Properties

Label 25.3.f.a.12.2
Level $25$
Weight $3$
Character 25.12
Analytic conductor $0.681$
Analytic rank $0$
Dimension $32$
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] = [25,3,Mod(2,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 25.f (of order \(20\), degree \(8\), 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: \(0.681200660901\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 12.2
Character \(\chi\) \(=\) 25.12
Dual form 25.3.f.a.23.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.312579 - 1.97355i) q^{2} +(-4.02069 - 2.04864i) q^{3} +(0.00704800 - 0.00229003i) q^{4} +(4.93389 + 0.810386i) q^{5} +(-2.78631 + 8.57538i) q^{6} +(3.91191 + 3.91191i) q^{7} +(-3.63528 - 7.13464i) q^{8} +(6.67894 + 9.19277i) q^{9} +O(q^{10})\) \(q+(-0.312579 - 1.97355i) q^{2} +(-4.02069 - 2.04864i) q^{3} +(0.00704800 - 0.00229003i) q^{4} +(4.93389 + 0.810386i) q^{5} +(-2.78631 + 8.57538i) q^{6} +(3.91191 + 3.91191i) q^{7} +(-3.63528 - 7.13464i) q^{8} +(6.67894 + 9.19277i) q^{9} +(0.0571038 - 9.99057i) q^{10} +(-2.73590 - 1.98775i) q^{11} +(-0.0330293 - 0.00523133i) q^{12} +(-3.13886 + 19.8180i) q^{13} +(6.49755 - 8.94311i) q^{14} +(-18.1775 - 13.3661i) q^{15} +(-12.9202 + 9.38711i) q^{16} +(17.7107 - 9.02407i) q^{17} +(16.0547 - 16.0547i) q^{18} +(-5.87938 - 1.91032i) q^{19} +(0.0366299 - 0.00558718i) q^{20} +(-7.71446 - 23.7427i) q^{21} +(-3.06773 + 6.02076i) q^{22} +(-13.6608 + 2.16366i) q^{23} +36.1336i q^{24} +(23.6865 + 7.99671i) q^{25} +40.0928 q^{26} +(-1.66800 - 10.5313i) q^{27} +(0.0365295 + 0.0186127i) q^{28} +(-29.3129 + 9.52435i) q^{29} +(-20.6967 + 40.0520i) q^{30} +(-0.774840 + 2.38471i) q^{31} +(-0.0838425 - 0.0838425i) q^{32} +(6.92803 + 13.5970i) q^{33} +(-23.3454 - 32.1322i) q^{34} +(16.1308 + 22.4711i) q^{35} +(0.0681249 + 0.0494957i) q^{36} +(-33.6313 - 5.32667i) q^{37} +(-1.93234 + 12.2003i) q^{38} +(53.2204 - 73.2515i) q^{39} +(-12.1543 - 38.1475i) q^{40} +(29.0354 - 21.0954i) q^{41} +(-44.4459 + 22.6463i) q^{42} +(23.3347 - 23.3347i) q^{43} +(-0.0238347 - 0.00774436i) q^{44} +(25.5035 + 50.7686i) q^{45} +(8.54016 + 26.2839i) q^{46} +(-19.2067 + 37.6953i) q^{47} +(71.1791 - 11.2737i) q^{48} -18.3940i q^{49} +(8.37796 - 49.2461i) q^{50} -89.6965 q^{51} +(0.0232612 + 0.146865i) q^{52} +(-73.4897 - 37.4449i) q^{53} +(-20.2627 + 6.58375i) q^{54} +(-11.8878 - 12.0245i) q^{55} +(13.6892 - 42.1309i) q^{56} +(19.7256 + 19.7256i) q^{57} +(27.9594 + 54.8733i) q^{58} +(1.53534 + 2.11322i) q^{59} +(-0.158724 - 0.0525773i) q^{60} +(21.8447 + 15.8711i) q^{61} +(4.94854 + 0.783771i) q^{62} +(-9.83388 + 62.0887i) q^{63} +(-37.6877 + 51.8727i) q^{64} +(-31.5470 + 95.2360i) q^{65} +(24.6688 - 17.9229i) q^{66} +(67.8430 - 34.5677i) q^{67} +(0.104160 - 0.104160i) q^{68} +(59.3584 + 19.2867i) q^{69} +(39.3056 - 38.8588i) q^{70} +(22.6659 + 69.7586i) q^{71} +(41.3073 - 81.0701i) q^{72} +(51.6598 - 8.18211i) q^{73} +68.0379i q^{74} +(-78.8539 - 80.6776i) q^{75} -0.0458126 q^{76} +(-2.92671 - 18.4785i) q^{77} +(-161.201 - 82.1359i) q^{78} +(-37.4103 + 12.1554i) q^{79} +(-71.3543 + 35.8446i) q^{80} +(16.7335 - 51.5004i) q^{81} +(-50.7087 - 50.7087i) q^{82} +(-22.8152 - 44.7773i) q^{83} +(-0.108743 - 0.149672i) q^{84} +(94.6958 - 30.1712i) q^{85} +(-53.3460 - 38.7581i) q^{86} +(137.370 + 21.7573i) q^{87} +(-4.23611 + 26.7457i) q^{88} +(-41.7155 + 57.4164i) q^{89} +(92.2224 - 66.2015i) q^{90} +(-89.8050 + 65.2472i) q^{91} +(-0.0913265 + 0.0465332i) q^{92} +(8.00082 - 8.00082i) q^{93} +(80.3971 + 26.1226i) q^{94} +(-27.4601 - 14.1899i) q^{95} +(0.165341 + 0.508868i) q^{96} +(-1.26842 + 2.48942i) q^{97} +(-36.3014 + 5.74957i) q^{98} -38.4266i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{9}{20}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.312579 1.97355i −0.156289 0.986773i −0.933772 0.357868i \(-0.883504\pi\)
0.777483 0.628905i \(-0.216496\pi\)
\(3\) −4.02069 2.04864i −1.34023 0.682881i −0.370907 0.928670i \(-0.620953\pi\)
−0.969323 + 0.245789i \(0.920953\pi\)
\(4\) 0.00704800 0.00229003i 0.00176200 0.000572509i
\(5\) 4.93389 + 0.810386i 0.986778 + 0.162077i
\(6\) −2.78631 + 8.57538i −0.464385 + 1.42923i
\(7\) 3.91191 + 3.91191i 0.558844 + 0.558844i 0.928978 0.370134i \(-0.120688\pi\)
−0.370134 + 0.928978i \(0.620688\pi\)
\(8\) −3.63528 7.13464i −0.454410 0.891830i
\(9\) 6.67894 + 9.19277i 0.742104 + 1.02142i
\(10\) 0.0571038 9.99057i 0.00571038 0.999057i
\(11\) −2.73590 1.98775i −0.248719 0.180705i 0.456440 0.889754i \(-0.349124\pi\)
−0.705159 + 0.709049i \(0.749124\pi\)
\(12\) −0.0330293 0.00523133i −0.00275244 0.000435944i
\(13\) −3.13886 + 19.8180i −0.241451 + 1.52446i 0.507394 + 0.861714i \(0.330609\pi\)
−0.748845 + 0.662746i \(0.769391\pi\)
\(14\) 6.49755 8.94311i 0.464111 0.638793i
\(15\) −18.1775 13.3661i −1.21183 0.891073i
\(16\) −12.9202 + 9.38711i −0.807515 + 0.586694i
\(17\) 17.7107 9.02407i 1.04181 0.530828i 0.152579 0.988291i \(-0.451242\pi\)
0.889228 + 0.457464i \(0.151242\pi\)
\(18\) 16.0547 16.0547i 0.891926 0.891926i
\(19\) −5.87938 1.91032i −0.309441 0.100543i 0.150180 0.988659i \(-0.452015\pi\)
−0.459621 + 0.888115i \(0.652015\pi\)
\(20\) 0.0366299 0.00558718i 0.00183149 0.000279359i
\(21\) −7.71446 23.7427i −0.367355 1.13060i
\(22\) −3.06773 + 6.02076i −0.139442 + 0.273671i
\(23\) −13.6608 + 2.16366i −0.593948 + 0.0940721i −0.446170 0.894948i \(-0.647212\pi\)
−0.147778 + 0.989021i \(0.547212\pi\)
\(24\) 36.1336i 1.50557i
\(25\) 23.6865 + 7.99671i 0.947462 + 0.319868i
\(26\) 40.0928 1.54203
\(27\) −1.66800 10.5313i −0.0617777 0.390049i
\(28\) 0.0365295 + 0.0186127i 0.00130463 + 0.000664740i
\(29\) −29.3129 + 9.52435i −1.01079 + 0.328426i −0.767170 0.641444i \(-0.778336\pi\)
−0.243622 + 0.969870i \(0.578336\pi\)
\(30\) −20.6967 + 40.0520i −0.689891 + 1.33507i
\(31\) −0.774840 + 2.38471i −0.0249948 + 0.0769262i −0.962776 0.270301i \(-0.912877\pi\)
0.937781 + 0.347227i \(0.112877\pi\)
\(32\) −0.0838425 0.0838425i −0.00262008 0.00262008i
\(33\) 6.92803 + 13.5970i 0.209940 + 0.412031i
\(34\) −23.3454 32.1322i −0.686630 0.945065i
\(35\) 16.1308 + 22.4711i 0.460879 + 0.642031i
\(36\) 0.0681249 + 0.0494957i 0.00189236 + 0.00137488i
\(37\) −33.6313 5.32667i −0.908954 0.143964i −0.315587 0.948897i \(-0.602202\pi\)
−0.593367 + 0.804932i \(0.702202\pi\)
\(38\) −1.93234 + 12.2003i −0.0508512 + 0.321062i
\(39\) 53.2204 73.2515i 1.36462 1.87824i
\(40\) −12.1543 38.1475i −0.303857 0.953688i
\(41\) 29.0354 21.0954i 0.708180 0.514523i −0.174406 0.984674i \(-0.555800\pi\)
0.882586 + 0.470151i \(0.155800\pi\)
\(42\) −44.4459 + 22.6463i −1.05823 + 0.539198i
\(43\) 23.3347 23.3347i 0.542667 0.542667i −0.381643 0.924310i \(-0.624642\pi\)
0.924310 + 0.381643i \(0.124642\pi\)
\(44\) −0.0238347 0.00774436i −0.000541697 0.000176008i
\(45\) 25.5035 + 50.7686i 0.566744 + 1.12819i
\(46\) 8.54016 + 26.2839i 0.185656 + 0.571389i
\(47\) −19.2067 + 37.6953i −0.408654 + 0.802029i −0.999990 0.00439647i \(-0.998601\pi\)
0.591336 + 0.806425i \(0.298601\pi\)
\(48\) 71.1791 11.2737i 1.48290 0.234868i
\(49\) 18.3940i 0.375387i
\(50\) 8.37796 49.2461i 0.167559 0.984922i
\(51\) −89.6965 −1.75875
\(52\) 0.0232612 + 0.146865i 0.000447330 + 0.00282433i
\(53\) −73.4897 37.4449i −1.38660 0.706507i −0.408134 0.912922i \(-0.633820\pi\)
−0.978465 + 0.206415i \(0.933820\pi\)
\(54\) −20.2627 + 6.58375i −0.375235 + 0.121921i
\(55\) −11.8878 12.0245i −0.216142 0.218627i
\(56\) 13.6892 42.1309i 0.244449 0.752338i
\(57\) 19.7256 + 19.7256i 0.346063 + 0.346063i
\(58\) 27.9594 + 54.8733i 0.482058 + 0.946092i
\(59\) 1.53534 + 2.11322i 0.0260228 + 0.0358173i 0.821830 0.569733i \(-0.192953\pi\)
−0.795807 + 0.605550i \(0.792953\pi\)
\(60\) −0.158724 0.0525773i −0.00264539 0.000876288i
\(61\) 21.8447 + 15.8711i 0.358110 + 0.260182i 0.752264 0.658862i \(-0.228962\pi\)
−0.394153 + 0.919045i \(0.628962\pi\)
\(62\) 4.94854 + 0.783771i 0.0798151 + 0.0126415i
\(63\) −9.83388 + 62.0887i −0.156093 + 0.985534i
\(64\) −37.6877 + 51.8727i −0.588870 + 0.810510i
\(65\) −31.5470 + 95.2360i −0.485338 + 1.46517i
\(66\) 24.6688 17.9229i 0.373770 0.271560i
\(67\) 67.8430 34.5677i 1.01258 0.515936i 0.132714 0.991154i \(-0.457631\pi\)
0.879868 + 0.475218i \(0.157631\pi\)
\(68\) 0.104160 0.104160i 0.00153176 0.00153176i
\(69\) 59.3584 + 19.2867i 0.860267 + 0.279518i
\(70\) 39.3056 38.8588i 0.561508 0.555126i
\(71\) 22.6659 + 69.7586i 0.319239 + 0.982516i 0.973974 + 0.226658i \(0.0727799\pi\)
−0.654736 + 0.755858i \(0.727220\pi\)
\(72\) 41.3073 81.0701i 0.573712 1.12597i
\(73\) 51.6598 8.18211i 0.707669 0.112084i 0.207783 0.978175i \(-0.433375\pi\)
0.499886 + 0.866091i \(0.333375\pi\)
\(74\) 68.0379i 0.919431i
\(75\) −78.8539 80.6776i −1.05138 1.07570i
\(76\) −0.0458126 −0.000602797
\(77\) −2.92671 18.4785i −0.0380092 0.239981i
\(78\) −161.201 82.1359i −2.06668 1.05302i
\(79\) −37.4103 + 12.1554i −0.473548 + 0.153865i −0.536061 0.844179i \(-0.680088\pi\)
0.0625131 + 0.998044i \(0.480088\pi\)
\(80\) −71.3543 + 35.8446i −0.891928 + 0.448057i
\(81\) 16.7335 51.5004i 0.206586 0.635807i
\(82\) −50.7087 50.7087i −0.618399 0.618399i
\(83\) −22.8152 44.7773i −0.274881 0.539485i 0.711754 0.702429i \(-0.247901\pi\)
−0.986635 + 0.162944i \(0.947901\pi\)
\(84\) −0.108743 0.149672i −0.00129456 0.00178181i
\(85\) 94.6958 30.1712i 1.11407 0.354956i
\(86\) −53.3460 38.7581i −0.620302 0.450676i
\(87\) 137.370 + 21.7573i 1.57897 + 0.250084i
\(88\) −4.23611 + 26.7457i −0.0481376 + 0.303929i
\(89\) −41.7155 + 57.4164i −0.468713 + 0.645128i −0.976287 0.216480i \(-0.930542\pi\)
0.507574 + 0.861608i \(0.330542\pi\)
\(90\) 92.2224 66.2015i 1.02469 0.735572i
\(91\) −89.8050 + 65.2472i −0.986868 + 0.717002i
\(92\) −0.0913265 + 0.0465332i −0.000992679 + 0.000505795i
\(93\) 8.00082 8.00082i 0.0860303 0.0860303i
\(94\) 80.3971 + 26.1226i 0.855288 + 0.277900i
\(95\) −27.4601 14.1899i −0.289054 0.149367i
\(96\) 0.165341 + 0.508868i 0.00172230 + 0.00530071i
\(97\) −1.26842 + 2.48942i −0.0130765 + 0.0256642i −0.897452 0.441111i \(-0.854584\pi\)
0.884376 + 0.466775i \(0.154584\pi\)
\(98\) −36.3014 + 5.74957i −0.370422 + 0.0586691i
\(99\) 38.4266i 0.388148i
\(100\) 0.185256 + 0.00211783i 0.00185256 + 2.11783e-5i
\(101\) −53.7631 −0.532308 −0.266154 0.963931i \(-0.585753\pi\)
−0.266154 + 0.963931i \(0.585753\pi\)
\(102\) 28.0372 + 177.020i 0.274875 + 1.73549i
\(103\) 104.783 + 53.3894i 1.01731 + 0.518344i 0.881397 0.472377i \(-0.156604\pi\)
0.135911 + 0.990721i \(0.456604\pi\)
\(104\) 152.805 49.6493i 1.46928 0.477397i
\(105\) −18.8216 123.395i −0.179253 1.17519i
\(106\) −50.9278 + 156.740i −0.480451 + 1.47868i
\(107\) 1.86245 + 1.86245i 0.0174060 + 0.0174060i 0.715756 0.698350i \(-0.246082\pi\)
−0.698350 + 0.715756i \(0.746082\pi\)
\(108\) −0.0358732 0.0704051i −0.000332159 0.000651899i
\(109\) −77.7078 106.956i −0.712915 0.981244i −0.999730 0.0232574i \(-0.992596\pi\)
0.286814 0.957986i \(-0.407404\pi\)
\(110\) −20.0150 + 27.2197i −0.181954 + 0.247452i
\(111\) 124.309 + 90.3154i 1.11990 + 0.813653i
\(112\) −87.2643 13.8213i −0.779145 0.123405i
\(113\) 6.99224 44.1473i 0.0618782 0.390684i −0.937239 0.348686i \(-0.886628\pi\)
0.999118 0.0419974i \(-0.0133721\pi\)
\(114\) 32.7635 45.0951i 0.287399 0.395571i
\(115\) −69.1543 0.395270i −0.601342 0.00343713i
\(116\) −0.184787 + 0.134255i −0.00159299 + 0.00115737i
\(117\) −203.146 + 103.508i −1.73629 + 0.884686i
\(118\) 3.69062 3.69062i 0.0312765 0.0312765i
\(119\) 104.584 + 33.9814i 0.878858 + 0.285558i
\(120\) −29.2821 + 178.279i −0.244018 + 1.48566i
\(121\) −33.8570 104.201i −0.279810 0.861167i
\(122\) 24.4942 48.0726i 0.200772 0.394037i
\(123\) −159.959 + 25.3351i −1.30048 + 0.205976i
\(124\) 0.0185819i 0.000149854i
\(125\) 110.386 + 58.6502i 0.883091 + 0.469201i
\(126\) 125.609 0.996894
\(127\) −26.6349 168.166i −0.209724 1.32415i −0.837793 0.545988i \(-0.816155\pi\)
0.628069 0.778158i \(-0.283845\pi\)
\(128\) 113.731 + 57.9488i 0.888522 + 0.452725i
\(129\) −141.626 + 46.0171i −1.09788 + 0.356722i
\(130\) 197.814 + 32.4907i 1.52164 + 0.249928i
\(131\) 16.2028 49.8672i 0.123686 0.380665i −0.869974 0.493098i \(-0.835864\pi\)
0.993659 + 0.112433i \(0.0358643\pi\)
\(132\) 0.0799664 + 0.0799664i 0.000605806 + 0.000605806i
\(133\) −15.5266 30.4726i −0.116741 0.229117i
\(134\) −89.4273 123.086i −0.667368 0.918553i
\(135\) 0.304720 53.3122i 0.00225718 0.394905i
\(136\) −128.767 93.5547i −0.946816 0.687902i
\(137\) 50.3103 + 7.96837i 0.367228 + 0.0581633i 0.337322 0.941389i \(-0.390479\pi\)
0.0299067 + 0.999553i \(0.490479\pi\)
\(138\) 19.5090 123.175i 0.141370 0.892574i
\(139\) −69.7880 + 96.0549i −0.502072 + 0.691043i −0.982557 0.185960i \(-0.940461\pi\)
0.480485 + 0.877003i \(0.340461\pi\)
\(140\) 0.165149 + 0.121436i 0.00117964 + 0.000867401i
\(141\) 154.449 112.214i 1.09538 0.795841i
\(142\) 130.587 66.5374i 0.919626 0.468573i
\(143\) 47.9808 47.9808i 0.335530 0.335530i
\(144\) −172.587 56.0769i −1.19852 0.389423i
\(145\) −152.345 + 23.2373i −1.05066 + 0.160257i
\(146\) −32.2955 99.3955i −0.221202 0.680791i
\(147\) −37.6827 + 73.9565i −0.256345 + 0.503105i
\(148\) −0.249232 + 0.0394744i −0.00168400 + 0.000266719i
\(149\) 64.0597i 0.429931i −0.976622 0.214965i \(-0.931036\pi\)
0.976622 0.214965i \(-0.0689639\pi\)
\(150\) −134.573 + 180.840i −0.897153 + 1.20560i
\(151\) 227.547 1.50693 0.753467 0.657486i \(-0.228380\pi\)
0.753467 + 0.657486i \(0.228380\pi\)
\(152\) 7.74370 + 48.8918i 0.0509454 + 0.321657i
\(153\) 201.245 + 102.540i 1.31533 + 0.670193i
\(154\) −35.5533 + 11.5520i −0.230866 + 0.0750129i
\(155\) −5.75551 + 11.1380i −0.0371323 + 0.0718580i
\(156\) 0.207349 0.638153i 0.00132916 0.00409073i
\(157\) −65.7370 65.7370i −0.418707 0.418707i 0.466051 0.884758i \(-0.345676\pi\)
−0.884758 + 0.466051i \(0.845676\pi\)
\(158\) 35.6828 + 70.0315i 0.225841 + 0.443237i
\(159\) 218.768 + 301.108i 1.37590 + 1.89376i
\(160\) −0.345725 0.481614i −0.00216078 0.00301009i
\(161\) −61.9038 44.9757i −0.384496 0.279352i
\(162\) −106.869 16.9264i −0.659685 0.104484i
\(163\) −19.9218 + 125.781i −0.122220 + 0.771664i 0.848100 + 0.529837i \(0.177747\pi\)
−0.970319 + 0.241827i \(0.922253\pi\)
\(164\) 0.156332 0.215173i 0.000953245 0.00131203i
\(165\) 23.1633 + 72.7006i 0.140384 + 0.440610i
\(166\) −81.2384 + 59.0232i −0.489388 + 0.355561i
\(167\) −71.6764 + 36.5209i −0.429200 + 0.218688i −0.655226 0.755433i \(-0.727427\pi\)
0.226026 + 0.974121i \(0.427427\pi\)
\(168\) −141.351 + 141.351i −0.841376 + 0.841376i
\(169\) −222.171 72.1878i −1.31462 0.427147i
\(170\) −89.1442 177.456i −0.524378 1.04386i
\(171\) −21.7068 66.8067i −0.126940 0.390682i
\(172\) 0.111026 0.217900i 0.000645498 0.00126686i
\(173\) 168.729 26.7241i 0.975314 0.154474i 0.351619 0.936143i \(-0.385631\pi\)
0.623694 + 0.781669i \(0.285631\pi\)
\(174\) 277.907i 1.59717i
\(175\) 61.3772 + 123.942i 0.350727 + 0.708240i
\(176\) 54.0078 0.306862
\(177\) −1.84391 11.6420i −0.0104176 0.0657739i
\(178\) 126.353 + 64.3802i 0.709850 + 0.361687i
\(179\) 250.316 81.3326i 1.39841 0.454372i 0.489736 0.871871i \(-0.337093\pi\)
0.908677 + 0.417499i \(0.137093\pi\)
\(180\) 0.296010 + 0.299414i 0.00164450 + 0.00166341i
\(181\) −42.4512 + 130.651i −0.234537 + 0.721830i 0.762646 + 0.646817i \(0.223900\pi\)
−0.997183 + 0.0750137i \(0.976100\pi\)
\(182\) 156.839 + 156.839i 0.861755 + 0.861755i
\(183\) −55.3166 108.565i −0.302277 0.593251i
\(184\) 65.0978 + 89.5994i 0.353792 + 0.486953i
\(185\) −161.616 53.5356i −0.873602 0.289381i
\(186\) −18.2909 13.2891i −0.0983380 0.0714467i
\(187\) −66.3925 10.5155i −0.355040 0.0562328i
\(188\) −0.0490455 + 0.309661i −0.000260880 + 0.00164713i
\(189\) 34.6725 47.7226i 0.183453 0.252501i
\(190\) −19.4210 + 58.6292i −0.102216 + 0.308575i
\(191\) −153.497 + 111.522i −0.803651 + 0.583886i −0.911983 0.410228i \(-0.865449\pi\)
0.108332 + 0.994115i \(0.465449\pi\)
\(192\) 257.799 131.355i 1.34270 0.684142i
\(193\) 46.3256 46.3256i 0.240029 0.240029i −0.576833 0.816862i \(-0.695712\pi\)
0.816862 + 0.576833i \(0.195712\pi\)
\(194\) 5.30947 + 1.72515i 0.0273684 + 0.00889254i
\(195\) 321.945 318.286i 1.65100 1.63224i
\(196\) −0.0421228 0.129641i −0.000214912 0.000661433i
\(197\) −124.210 + 243.776i −0.630508 + 1.23744i 0.325899 + 0.945405i \(0.394333\pi\)
−0.956407 + 0.292038i \(0.905667\pi\)
\(198\) −75.8367 + 12.0114i −0.383014 + 0.0606634i
\(199\) 198.243i 0.996197i 0.867120 + 0.498099i \(0.165968\pi\)
−0.867120 + 0.498099i \(0.834032\pi\)
\(200\) −29.0536 198.065i −0.145268 0.990326i
\(201\) −343.593 −1.70942
\(202\) 16.8052 + 106.104i 0.0831941 + 0.525267i
\(203\) −151.928 77.4111i −0.748413 0.381336i
\(204\) −0.632181 + 0.205408i −0.00309893 + 0.00100690i
\(205\) 160.353 80.5527i 0.782209 0.392940i
\(206\) 72.6137 223.482i 0.352494 1.08486i
\(207\) −111.130 111.130i −0.536858 0.536858i
\(208\) −145.479 285.518i −0.699417 1.37268i
\(209\) 12.2882 + 16.9132i 0.0587950 + 0.0809244i
\(210\) −237.643 + 75.7161i −1.13163 + 0.360553i
\(211\) 304.272 + 221.067i 1.44205 + 1.04771i 0.987609 + 0.156933i \(0.0501605\pi\)
0.454440 + 0.890777i \(0.349839\pi\)
\(212\) −0.603706 0.0956176i −0.00284767 0.000451026i
\(213\) 51.7778 326.912i 0.243088 1.53480i
\(214\) 3.09346 4.25778i 0.0144554 0.0198962i
\(215\) 134.041 96.2207i 0.623446 0.447538i
\(216\) −69.0736 + 50.1849i −0.319785 + 0.232338i
\(217\) −12.3599 + 6.29767i −0.0569579 + 0.0290215i
\(218\) −186.792 + 186.792i −0.856844 + 0.856844i
\(219\) −224.470 72.9348i −1.02498 0.333036i
\(220\) −0.111322 0.0575251i −0.000506008 0.000261478i
\(221\) 123.247 + 379.316i 0.557680 + 1.71636i
\(222\) 139.385 273.559i 0.627862 1.23225i
\(223\) −385.310 + 61.0271i −1.72785 + 0.273664i −0.939744 0.341878i \(-0.888937\pi\)
−0.788104 + 0.615542i \(0.788937\pi\)
\(224\) 0.655968i 0.00292843i
\(225\) 84.6891 + 271.155i 0.376396 + 1.20513i
\(226\) −89.3123 −0.395187
\(227\) −65.9806 416.585i −0.290663 1.83518i −0.510790 0.859706i \(-0.670647\pi\)
0.220127 0.975471i \(-0.429353\pi\)
\(228\) 0.184198 + 0.0938536i 0.000807886 + 0.000411639i
\(229\) 272.802 88.6388i 1.19128 0.387069i 0.354731 0.934968i \(-0.384572\pi\)
0.836544 + 0.547899i \(0.184572\pi\)
\(230\) 20.8361 + 136.603i 0.0905917 + 0.593925i
\(231\) −26.0885 + 80.2921i −0.112937 + 0.347585i
\(232\) 174.514 + 174.514i 0.752214 + 0.752214i
\(233\) 87.8729 + 172.460i 0.377137 + 0.740173i 0.999080 0.0428897i \(-0.0136564\pi\)
−0.621943 + 0.783063i \(0.713656\pi\)
\(234\) 267.778 + 368.564i 1.14435 + 1.57506i
\(235\) −125.312 + 170.420i −0.533241 + 0.725191i
\(236\) 0.0156605 + 0.0113780i 6.63579e−5 + 4.82118e-5i
\(237\) 175.317 + 27.7675i 0.739735 + 0.117163i
\(238\) 34.3731 217.023i 0.144425 0.911863i
\(239\) −34.9983 + 48.1710i −0.146436 + 0.201552i −0.875934 0.482431i \(-0.839754\pi\)
0.729498 + 0.683983i \(0.239754\pi\)
\(240\) 360.326 + 2.05954i 1.50136 + 0.00858142i
\(241\) 361.028 262.302i 1.49804 1.08839i 0.526889 0.849934i \(-0.323358\pi\)
0.971153 0.238457i \(-0.0766416\pi\)
\(242\) −195.063 + 99.3895i −0.806045 + 0.410701i
\(243\) −240.643 + 240.643i −0.990299 + 0.990299i
\(244\) 0.190307 + 0.0618346i 0.000779948 + 0.000253420i
\(245\) 14.9062 90.7539i 0.0608417 0.370424i
\(246\) 99.9999 + 307.768i 0.406504 + 1.25109i
\(247\) 56.3133 110.521i 0.227989 0.447454i
\(248\) 19.8308 3.14089i 0.0799630 0.0126649i
\(249\) 226.776i 0.910745i
\(250\) 81.2443 236.185i 0.324977 0.944742i
\(251\) −274.930 −1.09534 −0.547669 0.836695i \(-0.684485\pi\)
−0.547669 + 0.836695i \(0.684485\pi\)
\(252\) 0.0728760 + 0.460121i 0.000289190 + 0.00182588i
\(253\) 41.6755 + 21.2347i 0.164725 + 0.0839316i
\(254\) −323.559 + 105.131i −1.27385 + 0.413900i
\(255\) −442.553 72.6888i −1.73550 0.285054i
\(256\) −0.439685 + 1.35321i −0.00171752 + 0.00528598i
\(257\) 160.142 + 160.142i 0.623121 + 0.623121i 0.946328 0.323207i \(-0.104761\pi\)
−0.323207 + 0.946328i \(0.604761\pi\)
\(258\) 135.086 + 265.121i 0.523590 + 1.02760i
\(259\) −110.725 152.400i −0.427510 0.588417i
\(260\) −0.00424949 + 0.743468i −1.63442e−5 + 0.00285949i
\(261\) −283.335 205.855i −1.08557 0.788715i
\(262\) −103.480 16.3896i −0.394961 0.0625557i
\(263\) 65.5157 413.650i 0.249109 1.57281i −0.473018 0.881053i \(-0.656836\pi\)
0.722127 0.691760i \(-0.243164\pi\)
\(264\) 71.8245 98.8580i 0.272063 0.374462i
\(265\) −332.245 244.304i −1.25376 0.921902i
\(266\) −55.2858 + 40.1675i −0.207841 + 0.151005i
\(267\) 285.351 145.394i 1.06873 0.544545i
\(268\) 0.398996 0.398996i 0.00148879 0.00148879i
\(269\) −11.6319 3.77942i −0.0432412 0.0140499i 0.287317 0.957836i \(-0.407237\pi\)
−0.330558 + 0.943786i \(0.607237\pi\)
\(270\) −105.309 + 16.0629i −0.390034 + 0.0594922i
\(271\) −161.855 498.138i −0.597250 1.83815i −0.543189 0.839610i \(-0.682783\pi\)
−0.0540612 0.998538i \(-0.517217\pi\)
\(272\) −144.117 + 282.846i −0.529842 + 1.03987i
\(273\) 494.746 78.3601i 1.81226 0.287033i
\(274\) 101.780i 0.371461i
\(275\) −48.9087 68.9612i −0.177850 0.250768i
\(276\) 0.462525 0.00167582
\(277\) 68.2890 + 431.160i 0.246531 + 1.55653i 0.731402 + 0.681947i \(0.238867\pi\)
−0.484871 + 0.874586i \(0.661133\pi\)
\(278\) 211.383 + 107.705i 0.760371 + 0.387428i
\(279\) −27.0972 + 8.80442i −0.0971227 + 0.0315571i
\(280\) 101.683 196.776i 0.363154 0.702771i
\(281\) 31.8261 97.9506i 0.113260 0.348579i −0.878320 0.478073i \(-0.841335\pi\)
0.991580 + 0.129494i \(0.0413354\pi\)
\(282\) −269.736 269.736i −0.956510 0.956510i
\(283\) 96.0529 + 188.514i 0.339409 + 0.666129i 0.996119 0.0880149i \(-0.0280523\pi\)
−0.656710 + 0.754143i \(0.728052\pi\)
\(284\) 0.319499 + 0.439753i 0.00112500 + 0.00154843i
\(285\) 81.3385 + 113.309i 0.285398 + 0.397576i
\(286\) −109.690 79.6946i −0.383532 0.278652i
\(287\) 196.107 + 31.0603i 0.683300 + 0.108224i
\(288\) 0.210766 1.33072i 0.000731826 0.00462057i
\(289\) 62.3663 85.8398i 0.215800 0.297024i
\(290\) 93.4798 + 293.397i 0.322344 + 1.01171i
\(291\) 10.1999 7.41065i 0.0350512 0.0254662i
\(292\) 0.345361 0.175970i 0.00118274 0.000602638i
\(293\) −192.127 + 192.127i −0.655724 + 0.655724i −0.954365 0.298642i \(-0.903466\pi\)
0.298642 + 0.954365i \(0.403466\pi\)
\(294\) 157.735 + 51.2513i 0.536515 + 0.174324i
\(295\) 5.86270 + 11.6706i 0.0198736 + 0.0395614i
\(296\) 84.2553 + 259.311i 0.284646 + 0.876051i
\(297\) −16.3702 + 32.1283i −0.0551184 + 0.108176i
\(298\) −126.425 + 20.0237i −0.424244 + 0.0671937i
\(299\) 277.521i 0.928163i
\(300\) −0.740517 0.388038i −0.00246839 0.00129346i
\(301\) 182.566 0.606532
\(302\) −71.1264 449.075i −0.235518 1.48700i
\(303\) 216.165 + 110.141i 0.713415 + 0.363503i
\(304\) 93.8954 30.5085i 0.308866 0.100357i
\(305\) 94.9178 + 96.0091i 0.311206 + 0.314784i
\(306\) 139.461 429.218i 0.455756 1.40267i
\(307\) −37.7886 37.7886i −0.123090 0.123090i 0.642878 0.765968i \(-0.277740\pi\)
−0.765968 + 0.642878i \(0.777740\pi\)
\(308\) −0.0629438 0.123534i −0.000204363 0.000401085i
\(309\) −311.923 429.325i −1.00946 1.38940i
\(310\) 23.7804 + 7.87727i 0.0767109 + 0.0254105i
\(311\) 208.182 + 151.253i 0.669396 + 0.486345i 0.869823 0.493364i \(-0.164233\pi\)
−0.200427 + 0.979709i \(0.564233\pi\)
\(312\) −716.094 113.418i −2.29517 0.363520i
\(313\) −75.0087 + 473.586i −0.239644 + 1.51306i 0.515154 + 0.857098i \(0.327735\pi\)
−0.754798 + 0.655957i \(0.772265\pi\)
\(314\) −109.187 + 150.283i −0.347729 + 0.478608i
\(315\) −98.8350 + 298.369i −0.313762 + 0.947204i
\(316\) −0.235832 + 0.171342i −0.000746303 + 0.000542221i
\(317\) −175.952 + 89.6519i −0.555053 + 0.282814i −0.708933 0.705276i \(-0.750823\pi\)
0.153880 + 0.988090i \(0.450823\pi\)
\(318\) 525.869 525.869i 1.65368 1.65368i
\(319\) 99.1295 + 32.2091i 0.310751 + 0.100969i
\(320\) −227.984 + 225.392i −0.712449 + 0.704351i
\(321\) −3.67283 11.3038i −0.0114418 0.0352143i
\(322\) −69.4119 + 136.228i −0.215565 + 0.423070i
\(323\) −121.367 + 19.2226i −0.375749 + 0.0595128i
\(324\) 0.401295i 0.00123857i
\(325\) −232.827 + 444.319i −0.716392 + 1.36714i
\(326\) 254.462 0.780559
\(327\) 93.3250 + 589.231i 0.285397 + 1.80193i
\(328\) −256.060 130.469i −0.780671 0.397772i
\(329\) −222.596 + 72.3257i −0.676582 + 0.219835i
\(330\) 136.238 68.4385i 0.412841 0.207389i
\(331\) −91.8385 + 282.650i −0.277458 + 0.853927i 0.711101 + 0.703090i \(0.248197\pi\)
−0.988559 + 0.150837i \(0.951803\pi\)
\(332\) −0.263343 0.263343i −0.000793201 0.000793201i
\(333\) −175.654 344.741i −0.527491 1.03526i
\(334\) 94.4803 + 130.041i 0.282875 + 0.389344i
\(335\) 362.743 115.574i 1.08282 0.344998i
\(336\) 322.548 + 234.345i 0.959963 + 0.697454i
\(337\) 316.947 + 50.1994i 0.940495 + 0.148960i 0.607814 0.794080i \(-0.292047\pi\)
0.332681 + 0.943039i \(0.392047\pi\)
\(338\) −73.0199 + 461.030i −0.216035 + 1.36399i
\(339\) −118.556 + 163.178i −0.349722 + 0.481351i
\(340\) 0.598323 0.429504i 0.00175977 0.00126325i
\(341\) 6.86010 4.98416i 0.0201176 0.0146163i
\(342\) −125.061 + 63.7218i −0.365675 + 0.186321i
\(343\) 263.639 263.639i 0.768627 0.768627i
\(344\) −251.313 81.6564i −0.730560 0.237373i
\(345\) 277.238 + 143.262i 0.803589 + 0.415251i
\(346\) −105.482 324.642i −0.304863 0.938270i
\(347\) 207.859 407.947i 0.599019 1.17564i −0.370088 0.928997i \(-0.620672\pi\)
0.969106 0.246643i \(-0.0793276\pi\)
\(348\) 1.01801 0.161237i 0.00292532 0.000463325i
\(349\) 275.249i 0.788680i −0.918965 0.394340i \(-0.870973\pi\)
0.918965 0.394340i \(-0.129027\pi\)
\(350\) 225.420 159.872i 0.644057 0.456778i
\(351\) 213.945 0.609531
\(352\) 0.0627271 + 0.396043i 0.000178202 + 0.00112512i
\(353\) −365.927 186.449i −1.03662 0.528184i −0.149036 0.988832i \(-0.547617\pi\)
−0.887583 + 0.460648i \(0.847617\pi\)
\(354\) −22.3996 + 7.27808i −0.0632758 + 0.0205595i
\(355\) 55.2999 + 362.549i 0.155774 + 1.02127i
\(356\) −0.162525 + 0.500201i −0.000456531 + 0.00140506i
\(357\) −350.884 350.884i −0.982869 0.982869i
\(358\) −238.757 468.587i −0.666919 1.30890i
\(359\) −80.6575 111.015i −0.224673 0.309235i 0.681768 0.731568i \(-0.261211\pi\)
−0.906441 + 0.422333i \(0.861211\pi\)
\(360\) 269.504 366.516i 0.748622 1.01810i
\(361\) −261.137 189.727i −0.723372 0.525561i
\(362\) 271.116 + 42.9405i 0.748938 + 0.118620i
\(363\) −77.3426 + 488.322i −0.213065 + 1.34524i
\(364\) −0.483528 + 0.665519i −0.00132837 + 0.00182835i
\(365\) 261.515 + 1.49476i 0.716478 + 0.00409522i
\(366\) −196.967 + 143.105i −0.538162 + 0.390997i
\(367\) −468.126 + 238.522i −1.27555 + 0.649924i −0.954802 0.297242i \(-0.903933\pi\)
−0.320745 + 0.947166i \(0.603933\pi\)
\(368\) 156.190 156.190i 0.424430 0.424430i
\(369\) 387.851 + 126.021i 1.05109 + 0.341519i
\(370\) −55.1370 + 335.692i −0.149019 + 0.907274i
\(371\) −141.004 433.966i −0.380065 1.16972i
\(372\) 0.0380676 0.0747119i 0.000102332 0.000200839i
\(373\) 171.238 27.1214i 0.459083 0.0727116i 0.0773903 0.997001i \(-0.475341\pi\)
0.381693 + 0.924289i \(0.375341\pi\)
\(374\) 134.316i 0.359132i
\(375\) −323.676 461.957i −0.863137 1.23188i
\(376\) 338.765 0.900970
\(377\) −96.7442 610.819i −0.256616 1.62021i
\(378\) −105.021 53.5107i −0.277833 0.141563i
\(379\) 474.193 154.074i 1.25117 0.406529i 0.392829 0.919612i \(-0.371497\pi\)
0.858339 + 0.513083i \(0.171497\pi\)
\(380\) −0.226034 0.0371259i −0.000594827 9.76996e-5i
\(381\) −237.422 + 730.711i −0.623156 + 1.91788i
\(382\) 268.074 + 268.074i 0.701765 + 0.701765i
\(383\) 46.0664 + 90.4105i 0.120278 + 0.236059i 0.943293 0.331960i \(-0.107710\pi\)
−0.823015 + 0.568019i \(0.807710\pi\)
\(384\) −338.560 465.988i −0.881667 1.21351i
\(385\) 0.534668 93.5427i 0.00138875 0.242968i
\(386\) −105.906 76.9453i −0.274368 0.199340i
\(387\) 370.361 + 58.6595i 0.957006 + 0.151575i
\(388\) −0.00323899 + 0.0204502i −8.34792e−6 + 5.27067e-5i
\(389\) −40.2289 + 55.3703i −0.103416 + 0.142340i −0.857589 0.514336i \(-0.828038\pi\)
0.754172 + 0.656676i \(0.228038\pi\)
\(390\) −728.785 535.885i −1.86868 1.37406i
\(391\) −222.418 + 161.596i −0.568843 + 0.413289i
\(392\) −131.234 + 66.8673i −0.334782 + 0.170580i
\(393\) −167.307 + 167.307i −0.425716 + 0.425716i
\(394\) 519.929 + 168.935i 1.31962 + 0.428769i
\(395\) −194.429 + 29.6564i −0.492225 + 0.0750794i
\(396\) −0.0879983 0.270831i −0.000222218 0.000683916i
\(397\) −44.2700 + 86.8847i −0.111511 + 0.218853i −0.940017 0.341127i \(-0.889191\pi\)
0.828506 + 0.559980i \(0.189191\pi\)
\(398\) 391.242 61.9667i 0.983021 0.155695i
\(399\) 154.329i 0.386790i
\(400\) −381.102 + 119.029i −0.952755 + 0.297572i
\(401\) 145.737 0.363435 0.181717 0.983351i \(-0.441834\pi\)
0.181717 + 0.983351i \(0.441834\pi\)
\(402\) 107.400 + 678.096i 0.267164 + 1.68681i
\(403\) −44.8281 22.8410i −0.111236 0.0566775i
\(404\) −0.378922 + 0.123119i −0.000937927 + 0.000304751i
\(405\) 124.296 240.537i 0.306905 0.593918i
\(406\) −105.285 + 324.034i −0.259323 + 0.798113i
\(407\) 81.4239 + 81.4239i 0.200059 + 0.200059i
\(408\) 326.072 + 639.952i 0.799196 + 1.56851i
\(409\) 59.1584 + 81.4246i 0.144642 + 0.199082i 0.875191 0.483778i \(-0.160736\pi\)
−0.730549 + 0.682860i \(0.760736\pi\)
\(410\) −209.098 291.285i −0.509994 0.710451i
\(411\) −185.958 135.106i −0.452452 0.328726i
\(412\) 0.860772 + 0.136333i 0.00208925 + 0.000330905i
\(413\) −2.26060 + 14.2728i −0.00547360 + 0.0345590i
\(414\) −184.583 + 254.056i −0.445852 + 0.613663i
\(415\) −76.2806 239.415i −0.183809 0.576904i
\(416\) 1.92476 1.39842i 0.00462682 0.00336158i
\(417\) 477.378 243.236i 1.14479 0.583301i
\(418\) 29.5380 29.5380i 0.0706650 0.0706650i
\(419\) 330.195 + 107.287i 0.788054 + 0.256054i 0.675275 0.737566i \(-0.264025\pi\)
0.112779 + 0.993620i \(0.464025\pi\)
\(420\) −0.415234 0.826589i −0.000988653 0.00196807i
\(421\) −78.9442 242.965i −0.187516 0.577115i 0.812467 0.583008i \(-0.198124\pi\)
−0.999983 + 0.00589274i \(0.998124\pi\)
\(422\) 341.176 669.596i 0.808475 1.58672i
\(423\) −474.805 + 75.2018i −1.12247 + 0.177782i
\(424\) 660.445i 1.55765i
\(425\) 491.669 72.1214i 1.15687 0.169697i
\(426\) −661.361 −1.55249
\(427\) 23.3682 + 147.541i 0.0547264 + 0.345529i
\(428\) 0.0173916 + 0.00886145i 4.06345e−5 + 2.07043e-5i
\(429\) −291.212 + 94.6204i −0.678815 + 0.220560i
\(430\) −231.794 234.459i −0.539056 0.545254i
\(431\) 69.5257 213.978i 0.161312 0.496469i −0.837433 0.546540i \(-0.815945\pi\)
0.998746 + 0.0500709i \(0.0159447\pi\)
\(432\) 120.410 + 120.410i 0.278726 + 0.278726i
\(433\) 17.7029 + 34.7439i 0.0408843 + 0.0802399i 0.910545 0.413410i \(-0.135662\pi\)
−0.869661 + 0.493650i \(0.835662\pi\)
\(434\) 16.2922 + 22.4243i 0.0375396 + 0.0516688i
\(435\) 660.138 + 218.671i 1.51756 + 0.502692i
\(436\) −0.792616 0.575870i −0.00181793 0.00132080i
\(437\) 84.4503 + 13.3756i 0.193250 + 0.0306078i
\(438\) −73.7755 + 465.800i −0.168437 + 1.06347i
\(439\) 134.972 185.773i 0.307454 0.423174i −0.627131 0.778914i \(-0.715771\pi\)
0.934585 + 0.355740i \(0.115771\pi\)
\(440\) −42.5749 + 128.528i −0.0967610 + 0.292108i
\(441\) 169.092 122.852i 0.383428 0.278577i
\(442\) 710.073 361.800i 1.60650 0.818553i
\(443\) 514.933 514.933i 1.16238 1.16238i 0.178423 0.983954i \(-0.442900\pi\)
0.983954 0.178423i \(-0.0570995\pi\)
\(444\) 1.08295 + 0.351873i 0.00243908 + 0.000792506i
\(445\) −252.349 + 249.481i −0.567077 + 0.560631i
\(446\) 240.880 + 741.351i 0.540089 + 1.66222i
\(447\) −131.236 + 257.564i −0.293592 + 0.576206i
\(448\) −350.352 + 55.4903i −0.782035 + 0.123862i
\(449\) 747.530i 1.66488i 0.554117 + 0.832439i \(0.313056\pi\)
−0.554117 + 0.832439i \(0.686944\pi\)
\(450\) 508.664 251.895i 1.13036 0.559767i
\(451\) −121.371 −0.269114
\(452\) −0.0518174 0.327162i −0.000114640 0.000723811i
\(453\) −914.896 466.163i −2.01964 1.02906i
\(454\) −801.526 + 260.432i −1.76548 + 0.573638i
\(455\) −495.963 + 249.146i −1.09003 + 0.547573i
\(456\) 69.0269 212.443i 0.151375 0.465883i
\(457\) −131.867 131.867i −0.288549 0.288549i 0.547957 0.836506i \(-0.315406\pi\)
−0.836506 + 0.547957i \(0.815406\pi\)
\(458\) −260.205 510.681i −0.568133 1.11502i
\(459\) −124.577 171.465i −0.271409 0.373563i
\(460\) −0.488305 + 0.155580i −0.00106153 + 0.000338217i
\(461\) −146.995 106.798i −0.318861 0.231666i 0.416828 0.908985i \(-0.363142\pi\)
−0.735689 + 0.677319i \(0.763142\pi\)
\(462\) 166.615 + 26.3892i 0.360638 + 0.0571195i
\(463\) 70.5369 445.353i 0.152348 0.961885i −0.786510 0.617578i \(-0.788114\pi\)
0.938857 0.344307i \(-0.111886\pi\)
\(464\) 289.324 398.221i 0.623544 0.858234i
\(465\) 45.9589 32.9914i 0.0988364 0.0709493i
\(466\) 312.891 227.329i 0.671440 0.487830i
\(467\) −340.453 + 173.469i −0.729021 + 0.371455i −0.778772 0.627307i \(-0.784157\pi\)
0.0497511 + 0.998762i \(0.484157\pi\)
\(468\) −1.19474 + 1.19474i −0.00255286 + 0.00255286i
\(469\) 400.621 + 130.170i 0.854203 + 0.277547i
\(470\) 375.501 + 194.039i 0.798939 + 0.412848i
\(471\) 129.636 + 398.980i 0.275236 + 0.847091i
\(472\) 9.49566 18.6363i 0.0201179 0.0394837i
\(473\) −110.225 + 17.4579i −0.233034 + 0.0369089i
\(474\) 354.676i 0.748262i
\(475\) −123.986 92.2647i −0.261023 0.194241i
\(476\) 0.814927 0.00171203
\(477\) −146.611 925.666i −0.307361 1.94060i
\(478\) 106.007 + 54.0135i 0.221773 + 0.112999i
\(479\) −333.071 + 108.221i −0.695347 + 0.225932i −0.635302 0.772264i \(-0.719124\pi\)
−0.0600450 + 0.998196i \(0.519124\pi\)
\(480\) 0.403396 + 2.64469i 0.000840408 + 0.00550977i
\(481\) 211.128 649.784i 0.438935 1.35090i
\(482\) −630.515 630.515i −1.30812 1.30812i
\(483\) 156.757 + 307.652i 0.324548 + 0.636961i
\(484\) −0.477249 0.656877i −0.000986052 0.00135718i
\(485\) −8.27566 + 11.2546i −0.0170632 + 0.0232054i
\(486\) 550.139 + 399.699i 1.13197 + 0.822427i
\(487\) −798.213 126.425i −1.63904 0.259599i −0.732206 0.681084i \(-0.761509\pi\)
−0.906835 + 0.421485i \(0.861509\pi\)
\(488\) 33.8231 213.550i 0.0693095 0.437603i
\(489\) 337.780 464.915i 0.690757 0.950746i
\(490\) −183.766 1.05037i −0.375033 0.00214360i
\(491\) −426.270 + 309.703i −0.868166 + 0.630760i −0.930094 0.367321i \(-0.880275\pi\)
0.0619282 + 0.998081i \(0.480275\pi\)
\(492\) −1.06938 + 0.544874i −0.00217353 + 0.00110747i
\(493\) −433.205 + 433.205i −0.878713 + 0.878713i
\(494\) −235.721 76.5903i −0.477168 0.155041i
\(495\) 31.1404 189.593i 0.0629099 0.383016i
\(496\) −12.3744 38.0846i −0.0249484 0.0767834i
\(497\) −184.222 + 361.556i −0.370668 + 0.727477i
\(498\) 447.552 70.8853i 0.898699 0.142340i
\(499\) 568.734i 1.13975i −0.821732 0.569874i \(-0.806992\pi\)
0.821732 0.569874i \(-0.193008\pi\)
\(500\) 0.912315 + 0.160578i 0.00182463 + 0.000321155i
\(501\) 363.007 0.724565
\(502\) 85.9373 + 542.587i 0.171190 + 1.08085i
\(503\) 165.934 + 84.5473i 0.329888 + 0.168086i 0.611087 0.791563i \(-0.290732\pi\)
−0.281200 + 0.959649i \(0.590732\pi\)
\(504\) 478.729 155.549i 0.949859 0.308628i
\(505\) −265.261 43.5689i −0.525270 0.0862750i
\(506\) 28.8808 88.8860i 0.0570767 0.175664i
\(507\) 745.395 + 745.395i 1.47021 + 1.47021i
\(508\) −0.572830 1.12424i −0.00112762 0.00221308i
\(509\) 321.853 + 442.992i 0.632324 + 0.870319i 0.998177 0.0603538i \(-0.0192229\pi\)
−0.365854 + 0.930672i \(0.619223\pi\)
\(510\) −5.12201 + 896.119i −0.0100432 + 1.75710i
\(511\) 234.096 + 170.081i 0.458114 + 0.332839i
\(512\) 507.095 + 80.3159i 0.990419 + 0.156867i
\(513\) −10.3115 + 65.1041i −0.0201003 + 0.126909i
\(514\) 265.991 366.105i 0.517492 0.712266i
\(515\) 473.720 + 348.332i 0.919845 + 0.676373i
\(516\) −0.892800 + 0.648657i −0.00173023 + 0.00125709i
\(517\) 127.477 64.9526i 0.246570 0.125634i
\(518\) −266.158 + 266.158i −0.513818 + 0.513818i
\(519\) −733.156 238.217i −1.41263 0.458992i
\(520\) 794.157 121.133i 1.52723 0.232949i
\(521\) 140.714 + 433.072i 0.270084 + 0.831233i 0.990478 + 0.137668i \(0.0439607\pi\)
−0.720395 + 0.693564i \(0.756039\pi\)
\(522\) −317.699 + 623.520i −0.608619 + 1.19448i
\(523\) 946.845 149.965i 1.81041 0.286741i 0.842622 0.538506i \(-0.181011\pi\)
0.967788 + 0.251765i \(0.0810109\pi\)
\(524\) 0.388569i 0.000741544i
\(525\) 7.13434 624.072i 0.0135892 1.18871i
\(526\) −836.836 −1.59094
\(527\) 7.79682 + 49.2272i 0.0147947 + 0.0934103i
\(528\) −217.149 110.643i −0.411266 0.209551i
\(529\) −321.173 + 104.355i −0.607132 + 0.197269i
\(530\) −378.292 + 732.066i −0.713759 + 1.38126i
\(531\) −9.17188 + 28.2281i −0.0172728 + 0.0531604i
\(532\) −0.179214 0.179214i −0.000336869 0.000336869i
\(533\) 326.931 + 641.638i 0.613379 + 1.20382i
\(534\) −376.135 517.706i −0.704373 0.969487i
\(535\) 7.67980 + 10.6984i 0.0143548 + 0.0199970i
\(536\) −493.257 358.372i −0.920255 0.668604i
\(537\) −1173.06 185.795i −2.18448 0.345987i
\(538\) −3.82299 + 24.1374i −0.00710593 + 0.0448651i
\(539\) −36.5626 + 50.3242i −0.0678342 + 0.0933658i
\(540\) −0.119939 0.376442i −0.000222109 0.000697115i
\(541\) 134.635 97.8182i 0.248864 0.180810i −0.456359 0.889796i \(-0.650847\pi\)
0.705223 + 0.708986i \(0.250847\pi\)
\(542\) −932.506 + 475.136i −1.72049 + 0.876634i
\(543\) 438.341 438.341i 0.807258 0.807258i
\(544\) −2.24151 0.728311i −0.00412043 0.00133881i
\(545\) −296.726 590.680i −0.544452 1.08382i
\(546\) −309.295 951.911i −0.566474 1.74343i
\(547\) −107.533 + 211.046i −0.196587 + 0.385824i −0.968166 0.250310i \(-0.919467\pi\)
0.771579 + 0.636134i \(0.219467\pi\)
\(548\) 0.372835 0.0590513i 0.000680356 0.000107758i
\(549\) 306.816i 0.558863i
\(550\) −120.810 + 118.079i −0.219655 + 0.214690i
\(551\) 190.536 0.345801
\(552\) −78.1807 493.613i −0.141632 0.894227i
\(553\) −193.896 98.7951i −0.350626 0.178653i
\(554\) 829.567 269.543i 1.49741 0.486539i
\(555\) 540.134 + 546.344i 0.973215 + 0.984404i
\(556\) −0.271897 + 0.836812i −0.000489023 + 0.00150506i
\(557\) 443.386 + 443.386i 0.796026 + 0.796026i 0.982466 0.186441i \(-0.0596952\pi\)
−0.186441 + 0.982466i \(0.559695\pi\)
\(558\) 25.8460 + 50.7255i 0.0463189 + 0.0909060i
\(559\) 389.202 + 535.691i 0.696247 + 0.958302i
\(560\) −419.352 138.911i −0.748843 0.248055i
\(561\) 245.401 + 178.294i 0.437435 + 0.317815i
\(562\) −203.258 32.1929i −0.361669 0.0572828i
\(563\) −78.6829 + 496.784i −0.139757 + 0.882388i 0.813794 + 0.581154i \(0.197399\pi\)
−0.953550 + 0.301234i \(0.902601\pi\)
\(564\) 0.831582 1.14457i 0.00147444 0.00202939i
\(565\) 70.2753 212.151i 0.124381 0.375489i
\(566\) 342.018 248.490i 0.604272 0.439029i
\(567\) 266.925 136.005i 0.470767 0.239868i
\(568\) 415.305 415.305i 0.731172 0.731172i
\(569\) −780.470 253.590i −1.37165 0.445677i −0.471736 0.881740i \(-0.656373\pi\)
−0.899916 + 0.436063i \(0.856373\pi\)
\(570\) 198.196 195.943i 0.347712 0.343760i
\(571\) 119.477 + 367.712i 0.209241 + 0.643979i 0.999512 + 0.0312214i \(0.00993968\pi\)
−0.790271 + 0.612757i \(0.790060\pi\)
\(572\) 0.228291 0.448047i 0.000399110 0.000783298i
\(573\) 845.634 133.935i 1.47580 0.233744i
\(574\) 396.735i 0.691176i
\(575\) −340.879 57.9919i −0.592834 0.100855i
\(576\) −728.567 −1.26487
\(577\) 24.2091 + 152.850i 0.0419568 + 0.264905i 0.999745 0.0225689i \(-0.00718452\pi\)
−0.957788 + 0.287474i \(0.907185\pi\)
\(578\) −188.903 96.2510i −0.326822 0.166524i
\(579\) −281.165 + 91.3562i −0.485605 + 0.157783i
\(580\) −1.02052 + 0.512653i −0.00175951 + 0.000883884i
\(581\) 85.9137 264.415i 0.147872 0.455104i
\(582\) −17.8135 17.8135i −0.0306074 0.0306074i
\(583\) 126.630 + 248.525i 0.217204 + 0.426286i
\(584\) −246.174 338.830i −0.421531 0.580188i
\(585\) −1086.18 + 346.071i −1.85672 + 0.591575i
\(586\) 439.226 + 319.117i 0.749533 + 0.544568i
\(587\) 587.344 + 93.0261i 1.00059 + 0.158477i 0.635174 0.772369i \(-0.280928\pi\)
0.365412 + 0.930846i \(0.380928\pi\)
\(588\) −0.0962249 + 0.607540i −0.000163648 + 0.00103323i
\(589\) 9.11115 12.5404i 0.0154688 0.0212910i
\(590\) 21.2000 15.2183i 0.0359321 0.0257937i
\(591\) 998.821 725.686i 1.69005 1.22789i
\(592\) 484.527 246.879i 0.818457 0.417025i
\(593\) −151.299 + 151.299i −0.255142 + 0.255142i −0.823075 0.567933i \(-0.807743\pi\)
0.567933 + 0.823075i \(0.307743\pi\)
\(594\) 68.5236 + 22.2647i 0.115360 + 0.0374826i
\(595\) 488.468 + 252.414i 0.820955 + 0.424225i
\(596\) −0.146699 0.451493i −0.000246139 0.000757539i
\(597\) 406.130 797.075i 0.680285 1.33513i
\(598\) −547.700 + 86.7472i −0.915886 + 0.145062i
\(599\) 471.606i 0.787322i −0.919256 0.393661i \(-0.871208\pi\)
0.919256 0.393661i \(-0.128792\pi\)
\(600\) −288.950 + 855.880i −0.481583 + 1.42647i
\(601\) 12.2283 0.0203466 0.0101733 0.999948i \(-0.496762\pi\)
0.0101733 + 0.999948i \(0.496762\pi\)
\(602\) −57.0664 360.303i −0.0947946 0.598510i
\(603\) 770.893 + 392.789i 1.27843 + 0.651392i
\(604\) 1.60375 0.521091i 0.00265522 0.000862733i
\(605\) −82.6037 541.555i −0.136535 0.895132i
\(606\) 149.801 461.039i 0.247196 0.760790i
\(607\) −786.089 786.089i −1.29504 1.29504i −0.931629 0.363411i \(-0.881612\pi\)
−0.363411 0.931629i \(-0.618388\pi\)
\(608\) 0.332775 + 0.653108i 0.000547327 + 0.00107419i
\(609\) 452.267 + 622.492i 0.742639 + 1.02215i
\(610\) 159.809 217.335i 0.261982 0.356287i
\(611\) −686.758 498.959i −1.12399 0.816627i
\(612\) 1.65320 + 0.261840i 0.00270130 + 0.000427844i
\(613\) −9.63893 + 60.8578i −0.0157242 + 0.0992786i −0.994302 0.106597i \(-0.966004\pi\)
0.978578 + 0.205876i \(0.0660044\pi\)
\(614\) −62.7656 + 86.3895i −0.102224 + 0.140700i
\(615\) −809.753 4.62836i −1.31667 0.00752579i
\(616\) −121.198 + 88.0555i −0.196750 + 0.142947i
\(617\) 139.850 71.2571i 0.226661 0.115490i −0.336973 0.941514i \(-0.609403\pi\)
0.563634 + 0.826025i \(0.309403\pi\)
\(618\) −749.792 + 749.792i −1.21326 + 1.21326i
\(619\) −972.585 316.012i −1.57122 0.510520i −0.611444 0.791287i \(-0.709411\pi\)
−0.959776 + 0.280767i \(0.909411\pi\)
\(620\) −0.0150585 + 0.0916809i −2.42879e−5 + 0.000147872i
\(621\) 45.5724 + 140.257i 0.0733855 + 0.225857i
\(622\) 233.432 458.136i 0.375292 0.736552i
\(623\) −387.795 + 61.4207i −0.622463 + 0.0985885i
\(624\) 1446.01i 2.31733i
\(625\) 497.105 + 378.829i 0.795368 + 0.606126i
\(626\) 958.090 1.53050
\(627\) −14.7578 93.1768i −0.0235371 0.148607i
\(628\) −0.613854 0.312774i −0.000977475 0.000498048i
\(629\) −643.703 + 209.152i −1.02338 + 0.332515i
\(630\) 619.739 + 101.792i 0.983713 + 0.161574i
\(631\) 80.5107 247.786i 0.127592 0.392688i −0.866772 0.498704i \(-0.833809\pi\)
0.994364 + 0.106016i \(0.0338094\pi\)
\(632\) 222.721 + 222.721i 0.352407 + 0.352407i
\(633\) −770.498 1512.19i −1.21722 2.38892i
\(634\) 231.931 + 319.226i 0.365822 + 0.503510i
\(635\) 4.86583 851.299i 0.00766272 1.34063i
\(636\) 2.23143 + 1.62123i 0.00350853 + 0.00254910i
\(637\) 364.531 + 57.7361i 0.572263 + 0.0906375i
\(638\) 32.5804 205.704i 0.0510664 0.322421i
\(639\) −489.890 + 674.276i −0.766652 + 1.05521i
\(640\) 514.175 + 378.079i 0.803398 + 0.590748i
\(641\) −947.896 + 688.686i −1.47878 + 1.07439i −0.500828 + 0.865547i \(0.666971\pi\)
−0.977948 + 0.208847i \(0.933029\pi\)
\(642\) −21.1605 + 10.7818i −0.0329603 + 0.0167941i
\(643\) −268.108 + 268.108i −0.416965 + 0.416965i −0.884156 0.467191i \(-0.845266\pi\)
0.467191 + 0.884156i \(0.345266\pi\)
\(644\) −0.539294 0.175227i −0.000837413 0.000272092i
\(645\) −736.059 + 112.271i −1.14118 + 0.174064i
\(646\) 75.8735 + 233.515i 0.117451 + 0.361478i
\(647\) −540.483 + 1060.76i −0.835368 + 1.63950i −0.0685400 + 0.997648i \(0.521834\pi\)
−0.766828 + 0.641853i \(0.778166\pi\)
\(648\) −428.268 + 67.8310i −0.660907 + 0.104677i
\(649\) 8.83345i 0.0136109i
\(650\) 949.661 + 320.611i 1.46102 + 0.493247i
\(651\) 62.5969 0.0961550
\(652\) 0.147635 + 0.932128i 0.000226433 + 0.00142964i
\(653\) 402.175 + 204.918i 0.615888 + 0.313810i 0.733958 0.679195i \(-0.237671\pi\)
−0.118070 + 0.993005i \(0.537671\pi\)
\(654\) 1133.70 368.362i 1.73349 0.563245i
\(655\) 120.355 232.909i 0.183747 0.355586i
\(656\) −177.119 + 545.117i −0.269999 + 0.830971i
\(657\) 420.249 + 420.249i 0.639648 + 0.639648i
\(658\) 212.317 + 416.695i 0.322670 + 0.633275i
\(659\) 190.013 + 261.531i 0.288336 + 0.396860i 0.928473 0.371401i \(-0.121122\pi\)
−0.640137 + 0.768261i \(0.721122\pi\)
\(660\) 0.329742 + 0.459349i 0.000499609 + 0.000695984i
\(661\) 346.646 + 251.853i 0.524427 + 0.381018i 0.818269 0.574836i \(-0.194934\pi\)
−0.293842 + 0.955854i \(0.594934\pi\)
\(662\) 586.529 + 92.8971i 0.885996 + 0.140328i
\(663\) 281.545 1777.60i 0.424652 2.68115i
\(664\) −236.530 + 325.556i −0.356220 + 0.490295i
\(665\) −51.9118 162.931i −0.0780628 0.245009i
\(666\) −625.457 + 454.421i −0.939124 + 0.682314i
\(667\) 379.831 193.533i 0.569462 0.290155i
\(668\) −0.421541 + 0.421541i −0.000631049 + 0.000631049i
\(669\) 1674.24 + 543.992i 2.50259 + 0.813142i
\(670\) −341.477 679.764i −0.509668 1.01457i
\(671\) −28.2173 86.8438i −0.0420525 0.129424i
\(672\) −1.34384 + 2.63744i −0.00199977 + 0.00392477i
\(673\) −326.867 + 51.7706i −0.485686 + 0.0769252i −0.394476 0.918906i \(-0.629074\pi\)
−0.0912108 + 0.995832i \(0.529074\pi\)
\(674\) 641.200i 0.951336i
\(675\) 44.7069 262.789i 0.0662324 0.389318i
\(676\) −1.73118 −0.00256091
\(677\) 163.559 + 1032.67i 0.241593 + 1.52536i 0.748369 + 0.663282i \(0.230837\pi\)
−0.506776 + 0.862078i \(0.669163\pi\)
\(678\) 359.097 + 182.969i 0.529642 + 0.269866i
\(679\) −14.7004 + 4.77643i −0.0216500 + 0.00703451i
\(680\) −559.507 565.939i −0.822804 0.832264i
\(681\) −588.147 + 1810.13i −0.863652 + 2.65805i
\(682\) −11.9808 11.9808i −0.0175671 0.0175671i
\(683\) −76.1595 149.471i −0.111507 0.218845i 0.828508 0.559977i \(-0.189190\pi\)
−0.940016 + 0.341131i \(0.889190\pi\)
\(684\) −0.305979 0.421144i −0.000447338 0.000615708i
\(685\) 241.768 + 80.0858i 0.352946 + 0.116914i
\(686\) −602.712 437.896i −0.878588 0.638332i
\(687\) −1278.44 202.485i −1.86091 0.294738i
\(688\) −82.4447 + 520.535i −0.119832 + 0.756592i
\(689\) 972.756 1338.88i 1.41184 1.94323i
\(690\) 196.075 591.923i 0.284166 0.857859i
\(691\) −159.959 + 116.217i −0.231489 + 0.168187i −0.697483 0.716601i \(-0.745697\pi\)
0.465994 + 0.884788i \(0.345697\pi\)
\(692\) 1.12801 0.574747i 0.00163007 0.000830560i
\(693\) 150.321 150.321i 0.216914 0.216914i
\(694\) −870.075 282.704i −1.25371 0.407355i
\(695\) −422.168 + 417.369i −0.607436 + 0.600531i
\(696\) −344.149 1059.18i −0.494467 1.52181i
\(697\) 323.871 635.633i 0.464665 0.911956i
\(698\) −543.217 + 86.0371i −0.778248 + 0.123262i
\(699\) 873.430i 1.24954i
\(700\) 0.716418 + 0.732987i 0.00102345 + 0.00104712i
\(701\) 317.355 0.452718 0.226359 0.974044i \(-0.427318\pi\)
0.226359 + 0.974044i \(0.427318\pi\)
\(702\) −66.8748 422.231i −0.0952633 0.601468i
\(703\) 187.555 + 95.5642i 0.266793 + 0.135938i
\(704\) 206.220 67.0049i 0.292926 0.0951774i
\(705\) 852.969 428.486i 1.20989 0.607782i
\(706\) −253.584 + 780.453i −0.359185 + 1.10546i
\(707\) −210.316 210.316i −0.297477 0.297477i
\(708\) −0.0396564 0.0778301i −5.60119e−5 0.000109930i
\(709\) −600.695 826.785i −0.847242 1.16613i −0.984464 0.175588i \(-0.943817\pi\)
0.137221 0.990540i \(-0.456183\pi\)
\(710\) 698.222 222.462i 0.983412 0.313327i
\(711\) −361.603 262.720i −0.508583 0.369507i
\(712\) 561.293 + 88.9001i 0.788333 + 0.124860i
\(713\) 5.42523 34.2536i 0.00760902 0.0480415i
\(714\) −582.807 + 802.165i −0.816256 + 1.12348i
\(715\) 275.615 197.849i 0.385476 0.276712i
\(716\) 1.57797 1.14646i 0.00220387 0.00160121i
\(717\) 239.403 121.982i 0.333895 0.170128i
\(718\) −193.882 + 193.882i −0.270031 + 0.270031i
\(719\) 1129.58 + 367.024i 1.57105 + 0.510464i 0.959730 0.280923i \(-0.0906405\pi\)
0.611316 + 0.791387i \(0.290640\pi\)
\(720\) −806.082 416.540i −1.11956 0.578527i
\(721\) 201.046 + 618.755i 0.278843 + 0.858190i
\(722\) −292.810 + 574.672i −0.405554 + 0.795944i
\(723\) −1988.95 + 315.018i −2.75096 + 0.435710i
\(724\) 1.01805i 0.00140614i
\(725\) −770.486 8.80813i −1.06274 0.0121491i
\(726\) 987.901 1.36075
\(727\) 39.2430 + 247.771i 0.0539794 + 0.340813i 0.999867 + 0.0163178i \(0.00519433\pi\)
−0.945887 + 0.324495i \(0.894806\pi\)
\(728\) 791.981 + 403.535i 1.08789 + 0.554306i
\(729\) 997.037 323.957i 1.36768 0.444385i
\(730\) −78.7940 516.578i −0.107937 0.707641i
\(731\) 202.701 623.848i 0.277292 0.853417i
\(732\) −0.638489 0.638489i −0.000872253 0.000872253i
\(733\) −119.145 233.835i −0.162544 0.319011i 0.795341 0.606162i \(-0.207292\pi\)
−0.957885 + 0.287151i \(0.907292\pi\)
\(734\) 617.060 + 849.311i 0.840682 + 1.15710i
\(735\) −245.856 + 334.356i −0.334497 + 0.454906i
\(736\) 1.32676 + 0.963949i 0.00180267 + 0.00130971i
\(737\) −254.324 40.2810i −0.345080 0.0546553i
\(738\) 127.473 804.834i 0.172728 1.09056i
\(739\) −419.335 + 577.165i −0.567435 + 0.781008i −0.992248 0.124273i \(-0.960340\pi\)
0.424813 + 0.905281i \(0.360340\pi\)
\(740\) −1.26167 0.00721142i −0.00170496 9.74516e-6i
\(741\) −452.837 + 329.005i −0.611116 + 0.444002i
\(742\) −812.376 + 413.926i −1.09485 + 0.557852i
\(743\) −9.34501 + 9.34501i −0.0125774 + 0.0125774i −0.713368 0.700790i \(-0.752831\pi\)
0.700790 + 0.713368i \(0.252831\pi\)
\(744\) −86.1682 27.9977i −0.115817 0.0376314i
\(745\) 51.9131 316.064i 0.0696820 0.424246i
\(746\) −107.051 329.468i −0.143500 0.441647i
\(747\) 259.246 508.799i 0.347050 0.681123i
\(748\) −0.492015 + 0.0779276i −0.000657774 + 0.000104181i
\(749\) 14.5714i 0.0194545i
\(750\) −810.518 + 783.188i −1.08069 + 1.04425i
\(751\) −175.040 −0.233076 −0.116538 0.993186i \(-0.537180\pi\)
−0.116538 + 0.993186i \(0.537180\pi\)
\(752\) −105.694 667.329i −0.140551 0.887405i
\(753\) 1105.41 + 563.234i 1.46801 + 0.747986i
\(754\) −1175.24 + 381.858i −1.55867 + 0.506443i
\(755\) 1122.69 + 184.401i 1.48701 + 0.244240i
\(756\) 0.135086 0.415751i 0.000178685 0.000549935i
\(757\) −331.826 331.826i −0.438343 0.438343i 0.453111 0.891454i \(-0.350314\pi\)
−0.891454 + 0.453111i \(0.850314\pi\)
\(758\) −452.296 887.680i −0.596696 1.17108i
\(759\) −124.062 170.756i −0.163454 0.224975i
\(760\) −1.41466 + 247.502i −0.00186140 + 0.325661i
\(761\) 854.871 + 621.100i 1.12335 + 0.816163i 0.984714 0.174180i \(-0.0557274\pi\)
0.138638 + 0.990343i \(0.455727\pi\)
\(762\) 1516.30 + 240.159i 1.98990 + 0.315169i
\(763\) 114.415 722.386i 0.149954 0.946770i
\(764\) −0.826459 + 1.13752i −0.00108175 + 0.00148891i
\(765\) 909.825 + 669.005i 1.18931 + 0.874516i
\(766\) 164.030 119.175i 0.214138 0.155581i
\(767\) −46.6990 + 23.7943i −0.0608853 + 0.0310226i
\(768\) 4.54009 4.54009i 0.00591157 0.00591157i
\(769\) −407.934 132.546i −0.530474 0.172361i 0.0315195 0.999503i \(-0.489965\pi\)
−0.561993 + 0.827142i \(0.689965\pi\)
\(770\) −184.778 + 28.1843i −0.239971 + 0.0366030i
\(771\) −315.808 971.956i −0.409608 1.26064i
\(772\) 0.220416 0.432590i 0.000285512 0.000560350i
\(773\) 209.109 33.1196i 0.270516 0.0428456i −0.0197025 0.999806i \(-0.506272\pi\)
0.290219 + 0.956960i \(0.406272\pi\)
\(774\) 749.261i 0.968037i
\(775\) −37.4231 + 50.2894i −0.0482879 + 0.0648896i
\(776\) 22.3722 0.0288302
\(777\) 132.978 + 839.589i 0.171143 + 1.08055i
\(778\) 121.851 + 62.0859i 0.156620 + 0.0798020i
\(779\) −211.009 + 68.5610i −0.270872 + 0.0880116i
\(780\) 1.54019 2.98055i 0.00197460 0.00382121i
\(781\) 76.6509 235.907i 0.0981445 0.302058i
\(782\) 388.440 + 388.440i 0.496727 + 0.496727i
\(783\) 149.198 + 292.818i 0.190547 + 0.373969i
\(784\) 172.666 + 237.655i 0.220238 + 0.303131i
\(785\) −271.067 377.611i −0.345308 0.481034i
\(786\) 382.484 + 277.891i 0.486620 + 0.353550i
\(787\) −506.378 80.2023i −0.643428 0.101909i −0.173811 0.984779i \(-0.555608\pi\)
−0.469617 + 0.882870i \(0.655608\pi\)
\(788\) −0.317178 + 2.00258i −0.000402510 + 0.00254135i
\(789\) −1110.84 + 1528.94i −1.40791 + 1.93782i
\(790\) 119.303 + 374.445i 0.151016 + 0.473980i
\(791\) 200.053 145.347i 0.252911 0.183751i
\(792\) −274.160 + 139.692i −0.346162 + 0.176378i
\(793\) −383.101 + 383.101i −0.483104 + 0.483104i
\(794\) 185.309 + 60.2105i 0.233386 + 0.0758318i
\(795\) 835.364 + 1662.92i 1.05077 + 2.09173i
\(796\) 0.453984 + 1.39722i 0.000570332 + 0.00175530i
\(797\) 607.216 1191.73i 0.761878 1.49527i −0.103762 0.994602i \(-0.533088\pi\)
0.865640 0.500667i \(-0.166912\pi\)
\(798\) 304.576 48.2401i 0.381674 0.0604512i
\(799\) 840.935i 1.05248i
\(800\) −1.31547 2.65640i −0.00164434 0.00332050i
\(801\) −806.431 −1.00678
\(802\) −45.5544 287.619i −0.0568010 0.358628i
\(803\) −157.600 80.3014i −0.196264 0.100002i
\(804\) −2.42164 + 0.786839i −0.00301199 + 0.000978656i
\(805\) −268.979 272.071i −0.334135 0.337977i
\(806\) −31.0655 + 95.6099i −0.0385428 + 0.118623i
\(807\) 39.0255 + 39.0255i 0.0483587 + 0.0483587i
\(808\) 195.444 + 383.580i 0.241886 + 0.474728i
\(809\) −82.9765 114.207i −0.102567 0.141171i 0.754649 0.656129i \(-0.227807\pi\)
−0.857215 + 0.514958i \(0.827807\pi\)
\(810\) −513.563 170.118i −0.634028 0.210022i
\(811\) 105.885 + 76.9299i 0.130561 + 0.0948581i 0.651149 0.758950i \(-0.274287\pi\)
−0.520588 + 0.853808i \(0.674287\pi\)
\(812\) −1.24806 0.197674i −0.00153702 0.000243440i
\(813\) −369.739 + 2334.44i −0.454784 + 2.87139i
\(814\) 135.242 186.145i 0.166145 0.228680i
\(815\) −200.223 + 604.447i −0.245673 + 0.741652i
\(816\) 1158.90 841.990i 1.42022 1.03185i
\(817\) −181.770 + 92.6165i −0.222485 + 0.113362i
\(818\) 142.203 142.203i 0.173843 0.173843i
\(819\) −1199.60 389.775i −1.46472 0.475916i
\(820\) 0.945699 0.934950i 0.00115329 0.00114018i
\(821\) −223.412 687.591i −0.272122 0.837504i −0.989967 0.141301i \(-0.954871\pi\)
0.717845 0.696203i \(-0.245129\pi\)
\(822\) −208.512 + 409.228i −0.253664 + 0.497844i
\(823\) 1267.47 200.748i 1.54006 0.243922i 0.672065 0.740492i \(-0.265408\pi\)
0.867996 + 0.496571i \(0.165408\pi\)
\(824\) 941.672i 1.14281i
\(825\) 55.3696 + 377.468i 0.0671147 + 0.457537i
\(826\) 28.8747 0.0349573
\(827\) −26.4921 167.265i −0.0320340 0.202255i 0.966481 0.256740i \(-0.0826483\pi\)
−0.998515 + 0.0544850i \(0.982648\pi\)
\(828\) −1.03773 0.528751i −0.00125330 0.000638589i
\(829\) 1291.17 419.527i 1.55751 0.506064i 0.601366 0.798974i \(-0.294624\pi\)
0.956140 + 0.292910i \(0.0946235\pi\)
\(830\) −448.653 + 225.379i −0.540546 + 0.271541i
\(831\) 608.724 1873.46i 0.732519 2.25446i
\(832\) −909.715 909.715i −1.09341 1.09341i
\(833\) −165.988 325.771i −0.199266 0.391081i
\(834\) −629.257 866.097i −0.754504 1.03849i
\(835\) −383.239 + 122.105i −0.458969 + 0.146233i
\(836\) 0.125339 + 0.0910640i 0.000149927 + 0.000108928i
\(837\) 26.4066 + 4.18240i 0.0315491 + 0.00499689i
\(838\) 108.523 685.190i 0.129503 0.817649i
\(839\) −678.477 + 933.843i −0.808673 + 1.11304i 0.182853 + 0.983140i \(0.441467\pi\)
−0.991527 + 0.129903i \(0.958533\pi\)
\(840\) −811.960 + 582.862i −0.966619 + 0.693883i
\(841\) 88.1522 64.0464i 0.104818 0.0761550i
\(842\) −454.827 + 231.746i −0.540175 + 0.275233i
\(843\) −328.629 + 328.629i −0.389833 + 0.389833i
\(844\) 2.65076 + 0.861285i 0.00314071 + 0.00102048i
\(845\) −1037.67 536.211i −1.22801 0.634569i
\(846\) 296.828 + 913.544i 0.350861 + 1.07984i
\(847\) 275.180 540.071i 0.324888 0.637628i
\(848\) 1301.00 206.059i 1.53420 0.242994i
\(849\) 954.736i 1.12454i
\(850\) −296.020 947.788i −0.348259 1.11504i
\(851\) 470.955 0.553414
\(852\) −0.383710 2.42265i −0.000450364 0.00284349i
\(853\) 83.5286 + 42.5599i 0.0979233 + 0.0498944i 0.502266 0.864713i \(-0.332500\pi\)
−0.404343 + 0.914607i \(0.632500\pi\)
\(854\) 283.874 92.2364i 0.332406 0.108005i
\(855\) −52.9598 347.208i −0.0619413 0.406091i
\(856\) 6.51737 20.0584i 0.00761374 0.0234327i
\(857\) 178.447 + 178.447i 0.208223 + 0.208223i 0.803512 0.595289i \(-0.202962\pi\)
−0.595289 + 0.803512i \(0.702962\pi\)
\(858\) 277.764 + 545.143i 0.323735 + 0.635365i
\(859\) −192.730 265.270i −0.224366 0.308813i 0.681963 0.731387i \(-0.261127\pi\)
−0.906328 + 0.422574i \(0.861127\pi\)
\(860\) 0.724372 0.985122i 0.000842293 0.00114549i
\(861\) −724.855 526.638i −0.841875 0.611658i
\(862\) −444.028 70.3271i −0.515113 0.0815860i
\(863\) 18.8095 118.758i 0.0217954 0.137611i −0.974391 0.224860i \(-0.927808\pi\)
0.996187 + 0.0872489i \(0.0278075\pi\)
\(864\) −0.743124 + 1.02282i −0.000860097 + 0.00118382i
\(865\) 854.148 + 4.88211i 0.987455 + 0.00564406i
\(866\) 63.0351 45.7977i 0.0727888 0.0528842i
\(867\) −426.611 + 217.369i −0.492054 + 0.250714i
\(868\) −0.0726905 + 0.0726905i −8.37449e−5 + 8.37449e-5i
\(869\) 126.513 + 41.1065i 0.145584 + 0.0473033i
\(870\) 225.212 1371.16i 0.258865 1.57605i
\(871\) 472.113 + 1453.01i 0.542036 + 1.66821i
\(872\) −480.600 + 943.230i −0.551147 + 1.08169i
\(873\) −31.3564 + 4.96637i −0.0359180 + 0.00568886i
\(874\) 170.847i 0.195478i
\(875\) 202.387 + 661.255i 0.231300 + 0.755720i
\(876\) −1.74909 −0.00199668
\(877\) 142.712 + 901.047i 0.162727 + 1.02742i 0.924945 + 0.380100i \(0.124110\pi\)
−0.762218 + 0.647320i \(0.775890\pi\)
\(878\) −408.822 208.305i −0.465628 0.237249i
\(879\) 1166.08 378.883i 1.32660 0.431039i
\(880\) 266.469 + 43.7672i 0.302805 + 0.0497354i
\(881\) 422.625 1300.71i 0.479710 1.47640i −0.359788 0.933034i \(-0.617151\pi\)
0.839498 0.543363i \(-0.182849\pi\)
\(882\) −295.309 295.309i −0.334817 0.334817i
\(883\) 700.304 + 1374.42i 0.793096 + 1.55654i 0.830357 + 0.557232i \(0.188137\pi\)
−0.0372608 + 0.999306i \(0.511863\pi\)
\(884\) 1.73729 + 2.39118i 0.00196527 + 0.00270496i
\(885\) 0.336856 58.9345i 0.000380628 0.0665927i
\(886\) −1177.20 855.287i −1.32867 0.965335i
\(887\) 359.608 + 56.9563i 0.405421 + 0.0642123i 0.355815 0.934557i \(-0.384203\pi\)
0.0496060 + 0.998769i \(0.484203\pi\)
\(888\) 192.472 1215.22i 0.216747 1.36849i
\(889\) 553.658 762.045i 0.622787 0.857193i
\(890\) 571.241 + 420.040i 0.641843 + 0.471955i
\(891\) −148.151 + 107.638i −0.166275 + 0.120806i
\(892\) −2.57591 + 1.31249i −0.00288779 + 0.00147140i
\(893\) 184.934 184.934i 0.207093 0.207093i
\(894\) 549.336 + 178.490i 0.614470 + 0.199653i
\(895\) 1300.94 198.434i 1.45357 0.221713i
\(896\) 218.214 + 671.595i 0.243543 + 0.749548i
\(897\) −568.541 + 1115.83i −0.633825 + 1.24395i
\(898\) 1475.29 233.662i 1.64286 0.260203i
\(899\) 77.2828i 0.0859653i
\(900\) 1.21784 + 1.71716i 0.00135316 + 0.00190795i
\(901\) −1639.46 −1.81960
\(902\) 37.9379 + 239.530i 0.0420597 + 0.265555i
\(903\) −734.042 374.013i −0.812893 0.414190i
\(904\) −340.394 + 110.601i −0.376542 + 0.122346i
\(905\) −315.327 + 610.217i −0.348428 + 0.674273i
\(906\) −634.017 + 1951.30i −0.699798 + 2.15376i
\(907\) 45.1187 + 45.1187i 0.0497450 + 0.0497450i 0.731542 0.681797i \(-0.238801\pi\)
−0.681797 + 0.731542i \(0.738801\pi\)
\(908\) −1.41903 2.78500i −0.00156280 0.00306718i
\(909\) −359.080 494.232i −0.395028 0.543709i
\(910\) 646.728 + 900.929i 0.710690 + 0.990032i
\(911\) −274.452 199.401i −0.301265 0.218882i 0.426874 0.904311i \(-0.359615\pi\)
−0.728139 + 0.685429i \(0.759615\pi\)
\(912\) −440.025 69.6932i −0.482484 0.0764179i
\(913\) −26.5860 + 167.857i −0.0291193 + 0.183852i
\(914\) −219.027 + 301.465i −0.239636 + 0.329830i
\(915\) −184.947 580.476i −0.202127 0.634400i
\(916\) 1.71972 1.24945i 0.00187743 0.00136403i
\(917\) 258.460 131.692i 0.281853 0.143611i
\(918\) −299.455 + 299.455i −0.326204 + 0.326204i
\(919\) −240.689 78.2047i −0.261903 0.0850976i 0.175122 0.984547i \(-0.443968\pi\)
−0.437025 + 0.899449i \(0.643968\pi\)
\(920\) 248.575 + 494.828i 0.270190 + 0.537856i
\(921\) 74.5209 + 229.352i 0.0809130 + 0.249025i
\(922\) −164.823 + 323.484i −0.178767 + 0.350851i
\(923\) −1453.62 + 230.231i −1.57489 + 0.249437i
\(924\) 0.625642i 0.000677102i
\(925\) −754.013 395.110i −0.815150 0.427146i
\(926\) −900.972 −0.972972
\(927\) 209.040 + 1319.83i 0.225502 + 1.42376i
\(928\) 3.25622 + 1.65912i 0.00350885 + 0.00178785i
\(929\) −658.494 + 213.958i −0.708820 + 0.230310i −0.641169 0.767399i \(-0.721550\pi\)
−0.0676508 + 0.997709i \(0.521550\pi\)
\(930\) −79.4759 80.3896i −0.0854579 0.0864404i
\(931\) −35.1385 + 108.145i −0.0377427 + 0.116160i
\(932\) 1.01427 + 1.01427i 0.00108827 + 0.00108827i
\(933\) −527.172 1034.63i −0.565029 1.10893i
\(934\) 448.768 + 617.676i 0.480480 + 0.661324i
\(935\) −319.052 105.686i −0.341232 0.113033i
\(936\) 1476.99 + 1073.09i 1.57798 + 1.14647i
\(937\) 218.653 + 34.6312i 0.233354 + 0.0369596i 0.272016 0.962293i \(-0.412310\pi\)
−0.0386622 + 0.999252i \(0.512310\pi\)
\(938\) 131.670 831.333i 0.140373 0.886282i
\(939\) 1271.80 1750.48i 1.35442 1.86419i
\(940\) −0.492930 + 1.48809i −0.000524394 + 0.00158307i
\(941\) 164.559 119.559i 0.174876 0.127055i −0.496904 0.867805i \(-0.665530\pi\)
0.671780 + 0.740750i \(0.265530\pi\)
\(942\) 746.883 380.556i 0.792869 0.403987i
\(943\) −351.003 + 351.003i −0.372220 + 0.372220i
\(944\) −39.6741 12.8909i −0.0420276 0.0136556i
\(945\) 209.744 207.360i 0.221952 0.219429i
\(946\) 68.9080 + 212.077i 0.0728415 + 0.224183i
\(947\) 544.018 1067.69i 0.574464 1.12745i −0.402773 0.915300i \(-0.631954\pi\)
0.977237 0.212150i \(-0.0680464\pi\)
\(948\) 1.29923 0.205777i 0.00137049 0.000217064i
\(949\) 1049.48i 1.10588i
\(950\) −143.333 + 273.532i −0.150877 + 0.287928i
\(951\) 891.112 0.937026
\(952\) −137.747 869.701i −0.144692 0.913552i
\(953\) −863.782 440.119i −0.906382 0.461825i −0.0623115 0.998057i \(-0.519847\pi\)
−0.844071 + 0.536232i \(0.819847\pi\)
\(954\) −1781.02 + 578.688i −1.86689 + 0.606591i
\(955\) −847.715 + 425.847i −0.887660 + 0.445913i
\(956\) −0.136355 + 0.419657i −0.000142631 + 0.000438972i
\(957\) −332.584 332.584i −0.347528 0.347528i
\(958\) 317.691 + 623.504i 0.331619 + 0.650839i
\(959\) 165.638 + 227.981i 0.172719 + 0.237728i
\(960\) 1378.40 439.175i 1.43583 0.457474i
\(961\) 772.379 + 561.166i 0.803724 + 0.583940i
\(962\) −1348.37 213.561i −1.40164 0.221997i
\(963\) −4.68187 + 29.5602i −0.00486176 + 0.0306959i
\(964\) 1.94385 2.67547i 0.00201644 0.00277539i
\(965\) 266.107 191.024i 0.275758 0.197952i
\(966\) 558.167 405.532i 0.577813 0.419806i
\(967\) 394.896 201.209i 0.408372 0.208076i −0.237723 0.971333i \(-0.576401\pi\)
0.646095 + 0.763257i \(0.276401\pi\)
\(968\) −620.359 + 620.359i −0.640866 + 0.640866i
\(969\) 527.359 + 171.349i 0.544230 + 0.176831i
\(970\) 24.7983 + 12.8144i 0.0255653 + 0.0132108i
\(971\) 53.8408 + 165.705i 0.0554488 + 0.170654i 0.974946 0.222444i \(-0.0714034\pi\)
−0.919497 + 0.393098i \(0.871403\pi\)
\(972\) −1.14497 + 2.24713i −0.00117795 + 0.00231186i
\(973\) −648.762 + 102.754i −0.666765 + 0.105605i
\(974\) 1614.83i 1.65793i
\(975\) 1846.38 1309.49i 1.89372 1.34306i
\(976\) −431.223 −0.441827
\(977\) −257.214 1623.99i −0.263269 1.66222i −0.665289 0.746586i \(-0.731692\pi\)
0.402020 0.915631i \(-0.368308\pi\)
\(978\) −1023.11 521.302i −1.04613 0.533029i
\(979\) 228.259 74.1659i 0.233155 0.0757568i
\(980\) −0.102770 0.673769i −0.000104868 0.000687520i
\(981\) 464.213 1428.70i 0.473203 1.45637i
\(982\) 744.456 + 744.456i 0.758102 + 0.758102i
\(983\) 378.134 + 742.129i 0.384673 + 0.754964i 0.999430 0.0337529i \(-0.0107459\pi\)
−0.614757 + 0.788717i \(0.710746\pi\)
\(984\) 762.254 + 1049.15i 0.774648 + 1.06621i
\(985\) −810.392 + 1102.11i −0.822733 + 1.11889i
\(986\) 990.361 + 719.540i 1.00442 + 0.729756i
\(987\) 1043.16 + 165.220i 1.05690 + 0.167396i
\(988\) 0.143799 0.907912i 0.000145546 0.000918940i
\(989\) −268.282 + 369.259i −0.271266 + 0.373366i
\(990\) −383.904 2.19430i −0.387782 0.00221647i
\(991\) −238.832 + 173.522i −0.241001 + 0.175098i −0.701729 0.712444i \(-0.747588\pi\)
0.460728 + 0.887541i \(0.347588\pi\)
\(992\) 0.264905 0.134976i 0.000267041 0.000136064i
\(993\) 948.303 948.303i 0.954988 0.954988i
\(994\) 771.132 + 250.556i 0.775786 + 0.252068i
\(995\) −160.654 + 978.111i −0.161461 + 0.983026i
\(996\) 0.519324 + 1.59831i 0.000521410 + 0.00160473i
\(997\) 410.202 805.068i 0.411437 0.807490i −0.588563 0.808451i \(-0.700306\pi\)
1.00000 0.000961470i \(0.000306045\pi\)
\(998\) −1122.42 + 177.774i −1.12467 + 0.178131i
\(999\) 363.067i 0.363431i
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 25.3.f.a.12.2 32
3.2 odd 2 225.3.r.a.37.3 32
4.3 odd 2 400.3.bg.c.337.4 32
5.2 odd 4 125.3.f.b.43.3 32
5.3 odd 4 125.3.f.a.43.2 32
5.4 even 2 125.3.f.c.82.3 32
25.2 odd 20 125.3.f.c.93.3 32
25.11 even 5 125.3.f.a.32.2 32
25.14 even 10 125.3.f.b.32.3 32
25.23 odd 20 inner 25.3.f.a.23.2 yes 32
75.23 even 20 225.3.r.a.73.3 32
100.23 even 20 400.3.bg.c.273.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.3.f.a.12.2 32 1.1 even 1 trivial
25.3.f.a.23.2 yes 32 25.23 odd 20 inner
125.3.f.a.32.2 32 25.11 even 5
125.3.f.a.43.2 32 5.3 odd 4
125.3.f.b.32.3 32 25.14 even 10
125.3.f.b.43.3 32 5.2 odd 4
125.3.f.c.82.3 32 5.4 even 2
125.3.f.c.93.3 32 25.2 odd 20
225.3.r.a.37.3 32 3.2 odd 2
225.3.r.a.73.3 32 75.23 even 20
400.3.bg.c.273.4 32 100.23 even 20
400.3.bg.c.337.4 32 4.3 odd 2