1.07189 1.34411i
\(791\) 11395.5 + 1717.60i 0.512236 + 0.0772071i
\(792\) −5345.74 + 1648.94i −0.239839 + 0.0739806i
\(793\) 900.686 12018.8i 0.0403333 0.538210i
\(794\) −7034.91 + 4796.32i −0.314433 + 0.214377i
\(795\) −6670.32 + 29224.6i −0.297575 + 1.30376i
\(796\) −650.540 + 2850.20i −0.0289671 + 0.126913i
\(797\) 3112.94 2122.37i 0.138352 0.0943265i −0.492166 0.870501i \(-0.663795\pi\)
0.630518 + 0.776175i \(0.282843\pi\)
\(798\) −3319.02 + 44289.2i −0.147233 + 1.96469i
\(799\) 23948.7 7387.20i 1.06038 0.327084i
\(800\) −3298.37 497.150i −0.145769 0.0219711i
\(801\) 4360.50 5467.90i 0.192348 0.241197i
\(802\) −8106.24 5526.74i −0.356909 0.243337i
\(803\) 28730.8 26658.3i 1.26263 1.17155i
\(804\) 422.336 1076.10i 0.0185257 0.0472027i
\(805\) −9009.85 2779.17i −0.394479 0.121681i
\(806\) −12834.9 6180.96i −0.560905 0.270118i
\(807\) −1374.94 3503.29i −0.0599755 0.152815i
\(808\) −1038.82 13862.0i −0.0452295 0.603545i
\(809\) −7849.79 9843.32i −0.341142 0.427778i 0.581434 0.813593i \(-0.302492\pi\)
−0.922576 + 0.385815i \(0.873920\pi\)
\(810\) 15194.4 + 26317.5i 0.659108 + 1.14161i
\(811\) −14385.6 + 24916.6i −0.622869 + 1.07884i 0.366080 + 0.930584i \(0.380700\pi\)
−0.988949 + 0.148257i \(0.952634\pi\)
\(812\) −0.992435 + 0.149585i −4.28912e−5 + 6.46480e-6i
\(813\) −2244.84 + 1081.06i −0.0968389 + 0.0466352i
\(814\) −27816.1 25809.5i −1.19773 1.11133i
\(815\) 10996.3 + 48177.8i 0.472616 + 2.07067i
\(816\) 19078.9 0.818500
\(817\) −44736.9 5945.21i −1.91572 0.254586i
\(818\) 5197.94 0.222178
\(819\) 773.563 + 3389.20i 0.0330043 + 0.144601i
\(820\) 183.538 + 170.298i 0.00781636 + 0.00725252i
\(821\) −4185.18 + 2015.48i −0.177910 + 0.0856767i −0.520719 0.853728i \(-0.674336\pi\)
0.342809 + 0.939405i \(0.388622\pi\)
\(822\) −38014.2 + 5729.71i −1.61301 + 0.243123i
\(823\) 8054.93 13951.6i 0.341163 0.590912i −0.643486 0.765458i \(-0.722512\pi\)
0.984649 + 0.174546i \(0.0558458\pi\)
\(824\) −4828.76 8363.66i −0.204148 0.353595i
\(825\) 10599.4 + 13291.2i 0.447302 + 0.560899i
\(826\) −1915.02 25554.2i −0.0806683 1.07644i
\(827\) −5964.84 15198.2i −0.250808 0.639047i 0.748913 0.662668i \(-0.230576\pi\)
−0.999721 + 0.0236205i \(0.992481\pi\)
\(828\) 190.553 + 91.7657i 0.00799781 + 0.00385154i
\(829\) 30052.1 + 9269.84i 1.25905 + 0.388365i 0.851276 0.524718i \(-0.175829\pi\)
0.407773 + 0.913083i \(0.366305\pi\)
\(830\) −792.136 + 2018.33i −0.0331270 + 0.0844063i
\(831\) −13985.6 + 12976.7i −0.583819 + 0.541705i
\(832\) 16966.9 + 11567.8i 0.706997 + 0.482022i
\(833\) −256.027 + 321.047i −0.0106492 + 0.0133537i
\(834\) −13711.8 2066.72i −0.569305 0.0858090i
\(835\) −44133.6 + 13613.4i −1.82911 + 0.564206i
\(836\) −623.383 + 8318.46i −0.0257896 + 0.344139i
\(837\) −15274.5 + 10414.0i −0.630780 + 0.430058i
\(838\) −634.930 + 2781.81i −0.0261734 + 0.114673i
\(839\) −448.844 + 1966.51i −0.0184694 + 0.0809196i −0.983323 0.181869i \(-0.941785\pi\)
0.964853 + 0.262789i \(0.0846423\pi\)
\(840\) 28903.4 19706.0i 1.18722 0.809432i
\(841\) −1822.59 + 24320.8i −0.0747301 + 0.997204i
\(842\) −22427.0 + 6917.82i −0.917918 + 0.283140i
\(843\) 7050.75 + 1062.73i 0.288067 + 0.0434191i
\(844\) 3186.36 3995.57i 0.129952 0.162954i
\(845\) −9858.19 6721.20i −0.401340 0.273629i
\(846\) 3904.05 3622.43i 0.158657 0.147212i
\(847\) −5286.83 + 13470.6i −0.214472 + 0.546465i
\(848\) −19648.5 6060.75i −0.795673 0.245433i
\(849\) 23797.6 + 11460.3i 0.961994 + 0.463272i
\(850\) −3931.87 10018.3i −0.158661 0.404263i
\(851\) 862.197 + 11505.2i 0.0347306 + 0.463448i
\(852\) 1666.48 + 2089.70i 0.0670103 + 0.0840282i
\(853\) 20599.9 + 35680.1i 0.826880 + 1.43220i 0.900474 + 0.434910i \(0.143220\pi\)
−0.0735942 + 0.997288i \(0.523447\pi\)
\(854\) 8086.85 14006.8i 0.324035 0.561246i
\(855\) −11124.9 + 1676.82i −0.444989 + 0.0670712i
\(856\) 24744.1 11916.1i 0.988009 0.475800i
\(857\) −26020.3 24143.3i −1.03715 0.962333i −0.0378308 0.999284i \(-0.512045\pi\)
−0.999317 + 0.0369516i \(0.988235\pi\)
\(858\) −5531.03 24233.0i −0.220077 0.964222i
\(859\) −40702.2 −1.61669 −0.808347 0.588707i \(-0.799637\pi\)
−0.808347 + 0.588707i \(0.799637\pi\)
\(860\) 2276.51 + 3788.50i 0.0902653 + 0.150217i
\(861\) −1691.78 −0.0669637
\(862\) 5154.17 + 22581.9i 0.203656 + 0.892276i
\(863\) 6646.98 + 6167.50i 0.262185 + 0.243272i 0.800301 0.599599i \(-0.204673\pi\)
−0.538115 + 0.842871i \(0.680864\pi\)
\(864\) 5702.28 2746.07i 0.224532 0.108129i
\(865\) −24819.3 + 3740.90i −0.975584 + 0.147046i
\(866\) 2381.67 4125.17i 0.0934554 0.161870i
\(867\) 2743.17 + 4751.31i 0.107454 + 0.186116i
\(868\) 1972.57 + 2473.52i 0.0771351 + 0.0967243i
\(869\) 3620.39 + 48310.7i 0.141327 + 1.88588i
\(870\) 3.53595 + 9.00945i 0.000137793 + 0.000351091i
\(871\) 5907.38 + 2844.84i 0.229809 + 0.110670i
\(872\) 4388.96 + 1353.81i 0.170446 + 0.0525756i
\(873\) 1471.64 3749.67i 0.0570531 0.145369i
\(874\) −11234.5 + 10424.1i −0.434799 + 0.403434i
\(875\) 12702.8 + 8660.65i 0.490782 + 0.334610i
\(876\) 3427.64 4298.12i 0.132202 0.165776i
\(877\) −8197.42 1235.56i −0.315630 0.0475735i −0.0106829 0.999943i \(-0.503401\pi\)
−0.304947 + 0.952369i \(0.598639\pi\)
\(878\) −11622.0 + 3584.90i −0.446722 + 0.137795i
\(879\) −3305.03 + 44102.6i −0.126821 + 1.69231i
\(880\) −28048.8 + 19123.3i −1.07446 + 0.732554i
\(881\) 9160.28 40133.8i 0.350304 1.53478i −0.426177 0.904640i \(-0.640140\pi\)
0.776481 0.630141i \(-0.217003\pi\)
\(882\) −19.4173 + 85.0728i −0.000741287 + 0.00324779i
\(883\) −24756.7 + 16878.8i −0.943522 + 0.643282i −0.934229 0.356675i \(-0.883911\pi\)
−0.00929312 + 0.999957i \(0.502958\pi\)
\(884\) 194.611 2596.91i 0.00740439 0.0988048i
\(885\) 39080.2 12054.6i 1.48437 0.457867i
\(886\) 17445.6 + 2629.50i 0.661509 + 0.0997064i
\(887\) −5712.96 + 7163.82i −0.216260 + 0.271181i −0.878114 0.478451i \(-0.841198\pi\)
0.661854 + 0.749632i \(0.269770\pi\)
\(888\) −35367.7 24113.3i −1.33656 0.911249i
\(889\) 24792.3 23003.9i 0.935330 0.867859i
\(890\) 18132.7 46201.3i 0.682932 1.74008i
\(891\) −36853.3 11367.7i −1.38567 0.427423i
\(892\) −6685.35 3219.50i −0.250944 0.120848i
\(893\) −23333.6 59453.0i −0.874388 2.22790i
\(894\) −2461.21 32842.6i −0.0920752 1.22866i
\(895\) −11278.1 14142.3i −0.421213 0.528184i
\(896\) 9964.46 + 17258.9i 0.371528 + 0.643505i
\(897\) −3778.81 + 6545.10i −0.140659 + 0.243628i
\(898\) 18426.5 2777.34i 0.684743 0.103208i
\(899\) −6.34253 + 3.05440i −0.000235301 + 0.000113315i
\(900\) 277.451 + 257.437i 0.0102760 + 0.00953470i
\(901\) 5359.12 + 23479.9i 0.198156 + 0.868177i
\(902\) 1920.00 0.0708747
\(903\) −28687.7 8302.68i −1.05722 0.305976i
\(904\) −14754.0 −0.542821
\(905\) −2596.34 11375.3i −0.0953651 0.417822i
\(906\) −4969.06 4610.61i −0.182214 0.169070i
\(907\) −4713.83 + 2270.06i −0.172569 + 0.0831048i −0.518174 0.855275i \(-0.673388\pi\)
0.345605 + 0.938380i \(0.387674\pi\)
\(908\) −557.279 + 83.9963i −0.0203678 + 0.00306995i
\(909\) −1479.25 + 2562.13i −0.0539753 + 0.0934880i
\(910\) 12335.4 + 21365.5i 0.449355 + 0.778305i
\(911\) 5100.09 + 6395.31i 0.185481 + 0.232586i 0.865875 0.500261i \(-0.166762\pi\)
−0.680393 + 0.732847i \(0.738191\pi\)
\(912\) −3633.41 48484.5i −0.131923 1.76040i
\(913\) −1005.31 2561.48i −0.0364412 0.0928506i
\(914\) 6206.19 + 2988.74i 0.224598 + 0.108161i
\(915\) 24665.4 + 7608.28i 0.891163 + 0.274887i
\(916\) 498.702 1270.67i 0.0179886 0.0458343i
\(917\) 35519.9 32957.6i 1.27914 1.18687i
\(918\) 16872.0 + 11503.2i 0.606602 + 0.413574i
\(919\) 20206.2 25337.8i 0.725291 0.909486i −0.273334 0.961919i \(-0.588126\pi\)
0.998624 + 0.0524337i \(0.0166978\pi\)
\(920\) 11936.4 + 1799.12i 0.427751 + 0.0644731i
\(921\) 49316.5 15212.1i 1.76442 0.544252i
\(922\) −1944.12 + 25942.5i −0.0694427 + 0.926648i
\(923\) −12525.7 + 8539.88i −0.446683 + 0.304543i
\(924\) −1228.36 + 5381.80i −0.0437339 + 0.191611i
\(925\) −4594.38 + 20129.3i −0.163311 + 0.715510i
\(926\) 3048.78 2078.62i 0.108196 0.0737665i
\(927\) −153.599 + 2049.64i −0.00544214 + 0.0726203i
\(928\) 2.30300 0.710383i 8.14653e−5 2.51287e-5i
\(929\) −27779.9 4187.15i −0.981087 0.147875i −0.361134 0.932514i \(-0.617610\pi\)
−0.619953 + 0.784639i \(0.712848\pi\)
\(930\) 19022.1 23853.0i 0.670709 0.841043i
\(931\) 864.621 + 589.489i 0.0304370 + 0.0207516i
\(932\) 1115.40 1034.94i 0.0392018 0.0363740i
\(933\) 11106.0 28297.5i 0.389703 0.992946i
\(934\) −11723.5 3616.23i −0.410713 0.126688i
\(935\) 35824.2 + 17252.0i 1.25302 + 0.603424i
\(936\) −1626.00 4142.98i −0.0567815 0.144677i
\(937\) 1161.83 + 15503.5i 0.0405072 + 0.540532i 0.980135 + 0.198333i \(0.0635526\pi\)
−0.939628 + 0.342199i \(0.888828\pi\)
\(938\) 5485.87 + 6879.07i 0.190960 + 0.239456i
\(939\) −10436.9 18077.2i −0.362721 0.628250i
\(940\) −3127.49 + 5416.96i −0.108518 + 0.187959i
\(941\) −5015.43 + 755.955i −0.173750 + 0.0261885i −0.235341 0.971913i \(-0.575621\pi\)
0.0615911 + 0.998101i \(0.480383\pi\)
\(942\) −37203.3 + 17916.2i −1.28678 + 0.619682i
\(943\) −427.943 397.073i −0.0147781 0.0137121i
\(944\) 6242.42 + 27349.8i 0.215226 + 0.942967i
\(945\) 32015.4 1.10208
\(946\) 32557.6 + 9422.70i 1.11896 + 0.323846i
\(947\) 21296.0 0.730757 0.365378 0.930859i \(-0.380940\pi\)
0.365378 + 0.930859i \(0.380940\pi\)
\(948\) 1512.11 + 6624.98i 0.0518049 + 0.226972i
\(949\) 22857.3 + 21208.5i 0.781855 + 0.725455i
\(950\) −24710.2 + 11899.8i −0.843898 + 0.406400i
\(951\) 25350.1 3820.91i 0.864387 0.130285i
\(952\) 14052.7 24340.1i 0.478416 0.828641i
\(953\) 24237.9 + 41981.2i 0.823863 + 1.42697i 0.902785 + 0.430092i \(0.141519\pi\)
−0.0789215 + 0.996881i \(0.525148\pi\)
\(954\) 3190.91 + 4001.28i 0.108291 + 0.135793i
\(955\) −3249.54 43362.1i −0.110108 1.46928i
\(956\) −1530.75 3900.29i −0.0517866 0.131950i
\(957\) −11.0666 5.32941i −0.000373807 0.000180016i
\(958\) −14329.8 4420.16i −0.483272 0.149070i
\(959\) −17691.6 + 45077.4i −0.595715 + 1.51786i
\(960\) −32238.8 + 29913.2i −1.08386 + 1.00567i
\(961\) −6279.50 4281.29i −0.210785 0.143711i
\(962\) 18822.1 23602.2i 0.630820 0.791024i
\(963\) −5779.79 871.163i −0.193407 0.0291514i
\(964\) 1961.39 605.008i 0.0655311 0.0202137i
\(965\) −2284.66 + 30486.6i −0.0762132 + 1.01699i
\(966\) −8379.59 + 5713.10i −0.279098 + 0.190286i
\(967\) −6163.08 + 27002.2i −0.204955 + 0.897966i 0.762912 + 0.646502i \(0.223769\pi\)
−0.967867 + 0.251463i \(0.919088\pi\)
\(968\) 4122.54 18062.0i 0.136884 0.599727i
\(969\) −47052.5 + 32079.8i −1.55990 + 1.06352i
\(970\) 2136.26 28506.4i 0.0707125 0.943593i
\(971\) 15783.1 4868.44i 0.521631 0.160902i −0.0227478 0.999741i \(-0.507241\pi\)
0.544379 + 0.838839i \(0.316765\pi\)
\(972\) −1585.39 238.959i −0.0523162 0.00788540i
\(973\) −10890.5 + 13656.2i −0.358820 + 0.449947i
\(974\) 13342.7 + 9096.89i 0.438940 + 0.299264i
\(975\) −9914.37 + 9199.19i −0.325655 + 0.302164i
\(976\) −6468.63 + 16481.8i −0.212147 + 0.540543i
\(977\) −27211.1 8393.52i −0.891055 0.274854i −0.184770 0.982782i \(-0.559154\pi\)
−0.706285 + 0.707928i \(0.749630\pi\)
\(978\) 47890.2 + 23062.7i 1.56581 + 0.754054i
\(979\) 23012.4 + 58634.5i 0.751254 + 1.91416i
\(980\) −7.65876 102.199i −0.000249643 0.00333125i
\(981\) −609.474 764.256i −0.0198359 0.0248734i
\(982\) −13802.5 23906.7i −0.448530 0.776876i
\(983\) 5549.55 9612.09i 0.180064 0.311880i −0.761838 0.647768i \(-0.775703\pi\)
0.941902 + 0.335887i \(0.109036\pi\)
\(984\) 2141.72 322.813i 0.0693858 0.0104582i
\(985\) 19617.1 9447.12i 0.634573 0.305594i
\(986\) 5.70019 + 5.28900i 0.000184109 + 0.000170828i
\(987\) −9404.81 41205.1i −0.303301 1.32885i
\(988\) −6636.47 −0.213698
\(989\) −5307.98 8833.41i −0.170661 0.284010i
\(990\) 8449.46 0.271254
\(991\) −9464.88 41468.3i −0.303392 1.32925i −0.864970 0.501824i \(-0.832662\pi\)
0.561577 0.827424i \(-0.310195\pi\)
\(992\) −5569.14 5167.40i −0.178246 0.165388i
\(993\) 5414.05 2607.27i 0.173021 0.0833225i
\(994\) −20116.4 + 3032.06i −0.641904 + 0.0967515i
\(995\) 17756.0 30754.3i 0.565732 0.979877i
\(996\) −192.985 334.259i −0.00613951 0.0106339i
\(997\) −22898.6 28714.0i −0.727389 0.912116i 0.271342 0.962483i \(-0.412532\pi\)
−0.998731 + 0.0503666i \(0.983961\pi\)
\(998\) 322.124 + 4298.45i 0.0102171 + 0.136338i
\(999\) −14312.5 36467.6i −0.453281 1.15494i
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 43.4.g.a.10.4 120
43.13 even 21 inner 43.4.g.a.13.4 yes 120
43.20 odd 42 1849.4.a.k.1.20 60
43.23 even 21 1849.4.a.l.1.41 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.g.a.10.4 120 1.1 even 1 trivial
43.4.g.a.13.4 yes 120 43.13 even 21 inner
1849.4.a.k.1.20 60 43.20 odd 42
1849.4.a.l.1.41 60 43.23 even 21