Properties

Label 336.2.u.a.139.4
Level $336$
Weight $2$
Character 336.139
Analytic conductor $2.683$
Analytic rank $0$
Dimension $64$
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] = [336,2,Mod(139,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.139");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.u (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 139.4
Character \(\chi\) \(=\) 336.139
Dual form 336.2.u.a.307.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.27023 - 0.621708i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.22696 + 1.57942i) q^{4} +(-1.90169 + 1.90169i) q^{5} +(-1.33780 + 0.458573i) q^{6} +(2.22978 + 1.42411i) q^{7} +(-0.576579 - 2.76904i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-1.27023 - 0.621708i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.22696 + 1.57942i) q^{4} +(-1.90169 + 1.90169i) q^{5} +(-1.33780 + 0.458573i) q^{6} +(2.22978 + 1.42411i) q^{7} +(-0.576579 - 2.76904i) q^{8} -1.00000i q^{9} +(3.59788 - 1.23329i) q^{10} +(-3.56463 + 3.56463i) q^{11} +(1.98441 + 0.249229i) q^{12} +(-1.66932 - 1.66932i) q^{13} +(-1.94695 - 3.19522i) q^{14} +2.68940i q^{15} +(-0.989144 + 3.87577i) q^{16} +7.15496i q^{17} +(-0.621708 + 1.27023i) q^{18} +(-3.10260 + 3.10260i) q^{19} +(-5.33687 - 0.670275i) q^{20} +(2.58369 - 0.569692i) q^{21} +(6.74404 - 2.31173i) q^{22} +3.63389 q^{23} +(-2.36571 - 1.55030i) q^{24} -2.23286i q^{25} +(1.08259 + 3.15825i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.486574 + 5.26908i) q^{28} +(5.29845 - 5.29845i) q^{29} +(1.67202 - 3.41615i) q^{30} +0.906641 q^{31} +(3.66604 - 4.30815i) q^{32} +5.04114i q^{33} +(4.44830 - 9.08843i) q^{34} +(-6.94857 + 1.53213i) q^{35} +(1.57942 - 1.22696i) q^{36} +(2.51619 + 2.51619i) q^{37} +(5.86992 - 2.01210i) q^{38} -2.36078 q^{39} +(6.36233 + 4.16938i) q^{40} +2.37705 q^{41} +(-3.63606 - 0.882661i) q^{42} +(-1.93434 + 1.93434i) q^{43} +(-10.0037 - 1.25640i) q^{44} +(1.90169 + 1.90169i) q^{45} +(-4.61587 - 2.25922i) q^{46} +0.550905 q^{47} +(2.04115 + 3.44001i) q^{48} +(2.94382 + 6.35090i) q^{49} +(-1.38819 + 2.83624i) q^{50} +(5.05932 + 5.05932i) q^{51} +(0.588373 - 4.68475i) q^{52} +(3.05130 + 3.05130i) q^{53} +(0.458573 + 1.33780i) q^{54} -13.5576i q^{55} +(2.65777 - 6.99545i) q^{56} +4.38774i q^{57} +(-10.0243 + 3.43615i) q^{58} +(-9.17593 - 9.17593i) q^{59} +(-4.24769 + 3.29978i) q^{60} +(5.62319 + 5.62319i) q^{61} +(-1.15164 - 0.563666i) q^{62} +(1.42411 - 2.22978i) q^{63} +(-7.33511 + 3.19313i) q^{64} +6.34907 q^{65} +(3.13412 - 6.40340i) q^{66} +(1.68616 + 1.68616i) q^{67} +(-11.3007 + 8.77884i) q^{68} +(2.56955 - 2.56955i) q^{69} +(9.77880 + 2.37383i) q^{70} -11.6715 q^{71} +(-2.76904 + 0.576579i) q^{72} -8.41083 q^{73} +(-1.63180 - 4.76048i) q^{74} +(-1.57887 - 1.57887i) q^{75} +(-8.70707 - 1.09355i) q^{76} +(-13.0247 + 2.87190i) q^{77} +(2.99872 + 1.46771i) q^{78} -12.6448i q^{79} +(-5.48947 - 9.25157i) q^{80} -1.00000 q^{81} +(-3.01939 - 1.47783i) q^{82} +(3.82605 - 3.82605i) q^{83} +(4.06986 + 3.38175i) q^{84} +(-13.6065 - 13.6065i) q^{85} +(3.65964 - 1.25446i) q^{86} -7.49314i q^{87} +(11.9259 + 7.81529i) q^{88} +14.6937 q^{89} +(-1.23329 - 3.59788i) q^{90} +(-1.34492 - 6.09951i) q^{91} +(4.45864 + 5.73945i) q^{92} +(0.641092 - 0.641092i) q^{93} +(-0.699775 - 0.342502i) q^{94} -11.8004i q^{95} +(-0.454046 - 5.63860i) q^{96} -6.22825i q^{97} +(0.209087 - 9.89729i) q^{98} +(3.56463 + 3.56463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27023 0.621708i −0.898187 0.439614i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.22696 + 1.57942i 0.613479 + 0.789711i
\(5\) −1.90169 + 1.90169i −0.850462 + 0.850462i −0.990190 0.139728i \(-0.955377\pi\)
0.139728 + 0.990190i \(0.455377\pi\)
\(6\) −1.33780 + 0.458573i −0.546155 + 0.187212i
\(7\) 2.22978 + 1.42411i 0.842777 + 0.538263i
\(8\) −0.576579 2.76904i −0.203851 0.979002i
\(9\) 1.00000i 0.333333i
\(10\) 3.59788 1.23329i 1.13775 0.389999i
\(11\) −3.56463 + 3.56463i −1.07477 + 1.07477i −0.0778065 + 0.996968i \(0.524792\pi\)
−0.996968 + 0.0778065i \(0.975208\pi\)
\(12\) 1.98441 + 0.249229i 0.572850 + 0.0719461i
\(13\) −1.66932 1.66932i −0.462986 0.462986i 0.436647 0.899633i \(-0.356166\pi\)
−0.899633 + 0.436647i \(0.856166\pi\)
\(14\) −1.94695 3.19522i −0.520343 0.853957i
\(15\) 2.68940i 0.694400i
\(16\) −0.989144 + 3.87577i −0.247286 + 0.968943i
\(17\) 7.15496i 1.73533i 0.497147 + 0.867667i \(0.334381\pi\)
−0.497147 + 0.867667i \(0.665619\pi\)
\(18\) −0.621708 + 1.27023i −0.146538 + 0.299396i
\(19\) −3.10260 + 3.10260i −0.711785 + 0.711785i −0.966908 0.255123i \(-0.917884\pi\)
0.255123 + 0.966908i \(0.417884\pi\)
\(20\) −5.33687 0.670275i −1.19336 0.149878i
\(21\) 2.58369 0.569692i 0.563807 0.124317i
\(22\) 6.74404 2.31173i 1.43783 0.492863i
\(23\) 3.63389 0.757719 0.378860 0.925454i \(-0.376316\pi\)
0.378860 + 0.925454i \(0.376316\pi\)
\(24\) −2.36571 1.55030i −0.482898 0.316454i
\(25\) 2.23286i 0.446572i
\(26\) 1.08259 + 3.15825i 0.212313 + 0.619383i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0.486574 + 5.26908i 0.0919538 + 0.995763i
\(29\) 5.29845 5.29845i 0.983898 0.983898i −0.0159747 0.999872i \(-0.505085\pi\)
0.999872 + 0.0159747i \(0.00508512\pi\)
\(30\) 1.67202 3.41615i 0.305268 0.623701i
\(31\) 0.906641 0.162838 0.0814188 0.996680i \(-0.474055\pi\)
0.0814188 + 0.996680i \(0.474055\pi\)
\(32\) 3.66604 4.30815i 0.648070 0.761581i
\(33\) 5.04114i 0.877550i
\(34\) 4.44830 9.08843i 0.762876 1.55865i
\(35\) −6.94857 + 1.53213i −1.17452 + 0.258977i
\(36\) 1.57942 1.22696i 0.263237 0.204493i
\(37\) 2.51619 + 2.51619i 0.413660 + 0.413660i 0.883011 0.469352i \(-0.155512\pi\)
−0.469352 + 0.883011i \(0.655512\pi\)
\(38\) 5.86992 2.01210i 0.952226 0.326405i
\(39\) −2.36078 −0.378027
\(40\) 6.36233 + 4.16938i 1.00597 + 0.659236i
\(41\) 2.37705 0.371232 0.185616 0.982622i \(-0.440572\pi\)
0.185616 + 0.982622i \(0.440572\pi\)
\(42\) −3.63606 0.882661i −0.561056 0.136197i
\(43\) −1.93434 + 1.93434i −0.294984 + 0.294984i −0.839045 0.544062i \(-0.816886\pi\)
0.544062 + 0.839045i \(0.316886\pi\)
\(44\) −10.0037 1.25640i −1.50811 0.189409i
\(45\) 1.90169 + 1.90169i 0.283487 + 0.283487i
\(46\) −4.61587 2.25922i −0.680573 0.333104i
\(47\) 0.550905 0.0803577 0.0401789 0.999193i \(-0.487207\pi\)
0.0401789 + 0.999193i \(0.487207\pi\)
\(48\) 2.04115 + 3.44001i 0.294615 + 0.496523i
\(49\) 2.94382 + 6.35090i 0.420545 + 0.907272i
\(50\) −1.38819 + 2.83624i −0.196319 + 0.401106i
\(51\) 5.05932 + 5.05932i 0.708447 + 0.708447i
\(52\) 0.588373 4.68475i 0.0815927 0.649658i
\(53\) 3.05130 + 3.05130i 0.419128 + 0.419128i 0.884903 0.465775i \(-0.154224\pi\)
−0.465775 + 0.884903i \(0.654224\pi\)
\(54\) 0.458573 + 1.33780i 0.0624039 + 0.182052i
\(55\) 13.5576i 1.82811i
\(56\) 2.65777 6.99545i 0.355160 0.934806i
\(57\) 4.38774i 0.581170i
\(58\) −10.0243 + 3.43615i −1.31626 + 0.451189i
\(59\) −9.17593 9.17593i −1.19460 1.19460i −0.975760 0.218845i \(-0.929771\pi\)
−0.218845 0.975760i \(-0.570229\pi\)
\(60\) −4.24769 + 3.29978i −0.548375 + 0.426000i
\(61\) 5.62319 + 5.62319i 0.719976 + 0.719976i 0.968600 0.248624i \(-0.0799784\pi\)
−0.248624 + 0.968600i \(0.579978\pi\)
\(62\) −1.15164 0.563666i −0.146259 0.0715856i
\(63\) 1.42411 2.22978i 0.179421 0.280926i
\(64\) −7.33511 + 3.19313i −0.916889 + 0.399142i
\(65\) 6.34907 0.787505
\(66\) 3.13412 6.40340i 0.385783 0.788204i
\(67\) 1.68616 + 1.68616i 0.205997 + 0.205997i 0.802564 0.596567i \(-0.203469\pi\)
−0.596567 + 0.802564i \(0.703469\pi\)
\(68\) −11.3007 + 8.77884i −1.37041 + 1.06459i
\(69\) 2.56955 2.56955i 0.309338 0.309338i
\(70\) 9.77880 + 2.37383i 1.16879 + 0.283726i
\(71\) −11.6715 −1.38515 −0.692577 0.721344i \(-0.743525\pi\)
−0.692577 + 0.721344i \(0.743525\pi\)
\(72\) −2.76904 + 0.576579i −0.326334 + 0.0679505i
\(73\) −8.41083 −0.984414 −0.492207 0.870478i \(-0.663810\pi\)
−0.492207 + 0.870478i \(0.663810\pi\)
\(74\) −1.63180 4.76048i −0.189693 0.553394i
\(75\) −1.57887 1.57887i −0.182312 0.182312i
\(76\) −8.70707 1.09355i −0.998770 0.125439i
\(77\) −13.0247 + 2.87190i −1.48431 + 0.327283i
\(78\) 2.99872 + 1.46771i 0.339539 + 0.166186i
\(79\) 12.6448i 1.42265i −0.702862 0.711327i \(-0.748095\pi\)
0.702862 0.711327i \(-0.251905\pi\)
\(80\) −5.48947 9.25157i −0.613742 1.03436i
\(81\) −1.00000 −0.111111
\(82\) −3.01939 1.47783i −0.333436 0.163199i
\(83\) 3.82605 3.82605i 0.419964 0.419964i −0.465227 0.885191i \(-0.654027\pi\)
0.885191 + 0.465227i \(0.154027\pi\)
\(84\) 4.06986 + 3.38175i 0.444059 + 0.368979i
\(85\) −13.6065 13.6065i −1.47584 1.47584i
\(86\) 3.65964 1.25446i 0.394629 0.135272i
\(87\) 7.49314i 0.803349i
\(88\) 11.9259 + 7.81529i 1.27130 + 0.833112i
\(89\) 14.6937 1.55753 0.778765 0.627315i \(-0.215846\pi\)
0.778765 + 0.627315i \(0.215846\pi\)
\(90\) −1.23329 3.59788i −0.130000 0.379250i
\(91\) −1.34492 6.09951i −0.140986 0.639403i
\(92\) 4.45864 + 5.73945i 0.464845 + 0.598379i
\(93\) 0.641092 0.641092i 0.0664782 0.0664782i
\(94\) −0.699775 0.342502i −0.0721762 0.0353264i
\(95\) 11.8004i 1.21069i
\(96\) −0.454046 5.63860i −0.0463409 0.575487i
\(97\) 6.22825i 0.632383i −0.948695 0.316191i \(-0.897596\pi\)
0.948695 0.316191i \(-0.102404\pi\)
\(98\) 0.209087 9.89729i 0.0211209 0.999777i
\(99\) 3.56463 + 3.56463i 0.358258 + 0.358258i
\(100\) 3.52663 2.73963i 0.352663 0.273963i
\(101\) 13.7348 13.7348i 1.36666 1.36666i 0.501512 0.865150i \(-0.332777\pi\)
0.865150 0.501512i \(-0.167223\pi\)
\(102\) −3.28107 9.57191i −0.324875 0.947761i
\(103\) 2.12589i 0.209471i −0.994500 0.104735i \(-0.966600\pi\)
0.994500 0.104735i \(-0.0333995\pi\)
\(104\) −3.65991 + 5.58490i −0.358884 + 0.547645i
\(105\) −3.83000 + 5.99676i −0.373770 + 0.585224i
\(106\) −1.97883 5.77286i −0.192201 0.560710i
\(107\) −9.07831 + 9.07831i −0.877634 + 0.877634i −0.993289 0.115656i \(-0.963103\pi\)
0.115656 + 0.993289i \(0.463103\pi\)
\(108\) 0.249229 1.98441i 0.0239820 0.190950i
\(109\) −7.77089 + 7.77089i −0.744316 + 0.744316i −0.973405 0.229090i \(-0.926425\pi\)
0.229090 + 0.973405i \(0.426425\pi\)
\(110\) −8.42889 + 17.2213i −0.803663 + 1.64199i
\(111\) 3.55843 0.337752
\(112\) −7.72510 + 7.23345i −0.729953 + 0.683497i
\(113\) 7.32742 0.689306 0.344653 0.938730i \(-0.387997\pi\)
0.344653 + 0.938730i \(0.387997\pi\)
\(114\) 2.72789 5.57343i 0.255490 0.521999i
\(115\) −6.91054 + 6.91054i −0.644412 + 0.644412i
\(116\) 14.8695 + 1.86751i 1.38060 + 0.173394i
\(117\) −1.66932 + 1.66932i −0.154329 + 0.154329i
\(118\) 5.95078 + 17.3603i 0.547814 + 1.59814i
\(119\) −10.1895 + 15.9540i −0.934066 + 1.46250i
\(120\) 7.44704 1.55065i 0.679818 0.141554i
\(121\) 14.4131i 1.31028i
\(122\) −3.64675 10.6387i −0.330161 0.963184i
\(123\) 1.68083 1.68083i 0.151555 0.151555i
\(124\) 1.11241 + 1.43197i 0.0998975 + 0.128595i
\(125\) −5.26224 5.26224i −0.470669 0.470669i
\(126\) −3.19522 + 1.94695i −0.284652 + 0.173448i
\(127\) 14.6589i 1.30076i 0.759608 + 0.650382i \(0.225391\pi\)
−0.759608 + 0.650382i \(0.774609\pi\)
\(128\) 11.3025 + 0.504288i 0.999006 + 0.0445732i
\(129\) 2.73556i 0.240853i
\(130\) −8.06476 3.94726i −0.707326 0.346198i
\(131\) 5.52527 5.52527i 0.482745 0.482745i −0.423262 0.906007i \(-0.639115\pi\)
0.906007 + 0.423262i \(0.139115\pi\)
\(132\) −7.96209 + 6.18527i −0.693011 + 0.538359i
\(133\) −11.3365 + 2.49966i −0.983004 + 0.216748i
\(134\) −1.09351 3.19010i −0.0944646 0.275583i
\(135\) 2.68940 0.231467
\(136\) 19.8123 4.12540i 1.69889 0.353750i
\(137\) 3.43937i 0.293845i −0.989148 0.146923i \(-0.953063\pi\)
0.989148 0.146923i \(-0.0469368\pi\)
\(138\) −4.86143 + 1.66641i −0.413832 + 0.141854i
\(139\) 5.21179 + 5.21179i 0.442058 + 0.442058i 0.892703 0.450645i \(-0.148806\pi\)
−0.450645 + 0.892703i \(0.648806\pi\)
\(140\) −10.9455 9.09486i −0.925062 0.768656i
\(141\) 0.389548 0.389548i 0.0328059 0.0328059i
\(142\) 14.8255 + 7.25628i 1.24413 + 0.608933i
\(143\) 11.9010 0.995212
\(144\) 3.87577 + 0.989144i 0.322981 + 0.0824287i
\(145\) 20.1520i 1.67354i
\(146\) 10.6837 + 5.22908i 0.884187 + 0.432762i
\(147\) 6.57236 + 2.40917i 0.542079 + 0.198705i
\(148\) −0.886864 + 7.06139i −0.0728998 + 0.580443i
\(149\) 8.38511 + 8.38511i 0.686935 + 0.686935i 0.961553 0.274618i \(-0.0885514\pi\)
−0.274618 + 0.961553i \(0.588551\pi\)
\(150\) 1.02393 + 2.98712i 0.0836036 + 0.243898i
\(151\) 3.21093 0.261302 0.130651 0.991428i \(-0.458293\pi\)
0.130651 + 0.991428i \(0.458293\pi\)
\(152\) 10.3801 + 6.80231i 0.841937 + 0.551740i
\(153\) 7.15496 0.578444
\(154\) 18.3299 + 4.44962i 1.47706 + 0.358560i
\(155\) −1.72415 + 1.72415i −0.138487 + 0.138487i
\(156\) −2.89657 3.72866i −0.231912 0.298532i
\(157\) −0.574508 0.574508i −0.0458508 0.0458508i 0.683810 0.729660i \(-0.260322\pi\)
−0.729660 + 0.683810i \(0.760322\pi\)
\(158\) −7.86138 + 16.0618i −0.625418 + 1.27781i
\(159\) 4.31519 0.342217
\(160\) 1.22111 + 15.1644i 0.0965373 + 1.19885i
\(161\) 8.10277 + 5.17507i 0.638588 + 0.407852i
\(162\) 1.27023 + 0.621708i 0.0997985 + 0.0488460i
\(163\) −13.8383 13.8383i −1.08390 1.08390i −0.996142 0.0877597i \(-0.972029\pi\)
−0.0877597 0.996142i \(-0.527971\pi\)
\(164\) 2.91654 + 3.75436i 0.227743 + 0.293166i
\(165\) −9.58670 9.58670i −0.746323 0.746323i
\(166\) −7.23865 + 2.48127i −0.561828 + 0.192584i
\(167\) 9.71401i 0.751692i 0.926682 + 0.375846i \(0.122648\pi\)
−0.926682 + 0.375846i \(0.877352\pi\)
\(168\) −3.06720 6.82585i −0.236640 0.526626i
\(169\) 7.42674i 0.571287i
\(170\) 8.82411 + 25.7427i 0.676778 + 1.97437i
\(171\) 3.10260 + 3.10260i 0.237262 + 0.237262i
\(172\) −5.42848 0.681781i −0.413918 0.0519853i
\(173\) −3.57505 3.57505i −0.271806 0.271806i 0.558021 0.829827i \(-0.311561\pi\)
−0.829827 + 0.558021i \(0.811561\pi\)
\(174\) −4.65854 + 9.51800i −0.353163 + 0.721558i
\(175\) 3.17984 4.97879i 0.240374 0.376361i
\(176\) −10.2897 17.3416i −0.775618 1.30717i
\(177\) −12.9767 −0.975391
\(178\) −18.6644 9.13520i −1.39895 0.684712i
\(179\) 12.0824 + 12.0824i 0.903078 + 0.903078i 0.995701 0.0926229i \(-0.0295251\pi\)
−0.0926229 + 0.995701i \(0.529525\pi\)
\(180\) −0.670275 + 5.33687i −0.0499594 + 0.397787i
\(181\) 14.7072 14.7072i 1.09318 1.09318i 0.0979893 0.995187i \(-0.468759\pi\)
0.995187 0.0979893i \(-0.0312411\pi\)
\(182\) −2.08376 + 8.58392i −0.154459 + 0.636282i
\(183\) 7.95239 0.587858
\(184\) −2.09523 10.0624i −0.154462 0.741808i
\(185\) −9.57005 −0.703604
\(186\) −1.21291 + 0.415761i −0.0889345 + 0.0304851i
\(187\) −25.5048 25.5048i −1.86509 1.86509i
\(188\) 0.675937 + 0.870111i 0.0492978 + 0.0634593i
\(189\) −0.569692 2.58369i −0.0414390 0.187936i
\(190\) −7.33638 + 14.9892i −0.532237 + 1.08743i
\(191\) 4.83855i 0.350105i 0.984559 + 0.175052i \(0.0560095\pi\)
−0.984559 + 0.175052i \(0.943991\pi\)
\(192\) −2.92882 + 7.44460i −0.211369 + 0.537267i
\(193\) 23.3996 1.68434 0.842169 0.539213i \(-0.181278\pi\)
0.842169 + 0.539213i \(0.181278\pi\)
\(194\) −3.87215 + 7.91129i −0.278004 + 0.567998i
\(195\) 4.48947 4.48947i 0.321497 0.321497i
\(196\) −6.41881 + 12.4418i −0.458486 + 0.888701i
\(197\) 5.84458 + 5.84458i 0.416409 + 0.416409i 0.883964 0.467555i \(-0.154865\pi\)
−0.467555 + 0.883964i \(0.654865\pi\)
\(198\) −2.31173 6.74404i −0.164288 0.479278i
\(199\) 4.28359i 0.303655i −0.988407 0.151828i \(-0.951484\pi\)
0.988407 0.151828i \(-0.0485159\pi\)
\(200\) −6.18287 + 1.28742i −0.437195 + 0.0910344i
\(201\) 2.38459 0.168196
\(202\) −25.9853 + 8.90729i −1.82832 + 0.626715i
\(203\) 19.3600 4.26879i 1.35880 0.299610i
\(204\) −1.78322 + 14.1984i −0.124851 + 0.994086i
\(205\) −4.52041 + 4.52041i −0.315719 + 0.315719i
\(206\) −1.32168 + 2.70037i −0.0920861 + 0.188144i
\(207\) 3.63389i 0.252573i
\(208\) 8.12110 4.81870i 0.563097 0.334117i
\(209\) 22.1192i 1.53002i
\(210\) 8.59321 5.23611i 0.592988 0.361326i
\(211\) −5.34715 5.34715i −0.368113 0.368113i 0.498676 0.866789i \(-0.333820\pi\)
−0.866789 + 0.498676i \(0.833820\pi\)
\(212\) −1.07547 + 8.56311i −0.0738635 + 0.588117i
\(213\) −8.25301 + 8.25301i −0.565487 + 0.565487i
\(214\) 17.1756 5.88747i 1.17410 0.402459i
\(215\) 7.35702i 0.501745i
\(216\) −1.55030 + 2.36571i −0.105485 + 0.160966i
\(217\) 2.02161 + 1.29116i 0.137236 + 0.0876495i
\(218\) 14.7020 5.03958i 0.995746 0.341323i
\(219\) −5.94736 + 5.94736i −0.401885 + 0.401885i
\(220\) 21.4132 16.6347i 1.44368 1.12151i
\(221\) 11.9439 11.9439i 0.803435 0.803435i
\(222\) −4.52002 2.21231i −0.303364 0.148480i
\(223\) 28.4331 1.90402 0.952009 0.306070i \(-0.0990142\pi\)
0.952009 + 0.306070i \(0.0990142\pi\)
\(224\) 14.3097 4.38538i 0.956109 0.293011i
\(225\) −2.23286 −0.148857
\(226\) −9.30750 4.55552i −0.619126 0.303028i
\(227\) −19.1228 + 19.1228i −1.26923 + 1.26923i −0.322739 + 0.946488i \(0.604604\pi\)
−0.946488 + 0.322739i \(0.895396\pi\)
\(228\) −6.93009 + 5.38357i −0.458956 + 0.356536i
\(229\) −2.11755 + 2.11755i −0.139932 + 0.139932i −0.773603 0.633671i \(-0.781547\pi\)
0.633671 + 0.773603i \(0.281547\pi\)
\(230\) 13.0743 4.48163i 0.862094 0.295510i
\(231\) −7.17914 + 11.2406i −0.472353 + 0.739579i
\(232\) −17.7266 11.6166i −1.16381 0.762669i
\(233\) 23.1104i 1.51401i 0.653408 + 0.757006i \(0.273339\pi\)
−0.653408 + 0.757006i \(0.726661\pi\)
\(234\) 3.15825 1.08259i 0.206461 0.0707710i
\(235\) −1.04765 + 1.04765i −0.0683412 + 0.0683412i
\(236\) 3.23417 25.7512i 0.210527 1.67626i
\(237\) −8.94124 8.94124i −0.580796 0.580796i
\(238\) 22.8616 13.9303i 1.48190 0.902969i
\(239\) 9.94538i 0.643313i −0.946856 0.321657i \(-0.895760\pi\)
0.946856 0.321657i \(-0.104240\pi\)
\(240\) −10.4235 2.66020i −0.672833 0.171715i
\(241\) 11.4287i 0.736187i −0.929789 0.368093i \(-0.880011\pi\)
0.929789 0.368093i \(-0.119989\pi\)
\(242\) −8.96074 + 18.3079i −0.576018 + 1.17688i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −1.98196 + 15.7808i −0.126882 + 1.01026i
\(245\) −17.6757 6.47922i −1.12926 0.413942i
\(246\) −3.18001 + 1.09005i −0.202750 + 0.0694990i
\(247\) 10.3585 0.659093
\(248\) −0.522750 2.51052i −0.0331947 0.159418i
\(249\) 5.41086i 0.342899i
\(250\) 3.41267 + 9.95583i 0.215836 + 0.629662i
\(251\) 11.4020 + 11.4020i 0.719687 + 0.719687i 0.968541 0.248854i \(-0.0800540\pi\)
−0.248854 + 0.968541i \(0.580054\pi\)
\(252\) 5.26908 0.486574i 0.331921 0.0306513i
\(253\) −12.9535 + 12.9535i −0.814378 + 0.814378i
\(254\) 9.11352 18.6201i 0.571833 1.16833i
\(255\) −19.2425 −1.20501
\(256\) −14.0432 7.66739i −0.877699 0.479212i
\(257\) 8.41347i 0.524818i −0.964957 0.262409i \(-0.915483\pi\)
0.964957 0.262409i \(-0.0845169\pi\)
\(258\) 1.70072 3.47479i 0.105882 0.216331i
\(259\) 2.02721 + 9.19389i 0.125965 + 0.571280i
\(260\) 7.79004 + 10.0279i 0.483118 + 0.621901i
\(261\) −5.29845 5.29845i −0.327966 0.327966i
\(262\) −10.4535 + 3.58325i −0.645817 + 0.221374i
\(263\) −6.67247 −0.411442 −0.205721 0.978611i \(-0.565954\pi\)
−0.205721 + 0.978611i \(0.565954\pi\)
\(264\) 13.9591 2.90662i 0.859123 0.178890i
\(265\) −11.6053 −0.712906
\(266\) 15.9541 + 3.87288i 0.978206 + 0.237462i
\(267\) 10.3900 10.3900i 0.635859 0.635859i
\(268\) −0.594307 + 4.73200i −0.0363031 + 0.289053i
\(269\) −1.02225 1.02225i −0.0623274 0.0623274i 0.675256 0.737583i \(-0.264033\pi\)
−0.737583 + 0.675256i \(0.764033\pi\)
\(270\) −3.41615 1.67202i −0.207900 0.101756i
\(271\) 5.47375 0.332507 0.166253 0.986083i \(-0.446833\pi\)
0.166253 + 0.986083i \(0.446833\pi\)
\(272\) −27.7310 7.07729i −1.68144 0.429124i
\(273\) −5.26401 3.36201i −0.318592 0.203478i
\(274\) −2.13828 + 4.36878i −0.129178 + 0.263928i
\(275\) 7.95932 + 7.95932i 0.479965 + 0.479965i
\(276\) 7.21114 + 0.905671i 0.434059 + 0.0545150i
\(277\) 9.91118 + 9.91118i 0.595505 + 0.595505i 0.939113 0.343608i \(-0.111649\pi\)
−0.343608 + 0.939113i \(0.611649\pi\)
\(278\) −3.37995 9.86038i −0.202716 0.591386i
\(279\) 0.906641i 0.0542792i
\(280\) 8.24892 + 18.3574i 0.492967 + 1.09707i
\(281\) 19.6432i 1.17182i 0.810378 + 0.585908i \(0.199262\pi\)
−0.810378 + 0.585908i \(0.800738\pi\)
\(282\) −0.737001 + 0.252630i −0.0438877 + 0.0150439i
\(283\) 20.3051 + 20.3051i 1.20701 + 1.20701i 0.971990 + 0.235022i \(0.0755162\pi\)
0.235022 + 0.971990i \(0.424484\pi\)
\(284\) −14.3205 18.4343i −0.849764 1.09387i
\(285\) −8.34412 8.34412i −0.494263 0.494263i
\(286\) −15.1170 7.39895i −0.893886 0.437509i
\(287\) 5.30028 + 3.38518i 0.312866 + 0.199821i
\(288\) −4.30815 3.66604i −0.253860 0.216023i
\(289\) −34.1935 −2.01138
\(290\) 12.5287 25.5977i 0.735710 1.50315i
\(291\) −4.40404 4.40404i −0.258169 0.258169i
\(292\) −10.3197 13.2842i −0.603917 0.777402i
\(293\) 11.7526 11.7526i 0.686597 0.686597i −0.274881 0.961478i \(-0.588639\pi\)
0.961478 + 0.274881i \(0.0886385\pi\)
\(294\) −6.85059 7.14629i −0.399535 0.416780i
\(295\) 34.8996 2.03193
\(296\) 5.51664 8.41821i 0.320648 0.489299i
\(297\) 5.04114 0.292517
\(298\) −5.43792 15.8641i −0.315010 0.918983i
\(299\) −6.06613 6.06613i −0.350814 0.350814i
\(300\) 0.556493 4.43092i 0.0321292 0.255819i
\(301\) −7.06785 + 1.55843i −0.407384 + 0.0898264i
\(302\) −4.07861 1.99626i −0.234698 0.114872i
\(303\) 19.4239i 1.11588i
\(304\) −8.95604 15.0939i −0.513664 0.865693i
\(305\) −21.3871 −1.22462
\(306\) −9.08843 4.44830i −0.519551 0.254292i
\(307\) −19.0195 + 19.0195i −1.08550 + 1.08550i −0.0895163 + 0.995985i \(0.528532\pi\)
−0.995985 + 0.0895163i \(0.971468\pi\)
\(308\) −20.5168 17.0479i −1.16905 0.971392i
\(309\) −1.50323 1.50323i −0.0855160 0.0855160i
\(310\) 3.26199 1.11815i 0.185268 0.0635065i
\(311\) 13.7113i 0.777499i −0.921344 0.388749i \(-0.872907\pi\)
0.921344 0.388749i \(-0.127093\pi\)
\(312\) 1.36117 + 6.53707i 0.0770613 + 0.370089i
\(313\) 4.84337 0.273764 0.136882 0.990587i \(-0.456292\pi\)
0.136882 + 0.990587i \(0.456292\pi\)
\(314\) 0.372580 + 1.08693i 0.0210259 + 0.0613392i
\(315\) 1.53213 + 6.94857i 0.0863257 + 0.391508i
\(316\) 19.9715 15.5147i 1.12348 0.872768i
\(317\) −2.72533 + 2.72533i −0.153070 + 0.153070i −0.779488 0.626418i \(-0.784520\pi\)
0.626418 + 0.779488i \(0.284520\pi\)
\(318\) −5.48128 2.68279i −0.307375 0.150443i
\(319\) 37.7740i 2.11494i
\(320\) 7.87677 20.0215i 0.440325 1.11923i
\(321\) 12.8387i 0.716585i
\(322\) −7.07499 11.6111i −0.394274 0.647060i
\(323\) −22.1990 22.1990i −1.23518 1.23518i
\(324\) −1.22696 1.57942i −0.0681644 0.0877456i
\(325\) −3.72736 + 3.72736i −0.206757 + 0.206757i
\(326\) 8.97444 + 26.1812i 0.497048 + 1.45004i
\(327\) 10.9897i 0.607731i
\(328\) −1.37055 6.58212i −0.0756762 0.363437i
\(329\) 1.22839 + 0.784549i 0.0677236 + 0.0432536i
\(330\) 6.21717 + 18.1374i 0.342244 + 0.998432i
\(331\) 6.93803 6.93803i 0.381349 0.381349i −0.490239 0.871588i \(-0.663091\pi\)
0.871588 + 0.490239i \(0.163091\pi\)
\(332\) 10.7374 + 1.34854i 0.589289 + 0.0740108i
\(333\) 2.51619 2.51619i 0.137887 0.137887i
\(334\) 6.03927 12.3390i 0.330454 0.675160i
\(335\) −6.41310 −0.350385
\(336\) −0.347644 + 10.5773i −0.0189656 + 0.577039i
\(337\) 2.95698 0.161077 0.0805384 0.996752i \(-0.474336\pi\)
0.0805384 + 0.996752i \(0.474336\pi\)
\(338\) −4.61726 + 9.43365i −0.251146 + 0.513123i
\(339\) 5.18127 5.18127i 0.281408 0.281408i
\(340\) 4.79579 38.1851i 0.260088 2.07088i
\(341\) −3.23184 + 3.23184i −0.175014 + 0.175014i
\(342\) −2.01210 5.86992i −0.108802 0.317409i
\(343\) −2.48033 + 18.3534i −0.133925 + 0.990991i
\(344\) 6.47154 + 4.24095i 0.348922 + 0.228657i
\(345\) 9.77299i 0.526160i
\(346\) 2.31849 + 6.76376i 0.124643 + 0.363622i
\(347\) −3.16858 + 3.16858i −0.170098 + 0.170098i −0.787023 0.616924i \(-0.788378\pi\)
0.616924 + 0.787023i \(0.288378\pi\)
\(348\) 11.8348 9.19378i 0.634413 0.492838i
\(349\) −11.0951 11.0951i −0.593908 0.593908i 0.344777 0.938685i \(-0.387955\pi\)
−0.938685 + 0.344777i \(0.887955\pi\)
\(350\) −7.13448 + 4.34726i −0.381354 + 0.232371i
\(351\) 2.36078i 0.126009i
\(352\) 2.28891 + 28.4250i 0.121999 + 1.51506i
\(353\) 30.8984i 1.64455i 0.569087 + 0.822277i \(0.307297\pi\)
−0.569087 + 0.822277i \(0.692703\pi\)
\(354\) 16.4834 + 8.06773i 0.876083 + 0.428795i
\(355\) 22.1956 22.1956i 1.17802 1.17802i
\(356\) 18.0286 + 23.2076i 0.955513 + 1.23000i
\(357\) 4.07613 + 18.4862i 0.215732 + 0.978393i
\(358\) −7.83566 22.8591i −0.414127 1.20814i
\(359\) 0.943215 0.0497810 0.0248905 0.999690i \(-0.492076\pi\)
0.0248905 + 0.999690i \(0.492076\pi\)
\(360\) 4.16938 6.36233i 0.219745 0.335324i
\(361\) 0.252238i 0.0132757i
\(362\) −27.8251 + 9.53791i −1.46245 + 0.501301i
\(363\) −10.1916 10.1916i −0.534921 0.534921i
\(364\) 7.98354 9.60804i 0.418451 0.503598i
\(365\) 15.9948 15.9948i 0.837207 0.837207i
\(366\) −10.1014 4.94406i −0.528006 0.258430i
\(367\) −3.56906 −0.186304 −0.0931518 0.995652i \(-0.529694\pi\)
−0.0931518 + 0.995652i \(0.529694\pi\)
\(368\) −3.59444 + 14.0841i −0.187373 + 0.734186i
\(369\) 2.37705i 0.123744i
\(370\) 12.1561 + 5.94977i 0.631968 + 0.309314i
\(371\) 2.45833 + 11.1491i 0.127630 + 0.578833i
\(372\) 1.79915 + 0.225961i 0.0932815 + 0.0117155i
\(373\) −0.693026 0.693026i −0.0358835 0.0358835i 0.688937 0.724821i \(-0.258077\pi\)
−0.724821 + 0.688937i \(0.758077\pi\)
\(374\) 16.5404 + 48.2534i 0.855281 + 2.49512i
\(375\) −7.44194 −0.384300
\(376\) −0.317640 1.52547i −0.0163810 0.0786703i
\(377\) −17.6896 −0.911062
\(378\) −0.882661 + 3.63606i −0.0453992 + 0.187019i
\(379\) 6.55229 6.55229i 0.336569 0.336569i −0.518506 0.855074i \(-0.673511\pi\)
0.855074 + 0.518506i \(0.173511\pi\)
\(380\) 18.6378 14.4786i 0.956097 0.742735i
\(381\) 10.3654 + 10.3654i 0.531034 + 0.531034i
\(382\) 3.00816 6.14606i 0.153911 0.314460i
\(383\) −25.4405 −1.29995 −0.649975 0.759956i \(-0.725221\pi\)
−0.649975 + 0.759956i \(0.725221\pi\)
\(384\) 8.34863 7.63546i 0.426039 0.389646i
\(385\) 19.3076 30.2305i 0.984005 1.54069i
\(386\) −29.7228 14.5477i −1.51285 0.740459i
\(387\) 1.93434 + 1.93434i 0.0983278 + 0.0983278i
\(388\) 9.83703 7.64180i 0.499399 0.387954i
\(389\) −11.6405 11.6405i −0.590199 0.590199i 0.347486 0.937685i \(-0.387035\pi\)
−0.937685 + 0.347486i \(0.887035\pi\)
\(390\) −8.49379 + 2.91151i −0.430100 + 0.147430i
\(391\) 26.0004i 1.31490i
\(392\) 15.8885 11.8133i 0.802492 0.596663i
\(393\) 7.81392i 0.394160i
\(394\) −3.79033 11.0576i −0.190954 0.557072i
\(395\) 24.0465 + 24.0465i 1.20991 + 1.20991i
\(396\) −1.25640 + 10.0037i −0.0631363 + 0.502705i
\(397\) 18.3501 + 18.3501i 0.920963 + 0.920963i 0.997098 0.0761349i \(-0.0242580\pi\)
−0.0761349 + 0.997098i \(0.524258\pi\)
\(398\) −2.66314 + 5.44113i −0.133491 + 0.272739i
\(399\) −6.24862 + 9.78368i −0.312822 + 0.489797i
\(400\) 8.65406 + 2.20862i 0.432703 + 0.110431i
\(401\) 22.2529 1.11126 0.555630 0.831430i \(-0.312477\pi\)
0.555630 + 0.831430i \(0.312477\pi\)
\(402\) −3.02897 1.48252i −0.151071 0.0739412i
\(403\) −1.51347 1.51347i −0.0753916 0.0753916i
\(404\) 38.5450 + 4.84100i 1.91769 + 0.240849i
\(405\) 1.90169 1.90169i 0.0944958 0.0944958i
\(406\) −27.2455 6.61390i −1.35217 0.328242i
\(407\) −17.9386 −0.889182
\(408\) 11.0923 16.9265i 0.549153 0.837989i
\(409\) −27.1395 −1.34196 −0.670981 0.741475i \(-0.734127\pi\)
−0.670981 + 0.741475i \(0.734127\pi\)
\(410\) 8.55232 2.93158i 0.422369 0.144780i
\(411\) −2.43200 2.43200i −0.119962 0.119962i
\(412\) 3.35768 2.60838i 0.165421 0.128506i
\(413\) −7.39274 33.5278i −0.363773 1.64980i
\(414\) −2.25922 + 4.61587i −0.111035 + 0.226858i
\(415\) 14.5519i 0.714327i
\(416\) −13.3115 + 1.07190i −0.652649 + 0.0525543i
\(417\) 7.37059 0.360939
\(418\) −13.7517 + 28.0964i −0.672617 + 1.37424i
\(419\) 14.0335 14.0335i 0.685582 0.685582i −0.275670 0.961252i \(-0.588900\pi\)
0.961252 + 0.275670i \(0.0888997\pi\)
\(420\) −14.1707 + 1.30859i −0.691458 + 0.0638527i
\(421\) 18.7350 + 18.7350i 0.913087 + 0.913087i 0.996514 0.0834270i \(-0.0265866\pi\)
−0.0834270 + 0.996514i \(0.526587\pi\)
\(422\) 3.46774 + 10.1165i 0.168807 + 0.492462i
\(423\) 0.550905i 0.0267859i
\(424\) 6.68984 10.2085i 0.324887 0.495767i
\(425\) 15.9760 0.774952
\(426\) 15.6142 5.35225i 0.756509 0.259317i
\(427\) 4.53042 + 20.5465i 0.219242 + 0.994315i
\(428\) −25.4772 3.19977i −1.23149 0.154667i
\(429\) 8.41528 8.41528i 0.406294 0.406294i
\(430\) −4.57392 + 9.34510i −0.220574 + 0.450661i
\(431\) 24.5106i 1.18063i −0.807172 0.590317i \(-0.799003\pi\)
0.807172 0.590317i \(-0.200997\pi\)
\(432\) 3.44001 2.04115i 0.165508 0.0982050i
\(433\) 10.3532i 0.497542i −0.968562 0.248771i \(-0.919973\pi\)
0.968562 0.248771i \(-0.0800267\pi\)
\(434\) −1.76518 2.89691i −0.0847314 0.139056i
\(435\) 14.2496 + 14.2496i 0.683218 + 0.683218i
\(436\) −21.8081 2.73895i −1.04442 0.131172i
\(437\) −11.2745 + 11.2745i −0.539333 + 0.539333i
\(438\) 11.2520 3.85698i 0.537642 0.184294i
\(439\) 21.8589i 1.04327i −0.853170 0.521634i \(-0.825323\pi\)
0.853170 0.521634i \(-0.174677\pi\)
\(440\) −37.5416 + 7.81705i −1.78972 + 0.372663i
\(441\) 6.35090 2.94382i 0.302424 0.140182i
\(442\) −22.5971 + 7.74588i −1.07484 + 0.368434i
\(443\) 8.82244 8.82244i 0.419167 0.419167i −0.465750 0.884916i \(-0.654215\pi\)
0.884916 + 0.465750i \(0.154215\pi\)
\(444\) 4.36605 + 5.62027i 0.207204 + 0.266726i
\(445\) −27.9429 + 27.9429i −1.32462 + 1.32462i
\(446\) −36.1165 17.6771i −1.71016 0.837033i
\(447\) 11.8583 0.560880
\(448\) −20.9030 3.32603i −0.987576 0.157140i
\(449\) −15.3552 −0.724657 −0.362329 0.932050i \(-0.618018\pi\)
−0.362329 + 0.932050i \(0.618018\pi\)
\(450\) 2.83624 + 1.38819i 0.133702 + 0.0654398i
\(451\) −8.47328 + 8.47328i −0.398991 + 0.398991i
\(452\) 8.99045 + 11.5731i 0.422875 + 0.544352i
\(453\) 2.27047 2.27047i 0.106676 0.106676i
\(454\) 36.1792 12.4015i 1.69797 0.582033i
\(455\) 14.1570 + 9.04177i 0.663691 + 0.423885i
\(456\) 12.1498 2.52988i 0.568966 0.118472i
\(457\) 34.0509i 1.59283i −0.604748 0.796417i \(-0.706726\pi\)
0.604748 0.796417i \(-0.293274\pi\)
\(458\) 4.00627 1.37327i 0.187201 0.0641689i
\(459\) 5.05932 5.05932i 0.236149 0.236149i
\(460\) −19.3936 2.43571i −0.904232 0.113566i
\(461\) 17.5033 + 17.5033i 0.815210 + 0.815210i 0.985410 0.170200i \(-0.0544412\pi\)
−0.170200 + 0.985410i \(0.554441\pi\)
\(462\) 16.1075 9.81483i 0.749390 0.456627i
\(463\) 0.0530223i 0.00246416i 0.999999 + 0.00123208i \(0.000392183\pi\)
−0.999999 + 0.00123208i \(0.999608\pi\)
\(464\) 15.2946 + 25.7765i 0.710036 + 1.19664i
\(465\) 2.43832i 0.113074i
\(466\) 14.3679 29.3555i 0.665581 1.35987i
\(467\) 8.39635 8.39635i 0.388537 0.388537i −0.485629 0.874165i \(-0.661409\pi\)
0.874165 + 0.485629i \(0.161409\pi\)
\(468\) −4.68475 0.588373i −0.216553 0.0271976i
\(469\) 1.35848 + 6.16103i 0.0627288 + 0.284490i
\(470\) 1.98209 0.679423i 0.0914269 0.0313394i
\(471\) −0.812478 −0.0374370
\(472\) −20.1178 + 30.6991i −0.925998 + 1.41304i
\(473\) 13.7904i 0.634082i
\(474\) 5.79857 + 16.9162i 0.266337 + 0.776989i
\(475\) 6.92768 + 6.92768i 0.317864 + 0.317864i
\(476\) −37.7001 + 3.48142i −1.72798 + 0.159571i
\(477\) 3.05130 3.05130i 0.139709 0.139709i
\(478\) −6.18312 + 12.6329i −0.282809 + 0.577816i
\(479\) −36.9533 −1.68844 −0.844220 0.535997i \(-0.819936\pi\)
−0.844220 + 0.535997i \(0.819936\pi\)
\(480\) 11.5863 + 9.85943i 0.528842 + 0.450019i
\(481\) 8.40067i 0.383037i
\(482\) −7.10531 + 14.5170i −0.323638 + 0.661233i
\(483\) 9.38885 2.07020i 0.427208 0.0941974i
\(484\) 22.7644 17.6843i 1.03474 0.803831i
\(485\) 11.8442 + 11.8442i 0.537818 + 0.537818i
\(486\) 1.33780 0.458573i 0.0606839 0.0208013i
\(487\) 14.6233 0.662647 0.331324 0.943517i \(-0.392505\pi\)
0.331324 + 0.943517i \(0.392505\pi\)
\(488\) 12.3286 18.8130i 0.558089 0.851626i
\(489\) −19.5703 −0.885002
\(490\) 18.4240 + 19.2192i 0.832310 + 0.868235i
\(491\) 6.45924 6.45924i 0.291502 0.291502i −0.546172 0.837673i \(-0.683915\pi\)
0.837673 + 0.546172i \(0.183915\pi\)
\(492\) 4.71703 + 0.592428i 0.212660 + 0.0267087i
\(493\) 37.9102 + 37.9102i 1.70739 + 1.70739i
\(494\) −13.1576 6.43994i −0.591989 0.289747i
\(495\) −13.5576 −0.609370
\(496\) −0.896799 + 3.51393i −0.0402675 + 0.157780i
\(497\) −26.0249 16.6215i −1.16738 0.745578i
\(498\) −3.36397 + 6.87302i −0.150743 + 0.307987i
\(499\) 0.0937570 + 0.0937570i 0.00419714 + 0.00419714i 0.709202 0.705005i \(-0.249055\pi\)
−0.705005 + 0.709202i \(0.749055\pi\)
\(500\) 1.85474 14.7679i 0.0829467 0.660439i
\(501\) 6.86884 + 6.86884i 0.306877 + 0.306877i
\(502\) −7.39442 21.5718i −0.330029 0.962798i
\(503\) 8.91797i 0.397633i −0.980037 0.198816i \(-0.936290\pi\)
0.980037 0.198816i \(-0.0637097\pi\)
\(504\) −6.99545 2.65777i −0.311602 0.118387i
\(505\) 52.2387i 2.32459i
\(506\) 24.5071 8.40059i 1.08947 0.373452i
\(507\) −5.25150 5.25150i −0.233227 0.233227i
\(508\) −23.1525 + 17.9858i −1.02723 + 0.797991i
\(509\) 8.24799 + 8.24799i 0.365586 + 0.365586i 0.865864 0.500279i \(-0.166769\pi\)
−0.500279 + 0.865864i \(0.666769\pi\)
\(510\) 24.4424 + 11.9632i 1.08233 + 0.529741i
\(511\) −18.7543 11.9780i −0.829641 0.529874i
\(512\) 13.0712 + 18.4701i 0.577670 + 0.816271i
\(513\) 4.38774 0.193723
\(514\) −5.23072 + 10.6870i −0.230717 + 0.471384i
\(515\) 4.04279 + 4.04279i 0.178147 + 0.178147i
\(516\) −4.32061 + 3.35643i −0.190204 + 0.147758i
\(517\) −1.96377 + 1.96377i −0.0863664 + 0.0863664i
\(518\) 3.14089 12.9387i 0.138003 0.568492i
\(519\) −5.05588 −0.221929
\(520\) −3.66074 17.5808i −0.160534 0.770969i
\(521\) −22.1437 −0.970135 −0.485068 0.874477i \(-0.661205\pi\)
−0.485068 + 0.874477i \(0.661205\pi\)
\(522\) 3.43615 + 10.0243i 0.150396 + 0.438753i
\(523\) −1.49811 1.49811i −0.0655079 0.0655079i 0.673594 0.739102i \(-0.264750\pi\)
−0.739102 + 0.673594i \(0.764750\pi\)
\(524\) 15.5060 + 1.94745i 0.677383 + 0.0850748i
\(525\) −1.27204 5.76902i −0.0555166 0.251781i
\(526\) 8.47555 + 4.14832i 0.369552 + 0.180876i
\(527\) 6.48698i 0.282577i
\(528\) −19.5383 4.98642i −0.850296 0.217006i
\(529\) −9.79482 −0.425862
\(530\) 14.7413 + 7.21508i 0.640322 + 0.313403i
\(531\) −9.17593 + 9.17593i −0.398202 + 0.398202i
\(532\) −17.8575 14.8382i −0.774221 0.643318i
\(533\) −3.96805 3.96805i −0.171875 0.171875i
\(534\) −19.6573 + 6.73814i −0.850653 + 0.291588i
\(535\) 34.5283i 1.49279i
\(536\) 3.69683 5.64123i 0.159679 0.243664i
\(537\) 17.0870 0.737360
\(538\) 0.662947 + 1.93402i 0.0285817 + 0.0833817i
\(539\) −33.1322 12.1450i −1.42710 0.523121i
\(540\) 3.29978 + 4.24769i 0.142000 + 0.182792i
\(541\) 3.10477 3.10477i 0.133485 0.133485i −0.637208 0.770692i \(-0.719911\pi\)
0.770692 + 0.637208i \(0.219911\pi\)
\(542\) −6.95292 3.40308i −0.298653 0.146175i
\(543\) 20.7991i 0.892575i
\(544\) 30.8247 + 26.2303i 1.32160 + 1.12462i
\(545\) 29.5557i 1.26603i
\(546\) 4.59630 + 7.54319i 0.196704 + 0.322819i
\(547\) −1.79963 1.79963i −0.0769465 0.0769465i 0.667586 0.744533i \(-0.267328\pi\)
−0.744533 + 0.667586i \(0.767328\pi\)
\(548\) 5.43221 4.21996i 0.232053 0.180268i
\(549\) 5.62319 5.62319i 0.239992 0.239992i
\(550\) −5.16178 15.0585i −0.220099 0.642097i
\(551\) 32.8779i 1.40065i
\(552\) −8.59673 5.63363i −0.365901 0.239783i
\(553\) 18.0076 28.1951i 0.765762 1.19898i
\(554\) −6.42760 18.7513i −0.273083 0.796667i
\(555\) −6.76704 + 6.76704i −0.287245 + 0.287245i
\(556\) −1.83696 + 14.6263i −0.0779045 + 0.620292i
\(557\) −11.8995 + 11.8995i −0.504196 + 0.504196i −0.912739 0.408543i \(-0.866037\pi\)
0.408543 + 0.912739i \(0.366037\pi\)
\(558\) −0.563666 + 1.15164i −0.0238619 + 0.0487529i
\(559\) 6.45806 0.273147
\(560\) 0.934954 28.4466i 0.0395090 1.20209i
\(561\) −36.0692 −1.52284
\(562\) 12.2123 24.9514i 0.515146 1.05251i
\(563\) 0.635961 0.635961i 0.0268026 0.0268026i −0.693578 0.720381i \(-0.743967\pi\)
0.720381 + 0.693578i \(0.243967\pi\)
\(564\) 1.09322 + 0.137301i 0.0460329 + 0.00578143i
\(565\) −13.9345 + 13.9345i −0.586229 + 0.586229i
\(566\) −13.1683 38.4159i −0.553503 1.61474i
\(567\) −2.22978 1.42411i −0.0936419 0.0598070i
\(568\) 6.72955 + 32.3189i 0.282366 + 1.35607i
\(569\) 0.425156i 0.0178235i −0.999960 0.00891174i \(-0.997163\pi\)
0.999960 0.00891174i \(-0.00283673\pi\)
\(570\) 5.41133 + 15.7865i 0.226656 + 0.661226i
\(571\) −20.0961 + 20.0961i −0.840997 + 0.840997i −0.988989 0.147992i \(-0.952719\pi\)
0.147992 + 0.988989i \(0.452719\pi\)
\(572\) 14.6020 + 18.7967i 0.610542 + 0.785930i
\(573\) 3.42137 + 3.42137i 0.142930 + 0.142930i
\(574\) −4.62798 7.59517i −0.193168 0.317016i
\(575\) 8.11398i 0.338376i
\(576\) 3.19313 + 7.33511i 0.133047 + 0.305630i
\(577\) 10.2508i 0.426748i −0.976971 0.213374i \(-0.931555\pi\)
0.976971 0.213374i \(-0.0684453\pi\)
\(578\) 43.4335 + 21.2584i 1.80660 + 0.884231i
\(579\) 16.5460 16.5460i 0.687628 0.687628i
\(580\) −31.8286 + 24.7257i −1.32161 + 1.02668i
\(581\) 13.9800 3.08252i 0.579987 0.127885i
\(582\) 2.85611 + 8.33215i 0.118389 + 0.345379i
\(583\) −21.7535 −0.900937
\(584\) 4.84951 + 23.2899i 0.200674 + 0.963743i
\(585\) 6.34907i 0.262502i
\(586\) −22.2353 + 7.62183i −0.918530 + 0.314855i
\(587\) 19.3706 + 19.3706i 0.799510 + 0.799510i 0.983018 0.183508i \(-0.0587454\pi\)
−0.183508 + 0.983018i \(0.558745\pi\)
\(588\) 4.25891 + 13.3365i 0.175635 + 0.549987i
\(589\) −2.81294 + 2.81294i −0.115905 + 0.115905i
\(590\) −44.3304 21.6973i −1.82506 0.893266i
\(591\) 8.26548 0.339997
\(592\) −12.2411 + 7.26331i −0.503105 + 0.298520i
\(593\) 33.1941i 1.36312i 0.731764 + 0.681559i \(0.238698\pi\)
−0.731764 + 0.681559i \(0.761302\pi\)
\(594\) −6.40340 3.13412i −0.262735 0.128594i
\(595\) −10.9623 49.7167i −0.449412 2.03819i
\(596\) −2.95544 + 23.5318i −0.121060 + 0.963901i
\(597\) −3.02895 3.02895i −0.123967 0.123967i
\(598\) 3.93401 + 11.4767i 0.160874 + 0.469319i
\(599\) −1.68554 −0.0688694 −0.0344347 0.999407i \(-0.510963\pi\)
−0.0344347 + 0.999407i \(0.510963\pi\)
\(600\) −3.46161 + 5.28230i −0.141320 + 0.215649i
\(601\) −2.90830 −0.118632 −0.0593160 0.998239i \(-0.518892\pi\)
−0.0593160 + 0.998239i \(0.518892\pi\)
\(602\) 9.94667 + 2.41458i 0.405396 + 0.0984107i
\(603\) 1.68616 1.68616i 0.0686656 0.0686656i
\(604\) 3.93968 + 5.07141i 0.160303 + 0.206353i
\(605\) 27.4093 + 27.4093i 1.11435 + 1.11435i
\(606\) −12.0760 + 24.6728i −0.490554 + 1.00226i
\(607\) −21.5383 −0.874213 −0.437106 0.899410i \(-0.643997\pi\)
−0.437106 + 0.899410i \(0.643997\pi\)
\(608\) 1.99224 + 24.7407i 0.0807958 + 1.00337i
\(609\) 10.6711 16.7080i 0.432413 0.677044i
\(610\) 27.1666 + 13.2966i 1.09994 + 0.538362i
\(611\) −0.919637 0.919637i −0.0372045 0.0372045i
\(612\) 8.77884 + 11.3007i 0.354864 + 0.456804i
\(613\) 19.8687 + 19.8687i 0.802488 + 0.802488i 0.983484 0.180996i \(-0.0579321\pi\)
−0.180996 + 0.983484i \(0.557932\pi\)
\(614\) 35.9837 12.3345i 1.45218 0.497782i
\(615\) 6.39282i 0.257783i
\(616\) 15.4622 + 34.4101i 0.622989 + 1.38642i
\(617\) 31.7899i 1.27981i −0.768453 0.639906i \(-0.778973\pi\)
0.768453 0.639906i \(-0.221027\pi\)
\(618\) 0.974878 + 2.84402i 0.0392153 + 0.114403i
\(619\) 14.2152 + 14.2152i 0.571358 + 0.571358i 0.932508 0.361150i \(-0.117616\pi\)
−0.361150 + 0.932508i \(0.617616\pi\)
\(620\) −4.83863 0.607699i −0.194324 0.0244058i
\(621\) −2.56955 2.56955i −0.103113 0.103113i
\(622\) −8.52445 + 17.4165i −0.341799 + 0.698339i
\(623\) 32.7637 + 20.9255i 1.31265 + 0.838362i
\(624\) 2.33515 9.14983i 0.0934807 0.366286i
\(625\) 31.1786 1.24715
\(626\) −6.15219 3.01116i −0.245891 0.120350i
\(627\) −15.6406 15.6406i −0.624627 0.624627i
\(628\) 0.202493 1.61229i 0.00808034 0.0643373i
\(629\) −18.0033 + 18.0033i −0.717837 + 0.717837i
\(630\) 2.37383 9.77880i 0.0945755 0.389597i
\(631\) 7.63145 0.303803 0.151902 0.988396i \(-0.451460\pi\)
0.151902 + 0.988396i \(0.451460\pi\)
\(632\) −35.0139 + 7.29074i −1.39278 + 0.290010i
\(633\) −7.56202 −0.300563
\(634\) 5.15616 1.76743i 0.204777 0.0701938i
\(635\) −27.8766 27.8766i −1.10625 1.10625i
\(636\) 5.29456 + 6.81550i 0.209943 + 0.270252i
\(637\) 5.68752 15.5159i 0.225348 0.614761i
\(638\) 23.4844 47.9816i 0.929756 1.89961i
\(639\) 11.6715i 0.461718i
\(640\) −22.4528 + 20.5348i −0.887525 + 0.811709i
\(641\) −24.3462 −0.961616 −0.480808 0.876826i \(-0.659657\pi\)
−0.480808 + 0.876826i \(0.659657\pi\)
\(642\) 7.98190 16.3080i 0.315021 0.643627i
\(643\) 21.6002 21.6002i 0.851829 0.851829i −0.138529 0.990358i \(-0.544237\pi\)
0.990358 + 0.138529i \(0.0442374\pi\)
\(644\) 1.76816 + 19.1473i 0.0696752 + 0.754509i
\(645\) −5.20220 5.20220i −0.204836 0.204836i
\(646\) 14.3965 + 41.9990i 0.566422 + 1.65243i
\(647\) 34.5047i 1.35652i −0.734823 0.678259i \(-0.762735\pi\)
0.734823 0.678259i \(-0.237265\pi\)
\(648\) 0.576579 + 2.76904i 0.0226502 + 0.108778i
\(649\) 65.4175 2.56786
\(650\) 7.05193 2.41727i 0.276600 0.0948132i
\(651\) 2.34248 0.516507i 0.0918090 0.0202435i
\(652\) 4.87749 38.8356i 0.191017 1.52092i
\(653\) 10.7862 10.7862i 0.422097 0.422097i −0.463828 0.885925i \(-0.653525\pi\)
0.885925 + 0.463828i \(0.153525\pi\)
\(654\) 6.83238 13.9594i 0.267167 0.545856i
\(655\) 21.0147i 0.821113i
\(656\) −2.35124 + 9.21288i −0.0918005 + 0.359703i
\(657\) 8.41083i 0.328138i
\(658\) −1.07258 1.76026i −0.0418136 0.0686221i
\(659\) −14.5491 14.5491i −0.566754 0.566754i 0.364464 0.931217i \(-0.381252\pi\)
−0.931217 + 0.364464i \(0.881252\pi\)
\(660\) 3.37895 26.9039i 0.131526 1.04723i
\(661\) 25.2625 25.2625i 0.982596 0.982596i −0.0172555 0.999851i \(-0.505493\pi\)
0.999851 + 0.0172555i \(0.00549287\pi\)
\(662\) −13.1263 + 4.49946i −0.510169 + 0.174876i
\(663\) 16.8913i 0.656002i
\(664\) −12.8005 8.38845i −0.496756 0.325535i
\(665\) 16.8050 26.3122i 0.651671 1.02034i
\(666\) −4.76048 + 1.63180i −0.184465 + 0.0632310i
\(667\) 19.2540 19.2540i 0.745518 0.745518i
\(668\) −15.3425 + 11.9187i −0.593620 + 0.461148i
\(669\) 20.1052 20.1052i 0.777312 0.777312i
\(670\) 8.14610 + 3.98708i 0.314711 + 0.154034i
\(671\) −40.0891 −1.54762
\(672\) 7.01757 13.2194i 0.270709 0.509951i
\(673\) 10.5919 0.408287 0.204144 0.978941i \(-0.434559\pi\)
0.204144 + 0.978941i \(0.434559\pi\)
\(674\) −3.75603 1.83838i −0.144677 0.0708116i
\(675\) −1.57887 + 1.57887i −0.0607708 + 0.0607708i
\(676\) 11.7299 9.11230i 0.451152 0.350473i
\(677\) −27.0595 + 27.0595i −1.03998 + 1.03998i −0.0408138 + 0.999167i \(0.512995\pi\)
−0.999167 + 0.0408138i \(0.987005\pi\)
\(678\) −9.80263 + 3.36016i −0.376468 + 0.129046i
\(679\) 8.86971 13.8876i 0.340388 0.532957i
\(680\) −29.8317 + 45.5222i −1.14399 + 1.74570i
\(681\) 27.0438i 1.03632i
\(682\) 6.11443 2.09591i 0.234133 0.0802566i
\(683\) 28.1993 28.1993i 1.07901 1.07901i 0.0824168 0.996598i \(-0.473736\pi\)
0.996598 0.0824168i \(-0.0262639\pi\)
\(684\) −1.09355 + 8.70707i −0.0418129 + 0.332923i
\(685\) 6.54062 + 6.54062i 0.249904 + 0.249904i
\(686\) 14.5611 21.7710i 0.555943 0.831220i
\(687\) 2.99467i 0.114254i
\(688\) −5.58371 9.41038i −0.212877 0.358767i
\(689\) 10.1872i 0.388101i
\(690\) 6.07594 12.4139i 0.231307 0.472590i
\(691\) −2.94281 + 2.94281i −0.111950 + 0.111950i −0.760863 0.648913i \(-0.775224\pi\)
0.648913 + 0.760863i \(0.275224\pi\)
\(692\) 1.26007 10.0329i 0.0479007 0.381395i
\(693\) 2.87190 + 13.0247i 0.109094 + 0.494769i
\(694\) 5.99475 2.05489i 0.227558 0.0780025i
\(695\) −19.8224 −0.751908
\(696\) −20.7488 + 4.32039i −0.786480 + 0.163764i
\(697\) 17.0077i 0.644211i
\(698\) 7.19541 + 20.9913i 0.272350 + 0.794531i
\(699\) 16.3415 + 16.3415i 0.618093 + 0.618093i
\(700\) 11.7651 1.08645i 0.444680 0.0410641i
\(701\) 14.0610 14.0610i 0.531077 0.531077i −0.389816 0.920893i \(-0.627461\pi\)
0.920893 + 0.389816i \(0.127461\pi\)
\(702\) 1.46771 2.99872i 0.0553953 0.113180i
\(703\) −15.6135 −0.588873
\(704\) 14.7646 37.5293i 0.556462 1.41444i
\(705\) 1.48160i 0.0558004i
\(706\) 19.2098 39.2480i 0.722969 1.47712i
\(707\) 50.1854 11.0657i 1.88742 0.416167i
\(708\) −15.9219 20.4957i −0.598382 0.770276i
\(709\) −17.0650 17.0650i −0.640890 0.640890i 0.309884 0.950774i \(-0.399710\pi\)
−0.950774 + 0.309884i \(0.899710\pi\)
\(710\) −41.9927 + 14.3943i −1.57596 + 0.540209i
\(711\) −12.6448 −0.474218
\(712\) −8.47209 40.6874i −0.317505 1.52483i
\(713\) 3.29464 0.123385
\(714\) 6.31540 26.0158i 0.236348 0.973619i
\(715\) −22.6320 + 22.6320i −0.846390 + 0.846390i
\(716\) −4.25858 + 33.9077i −0.159151 + 1.26719i
\(717\) −7.03245 7.03245i −0.262632 0.262632i
\(718\) −1.19810 0.586404i −0.0447126 0.0218844i
\(719\) −4.08011 −0.152162 −0.0760812 0.997102i \(-0.524241\pi\)
−0.0760812 + 0.997102i \(0.524241\pi\)
\(720\) −9.25157 + 5.48947i −0.344786 + 0.204581i
\(721\) 3.02751 4.74027i 0.112750 0.176537i
\(722\) −0.156819 + 0.320400i −0.00583618 + 0.0119241i
\(723\) −8.08131 8.08131i −0.300547 0.300547i
\(724\) 41.2740 + 5.18373i 1.53393 + 0.192652i
\(725\) −11.8307 11.8307i −0.439382 0.439382i
\(726\) 6.60946 + 19.2819i 0.245300 + 0.715617i
\(727\) 29.7494i 1.10334i −0.834061 0.551672i \(-0.813990\pi\)
0.834061 0.551672i \(-0.186010\pi\)
\(728\) −16.1143 + 7.24097i −0.597236 + 0.268368i
\(729\) 1.00000i 0.0370370i
\(730\) −30.2612 + 10.3730i −1.12002 + 0.383920i
\(731\) −13.8401 13.8401i −0.511895 0.511895i
\(732\) 9.75726 + 12.5602i 0.360639 + 0.464238i
\(733\) −12.3461 12.3461i −0.456014 0.456014i 0.441330 0.897345i \(-0.354507\pi\)
−0.897345 + 0.441330i \(0.854507\pi\)
\(734\) 4.53352 + 2.21891i 0.167335 + 0.0819016i
\(735\) −17.0801 + 7.91709i −0.630009 + 0.292026i
\(736\) 13.3220 15.6554i 0.491055 0.577065i
\(737\) −12.0210 −0.442801
\(738\) −1.47783 + 3.01939i −0.0543996 + 0.111145i
\(739\) −12.7621 12.7621i −0.469462 0.469462i 0.432278 0.901740i \(-0.357710\pi\)
−0.901740 + 0.432278i \(0.857710\pi\)
\(740\) −11.7421 15.1151i −0.431646 0.555643i
\(741\) 7.32454 7.32454i 0.269074 0.269074i
\(742\) 3.80885 15.6903i 0.139827 0.576008i
\(743\) −14.3254 −0.525547 −0.262774 0.964858i \(-0.584637\pi\)
−0.262774 + 0.964858i \(0.584637\pi\)
\(744\) −2.14485 1.40557i −0.0786339 0.0515306i
\(745\) −31.8918 −1.16843
\(746\) 0.449441 + 1.31116i 0.0164552 + 0.0480050i
\(747\) −3.82605 3.82605i −0.139988 0.139988i
\(748\) 8.98947 71.5760i 0.328688 2.61708i
\(749\) −33.1711 + 7.31409i −1.21205 + 0.267251i
\(750\) 9.45296 + 4.62671i 0.345173 + 0.168944i
\(751\) 51.1794i 1.86756i 0.357846 + 0.933781i \(0.383511\pi\)
−0.357846 + 0.933781i \(0.616489\pi\)
\(752\) −0.544924 + 2.13518i −0.0198713 + 0.0778620i
\(753\) 16.1248 0.587622
\(754\) 22.4699 + 10.9978i 0.818304 + 0.400516i
\(755\) −6.10620 + 6.10620i −0.222227 + 0.222227i
\(756\) 3.38175 4.06986i 0.122993 0.148020i
\(757\) −14.4521 14.4521i −0.525271 0.525271i 0.393888 0.919159i \(-0.371130\pi\)
−0.919159 + 0.393888i \(0.871130\pi\)
\(758\) −12.3965 + 4.24929i −0.450262 + 0.154341i
\(759\) 18.3190i 0.664936i
\(760\) −32.6756 + 6.80385i −1.18527 + 0.246801i
\(761\) −6.59268 −0.238985 −0.119492 0.992835i \(-0.538127\pi\)
−0.119492 + 0.992835i \(0.538127\pi\)
\(762\) −6.72216 19.6106i −0.243518 0.710418i
\(763\) −28.3939 + 6.26074i −1.02793 + 0.226654i
\(764\) −7.64210 + 5.93670i −0.276482 + 0.214782i
\(765\) −13.6065 + 13.6065i −0.491945 + 0.491945i
\(766\) 32.3153 + 15.8166i 1.16760 + 0.571476i
\(767\) 30.6351i 1.10617i
\(768\) −15.3517 + 4.50837i −0.553957 + 0.162682i
\(769\) 2.21522i 0.0798829i 0.999202 + 0.0399414i \(0.0127171\pi\)
−0.999202 + 0.0399414i \(0.987283\pi\)
\(770\) −43.3196 + 26.3960i −1.56113 + 0.951245i
\(771\) −5.94922 5.94922i −0.214256 0.214256i
\(772\) 28.7103 + 36.9578i 1.03331 + 1.33014i
\(773\) 17.1592 17.1592i 0.617173 0.617173i −0.327633 0.944805i \(-0.606251\pi\)
0.944805 + 0.327633i \(0.106251\pi\)
\(774\) −1.25446 3.65964i −0.0450905 0.131543i
\(775\) 2.02440i 0.0727188i
\(776\) −17.2462 + 3.59108i −0.619104 + 0.128912i
\(777\) 7.93452 + 5.06760i 0.284649 + 0.181799i
\(778\) 7.54913 + 22.0232i 0.270649 + 0.789568i
\(779\) −7.37502 + 7.37502i −0.264237 + 0.264237i
\(780\) 12.5992 + 1.58237i 0.451122 + 0.0566579i
\(781\) 41.6046 41.6046i 1.48873 1.48873i
\(782\) 16.1646 33.0264i 0.578046 1.18102i
\(783\) −7.49314 −0.267783
\(784\) −27.5265 + 5.12760i −0.983089 + 0.183129i
\(785\) 2.18508 0.0779887
\(786\) −4.85797 + 9.92546i −0.173278 + 0.354029i
\(787\) −18.9133 + 18.9133i −0.674188 + 0.674188i −0.958679 0.284491i \(-0.908175\pi\)
0.284491 + 0.958679i \(0.408175\pi\)
\(788\) −2.06000 + 16.4021i −0.0733843 + 0.584301i
\(789\) −4.71815 + 4.71815i −0.167970 + 0.167970i
\(790\) −15.5947 45.4945i −0.554834 1.61862i
\(791\) 16.3385 + 10.4351i 0.580931 + 0.371028i
\(792\) 7.81529 11.9259i 0.277704 0.423767i
\(793\) 18.7738i 0.666678i
\(794\) −11.9004 34.7171i −0.422329 1.23206i
\(795\) −8.20616 + 8.20616i −0.291043 + 0.291043i
\(796\) 6.76559 5.25578i 0.239800 0.186286i
\(797\) 0.285537 + 0.285537i 0.0101142 + 0.0101142i 0.712146 0.702032i \(-0.247723\pi\)
−0.702032 + 0.712146i \(0.747723\pi\)
\(798\) 14.0198 8.54268i 0.496294 0.302408i
\(799\) 3.94170i 0.139447i
\(800\) −9.61951 8.18575i −0.340101 0.289410i
\(801\) 14.6937i 0.519177i
\(802\) −28.2663 13.8348i −0.998118 0.488525i
\(803\) 29.9815 29.9815i 1.05802 1.05802i
\(804\) 2.92579 + 3.76627i 0.103185 + 0.132826i
\(805\) −25.2504 + 5.56760i −0.889958 + 0.196232i
\(806\) 0.981519 + 2.86340i 0.0345725 + 0.100859i
\(807\) −1.44567 −0.0508901
\(808\) −45.9513 30.1129i −1.61656 1.05937i
\(809\) 20.9610i 0.736948i 0.929638 + 0.368474i \(0.120120\pi\)
−0.929638 + 0.368474i \(0.879880\pi\)
\(810\) −3.59788 + 1.23329i −0.126417 + 0.0433332i
\(811\) −8.09740 8.09740i −0.284338 0.284338i 0.550498 0.834836i \(-0.314438\pi\)
−0.834836 + 0.550498i \(0.814438\pi\)
\(812\) 30.4961 + 25.3399i 1.07020 + 0.889256i
\(813\) 3.87053 3.87053i 0.135745 0.135745i
\(814\) 22.7861 + 11.1525i 0.798651 + 0.390897i
\(815\) 52.6325 1.84363
\(816\) −24.6132 + 14.6044i −0.861633 + 0.511255i
\(817\) 12.0029i 0.419930i
\(818\) 34.4734 + 16.8728i 1.20533 + 0.589945i
\(819\) −6.09951 + 1.34492i −0.213134 + 0.0469952i
\(820\) −12.6860 1.59327i −0.443014 0.0556396i
\(821\) −33.6935 33.6935i −1.17591 1.17591i −0.980776 0.195136i \(-0.937485\pi\)
−0.195136 0.980776i \(-0.562515\pi\)
\(822\) 1.57720 + 4.60119i 0.0550112 + 0.160485i
\(823\) −46.3245 −1.61477 −0.807386 0.590023i \(-0.799118\pi\)
−0.807386 + 0.590023i \(0.799118\pi\)
\(824\) −5.88668 + 1.22575i −0.205072 + 0.0427009i
\(825\) 11.2562 0.391890
\(826\) −11.4540 + 47.1841i −0.398537 + 1.64175i
\(827\) −13.5597 + 13.5597i −0.471516 + 0.471516i −0.902405 0.430889i \(-0.858200\pi\)
0.430889 + 0.902405i \(0.358200\pi\)
\(828\) 5.73945 4.45864i 0.199460 0.154948i
\(829\) 19.5380 + 19.5380i 0.678582 + 0.678582i 0.959679 0.281097i \(-0.0906983\pi\)
−0.281097 + 0.959679i \(0.590698\pi\)
\(830\) 9.04706 18.4843i 0.314028 0.641599i
\(831\) 14.0165 0.486228
\(832\) 17.5750 + 6.91429i 0.609304 + 0.239710i
\(833\) −45.4405 + 21.0629i −1.57442 + 0.729786i
\(834\) −9.36233 4.58235i −0.324191 0.158674i
\(835\) −18.4730 18.4730i −0.639286 0.639286i
\(836\) 34.9355 27.1394i 1.20827 0.938634i
\(837\) −0.641092 0.641092i −0.0221594 0.0221594i
\(838\) −26.5505 + 9.10102i −0.917173 + 0.314390i
\(839\) 1.94803i 0.0672534i −0.999434 0.0336267i \(-0.989294\pi\)
0.999434 0.0336267i \(-0.0107057\pi\)
\(840\) 18.8135 + 7.14780i 0.649129 + 0.246623i
\(841\) 27.1472i 0.936109i
\(842\) −12.1500 35.4454i −0.418717 1.22153i
\(843\) 13.8898 + 13.8898i 0.478392 + 0.478392i
\(844\) 1.88467 15.0061i 0.0648731 0.516533i
\(845\) 14.1234 + 14.1234i 0.485858 + 0.485858i
\(846\) −0.342502 + 0.699775i −0.0117755 + 0.0240587i
\(847\) 20.5259 32.1380i 0.705277 1.10428i
\(848\) −14.8443 + 8.80796i −0.509756 + 0.302467i
\(849\) 28.7157 0.985521
\(850\) −20.2932 9.93243i −0.696052 0.340680i
\(851\) 9.14358 + 9.14358i 0.313438 + 0.313438i
\(852\) −23.1611 2.90888i −0.793486 0.0996565i
\(853\) −15.1509 + 15.1509i −0.518756 + 0.518756i −0.917195 0.398439i \(-0.869552\pi\)
0.398439 + 0.917195i \(0.369552\pi\)
\(854\) 7.01926 28.9154i 0.240194 0.989463i
\(855\) −11.8004 −0.403564
\(856\) 30.3725 + 19.9038i 1.03811 + 0.680298i
\(857\) 28.4917 0.973259 0.486629 0.873609i \(-0.338226\pi\)
0.486629 + 0.873609i \(0.338226\pi\)
\(858\) −15.9212 + 5.45748i −0.543540 + 0.186315i
\(859\) −4.12583 4.12583i −0.140772 0.140772i 0.633209 0.773981i \(-0.281737\pi\)
−0.773981 + 0.633209i \(0.781737\pi\)
\(860\) 11.6198 9.02676i 0.396233 0.307810i
\(861\) 6.14155 1.35418i 0.209303 0.0461505i
\(862\) −15.2384 + 31.1340i −0.519023 + 1.06043i
\(863\) 13.9231i 0.473949i 0.971516 + 0.236974i \(0.0761557\pi\)
−0.971516 + 0.236974i \(0.923844\pi\)
\(864\) −5.63860 + 0.454046i −0.191829 + 0.0154470i
\(865\) 13.5973 0.462321
\(866\) −6.43666 + 13.1509i −0.218726 + 0.446886i
\(867\) −24.1784 + 24.1784i −0.821143 + 0.821143i
\(868\) 0.441148 + 4.77717i 0.0149735 + 0.162148i
\(869\) 45.0740 + 45.0740i 1.52903 + 1.52903i
\(870\) −9.24118 26.9594i −0.313305 0.914010i
\(871\) 5.62947i 0.190747i
\(872\) 25.9984 + 17.0373i 0.880416 + 0.576957i
\(873\) −6.22825 −0.210794
\(874\) 21.3307 7.31175i 0.721520 0.247324i
\(875\) −4.23961 19.2276i −0.143325 0.650013i
\(876\) −16.6905 2.09622i −0.563921 0.0708247i
\(877\) 28.6830 28.6830i 0.968557 0.968557i −0.0309635 0.999521i \(-0.509858\pi\)
0.999521 + 0.0309635i \(0.00985756\pi\)
\(878\) −13.5898 + 27.7658i −0.458635 + 0.937049i
\(879\) 16.6208i 0.560604i
\(880\) 52.5463 + 13.4105i 1.77133 + 0.452066i
\(881\) 4.92697i 0.165994i −0.996550 0.0829969i \(-0.973551\pi\)
0.996550 0.0829969i \(-0.0264492\pi\)
\(882\) −9.89729 0.209087i −0.333259 0.00704031i
\(883\) 33.0133 + 33.0133i 1.11099 + 1.11099i 0.993017 + 0.117971i \(0.0376389\pi\)
0.117971 + 0.993017i \(0.462361\pi\)
\(884\) 33.5192 + 4.20979i 1.12737 + 0.141590i
\(885\) 24.6777 24.6777i 0.829533 0.829533i
\(886\) −16.6915 + 5.72153i −0.560762 + 0.192219i
\(887\) 6.48099i 0.217610i −0.994063 0.108805i \(-0.965298\pi\)
0.994063 0.108805i \(-0.0347025\pi\)
\(888\) −2.05172 9.85343i −0.0688511 0.330659i
\(889\) −20.8758 + 32.6860i −0.700153 + 1.09625i
\(890\) 52.8662 18.1215i 1.77208 0.607436i
\(891\) 3.56463 3.56463i 0.119419 0.119419i
\(892\) 34.8862 + 44.9078i 1.16808 + 1.50362i
\(893\) −1.70924 + 1.70924i −0.0571974 + 0.0571974i
\(894\) −15.0628 7.37242i −0.503775 0.246571i
\(895\) −45.9539 −1.53607
\(896\) 24.4838 + 17.2204i 0.817947 + 0.575294i
\(897\) −8.57881 −0.286438
\(898\) 19.5046 + 9.54646i 0.650878 + 0.318569i
\(899\) 4.80379 4.80379i 0.160216 0.160216i
\(900\) −2.73963 3.52663i −0.0913210 0.117554i
\(901\) −21.8319 + 21.8319i −0.727327 + 0.727327i
\(902\) 16.0309 5.49509i 0.533770 0.182967i
\(903\) −3.89575 + 6.09970i −0.129642 + 0.202985i
\(904\) −4.22484 20.2899i −0.140516 0.674832i
\(905\) 55.9371i 1.85941i
\(906\) −4.29558 + 1.47245i −0.142711 + 0.0489187i
\(907\) 33.5078 33.5078i 1.11261 1.11261i 0.119810 0.992797i \(-0.461771\pi\)
0.992797 0.119810i \(-0.0382286\pi\)
\(908\) −53.6659 6.74008i −1.78097 0.223678i
\(909\) −13.7348 13.7348i −0.455554 0.455554i
\(910\) −12.3613 20.2866i −0.409773 0.672495i
\(911\) 12.4867i 0.413702i 0.978372 + 0.206851i \(0.0663215\pi\)
−0.978372 + 0.206851i \(0.933679\pi\)
\(912\) −17.0059 4.34010i −0.563120 0.143715i
\(913\) 27.2769i 0.902733i
\(914\) −21.1697 + 43.2524i −0.700232 + 1.43066i
\(915\) −15.1230 + 15.1230i −0.499951 + 0.499951i
\(916\) −5.94265 0.746357i −0.196351 0.0246603i
\(917\) 20.1887 4.45153i 0.666691 0.147002i
\(918\) −9.57191 + 3.28107i −0.315920 + 0.108292i
\(919\) −23.3667 −0.770796 −0.385398 0.922751i \(-0.625936\pi\)
−0.385398 + 0.922751i \(0.625936\pi\)
\(920\) 23.1200 + 15.1511i 0.762244 + 0.499516i
\(921\) 26.8977i 0.886308i
\(922\) −11.3512 33.1151i −0.373833 1.09059i
\(923\) 19.4835 + 19.4835i 0.641308 + 0.641308i
\(924\) −26.5622 + 2.45289i −0.873832 + 0.0806941i
\(925\) 5.61831 5.61831i 0.184729 0.184729i
\(926\) 0.0329644 0.0673505i 0.00108328 0.00221327i
\(927\) −2.12589 −0.0698235
\(928\) −3.40223 42.2509i −0.111684 1.38695i
\(929\) 22.6572i 0.743357i 0.928361 + 0.371679i \(0.121218\pi\)
−0.928361 + 0.371679i \(0.878782\pi\)
\(930\) 1.51592 3.09722i 0.0497090 0.101562i
\(931\) −28.8378 10.5708i −0.945120 0.346445i
\(932\) −36.5011 + 28.3555i −1.19563 + 0.928815i
\(933\) −9.69538 9.69538i −0.317413 0.317413i
\(934\) −15.8854 + 5.44520i −0.519785 + 0.178172i
\(935\) 97.0044 3.17238
\(936\) 5.58490 + 3.65991i 0.182548 + 0.119628i
\(937\) −23.8889 −0.780417 −0.390208 0.920727i \(-0.627597\pi\)
−0.390208 + 0.920727i \(0.627597\pi\)
\(938\) 2.10478 8.67049i 0.0687235 0.283102i
\(939\) 3.42478 3.42478i 0.111764 0.111764i
\(940\) −2.94011 0.369258i −0.0958957 0.0120439i
\(941\) −13.2546 13.2546i −0.432088 0.432088i 0.457250 0.889338i \(-0.348834\pi\)
−0.889338 + 0.457250i \(0.848834\pi\)
\(942\) 1.03203 + 0.505124i 0.0336254 + 0.0164578i
\(943\) 8.63793 0.281290
\(944\) 44.6401 26.4875i 1.45291 0.862094i
\(945\) 5.99676 + 3.83000i 0.195075 + 0.124590i
\(946\) −8.57358 + 17.5169i −0.278751 + 0.569524i
\(947\) 7.30455 + 7.30455i 0.237366 + 0.237366i 0.815759 0.578393i \(-0.196320\pi\)
−0.578393 + 0.815759i \(0.696320\pi\)
\(948\) 3.15145 25.0925i 0.102354 0.814967i
\(949\) 14.0404 + 14.0404i 0.455770 + 0.455770i
\(950\) −4.49274 13.1067i −0.145764 0.425238i
\(951\) 3.85421i 0.124981i
\(952\) 50.0521 + 19.0162i 1.62220 + 0.616320i
\(953\) 27.8206i 0.901198i −0.892726 0.450599i \(-0.851210\pi\)
0.892726 0.450599i \(-0.148790\pi\)
\(954\) −5.77286 + 1.97883i −0.186903 + 0.0640670i
\(955\) −9.20142 9.20142i −0.297751 0.297751i
\(956\) 15.7080 12.2026i 0.508031 0.394660i
\(957\) 26.7102 + 26.7102i 0.863419 + 0.863419i
\(958\) 46.9391 + 22.9742i 1.51653 + 0.742262i
\(959\) 4.89804 7.66903i 0.158166 0.247646i
\(960\) −8.58761 19.7270i −0.277164 0.636687i
\(961\) −30.1780 −0.973484
\(962\) −5.22276 + 10.6708i −0.168389 + 0.344039i
\(963\) 9.07831 + 9.07831i 0.292545 + 0.292545i
\(964\) 18.0507 14.0225i 0.581375 0.451635i
\(965\) −44.4988 + 44.4988i −1.43247 + 1.43247i
\(966\) −13.2130 3.20749i −0.425123 0.103199i
\(967\) 23.9412 0.769898 0.384949 0.922938i \(-0.374219\pi\)
0.384949 + 0.922938i \(0.374219\pi\)
\(968\) −39.9104 + 8.31029i −1.28277 + 0.267103i
\(969\) −31.3941 −1.00852
\(970\) −7.68121 22.4085i −0.246629 0.719493i
\(971\) −18.4212 18.4212i −0.591165 0.591165i 0.346781 0.937946i \(-0.387275\pi\)
−0.937946 + 0.346781i \(0.887275\pi\)
\(972\) −1.98441 0.249229i −0.0636500 0.00799401i
\(973\) 4.19897 + 19.0433i 0.134613 + 0.610500i
\(974\) −18.5750 9.09145i −0.595181 0.291309i
\(975\) 5.27129i 0.168816i
\(976\) −27.3563 + 16.2320i −0.875655 + 0.519575i
\(977\) 41.8758 1.33973 0.669863 0.742484i \(-0.266353\pi\)
0.669863 + 0.742484i \(0.266353\pi\)
\(978\) 24.8588 + 12.1670i 0.794897 + 0.389059i
\(979\) −52.3776 + 52.3776i −1.67399 + 1.67399i
\(980\) −11.4539 35.8671i −0.365882 1.14573i
\(981\) 7.77089 + 7.77089i 0.248105 + 0.248105i
\(982\) −12.2205 + 4.18895i −0.389971 + 0.133675i
\(983\) 28.1376i 0.897450i −0.893670 0.448725i \(-0.851878\pi\)
0.893670 0.448725i \(-0.148122\pi\)
\(984\) −5.62339 3.68514i −0.179267 0.117478i
\(985\) −22.2292 −0.708281
\(986\) −24.5855 71.7237i −0.782963 2.28415i
\(987\) 1.42337 0.313846i 0.0453063 0.00998983i
\(988\) 12.7094 + 16.3604i 0.404340 + 0.520493i
\(989\) −7.02917 + 7.02917i −0.223515 + 0.223515i
\(990\) 17.2213 + 8.42889i 0.547329 + 0.267888i
\(991\) 57.5245i 1.82733i −0.406473 0.913663i \(-0.633242\pi\)
0.406473 0.913663i \(-0.366758\pi\)
\(992\) 3.32378 3.90595i 0.105530 0.124014i
\(993\) 9.81186i 0.311370i
\(994\) 22.7238 + 37.2930i 0.720756 + 1.18286i
\(995\) 8.14606 + 8.14606i 0.258248 + 0.258248i
\(996\) 8.54602 6.63890i 0.270791 0.210361i
\(997\) 31.2570 31.2570i 0.989919 0.989919i −0.0100311 0.999950i \(-0.503193\pi\)
0.999950 + 0.0100311i \(0.00319307\pi\)
\(998\) −0.0608033 0.177382i −0.00192470 0.00561494i
\(999\) 3.55843i 0.112584i
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 336.2.u.a.139.4 yes 64
4.3 odd 2 1344.2.u.a.1231.14 64
7.6 odd 2 inner 336.2.u.a.139.3 64
16.3 odd 4 inner 336.2.u.a.307.3 yes 64
16.13 even 4 1344.2.u.a.559.19 64
28.27 even 2 1344.2.u.a.1231.19 64
112.13 odd 4 1344.2.u.a.559.14 64
112.83 even 4 inner 336.2.u.a.307.4 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.u.a.139.3 64 7.6 odd 2 inner
336.2.u.a.139.4 yes 64 1.1 even 1 trivial
336.2.u.a.307.3 yes 64 16.3 odd 4 inner
336.2.u.a.307.4 yes 64 112.83 even 4 inner
1344.2.u.a.559.14 64 112.13 odd 4
1344.2.u.a.559.19 64 16.13 even 4
1344.2.u.a.1231.14 64 4.3 odd 2
1344.2.u.a.1231.19 64 28.27 even 2