Properties

Label 49.2.g.a.25.1
Level $49$
Weight $2$
Character 49.25
Analytic conductor $0.391$
Analytic rank $0$
Dimension $48$
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] = [49,2,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, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
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: \(0.391266969904\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 25.1
Character \(\chi\) \(=\) 49.25
Dual form 49.2.g.a.2.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.50546 + 0.772833i) q^{2} +(-0.539916 - 1.37568i) q^{3} +(4.02760 - 2.74597i) q^{4} +(2.04183 + 0.307757i) q^{5} +(2.41591 + 3.02946i) q^{6} +(0.189789 - 2.63894i) q^{7} +(-4.69930 + 5.89274i) q^{8} +(0.598158 - 0.555009i) q^{9} +O(q^{10})\) \(q+(-2.50546 + 0.772833i) q^{2} +(-0.539916 - 1.37568i) q^{3} +(4.02760 - 2.74597i) q^{4} +(2.04183 + 0.307757i) q^{5} +(2.41591 + 3.02946i) q^{6} +(0.189789 - 2.63894i) q^{7} +(-4.69930 + 5.89274i) q^{8} +(0.598158 - 0.555009i) q^{9} +(-5.35358 + 0.806922i) q^{10} +(-1.36984 - 1.27103i) q^{11} +(-5.95215 - 4.05811i) q^{12} +(-0.677236 + 2.96716i) q^{13} +(1.56395 + 6.75843i) q^{14} +(-0.679042 - 2.97508i) q^{15} +(3.65803 - 9.32052i) q^{16} +(-0.104929 + 1.40017i) q^{17} +(-1.06973 + 1.85283i) q^{18} +(2.73229 + 4.73247i) q^{19} +(9.06877 - 4.36729i) q^{20} +(-3.73281 + 1.16371i) q^{21} +(4.41439 + 2.12586i) q^{22} +(-0.0152199 - 0.203095i) q^{23} +(10.6438 + 3.28317i) q^{24} +(-0.703500 - 0.217001i) q^{25} +(-0.596333 - 7.95751i) q^{26} +(-5.08094 - 2.44685i) q^{27} +(-6.48204 - 11.1497i) q^{28} +(1.62320 - 0.781691i) q^{29} +(4.00056 + 6.92917i) q^{30} +(-2.57807 + 4.46535i) q^{31} +(-0.835369 + 11.1472i) q^{32} +(-1.00893 + 2.57072i) q^{33} +(-0.819206 - 3.58918i) q^{34} +(1.19967 - 5.32985i) q^{35} +(0.885100 - 3.87788i) q^{36} +(6.23369 + 4.25006i) q^{37} +(-10.5031 - 9.74542i) q^{38} +(4.44753 - 0.670357i) q^{39} +(-11.4087 + 10.5857i) q^{40} +(-5.90598 + 7.40586i) q^{41} +(8.45307 - 5.80048i) q^{42} +(1.60000 + 2.00633i) q^{43} +(-9.00739 - 1.35765i) q^{44} +(1.39215 - 0.949149i) q^{45} +(0.195091 + 0.497084i) q^{46} +(1.58858 - 0.490011i) q^{47} -14.7971 q^{48} +(-6.92796 - 1.00168i) q^{49} +1.93030 q^{50} +(1.98285 - 0.611628i) q^{51} +(5.42011 + 13.8102i) q^{52} +(5.98035 - 4.07733i) q^{53} +(14.6211 + 2.20378i) q^{54} +(-2.40583 - 3.01681i) q^{55} +(14.6587 + 13.5195i) q^{56} +(5.03517 - 6.31391i) q^{57} +(-3.46275 + 3.21296i) q^{58} +(8.25485 - 1.24422i) q^{59} +(-10.9044 - 10.1178i) q^{60} +(-5.45679 - 3.72038i) q^{61} +(3.00829 - 13.1802i) q^{62} +(-1.35111 - 1.68383i) q^{63} +(-2.06590 - 9.05131i) q^{64} +(-2.29597 + 5.85003i) q^{65} +(0.541109 - 7.22059i) q^{66} +(-1.78982 + 3.10006i) q^{67} +(3.42222 + 5.92747i) q^{68} +(-0.271177 + 0.130592i) q^{69} +(1.11337 + 14.2809i) q^{70} +(-6.02101 - 2.89956i) q^{71} +(0.459601 + 6.13295i) q^{72} +(-0.168909 - 0.0521016i) q^{73} +(-18.9029 - 5.83076i) q^{74} +(0.0813062 + 1.08496i) q^{75} +(23.9998 + 11.5577i) q^{76} +(-3.61415 + 3.37370i) q^{77} +(-10.6251 + 5.11676i) q^{78} +(-7.82581 - 13.5547i) q^{79} +(10.3375 - 17.9052i) q^{80} +(-0.439878 + 5.86976i) q^{81} +(9.07372 - 23.1194i) q^{82} +(2.14456 + 9.39591i) q^{83} +(-11.8387 + 14.9372i) q^{84} +(-0.645159 + 2.82663i) q^{85} +(-5.55929 - 3.79026i) q^{86} +(-1.95175 - 1.81096i) q^{87} +(13.9272 - 2.09918i) q^{88} +(0.911046 - 0.845327i) q^{89} +(-2.75444 + 3.45395i) q^{90} +(7.70162 + 2.35032i) q^{91} +(-0.618992 - 0.776191i) q^{92} +(7.53485 + 1.13570i) q^{93} +(-3.60142 + 2.45541i) q^{94} +(4.12243 + 10.5038i) q^{95} +(15.7861 - 4.86936i) q^{96} +13.9109 q^{97} +(18.1319 - 2.84448i) q^{98} -1.52482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{8}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50546 + 0.772833i −1.77163 + 0.546475i −0.996367 0.0851631i \(-0.972859\pi\)
−0.775263 + 0.631639i \(0.782383\pi\)
\(3\) −0.539916 1.37568i −0.311721 0.794252i −0.997773 0.0666995i \(-0.978753\pi\)
0.686052 0.727552i \(-0.259342\pi\)
\(4\) 4.02760 2.74597i 2.01380 1.37298i
\(5\) 2.04183 + 0.307757i 0.913135 + 0.137633i 0.588772 0.808300i \(-0.299612\pi\)
0.324364 + 0.945932i \(0.394850\pi\)
\(6\) 2.41591 + 3.02946i 0.986293 + 1.23677i
\(7\) 0.189789 2.63894i 0.0717335 0.997424i
\(8\) −4.69930 + 5.89274i −1.66146 + 2.08340i
\(9\) 0.598158 0.555009i 0.199386 0.185003i
\(10\) −5.35358 + 0.806922i −1.69295 + 0.255171i
\(11\) −1.36984 1.27103i −0.413024 0.383230i 0.446113 0.894977i \(-0.352808\pi\)
−0.859136 + 0.511747i \(0.828999\pi\)
\(12\) −5.95215 4.05811i −1.71824 1.17148i
\(13\) −0.677236 + 2.96716i −0.187831 + 0.822943i 0.789926 + 0.613203i \(0.210119\pi\)
−0.977757 + 0.209741i \(0.932738\pi\)
\(14\) 1.56395 + 6.75843i 0.417983 + 1.80627i
\(15\) −0.679042 2.97508i −0.175328 0.768162i
\(16\) 3.65803 9.32052i 0.914509 2.33013i
\(17\) −0.104929 + 1.40017i −0.0254489 + 0.339592i 0.969917 + 0.243435i \(0.0782742\pi\)
−0.995366 + 0.0961572i \(0.969345\pi\)
\(18\) −1.06973 + 1.85283i −0.252139 + 0.436717i
\(19\) 2.73229 + 4.73247i 0.626831 + 1.08570i 0.988184 + 0.153274i \(0.0489816\pi\)
−0.361353 + 0.932429i \(0.617685\pi\)
\(20\) 9.06877 4.36729i 2.02784 0.976555i
\(21\) −3.73281 + 1.16371i −0.814566 + 0.253943i
\(22\) 4.41439 + 2.12586i 0.941151 + 0.453234i
\(23\) −0.0152199 0.203095i −0.00317356 0.0423482i 0.995392 0.0958873i \(-0.0305689\pi\)
−0.998566 + 0.0535391i \(0.982950\pi\)
\(24\) 10.6438 + 3.28317i 2.17265 + 0.670175i
\(25\) −0.703500 0.217001i −0.140700 0.0434002i
\(26\) −0.596333 7.95751i −0.116951 1.56060i
\(27\) −5.08094 2.44685i −0.977828 0.470897i
\(28\) −6.48204 11.1497i −1.22499 2.10710i
\(29\) 1.62320 0.781691i 0.301420 0.145156i −0.277060 0.960853i \(-0.589360\pi\)
0.578480 + 0.815696i \(0.303646\pi\)
\(30\) 4.00056 + 6.92917i 0.730398 + 1.26509i
\(31\) −2.57807 + 4.46535i −0.463035 + 0.802000i −0.999110 0.0421697i \(-0.986573\pi\)
0.536075 + 0.844170i \(0.319906\pi\)
\(32\) −0.835369 + 11.1472i −0.147674 + 1.97057i
\(33\) −1.00893 + 2.57072i −0.175633 + 0.447506i
\(34\) −0.819206 3.58918i −0.140493 0.615539i
\(35\) 1.19967 5.32985i 0.202781 0.900910i
\(36\) 0.885100 3.87788i 0.147517 0.646313i
\(37\) 6.23369 + 4.25006i 1.02481 + 0.698705i 0.954314 0.298807i \(-0.0965886\pi\)
0.0704986 + 0.997512i \(0.477541\pi\)
\(38\) −10.5031 9.74542i −1.70382 1.58092i
\(39\) 4.44753 0.670357i 0.712175 0.107343i
\(40\) −11.4087 + 10.5857i −1.80388 + 1.67375i
\(41\) −5.90598 + 7.40586i −0.922359 + 1.15660i 0.0649659 + 0.997887i \(0.479306\pi\)
−0.987325 + 0.158714i \(0.949265\pi\)
\(42\) 8.45307 5.80048i 1.30434 0.895034i
\(43\) 1.60000 + 2.00633i 0.243997 + 0.305963i 0.888717 0.458456i \(-0.151597\pi\)
−0.644720 + 0.764419i \(0.723026\pi\)
\(44\) −9.00739 1.35765i −1.35792 0.204673i
\(45\) 1.39215 0.949149i 0.207529 0.141491i
\(46\) 0.195091 + 0.497084i 0.0287646 + 0.0732911i
\(47\) 1.58858 0.490011i 0.231718 0.0714754i −0.176722 0.984261i \(-0.556549\pi\)
0.408439 + 0.912785i \(0.366073\pi\)
\(48\) −14.7971 −2.13578
\(49\) −6.92796 1.00168i −0.989709 0.143097i
\(50\) 1.93030 0.272985
\(51\) 1.98285 0.611628i 0.277655 0.0856451i
\(52\) 5.42011 + 13.8102i 0.751634 + 1.91513i
\(53\) 5.98035 4.07733i 0.821464 0.560065i −0.0780537 0.996949i \(-0.524871\pi\)
0.899518 + 0.436885i \(0.143918\pi\)
\(54\) 14.6211 + 2.20378i 1.98968 + 0.299896i
\(55\) −2.40583 3.01681i −0.324401 0.406786i
\(56\) 14.6587 + 13.5195i 1.95885 + 1.80662i
\(57\) 5.03517 6.31391i 0.666925 0.836298i
\(58\) −3.46275 + 3.21296i −0.454681 + 0.421882i
\(59\) 8.25485 1.24422i 1.07469 0.161983i 0.412229 0.911080i \(-0.364750\pi\)
0.662460 + 0.749097i \(0.269512\pi\)
\(60\) −10.9044 10.1178i −1.40775 1.30620i
\(61\) −5.45679 3.72038i −0.698671 0.476345i 0.161158 0.986929i \(-0.448477\pi\)
−0.859828 + 0.510583i \(0.829430\pi\)
\(62\) 3.00829 13.1802i 0.382053 1.67389i
\(63\) −1.35111 1.68383i −0.170224 0.212143i
\(64\) −2.06590 9.05131i −0.258238 1.13141i
\(65\) −2.29597 + 5.85003i −0.284780 + 0.725607i
\(66\) 0.541109 7.22059i 0.0666059 0.888793i
\(67\) −1.78982 + 3.10006i −0.218661 + 0.378732i −0.954399 0.298534i \(-0.903502\pi\)
0.735738 + 0.677267i \(0.236836\pi\)
\(68\) 3.42222 + 5.92747i 0.415006 + 0.718811i
\(69\) −0.271177 + 0.130592i −0.0326459 + 0.0157214i
\(70\) 1.11337 + 14.2809i 0.133073 + 1.70689i
\(71\) −6.02101 2.89956i −0.714562 0.344115i 0.0410295 0.999158i \(-0.486936\pi\)
−0.755592 + 0.655043i \(0.772651\pi\)
\(72\) 0.459601 + 6.13295i 0.0541645 + 0.722775i
\(73\) −0.168909 0.0521016i −0.0197693 0.00609804i 0.284855 0.958571i \(-0.408055\pi\)
−0.304624 + 0.952473i \(0.598531\pi\)
\(74\) −18.9029 5.83076i −2.19741 0.677812i
\(75\) 0.0813062 + 1.08496i 0.00938843 + 0.125280i
\(76\) 23.9998 + 11.5577i 2.75296 + 1.32576i
\(77\) −3.61415 + 3.37370i −0.411870 + 0.384469i
\(78\) −10.6251 + 5.11676i −1.20305 + 0.579358i
\(79\) −7.82581 13.5547i −0.880473 1.52502i −0.850816 0.525463i \(-0.823892\pi\)
−0.0296560 0.999560i \(-0.509441\pi\)
\(80\) 10.3375 17.9052i 1.15577 2.00186i
\(81\) −0.439878 + 5.86976i −0.0488753 + 0.652196i
\(82\) 9.07372 23.1194i 1.00202 2.55312i
\(83\) 2.14456 + 9.39591i 0.235396 + 1.03134i 0.945086 + 0.326822i \(0.105978\pi\)
−0.709691 + 0.704514i \(0.751165\pi\)
\(84\) −11.8387 + 14.9372i −1.29171 + 1.62978i
\(85\) −0.645159 + 2.82663i −0.0699773 + 0.306591i
\(86\) −5.55929 3.79026i −0.599474 0.408714i
\(87\) −1.95175 1.81096i −0.209250 0.194155i
\(88\) 13.9272 2.09918i 1.48464 0.223774i
\(89\) 0.911046 0.845327i 0.0965706 0.0896045i −0.630410 0.776262i \(-0.717113\pi\)
0.726981 + 0.686658i \(0.240923\pi\)
\(90\) −2.75444 + 3.45395i −0.290343 + 0.364079i
\(91\) 7.70162 + 2.35032i 0.807349 + 0.246380i
\(92\) −0.618992 0.776191i −0.0645344 0.0809235i
\(93\) 7.53485 + 1.13570i 0.781328 + 0.117766i
\(94\) −3.60142 + 2.45541i −0.371458 + 0.253256i
\(95\) 4.12243 + 10.5038i 0.422953 + 1.07767i
\(96\) 15.7861 4.86936i 1.61116 0.496977i
\(97\) 13.9109 1.41244 0.706218 0.707995i \(-0.250400\pi\)
0.706218 + 0.707995i \(0.250400\pi\)
\(98\) 18.1319 2.84448i 1.83160 0.287336i
\(99\) −1.52482 −0.153250
\(100\) −3.42929 + 1.05780i −0.342929 + 0.105780i
\(101\) −0.487085 1.24107i −0.0484667 0.123491i 0.904590 0.426282i \(-0.140177\pi\)
−0.953057 + 0.302791i \(0.902082\pi\)
\(102\) −4.49527 + 3.06482i −0.445098 + 0.303463i
\(103\) −7.54399 1.13707i −0.743331 0.112039i −0.233552 0.972344i \(-0.575035\pi\)
−0.509779 + 0.860305i \(0.670273\pi\)
\(104\) −14.3022 17.9344i −1.40245 1.75861i
\(105\) −7.97992 + 1.22731i −0.778760 + 0.119773i
\(106\) −11.8324 + 14.8374i −1.14927 + 1.44114i
\(107\) −1.18174 + 1.09649i −0.114243 + 0.106002i −0.735226 0.677822i \(-0.762924\pi\)
0.620983 + 0.783824i \(0.286734\pi\)
\(108\) −27.1830 + 4.09717i −2.61568 + 0.394251i
\(109\) −7.47506 6.93584i −0.715981 0.664333i 0.235558 0.971860i \(-0.424308\pi\)
−0.951539 + 0.307527i \(0.900499\pi\)
\(110\) 8.35920 + 5.69920i 0.797018 + 0.543398i
\(111\) 2.48107 10.8703i 0.235492 1.03176i
\(112\) −23.9020 11.4222i −2.25853 1.07930i
\(113\) −1.56953 6.87656i −0.147649 0.646893i −0.993535 0.113528i \(-0.963785\pi\)
0.845886 0.533364i \(-0.179072\pi\)
\(114\) −7.73585 + 19.7106i −0.724528 + 1.84607i
\(115\) 0.0314274 0.419370i 0.00293062 0.0391064i
\(116\) 4.39109 7.60559i 0.407702 0.706161i
\(117\) 1.24171 + 2.15070i 0.114796 + 0.198833i
\(118\) −19.7206 + 9.49696i −1.81543 + 0.874266i
\(119\) 3.67505 + 0.542637i 0.336892 + 0.0497435i
\(120\) 20.7224 + 9.97938i 1.89169 + 0.910989i
\(121\) −0.561074 7.48701i −0.0510067 0.680638i
\(122\) 16.5470 + 5.10408i 1.49810 + 0.462102i
\(123\) 13.3769 + 4.12622i 1.20615 + 0.372048i
\(124\) 1.87828 + 25.0639i 0.168675 + 2.25081i
\(125\) −10.6717 5.13921i −0.954504 0.459665i
\(126\) 4.68648 + 3.17460i 0.417505 + 0.282816i
\(127\) −0.0652974 + 0.0314456i −0.00579421 + 0.00279034i −0.436779 0.899569i \(-0.643881\pi\)
0.430984 + 0.902359i \(0.358166\pi\)
\(128\) 0.992721 + 1.71944i 0.0877450 + 0.151979i
\(129\) 1.89622 3.28434i 0.166952 0.289170i
\(130\) 1.23137 16.4314i 0.107998 1.44113i
\(131\) −6.79968 + 17.3253i −0.594090 + 1.51372i 0.244887 + 0.969552i \(0.421249\pi\)
−0.838977 + 0.544166i \(0.816846\pi\)
\(132\) 2.99555 + 13.1243i 0.260729 + 1.14233i
\(133\) 13.0072 6.31217i 1.12787 0.547335i
\(134\) 2.08850 9.15032i 0.180419 0.790467i
\(135\) −9.62140 6.55976i −0.828078 0.564574i
\(136\) −7.75777 7.19816i −0.665223 0.617237i
\(137\) −7.87758 + 1.18735i −0.673027 + 0.101443i −0.476660 0.879088i \(-0.658153\pi\)
−0.196367 + 0.980530i \(0.562915\pi\)
\(138\) 0.578498 0.536768i 0.0492450 0.0456927i
\(139\) 11.8104 14.8098i 1.00175 1.25615i 0.0352743 0.999378i \(-0.488770\pi\)
0.966472 0.256772i \(-0.0826590\pi\)
\(140\) −9.80384 24.7608i −0.828576 2.09267i
\(141\) −1.53180 1.92081i −0.129001 0.161762i
\(142\) 17.3263 + 2.61152i 1.45399 + 0.219154i
\(143\) 4.69906 3.20377i 0.392955 0.267912i
\(144\) −2.98489 7.60539i −0.248741 0.633782i
\(145\) 3.55487 1.09653i 0.295216 0.0910620i
\(146\) 0.463462 0.0383564
\(147\) 2.36252 + 10.0715i 0.194857 + 0.830684i
\(148\) 36.7773 3.02308
\(149\) 22.5849 6.96653i 1.85023 0.570720i 0.851290 0.524696i \(-0.175821\pi\)
0.998940 0.0460243i \(-0.0146552\pi\)
\(150\) −1.04220 2.65548i −0.0850952 0.216819i
\(151\) −7.34454 + 5.00742i −0.597690 + 0.407498i −0.824027 0.566551i \(-0.808277\pi\)
0.226337 + 0.974049i \(0.427325\pi\)
\(152\) −40.7271 6.13862i −3.30340 0.497908i
\(153\) 0.714346 + 0.895761i 0.0577514 + 0.0724180i
\(154\) 6.44780 11.2458i 0.519579 0.906214i
\(155\) −6.63823 + 8.32408i −0.533195 + 0.668606i
\(156\) 16.0721 14.9127i 1.28680 1.19397i
\(157\) 1.56441 0.235797i 0.124853 0.0188186i −0.0863183 0.996268i \(-0.527510\pi\)
0.211172 + 0.977449i \(0.432272\pi\)
\(158\) 30.0828 + 27.9128i 2.39326 + 2.22062i
\(159\) −8.83801 6.02565i −0.700900 0.477865i
\(160\) −5.13631 + 22.5037i −0.406061 + 1.77907i
\(161\) −0.538843 + 0.00161907i −0.0424668 + 0.000127600i
\(162\) −3.43425 15.0464i −0.269820 1.18216i
\(163\) −5.73215 + 14.6053i −0.448976 + 1.14397i 0.509921 + 0.860221i \(0.329674\pi\)
−0.958898 + 0.283752i \(0.908421\pi\)
\(164\) −3.45063 + 46.0455i −0.269449 + 3.59555i
\(165\) −2.85123 + 4.93848i −0.221968 + 0.384460i
\(166\) −12.6346 21.8837i −0.980633 1.69851i
\(167\) −6.00479 + 2.89175i −0.464664 + 0.223771i −0.651542 0.758613i \(-0.725878\pi\)
0.186877 + 0.982383i \(0.440163\pi\)
\(168\) 10.6842 27.4651i 0.824300 2.11898i
\(169\) 3.36718 + 1.62155i 0.259014 + 0.124735i
\(170\) −0.568088 7.58061i −0.0435704 0.581406i
\(171\) 4.26091 + 1.31432i 0.325840 + 0.100508i
\(172\) 11.9535 + 3.68716i 0.911444 + 0.281143i
\(173\) −1.57547 21.0232i −0.119781 1.59837i −0.656315 0.754487i \(-0.727886\pi\)
0.536534 0.843879i \(-0.319733\pi\)
\(174\) 6.28961 + 3.02892i 0.476814 + 0.229622i
\(175\) −0.706168 + 1.81531i −0.0533813 + 0.137224i
\(176\) −16.8576 + 8.11819i −1.27069 + 0.611932i
\(177\) −6.16858 10.6843i −0.463659 0.803080i
\(178\) −1.62929 + 2.82202i −0.122121 + 0.211519i
\(179\) −1.49710 + 19.9774i −0.111899 + 1.49318i 0.605123 + 0.796132i \(0.293124\pi\)
−0.717022 + 0.697051i \(0.754495\pi\)
\(180\) 3.00067 7.64558i 0.223657 0.569868i
\(181\) 1.67180 + 7.32462i 0.124264 + 0.544435i 0.998285 + 0.0585468i \(0.0186467\pi\)
−0.874021 + 0.485888i \(0.838496\pi\)
\(182\) −21.1125 + 0.0634371i −1.56497 + 0.00470227i
\(183\) −2.17185 + 9.51551i −0.160548 + 0.703407i
\(184\) 1.26831 + 0.864718i 0.0935009 + 0.0637479i
\(185\) 11.4202 + 10.5964i 0.839627 + 0.779060i
\(186\) −19.7560 + 2.97774i −1.44858 + 0.218338i
\(187\) 1.92340 1.78465i 0.140653 0.130507i
\(188\) 5.05259 6.33575i 0.368498 0.462082i
\(189\) −7.42139 + 12.9439i −0.539827 + 0.941530i
\(190\) −18.4463 23.1309i −1.33823 1.67809i
\(191\) 4.59992 + 0.693327i 0.332839 + 0.0501674i 0.313336 0.949642i \(-0.398554\pi\)
0.0195030 + 0.999810i \(0.493792\pi\)
\(192\) −11.3363 + 7.72898i −0.818129 + 0.557791i
\(193\) −8.01876 20.4315i −0.577203 1.47069i −0.859385 0.511329i \(-0.829153\pi\)
0.282182 0.959361i \(-0.408942\pi\)
\(194\) −34.8532 + 10.7508i −2.50231 + 0.771861i
\(195\) 9.28742 0.665086
\(196\) −30.6536 + 14.9896i −2.18954 + 1.07069i
\(197\) −14.4765 −1.03141 −0.515705 0.856766i \(-0.672470\pi\)
−0.515705 + 0.856766i \(0.672470\pi\)
\(198\) 3.82037 1.17843i 0.271502 0.0837473i
\(199\) −2.35273 5.99466i −0.166781 0.424951i 0.822910 0.568172i \(-0.192349\pi\)
−0.989691 + 0.143221i \(0.954254\pi\)
\(200\) 4.58469 3.12579i 0.324186 0.221027i
\(201\) 5.23106 + 0.788455i 0.368970 + 0.0556133i
\(202\) 2.17951 + 2.73302i 0.153350 + 0.192295i
\(203\) −1.75477 4.43187i −0.123160 0.311056i
\(204\) 6.30661 7.90824i 0.441551 0.553687i
\(205\) −14.3382 + 13.3039i −1.00142 + 0.929186i
\(206\) 19.7799 2.98135i 1.37813 0.207720i
\(207\) −0.121823 0.113036i −0.00846732 0.00785652i
\(208\) 25.1782 + 17.1662i 1.74579 + 1.19026i
\(209\) 2.27229 9.95557i 0.157178 0.688642i
\(210\) 19.0449 9.24213i 1.31422 0.637767i
\(211\) 2.96277 + 12.9808i 0.203966 + 0.893632i 0.968493 + 0.249041i \(0.0801154\pi\)
−0.764527 + 0.644591i \(0.777028\pi\)
\(212\) 12.8902 32.8437i 0.885303 2.25571i
\(213\) −0.738045 + 9.84853i −0.0505700 + 0.674810i
\(214\) 2.11340 3.66051i 0.144469 0.250227i
\(215\) 2.64946 + 4.58900i 0.180692 + 0.312967i
\(216\) 38.2956 18.4422i 2.60568 1.25483i
\(217\) 11.2945 + 7.65084i 0.766719 + 0.519373i
\(218\) 24.0887 + 11.6005i 1.63150 + 0.785687i
\(219\) 0.0195215 + 0.260497i 0.00131914 + 0.0176027i
\(220\) −17.9738 5.54417i −1.21179 0.373788i
\(221\) −4.08348 1.25959i −0.274685 0.0847291i
\(222\) 2.18468 + 29.1525i 0.146626 + 1.95659i
\(223\) −14.7151 7.08644i −0.985399 0.474543i −0.129440 0.991587i \(-0.541318\pi\)
−0.855959 + 0.517044i \(0.827032\pi\)
\(224\) 29.2582 + 4.32010i 1.95490 + 0.288649i
\(225\) −0.541241 + 0.260648i −0.0360828 + 0.0173765i
\(226\) 9.24684 + 16.0160i 0.615090 + 1.06537i
\(227\) 7.36693 12.7599i 0.488960 0.846904i −0.510959 0.859605i \(-0.670710\pi\)
0.999919 + 0.0127013i \(0.00404304\pi\)
\(228\) 2.94185 39.2563i 0.194829 2.59981i
\(229\) 2.42402 6.17631i 0.160184 0.408142i −0.828138 0.560525i \(-0.810599\pi\)
0.988322 + 0.152383i \(0.0486947\pi\)
\(230\) 0.245362 + 1.07500i 0.0161787 + 0.0708836i
\(231\) 6.59249 + 3.15041i 0.433754 + 0.207282i
\(232\) −3.02160 + 13.2385i −0.198378 + 0.869149i
\(233\) −2.06376 1.40705i −0.135202 0.0921788i 0.493831 0.869558i \(-0.335596\pi\)
−0.629032 + 0.777379i \(0.716549\pi\)
\(234\) −4.77319 4.42888i −0.312034 0.289525i
\(235\) 3.39441 0.511625i 0.221427 0.0333747i
\(236\) 29.8306 27.6788i 1.94181 1.80173i
\(237\) −14.4217 + 18.0842i −0.936791 + 1.17470i
\(238\) −9.62708 + 1.48065i −0.624031 + 0.0959760i
\(239\) 8.40358 + 10.5378i 0.543583 + 0.681631i 0.975428 0.220316i \(-0.0707090\pi\)
−0.431846 + 0.901947i \(0.642138\pi\)
\(240\) −30.2132 4.55391i −1.95026 0.293954i
\(241\) −20.0165 + 13.6470i −1.28938 + 0.879082i −0.997014 0.0772251i \(-0.975394\pi\)
−0.292363 + 0.956307i \(0.594442\pi\)
\(242\) 7.19196 + 18.3248i 0.462317 + 1.17796i
\(243\) −7.85419 + 2.42270i −0.503847 + 0.155416i
\(244\) −32.1938 −2.06100
\(245\) −13.8375 4.17739i −0.884043 0.266884i
\(246\) −36.7041 −2.34017
\(247\) −15.8924 + 4.90216i −1.01121 + 0.311917i
\(248\) −14.1980 36.1759i −0.901575 2.29717i
\(249\) 11.7679 8.02324i 0.745762 0.508452i
\(250\) 30.7092 + 4.62867i 1.94222 + 0.292743i
\(251\) 5.00516 + 6.27627i 0.315923 + 0.396155i 0.914285 0.405071i \(-0.132753\pi\)
−0.598362 + 0.801226i \(0.704182\pi\)
\(252\) −10.0655 3.07170i −0.634066 0.193499i
\(253\) −0.237291 + 0.297553i −0.0149183 + 0.0187070i
\(254\) 0.139298 0.129250i 0.00874034 0.00810985i
\(255\) 4.23688 0.638607i 0.265324 0.0399911i
\(256\) 9.79536 + 9.08877i 0.612210 + 0.568048i
\(257\) 14.6378 + 9.97992i 0.913084 + 0.622530i 0.926056 0.377386i \(-0.123177\pi\)
−0.0129722 + 0.999916i \(0.504129\pi\)
\(258\) −2.21265 + 9.69426i −0.137754 + 0.603538i
\(259\) 12.3987 15.6437i 0.770419 0.972052i
\(260\) 6.81677 + 29.8662i 0.422758 + 1.85222i
\(261\) 0.537083 1.36846i 0.0332446 0.0847058i
\(262\) 3.64678 48.6629i 0.225299 3.00640i
\(263\) 9.69503 16.7923i 0.597821 1.03546i −0.395321 0.918543i \(-0.629367\pi\)
0.993142 0.116913i \(-0.0373000\pi\)
\(264\) −10.4073 18.0260i −0.640526 1.10942i
\(265\) 13.4657 6.48473i 0.827191 0.398354i
\(266\) −27.7109 + 25.8673i −1.69906 + 1.58603i
\(267\) −1.65479 0.796905i −0.101272 0.0487698i
\(268\) 1.30399 + 17.4006i 0.0796541 + 1.06291i
\(269\) −27.3429 8.43417i −1.66713 0.514241i −0.689446 0.724337i \(-0.742146\pi\)
−0.977681 + 0.210096i \(0.932622\pi\)
\(270\) 29.1756 + 8.99950i 1.77557 + 0.547692i
\(271\) −2.00695 26.7808i −0.121913 1.62682i −0.637827 0.770179i \(-0.720167\pi\)
0.515914 0.856640i \(-0.327452\pi\)
\(272\) 12.6665 + 6.09987i 0.768020 + 0.369859i
\(273\) −0.924938 11.8640i −0.0559798 0.718040i
\(274\) 18.8194 9.06293i 1.13692 0.547512i
\(275\) 0.687871 + 1.19143i 0.0414802 + 0.0718457i
\(276\) −0.733590 + 1.27062i −0.0441569 + 0.0764821i
\(277\) 0.817360 10.9069i 0.0491104 0.655333i −0.917278 0.398247i \(-0.869619\pi\)
0.966389 0.257086i \(-0.0827623\pi\)
\(278\) −18.1451 + 46.2329i −1.08827 + 2.77286i
\(279\) 0.936218 + 4.10184i 0.0560499 + 0.245571i
\(280\) 25.7699 + 32.1159i 1.54004 + 1.91929i
\(281\) 5.11979 22.4313i 0.305421 1.33814i −0.556396 0.830917i \(-0.687816\pi\)
0.861817 0.507219i \(-0.169327\pi\)
\(282\) 5.32233 + 3.62871i 0.316940 + 0.216086i
\(283\) 0.959396 + 0.890190i 0.0570302 + 0.0529163i 0.708173 0.706039i \(-0.249520\pi\)
−0.651143 + 0.758955i \(0.725710\pi\)
\(284\) −32.2123 + 4.85523i −1.91145 + 0.288105i
\(285\) 12.2241 11.3423i 0.724095 0.671862i
\(286\) −9.29735 + 11.6585i −0.549764 + 0.689382i
\(287\) 18.4227 + 16.9910i 1.08746 + 1.00295i
\(288\) 5.68713 + 7.13144i 0.335117 + 0.420224i
\(289\) 14.8606 + 2.23988i 0.874156 + 0.131758i
\(290\) −8.05915 + 5.49464i −0.473250 + 0.322656i
\(291\) −7.51071 19.1370i −0.440285 1.12183i
\(292\) −0.823369 + 0.253976i −0.0481840 + 0.0148628i
\(293\) 4.00258 0.233833 0.116917 0.993142i \(-0.462699\pi\)
0.116917 + 0.993142i \(0.462699\pi\)
\(294\) −13.7028 23.4080i −0.799164 1.36518i
\(295\) 17.2379 1.00363
\(296\) −54.3385 + 16.7612i −3.15836 + 0.974225i
\(297\) 3.85008 + 9.80984i 0.223404 + 0.569225i
\(298\) −51.2018 + 34.9088i −2.96604 + 2.02221i
\(299\) 0.612923 + 0.0923833i 0.0354463 + 0.00534266i
\(300\) 3.30672 + 4.14650i 0.190914 + 0.239398i
\(301\) 5.59824 3.84151i 0.322677 0.221421i
\(302\) 14.5316 18.2220i 0.836198 1.04856i
\(303\) −1.44434 + 1.34015i −0.0829750 + 0.0769896i
\(304\) 54.1039 8.15485i 3.10307 0.467713i
\(305\) −9.99688 9.27575i −0.572420 0.531128i
\(306\) −2.48204 1.69223i −0.141889 0.0967382i
\(307\) 3.97135 17.3996i 0.226657 0.993049i −0.725687 0.688025i \(-0.758478\pi\)
0.952344 0.305025i \(-0.0986647\pi\)
\(308\) −5.29224 + 23.5123i −0.301554 + 1.33974i
\(309\) 2.50887 + 10.9921i 0.142724 + 0.625317i
\(310\) 10.1987 25.9859i 0.579248 1.47590i
\(311\) 0.426099 5.68590i 0.0241619 0.322418i −0.972006 0.234956i \(-0.924505\pi\)
0.996168 0.0874617i \(-0.0278756\pi\)
\(312\) −16.9501 + 29.3584i −0.959608 + 1.66209i
\(313\) 10.7377 + 18.5983i 0.606933 + 1.05124i 0.991743 + 0.128242i \(0.0409335\pi\)
−0.384810 + 0.922996i \(0.625733\pi\)
\(314\) −3.73734 + 1.79981i −0.210910 + 0.101569i
\(315\) −2.24053 3.85392i −0.126240 0.217144i
\(316\) −68.7400 33.1034i −3.86693 1.86221i
\(317\) 0.462158 + 6.16707i 0.0259574 + 0.346377i 0.995028 + 0.0995942i \(0.0317545\pi\)
−0.969071 + 0.246783i \(0.920627\pi\)
\(318\) 26.8001 + 8.26674i 1.50288 + 0.463576i
\(319\) −3.21708 0.992338i −0.180122 0.0555603i
\(320\) −1.43263 19.1171i −0.0800862 1.06868i
\(321\) 2.14647 + 1.03369i 0.119804 + 0.0576947i
\(322\) 1.34880 0.420492i 0.0751657 0.0234331i
\(323\) −6.91298 + 3.32911i −0.384648 + 0.185237i
\(324\) 14.3465 + 24.8489i 0.797030 + 1.38050i
\(325\) 1.12031 1.94044i 0.0621437 0.107636i
\(326\) 3.07425 41.0230i 0.170267 2.27205i
\(327\) −5.50562 + 14.0281i −0.304462 + 0.775756i
\(328\) −15.8868 69.6048i −0.877204 3.84328i
\(329\) −0.991613 4.28515i −0.0546694 0.236248i
\(330\) 3.32704 14.5767i 0.183147 0.802421i
\(331\) −0.972462 0.663014i −0.0534514 0.0364425i 0.536300 0.844028i \(-0.319822\pi\)
−0.589751 + 0.807585i \(0.700774\pi\)
\(332\) 34.4383 + 31.9541i 1.89005 + 1.75371i
\(333\) 6.08755 0.917551i 0.333596 0.0502815i
\(334\) 12.8099 11.8859i 0.700928 0.650366i
\(335\) −4.60858 + 5.77897i −0.251793 + 0.315739i
\(336\) −2.80833 + 39.0487i −0.153207 + 2.13028i
\(337\) −3.39407 4.25603i −0.184887 0.231841i 0.680747 0.732519i \(-0.261655\pi\)
−0.865634 + 0.500678i \(0.833084\pi\)
\(338\) −9.68954 1.46046i −0.527041 0.0794387i
\(339\) −8.61256 + 5.87195i −0.467770 + 0.318920i
\(340\) 5.16339 + 13.1561i 0.280024 + 0.713490i
\(341\) 9.20715 2.84003i 0.498595 0.153796i
\(342\) −11.6913 −0.632193
\(343\) −3.95822 + 18.0923i −0.213724 + 0.976894i
\(344\) −19.3417 −1.04283
\(345\) −0.593888 + 0.183190i −0.0319739 + 0.00986263i
\(346\) 20.1947 + 51.4553i 1.08568 + 2.76626i
\(347\) −3.06046 + 2.08658i −0.164294 + 0.112014i −0.642676 0.766138i \(-0.722176\pi\)
0.478382 + 0.878152i \(0.341223\pi\)
\(348\) −12.8337 1.93437i −0.687959 0.103693i
\(349\) 15.1210 + 18.9611i 0.809406 + 1.01496i 0.999449 + 0.0331876i \(0.0105659\pi\)
−0.190043 + 0.981776i \(0.560863\pi\)
\(350\) 0.366349 5.09393i 0.0195822 0.272282i
\(351\) 10.7012 13.4189i 0.571188 0.716247i
\(352\) 15.3128 14.2082i 0.816174 0.757299i
\(353\) −29.6433 + 4.46801i −1.57775 + 0.237808i −0.878741 0.477299i \(-0.841616\pi\)
−0.699014 + 0.715108i \(0.746378\pi\)
\(354\) 23.7123 + 22.0018i 1.26030 + 1.16938i
\(355\) −11.4015 7.77343i −0.605130 0.412571i
\(356\) 1.34808 5.90634i 0.0714483 0.313035i
\(357\) −1.23772 5.34869i −0.0655073 0.283083i
\(358\) −11.6883 51.2097i −0.617745 2.70652i
\(359\) 3.58266 9.12846i 0.189085 0.481782i −0.804622 0.593787i \(-0.797632\pi\)
0.993708 + 0.112005i \(0.0357274\pi\)
\(360\) −0.949028 + 12.6639i −0.0500182 + 0.667446i
\(361\) −5.43084 + 9.40650i −0.285834 + 0.495079i
\(362\) −9.84934 17.0596i −0.517670 0.896630i
\(363\) −9.99683 + 4.81422i −0.524698 + 0.252681i
\(364\) 37.4729 11.6823i 1.96412 0.612318i
\(365\) −0.328850 0.158366i −0.0172128 0.00828925i
\(366\) −1.91240 25.5193i −0.0999629 1.33391i
\(367\) −15.4383 4.76209i −0.805874 0.248579i −0.135668 0.990754i \(-0.543318\pi\)
−0.670206 + 0.742175i \(0.733794\pi\)
\(368\) −1.94862 0.601071i −0.101579 0.0313330i
\(369\) 0.577616 + 7.70775i 0.0300695 + 0.401249i
\(370\) −36.8020 17.7229i −1.91325 0.921371i
\(371\) −9.62481 16.5556i −0.499695 0.859523i
\(372\) 33.4659 16.1163i 1.73513 0.835594i
\(373\) 9.46448 + 16.3930i 0.490052 + 0.848795i 0.999934 0.0114488i \(-0.00364435\pi\)
−0.509882 + 0.860244i \(0.670311\pi\)
\(374\) −3.43977 + 5.95785i −0.177866 + 0.308073i
\(375\) −1.30812 + 17.4556i −0.0675508 + 0.901403i
\(376\) −4.57770 + 11.6638i −0.236077 + 0.601514i
\(377\) 1.22012 + 5.34568i 0.0628392 + 0.275317i
\(378\) 8.59056 38.1659i 0.441851 1.96304i
\(379\) −4.39197 + 19.2425i −0.225600 + 0.988420i 0.727581 + 0.686021i \(0.240644\pi\)
−0.953182 + 0.302398i \(0.902213\pi\)
\(380\) 45.4466 + 30.9850i 2.33136 + 1.58949i
\(381\) 0.0785143 + 0.0728506i 0.00402241 + 0.00373225i
\(382\) −12.0608 + 1.81787i −0.617082 + 0.0930102i
\(383\) 7.58783 7.04048i 0.387720 0.359752i −0.462097 0.886829i \(-0.652903\pi\)
0.849817 + 0.527078i \(0.176712\pi\)
\(384\) 1.82943 2.29403i 0.0933575 0.117067i
\(385\) −8.41776 + 5.77626i −0.429009 + 0.294385i
\(386\) 35.8808 + 44.9931i 1.82629 + 2.29009i
\(387\) 2.07058 + 0.312090i 0.105254 + 0.0158644i
\(388\) 56.0274 38.1988i 2.84436 1.93925i
\(389\) 6.88950 + 17.5542i 0.349312 + 0.890032i 0.992266 + 0.124127i \(0.0396132\pi\)
−0.642955 + 0.765904i \(0.722292\pi\)
\(390\) −23.2693 + 7.17762i −1.17829 + 0.363453i
\(391\) 0.285965 0.0144619
\(392\) 38.4592 36.1175i 1.94249 1.82421i
\(393\) 27.5054 1.38746
\(394\) 36.2704 11.1879i 1.82728 0.563641i
\(395\) −11.8074 30.0849i −0.594097 1.51373i
\(396\) −6.14135 + 4.18710i −0.308614 + 0.210410i
\(397\) 0.334401 + 0.0504029i 0.0167831 + 0.00252965i 0.157428 0.987530i \(-0.449680\pi\)
−0.140645 + 0.990060i \(0.544918\pi\)
\(398\) 10.5276 + 13.2011i 0.527699 + 0.661713i
\(399\) −15.7064 14.4858i −0.786302 0.725198i
\(400\) −4.59599 + 5.76319i −0.229799 + 0.288159i
\(401\) −17.0641 + 15.8332i −0.852141 + 0.790671i −0.979555 0.201179i \(-0.935523\pi\)
0.127414 + 0.991850i \(0.459332\pi\)
\(402\) −13.7156 + 2.06729i −0.684070 + 0.103107i
\(403\) −11.5035 10.6737i −0.573028 0.531693i
\(404\) −5.36973 3.66102i −0.267154 0.182142i
\(405\) −2.70462 + 11.8497i −0.134393 + 0.588816i
\(406\) 7.82160 + 9.74774i 0.388179 + 0.483772i
\(407\) −3.13724 13.7451i −0.155507 0.681321i
\(408\) −5.71385 + 14.5586i −0.282878 + 0.720760i
\(409\) −1.01859 + 13.5921i −0.0503660 + 0.672087i 0.913694 + 0.406403i \(0.133217\pi\)
−0.964060 + 0.265684i \(0.914402\pi\)
\(410\) 25.6422 44.4135i 1.26638 2.19343i
\(411\) 5.88666 + 10.1960i 0.290368 + 0.502931i
\(412\) −33.5065 + 16.1359i −1.65075 + 0.794958i
\(413\) −1.71673 22.0201i −0.0844749 1.08354i
\(414\) 0.392582 + 0.189057i 0.0192943 + 0.00929167i
\(415\) 1.48717 + 19.8449i 0.0730022 + 0.974147i
\(416\) −32.5099 10.0280i −1.59393 0.491662i
\(417\) −26.7502 8.25135i −1.30996 0.404071i
\(418\) 2.00085 + 26.6994i 0.0978646 + 1.30591i
\(419\) 7.73651 + 3.72571i 0.377953 + 0.182013i 0.613209 0.789921i \(-0.289878\pi\)
−0.235256 + 0.971934i \(0.575593\pi\)
\(420\) −28.7697 + 26.8557i −1.40382 + 1.31043i
\(421\) 5.75293 2.77046i 0.280381 0.135024i −0.288409 0.957507i \(-0.593126\pi\)
0.568789 + 0.822483i \(0.307412\pi\)
\(422\) −17.4551 30.2331i −0.849700 1.47172i
\(423\) 0.678259 1.17478i 0.0329781 0.0571197i
\(424\) −4.07681 + 54.4013i −0.197987 + 2.64196i
\(425\) 0.377656 0.962252i 0.0183190 0.0466761i
\(426\) −5.76212 25.2455i −0.279176 1.22315i
\(427\) −10.8535 + 13.6940i −0.525236 + 0.662701i
\(428\) −1.74863 + 7.66126i −0.0845233 + 0.370321i
\(429\) −6.94447 4.73466i −0.335282 0.228592i
\(430\) −10.1847 9.44999i −0.491148 0.455719i
\(431\) 38.2551 5.76603i 1.84268 0.277740i 0.867223 0.497919i \(-0.165902\pi\)
0.975459 + 0.220180i \(0.0706643\pi\)
\(432\) −41.3922 + 38.4063i −1.99148 + 1.84783i
\(433\) 0.316460 0.396828i 0.0152081 0.0190703i −0.774169 0.632979i \(-0.781832\pi\)
0.789377 + 0.613908i \(0.210404\pi\)
\(434\) −34.2107 10.4401i −1.64217 0.501143i
\(435\) −3.42781 4.29834i −0.164351 0.206090i
\(436\) −49.1522 7.40850i −2.35396 0.354803i
\(437\) 0.919555 0.626942i 0.0439883 0.0299907i
\(438\) −0.250231 0.637578i −0.0119565 0.0304646i
\(439\) −5.55861 + 1.71460i −0.265298 + 0.0818335i −0.424550 0.905404i \(-0.639568\pi\)
0.159252 + 0.987238i \(0.449092\pi\)
\(440\) 29.0830 1.38648
\(441\) −4.69996 + 3.24592i −0.223807 + 0.154568i
\(442\) 11.2045 0.532942
\(443\) −6.23804 + 1.92418i −0.296378 + 0.0914206i −0.439378 0.898302i \(-0.644801\pi\)
0.143000 + 0.989723i \(0.454325\pi\)
\(444\) −19.8567 50.5940i −0.942356 2.40108i
\(445\) 2.12036 1.44563i 0.100515 0.0685297i
\(446\) 42.3449 + 6.38247i 2.00509 + 0.302218i
\(447\) −21.7777 27.3084i −1.03005 1.29164i
\(448\) −24.2779 + 3.73395i −1.14702 + 0.176412i
\(449\) −10.3649 + 12.9972i −0.489152 + 0.613377i −0.963744 0.266829i \(-0.914024\pi\)
0.474592 + 0.880206i \(0.342596\pi\)
\(450\) 1.15462 1.07133i 0.0544295 0.0505032i
\(451\) 17.5033 2.63821i 0.824200 0.124228i
\(452\) −25.2043 23.3861i −1.18551 1.09999i
\(453\) 10.8541 + 7.40017i 0.509968 + 0.347691i
\(454\) −8.59630 + 37.6628i −0.403444 + 1.76760i
\(455\) 15.0021 + 7.16918i 0.703309 + 0.336096i
\(456\) 13.5444 + 59.3420i 0.634275 + 2.77894i
\(457\) −14.7119 + 37.4853i −0.688193 + 1.75349i −0.0312913 + 0.999510i \(0.509962\pi\)
−0.656902 + 0.753976i \(0.728133\pi\)
\(458\) −1.30004 + 17.3479i −0.0607471 + 0.810613i
\(459\) 3.95915 6.85746i 0.184798 0.320079i
\(460\) −1.02500 1.77535i −0.0477908 0.0827762i
\(461\) 4.28753 2.06477i 0.199690 0.0961657i −0.331366 0.943502i \(-0.607510\pi\)
0.531056 + 0.847337i \(0.321795\pi\)
\(462\) −18.9520 2.79834i −0.881726 0.130191i
\(463\) 21.6387 + 10.4207i 1.00564 + 0.484289i 0.862848 0.505464i \(-0.168679\pi\)
0.142789 + 0.989753i \(0.454393\pi\)
\(464\) −1.34805 17.9885i −0.0625817 0.835095i
\(465\) 15.0354 + 4.63780i 0.697249 + 0.215073i
\(466\) 6.25809 + 1.93037i 0.289901 + 0.0894225i
\(467\) −1.44844 19.3281i −0.0670259 0.894398i −0.924820 0.380405i \(-0.875785\pi\)
0.857794 0.513993i \(-0.171834\pi\)
\(468\) 10.9069 + 5.25248i 0.504171 + 0.242796i
\(469\) 7.84117 + 5.31158i 0.362071 + 0.245266i
\(470\) −8.10917 + 3.90517i −0.374048 + 0.180132i
\(471\) −1.16903 2.02482i −0.0538661 0.0932988i
\(472\) −31.4602 + 54.4906i −1.44807 + 2.50813i
\(473\) 0.358362 4.78201i 0.0164775 0.219877i
\(474\) 22.1570 56.4550i 1.01770 2.59306i
\(475\) −0.895217 3.92220i −0.0410754 0.179963i
\(476\) 16.2917 7.90606i 0.746729 0.362374i
\(477\) 1.31423 5.75804i 0.0601747 0.263642i
\(478\) −29.1988 19.9074i −1.33552 0.910544i
\(479\) 1.65200 + 1.53283i 0.0754817 + 0.0700368i 0.717012 0.697061i \(-0.245509\pi\)
−0.641530 + 0.767098i \(0.721700\pi\)
\(480\) 33.7311 5.08415i 1.53961 0.232059i
\(481\) −16.8323 + 15.6181i −0.767487 + 0.712124i
\(482\) 39.6038 49.6615i 1.80390 2.26202i
\(483\) 0.293157 + 0.740403i 0.0133391 + 0.0336895i
\(484\) −22.8189 28.6140i −1.03722 1.30064i
\(485\) 28.4037 + 4.28116i 1.28974 + 0.194398i
\(486\) 17.8060 12.1400i 0.807699 0.550680i
\(487\) −1.83221 4.66839i −0.0830253 0.211545i 0.883332 0.468747i \(-0.155295\pi\)
−0.966358 + 0.257202i \(0.917199\pi\)
\(488\) 47.5663 14.6723i 2.15323 0.664183i
\(489\) 23.1871 1.04856
\(490\) 37.8977 0.227745i 1.71204 0.0102885i
\(491\) −3.79212 −0.171136 −0.0855680 0.996332i \(-0.527270\pi\)
−0.0855680 + 0.996332i \(0.527270\pi\)
\(492\) 65.2071 20.1137i 2.93976 0.906796i
\(493\) 0.924183 + 2.35478i 0.0416231 + 0.106054i
\(494\) 36.0293 24.5644i 1.62104 1.10520i
\(495\) −3.11342 0.469273i −0.139938 0.0210922i
\(496\) 32.1887 + 40.3634i 1.44532 + 1.81237i
\(497\) −8.79448 + 15.3387i −0.394487 + 0.688037i
\(498\) −23.2835 + 29.1966i −1.04336 + 1.30833i
\(499\) 20.0801 18.6316i 0.898907 0.834064i −0.0878725 0.996132i \(-0.528007\pi\)
0.986780 + 0.162068i \(0.0518163\pi\)
\(500\) −57.0933 + 8.60543i −2.55329 + 0.384847i
\(501\) 7.22022 + 6.69939i 0.322576 + 0.299307i
\(502\) −17.3908 11.8568i −0.776188 0.529196i
\(503\) −2.00879 + 8.80109i −0.0895676 + 0.392421i −0.999763 0.0217571i \(-0.993074\pi\)
0.910196 + 0.414179i \(0.135931\pi\)
\(504\) 16.2717 0.0488917i 0.724798 0.00217781i
\(505\) −0.612597 2.68396i −0.0272602 0.119435i
\(506\) 0.364564 0.928895i 0.0162069 0.0412944i
\(507\) 0.412744 5.50768i 0.0183306 0.244605i
\(508\) −0.176643 + 0.305955i −0.00783727 + 0.0135745i
\(509\) −12.0418 20.8569i −0.533741 0.924467i −0.999223 0.0394096i \(-0.987452\pi\)
0.465482 0.885057i \(-0.345881\pi\)
\(510\) −10.1218 + 4.87441i −0.448201 + 0.215842i
\(511\) −0.169550 + 0.435853i −0.00750045 + 0.0192810i
\(512\) −35.1437 16.9243i −1.55315 0.747955i
\(513\) −2.30296 30.7309i −0.101678 1.35680i
\(514\) −44.3874 13.6917i −1.95784 0.603915i
\(515\) −15.0536 4.64342i −0.663341 0.204614i
\(516\) −1.38151 18.4350i −0.0608175 0.811554i
\(517\) −2.79892 1.34789i −0.123096 0.0592801i
\(518\) −18.9746 + 48.7768i −0.833694 + 2.14313i
\(519\) −28.0707 + 13.5181i −1.23217 + 0.593380i
\(520\) −23.6833 41.0206i −1.03858 1.79887i
\(521\) 9.12162 15.7991i 0.399626 0.692172i −0.594054 0.804425i \(-0.702473\pi\)
0.993680 + 0.112253i \(0.0358068\pi\)
\(522\) −0.288046 + 3.84371i −0.0126075 + 0.168235i
\(523\) 1.49748 3.81551i 0.0654801 0.166841i −0.894388 0.447291i \(-0.852389\pi\)
0.959868 + 0.280451i \(0.0904839\pi\)
\(524\) 20.1884 + 88.4510i 0.881933 + 3.86400i
\(525\) 2.87856 0.00864924i 0.125631 0.000377484i
\(526\) −11.3129 + 49.5651i −0.493266 + 2.16114i
\(527\) −5.98175 4.07829i −0.260569 0.177653i
\(528\) 20.2698 + 18.8076i 0.882128 + 0.818495i
\(529\) 22.7021 3.42179i 0.987048 0.148773i
\(530\) −28.7262 + 26.6540i −1.24779 + 1.15778i
\(531\) 4.24715 5.32576i 0.184311 0.231118i
\(532\) 35.0549 61.1404i 1.51982 2.65077i
\(533\) −17.9747 22.5395i −0.778569 0.976295i
\(534\) 4.76189 + 0.717740i 0.206067 + 0.0310596i
\(535\) −2.75037 + 1.87517i −0.118909 + 0.0810706i
\(536\) −9.85694 25.1151i −0.425755 1.08481i
\(537\) 28.2909 8.72660i 1.22084 0.376580i
\(538\) 75.0249 3.23455
\(539\) 8.21706 + 10.1778i 0.353934 + 0.438389i
\(540\) −56.7640 −2.44273
\(541\) 15.9875 4.93151i 0.687358 0.212022i 0.0686478 0.997641i \(-0.478132\pi\)
0.618711 + 0.785619i \(0.287655\pi\)
\(542\) 25.7254 + 65.5474i 1.10500 + 2.81550i
\(543\) 9.17374 6.25455i 0.393683 0.268408i
\(544\) −15.5204 2.33932i −0.665431 0.100298i
\(545\) −13.1283 16.4623i −0.562353 0.705169i
\(546\) 11.4863 + 29.0099i 0.491567 + 1.24151i
\(547\) 0.569364 0.713960i 0.0243443 0.0305267i −0.769510 0.638634i \(-0.779500\pi\)
0.793855 + 0.608108i \(0.208071\pi\)
\(548\) −28.4673 + 26.4138i −1.21606 + 1.12834i
\(549\) −5.32887 + 0.803198i −0.227431 + 0.0342796i
\(550\) −2.64421 2.45347i −0.112749 0.104616i
\(551\) 8.13438 + 5.54592i 0.346536 + 0.236264i
\(552\) 0.504799 2.21167i 0.0214857 0.0941348i
\(553\) −37.2552 + 18.0793i −1.58425 + 0.768809i
\(554\) 6.38136 + 27.9586i 0.271118 + 1.18785i
\(555\) 8.41132 21.4317i 0.357041 0.909725i
\(556\) 6.90036 92.0789i 0.292640 3.90502i
\(557\) −22.5492 + 39.0564i −0.955442 + 1.65487i −0.222089 + 0.975026i \(0.571288\pi\)
−0.733353 + 0.679848i \(0.762046\pi\)
\(558\) −5.51570 9.55346i −0.233498 0.404430i
\(559\) −7.03669 + 3.38869i −0.297620 + 0.143326i
\(560\) −45.2886 30.6783i −1.91379 1.29640i
\(561\) −3.49359 1.68243i −0.147500 0.0710321i
\(562\) 4.50818 + 60.1574i 0.190166 + 2.53759i
\(563\) 30.1839 + 9.31050i 1.27210 + 0.392391i 0.856022 0.516939i \(-0.172928\pi\)
0.416077 + 0.909329i \(0.363405\pi\)
\(564\) −11.4440 3.53000i −0.481878 0.148640i
\(565\) −1.08841 14.5238i −0.0457898 0.611022i
\(566\) −3.09170 1.48888i −0.129954 0.0625825i
\(567\) 15.4064 + 2.27483i 0.647010 + 0.0955337i
\(568\) 45.3809 21.8543i 1.90414 0.916986i
\(569\) −8.43410 14.6083i −0.353576 0.612412i 0.633297 0.773909i \(-0.281701\pi\)
−0.986873 + 0.161497i \(0.948368\pi\)
\(570\) −21.8614 + 37.8650i −0.915672 + 1.58599i
\(571\) 0.703121 9.38249i 0.0294247 0.392645i −0.962975 0.269590i \(-0.913112\pi\)
0.992400 0.123055i \(-0.0392692\pi\)
\(572\) 10.1285 25.8070i 0.423493 1.07904i
\(573\) −1.52977 6.70238i −0.0639072 0.279996i
\(574\) −59.2886 28.3328i −2.47466 1.18259i
\(575\) −0.0333646 + 0.146180i −0.00139140 + 0.00609612i
\(576\) −6.25930 4.26752i −0.260804 0.177813i
\(577\) 8.39507 + 7.78949i 0.349491 + 0.324281i 0.835310 0.549779i \(-0.185288\pi\)
−0.485819 + 0.874060i \(0.661479\pi\)
\(578\) −38.9639 + 5.87286i −1.62068 + 0.244279i
\(579\) −23.7778 + 22.0626i −0.988172 + 0.916889i
\(580\) 11.3065 14.1779i 0.469478 0.588707i
\(581\) 25.2022 3.87610i 1.04556 0.160808i
\(582\) 33.6075 + 42.1424i 1.39307 + 1.74686i
\(583\) −13.3746 2.01589i −0.553918 0.0834896i
\(584\) 1.10078 0.750498i 0.0455505 0.0310558i
\(585\) 1.87347 + 4.77352i 0.0774584 + 0.197361i
\(586\) −10.0283 + 3.09332i −0.414266 + 0.127784i
\(587\) −28.6455 −1.18233 −0.591163 0.806552i \(-0.701331\pi\)
−0.591163 + 0.806552i \(0.701331\pi\)
\(588\) 37.1713 + 34.0766i 1.53292 + 1.40529i
\(589\) −28.1762 −1.16098
\(590\) −43.1890 + 13.3220i −1.77806 + 0.548460i
\(591\) 7.81612 + 19.9151i 0.321512 + 0.819200i
\(592\) 62.4158 42.5544i 2.56527 1.74897i
\(593\) −41.3362 6.23043i −1.69747 0.255853i −0.772262 0.635304i \(-0.780875\pi\)
−0.925212 + 0.379451i \(0.876113\pi\)
\(594\) −17.2276 21.6027i −0.706857 0.886370i
\(595\) 7.33684 + 2.23900i 0.300781 + 0.0917899i
\(596\) 71.8331 90.0759i 2.94240 3.68965i
\(597\) −6.97649 + 6.47323i −0.285529 + 0.264932i
\(598\) −1.60705 + 0.242224i −0.0657173 + 0.00990529i
\(599\) 6.25486 + 5.80366i 0.255567 + 0.237131i 0.797542 0.603263i \(-0.206133\pi\)
−0.541976 + 0.840394i \(0.682324\pi\)
\(600\) −6.77545 4.61942i −0.276606 0.188587i
\(601\) 3.88880 17.0379i 0.158627 0.694992i −0.831582 0.555402i \(-0.812564\pi\)
0.990209 0.139590i \(-0.0445784\pi\)
\(602\) −11.0573 + 13.9513i −0.450664 + 0.568611i
\(603\) 0.649967 + 2.84769i 0.0264687 + 0.115967i
\(604\) −15.8306 + 40.3357i −0.644138 + 1.64124i
\(605\) 1.15856 15.4599i 0.0471021 0.628534i
\(606\) 2.58302 4.47393i 0.104928 0.181741i
\(607\) 13.3329 + 23.0932i 0.541164 + 0.937324i 0.998838 + 0.0482033i \(0.0153495\pi\)
−0.457673 + 0.889120i \(0.651317\pi\)
\(608\) −55.0363 + 26.5041i −2.23202 + 1.07488i
\(609\) −5.14943 + 4.80684i −0.208665 + 0.194783i
\(610\) 32.2154 + 15.5141i 1.30436 + 0.628149i
\(611\) 0.378102 + 5.04542i 0.0152964 + 0.204116i
\(612\) 5.33683 + 1.64619i 0.215729 + 0.0665435i
\(613\) 23.1123 + 7.12919i 0.933496 + 0.287945i 0.723949 0.689853i \(-0.242325\pi\)
0.209547 + 0.977799i \(0.432801\pi\)
\(614\) 3.49693 + 46.6633i 0.141125 + 1.88318i
\(615\) 26.0434 + 12.5419i 1.05017 + 0.505736i
\(616\) −2.89639 37.1513i −0.116699 1.49687i
\(617\) 24.7579 11.9228i 0.996717 0.479994i 0.136894 0.990586i \(-0.456288\pi\)
0.859823 + 0.510592i \(0.170574\pi\)
\(618\) −14.7809 25.6013i −0.594575 1.02983i
\(619\) −4.78591 + 8.28944i −0.192362 + 0.333181i −0.946033 0.324072i \(-0.894948\pi\)
0.753671 + 0.657252i \(0.228281\pi\)
\(620\) −3.87846 + 51.7544i −0.155763 + 2.07851i
\(621\) −0.419612 + 1.06915i −0.0168384 + 0.0429037i
\(622\) 3.32667 + 14.5751i 0.133387 + 0.584409i
\(623\) −2.05786 2.56462i −0.0824463 0.102749i
\(624\) 10.0211 43.9055i 0.401167 1.75763i
\(625\) −17.1667 11.7041i −0.686669 0.468163i
\(626\) −41.2764 38.2989i −1.64974 1.53073i
\(627\) −14.9226 + 2.24922i −0.595950 + 0.0898251i
\(628\) 5.65332 5.24551i 0.225592 0.209319i
\(629\) −6.60491 + 8.28230i −0.263355 + 0.330237i
\(630\) 8.59200 + 7.92430i 0.342314 + 0.315712i
\(631\) 4.68739 + 5.87780i 0.186602 + 0.233992i 0.866329 0.499474i \(-0.166473\pi\)
−0.679727 + 0.733465i \(0.737902\pi\)
\(632\) 116.650 + 17.5822i 4.64010 + 0.699382i
\(633\) 16.2578 11.0844i 0.646189 0.440564i
\(634\) −5.92404 15.0942i −0.235274 0.599467i
\(635\) −0.143004 + 0.0441109i −0.00567494 + 0.00175049i
\(636\) −52.1422 −2.06757
\(637\) 7.66402 19.8780i 0.303659 0.787596i
\(638\) 8.82719 0.349472
\(639\) −5.21080 + 1.60732i −0.206136 + 0.0635846i
\(640\) 1.49780 + 3.81633i 0.0592057 + 0.150854i
\(641\) 1.40677 0.959120i 0.0555641 0.0378830i −0.535219 0.844713i \(-0.679771\pi\)
0.590784 + 0.806830i \(0.298819\pi\)
\(642\) −6.17677 0.930998i −0.243778 0.0367436i
\(643\) 1.53076 + 1.91951i 0.0603672 + 0.0756981i 0.811098 0.584910i \(-0.198870\pi\)
−0.750731 + 0.660608i \(0.770299\pi\)
\(644\) −2.16580 + 1.48617i −0.0853443 + 0.0585632i
\(645\) 4.88253 6.12250i 0.192250 0.241073i
\(646\) 14.7474 13.6835i 0.580227 0.538372i
\(647\) 28.2193 4.25337i 1.10941 0.167217i 0.431325 0.902197i \(-0.358046\pi\)
0.678090 + 0.734979i \(0.262808\pi\)
\(648\) −32.5219 30.1759i −1.27758 1.18542i
\(649\) −12.8893 8.78777i −0.505949 0.344950i
\(650\) −1.30727 + 5.72751i −0.0512752 + 0.224651i
\(651\) 4.42706 19.6684i 0.173510 0.770867i
\(652\) 17.0188 + 74.5644i 0.666510 + 2.92017i
\(653\) 3.07373 7.83175i 0.120285 0.306480i −0.858032 0.513597i \(-0.828313\pi\)
0.978316 + 0.207117i \(0.0664080\pi\)
\(654\) 2.95276 39.4018i 0.115462 1.54073i
\(655\) −19.2158 + 33.2827i −0.750822 + 1.30046i
\(656\) 47.4222 + 82.1377i 1.85153 + 3.20694i
\(657\) −0.129951 + 0.0625813i −0.00506989 + 0.00244153i
\(658\) 5.79616 + 9.96993i 0.225958 + 0.388668i
\(659\) −24.6195 11.8561i −0.959039 0.461849i −0.112193 0.993686i \(-0.535787\pi\)
−0.846846 + 0.531838i \(0.821502\pi\)
\(660\) 2.07730 + 27.7196i 0.0808587 + 1.07898i
\(661\) −19.4064 5.98607i −0.754820 0.232831i −0.106619 0.994300i \(-0.534002\pi\)
−0.648202 + 0.761469i \(0.724479\pi\)
\(662\) 2.94887 + 0.909605i 0.114611 + 0.0353528i
\(663\) 0.471944 + 6.29766i 0.0183288 + 0.244581i
\(664\) −65.4456 31.5169i −2.53978 1.22309i
\(665\) 28.5012 8.88533i 1.10523 0.344558i
\(666\) −14.5430 + 7.00355i −0.563531 + 0.271382i
\(667\) −0.183462 0.317766i −0.00710368 0.0123039i
\(668\) −16.2442 + 28.1358i −0.628507 + 1.08861i
\(669\) −1.80376 + 24.0695i −0.0697373 + 0.930580i
\(670\) 7.08044 18.0407i 0.273541 0.696971i
\(671\) 2.74625 + 12.0321i 0.106018 + 0.464494i
\(672\) −9.85391 42.5826i −0.380123 1.64266i
\(673\) 2.17126 9.51293i 0.0836961 0.366697i −0.915684 0.401899i \(-0.868350\pi\)
0.999380 + 0.0352021i \(0.0112075\pi\)
\(674\) 11.7929 + 8.04028i 0.454247 + 0.309700i
\(675\) 3.04347 + 2.82393i 0.117143 + 0.108693i
\(676\) 18.0144 2.71523i 0.692861 0.104432i
\(677\) −18.8355 + 17.4768i −0.723906 + 0.671686i −0.953429 0.301617i \(-0.902474\pi\)
0.229524 + 0.973303i \(0.426283\pi\)
\(678\) 17.0404 21.3680i 0.654434 0.820634i
\(679\) 2.64013 36.7099i 0.101319 1.40880i
\(680\) −13.6248 17.0849i −0.522487 0.655178i
\(681\) −21.5311 3.24529i −0.825074 0.124360i
\(682\) −20.8733 + 14.2312i −0.799280 + 0.544940i
\(683\) 8.98140 + 22.8842i 0.343664 + 0.875640i 0.993318 + 0.115411i \(0.0368184\pi\)
−0.649654 + 0.760230i \(0.725086\pi\)
\(684\) 20.7703 6.40679i 0.794172 0.244970i
\(685\) −16.4501 −0.628527
\(686\) −4.06517 48.3887i −0.155209 1.84749i
\(687\) −9.80542 −0.374100
\(688\) 24.5529 7.57357i 0.936071 0.288740i
\(689\) 8.04801 + 20.5060i 0.306605 + 0.781216i
\(690\) 1.34639 0.917953i 0.0512562 0.0349459i
\(691\) −2.94075 0.443247i −0.111872 0.0168619i 0.0928678 0.995678i \(-0.470397\pi\)
−0.204739 + 0.978817i \(0.565635\pi\)
\(692\) −64.0745 80.3469i −2.43575 3.05433i
\(693\) −0.289393 + 4.02389i −0.0109931 + 0.152855i
\(694\) 6.05528 7.59308i 0.229855 0.288229i
\(695\) 28.6727 26.6044i 1.08762 1.00916i
\(696\) 19.8434 2.99091i 0.752162 0.113370i
\(697\) −9.74979 9.04648i −0.369300 0.342660i
\(698\) −52.5388 35.8203i −1.98862 1.35582i
\(699\) −0.821396 + 3.59877i −0.0310681 + 0.136118i
\(700\) 2.14061 + 9.25044i 0.0809076 + 0.349634i
\(701\) 0.282827 + 1.23914i 0.0106822 + 0.0468018i 0.979988 0.199056i \(-0.0637875\pi\)
−0.969306 + 0.245858i \(0.920930\pi\)
\(702\) −16.4409 + 41.8908i −0.620523 + 1.58107i
\(703\) −3.08100 + 41.1131i −0.116202 + 1.55061i
\(704\) −8.67453 + 15.0247i −0.326933 + 0.566265i
\(705\) −2.53653 4.39340i −0.0955313 0.165465i
\(706\) 70.8172 34.1038i 2.66524 1.28351i
\(707\) −3.36755 + 1.04984i −0.126650 + 0.0394834i
\(708\) −54.1833 26.0933i −2.03633 0.980646i
\(709\) −3.51668 46.9269i −0.132072 1.76238i −0.532859 0.846204i \(-0.678882\pi\)
0.400787 0.916171i \(-0.368737\pi\)
\(710\) 34.5737 + 10.6646i 1.29753 + 0.400234i
\(711\) −12.2041 3.76445i −0.457688 0.141178i
\(712\) 0.700011 + 9.34100i 0.0262340 + 0.350069i
\(713\) 0.946127 + 0.455631i 0.0354327 + 0.0170635i
\(714\) 7.23472 + 12.4444i 0.270753 + 0.465720i
\(715\) 10.5807 5.09539i 0.395695 0.190557i
\(716\) 48.8277 + 84.5720i 1.82478 + 3.16060i
\(717\) 9.95940 17.2502i 0.371941 0.644220i
\(718\) −1.92144 + 25.6398i −0.0717075 + 0.956870i
\(719\) 3.94929 10.0626i 0.147284 0.375273i −0.838125 0.545478i \(-0.816348\pi\)
0.985409 + 0.170206i \(0.0544433\pi\)
\(720\) −3.75404 16.4475i −0.139905 0.612964i
\(721\) −4.43243 + 19.6923i −0.165072 + 0.733379i
\(722\) 6.33713 27.7648i 0.235843 1.03330i
\(723\) 29.5812 + 20.1681i 1.10014 + 0.750061i
\(724\) 26.8465 + 24.9099i 0.997743 + 0.925770i
\(725\) −1.31155 + 0.197684i −0.0487096 + 0.00734179i
\(726\) 21.3261 19.7877i 0.791486 0.734392i
\(727\) 15.0795 18.9091i 0.559268 0.701300i −0.419155 0.907915i \(-0.637673\pi\)
0.978422 + 0.206615i \(0.0662449\pi\)
\(728\) −50.0421 + 34.3388i −1.85468 + 1.27268i
\(729\) 18.5835 + 23.3029i 0.688277 + 0.863072i
\(730\) 0.946312 + 0.142634i 0.0350246 + 0.00527911i
\(731\) −2.97710 + 2.02975i −0.110112 + 0.0750731i
\(732\) 17.3820 + 44.2885i 0.642456 + 1.63695i
\(733\) 21.3609 6.58895i 0.788981 0.243368i 0.126025 0.992027i \(-0.459778\pi\)
0.662956 + 0.748659i \(0.269302\pi\)
\(734\) 42.3605 1.56355
\(735\) 1.72430 + 21.2914i 0.0636017 + 0.785346i
\(736\) 2.27666 0.0839187
\(737\) 6.39204 1.97168i 0.235454 0.0726279i
\(738\) −7.40400 18.8651i −0.272545 0.694433i
\(739\) −0.514420 + 0.350725i −0.0189232 + 0.0129016i −0.572745 0.819734i \(-0.694121\pi\)
0.553822 + 0.832635i \(0.313169\pi\)
\(740\) 75.0931 + 11.3185i 2.76048 + 0.416075i
\(741\) 15.3244 + 19.2162i 0.562956 + 0.705924i
\(742\) 36.9093 + 34.0410i 1.35498 + 1.24969i
\(743\) −14.6375 + 18.3549i −0.536999 + 0.673375i −0.974121 0.226027i \(-0.927426\pi\)
0.437122 + 0.899402i \(0.355998\pi\)
\(744\) −42.1009 + 39.0640i −1.54350 + 1.43215i
\(745\) 48.2586 7.27382i 1.76806 0.266492i
\(746\) −36.3819 33.7575i −1.33204 1.23595i
\(747\) 6.49760 + 4.42999i 0.237735 + 0.162085i
\(748\) 2.84607 12.4695i 0.104063 0.455929i
\(749\) 2.66930 + 3.32664i 0.0975339 + 0.121553i
\(750\) −10.2128 44.7453i −0.372920 1.63387i
\(751\) 17.4097 44.3591i 0.635288 1.61869i −0.142236 0.989833i \(-0.545429\pi\)
0.777524 0.628854i \(-0.216476\pi\)
\(752\) 1.24391 16.5988i 0.0453608 0.605297i
\(753\) 5.93180 10.2742i 0.216167 0.374412i
\(754\) −7.18828 12.4505i −0.261782 0.453419i
\(755\) −16.5374 + 7.96398i −0.601857 + 0.289839i
\(756\) 5.65315 + 72.5117i 0.205603 + 2.63723i
\(757\) −3.64606 1.75585i −0.132518 0.0638175i 0.366450 0.930438i \(-0.380573\pi\)
−0.498968 + 0.866620i \(0.666287\pi\)
\(758\) −3.86730 51.6056i −0.140467 1.87440i
\(759\) 0.537457 + 0.165783i 0.0195084 + 0.00601756i
\(760\) −81.2687 25.0681i −2.94793 0.909314i
\(761\) 2.85207 + 38.0583i 0.103388 + 1.37961i 0.771821 + 0.635839i \(0.219346\pi\)
−0.668434 + 0.743772i \(0.733035\pi\)
\(762\) −0.253016 0.121846i −0.00916581 0.00441402i
\(763\) −19.7219 + 18.4099i −0.713982 + 0.666482i
\(764\) 20.4305 9.83880i 0.739149 0.355955i
\(765\) 1.18290 + 2.04884i 0.0427678 + 0.0740759i
\(766\) −13.5699 + 23.5038i −0.490301 + 0.849227i
\(767\) −1.89868 + 25.3361i −0.0685573 + 0.914834i
\(768\) 7.21460 18.3825i 0.260334 0.663321i
\(769\) −9.16664 40.1617i −0.330558 1.44827i −0.818054 0.575142i \(-0.804947\pi\)
0.487496 0.873125i \(-0.337910\pi\)
\(770\) 16.6263 20.9777i 0.599171 0.755985i
\(771\) 5.82600 25.5254i 0.209818 0.919274i
\(772\) −88.4006 60.2705i −3.18161 2.16918i
\(773\) −9.81326 9.10537i −0.352958 0.327498i 0.483688 0.875240i \(-0.339297\pi\)
−0.836647 + 0.547743i \(0.815487\pi\)
\(774\) −5.42897 + 0.818285i −0.195140 + 0.0294127i
\(775\) 2.78266 2.58193i 0.0999560 0.0927456i
\(776\) −65.3714 + 81.9732i −2.34670 + 2.94267i
\(777\) −28.2150 8.61043i −1.01221 0.308897i
\(778\) −30.8278 38.6569i −1.10523 1.38592i
\(779\) −51.1849 7.71488i −1.83389 0.276414i
\(780\) 37.4060 25.5030i 1.33935 0.913153i
\(781\) 4.56241 + 11.6248i 0.163256 + 0.415969i
\(782\) −0.716475 + 0.221003i −0.0256211 + 0.00790306i
\(783\) −10.1601 −0.363091
\(784\) −34.6789 + 60.9080i −1.23853 + 2.17529i
\(785\) 3.26683 0.116598
\(786\) −68.9137 + 21.2571i −2.45807 + 0.758215i
\(787\) −9.28323 23.6533i −0.330912 0.843149i −0.995396 0.0958469i \(-0.969444\pi\)
0.664485 0.747302i \(-0.268651\pi\)
\(788\) −58.3057 + 39.7521i −2.07705 + 1.41611i
\(789\) −28.3354 4.27087i −1.00877 0.152047i
\(790\) 52.8337 + 66.2514i 1.87974 + 2.35712i
\(791\) −18.4447 + 2.83679i −0.655818 + 0.100865i
\(792\) 7.16558 8.98536i 0.254618 0.319281i
\(793\) 14.7345 13.6716i 0.523238 0.485493i
\(794\) −0.876783 + 0.132154i −0.0311159 + 0.00468996i
\(795\) −16.1913 15.0233i −0.574246 0.532822i
\(796\) −25.9370 17.6836i −0.919314 0.626777i
\(797\) −1.31373 + 5.75582i −0.0465347 + 0.203882i −0.992851 0.119360i \(-0.961916\pi\)
0.946316 + 0.323242i \(0.104773\pi\)
\(798\) 50.5469 + 24.1553i 1.78934 + 0.855087i
\(799\) 0.519414 + 2.27570i 0.0183755 + 0.0805085i
\(800\) 3.00664 7.66079i 0.106301 0.270850i
\(801\) 0.0757848 1.01128i 0.00267772 0.0357317i
\(802\) 30.5171 52.8571i 1.07760 1.86645i
\(803\) 0.165157 + 0.286060i 0.00582826 + 0.0100948i
\(804\) 23.2337 11.1887i 0.819388 0.394596i
\(805\) −1.10072 0.162527i −0.0387955 0.00572831i
\(806\) 37.0705 + 17.8522i 1.30575 + 0.628817i
\(807\) 3.16013 + 42.1690i 0.111242 + 1.48442i
\(808\) 9.60227 + 2.96191i 0.337807 + 0.104200i
\(809\) 10.7765 + 3.32412i 0.378883 + 0.116870i 0.478346 0.878171i \(-0.341236\pi\)
−0.0994633 + 0.995041i \(0.531713\pi\)
\(810\) −2.38152 31.7792i −0.0836781 1.11661i
\(811\) 16.3734 + 7.88502i 0.574948 + 0.276881i 0.698679 0.715435i \(-0.253772\pi\)
−0.123731 + 0.992316i \(0.539486\pi\)
\(812\) −19.2373 13.0313i −0.675096 0.457307i
\(813\) −35.7584 + 17.2203i −1.25410 + 0.603943i
\(814\) 18.4829 + 32.0134i 0.647826 + 1.12207i
\(815\) −16.1989 + 28.0574i −0.567424 + 0.982808i
\(816\) 1.55264 20.7185i 0.0543533 0.725294i
\(817\) −5.12325 + 13.0538i −0.179240 + 0.456695i
\(818\) −7.95240 34.8418i −0.278049 1.21821i
\(819\) 5.91123 2.86861i 0.206555 0.100237i
\(820\) −21.2164 + 92.9552i −0.740909 + 3.24613i
\(821\) 39.3340 + 26.8175i 1.37277 + 0.935936i 0.999968 + 0.00802310i \(0.00255386\pi\)
0.372798 + 0.927913i \(0.378399\pi\)
\(822\) −22.6286 20.9963i −0.789263 0.732330i
\(823\) 11.6636 1.75800i 0.406567 0.0612801i 0.0574245 0.998350i \(-0.481711\pi\)
0.349142 + 0.937070i \(0.386473\pi\)
\(824\) 42.1520 39.1113i 1.46843 1.36251i
\(825\) 1.26763 1.58956i 0.0441334 0.0553415i
\(826\) 21.3191 + 53.8439i 0.741787 + 1.87347i
\(827\) −16.1389 20.2376i −0.561206 0.703730i 0.417575 0.908643i \(-0.362880\pi\)
−0.978780 + 0.204913i \(0.934309\pi\)
\(828\) −0.801048 0.120739i −0.0278384 0.00419596i
\(829\) 9.36981 6.38823i 0.325427 0.221872i −0.389575 0.920995i \(-0.627378\pi\)
0.715002 + 0.699122i \(0.246426\pi\)
\(830\) −19.0628 48.5713i −0.661680 1.68593i
\(831\) −15.4458 + 4.76439i −0.535808 + 0.165275i
\(832\) 28.2558 0.979595
\(833\) 2.12947 9.59524i 0.0737817 0.332455i
\(834\) 73.3986 2.54159
\(835\) −13.1507 + 4.05646i −0.455100 + 0.140380i
\(836\) −18.1858 46.3367i −0.628970 1.60259i
\(837\) 24.0251 16.3800i 0.830428 0.566176i
\(838\) −22.2629 3.35559i −0.769059 0.115917i
\(839\) 11.7264 + 14.7044i 0.404840 + 0.507654i 0.941901 0.335890i \(-0.109037\pi\)
−0.537061 + 0.843543i \(0.680465\pi\)
\(840\) 30.2678 52.7911i 1.04434 1.82147i
\(841\) −16.0575 + 20.1354i −0.553706 + 0.694325i
\(842\) −12.2726 + 11.3873i −0.422943 + 0.392434i
\(843\) −33.6226 + 5.06779i −1.15802 + 0.174544i
\(844\) 47.5776 + 44.1456i 1.63769 + 1.51955i
\(845\) 6.37618 + 4.34720i 0.219347 + 0.149548i
\(846\) −0.791445 + 3.46755i −0.0272104 + 0.119217i
\(847\) −19.8642 + 0.0596863i −0.682543 + 0.00205084i
\(848\) −16.1265 70.6550i −0.553787 2.42630i
\(849\) 0.706626 1.80045i 0.0242514 0.0617914i
\(850\) −0.202543 + 2.70275i −0.00694718 + 0.0927037i
\(851\) 0.768289 1.33072i 0.0263366 0.0456163i
\(852\) 24.0712 + 41.6926i 0.824666 + 1.42836i
\(853\) −8.23650 + 3.96649i −0.282012 + 0.135810i −0.569543 0.821961i \(-0.692880\pi\)
0.287531 + 0.957771i \(0.407166\pi\)
\(854\) 16.6098 42.6978i 0.568375 1.46109i
\(855\) 8.29557 + 3.99494i 0.283702 + 0.136624i
\(856\) −0.908002 12.1164i −0.0310349 0.414131i
\(857\) 16.6993 + 5.15105i 0.570437 + 0.175956i 0.566537 0.824036i \(-0.308283\pi\)
0.00389923 + 0.999992i \(0.498759\pi\)
\(858\) 21.0582 + 6.49560i 0.718916 + 0.221756i
\(859\) −0.959712 12.8065i −0.0327449 0.436951i −0.989349 0.145561i \(-0.953501\pi\)
0.956604 0.291390i \(-0.0941177\pi\)
\(860\) 23.2722 + 11.2073i 0.793577 + 0.382166i
\(861\) 13.4276 34.5176i 0.457611 1.17636i
\(862\) −91.3905 + 44.0114i −3.11277 + 1.49903i
\(863\) 20.1744 + 34.9430i 0.686743 + 1.18947i 0.972886 + 0.231287i \(0.0742936\pi\)
−0.286142 + 0.958187i \(0.592373\pi\)
\(864\) 31.5201 54.5944i 1.07233 1.85734i
\(865\) 3.25319 43.4108i 0.110612 1.47601i
\(866\) −0.486197 + 1.23881i −0.0165216 + 0.0420964i
\(867\) −4.94213 21.6529i −0.167844 0.735371i
\(868\) 66.4986 0.199809i 2.25711 0.00678196i
\(869\) −6.50829 + 28.5147i −0.220779 + 0.967294i
\(870\) 11.9102 + 8.12021i 0.403792 + 0.275301i
\(871\) −7.98625 7.41016i −0.270604 0.251084i
\(872\) 75.9987 11.4550i 2.57364 0.387914i
\(873\) 8.32090 7.72067i 0.281620 0.261305i
\(874\) −1.81939 + 2.28144i −0.0615418 + 0.0771710i
\(875\) −15.5874 + 27.1865i −0.526950 + 0.919071i
\(876\) 0.793940 + 0.995570i 0.0268248 + 0.0336372i
\(877\) −24.0921 3.63130i −0.813533 0.122620i −0.270919 0.962602i \(-0.587327\pi\)
−0.542614 + 0.839982i \(0.682566\pi\)
\(878\) 12.6018 8.59175i 0.425290 0.289958i
\(879\) −2.16106 5.50628i −0.0728906 0.185722i
\(880\) −36.9188 + 11.3879i −1.24453 + 0.383888i
\(881\) −55.9997 −1.88668 −0.943339 0.331831i \(-0.892334\pi\)
−0.943339 + 0.331831i \(0.892334\pi\)
\(882\) 9.26702 11.7648i 0.312037 0.396142i
\(883\) 4.69302 0.157933 0.0789663 0.996877i \(-0.474838\pi\)
0.0789663 + 0.996877i \(0.474838\pi\)
\(884\) −19.9054 + 6.14001i −0.669492 + 0.206511i
\(885\) −9.30704 23.7139i −0.312853 0.797136i
\(886\) 14.1421 9.64193i 0.475113 0.323927i
\(887\) 47.6940 + 7.18872i 1.60141 + 0.241373i 0.888159 0.459537i \(-0.151985\pi\)
0.713249 + 0.700910i \(0.247223\pi\)
\(888\) 52.3964 + 65.7030i 1.75831 + 2.20485i
\(889\) 0.0705901 + 0.178284i 0.00236752 + 0.00597944i
\(890\) −4.19524 + 5.26067i −0.140625 + 0.176338i
\(891\) 8.06321 7.48157i 0.270128 0.250642i
\(892\) −78.7258 + 11.8660i −2.63594 + 0.397303i
\(893\) 6.65942 + 6.17904i 0.222849 + 0.206774i
\(894\) 75.6681 + 51.5896i 2.53072 + 1.72542i
\(895\) −9.20501 + 40.3298i −0.307690 + 1.34808i
\(896\) 4.72591 2.29340i 0.157882 0.0766170i
\(897\) −0.203837 0.893068i −0.00680592 0.0298187i
\(898\) 15.9243 40.5745i 0.531401 1.35399i
\(899\) −0.694196 + 9.26340i −0.0231527 + 0.308952i
\(900\) −1.46417 + 2.53602i −0.0488057 + 0.0845339i
\(901\) 5.08146 + 8.80135i 0.169288 + 0.293216i
\(902\) −41.8151 + 20.1371i −1.39229 + 0.670492i
\(903\) −8.30729 5.62732i −0.276449 0.187266i
\(904\) 47.8975 + 23.0662i 1.59305 + 0.767171i
\(905\) 1.15933 + 15.4702i 0.0385374 + 0.514246i
\(906\) −32.9136 10.1525i −1.09348 0.337294i
\(907\) 18.9530 + 5.84622i 0.629324 + 0.194121i 0.592978 0.805219i \(-0.297952\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(908\) −5.36726 71.6211i −0.178119 2.37683i
\(909\) −0.980160 0.472020i −0.0325099 0.0156559i
\(910\) −43.1278 6.36800i −1.42967 0.211097i
\(911\) 32.7621 15.7774i 1.08546 0.522728i 0.196398 0.980524i \(-0.437075\pi\)
0.889057 + 0.457797i \(0.151361\pi\)
\(912\) −40.4301 70.0269i −1.33877 2.31882i
\(913\) 9.00478 15.5967i 0.298015 0.516177i
\(914\) 7.89023 105.288i 0.260986 3.48261i
\(915\) −7.36302 + 18.7607i −0.243414 + 0.620209i
\(916\) −7.19697 31.5320i −0.237795 1.04185i
\(917\) 44.4298 + 21.2321i 1.46720 + 0.701144i
\(918\) −4.61985 + 20.2409i −0.152478 + 0.668048i
\(919\) 17.1911 + 11.7207i 0.567083 + 0.386631i 0.812653 0.582748i \(-0.198023\pi\)
−0.245569 + 0.969379i \(0.578975\pi\)
\(920\) 2.32355 + 2.15594i 0.0766052 + 0.0710792i
\(921\) −26.0806 + 3.93102i −0.859385 + 0.129531i
\(922\) −9.14653 + 8.48674i −0.301225 + 0.279496i
\(923\) 12.6811 15.9016i 0.417404 0.523409i
\(924\) 35.2028 5.41420i 1.15809 0.178114i
\(925\) −3.46313 4.34263i −0.113867 0.142785i
\(926\) −62.2685 9.38547i −2.04627 0.308426i
\(927\) −5.14358 + 3.50683i −0.168937 + 0.115180i
\(928\) 7.35771 + 18.7471i 0.241529 + 0.615405i
\(929\) 0.170729 0.0526630i 0.00560145 0.00172782i −0.291953 0.956433i \(-0.594305\pi\)
0.297555 + 0.954705i \(0.403829\pi\)
\(930\) −41.2549 −1.35280
\(931\) −14.1888 35.5232i −0.465019 1.16423i
\(932\) −12.1757 −0.398829
\(933\) −8.05206 + 2.48373i −0.263613 + 0.0813137i
\(934\) 18.5664 + 47.3065i 0.607512 + 1.54791i
\(935\) 4.47650 3.05202i 0.146397 0.0998119i
\(936\) −18.5087 2.78974i −0.604977 0.0911855i
\(937\) 9.09326 + 11.4026i 0.297064 + 0.372506i 0.907854 0.419286i \(-0.137720\pi\)
−0.610790 + 0.791792i \(0.709148\pi\)
\(938\) −23.7507 7.24804i −0.775488 0.236657i
\(939\) 19.7879 24.8133i 0.645754 0.809750i
\(940\) 12.2664 11.3816i 0.400086 0.371226i
\(941\) −27.8070 + 4.19122i −0.906481 + 0.136630i −0.585704 0.810525i \(-0.699182\pi\)
−0.320777 + 0.947155i \(0.603944\pi\)
\(942\) 4.49381 + 4.16965i 0.146416 + 0.135855i
\(943\) 1.59398 + 1.08676i 0.0519071 + 0.0353897i
\(944\) 18.5998 81.4908i 0.605370 2.65230i
\(945\) −19.1368 + 24.1453i −0.622520 + 0.785446i
\(946\) 2.79783 + 12.2581i 0.0909653 + 0.398545i
\(947\) −5.77481 + 14.7140i −0.187656 + 0.478140i −0.993479 0.114017i \(-0.963628\pi\)
0.805823 + 0.592157i \(0.201723\pi\)
\(948\) −8.42604 + 112.438i −0.273665 + 3.65181i
\(949\) 0.268986 0.465897i 0.00873164 0.0151236i
\(950\) 5.27414 + 9.13508i 0.171116 + 0.296381i
\(951\) 8.23442 3.96549i 0.267019 0.128590i
\(952\) −20.4678 + 19.1061i −0.663366 + 0.619233i
\(953\) 40.6458 + 19.5740i 1.31665 + 0.634064i 0.954543 0.298074i \(-0.0963442\pi\)
0.362104 + 0.932138i \(0.382058\pi\)
\(954\) 1.15724 + 15.4422i 0.0374669 + 0.499961i
\(955\) 9.17889 + 2.83131i 0.297022 + 0.0916192i
\(956\) 62.7826 + 19.3659i 2.03054 + 0.626337i
\(957\) 0.371811 + 4.96147i 0.0120189 + 0.160381i
\(958\) −5.32364 2.56373i −0.171999 0.0828304i
\(959\) 1.63827 + 21.0138i 0.0529026 + 0.678570i
\(960\) −25.5255 + 12.2925i −0.823833 + 0.396737i
\(961\) 2.20710 + 3.82281i 0.0711969 + 0.123317i
\(962\) 30.1025 52.1391i 0.970544 1.68103i
\(963\) −0.0983023 + 1.31175i −0.00316775 + 0.0422707i
\(964\) −43.1441 + 109.929i −1.38958 + 3.54059i
\(965\) −10.0850 44.1855i −0.324649 1.42238i
\(966\) −1.30670 1.62849i −0.0420425 0.0523959i
\(967\) 11.5268 50.5020i 0.370675 1.62403i −0.354210 0.935166i \(-0.615250\pi\)
0.724886 0.688869i \(-0.241893\pi\)
\(968\) 46.7557 + 31.8775i 1.50278 + 1.02458i
\(969\) 8.31224 + 7.71263i 0.267028 + 0.247765i
\(970\) −74.4730 + 11.2250i −2.39118 + 0.360413i
\(971\) 29.4461 27.3219i 0.944969 0.876803i −0.0475530 0.998869i \(-0.515142\pi\)
0.992522 + 0.122066i \(0.0389518\pi\)
\(972\) −24.9809 + 31.3250i −0.801262 + 1.00475i
\(973\) −36.8406 33.9777i −1.18106 1.08927i
\(974\) 8.19842 + 10.2805i 0.262694 + 0.329408i
\(975\) −3.27430 0.493522i −0.104862 0.0158054i
\(976\) −54.6370 + 37.2509i −1.74889 + 1.19237i
\(977\) −8.28272 21.1040i −0.264988 0.675177i 0.735008 0.678058i \(-0.237178\pi\)
−0.999996 + 0.00288075i \(0.999083\pi\)
\(978\) −58.0945 + 17.9198i −1.85766 + 0.573011i
\(979\) −2.32243 −0.0742251
\(980\) −67.2027 + 21.1724i −2.14671 + 0.676327i
\(981\) −8.32073 −0.265660
\(982\) 9.50102 2.93068i 0.303190 0.0935217i
\(983\) −6.48720 16.5291i −0.206909 0.527197i 0.789317 0.613986i \(-0.210435\pi\)
−0.996227 + 0.0867888i \(0.972339\pi\)
\(984\) −87.1767 + 59.4360i −2.77909 + 1.89475i
\(985\) −29.5587 4.45525i −0.941817 0.141956i
\(986\) −4.13536 5.18558i −0.131697 0.165142i
\(987\) −5.35962 + 3.67777i −0.170599 + 0.117065i
\(988\) −50.5471 + 63.3840i −1.60812 + 2.01651i
\(989\) 0.383124 0.355487i 0.0121826 0.0113038i
\(990\) 8.16323 1.23041i 0.259445 0.0391050i
\(991\) 6.33519 + 5.87819i 0.201244 + 0.186727i 0.774356 0.632750i \(-0.218074\pi\)
−0.573113 + 0.819477i \(0.694264\pi\)
\(992\) −47.6226 32.4685i −1.51202 1.03088i
\(993\) −0.387049 + 1.69577i −0.0122826 + 0.0538137i
\(994\) 10.1800 45.2273i 0.322889 1.43452i
\(995\) −2.95899 12.9642i −0.0938062 0.410992i
\(996\) 25.3649 64.6287i 0.803718 2.04784i
\(997\) 0.894504 11.9363i 0.0283292 0.378027i −0.964962 0.262389i \(-0.915490\pi\)
0.993291 0.115638i \(-0.0368913\pi\)
\(998\) −35.9108 + 62.1993i −1.13674 + 1.96888i
\(999\) −21.2738 36.8472i −0.673072 1.16579i
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 49.2.g.a.25.1 yes 48
3.2 odd 2 441.2.bb.d.172.4 48
4.3 odd 2 784.2.bg.c.417.3 48
7.2 even 3 343.2.g.i.177.4 48
7.3 odd 6 343.2.e.c.99.8 48
7.4 even 3 343.2.e.d.99.8 48
7.5 odd 6 343.2.g.h.177.4 48
7.6 odd 2 343.2.g.g.67.1 48
49.2 even 21 inner 49.2.g.a.2.1 48
49.10 odd 42 2401.2.a.i.1.1 24
49.11 even 21 343.2.e.d.246.8 48
49.13 odd 14 343.2.g.h.312.4 48
49.36 even 7 343.2.g.i.312.4 48
49.38 odd 42 343.2.e.c.246.8 48
49.39 even 21 2401.2.a.h.1.1 24
49.47 odd 42 343.2.g.g.128.1 48
147.2 odd 42 441.2.bb.d.100.4 48
196.51 odd 42 784.2.bg.c.737.3 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.2.g.a.2.1 48 49.2 even 21 inner
49.2.g.a.25.1 yes 48 1.1 even 1 trivial
343.2.e.c.99.8 48 7.3 odd 6
343.2.e.c.246.8 48 49.38 odd 42
343.2.e.d.99.8 48 7.4 even 3
343.2.e.d.246.8 48 49.11 even 21
343.2.g.g.67.1 48 7.6 odd 2
343.2.g.g.128.1 48 49.47 odd 42
343.2.g.h.177.4 48 7.5 odd 6
343.2.g.h.312.4 48 49.13 odd 14
343.2.g.i.177.4 48 7.2 even 3
343.2.g.i.312.4 48 49.36 even 7
441.2.bb.d.100.4 48 147.2 odd 42
441.2.bb.d.172.4 48 3.2 odd 2
784.2.bg.c.417.3 48 4.3 odd 2
784.2.bg.c.737.3 48 196.51 odd 42
2401.2.a.h.1.1 24 49.39 even 21
2401.2.a.i.1.1 24 49.10 odd 42