Properties

Label 338.4.c.l.315.2
Level $338$
Weight $4$
Character 338.315
Analytic conductor $19.943$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [338,4,Mod(191,338)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(338, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("338.191");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 338.c (of order \(3\), degree \(2\), not 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: \(19.9426455819\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 315.2
Root \(0.900969 + 1.56052i\) of defining polynomial
Character \(\chi\) \(=\) 338.315
Dual form 338.4.c.l.191.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(1.83244 + 3.17387i) q^{3} +(-2.00000 + 3.46410i) q^{4} -8.53079 q^{5} +(-3.66487 + 6.34775i) q^{6} +(-2.10052 + 3.63821i) q^{7} -8.00000 q^{8} +(6.78435 - 11.7508i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(1.83244 + 3.17387i) q^{3} +(-2.00000 + 3.46410i) q^{4} -8.53079 q^{5} +(-3.66487 + 6.34775i) q^{6} +(-2.10052 + 3.63821i) q^{7} -8.00000 q^{8} +(6.78435 - 11.7508i) q^{9} +(-8.53079 - 14.7758i) q^{10} +(-32.6863 - 56.6143i) q^{11} -14.6595 q^{12} -8.40209 q^{14} +(-15.6321 - 27.0757i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(13.4510 - 23.2977i) q^{17} +27.1374 q^{18} +(-6.68648 + 11.5813i) q^{19} +(17.0616 - 29.5515i) q^{20} -15.3963 q^{21} +(65.3726 - 113.229i) q^{22} +(-79.9645 - 138.503i) q^{23} +(-14.6595 - 25.3910i) q^{24} -52.2255 q^{25} +148.679 q^{27} +(-8.40209 - 14.5529i) q^{28} +(150.644 + 260.923i) q^{29} +(31.2643 - 54.1513i) q^{30} +73.0232 q^{31} +(16.0000 - 27.7128i) q^{32} +(119.791 - 207.484i) q^{33} +53.8038 q^{34} +(17.9191 - 31.0368i) q^{35} +(27.1374 + 47.0033i) q^{36} +(-59.3904 - 102.867i) q^{37} -26.7459 q^{38} +68.2464 q^{40} +(-216.451 - 374.903i) q^{41} +(-15.3963 - 26.6672i) q^{42} +(178.254 - 308.745i) q^{43} +261.490 q^{44} +(-57.8759 + 100.244i) q^{45} +(159.929 - 277.005i) q^{46} -588.614 q^{47} +(29.3190 - 50.7820i) q^{48} +(162.676 + 281.762i) q^{49} +(-52.2255 - 90.4573i) q^{50} +98.5921 q^{51} -269.462 q^{53} +(148.679 + 257.520i) q^{54} +(278.840 + 482.965i) q^{55} +(16.8042 - 29.1057i) q^{56} -49.0102 q^{57} +(-301.288 + 521.846i) q^{58} +(115.170 - 199.480i) q^{59} +125.057 q^{60} +(190.408 - 329.796i) q^{61} +(73.0232 + 126.480i) q^{62} +(28.5014 + 49.3658i) q^{63} +64.0000 q^{64} +479.164 q^{66} +(217.924 + 377.456i) q^{67} +(53.8038 + 93.1909i) q^{68} +(293.060 - 507.595i) q^{69} +71.6765 q^{70} +(32.9811 - 57.1249i) q^{71} +(-54.2748 + 94.0067i) q^{72} -885.517 q^{73} +(118.781 - 205.735i) q^{74} +(-95.7000 - 165.757i) q^{75} +(-26.7459 - 46.3253i) q^{76} +274.633 q^{77} -385.463 q^{79} +(68.2464 + 118.206i) q^{80} +(89.2679 + 154.616i) q^{81} +(432.901 - 749.807i) q^{82} +254.207 q^{83} +(30.7926 - 53.3344i) q^{84} +(-114.747 + 198.748i) q^{85} +713.016 q^{86} +(-552.091 + 956.250i) q^{87} +(261.490 + 452.914i) q^{88} +(-186.306 - 322.692i) q^{89} -231.504 q^{90} +639.716 q^{92} +(133.810 + 231.766i) q^{93} +(-588.614 - 1019.51i) q^{94} +(57.0410 - 98.7979i) q^{95} +117.276 q^{96} +(656.942 - 1137.86i) q^{97} +(-325.351 + 563.525i) q^{98} -887.020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 12 q^{3} - 12 q^{4} + 24 q^{5} - 24 q^{6} + 27 q^{7} - 48 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 12 q^{3} - 12 q^{4} + 24 q^{5} - 24 q^{6} + 27 q^{7} - 48 q^{8} - 9 q^{9} + 24 q^{10} - 82 q^{11} - 96 q^{12} + 108 q^{14} + 90 q^{15} - 48 q^{16} + 90 q^{17} - 36 q^{18} - 130 q^{19} - 48 q^{20} + 468 q^{21} + 164 q^{22} - 19 q^{23} - 96 q^{24} - 122 q^{25} - 138 q^{27} + 108 q^{28} + 101 q^{29} - 180 q^{30} + 1038 q^{31} + 96 q^{32} + 146 q^{33} + 360 q^{34} + 458 q^{35} - 36 q^{36} - 84 q^{37} - 520 q^{38} - 192 q^{40} - 187 q^{41} + 468 q^{42} + 1205 q^{43} + 656 q^{44} - 645 q^{45} + 38 q^{46} - 1072 q^{47} + 192 q^{48} + 184 q^{49} - 122 q^{50} - 414 q^{51} - 2190 q^{53} - 138 q^{54} + 526 q^{55} - 216 q^{56} - 2818 q^{57} - 202 q^{58} + 1413 q^{59} - 720 q^{60} + 1108 q^{61} + 1038 q^{62} + 1404 q^{63} + 384 q^{64} + 584 q^{66} + 1605 q^{67} + 360 q^{68} + 314 q^{69} + 1832 q^{70} + 909 q^{71} + 72 q^{72} + 574 q^{73} + 168 q^{74} + 505 q^{75} - 520 q^{76} + 960 q^{77} - 3922 q^{79} - 192 q^{80} - 915 q^{81} + 374 q^{82} + 382 q^{83} - 936 q^{84} - 67 q^{85} + 4820 q^{86} - 1636 q^{87} + 656 q^{88} - 1091 q^{89} - 2580 q^{90} + 152 q^{92} + 1614 q^{93} - 1072 q^{94} - 1829 q^{95} + 768 q^{96} + 947 q^{97} - 368 q^{98} - 4114 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).

\(n\) \(171\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 1.83244 + 3.17387i 0.352653 + 0.610812i 0.986713 0.162471i \(-0.0519464\pi\)
−0.634061 + 0.773283i \(0.718613\pi\)
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −8.53079 −0.763017 −0.381509 0.924365i \(-0.624595\pi\)
−0.381509 + 0.924365i \(0.624595\pi\)
\(6\) −3.66487 + 6.34775i −0.249363 + 0.431910i
\(7\) −2.10052 + 3.63821i −0.113418 + 0.196445i −0.917146 0.398551i \(-0.869513\pi\)
0.803729 + 0.594996i \(0.202846\pi\)
\(8\) −8.00000 −0.353553
\(9\) 6.78435 11.7508i 0.251272 0.435216i
\(10\) −8.53079 14.7758i −0.269767 0.467251i
\(11\) −32.6863 56.6143i −0.895935 1.55180i −0.832643 0.553810i \(-0.813174\pi\)
−0.0632915 0.997995i \(-0.520160\pi\)
\(12\) −14.6595 −0.352653
\(13\) 0 0
\(14\) −8.40209 −0.160397
\(15\) −15.6321 27.0757i −0.269080 0.466061i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 13.4510 23.2977i 0.191902 0.332384i −0.753979 0.656899i \(-0.771868\pi\)
0.945881 + 0.324515i \(0.105201\pi\)
\(18\) 27.1374 0.355352
\(19\) −6.68648 + 11.5813i −0.0807360 + 0.139839i −0.903566 0.428448i \(-0.859060\pi\)
0.822830 + 0.568287i \(0.192394\pi\)
\(20\) 17.0616 29.5515i 0.190754 0.330396i
\(21\) −15.3963 −0.159988
\(22\) 65.3726 113.229i 0.633522 1.09729i
\(23\) −79.9645 138.503i −0.724946 1.25564i −0.958996 0.283419i \(-0.908531\pi\)
0.234050 0.972225i \(-0.424802\pi\)
\(24\) −14.6595 25.3910i −0.124682 0.215955i
\(25\) −52.2255 −0.417804
\(26\) 0 0
\(27\) 148.679 1.05975
\(28\) −8.40209 14.5529i −0.0567088 0.0982225i
\(29\) 150.644 + 260.923i 0.964616 + 1.67076i 0.710643 + 0.703553i \(0.248404\pi\)
0.253973 + 0.967211i \(0.418262\pi\)
\(30\) 31.2643 54.1513i 0.190268 0.329555i
\(31\) 73.0232 0.423076 0.211538 0.977370i \(-0.432153\pi\)
0.211538 + 0.977370i \(0.432153\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 119.791 207.484i 0.631908 1.09450i
\(34\) 53.8038 0.271390
\(35\) 17.9191 31.0368i 0.0865396 0.149891i
\(36\) 27.1374 + 47.0033i 0.125636 + 0.217608i
\(37\) −59.3904 102.867i −0.263885 0.457061i 0.703386 0.710808i \(-0.251670\pi\)
−0.967271 + 0.253746i \(0.918337\pi\)
\(38\) −26.7459 −0.114178
\(39\) 0 0
\(40\) 68.2464 0.269767
\(41\) −216.451 374.903i −0.824486 1.42805i −0.902312 0.431084i \(-0.858131\pi\)
0.0778262 0.996967i \(-0.475202\pi\)
\(42\) −15.3963 26.6672i −0.0565643 0.0979723i
\(43\) 178.254 308.745i 0.632174 1.09496i −0.354933 0.934892i \(-0.615496\pi\)
0.987106 0.160065i \(-0.0511704\pi\)
\(44\) 261.490 0.895935
\(45\) −57.8759 + 100.244i −0.191725 + 0.332078i
\(46\) 159.929 277.005i 0.512614 0.887874i
\(47\) −588.614 −1.82677 −0.913385 0.407096i \(-0.866541\pi\)
−0.913385 + 0.407096i \(0.866541\pi\)
\(48\) 29.3190 50.7820i 0.0881632 0.152703i
\(49\) 162.676 + 281.762i 0.474273 + 0.821465i
\(50\) −52.2255 90.4573i −0.147716 0.255852i
\(51\) 98.5921 0.270699
\(52\) 0 0
\(53\) −269.462 −0.698366 −0.349183 0.937054i \(-0.613541\pi\)
−0.349183 + 0.937054i \(0.613541\pi\)
\(54\) 148.679 + 257.520i 0.374679 + 0.648963i
\(55\) 278.840 + 482.965i 0.683614 + 1.18405i
\(56\) 16.8042 29.1057i 0.0400992 0.0694538i
\(57\) −49.0102 −0.113887
\(58\) −301.288 + 521.846i −0.682087 + 1.18141i
\(59\) 115.170 199.480i 0.254133 0.440171i −0.710527 0.703670i \(-0.751543\pi\)
0.964660 + 0.263499i \(0.0848767\pi\)
\(60\) 125.057 0.269080
\(61\) 190.408 329.796i 0.399659 0.692230i −0.594024 0.804447i \(-0.702462\pi\)
0.993684 + 0.112217i \(0.0357951\pi\)
\(62\) 73.0232 + 126.480i 0.149580 + 0.259080i
\(63\) 28.5014 + 49.3658i 0.0569974 + 0.0987223i
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) 479.164 0.893652
\(67\) 217.924 + 377.456i 0.397368 + 0.688262i 0.993400 0.114699i \(-0.0365903\pi\)
−0.596032 + 0.802961i \(0.703257\pi\)
\(68\) 53.8038 + 93.1909i 0.0959510 + 0.166192i
\(69\) 293.060 507.595i 0.511308 0.885612i
\(70\) 71.6765 0.122385
\(71\) 32.9811 57.1249i 0.0551287 0.0954857i −0.837144 0.546982i \(-0.815776\pi\)
0.892273 + 0.451497i \(0.149110\pi\)
\(72\) −54.2748 + 94.0067i −0.0888381 + 0.153872i
\(73\) −885.517 −1.41975 −0.709876 0.704326i \(-0.751249\pi\)
−0.709876 + 0.704326i \(0.751249\pi\)
\(74\) 118.781 205.735i 0.186595 0.323191i
\(75\) −95.7000 165.757i −0.147340 0.255200i
\(76\) −26.7459 46.3253i −0.0403680 0.0699194i
\(77\) 274.633 0.406459
\(78\) 0 0
\(79\) −385.463 −0.548962 −0.274481 0.961592i \(-0.588506\pi\)
−0.274481 + 0.961592i \(0.588506\pi\)
\(80\) 68.2464 + 118.206i 0.0953772 + 0.165198i
\(81\) 89.2679 + 154.616i 0.122452 + 0.212094i
\(82\) 432.901 749.807i 0.582999 1.00978i
\(83\) 254.207 0.336179 0.168089 0.985772i \(-0.446240\pi\)
0.168089 + 0.985772i \(0.446240\pi\)
\(84\) 30.7926 53.3344i 0.0399970 0.0692769i
\(85\) −114.747 + 198.748i −0.146425 + 0.253615i
\(86\) 713.016 0.894029
\(87\) −552.091 + 956.250i −0.680349 + 1.17840i
\(88\) 261.490 + 452.914i 0.316761 + 0.548646i
\(89\) −186.306 322.692i −0.221892 0.384329i 0.733490 0.679700i \(-0.237890\pi\)
−0.955383 + 0.295371i \(0.904557\pi\)
\(90\) −231.504 −0.271140
\(91\) 0 0
\(92\) 639.716 0.724946
\(93\) 133.810 + 231.766i 0.149199 + 0.258420i
\(94\) −588.614 1019.51i −0.645861 1.11866i
\(95\) 57.0410 98.7979i 0.0616030 0.106699i
\(96\) 117.276 0.124682
\(97\) 656.942 1137.86i 0.687653 1.19105i −0.284942 0.958545i \(-0.591974\pi\)
0.972595 0.232506i \(-0.0746924\pi\)
\(98\) −325.351 + 563.525i −0.335362 + 0.580863i
\(99\) −887.020 −0.900494
\(100\) 104.451 180.915i 0.104451 0.180915i
\(101\) −731.861 1267.62i −0.721019 1.24884i −0.960592 0.277963i \(-0.910341\pi\)
0.239573 0.970878i \(-0.422993\pi\)
\(102\) 98.5921 + 170.767i 0.0957066 + 0.165769i
\(103\) 210.886 0.201740 0.100870 0.994900i \(-0.467837\pi\)
0.100870 + 0.994900i \(0.467837\pi\)
\(104\) 0 0
\(105\) 131.343 0.122074
\(106\) −269.462 466.722i −0.246910 0.427660i
\(107\) −195.531 338.669i −0.176660 0.305985i 0.764074 0.645128i \(-0.223196\pi\)
−0.940735 + 0.339144i \(0.889863\pi\)
\(108\) −297.358 + 515.040i −0.264938 + 0.458886i
\(109\) −1331.40 −1.16996 −0.584978 0.811049i \(-0.698897\pi\)
−0.584978 + 0.811049i \(0.698897\pi\)
\(110\) −557.680 + 965.930i −0.483388 + 0.837253i
\(111\) 217.658 376.996i 0.186119 0.322368i
\(112\) 67.2167 0.0567088
\(113\) 355.956 616.534i 0.296332 0.513263i −0.678962 0.734174i \(-0.737570\pi\)
0.975294 + 0.220911i \(0.0709031\pi\)
\(114\) −49.0102 84.8882i −0.0402652 0.0697413i
\(115\) 682.161 + 1181.54i 0.553146 + 0.958078i
\(116\) −1205.15 −0.964616
\(117\) 0 0
\(118\) 460.679 0.359398
\(119\) 56.5081 + 97.8748i 0.0435301 + 0.0753964i
\(120\) 125.057 + 216.605i 0.0951342 + 0.164777i
\(121\) −1471.29 + 2548.34i −1.10540 + 1.91461i
\(122\) 761.631 0.565204
\(123\) 793.264 1373.97i 0.581514 1.00721i
\(124\) −146.046 + 252.960i −0.105769 + 0.183197i
\(125\) 1511.87 1.08181
\(126\) −57.0027 + 98.7316i −0.0403032 + 0.0698072i
\(127\) 585.852 + 1014.73i 0.409338 + 0.708995i 0.994816 0.101694i \(-0.0324262\pi\)
−0.585477 + 0.810689i \(0.699093\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 1306.56 0.891751
\(130\) 0 0
\(131\) −1128.61 −0.752726 −0.376363 0.926472i \(-0.622825\pi\)
−0.376363 + 0.926472i \(0.622825\pi\)
\(132\) 479.164 + 829.937i 0.315954 + 0.547248i
\(133\) −28.0902 48.6537i −0.0183138 0.0317204i
\(134\) −435.848 + 754.911i −0.280982 + 0.486675i
\(135\) −1268.35 −0.808610
\(136\) −107.608 + 186.382i −0.0678476 + 0.117516i
\(137\) −873.967 + 1513.76i −0.545022 + 0.944006i 0.453583 + 0.891214i \(0.350145\pi\)
−0.998606 + 0.0527923i \(0.983188\pi\)
\(138\) 1172.24 0.723099
\(139\) −838.268 + 1451.92i −0.511518 + 0.885975i 0.488393 + 0.872624i \(0.337583\pi\)
−0.999911 + 0.0133509i \(0.995750\pi\)
\(140\) 71.6765 + 124.147i 0.0432698 + 0.0749455i
\(141\) −1078.60 1868.19i −0.644216 1.11581i
\(142\) 131.924 0.0779637
\(143\) 0 0
\(144\) −217.099 −0.125636
\(145\) −1285.11 2225.88i −0.736019 1.27482i
\(146\) −885.517 1533.76i −0.501958 0.869417i
\(147\) −596.186 + 1032.62i −0.334507 + 0.579384i
\(148\) 475.124 0.263885
\(149\) −448.481 + 776.791i −0.246584 + 0.427095i −0.962576 0.271013i \(-0.912641\pi\)
0.715992 + 0.698108i \(0.245975\pi\)
\(150\) 191.400 331.515i 0.104185 0.180454i
\(151\) 2078.28 1.12005 0.560027 0.828475i \(-0.310791\pi\)
0.560027 + 0.828475i \(0.310791\pi\)
\(152\) 53.4918 92.6506i 0.0285445 0.0494405i
\(153\) −182.512 316.120i −0.0964393 0.167038i
\(154\) 274.633 + 475.679i 0.143705 + 0.248904i
\(155\) −622.946 −0.322814
\(156\) 0 0
\(157\) −3494.75 −1.77650 −0.888252 0.459357i \(-0.848080\pi\)
−0.888252 + 0.459357i \(0.848080\pi\)
\(158\) −385.463 667.642i −0.194087 0.336169i
\(159\) −493.772 855.238i −0.246281 0.426571i
\(160\) −136.493 + 236.412i −0.0674419 + 0.116813i
\(161\) 671.869 0.328887
\(162\) −178.536 + 309.233i −0.0865870 + 0.149973i
\(163\) −225.627 + 390.797i −0.108420 + 0.187789i −0.915130 0.403158i \(-0.867912\pi\)
0.806710 + 0.590947i \(0.201246\pi\)
\(164\) 1731.61 0.824486
\(165\) −1021.91 + 1770.01i −0.482157 + 0.835120i
\(166\) 254.207 + 440.299i 0.118857 + 0.205867i
\(167\) 1601.68 + 2774.18i 0.742164 + 1.28547i 0.951508 + 0.307624i \(0.0995338\pi\)
−0.209344 + 0.977842i \(0.567133\pi\)
\(168\) 123.170 0.0565643
\(169\) 0 0
\(170\) −458.989 −0.207076
\(171\) 90.7268 + 157.143i 0.0405734 + 0.0702752i
\(172\) 713.016 + 1234.98i 0.316087 + 0.547478i
\(173\) −949.691 + 1644.91i −0.417362 + 0.722893i −0.995673 0.0929237i \(-0.970379\pi\)
0.578311 + 0.815816i \(0.303712\pi\)
\(174\) −2208.36 −0.962159
\(175\) 109.701 190.008i 0.0473864 0.0820756i
\(176\) −522.980 + 905.829i −0.223984 + 0.387951i
\(177\) 844.165 0.358482
\(178\) 372.612 645.384i 0.156902 0.271762i
\(179\) −1325.45 2295.74i −0.553455 0.958612i −0.998022 0.0628664i \(-0.979976\pi\)
0.444567 0.895746i \(-0.353358\pi\)
\(180\) −231.504 400.976i −0.0958625 0.166039i
\(181\) −2289.94 −0.940387 −0.470194 0.882563i \(-0.655816\pi\)
−0.470194 + 0.882563i \(0.655816\pi\)
\(182\) 0 0
\(183\) 1395.64 0.563764
\(184\) 639.716 + 1108.02i 0.256307 + 0.443937i
\(185\) 506.648 + 877.539i 0.201349 + 0.348746i
\(186\) −267.621 + 463.533i −0.105500 + 0.182731i
\(187\) −1758.65 −0.687727
\(188\) 1177.23 2039.02i 0.456693 0.791015i
\(189\) −312.304 + 540.926i −0.120195 + 0.208183i
\(190\) 228.164 0.0871198
\(191\) 169.157 292.988i 0.0640825 0.110994i −0.832204 0.554469i \(-0.812921\pi\)
0.896287 + 0.443475i \(0.146255\pi\)
\(192\) 117.276 + 203.128i 0.0440816 + 0.0763515i
\(193\) 1342.03 + 2324.46i 0.500524 + 0.866933i 1.00000 0.000605201i \(0.000192642\pi\)
−0.499476 + 0.866328i \(0.666474\pi\)
\(194\) 2627.77 0.972489
\(195\) 0 0
\(196\) −1301.40 −0.474273
\(197\) 948.620 + 1643.06i 0.343078 + 0.594229i 0.985003 0.172539i \(-0.0551971\pi\)
−0.641925 + 0.766768i \(0.721864\pi\)
\(198\) −887.020 1536.36i −0.318373 0.551438i
\(199\) 1207.80 2091.97i 0.430245 0.745207i −0.566649 0.823959i \(-0.691760\pi\)
0.996894 + 0.0787527i \(0.0250937\pi\)
\(200\) 417.804 0.147716
\(201\) −798.665 + 1383.33i −0.280266 + 0.485435i
\(202\) 1463.72 2535.24i 0.509837 0.883064i
\(203\) −1265.72 −0.437618
\(204\) −197.184 + 341.533i −0.0676748 + 0.117216i
\(205\) 1846.50 + 3198.22i 0.629097 + 1.08963i
\(206\) 210.886 + 365.265i 0.0713258 + 0.123540i
\(207\) −2170.03 −0.728635
\(208\) 0 0
\(209\) 874.225 0.289337
\(210\) 131.343 + 227.492i 0.0431596 + 0.0747546i
\(211\) −1334.21 2310.92i −0.435312 0.753982i 0.562009 0.827131i \(-0.310028\pi\)
−0.997321 + 0.0731491i \(0.976695\pi\)
\(212\) 538.924 933.443i 0.174592 0.302402i
\(213\) 241.743 0.0777651
\(214\) 391.061 677.338i 0.124918 0.216364i
\(215\) −1520.65 + 2633.84i −0.482360 + 0.835471i
\(216\) −1189.43 −0.374679
\(217\) −153.387 + 265.674i −0.0479842 + 0.0831112i
\(218\) −1331.40 2306.06i −0.413642 0.716449i
\(219\) −1622.65 2810.52i −0.500680 0.867202i
\(220\) −2230.72 −0.683614
\(221\) 0 0
\(222\) 870.634 0.263212
\(223\) −143.179 247.993i −0.0429953 0.0744701i 0.843727 0.536773i \(-0.180357\pi\)
−0.886722 + 0.462303i \(0.847023\pi\)
\(224\) 67.2167 + 116.423i 0.0200496 + 0.0347269i
\(225\) −354.316 + 613.694i −0.104983 + 0.181835i
\(226\) 1423.82 0.419077
\(227\) 2600.62 4504.41i 0.760393 1.31704i −0.182255 0.983251i \(-0.558340\pi\)
0.942648 0.333788i \(-0.108327\pi\)
\(228\) 98.0204 169.776i 0.0284718 0.0493145i
\(229\) −890.458 −0.256957 −0.128478 0.991712i \(-0.541009\pi\)
−0.128478 + 0.991712i \(0.541009\pi\)
\(230\) −1364.32 + 2363.08i −0.391134 + 0.677463i
\(231\) 503.248 + 871.651i 0.143339 + 0.248270i
\(232\) −1205.15 2087.38i −0.341043 0.590704i
\(233\) 4753.11 1.33642 0.668212 0.743971i \(-0.267060\pi\)
0.668212 + 0.743971i \(0.267060\pi\)
\(234\) 0 0
\(235\) 5021.35 1.39386
\(236\) 460.679 + 797.919i 0.127066 + 0.220085i
\(237\) −706.337 1223.41i −0.193593 0.335313i
\(238\) −113.016 + 195.750i −0.0307805 + 0.0533133i
\(239\) 2292.62 0.620491 0.310245 0.950656i \(-0.399589\pi\)
0.310245 + 0.950656i \(0.399589\pi\)
\(240\) −250.114 + 433.211i −0.0672700 + 0.116515i
\(241\) 987.604 1710.58i 0.263972 0.457212i −0.703322 0.710871i \(-0.748301\pi\)
0.967294 + 0.253659i \(0.0816341\pi\)
\(242\) −5885.14 −1.56327
\(243\) 1680.01 2909.87i 0.443510 0.768182i
\(244\) 761.631 + 1319.18i 0.199830 + 0.346115i
\(245\) −1387.75 2403.66i −0.361879 0.626792i
\(246\) 3173.06 0.822385
\(247\) 0 0
\(248\) −584.186 −0.149580
\(249\) 465.818 + 806.821i 0.118554 + 0.205342i
\(250\) 1511.87 + 2618.64i 0.382477 + 0.662470i
\(251\) 3732.87 6465.52i 0.938711 1.62590i 0.170833 0.985300i \(-0.445354\pi\)
0.767879 0.640595i \(-0.221312\pi\)
\(252\) −228.011 −0.0569974
\(253\) −5227.49 + 9054.27i −1.29901 + 2.24995i
\(254\) −1171.70 + 2029.45i −0.289446 + 0.501335i
\(255\) −841.069 −0.206548
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 277.483 + 480.615i 0.0673499 + 0.116653i 0.897734 0.440538i \(-0.145212\pi\)
−0.830384 + 0.557191i \(0.811879\pi\)
\(258\) 1306.56 + 2263.02i 0.315282 + 0.546084i
\(259\) 499.004 0.119717
\(260\) 0 0
\(261\) 4088.08 0.969525
\(262\) −1128.61 1954.81i −0.266129 0.460949i
\(263\) 996.534 + 1726.05i 0.233646 + 0.404687i 0.958878 0.283817i \(-0.0916010\pi\)
−0.725232 + 0.688504i \(0.758268\pi\)
\(264\) −958.329 + 1659.87i −0.223413 + 0.386963i
\(265\) 2298.72 0.532866
\(266\) 56.1804 97.3074i 0.0129498 0.0224297i
\(267\) 682.789 1182.63i 0.156502 0.271069i
\(268\) −1743.39 −0.397368
\(269\) 2603.88 4510.06i 0.590191 1.02224i −0.404015 0.914752i \(-0.632386\pi\)
0.994206 0.107489i \(-0.0342811\pi\)
\(270\) −1268.35 2196.85i −0.285887 0.495170i
\(271\) 2042.45 + 3537.63i 0.457823 + 0.792972i 0.998846 0.0480356i \(-0.0152961\pi\)
−0.541023 + 0.841008i \(0.681963\pi\)
\(272\) −430.430 −0.0959510
\(273\) 0 0
\(274\) −3495.87 −0.770778
\(275\) 1707.06 + 2956.71i 0.374325 + 0.648351i
\(276\) 1172.24 + 2030.38i 0.255654 + 0.442806i
\(277\) −218.996 + 379.313i −0.0475026 + 0.0822769i −0.888799 0.458297i \(-0.848460\pi\)
0.841296 + 0.540574i \(0.181793\pi\)
\(278\) −3353.07 −0.723395
\(279\) 495.415 858.083i 0.106307 0.184129i
\(280\) −143.353 + 248.295i −0.0305964 + 0.0529945i
\(281\) −5462.34 −1.15963 −0.579815 0.814748i \(-0.696875\pi\)
−0.579815 + 0.814748i \(0.696875\pi\)
\(282\) 2157.20 3736.38i 0.455529 0.789000i
\(283\) 398.338 + 689.941i 0.0836704 + 0.144921i 0.904824 0.425786i \(-0.140002\pi\)
−0.821153 + 0.570707i \(0.806669\pi\)
\(284\) 131.924 + 228.500i 0.0275643 + 0.0477428i
\(285\) 418.096 0.0868978
\(286\) 0 0
\(287\) 1818.64 0.374045
\(288\) −217.099 376.027i −0.0444191 0.0769361i
\(289\) 2094.64 + 3628.03i 0.426347 + 0.738455i
\(290\) 2570.22 4451.76i 0.520444 0.901436i
\(291\) 4815.22 0.970011
\(292\) 1771.03 3067.52i 0.354938 0.614771i
\(293\) 848.662 1469.93i 0.169213 0.293085i −0.768931 0.639332i \(-0.779211\pi\)
0.938143 + 0.346247i \(0.112544\pi\)
\(294\) −2384.74 −0.473065
\(295\) −982.490 + 1701.72i −0.193908 + 0.335858i
\(296\) 475.124 + 822.938i 0.0932973 + 0.161596i
\(297\) −4859.77 8417.37i −0.949469 1.64453i
\(298\) −1793.92 −0.348722
\(299\) 0 0
\(300\) 765.600 0.147340
\(301\) 748.853 + 1297.05i 0.143399 + 0.248375i
\(302\) 2078.28 + 3599.69i 0.395999 + 0.685890i
\(303\) 2682.18 4645.67i 0.508538 0.880814i
\(304\) 213.967 0.0403680
\(305\) −1624.33 + 2813.42i −0.304947 + 0.528184i
\(306\) 365.024 632.240i 0.0681929 0.118114i
\(307\) 9385.86 1.74488 0.872442 0.488718i \(-0.162535\pi\)
0.872442 + 0.488718i \(0.162535\pi\)
\(308\) −549.266 + 951.357i −0.101615 + 0.176002i
\(309\) 386.435 + 669.325i 0.0711441 + 0.123225i
\(310\) −622.946 1078.97i −0.114132 0.197683i
\(311\) −3282.65 −0.598527 −0.299264 0.954170i \(-0.596741\pi\)
−0.299264 + 0.954170i \(0.596741\pi\)
\(312\) 0 0
\(313\) −5924.67 −1.06991 −0.534955 0.844880i \(-0.679672\pi\)
−0.534955 + 0.844880i \(0.679672\pi\)
\(314\) −3494.75 6053.08i −0.628089 1.08788i
\(315\) −243.139 421.130i −0.0434900 0.0753269i
\(316\) 770.927 1335.28i 0.137241 0.237708i
\(317\) 6467.88 1.14597 0.572985 0.819566i \(-0.305785\pi\)
0.572985 + 0.819566i \(0.305785\pi\)
\(318\) 987.544 1710.48i 0.174147 0.301631i
\(319\) 9847.98 17057.2i 1.72847 2.99379i
\(320\) −545.971 −0.0953772
\(321\) 716.595 1241.18i 0.124599 0.215813i
\(322\) 671.869 + 1163.71i 0.116279 + 0.201401i
\(323\) 179.879 + 311.560i 0.0309868 + 0.0536707i
\(324\) −714.143 −0.122452
\(325\) 0 0
\(326\) −902.508 −0.153329
\(327\) −2439.71 4225.70i −0.412588 0.714624i
\(328\) 1731.61 + 2999.23i 0.291500 + 0.504892i
\(329\) 1236.40 2141.50i 0.207188 0.358860i
\(330\) −4087.65 −0.681872
\(331\) −1754.62 + 3039.09i −0.291368 + 0.504664i −0.974133 0.225974i \(-0.927444\pi\)
0.682766 + 0.730637i \(0.260777\pi\)
\(332\) −508.414 + 880.599i −0.0840447 + 0.145570i
\(333\) −1611.70 −0.265227
\(334\) −3203.35 + 5548.37i −0.524789 + 0.908962i
\(335\) −1859.07 3220.00i −0.303199 0.525156i
\(336\) 123.170 + 213.337i 0.0199985 + 0.0346384i
\(337\) −1834.82 −0.296584 −0.148292 0.988944i \(-0.547378\pi\)
−0.148292 + 0.988944i \(0.547378\pi\)
\(338\) 0 0
\(339\) 2609.07 0.418010
\(340\) −458.989 794.993i −0.0732123 0.126807i
\(341\) −2386.86 4134.16i −0.379048 0.656531i
\(342\) −181.454 + 314.287i −0.0286897 + 0.0496921i
\(343\) −2807.77 −0.441999
\(344\) −1426.03 + 2469.96i −0.223507 + 0.387126i
\(345\) −2500.03 + 4330.19i −0.390137 + 0.675737i
\(346\) −3798.76 −0.590239
\(347\) 3629.65 6286.74i 0.561527 0.972593i −0.435837 0.900026i \(-0.643547\pi\)
0.997364 0.0725673i \(-0.0231192\pi\)
\(348\) −2208.36 3825.00i −0.340175 0.589200i
\(349\) 897.618 + 1554.72i 0.137674 + 0.238459i 0.926616 0.376009i \(-0.122704\pi\)
−0.788942 + 0.614468i \(0.789371\pi\)
\(350\) 438.804 0.0670144
\(351\) 0 0
\(352\) −2091.92 −0.316761
\(353\) 2276.19 + 3942.47i 0.343199 + 0.594438i 0.985025 0.172412i \(-0.0551561\pi\)
−0.641826 + 0.766850i \(0.721823\pi\)
\(354\) 844.165 + 1462.14i 0.126743 + 0.219525i
\(355\) −281.355 + 487.321i −0.0420641 + 0.0728572i
\(356\) 1490.45 0.221892
\(357\) −207.095 + 358.699i −0.0307020 + 0.0531775i
\(358\) 2650.89 4591.48i 0.391352 0.677841i
\(359\) 10165.4 1.49445 0.747227 0.664569i \(-0.231385\pi\)
0.747227 + 0.664569i \(0.231385\pi\)
\(360\) 463.007 801.952i 0.0677850 0.117407i
\(361\) 3340.08 + 5785.19i 0.486963 + 0.843445i
\(362\) −2289.94 3966.30i −0.332477 0.575867i
\(363\) −10784.2 −1.55929
\(364\) 0 0
\(365\) 7554.16 1.08330
\(366\) 1395.64 + 2417.32i 0.199321 + 0.345233i
\(367\) 5200.78 + 9008.01i 0.739723 + 1.28124i 0.952620 + 0.304163i \(0.0983769\pi\)
−0.212897 + 0.977075i \(0.568290\pi\)
\(368\) −1279.43 + 2216.04i −0.181237 + 0.313911i
\(369\) −5873.91 −0.828681
\(370\) −1013.30 + 1755.08i −0.142375 + 0.246601i
\(371\) 566.011 980.359i 0.0792070 0.137191i
\(372\) −1070.48 −0.149199
\(373\) 3976.70 6887.85i 0.552027 0.956138i −0.446101 0.894982i \(-0.647188\pi\)
0.998128 0.0611560i \(-0.0194787\pi\)
\(374\) −1758.65 3046.06i −0.243148 0.421145i
\(375\) 2770.42 + 4798.50i 0.381503 + 0.660783i
\(376\) 4708.91 0.645861
\(377\) 0 0
\(378\) −1249.22 −0.169981
\(379\) −4507.41 7807.06i −0.610897 1.05810i −0.991090 0.133197i \(-0.957476\pi\)
0.380193 0.924907i \(-0.375858\pi\)
\(380\) 228.164 + 395.192i 0.0308015 + 0.0533497i
\(381\) −2147.07 + 3718.84i −0.288709 + 0.500058i
\(382\) 676.627 0.0906263
\(383\) 1248.12 2161.81i 0.166517 0.288415i −0.770676 0.637227i \(-0.780081\pi\)
0.937193 + 0.348812i \(0.113415\pi\)
\(384\) −234.552 + 406.256i −0.0311704 + 0.0539887i
\(385\) −2342.84 −0.310135
\(386\) −2684.05 + 4648.91i −0.353924 + 0.613014i
\(387\) −2418.67 4189.26i −0.317695 0.550264i
\(388\) 2627.77 + 4551.43i 0.343827 + 0.595525i
\(389\) 10896.9 1.42029 0.710145 0.704056i \(-0.248629\pi\)
0.710145 + 0.704056i \(0.248629\pi\)
\(390\) 0 0
\(391\) −4302.40 −0.556475
\(392\) −1301.40 2254.10i −0.167681 0.290432i
\(393\) −2068.11 3582.07i −0.265451 0.459774i
\(394\) −1897.24 + 3286.12i −0.242593 + 0.420183i
\(395\) 3288.31 0.418868
\(396\) 1774.04 3072.73i 0.225123 0.389925i
\(397\) −5443.57 + 9428.55i −0.688174 + 1.19195i 0.284254 + 0.958749i \(0.408254\pi\)
−0.972428 + 0.233203i \(0.925079\pi\)
\(398\) 4831.21 0.608459
\(399\) 102.947 178.310i 0.0129168 0.0223725i
\(400\) 417.804 + 723.658i 0.0522255 + 0.0904573i
\(401\) −4984.38 8633.20i −0.620718 1.07512i −0.989352 0.145541i \(-0.953508\pi\)
0.368634 0.929575i \(-0.379826\pi\)
\(402\) −3194.66 −0.396356
\(403\) 0 0
\(404\) 5854.89 0.721019
\(405\) −761.526 1319.00i −0.0934334 0.161831i
\(406\) −1265.72 2192.30i −0.154721 0.267985i
\(407\) −3882.50 + 6724.70i −0.472847 + 0.818994i
\(408\) −788.737 −0.0957066
\(409\) −2018.16 + 3495.56i −0.243989 + 0.422602i −0.961847 0.273588i \(-0.911790\pi\)
0.717858 + 0.696190i \(0.245123\pi\)
\(410\) −3692.99 + 6396.45i −0.444839 + 0.770483i
\(411\) −6405.96 −0.768814
\(412\) −421.772 + 730.530i −0.0504350 + 0.0873559i
\(413\) 483.833 + 838.024i 0.0576462 + 0.0998462i
\(414\) −2170.03 3758.60i −0.257611 0.446196i
\(415\) −2168.59 −0.256510
\(416\) 0 0
\(417\) −6144.29 −0.721552
\(418\) 874.225 + 1514.20i 0.102296 + 0.177182i
\(419\) −7597.43 13159.1i −0.885821 1.53429i −0.844770 0.535129i \(-0.820263\pi\)
−0.0410504 0.999157i \(-0.513070\pi\)
\(420\) −262.685 + 454.985i −0.0305184 + 0.0528595i
\(421\) 10154.8 1.17556 0.587782 0.809019i \(-0.300001\pi\)
0.587782 + 0.809019i \(0.300001\pi\)
\(422\) 2668.42 4621.84i 0.307812 0.533146i
\(423\) −3993.36 + 6916.71i −0.459017 + 0.795040i
\(424\) 2155.69 0.246910
\(425\) −702.483 + 1216.74i −0.0801775 + 0.138872i
\(426\) 241.743 + 418.711i 0.0274941 + 0.0476212i
\(427\) 799.912 + 1385.49i 0.0906568 + 0.157022i
\(428\) 1564.24 0.176660
\(429\) 0 0
\(430\) −6082.59 −0.682159
\(431\) 3308.42 + 5730.35i 0.369747 + 0.640420i 0.989526 0.144356i \(-0.0461111\pi\)
−0.619779 + 0.784776i \(0.712778\pi\)
\(432\) −1189.43 2060.16i −0.132469 0.229443i
\(433\) −2848.80 + 4934.27i −0.316177 + 0.547635i −0.979687 0.200533i \(-0.935733\pi\)
0.663510 + 0.748167i \(0.269066\pi\)
\(434\) −613.548 −0.0678600
\(435\) 4709.77 8157.57i 0.519118 0.899139i
\(436\) 2662.81 4612.11i 0.292489 0.506606i
\(437\) 2138.73 0.234117
\(438\) 3245.31 5621.04i 0.354034 0.613205i
\(439\) −218.004 377.593i −0.0237010 0.0410513i 0.853932 0.520385i \(-0.174212\pi\)
−0.877633 + 0.479334i \(0.840878\pi\)
\(440\) −2230.72 3863.72i −0.241694 0.418626i
\(441\) 4414.59 0.476686
\(442\) 0 0
\(443\) 6609.58 0.708873 0.354436 0.935080i \(-0.384673\pi\)
0.354436 + 0.935080i \(0.384673\pi\)
\(444\) 870.634 + 1507.98i 0.0930596 + 0.161184i
\(445\) 1589.34 + 2752.82i 0.169308 + 0.293250i
\(446\) 286.358 495.986i 0.0304023 0.0526583i
\(447\) −3287.25 −0.347833
\(448\) −134.433 + 232.846i −0.0141772 + 0.0245556i
\(449\) −4007.65 + 6941.46i −0.421231 + 0.729594i −0.996060 0.0886795i \(-0.971735\pi\)
0.574829 + 0.818274i \(0.305069\pi\)
\(450\) −1417.26 −0.148468
\(451\) −14149.9 + 24508.4i −1.47737 + 2.55888i
\(452\) 1423.82 + 2466.14i 0.148166 + 0.256631i
\(453\) 3808.32 + 6596.20i 0.394990 + 0.684142i
\(454\) 10402.5 1.07536
\(455\) 0 0
\(456\) 392.082 0.0402652
\(457\) 2253.52 + 3903.21i 0.230668 + 0.399528i 0.958005 0.286752i \(-0.0925757\pi\)
−0.727337 + 0.686280i \(0.759242\pi\)
\(458\) −890.458 1542.32i −0.0908480 0.157353i
\(459\) 1999.88 3463.89i 0.203369 0.352245i
\(460\) −5457.29 −0.553146
\(461\) −1051.78 + 1821.73i −0.106260 + 0.184048i −0.914252 0.405145i \(-0.867221\pi\)
0.807992 + 0.589193i \(0.200554\pi\)
\(462\) −1006.50 + 1743.30i −0.101356 + 0.175554i
\(463\) 5468.28 0.548883 0.274441 0.961604i \(-0.411507\pi\)
0.274441 + 0.961604i \(0.411507\pi\)
\(464\) 2410.30 4174.77i 0.241154 0.417691i
\(465\) −1141.51 1977.15i −0.113841 0.197179i
\(466\) 4753.11 + 8232.63i 0.472497 + 0.818389i
\(467\) −6043.79 −0.598872 −0.299436 0.954116i \(-0.596799\pi\)
−0.299436 + 0.954116i \(0.596799\pi\)
\(468\) 0 0
\(469\) −1831.02 −0.180274
\(470\) 5021.35 + 8697.23i 0.492803 + 0.853560i
\(471\) −6403.90 11091.9i −0.626489 1.08511i
\(472\) −921.358 + 1595.84i −0.0898495 + 0.155624i
\(473\) −23305.8 −2.26555
\(474\) 1412.67 2446.82i 0.136891 0.237102i
\(475\) 349.205 604.841i 0.0337318 0.0584253i
\(476\) −452.065 −0.0435301
\(477\) −1828.12 + 3166.40i −0.175480 + 0.303940i
\(478\) 2292.62 + 3970.94i 0.219377 + 0.379972i
\(479\) 4240.65 + 7345.02i 0.404510 + 0.700632i 0.994264 0.106951i \(-0.0341088\pi\)
−0.589754 + 0.807583i \(0.700775\pi\)
\(480\) −1000.46 −0.0951342
\(481\) 0 0
\(482\) 3950.42 0.373312
\(483\) 1231.16 + 2132.43i 0.115983 + 0.200888i
\(484\) −5885.14 10193.4i −0.552699 0.957303i
\(485\) −5604.24 + 9706.83i −0.524691 + 0.908792i
\(486\) 6720.05 0.627218
\(487\) 3311.68 5735.99i 0.308145 0.533722i −0.669812 0.742531i \(-0.733625\pi\)
0.977957 + 0.208809i \(0.0669586\pi\)
\(488\) −1523.26 + 2638.37i −0.141301 + 0.244740i
\(489\) −1653.79 −0.152939
\(490\) 2775.50 4807.31i 0.255887 0.443209i
\(491\) −8189.68 14184.9i −0.752739 1.30378i −0.946490 0.322732i \(-0.895399\pi\)
0.193751 0.981051i \(-0.437935\pi\)
\(492\) 3173.06 + 5495.90i 0.290757 + 0.503606i
\(493\) 8105.21 0.740447
\(494\) 0 0
\(495\) 7566.99 0.687093
\(496\) −584.186 1011.84i −0.0528845 0.0915986i
\(497\) 138.555 + 239.985i 0.0125051 + 0.0216595i
\(498\) −931.637 + 1613.64i −0.0838306 + 0.145199i
\(499\) −7915.70 −0.710131 −0.355065 0.934841i \(-0.615541\pi\)
−0.355065 + 0.934841i \(0.615541\pi\)
\(500\) −3023.75 + 5237.29i −0.270452 + 0.468437i
\(501\) −5869.94 + 10167.0i −0.523452 + 0.906646i
\(502\) 14931.5 1.32754
\(503\) 239.755 415.269i 0.0212528 0.0368110i −0.855203 0.518293i \(-0.826568\pi\)
0.876456 + 0.481482i \(0.159901\pi\)
\(504\) −228.011 394.926i −0.0201516 0.0349036i
\(505\) 6243.36 + 10813.8i 0.550150 + 0.952888i
\(506\) −20909.9 −1.83708
\(507\) 0 0
\(508\) −4686.82 −0.409338
\(509\) −596.164 1032.59i −0.0519145 0.0899186i 0.838900 0.544285i \(-0.183199\pi\)
−0.890815 + 0.454366i \(0.849866\pi\)
\(510\) −841.069 1456.77i −0.0730258 0.126484i
\(511\) 1860.05 3221.70i 0.161025 0.278903i
\(512\) −512.000 −0.0441942
\(513\) −994.140 + 1721.90i −0.0855602 + 0.148195i
\(514\) −554.966 + 961.229i −0.0476236 + 0.0824864i
\(515\) −1799.02 −0.153931
\(516\) −2613.11 + 4526.04i −0.222938 + 0.386140i
\(517\) 19239.6 + 33324.0i 1.63667 + 2.83479i
\(518\) 499.004 + 864.300i 0.0423262 + 0.0733111i
\(519\) −6961.00 −0.588736
\(520\) 0 0
\(521\) −23238.5 −1.95412 −0.977062 0.212955i \(-0.931691\pi\)
−0.977062 + 0.212955i \(0.931691\pi\)
\(522\) 4088.08 + 7080.77i 0.342779 + 0.593710i
\(523\) 5513.14 + 9549.03i 0.460942 + 0.798375i 0.999008 0.0445277i \(-0.0141783\pi\)
−0.538066 + 0.842903i \(0.680845\pi\)
\(524\) 2257.22 3909.62i 0.188181 0.325940i
\(525\) 804.080 0.0668437
\(526\) −1993.07 + 3452.10i −0.165213 + 0.286157i
\(527\) 982.231 1701.27i 0.0811891 0.140624i
\(528\) −3833.32 −0.315954
\(529\) −6705.15 + 11613.7i −0.551093 + 0.954522i
\(530\) 2298.72 + 3981.51i 0.188397 + 0.326312i
\(531\) −1562.70 2706.68i −0.127713 0.221205i
\(532\) 224.722 0.0183138
\(533\) 0 0
\(534\) 2731.16 0.221327
\(535\) 1668.03 + 2889.11i 0.134795 + 0.233472i
\(536\) −1743.39 3019.65i −0.140491 0.243337i
\(537\) 4857.59 8413.59i 0.390355 0.676114i
\(538\) 10415.5 0.834657
\(539\) 10634.5 18419.5i 0.849835 1.47196i
\(540\) 2536.70 4393.70i 0.202152 0.350138i
\(541\) 8987.70 0.714254 0.357127 0.934056i \(-0.383756\pi\)
0.357127 + 0.934056i \(0.383756\pi\)
\(542\) −4084.90 + 7075.25i −0.323730 + 0.560716i
\(543\) −4196.17 7267.99i −0.331630 0.574400i
\(544\) −430.430 745.527i −0.0339238 0.0587578i
\(545\) 11357.9 0.892697
\(546\) 0 0
\(547\) −10734.8 −0.839101 −0.419550 0.907732i \(-0.637812\pi\)
−0.419550 + 0.907732i \(0.637812\pi\)
\(548\) −3495.87 6055.02i −0.272511 0.472003i
\(549\) −2583.59 4474.90i −0.200847 0.347876i
\(550\) −3414.12 + 5913.42i −0.264688 + 0.458453i
\(551\) −4029.11 −0.311517
\(552\) −2344.48 + 4060.76i −0.180775 + 0.313111i
\(553\) 809.675 1402.40i 0.0622620 0.107841i
\(554\) −875.985 −0.0671788
\(555\) −1856.80 + 3216.07i −0.142012 + 0.245972i
\(556\) −3353.07 5807.69i −0.255759 0.442987i
\(557\) −6614.13 11456.0i −0.503141 0.871466i −0.999993 0.00363111i \(-0.998844\pi\)
0.496852 0.867835i \(-0.334489\pi\)
\(558\) 1981.66 0.150341
\(559\) 0 0
\(560\) −573.412 −0.0432698
\(561\) −3222.61 5581.72i −0.242529 0.420072i
\(562\) −5462.34 9461.06i −0.409991 0.710126i
\(563\) −5366.98 + 9295.89i −0.401761 + 0.695870i −0.993939 0.109937i \(-0.964935\pi\)
0.592178 + 0.805807i \(0.298268\pi\)
\(564\) 8628.79 0.644216
\(565\) −3036.59 + 5259.53i −0.226107 + 0.391628i
\(566\) −796.676 + 1379.88i −0.0591639 + 0.102475i
\(567\) −750.037 −0.0555531
\(568\) −263.849 + 457.000i −0.0194909 + 0.0337593i
\(569\) −2656.73 4601.58i −0.195739 0.339031i 0.751403 0.659843i \(-0.229377\pi\)
−0.947143 + 0.320813i \(0.896044\pi\)
\(570\) 418.096 + 724.164i 0.0307230 + 0.0532138i
\(571\) 4629.37 0.339287 0.169644 0.985505i \(-0.445738\pi\)
0.169644 + 0.985505i \(0.445738\pi\)
\(572\) 0 0
\(573\) 1239.88 0.0903954
\(574\) 1818.64 + 3149.97i 0.132245 + 0.229055i
\(575\) 4176.19 + 7233.37i 0.302886 + 0.524613i
\(576\) 434.198 752.053i 0.0314090 0.0544020i
\(577\) −504.750 −0.0364177 −0.0182088 0.999834i \(-0.505796\pi\)
−0.0182088 + 0.999834i \(0.505796\pi\)
\(578\) −4189.29 + 7256.06i −0.301473 + 0.522167i
\(579\) −4918.36 + 8518.84i −0.353022 + 0.611453i
\(580\) 10280.9 0.736019
\(581\) −533.968 + 924.859i −0.0381286 + 0.0660407i
\(582\) 4815.22 + 8340.21i 0.342951 + 0.594008i
\(583\) 8807.70 + 15255.4i 0.625691 + 1.08373i
\(584\) 7084.14 0.501958
\(585\) 0 0
\(586\) 3394.65 0.239303
\(587\) −2766.47 4791.66i −0.194522 0.336922i 0.752222 0.658910i \(-0.228982\pi\)
−0.946744 + 0.321988i \(0.895649\pi\)
\(588\) −2384.74 4130.50i −0.167254 0.289692i
\(589\) −488.268 + 845.705i −0.0341575 + 0.0591624i
\(590\) −3929.96 −0.274227
\(591\) −3476.57 + 6021.60i −0.241975 + 0.419113i
\(592\) −950.247 + 1645.88i −0.0659711 + 0.114265i
\(593\) −18079.8 −1.25202 −0.626009 0.779816i \(-0.715313\pi\)
−0.626009 + 0.779816i \(0.715313\pi\)
\(594\) 9719.54 16834.7i 0.671376 1.16286i
\(595\) −482.059 834.950i −0.0332143 0.0575288i
\(596\) −1793.92 3107.16i −0.123292 0.213548i
\(597\) 8852.88 0.606909
\(598\) 0 0
\(599\) −1837.55 −0.125342 −0.0626712 0.998034i \(-0.519962\pi\)
−0.0626712 + 0.998034i \(0.519962\pi\)
\(600\) 765.600 + 1326.06i 0.0520925 + 0.0902268i
\(601\) 11743.6 + 20340.6i 0.797060 + 1.38055i 0.921523 + 0.388324i \(0.126946\pi\)
−0.124463 + 0.992224i \(0.539721\pi\)
\(602\) −1497.71 + 2594.10i −0.101399 + 0.175627i
\(603\) 5913.89 0.399390
\(604\) −4156.56 + 7199.37i −0.280013 + 0.484997i
\(605\) 12551.2 21739.4i 0.843438 1.46088i
\(606\) 10728.7 0.719182
\(607\) 8155.42 14125.6i 0.545335 0.944548i −0.453251 0.891383i \(-0.649736\pi\)
0.998586 0.0531648i \(-0.0169309\pi\)
\(608\) 213.967 + 370.602i 0.0142722 + 0.0247202i
\(609\) −2319.36 4017.25i −0.154327 0.267302i
\(610\) −6497.32 −0.431260
\(611\) 0 0
\(612\) 1460.09 0.0964393
\(613\) −4226.56 7320.61i −0.278481 0.482344i 0.692526 0.721393i \(-0.256498\pi\)
−0.971008 + 0.239049i \(0.923164\pi\)
\(614\) 9385.86 + 16256.8i 0.616910 + 1.06852i
\(615\) −6767.18 + 11721.1i −0.443705 + 0.768520i
\(616\) −2197.06 −0.143705
\(617\) 6705.17 11613.7i 0.437504 0.757779i −0.559992 0.828498i \(-0.689196\pi\)
0.997496 + 0.0707186i \(0.0225292\pi\)
\(618\) −772.870 + 1338.65i −0.0503065 + 0.0871334i
\(619\) −890.135 −0.0577990 −0.0288995 0.999582i \(-0.509200\pi\)
−0.0288995 + 0.999582i \(0.509200\pi\)
\(620\) 1245.89 2157.95i 0.0807036 0.139783i
\(621\) −11889.1 20592.5i −0.768263 1.33067i
\(622\) −3282.65 5685.72i −0.211611 0.366522i
\(623\) 1565.36 0.100666
\(624\) 0 0
\(625\) −6369.30 −0.407635
\(626\) −5924.67 10261.8i −0.378271 0.655184i
\(627\) 1601.96 + 2774.68i 0.102035 + 0.176730i
\(628\) 6989.49 12106.2i 0.444126 0.769249i
\(629\) −3195.43 −0.202560
\(630\) 486.278 842.259i 0.0307521 0.0532641i
\(631\) 5291.22 9164.66i 0.333819 0.578192i −0.649438 0.760415i \(-0.724996\pi\)
0.983257 + 0.182222i \(0.0583291\pi\)
\(632\) 3083.71 0.194087
\(633\) 4889.71 8469.22i 0.307028 0.531787i
\(634\) 6467.88 + 11202.7i 0.405161 + 0.701760i
\(635\) −4997.78 8656.42i −0.312332 0.540975i
\(636\) 3950.17 0.246281
\(637\) 0 0
\(638\) 39391.9 2.44442
\(639\) −447.510 775.111i −0.0277046 0.0479858i
\(640\) −545.971 945.649i −0.0337209 0.0584064i
\(641\) −13442.1 + 23282.4i −0.828286 + 1.43463i 0.0710952 + 0.997470i \(0.477351\pi\)
−0.899382 + 0.437164i \(0.855983\pi\)
\(642\) 2866.38 0.176210
\(643\) −2845.56 + 4928.66i −0.174523 + 0.302282i −0.939996 0.341186i \(-0.889172\pi\)
0.765473 + 0.643468i \(0.222505\pi\)
\(644\) −1343.74 + 2327.42i −0.0822216 + 0.142412i
\(645\) −11146.0 −0.680422
\(646\) −359.758 + 623.119i −0.0219110 + 0.0379509i
\(647\) −904.896 1567.33i −0.0549847 0.0952364i 0.837223 0.546862i \(-0.184178\pi\)
−0.892208 + 0.451625i \(0.850844\pi\)
\(648\) −714.143 1236.93i −0.0432935 0.0749865i
\(649\) −15057.9 −0.910745
\(650\) 0 0
\(651\) −1124.29 −0.0676871
\(652\) −902.508 1563.19i −0.0542100 0.0938945i
\(653\) −4729.58 8191.88i −0.283435 0.490923i 0.688794 0.724957i \(-0.258141\pi\)
−0.972228 + 0.234034i \(0.924807\pi\)
\(654\) 4879.42 8451.41i 0.291744 0.505315i
\(655\) 9627.94 0.574343
\(656\) −3463.21 + 5998.46i −0.206121 + 0.357013i
\(657\) −6007.66 + 10405.6i −0.356744 + 0.617899i
\(658\) 4945.59 0.293008
\(659\) −507.660 + 879.293i −0.0300085 + 0.0519763i −0.880640 0.473787i \(-0.842887\pi\)
0.850631 + 0.525763i \(0.176220\pi\)
\(660\) −4087.65 7080.02i −0.241078 0.417560i
\(661\) −11824.2 20480.2i −0.695778 1.20512i −0.969918 0.243433i \(-0.921727\pi\)
0.274140 0.961690i \(-0.411607\pi\)
\(662\) −7018.49 −0.412056
\(663\) 0 0
\(664\) −2033.66 −0.118857
\(665\) 239.632 + 415.055i 0.0139737 + 0.0242032i
\(666\) −1611.70 2791.55i −0.0937720 0.162418i
\(667\) 24092.3 41729.2i 1.39859 2.42243i
\(668\) −12813.4 −0.742164
\(669\) 524.732 908.863i 0.0303248 0.0525242i
\(670\) 3718.13 6439.99i 0.214394 0.371341i
\(671\) −24894.9 −1.43228
\(672\) −246.341 + 426.675i −0.0141411 + 0.0244931i
\(673\) −8873.48 15369.3i −0.508243 0.880303i −0.999954 0.00954455i \(-0.996962\pi\)
0.491711 0.870758i \(-0.336372\pi\)
\(674\) −1834.82 3178.00i −0.104858 0.181620i
\(675\) −7764.85 −0.442769
\(676\) 0 0
\(677\) 10754.2 0.610511 0.305256 0.952270i \(-0.401258\pi\)
0.305256 + 0.952270i \(0.401258\pi\)
\(678\) 2609.07 + 4519.04i 0.147789 + 0.255977i
\(679\) 2759.84 + 4780.19i 0.155984 + 0.270172i
\(680\) 917.978 1589.99i 0.0517689 0.0896664i
\(681\) 19061.9 1.07262
\(682\) 4773.71 8268.31i 0.268028 0.464238i
\(683\) 11990.9 20768.8i 0.671768 1.16354i −0.305635 0.952149i \(-0.598869\pi\)
0.977402 0.211387i \(-0.0677980\pi\)
\(684\) −725.815 −0.0405734
\(685\) 7455.63 12913.5i 0.415862 0.720293i
\(686\) −2807.77 4863.21i −0.156270 0.270668i
\(687\) −1631.71 2826.20i −0.0906166 0.156953i
\(688\) −5704.13 −0.316087
\(689\) 0 0
\(690\) −10000.1 −0.551737
\(691\) −14500.7 25116.0i −0.798312 1.38272i −0.920715 0.390236i \(-0.872393\pi\)
0.122403 0.992480i \(-0.460940\pi\)
\(692\) −3798.76 6579.65i −0.208681 0.361446i
\(693\) 1863.21 3227.17i 0.102132 0.176898i
\(694\) 14518.6 0.794119
\(695\) 7151.09 12386.1i 0.390297 0.676014i
\(696\) 4416.73 7650.00i 0.240540 0.416627i
\(697\) −11645.9 −0.632882
\(698\) −1795.24 + 3109.44i −0.0973505 + 0.168616i
\(699\) 8709.78 + 15085.8i 0.471293 + 0.816304i
\(700\) 438.804 + 760.030i 0.0236932 + 0.0410378i
\(701\) −31031.5 −1.67196 −0.835979 0.548761i \(-0.815100\pi\)
−0.835979 + 0.548761i \(0.815100\pi\)
\(702\) 0 0
\(703\) 1588.45 0.0852199
\(704\) −2091.92 3623.31i −0.111992 0.193976i
\(705\) 9201.30 + 15937.1i 0.491548 + 0.851386i
\(706\) −4552.38 + 7884.94i −0.242678 + 0.420331i
\(707\) 6149.16 0.327105
\(708\) −1688.33 + 2924.27i −0.0896206 + 0.155227i
\(709\) 2191.29 3795.43i 0.116073 0.201044i −0.802135 0.597143i \(-0.796303\pi\)
0.918208 + 0.396098i \(0.129636\pi\)
\(710\) −1125.42 −0.0594877
\(711\) −2615.12 + 4529.52i −0.137939 + 0.238917i
\(712\) 1490.45 + 2581.54i 0.0784508 + 0.135881i
\(713\) −5839.27 10113.9i −0.306707 0.531232i
\(714\) −828.380 −0.0434192
\(715\) 0 0
\(716\) 10603.6 0.553455
\(717\) 4201.08 + 7276.49i 0.218818 + 0.379004i
\(718\) 10165.4 + 17607.0i 0.528369 + 0.915162i
\(719\) 14382.3 24910.9i 0.745994 1.29210i −0.203735 0.979026i \(-0.565308\pi\)
0.949729 0.313073i \(-0.101358\pi\)
\(720\) 1852.03 0.0958625
\(721\) −442.971 + 767.248i −0.0228808 + 0.0396308i
\(722\) −6680.16 + 11570.4i −0.344335 + 0.596406i
\(723\) 7238.89 0.372361
\(724\) 4579.88 7932.59i 0.235097 0.407200i
\(725\) −7867.46 13626.8i −0.403021 0.698052i
\(726\) −10784.2 18678.7i −0.551291 0.954864i
\(727\) 25408.5 1.29621 0.648107 0.761549i \(-0.275561\pi\)
0.648107 + 0.761549i \(0.275561\pi\)
\(728\) 0 0
\(729\) 17134.5 0.870525
\(730\) 7554.16 + 13084.2i 0.383003 + 0.663381i
\(731\) −4795.37 8305.82i −0.242631 0.420249i
\(732\) −2791.28 + 4834.64i −0.140941 + 0.244117i
\(733\) −22341.8 −1.12580 −0.562902 0.826524i \(-0.690315\pi\)
−0.562902 + 0.826524i \(0.690315\pi\)
\(734\) −10401.6 + 18016.0i −0.523063 + 0.905972i
\(735\) 5085.94 8809.10i 0.255235 0.442080i
\(736\) −5117.73 −0.256307
\(737\) 14246.3 24675.2i 0.712032 1.23328i
\(738\) −5873.91 10173.9i −0.292983 0.507461i
\(739\) 4105.45 + 7110.84i 0.204359 + 0.353960i 0.949928 0.312468i \(-0.101156\pi\)
−0.745569 + 0.666428i \(0.767822\pi\)
\(740\) −4053.18 −0.201349
\(741\) 0 0
\(742\) 2264.04 0.112016
\(743\) 16376.1 + 28364.3i 0.808590 + 1.40052i 0.913841 + 0.406073i \(0.133102\pi\)
−0.105251 + 0.994446i \(0.533565\pi\)
\(744\) −1070.48 1854.13i −0.0527498 0.0913653i
\(745\) 3825.90 6626.65i 0.188148 0.325881i
\(746\) 15906.8 0.780684
\(747\) 1724.63 2987.14i 0.0844724 0.146310i
\(748\) 3517.29 6092.13i 0.171932 0.297794i
\(749\) 1642.87 0.0801455
\(750\) −5540.83 + 9597.00i −0.269763 + 0.467244i
\(751\) −4453.70 7714.04i −0.216402 0.374819i 0.737303 0.675562i \(-0.236099\pi\)
−0.953705 + 0.300742i \(0.902766\pi\)
\(752\) 4708.91 + 8156.08i 0.228346 + 0.395507i
\(753\) 27361.0 1.32416
\(754\) 0 0
\(755\) −17729.4 −0.854620
\(756\) −1249.22 2163.71i −0.0600973 0.104092i
\(757\) 5372.32 + 9305.13i 0.257940 + 0.446765i 0.965690 0.259698i \(-0.0836231\pi\)
−0.707750 + 0.706463i \(0.750290\pi\)
\(758\) 9014.81 15614.1i 0.431969 0.748193i
\(759\) −38316.2 −1.83240
\(760\) −456.328 + 790.383i −0.0217799 + 0.0377240i
\(761\) 8498.89 14720.5i 0.404841 0.701206i −0.589462 0.807796i \(-0.700660\pi\)
0.994303 + 0.106590i \(0.0339934\pi\)
\(762\) −8588.30 −0.408296
\(763\) 2796.64 4843.93i 0.132694 0.229832i
\(764\) 676.627 + 1171.95i 0.0320412 + 0.0554970i
\(765\) 1556.97 + 2696.75i 0.0735849 + 0.127453i
\(766\) 4992.48 0.235490
\(767\) 0 0
\(768\) −938.208 −0.0440816
\(769\) −9516.21 16482.6i −0.446246 0.772921i 0.551892 0.833916i \(-0.313906\pi\)
−0.998138 + 0.0609948i \(0.980573\pi\)
\(770\) −2342.84 4057.92i −0.109649 0.189918i
\(771\)