Properties

Label 147.4.o.a.101.27
Level $147$
Weight $4$
Character 147.101
Analytic conductor $8.673$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,4,Mod(5,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 29]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.o (of order \(42\), 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: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 101.27
Character \(\chi\) \(=\) 147.101
Dual form 147.4.o.a.131.27

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.283103 - 0.111110i) q^{2} +(-4.90886 + 1.70386i) q^{3} +(-5.79661 - 5.37847i) q^{4} +(-14.9795 - 10.2129i) q^{5} +(1.57903 + 0.0630541i) q^{6} +(-13.0100 + 13.1810i) q^{7} +(2.09908 + 4.35878i) q^{8} +(21.1937 - 16.7280i) q^{9} +O(q^{10})\) \(q+(-0.283103 - 0.111110i) q^{2} +(-4.90886 + 1.70386i) q^{3} +(-5.79661 - 5.37847i) q^{4} +(-14.9795 - 10.2129i) q^{5} +(1.57903 + 0.0630541i) q^{6} +(-13.0100 + 13.1810i) q^{7} +(2.09908 + 4.35878i) q^{8} +(21.1937 - 16.7280i) q^{9} +(3.10600 + 4.55566i) q^{10} +(4.06296 + 26.9560i) q^{11} +(37.6189 + 16.5255i) q^{12} +(40.2721 - 32.1159i) q^{13} +(5.14771 - 2.28604i) q^{14} +(90.9335 + 24.6105i) q^{15} +(4.61748 + 61.6160i) q^{16} +(-81.2257 - 25.0548i) q^{17} +(-7.85865 + 2.38091i) q^{18} +(94.1016 - 54.3296i) q^{19} +(31.9009 + 139.767i) q^{20} +(41.4057 - 86.8710i) q^{21} +(1.84483 - 8.08274i) q^{22} +(8.40103 + 27.2355i) q^{23} +(-17.7308 - 17.8201i) q^{24} +(74.4157 + 189.608i) q^{25} +(-14.9695 + 4.61749i) q^{26} +(-75.5348 + 118.226i) q^{27} +(146.308 - 6.43121i) q^{28} +(-251.444 + 57.3904i) q^{29} +(-23.0091 - 17.0709i) q^{30} +(33.3614 + 19.2612i) q^{31} +(16.9468 - 54.9403i) q^{32} +(-65.8736 - 125.400i) q^{33} +(20.2114 + 16.1180i) q^{34} +(329.500 - 64.5757i) q^{35} +(-212.823 - 17.0241i) q^{36} +(-84.6140 + 78.5103i) q^{37} +(-32.6770 + 4.92526i) q^{38} +(-142.969 + 226.270i) q^{39} +(13.0725 - 86.7301i) q^{40} +(416.591 - 200.620i) q^{41} +(-21.3743 + 19.9928i) q^{42} +(296.963 + 143.010i) q^{43} +(121.430 - 178.106i) q^{44} +(-488.312 + 34.1286i) q^{45} +(0.647769 - 8.64388i) q^{46} +(67.7263 - 172.564i) q^{47} +(-127.651 - 294.596i) q^{48} +(-4.47846 - 342.971i) q^{49} -61.9469i q^{50} +(441.415 - 15.4067i) q^{51} +(-406.176 - 30.4387i) q^{52} +(-200.228 + 215.795i) q^{53} +(34.5202 - 25.0776i) q^{54} +(214.436 - 445.282i) q^{55} +(-84.7623 - 29.0399i) q^{56} +(-369.361 + 427.032i) q^{57} +(77.5610 + 11.6904i) q^{58} +(-433.618 + 295.636i) q^{59} +(-394.740 - 631.741i) q^{60} +(467.341 + 503.674i) q^{61} +(-7.30461 - 9.15969i) q^{62} +(-55.2390 + 496.987i) q^{63} +(297.295 - 372.796i) q^{64} +(-931.252 + 69.7877i) q^{65} +(4.71583 + 42.8204i) q^{66} +(-123.279 + 213.526i) q^{67} +(336.077 + 582.103i) q^{68} +(-87.6448 - 119.381i) q^{69} +(-100.457 - 18.3291i) q^{70} +(306.770 + 70.0182i) q^{71} +(117.401 + 57.2655i) q^{72} +(-263.143 + 103.276i) q^{73} +(32.6777 - 12.8251i) q^{74} +(-688.361 - 803.965i) q^{75} +(-837.680 - 191.195i) q^{76} +(-408.166 - 297.144i) q^{77} +(65.6157 - 48.1726i) q^{78} +(52.8640 + 91.5632i) q^{79} +(560.107 - 970.135i) q^{80} +(169.348 - 709.057i) q^{81} +(-140.229 + 10.5087i) q^{82} +(280.931 - 352.277i) q^{83} +(-707.246 + 280.858i) q^{84} +(960.840 + 1204.86i) q^{85} +(-68.1814 - 73.4821i) q^{86} +(1136.52 - 710.146i) q^{87} +(-108.967 + 74.2923i) q^{88} +(1028.52 + 155.025i) q^{89} +(142.035 + 44.5943i) q^{90} +(-100.620 + 948.656i) q^{91} +(97.7877 - 203.058i) q^{92} +(-196.585 - 37.7074i) q^{93} +(-38.3470 + 41.3283i) q^{94} +(-1964.46 - 147.216i) q^{95} +(10.4209 + 298.569i) q^{96} -214.821i q^{97} +(-36.8395 + 97.5936i) q^{98} +(537.028 + 503.332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9} - 58 q^{10} - 207 q^{12} - 28 q^{13} - 148 q^{15} + 726 q^{16} - 81 q^{18} - 342 q^{19} - 371 q^{21} - 156 q^{22} - 428 q^{24} + 1250 q^{25} - 56 q^{27} + 700 q^{28} + 389 q^{30} + 888 q^{31} + 841 q^{33} - 532 q^{34} - 38 q^{36} + 1178 q^{37} - 180 q^{39} + 194 q^{40} + 56 q^{42} + 1296 q^{43} - 617 q^{45} - 6756 q^{46} - 2380 q^{49} + 787 q^{51} - 5204 q^{52} + 4144 q^{54} - 5698 q^{55} + 863 q^{57} - 3066 q^{58} + 2820 q^{60} + 1492 q^{61} - 1085 q^{63} + 7648 q^{64} + 2568 q^{66} + 142 q^{67} - 5474 q^{69} + 5180 q^{70} + 1278 q^{72} + 2876 q^{73} - 1754 q^{75} + 7644 q^{76} + 936 q^{78} - 992 q^{79} + 911 q^{81} + 1022 q^{82} + 7868 q^{84} + 2672 q^{85} - 196 q^{87} + 370 q^{88} - 18767 q^{90} - 2254 q^{91} - 11096 q^{93} - 3628 q^{94} - 24248 q^{96} + 10982 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.283103 0.111110i −0.100092 0.0392832i 0.314767 0.949169i \(-0.398074\pi\)
−0.414859 + 0.909886i \(0.636169\pi\)
\(3\) −4.90886 + 1.70386i −0.944710 + 0.327908i
\(4\) −5.79661 5.37847i −0.724577 0.672309i
\(5\) −14.9795 10.2129i −1.33981 0.913466i −0.340170 0.940364i \(-0.610485\pi\)
−0.999638 + 0.0268981i \(0.991437\pi\)
\(6\) 1.57903 + 0.0630541i 0.107439 + 0.00429029i
\(7\) −13.0100 + 13.1810i −0.702475 + 0.711708i
\(8\) 2.09908 + 4.35878i 0.0927671 + 0.192633i
\(9\) 21.1937 16.7280i 0.784953 0.619555i
\(10\) 3.10600 + 4.55566i 0.0982202 + 0.144063i
\(11\) 4.06296 + 26.9560i 0.111366 + 0.738866i 0.972910 + 0.231183i \(0.0742597\pi\)
−0.861544 + 0.507683i \(0.830502\pi\)
\(12\) 37.6189 + 16.5255i 0.904970 + 0.397542i
\(13\) 40.2721 32.1159i 0.859190 0.685181i −0.0913380 0.995820i \(-0.529114\pi\)
0.950528 + 0.310639i \(0.100543\pi\)
\(14\) 5.14771 2.28604i 0.0982703 0.0436408i
\(15\) 90.9335 + 24.6105i 1.56526 + 0.423626i
\(16\) 4.61748 + 61.6160i 0.0721481 + 0.962749i
\(17\) −81.2257 25.0548i −1.15883 0.357452i −0.345028 0.938593i \(-0.612130\pi\)
−0.813803 + 0.581141i \(0.802607\pi\)
\(18\) −7.85865 + 2.38091i −0.102906 + 0.0311770i
\(19\) 94.1016 54.3296i 1.13623 0.656003i 0.190736 0.981641i \(-0.438913\pi\)
0.945494 + 0.325638i \(0.105579\pi\)
\(20\) 31.9009 + 139.767i 0.356663 + 1.56264i
\(21\) 41.4057 86.8710i 0.430261 0.902705i
\(22\) 1.84483 8.08274i 0.0178782 0.0783294i
\(23\) 8.40103 + 27.2355i 0.0761624 + 0.246913i 0.985645 0.168829i \(-0.0539984\pi\)
−0.909483 + 0.415741i \(0.863522\pi\)
\(24\) −17.7308 17.8201i −0.150804 0.151563i
\(25\) 74.4157 + 189.608i 0.595325 + 1.51686i
\(26\) −14.9695 + 4.61749i −0.112914 + 0.0348294i
\(27\) −75.5348 + 118.226i −0.538396 + 0.842692i
\(28\) 146.308 6.43121i 0.987485 0.0434066i
\(29\) −251.444 + 57.3904i −1.61007 + 0.367487i −0.930547 0.366171i \(-0.880668\pi\)
−0.679518 + 0.733658i \(0.737811\pi\)
\(30\) −23.0091 17.0709i −0.140029 0.103890i
\(31\) 33.3614 + 19.2612i 0.193287 + 0.111594i 0.593520 0.804819i \(-0.297738\pi\)
−0.400234 + 0.916413i \(0.631071\pi\)
\(32\) 16.9468 54.9403i 0.0936190 0.303505i
\(33\) −65.8736 125.400i −0.347489 0.661496i
\(34\) 20.2114 + 16.1180i 0.101948 + 0.0813007i
\(35\) 329.500 64.5757i 1.59130 0.311865i
\(36\) −212.823 17.0241i −0.985291 0.0788155i
\(37\) −84.6140 + 78.5103i −0.375958 + 0.348838i −0.845408 0.534121i \(-0.820643\pi\)
0.469450 + 0.882959i \(0.344452\pi\)
\(38\) −32.6770 + 4.92526i −0.139497 + 0.0210259i
\(39\) −142.969 + 226.270i −0.587009 + 0.929032i
\(40\) 13.0725 86.7301i 0.0516734 0.342831i
\(41\) 416.591 200.620i 1.58684 0.764184i 0.587848 0.808971i \(-0.299975\pi\)
0.998997 + 0.0447873i \(0.0142610\pi\)
\(42\) −21.3743 + 19.9928i −0.0785268 + 0.0734515i
\(43\) 296.963 + 143.010i 1.05317 + 0.507182i 0.878648 0.477470i \(-0.158446\pi\)
0.174527 + 0.984652i \(0.444161\pi\)
\(44\) 121.430 178.106i 0.416053 0.610238i
\(45\) −488.312 + 34.1286i −1.61763 + 0.113058i
\(46\) 0.647769 8.64388i 0.00207627 0.0277059i
\(47\) 67.7263 172.564i 0.210189 0.535554i −0.786433 0.617676i \(-0.788074\pi\)
0.996622 + 0.0821219i \(0.0261697\pi\)
\(48\) −127.651 294.596i −0.383852 0.885861i
\(49\) −4.47846 342.971i −0.0130567 0.999915i
\(50\) 61.9469i 0.175212i
\(51\) 441.415 15.4067i 1.21197 0.0423013i
\(52\) −406.176 30.4387i −1.08320 0.0811748i
\(53\) −200.228 + 215.795i −0.518933 + 0.559277i −0.937085 0.349100i \(-0.886487\pi\)
0.418152 + 0.908377i \(0.362678\pi\)
\(54\) 34.5202 25.0776i 0.0869927 0.0631968i
\(55\) 214.436 445.282i 0.525720 1.09167i
\(56\) −84.7623 29.0399i −0.202265 0.0692968i
\(57\) −369.361 + 427.032i −0.858299 + 0.992311i
\(58\) 77.5610 + 11.6904i 0.175591 + 0.0264660i
\(59\) −433.618 + 295.636i −0.956818 + 0.652348i −0.937691 0.347469i \(-0.887041\pi\)
−0.0191270 + 0.999817i \(0.506089\pi\)
\(60\) −394.740 631.741i −0.849345 1.35929i
\(61\) 467.341 + 503.674i 0.980933 + 1.05719i 0.998354 + 0.0573463i \(0.0182639\pi\)
−0.0174212 + 0.999848i \(0.505546\pi\)
\(62\) −7.30461 9.15969i −0.0149627 0.0187626i
\(63\) −55.2390 + 496.987i −0.110468 + 0.993880i
\(64\) 297.295 372.796i 0.580654 0.728118i
\(65\) −931.252 + 69.7877i −1.77704 + 0.133171i
\(66\) 4.71583 + 42.8204i 0.00879513 + 0.0798609i
\(67\) −123.279 + 213.526i −0.224791 + 0.389349i −0.956257 0.292529i \(-0.905503\pi\)
0.731466 + 0.681878i \(0.238836\pi\)
\(68\) 336.077 + 582.103i 0.599344 + 1.03809i
\(69\) −87.6448 119.381i −0.152916 0.208286i
\(70\) −100.457 18.3291i −0.171528 0.0312963i
\(71\) 306.770 + 70.0182i 0.512773 + 0.117037i 0.471075 0.882093i \(-0.343866\pi\)
0.0416979 + 0.999130i \(0.486723\pi\)
\(72\) 117.401 + 57.2655i 0.192165 + 0.0937334i
\(73\) −263.143 + 103.276i −0.421899 + 0.165583i −0.566786 0.823865i \(-0.691813\pi\)
0.144887 + 0.989448i \(0.453718\pi\)
\(74\) 32.6777 12.8251i 0.0513339 0.0201471i
\(75\) −688.361 803.965i −1.05980 1.23778i
\(76\) −837.680 191.195i −1.26432 0.288573i
\(77\) −408.166 297.144i −0.604089 0.439775i
\(78\) 65.6157 48.1726i 0.0952503 0.0699291i
\(79\) 52.8640 + 91.5632i 0.0752870 + 0.130401i 0.901211 0.433381i \(-0.142679\pi\)
−0.825924 + 0.563781i \(0.809346\pi\)
\(80\) 560.107 970.135i 0.782774 1.35580i
\(81\) 169.348 709.057i 0.232302 0.972644i
\(82\) −140.229 + 10.5087i −0.188850 + 0.0141524i
\(83\) 280.931 352.277i 0.371521 0.465872i −0.560565 0.828110i \(-0.689416\pi\)
0.932085 + 0.362238i \(0.117987\pi\)
\(84\) −707.246 + 280.858i −0.918653 + 0.364811i
\(85\) 960.840 + 1204.86i 1.22609 + 1.53747i
\(86\) −68.1814 73.4821i −0.0854906 0.0921369i
\(87\) 1136.52 710.146i 1.40054 0.875122i
\(88\) −108.967 + 74.2923i −0.131999 + 0.0899953i
\(89\) 1028.52 + 155.025i 1.22498 + 0.184636i 0.729499 0.683982i \(-0.239753\pi\)
0.495482 + 0.868618i \(0.334992\pi\)
\(90\) 142.035 + 44.5943i 0.166353 + 0.0522295i
\(91\) −100.620 + 948.656i −0.115911 + 1.09282i
\(92\) 97.7877 203.058i 0.110816 0.230112i
\(93\) −196.585 37.7074i −0.219193 0.0420439i
\(94\) −38.3470 + 41.3283i −0.0420765 + 0.0453477i
\(95\) −1964.46 147.216i −2.12157 0.158989i
\(96\) 10.4209 + 298.569i 0.0110790 + 0.317423i
\(97\) 214.821i 0.224863i −0.993659 0.112432i \(-0.964136\pi\)
0.993659 0.112432i \(-0.0358639\pi\)
\(98\) −36.8395 + 97.5936i −0.0379730 + 0.100596i
\(99\) 537.028 + 503.332i 0.545186 + 0.510978i
\(100\) 588.442 1499.33i 0.588442 1.49933i
\(101\) −87.7814 + 1171.36i −0.0864809 + 1.15401i 0.770075 + 0.637953i \(0.220219\pi\)
−0.856556 + 0.516054i \(0.827400\pi\)
\(102\) −126.678 44.6838i −0.122970 0.0433760i
\(103\) −375.857 + 551.281i −0.359556 + 0.527372i −0.962811 0.270177i \(-0.912918\pi\)
0.603255 + 0.797549i \(0.293870\pi\)
\(104\) 224.521 + 108.123i 0.211693 + 0.101946i
\(105\) −1507.44 + 878.414i −1.40106 + 0.816423i
\(106\) 80.6620 38.8448i 0.0739112 0.0355938i
\(107\) −59.1189 + 392.228i −0.0534135 + 0.354375i 0.946120 + 0.323818i \(0.104966\pi\)
−0.999533 + 0.0305577i \(0.990272\pi\)
\(108\) 1073.72 279.051i 0.956658 0.248627i
\(109\) 1275.95 192.319i 1.12123 0.168999i 0.437842 0.899052i \(-0.355743\pi\)
0.683390 + 0.730053i \(0.260505\pi\)
\(110\) −110.183 + 102.235i −0.0955045 + 0.0886153i
\(111\) 281.587 529.566i 0.240785 0.452831i
\(112\) −872.235 740.762i −0.735879 0.624959i
\(113\) −753.352 600.778i −0.627163 0.500146i 0.257561 0.966262i \(-0.417081\pi\)
−0.884723 + 0.466117i \(0.845653\pi\)
\(114\) 152.015 79.8543i 0.124890 0.0656056i
\(115\) 152.309 493.773i 0.123503 0.400387i
\(116\) 1766.19 + 1019.71i 1.41368 + 0.816189i
\(117\) 316.281 1354.33i 0.249916 1.07015i
\(118\) 155.607 35.5162i 0.121396 0.0277079i
\(119\) 1387.00 744.674i 1.06845 0.573648i
\(120\) 83.6050 + 448.019i 0.0636005 + 0.340820i
\(121\) 561.751 173.277i 0.422052 0.130186i
\(122\) −76.3426 194.518i −0.0566535 0.144351i
\(123\) −1703.16 + 1694.63i −1.24853 + 1.24227i
\(124\) −89.7874 291.083i −0.0650253 0.210807i
\(125\) 317.448 1390.83i 0.227147 0.995198i
\(126\) 70.8583 134.561i 0.0500997 0.0951399i
\(127\) 464.885 + 2036.79i 0.324818 + 1.42312i 0.828867 + 0.559445i \(0.188986\pi\)
−0.504050 + 0.863675i \(0.668157\pi\)
\(128\) −523.921 + 302.486i −0.361785 + 0.208877i
\(129\) −1701.42 196.032i −1.16125 0.133796i
\(130\) 271.394 + 83.7140i 0.183099 + 0.0564785i
\(131\) 117.404 + 1566.64i 0.0783024 + 1.04487i 0.888548 + 0.458783i \(0.151714\pi\)
−0.810246 + 0.586090i \(0.800667\pi\)
\(132\) −292.618 + 1081.20i −0.192948 + 0.712924i
\(133\) −508.145 + 1947.18i −0.331291 + 1.26949i
\(134\) 58.6256 46.7523i 0.0377946 0.0301402i
\(135\) 2338.90 999.548i 1.49112 0.637240i
\(136\) −61.2907 406.637i −0.0386444 0.256389i
\(137\) 345.472 + 506.714i 0.215443 + 0.315996i 0.918713 0.394926i \(-0.129230\pi\)
−0.703270 + 0.710923i \(0.748278\pi\)
\(138\) 11.5481 + 43.5352i 0.00712350 + 0.0268548i
\(139\) −1050.32 2181.00i −0.640910 1.33086i −0.927864 0.372920i \(-0.878357\pi\)
0.286953 0.957945i \(-0.407358\pi\)
\(140\) −2257.30 1397.88i −1.36269 0.843877i
\(141\) −38.4343 + 962.487i −0.0229557 + 0.574866i
\(142\) −79.0677 53.9074i −0.0467269 0.0318578i
\(143\) 1029.34 + 955.087i 0.601942 + 0.558520i
\(144\) 1128.57 + 1228.63i 0.653109 + 0.711013i
\(145\) 4352.62 + 1708.28i 2.49287 + 0.978378i
\(146\) 85.9716 0.0487333
\(147\) 606.358 + 1675.96i 0.340215 + 0.940348i
\(148\) 912.740 0.506938
\(149\) 3025.60 + 1187.46i 1.66353 + 0.652889i 0.995804 0.0915155i \(-0.0291711\pi\)
0.667729 + 0.744404i \(0.267266\pi\)
\(150\) 105.549 + 304.088i 0.0574535 + 0.165525i
\(151\) 282.104 + 261.754i 0.152035 + 0.141068i 0.752523 0.658566i \(-0.228837\pi\)
−0.600488 + 0.799634i \(0.705027\pi\)
\(152\) 434.337 + 296.126i 0.231773 + 0.158020i
\(153\) −2140.59 + 827.738i −1.13109 + 0.437377i
\(154\) 82.5374 + 129.473i 0.0431887 + 0.0677485i
\(155\) −303.026 629.240i −0.157030 0.326076i
\(156\) 2045.72 542.648i 1.04993 0.278504i
\(157\) −1427.60 2093.91i −0.725701 1.06441i −0.994855 0.101311i \(-0.967696\pi\)
0.269153 0.963097i \(-0.413256\pi\)
\(158\) −4.79240 31.7955i −0.00241306 0.0160096i
\(159\) 615.208 1400.47i 0.306850 0.698517i
\(160\) −814.953 + 649.903i −0.402673 + 0.321121i
\(161\) −468.289 243.600i −0.229232 0.119245i
\(162\) −126.726 + 181.920i −0.0614602 + 0.0882282i
\(163\) −28.3617 378.461i −0.0136286 0.181861i −0.999864 0.0165118i \(-0.994744\pi\)
0.986235 0.165349i \(-0.0528752\pi\)
\(164\) −3493.85 1077.71i −1.66356 0.513140i
\(165\) −293.940 + 2551.19i −0.138686 + 1.20370i
\(166\) −118.674 + 68.5163i −0.0554872 + 0.0320355i
\(167\) 337.252 + 1477.60i 0.156271 + 0.684670i 0.990984 + 0.133984i \(0.0427769\pi\)
−0.834712 + 0.550687i \(0.814366\pi\)
\(168\) 465.566 1.87037i 0.213805 0.000858943i
\(169\) 101.531 444.835i 0.0462133 0.202474i
\(170\) −138.145 447.857i −0.0623251 0.202053i
\(171\) 1085.54 2725.58i 0.485457 1.21889i
\(172\) −952.207 2426.18i −0.422123 1.07555i
\(173\) −3915.54 + 1207.78i −1.72077 + 0.530787i −0.988630 0.150369i \(-0.951954\pi\)
−0.732138 + 0.681156i \(0.761477\pi\)
\(174\) −400.655 + 74.7663i −0.174561 + 0.0325748i
\(175\) −3467.38 1485.93i −1.49777 0.641862i
\(176\) −1642.16 + 374.812i −0.703308 + 0.160525i
\(177\) 1624.85 2190.06i 0.690006 0.930027i
\(178\) −273.953 158.167i −0.115358 0.0666018i
\(179\) 544.149 1764.09i 0.227216 0.736615i −0.768134 0.640289i \(-0.778815\pi\)
0.995350 0.0963263i \(-0.0307092\pi\)
\(180\) 3014.12 + 2428.54i 1.24811 + 1.00563i
\(181\) −1066.13 850.213i −0.437818 0.349148i 0.379642 0.925134i \(-0.376047\pi\)
−0.817460 + 0.575985i \(0.804619\pi\)
\(182\) 133.891 257.387i 0.0545310 0.104829i
\(183\) −3152.30 1676.18i −1.27336 0.677086i
\(184\) −101.079 + 93.7877i −0.0404981 + 0.0375767i
\(185\) 2069.29 311.895i 0.822364 0.123951i
\(186\) 51.4641 + 32.5176i 0.0202878 + 0.0128188i
\(187\) 345.360 2291.31i 0.135055 0.896029i
\(188\) −1320.71 + 636.022i −0.512356 + 0.246738i
\(189\) −575.635 2533.75i −0.221541 0.975151i
\(190\) 539.786 + 259.947i 0.206106 + 0.0992555i
\(191\) 1185.93 1739.45i 0.449273 0.658963i −0.533066 0.846074i \(-0.678960\pi\)
0.982339 + 0.187111i \(0.0599125\pi\)
\(192\) −824.186 + 2336.55i −0.309794 + 0.878261i
\(193\) −320.793 + 4280.69i −0.119643 + 1.59653i 0.537830 + 0.843053i \(0.319244\pi\)
−0.657474 + 0.753478i \(0.728375\pi\)
\(194\) −23.8687 + 60.8164i −0.00883335 + 0.0225070i
\(195\) 4452.47 1929.30i 1.63512 0.708513i
\(196\) −1818.70 + 2012.16i −0.662791 + 0.733293i
\(197\) 2715.19i 0.981976i 0.871166 + 0.490988i \(0.163364\pi\)
−0.871166 + 0.490988i \(0.836636\pi\)
\(198\) −96.1092 202.164i −0.0344959 0.0725614i
\(199\) −938.098 70.3007i −0.334171 0.0250426i −0.0934117 0.995628i \(-0.529777\pi\)
−0.240759 + 0.970585i \(0.577396\pi\)
\(200\) −670.256 + 722.364i −0.236971 + 0.255394i
\(201\) 241.342 1258.22i 0.0846914 0.441532i
\(202\) 155.001 321.862i 0.0539892 0.112110i
\(203\) 2514.82 4060.93i 0.869488 1.40405i
\(204\) −2641.58 2284.83i −0.906605 0.784168i
\(205\) −8289.24 1249.40i −2.82412 0.425668i
\(206\) 167.659 114.308i 0.0567055 0.0386612i
\(207\) 633.644 + 436.689i 0.212760 + 0.146628i
\(208\) 2164.81 + 2333.11i 0.721647 + 0.777750i
\(209\) 1846.84 + 2315.86i 0.611236 + 0.766466i
\(210\) 524.360 81.1904i 0.172306 0.0266794i
\(211\) 842.011 1055.85i 0.274723 0.344491i −0.625260 0.780416i \(-0.715007\pi\)
0.899983 + 0.435925i \(0.143579\pi\)
\(212\) 2321.29 173.957i 0.752014 0.0563556i
\(213\) −1625.19 + 178.983i −0.522799 + 0.0575762i
\(214\) 60.3171 104.472i 0.0192673 0.0333719i
\(215\) −2987.83 5175.07i −0.947758 1.64157i
\(216\) −673.877 81.0733i −0.212276 0.0255386i
\(217\) −687.916 + 189.149i −0.215202 + 0.0591716i
\(218\) −382.595 87.3248i −0.118865 0.0271302i
\(219\) 1115.77 955.327i 0.344276 0.294772i
\(220\) −3637.94 + 1427.79i −1.11486 + 0.437551i
\(221\) −4075.79 + 1599.63i −1.24058 + 0.486890i
\(222\) −138.558 + 118.635i −0.0418892 + 0.0358659i
\(223\) 1606.92 + 366.769i 0.482544 + 0.110138i 0.456871 0.889533i \(-0.348970\pi\)
0.0256731 + 0.999670i \(0.491827\pi\)
\(224\) 503.690 + 938.152i 0.150242 + 0.279834i
\(225\) 4748.91 + 2773.68i 1.40708 + 0.821830i
\(226\) 146.524 + 253.787i 0.0431266 + 0.0746975i
\(227\) 2265.31 3923.63i 0.662351 1.14723i −0.317645 0.948210i \(-0.602892\pi\)
0.979996 0.199016i \(-0.0637747\pi\)
\(228\) 4437.82 488.740i 1.28904 0.141963i
\(229\) −5615.32 + 420.810i −1.62040 + 0.121432i −0.853766 0.520656i \(-0.825687\pi\)
−0.766631 + 0.642088i \(0.778068\pi\)
\(230\) −97.9819 + 122.865i −0.0280902 + 0.0352240i
\(231\) 2509.92 + 763.179i 0.714894 + 0.217374i
\(232\) −777.953 975.522i −0.220151 0.276061i
\(233\) 395.637 + 426.395i 0.111240 + 0.119889i 0.786217 0.617950i \(-0.212037\pi\)
−0.674977 + 0.737839i \(0.735846\pi\)
\(234\) −240.019 + 348.272i −0.0670535 + 0.0972960i
\(235\) −2776.88 + 1893.24i −0.770824 + 0.525539i
\(236\) 4103.59 + 618.516i 1.13187 + 0.170602i
\(237\) −415.513 359.398i −0.113884 0.0985038i
\(238\) −475.403 + 56.7105i −0.129478 + 0.0154454i
\(239\) 72.3809 150.301i 0.0195897 0.0406784i −0.890944 0.454112i \(-0.849956\pi\)
0.910534 + 0.413434i \(0.135671\pi\)
\(240\) −1096.51 + 5716.60i −0.294915 + 1.53752i
\(241\) 771.462 831.438i 0.206200 0.222231i −0.621481 0.783429i \(-0.713469\pi\)
0.827682 + 0.561198i \(0.189659\pi\)
\(242\) −178.286 13.3607i −0.0473581 0.00354900i
\(243\) 376.827 + 3769.21i 0.0994792 + 0.995040i
\(244\) 5433.19i 1.42551i
\(245\) −3435.63 + 5183.27i −0.895894 + 1.35162i
\(246\) 670.458 290.516i 0.173768 0.0752952i
\(247\) 2044.82 5210.12i 0.526757 1.34215i
\(248\) −13.9272 + 185.846i −0.00356605 + 0.0475857i
\(249\) −778.821 + 2207.94i −0.198216 + 0.561938i
\(250\) −244.405 + 358.477i −0.0618302 + 0.0906882i
\(251\) −3706.03 1784.73i −0.931963 0.448810i −0.0946358 0.995512i \(-0.530169\pi\)
−0.837327 + 0.546702i \(0.815883\pi\)
\(252\) 2993.23 2583.74i 0.748236 0.645874i
\(253\) −700.025 + 337.114i −0.173953 + 0.0837715i
\(254\) 94.6973 628.275i 0.0233930 0.155203i
\(255\) −6769.53 4277.32i −1.66245 1.05042i
\(256\) −3590.06 + 541.114i −0.876478 + 0.132108i
\(257\) 2091.82 1940.92i 0.507719 0.471095i −0.384225 0.923239i \(-0.625531\pi\)
0.891945 + 0.452145i \(0.149341\pi\)
\(258\) 459.896 + 244.541i 0.110976 + 0.0590096i
\(259\) 65.9844 2136.72i 0.0158304 0.512623i
\(260\) 5773.46 + 4604.18i 1.37713 + 1.09823i
\(261\) −4369.00 + 5422.46i −1.03615 + 1.28599i
\(262\) 140.832 456.566i 0.0332085 0.107659i
\(263\) 2849.11 + 1644.93i 0.667999 + 0.385669i 0.795318 0.606193i \(-0.207304\pi\)
−0.127319 + 0.991862i \(0.540637\pi\)
\(264\) 408.318 550.354i 0.0951904 0.128303i
\(265\) 5203.20 1187.60i 1.20615 0.275296i
\(266\) 360.208 494.793i 0.0830292 0.114052i
\(267\) −5313.01 + 991.464i −1.21779 + 0.227253i
\(268\) 1863.05 574.674i 0.424641 0.130984i
\(269\) −156.697 399.259i −0.0355168 0.0904953i 0.912015 0.410157i \(-0.134526\pi\)
−0.947532 + 0.319662i \(0.896431\pi\)
\(270\) −773.210 + 23.0999i −0.174282 + 0.00520672i
\(271\) 153.780 + 498.541i 0.0344703 + 0.111750i 0.971173 0.238376i \(-0.0766150\pi\)
−0.936703 + 0.350126i \(0.886139\pi\)
\(272\) 1168.72 5120.49i 0.260529 1.14145i
\(273\) −1122.45 4828.26i −0.248841 1.07040i
\(274\) −41.5032 181.837i −0.00915073 0.0400920i
\(275\) −4808.72 + 2776.32i −1.05446 + 0.608793i
\(276\) −134.043 + 1163.40i −0.0292335 + 0.253726i
\(277\) 2785.26 + 859.140i 0.604153 + 0.186356i 0.581716 0.813392i \(-0.302381\pi\)
0.0224366 + 0.999748i \(0.492858\pi\)
\(278\) 55.0168 + 734.148i 0.0118694 + 0.158386i
\(279\) 1029.26 149.853i 0.220860 0.0321557i
\(280\) 973.118 + 1300.67i 0.207696 + 0.277606i
\(281\) 3876.74 3091.60i 0.823014 0.656332i −0.118631 0.992938i \(-0.537851\pi\)
0.941645 + 0.336607i \(0.109279\pi\)
\(282\) 117.823 268.212i 0.0248802 0.0566377i
\(283\) 1297.76 + 8610.05i 0.272592 + 1.80853i 0.536409 + 0.843958i \(0.319780\pi\)
−0.263817 + 0.964573i \(0.584982\pi\)
\(284\) −1401.63 2055.82i −0.292858 0.429544i
\(285\) 9894.06 2624.49i 2.05640 0.545479i
\(286\) −185.289 384.758i −0.0383091 0.0795496i
\(287\) −2775.49 + 8101.17i −0.570843 + 1.66619i
\(288\) −559.874 1447.88i −0.114552 0.296239i
\(289\) 1910.56 + 1302.60i 0.388878 + 0.265133i
\(290\) −1042.43 967.237i −0.211082 0.195856i
\(291\) 366.024 + 1054.52i 0.0737345 + 0.212431i
\(292\) 2080.81 + 816.657i 0.417021 + 0.163669i
\(293\) 1019.76 0.203327 0.101664 0.994819i \(-0.467583\pi\)
0.101664 + 0.994819i \(0.467583\pi\)
\(294\) 14.5541 541.842i 0.00288712 0.107486i
\(295\) 9514.68 1.87785
\(296\) −519.821 204.015i −0.102074 0.0400612i
\(297\) −3493.80 1555.76i −0.682596 0.303955i
\(298\) −724.616 672.346i −0.140859 0.130698i
\(299\) 1213.02 + 827.023i 0.234618 + 0.159960i
\(300\) −333.938 + 8362.60i −0.0642663 + 1.60938i
\(301\) −5748.52 + 2053.72i −1.10079 + 0.393270i
\(302\) −50.7810 105.448i −0.00967589 0.0200922i
\(303\) −1564.93 5899.61i −0.296709 1.11856i
\(304\) 3782.08 + 5547.29i 0.713543 + 1.04658i
\(305\) −1856.59 12317.7i −0.348551 2.31249i
\(306\) 697.977 + 3.50549i 0.130394 + 0.000654886i
\(307\) 3146.10 2508.93i 0.584877 0.466424i −0.285793 0.958291i \(-0.592257\pi\)
0.870670 + 0.491868i \(0.163686\pi\)
\(308\) 767.802 + 3917.74i 0.142044 + 0.724785i
\(309\) 905.723 3346.57i 0.166747 0.616115i
\(310\) 15.8729 + 211.809i 0.00290812 + 0.0388062i
\(311\) 7989.76 + 2464.51i 1.45678 + 0.449356i 0.919177 0.393844i \(-0.128855\pi\)
0.537600 + 0.843200i \(0.319331\pi\)
\(312\) −1286.37 148.211i −0.233417 0.0268936i
\(313\) −2046.55 + 1181.58i −0.369578 + 0.213376i −0.673274 0.739393i \(-0.735113\pi\)
0.303696 + 0.952769i \(0.401779\pi\)
\(314\) 171.505 + 751.412i 0.0308235 + 0.135047i
\(315\) 5903.11 6880.47i 1.05588 1.23070i
\(316\) 186.038 815.084i 0.0331185 0.145101i
\(317\) 431.124 + 1397.67i 0.0763859 + 0.247637i 0.985710 0.168452i \(-0.0538767\pi\)
−0.909324 + 0.416089i \(0.863401\pi\)
\(318\) −329.772 + 328.120i −0.0581532 + 0.0578619i
\(319\) −2568.62 6544.73i −0.450831 1.14870i
\(320\) −8260.65 + 2548.07i −1.44308 + 0.445130i
\(321\) −378.096 2026.12i −0.0657422 0.352297i
\(322\) 105.508 + 120.995i 0.0182600 + 0.0209404i
\(323\) −9004.68 + 2055.26i −1.55119 + 0.354049i
\(324\) −4795.29 + 3199.29i −0.822238 + 0.548576i
\(325\) 9086.31 + 5245.99i 1.55082 + 0.895369i
\(326\) −34.0214 + 110.295i −0.00577998 + 0.0187382i
\(327\) −5935.79 + 3118.11i −1.00382 + 0.527315i
\(328\) 1748.92 + 1394.71i 0.294414 + 0.234787i
\(329\) 1393.45 + 3137.76i 0.233505 + 0.525807i
\(330\) 366.677 689.590i 0.0611664 0.115032i
\(331\) −1712.51 + 1588.97i −0.284374 + 0.263861i −0.809442 0.587200i \(-0.800230\pi\)
0.525068 + 0.851060i \(0.324040\pi\)
\(332\) −3523.16 + 531.031i −0.582405 + 0.0877834i
\(333\) −479.966 + 3079.35i −0.0789849 + 0.506749i
\(334\) 68.6984 455.784i 0.0112545 0.0746688i
\(335\) 4027.38 1939.48i 0.656833 0.316314i
\(336\) 5543.83 + 2150.13i 0.900121 + 0.349105i
\(337\) 3315.98 + 1596.89i 0.536002 + 0.258125i 0.682245 0.731124i \(-0.261004\pi\)
−0.146243 + 0.989249i \(0.546718\pi\)
\(338\) −78.1691 + 114.653i −0.0125794 + 0.0184506i
\(339\) 4721.74 + 1665.53i 0.756488 + 0.266841i
\(340\) 910.661 12151.9i 0.145257 1.93833i
\(341\) −383.659 + 977.547i −0.0609276 + 0.155241i
\(342\) −610.157 + 651.005i −0.0964722 + 0.102931i
\(343\) 4578.97 + 4403.03i 0.720819 + 0.693123i
\(344\) 1594.59i 0.249926i
\(345\) 93.6575 + 2683.37i 0.0146155 + 0.418747i
\(346\) 1242.70 + 93.1272i 0.193086 + 0.0144698i
\(347\) 3000.41 3233.67i 0.464180 0.500267i −0.456966 0.889484i \(-0.651064\pi\)
0.921146 + 0.389217i \(0.127254\pi\)
\(348\) −10407.4 1996.28i −1.60315 0.307505i
\(349\) −1517.20 + 3150.50i −0.232705 + 0.483217i −0.984322 0.176384i \(-0.943560\pi\)
0.751617 + 0.659600i \(0.229274\pi\)
\(350\) 816.523 + 805.930i 0.124700 + 0.123082i
\(351\) 755.006 + 7187.10i 0.114813 + 1.09293i
\(352\) 1549.82 + 233.598i 0.234676 + 0.0353717i
\(353\) −4104.36 + 2798.30i −0.618846 + 0.421922i −0.831750 0.555151i \(-0.812660\pi\)
0.212903 + 0.977073i \(0.431708\pi\)
\(354\) −703.336 + 439.475i −0.105598 + 0.0659826i
\(355\) −3880.17 4181.83i −0.580108 0.625208i
\(356\) −5128.16 6430.50i −0.763460 0.957348i
\(357\) −5539.75 + 6018.74i −0.821273 + 0.892284i
\(358\) −350.057 + 438.958i −0.0516791 + 0.0648035i
\(359\) −3152.26 + 236.229i −0.463426 + 0.0347290i −0.304398 0.952545i \(-0.598455\pi\)
−0.159028 + 0.987274i \(0.550836\pi\)
\(360\) −1173.77 2056.81i −0.171841 0.301121i
\(361\) 2473.90 4284.92i 0.360680 0.624715i
\(362\) 207.359 + 359.156i 0.0301064 + 0.0521459i
\(363\) −2462.32 + 1807.74i −0.356028 + 0.261382i
\(364\) 5685.58 4957.81i 0.818696 0.713901i
\(365\) 4996.51 + 1140.42i 0.716518 + 0.163541i
\(366\) 706.185 + 824.782i 0.100855 + 0.117793i
\(367\) 5926.58 2326.01i 0.842956 0.330836i 0.0957310 0.995407i \(-0.469481\pi\)
0.747225 + 0.664572i \(0.231386\pi\)
\(368\) −1639.35 + 643.397i −0.232220 + 0.0911396i
\(369\) 5473.16 11220.6i 0.772144 1.58299i
\(370\) −620.477 141.620i −0.0871812 0.0198985i
\(371\) −239.419 5446.71i −0.0335041 0.762207i
\(372\) 936.718 + 1275.90i 0.130555 + 0.177829i
\(373\) 2671.45 + 4627.08i 0.370837 + 0.642309i 0.989695 0.143194i \(-0.0457374\pi\)
−0.618857 + 0.785503i \(0.712404\pi\)
\(374\) −352.359 + 610.304i −0.0487168 + 0.0843799i
\(375\) 811.473 + 7368.28i 0.111745 + 1.01466i
\(376\) 894.332 67.0209i 0.122664 0.00919239i
\(377\) −8283.02 + 10386.6i −1.13156 + 1.41893i
\(378\) −118.561 + 781.272i −0.0161326 + 0.106308i
\(379\) 471.925 + 591.775i 0.0639608 + 0.0802043i 0.812783 0.582567i \(-0.197952\pi\)
−0.748822 + 0.662771i \(0.769380\pi\)
\(380\) 10595.4 + 11419.1i 1.43035 + 1.54155i
\(381\) −5752.46 9206.23i −0.773510 1.23792i
\(382\) −529.010 + 360.673i −0.0708548 + 0.0483080i
\(383\) 813.016 + 122.542i 0.108468 + 0.0163489i 0.203052 0.979168i \(-0.434914\pi\)
−0.0945840 + 0.995517i \(0.530152\pi\)
\(384\) 2056.46 2377.55i 0.273290 0.315960i
\(385\) 3079.44 + 8619.61i 0.407644 + 1.14103i
\(386\) 566.443 1176.23i 0.0746922 0.155100i
\(387\) 8686.03 1936.69i 1.14092 0.254386i
\(388\) −1155.41 + 1245.23i −0.151178 + 0.162931i
\(389\) 2861.94 + 214.473i 0.373024 + 0.0279542i 0.259923 0.965629i \(-0.416303\pi\)
0.113100 + 0.993584i \(0.463922\pi\)
\(390\) −1474.87 + 51.4773i −0.191495 + 0.00668373i
\(391\) 2422.71i 0.313354i
\(392\) 1485.53 739.444i 0.191405 0.0952743i
\(393\) −3245.66 7490.39i −0.416595 0.961425i
\(394\) 301.684 768.678i 0.0385752 0.0982879i
\(395\) 143.245 1911.47i 0.0182466 0.243484i
\(396\) −405.788 5806.01i −0.0514940 0.736776i
\(397\) −7369.60 + 10809.2i −0.931661 + 1.36650i −0.00124201 + 0.999999i \(0.500395\pi\)
−0.930419 + 0.366497i \(0.880557\pi\)
\(398\) 257.767 + 124.134i 0.0324641 + 0.0156339i
\(399\) −823.316 10424.2i −0.103302 1.30793i
\(400\) −11339.3 + 5460.70i −1.41741 + 0.682588i
\(401\) 1239.19 8221.46i 0.154319 1.02384i −0.768845 0.639435i \(-0.779168\pi\)
0.923164 0.384406i \(-0.125594\pi\)
\(402\) −208.125 + 329.390i −0.0258217 + 0.0408669i
\(403\) 1962.13 295.743i 0.242532 0.0365559i
\(404\) 6808.97 6317.80i 0.838512 0.778025i
\(405\) −9778.26 + 8891.80i −1.19972 + 1.09096i
\(406\) −1163.16 + 870.240i −0.142184 + 0.106378i
\(407\) −2460.10 1961.87i −0.299614 0.238934i
\(408\) 993.720 + 1891.69i 0.120580 + 0.229541i
\(409\) 2354.98 7634.66i 0.284710 0.923006i −0.694385 0.719603i \(-0.744324\pi\)
0.979095 0.203403i \(-0.0652002\pi\)
\(410\) 2207.89 + 1274.72i 0.265950 + 0.153547i
\(411\) −2559.24 1898.75i −0.307148 0.227879i
\(412\) 5143.75 1174.03i 0.615083 0.140389i
\(413\) 1744.60 9561.76i 0.207860 1.13923i
\(414\) −130.866 194.032i −0.0155355 0.0230342i
\(415\) −7805.96 + 2407.82i −0.923324 + 0.284808i
\(416\) −1081.97 2756.83i −0.127520 0.324915i
\(417\) 8871.96 + 8916.63i 1.04188 + 1.04712i
\(418\) −265.530 860.828i −0.0310706 0.100728i
\(419\) −1920.25 + 8413.15i −0.223891 + 0.980929i 0.730627 + 0.682776i \(0.239228\pi\)
−0.954518 + 0.298153i \(0.903629\pi\)
\(420\) 13462.6 + 3015.89i 1.56406 + 0.350382i
\(421\) −2929.31 12834.1i −0.339111 1.48574i −0.800925 0.598764i \(-0.795659\pi\)
0.461815 0.886977i \(-0.347199\pi\)
\(422\) −355.691 + 205.358i −0.0410302 + 0.0236888i
\(423\) −1451.27 4790.20i −0.166816 0.550609i
\(424\) −1360.90 419.781i −0.155875 0.0480811i
\(425\) −1293.87 17265.5i −0.147675 1.97059i
\(426\) 479.983 + 129.904i 0.0545897 + 0.0147743i
\(427\) −12719.1 392.780i −1.44150 0.0445151i
\(428\) 2452.28 1955.63i 0.276952 0.220862i
\(429\) −6680.21 2934.54i −0.751804 0.330258i
\(430\) 270.862 + 1797.05i 0.0303770 + 0.201539i
\(431\) 7951.76 + 11663.1i 0.888684 + 1.30346i 0.952199 + 0.305479i \(0.0988167\pi\)
−0.0635146 + 0.997981i \(0.520231\pi\)
\(432\) −7633.42 4108.24i −0.850146 0.457541i
\(433\) 2570.16 + 5336.99i 0.285251 + 0.592331i 0.993526 0.113607i \(-0.0362403\pi\)
−0.708274 + 0.705937i \(0.750526\pi\)
\(434\) 215.767 + 22.8856i 0.0238644 + 0.00253121i
\(435\) −24277.1 969.438i −2.67585 0.106853i
\(436\) −8430.60 5747.89i −0.926038 0.631362i
\(437\) 2270.24 + 2106.48i 0.248513 + 0.230587i
\(438\) −422.022 + 146.484i −0.0460388 + 0.0159800i
\(439\) −122.752 48.1768i −0.0133455 0.00523771i 0.358659 0.933469i \(-0.383234\pi\)
−0.372004 + 0.928231i \(0.621329\pi\)
\(440\) 2391.01 0.259061
\(441\) −5832.13 7193.91i −0.629751 0.776797i
\(442\) 1331.60 0.143298
\(443\) −8415.92 3303.01i −0.902602 0.354245i −0.131767 0.991281i \(-0.542065\pi\)
−0.770834 + 0.637036i \(0.780160\pi\)
\(444\) −4480.51 + 1555.18i −0.478909 + 0.166229i
\(445\) −13823.5 12826.4i −1.47258 1.36635i
\(446\) −414.172 282.378i −0.0439723 0.0299798i
\(447\) −16875.5 673.876i −1.78564 0.0713048i
\(448\) 1046.02 + 8768.74i 0.110312 + 0.924741i
\(449\) −4736.96 9836.41i −0.497887 1.03387i −0.986861 0.161574i \(-0.948343\pi\)
0.488974 0.872298i \(-0.337371\pi\)
\(450\) −1036.25 1312.89i −0.108554 0.137533i
\(451\) 7100.49 + 10414.5i 0.741351 + 1.08736i
\(452\) 1135.62 + 7534.36i 0.118175 + 0.784041i
\(453\) −1830.80 804.249i −0.189886 0.0834148i
\(454\) −1077.27 + 859.093i −0.111363 + 0.0888088i
\(455\) 11195.7 13182.8i 1.15355 1.35828i
\(456\) −2636.66 713.591i −0.270774 0.0732829i
\(457\) 295.389 + 3941.69i 0.0302357 + 0.403467i 0.991703 + 0.128548i \(0.0410318\pi\)
−0.961468 + 0.274918i \(0.911349\pi\)
\(458\) 1636.47 + 504.784i 0.166959 + 0.0515000i
\(459\) 9097.51 7710.51i 0.925131 0.784087i
\(460\) −3538.62 + 2043.02i −0.358671 + 0.207079i
\(461\) 1744.77 + 7644.33i 0.176273 + 0.772304i 0.983330 + 0.181830i \(0.0582020\pi\)
−0.807057 + 0.590474i \(0.798941\pi\)
\(462\) −625.769 494.934i −0.0630160 0.0498408i
\(463\) 1412.24 6187.44i 0.141755 0.621068i −0.853272 0.521465i \(-0.825386\pi\)
0.995027 0.0996030i \(-0.0317573\pi\)
\(464\) −4697.20 15227.9i −0.469961 1.52358i
\(465\) 2559.65 + 2572.53i 0.255270 + 0.256556i
\(466\) −64.6292 164.673i −0.00642466 0.0163698i
\(467\) −1219.35 + 376.119i −0.120824 + 0.0372692i −0.354577 0.935027i \(-0.615375\pi\)
0.233754 + 0.972296i \(0.424899\pi\)
\(468\) −9117.57 + 6149.41i −0.900555 + 0.607385i
\(469\) −1210.62 4402.93i −0.119193 0.433493i
\(470\) 996.500 227.445i 0.0977981 0.0223218i
\(471\) 10575.6 + 7846.26i 1.03460 + 0.767594i
\(472\) −2198.81 1269.48i −0.214425 0.123798i
\(473\) −2648.42 + 8585.98i −0.257452 + 0.834638i
\(474\) 77.7003 + 147.914i 0.00752931 + 0.0143332i
\(475\) 17304.0 + 13799.4i 1.67149 + 1.33297i
\(476\) −12045.1 3143.33i −1.15984 0.302677i
\(477\) −633.770 + 7922.91i −0.0608351 + 0.760514i
\(478\) −37.1911 + 34.5083i −0.00355875 + 0.00330203i
\(479\) 1127.14 169.888i 0.107516 0.0162054i −0.0950639 0.995471i \(-0.530306\pi\)
0.202580 + 0.979266i \(0.435067\pi\)
\(480\) 2893.14 4578.85i 0.275111 0.435406i
\(481\) −886.152 + 5879.23i −0.0840022 + 0.557318i
\(482\) −310.784 + 149.666i −0.0293689 + 0.0141433i
\(483\) 2713.82 + 397.899i 0.255659 + 0.0374846i
\(484\) −4188.22 2016.94i −0.393334 0.189420i
\(485\) −2193.93 + 3217.91i −0.205405 + 0.301274i
\(486\) 312.115 1108.94i 0.0291313 0.103503i
\(487\) −1021.87 + 13635.9i −0.0950831 + 1.26880i 0.721845 + 0.692055i \(0.243295\pi\)
−0.816928 + 0.576740i \(0.804325\pi\)
\(488\) −1214.42 + 3094.29i −0.112652 + 0.287033i
\(489\) 784.068 + 1809.49i 0.0725088 + 0.167337i
\(490\) 1548.55 1085.67i 0.142768 0.100093i
\(491\) 11454.5i 1.05282i 0.850231 + 0.526410i \(0.176462\pi\)
−0.850231 + 0.526410i \(0.823538\pi\)
\(492\) 18987.1 662.704i 1.73984 0.0607256i
\(493\) 21861.6 + 1638.30i 1.99715 + 0.149666i
\(494\) −1157.79 + 1247.80i −0.105448 + 0.113646i
\(495\) −2903.96 13024.3i −0.263684 1.18262i
\(496\) −1032.75 + 2144.54i −0.0934920 + 0.194138i
\(497\) −4913.99 + 3132.60i −0.443506 + 0.282729i
\(498\) 465.810 538.540i 0.0419146 0.0484589i
\(499\) −17602.4 2653.13i −1.57914 0.238017i −0.699844 0.714296i \(-0.746747\pi\)
−0.879294 + 0.476279i \(0.841985\pi\)
\(500\) −9320.67 + 6354.73i −0.833666 + 0.568384i
\(501\) −4173.14 6678.68i −0.372140 0.595572i
\(502\) 850.887 + 917.038i 0.0756513 + 0.0815327i
\(503\) 705.338 + 884.466i 0.0625238 + 0.0784024i 0.812110 0.583504i \(-0.198319\pi\)
−0.749586 + 0.661907i \(0.769747\pi\)
\(504\) −2282.21 + 802.440i −0.201702 + 0.0709197i
\(505\) 13277.9 16649.9i 1.17001 1.46715i
\(506\) 235.636 17.6585i 0.0207022 0.00155141i
\(507\) 259.537 + 2356.63i 0.0227346 + 0.206433i
\(508\) 8260.08 14306.9i 0.721421 1.24954i
\(509\) 10834.9 + 18766.6i 0.943513 + 1.63421i 0.758702 + 0.651438i \(0.225834\pi\)
0.184810 + 0.982774i \(0.440833\pi\)
\(510\) 1441.22 + 1963.08i 0.125134 + 0.170445i
\(511\) 2062.22 4812.12i 0.178527 0.416587i
\(512\) 5794.91 + 1322.65i 0.500198 + 0.114167i
\(513\) −684.754 + 15229.1i −0.0589330 + 1.31068i
\(514\) −807.854 + 317.059i −0.0693248 + 0.0272080i
\(515\) 11260.3 4419.34i 0.963473 0.378135i
\(516\) 8808.12 + 10287.4i 0.751465 + 0.877666i
\(517\) 4926.79 + 1124.51i 0.419111 + 0.0956593i
\(518\) −256.091 + 597.580i −0.0217220 + 0.0506876i
\(519\) 17162.9 12600.4i 1.45158 1.06569i
\(520\) −2258.96 3912.64i −0.190504 0.329962i
\(521\) −8883.34 + 15386.4i −0.746999 + 1.29384i 0.202256 + 0.979333i \(0.435173\pi\)
−0.949255 + 0.314507i \(0.898161\pi\)
\(522\) 1839.37 1049.68i 0.154228 0.0880136i
\(523\) −2743.26 + 205.579i −0.229358 + 0.0171880i −0.188913 0.981994i \(-0.560496\pi\)
−0.0404447 + 0.999182i \(0.512877\pi\)
\(524\) 7745.60 9712.68i 0.645741 0.809734i
\(525\) 19552.7 + 1386.30i 1.62543 + 0.115244i
\(526\) −623.823 782.249i −0.0517110 0.0648435i
\(527\) −2227.22 2400.37i −0.184097 0.198410i
\(528\) 7422.48 4637.90i 0.611784 0.382270i
\(529\) 9381.65 6396.30i 0.771074 0.525709i
\(530\) −1604.99 241.914i −0.131541 0.0198266i
\(531\) −4244.59 + 13519.2i −0.346892 + 1.10486i
\(532\) 13418.4 8554.03i 1.09354 0.697113i
\(533\) 10333.9 21458.6i 0.839797 1.74386i
\(534\) 1614.29 + 309.641i 0.130819 + 0.0250927i
\(535\) 4891.35 5271.62i 0.395274 0.426004i
\(536\) −1189.49 89.1398i −0.0958546 0.00718331i
\(537\) 334.608 + 9586.81i 0.0268890 + 0.770393i
\(538\) 130.442i 0.0104531i
\(539\) 9226.91 1514.20i 0.737349 0.121004i
\(540\) −18933.8 6785.74i −1.50885 0.540762i
\(541\) −5060.73 + 12894.5i −0.402177 + 1.02473i 0.576091 + 0.817386i \(0.304577\pi\)
−0.978268 + 0.207345i \(0.933518\pi\)
\(542\) 11.8573 158.225i 0.000939696 0.0125394i
\(543\) 6682.14 + 2357.03i 0.528100 + 0.186280i
\(544\) −2753.04 + 4037.96i −0.216977 + 0.318247i
\(545\) −21077.3 10150.3i −1.65661 0.797782i
\(546\) −218.699 + 1491.61i −0.0171419 + 0.116914i
\(547\) −9067.68 + 4366.77i −0.708786 + 0.341334i −0.753302 0.657675i \(-0.771540\pi\)
0.0445153 + 0.999009i \(0.485826\pi\)
\(548\) 722.780 4795.33i 0.0563424 0.373808i
\(549\) 18330.2 + 2857.05i 1.42498 + 0.222106i
\(550\) 1669.84 251.688i 0.129458 0.0195127i
\(551\) −20543.2 + 19061.3i −1.58833 + 1.47376i
\(552\) 336.382 632.615i 0.0259372 0.0487788i
\(553\) −1894.66 494.438i −0.145695 0.0380210i
\(554\) −693.057 552.695i −0.0531502 0.0423858i
\(555\) −9626.42 + 5056.83i −0.736250 + 0.386758i
\(556\) −5642.18 + 18291.5i −0.430363 + 1.39520i
\(557\) −21167.4 12221.0i −1.61022 0.929658i −0.989319 0.145765i \(-0.953436\pi\)
−0.620896 0.783893i \(-0.713231\pi\)
\(558\) −308.035 71.9365i −0.0233695 0.00545756i
\(559\) 16552.2 3777.94i 1.25239 0.285850i
\(560\) 5500.35 + 20004.3i 0.415057 + 1.50953i
\(561\) 2208.75 + 11836.2i 0.166227 + 0.890773i
\(562\) −1441.02 + 444.497i −0.108160 + 0.0333629i
\(563\) 3302.37 + 8414.30i 0.247208 + 0.629876i 0.999584 0.0288583i \(-0.00918717\pi\)
−0.752375 + 0.658735i \(0.771092\pi\)
\(564\) 5399.50 5372.45i 0.403120 0.401101i
\(565\) 5149.18 + 16693.2i 0.383412 + 1.24299i
\(566\) 589.261 2581.72i 0.0437606 0.191728i
\(567\) 7142.87 + 11457.0i 0.529052 + 0.848590i
\(568\) 338.740 + 1484.12i 0.0250233 + 0.109634i
\(569\) −4099.82 + 2367.03i −0.302062 + 0.174396i −0.643369 0.765556i \(-0.722464\pi\)
0.341307 + 0.939952i \(0.389131\pi\)
\(570\) −3092.64 356.324i −0.227257 0.0261838i
\(571\) 10214.1 + 3150.65i 0.748597 + 0.230912i 0.645500 0.763760i \(-0.276649\pi\)
0.103096 + 0.994671i \(0.467125\pi\)
\(572\) −829.773 11072.5i −0.0606548 0.809382i
\(573\) −2857.81 + 10559.4i −0.208354 + 0.769849i
\(574\) 1685.87 1985.08i 0.122590 0.144348i
\(575\) −4538.90 + 3619.65i −0.329191 + 0.262521i
\(576\) 64.6582 12874.1i 0.00467724 0.931286i
\(577\) −396.208 2628.67i −0.0285864 0.189659i 0.969980 0.243185i \(-0.0781921\pi\)
−0.998566 + 0.0535261i \(0.982954\pi\)
\(578\) −396.153 581.050i −0.0285083 0.0418140i
\(579\) −5718.96 21559.9i −0.410487 1.54749i
\(580\) −16042.5 33312.7i −1.14850 2.38489i
\(581\) 988.442 + 8286.09i 0.0705808 + 0.591678i
\(582\) 13.5453 339.208i 0.000964729 0.0241591i
\(583\) −6630.47 4520.58i −0.471022 0.321138i
\(584\) −1002.52 930.200i −0.0710351 0.0659109i
\(585\) −18569.3 + 17057.0i −1.31239 + 1.20551i
\(586\) −288.696 113.305i −0.0203514 0.00798735i
\(587\) 20847.9 1.46590 0.732951 0.680281i \(-0.238142\pi\)
0.732951 + 0.680281i \(0.238142\pi\)
\(588\) 5499.30 12976.2i 0.385693 0.910083i
\(589\) 4185.82 0.292824
\(590\) −2693.63 1057.17i −0.187958 0.0737680i
\(591\) −4626.30 13328.5i −0.321998 0.927682i
\(592\) −5228.19 4851.05i −0.362968 0.336786i
\(593\) 21722.3 + 14810.0i 1.50426 + 1.02559i 0.985308 + 0.170785i \(0.0546302\pi\)
0.518952 + 0.854803i \(0.326322\pi\)
\(594\) 816.245 + 828.637i 0.0563820 + 0.0572380i
\(595\) −28381.8 3010.35i −1.95553 0.207416i
\(596\) −11151.5 23156.3i −0.766414 1.59148i
\(597\) 4724.77 1253.29i 0.323906 0.0859192i
\(598\) −251.519 368.911i −0.0171996 0.0252272i
\(599\) 4162.63 + 27617.2i 0.283940 + 1.88382i 0.442952 + 0.896545i \(0.353931\pi\)
−0.159012 + 0.987277i \(0.550831\pi\)
\(600\) 2059.38 4688.00i 0.140123 0.318978i
\(601\) −10898.3 + 8691.11i −0.739686 + 0.589880i −0.919161 0.393883i \(-0.871132\pi\)
0.179475 + 0.983763i \(0.442560\pi\)
\(602\) 1855.61 + 57.3034i 0.125630 + 0.00387959i
\(603\) 959.114 + 6587.63i 0.0647731 + 0.444891i
\(604\) −227.410 3034.58i −0.0153198 0.204429i
\(605\) −10184.4 3141.48i −0.684389 0.211106i
\(606\) −212.468 + 1844.07i −0.0142425 + 0.123615i
\(607\) −6202.40 + 3580.96i −0.414741 + 0.239451i −0.692825 0.721106i \(-0.743634\pi\)
0.278084 + 0.960557i \(0.410301\pi\)
\(608\) −1390.16 6090.68i −0.0927276 0.406266i
\(609\) −5425.65 + 24219.4i −0.361016 + 1.61153i
\(610\) −843.007 + 3693.46i −0.0559547 + 0.245154i
\(611\) −2814.57 9124.60i −0.186359 0.604160i
\(612\) 16860.1 + 6715.03i 1.11361 + 0.443528i
\(613\) −2799.55 7133.13i −0.184458 0.469991i 0.808495 0.588504i \(-0.200283\pi\)
−0.992953 + 0.118512i \(0.962187\pi\)
\(614\) −1169.44 + 360.723i −0.0768641 + 0.0237094i
\(615\) 42819.5 7990.56i 2.80756 0.523919i
\(616\) 438.412 2402.84i 0.0286756 0.157164i
\(617\) 255.218 58.2520i 0.0166527 0.00380087i −0.214186 0.976793i \(-0.568710\pi\)
0.230839 + 0.972992i \(0.425853\pi\)
\(618\) −628.248 + 846.788i −0.0408930 + 0.0551178i
\(619\) −3455.35 1994.94i −0.224365 0.129537i 0.383605 0.923497i \(-0.374683\pi\)
−0.607970 + 0.793960i \(0.708016\pi\)
\(620\) −1627.82 + 5277.27i −0.105443 + 0.341839i
\(621\) −3854.52 1064.00i −0.249077 0.0687552i
\(622\) −1988.09 1585.45i −0.128160 0.102204i
\(623\) −15424.5 + 11540.1i −0.991926 + 0.742126i
\(624\) −14602.0 7764.37i −0.936777 0.498115i
\(625\) −295.326 + 274.023i −0.0189009 + 0.0175375i
\(626\) 710.669 107.116i 0.0453738 0.00683901i
\(627\) −13011.7 8221.47i −0.828771 0.523659i
\(628\) −2986.77 + 19815.9i −0.189785 + 1.25914i
\(629\) 8839.89 4257.07i 0.560365 0.269857i
\(630\) −2435.67 + 1291.99i −0.154031 + 0.0817048i
\(631\) 18903.1 + 9103.27i 1.19259 + 0.574319i 0.921554 0.388251i \(-0.126921\pi\)
0.271033 + 0.962570i \(0.412635\pi\)
\(632\) −288.138 + 422.621i −0.0181353 + 0.0265996i
\(633\) −2334.30 + 6617.68i −0.146572 + 0.415528i
\(634\) 33.2422 443.586i 0.00208236 0.0277872i
\(635\) 13837.7 35258.0i 0.864778 2.20342i
\(636\) −11098.5 + 4809.08i −0.691955 + 0.299831i
\(637\) −11195.2 13668.3i −0.696341 0.850171i
\(638\) 2138.23i 0.132685i
\(639\) 7672.86 3647.70i 0.475013 0.225823i
\(640\) 10937.3 + 819.639i 0.675525 + 0.0506236i
\(641\) 13952.8 15037.6i 0.859757 0.926598i −0.138205 0.990404i \(-0.544133\pi\)
0.997962 + 0.0638058i \(0.0203238\pi\)
\(642\) −118.082 + 615.611i −0.00725907 + 0.0378446i
\(643\) −7340.55 + 15242.8i −0.450207 + 0.934865i 0.545125 + 0.838355i \(0.316482\pi\)
−0.995332 + 0.0965099i \(0.969232\pi\)
\(644\) 1404.29 + 3930.73i 0.0859269 + 0.240516i
\(645\) 23484.4 + 20312.8i 1.43364 + 1.24003i
\(646\) 2777.61 + 418.657i 0.169170 + 0.0254982i
\(647\) 24032.6 16385.2i 1.46031 0.995623i 0.466502 0.884520i \(-0.345514\pi\)
0.993809 0.111102i \(-0.0354382\pi\)
\(648\) 3446.10 750.215i 0.208913 0.0454803i
\(649\) −9730.92 10487.4i −0.588555 0.634311i
\(650\) −1989.48 2494.73i −0.120052 0.150541i
\(651\) 3054.60 2100.61i 0.183900 0.126466i
\(652\) −1871.14 + 2346.34i −0.112392 + 0.140935i
\(653\) −111.166 + 8.33075i −0.00666197 + 0.000499245i −0.0780607 0.996949i \(-0.524873\pi\)
0.0713987 + 0.997448i \(0.477254\pi\)
\(654\) 2026.89 223.223i 0.121189 0.0133466i
\(655\) 14241.3 24666.6i 0.849545 1.47146i
\(656\) 14285.0 + 24742.3i 0.850206 + 1.47260i
\(657\) −3849.39 + 6590.67i −0.228583 + 0.391365i
\(658\) −45.8528 1043.13i −0.00271661 0.0618019i
\(659\) −7616.93 1738.51i −0.450248 0.102766i −0.00861687 0.999963i \(-0.502743\pi\)
−0.441631 + 0.897197i \(0.645600\pi\)
\(660\) 15425.4 13207.3i 0.909745 0.778931i
\(661\) −20924.1 + 8212.10i −1.23124 + 0.483228i −0.889660 0.456623i \(-0.849059\pi\)
−0.341585 + 0.939851i \(0.610964\pi\)
\(662\) 661.366 259.567i 0.0388289 0.0152392i
\(663\) 17281.9 14796.9i 1.01233 0.866764i
\(664\) 2125.19 + 485.062i 0.124207 + 0.0283495i
\(665\) 27498.1 23978.2i 1.60350 1.39825i
\(666\) 478.025 818.443i 0.0278125 0.0476187i
\(667\) −3675.44 6366.05i −0.213364 0.369557i
\(668\) 5992.30 10379.0i 0.347079 0.601159i
\(669\) −8513.07 + 937.549i −0.491979 + 0.0541820i
\(670\) −1355.66 + 101.592i −0.0781696 + 0.00585800i
\(671\) −11678.2 + 14644.0i −0.671883 + 0.842514i
\(672\) −4071.02 3747.03i −0.233695 0.215097i
\(673\) 13149.3 + 16488.6i 0.753145 + 0.944414i 0.999695 0.0247162i \(-0.00786821\pi\)
−0.246549 + 0.969130i \(0.579297\pi\)
\(674\) −761.332 820.521i −0.0435095 0.0468921i
\(675\) −28037.7 5524.11i −1.59877 0.314997i
\(676\) −2981.07 + 2032.46i −0.169610 + 0.115638i
\(677\) −23396.3 3526.43i −1.32820 0.200195i −0.553675 0.832733i \(-0.686775\pi\)
−0.774529 + 0.632538i \(0.782013\pi\)
\(678\) −1151.68 996.146i −0.0652361 0.0564259i
\(679\) 2831.56 + 2794.82i 0.160037 + 0.157961i
\(680\) −3234.82 + 6717.18i −0.182426 + 0.378812i
\(681\) −4434.76 + 23120.3i −0.249545 + 1.30099i
\(682\) 217.230 234.118i 0.0121967 0.0131449i
\(683\) −3940.78 295.320i −0.220775 0.0165448i −0.0361169 0.999348i \(-0.511499\pi\)
−0.184658 + 0.982803i \(0.559118\pi\)
\(684\) −20951.9 + 9960.57i −1.17122 + 0.556801i
\(685\) 11118.6i 0.620174i
\(686\) −807.100 1755.28i −0.0449201 0.0976921i
\(687\) 26847.8 11633.4i 1.49099 0.646059i
\(688\) −7440.48 + 18958.0i −0.412305 + 1.05054i
\(689\) −1133.16 + 15121.0i −0.0626562 + 0.836088i
\(690\) 271.634 770.076i 0.0149868 0.0424874i
\(691\) 10913.7 16007.4i 0.600833 0.881259i −0.398523 0.917158i \(-0.630477\pi\)
0.999355 + 0.0358989i \(0.0114294\pi\)
\(692\) 29192.9 + 14058.6i 1.60368 + 0.772292i
\(693\) −13621.2 + 530.215i −0.746646 + 0.0290638i
\(694\) −1208.72 + 582.088i −0.0661128 + 0.0318383i
\(695\) −6541.05 + 43397.1i −0.357002 + 2.36855i
\(696\) 5481.01 + 3463.17i 0.298502 + 0.188608i
\(697\) −38864.4 + 5857.87i −2.11204 + 0.318339i
\(698\) 779.576 723.341i 0.0422742 0.0392247i
\(699\) −2668.64 1419.00i −0.144402 0.0767834i
\(700\) 12107.0 + 27262.6i 0.653717 + 1.47204i
\(701\) 13162.4 + 10496.6i 0.709180 + 0.565552i 0.910267 0.414021i \(-0.135876\pi\)
−0.201087 + 0.979573i \(0.564447\pi\)
\(702\) 584.812 2118.58i 0.0314420 0.113904i
\(703\) −3696.88 + 11985.0i −0.198336 + 0.642990i
\(704\) 11257.0 + 6499.22i 0.602647 + 0.347938i
\(705\) 10405.5 14025.1i 0.555876 0.749240i
\(706\) 1472.87 336.174i 0.0785160 0.0179208i
\(707\) −14297.7 16396.5i −0.760566 0.872211i
\(708\) −21197.8 + 3955.73i −1.12523 + 0.209979i
\(709\) −19887.8 + 6134.58i −1.05346 + 0.324949i −0.772662 0.634818i \(-0.781075\pi\)
−0.280797 + 0.959767i \(0.590599\pi\)
\(710\) 633.846 + 1615.01i 0.0335040 + 0.0853668i
\(711\) 2652.05 + 1056.26i 0.139887 + 0.0557141i
\(712\) 1483.23 + 4808.52i 0.0780709 + 0.253100i
\(713\) −244.318 + 1070.43i −0.0128328 + 0.0562242i
\(714\) 2237.06 1088.40i 0.117255 0.0570483i
\(715\) −5664.83 24819.2i −0.296297 1.29816i
\(716\) −12642.3 + 7299.05i −0.659868 + 0.380975i
\(717\) −99.2166 + 861.131i −0.00516780 + 0.0448529i
\(718\) 918.661 + 283.369i 0.0477495 + 0.0147288i
\(719\) −1320.43 17620.0i −0.0684894 0.913928i −0.920585 0.390542i \(-0.872288\pi\)
0.852096 0.523386i \(-0.175331\pi\)
\(720\) −4357.64 29930.2i −0.225555 1.54921i
\(721\) −2376.53 12126.4i −0.122756 0.626365i
\(722\) −1176.46 + 938.200i −0.0606420 + 0.0483603i
\(723\) −2370.34 + 5395.87i −0.121928 + 0.277558i
\(724\) 1607.12 + 10662.5i 0.0824973 + 0.547334i
\(725\) −29593.0 43405.0i −1.51594 2.22348i
\(726\) 897.946 238.189i 0.0459034 0.0121763i
\(727\) −15202.2 31567.6i −0.775540 1.61043i −0.791970 0.610560i \(-0.790944\pi\)
0.0164300 0.999865i \(-0.494770\pi\)
\(728\) −4346.20 + 1552.72i −0.221265 + 0.0790491i
\(729\) −8271.98 17860.4i −0.420260 0.907404i
\(730\) −1287.81 878.016i −0.0652933 0.0445162i
\(731\) −20538.0 19056.5i −1.03916 0.964197i
\(732\) 9257.38 + 26670.7i 0.467435 + 1.34669i
\(733\) −25225.1 9900.11i −1.27109 0.498866i −0.368604 0.929586i \(-0.620164\pi\)
−0.902485 + 0.430720i \(0.858260\pi\)
\(734\) −1936.27 −0.0973694
\(735\) 8033.43 31297.8i 0.403153 1.57066i
\(736\) 1638.70 0.0820695
\(737\) −6256.68 2455.57i −0.312711 0.122730i
\(738\) −2796.19 + 2568.47i −0.139470 + 0.128112i
\(739\) 2313.66 + 2146.77i 0.115168 + 0.106861i 0.735655 0.677356i \(-0.236874\pi\)
−0.620487 + 0.784217i \(0.713065\pi\)
\(740\) −13672.4 9321.68i −0.679199 0.463070i
\(741\) −1160.43 + 29059.8i −0.0575294 + 1.44067i
\(742\) −537.401 + 1568.58i −0.0265884 + 0.0776070i
\(743\) 5049.09 + 10484.5i 0.249304 + 0.517686i 0.987638 0.156749i \(-0.0501015\pi\)
−0.738334 + 0.674435i \(0.764387\pi\)
\(744\) −248.289 936.022i −0.0122348 0.0461240i
\(745\) −33194.6 48687.5i −1.63242 2.39433i
\(746\) −242.181 1606.76i −0.0118859 0.0788577i
\(747\) 61.0992 12165.5i 0.00299264 0.595865i
\(748\) −14325.7 + 11424.3i −0.700266 + 0.558443i
\(749\) −4400.83 5882.15i −0.214690 0.286955i
\(750\) 588.957 2176.14i 0.0286742 0.105949i
\(751\) −114.508 1528.00i −0.00556384 0.0742443i 0.993731 0.111800i \(-0.0356617\pi\)
−0.999295 + 0.0375562i \(0.988043\pi\)
\(752\) 10945.4 + 3376.21i 0.530769 + 0.163721i
\(753\) 21233.3 + 2446.43i 1.02760 + 0.118397i
\(754\) 3499.00 2020.15i 0.169000 0.0975721i
\(755\) −1552.52 6802.04i −0.0748371 0.327883i
\(756\) −10291.0 + 17783.2i −0.495079 + 0.855516i
\(757\) −2359.27 + 10336.6i −0.113275 + 0.496290i 0.886182 + 0.463337i \(0.153348\pi\)
−0.999457 + 0.0329527i \(0.989509\pi\)
\(758\) −67.8513 219.969i −0.00325128 0.0105404i
\(759\) 2861.93 2847.59i 0.136866 0.136180i
\(760\) −3481.87 8871.65i −0.166185 0.423433i
\(761\) 12590.1 3883.53i 0.599724 0.184990i 0.0199956 0.999800i \(-0.493635\pi\)
0.579729 + 0.814810i \(0.303159\pi\)
\(762\) 605.637 + 3245.46i 0.0287925 + 0.154292i
\(763\) −14065.2 + 19320.5i −0.667360 + 0.916707i
\(764\) −16230.0 + 3704.38i −0.768559 + 0.175419i
\(765\) 40518.6 + 9462.45i 1.91497 + 0.447210i
\(766\) −216.551 125.026i −0.0102145 0.00589735i
\(767\) −7968.09 + 25831.9i −0.375112 + 1.21608i
\(768\) 16701.1 8773.20i 0.784698 0.412208i
\(769\) −19452.5 15512.9i −0.912193 0.727450i 0.0503062 0.998734i \(-0.483980\pi\)
−0.962499 + 0.271284i \(0.912552\pi\)
\(770\) 85.9236 2782.39i 0.00402139 0.130221i
\(771\) −6961.37 + 13091.9i −0.325172 + 0.611533i
\(772\) 24883.1 23088.1i 1.16005 1.07637i
\(773\) −13743.8 + 2071.55i −0.639496 + 0.0963885i −0.460783 0.887513i \(-0.652431\pi\)
−0.178713 + 0.983901i \(0.557193\pi\)
\(774\) −2674.23 416.821i −0.124190 0.0193570i
\(775\) −1169.47 + 7758.94i −0.0542047 + 0.359625i
\(776\) 936.358 450.926i 0.0433161 0.0208599i
\(777\) 3316.76 + 10601.3i 0.153138 + 0.489471i
\(778\) −786.394 378.707i −0.0362385 0.0174516i
\(779\) 28302.3 41511.9i 1.30171 1.90926i
\(780\) −36185.9 12764.1i −1.66111 0.585933i
\(781\) −641.015 + 8553.75i −0.0293692 + 0.391904i
\(782\) −269.186 + 685.875i −0.0123096 + 0.0313642i
\(783\) 12207.7 34062.3i 0.557174 1.55464i
\(784\) 21111.8 1859.60i 0.961725 0.0847123i
\(785\) 45945.6i 2.08901i
\(786\) 86.6002 + 2481.17i 0.00392993 + 0.112596i
\(787\) 2754.61 + 206.429i 0.124766 + 0.00934994i 0.136967 0.990576i \(-0.456265\pi\)
−0.0122006 + 0.999926i \(0.503884\pi\)
\(788\) 14603.6 15738.9i 0.660191 0.711517i
\(789\) −16788.6 3220.26i −0.757529 0.145303i
\(790\) −252.935 + 525.225i −0.0113912 + 0.0236540i
\(791\) 17720.0 2113.81i 0.796524 0.0950168i
\(792\) −1066.65 + 3397.33i −0.0478558 + 0.152423i
\(793\) 34996.8 + 5274.92i 1.56718 + 0.236214i
\(794\) 3287.36 2241.29i 0.146932 0.100177i
\(795\) −23518.3 + 14695.3i −1.04919 + 0.655581i
\(796\) 5059.68 + 5453.04i 0.225296 + 0.242811i
\(797\) −2211.58 2773.23i −0.0982912 0.123253i 0.730253 0.683177i \(-0.239402\pi\)
−0.828544 + 0.559923i \(0.810831\pi\)
\(798\) −925.152 + 3042.61i −0.0410401 + 0.134972i
\(799\) −9824.67 + 12319.7i −0.435009 + 0.545484i
\(800\) 11678.2 875.163i 0.516110 0.0386771i
\(801\) 24391.5 13919.6i 1.07594 0.614013i
\(802\) −1264.30 + 2189.83i −0.0556658 + 0.0964161i
\(803\) −3853.05 6673.68i −0.169329 0.293286i
\(804\) −8166.27 + 5995.36i −0.358211 + 0.262985i
\(805\) 4526.89 + 8431.58i 0.198201 + 0.369160i
\(806\) −588.344 134.286i −0.0257116 0.00586850i
\(807\) 1449.49 + 1692.91i 0.0632272 + 0.0738455i
\(808\) −5289.97 + 2076.16i −0.230322 + 0.0903949i
\(809\) 24932.4 9785.23i 1.08353 0.425254i 0.244672 0.969606i \(-0.421320\pi\)
0.838857 + 0.544352i \(0.183224\pi\)
\(810\) 3756.22 1430.83i 0.162938 0.0620672i
\(811\) 28427.4 + 6488.38i 1.23085 + 0.280934i 0.788009 0.615664i \(-0.211112\pi\)
0.442845 + 0.896598i \(0.353969\pi\)
\(812\) −36419.1 + 10013.7i −1.57396 + 0.432775i
\(813\) −1604.33 2185.25i −0.0692081 0.0942682i
\(814\) 478.480 + 828.752i 0.0206028 + 0.0356852i
\(815\) −3440.33 + 5958.82i −0.147864 + 0.256108i
\(816\) 2987.52 + 27127.1i 0.128167 + 1.16377i
\(817\) 35714.4 2676.42i 1.52936 0.114610i
\(818\) −1514.99 + 1899.73i −0.0647558 + 0.0812012i
\(819\) 13736.6 + 21788.7i 0.586075 + 0.929622i
\(820\) 41329.6 + 51825.7i 1.76011 + 2.20711i
\(821\) 11451.1 + 12341.3i 0.486779 + 0.524623i 0.927902 0.372824i \(-0.121610\pi\)
−0.441123 + 0.897446i \(0.645420\pi\)
\(822\) 513.559 + 821.898i 0.0217913 + 0.0348747i
\(823\) −26884.8 + 18329.8i −1.13869 + 0.776349i −0.977575 0.210586i \(-0.932463\pi\)
−0.161120 + 0.986935i \(0.551510\pi\)
\(824\) −3191.87 481.097i −0.134944 0.0203396i
\(825\) 18874.9 21821.9i 0.796531 0.920899i
\(826\) −1556.31 + 2513.12i −0.0655579 + 0.105863i
\(827\) −254.781 + 529.058i −0.0107129 + 0.0222456i −0.906257 0.422728i \(-0.861073\pi\)
0.895544 + 0.444973i \(0.146787\pi\)
\(828\) −1324.27 5939.35i −0.0555816 0.249284i
\(829\) 27760.7 29918.9i 1.16305 1.25347i 0.201302 0.979529i \(-0.435483\pi\)
0.961747 0.273939i \(-0.0883268\pi\)
\(830\) 2477.42 + 185.657i 0.103606 + 0.00776416i
\(831\) −15136.3 + 528.302i −0.631857 + 0.0220536i
\(832\) 24561.2i 1.02344i
\(833\) −8229.30 + 27970.2i −0.342291 + 1.16340i
\(834\) −1520.95 3510.09i −0.0631491 0.145737i
\(835\) 10038.6 25578.0i 0.416049 1.06008i
\(836\) 1750.39 23357.3i 0.0724144 0.966302i
\(837\) −4797.14 + 2489.31i −0.198104 + 0.102799i
\(838\) 1478.41 2168.43i 0.0609437 0.0893880i
\(839\) −16073.6 7740.65i −0.661410 0.318518i 0.0728933 0.997340i \(-0.476777\pi\)
−0.734303 + 0.678821i \(0.762491\pi\)
\(840\) −6993.05 4726.74i −0.287242 0.194152i
\(841\) 37956.5 18278.9i 1.55630 0.749473i
\(842\) −596.701 + 3958.85i −0.0244224 + 0.162032i
\(843\) −13762.7 + 21781.6i −0.562293 + 0.889916i
\(844\) −10559.7 + 1591.61i −0.430662 + 0.0649119i
\(845\) −6063.92 + 5626.49i −0.246870 + 0.229062i
\(846\) −121.378 + 1517.37i −0.00493268 + 0.0616646i
\(847\) −5024.43 + 9658.80i −0.203827 + 0.391830i
\(848\) −14220.9 11340.8i −0.575884 0.459252i
\(849\) −21040.8 40054.3i −0.850552 1.61915i
\(850\) −1552.07 + 5031.68i −0.0626300 + 0.203041i
\(851\) −2849.11 1644.93i −0.114766 0.0662604i
\(852\) 10383.3 + 7703.54i 0.417517 + 0.309764i
\(853\) 7516.35 1715.56i 0.301706 0.0688624i −0.0689881 0.997617i \(-0.521977\pi\)
0.370694 + 0.928755i \(0.379120\pi\)
\(854\) 3557.16 + 1524.41i 0.142533 + 0.0610822i
\(855\) −44096.8 + 29741.4i −1.76383 + 1.18963i
\(856\) −1833.73 + 565.632i −0.0732193 + 0.0225852i
\(857\) −3584.43 9132.97i −0.142872 0.364033i 0.841469 0.540305i \(-0.181691\pi\)
−0.984341 + 0.176272i \(0.943596\pi\)
\(858\) 1565.13 + 1573.01i 0.0622759 + 0.0625895i
\(859\) 1263.10 + 4094.86i 0.0501703 + 0.162648i 0.977191 0.212362i \(-0.0681155\pi\)
−0.927021 + 0.375010i \(0.877639\pi\)
\(860\) −10514.7 + 46067.8i −0.416916 + 1.82663i
\(861\) −178.761 44496.5i −0.00707568 1.76125i
\(862\) −955.284 4185.37i −0.0377461 0.165376i
\(863\) 4287.97 2475.66i 0.169136 0.0976506i −0.413042 0.910712i \(-0.635534\pi\)
0.582178 + 0.813061i \(0.302201\pi\)
\(864\) 5215.32 + 6153.47i 0.205357 + 0.242298i
\(865\) 70987.8 + 21896.8i 2.79035 + 0.860710i
\(866\) −134.628 1796.49i −0.00528273 0.0704931i
\(867\) −11598.1 3138.94i −0.454316 0.122957i
\(868\) 5004.91 + 2603.51i 0.195712 + 0.101808i
\(869\) −2253.39 + 1797.02i −0.0879643 + 0.0701492i
\(870\) 6765.19 + 2971.87i 0.263634 + 0.115811i
\(871\) 1892.87 + 12558.4i 0.0736366 + 0.488547i
\(872\) 3516.61 + 5157.92i 0.136568 + 0.200309i
\(873\) −3593.52 4552.85i −0.139315 0.176507i
\(874\) −408.662 848.595i −0.0158160 0.0328423i
\(875\) 14202.6 + 22279.0i 0.548725 + 0.860765i
\(876\) −11605.9 463.448i −0.447632 0.0178750i
\(877\) −6176.45 4211.03i −0.237815 0.162140i 0.438548 0.898708i \(-0.355493\pi\)
−0.676364 + 0.736568i \(0.736445\pi\)
\(878\) 29.3987 + 27.2780i 0.00113002 + 0.00104850i
\(879\) −5005.84 + 1737.52i −0.192085 + 0.0666726i
\(880\) 28426.6 + 11156.6i 1.08893 + 0.427375i
\(881\) −25868.4 −0.989250 −0.494625 0.869106i \(-0.664695\pi\)
−0.494625 + 0.869106i \(0.664695\pi\)
\(882\) 851.779 + 2684.62i 0.0325180 + 0.102490i
\(883\) 13142.7 0.500890 0.250445 0.968131i \(-0.419423\pi\)
0.250445 + 0.968131i \(0.419423\pi\)
\(884\) 32229.3 + 12649.1i 1.22623 + 0.481261i
\(885\) −46706.2 + 16211.7i −1.77402 + 0.615762i
\(886\) 2015.58 + 1870.18i 0.0764273 + 0.0709142i
\(887\) 28999.1 + 19771.3i 1.09774 + 0.748427i 0.969933 0.243372i \(-0.0782537\pi\)
0.127807 + 0.991799i \(0.459206\pi\)
\(888\) 2899.34 + 115.777i 0.109567 + 0.00437526i
\(889\) −32895.2 20371.1i −1.24102 0.768531i
\(890\) 2488.35 + 5167.11i 0.0937187 + 0.194609i
\(891\) 19801.4 + 1684.08i 0.744524 + 0.0633207i
\(892\) −7342.04 10768.8i −0.275594 0.404222i
\(893\) −3002.17 19918.1i −0.112501 0.746397i
\(894\) 4702.62 + 2065.80i 0.175927 + 0.0772828i
\(895\) −26167.5 + 20867.9i −0.977298 + 0.779369i
\(896\) 2829.15 10841.2i 0.105486 0.404216i
\(897\) −7363.67 1992.92i −0.274098 0.0741825i
\(898\) 248.128 + 3311.04i 0.00922064 + 0.123041i
\(899\) −9493.93 2928.49i −0.352214 0.108644i
\(900\) −12609.4 41619.8i −0.467016 1.54147i
\(901\) 21670.4 12511.4i 0.801270 0.462614i
\(902\) −853.017 3737.31i −0.0314882 0.137959i
\(903\) 24719.4 19876.1i 0.910975 0.732485i
\(904\) 1037.32 4544.78i 0.0381644 0.167209i
\(905\) 7287.06 + 23624.1i 0.267657 + 0.867724i
\(906\) 428.945 + 431.105i 0.0157293 + 0.0158085i
\(907\) 13570.0 + 34575.8i 0.496786 + 1.26579i 0.931013 + 0.364987i \(0.118926\pi\)
−0.434227 + 0.900804i \(0.642978\pi\)
\(908\) −34234.2 + 10559.9i −1.25121 + 0.385949i
\(909\) 17734.1 + 26293.9i 0.647088 + 0.959421i
\(910\) −4634.28 + 2488.13i −0.168819 + 0.0906381i
\(911\) 25773.8 5882.71i 0.937349 0.213944i 0.273553 0.961857i \(-0.411801\pi\)
0.663797 + 0.747913i \(0.268944\pi\)
\(912\) −28017.5 20786.7i −1.01727 0.754734i
\(913\) 10637.4 + 6141.48i 0.385592 + 0.222622i
\(914\) 354.334 1148.72i 0.0128231 0.0415716i
\(915\) 30101.3 + 57302.4i 1.08756 + 2.07034i
\(916\) 34813.2 + 27762.6i 1.25574 + 1.00142i
\(917\) −22177.4 18834.6i −0.798650 0.678269i
\(918\) −3432.24 + 1172.05i −0.123400 + 0.0421387i
\(919\) −21663.4 + 20100.7i −0.777593 + 0.721501i −0.965420 0.260701i \(-0.916046\pi\)
0.187826 + 0.982202i \(0.439856\pi\)
\(920\) 2471.96 372.587i 0.0885848 0.0133520i
\(921\) −11168.9 + 17676.5i −0.399595 + 0.632421i
\(922\) 355.410 2357.99i 0.0126950 0.0842260i
\(923\) 14603.0 7032.42i 0.520761 0.250785i
\(924\) −10444.3 17923.4i −0.371853 0.638134i
\(925\) −21182.8 10201.1i −0.752958 0.362605i
\(926\) −1087.29 + 1594.77i −0.0385861 + 0.0565954i
\(927\) 1256.01 + 17971.0i 0.0445015 + 0.636727i
\(928\) −1108.13 + 14787.0i −0.0391985 + 0.523067i
\(929\) −5888.11 + 15002.7i −0.207947 + 0.529840i −0.996354 0.0853138i \(-0.972811\pi\)
0.788407 + 0.615153i \(0.210906\pi\)
\(930\) −438.810 1012.69i −0.0154722 0.0357070i
\(931\) −19054.9 32030.8i −0.670782 1.12757i
\(932\) 4599.57i 0.161656i
\(933\) −43419.8 + 1515.48i −1.52358 + 0.0531773i
\(934\) 386.991 + 29.0010i 0.0135575 + 0.00101600i
\(935\) −28574.2 + 30795.6i −0.999439 + 1.07714i
\(936\) 6567.12 1464.24i 0.229330 0.0511327i
\(937\) 14289.4 29672.3i 0.498202 1.03453i −0.488587 0.872515i \(-0.662488\pi\)
0.986789 0.162011i \(-0.0517981\pi\)
\(938\) −146.477 + 1380.99i −0.00509876 + 0.0480715i
\(939\) 8032.98 9287.22i 0.279176 0.322766i
\(940\) 26279.2 + 3960.96i 0.911845 + 0.137439i
\(941\) 36118.9 24625.4i 1.25127 0.853099i 0.257686 0.966229i \(-0.417040\pi\)
0.993580 + 0.113130i \(0.0360875\pi\)
\(942\) −2122.19 3396.35i −0.0734021 0.117473i
\(943\) 8963.77 + 9660.65i 0.309545 + 0.333610i
\(944\) −20218.1 25352.7i −0.697080 0.874111i
\(945\) −17254.2 + 43833.3i −0.593945 + 1.50889i
\(946\) 1703.76 2136.45i 0.0585561 0.0734270i
\(947\) 25659.7 1922.93i 0.880495 0.0659839i 0.373194 0.927753i \(-0.378263\pi\)
0.507300 + 0.861769i \(0.330643\pi\)
\(948\) 475.556 + 4318.11i 0.0162926 + 0.147939i
\(949\) −7280.53 + 12610.2i −0.249037 + 0.431344i
\(950\) −3365.55 5829.30i −0.114940 0.199081i
\(951\) −4497.76 6126.39i −0.153365 0.208898i
\(952\) 6157.29 + 4482.49i 0.209621 + 0.152603i
\(953\) 11507.0 + 2626.39i 0.391131 + 0.0892731i 0.413564 0.910475i \(-0.364284\pi\)
−0.0224325 + 0.999748i \(0.507141\pi\)
\(954\) 1059.73 2172.58i 0.0359645 0.0737315i
\(955\) −35529.4 + 13944.3i −1.20388 + 0.472488i
\(956\) −1227.95 + 481.935i −0.0415427 + 0.0163043i
\(957\) 23760.3 + 27750.6i 0.802571 + 0.937355i
\(958\) −337.971 77.1398i −0.0113981 0.00260154i
\(959\) −11173.6 2038.69i −0.376240 0.0686474i
\(960\) 36208.8 26583.1i 1.21733 0.893715i
\(961\) −14153.5 24514.6i −0.475093 0.822886i
\(962\) 904.112 1565.97i 0.0303012 0.0524832i
\(963\) 5308.25 + 9301.73i 0.177628 + 0.311261i
\(964\) −8943.73 + 670.240i −0.298816 + 0.0223931i
\(965\) 48523.4 60846.4i 1.61868 2.02976i
\(966\) −724.080 414.178i −0.0241169 0.0137950i
\(967\) 6368.16 + 7985.42i 0.211775 + 0.265557i 0.876362 0.481654i \(-0.159964\pi\)
−0.664587 + 0.747211i \(0.731392\pi\)
\(968\) 1934.44 + 2084.83i 0.0642306 + 0.0692241i
\(969\) 40700.8 25431.7i 1.34933 0.843120i
\(970\) 978.650 667.232i 0.0323944 0.0220861i
\(971\) 5736.94 + 864.704i 0.189606 + 0.0285784i 0.243159 0.969987i \(-0.421816\pi\)
−0.0535529 + 0.998565i \(0.517055\pi\)
\(972\) 18088.2 23875.4i 0.596894 0.787863i
\(973\) 42412.4 + 14530.7i 1.39741 + 0.478758i
\(974\) 1804.38 3746.83i 0.0593594 0.123261i
\(975\) −53541.8 10270.0i −1.75868 0.337336i
\(976\) −28876.4 + 31121.4i −0.947041 + 1.02067i
\(977\) −37874.7 2838.32i −1.24025 0.0929435i −0.561599 0.827409i \(-0.689814\pi\)
−0.678646 + 0.734466i \(0.737433\pi\)
\(978\) −20.9204 599.389i −0.000684009 0.0195975i
\(979\) 28354.7i 0.925659i
\(980\) 47793.1 11567.0i 1.55785 0.377035i
\(981\) 23825.1 25420.1i 0.775411 0.827321i
\(982\) 1272.71 3242.80i 0.0413581 0.105379i
\(983\) 3328.99 44422.3i 0.108015 1.44136i −0.635223 0.772328i \(-0.719092\pi\)
0.743238 0.669027i \(-0.233289\pi\)
\(984\) −10961.6 3866.55i −0.355124 0.125265i
\(985\) 27729.9 40672.2i 0.897002 1.31566i
\(986\) −6007.05 2892.84i −0.194020 0.0934349i
\(987\) −12186.5 13028.6i −0.393011 0.420167i
\(988\) −39875.5 + 19203.1i −1.28402 + 0.618351i
\(989\) −1400.15 + 9289.37i −0.0450173 + 0.298670i
\(990\) −625.002 + 4009.87i −0.0200645 + 0.128729i
\(991\) 29520.6 4449.52i 0.946270 0.142627i 0.342261 0.939605i \(-0.388807\pi\)
0.604009 + 0.796978i \(0.293569\pi\)
\(992\) 1623.59 1506.47i 0.0519647 0.0482162i
\(993\) 5699.06 10717.9i 0.182129 0.342520i
\(994\) 1739.23 340.855i 0.0554979 0.0108765i
\(995\) 13334.3 + 10633.7i 0.424849 + 0.338806i
\(996\) 16389.9 8609.72i 0.521419 0.273905i
\(997\) 12388.1 40161.1i 0.393515 1.27574i −0.514748 0.857342i \(-0.672114\pi\)
0.908262 0.418401i \(-0.137409\pi\)
\(998\) 4688.49 + 2706.90i 0.148709 + 0.0858572i
\(999\) −2890.69 15933.9i −0.0915490 0.504630i
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 147.4.o.a.101.27 648
3.2 odd 2 inner 147.4.o.a.101.28 yes 648
49.33 odd 42 inner 147.4.o.a.131.28 yes 648
147.131 even 42 inner 147.4.o.a.131.27 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.4.o.a.101.27 648 1.1 even 1 trivial
147.4.o.a.101.28 yes 648 3.2 odd 2 inner
147.4.o.a.131.27 yes 648 147.131 even 42 inner
147.4.o.a.131.28 yes 648 49.33 odd 42 inner