Properties

Label 61.2.g.a.52.2
Level $61$
Weight $2$
Character 61.52
Analytic conductor $0.487$
Analytic rank $0$
Dimension $16$
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] = [61,2,Mod(3,61)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(61, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("61.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 61.g (of order \(10\), 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: \(0.487087452330\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 17x^{14} + 111x^{12} + 361x^{10} + 624x^{8} + 558x^{6} + 229x^{4} + 34x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 52.2
Root \(-1.25523i\) of defining polynomial
Character \(\chi\) \(=\) 61.52
Dual form 61.2.g.a.27.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.737805 + 1.01550i) q^{2} +(-0.446713 - 0.324556i) q^{3} +(0.131147 + 0.403630i) q^{4} +(0.620635 + 1.91012i) q^{5} +(0.659173 - 0.214178i) q^{6} +(1.40505 + 1.93389i) q^{7} +(-2.89423 - 0.940394i) q^{8} +(-0.832835 - 2.56320i) q^{9} +O(q^{10})\) \(q+(-0.737805 + 1.01550i) q^{2} +(-0.446713 - 0.324556i) q^{3} +(0.131147 + 0.403630i) q^{4} +(0.620635 + 1.91012i) q^{5} +(0.659173 - 0.214178i) q^{6} +(1.40505 + 1.93389i) q^{7} +(-2.89423 - 0.940394i) q^{8} +(-0.832835 - 2.56320i) q^{9} +(-2.39763 - 0.779038i) q^{10} -3.52926i q^{11} +(0.0724152 - 0.222871i) q^{12} +4.88471 q^{13} -3.00052 q^{14} +(0.342694 - 1.05470i) q^{15} +(2.40365 - 1.74636i) q^{16} +(-0.242658 + 0.0788443i) q^{17} +(3.21741 + 1.04540i) q^{18} +(-4.30389 - 3.12696i) q^{19} +(-0.689585 + 0.501013i) q^{20} -1.31991i q^{21} +(3.58396 + 2.60390i) q^{22} +(-1.09816 + 0.356815i) q^{23} +(0.987681 + 1.35943i) q^{24} +(0.781726 - 0.567958i) q^{25} +(-3.60396 + 4.96043i) q^{26} +(-0.971751 + 2.99074i) q^{27} +(-0.596306 + 0.820745i) q^{28} +6.09997i q^{29} +(0.818211 + 1.12617i) q^{30} +(-2.59754 - 3.57520i) q^{31} -2.35697i q^{32} +(-1.14544 + 1.57656i) q^{33} +(0.0989676 - 0.304591i) q^{34} +(-2.82193 + 3.88405i) q^{35} +(0.925361 - 0.672314i) q^{36} +(5.80482 + 7.98965i) q^{37} +(6.35086 - 2.06352i) q^{38} +(-2.18206 - 1.58536i) q^{39} -6.11197i q^{40} +(0.148301 - 0.107747i) q^{41} +(1.34037 + 0.973836i) q^{42} +(-5.29667 - 1.72099i) q^{43} +(1.42451 - 0.462852i) q^{44} +(4.37913 - 3.18163i) q^{45} +(0.447884 - 1.37845i) q^{46} +3.83056 q^{47} -1.64053 q^{48} +(0.397366 - 1.22297i) q^{49} +1.21289i q^{50} +(0.133988 + 0.0435352i) q^{51} +(0.640616 + 1.97161i) q^{52} +(-13.6262 - 4.42743i) q^{53} +(-2.32014 - 3.19340i) q^{54} +(6.74129 - 2.19038i) q^{55} +(-2.24793 - 6.91843i) q^{56} +(0.907729 + 2.79370i) q^{57} +(-6.19452 - 4.50059i) q^{58} +(3.02806 - 4.16777i) q^{59} +0.470653 q^{60} +(-7.52310 + 2.09834i) q^{61} +5.54710 q^{62} +(3.78677 - 5.21204i) q^{63} +(7.20082 + 5.23170i) q^{64} +(3.03162 + 9.33036i) q^{65} +(-0.755890 - 2.32639i) q^{66} +(-11.9252 + 3.87475i) q^{67} +(-0.0636478 - 0.0876037i) q^{68} +(0.606369 + 0.197021i) q^{69} +(-1.86223 - 5.73134i) q^{70} +(1.81332 + 0.589183i) q^{71} +8.20170i q^{72} +(-0.832448 + 2.56201i) q^{73} -12.3963 q^{74} -0.533541 q^{75} +(0.697690 - 2.14727i) q^{76} +(6.82519 - 4.95879i) q^{77} +(3.21987 - 1.04620i) q^{78} +(-7.35678 - 2.39036i) q^{79} +(4.82754 + 3.50741i) q^{80} +(-5.13642 + 3.73183i) q^{81} +0.230096i q^{82} +(12.5362 + 9.10809i) q^{83} +(0.532755 - 0.173103i) q^{84} +(-0.301204 - 0.414571i) q^{85} +(5.65558 - 4.10902i) q^{86} +(1.97978 - 2.72493i) q^{87} +(-3.31889 + 10.2145i) q^{88} +(9.09752 - 12.5217i) q^{89} +6.79443i q^{90} +(6.86327 + 9.44648i) q^{91} +(-0.288042 - 0.396456i) q^{92} +2.44013i q^{93} +(-2.82621 + 3.88994i) q^{94} +(3.30171 - 10.1616i) q^{95} +(-0.764968 + 1.05289i) q^{96} +(3.36013 - 2.44127i) q^{97} +(0.948746 + 1.30584i) q^{98} +(-9.04620 + 2.93929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/61\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.737805 + 1.01550i −0.521707 + 0.718068i −0.985838 0.167699i \(-0.946366\pi\)
0.464132 + 0.885766i \(0.346366\pi\)
\(3\) −0.446713 0.324556i −0.257910 0.187382i 0.451315 0.892365i \(-0.350955\pi\)
−0.709225 + 0.704982i \(0.750955\pi\)
\(4\) 0.131147 + 0.403630i 0.0655736 + 0.201815i
\(5\) 0.620635 + 1.91012i 0.277556 + 0.854230i 0.988532 + 0.151013i \(0.0482537\pi\)
−0.710976 + 0.703217i \(0.751746\pi\)
\(6\) 0.659173 0.214178i 0.269106 0.0874380i
\(7\) 1.40505 + 1.93389i 0.531060 + 0.730941i 0.987291 0.158920i \(-0.0508012\pi\)
−0.456232 + 0.889861i \(0.650801\pi\)
\(8\) −2.89423 0.940394i −1.02327 0.332479i
\(9\) −0.832835 2.56320i −0.277612 0.854401i
\(10\) −2.39763 0.779038i −0.758198 0.246353i
\(11\) 3.52926i 1.06411i −0.846710 0.532055i \(-0.821420\pi\)
0.846710 0.532055i \(-0.178580\pi\)
\(12\) 0.0724152 0.222871i 0.0209045 0.0643373i
\(13\) 4.88471 1.35477 0.677387 0.735627i \(-0.263112\pi\)
0.677387 + 0.735627i \(0.263112\pi\)
\(14\) −3.00052 −0.801923
\(15\) 0.342694 1.05470i 0.0884832 0.272323i
\(16\) 2.40365 1.74636i 0.600914 0.436589i
\(17\) −0.242658 + 0.0788443i −0.0588532 + 0.0191226i −0.338296 0.941040i \(-0.609850\pi\)
0.279442 + 0.960162i \(0.409850\pi\)
\(18\) 3.21741 + 1.04540i 0.758350 + 0.246403i
\(19\) −4.30389 3.12696i −0.987379 0.717373i −0.0280337 0.999607i \(-0.508925\pi\)
−0.959346 + 0.282234i \(0.908925\pi\)
\(20\) −0.689585 + 0.501013i −0.154196 + 0.112030i
\(21\) 1.31991i 0.288028i
\(22\) 3.58396 + 2.60390i 0.764103 + 0.555154i
\(23\) −1.09816 + 0.356815i −0.228983 + 0.0744010i −0.421261 0.906939i \(-0.638412\pi\)
0.192278 + 0.981340i \(0.438412\pi\)
\(24\) 0.987681 + 1.35943i 0.201609 + 0.277492i
\(25\) 0.781726 0.567958i 0.156345 0.113592i
\(26\) −3.60396 + 4.96043i −0.706795 + 0.972820i
\(27\) −0.971751 + 2.99074i −0.187014 + 0.575569i
\(28\) −0.596306 + 0.820745i −0.112691 + 0.155106i
\(29\) 6.09997i 1.13274i 0.824153 + 0.566368i \(0.191652\pi\)
−0.824153 + 0.566368i \(0.808348\pi\)
\(30\) 0.818211 + 1.12617i 0.149384 + 0.205610i
\(31\) −2.59754 3.57520i −0.466531 0.642125i 0.509316 0.860580i \(-0.329899\pi\)
−0.975847 + 0.218454i \(0.929899\pi\)
\(32\) 2.35697i 0.416657i
\(33\) −1.14544 + 1.57656i −0.199395 + 0.274444i
\(34\) 0.0989676 0.304591i 0.0169728 0.0522369i
\(35\) −2.82193 + 3.88405i −0.476993 + 0.656525i
\(36\) 0.925361 0.672314i 0.154227 0.112052i
\(37\) 5.80482 + 7.98965i 0.954307 + 1.31349i 0.949588 + 0.313502i \(0.101502\pi\)
0.00471946 + 0.999989i \(0.498498\pi\)
\(38\) 6.35086 2.06352i 1.03024 0.334747i
\(39\) −2.18206 1.58536i −0.349409 0.253861i
\(40\) 6.11197i 0.966387i
\(41\) 0.148301 0.107747i 0.0231607 0.0168272i −0.576145 0.817348i \(-0.695444\pi\)
0.599305 + 0.800520i \(0.295444\pi\)
\(42\) 1.34037 + 0.973836i 0.206824 + 0.150266i
\(43\) −5.29667 1.72099i −0.807735 0.262449i −0.124097 0.992270i \(-0.539603\pi\)
−0.683638 + 0.729821i \(0.739603\pi\)
\(44\) 1.42451 0.462852i 0.214753 0.0697776i
\(45\) 4.37913 3.18163i 0.652802 0.474289i
\(46\) 0.447884 1.37845i 0.0660369 0.203241i
\(47\) 3.83056 0.558745 0.279372 0.960183i \(-0.409874\pi\)
0.279372 + 0.960183i \(0.409874\pi\)
\(48\) −1.64053 −0.236791
\(49\) 0.397366 1.22297i 0.0567666 0.174710i
\(50\) 1.21289i 0.171528i
\(51\) 0.133988 + 0.0435352i 0.0187620 + 0.00609615i
\(52\) 0.640616 + 1.97161i 0.0888375 + 0.273414i
\(53\) −13.6262 4.42743i −1.87171 0.608155i −0.990885 0.134709i \(-0.956990\pi\)
−0.880823 0.473446i \(-0.843010\pi\)
\(54\) −2.32014 3.19340i −0.315731 0.434567i
\(55\) 6.74129 2.19038i 0.908995 0.295350i
\(56\) −2.24793 6.91843i −0.300393 0.924514i
\(57\) 0.907729 + 2.79370i 0.120232 + 0.370035i
\(58\) −6.19452 4.50059i −0.813381 0.590956i
\(59\) 3.02806 4.16777i 0.394220 0.542597i −0.565062 0.825049i \(-0.691148\pi\)
0.959282 + 0.282452i \(0.0911477\pi\)
\(60\) 0.470653 0.0607611
\(61\) −7.52310 + 2.09834i −0.963234 + 0.268665i
\(62\) 5.54710 0.704482
\(63\) 3.78677 5.21204i 0.477088 0.656656i
\(64\) 7.20082 + 5.23170i 0.900102 + 0.653962i
\(65\) 3.03162 + 9.33036i 0.376026 + 1.15729i
\(66\) −0.755890 2.32639i −0.0930437 0.286359i
\(67\) −11.9252 + 3.87475i −1.45690 + 0.473376i −0.927122 0.374760i \(-0.877725\pi\)
−0.529779 + 0.848136i \(0.677725\pi\)
\(68\) −0.0636478 0.0876037i −0.00771843 0.0106235i
\(69\) 0.606369 + 0.197021i 0.0729983 + 0.0237186i
\(70\) −1.86223 5.73134i −0.222579 0.685027i
\(71\) 1.81332 + 0.589183i 0.215201 + 0.0699231i 0.414634 0.909988i \(-0.363910\pi\)
−0.199432 + 0.979912i \(0.563910\pi\)
\(72\) 8.20170i 0.966580i
\(73\) −0.832448 + 2.56201i −0.0974307 + 0.299861i −0.987880 0.155223i \(-0.950391\pi\)
0.890449 + 0.455083i \(0.150391\pi\)
\(74\) −12.3963 −1.44104
\(75\) −0.533541 −0.0616080
\(76\) 0.697690 2.14727i 0.0800305 0.246309i
\(77\) 6.82519 4.95879i 0.777802 0.565106i
\(78\) 3.21987 1.04620i 0.364578 0.118459i
\(79\) −7.35678 2.39036i −0.827702 0.268937i −0.135625 0.990760i \(-0.543304\pi\)
−0.692077 + 0.721823i \(0.743304\pi\)
\(80\) 4.82754 + 3.50741i 0.539735 + 0.392140i
\(81\) −5.13642 + 3.73183i −0.570713 + 0.414647i
\(82\) 0.230096i 0.0254098i
\(83\) 12.5362 + 9.10809i 1.37603 + 0.999743i 0.997239 + 0.0742597i \(0.0236594\pi\)
0.378789 + 0.925483i \(0.376341\pi\)
\(84\) 0.532755 0.173103i 0.0581283 0.0188870i
\(85\) −0.301204 0.414571i −0.0326701 0.0449666i
\(86\) 5.65558 4.10902i 0.609857 0.443087i
\(87\) 1.97978 2.72493i 0.212255 0.292143i
\(88\) −3.31889 + 10.2145i −0.353795 + 1.08887i
\(89\) 9.09752 12.5217i 0.964335 1.32729i 0.0194775 0.999810i \(-0.493800\pi\)
0.944857 0.327483i \(-0.106200\pi\)
\(90\) 6.79443i 0.716196i
\(91\) 6.86327 + 9.44648i 0.719466 + 0.990260i
\(92\) −0.288042 0.396456i −0.0300305 0.0413334i
\(93\) 2.44013i 0.253030i
\(94\) −2.82621 + 3.88994i −0.291501 + 0.401217i
\(95\) 3.30171 10.1616i 0.338748 1.04256i
\(96\) −0.764968 + 1.05289i −0.0780742 + 0.107460i
\(97\) 3.36013 2.44127i 0.341169 0.247874i −0.403986 0.914765i \(-0.632376\pi\)
0.745155 + 0.666891i \(0.232376\pi\)
\(98\) 0.948746 + 1.30584i 0.0958379 + 0.131910i
\(99\) −9.04620 + 2.93929i −0.909177 + 0.295410i
\(100\) 0.331766 + 0.241042i 0.0331766 + 0.0241042i
\(101\) 9.26984i 0.922383i 0.887301 + 0.461192i \(0.152578\pi\)
−0.887301 + 0.461192i \(0.847422\pi\)
\(102\) −0.143067 + 0.103944i −0.0141657 + 0.0102920i
\(103\) −11.6371 8.45482i −1.14663 0.833078i −0.158604 0.987342i \(-0.550699\pi\)
−0.988030 + 0.154264i \(0.950699\pi\)
\(104\) −14.1375 4.59355i −1.38629 0.450434i
\(105\) 2.52118 0.819182i 0.246042 0.0799439i
\(106\) 14.5496 10.5709i 1.41318 1.02673i
\(107\) −4.82546 + 14.8513i −0.466495 + 1.43572i 0.390597 + 0.920562i \(0.372269\pi\)
−0.857092 + 0.515163i \(0.827731\pi\)
\(108\) −1.33460 −0.128421
\(109\) 1.76843 0.169385 0.0846924 0.996407i \(-0.473009\pi\)
0.0846924 + 0.996407i \(0.473009\pi\)
\(110\) −2.74942 + 8.46186i −0.262147 + 0.806807i
\(111\) 5.45307i 0.517582i
\(112\) 6.75452 + 2.19468i 0.638242 + 0.207377i
\(113\) −0.0110103 0.0338863i −0.00103576 0.00318776i 0.950537 0.310610i \(-0.100533\pi\)
−0.951573 + 0.307423i \(0.900533\pi\)
\(114\) −3.50673 1.13941i −0.328436 0.106715i
\(115\) −1.36312 1.87617i −0.127111 0.174954i
\(116\) −2.46213 + 0.799994i −0.228603 + 0.0742776i
\(117\) −4.06816 12.5205i −0.376101 1.15752i
\(118\) 1.99825 + 6.14999i 0.183954 + 0.566153i
\(119\) −0.493423 0.358493i −0.0452320 0.0328630i
\(120\) −1.98367 + 2.73029i −0.181084 + 0.249240i
\(121\) −1.45564 −0.132331
\(122\) 3.41971 9.18788i 0.309606 0.831831i
\(123\) −0.101218 −0.00912649
\(124\) 1.10240 1.51732i 0.0989983 0.136259i
\(125\) 9.69424 + 7.04328i 0.867079 + 0.629970i
\(126\) 2.49894 + 7.69094i 0.222623 + 0.685164i
\(127\) 2.01970 + 6.21599i 0.179219 + 0.551580i 0.999801 0.0199492i \(-0.00635045\pi\)
−0.820582 + 0.571529i \(0.806350\pi\)
\(128\) −6.14237 + 1.99578i −0.542914 + 0.176403i
\(129\) 1.80753 + 2.48785i 0.159144 + 0.219043i
\(130\) −11.7117 3.80537i −1.02719 0.333753i
\(131\) −0.565003 1.73890i −0.0493646 0.151928i 0.923336 0.383994i \(-0.125452\pi\)
−0.972700 + 0.232065i \(0.925452\pi\)
\(132\) −0.786569 0.255572i −0.0684620 0.0222447i
\(133\) 12.7168i 1.10268i
\(134\) 4.86369 14.9689i 0.420159 1.29312i
\(135\) −6.31577 −0.543575
\(136\) 0.776453 0.0665803
\(137\) 4.03793 12.4275i 0.344984 1.06175i −0.616608 0.787270i \(-0.711494\pi\)
0.961592 0.274482i \(-0.0885062\pi\)
\(138\) −0.647458 + 0.470405i −0.0551152 + 0.0400436i
\(139\) 11.0028 3.57502i 0.933243 0.303229i 0.197355 0.980332i \(-0.436765\pi\)
0.735888 + 0.677103i \(0.236765\pi\)
\(140\) −1.93781 0.629632i −0.163775 0.0532136i
\(141\) −1.71116 1.24323i −0.144106 0.104699i
\(142\) −1.93619 + 1.40672i −0.162481 + 0.118050i
\(143\) 17.2394i 1.44163i
\(144\) −6.47812 4.70663i −0.539843 0.392219i
\(145\) −11.6516 + 3.78585i −0.967617 + 0.314398i
\(146\) −1.98754 2.73562i −0.164490 0.226401i
\(147\) −0.574430 + 0.417348i −0.0473782 + 0.0344222i
\(148\) −2.46358 + 3.39082i −0.202505 + 0.278724i
\(149\) 1.54164 4.74467i 0.126296 0.388698i −0.867839 0.496845i \(-0.834492\pi\)
0.994135 + 0.108147i \(0.0344917\pi\)
\(150\) 0.393649 0.541811i 0.0321413 0.0442387i
\(151\) 19.5832i 1.59366i 0.604203 + 0.796830i \(0.293492\pi\)
−0.604203 + 0.796830i \(0.706508\pi\)
\(152\) 9.51589 + 13.0975i 0.771840 + 1.06235i
\(153\) 0.404188 + 0.556317i 0.0326767 + 0.0449756i
\(154\) 10.5896i 0.853334i
\(155\) 5.21693 7.18049i 0.419034 0.576751i
\(156\) 0.353727 1.08866i 0.0283208 0.0871626i
\(157\) 1.42877 1.96654i 0.114028 0.156947i −0.748188 0.663487i \(-0.769076\pi\)
0.862216 + 0.506540i \(0.169076\pi\)
\(158\) 7.85528 5.70720i 0.624933 0.454040i
\(159\) 4.65006 + 6.40026i 0.368774 + 0.507574i
\(160\) 4.50209 1.46282i 0.355921 0.115646i
\(161\) −2.23302 1.62238i −0.175986 0.127862i
\(162\) 7.96940i 0.626135i
\(163\) 11.6916 8.49445i 0.915757 0.665337i −0.0267070 0.999643i \(-0.508502\pi\)
0.942464 + 0.334307i \(0.108502\pi\)
\(164\) 0.0629391 + 0.0457279i 0.00491471 + 0.00357075i
\(165\) −3.72232 1.20945i −0.289782 0.0941559i
\(166\) −18.4986 + 6.01054i −1.43577 + 0.466509i
\(167\) 7.43108 5.39900i 0.575035 0.417787i −0.261896 0.965096i \(-0.584348\pi\)
0.836931 + 0.547309i \(0.184348\pi\)
\(168\) −1.24123 + 3.82013i −0.0957633 + 0.294729i
\(169\) 10.8604 0.835413
\(170\) 0.643227 0.0493333
\(171\) −4.43060 + 13.6360i −0.338816 + 1.04277i
\(172\) 2.36360i 0.180223i
\(173\) −3.83370 1.24565i −0.291471 0.0947047i 0.159632 0.987177i \(-0.448969\pi\)
−0.451103 + 0.892472i \(0.648969\pi\)
\(174\) 1.30648 + 4.02094i 0.0990441 + 0.304826i
\(175\) 2.19673 + 0.713762i 0.166057 + 0.0539553i
\(176\) −6.16334 8.48311i −0.464579 0.639439i
\(177\) −2.70534 + 0.879019i −0.203346 + 0.0660711i
\(178\) 6.00357 + 18.4771i 0.449986 + 1.38492i
\(179\) 7.04388 + 21.6788i 0.526484 + 1.62035i 0.761363 + 0.648326i \(0.224531\pi\)
−0.234879 + 0.972025i \(0.575469\pi\)
\(180\) 1.85851 + 1.35029i 0.138525 + 0.100644i
\(181\) −6.96035 + 9.58010i −0.517359 + 0.712084i −0.985139 0.171762i \(-0.945054\pi\)
0.467780 + 0.883845i \(0.345054\pi\)
\(182\) −14.6567 −1.08642
\(183\) 4.04169 + 1.50431i 0.298770 + 0.111202i
\(184\) 3.51389 0.259047
\(185\) −11.6585 + 16.0465i −0.857150 + 1.17977i
\(186\) −2.47796 1.80034i −0.181693 0.132007i
\(187\) 0.278262 + 0.856402i 0.0203485 + 0.0626263i
\(188\) 0.502368 + 1.54613i 0.0366389 + 0.112763i
\(189\) −7.14912 + 2.32289i −0.520022 + 0.168965i
\(190\) 7.88312 + 10.8502i 0.571902 + 0.787155i
\(191\) 9.15352 + 2.97416i 0.662326 + 0.215203i 0.620841 0.783936i \(-0.286791\pi\)
0.0414847 + 0.999139i \(0.486791\pi\)
\(192\) −1.51872 4.67413i −0.109604 0.337326i
\(193\) −11.5824 3.76334i −0.833717 0.270891i −0.139107 0.990277i \(-0.544423\pi\)
−0.694610 + 0.719386i \(0.744423\pi\)
\(194\) 5.21340i 0.374300i
\(195\) 1.67396 5.15192i 0.119875 0.368937i
\(196\) 0.545740 0.0389814
\(197\) −8.80635 −0.627427 −0.313713 0.949518i \(-0.601573\pi\)
−0.313713 + 0.949518i \(0.601573\pi\)
\(198\) 3.68948 11.3550i 0.262200 0.806968i
\(199\) 19.9215 14.4738i 1.41220 1.02602i 0.419198 0.907895i \(-0.362311\pi\)
0.992999 0.118126i \(-0.0376885\pi\)
\(200\) −2.79660 + 0.908671i −0.197750 + 0.0642528i
\(201\) 6.58473 + 2.13951i 0.464451 + 0.150909i
\(202\) −9.41353 6.83933i −0.662334 0.481214i
\(203\) −11.7967 + 8.57077i −0.827963 + 0.601550i
\(204\) 0.0597909i 0.00418620i
\(205\) 0.297850 + 0.216400i 0.0208027 + 0.0151141i
\(206\) 17.1718 5.57944i 1.19641 0.388738i
\(207\) 1.82918 + 2.51765i 0.127137 + 0.174989i
\(208\) 11.7412 8.53045i 0.814102 0.591480i
\(209\) −11.0358 + 15.1895i −0.763364 + 1.05068i
\(210\) −1.02826 + 3.16466i −0.0709567 + 0.218382i
\(211\) −7.23167 + 9.95355i −0.497849 + 0.685230i −0.981811 0.189858i \(-0.939197\pi\)
0.483963 + 0.875089i \(0.339197\pi\)
\(212\) 6.08060i 0.417618i
\(213\) −0.618809 0.851718i −0.0424001 0.0583588i
\(214\) −11.5212 15.8576i −0.787574 1.08400i
\(215\) 11.1854i 0.762836i
\(216\) 5.62495 7.74208i 0.382729 0.526782i
\(217\) 3.26437 10.0467i 0.221600 0.682014i
\(218\) −1.30476 + 1.79584i −0.0883692 + 0.121630i
\(219\) 1.20338 0.874307i 0.0813169 0.0590802i
\(220\) 1.76820 + 2.43372i 0.119212 + 0.164082i
\(221\) −1.18531 + 0.385131i −0.0797328 + 0.0259067i
\(222\) 5.53760 + 4.02330i 0.371659 + 0.270026i
\(223\) 2.62388i 0.175708i −0.996133 0.0878541i \(-0.971999\pi\)
0.996133 0.0878541i \(-0.0280009\pi\)
\(224\) 4.55812 3.31167i 0.304552 0.221270i
\(225\) −2.10684 1.53071i −0.140456 0.102047i
\(226\) 0.0425351 + 0.0138205i 0.00282939 + 0.000919325i
\(227\) −10.4947 + 3.40994i −0.696559 + 0.226326i −0.635831 0.771828i \(-0.719342\pi\)
−0.0607285 + 0.998154i \(0.519342\pi\)
\(228\) −1.00858 + 0.732773i −0.0667945 + 0.0485291i
\(229\) 8.75958 26.9592i 0.578849 1.78152i −0.0438306 0.999039i \(-0.513956\pi\)
0.622680 0.782477i \(-0.286044\pi\)
\(230\) 2.91096 0.191943
\(231\) −4.65830 −0.306494
\(232\) 5.73637 17.6547i 0.376611 1.15909i
\(233\) 4.83039i 0.316449i 0.987403 + 0.158225i \(0.0505770\pi\)
−0.987403 + 0.158225i \(0.949423\pi\)
\(234\) 15.7161 + 5.10647i 1.02739 + 0.333820i
\(235\) 2.37738 + 7.31682i 0.155083 + 0.477297i
\(236\) 2.07936 + 0.675624i 0.135355 + 0.0439794i
\(237\) 2.51056 + 3.45549i 0.163078 + 0.224458i
\(238\) 0.728100 0.236574i 0.0471957 0.0153348i
\(239\) 0.405160 + 1.24695i 0.0262076 + 0.0806588i 0.963305 0.268410i \(-0.0864981\pi\)
−0.937097 + 0.349068i \(0.886498\pi\)
\(240\) −1.01817 3.13361i −0.0657227 0.202274i
\(241\) −18.5731 13.4942i −1.19640 0.869236i −0.202474 0.979288i \(-0.564898\pi\)
−0.993926 + 0.110052i \(0.964898\pi\)
\(242\) 1.07398 1.47821i 0.0690381 0.0950228i
\(243\) 12.9396 0.830079
\(244\) −1.83359 2.76135i −0.117383 0.176778i
\(245\) 2.58263 0.164998
\(246\) 0.0746789 0.102787i 0.00476135 0.00655344i
\(247\) −21.0232 15.2743i −1.33768 0.971879i
\(248\) 4.15578 + 12.7902i 0.263892 + 0.812177i
\(249\) −2.64400 8.13740i −0.167557 0.515687i
\(250\) −14.3049 + 4.64795i −0.904722 + 0.293962i
\(251\) −9.34235 12.8586i −0.589684 0.811630i 0.405031 0.914303i \(-0.367261\pi\)
−0.994715 + 0.102673i \(0.967261\pi\)
\(252\) 2.60036 + 0.844909i 0.163807 + 0.0532242i
\(253\) 1.25929 + 3.87570i 0.0791709 + 0.243663i
\(254\) −7.80249 2.53518i −0.489572 0.159071i
\(255\) 0.282952i 0.0177191i
\(256\) −2.99578 + 9.22006i −0.187236 + 0.576254i
\(257\) 2.44266 0.152369 0.0761843 0.997094i \(-0.475726\pi\)
0.0761843 + 0.997094i \(0.475726\pi\)
\(258\) −3.86002 −0.240315
\(259\) −7.29502 + 22.4518i −0.453290 + 1.39508i
\(260\) −3.36842 + 2.44730i −0.208901 + 0.151775i
\(261\) 15.6355 5.08027i 0.967811 0.314461i
\(262\) 2.18272 + 0.709208i 0.134849 + 0.0438150i
\(263\) 5.65529 + 4.10881i 0.348720 + 0.253360i 0.748332 0.663324i \(-0.230855\pi\)
−0.399612 + 0.916684i \(0.630855\pi\)
\(264\) 4.79776 3.48578i 0.295282 0.214535i
\(265\) 28.7755i 1.76767i
\(266\) 12.9139 + 9.38250i 0.791802 + 0.575278i
\(267\) −8.12795 + 2.64093i −0.497422 + 0.161622i
\(268\) −3.12793 4.30522i −0.191069 0.262983i
\(269\) −13.9956 + 10.1684i −0.853326 + 0.619978i −0.926061 0.377374i \(-0.876827\pi\)
0.0727351 + 0.997351i \(0.476827\pi\)
\(270\) 4.65981 6.41367i 0.283587 0.390324i
\(271\) −4.58539 + 14.1124i −0.278543 + 0.857266i 0.709718 + 0.704486i \(0.248822\pi\)
−0.988260 + 0.152780i \(0.951178\pi\)
\(272\) −0.445575 + 0.613282i −0.0270170 + 0.0371857i
\(273\) 6.44737i 0.390213i
\(274\) 9.64092 + 13.2696i 0.582429 + 0.801645i
\(275\) −2.00447 2.75891i −0.120874 0.166369i
\(276\) 0.270588i 0.0162875i
\(277\) −2.67671 + 3.68417i −0.160828 + 0.221361i −0.881824 0.471578i \(-0.843684\pi\)
0.720996 + 0.692939i \(0.243684\pi\)
\(278\) −4.48747 + 13.8110i −0.269140 + 0.828329i
\(279\) −7.00065 + 9.63557i −0.419118 + 0.576866i
\(280\) 11.8199 8.58763i 0.706372 0.513209i
\(281\) 9.25243 + 12.7349i 0.551954 + 0.759699i 0.990276 0.139119i \(-0.0444270\pi\)
−0.438322 + 0.898818i \(0.644427\pi\)
\(282\) 2.52500 0.820423i 0.150362 0.0488555i
\(283\) 11.7365 + 8.52706i 0.697662 + 0.506881i 0.879170 0.476508i \(-0.158098\pi\)
−0.181508 + 0.983389i \(0.558098\pi\)
\(284\) 0.809179i 0.0480159i
\(285\) −4.77293 + 3.46774i −0.282724 + 0.205411i
\(286\) 17.5066 + 12.7193i 1.03519 + 0.752108i
\(287\) 0.416741 + 0.135407i 0.0245994 + 0.00799283i
\(288\) −6.04140 + 1.96297i −0.355993 + 0.115669i
\(289\) −13.7006 + 9.95408i −0.805919 + 0.585534i
\(290\) 4.75211 14.6255i 0.279053 0.858838i
\(291\) −2.29334 −0.134438
\(292\) −1.14328 −0.0669053
\(293\) −5.41202 + 16.6565i −0.316173 + 0.973082i 0.659095 + 0.752059i \(0.270939\pi\)
−0.975269 + 0.221022i \(0.929061\pi\)
\(294\) 0.891255i 0.0519790i
\(295\) 9.84024 + 3.19729i 0.572921 + 0.186153i
\(296\) −9.28710 28.5827i −0.539802 1.66134i
\(297\) 10.5551 + 3.42956i 0.612469 + 0.199003i
\(298\) 3.68079 + 5.06617i 0.213222 + 0.293475i
\(299\) −5.36420 + 1.74294i −0.310220 + 0.100797i
\(300\) −0.0699724 0.215353i −0.00403986 0.0124334i
\(301\) −4.11389 12.6613i −0.237121 0.729783i
\(302\) −19.8868 14.4486i −1.14436 0.831423i
\(303\) 3.00858 4.14095i 0.172838 0.237892i
\(304\) −15.8058 −0.906527
\(305\) −8.67717 13.0677i −0.496853 0.748254i
\(306\) −0.863153 −0.0493431
\(307\) −11.4833 + 15.8053i −0.655384 + 0.902058i −0.999318 0.0369354i \(-0.988240\pi\)
0.343934 + 0.938994i \(0.388240\pi\)
\(308\) 2.89662 + 2.10452i 0.165050 + 0.119916i
\(309\) 2.45436 + 7.55375i 0.139624 + 0.429718i
\(310\) 3.44272 + 10.5956i 0.195533 + 0.601790i
\(311\) 21.3585 6.93979i 1.21113 0.393519i 0.367284 0.930109i \(-0.380288\pi\)
0.843843 + 0.536590i \(0.180288\pi\)
\(312\) 4.82453 + 6.64040i 0.273135 + 0.375938i
\(313\) 12.2136 + 3.96845i 0.690355 + 0.224310i 0.633123 0.774051i \(-0.281773\pi\)
0.0572318 + 0.998361i \(0.481773\pi\)
\(314\) 0.942865 + 2.90184i 0.0532089 + 0.163760i
\(315\) 12.3058 + 3.99840i 0.693354 + 0.225284i
\(316\) 3.28290i 0.184678i
\(317\) −0.930921 + 2.86508i −0.0522857 + 0.160919i −0.973790 0.227450i \(-0.926961\pi\)
0.921504 + 0.388369i \(0.126961\pi\)
\(318\) −9.93032 −0.556864
\(319\) 21.5283 1.20536
\(320\) −5.52408 + 17.0014i −0.308805 + 0.950406i
\(321\) 6.97565 5.06811i 0.389343 0.282874i
\(322\) 3.29506 1.07063i 0.183626 0.0596639i
\(323\) 1.29091 + 0.419444i 0.0718284 + 0.0233385i
\(324\) −2.17990 1.58379i −0.121106 0.0879885i
\(325\) 3.81851 2.77431i 0.211813 0.153891i
\(326\) 18.1401i 1.00469i
\(327\) −0.789980 0.573954i −0.0436860 0.0317397i
\(328\) −0.530541 + 0.172383i −0.0292943 + 0.00951828i
\(329\) 5.38214 + 7.40788i 0.296727 + 0.408409i
\(330\) 3.97455 2.88768i 0.218792 0.158961i
\(331\) 11.0764 15.2454i 0.608815 0.837962i −0.387665 0.921801i \(-0.626718\pi\)
0.996479 + 0.0838389i \(0.0267181\pi\)
\(332\) −2.03221 + 6.25449i −0.111532 + 0.343260i
\(333\) 15.6446 21.5330i 0.857321 1.18000i
\(334\) 11.5297i 0.630876i
\(335\) −14.8024 20.3738i −0.808744 1.11314i
\(336\) −2.30503 3.17261i −0.125750 0.173080i
\(337\) 12.5489i 0.683580i −0.939776 0.341790i \(-0.888967\pi\)
0.939776 0.341790i \(-0.111033\pi\)
\(338\) −8.01284 + 11.0287i −0.435841 + 0.599883i
\(339\) −0.00607954 + 0.0187109i −0.000330195 + 0.00101624i
\(340\) 0.127831 0.175945i 0.00693262 0.00954194i
\(341\) −12.6178 + 9.16737i −0.683292 + 0.496441i
\(342\) −10.5784 14.5600i −0.572016 0.787313i
\(343\) 18.8374 6.12063i 1.01712 0.330483i
\(344\) 13.7114 + 9.96191i 0.739269 + 0.537110i
\(345\) 1.28051i 0.0689406i
\(346\) 4.09348 2.97409i 0.220067 0.159888i
\(347\) −11.5376 8.38259i −0.619373 0.450001i 0.233329 0.972398i \(-0.425038\pi\)
−0.852703 + 0.522397i \(0.825038\pi\)
\(348\) 1.35951 + 0.441730i 0.0728772 + 0.0236792i
\(349\) 13.1239 4.26420i 0.702504 0.228257i 0.0640828 0.997945i \(-0.479588\pi\)
0.638421 + 0.769687i \(0.279588\pi\)
\(350\) −2.34559 + 1.70417i −0.125377 + 0.0910916i
\(351\) −4.74672 + 14.6089i −0.253361 + 0.779766i
\(352\) −8.31835 −0.443370
\(353\) −0.783067 −0.0416785 −0.0208392 0.999783i \(-0.506634\pi\)
−0.0208392 + 0.999783i \(0.506634\pi\)
\(354\) 1.10337 3.39582i 0.0586435 0.180486i
\(355\) 3.82932i 0.203239i
\(356\) 6.24723 + 2.02985i 0.331102 + 0.107582i
\(357\) 0.104067 + 0.320286i 0.00550783 + 0.0169514i
\(358\) −27.2119 8.84167i −1.43819 0.467297i
\(359\) −7.44237 10.2435i −0.392793 0.540633i 0.566124 0.824320i \(-0.308442\pi\)
−0.958917 + 0.283687i \(0.908442\pi\)
\(360\) −15.6662 + 5.09026i −0.825682 + 0.268280i
\(361\) 2.87426 + 8.84606i 0.151277 + 0.465582i
\(362\) −4.59323 14.1365i −0.241415 0.742998i
\(363\) 0.650254 + 0.472437i 0.0341295 + 0.0247965i
\(364\) −2.91278 + 4.00910i −0.152671 + 0.210134i
\(365\) −5.41039 −0.283193
\(366\) −4.50960 + 2.99445i −0.235721 + 0.156523i
\(367\) −19.0239 −0.993040 −0.496520 0.868025i \(-0.665389\pi\)
−0.496520 + 0.868025i \(0.665389\pi\)
\(368\) −2.01648 + 2.77544i −0.105116 + 0.144680i
\(369\) −0.399687 0.290390i −0.0208069 0.0151171i
\(370\) −7.69359 23.6784i −0.399971 1.23098i
\(371\) −10.5834 32.5724i −0.549464 1.69107i
\(372\) −0.984910 + 0.320017i −0.0510652 + 0.0165921i
\(373\) −5.41223 7.44929i −0.280235 0.385710i 0.645577 0.763695i \(-0.276617\pi\)
−0.925812 + 0.377985i \(0.876617\pi\)
\(374\) −1.07498 0.349282i −0.0555859 0.0180609i
\(375\) −2.04460 6.29264i −0.105583 0.324951i
\(376\) −11.0865 3.60224i −0.571745 0.185771i
\(377\) 29.7966i 1.53460i
\(378\) 2.91576 8.97378i 0.149970 0.461562i
\(379\) 25.8699 1.32885 0.664424 0.747356i \(-0.268677\pi\)
0.664424 + 0.747356i \(0.268677\pi\)
\(380\) 4.53454 0.232617
\(381\) 1.11521 3.43226i 0.0571340 0.175840i
\(382\) −9.77378 + 7.10106i −0.500070 + 0.363322i
\(383\) 6.65914 2.16369i 0.340266 0.110559i −0.133899 0.990995i \(-0.542750\pi\)
0.474165 + 0.880436i \(0.342750\pi\)
\(384\) 3.39161 + 1.10200i 0.173078 + 0.0562363i
\(385\) 13.7078 + 9.95931i 0.698615 + 0.507573i
\(386\) 12.3672 8.98530i 0.629474 0.457340i
\(387\) 15.0098i 0.762989i
\(388\) 1.42604 + 1.03608i 0.0723963 + 0.0525990i
\(389\) −3.42124 + 1.11163i −0.173464 + 0.0563618i −0.394461 0.918913i \(-0.629069\pi\)
0.220998 + 0.975274i \(0.429069\pi\)
\(390\) 3.99672 + 5.50102i 0.202382 + 0.278555i
\(391\) 0.238345 0.173168i 0.0120536 0.00875747i
\(392\) −2.30014 + 3.16587i −0.116175 + 0.159901i
\(393\) −0.311976 + 0.960164i −0.0157371 + 0.0484339i
\(394\) 6.49737 8.94286i 0.327333 0.450535i
\(395\) 15.5358i 0.781693i
\(396\) −2.37277 3.26584i −0.119236 0.164114i
\(397\) 10.1841 + 14.0172i 0.511126 + 0.703504i 0.984109 0.177567i \(-0.0568227\pi\)
−0.472983 + 0.881072i \(0.656823\pi\)
\(398\) 30.9091i 1.54933i
\(399\) −4.12730 + 5.68074i −0.206623 + 0.284393i
\(400\) 0.887144 2.73035i 0.0443572 0.136517i
\(401\) 12.0486 16.5835i 0.601678 0.828138i −0.394183 0.919032i \(-0.628972\pi\)
0.995861 + 0.0908937i \(0.0289723\pi\)
\(402\) −7.03092 + 5.10826i −0.350670 + 0.254777i
\(403\) −12.6882 17.4638i −0.632045 0.869935i
\(404\) −3.74158 + 1.21571i −0.186151 + 0.0604840i
\(405\) −10.3161 7.49506i −0.512609 0.372432i
\(406\) 18.3031i 0.908366i
\(407\) 28.1975 20.4867i 1.39770 1.01549i
\(408\) −0.346851 0.252002i −0.0171717 0.0124760i
\(409\) 21.8989 + 7.11537i 1.08283 + 0.351833i 0.795472 0.605991i \(-0.207223\pi\)
0.287358 + 0.957823i \(0.407223\pi\)
\(410\) −0.439510 + 0.142805i −0.0217058 + 0.00705265i
\(411\) −5.83721 + 4.24098i −0.287928 + 0.209192i
\(412\) 1.88645 5.80589i 0.0929386 0.286036i
\(413\) 12.3146 0.605961
\(414\) −3.90625 −0.191982
\(415\) −9.61711 + 29.5984i −0.472085 + 1.45293i
\(416\) 11.5131i 0.564477i
\(417\) −6.07537 1.97401i −0.297512 0.0966676i
\(418\) −7.28268 22.4138i −0.356208 1.09629i
\(419\) 19.1455 + 6.22074i 0.935317 + 0.303903i 0.736735 0.676181i \(-0.236366\pi\)
0.198582 + 0.980084i \(0.436366\pi\)
\(420\) 0.661292 + 0.910191i 0.0322678 + 0.0444128i
\(421\) −28.5022 + 9.26093i −1.38911 + 0.451350i −0.905654 0.424017i \(-0.860620\pi\)
−0.483459 + 0.875367i \(0.660620\pi\)
\(422\) −4.77227 14.6875i −0.232311 0.714979i
\(423\) −3.19023 9.81851i −0.155114 0.477392i
\(424\) 35.2740 + 25.6281i 1.71306 + 1.24461i
\(425\) −0.144912 + 0.199454i −0.00702926 + 0.00967494i
\(426\) 1.32148 0.0640260
\(427\) −14.6283 11.6005i −0.707913 0.561390i
\(428\) −6.62725 −0.320340
\(429\) −5.59514 + 7.70105i −0.270136 + 0.371810i
\(430\) 11.3588 + 8.25262i 0.547768 + 0.397977i
\(431\) 4.35017 + 13.3885i 0.209540 + 0.644899i 0.999496 + 0.0317355i \(0.0101034\pi\)
−0.789956 + 0.613164i \(0.789897\pi\)
\(432\) 2.88715 + 8.88574i 0.138908 + 0.427515i
\(433\) 4.00362 1.30085i 0.192401 0.0625150i −0.211231 0.977436i \(-0.567747\pi\)
0.403633 + 0.914921i \(0.367747\pi\)
\(434\) 7.79396 + 10.7275i 0.374122 + 0.514935i
\(435\) 6.43366 + 2.09042i 0.308470 + 0.100228i
\(436\) 0.231925 + 0.713791i 0.0111072 + 0.0341844i
\(437\) 5.84211 + 1.89822i 0.279466 + 0.0908041i
\(438\) 1.86710i 0.0892136i
\(439\) −1.02979 + 3.16938i −0.0491494 + 0.151266i −0.972619 0.232405i \(-0.925340\pi\)
0.923470 + 0.383671i \(0.125340\pi\)
\(440\) −21.5707 −1.02834
\(441\) −3.46566 −0.165031
\(442\) 0.483428 1.48784i 0.0229943 0.0707693i
\(443\) −7.22885 + 5.25207i −0.343453 + 0.249533i −0.746117 0.665815i \(-0.768084\pi\)
0.402664 + 0.915348i \(0.368084\pi\)
\(444\) 2.20102 0.715155i 0.104456 0.0339397i
\(445\) 29.5641 + 9.60594i 1.40147 + 0.455365i
\(446\) 2.66455 + 1.93591i 0.126170 + 0.0916681i
\(447\) −2.22858 + 1.61916i −0.105408 + 0.0765835i
\(448\) 21.2764i 1.00521i
\(449\) −29.4981 21.4317i −1.39210 1.01142i −0.995631 0.0933760i \(-0.970234\pi\)
−0.396473 0.918046i \(-0.629766\pi\)
\(450\) 3.10887 1.01013i 0.146554 0.0476182i
\(451\) −0.380266 0.523391i −0.0179060 0.0246455i
\(452\) 0.0122336 0.00888820i 0.000575418 0.000418066i
\(453\) 6.35585 8.74807i 0.298624 0.411020i
\(454\) 4.28026 13.1733i 0.200882 0.618253i
\(455\) −13.7843 + 18.9725i −0.646218 + 0.889443i
\(456\) 8.93925i 0.418619i
\(457\) 4.53332 + 6.23958i 0.212060 + 0.291875i 0.901775 0.432205i \(-0.142264\pi\)
−0.689715 + 0.724081i \(0.742264\pi\)
\(458\) 20.9143 + 28.7860i 0.977259 + 1.34508i
\(459\) 0.802344i 0.0374502i
\(460\) 0.578508 0.796248i 0.0269731 0.0371253i
\(461\) 7.48218 23.0278i 0.348480 1.07251i −0.611215 0.791465i \(-0.709319\pi\)
0.959694 0.281045i \(-0.0906812\pi\)
\(462\) 3.43692 4.73051i 0.159900 0.220083i
\(463\) −20.6003 + 14.9670i −0.957375 + 0.695574i −0.952540 0.304415i \(-0.901539\pi\)
−0.00483540 + 0.999988i \(0.501539\pi\)
\(464\) 10.6527 + 14.6622i 0.494540 + 0.680676i
\(465\) −4.66094 + 1.51443i −0.216146 + 0.0702300i
\(466\) −4.90526 3.56388i −0.227232 0.165094i
\(467\) 4.87498i 0.225587i −0.993618 0.112794i \(-0.964020\pi\)
0.993618 0.112794i \(-0.0359799\pi\)
\(468\) 4.52012 3.28406i 0.208943 0.151806i
\(469\) −24.2489 17.6179i −1.11971 0.813518i
\(470\) −9.18428 2.98415i −0.423639 0.137649i
\(471\) −1.27650 + 0.414760i −0.0588181 + 0.0191111i
\(472\) −12.6833 + 9.21492i −0.583794 + 0.424151i
\(473\) −6.07382 + 18.6933i −0.279275 + 0.859519i
\(474\) −5.36136 −0.246255
\(475\) −5.14044 −0.235860
\(476\) 0.0799873 0.246176i 0.00366621 0.0112834i
\(477\) 38.6142i 1.76802i
\(478\) −1.56521 0.508568i −0.0715911 0.0232614i
\(479\) −2.21313 6.81133i −0.101121 0.311217i 0.887680 0.460461i \(-0.152316\pi\)
−0.988800 + 0.149244i \(0.952316\pi\)
\(480\) −2.48591 0.807720i −0.113466 0.0368672i
\(481\) 28.3549 + 39.0271i 1.29287 + 1.77948i
\(482\) 27.4067 8.90497i 1.24834 0.405610i
\(483\) 0.470963 + 1.44948i 0.0214296 + 0.0659534i
\(484\) −0.190904 0.587541i −0.00867744 0.0267064i
\(485\) 6.74853 + 4.90309i 0.306435 + 0.222638i
\(486\) −9.54693 + 13.1402i −0.433058 + 0.596053i
\(487\) 2.83599 0.128511 0.0642555 0.997933i \(-0.479533\pi\)
0.0642555 + 0.997933i \(0.479533\pi\)
\(488\) 23.7469 + 1.00158i 1.07497 + 0.0453396i
\(489\) −7.97971 −0.360855
\(490\) −1.90548 + 2.62266i −0.0860807 + 0.118480i
\(491\) −18.9613 13.7762i −0.855710 0.621710i 0.0710045 0.997476i \(-0.477380\pi\)
−0.926714 + 0.375766i \(0.877380\pi\)
\(492\) −0.0132744 0.0408544i −0.000598457 0.00184186i
\(493\) −0.480948 1.48021i −0.0216608 0.0666651i
\(494\) 31.0221 10.0797i 1.39575 0.453506i
\(495\) −11.2288 15.4551i −0.504696 0.694654i
\(496\) −12.4872 4.05732i −0.560690 0.182179i
\(497\) 1.40839 + 4.33459i 0.0631750 + 0.194433i
\(498\) 10.2143 + 3.31882i 0.457713 + 0.148720i
\(499\) 4.02101i 0.180005i −0.995942 0.0900026i \(-0.971312\pi\)
0.995942 0.0900026i \(-0.0286875\pi\)
\(500\) −1.57150 + 4.83659i −0.0702798 + 0.216299i
\(501\) −5.07183 −0.226593
\(502\) 19.9508 0.890448
\(503\) −0.844107 + 2.59790i −0.0376369 + 0.115834i −0.968110 0.250526i \(-0.919396\pi\)
0.930473 + 0.366361i \(0.119396\pi\)
\(504\) −15.8612 + 11.5238i −0.706513 + 0.513312i
\(505\) −17.7065 + 5.75318i −0.787928 + 0.256013i
\(506\) −4.86489 1.58070i −0.216271 0.0702706i
\(507\) −4.85146 3.52480i −0.215461 0.156542i
\(508\) −2.24408 + 1.63042i −0.0995650 + 0.0723382i
\(509\) 21.9223i 0.971688i −0.874045 0.485844i \(-0.838512\pi\)
0.874045 0.485844i \(-0.161488\pi\)
\(510\) −0.287338 0.208763i −0.0127235 0.00924418i
\(511\) −6.12428 + 1.98990i −0.270922 + 0.0880279i
\(512\) −14.7451 20.2948i −0.651646 0.896914i
\(513\) 13.5342 9.83319i 0.597551 0.434146i
\(514\) −1.80220 + 2.48052i −0.0794918 + 0.109411i
\(515\) 8.92733 27.4755i 0.393385 1.21072i
\(516\) −0.767119 + 1.05585i −0.0337705 + 0.0464812i
\(517\) 13.5190i 0.594566i
\(518\) −17.4175 23.9731i −0.765280 1.05332i
\(519\) 1.30828 + 1.80070i 0.0574272 + 0.0790418i
\(520\) 29.8552i 1.30924i
\(521\) −0.644761 + 0.887437i −0.0282475 + 0.0388793i −0.822907 0.568176i \(-0.807649\pi\)
0.794660 + 0.607055i \(0.207649\pi\)
\(522\) −6.37690 + 19.6261i −0.279109 + 0.859010i
\(523\) −0.440254 + 0.605958i −0.0192510 + 0.0264967i −0.818534 0.574458i \(-0.805213\pi\)
0.799283 + 0.600955i \(0.205213\pi\)
\(524\) 0.627774 0.456104i 0.0274244 0.0199250i
\(525\) −0.749653 1.03181i −0.0327175 0.0450318i
\(526\) −8.34500 + 2.71146i −0.363859 + 0.118225i
\(527\) 0.912197 + 0.662750i 0.0397359 + 0.0288698i
\(528\) 5.78986i 0.251971i
\(529\) −17.5287 + 12.7354i −0.762119 + 0.553712i
\(530\) 29.2216 + 21.2307i 1.26930 + 0.922204i
\(531\) −13.2047 4.29047i −0.573035 0.186190i
\(532\) 5.13287 1.66777i 0.222538 0.0723070i
\(533\) 0.724406 0.526312i 0.0313775 0.0227971i
\(534\) 3.31497 10.2024i 0.143453 0.441502i
\(535\) −31.3625 −1.35592
\(536\) 38.1582 1.64818
\(537\) 3.88940 11.9703i 0.167840 0.516558i
\(538\) 21.7148i 0.936192i
\(539\) −4.31617 1.40241i −0.185910 0.0604060i
\(540\) −0.828296 2.54923i −0.0356442 0.109702i
\(541\) 29.4720 + 9.57603i 1.26710 + 0.411706i 0.864019 0.503459i \(-0.167939\pi\)
0.403081 + 0.915165i \(0.367939\pi\)
\(542\) −10.9480 15.0686i −0.470257 0.647254i
\(543\) 6.21855 2.02053i 0.266864 0.0867093i
\(544\) 0.185834 + 0.571937i 0.00796756 + 0.0245216i
\(545\) 1.09755 + 3.37791i 0.0470138 + 0.144694i
\(546\) 6.54732 + 4.75690i 0.280199 + 0.203577i
\(547\) 14.5034 19.9623i 0.620122 0.853525i −0.377239 0.926116i \(-0.623127\pi\)
0.997362 + 0.0725904i \(0.0231266\pi\)
\(548\) 5.54567 0.236899
\(549\) 11.6440 + 17.5357i 0.496953 + 0.748403i
\(550\) 4.28058 0.182525
\(551\) 19.0743 26.2536i 0.812594 1.11844i
\(552\) −1.56970 1.14045i −0.0668107 0.0485408i
\(553\) −5.71396 17.5858i −0.242982 0.747823i
\(554\) −1.76639 5.43640i −0.0750469 0.230971i
\(555\) 10.4160 3.38436i 0.442134 0.143658i
\(556\) 2.88597 + 3.97220i 0.122392 + 0.168459i
\(557\) 31.9393 + 10.3777i 1.35331 + 0.439717i 0.893804 0.448457i \(-0.148026\pi\)
0.459507 + 0.888174i \(0.348026\pi\)
\(558\) −4.61982 14.2183i −0.195572 0.601910i
\(559\) −25.8727 8.40655i −1.09430 0.355559i
\(560\) 14.2640i 0.602765i
\(561\) 0.153647 0.472877i 0.00648698 0.0199649i
\(562\) −19.7588 −0.833474
\(563\) −33.6701 −1.41903 −0.709513 0.704692i \(-0.751085\pi\)
−0.709513 + 0.704692i \(0.751085\pi\)
\(564\) 0.277391 0.853721i 0.0116803 0.0359481i
\(565\) 0.0578934 0.0420620i 0.00243559 0.00176956i
\(566\) −17.3185 + 5.62712i −0.727950 + 0.236525i
\(567\) −14.4339 4.68985i −0.606165 0.196955i
\(568\) −4.69410 3.41047i −0.196960 0.143100i
\(569\) 8.09730 5.88303i 0.339456 0.246630i −0.404976 0.914327i \(-0.632720\pi\)
0.744432 + 0.667698i \(0.232720\pi\)
\(570\) 7.40543i 0.310179i
\(571\) −10.8513 7.88391i −0.454112 0.329931i 0.337105 0.941467i \(-0.390552\pi\)
−0.791217 + 0.611535i \(0.790552\pi\)
\(572\) 6.95833 2.26090i 0.290942 0.0945329i
\(573\) −3.12371 4.29942i −0.130495 0.179611i
\(574\) −0.444979 + 0.323296i −0.0185731 + 0.0134941i
\(575\) −0.655807 + 0.902641i −0.0273491 + 0.0376427i
\(576\) 7.41281 22.8143i 0.308867 0.950596i
\(577\) 5.97826 8.22837i 0.248878 0.342552i −0.666240 0.745738i \(-0.732097\pi\)
0.915118 + 0.403186i \(0.132097\pi\)
\(578\) 21.2572i 0.884182i
\(579\) 3.95257 + 5.44025i 0.164263 + 0.226089i
\(580\) −3.05616 4.20645i −0.126900 0.174663i
\(581\) 37.0410i 1.53672i
\(582\) 1.69204 2.32889i 0.0701372 0.0965356i
\(583\) −15.6255 + 48.0905i −0.647144 + 1.99170i
\(584\) 4.81860 6.63223i 0.199395 0.274444i
\(585\) 21.3908 15.5413i 0.884400 0.642554i
\(586\) −12.9217 17.7851i −0.533789 0.734697i
\(587\) −24.6772 + 8.01811i −1.01854 + 0.330943i −0.770249 0.637743i \(-0.779868\pi\)
−0.248289 + 0.968686i \(0.579868\pi\)
\(588\) −0.243789 0.177123i −0.0100537 0.00730443i
\(589\) 23.5097i 0.968698i
\(590\) −10.5070 + 7.63380i −0.432567 + 0.314278i
\(591\) 3.93391 + 2.85815i 0.161819 + 0.117569i
\(592\) 27.9056 + 9.06707i 1.14691 + 0.372654i
\(593\) −6.35039 + 2.06337i −0.260779 + 0.0847323i −0.436489 0.899710i \(-0.643778\pi\)
0.175709 + 0.984442i \(0.443778\pi\)
\(594\) −11.2703 + 8.18837i −0.462427 + 0.335973i
\(595\) 0.378528 1.16499i 0.0155181 0.0477599i
\(596\) 2.11727 0.0867268
\(597\) −13.5967 −0.556477
\(598\) 2.18778 6.73330i 0.0894651 0.275345i
\(599\) 19.6048i 0.801032i 0.916290 + 0.400516i \(0.131169\pi\)
−0.916290 + 0.400516i \(0.868831\pi\)
\(600\) 1.54419 + 0.501738i 0.0630414 + 0.0204834i
\(601\) 11.2805 + 34.7179i 0.460142 + 1.41617i 0.864990 + 0.501788i \(0.167324\pi\)
−0.404848 + 0.914384i \(0.632676\pi\)
\(602\) 15.8928 + 5.16387i 0.647741 + 0.210464i
\(603\) 19.8635 + 27.3398i 0.808906 + 1.11336i
\(604\) −7.90437 + 2.56829i −0.321624 + 0.104502i
\(605\) −0.903423 2.78045i −0.0367294 0.113041i
\(606\) 1.98540 + 6.11043i 0.0806513 + 0.248219i
\(607\) −2.93759 2.13429i −0.119233 0.0866280i 0.526571 0.850131i \(-0.323478\pi\)
−0.645804 + 0.763503i \(0.723478\pi\)
\(608\) −7.37015 + 10.1441i −0.298899 + 0.411399i
\(609\) 8.05141 0.326259
\(610\) 19.6723 + 0.829729i 0.796508 + 0.0335947i
\(611\) 18.7112 0.756973
\(612\) −0.171538 + 0.236102i −0.00693401 + 0.00954385i
\(613\) −17.5058 12.7187i −0.707055 0.513705i 0.175168 0.984539i \(-0.443953\pi\)
−0.882222 + 0.470833i \(0.843953\pi\)
\(614\) −7.57794 23.3225i −0.305821 0.941220i
\(615\) −0.0628192 0.193337i −0.00253311 0.00779612i
\(616\) −24.4169 + 7.93353i −0.983785 + 0.319651i
\(617\) −2.05889 2.83382i −0.0828879 0.114085i 0.765560 0.643365i \(-0.222462\pi\)
−0.848447 + 0.529280i \(0.822462\pi\)
\(618\) −9.48168 3.08078i −0.381409 0.123927i
\(619\) 8.73648 + 26.8881i 0.351149 + 1.08073i 0.958209 + 0.286069i \(0.0923487\pi\)
−0.607060 + 0.794656i \(0.707651\pi\)
\(620\) 3.58245 + 1.16401i 0.143875 + 0.0467477i
\(621\) 3.63106i 0.145709i
\(622\) −8.71102 + 26.8098i −0.349280 + 1.07497i
\(623\) 36.9980 1.48229
\(624\) −8.01352 −0.320798
\(625\) −5.94394 + 18.2936i −0.237758 + 0.731743i
\(626\) −13.0412 + 9.47501i −0.521233 + 0.378698i
\(627\) 9.85969 3.20361i 0.393758 0.127940i
\(628\) 0.981132 + 0.318789i 0.0391514 + 0.0127211i
\(629\) −2.03852 1.48107i −0.0812813 0.0590543i
\(630\) −13.1397 + 9.54653i −0.523497 + 0.380343i
\(631\) 1.49128i 0.0593671i 0.999559 + 0.0296836i \(0.00944996\pi\)
−0.999559 + 0.0296836i \(0.990550\pi\)
\(632\) 19.0444 + 13.8365i 0.757544 + 0.550388i
\(633\) 6.46096 2.09929i 0.256800 0.0834394i
\(634\) −2.22266 3.05922i −0.0882729 0.121497i
\(635\) −10.6198 + 7.71571i −0.421433 + 0.306189i
\(636\) −1.97349 + 2.71628i −0.0782541 + 0.107708i
\(637\) 1.94102 5.97384i 0.0769060 0.236692i
\(638\) −15.8837 + 21.8621i −0.628842 + 0.865527i
\(639\) 5.13860i 0.203280i
\(640\) −7.62433 10.4940i −0.301378 0.414811i
\(641\) −10.4584 14.3948i −0.413082 0.568559i 0.550884 0.834582i \(-0.314291\pi\)
−0.963967 + 0.266022i \(0.914291\pi\)
\(642\) 10.8231i 0.427152i
\(643\) 8.72980 12.0155i 0.344270 0.473846i −0.601413 0.798938i \(-0.705395\pi\)
0.945682 + 0.325092i \(0.105395\pi\)
\(644\) 0.361987 1.11408i 0.0142643 0.0439010i
\(645\) −3.63028 + 4.99664i −0.142942 + 0.196743i
\(646\) −1.37839 + 1.00146i −0.0542320 + 0.0394018i
\(647\) −10.5750 14.5552i −0.415745 0.572224i 0.548863 0.835912i \(-0.315061\pi\)
−0.964608 + 0.263689i \(0.915061\pi\)
\(648\) 18.3754 5.97052i 0.721853 0.234544i
\(649\) −14.7091 10.6868i −0.577383 0.419493i
\(650\) 5.92459i 0.232382i
\(651\) −4.71894 + 3.42851i −0.184950 + 0.134374i
\(652\) 4.96194 + 3.60506i 0.194324 + 0.141185i
\(653\) 32.7027 + 10.6258i 1.27976 + 0.415818i 0.868494 0.495700i \(-0.165088\pi\)
0.411261 + 0.911517i \(0.365088\pi\)
\(654\) 1.16570 0.378759i 0.0455825 0.0148107i
\(655\) 2.97084 2.15844i 0.116080 0.0843374i
\(656\) 0.168299 0.517972i 0.00657099 0.0202234i
\(657\) 7.26025 0.283249
\(658\) −11.4937 −0.448070
\(659\) 9.94999 30.6229i 0.387596 1.19290i −0.546983 0.837144i \(-0.684224\pi\)
0.934579 0.355755i \(-0.115776\pi\)
\(660\) 1.66106i 0.0646565i
\(661\) −22.8551 7.42607i −0.888960 0.288840i −0.171287 0.985221i \(-0.554793\pi\)
−0.717673 + 0.696381i \(0.754793\pi\)
\(662\) 7.30947 + 22.4962i 0.284090 + 0.874340i
\(663\) 0.654491 + 0.212657i 0.0254183 + 0.00825891i
\(664\) −27.7175 38.1499i −1.07565 1.48050i
\(665\) 24.2905 7.89247i 0.941946 0.306057i
\(666\) 10.3241 + 31.7743i 0.400051 + 1.23123i
\(667\) −2.17656 6.69876i −0.0842767 0.259377i
\(668\) 3.15376 + 2.29134i 0.122023 + 0.0886547i
\(669\) −0.851596 + 1.17212i −0.0329246 + 0.0453168i
\(670\) 31.6109 1.22124
\(671\) 7.40558 + 26.5509i 0.285889 + 1.02499i
\(672\) −3.11099 −0.120009
\(673\) 10.0946 13.8940i 0.389117 0.535573i −0.568854 0.822438i \(-0.692613\pi\)
0.957971 + 0.286865i \(0.0926132\pi\)
\(674\) 12.7434 + 9.25861i 0.490857 + 0.356628i
\(675\) 0.938971 + 2.88986i 0.0361410 + 0.111231i
\(676\) 1.42431 + 4.38357i 0.0547811 + 0.168599i
\(677\) 10.1805 3.30785i 0.391269 0.127131i −0.106774 0.994283i \(-0.534052\pi\)
0.498043 + 0.867152i \(0.334052\pi\)
\(678\) −0.0145154 0.0199788i −0.000557462 0.000767280i
\(679\) 9.44230 + 3.06799i 0.362362 + 0.117739i
\(680\) 0.481894 + 1.48312i 0.0184798 + 0.0568749i
\(681\) 5.79484 + 1.88286i 0.222059 + 0.0721513i
\(682\) 19.5771i 0.749647i
\(683\) 1.46127 4.49733i 0.0559140 0.172086i −0.919199 0.393793i \(-0.871163\pi\)
0.975113 + 0.221707i \(0.0711628\pi\)
\(684\) −6.08495 −0.232664
\(685\) 26.2440 1.00273
\(686\) −7.68279 + 23.6452i −0.293330 + 0.902777i
\(687\) −12.6628 + 9.20005i −0.483115 + 0.351004i
\(688\) −15.7368 + 5.11321i −0.599961 + 0.194939i
\(689\) −66.5602 21.6267i −2.53574 0.823913i
\(690\) −1.30036 0.944770i −0.0495040 0.0359668i
\(691\) 23.9273 17.3842i 0.910239 0.661327i −0.0308365 0.999524i \(-0.509817\pi\)
0.941075 + 0.338197i \(0.109817\pi\)
\(692\) 1.71076i 0.0650333i
\(693\) −18.3946 13.3645i −0.698754 0.507675i
\(694\) 17.0251 5.53178i 0.646263 0.209983i
\(695\) 13.6574 + 18.7978i 0.518055 + 0.713042i
\(696\) −8.29245 + 6.02482i −0.314325 + 0.228370i
\(697\) −0.0274911 + 0.0378383i −0.00104130 + 0.00143323i
\(698\) −5.35254 + 16.4734i −0.202597 + 0.623529i
\(699\) 1.56773 2.15779i 0.0592970 0.0816153i
\(700\) 0.980275i 0.0370509i
\(701\) −28.1898 38.7999i −1.06471 1.46545i −0.875316 0.483551i \(-0.839347\pi\)
−0.189397 0.981901i \(-0.560653\pi\)
\(702\) −11.3332 15.5988i −0.427744 0.588740i
\(703\) 52.5380i 1.98151i
\(704\) 18.4640 25.4135i 0.695888 0.957808i
\(705\) 1.31271 4.04011i 0.0494395 0.152159i
\(706\) 0.577751 0.795206i 0.0217439 0.0299280i
\(707\) −17.9268 + 13.0246i −0.674208 + 0.489841i
\(708\) −0.709597 0.976676i −0.0266683 0.0367057i
\(709\) 13.2695 4.31152i 0.498347 0.161923i −0.0490494 0.998796i \(-0.515619\pi\)
0.547396 + 0.836874i \(0.315619\pi\)
\(710\) −3.88868 2.82529i −0.145939 0.106031i
\(711\) 20.8477i 0.781850i
\(712\) −38.1056 + 27.6854i −1.42807 + 1.03755i
\(713\) 4.12820 + 2.99931i 0.154602 + 0.112325i
\(714\) −0.402033 0.130628i −0.0150457 0.00488864i
\(715\) 32.9292 10.6994i 1.23148 0.400133i
\(716\) −7.82643 + 5.68624i −0.292487 + 0.212505i
\(717\) 0.223716 0.688527i 0.00835483 0.0257135i
\(718\) 15.8933 0.593134
\(719\) −19.0866 −0.711811 −0.355906 0.934522i \(-0.615828\pi\)
−0.355906 + 0.934522i \(0.615828\pi\)
\(720\) 4.96966 15.2951i 0.185208 0.570013i
\(721\) 34.3842i 1.28054i
\(722\) −11.1038 3.60785i −0.413242 0.134270i
\(723\) 3.91724 + 12.0560i 0.145684 + 0.448368i
\(724\) −4.77965 1.55300i −0.177634 0.0577168i
\(725\) 3.46452 + 4.76851i 0.128669 + 0.177098i
\(726\) −0.959522 + 0.311767i −0.0356112 + 0.0115708i
\(727\) 9.57763 + 29.4769i 0.355215 + 1.09324i 0.955885 + 0.293741i \(0.0949004\pi\)
−0.600670 + 0.799497i \(0.705100\pi\)
\(728\) −10.9805 33.7945i −0.406964 1.25251i
\(729\) 9.62895 + 6.99584i 0.356628 + 0.259105i
\(730\) 3.99181 5.49426i 0.147744 0.203352i
\(731\) 1.42097 0.0525565
\(732\) −0.0771271 + 1.82863i −0.00285070 + 0.0675882i
\(733\) 17.5817 0.649393 0.324697 0.945818i \(-0.394738\pi\)
0.324697 + 0.945818i \(0.394738\pi\)
\(734\) 14.0359 19.3188i 0.518076 0.713070i
\(735\) −1.15369 0.838207i −0.0425546 0.0309177i
\(736\) 0.841002 + 2.58834i 0.0309997 + 0.0954074i
\(737\) 13.6750 + 42.0872i 0.503724 + 1.55030i
\(738\) 0.589782 0.191632i 0.0217102 0.00705406i
\(739\) −11.1192 15.3043i −0.409027 0.562978i 0.553954 0.832548i \(-0.313118\pi\)
−0.962981 + 0.269570i \(0.913118\pi\)
\(740\) −8.00584 2.60126i −0.294301 0.0956241i
\(741\) 4.43399 + 13.6464i 0.162887 + 0.501314i
\(742\) 40.8858 + 13.2846i 1.50097 + 0.487693i
\(743\) 32.3581i 1.18711i −0.804795 0.593553i \(-0.797725\pi\)
0.804795 0.593553i \(-0.202275\pi\)
\(744\) 2.29469 7.06232i 0.0841272 0.258917i
\(745\) 10.0197 0.367092
\(746\) 11.5579 0.423166
\(747\) 12.9053 39.7184i 0.472180 1.45322i
\(748\) −0.309176 + 0.224629i −0.0113046 + 0.00821327i
\(749\) −35.5007 + 11.5349i −1.29717 + 0.421475i
\(750\) 7.89870 + 2.56644i 0.288420 + 0.0937133i
\(751\) 12.7216 + 9.24278i 0.464218 + 0.337274i 0.795183 0.606369i \(-0.207375\pi\)
−0.330966 + 0.943643i \(0.607375\pi\)
\(752\) 9.20735 6.68953i 0.335757 0.243942i
\(753\) 8.77623i 0.319824i
\(754\) −30.2584 21.9840i −1.10195 0.800612i
\(755\) −37.4063 + 12.1540i −1.36135 + 0.442330i
\(756\) −1.87518 2.58096i −0.0681995 0.0938686i
\(757\) −38.1540 + 27.7205i −1.38673 + 1.00752i −0.390514 + 0.920597i \(0.627703\pi\)
−0.996215 + 0.0869206i \(0.972297\pi\)
\(758\) −19.0870 + 26.2709i −0.693269 + 0.954203i
\(759\) 0.695339 2.14003i 0.0252392 0.0776782i
\(760\) −19.1119 + 26.3052i −0.693260 + 0.954190i
\(761\) 8.31072i 0.301263i −0.988590 0.150632i \(-0.951869\pi\)
0.988590 0.150632i \(-0.0481308\pi\)
\(762\) 2.66266 + 3.66484i 0.0964580 + 0.132763i
\(763\) 2.48474 + 3.41994i 0.0899535 + 0.123810i
\(764\) 4.08469i 0.147779i
\(765\) −0.811778 + 1.11732i −0.0293499 + 0.0403966i
\(766\) −2.71592 + 8.35875i −0.0981302 + 0.302014i
\(767\) 14.7912 20.3583i 0.534079 0.735096i
\(768\) 4.33067 3.14642i 0.156270 0.113537i
\(769\) −8.97573 12.3540i −0.323673 0.445498i 0.615911 0.787816i \(-0.288788\pi\)
−0.939584 + 0.342318i \(0.888788\pi\)
\(770\) −20.2274 + 6.57227i −0.728944 + 0.236848i
\(771\) −1.09116 0.792778i −0.0392973 0.0285512i
\(772\) 5.16854i 0.186020i
\(773\) −23.2033 + 16.8582i −0.834564 + 0.606346i −0.920847 0.389924i \(-0.872501\pi\)
0.0862829 + 0.996271i \(0.472501\pi\)
\(774\) −15.2424 11.0743i −0.547877 0.398056i
\(775\) −4.06113 1.31954i −0.145880 0.0473993i
\(776\) −12.0207 + 3.90578i −0.431520 + 0.140209i
\(777\) 10.5456 7.66184i 0.378322 0.274867i
\(778\) 1.39535 4.29444i 0.0500256 0.153963i
\(779\) −0.975189 −0.0349398
\(780\) 2.29900 0.0823175
\(781\) 2.07938 6.39966i 0.0744059 0.228998i
\(782\) 0.369804i 0.0132242i
\(783\) −18.2434 5.92765i −0.651967 0.211837i
\(784\) −1.18061 3.63354i −0.0421645 0.129769i
\(785\) 4.64306 + 1.50862i 0.165718 + 0.0538450i
\(786\) −0.744870 1.02523i −0.0265686 0.0365686i
\(787\) 47.0311 15.2813i 1.67648 0.544721i 0.692256 0.721652i \(-0.256617\pi\)
0.984223 + 0.176931i \(0.0566169\pi\)
\(788\) −1.15493 3.55451i −0.0411426 0.126624i
\(789\) −1.19275 3.67091i −0.0424631 0.130688i
\(790\) 15.7767 + 11.4624i 0.561309 + 0.407815i
\(791\) 0.0500623 0.0689048i 0.00178001 0.00244997i
\(792\) 28.9459 1.02855
\(793\) −36.7481 + 10.2498i −1.30496 + 0.363980i
\(794\) −21.7484 −0.771822
\(795\) −9.33926 + 12.8544i −0.331229 + 0.455898i
\(796\) 8.45471 + 6.14270i 0.299669 + 0.217722i
\(797\) −15.9355 49.0444i −0.564464 1.73724i −0.669539 0.742777i \(-0.733508\pi\)
0.105075 0.994464i \(-0.466492\pi\)
\(798\) −2.72366 8.38256i −0.0964165 0.296739i
\(799\) −0.929516 + 0.302018i −0.0328839 + 0.0106846i
\(800\) −1.33866 1.84251i −0.0473288 0.0651424i
\(801\) −39.6723 12.8903i −1.40175 0.455457i
\(802\) 7.95102 + 24.4707i 0.280760 + 0.864091i
\(803\) 9.04200 + 2.93792i 0.319085 + 0.103677i
\(804\) 2.93838i 0.103629i
\(805\) 1.71305 5.27223i 0.0603771 0.185822i
\(806\) 27.0959 0.954414
\(807\) 9.55221 0.336254
\(808\) 8.71730 26.8291i 0.306673 0.943844i
\(809\) 10.2459 7.44408i 0.360227 0.261720i −0.392920 0.919573i \(-0.628535\pi\)
0.753147 + 0.657853i \(0.228535\pi\)
\(810\) 15.2225 4.94608i 0.534863 0.173788i
\(811\) 46.1020 + 14.9794i 1.61886 + 0.525999i 0.971672 0.236332i \(-0.0759452\pi\)
0.647187 + 0.762331i \(0.275945\pi\)
\(812\) −5.00652 3.63745i −0.175694 0.127649i
\(813\) 6.62860 4.81596i 0.232475 0.168903i
\(814\) 43.7498i 1.53343i
\(815\) 23.4816 + 17.0604i 0.822525 + 0.597599i
\(816\) 0.398088 0.129347i 0.0139359 0.00452804i
\(817\) 17.4148 + 23.9694i 0.609267 + 0.838584i
\(818\) −23.3828 + 16.9886i −0.817559 + 0.593991i
\(819\) 18.4973 25.4593i 0.646347 0.889621i
\(820\) −0.0482835 + 0.148601i −0.00168613 + 0.00518938i
\(821\) −19.7460 + 27.1780i −0.689140 + 0.948520i −0.999998 0.00193620i \(-0.999384\pi\)
0.310858 + 0.950456i \(0.399384\pi\)
\(822\) 9.05670i 0.315889i
\(823\) 15.3973 + 21.1926i 0.536716 + 0.738726i 0.988135 0.153586i \(-0.0490822\pi\)
−0.451419 + 0.892312i \(0.649082\pi\)
\(824\) 25.7295 + 35.4136i 0.896330 + 1.23369i
\(825\) 1.88300i 0.0655577i
\(826\) −9.08575 + 12.5055i −0.316134 + 0.435121i
\(827\) 9.76503 30.0537i 0.339563 1.04507i −0.624867 0.780731i \(-0.714847\pi\)
0.964430 0.264338i \(-0.0851533\pi\)
\(828\) −0.776306 + 1.06849i −0.0269785 + 0.0371327i
\(829\) 19.6250 14.2584i 0.681606 0.495216i −0.192284 0.981339i \(-0.561589\pi\)
0.873890 + 0.486123i \(0.161589\pi\)
\(830\) −22.9617 31.6040i −0.797012 1.09699i
\(831\) 2.39144 0.777026i 0.0829581 0.0269547i
\(832\) 35.1739 + 25.5553i 1.21943 + 0.885971i
\(833\) 0.328093i 0.0113677i
\(834\) 6.48705 4.71311i 0.224628 0.163202i
\(835\) 14.9247 + 10.8434i 0.516491 + 0.375252i
\(836\) −7.57826 2.46233i −0.262100 0.0851613i
\(837\) 13.2167 4.29436i 0.456835 0.148435i
\(838\) −20.4428 + 14.8526i −0.706184 + 0.513073i
\(839\) −14.6860 + 45.1990i −0.507018 + 1.56044i 0.290333 + 0.956926i \(0.406234\pi\)
−0.797351 + 0.603516i \(0.793766\pi\)
\(840\) −8.06724 −0.278346
\(841\) −8.20960 −0.283090
\(842\) 11.6246 35.7768i 0.400610 1.23295i
\(843\) 8.69176i 0.299360i
\(844\) −4.96596 1.61354i −0.170935 0.0555403i
\(845\) 6.74032 + 20.7446i 0.231874 + 0.713635i
\(846\) 12.3245 + 4.00446i 0.423724 + 0.137676i
\(847\) −2.04526 2.81505i −0.0702758 0.0967264i
\(848\) −40.4847 + 13.1543i −1.39025 + 0.451719i
\(849\) −2.47533 7.61829i −0.0849532 0.261459i
\(850\) −0.0956292 0.294316i −0.00328005 0.0100950i
\(851\) −9.22547 6.70269i −0.316245 0.229765i
\(852\) 0.262624 0.361470i 0.00899734 0.0123838i
\(853\) −22.7667 −0.779516 −0.389758 0.920917i \(-0.627441\pi\)
−0.389758 + 0.920917i \(0.627441\pi\)
\(854\) 22.5732 6.29611i 0.772439 0.215449i
\(855\) −28.7961 −0.984805
\(856\) 27.9320 38.4452i 0.954698 1.31403i
\(857\) 42.9379 + 31.1962i 1.46673 + 1.06564i 0.981545 + 0.191229i \(0.0612474\pi\)
0.485184 + 0.874412i \(0.338753\pi\)
\(858\) −3.69230 11.3637i −0.126053 0.387952i
\(859\) 1.44916 + 4.46005i 0.0494446 + 0.152175i 0.972730 0.231939i \(-0.0745070\pi\)
−0.923286 + 0.384114i \(0.874507\pi\)
\(860\) 4.51475 1.46693i 0.153952 0.0500219i
\(861\) −0.142216 0.195744i −0.00484671 0.00667092i
\(862\) −16.8056 5.46046i −0.572400 0.185984i
\(863\) 3.42592 + 10.5439i 0.116620 + 0.358918i 0.992281 0.124007i \(-0.0395744\pi\)
−0.875662 + 0.482925i \(0.839574\pi\)
\(864\) 7.04909 + 2.29039i 0.239815 + 0.0779206i
\(865\) 8.09591i 0.275269i
\(866\) −1.63287 + 5.02545i −0.0554871 + 0.170772i
\(867\) 9.35089 0.317573
\(868\) 4.48326 0.152172
\(869\) −8.43620 + 25.9640i −0.286178 + 0.880767i
\(870\) −6.86961 + 4.99106i −0.232902 + 0.169213i
\(871\) −58.2513 + 18.9270i −1.97377 + 0.641317i
\(872\) −5.11825 1.66302i −0.173326 0.0563170i
\(873\) −9.05591 6.57951i −0.306496 0.222683i
\(874\) −6.23798 + 4.53216i −0.211003 + 0.153303i
\(875\) 28.6438i 0.968336i
\(876\) 0.510716 + 0.371057i 0.0172555 + 0.0125369i
\(877\) 36.8856 11.9849i 1.24554 0.404700i 0.389219 0.921145i \(-0.372745\pi\)
0.856320 + 0.516445i \(0.172745\pi\)
\(878\) −2.45872 3.38414i −0.0829779 0.114209i
\(879\) 7.82357 5.68416i 0.263882 0.191722i
\(880\) 12.3785 17.0376i 0.417281 0.574338i
\(881\) 5.65144 17.3933i 0.190402 0.585996i −0.809598 0.586985i \(-0.800315\pi\)
1.00000 0.000988752i \(0.000314730\pi\)
\(882\) 2.55698 3.51938i 0.0860979 0.118504i
\(883\) 11.4786i 0.386287i 0.981171 + 0.193143i \(0.0618683\pi\)
−0.981171 + 0.193143i \(0.938132\pi\)
\(884\) −0.310901 0.427919i −0.0104567 0.0143925i
\(885\) −3.35806 4.62197i −0.112880 0.155366i
\(886\) 11.2159i 0.376806i
\(887\) −21.9563 + 30.2203i −0.737221 + 1.01470i 0.261552 + 0.965189i \(0.415766\pi\)
−0.998774 + 0.0495088i \(0.984234\pi\)
\(888\) −5.12803 + 15.7825i −0.172085 + 0.529624i
\(889\) −9.18325 + 12.6397i −0.307996 + 0.423920i
\(890\) −31.5673 + 22.9350i −1.05814 + 0.768784i
\(891\) 13.1706 + 18.1277i 0.441231 + 0.607302i
\(892\) 1.05908 0.344115i 0.0354605 0.0115218i
\(893\) −16.4863 11.9780i −0.551693 0.400828i
\(894\) 3.45774i 0.115644i
\(895\) −37.0374 + 26.9092i −1.23802 + 0.899477i
\(896\) −12.4900 9.07448i −0.417260 0.303157i
\(897\) 2.96194 + 0.962392i 0.0988962 + 0.0321333i
\(898\) 43.5277 14.1430i 1.45254 0.471959i
\(899\) 21.8086 15.8449i 0.727358 0.528457i
\(900\) 0.341533 1.05113i 0.0113844 0.0350377i
\(901\) 3.65559 0.121785
\(902\) 0.812066 0.0270389
\(903\) −2.27156 + 6.99113i −0.0755926 + 0.232650i
\(904\) 0.108429i 0.00360629i
\(905\) −22.6190 7.34934i −0.751879 0.244300i
\(906\) 4.19430 + 12.9087i 0.139346 + 0.428864i
\(907\) −28.7648 9.34625i −0.955119 0.310337i −0.210325 0.977631i \(-0.567452\pi\)
−0.744794 + 0.667294i \(0.767452\pi\)
\(908\) −2.75271 3.78878i −0.0913519 0.125735i
\(909\) 23.7605 7.72025i 0.788085 0.256064i
\(910\) −9.09643 27.9959i −0.301544 0.928056i
\(911\) 7.37466 + 22.6969i 0.244333 + 0.751981i 0.995745 + 0.0921477i \(0.0293732\pi\)
−0.751412 + 0.659833i \(0.770627\pi\)
\(912\) 7.06067 + 5.12988i 0.233802 + 0.169867i
\(913\) 32.1448 44.2435i 1.06384 1.46425i
\(914\) −9.68101 −0.320219
\(915\) −0.364992 + 8.65372i −0.0120663 + 0.286083i
\(916\) 12.0303 0.397494
\(917\) 2.56898 3.53590i 0.0848352 0.116766i
\(918\) 0.814782 + 0.591973i 0.0268918 + 0.0195380i
\(919\) −7.70856 23.7245i −0.254282 0.782599i −0.993970 0.109650i \(-0.965027\pi\)
0.739688 0.672949i \(-0.234973\pi\)
\(920\) 2.18084 + 6.71193i 0.0719001 + 0.221286i
\(921\) 10.2594 3.33349i 0.338060 0.109842i
\(922\) 17.8643 + 24.5882i 0.588331 + 0.809768i
\(923\) 8.85753 + 2.87799i 0.291549 + 0.0947301i
\(924\) −0.610923 1.88023i −0.0200979 0.0618550i
\(925\) 9.07557 + 2.94883i 0.298403 + 0.0969570i
\(926\) 31.9623i 1.05035i
\(927\) −11.9797 + 36.8696i −0.393464 + 1.21096i
\(928\) 14.3774 0.471963
\(929\) −52.0441 −1.70751 −0.853756 0.520674i \(-0.825681\pi\)
−0.853756 + 0.520674i \(0.825681\pi\)
\(930\) 1.90096 5.85054i 0.0623348 0.191847i
\(931\) −5.53439 + 4.02097i −0.181382 + 0.131782i
\(932\) −1.94969 + 0.633492i −0.0638641 + 0.0207507i
\(933\) −11.7934 3.83192i −0.386100 0.125451i
\(934\) 4.95055 + 3.59679i 0.161987 + 0.117690i
\(935\) −1.46313 + 1.06302i −0.0478494 + 0.0347646i
\(936\) 40.0629i 1.30950i
\(937\) −23.7282 17.2395i −0.775166 0.563191i 0.128358 0.991728i \(-0.459029\pi\)
−0.903524 + 0.428537i \(0.859029\pi\)
\(938\) 35.7819 11.6263i 1.16832 0.379611i
\(939\) −4.16800 5.73676i −0.136018 0.187212i
\(940\) −2.64150 + 1.91916i −0.0861562 + 0.0625961i
\(941\) 18.9947 26.1439i 0.619208 0.852267i −0.378087 0.925770i \(-0.623418\pi\)
0.997295 + 0.0735029i \(0.0234178\pi\)
\(942\) 0.520619 1.60230i 0.0169627 0.0522058i
\(943\) −0.124413 + 0.171239i −0.00405144 + 0.00557632i
\(944\) 15.3059i 0.498166i
\(945\) −8.87399 12.2140i −0.288671 0.397321i
\(946\) −14.5018 19.9600i −0.471494 0.648955i
\(947\) 14.8438i 0.482358i 0.970481 + 0.241179i \(0.0775341\pi\)
−0.970481 + 0.241179i \(0.922466\pi\)
\(948\) −1.06549 + 1.46651i −0.0346054 + 0.0476302i
\(949\) −4.06627 + 12.5147i −0.131997 + 0.406244i
\(950\) 3.79264 5.22012i 0.123050 0.169363i
\(951\) 1.34573 0.977732i 0.0436384 0.0317051i
\(952\) 1.09096 + 1.50157i 0.0353581 + 0.0486663i
\(953\) −26.0333 + 8.45873i −0.843301 + 0.274005i −0.698638 0.715476i \(-0.746210\pi\)
−0.144664 + 0.989481i \(0.546210\pi\)
\(954\) −39.2127 28.4897i −1.26956 0.922388i
\(955\) 19.3302i 0.625509i
\(956\) −0.450172 + 0.327069i −0.0145596 + 0.0105782i
\(957\) −9.61698 6.98715i −0.310873 0.225862i
\(958\) 8.54977 + 2.77799i 0.276231 + 0.0897527i
\(959\) 29.7069 9.65235i 0.959285 0.311691i
\(960\) 7.98557 5.80185i 0.257733 0.187254i
\(961\) 3.54465 10.9093i 0.114344 0.351913i
\(962\) −60.5524 −1.95229
\(963\) 42.0856 1.35619
\(964\) 3.01083 9.26639i 0.0969724 0.298450i
\(965\) 24.4593i 0.787374i
\(966\) −1.81942 0.591166i −0.0585390 0.0190205i
\(967\) −5.05294 15.5514i −0.162492 0.500098i 0.836351 0.548194i \(-0.184685\pi\)
−0.998843 + 0.0480963i \(0.984685\pi\)
\(968\) 4.21297 + 1.36888i 0.135410 + 0.0439974i
\(969\) −0.440535 0.606344i −0.0141520 0.0194786i
\(970\) −9.95819 + 3.23561i −0.319738 + 0.103889i
\(971\) −14.8704 45.7663i −0.477213 1.46871i −0.842950 0.537991i \(-0.819183\pi\)
0.365738 0.930718i \(-0.380817\pi\)
\(972\) 1.69700 + 5.22283i 0.0544313 + 0.167522i
\(973\) 22.3732 + 16.2551i 0.717251 + 0.521113i
\(974\) −2.09241 + 2.87995i −0.0670451 + 0.0922796i
\(975\) −2.60619 −0.0834649
\(976\) −14.4185 + 18.1817i −0.461524 + 0.581982i
\(977\) 14.2862 0.457058 0.228529 0.973537i \(-0.426608\pi\)
0.228529 + 0.973537i \(0.426608\pi\)
\(978\) 5.88747 8.10340i 0.188260 0.259118i
\(979\) −44.1921 32.1075i −1.41239 1.02616i
\(980\) 0.338705 + 1.04243i 0.0108195 + 0.0332991i
\(981\) −1.47281 4.53284i −0.0470232 0.144723i
\(982\) 27.9794 9.09107i 0.892859 0.290108i
\(983\) −0.478789 0.658996i −0.0152710 0.0210187i 0.801313 0.598245i \(-0.204135\pi\)
−0.816584 + 0.577226i \(0.804135\pi\)
\(984\) 0.292948 + 0.0951844i 0.00933883 + 0.00303437i
\(985\) −5.46553 16.8212i −0.174146 0.535967i
\(986\) 1.85800 + 0.603699i 0.0591706 + 0.0192257i
\(987\) 5.05599i 0.160934i
\(988\) 3.40801 10.4888i 0.108423 0.333693i
\(989\) 6.43068 0.204484
\(990\) 23.9793 0.762112
\(991\) 5.32256 16.3812i 0.169077 0.520365i −0.830237 0.557411i \(-0.811795\pi\)
0.999314 + 0.0370460i \(0.0117948\pi\)
\(992\) −8.42665 + 6.12232i −0.267546 + 0.194384i
\(993\) −9.89595 + 3.21539i −0.314038 + 0.102037i
\(994\) −5.44090 1.76785i −0.172575 0.0560729i
\(995\) 40.0106 + 29.0694i 1.26842 + 0.921562i
\(996\) 2.93774 2.13439i 0.0930859 0.0676309i
\(997\) 9.58063i 0.303422i 0.988425 + 0.151711i \(0.0484782\pi\)
−0.988425 + 0.151711i \(0.951522\pi\)
\(998\) 4.08334 + 2.96672i 0.129256 + 0.0939100i
\(999\) −29.5358 + 9.59678i −0.934473 + 0.303629i
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 61.2.g.a.52.2 yes 16
3.2 odd 2 549.2.y.b.235.3 16
4.3 odd 2 976.2.bd.b.113.3 16
61.24 odd 20 3721.2.a.k.1.5 16
61.27 even 10 inner 61.2.g.a.27.2 16
61.37 odd 20 3721.2.a.k.1.12 16
183.149 odd 10 549.2.y.b.271.3 16
244.27 odd 10 976.2.bd.b.881.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
61.2.g.a.27.2 16 61.27 even 10 inner
61.2.g.a.52.2 yes 16 1.1 even 1 trivial
549.2.y.b.235.3 16 3.2 odd 2
549.2.y.b.271.3 16 183.149 odd 10
976.2.bd.b.113.3 16 4.3 odd 2
976.2.bd.b.881.3 16 244.27 odd 10
3721.2.a.k.1.5 16 61.24 odd 20
3721.2.a.k.1.12 16 61.37 odd 20