Properties

Label 429.2.be.a.89.13
Level $429$
Weight $2$
Character 429.89
Analytic conductor $3.426$
Analytic rank $0$
Dimension $184$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(89,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.be (of order \(12\), degree \(4\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(184\)
Relative dimension: \(46\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 89.13
Character \(\chi\) \(=\) 429.89
Dual form 429.2.be.a.188.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50551 - 0.403401i) q^{2} +(0.00525696 + 1.73204i) q^{3} +(0.371782 + 0.214648i) q^{4} +(-0.722785 + 0.722785i) q^{5} +(0.690793 - 2.60973i) q^{6} +(1.16889 + 4.36236i) q^{7} +(1.73109 + 1.73109i) q^{8} +(-2.99994 + 0.0182105i) q^{9} +O(q^{10})\) \(q+(-1.50551 - 0.403401i) q^{2} +(0.00525696 + 1.73204i) q^{3} +(0.371782 + 0.214648i) q^{4} +(-0.722785 + 0.722785i) q^{5} +(0.690793 - 2.60973i) q^{6} +(1.16889 + 4.36236i) q^{7} +(1.73109 + 1.73109i) q^{8} +(-2.99994 + 0.0182105i) q^{9} +(1.37973 - 0.796589i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(-0.369826 + 0.645070i) q^{12} +(-1.89064 - 3.07010i) q^{13} -7.03911i q^{14} +(-1.25569 - 1.24809i) q^{15} +(-2.33715 - 4.04806i) q^{16} +(0.404937 - 0.701372i) q^{17} +(4.52380 + 1.18276i) q^{18} +(2.03350 - 0.544876i) q^{19} +(-0.423863 + 0.113574i) q^{20} +(-7.54965 + 2.04750i) q^{21} +(0.779310 - 1.34980i) q^{22} +(2.19342 + 3.79912i) q^{23} +(-2.98922 + 3.00742i) q^{24} +3.95516i q^{25} +(1.60790 + 5.38475i) q^{26} +(-0.0473120 - 5.19594i) q^{27} +(-0.501801 + 1.87275i) q^{28} +(-6.01241 + 3.47127i) q^{29} +(1.38698 + 2.38557i) q^{30} +(-4.79999 - 4.79999i) q^{31} +(0.618369 + 2.30778i) q^{32} +(-1.67439 - 0.443208i) q^{33} +(-0.892572 + 0.892572i) q^{34} +(-3.99790 - 2.30819i) q^{35} +(-1.11923 - 0.637163i) q^{36} +(-0.702201 - 0.188154i) q^{37} -3.28127 q^{38} +(5.30760 - 3.29080i) q^{39} -2.50241 q^{40} +(-7.82744 - 2.09736i) q^{41} +(12.1920 - 0.0370043i) q^{42} +(-8.47216 - 4.89141i) q^{43} +(-0.303559 + 0.303559i) q^{44} +(2.15515 - 2.18148i) q^{45} +(-1.76966 - 6.60445i) q^{46} +(3.43483 + 3.43483i) q^{47} +(6.99913 - 4.06932i) q^{48} +(-11.6017 + 6.69824i) q^{49} +(1.59552 - 5.95454i) q^{50} +(1.21694 + 0.697682i) q^{51} +(-0.0439135 - 1.54723i) q^{52} -0.398917i q^{53} +(-2.02482 + 7.84163i) q^{54} +(-0.511086 - 0.885227i) q^{55} +(-5.52818 + 9.57509i) q^{56} +(0.954438 + 3.51925i) q^{57} +(10.4521 - 2.80062i) q^{58} +(9.09289 - 2.43643i) q^{59} +(-0.198943 - 0.733552i) q^{60} +(-0.865584 + 1.49924i) q^{61} +(5.29012 + 9.16276i) q^{62} +(-3.58605 - 13.0656i) q^{63} +5.62475i q^{64} +(3.58554 + 0.852495i) q^{65} +(2.34202 + 1.34270i) q^{66} +(-1.65798 + 6.18768i) q^{67} +(0.301097 - 0.173838i) q^{68} +(-6.56871 + 3.81908i) q^{69} +(5.08776 + 5.08776i) q^{70} +(2.03515 + 7.59530i) q^{71} +(-5.22470 - 5.16165i) q^{72} +(7.79914 - 7.79914i) q^{73} +(0.981270 + 0.566536i) q^{74} +(-6.85051 + 0.0207921i) q^{75} +(0.872976 + 0.233913i) q^{76} -4.51625 q^{77} +(-9.31816 + 2.81325i) q^{78} +2.80316 q^{79} +(4.61513 + 1.23662i) q^{80} +(8.99934 - 0.109261i) q^{81} +(10.9382 + 6.31519i) q^{82} +(7.49577 - 7.49577i) q^{83} +(-3.24631 - 0.859295i) q^{84} +(0.214259 + 0.799624i) q^{85} +(10.7817 + 10.7817i) q^{86} +(-6.04399 - 10.3955i) q^{87} +(-2.12014 + 1.22406i) q^{88} +(-3.27018 + 12.2045i) q^{89} +(-4.12462 + 2.41485i) q^{90} +(11.1829 - 11.8362i) q^{91} +1.88326i q^{92} +(8.28856 - 8.33903i) q^{93} +(-3.78557 - 6.55679i) q^{94} +(-1.07596 + 1.86361i) q^{95} +(-3.99393 + 1.08317i) q^{96} +(4.11504 - 1.10262i) q^{97} +(20.1686 - 5.40415i) q^{98} +(0.758853 - 2.90244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50551 0.403401i −1.06456 0.285247i −0.316302 0.948658i \(-0.602441\pi\)
−0.748255 + 0.663411i \(0.769108\pi\)
\(3\) 0.00525696 + 1.73204i 0.00303510 + 0.999995i
\(4\) 0.371782 + 0.214648i 0.185891 + 0.107324i
\(5\) −0.722785 + 0.722785i −0.323239 + 0.323239i −0.850008 0.526769i \(-0.823403\pi\)
0.526769 + 0.850008i \(0.323403\pi\)
\(6\) 0.690793 2.60973i 0.282015 1.06542i
\(7\) 1.16889 + 4.36236i 0.441799 + 1.64882i 0.724252 + 0.689536i \(0.242185\pi\)
−0.282453 + 0.959281i \(0.591148\pi\)
\(8\) 1.73109 + 1.73109i 0.612032 + 0.612032i
\(9\) −2.99994 + 0.0182105i −0.999982 + 0.00607018i
\(10\) 1.37973 0.796589i 0.436310 0.251904i
\(11\) −0.258819 + 0.965926i −0.0780369 + 0.291238i
\(12\) −0.369826 + 0.645070i −0.106759 + 0.186216i
\(13\) −1.89064 3.07010i −0.524368 0.851492i
\(14\) 7.03911i 1.88128i
\(15\) −1.25569 1.24809i −0.324219 0.322257i
\(16\) −2.33715 4.04806i −0.584287 1.01202i
\(17\) 0.404937 0.701372i 0.0982118 0.170108i −0.812733 0.582637i \(-0.802021\pi\)
0.910945 + 0.412529i \(0.135354\pi\)
\(18\) 4.52380 + 1.18276i 1.06627 + 0.278780i
\(19\) 2.03350 0.544876i 0.466518 0.125003i −0.0179001 0.999840i \(-0.505698\pi\)
0.484418 + 0.874837i \(0.339031\pi\)
\(20\) −0.423863 + 0.113574i −0.0947786 + 0.0253959i
\(21\) −7.54965 + 2.04750i −1.64747 + 0.446801i
\(22\) 0.779310 1.34980i 0.166149 0.287779i
\(23\) 2.19342 + 3.79912i 0.457361 + 0.792172i 0.998821 0.0485547i \(-0.0154615\pi\)
−0.541460 + 0.840727i \(0.682128\pi\)
\(24\) −2.98922 + 3.00742i −0.610172 + 0.613887i
\(25\) 3.95516i 0.791033i
\(26\) 1.60790 + 5.38475i 0.315335 + 1.05604i
\(27\) −0.0473120 5.19594i −0.00910520 0.999959i
\(28\) −0.501801 + 1.87275i −0.0948314 + 0.353916i
\(29\) −6.01241 + 3.47127i −1.11648 + 0.644598i −0.940499 0.339796i \(-0.889642\pi\)
−0.175978 + 0.984394i \(0.556309\pi\)
\(30\) 1.38698 + 2.38557i 0.253227 + 0.435543i
\(31\) −4.79999 4.79999i −0.862104 0.862104i 0.129478 0.991582i \(-0.458670\pi\)
−0.991582 + 0.129478i \(0.958670\pi\)
\(32\) 0.618369 + 2.30778i 0.109313 + 0.407963i
\(33\) −1.67439 0.443208i −0.291473 0.0771526i
\(34\) −0.892572 + 0.892572i −0.153075 + 0.153075i
\(35\) −3.99790 2.30819i −0.675769 0.390156i
\(36\) −1.11923 0.637163i −0.186539 0.106194i
\(37\) −0.702201 0.188154i −0.115441 0.0309324i 0.200636 0.979666i \(-0.435699\pi\)
−0.316077 + 0.948734i \(0.602366\pi\)
\(38\) −3.28127 −0.532292
\(39\) 5.30760 3.29080i 0.849896 0.526950i
\(40\) −2.50241 −0.395666
\(41\) −7.82744 2.09736i −1.22244 0.327552i −0.410809 0.911721i \(-0.634754\pi\)
−0.811632 + 0.584169i \(0.801420\pi\)
\(42\) 12.1920 0.0370043i 1.88127 0.00570989i
\(43\) −8.47216 4.89141i −1.29199 0.745933i −0.312986 0.949758i \(-0.601329\pi\)
−0.979007 + 0.203825i \(0.934663\pi\)
\(44\) −0.303559 + 0.303559i −0.0457632 + 0.0457632i
\(45\) 2.15515 2.18148i 0.321271 0.325195i
\(46\) −1.76966 6.60445i −0.260922 0.973773i
\(47\) 3.43483 + 3.43483i 0.501022 + 0.501022i 0.911755 0.410733i \(-0.134727\pi\)
−0.410733 + 0.911755i \(0.634727\pi\)
\(48\) 6.99913 4.06932i 1.01024 0.587356i
\(49\) −11.6017 + 6.69824i −1.65738 + 0.956892i
\(50\) 1.59552 5.95454i 0.225640 0.842100i
\(51\) 1.21694 + 0.697682i 0.170405 + 0.0976950i
\(52\) −0.0439135 1.54723i −0.00608970 0.214562i
\(53\) 0.398917i 0.0547954i −0.999625 0.0273977i \(-0.991278\pi\)
0.999625 0.0273977i \(-0.00872206\pi\)
\(54\) −2.02482 + 7.84163i −0.275542 + 1.06711i
\(55\) −0.511086 0.885227i −0.0689148 0.119364i
\(56\) −5.52818 + 9.57509i −0.738734 + 1.27952i
\(57\) 0.954438 + 3.51925i 0.126418 + 0.466136i
\(58\) 10.4521 2.80062i 1.37242 0.367740i
\(59\) 9.09289 2.43643i 1.18379 0.317197i 0.387364 0.921927i \(-0.373386\pi\)
0.796430 + 0.604730i \(0.206719\pi\)
\(60\) −0.198943 0.733552i −0.0256834 0.0947011i
\(61\) −0.865584 + 1.49924i −0.110827 + 0.191957i −0.916104 0.400941i \(-0.868683\pi\)
0.805277 + 0.592899i \(0.202017\pi\)
\(62\) 5.29012 + 9.16276i 0.671846 + 1.16367i
\(63\) −3.58605 13.0656i −0.451800 1.64610i
\(64\) 5.62475i 0.703094i
\(65\) 3.58554 + 0.852495i 0.444732 + 0.105739i
\(66\) 2.34202 + 1.34270i 0.288282 + 0.165275i
\(67\) −1.65798 + 6.18768i −0.202555 + 0.755946i 0.787626 + 0.616154i \(0.211310\pi\)
−0.990181 + 0.139792i \(0.955357\pi\)
\(68\) 0.301097 0.173838i 0.0365133 0.0210810i
\(69\) −6.56871 + 3.81908i −0.790780 + 0.459763i
\(70\) 5.08776 + 5.08776i 0.608104 + 0.608104i
\(71\) 2.03515 + 7.59530i 0.241528 + 0.901396i 0.975097 + 0.221780i \(0.0711868\pi\)
−0.733568 + 0.679616i \(0.762147\pi\)
\(72\) −5.22470 5.16165i −0.615736 0.608306i
\(73\) 7.79914 7.79914i 0.912820 0.912820i −0.0836728 0.996493i \(-0.526665\pi\)
0.996493 + 0.0836728i \(0.0266651\pi\)
\(74\) 0.981270 + 0.566536i 0.114070 + 0.0658585i
\(75\) −6.85051 + 0.0207921i −0.791029 + 0.00240087i
\(76\) 0.872976 + 0.233913i 0.100137 + 0.0268317i
\(77\) −4.51625 −0.514674
\(78\) −9.31816 + 2.81325i −1.05507 + 0.318538i
\(79\) 2.80316 0.315380 0.157690 0.987489i \(-0.449595\pi\)
0.157690 + 0.987489i \(0.449595\pi\)
\(80\) 4.61513 + 1.23662i 0.515988 + 0.138258i
\(81\) 8.99934 0.109261i 0.999926 0.0121401i
\(82\) 10.9382 + 6.31519i 1.20793 + 0.697396i
\(83\) 7.49577 7.49577i 0.822768 0.822768i −0.163736 0.986504i \(-0.552355\pi\)
0.986504 + 0.163736i \(0.0523545\pi\)
\(84\) −3.24631 0.859295i −0.354202 0.0937568i
\(85\) 0.214259 + 0.799624i 0.0232396 + 0.0867314i
\(86\) 10.7817 + 10.7817i 1.16263 + 1.16263i
\(87\) −6.04399 10.3955i −0.647984 1.11452i
\(88\) −2.12014 + 1.22406i −0.226008 + 0.130486i
\(89\) −3.27018 + 12.2045i −0.346638 + 1.29367i 0.544048 + 0.839054i \(0.316891\pi\)
−0.890687 + 0.454618i \(0.849776\pi\)
\(90\) −4.12462 + 2.41485i −0.434773 + 0.254547i
\(91\) 11.1829 11.8362i 1.17229 1.24078i
\(92\) 1.88326i 0.196343i
\(93\) 8.28856 8.33903i 0.859484 0.864717i
\(94\) −3.78557 6.55679i −0.390451 0.676282i
\(95\) −1.07596 + 1.86361i −0.110391 + 0.191203i
\(96\) −3.99393 + 1.08317i −0.407629 + 0.110551i
\(97\) 4.11504 1.10262i 0.417819 0.111954i −0.0437835 0.999041i \(-0.513941\pi\)
0.461603 + 0.887087i \(0.347275\pi\)
\(98\) 20.1686 5.40415i 2.03733 0.545901i
\(99\) 0.758853 2.90244i 0.0762676 0.291706i
\(100\) −0.848969 + 1.47046i −0.0848969 + 0.147046i
\(101\) −4.45621 7.71838i −0.443409 0.768008i 0.554530 0.832163i \(-0.312898\pi\)
−0.997940 + 0.0641557i \(0.979565\pi\)
\(102\) −1.55067 1.54128i −0.153539 0.152610i
\(103\) 8.53582i 0.841059i 0.907279 + 0.420530i \(0.138156\pi\)
−0.907279 + 0.420530i \(0.861844\pi\)
\(104\) 2.04175 8.58747i 0.200210 0.842071i
\(105\) 3.97687 6.93668i 0.388103 0.676950i
\(106\) −0.160923 + 0.600574i −0.0156303 + 0.0583329i
\(107\) −11.0916 + 6.40373i −1.07226 + 0.619072i −0.928799 0.370583i \(-0.879158\pi\)
−0.143465 + 0.989655i \(0.545824\pi\)
\(108\) 1.09771 1.94191i 0.105627 0.186860i
\(109\) 11.8317 + 11.8317i 1.13327 + 1.13327i 0.989630 + 0.143639i \(0.0458805\pi\)
0.143639 + 0.989630i \(0.454120\pi\)
\(110\) 0.412345 + 1.53889i 0.0393155 + 0.146728i
\(111\) 0.322200 1.21723i 0.0305818 0.115534i
\(112\) 14.9272 14.9272i 1.41049 1.41049i
\(113\) 4.03931 + 2.33210i 0.379986 + 0.219385i 0.677812 0.735235i \(-0.262928\pi\)
−0.297826 + 0.954620i \(0.596262\pi\)
\(114\) −0.0172495 5.68329i −0.00161556 0.532289i
\(115\) −4.33132 1.16057i −0.403898 0.108224i
\(116\) −2.98041 −0.276724
\(117\) 5.72772 + 9.17569i 0.529527 + 0.848293i
\(118\) −14.6723 −1.35070
\(119\) 3.53297 + 0.946655i 0.323866 + 0.0867797i
\(120\) −0.0131551 4.33428i −0.00120089 0.395664i
\(121\) −0.866025 0.500000i −0.0787296 0.0454545i
\(122\) 1.90794 1.90794i 0.172737 0.172737i
\(123\) 3.59156 13.5685i 0.323840 1.22343i
\(124\) −0.754239 2.81486i −0.0677327 0.252782i
\(125\) −6.47266 6.47266i −0.578932 0.578932i
\(126\) 0.128186 + 21.1169i 0.0114197 + 1.88125i
\(127\) −9.62330 + 5.55602i −0.853930 + 0.493017i −0.861975 0.506951i \(-0.830773\pi\)
0.00804484 + 0.999968i \(0.497439\pi\)
\(128\) 3.50576 13.0837i 0.309869 1.15645i
\(129\) 8.42759 14.6999i 0.742008 1.29425i
\(130\) −5.05418 2.72985i −0.443281 0.239424i
\(131\) 5.82057i 0.508546i −0.967133 0.254273i \(-0.918164\pi\)
0.967133 0.254273i \(-0.0818361\pi\)
\(132\) −0.527372 0.524181i −0.0459019 0.0456241i
\(133\) 4.75389 + 8.23397i 0.412214 + 0.713976i
\(134\) 4.99223 8.64680i 0.431263 0.746969i
\(135\) 3.78974 + 3.72135i 0.326169 + 0.320283i
\(136\) 1.91512 0.513155i 0.164220 0.0440027i
\(137\) 14.8431 3.97720i 1.26813 0.339795i 0.438818 0.898576i \(-0.355397\pi\)
0.829315 + 0.558781i \(0.188731\pi\)
\(138\) 11.4299 3.09984i 0.972977 0.263876i
\(139\) −6.55271 + 11.3496i −0.555793 + 0.962662i 0.442048 + 0.896991i \(0.354252\pi\)
−0.997841 + 0.0656709i \(0.979081\pi\)
\(140\) −0.990899 1.71629i −0.0837462 0.145053i
\(141\) −5.93122 + 5.96734i −0.499499 + 0.502540i
\(142\) 12.2558i 1.02848i
\(143\) 3.45482 1.03162i 0.288906 0.0862681i
\(144\) 7.08503 + 12.1014i 0.590420 + 1.00845i
\(145\) 1.83670 6.85466i 0.152530 0.569249i
\(146\) −14.8879 + 8.59552i −1.23213 + 0.711370i
\(147\) −11.6626 20.0594i −0.961918 1.65447i
\(148\) −0.220679 0.220679i −0.0181397 0.0181397i
\(149\) −3.46544 12.9332i −0.283900 1.05953i −0.949640 0.313344i \(-0.898551\pi\)
0.665740 0.746184i \(-0.268116\pi\)
\(150\) 10.3219 + 2.73220i 0.842781 + 0.223083i
\(151\) 8.63945 8.63945i 0.703069 0.703069i −0.261999 0.965068i \(-0.584382\pi\)
0.965068 + 0.261999i \(0.0843818\pi\)
\(152\) 4.46341 + 2.57695i 0.362030 + 0.209018i
\(153\) −1.20202 + 2.11145i −0.0971774 + 0.170701i
\(154\) 6.79926 + 1.82186i 0.547900 + 0.146809i
\(155\) 6.93872 0.557332
\(156\) 2.67963 0.0841937i 0.214542 0.00674089i
\(157\) 5.04318 0.402490 0.201245 0.979541i \(-0.435501\pi\)
0.201245 + 0.979541i \(0.435501\pi\)
\(158\) −4.22019 1.13080i −0.335741 0.0899614i
\(159\) 0.690941 0.00209709i 0.0547952 0.000166310i
\(160\) −2.11498 1.22108i −0.167204 0.0965352i
\(161\) −14.0093 + 14.0093i −1.10408 + 1.10408i
\(162\) −13.5927 3.46584i −1.06794 0.272302i
\(163\) 1.78888 + 6.67618i 0.140116 + 0.522919i 0.999924 + 0.0123023i \(0.00391606\pi\)
−0.859809 + 0.510616i \(0.829417\pi\)
\(164\) −2.45991 2.45991i −0.192086 0.192086i
\(165\) 1.53056 0.889877i 0.119154 0.0692768i
\(166\) −14.3088 + 8.26117i −1.11058 + 0.641191i
\(167\) −6.43757 + 24.0254i −0.498154 + 1.85914i 0.0134389 + 0.999910i \(0.495722\pi\)
−0.511593 + 0.859228i \(0.670945\pi\)
\(168\) −16.6135 9.52471i −1.28176 0.734847i
\(169\) −5.85098 + 11.6089i −0.450076 + 0.892990i
\(170\) 1.29028i 0.0989596i
\(171\) −6.09048 + 1.67163i −0.465750 + 0.127833i
\(172\) −2.09986 3.63707i −0.160113 0.277324i
\(173\) −2.16899 + 3.75679i −0.164905 + 0.285624i −0.936622 0.350343i \(-0.886065\pi\)
0.771717 + 0.635967i \(0.219398\pi\)
\(174\) 4.90575 + 18.0887i 0.371904 + 1.37130i
\(175\) −17.2538 + 4.62315i −1.30427 + 0.349478i
\(176\) 4.51502 1.20980i 0.340333 0.0911919i
\(177\) 4.26781 + 15.7365i 0.320788 + 1.18283i
\(178\) 9.84659 17.0548i 0.738033 1.27831i
\(179\) 0.747073 + 1.29397i 0.0558388 + 0.0967157i 0.892594 0.450862i \(-0.148883\pi\)
−0.836755 + 0.547578i \(0.815550\pi\)
\(180\) 1.26950 0.348434i 0.0946227 0.0259707i
\(181\) 20.4957i 1.52344i 0.647908 + 0.761719i \(0.275644\pi\)
−0.647908 + 0.761719i \(0.724356\pi\)
\(182\) −21.6108 + 13.3084i −1.60190 + 0.986485i
\(183\) −2.60129 1.49135i −0.192293 0.110244i
\(184\) −2.77961 + 10.3736i −0.204915 + 0.764755i
\(185\) 0.643535 0.371545i 0.0473137 0.0273166i
\(186\) −15.8425 + 9.21089i −1.16163 + 0.675375i
\(187\) 0.572668 + 0.572668i 0.0418776 + 0.0418776i
\(188\) 0.539727 + 2.01429i 0.0393637 + 0.146907i
\(189\) 22.6112 6.27987i 1.64473 0.456794i
\(190\) 2.37165 2.37165i 0.172058 0.172058i
\(191\) −17.1541 9.90393i −1.24123 0.716624i −0.271884 0.962330i \(-0.587647\pi\)
−0.969344 + 0.245707i \(0.920980\pi\)
\(192\) −9.74231 + 0.0295691i −0.703090 + 0.00213396i
\(193\) −17.0048 4.55643i −1.22403 0.327979i −0.411780 0.911283i \(-0.635093\pi\)
−0.812254 + 0.583304i \(0.801760\pi\)
\(194\) −6.64004 −0.476727
\(195\) −1.45771 + 6.21480i −0.104389 + 0.445051i
\(196\) −5.75106 −0.410790
\(197\) 14.5311 + 3.89359i 1.03530 + 0.277407i 0.736162 0.676805i \(-0.236636\pi\)
0.299133 + 0.954211i \(0.403303\pi\)
\(198\) −2.31331 + 4.06353i −0.164400 + 0.288783i
\(199\) 15.1371 + 8.73940i 1.07304 + 0.619520i 0.929010 0.370053i \(-0.120661\pi\)
0.144030 + 0.989573i \(0.453994\pi\)
\(200\) −6.84674 + 6.84674i −0.484138 + 0.484138i
\(201\) −10.7260 2.83917i −0.756557 0.200260i
\(202\) 3.59528 + 13.4178i 0.252963 + 0.944070i
\(203\) −22.1708 22.1708i −1.55608 1.55608i
\(204\) 0.302678 + 0.520599i 0.0211917 + 0.0364492i
\(205\) 7.17350 4.14162i 0.501019 0.289263i
\(206\) 3.44335 12.8508i 0.239910 0.895356i
\(207\) −6.64934 11.3572i −0.462161 0.789381i
\(208\) −8.00924 + 14.8287i −0.555341 + 1.02818i
\(209\) 2.10524i 0.145622i
\(210\) −8.78548 + 8.83897i −0.606256 + 0.609947i
\(211\) 5.99424 + 10.3823i 0.412661 + 0.714749i 0.995180 0.0980679i \(-0.0312662\pi\)
−0.582519 + 0.812817i \(0.697933\pi\)
\(212\) 0.0856268 0.148310i 0.00588087 0.0101860i
\(213\) −13.1447 + 3.56490i −0.900659 + 0.244263i
\(214\) 19.2818 5.16654i 1.31808 0.353177i
\(215\) 9.65899 2.58812i 0.658738 0.176508i
\(216\) 8.91273 9.07653i 0.606434 0.617580i
\(217\) 15.3286 26.5500i 1.04057 1.80233i
\(218\) −13.0398 22.5856i −0.883168 1.52969i
\(219\) 13.5494 + 13.4674i 0.915587 + 0.910046i
\(220\) 0.438815i 0.0295849i
\(221\) −2.91887 + 0.0828435i −0.196344 + 0.00557265i
\(222\) −0.976107 + 1.70258i −0.0655120 + 0.114270i
\(223\) 4.32068 16.1250i 0.289334 1.07981i −0.656280 0.754518i \(-0.727871\pi\)
0.945614 0.325292i \(-0.105462\pi\)
\(224\) −9.34458 + 5.39510i −0.624361 + 0.360475i
\(225\) −0.0720257 11.8653i −0.00480171 0.791018i
\(226\) −5.14046 5.14046i −0.341938 0.341938i
\(227\) 0.716073 + 2.67242i 0.0475274 + 0.177375i 0.985609 0.169038i \(-0.0540662\pi\)
−0.938082 + 0.346413i \(0.887400\pi\)
\(228\) −0.400559 + 1.51326i −0.0265276 + 0.100218i
\(229\) −12.0728 + 12.0728i −0.797790 + 0.797790i −0.982747 0.184957i \(-0.940786\pi\)
0.184957 + 0.982747i \(0.440786\pi\)
\(230\) 6.05268 + 3.49452i 0.399102 + 0.230422i
\(231\) −0.0237417 7.82233i −0.00156209 0.514672i
\(232\) −16.4171 4.39895i −1.07784 0.288805i
\(233\) −27.4881 −1.80081 −0.900404 0.435055i \(-0.856729\pi\)
−0.900404 + 0.435055i \(0.856729\pi\)
\(234\) −4.92166 16.1247i −0.321739 1.05410i
\(235\) −4.96529 −0.323900
\(236\) 3.90355 + 1.04595i 0.254099 + 0.0680857i
\(237\) 0.0147361 + 4.85520i 0.000957212 + 0.315379i
\(238\) −4.93704 2.85040i −0.320021 0.184764i
\(239\) −0.543789 + 0.543789i −0.0351748 + 0.0351748i −0.724475 0.689301i \(-0.757918\pi\)
0.689301 + 0.724475i \(0.257918\pi\)
\(240\) −2.11762 + 8.00011i −0.136692 + 0.516405i
\(241\) 4.08323 + 15.2388i 0.263024 + 0.981619i 0.963449 + 0.267893i \(0.0863273\pi\)
−0.700425 + 0.713726i \(0.747006\pi\)
\(242\) 1.10211 + 1.10211i 0.0708464 + 0.0708464i
\(243\) 0.236554 + 15.5867i 0.0151750 + 0.999885i
\(244\) −0.643617 + 0.371592i −0.0412033 + 0.0237888i
\(245\) 3.54414 13.2269i 0.226427 0.845037i
\(246\) −10.8807 + 18.9787i −0.693727 + 1.21004i
\(247\) −5.51744 5.21289i −0.351066 0.331688i
\(248\) 16.6184i 1.05527i
\(249\) 13.0224 + 12.9436i 0.825262 + 0.820267i
\(250\) 7.13359 + 12.3557i 0.451168 + 0.781445i
\(251\) 9.48111 16.4218i 0.598443 1.03653i −0.394609 0.918849i \(-0.629120\pi\)
0.993051 0.117684i \(-0.0375469\pi\)
\(252\) 1.47127 5.62727i 0.0926813 0.354485i
\(253\) −4.23737 + 1.13540i −0.266401 + 0.0713820i
\(254\) 16.7293 4.48260i 1.04969 0.281263i
\(255\) −1.38386 + 0.375309i −0.0866605 + 0.0235027i
\(256\) −4.93119 + 8.54107i −0.308199 + 0.533817i
\(257\) 11.4432 + 19.8202i 0.713807 + 1.23635i 0.963418 + 0.268003i \(0.0863638\pi\)
−0.249611 + 0.968346i \(0.580303\pi\)
\(258\) −18.6178 + 18.7311i −1.15909 + 1.16615i
\(259\) 3.28318i 0.204007i
\(260\) 1.15005 + 1.08657i 0.0713233 + 0.0673864i
\(261\) 17.9737 10.5231i 1.11254 0.651364i
\(262\) −2.34802 + 8.76294i −0.145061 + 0.541376i
\(263\) 4.36016 2.51734i 0.268859 0.155226i −0.359510 0.933141i \(-0.617056\pi\)
0.628369 + 0.777915i \(0.283723\pi\)
\(264\) −2.13128 3.66574i −0.131171 0.225611i
\(265\) 0.288331 + 0.288331i 0.0177120 + 0.0177120i
\(266\) −3.83544 14.3141i −0.235166 0.877652i
\(267\) −21.1559 5.59993i −1.29472 0.342710i
\(268\) −1.94458 + 1.94458i −0.118784 + 0.118784i
\(269\) 23.6873 + 13.6759i 1.44424 + 0.833834i 0.998129 0.0611419i \(-0.0194742\pi\)
0.446114 + 0.894976i \(0.352808\pi\)
\(270\) −4.20430 7.13132i −0.255866 0.433998i
\(271\) −9.98415 2.67525i −0.606494 0.162510i −0.0575135 0.998345i \(-0.518317\pi\)
−0.548981 + 0.835835i \(0.684984\pi\)
\(272\) −3.78560 −0.229536
\(273\) 20.5597 + 19.3071i 1.24433 + 1.16852i
\(274\) −23.9509 −1.44693
\(275\) −3.82039 1.02367i −0.230378 0.0617297i
\(276\) −3.26189 + 0.00990021i −0.196342 + 0.000595923i
\(277\) 17.4479 + 10.0736i 1.04834 + 0.605262i 0.922185 0.386748i \(-0.126402\pi\)
0.126159 + 0.992010i \(0.459735\pi\)
\(278\) 14.4436 14.4436i 0.866271 0.866271i
\(279\) 14.4871 + 14.3123i 0.867321 + 0.856855i
\(280\) −2.92504 10.9164i −0.174805 0.652381i
\(281\) 10.6385 + 10.6385i 0.634639 + 0.634639i 0.949228 0.314589i \(-0.101867\pi\)
−0.314589 + 0.949228i \(0.601867\pi\)
\(282\) 11.3367 6.59123i 0.675094 0.392502i
\(283\) −1.40406 + 0.810632i −0.0834624 + 0.0481871i −0.541150 0.840926i \(-0.682011\pi\)
0.457688 + 0.889113i \(0.348678\pi\)
\(284\) −0.873685 + 3.26064i −0.0518437 + 0.193483i
\(285\) −3.23352 1.85381i −0.191537 0.109810i
\(286\) −5.61742 + 0.159434i −0.332165 + 0.00942752i
\(287\) 36.5977i 2.16029i
\(288\) −1.89710 6.91197i −0.111788 0.407291i
\(289\) 8.17205 + 14.1544i 0.480709 + 0.832612i
\(290\) −5.53035 + 9.57885i −0.324753 + 0.562489i
\(291\) 1.93142 + 7.12164i 0.113222 + 0.417478i
\(292\) 4.57365 1.22551i 0.267653 0.0717173i
\(293\) −19.4523 + 5.21222i −1.13641 + 0.304501i −0.777509 0.628872i \(-0.783517\pi\)
−0.358906 + 0.933374i \(0.616850\pi\)
\(294\) 9.46624 + 34.9044i 0.552082 + 2.03567i
\(295\) −4.81119 + 8.33322i −0.280118 + 0.485179i
\(296\) −0.889861 1.54128i −0.0517221 0.0895853i
\(297\) 5.03114 + 1.29911i 0.291936 + 0.0753819i
\(298\) 20.8690i 1.20891i
\(299\) 7.51670 13.9168i 0.434702 0.804829i
\(300\) −2.55136 1.46272i −0.147303 0.0844502i
\(301\) 11.4350 42.6761i 0.659105 2.45981i
\(302\) −16.4920 + 9.52164i −0.949005 + 0.547909i
\(303\) 13.3451 7.75892i 0.766658 0.445738i
\(304\) −6.95829 6.95829i −0.399085 0.399085i
\(305\) −0.457994 1.70926i −0.0262247 0.0978717i
\(306\) 2.66141 2.69392i 0.152143 0.154001i
\(307\) 8.39109 8.39109i 0.478905 0.478905i −0.425876 0.904781i \(-0.640034\pi\)
0.904781 + 0.425876i \(0.140034\pi\)
\(308\) −1.67906 0.969405i −0.0956732 0.0552370i
\(309\) −14.7844 + 0.0448724i −0.841055 + 0.00255270i
\(310\) −10.4463 2.79909i −0.593312 0.158977i
\(311\) −3.94294 −0.223584 −0.111792 0.993732i \(-0.535659\pi\)
−0.111792 + 0.993732i \(0.535659\pi\)
\(312\) 14.8846 + 3.49125i 0.842675 + 0.197653i
\(313\) −4.72509 −0.267078 −0.133539 0.991044i \(-0.542634\pi\)
−0.133539 + 0.991044i \(0.542634\pi\)
\(314\) −7.59257 2.03442i −0.428474 0.114809i
\(315\) 12.0355 + 6.85164i 0.678125 + 0.386046i
\(316\) 1.04216 + 0.601694i 0.0586263 + 0.0338479i
\(317\) −8.92744 + 8.92744i −0.501415 + 0.501415i −0.911878 0.410462i \(-0.865367\pi\)
0.410462 + 0.911878i \(0.365367\pi\)
\(318\) −1.04107 0.275569i −0.0583801 0.0154531i
\(319\) −1.79686 6.70598i −0.100605 0.375463i
\(320\) −4.06548 4.06548i −0.227267 0.227267i
\(321\) −11.1498 19.1774i −0.622324 1.07038i
\(322\) 26.7425 15.4398i 1.49030 0.860424i
\(323\) 0.441281 1.64688i 0.0245535 0.0916351i
\(324\) 3.36924 + 1.89107i 0.187180 + 0.105059i
\(325\) 12.1427 7.47778i 0.673558 0.414793i
\(326\) 10.7727i 0.596644i
\(327\) −20.4308 + 20.5552i −1.12982 + 1.13670i
\(328\) −9.91929 17.1807i −0.547701 0.948646i
\(329\) −10.9690 + 18.9989i −0.604742 + 1.04744i
\(330\) −2.66326 + 0.722289i −0.146608 + 0.0397607i
\(331\) −1.38854 + 0.372059i −0.0763212 + 0.0204502i −0.296778 0.954947i \(-0.595912\pi\)
0.220456 + 0.975397i \(0.429245\pi\)
\(332\) 4.39575 1.17784i 0.241248 0.0646422i
\(333\) 2.10999 + 0.551665i 0.115627 + 0.0302310i
\(334\) 19.3837 33.5735i 1.06063 1.83706i
\(335\) −3.27400 5.67073i −0.178878 0.309825i
\(336\) 25.9331 + 25.7761i 1.41476 + 1.40620i
\(337\) 4.60938i 0.251089i −0.992088 0.125544i \(-0.959932\pi\)
0.992088 0.125544i \(-0.0400678\pi\)
\(338\) 13.4917 15.1170i 0.733854 0.822257i
\(339\) −4.01805 + 7.00851i −0.218231 + 0.380650i
\(340\) −0.0919805 + 0.343276i −0.00498834 + 0.0186167i
\(341\) 5.87877 3.39411i 0.318353 0.183801i
\(342\) 9.84362 0.0597536i 0.532282 0.00323111i
\(343\) −20.4270 20.4270i −1.10295 1.10295i
\(344\) −6.19861 23.1335i −0.334207 1.24728i
\(345\) 1.98740 7.50814i 0.106998 0.404225i
\(346\) 4.78092 4.78092i 0.257024 0.257024i
\(347\) −6.58151 3.79984i −0.353314 0.203986i 0.312830 0.949809i \(-0.398723\pi\)
−0.666144 + 0.745823i \(0.732056\pi\)
\(348\) −0.0156679 5.16219i −0.000839886 0.276723i
\(349\) 24.6650 + 6.60896i 1.32029 + 0.353769i 0.849085 0.528257i \(-0.177154\pi\)
0.471201 + 0.882026i \(0.343821\pi\)
\(350\) 27.8408 1.48816
\(351\) −15.8626 + 9.96888i −0.846682 + 0.532100i
\(352\) −2.38919 −0.127344
\(353\) 5.98040 + 1.60244i 0.318304 + 0.0852894i 0.414434 0.910079i \(-0.363980\pi\)
−0.0961295 + 0.995369i \(0.530646\pi\)
\(354\) −0.0771317 25.4131i −0.00409950 1.35069i
\(355\) −6.96075 4.01879i −0.369438 0.213295i
\(356\) −3.83546 + 3.83546i −0.203279 + 0.203279i
\(357\) −1.62107 + 6.12422i −0.0857964 + 0.324128i
\(358\) −0.602739 2.24945i −0.0318558 0.118887i
\(359\) 11.0013 + 11.0013i 0.580627 + 0.580627i 0.935076 0.354448i \(-0.115331\pi\)
−0.354448 + 0.935076i \(0.615331\pi\)
\(360\) 7.50709 0.0455703i 0.395659 0.00240176i
\(361\) −12.6162 + 7.28399i −0.664012 + 0.383368i
\(362\) 8.26800 30.8566i 0.434556 1.62179i
\(363\) 0.861469 1.50262i 0.0452154 0.0788672i
\(364\) 6.69823 2.00011i 0.351083 0.104834i
\(365\) 11.2742i 0.590119i
\(366\) 3.31466 + 3.29460i 0.173260 + 0.172212i
\(367\) −5.37126 9.30330i −0.280378 0.485628i 0.691100 0.722759i \(-0.257126\pi\)
−0.971478 + 0.237131i \(0.923793\pi\)
\(368\) 10.2527 17.7582i 0.534460 0.925712i
\(369\) 23.5201 + 6.14941i 1.22441 + 0.320126i
\(370\) −1.11873 + 0.299763i −0.0581601 + 0.0155839i
\(371\) 1.74022 0.466290i 0.0903476 0.0242086i
\(372\) 4.87149 1.32117i 0.252575 0.0684996i
\(373\) 11.4605 19.8501i 0.593400 1.02780i −0.400370 0.916353i \(-0.631118\pi\)
0.993771 0.111446i \(-0.0355482\pi\)
\(374\) −0.631144 1.09317i −0.0326357 0.0565266i
\(375\) 11.1769 11.2449i 0.577172 0.580687i
\(376\) 11.8920i 0.613283i
\(377\) 22.0244 + 11.8958i 1.13432 + 0.612664i
\(378\) −36.5748 + 0.333035i −1.88120 + 0.0171295i
\(379\) −1.97646 + 7.37626i −0.101524 + 0.378893i −0.997928 0.0643457i \(-0.979504\pi\)
0.896404 + 0.443239i \(0.146171\pi\)
\(380\) −0.800043 + 0.461905i −0.0410413 + 0.0236952i
\(381\) −9.67385 16.6388i −0.495606 0.852430i
\(382\) 21.8305 + 21.8305i 1.11694 + 1.11694i
\(383\) 8.44711 + 31.5251i 0.431627 + 1.61085i 0.749011 + 0.662558i \(0.230529\pi\)
−0.317384 + 0.948297i \(0.602804\pi\)
\(384\) 22.6799 + 6.00335i 1.15738 + 0.306357i
\(385\) 3.26428 3.26428i 0.166363 0.166363i
\(386\) 23.7629 + 13.7195i 1.20950 + 0.698305i
\(387\) 25.5051 + 14.5197i 1.29650 + 0.738076i
\(388\) 1.76657 + 0.473352i 0.0896842 + 0.0240308i
\(389\) −14.9885 −0.759946 −0.379973 0.924998i \(-0.624067\pi\)
−0.379973 + 0.924998i \(0.624067\pi\)
\(390\) 4.70165 8.76841i 0.238077 0.444006i
\(391\) 3.55280 0.179673
\(392\) −31.6788 8.48832i −1.60002 0.428725i
\(393\) 10.0815 0.0305985i 0.508543 0.00154349i
\(394\) −20.3060 11.7237i −1.02300 0.590630i
\(395\) −2.02608 + 2.02608i −0.101943 + 0.101943i
\(396\) 0.905131 0.916187i 0.0454845 0.0460401i
\(397\) −9.39379 35.0581i −0.471461 1.75952i −0.634526 0.772901i \(-0.718805\pi\)
0.163065 0.986615i \(-0.447862\pi\)
\(398\) −19.2636 19.2636i −0.965596 0.965596i
\(399\) −14.2366 + 8.27722i −0.712722 + 0.414379i
\(400\) 16.0107 9.24381i 0.800537 0.462190i
\(401\) −5.09693 + 19.0220i −0.254529 + 0.949914i 0.713824 + 0.700326i \(0.246962\pi\)
−0.968352 + 0.249588i \(0.919705\pi\)
\(402\) 15.0029 + 8.60130i 0.748275 + 0.428994i
\(403\) −5.66139 + 23.8115i −0.282014 + 1.18613i
\(404\) 3.82607i 0.190354i
\(405\) −6.42561 + 6.58356i −0.319291 + 0.327140i
\(406\) 24.4346 + 42.3221i 1.21267 + 2.10041i
\(407\) 0.363486 0.629576i 0.0180173 0.0312069i
\(408\) 0.898874 + 3.31437i 0.0445009 + 0.164086i
\(409\) −21.5721 + 5.78021i −1.06667 + 0.285813i −0.749124 0.662430i \(-0.769525\pi\)
−0.317545 + 0.948243i \(0.602859\pi\)
\(410\) −12.4705 + 3.34146i −0.615875 + 0.165023i
\(411\) 6.96671 + 25.6880i 0.343643 + 1.26710i
\(412\) −1.83220 + 3.17346i −0.0902660 + 0.156345i
\(413\) 21.2572 + 36.8185i 1.04600 + 1.81172i
\(414\) 5.42915 + 19.7808i 0.266828 + 0.972172i
\(415\) 10.8357i 0.531902i
\(416\) 5.91601 6.26164i 0.290056 0.307002i
\(417\) −19.6925 11.2899i −0.964345 0.552869i
\(418\) 0.849254 3.16946i 0.0415384 0.155023i
\(419\) 10.5327 6.08107i 0.514557 0.297079i −0.220148 0.975466i \(-0.570654\pi\)
0.734705 + 0.678387i \(0.237321\pi\)
\(420\) 2.96747 1.72530i 0.144798 0.0841861i
\(421\) −9.51904 9.51904i −0.463930 0.463930i 0.436012 0.899941i \(-0.356391\pi\)
−0.899941 + 0.436012i \(0.856391\pi\)
\(422\) −4.83616 18.0488i −0.235421 0.878602i
\(423\) −10.3669 10.2418i −0.504054 0.497971i
\(424\) 0.690561 0.690561i 0.0335366 0.0335366i
\(425\) 2.77404 + 1.60159i 0.134561 + 0.0776887i
\(426\) 21.2276 0.0644282i 1.02848 0.00312155i
\(427\) −7.55198 2.02355i −0.365466 0.0979263i
\(428\) −5.49820 −0.265766
\(429\) 1.80496 + 5.97847i 0.0871445 + 0.288643i
\(430\) −15.5858 −0.751612
\(431\) 0.337862 + 0.0905298i 0.0162742 + 0.00436067i 0.266947 0.963711i \(-0.413985\pi\)
−0.250673 + 0.968072i \(0.580652\pi\)
\(432\) −20.9229 + 12.3352i −1.00665 + 0.593478i
\(433\) −9.19071 5.30626i −0.441677 0.255003i 0.262631 0.964896i \(-0.415410\pi\)
−0.704309 + 0.709894i \(0.748743\pi\)
\(434\) −33.7877 + 33.7877i −1.62186 + 1.62186i
\(435\) 11.8822 + 3.14521i 0.569709 + 0.150801i
\(436\) 1.85915 + 6.93845i 0.0890373 + 0.332292i
\(437\) 6.53039 + 6.53039i 0.312391 + 0.312391i
\(438\) −14.9661 25.7412i −0.715107 1.22996i
\(439\) −11.4072 + 6.58593i −0.544434 + 0.314329i −0.746874 0.664965i \(-0.768446\pi\)
0.202440 + 0.979295i \(0.435113\pi\)
\(440\) 0.647672 2.41714i 0.0308765 0.115233i
\(441\) 34.6825 20.3056i 1.65155 0.966935i
\(442\) 4.42781 + 1.05275i 0.210610 + 0.0500743i
\(443\) 23.3072i 1.10736i −0.832731 0.553678i \(-0.813224\pi\)
0.832731 0.553678i \(-0.186776\pi\)
\(444\) 0.381065 0.383385i 0.0180845 0.0181946i
\(445\) −6.45758 11.1848i −0.306118 0.530213i
\(446\) −13.0097 + 22.5334i −0.616025 + 1.06699i
\(447\) 22.3826 6.07028i 1.05866 0.287114i
\(448\) −24.5372 + 6.57472i −1.15927 + 0.310626i
\(449\) −24.0621 + 6.44742i −1.13556 + 0.304273i −0.777165 0.629297i \(-0.783343\pi\)
−0.358396 + 0.933570i \(0.616676\pi\)
\(450\) −4.67802 + 17.8924i −0.220524 + 0.843454i
\(451\) 4.05178 7.01789i 0.190791 0.330460i
\(452\) 1.00116 + 1.73406i 0.0470906 + 0.0815634i
\(453\) 15.0093 + 14.9185i 0.705199 + 0.700932i
\(454\) 4.31222i 0.202383i
\(455\) 0.472217 + 16.6379i 0.0221379 + 0.779997i
\(456\) −4.43992 + 7.74436i −0.207918 + 0.362663i
\(457\) 5.56709 20.7767i 0.260418 0.971892i −0.704578 0.709626i \(-0.748864\pi\)
0.964996 0.262265i \(-0.0844696\pi\)
\(458\) 23.0458 13.3055i 1.07686 0.621726i
\(459\) −3.66344 2.07085i −0.170995 0.0966588i
\(460\) −1.36119 1.36119i −0.0634659 0.0634659i
\(461\) 7.06327 + 26.3605i 0.328969 + 1.22773i 0.910261 + 0.414035i \(0.135881\pi\)
−0.581292 + 0.813695i \(0.697453\pi\)
\(462\) −3.11979 + 11.7862i −0.145146 + 0.548343i
\(463\) 9.49329 9.49329i 0.441191 0.441191i −0.451221 0.892412i \(-0.649011\pi\)
0.892412 + 0.451221i \(0.149011\pi\)
\(464\) 28.1038 + 16.2257i 1.30469 + 0.753261i
\(465\) 0.0364766 + 12.0182i 0.00169156 + 0.557329i
\(466\) 41.3837 + 11.0887i 1.91706 + 0.513676i
\(467\) 32.2721 1.49338 0.746688 0.665174i \(-0.231643\pi\)
0.746688 + 0.665174i \(0.231643\pi\)
\(468\) 0.159914 + 4.64080i 0.00739202 + 0.214521i
\(469\) −28.9309 −1.33590
\(470\) 7.47530 + 2.00300i 0.344810 + 0.0923916i
\(471\) 0.0265118 + 8.73501i 0.00122160 + 0.402488i
\(472\) 19.9583 + 11.5229i 0.918655 + 0.530386i
\(473\) 6.91749 6.91749i 0.318067 0.318067i
\(474\) 1.93640 7.31550i 0.0889420 0.336012i
\(475\) 2.15507 + 8.04284i 0.0988815 + 0.369031i
\(476\) 1.11029 + 1.11029i 0.0508903 + 0.0508903i
\(477\) 0.00726449 + 1.19673i 0.000332618 + 0.0547944i
\(478\) 1.03805 0.599316i 0.0474791 0.0274121i
\(479\) −1.35986 + 5.07505i −0.0621334 + 0.231885i −0.990009 0.141005i \(-0.954967\pi\)
0.927875 + 0.372890i \(0.121633\pi\)
\(480\) 2.10385 3.66965i 0.0960273 0.167496i
\(481\) 0.749956 + 2.51156i 0.0341950 + 0.114517i
\(482\) 24.5894i 1.12002i
\(483\) −24.3383 24.1910i −1.10743 1.10073i
\(484\) −0.214648 0.371782i −0.00975674 0.0168992i
\(485\) −2.17733 + 3.77125i −0.0988676 + 0.171244i
\(486\) 5.93153 23.5613i 0.269060 1.06876i
\(487\) 11.8773 3.18253i 0.538214 0.144214i 0.0205353 0.999789i \(-0.493463\pi\)
0.517679 + 0.855575i \(0.326796\pi\)
\(488\) −4.09371 + 1.09691i −0.185314 + 0.0496547i
\(489\) −11.5540 + 3.13351i −0.522491 + 0.141702i
\(490\) −10.6715 + 18.4836i −0.482089 + 0.835003i
\(491\) −14.3315 24.8229i −0.646772 1.12024i −0.983889 0.178780i \(-0.942785\pi\)
0.337117 0.941463i \(-0.390548\pi\)
\(492\) 4.24773 4.27359i 0.191503 0.192669i
\(493\) 5.62259i 0.253229i
\(494\) 6.20368 + 10.0738i 0.279117 + 0.453242i
\(495\) 1.54935 + 2.64633i 0.0696381 + 0.118943i
\(496\) −8.21236 + 30.6490i −0.368746 + 1.37618i
\(497\) −30.7546 + 17.7561i −1.37953 + 0.796472i
\(498\) −14.3839 24.7400i −0.644559 1.10863i
\(499\) −15.5915 15.5915i −0.697973 0.697973i 0.266000 0.963973i \(-0.414298\pi\)
−0.963973 + 0.266000i \(0.914298\pi\)
\(500\) −1.01707 3.79576i −0.0454848 0.169752i
\(501\) −41.6468 11.0239i −1.86064 0.492509i
\(502\) −20.8985 + 20.8985i −0.932745 + 0.932745i
\(503\) 25.2920 + 14.6023i 1.12771 + 0.651085i 0.943359 0.331775i \(-0.107647\pi\)
0.184354 + 0.982860i \(0.440981\pi\)
\(504\) 16.4099 28.8254i 0.730953 1.28399i
\(505\) 8.79961 + 2.35785i 0.391578 + 0.104923i
\(506\) 6.83743 0.303961
\(507\) −20.1378 10.0731i −0.894352 0.447363i
\(508\) −4.77036 −0.211650
\(509\) 28.0102 + 7.50531i 1.24153 + 0.332667i 0.819059 0.573710i \(-0.194496\pi\)
0.422471 + 0.906377i \(0.361163\pi\)
\(510\) 2.23481 0.00678292i 0.0989591 0.000300353i
\(511\) 43.1390 + 24.9063i 1.90836 + 1.10179i
\(512\) −8.28642 + 8.28642i −0.366212 + 0.366212i
\(513\) −2.92735 10.5402i −0.129246 0.465360i
\(514\) −9.23238 34.4557i −0.407223 1.51978i
\(515\) −6.16956 6.16956i −0.271863 0.271863i
\(516\) 6.28852 3.65617i 0.276837 0.160954i
\(517\) −4.20679 + 2.42879i −0.185015 + 0.106818i
\(518\) −1.32444 + 4.94287i −0.0581925 + 0.217177i
\(519\) −6.51833 3.73703i −0.286123 0.164037i
\(520\) 4.73115 + 7.68264i 0.207475 + 0.336906i
\(521\) 31.0806i 1.36167i −0.732438 0.680833i \(-0.761618\pi\)
0.732438 0.680833i \(-0.238382\pi\)
\(522\) −31.3046 + 8.59205i −1.37017 + 0.376064i
\(523\) −17.3773 30.0984i −0.759857 1.31611i −0.942923 0.333010i \(-0.891936\pi\)
0.183067 0.983100i \(-0.441398\pi\)
\(524\) 1.24938 2.16398i 0.0545792 0.0945340i
\(525\) −8.09820 29.8601i −0.353435 1.30320i
\(526\) −7.57976 + 2.03099i −0.330493 + 0.0885555i
\(527\) −5.31028 + 1.42288i −0.231319 + 0.0619818i
\(528\) 2.11916 + 7.81386i 0.0922244 + 0.340054i
\(529\) 1.87778 3.25240i 0.0816424 0.141409i
\(530\) −0.317773 0.550399i −0.0138032 0.0239078i
\(531\) −27.2338 + 7.47475i −1.18185 + 0.324377i
\(532\) 4.08166i 0.176962i
\(533\) 8.35977 + 27.9963i 0.362102 + 1.21266i
\(534\) 29.5914 + 16.9651i 1.28054 + 0.734150i
\(535\) 3.38831 12.6454i 0.146490 0.546706i
\(536\) −13.5816 + 7.84131i −0.586634 + 0.338693i
\(537\) −2.23728 + 1.30076i −0.0965458 + 0.0561321i
\(538\) −30.1447 30.1447i −1.29963 1.29963i
\(539\) −3.46726 12.9400i −0.149346 0.557366i
\(540\) 0.610176 + 2.19699i 0.0262578 + 0.0945434i
\(541\) 22.0484 22.0484i 0.947933 0.947933i −0.0507774 0.998710i \(-0.516170\pi\)
0.998710 + 0.0507774i \(0.0161699\pi\)
\(542\) 13.9521 + 8.05523i 0.599292 + 0.346002i
\(543\) −35.4995 + 0.107745i −1.52343 + 0.00462379i
\(544\) 1.86902 + 0.500802i 0.0801334 + 0.0214717i
\(545\) −17.1035 −0.732634
\(546\) −23.1643 37.3608i −0.991342 1.59889i
\(547\) 22.6047 0.966505 0.483253 0.875481i \(-0.339455\pi\)
0.483253 + 0.875481i \(0.339455\pi\)
\(548\) 6.37210 + 1.70740i 0.272203 + 0.0729365i
\(549\) 2.56940 4.51339i 0.109659 0.192627i
\(550\) 5.33870 + 3.08230i 0.227643 + 0.131430i
\(551\) −10.3349 + 10.3349i −0.440280 + 0.440280i
\(552\) −17.9822 4.75987i −0.765373 0.202593i
\(553\) 3.27659 + 12.2284i 0.139335 + 0.520005i
\(554\) −22.2044 22.2044i −0.943373 0.943373i
\(555\) 0.646915 + 1.11268i 0.0274600 + 0.0472305i
\(556\) −4.87235 + 2.81305i −0.206634 + 0.119300i
\(557\) 4.95821 18.5043i 0.210086 0.784051i −0.777753 0.628570i \(-0.783641\pi\)
0.987839 0.155481i \(-0.0496928\pi\)
\(558\) −16.0369 27.3914i −0.678898 1.15957i
\(559\) 1.00070 + 35.2582i 0.0423251 + 1.49126i
\(560\) 21.5783i 0.911851i
\(561\) −0.988875 + 0.994896i −0.0417503 + 0.0420045i
\(562\) −11.7248 20.3079i −0.494580 0.856638i
\(563\) 21.3106 36.9111i 0.898136 1.55562i 0.0682604 0.997668i \(-0.478255\pi\)
0.829875 0.557949i \(-0.188412\pi\)
\(564\) −3.48600 + 0.945420i −0.146787 + 0.0398094i
\(565\) −4.60515 + 1.23395i −0.193740 + 0.0519126i
\(566\) 2.44083 0.654019i 0.102596 0.0274905i
\(567\) 10.9959 + 39.1306i 0.461783 + 1.64333i
\(568\) −9.62511 + 16.6712i −0.403861 + 0.699507i
\(569\) −18.6305 32.2690i −0.781033 1.35279i −0.931340 0.364150i \(-0.881360\pi\)
0.150308 0.988639i \(-0.451974\pi\)
\(570\) 4.12027 + 4.09533i 0.172579 + 0.171535i
\(571\) 36.4187i 1.52407i −0.647534 0.762037i \(-0.724199\pi\)
0.647534 0.762037i \(-0.275801\pi\)
\(572\) 1.50587 + 0.358035i 0.0629637 + 0.0149702i
\(573\) 17.0639 29.7637i 0.712853 1.24340i
\(574\) −14.7635 + 55.0982i −0.616218 + 2.29976i
\(575\) −15.0262 + 8.67535i −0.626634 + 0.361787i
\(576\) −0.102430 16.8739i −0.00426791 0.703081i
\(577\) 26.8286 + 26.8286i 1.11689 + 1.11689i 0.992195 + 0.124692i \(0.0397943\pi\)
0.124692 + 0.992195i \(0.460206\pi\)
\(578\) −6.59322 24.6062i −0.274242 1.02348i
\(579\) 7.80254 29.4770i 0.324262 1.22502i
\(580\) 2.15419 2.15419i 0.0894480 0.0894480i
\(581\) 41.4610 + 23.9375i 1.72009 + 0.993096i
\(582\) −0.0349064 11.5008i −0.00144692 0.476725i
\(583\) 0.385324 + 0.103247i 0.0159585 + 0.00427607i
\(584\) 27.0020 1.11735
\(585\) −10.7720 2.49214i −0.445366 0.103037i
\(586\) 31.3883 1.29664
\(587\) 20.4373 + 5.47617i 0.843539 + 0.226026i 0.654611 0.755966i \(-0.272832\pi\)
0.188927 + 0.981991i \(0.439499\pi\)
\(588\) −0.0302331 9.96109i −0.00124679 0.410788i
\(589\) −12.3762 7.14540i −0.509953 0.294421i
\(590\) 10.6049 10.6049i 0.436598 0.436598i
\(591\) −6.66747 + 25.1889i −0.274263 + 1.03613i
\(592\) 0.879489 + 3.28230i 0.0361468 + 0.134902i
\(593\) 5.72278 + 5.72278i 0.235007 + 0.235007i 0.814779 0.579772i \(-0.196858\pi\)
−0.579772 + 0.814779i \(0.696858\pi\)
\(594\) −7.05037 3.98538i −0.289280 0.163522i
\(595\) −3.23780 + 1.86935i −0.132737 + 0.0766357i
\(596\) 1.48770 5.55217i 0.0609386 0.227426i
\(597\) −15.0574 + 26.2640i −0.616260 + 1.07492i
\(598\) −16.9305 + 17.9196i −0.692341 + 0.732789i
\(599\) 3.91773i 0.160074i 0.996792 + 0.0800371i \(0.0255039\pi\)
−0.996792 + 0.0800371i \(0.974496\pi\)
\(600\) −11.8948 11.8229i −0.485605 0.482666i
\(601\) −3.14233 5.44268i −0.128178 0.222012i 0.794792 0.606881i \(-0.207580\pi\)
−0.922971 + 0.384870i \(0.874246\pi\)
\(602\) −34.4312 + 59.6365i −1.40331 + 2.43060i
\(603\) 4.86118 18.5929i 0.197963 0.757161i
\(604\) 5.06644 1.35755i 0.206150 0.0552378i
\(605\) 0.987343 0.264558i 0.0401412 0.0107558i
\(606\) −23.2212 + 6.29771i −0.943298 + 0.255827i
\(607\) −19.9662 + 34.5825i −0.810404 + 1.40366i 0.102178 + 0.994766i \(0.467419\pi\)
−0.912582 + 0.408894i \(0.865914\pi\)
\(608\) 2.51491 + 4.35595i 0.101993 + 0.176657i
\(609\) 38.2842 38.5173i 1.55135 1.56080i
\(610\) 2.75806i 0.111671i
\(611\) 4.05125 17.0393i 0.163896 0.689336i
\(612\) −0.900108 + 0.526988i −0.0363847 + 0.0213022i
\(613\) 6.98427 26.0657i 0.282092 1.05278i −0.668846 0.743401i \(-0.733211\pi\)
0.950938 0.309381i \(-0.100122\pi\)
\(614\) −16.0179 + 9.24791i −0.646428 + 0.373215i
\(615\) 7.21117 + 12.4030i 0.290783 + 0.500138i
\(616\) −7.81803 7.81803i −0.314997 0.314997i
\(617\) −4.15340 15.5007i −0.167210 0.624035i −0.997748 0.0670735i \(-0.978634\pi\)
0.830538 0.556961i \(-0.188033\pi\)
\(618\) 22.2762 + 5.89648i 0.896080 + 0.237191i
\(619\) −11.0819 + 11.0819i −0.445418 + 0.445418i −0.893828 0.448410i \(-0.851990\pi\)
0.448410 + 0.893828i \(0.351990\pi\)
\(620\) 2.57969 + 1.48939i 0.103603 + 0.0598152i
\(621\) 19.6362 11.5766i 0.787975 0.464555i
\(622\) 5.93614 + 1.59058i 0.238018 + 0.0637766i
\(623\) −57.0628 −2.28617
\(624\) −25.7260 13.7944i −1.02987 0.552217i
\(625\) −10.4191 −0.416766
\(626\) 7.11367 + 1.90610i 0.284319 + 0.0761832i
\(627\) −3.64636 + 0.0110671i −0.145622 + 0.000441979i
\(628\) 1.87496 + 1.08251i 0.0748192 + 0.0431969i
\(629\) −0.416314 + 0.416314i −0.0165995 + 0.0165995i
\(630\) −15.3557 15.1704i −0.611784 0.604402i
\(631\) 8.21544 + 30.6604i 0.327051 + 1.22057i 0.912234 + 0.409671i \(0.134356\pi\)
−0.585182 + 0.810902i \(0.698977\pi\)
\(632\) 4.85252 + 4.85252i 0.193023 + 0.193023i
\(633\) −17.9511 + 10.4369i −0.713493 + 0.414828i
\(634\) 17.0417 9.83903i 0.676812 0.390758i
\(635\) 2.93977 10.9714i 0.116661 0.435386i
\(636\) 0.257329 + 0.147530i 0.0102038 + 0.00584993i
\(637\) 42.4988 + 22.9544i 1.68387 + 0.909485i
\(638\) 10.8208i 0.428399i
\(639\) −6.24367 22.7484i −0.246996 0.899914i
\(640\) 6.92278 + 11.9906i 0.273647 + 0.473970i
\(641\) −1.23655 + 2.14176i −0.0488406 + 0.0845945i −0.889412 0.457106i \(-0.848886\pi\)
0.840572 + 0.541701i \(0.182219\pi\)
\(642\) 9.05003 + 33.3697i 0.357176 + 1.31700i
\(643\) 13.4906 3.61479i 0.532016 0.142553i 0.0171972 0.999852i \(-0.494526\pi\)
0.514819 + 0.857299i \(0.327859\pi\)
\(644\) −8.21545 + 2.20132i −0.323734 + 0.0867443i
\(645\) 4.53351 + 16.7162i 0.178507 + 0.658199i
\(646\) −1.32871 + 2.30139i −0.0522773 + 0.0905470i
\(647\) 2.30184 + 3.98690i 0.0904946 + 0.156741i 0.907719 0.419578i \(-0.137822\pi\)
−0.817225 + 0.576319i \(0.804489\pi\)
\(648\) 15.7678 + 15.3895i 0.619418 + 0.604557i
\(649\) 9.41366i 0.369518i
\(650\) −21.2976 + 6.35950i −0.835359 + 0.249440i
\(651\) 46.0662 + 26.4103i 1.80548 + 1.03510i
\(652\) −0.767959 + 2.86606i −0.0300756 + 0.112244i
\(653\) −4.09778 + 2.36586i −0.160359 + 0.0925831i −0.578032 0.816014i \(-0.696179\pi\)
0.417673 + 0.908597i \(0.362846\pi\)
\(654\) 39.0507 22.7043i 1.52700 0.887807i
\(655\) 4.20702 + 4.20702i 0.164382 + 0.164382i
\(656\) 9.80367 + 36.5878i 0.382769 + 1.42851i
\(657\) −23.2550 + 23.5390i −0.907263 + 0.918345i
\(658\) 24.1782 24.1782i 0.942564 0.942564i
\(659\) −35.7398 20.6344i −1.39223 0.803802i −0.398665 0.917097i \(-0.630526\pi\)
−0.993561 + 0.113295i \(0.963860\pi\)
\(660\) 0.760047 0.00230683i 0.0295848 8.97933e-5i
\(661\) 18.1856 + 4.87280i 0.707336 + 0.189530i 0.594514 0.804085i \(-0.297344\pi\)
0.112822 + 0.993615i \(0.464011\pi\)
\(662\) 2.24056 0.0870816
\(663\) −0.158833 5.05517i −0.00616855 0.196327i
\(664\) 25.9517 1.00712
\(665\) −9.38743 2.51535i −0.364029 0.0975413i
\(666\) −2.95407 1.68171i −0.114468 0.0651649i
\(667\) −26.3756 15.2279i −1.02127 0.589628i
\(668\) −7.55037 + 7.55037i −0.292133 + 0.292133i
\(669\) 27.9519 + 7.39883i 1.08068 + 0.286055i
\(670\) 2.64147 + 9.85808i 0.102049 + 0.380851i
\(671\) −1.22412 1.22412i −0.0472567 0.0472567i
\(672\) −9.39366 16.1569i −0.362368 0.623264i
\(673\) 25.4604 14.6996i 0.981427 0.566627i 0.0787261 0.996896i \(-0.474915\pi\)
0.902701 + 0.430269i \(0.141581\pi\)
\(674\) −1.85943 + 6.93947i −0.0716224 + 0.267299i
\(675\) 20.5508 0.187127i 0.791000 0.00720251i
\(676\) −4.66711 + 3.06006i −0.179504 + 0.117695i
\(677\) 23.6108i 0.907435i 0.891146 + 0.453718i \(0.149902\pi\)
−0.891146 + 0.453718i \(0.850098\pi\)
\(678\) 8.87647 8.93051i 0.340899 0.342974i
\(679\) 9.62007 + 16.6625i 0.369185 + 0.639446i
\(680\) −1.01332 + 1.75512i −0.0388590 + 0.0673058i
\(681\) −4.62498 + 1.25432i −0.177230 + 0.0480656i
\(682\) −10.2197 + 2.73837i −0.391334 + 0.104858i
\(683\) −4.04949 + 1.08506i −0.154949 + 0.0415185i −0.335460 0.942055i \(-0.608892\pi\)
0.180511 + 0.983573i \(0.442225\pi\)
\(684\) −2.62314 0.685830i −0.100298 0.0262234i
\(685\) −7.85372 + 13.6030i −0.300075 + 0.519746i
\(686\) 22.5128 + 38.9933i 0.859542 + 1.48877i
\(687\) −20.9740 20.8471i −0.800208 0.795365i
\(688\) 45.7278i 1.74336i
\(689\) −1.22471 + 0.754207i −0.0466579 + 0.0287330i
\(690\) −6.02083 + 10.5019i −0.229209 + 0.399799i
\(691\) 8.50823 31.7531i 0.323668 1.20795i −0.591976 0.805956i \(-0.701652\pi\)
0.915644 0.401990i \(-0.131681\pi\)
\(692\) −1.61278 + 0.931138i −0.0613086 + 0.0353966i
\(693\) 13.5485 0.0822433i 0.514665 0.00312416i
\(694\) 8.37569 + 8.37569i 0.317937 + 0.317937i
\(695\) −3.46714 12.9395i −0.131516 0.490824i
\(696\) 7.53286 28.4582i 0.285532 1.07871i
\(697\) −4.64065 + 4.64065i −0.175777 + 0.175777i
\(698\) −34.4673 19.8997i −1.30461 0.753216i
\(699\) −0.144504 47.6106i −0.00546564 1.80080i
\(700\) −7.40702 1.98470i −0.279959 0.0750148i
\(701\) −41.5939 −1.57098 −0.785490 0.618875i \(-0.787589\pi\)
−0.785490 + 0.618875i \(0.787589\pi\)
\(702\) 27.9027 8.60930i 1.05312 0.324937i
\(703\) −1.53045 −0.0577220
\(704\) −5.43309 1.45579i −0.204767 0.0548672i
\(705\) −0.0261023 8.60010i −0.000983070 0.323898i
\(706\) −8.35713 4.82499i −0.314525 0.181591i
\(707\) 28.4615 28.4615i 1.07041 1.07041i
\(708\) −1.79111 + 6.76661i −0.0673142 + 0.254305i
\(709\) −0.479146 1.78820i −0.0179947 0.0671572i 0.956345 0.292241i \(-0.0944010\pi\)
−0.974339 + 0.225084i \(0.927734\pi\)
\(710\) 8.85830 + 8.85830i 0.332446 + 0.332446i
\(711\) −8.40933 + 0.0510471i −0.315375 + 0.00191442i
\(712\) −26.7880 + 15.4661i −1.00392 + 0.579615i
\(713\) 7.70734 28.7642i 0.288642 1.07723i
\(714\) 4.91106 8.56615i 0.183792 0.320580i
\(715\) −1.75145 + 3.24273i −0.0655007 + 0.121271i
\(716\) 0.641432i 0.0239714i
\(717\) −0.944725 0.939008i −0.0352814 0.0350679i
\(718\) −12.1247 21.0005i −0.452489 0.783733i
\(719\) −1.00585 + 1.74219i −0.0375121 + 0.0649728i −0.884172 0.467162i \(-0.845277\pi\)
0.846660 + 0.532134i \(0.178610\pi\)
\(720\) −13.8677 3.62575i −0.516817 0.135124i
\(721\) −37.2363 + 9.97744i −1.38675 + 0.371579i
\(722\) 21.9322 5.87673i 0.816234 0.218709i
\(723\) −26.3728 + 7.15244i −0.980816 + 0.266002i
\(724\) −4.39938 + 7.61995i −0.163502 + 0.283193i
\(725\) −13.7294 23.7801i −0.509898 0.883170i
\(726\) −1.90311 + 1.91470i −0.0706310 + 0.0710611i
\(727\) 25.8467i 0.958603i −0.877650 0.479301i \(-0.840890\pi\)
0.877650 0.479301i \(-0.159110\pi\)
\(728\) 39.8482 1.13097i 1.47687 0.0419167i
\(729\) −26.9955 + 0.491661i −0.999834 + 0.0182096i
\(730\) 4.54802 16.9734i 0.168330 0.628215i
\(731\) −6.86139 + 3.96143i −0.253778 + 0.146519i
\(732\) −0.646997 1.11282i −0.0239137 0.0411310i
\(733\) 26.4081 + 26.4081i 0.975406 + 0.975406i 0.999705 0.0242989i \(-0.00773535\pi\)
−0.0242989 + 0.999705i \(0.507735\pi\)
\(734\) 4.33354 + 16.1730i 0.159954 + 0.596956i
\(735\) 22.9282 + 6.06907i 0.845720 + 0.223861i
\(736\) −7.41121 + 7.41121i −0.273181 + 0.273181i
\(737\) −5.54772 3.20298i −0.204353 0.117983i
\(738\) −32.9291 18.7460i −1.21214 0.690051i
\(739\) −30.6537 8.21364i −1.12761 0.302144i −0.353654 0.935376i \(-0.615061\pi\)
−0.773961 + 0.633233i \(0.781728\pi\)
\(740\) 0.319006 0.0117269
\(741\) 8.99995 9.58384i 0.330621 0.352071i
\(742\) −2.80802 −0.103086
\(743\) 33.8281 + 9.06420i 1.24103 + 0.332533i 0.818866 0.573985i \(-0.194603\pi\)
0.422166 + 0.906519i \(0.361270\pi\)
\(744\) 28.7838 0.0873623i 1.05527 0.00320286i
\(745\) 11.8527 + 6.84315i 0.434249 + 0.250714i
\(746\) −25.2614 + 25.2614i −0.924886 + 0.924886i
\(747\) −22.3504 + 22.6234i −0.817759 + 0.827747i
\(748\) 0.0899853 + 0.335830i 0.00329019 + 0.0122792i
\(749\) −40.9002 40.9002i −1.49446 1.49446i
\(750\) −21.3632 + 12.4206i −0.780072 + 0.453537i
\(751\) 9.09928 5.25347i 0.332037 0.191702i −0.324708 0.945814i \(-0.605266\pi\)
0.656745 + 0.754112i \(0.271933\pi\)
\(752\) 5.87670 21.9321i 0.214301 0.799783i
\(753\) 28.4931 + 16.3354i 1.03834 + 0.595294i
\(754\) −28.3593 26.7939i −1.03278 0.975776i
\(755\) 12.4889i 0.454519i
\(756\) 9.75441 + 2.51872i 0.354765 + 0.0916050i
\(757\) 3.10530 + 5.37853i 0.112864 + 0.195486i 0.916924 0.399062i \(-0.130664\pi\)
−0.804060 + 0.594548i \(0.797331\pi\)
\(758\) 5.95118 10.3077i 0.216157 0.374394i
\(759\) −1.98884 7.33334i −0.0721902 0.266183i
\(760\) −5.08866 + 1.36350i −0.184585 + 0.0494594i
\(761\) −36.1674 + 9.69104i −1.31107 + 0.351300i −0.845625 0.533778i \(-0.820772\pi\)
−0.465444 + 0.885077i \(0.654105\pi\)
\(762\) 7.85200 + 28.9523i 0.284448 + 1.04883i
\(763\) −37.7841 + 65.4440i −1.36788 + 2.36923i
\(764\) −4.25173 7.36420i −0.153822 0.266428i
\(765\) −0.657326 2.39493i −0.0237657 0.0865887i
\(766\) 50.8689i 1.83797i
\(767\) −24.6714 23.3096i −0.890834 0.841663i
\(768\) −14.8194 8.49613i −0.534750 0.306578i
\(769\) −1.27566 + 4.76085i −0.0460016 + 0.171680i −0.985105 0.171955i \(-0.944992\pi\)
0.939103 + 0.343635i \(0.111658\pi\)
\(770\) −6.23121 + 3.59759i −0.224557 + 0.129648i
\(771\) −34.2693 + 19.9243i −1.23418 + 0.717556i
\(772\) −5.34405 5.34405i −0.192337 0.192337i
\(773\) 8.65504 + 32.3011i 0.311300 + 1.16179i 0.927385 + 0.374108i \(0.122051\pi\)
−0.616085 + 0.787680i \(0.711282\pi\)
\(774\) −32.5410 32.1483i −1.16966 1.15555i
\(775\) 18.9848 18.9848i 0.681953 0.681953i
\(776\) 9.03225 + 5.21477i 0.324239 + 0.187199i
\(777\) 5.68662 0.0172596i 0.204006 0.000619183i
\(778\) 22.5653 + 6.04636i 0.809006 + 0.216772i
\(779\) −17.0599 −0.611236
\(780\) −1.87595 + 1.99765i −0.0671696 + 0.0715275i
\(781\) −7.86323 −0.281369
\(782\) −5.34878 1.43320i −0.191272 0.0512512i
\(783\) 18.3210 + 31.0759i 0.654737 + 1.11056i
\(784\) 54.2298 + 31.3096i 1.93678 + 1.11820i
\(785\) −3.64514 + 3.64514i −0.130101 + 0.130101i
\(786\) −15.1901 4.02081i −0.541814 0.143417i
\(787\) 0.708971 + 2.64592i 0.0252721 + 0.0943168i 0.977410 0.211352i \(-0.0677866\pi\)
−0.952138 + 0.305669i \(0.901120\pi\)
\(788\) 4.56663 + 4.56663i 0.162680 + 0.162680i
\(789\) 4.38306 + 7.53875i 0.156041 + 0.268387i
\(790\) 3.86762 2.23297i 0.137604 0.0794455i
\(791\) −5.45193 + 20.3469i −0.193848 + 0.723452i
\(792\) 6.33802 3.71074i 0.225212 0.131855i
\(793\) 6.23930 0.177084i 0.221564 0.00628844i
\(794\) 56.5699i 2.00759i
\(795\) −0.497886 + 0.500918i −0.0176582 + 0.0177657i
\(796\) 3.75180 + 6.49830i 0.132979 + 0.230326i
\(797\) −8.15570 + 14.1261i −0.288890 + 0.500372i −0.973545 0.228495i \(-0.926619\pi\)
0.684655 + 0.728867i \(0.259953\pi\)
\(798\) 24.7724 6.71840i 0.876934 0.237829i
\(799\) 3.79999 1.01820i 0.134434 0.0360215i
\(800\) −9.12767 + 2.44575i −0.322712 + 0.0864703i
\(801\) 9.58811 36.6723i 0.338779 1.29575i
\(802\) 15.3470 26.5817i 0.541921 0.938634i
\(803\) 5.51483 + 9.55196i 0.194614 + 0.337081i
\(804\) −3.37833 3.35788i −0.119144 0.118423i
\(805\) 20.2514i 0.713767i
\(806\) 18.1289 33.5646i 0.638562 1.18226i
\(807\) −23.5627 + 41.0994i −0.829447 + 1.44677i
\(808\) 5.64711 21.0753i 0.198665 0.741427i
\(809\) −12.4149 + 7.16776i −0.436485 + 0.252005i −0.702106 0.712073i \(-0.747757\pi\)
0.265620 + 0.964078i \(0.414423\pi\)
\(810\) 12.3296 7.31953i 0.433220 0.257182i
\(811\) 5.06572 + 5.06572i 0.177881 + 0.177881i 0.790432 0.612550i \(-0.209856\pi\)
−0.612550 + 0.790432i \(0.709856\pi\)
\(812\) −3.48377 13.0016i −0.122256 0.456267i
\(813\) 4.58115 17.3070i 0.160668 0.606985i
\(814\) −0.801204 + 0.801204i −0.0280822 + 0.0280822i
\(815\) −6.11841 3.53247i −0.214319 0.123737i
\(816\) −0.0199007 6.55682i −0.000696664 0.229534i
\(817\) −19.8934 5.33042i −0.695982 0.186488i
\(818\) 34.8087 1.21706
\(819\) −33.3326 + 35.7117i −1.16473 + 1.24787i
\(820\) 3.55597 0.124180
\(821\) 46.4920 + 12.4575i 1.62258 + 0.434770i 0.951759 0.306847i \(-0.0992741\pi\)
0.670824 + 0.741617i \(0.265941\pi\)
\(822\) −0.125909 41.4840i −0.00439157 1.44692i
\(823\) 19.8631 + 11.4680i 0.692384 + 0.399748i 0.804505 0.593946i \(-0.202431\pi\)
−0.112120 + 0.993695i \(0.535764\pi\)
\(824\) −14.7763 + 14.7763i −0.514756 + 0.514756i
\(825\) 1.75296 6.62247i 0.0610302 0.230565i
\(826\) −17.1503 64.0059i −0.596736 2.22705i
\(827\) 18.1940 + 18.1940i 0.632667 + 0.632667i 0.948736 0.316069i \(-0.102363\pi\)
−0.316069 + 0.948736i \(0.602363\pi\)
\(828\) −0.0342952 5.64967i −0.00119184 0.196340i
\(829\) −5.05604 + 2.91911i −0.175604 + 0.101385i −0.585225 0.810871i \(-0.698994\pi\)
0.409622 + 0.912255i \(0.365661\pi\)
\(830\) 4.37111 16.3132i 0.151724 0.566240i
\(831\) −17.3561 + 30.2735i −0.602077 + 1.05018i
\(832\) 17.2685 10.6344i 0.598678 0.368680i
\(833\) 10.8495i 0.375912i
\(834\) 25.0929 + 24.9410i 0.868896 + 0.863637i
\(835\) −12.7122 22.0181i −0.439923 0.761969i
\(836\) −0.451886 + 0.782689i −0.0156288 + 0.0270699i
\(837\) −24.7134 + 25.1676i −0.854219 + 0.869918i
\(838\) −18.3102 + 4.90621i −0.632516 + 0.169482i
\(839\) −25.9687 + 6.95830i −0.896540 + 0.240227i −0.677530 0.735495i \(-0.736950\pi\)
−0.219010 + 0.975723i \(0.570283\pi\)
\(840\) 18.8923 5.12369i 0.651847 0.176784i
\(841\) 9.59941 16.6267i 0.331014 0.573333i
\(842\) 10.4910 + 18.1710i 0.361545 + 0.626214i
\(843\) −18.3704 + 18.4822i −0.632710 + 0.636562i
\(844\) 5.14661i 0.177154i
\(845\) −4.16172 12.6197i −0.143167 0.434132i
\(846\) 11.4759 + 19.6011i 0.394549 + 0.673899i
\(847\) 1.16889 4.36236i 0.0401636 0.149892i
\(848\) −1.61484 + 0.932328i −0.0554538 + 0.0320163i
\(849\) −1.41143 2.42762i −0.0484402 0.0833158i
\(850\) −3.53027 3.53027i −0.121087 0.121087i
\(851\) −0.825404 3.08045i −0.0282945 0.105596i
\(852\) −5.65215 1.49612i −0.193640 0.0512562i
\(853\) −24.1938 + 24.1938i −0.828378 + 0.828378i −0.987292 0.158914i \(-0.949201\pi\)
0.158914 + 0.987292i \(0.449201\pi\)
\(854\) 10.5533 + 6.09294i 0.361126 + 0.208496i
\(855\) 3.19388 5.61033i 0.109228 0.191869i
\(856\) −30.2860 8.11510i −1.03515 0.277368i
\(857\) 35.1936 1.20219 0.601095 0.799178i \(-0.294731\pi\)
0.601095 + 0.799178i \(0.294731\pi\)
\(858\) −0.305677 9.72878i −0.0104356 0.332135i
\(859\) −25.1566 −0.858332 −0.429166 0.903226i \(-0.641192\pi\)
−0.429166 + 0.903226i \(0.641192\pi\)
\(860\) 4.14657 + 1.11107i 0.141397 + 0.0378872i
\(861\) 63.3888 0.192392i 2.16028 0.00655672i
\(862\) −0.472135 0.272587i −0.0160810 0.00928436i
\(863\) 27.2191 27.2191i 0.926548 0.926548i −0.0709328 0.997481i \(-0.522598\pi\)
0.997481 + 0.0709328i \(0.0225976\pi\)
\(864\) 11.9618 3.32219i 0.406950 0.113023i
\(865\) −1.14764 4.28306i −0.0390210 0.145629i
\(866\) 11.6962 + 11.6962i 0.397452 + 0.397452i
\(867\) −24.4731 + 14.2288i −0.831149 + 0.483234i
\(868\) 11.3978 6.58053i 0.386867 0.223358i
\(869\) −0.725512 + 2.70765i −0.0246113 + 0.0918506i
\(870\) −16.6200 9.52845i −0.563472 0.323045i
\(871\) 22.1314 6.60849i 0.749895 0.223920i
\(872\) 40.9634i 1.38720i
\(873\) −12.3248 + 3.38274i −0.417132 + 0.114489i
\(874\) −7.19721 12.4659i −0.243449 0.421667i
\(875\) 20.6702 35.8019i 0.698781 1.21032i
\(876\) 2.14667 + 7.91532i 0.0725293 + 0.267434i
\(877\) −0.898838 + 0.240843i −0.0303516 + 0.00813269i −0.273963 0.961740i \(-0.588335\pi\)
0.243611 + 0.969873i \(0.421668\pi\)
\(878\) 19.8304 5.31354i 0.669243 0.179323i
\(879\) −9.13006 33.6648i −0.307949 1.13549i
\(880\) −2.38897 + 4.13782i −0.0805321 + 0.139486i
\(881\) −0.0815511 0.141251i −0.00274753 0.00475885i 0.864648 0.502378i \(-0.167541\pi\)
−0.867396 + 0.497619i \(0.834208\pi\)
\(882\) −60.4061 + 16.5794i −2.03398 + 0.558258i
\(883\) 41.4147i 1.39371i 0.717210 + 0.696857i \(0.245419\pi\)
−0.717210 + 0.696857i \(0.754581\pi\)
\(884\) −1.10296 0.595731i −0.0370967 0.0200366i
\(885\) −14.4588 8.28938i −0.486027 0.278644i
\(886\) −9.40212 + 35.0892i −0.315871 + 1.17884i
\(887\) 22.2200 12.8287i 0.746073 0.430746i −0.0782002 0.996938i \(-0.524917\pi\)
0.824273 + 0.566192i \(0.191584\pi\)
\(888\) 2.66489 1.54938i 0.0894279 0.0519938i
\(889\) −35.4859 35.4859i −1.19016 1.19016i
\(890\) 5.20998 + 19.4439i 0.174639 + 0.651761i
\(891\) −2.22366 + 8.72097i −0.0744955 + 0.292164i
\(892\) 5.06755 5.06755i 0.169674 0.169674i
\(893\) 8.85631 + 5.11319i 0.296365 + 0.171106i
\(894\) −36.1460 + 0.109708i −1.20890 + 0.00366917i
\(895\) −1.47523 0.395288i −0.0493116 0.0132130i
\(896\) 61.1736 2.04367
\(897\) 24.1440 + 12.9461i 0.806144 + 0.432257i
\(898\) 38.8267 1.29566
\(899\) 45.5216 + 12.1975i 1.51823 + 0.406809i
\(900\) 2.52008 4.42675i 0.0840028 0.147558i
\(901\) −0.279789 0.161536i −0.00932113 0.00538156i
\(902\) −8.93103 + 8.93103i −0.297371 + 0.297371i
\(903\) 73.9770 + 19.5816i 2.46180 + 0.651636i
\(904\) 2.95534 + 11.0295i 0.0982930 + 0.366835i
\(905\) −14.8140 14.8140i −0.492435 0.492435i
\(906\) −16.5786 28.5147i −0.550786 0.947338i
\(907\) 36.9696 21.3444i 1.22756 0.708730i 0.261039 0.965328i \(-0.415935\pi\)
0.966518 + 0.256598i \(0.0826017\pi\)
\(908\) −0.307408 + 1.14726i −0.0102017 + 0.0380732i
\(909\) 13.5089 + 23.0736i 0.448063 + 0.765302i
\(910\) 6.00081 25.2390i 0.198925 0.836666i
\(911\) 25.3129i 0.838653i 0.907836 + 0.419326i \(0.137734\pi\)
−0.907836 + 0.419326i \(0.862266\pi\)
\(912\) 12.0155 12.0886i 0.397872 0.400295i
\(913\) 5.30031 + 9.18041i 0.175415 + 0.303827i
\(914\) −16.7626 + 29.0338i −0.554459 + 0.960351i
\(915\) 2.95810 0.802250i 0.0977917 0.0265216i
\(916\) −7.07983 + 1.89703i −0.233924 + 0.0626798i
\(917\) 25.3914 6.80361i 0.838499 0.224675i
\(918\) 4.67998 + 4.59552i 0.154462 + 0.151675i
\(919\) 4.22673 7.32090i 0.139427 0.241494i −0.787853 0.615863i \(-0.788807\pi\)
0.927280 + 0.374369i \(0.122141\pi\)
\(920\) −5.48885 9.50697i −0.180962 0.313435i
\(921\) 14.5778 + 14.4896i 0.480356 + 0.477449i
\(922\) 42.5353i 1.40083i
\(923\) 19.4706 20.6081i 0.640881 0.678323i
\(924\) 1.67022 2.91330i 0.0549463 0.0958404i
\(925\) 0.744181 2.77732i 0.0244685 0.0913177i
\(926\) −18.1219 + 10.4627i −0.595521 + 0.343824i
\(927\) −0.155442 25.6070i −0.00510538 0.841044i
\(928\) −11.7288 11.7288i −0.385018 0.385018i
\(929\) 4.77136 + 17.8070i 0.156543 + 0.584228i 0.998968 + 0.0454139i \(0.0144607\pi\)
−0.842425 + 0.538814i \(0.818873\pi\)
\(930\) 4.79322 18.1082i 0.157176 0.593791i
\(931\) −19.9424 + 19.9424i −0.653585 + 0.653585i
\(932\) −10.2196 5.90028i −0.334754 0.193270i
\(933\) −0.0207279 6.82934i −0.000678600 0.223583i
\(934\) −48.5861 13.0186i −1.58979 0.425982i
\(935\) −0.827832 −0.0270730
\(936\) −5.96875 + 25.7991i −0.195095 + 0.843271i
\(937\) −49.9817 −1.63283 −0.816415 0.577465i \(-0.804042\pi\)
−0.816415 + 0.577465i \(0.804042\pi\)
\(938\) 43.5558 + 11.6707i 1.42215 + 0.381063i
\(939\) −0.0248396 8.18405i −0.000810609 0.267076i
\(940\) −1.84601 1.06579i −0.0602100 0.0347623i
\(941\) 19.6154 19.6154i 0.639444 0.639444i −0.310974 0.950418i \(-0.600655\pi\)
0.950418 + 0.310974i \(0.100655\pi\)
\(942\) 3.48379 13.1614i 0.113508 0.428820i
\(943\) −9.20079 34.3378i −0.299619 1.11819i
\(944\) −31.1143 31.1143i −1.01268 1.01268i
\(945\) −11.8041 + 20.8821i −0.383986 + 0.679294i
\(946\) −13.2049 + 7.62384i −0.429328 + 0.247873i
\(947\) 10.0243 37.4113i 0.325747 1.21570i −0.587812 0.808998i \(-0.700010\pi\)
0.913559 0.406707i \(-0.133323\pi\)
\(948\) −1.03668 + 1.80824i −0.0336698 + 0.0587288i
\(949\) −38.6895 9.19877i −1.25591 0.298605i
\(950\) 12.9779i 0.421060i
\(951\) −15.5096 15.4158i −0.502935 0.499891i
\(952\) 4.47713 + 7.75462i 0.145105 + 0.251329i
\(953\) −7.57483 + 13.1200i −0.245373 + 0.424998i −0.962236 0.272215i \(-0.912244\pi\)
0.716864 + 0.697213i \(0.245577\pi\)
\(954\) 0.471824 1.80462i 0.0152759 0.0584267i
\(955\) 19.5572 5.24032i 0.632855 0.169573i
\(956\) −0.318894 + 0.0854475i −0.0103138 + 0.00276357i
\(957\) 11.6056 3.14749i 0.375155 0.101744i
\(958\) 4.09456 7.09199i 0.132289 0.229132i
\(959\) 34.7000 + 60.1021i 1.12052 + 1.94080i
\(960\) 7.02022 7.06296i 0.226577 0.227956i
\(961\) 15.0799i 0.486447i
\(962\) −0.115904 4.08371i −0.00373689 0.131664i
\(963\) 33.1575 19.4128i 1.06849 0.625569i
\(964\) −1.75292 + 6.54198i −0.0564577 + 0.210703i
\(965\) 15.5841 8.99751i 0.501672 0.289640i
\(966\) 26.8829 + 46.2379i 0.864944 + 1.48768i
\(967\) 12.5415 + 12.5415i 0.403306 + 0.403306i 0.879396 0.476090i \(-0.157946\pi\)
−0.476090 + 0.879396i \(0.657946\pi\)
\(968\) −0.633623 2.36471i −0.0203654 0.0760047i
\(969\) 2.85479 + 0.755660i 0.0917092 + 0.0242753i
\(970\) 4.79932 4.79932i 0.154097 0.154097i
\(971\) −6.82710 3.94163i −0.219092 0.126493i 0.386438 0.922316i \(-0.373705\pi\)
−0.605530 + 0.795823i \(0.707039\pi\)
\(972\) −3.25770 + 5.84561i −0.104491 + 0.187498i
\(973\) −57.1705 15.3188i −1.83280 0.491098i
\(974\) −19.1653 −0.614096
\(975\) 13.0157 + 20.9924i 0.416835 + 0.672296i
\(976\) 8.09200 0.259018
\(977\) −46.0147 12.3296i −1.47214 0.394459i −0.568476 0.822700i \(-0.692467\pi\)
−0.903665 + 0.428241i \(0.859133\pi\)
\(978\) 18.6588 0.0566316i 0.596642 0.00181088i
\(979\) −10.9422 6.31750i −0.349715 0.201908i
\(980\) 4.15678 4.15678i 0.132784 0.132784i
\(981\) −35.7098 35.2789i −1.14013 1.12637i
\(982\) 11.5627 + 43.1525i 0.368980 + 1.37705i
\(983\) 2.90704 + 2.90704i 0.0927203 + 0.0927203i 0.751946 0.659225i \(-0.229116\pi\)
−0.659225 + 0.751946i \(0.729116\pi\)
\(984\) 29.7056 17.2710i 0.946979 0.550578i
\(985\) −13.3171 + 7.68861i −0.424317 + 0.244979i
\(986\) 2.26815 8.46487i 0.0722328 0.269576i
\(987\) −32.9646 18.8990i −1.04928 0.601560i
\(988\) −0.932345 3.12237i −0.0296618 0.0993357i
\(989\) 42.9157i 1.36464i
\(990\) −1.26504 4.60908i −0.0402055 0.146486i
\(991\) −3.51621 6.09025i −0.111696 0.193463i 0.804758 0.593603i \(-0.202295\pi\)
−0.916454 + 0.400140i \(0.868962\pi\)
\(992\) 8.10918 14.0455i 0.257467 0.445946i
\(993\) −0.651721 2.40306i −0.0206818 0.0762588i
\(994\) 53.4642 14.3257i 1.69578 0.454383i
\(995\) −17.2576 + 4.62415i −0.547102 + 0.146596i
\(996\) 2.06317 + 7.60743i 0.0653741 + 0.241051i
\(997\) 6.46839 11.2036i 0.204856 0.354821i −0.745231 0.666807i \(-0.767661\pi\)
0.950087 + 0.311985i \(0.100994\pi\)
\(998\) 17.1836 + 29.7629i 0.543938 + 0.942128i
\(999\) −0.944415 + 3.65749i −0.0298800 + 0.115718i
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 429.2.be.a.89.13 184
3.2 odd 2 inner 429.2.be.a.89.34 yes 184
13.6 odd 12 inner 429.2.be.a.188.34 yes 184
39.32 even 12 inner 429.2.be.a.188.13 yes 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.be.a.89.13 184 1.1 even 1 trivial
429.2.be.a.89.34 yes 184 3.2 odd 2 inner
429.2.be.a.188.13 yes 184 39.32 even 12 inner
429.2.be.a.188.34 yes 184 13.6 odd 12 inner