Properties

Label 49.4.g.a.2.2
Level $49$
Weight $4$
Character 49.2
Analytic conductor $2.891$
Analytic rank $0$
Dimension $156$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [49,4,Mod(2,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([26]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.2");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 49.g (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.89109359028\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(13\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 2.2
Character \(\chi\) \(=\) 49.2
Dual form 49.4.g.a.25.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.56991 - 1.40963i) q^{2} +(2.47210 - 6.29880i) q^{3} +(12.2871 + 8.37722i) q^{4} +(16.6312 - 2.50675i) q^{5} +(-20.1763 + 25.3002i) q^{6} +(-5.68057 - 17.6276i) q^{7} +(-20.4882 - 25.6914i) q^{8} +(-13.7713 - 12.7779i) q^{9} +O(q^{10})\) \(q+(-4.56991 - 1.40963i) q^{2} +(2.47210 - 6.29880i) q^{3} +(12.2871 + 8.37722i) q^{4} +(16.6312 - 2.50675i) q^{5} +(-20.1763 + 25.3002i) q^{6} +(-5.68057 - 17.6276i) q^{7} +(-20.4882 - 25.6914i) q^{8} +(-13.7713 - 12.7779i) q^{9} +(-79.5368 - 11.9882i) q^{10} +(-12.9486 + 12.0146i) q^{11} +(83.1415 - 56.6849i) q^{12} +(-12.6098 - 55.2471i) q^{13} +(1.11133 + 88.5639i) q^{14} +(25.3245 - 110.954i) q^{15} +(13.9495 + 35.5427i) q^{16} +(9.35333 + 124.812i) q^{17} +(44.9214 + 77.8061i) q^{18} +(-24.2655 + 42.0291i) q^{19} +(225.349 + 108.523i) q^{20} +(-125.076 - 7.79630i) q^{21} +(76.1101 - 36.6527i) q^{22} +(9.85237 - 131.471i) q^{23} +(-212.474 + 65.5395i) q^{24} +(150.867 - 46.5363i) q^{25} +(-20.2524 + 270.249i) q^{26} +(50.0750 - 24.1149i) q^{27} +(77.8722 - 264.180i) q^{28} +(-24.3814 - 11.7415i) q^{29} +(-272.134 + 471.350i) q^{30} +(14.2088 + 24.6104i) q^{31} +(5.99953 + 80.0582i) q^{32} +(43.6671 + 111.262i) q^{33} +(133.194 - 583.562i) q^{34} +(-138.663 - 278.928i) q^{35} +(-62.1663 - 272.368i) q^{36} +(80.0525 - 54.5789i) q^{37} +(170.137 - 157.864i) q^{38} +(-379.163 - 57.1496i) q^{39} +(-405.145 - 375.920i) q^{40} +(216.523 + 271.511i) q^{41} +(560.594 + 211.939i) q^{42} +(-24.3736 + 30.5635i) q^{43} +(-259.750 + 39.1510i) q^{44} +(-261.064 - 177.990i) q^{45} +(-230.350 + 586.921i) q^{46} +(-137.491 - 42.4104i) q^{47} +258.361 q^{48} +(-278.462 + 200.269i) q^{49} -755.047 q^{50} +(809.286 + 249.632i) q^{51} +(307.879 - 784.463i) q^{52} +(625.536 + 426.483i) q^{53} +(-262.831 + 39.6155i) q^{54} +(-185.234 + 232.276i) q^{55} +(-336.492 + 507.098i) q^{56} +(204.746 + 256.744i) q^{57} +(94.8698 + 88.0263i) q^{58} +(181.962 + 27.4264i) q^{59} +(1240.65 - 1151.15i) q^{60} +(417.657 - 284.753i) q^{61} +(-30.2415 - 132.496i) q^{62} +(-147.014 + 315.339i) q^{63} +(153.406 - 672.114i) q^{64} +(-348.207 - 887.216i) q^{65} +(-42.7165 - 570.012i) q^{66} +(173.718 + 300.888i) q^{67} +(-930.648 + 1611.93i) q^{68} +(-803.752 - 387.067i) q^{69} +(240.491 + 1470.14i) q^{70} +(106.596 - 51.3340i) q^{71} +(-46.1327 + 615.598i) q^{72} +(-711.381 + 219.432i) q^{73} +(-442.769 + 136.576i) q^{74} +(79.8349 - 1065.32i) q^{75} +(-650.240 + 313.139i) q^{76} +(285.343 + 160.003i) q^{77} +(1652.18 + 795.649i) q^{78} +(-54.8915 + 95.0748i) q^{79} +(321.094 + 556.150i) q^{80} +(-66.0095 - 880.836i) q^{81} +(-606.760 - 1546.00i) q^{82} +(246.585 - 1080.36i) q^{83} +(-1471.51 - 1143.58i) q^{84} +(468.429 + 2052.32i) q^{85} +(154.468 - 105.315i) q^{86} +(-134.231 + 124.548i) q^{87} +(573.964 + 86.5111i) q^{88} +(-10.0282 - 9.30481i) q^{89} +(942.138 + 1181.40i) q^{90} +(-902.241 + 536.115i) q^{91} +(1222.42 - 1532.86i) q^{92} +(190.142 - 28.6592i) q^{93} +(568.539 + 387.623i) q^{94} +(-298.208 + 759.822i) q^{95} +(519.102 + 160.122i) q^{96} +270.559 q^{97} +(1554.85 - 522.683i) q^{98} +331.839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 156 q - 13 q^{2} - 7 q^{3} + 35 q^{4} - 7 q^{5} - 70 q^{6} - 42 q^{7} + 16 q^{8} + 198 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 156 q - 13 q^{2} - 7 q^{3} + 35 q^{4} - 7 q^{5} - 70 q^{6} - 42 q^{7} + 16 q^{8} + 198 q^{9} + 85 q^{11} - 427 q^{12} + 14 q^{13} - 203 q^{14} + 230 q^{15} + 127 q^{16} + 189 q^{17} - 16 q^{18} - 490 q^{19} - 406 q^{20} + 231 q^{21} + 590 q^{22} - 377 q^{23} - 812 q^{24} + 142 q^{25} + 490 q^{26} + 14 q^{27} - 280 q^{28} + 172 q^{29} - 39 q^{30} - 1162 q^{31} - 1099 q^{32} - 49 q^{33} + 882 q^{34} + 847 q^{35} + 812 q^{36} - 377 q^{37} - 1596 q^{38} - 770 q^{39} - 1694 q^{40} - 938 q^{41} - 3290 q^{42} - 10 q^{43} + 4354 q^{44} + 1176 q^{45} + 3408 q^{46} + 1379 q^{47} + 9604 q^{48} + 2576 q^{49} - 6184 q^{50} + 2271 q^{51} + 6874 q^{52} + 1905 q^{53} + 1617 q^{54} - 1834 q^{55} + 1736 q^{56} + 2673 q^{57} - 4716 q^{58} + 63 q^{59} - 10850 q^{60} - 2625 q^{61} - 4298 q^{62} - 1806 q^{63} - 2756 q^{64} - 196 q^{65} + 2100 q^{66} - 202 q^{67} - 5635 q^{68} - 3248 q^{69} + 6650 q^{70} + 2608 q^{71} - 6424 q^{72} - 2471 q^{73} + 2582 q^{74} + 3612 q^{75} - 4529 q^{76} - 1281 q^{77} + 5040 q^{78} - 608 q^{79} - 12348 q^{80} - 17375 q^{81} - 3234 q^{82} - 9842 q^{83} - 11564 q^{84} - 512 q^{85} - 2301 q^{86} + 2254 q^{87} + 4033 q^{88} + 4977 q^{89} + 18312 q^{90} - 8932 q^{91} + 7714 q^{92} + 14164 q^{93} + 2506 q^{94} + 11504 q^{95} + 12642 q^{96} + 11116 q^{97} + 29771 q^{98} - 10804 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{13}{21}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.56991 1.40963i −1.61571 0.498380i −0.650422 0.759573i \(-0.725408\pi\)
−0.965286 + 0.261194i \(0.915884\pi\)
\(3\) 2.47210 6.29880i 0.475756 1.21221i −0.468639 0.883390i \(-0.655255\pi\)
0.944394 0.328815i \(-0.106649\pi\)
\(4\) 12.2871 + 8.37722i 1.53589 + 1.04715i
\(5\) 16.6312 2.50675i 1.48754 0.224211i 0.645556 0.763713i \(-0.276625\pi\)
0.841984 + 0.539502i \(0.181387\pi\)
\(6\) −20.1763 + 25.3002i −1.37282 + 1.72146i
\(7\) −5.68057 17.6276i −0.306722 0.951799i
\(8\) −20.4882 25.6914i −0.905458 1.13541i
\(9\) −13.7713 12.7779i −0.510047 0.473254i
\(10\) −79.5368 11.9882i −2.51517 0.379101i
\(11\) −12.9486 + 12.0146i −0.354923 + 0.329320i −0.837402 0.546587i \(-0.815927\pi\)
0.482479 + 0.875907i \(0.339736\pi\)
\(12\) 83.1415 56.6849i 2.00007 1.36363i
\(13\) −12.6098 55.2471i −0.269025 1.17868i −0.911150 0.412075i \(-0.864804\pi\)
0.642125 0.766600i \(-0.278053\pi\)
\(14\) 1.11133 + 88.5639i 0.0212153 + 1.69069i
\(15\) 25.3245 110.954i 0.435916 1.90987i
\(16\) 13.9495 + 35.5427i 0.217961 + 0.555355i
\(17\) 9.35333 + 124.812i 0.133442 + 1.78066i 0.515861 + 0.856672i \(0.327472\pi\)
−0.382419 + 0.923989i \(0.624909\pi\)
\(18\) 44.9214 + 77.8061i 0.588226 + 1.01884i
\(19\) −24.2655 + 42.0291i −0.292994 + 0.507481i −0.974516 0.224317i \(-0.927985\pi\)
0.681522 + 0.731798i \(0.261318\pi\)
\(20\) 225.349 + 108.523i 2.51948 + 1.21332i
\(21\) −125.076 7.79630i −1.29970 0.0810139i
\(22\) 76.1101 36.6527i 0.737579 0.355199i
\(23\) 9.85237 131.471i 0.0893200 1.19189i −0.754879 0.655864i \(-0.772305\pi\)
0.844199 0.536029i \(-0.180076\pi\)
\(24\) −212.474 + 65.5395i −1.80713 + 0.557424i
\(25\) 150.867 46.5363i 1.20693 0.372290i
\(26\) −20.2524 + 270.249i −0.152762 + 2.03847i
\(27\) 50.0750 24.1149i 0.356924 0.171885i
\(28\) 77.8722 264.180i 0.525588 1.78304i
\(29\) −24.3814 11.7415i −0.156121 0.0751840i 0.354192 0.935173i \(-0.384756\pi\)
−0.510313 + 0.859989i \(0.670470\pi\)
\(30\) −272.134 + 471.350i −1.65616 + 2.86855i
\(31\) 14.2088 + 24.6104i 0.0823219 + 0.142586i 0.904247 0.427010i \(-0.140433\pi\)
−0.821925 + 0.569596i \(0.807100\pi\)
\(32\) 5.99953 + 80.0582i 0.0331430 + 0.442263i
\(33\) 43.6671 + 111.262i 0.230347 + 0.586916i
\(34\) 133.194 583.562i 0.671842 2.94353i
\(35\) −138.663 278.928i −0.669665 1.34707i
\(36\) −62.1663 272.368i −0.287807 1.26096i
\(37\) 80.0525 54.5789i 0.355691 0.242506i −0.372270 0.928124i \(-0.621421\pi\)
0.727961 + 0.685619i \(0.240468\pi\)
\(38\) 170.137 157.864i 0.726311 0.673918i
\(39\) −379.163 57.1496i −1.55679 0.234648i
\(40\) −405.145 375.920i −1.60148 1.48595i
\(41\) 216.523 + 271.511i 0.824760 + 1.03422i 0.998775 + 0.0494737i \(0.0157544\pi\)
−0.174015 + 0.984743i \(0.555674\pi\)
\(42\) 560.594 + 211.939i 2.05956 + 0.778640i
\(43\) −24.3736 + 30.5635i −0.0864403 + 0.108393i −0.823171 0.567794i \(-0.807797\pi\)
0.736731 + 0.676186i \(0.236369\pi\)
\(44\) −259.750 + 39.1510i −0.889972 + 0.134142i
\(45\) −261.064 177.990i −0.864824 0.589627i
\(46\) −230.350 + 586.921i −0.738331 + 1.88124i
\(47\) −137.491 42.4104i −0.426705 0.131621i 0.0739619 0.997261i \(-0.476436\pi\)
−0.500667 + 0.865640i \(0.666912\pi\)
\(48\) 258.361 0.776900
\(49\) −278.462 + 200.269i −0.811843 + 0.583875i
\(50\) −755.047 −2.13560
\(51\) 809.286 + 249.632i 2.22201 + 0.685400i
\(52\) 307.879 784.463i 0.821060 2.09203i
\(53\) 625.536 + 426.483i 1.62121 + 1.10532i 0.919675 + 0.392680i \(0.128452\pi\)
0.701531 + 0.712639i \(0.252500\pi\)
\(54\) −262.831 + 39.6155i −0.662349 + 0.0998330i
\(55\) −185.234 + 232.276i −0.454125 + 0.569455i
\(56\) −336.492 + 507.098i −0.802957 + 1.21007i
\(57\) 204.746 + 256.744i 0.475777 + 0.596606i
\(58\) 94.8698 + 88.0263i 0.214776 + 0.199283i
\(59\) 181.962 + 27.4264i 0.401516 + 0.0605188i 0.346696 0.937978i \(-0.387304\pi\)
0.0548196 + 0.998496i \(0.482542\pi\)
\(60\) 1240.65 1151.15i 2.66945 2.47689i
\(61\) 417.657 284.753i 0.876647 0.597688i −0.0391929 0.999232i \(-0.512479\pi\)
0.915840 + 0.401544i \(0.131526\pi\)
\(62\) −30.2415 132.496i −0.0619463 0.271404i
\(63\) −147.014 + 315.339i −0.294000 + 0.630619i
\(64\) 153.406 672.114i 0.299621 1.31272i
\(65\) −348.207 887.216i −0.664457 1.69301i
\(66\) −42.7165 570.012i −0.0796672 1.06308i
\(67\) 173.718 + 300.888i 0.316762 + 0.548647i 0.979810 0.199929i \(-0.0640711\pi\)
−0.663049 + 0.748576i \(0.730738\pi\)
\(68\) −930.648 + 1611.93i −1.65967 + 2.87464i
\(69\) −803.752 387.067i −1.40232 0.675324i
\(70\) 240.491 + 1470.14i 0.410630 + 2.51022i
\(71\) 106.596 51.3340i 0.178178 0.0858060i −0.342668 0.939456i \(-0.611331\pi\)
0.520846 + 0.853650i \(0.325616\pi\)
\(72\) −46.1327 + 615.598i −0.0755109 + 1.00762i
\(73\) −711.381 + 219.432i −1.14056 + 0.351816i −0.806790 0.590838i \(-0.798797\pi\)
−0.333770 + 0.942654i \(0.608321\pi\)
\(74\) −442.769 + 136.576i −0.695552 + 0.214550i
\(75\) 79.8349 1065.32i 0.122914 1.64017i
\(76\) −650.240 + 313.139i −0.981417 + 0.472626i
\(77\) 285.343 + 160.003i 0.422310 + 0.236806i
\(78\) 1652.18 + 795.649i 2.39837 + 1.15499i
\(79\) −54.8915 + 95.0748i −0.0781744 + 0.135402i −0.902462 0.430769i \(-0.858242\pi\)
0.824288 + 0.566171i \(0.191576\pi\)
\(80\) 321.094 + 556.150i 0.448742 + 0.777244i
\(81\) −66.0095 880.836i −0.0905481 1.20828i
\(82\) −606.760 1546.00i −0.817139 2.08204i
\(83\) 246.585 1080.36i 0.326099 1.42873i −0.500399 0.865795i \(-0.666813\pi\)
0.826498 0.562939i \(-0.190329\pi\)
\(84\) −1471.51 1143.58i −1.91136 1.48541i
\(85\) 468.429 + 2052.32i 0.597744 + 2.61889i
\(86\) 154.468 105.315i 0.193683 0.132051i
\(87\) −134.231 + 124.548i −0.165414 + 0.153482i
\(88\) 573.964 + 86.5111i 0.695281 + 0.104797i
\(89\) −10.0282 9.30481i −0.0119437 0.0110821i 0.674178 0.738569i \(-0.264498\pi\)
−0.686122 + 0.727486i \(0.740688\pi\)
\(90\) 942.138 + 1181.40i 1.10344 + 1.38368i
\(91\) −902.241 + 536.115i −1.03935 + 0.617583i
\(92\) 1222.42 1532.86i 1.38528 1.73709i
\(93\) 190.142 28.6592i 0.212008 0.0319551i
\(94\) 568.539 + 387.623i 0.623833 + 0.425322i
\(95\) −298.208 + 759.822i −0.322058 + 0.820591i
\(96\) 519.102 + 160.122i 0.551882 + 0.170233i
\(97\) 270.559 0.283208 0.141604 0.989923i \(-0.454774\pi\)
0.141604 + 0.989923i \(0.454774\pi\)
\(98\) 1554.85 522.683i 1.60269 0.538765i
\(99\) 331.839 0.336880
\(100\) 2243.56 + 692.048i 2.24356 + 0.692048i
\(101\) −347.522 + 885.471i −0.342373 + 0.872353i 0.651173 + 0.758929i \(0.274277\pi\)
−0.993547 + 0.113424i \(0.963818\pi\)
\(102\) −3346.48 2281.59i −3.24853 2.21481i
\(103\) −170.941 + 25.7651i −0.163527 + 0.0246477i −0.230295 0.973121i \(-0.573969\pi\)
0.0667684 + 0.997768i \(0.478731\pi\)
\(104\) −1161.02 + 1455.87i −1.09469 + 1.37269i
\(105\) −2099.70 + 183.871i −1.95152 + 0.170895i
\(106\) −2257.46 2830.76i −2.06853 2.59385i
\(107\) 147.600 + 136.952i 0.133355 + 0.123735i 0.744031 0.668145i \(-0.232912\pi\)
−0.610676 + 0.791881i \(0.709102\pi\)
\(108\) 817.294 + 123.187i 0.728186 + 0.109756i
\(109\) 189.088 175.448i 0.166160 0.154174i −0.592711 0.805416i \(-0.701942\pi\)
0.758870 + 0.651242i \(0.225752\pi\)
\(110\) 1173.92 800.368i 1.01754 0.693746i
\(111\) −145.884 639.160i −0.124745 0.546544i
\(112\) 547.290 447.798i 0.461733 0.377794i
\(113\) −229.566 + 1005.80i −0.191113 + 0.837321i 0.784902 + 0.619620i \(0.212713\pi\)
−0.976015 + 0.217702i \(0.930144\pi\)
\(114\) −573.759 1461.91i −0.471381 1.20106i
\(115\) −165.708 2211.22i −0.134368 1.79302i
\(116\) −201.217 348.518i −0.161056 0.278957i
\(117\) −532.287 + 921.948i −0.420598 + 0.728497i
\(118\) −792.889 381.835i −0.618571 0.297888i
\(119\) 2146.99 873.877i 1.65390 0.673178i
\(120\) −3369.40 + 1622.62i −2.56319 + 1.23437i
\(121\) −76.1488 + 1016.13i −0.0572117 + 0.763437i
\(122\) −2310.05 + 712.557i −1.71428 + 0.528786i
\(123\) 2245.46 692.633i 1.64607 0.507745i
\(124\) −31.5812 + 421.421i −0.0228715 + 0.305200i
\(125\) 498.262 239.950i 0.356527 0.171694i
\(126\) 1116.35 1233.84i 0.789307 0.872373i
\(127\) 672.862 + 324.033i 0.470133 + 0.226404i 0.653922 0.756562i \(-0.273122\pi\)
−0.183790 + 0.982966i \(0.558837\pi\)
\(128\) −1327.35 + 2299.04i −0.916582 + 1.58757i
\(129\) 132.260 + 229.080i 0.0902698 + 0.156352i
\(130\) 340.626 + 4545.34i 0.229807 + 3.06656i
\(131\) 358.344 + 913.046i 0.238997 + 0.608956i 0.999169 0.0407672i \(-0.0129802\pi\)
−0.760171 + 0.649723i \(0.774885\pi\)
\(132\) −395.523 + 1732.90i −0.260802 + 1.14265i
\(133\) 878.713 + 188.993i 0.572888 + 0.123216i
\(134\) −369.734 1619.91i −0.238360 1.04432i
\(135\) 772.358 526.585i 0.492400 0.335713i
\(136\) 3014.95 2797.46i 1.90095 1.76383i
\(137\) −2747.24 414.079i −1.71323 0.258228i −0.782161 0.623076i \(-0.785883\pi\)
−0.931067 + 0.364849i \(0.881121\pi\)
\(138\) 3127.46 + 2901.86i 1.92918 + 1.79002i
\(139\) −58.5598 73.4317i −0.0357337 0.0448086i 0.763644 0.645638i \(-0.223409\pi\)
−0.799377 + 0.600829i \(0.794837\pi\)
\(140\) 632.876 4588.83i 0.382056 2.77019i
\(141\) −607.026 + 761.187i −0.362559 + 0.454635i
\(142\) −559.497 + 84.3306i −0.330648 + 0.0498371i
\(143\) 827.048 + 563.872i 0.483645 + 0.329744i
\(144\) 262.058 667.712i 0.151654 0.386408i
\(145\) −434.926 134.157i −0.249094 0.0768353i
\(146\) 3560.27 2.01815
\(147\) 573.070 + 2249.06i 0.321538 + 1.26190i
\(148\) 1440.84 0.800243
\(149\) −2832.33 873.659i −1.55727 0.480356i −0.607771 0.794112i \(-0.707936\pi\)
−0.949503 + 0.313757i \(0.898412\pi\)
\(150\) −1866.55 + 4755.89i −1.01602 + 2.58878i
\(151\) 435.928 + 297.211i 0.234936 + 0.160177i 0.675066 0.737757i \(-0.264115\pi\)
−0.440130 + 0.897934i \(0.645068\pi\)
\(152\) 1576.94 237.686i 0.841492 0.126835i
\(153\) 1466.02 1838.33i 0.774644 0.971372i
\(154\) −1078.45 1133.43i −0.564310 0.593079i
\(155\) 298.002 + 373.683i 0.154426 + 0.193645i
\(156\) −4180.07 3878.54i −2.14534 1.99059i
\(157\) 736.273 + 110.975i 0.374274 + 0.0564127i 0.333486 0.942755i \(-0.391775\pi\)
0.0407879 + 0.999168i \(0.487013\pi\)
\(158\) 384.870 357.107i 0.193789 0.179809i
\(159\) 4232.72 2885.82i 2.11117 1.43937i
\(160\) 300.466 + 1316.43i 0.148462 + 0.650454i
\(161\) −2373.48 + 573.155i −1.16184 + 0.280565i
\(162\) −939.996 + 4118.39i −0.455883 + 1.99736i
\(163\) 97.0433 + 247.262i 0.0466320 + 0.118816i 0.952292 0.305188i \(-0.0987193\pi\)
−0.905660 + 0.424004i \(0.860624\pi\)
\(164\) 385.935 + 5149.95i 0.183759 + 2.45209i
\(165\) 1005.14 + 1740.96i 0.474244 + 0.821415i
\(166\) −2649.78 + 4589.56i −1.23893 + 2.14590i
\(167\) −3424.29 1649.05i −1.58670 0.764116i −0.587715 0.809068i \(-0.699972\pi\)
−0.998989 + 0.0449519i \(0.985687\pi\)
\(168\) 2362.27 + 3373.09i 1.08484 + 1.54905i
\(169\) −913.804 + 440.065i −0.415933 + 0.200303i
\(170\) 752.337 10039.2i 0.339421 4.52926i
\(171\) 871.209 268.732i 0.389608 0.120178i
\(172\) −555.518 + 171.355i −0.246267 + 0.0759632i
\(173\) −12.5456 + 167.410i −0.00551344 + 0.0735718i −0.999282 0.0378933i \(-0.987935\pi\)
0.993768 + 0.111465i \(0.0355543\pi\)
\(174\) 788.988 379.957i 0.343753 0.165543i
\(175\) −1677.33 2395.06i −0.724539 1.03457i
\(176\) −607.656 292.632i −0.260249 0.125329i
\(177\) 622.581 1078.34i 0.264385 0.457927i
\(178\) 32.7116 + 56.6582i 0.0137744 + 0.0238579i
\(179\) 236.538 + 3156.38i 0.0987691 + 1.31798i 0.797814 + 0.602904i \(0.205990\pi\)
−0.699044 + 0.715078i \(0.746391\pi\)
\(180\) −1716.66 4373.98i −0.710846 1.81121i
\(181\) −354.098 + 1551.41i −0.145414 + 0.637100i 0.848711 + 0.528857i \(0.177379\pi\)
−0.994125 + 0.108242i \(0.965478\pi\)
\(182\) 4878.89 1178.17i 1.98707 0.479845i
\(183\) −761.118 3334.68i −0.307451 1.34703i
\(184\) −3579.52 + 2440.48i −1.43416 + 0.977795i
\(185\) 1194.56 1108.39i 0.474732 0.440487i
\(186\) −909.329 137.059i −0.358469 0.0540305i
\(187\) −1620.67 1503.76i −0.633770 0.588053i
\(188\) −1334.09 1672.90i −0.517545 0.648981i
\(189\) −709.541 745.715i −0.273077 0.286999i
\(190\) 2433.86 3051.96i 0.929318 1.16533i
\(191\) 454.857 68.5586i 0.172316 0.0259724i −0.0623176 0.998056i \(-0.519849\pi\)
0.234633 + 0.972084i \(0.424611\pi\)
\(192\) −3854.28 2627.81i −1.44874 0.987737i
\(193\) 970.758 2473.45i 0.362055 0.922502i −0.627535 0.778588i \(-0.715936\pi\)
0.989590 0.143914i \(-0.0459687\pi\)
\(194\) −1236.43 381.389i −0.457581 0.141145i
\(195\) −6449.20 −2.36839
\(196\) −5099.20 + 127.993i −1.85831 + 0.0466446i
\(197\) −529.338 −0.191440 −0.0957201 0.995408i \(-0.530515\pi\)
−0.0957201 + 0.995408i \(0.530515\pi\)
\(198\) −1516.48 467.771i −0.544299 0.167894i
\(199\) −228.370 + 581.878i −0.0813505 + 0.207278i −0.965762 0.259431i \(-0.916465\pi\)
0.884411 + 0.466709i \(0.154560\pi\)
\(200\) −4286.57 2922.53i −1.51553 1.03327i
\(201\) 2324.68 350.390i 0.815774 0.122958i
\(202\) 2836.33 3556.65i 0.987938 1.23884i
\(203\) −68.4733 + 496.483i −0.0236743 + 0.171657i
\(204\) 7852.58 + 9846.82i 2.69505 + 3.37949i
\(205\) 4281.65 + 3972.79i 1.45875 + 1.35352i
\(206\) 817.502 + 123.219i 0.276496 + 0.0416750i
\(207\) −1815.59 + 1684.63i −0.609626 + 0.565650i
\(208\) 1787.73 1218.85i 0.595946 0.406309i
\(209\) −190.756 835.758i −0.0631334 0.276606i
\(210\) 9854.64 + 2119.53i 3.23826 + 0.696482i
\(211\) 1119.70 4905.72i 0.365323 1.60059i −0.374129 0.927377i \(-0.622058\pi\)
0.739452 0.673209i \(-0.235085\pi\)
\(212\) 4113.29 + 10480.5i 1.33256 + 3.39530i
\(213\) −59.8266 798.331i −0.0192453 0.256811i
\(214\) −481.465 833.921i −0.153795 0.266382i
\(215\) −328.747 + 569.406i −0.104281 + 0.180619i
\(216\) −1645.49 792.426i −0.518340 0.249619i
\(217\) 353.107 390.268i 0.110463 0.122088i
\(218\) −1111.44 + 535.239i −0.345302 + 0.166289i
\(219\) −376.445 + 5023.31i −0.116154 + 1.54997i
\(220\) −4221.81 + 1302.26i −1.29379 + 0.399082i
\(221\) 6777.53 2090.59i 2.06292 0.636327i
\(222\) −234.302 + 3126.55i −0.0708349 + 0.945226i
\(223\) −1424.68 + 686.092i −0.427820 + 0.206027i −0.635388 0.772193i \(-0.719160\pi\)
0.207567 + 0.978221i \(0.433445\pi\)
\(224\) 1377.15 560.533i 0.410780 0.167197i
\(225\) −2672.26 1286.89i −0.791781 0.381302i
\(226\) 2466.90 4272.79i 0.726087 1.25762i
\(227\) −366.691 635.128i −0.107217 0.185704i 0.807425 0.589970i \(-0.200860\pi\)
−0.914642 + 0.404266i \(0.867527\pi\)
\(228\) 364.945 + 4869.85i 0.106005 + 1.41453i
\(229\) −1323.84 3373.09i −0.382017 0.973363i −0.984524 0.175250i \(-0.943927\pi\)
0.602507 0.798114i \(-0.294169\pi\)
\(230\) −2359.73 + 10338.6i −0.676504 + 2.96396i
\(231\) 1713.22 1401.78i 0.487973 0.399264i
\(232\) 197.877 + 866.954i 0.0559967 + 0.245337i
\(233\) 4133.19 2817.96i 1.16212 0.792322i 0.180579 0.983561i \(-0.442203\pi\)
0.981544 + 0.191239i \(0.0612505\pi\)
\(234\) 3732.11 3462.89i 1.04263 0.967421i
\(235\) −2392.96 360.680i −0.664252 0.100120i
\(236\) 2006.03 + 1861.33i 0.553312 + 0.513398i
\(237\) 463.161 + 580.785i 0.126943 + 0.159182i
\(238\) −11043.4 + 967.074i −3.00772 + 0.263387i
\(239\) −2494.19 + 3127.62i −0.675045 + 0.846480i −0.994887 0.100991i \(-0.967799\pi\)
0.319842 + 0.947471i \(0.396370\pi\)
\(240\) 4296.86 647.647i 1.15567 0.174189i
\(241\) −1377.69 939.294i −0.368236 0.251059i 0.365038 0.930993i \(-0.381056\pi\)
−0.733274 + 0.679934i \(0.762009\pi\)
\(242\) 1780.37 4536.30i 0.472919 1.20498i
\(243\) −4277.43 1319.41i −1.12921 0.348314i
\(244\) 7517.24 1.97230
\(245\) −4129.14 + 4028.76i −1.07674 + 1.05056i
\(246\) −11237.9 −2.91261
\(247\) 2627.97 + 810.621i 0.676978 + 0.208820i
\(248\) 341.162 869.266i 0.0873540 0.222574i
\(249\) −6195.39 4223.95i −1.57678 1.07503i
\(250\) −2615.25 + 394.186i −0.661613 + 0.0997220i
\(251\) −2372.34 + 2974.82i −0.596576 + 0.748082i −0.984840 0.173466i \(-0.944503\pi\)
0.388264 + 0.921548i \(0.373075\pi\)
\(252\) −4448.05 + 2643.05i −1.11191 + 0.660699i
\(253\) 1451.99 + 1820.74i 0.360813 + 0.452445i
\(254\) −2618.15 2429.29i −0.646762 0.600107i
\(255\) 14085.2 + 2123.00i 3.45901 + 0.521362i
\(256\) 5263.77 4884.06i 1.28510 1.19240i
\(257\) −433.298 + 295.418i −0.105169 + 0.0717029i −0.614762 0.788712i \(-0.710748\pi\)
0.509594 + 0.860415i \(0.329796\pi\)
\(258\) −281.496 1233.31i −0.0679270 0.297608i
\(259\) −1416.84 1101.09i −0.339915 0.264164i
\(260\) 3153.95 13818.3i 0.752306 3.29607i
\(261\) 185.732 + 473.237i 0.0440480 + 0.112232i
\(262\) −350.543 4677.67i −0.0826589 1.10301i
\(263\) −2614.20 4527.92i −0.612922 1.06161i −0.990745 0.135734i \(-0.956661\pi\)
0.377824 0.925877i \(-0.376672\pi\)
\(264\) 1963.81 3401.42i 0.457819 0.792966i
\(265\) 11472.5 + 5524.87i 2.65943 + 1.28072i
\(266\) −3749.23 2102.34i −0.864211 0.484597i
\(267\) −83.3999 + 40.1633i −0.0191161 + 0.00920581i
\(268\) −386.114 + 5152.33i −0.0880061 + 1.17436i
\(269\) 5028.36 1551.04i 1.13972 0.351557i 0.333254 0.942837i \(-0.391853\pi\)
0.806466 + 0.591280i \(0.201377\pi\)
\(270\) −4271.90 + 1317.71i −0.962887 + 0.297011i
\(271\) −367.711 + 4906.76i −0.0824237 + 1.09987i 0.790646 + 0.612273i \(0.209745\pi\)
−0.873070 + 0.487595i \(0.837874\pi\)
\(272\) −4305.66 + 2073.50i −0.959814 + 0.462222i
\(273\) 1146.45 + 7008.37i 0.254163 + 1.55372i
\(274\) 11970.9 + 5764.90i 2.63938 + 1.27106i
\(275\) −1394.40 + 2415.18i −0.305766 + 0.529603i
\(276\) −6633.26 11489.1i −1.44665 2.50567i
\(277\) −62.3335 831.783i −0.0135208 0.180422i −0.999875 0.0157875i \(-0.994974\pi\)
0.986355 0.164635i \(-0.0526446\pi\)
\(278\) 164.102 + 418.124i 0.0354035 + 0.0902066i
\(279\) 118.795 520.474i 0.0254913 0.111685i
\(280\) −4325.10 + 9277.16i −0.923121 + 1.98006i
\(281\) 1045.56 + 4580.88i 0.221967 + 0.972501i 0.955995 + 0.293382i \(0.0947807\pi\)
−0.734028 + 0.679119i \(0.762362\pi\)
\(282\) 3847.05 2622.87i 0.812370 0.553865i
\(283\) −6763.02 + 6275.17i −1.42057 + 1.31809i −0.542077 + 0.840329i \(0.682362\pi\)
−0.878488 + 0.477764i \(0.841448\pi\)
\(284\) 1739.80 + 262.232i 0.363514 + 0.0547909i
\(285\) 4048.77 + 3756.71i 0.841504 + 0.780801i
\(286\) −2984.69 3742.68i −0.617092 0.773808i
\(287\) 3556.11 5359.11i 0.731395 1.10222i
\(288\) 940.352 1179.16i 0.192398 0.241260i
\(289\) −10632.3 + 1602.56i −2.16412 + 0.326188i
\(290\) 1798.46 + 1226.17i 0.364170 + 0.248287i
\(291\) 668.849 1704.20i 0.134738 0.343306i
\(292\) −10579.1 3263.21i −2.12018 0.653989i
\(293\) −4854.63 −0.967955 −0.483977 0.875081i \(-0.660808\pi\)
−0.483977 + 0.875081i \(0.660808\pi\)
\(294\) 551.471 11085.8i 0.109396 2.19911i
\(295\) 3095.00 0.610840
\(296\) −3042.34 938.437i −0.597406 0.184275i
\(297\) −358.673 + 913.883i −0.0700751 + 0.178548i
\(298\) 11712.0 + 7985.09i 2.27670 + 1.55223i
\(299\) −7387.61 + 1113.50i −1.42888 + 0.215370i
\(300\) 9905.39 12421.0i 1.90629 2.39042i
\(301\) 677.215 + 256.029i 0.129681 + 0.0490274i
\(302\) −1573.20 1972.73i −0.299759 0.375886i
\(303\) 4718.30 + 4377.94i 0.894585 + 0.830054i
\(304\) −1832.32 276.178i −0.345693 0.0521048i
\(305\) 6232.33 5782.76i 1.17004 1.08564i
\(306\) −9290.94 + 6334.45i −1.73571 + 1.18339i
\(307\) −1468.92 6435.76i −0.273080 1.19644i −0.906355 0.422516i \(-0.861147\pi\)
0.633275 0.773927i \(-0.281710\pi\)
\(308\) 2165.66 + 4356.36i 0.400650 + 0.805930i
\(309\) −260.292 + 1140.41i −0.0479207 + 0.209954i
\(310\) −835.088 2127.77i −0.152999 0.389836i
\(311\) 461.972 + 6164.59i 0.0842316 + 1.12399i 0.865873 + 0.500264i \(0.166764\pi\)
−0.781641 + 0.623728i \(0.785617\pi\)
\(312\) 6300.11 + 10912.1i 1.14318 + 1.98005i
\(313\) 3441.16 5960.26i 0.621424 1.07634i −0.367797 0.929906i \(-0.619888\pi\)
0.989221 0.146432i \(-0.0467789\pi\)
\(314\) −3208.27 1545.02i −0.576602 0.277677i
\(315\) −1654.54 + 5613.00i −0.295946 + 1.00399i
\(316\) −1470.92 + 708.359i −0.261854 + 0.126102i
\(317\) −259.804 + 3466.84i −0.0460317 + 0.614250i 0.925715 + 0.378223i \(0.123465\pi\)
−0.971746 + 0.236028i \(0.924154\pi\)
\(318\) −23411.1 + 7221.36i −4.12839 + 1.27344i
\(319\) 456.774 140.896i 0.0801707 0.0247294i
\(320\) 866.499 11562.6i 0.151371 2.01991i
\(321\) 1227.52 591.141i 0.213437 0.102786i
\(322\) 11654.5 + 726.458i 2.01702 + 0.125726i
\(323\) −5472.68 2635.50i −0.942749 0.454004i
\(324\) 6567.89 11375.9i 1.12618 1.95060i
\(325\) −4473.39 7748.14i −0.763505 1.32243i
\(326\) −94.9307 1266.76i −0.0161280 0.215213i
\(327\) −637.670 1624.76i −0.107839 0.274768i
\(328\) 2539.33 11125.5i 0.427473 1.87288i
\(329\) 33.4355 + 2664.55i 0.00560292 + 0.446509i
\(330\) −2139.31 9372.91i −0.356863 1.56352i
\(331\) −5520.83 + 3764.04i −0.916774 + 0.625046i −0.927065 0.374901i \(-0.877677\pi\)
0.0102911 + 0.999947i \(0.496724\pi\)
\(332\) 12080.2 11208.8i 1.99696 1.85290i
\(333\) −1799.83 271.280i −0.296186 0.0446428i
\(334\) 13324.2 + 12363.0i 2.18283 + 2.02537i
\(335\) 3643.39 + 4568.67i 0.594208 + 0.745114i
\(336\) −1467.64 4554.28i −0.238292 0.739453i
\(337\) 2120.79 2659.39i 0.342810 0.429870i −0.580302 0.814401i \(-0.697066\pi\)
0.923112 + 0.384532i \(0.125637\pi\)
\(338\) 4796.33 722.931i 0.771852 0.116338i
\(339\) 5767.80 + 3932.42i 0.924082 + 0.630029i
\(340\) −11437.1 + 29141.3i −1.82431 + 4.64825i
\(341\) −479.667 147.958i −0.0761743 0.0234967i
\(342\) −4360.16 −0.689387
\(343\) 5112.08 + 3770.97i 0.804742 + 0.593625i
\(344\) 1284.59 0.201338
\(345\) −14337.7 4422.58i −2.23743 0.690156i
\(346\) 293.318 747.363i 0.0455748 0.116123i
\(347\) 4512.68 + 3076.69i 0.698136 + 0.475981i 0.859646 0.510890i \(-0.170684\pi\)
−0.161510 + 0.986871i \(0.551636\pi\)
\(348\) −2692.67 + 405.855i −0.414777 + 0.0625176i
\(349\) 537.353 673.819i 0.0824179 0.103349i −0.738913 0.673801i \(-0.764661\pi\)
0.821331 + 0.570452i \(0.193232\pi\)
\(350\) 4289.10 + 13309.6i 0.655034 + 2.03266i
\(351\) −1963.71 2462.41i −0.298619 0.374456i
\(352\) −1039.55 964.561i −0.157410 0.146055i
\(353\) −9090.25 1370.13i −1.37061 0.206586i −0.577861 0.816135i \(-0.696113\pi\)
−0.792748 + 0.609549i \(0.791351\pi\)
\(354\) −4365.21 + 4050.32i −0.655390 + 0.608113i
\(355\) 1644.14 1120.96i 0.245808 0.167589i
\(356\) −45.2693 198.338i −0.00673952 0.0295278i
\(357\) −196.805 15683.8i −0.0291765 2.32514i
\(358\) 3368.37 14757.8i 0.497274 2.17870i
\(359\) 1025.39 + 2612.66i 0.150747 + 0.384097i 0.986221 0.165433i \(-0.0529021\pi\)
−0.835474 + 0.549530i \(0.814807\pi\)
\(360\) 775.908 + 10353.8i 0.113594 + 1.51581i
\(361\) 2251.87 + 3900.35i 0.328309 + 0.568648i
\(362\) 3805.11 6590.64i 0.552464 0.956896i
\(363\) 6212.19 + 2991.63i 0.898224 + 0.432562i
\(364\) −15577.1 970.963i −2.24303 0.139814i
\(365\) −11281.1 + 5432.68i −1.61775 + 0.779067i
\(366\) −1222.42 + 16312.1i −0.174582 + 2.32963i
\(367\) −848.876 + 261.843i −0.120738 + 0.0372428i −0.354536 0.935043i \(-0.615361\pi\)
0.233797 + 0.972285i \(0.424885\pi\)
\(368\) 4810.26 1483.77i 0.681392 0.210182i
\(369\) 487.538 6505.75i 0.0687811 0.917820i
\(370\) −7021.43 + 3381.34i −0.986558 + 0.475101i
\(371\) 3964.46 13449.3i 0.554783 1.88209i
\(372\) 2576.38 + 1240.72i 0.359083 + 0.172925i
\(373\) 4149.02 7186.32i 0.575947 0.997570i −0.419991 0.907528i \(-0.637967\pi\)
0.995938 0.0900416i \(-0.0287000\pi\)
\(374\) 5286.56 + 9156.60i 0.730913 + 1.26598i
\(375\) −279.647 3731.63i −0.0385091 0.513869i
\(376\) 1727.36 + 4401.25i 0.236920 + 0.603662i
\(377\) −341.238 + 1495.06i −0.0466171 + 0.204243i
\(378\) 2191.36 + 4408.04i 0.298178 + 0.599802i
\(379\) 337.696 + 1479.54i 0.0457685 + 0.200525i 0.992643 0.121079i \(-0.0386353\pi\)
−0.946874 + 0.321604i \(0.895778\pi\)
\(380\) −10029.3 + 6837.88i −1.35393 + 0.923094i
\(381\) 3704.40 3437.18i 0.498116 0.462184i
\(382\) −2175.30 327.873i −0.291356 0.0439148i
\(383\) −10122.2 9392.03i −1.35045 1.25303i −0.940013 0.341139i \(-0.889187\pi\)
−0.410432 0.911891i \(-0.634622\pi\)
\(384\) 11199.9 + 14044.2i 1.48839 + 1.86638i
\(385\) 5146.69 + 1945.76i 0.681297 + 0.257572i
\(386\) −7922.93 + 9935.04i −1.04473 + 1.31005i
\(387\) 726.191 109.456i 0.0953859 0.0143771i
\(388\) 3324.40 + 2266.54i 0.434976 + 0.296562i
\(389\) −948.632 + 2417.07i −0.123644 + 0.315040i −0.979271 0.202552i \(-0.935076\pi\)
0.855627 + 0.517592i \(0.173172\pi\)
\(390\) 29472.3 + 9091.00i 3.82663 + 1.18036i
\(391\) 16501.2 2.13428
\(392\) 10850.4 + 3050.93i 1.39803 + 0.393099i
\(393\) 6636.96 0.851884
\(394\) 2419.03 + 746.171i 0.309312 + 0.0954100i
\(395\) −674.583 + 1718.81i −0.0859290 + 0.218943i
\(396\) 4077.35 + 2779.89i 0.517410 + 0.352764i
\(397\) −2942.29 + 443.479i −0.371963 + 0.0560644i −0.332364 0.943151i \(-0.607846\pi\)
−0.0395991 + 0.999216i \(0.512608\pi\)
\(398\) 1863.87 2337.21i 0.234742 0.294357i
\(399\) 3362.69 5067.63i 0.421918 0.635837i
\(400\) 3758.54 + 4713.06i 0.469817 + 0.589132i
\(401\) 9180.74 + 8518.48i 1.14330 + 1.06083i 0.997439 + 0.0715244i \(0.0227864\pi\)
0.145863 + 0.989305i \(0.453404\pi\)
\(402\) −11117.5 1675.70i −1.37933 0.207901i
\(403\) 1180.48 1095.33i 0.145916 0.135390i
\(404\) −11687.8 + 7968.63i −1.43933 + 0.981322i
\(405\) −3305.86 14483.9i −0.405603 1.77706i
\(406\) 1012.78 2172.36i 0.123801 0.265548i
\(407\) −380.828 + 1668.52i −0.0463807 + 0.203207i
\(408\) −10167.4 25906.2i −1.23373 3.14349i
\(409\) −682.883 9112.43i −0.0825584 1.10166i −0.872543 0.488538i \(-0.837530\pi\)
0.789984 0.613127i \(-0.210089\pi\)
\(410\) −13966.6 24190.8i −1.68234 2.91390i
\(411\) −9399.64 + 16280.7i −1.12810 + 1.95393i
\(412\) −2316.21 1115.43i −0.276969 0.133381i
\(413\) −550.187 3363.34i −0.0655519 0.400725i
\(414\) 10671.8 5139.27i 1.26689 0.610100i
\(415\) 1392.81 18585.8i 0.164748 2.19841i
\(416\) 4347.33 1340.97i 0.512369 0.158045i
\(417\) −607.298 + 187.327i −0.0713177 + 0.0219986i
\(418\) −306.371 + 4088.24i −0.0358495 + 0.478378i
\(419\) −8615.21 + 4148.87i −1.00449 + 0.483736i −0.862459 0.506127i \(-0.831077\pi\)
−0.142029 + 0.989863i \(0.545363\pi\)
\(420\) −27339.6 15330.4i −3.17628 1.78107i
\(421\) −7401.55 3564.40i −0.856839 0.412632i −0.0467276 0.998908i \(-0.514879\pi\)
−0.810112 + 0.586276i \(0.800594\pi\)
\(422\) −12032.2 + 20840.3i −1.38796 + 2.40401i
\(423\) 1351.51 + 2340.89i 0.155349 + 0.269073i
\(424\) −1859.16 24808.7i −0.212945 2.84155i
\(425\) 7219.37 + 18394.7i 0.823978 + 2.09946i
\(426\) −851.950 + 3732.64i −0.0968946 + 0.424523i
\(427\) −7392.04 5744.71i −0.837765 0.651068i
\(428\) 666.294 + 2919.22i 0.0752489 + 0.329687i
\(429\) 5596.26 3815.47i 0.629814 0.429400i
\(430\) 2305.00 2138.72i 0.258504 0.239857i
\(431\) 5284.27 + 796.476i 0.590567 + 0.0890137i 0.437526 0.899206i \(-0.355855\pi\)
0.153042 + 0.988220i \(0.451093\pi\)
\(432\) 1555.63 + 1443.41i 0.173253 + 0.160755i
\(433\) −1821.02 2283.48i −0.202107 0.253434i 0.670441 0.741963i \(-0.266105\pi\)
−0.872548 + 0.488529i \(0.837534\pi\)
\(434\) −2163.80 + 1285.74i −0.239322 + 0.142206i
\(435\) −1920.21 + 2407.86i −0.211648 + 0.265398i
\(436\) 3793.12 571.722i 0.416646 0.0627993i
\(437\) 5286.52 + 3604.29i 0.578693 + 0.394546i
\(438\) 8801.34 22425.4i 0.960146 2.44641i
\(439\) −7382.12 2277.08i −0.802573 0.247561i −0.133781 0.991011i \(-0.542712\pi\)
−0.668791 + 0.743450i \(0.733188\pi\)
\(440\) 9762.58 1.05776
\(441\) 6393.79 + 800.194i 0.690399 + 0.0864047i
\(442\) −33919.7 −3.65021
\(443\) −5363.29 1654.35i −0.575209 0.177428i −0.00651640 0.999979i \(-0.502074\pi\)
−0.568692 + 0.822550i \(0.692550\pi\)
\(444\) 3561.89 9075.54i 0.380720 0.970059i
\(445\) −190.106 129.612i −0.0202514 0.0138072i
\(446\) 7477.82 1127.10i 0.793913 0.119663i
\(447\) −12504.8 + 15680.5i −1.32317 + 1.65920i
\(448\) −12719.2 + 1113.82i −1.34135 + 0.117462i
\(449\) 5766.71 + 7231.23i 0.606120 + 0.760051i 0.986318 0.164854i \(-0.0527154\pi\)
−0.380197 + 0.924905i \(0.624144\pi\)
\(450\) 10398.0 + 9647.89i 1.08925 + 1.01068i
\(451\) −6065.75 914.265i −0.633315 0.0954569i
\(452\) −11246.5 + 10435.2i −1.17033 + 1.08591i
\(453\) 2949.73 2011.09i 0.305939 0.208586i
\(454\) 780.451 + 3419.38i 0.0806792 + 0.353479i
\(455\) −13661.5 + 11177.9i −1.40760 + 1.15171i
\(456\) 2401.22 10520.4i 0.246595 1.08040i
\(457\) 1844.50 + 4699.72i 0.188801 + 0.481058i 0.993662 0.112405i \(-0.0358555\pi\)
−0.804861 + 0.593463i \(0.797760\pi\)
\(458\) 1295.02 + 17280.9i 0.132123 + 1.76306i
\(459\) 3478.18 + 6024.38i 0.353698 + 0.612624i
\(460\) 16487.8 28557.7i 1.67119 2.89458i
\(461\) 1.44924 + 0.697918i 0.000146416 + 7.05103e-5i 0.433957 0.900934i \(-0.357117\pi\)
−0.433811 + 0.901004i \(0.642831\pi\)
\(462\) −9805.27 + 3990.98i −0.987408 + 0.401899i
\(463\) 11108.6 5349.60i 1.11503 0.536969i 0.216675 0.976244i \(-0.430479\pi\)
0.898353 + 0.439274i \(0.144764\pi\)
\(464\) 77.2155 1030.37i 0.00772552 0.103090i
\(465\) 3090.44 953.275i 0.308206 0.0950690i
\(466\) −22860.6 + 7051.57i −2.27253 + 0.700982i
\(467\) 630.982 8419.86i 0.0625232 0.834314i −0.874495 0.485034i \(-0.838807\pi\)
0.937018 0.349280i \(-0.113574\pi\)
\(468\) −14263.6 + 6869.01i −1.40884 + 0.678461i
\(469\) 4317.11 4771.44i 0.425044 0.469776i
\(470\) 10427.2 + 5021.46i 1.02334 + 0.492814i
\(471\) 2519.15 4363.29i 0.246446 0.426858i
\(472\) −3023.45 5236.77i −0.294842 0.510682i
\(473\) −51.6028 688.592i −0.00501628 0.0669376i
\(474\) −1297.91 3307.02i −0.125770 0.320457i
\(475\) −1704.98 + 7470.02i −0.164695 + 0.721575i
\(476\) 33701.0 + 7248.39i 3.24513 + 0.697961i
\(477\) −3164.87 13866.2i −0.303794 1.33101i
\(478\) 15807.0 10777.0i 1.51254 1.03124i
\(479\) −3443.66 + 3195.25i −0.328486 + 0.304791i −0.827124 0.562020i \(-0.810024\pi\)
0.498638 + 0.866811i \(0.333834\pi\)
\(480\) 9034.69 + 1361.76i 0.859115 + 0.129491i
\(481\) −4024.77 3734.44i −0.381525 0.354004i
\(482\) 4971.87 + 6234.53i 0.469839 + 0.589160i
\(483\) −2257.28 + 16367.0i −0.212649 + 1.54187i
\(484\) −9448.03 + 11847.5i −0.887306 + 1.11265i
\(485\) 4499.73 678.225i 0.421283 0.0634982i
\(486\) 17687.6 + 12059.2i 1.65088 + 1.12555i
\(487\) 3994.57 10178.0i 0.371686 0.947041i −0.615596 0.788062i \(-0.711085\pi\)
0.987282 0.158979i \(-0.0508202\pi\)
\(488\) −15872.7 4896.09i −1.47239 0.454171i
\(489\) 1797.36 0.166215
\(490\) 24548.9 12590.5i 2.26328 1.16078i
\(491\) 14324.0 1.31657 0.658284 0.752770i \(-0.271283\pi\)
0.658284 + 0.752770i \(0.271283\pi\)
\(492\) 33392.6 + 10300.2i 3.05987 + 0.943844i
\(493\) 1237.42 3152.90i 0.113044 0.288032i
\(494\) −10866.9 7408.93i −0.989727 0.674784i
\(495\) 5518.89 831.838i 0.501122 0.0755320i
\(496\) −676.514 + 848.322i −0.0612427 + 0.0767959i
\(497\) −1510.42 1587.42i −0.136321 0.143271i
\(498\) 22358.2 + 28036.3i 2.01184 + 2.52276i
\(499\) −14428.0 13387.2i −1.29436 1.20099i −0.966617 0.256224i \(-0.917521\pi\)
−0.327743 0.944767i \(-0.606288\pi\)
\(500\) 8132.32 + 1225.75i 0.727377 + 0.109634i
\(501\) −18852.2 + 17492.3i −1.68115 + 1.55988i
\(502\) 15034.8 10250.5i 1.33672 0.911361i
\(503\) −2001.49 8769.08i −0.177419 0.777324i −0.982816 0.184588i \(-0.940905\pi\)
0.805397 0.592736i \(-0.201952\pi\)
\(504\) 11113.5 2683.74i 0.982216 0.237189i
\(505\) −3560.05 + 15597.6i −0.313703 + 1.37442i
\(506\) −4068.89 10367.4i −0.357479 0.910841i
\(507\) 512.869 + 6843.76i 0.0449256 + 0.599491i
\(508\) 5553.04 + 9618.15i 0.484993 + 0.840032i
\(509\) 1975.73 3422.06i 0.172048 0.297996i −0.767088 0.641542i \(-0.778295\pi\)
0.939136 + 0.343546i \(0.111628\pi\)
\(510\) −61375.3 29556.8i −5.32891 2.56627i
\(511\) 7909.11 + 11293.4i 0.684693 + 0.977675i
\(512\) −11805.2 + 5685.10i −1.01899 + 0.490719i
\(513\) −201.570 + 2689.77i −0.0173480 + 0.231493i
\(514\) 2396.56 739.242i 0.205657 0.0634369i
\(515\) −2778.36 + 857.011i −0.237727 + 0.0733290i
\(516\) −293.966 + 3922.70i −0.0250797 + 0.334666i
\(517\) 2289.86 1102.74i 0.194793 0.0938073i
\(518\) 4922.69 + 7029.11i 0.417549 + 0.596219i
\(519\) 1023.47 + 492.876i 0.0865611 + 0.0416856i
\(520\) −15659.7 + 27123.4i −1.32062 + 2.28738i
\(521\) −1210.62 2096.85i −0.101801 0.176324i 0.810626 0.585564i \(-0.199127\pi\)
−0.912427 + 0.409240i \(0.865794\pi\)
\(522\) −181.689 2424.47i −0.0152343 0.203287i
\(523\) 7719.85 + 19669.9i 0.645441 + 1.64456i 0.759051 + 0.651031i \(0.225663\pi\)
−0.113610 + 0.993525i \(0.536241\pi\)
\(524\) −3245.77 + 14220.6i −0.270595 + 1.18556i
\(525\) −19232.6 + 4644.34i −1.59881 + 0.386087i
\(526\) 5563.95 + 24377.3i 0.461216 + 2.02072i
\(527\) −2938.76 + 2003.61i −0.242912 + 0.165614i
\(528\) −3345.42 + 3104.09i −0.275740 + 0.255849i
\(529\) −5156.38 777.199i −0.423800 0.0638776i
\(530\) −44640.3 41420.1i −3.65859 3.39467i
\(531\) −2155.40 2702.78i −0.176151 0.220886i
\(532\) 9213.62 + 9683.35i 0.750867 + 0.789147i
\(533\) 12269.9 15385.9i 0.997125 1.25035i
\(534\) 437.745 65.9795i 0.0354740 0.00534684i
\(535\) 2798.06 + 1907.69i 0.226114 + 0.154162i
\(536\) 4171.07 10627.7i 0.336124 0.856431i
\(537\) 20466.2 + 6312.97i 1.64466 + 0.507309i
\(538\) −25165.6 −2.01666
\(539\) 1199.55 5938.81i 0.0958599 0.474587i
\(540\) 13901.4 1.10782
\(541\) 20502.5 + 6324.19i 1.62934 + 0.502584i 0.968724 0.248142i \(-0.0798199\pi\)
0.660614 + 0.750726i \(0.270296\pi\)
\(542\) 8597.12 21905.1i 0.681325 1.73599i
\(543\) 8896.63 + 6065.62i 0.703114 + 0.479375i
\(544\) −9936.07 + 1497.62i −0.783098 + 0.118033i
\(545\) 2704.96 3391.92i 0.212602 0.266594i
\(546\) 4640.02 33643.7i 0.363690 2.63703i
\(547\) 8422.85 + 10561.9i 0.658382 + 0.825586i 0.993166 0.116710i \(-0.0372347\pi\)
−0.334784 + 0.942295i \(0.608663\pi\)
\(548\) −30286.8 28102.0i −2.36093 2.19062i
\(549\) −9390.20 1415.34i −0.729989 0.110028i
\(550\) 9776.81 9071.56i 0.757972 0.703295i
\(551\) 1085.11 739.816i 0.0838971 0.0572001i
\(552\) 6523.15 + 28579.8i 0.502978 + 2.20369i
\(553\) 1987.75 + 427.524i 0.152853 + 0.0328756i
\(554\) −887.649 + 3889.04i −0.0680732 + 0.298248i
\(555\) −4028.44 10264.3i −0.308104 0.785037i
\(556\) −104.378 1392.83i −0.00796157 0.106240i
\(557\) 2096.85 + 3631.86i 0.159509 + 0.276278i 0.934692 0.355459i \(-0.115676\pi\)
−0.775183 + 0.631737i \(0.782342\pi\)
\(558\) −1276.56 + 2211.06i −0.0968477 + 0.167745i
\(559\) 1995.89 + 961.169i 0.151014 + 0.0727247i
\(560\) 7979.58 8819.35i 0.602141 0.665510i
\(561\) −13478.3 + 6490.83i −1.01436 + 0.488490i
\(562\) 1679.25 22408.1i 0.126041 1.68190i
\(563\) −12914.6 + 3983.62i −0.966758 + 0.298205i −0.737641 0.675194i \(-0.764060\pi\)
−0.229117 + 0.973399i \(0.573584\pi\)
\(564\) −13835.2 + 4267.61i −1.03292 + 0.318615i
\(565\) −1296.69 + 17303.1i −0.0965522 + 1.28840i
\(566\) 39752.1 19143.6i 2.95213 1.42167i
\(567\) −15152.0 + 6167.24i −1.12227 + 0.456789i
\(568\) −3502.80 1686.86i −0.258758 0.124611i
\(569\) 11043.5 19127.8i 0.813648 1.40928i −0.0966472 0.995319i \(-0.530812\pi\)
0.910295 0.413960i \(-0.135855\pi\)
\(570\) −13207.0 22875.1i −0.970489 1.68094i
\(571\) −853.790 11393.0i −0.0625744 0.834998i −0.936887 0.349633i \(-0.886306\pi\)
0.874312 0.485364i \(-0.161313\pi\)
\(572\) 5438.37 + 13856.7i 0.397534 + 1.01290i
\(573\) 692.613 3034.54i 0.0504962 0.221238i
\(574\) −23805.5 + 19477.8i −1.73105 + 1.41636i
\(575\) −4631.76 20293.1i −0.335927 1.47179i
\(576\) −10700.8 + 7295.66i −0.774072 + 0.527754i
\(577\) 2672.08 2479.33i 0.192791 0.178884i −0.577871 0.816128i \(-0.696116\pi\)
0.770662 + 0.637244i \(0.219926\pi\)
\(578\) 50847.7 + 7664.06i 3.65915 + 0.551528i
\(579\) −13180.0 12229.2i −0.946012 0.877771i
\(580\) −4220.13 5291.87i −0.302123 0.378850i
\(581\) −20444.9 + 1790.36i −1.45989 + 0.127843i
\(582\) −5458.88 + 6845.21i −0.388793 + 0.487531i
\(583\) −13223.8 + 1993.17i −0.939408 + 0.141593i
\(584\) 20212.4 + 13780.6i 1.43218 + 0.976447i
\(585\) −6541.48 + 16667.4i −0.462320 + 1.17797i
\(586\) 22185.2 + 6843.24i 1.56393 + 0.482409i
\(587\) −3005.17 −0.211306 −0.105653 0.994403i \(-0.533693\pi\)
−0.105653 + 0.994403i \(0.533693\pi\)
\(588\) −11799.5 + 32435.3i −0.827558 + 2.27484i
\(589\) −1379.14 −0.0964793
\(590\) −14143.9 4362.81i −0.986939 0.304430i
\(591\) −1308.57 + 3334.19i −0.0910788 + 0.232065i
\(592\) 3056.57 + 2083.94i 0.212203 + 0.144678i
\(593\) 16712.7 2519.03i 1.15735 0.174442i 0.457817 0.889046i \(-0.348631\pi\)
0.699529 + 0.714604i \(0.253393\pi\)
\(594\) 2927.34 3670.77i 0.202206 0.253558i
\(595\) 33516.5 19915.6i 2.30931 1.37220i
\(596\) −27482.4 34461.9i −1.88880 2.36848i
\(597\) 3100.58 + 2876.92i 0.212560 + 0.197227i
\(598\) 35330.4 + 5325.19i 2.41600 + 0.364153i
\(599\) 4748.25 4405.74i 0.323887 0.300523i −0.501424 0.865202i \(-0.667190\pi\)
0.825311 + 0.564678i \(0.191000\pi\)
\(600\) −29005.3 + 19775.5i −1.97356 + 1.34555i
\(601\) −120.455 527.746i −0.00817545 0.0358190i 0.970676 0.240393i \(-0.0772763\pi\)
−0.978851 + 0.204574i \(0.934419\pi\)
\(602\) −2733.91 2124.65i −0.185093 0.143844i
\(603\) 1452.39 6363.36i 0.0980864 0.429744i
\(604\) 2866.51 + 7303.74i 0.193107 + 0.492028i
\(605\) 1280.75 + 17090.4i 0.0860660 + 1.14847i
\(606\) −15390.9 26657.9i −1.03171 1.78697i
\(607\) 653.893 1132.58i 0.0437244 0.0757328i −0.843335 0.537388i \(-0.819411\pi\)
0.887059 + 0.461655i \(0.152744\pi\)
\(608\) −3510.36 1690.50i −0.234151 0.112761i
\(609\) 2957.98 + 1658.66i 0.196820 + 0.110365i
\(610\) −36632.8 + 17641.4i −2.43150 + 1.17095i
\(611\) −609.317 + 8130.77i −0.0403442 + 0.538356i
\(612\) 33413.2 10306.6i 2.20694 0.680752i
\(613\) −19767.4 + 6097.44i −1.30244 + 0.401751i −0.866929 0.498431i \(-0.833910\pi\)
−0.435514 + 0.900182i \(0.643433\pi\)
\(614\) −2359.21 + 31481.5i −0.155065 + 2.06920i
\(615\) 35608.5 17148.1i 2.33475 1.12436i
\(616\) −1735.46 10609.0i −0.113512 0.693912i
\(617\) −1956.48 942.190i −0.127658 0.0614767i 0.368965 0.929443i \(-0.379712\pi\)
−0.496622 + 0.867967i \(0.665427\pi\)
\(618\) 2797.08 4844.68i 0.182063 0.315342i
\(619\) −5922.52 10258.1i −0.384566 0.666087i 0.607143 0.794592i \(-0.292315\pi\)
−0.991709 + 0.128505i \(0.958982\pi\)
\(620\) 531.166 + 7087.91i 0.0344067 + 0.459125i
\(621\) −2677.04 6820.99i −0.172989 0.440768i
\(622\) 6578.62 28822.8i 0.424081 1.85802i
\(623\) −107.055 + 229.629i −0.00688456 + 0.0147671i
\(624\) −3257.88 14273.7i −0.209006 0.915713i
\(625\) −8620.73 + 5877.51i −0.551727 + 0.376161i
\(626\) −24127.6 + 22387.1i −1.54047 + 1.42934i
\(627\) −5735.84 864.539i −0.365339 0.0550660i
\(628\) 8117.01 + 7531.49i 0.515771 + 0.478565i
\(629\) 7560.83 + 9480.99i 0.479285 + 0.601004i
\(630\) 15473.4 23318.6i 0.978531 1.47466i
\(631\) 12544.5 15730.3i 0.791425 0.992415i −0.208472 0.978028i \(-0.566849\pi\)
0.999897 0.0143870i \(-0.00457970\pi\)
\(632\) 3567.23 537.673i 0.224520 0.0338410i
\(633\) −28132.2 19180.2i −1.76643 1.20433i
\(634\) 6074.25 15476.9i 0.380504 0.969508i
\(635\) 12002.8 + 3702.37i 0.750104 + 0.231376i
\(636\) 76183.1 4.74977
\(637\) 14575.6 + 12858.9i 0.906606 + 0.799823i
\(638\) −2286.03 −0.141857
\(639\) −2123.90 655.137i −0.131487 0.0405584i
\(640\) −16312.4 + 41563.2i −1.00750 + 2.56708i
\(641\) −14538.8 9912.41i −0.895865 0.610790i 0.0254208 0.999677i \(-0.491907\pi\)
−0.921286 + 0.388886i \(0.872860\pi\)
\(642\) −6442.93 + 971.116i −0.396078 + 0.0596992i
\(643\) −12549.1 + 15736.1i −0.769658 + 0.965120i −0.999968 0.00799685i \(-0.997454\pi\)
0.230310 + 0.973117i \(0.426026\pi\)
\(644\) −33964.7 12840.7i −2.07825 0.785706i
\(645\) 2773.88 + 3478.34i 0.169336 + 0.212340i
\(646\) 21294.6 + 19758.5i 1.29694 + 1.20339i
\(647\) −16481.4 2484.17i −1.00147 0.150947i −0.372214 0.928147i \(-0.621401\pi\)
−0.629253 + 0.777200i \(0.716639\pi\)
\(648\) −21277.5 + 19742.6i −1.28990 + 1.19686i
\(649\) −2685.67 + 1831.06i −0.162437 + 0.110748i
\(650\) 9520.98 + 41714.1i 0.574529 + 2.51717i
\(651\) −1585.30 3188.93i −0.0954424 0.191988i
\(652\) −878.987 + 3851.10i −0.0527972 + 0.231320i
\(653\) 4728.67 + 12048.5i 0.283380 + 0.722041i 0.999705 + 0.0242742i \(0.00772749\pi\)
−0.716325 + 0.697767i \(0.754177\pi\)
\(654\) 623.788 + 8323.88i 0.0372967 + 0.497690i
\(655\) 8248.48 + 14286.8i 0.492053 + 0.852261i
\(656\) −6629.85 + 11483.2i −0.394592 + 0.683453i
\(657\) 12600.5 + 6068.08i 0.748238 + 0.360332i
\(658\) 3603.23 12223.9i 0.213478 0.724220i
\(659\) −834.082 + 401.673i −0.0493038 + 0.0237435i −0.458373 0.888760i \(-0.651568\pi\)
0.409069 + 0.912503i \(0.365853\pi\)
\(660\) −2234.08 + 29811.7i −0.131760 + 1.75821i
\(661\) −11706.1 + 3610.87i −0.688829 + 0.212476i −0.619359 0.785108i \(-0.712607\pi\)
−0.0694708 + 0.997584i \(0.522131\pi\)
\(662\) 30535.6 9418.98i 1.79275 0.552990i
\(663\) 3586.50 47858.5i 0.210087 2.80342i
\(664\) −32808.0 + 15799.5i −1.91747 + 0.923403i
\(665\) 15087.8 + 940.465i 0.879820 + 0.0548416i
\(666\) 7842.64 + 3776.82i 0.456301 + 0.219743i
\(667\) −1783.88 + 3089.76i −0.103556 + 0.179364i
\(668\) −28260.2 48948.1i −1.63686 2.83512i
\(669\) 799.598 + 10669.9i 0.0462096 + 0.616625i
\(670\) −10209.8 26014.3i −0.588718 1.50003i
\(671\) −1986.89 + 8705.12i −0.114311 + 0.500831i
\(672\) −126.237 10060.1i −0.00724658 0.577495i
\(673\) 4821.32 + 21123.6i 0.276149 + 1.20989i 0.902618 + 0.430442i \(0.141642\pi\)
−0.626469 + 0.779446i \(0.715501\pi\)
\(674\) −13440.6 + 9163.63i −0.768118 + 0.523694i
\(675\) 6432.44 5968.44i 0.366792 0.340334i
\(676\) −14914.5 2248.01i −0.848575 0.127902i
\(677\) 24286.3 + 22534.4i 1.37873 + 1.27927i 0.920665 + 0.390353i \(0.127647\pi\)
0.458063 + 0.888920i \(0.348543\pi\)
\(678\) −20815.1 26101.3i −1.17905 1.47849i
\(679\) −1536.93 4769.30i −0.0868660 0.269557i
\(680\) 43129.7 54082.9i 2.43228 3.04998i
\(681\) −4907.04 + 739.618i −0.276121 + 0.0416185i
\(682\) 1983.47 + 1352.31i 0.111365 + 0.0759275i
\(683\) −3578.81 + 9118.67i −0.200497 + 0.510858i −0.995392 0.0958889i \(-0.969431\pi\)
0.794895 + 0.606747i \(0.207526\pi\)
\(684\) 12955.9 + 3996.36i 0.724241 + 0.223399i
\(685\) −46727.9 −2.60639
\(686\) −18046.1 24439.2i −1.00438 1.36019i
\(687\) −24519.1 −1.36166
\(688\) −1426.31 439.957i −0.0790370 0.0243797i
\(689\) 15674.1 39936.9i 0.866668 2.20823i
\(690\) 59287.6 + 40421.6i 3.27107 + 2.23018i
\(691\) 18710.0 2820.08i 1.03005 0.155255i 0.387794 0.921746i \(-0.373237\pi\)
0.642255 + 0.766491i \(0.277999\pi\)
\(692\) −1556.58 + 1951.89i −0.0855090 + 0.107225i
\(693\) −1885.03 5849.52i −0.103328 0.320642i
\(694\) −16285.5 20421.4i −0.890765 1.11698i
\(695\) −1158.00 1074.46i −0.0632019 0.0586428i
\(696\) 5949.94 + 896.809i 0.324040 + 0.0488412i
\(697\) −31862.5 + 29564.1i −1.73153 + 1.60663i
\(698\) −3405.49 + 2321.82i −0.184670 + 0.125906i
\(699\) −7532.14 33000.5i −0.407570 1.78568i
\(700\) −545.598 43479.8i −0.0294595 2.34769i
\(701\) 2322.04 10173.5i 0.125110 0.548144i −0.873056 0.487619i \(-0.837865\pi\)
0.998167 0.0605249i \(-0.0192774\pi\)
\(702\) 5502.89 + 14021.1i 0.295859 + 0.753837i
\(703\) 351.386 + 4688.92i 0.0188517 + 0.251559i
\(704\) 6088.76 + 10546.0i 0.325964 + 0.564587i
\(705\) −8187.48 + 14181.1i −0.437387 + 0.757577i
\(706\) 39610.3 + 19075.3i 2.11155 + 1.01687i
\(707\) 17582.8 + 1095.99i 0.935318 + 0.0583009i
\(708\) 16683.2 8034.23i 0.885586 0.426476i
\(709\) 1953.73 26070.8i 0.103489 1.38097i −0.667731 0.744402i \(-0.732735\pi\)
0.771221 0.636568i \(-0.219646\pi\)
\(710\) −9093.72 + 2805.04i −0.480678 + 0.148269i
\(711\) 1970.78 607.905i 0.103952 0.0320650i
\(712\) −33.5937 + 448.277i −0.00176823 + 0.0235953i
\(713\) 3375.54 1625.57i 0.177300 0.0853831i
\(714\) −21209.0 + 71951.0i −1.11166 + 3.77128i
\(715\) 15168.3 + 7304.67i 0.793374 + 0.382069i
\(716\) −23535.3 + 40764.4i −1.22843 + 2.12770i
\(717\) 13534.4 + 23442.2i 0.704951 + 1.22101i
\(718\) −1003.07 13385.0i −0.0521369 0.695718i
\(719\) 8831.79 + 22503.0i 0.458095 + 1.16721i 0.954260 + 0.298979i \(0.0966459\pi\)
−0.496165 + 0.868228i \(0.665259\pi\)
\(720\) 2684.55 11761.8i 0.138955 0.608800i
\(721\) 1425.22 + 2866.90i 0.0736169 + 0.148085i
\(722\) −4792.79 20998.6i −0.247049 1.08239i
\(723\) −9322.22 + 6355.78i −0.479526 + 0.326935i
\(724\) −17347.3 + 16096.0i −0.890481 + 0.826245i
\(725\) −4224.75 636.779i −0.216418 0.0326198i
\(726\) −24172.0 22428.4i −1.23569 1.14655i
\(727\) 15214.4 + 19078.2i 0.776161 + 0.973275i 0.999999 0.00135096i \(-0.000430023\pi\)
−0.223838 + 0.974626i \(0.571859\pi\)
\(728\) 32258.8 + 12195.8i 1.64229 + 0.620887i
\(729\) −4015.18 + 5034.87i −0.203992 + 0.255798i
\(730\) 59211.6 8924.71i 3.00208 0.452491i
\(731\) −4042.65 2756.23i −0.204545 0.139457i
\(732\) 18583.4 47349.6i 0.938335 2.39084i
\(733\) 6361.18 + 1962.16i 0.320539 + 0.0988733i 0.450850 0.892600i \(-0.351121\pi\)
−0.130310 + 0.991473i \(0.541597\pi\)
\(734\) 4248.39 0.213639
\(735\) 15168.7 + 35968.1i 0.761233 + 1.80504i
\(736\) 10584.4 0.530091
\(737\) −5864.45 1808.94i −0.293107 0.0904115i
\(738\) −11398.7 + 29043.4i −0.568553 + 1.44865i
\(739\) −4648.79 3169.49i −0.231405 0.157770i 0.442067 0.896982i \(-0.354245\pi\)
−0.673472 + 0.739213i \(0.735198\pi\)
\(740\) 23962.8 3611.82i 1.19039 0.179423i
\(741\) 11602.5 14549.1i 0.575209 0.721289i
\(742\) −37075.8 + 55873.9i −1.83436 + 2.76441i
\(743\) −13574.6 17022.1i −0.670263 0.840483i 0.324154 0.946004i \(-0.394920\pi\)
−0.994417 + 0.105521i \(0.966349\pi\)
\(744\) −4631.95 4297.82i −0.228247 0.211782i
\(745\) −49295.2 7430.06i −2.42421 0.365391i
\(746\) −29090.7 + 26992.3i −1.42773 + 1.32474i
\(747\) −17200.5 + 11727.1i −0.842480 + 0.574393i
\(748\) −7316.02 32053.6i −0.357621 1.56684i
\(749\) 1575.69 3379.79i 0.0768683 0.164879i
\(750\) −3982.26 + 17447.4i −0.193882 + 0.849454i
\(751\) 13922.8 + 35474.6i 0.676497 + 1.72369i 0.690034 + 0.723777i \(0.257596\pi\)
−0.0135371 + 0.999908i \(0.504309\pi\)
\(752\) −410.550 5478.41i −0.0199085 0.265661i
\(753\) 12873.1 + 22296.9i 0.623005 + 1.07908i
\(754\) 3666.91 6351.27i 0.177110 0.306764i
\(755\) 7995.05 + 3850.21i 0.385390 + 0.185594i
\(756\) −2471.20 15106.7i −0.118885 0.726752i
\(757\) 16774.1 8077.97i 0.805369 0.387845i 0.0145490 0.999894i \(-0.495369\pi\)
0.790820 + 0.612049i \(0.209654\pi\)
\(758\) 542.369 7237.41i 0.0259891 0.346800i
\(759\) 15057.9 4644.75i 0.720115 0.222126i
\(760\) 25630.6 7906.00i 1.22332 0.377343i
\(761\) 2281.69 30447.1i 0.108688 1.45034i −0.630161 0.776465i \(-0.717011\pi\)
0.738848 0.673872i \(-0.235370\pi\)
\(762\) −21774.0 + 10485.8i −1.03515 + 0.498504i
\(763\) −4166.86 2336.52i −0.197707 0.110862i
\(764\) 6163.21 + 2968.05i 0.291855 + 0.140550i
\(765\) 19773.4 34248.6i 0.934522 1.61864i
\(766\) 33018.3 + 57189.3i 1.55744 + 2.69756i
\(767\) −779.275 10398.7i −0.0366858 0.489538i
\(768\) −17751.2 45229.3i −0.834038 2.12510i
\(769\) 6347.45 27810.0i 0.297653 1.30410i −0.575959 0.817478i \(-0.695371\pi\)
0.873612 0.486623i \(-0.161772\pi\)
\(770\) −20777.1 16146.9i −0.972409 0.755706i
\(771\) 789.622 + 3459.56i 0.0368840 + 0.161599i
\(772\) 32648.5 22259.3i 1.52208 1.03774i
\(773\) −11279.1 + 10465.5i −0.524813 + 0.486955i −0.897508 0.440999i \(-0.854624\pi\)
0.372695 + 0.927954i \(0.378434\pi\)
\(774\) −3472.92 523.458i −0.161281 0.0243092i
\(775\) 3288.91 + 3051.67i 0.152440 + 0.141444i
\(776\) −5543.27 6951.04i −0.256433 0.321556i
\(777\) −10438.1 + 6202.37i −0.481938 + 0.286369i
\(778\) 7742.35 9708.59i 0.356782 0.447391i
\(779\) −16665.4 + 2511.90i −0.766495 + 0.115531i
\(780\) −79242.2 54026.4i −3.63760 2.48007i
\(781\) −763.517 + 1945.41i −0.0349818 + 0.0891322i
\(782\) −75409.1 23260.6i −3.44837 1.06368i
\(783\) −1504.04 −0.0686464
\(784\) −11002.5 7103.65i −0.501208 0.323599i
\(785\) 12523.3 0.569396
\(786\) −30330.3 9355.66i −1.37640 0.424562i
\(787\) 2059.60 5247.78i 0.0932871 0.237692i −0.876612 0.481197i \(-0.840202\pi\)
0.969900 + 0.243505i \(0.0782974\pi\)
\(788\) −6504.04 4434.38i −0.294031 0.200467i
\(789\) −34983.1 + 5272.85i −1.57849 + 0.237919i
\(790\) 5505.67 6903.89i 0.247953 0.310923i
\(791\) 19033.8 1666.80i 0.855580 0.0749234i
\(792\) −6798.78 8525.40i −0.305030 0.382496i
\(793\) −20998.4 19483.6i −0.940320 0.872489i
\(794\) 14071.1 + 2120.88i 0.628925 + 0.0947952i
\(795\) 63161.2 58605.0i 2.81773 2.61447i
\(796\) −7680.54 + 5236.50i −0.341997 + 0.233170i
\(797\) −6084.93 26659.8i −0.270438 1.18487i −0.909497 0.415709i \(-0.863533\pi\)
0.639059 0.769157i \(-0.279324\pi\)
\(798\) −22510.7 + 18418.5i −0.998584 + 0.817051i
\(799\) 4007.31 17557.2i 0.177432 0.777381i
\(800\) 4630.74 + 11798.9i 0.204652 + 0.521444i
\(801\) 19.2054 + 256.278i 0.000847177 + 0.0113048i
\(802\) −29947.2 51870.1i −1.31855 2.28379i
\(803\) 6575.02 11388.3i 0.288951 0.500478i
\(804\) 31499.0 + 15169.1i 1.38170 + 0.665390i
\(805\) −38037.0 + 15482.0i −1.66538 + 0.677849i
\(806\) −6938.70 + 3341.50i −0.303233 + 0.146029i
\(807\) 2660.88 35507.0i 0.116069 1.54883i
\(808\) 29869.0 9213.38i 1.30048 0.401146i
\(809\) 41434.2 12780.8i 1.80068 0.555436i 0.801580 0.597887i \(-0.203993\pi\)
0.999099 + 0.0424510i \(0.0135166\pi\)
\(810\) −5309.49 + 70850.2i −0.230317 + 3.07336i
\(811\) −28970.8 + 13951.6i −1.25438 + 0.604078i −0.938683 0.344781i \(-0.887953\pi\)
−0.315698 + 0.948860i \(0.602239\pi\)
\(812\) −5000.49 + 5526.74i −0.216112 + 0.238855i
\(813\) 29997.7 + 14446.1i 1.29405 + 0.623183i
\(814\) 4092.34 7088.15i 0.176212 0.305208i
\(815\) 2233.77 + 3869.01i 0.0960069 + 0.166289i
\(816\) 2416.54 + 32246.4i 0.103671 + 1.38340i
\(817\) −693.118 1766.04i −0.0296807 0.0756252i
\(818\) −9724.46 + 42605.6i −0.415657 + 1.82111i
\(819\) 19275.4 + 4145.74i 0.822389 + 0.176879i
\(820\) 19328.2 + 84682.4i 0.823135 + 3.60639i
\(821\) 2299.79 1567.97i 0.0977627 0.0666535i −0.513452 0.858118i \(-0.671634\pi\)
0.611215 + 0.791465i \(0.290681\pi\)
\(822\) 65905.3 61151.1i 2.79648 2.59476i
\(823\) −23670.7 3567.78i −1.00256 0.151112i −0.372810 0.927908i \(-0.621606\pi\)
−0.629752 + 0.776796i \(0.716844\pi\)
\(824\) 4164.20 + 3863.81i 0.176052 + 0.163352i
\(825\) 11765.6 + 14753.6i 0.496517 + 0.622613i
\(826\) −2226.77 + 16145.7i −0.0938004 + 0.680124i
\(827\) −22913.9 + 28733.1i −0.963474 + 1.20816i 0.0145980 + 0.999893i \(0.495353\pi\)
−0.978072 + 0.208265i \(0.933218\pi\)
\(828\) −36420.9 + 5489.57i −1.52864 + 0.230406i
\(829\) 28112.9 + 19167.1i 1.17781 + 0.803015i 0.984025 0.178030i \(-0.0569724\pi\)
0.193781 + 0.981045i \(0.437925\pi\)
\(830\) −32564.2 + 82972.2i −1.36183 + 3.46989i
\(831\) −5393.33 1663.62i −0.225142 0.0694470i
\(832\) −39066.8 −1.62788
\(833\) −27600.5 32882.1i −1.14802 1.36770i
\(834\) 3039.36 0.126192
\(835\) −61083.9 18841.9i −2.53161 0.780898i
\(836\) 4657.48 11867.1i 0.192682 0.490946i
\(837\) 1304.98 + 889.722i 0.0538910 + 0.0367423i
\(838\) 45219.1 6815.69i 1.86404 0.280959i
\(839\) 27592.2 34599.5i 1.13538 1.42373i 0.244411 0.969672i \(-0.421405\pi\)
0.890973 0.454056i \(-0.150023\pi\)
\(840\) 47743.0 + 50177.0i 1.96106 + 2.06104i
\(841\) −14749.7 18495.5i −0.604769 0.758356i
\(842\) 28799.9 + 26722.4i 1.17875 + 1.09372i
\(843\) 31438.8 + 4738.64i 1.28447 + 0.193603i
\(844\) 54854.2 50897.2i 2.23715 2.07578i
\(845\) −14094.5 + 9609.49i −0.573807 + 0.391215i
\(846\) −2876.50 12602.8i −0.116899 0.512166i
\(847\) 18344.5 4429.90i 0.744187 0.179709i
\(848\) −6432.46 + 28182.4i −0.260485 + 1.14126i
\(849\) 22807.2 + 58111.8i 0.921957 + 2.34911i
\(850\) −7062.21 94238.6i −0.284978 3.80277i
\(851\) −6386.82 11062.3i −0.257271 0.445606i
\(852\) 5952.70 10310.4i 0.239362 0.414586i
\(853\) −5397.95 2599.51i −0.216673 0.104344i 0.322399 0.946604i \(-0.395511\pi\)
−0.539072 + 0.842260i \(0.681225\pi\)
\(854\) 25683.0 + 36672.9i 1.02911 + 1.46946i
\(855\) 13815.6 6653.25i 0.552613 0.266124i
\(856\) 494.447 6597.94i 0.0197428 0.263450i
\(857\) 29960.0 9241.43i 1.19418 0.368356i 0.366962 0.930236i \(-0.380398\pi\)
0.827219 + 0.561880i \(0.189922\pi\)
\(858\) −30952.8 + 9547.69i −1.23160 + 0.379898i
\(859\) −2461.87 + 32851.4i −0.0977859 + 1.30486i 0.705262 + 0.708947i \(0.250829\pi\)
−0.803048 + 0.595915i \(0.796790\pi\)
\(860\) −8809.40 + 4242.38i −0.349300 + 0.168214i
\(861\) −24964.9 35647.4i −0.988156 1.41099i
\(862\) −23025.9 11088.7i −0.909822 0.438147i
\(863\) 5805.06 10054.7i 0.228976 0.396598i −0.728529 0.685015i \(-0.759796\pi\)
0.957505 + 0.288417i \(0.0931289\pi\)
\(864\) 2231.02 + 3864.24i 0.0878481 + 0.152157i
\(865\) 211.006 + 2815.67i 0.00829411 + 0.110677i
\(866\) 5103.01 + 13002.3i 0.200240 + 0.510202i
\(867\) −16189.9 + 70932.5i −0.634184 + 2.77854i
\(868\) 7608.03 1837.21i 0.297504 0.0718423i
\(869\) −431.513 1890.58i −0.0168448 0.0738017i
\(870\) 12169.4 8296.94i 0.474230 0.323325i
\(871\) 14432.7 13391.5i 0.561460 0.520959i
\(872\) −8381.59 1263.32i −0.325500 0.0490613i
\(873\) −3725.94 3457.17i −0.144449 0.134029i
\(874\) −19078.2 23923.3i −0.738365 0.925880i
\(875\) −7060.15 7420.09i −0.272773 0.286680i
\(876\) −46706.8 + 58568.5i −1.80146 + 2.25896i
\(877\) 4717.24 711.010i 0.181630 0.0273764i −0.0575971 0.998340i \(-0.518344\pi\)
0.239228 + 0.970964i \(0.423106\pi\)
\(878\) 30525.8 + 20812.1i 1.17334 + 0.799972i
\(879\) −12001.1 + 30578.4i −0.460510 + 1.17336i
\(880\) −10839.6 3343.58i −0.415231 0.128082i
\(881\) −37538.9 −1.43555 −0.717773 0.696277i \(-0.754838\pi\)
−0.717773 + 0.696277i \(0.754838\pi\)
\(882\) −28091.1 12669.7i −1.07242 0.483686i
\(883\) −26101.4 −0.994769 −0.497384 0.867530i \(-0.665706\pi\)
−0.497384 + 0.867530i \(0.665706\pi\)
\(884\) 100790. + 31089.5i 3.83476 + 1.18287i
\(885\) 7651.14 19494.8i 0.290611 0.740464i
\(886\) 22177.7 + 15120.5i 0.840942 + 0.573345i
\(887\) −32808.9 + 4945.14i −1.24196 + 0.187195i −0.736966 0.675930i \(-0.763742\pi\)
−0.504990 + 0.863125i \(0.668504\pi\)
\(888\) −13432.0 + 16843.2i −0.507599 + 0.636509i
\(889\) 1889.68 13701.6i 0.0712911 0.516915i
\(890\) 686.062 + 860.295i 0.0258392 + 0.0324013i
\(891\) 11437.6 + 10612.5i 0.430049 + 0.399027i
\(892\) −23252.8 3504.80i −0.872828 0.131558i
\(893\) 5118.76 4749.52i 0.191817 0.177980i
\(894\) 79249.7 54031.5i 2.96477 2.02135i
\(895\) 11846.2 + 51901.5i 0.442429 + 1.93841i
\(896\) 48066.7 + 10338.1i 1.79218 + 0.385461i
\(897\) −11249.2 + 49285.8i −0.418727 + 1.83456i
\(898\) −16160.0 41175.0i −0.600520 1.53010i
\(899\) −57.4689 766.869i −0.00213203 0.0284499i
\(900\) −22053.8 38198.3i −0.816808 1.41475i
\(901\) −47379.1 + 82063.1i −1.75186 + 3.03431i
\(902\) 26431.2 + 12728.6i 0.975678 + 0.469862i
\(903\) 3286.82 3632.72i 0.121128 0.133875i
\(904\) 30543.7 14709.1i 1.12375 0.541168i
\(905\) −2000.09 + 26689.4i −0.0734645 + 0.980316i
\(906\) −16314.9 + 5032.48i −0.598263 + 0.184540i
\(907\) −10437.1 + 3219.43i −0.382094 + 0.117860i −0.479851 0.877350i \(-0.659309\pi\)
0.0977572 + 0.995210i \(0.468833\pi\)
\(908\) 815.025 10875.7i 0.0297880 0.397494i
\(909\) 16100.2 7753.47i 0.587471 0.282911i
\(910\) 78188.4 31824.5i 2.84826 1.15931i
\(911\) −13214.6 6363.81i −0.480592 0.231441i 0.177872 0.984054i \(-0.443079\pi\)
−0.658463 + 0.752613i \(0.728793\pi\)
\(912\) −6269.26 + 10858.7i −0.227627 + 0.394262i
\(913\) 9787.11 + 16951.8i 0.354771 + 0.614482i
\(914\) −1804.35 24077.4i −0.0652982 0.871344i
\(915\) −21017.5 53551.8i −0.759364 1.93483i
\(916\) 11990.9 52535.7i 0.432524 1.89501i
\(917\) 14059.2 11503.4i 0.506298 0.414258i
\(918\) −7402.82 32433.9i −0.266154 1.16610i
\(919\) 34909.4 23800.8i 1.25305 0.854317i 0.259287 0.965800i \(-0.416513\pi\)
0.993766 + 0.111483i \(0.0355602\pi\)
\(920\) −53414.1 + 49561.0i −1.91414 + 1.77606i
\(921\) −44168.9 6657.39i −1.58025 0.238185i
\(922\) −5.63910 5.23232i −0.000201425 0.000186895i
\(923\) −4180.21 5241.81i −0.149072 0.186930i
\(924\) 32793.6 2871.74i 1.16756 0.102244i
\(925\) 9537.38 11959.5i 0.339013 0.425109i
\(926\) −58306.1 + 8788.22i −2.06917 + 0.311878i
\(927\) 2683.29 + 1829.44i 0.0950710 + 0.0648183i
\(928\) 793.724 2022.38i 0.0280768 0.0715385i
\(929\) −23649.8 7294.99i −0.835225 0.257633i −0.152495 0.988304i \(-0.548731\pi\)
−0.682729 + 0.730672i \(0.739207\pi\)
\(930\) −15466.8 −0.545352
\(931\) −1660.10 16563.2i −0.0584401 0.583067i
\(932\) 74391.8 2.61458
\(933\) 39971.6 + 12329.6i 1.40258 + 0.432640i
\(934\) −14752.4 + 37588.6i −0.516825 + 1.31685i
\(935\) −30723.2 20946.7i −1.07461 0.732654i
\(936\) 34591.7 5213.86i 1.20798 0.182073i
\(937\) 8344.99 10464.3i 0.290949 0.364838i −0.614778 0.788700i \(-0.710754\pi\)
0.905727 + 0.423862i \(0.139326\pi\)
\(938\) −26454.8 + 15719.5i −0.920874 + 0.547187i
\(939\) −29035.6 36409.5i −1.00910 1.26537i
\(940\) −26381.1 24478.0i −0.915378 0.849347i
\(941\) 14614.0 + 2202.70i 0.506272 + 0.0763083i 0.397212 0.917727i \(-0.369978\pi\)
0.109060 + 0.994035i \(0.465216\pi\)
\(942\) −17662.9 + 16388.8i −0.610923 + 0.566854i
\(943\) 37829.0 25791.4i 1.30634 0.890650i
\(944\) 1563.47 + 6850.00i 0.0539053 + 0.236174i
\(945\) −13669.8 10623.5i −0.470561 0.365696i
\(946\) −734.840 + 3219.55i −0.0252555 + 0.110652i
\(947\) 9879.69 + 25173.1i 0.339015 + 0.863795i 0.994123 + 0.108260i \(0.0345279\pi\)
−0.655108 + 0.755535i \(0.727377\pi\)
\(948\) 825.548 + 11016.2i 0.0282833 + 0.377414i
\(949\) 21093.3 + 36534.8i 0.721516 + 1.24970i
\(950\) 18321.6 31734.0i 0.625717 1.08377i
\(951\) 21194.7 + 10206.8i 0.722697 + 0.348033i
\(952\) −66439.0 37255.0i −2.26187 1.26832i
\(953\) 13953.3 6719.58i 0.474285 0.228403i −0.181442 0.983402i \(-0.558077\pi\)
0.655727 + 0.754998i \(0.272362\pi\)
\(954\) −5083.06 + 67828.7i −0.172505 + 2.30192i
\(955\) 7392.96 2280.43i 0.250503 0.0772700i
\(956\) −56847.2 + 17535.0i −1.92319 + 0.593225i
\(957\) 241.713 3225.44i 0.00816456 0.108948i
\(958\) 20241.3 9747.72i 0.682639 0.328742i
\(959\) 8306.65 + 50779.3i 0.279704 + 1.70985i
\(960\) −70688.6 34041.9i −2.37653 1.14448i
\(961\) 14491.7 25100.4i 0.486446 0.842550i
\(962\) 13128.7 + 22739.5i 0.440005 + 0.762111i
\(963\) −282.673 3772.01i −0.00945900 0.126222i
\(964\) −9059.19 23082.4i −0.302673 0.771199i
\(965\) 9944.55 43569.9i 0.331737 1.45344i
\(966\) 33386.9 71613.6i 1.11202 2.38523i
\(967\) −3056.81 13392.7i −0.101655 0.445379i −0.999982 0.00605135i \(-0.998074\pi\)
0.898327 0.439328i \(-0.144783\pi\)
\(968\) 27666.0 18862.4i 0.918616 0.626302i
\(969\) −30129.5 + 27956.1i −0.998864 + 0.926811i
\(970\) −21519.4 3243.53i −0.712316 0.107364i
\(971\) 8536.54 + 7920.75i 0.282133 + 0.261781i 0.808526 0.588460i \(-0.200266\pi\)
−0.526394 + 0.850241i \(0.676456\pi\)
\(972\) −41504.3 52044.8i −1.36960 1.71742i
\(973\) −961.769 + 1449.40i −0.0316885 + 0.0477551i
\(974\) −32602.0 + 40881.7i −1.07252 + 1.34490i
\(975\) −59862.7 + 9022.85i −1.96630 + 0.296372i
\(976\) 15947.0 + 10872.5i 0.523003 + 0.356578i
\(977\) 10823.8 27578.6i 0.354436 0.903089i −0.636805 0.771025i \(-0.719744\pi\)
0.991241 0.132064i \(-0.0421604\pi\)
\(978\) −8213.76 2533.61i −0.268555 0.0828384i
\(979\) 241.644 0.00788865
\(980\) −84485.1 + 14911.1i −2.75385 + 0.486039i
\(981\) −4845.84 −0.157712
\(982\) −65459.6 20191.6i −2.12719 0.656151i
\(983\) −16893.7 + 43044.3i −0.548142 + 1.39664i 0.341455 + 0.939898i \(0.389080\pi\)
−0.889597 + 0.456746i \(0.849015\pi\)
\(984\) −63800.1 43498.1i −2.06694 1.40922i
\(985\) −8803.53 + 1326.92i −0.284775 + 0.0429230i
\(986\) −10099.4 + 12664.2i −0.326196 + 0.409036i
\(987\) 16866.1 + 6376.42i 0.543926 + 0.205637i
\(988\) 25499.4 + 31975.3i 0.821098 + 1.02962i
\(989\) 3778.07 + 3505.53i 0.121472 + 0.112709i
\(990\) −26393.4 3978.17i −0.847311 0.127712i
\(991\) 34318.9 31843.3i 1.10008 1.02072i 0.100408 0.994946i \(-0.467985\pi\)
0.999668 0.0257752i \(-0.00820540\pi\)
\(992\) −1885.02 + 1285.18i −0.0603320 + 0.0411337i
\(993\) 10060.9 + 44079.7i 0.321524 + 1.40869i
\(994\) 4664.80 + 9383.53i 0.148852 + 0.299424i
\(995\) −2339.45 + 10249.8i −0.0745383 + 0.326574i
\(996\) −40738.6 103800.i −1.29604 3.30225i
\(997\) −380.869 5082.35i −0.0120985 0.161444i −0.999981 0.00623707i \(-0.998015\pi\)
0.987882 0.155207i \(-0.0496044\pi\)
\(998\) 47063.6 + 81516.6i 1.49276 + 2.58553i
\(999\) 2692.47 4663.50i 0.0852713 0.147694i
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 49.4.g.a.2.2 156
49.5 odd 42 2401.4.a.f.1.7 78
49.25 even 21 inner 49.4.g.a.25.2 yes 156
49.44 even 21 2401.4.a.g.1.7 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.4.g.a.2.2 156 1.1 even 1 trivial
49.4.g.a.25.2 yes 156 49.25 even 21 inner
2401.4.a.f.1.7 78 49.5 odd 42
2401.4.a.g.1.7 78 49.44 even 21