Properties

Label 350.2.m.a.309.2
Level $350$
Weight $2$
Character 350.309
Analytic conductor $2.795$
Analytic rank $0$
Dimension $24$
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] = [350,2,Mod(29,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.m (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: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 309.2
Character \(\chi\) \(=\) 350.309
Dual form 350.2.m.a.239.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 + 0.809017i) q^{2} +(0.195447 - 0.0635047i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.0419655 + 2.23567i) q^{5} +(-0.0635047 + 0.195447i) q^{6} +1.00000i q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.39288 + 1.73853i) q^{9} +O(q^{10})\) \(q+(-0.587785 + 0.809017i) q^{2} +(0.195447 - 0.0635047i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.0419655 + 2.23567i) q^{5} +(-0.0635047 + 0.195447i) q^{6} +1.00000i q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.39288 + 1.73853i) q^{9} +(-1.83337 - 1.28015i) q^{10} +(0.483397 + 0.351209i) q^{11} +(-0.120793 - 0.166258i) q^{12} +(-1.59798 - 2.19943i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(0.150178 + 0.434292i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.72127 + 0.559274i) q^{17} -2.95777i q^{18} +(-2.23744 + 6.88612i) q^{19} +(2.11328 - 0.730773i) q^{20} +(0.0635047 + 0.195447i) q^{21} +(-0.568268 + 0.184641i) q^{22} +(-0.516806 + 0.711323i) q^{23} +0.205506 q^{24} +(-4.99648 + 0.187642i) q^{25} +2.71865 q^{26} +(-0.719658 + 0.990524i) q^{27} +(0.951057 - 0.309017i) q^{28} +(1.25308 + 3.85659i) q^{29} +(-0.439622 - 0.133774i) q^{30} +(-1.36453 + 4.19959i) q^{31} -1.00000i q^{32} +(0.116782 + 0.0379448i) q^{33} +(-1.46420 + 1.06380i) q^{34} +(-2.23567 + 0.0419655i) q^{35} +(2.39288 + 1.73853i) q^{36} +(-2.27805 - 3.13546i) q^{37} +(-4.25586 - 5.85769i) q^{38} +(-0.451996 - 0.328394i) q^{39} +(-0.650950 + 2.13922i) q^{40} +(4.93070 - 3.58236i) q^{41} +(-0.195447 - 0.0635047i) q^{42} -0.789626i q^{43} +(0.184641 - 0.568268i) q^{44} +(-3.98721 - 5.27675i) q^{45} +(-0.271701 - 0.836210i) q^{46} +(0.430533 - 0.139889i) q^{47} +(-0.120793 + 0.166258i) q^{48} -1.00000 q^{49} +(2.78505 - 4.15253i) q^{50} +0.371934 q^{51} +(-1.59798 + 2.19943i) q^{52} +(9.74573 - 3.16658i) q^{53} +(-0.378346 - 1.16443i) q^{54} +(-0.764902 + 1.09546i) q^{55} +(-0.309017 + 0.951057i) q^{56} +1.48796i q^{57} +(-3.85659 - 1.25308i) q^{58} +(1.21560 - 0.883186i) q^{59} +(0.366629 - 0.277031i) q^{60} +(9.35755 + 6.79866i) q^{61} +(-2.59549 - 3.57238i) q^{62} +(-1.73853 - 2.39288i) q^{63} +(0.809017 + 0.587785i) q^{64} +(4.85016 - 3.66487i) q^{65} +(-0.0993408 + 0.0721753i) q^{66} +(-3.66555 - 1.19101i) q^{67} -1.80985i q^{68} +(-0.0558361 + 0.171846i) q^{69} +(1.28015 - 1.83337i) q^{70} +(-0.329896 - 1.01532i) q^{71} +(-2.81300 + 0.914000i) q^{72} +(4.35351 - 5.99209i) q^{73} +3.87565 q^{74} +(-0.964633 + 0.353974i) q^{75} +7.24050 q^{76} +(-0.351209 + 0.483397i) q^{77} +(0.531353 - 0.172647i) q^{78} +(1.32550 + 4.07947i) q^{79} +(-1.34805 - 1.78403i) q^{80} +(2.66425 - 8.19972i) q^{81} +6.09468i q^{82} +(0.811986 + 0.263830i) q^{83} +(0.166258 - 0.120793i) q^{84} +(-1.17812 + 3.87167i) q^{85} +(0.638821 + 0.464130i) q^{86} +(0.489824 + 0.674185i) q^{87} +(0.351209 + 0.483397i) q^{88} +(9.67930 + 7.03242i) q^{89} +(6.61260 - 0.124124i) q^{90} +(2.19943 - 1.59798i) q^{91} +(0.836210 + 0.271701i) q^{92} +0.907452i q^{93} +(-0.139889 + 0.430533i) q^{94} +(-15.4890 - 4.71320i) q^{95} +(-0.0635047 - 0.195447i) q^{96} +(3.27298 - 1.06346i) q^{97} +(0.587785 - 0.809017i) q^{98} -1.76730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 + 0.809017i −0.415627 + 0.572061i
\(3\) 0.195447 0.0635047i 0.112842 0.0366645i −0.252052 0.967714i \(-0.581105\pi\)
0.364894 + 0.931049i \(0.381105\pi\)
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) 0.0419655 + 2.23567i 0.0187675 + 0.999824i
\(6\) −0.0635047 + 0.195447i −0.0259257 + 0.0797911i
\(7\) 1.00000i 0.377964i
\(8\) 0.951057 + 0.309017i 0.336249 + 0.109254i
\(9\) −2.39288 + 1.73853i −0.797628 + 0.579511i
\(10\) −1.83337 1.28015i −0.579761 0.404818i
\(11\) 0.483397 + 0.351209i 0.145750 + 0.105893i 0.658271 0.752781i \(-0.271288\pi\)
−0.512521 + 0.858675i \(0.671288\pi\)
\(12\) −0.120793 0.166258i −0.0348700 0.0479944i
\(13\) −1.59798 2.19943i −0.443201 0.610013i 0.527719 0.849419i \(-0.323047\pi\)
−0.970920 + 0.239406i \(0.923047\pi\)
\(14\) −0.809017 0.587785i −0.216219 0.157092i
\(15\) 0.150178 + 0.434292i 0.0387758 + 0.112134i
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) 1.72127 + 0.559274i 0.417469 + 0.135644i 0.510217 0.860046i \(-0.329565\pi\)
−0.0927479 + 0.995690i \(0.529565\pi\)
\(18\) 2.95777i 0.697152i
\(19\) −2.23744 + 6.88612i −0.513303 + 1.57978i 0.273045 + 0.962001i \(0.411969\pi\)
−0.786348 + 0.617784i \(0.788031\pi\)
\(20\) 2.11328 0.730773i 0.472545 0.163406i
\(21\) 0.0635047 + 0.195447i 0.0138579 + 0.0426501i
\(22\) −0.568268 + 0.184641i −0.121155 + 0.0393657i
\(23\) −0.516806 + 0.711323i −0.107762 + 0.148321i −0.859492 0.511150i \(-0.829220\pi\)
0.751730 + 0.659471i \(0.229220\pi\)
\(24\) 0.205506 0.0419487
\(25\) −4.99648 + 0.187642i −0.999296 + 0.0375285i
\(26\) 2.71865 0.533171
\(27\) −0.719658 + 0.990524i −0.138498 + 0.190626i
\(28\) 0.951057 0.309017i 0.179733 0.0583987i
\(29\) 1.25308 + 3.85659i 0.232692 + 0.716151i 0.997419 + 0.0717976i \(0.0228736\pi\)
−0.764728 + 0.644354i \(0.777126\pi\)
\(30\) −0.439622 0.133774i −0.0802636 0.0244236i
\(31\) −1.36453 + 4.19959i −0.245077 + 0.754268i 0.750547 + 0.660817i \(0.229790\pi\)
−0.995624 + 0.0934513i \(0.970210\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.116782 + 0.0379448i 0.0203292 + 0.00660535i
\(34\) −1.46420 + 1.06380i −0.251108 + 0.182441i
\(35\) −2.23567 + 0.0419655i −0.377898 + 0.00709346i
\(36\) 2.39288 + 1.73853i 0.398814 + 0.289755i
\(37\) −2.27805 3.13546i −0.374509 0.515467i 0.579611 0.814894i \(-0.303205\pi\)
−0.954119 + 0.299426i \(0.903205\pi\)
\(38\) −4.25586 5.85769i −0.690391 0.950242i
\(39\) −0.451996 0.328394i −0.0723773 0.0525852i
\(40\) −0.650950 + 2.13922i −0.102924 + 0.338240i
\(41\) 4.93070 3.58236i 0.770046 0.559471i −0.131929 0.991259i \(-0.542117\pi\)
0.901975 + 0.431788i \(0.142117\pi\)
\(42\) −0.195447 0.0635047i −0.0301582 0.00979899i
\(43\) 0.789626i 0.120417i −0.998186 0.0602084i \(-0.980823\pi\)
0.998186 0.0602084i \(-0.0191765\pi\)
\(44\) 0.184641 0.568268i 0.0278357 0.0856696i
\(45\) −3.98721 5.27675i −0.594378 0.786612i
\(46\) −0.271701 0.836210i −0.0400602 0.123292i
\(47\) 0.430533 0.139889i 0.0627998 0.0204049i −0.277449 0.960740i \(-0.589489\pi\)
0.340248 + 0.940336i \(0.389489\pi\)
\(48\) −0.120793 + 0.166258i −0.0174350 + 0.0239972i
\(49\) −1.00000 −0.142857
\(50\) 2.78505 4.15253i 0.393866 0.587256i
\(51\) 0.371934 0.0520812
\(52\) −1.59798 + 2.19943i −0.221600 + 0.305007i
\(53\) 9.74573 3.16658i 1.33868 0.434963i 0.449809 0.893125i \(-0.351492\pi\)
0.888869 + 0.458162i \(0.151492\pi\)
\(54\) −0.378346 1.16443i −0.0514864 0.158459i
\(55\) −0.764902 + 1.09546i −0.103139 + 0.147711i
\(56\) −0.309017 + 0.951057i −0.0412941 + 0.127090i
\(57\) 1.48796i 0.197085i
\(58\) −3.85659 1.25308i −0.506396 0.164538i
\(59\) 1.21560 0.883186i 0.158258 0.114981i −0.505838 0.862628i \(-0.668817\pi\)
0.664096 + 0.747647i \(0.268817\pi\)
\(60\) 0.366629 0.277031i 0.0473315 0.0357646i
\(61\) 9.35755 + 6.79866i 1.19811 + 0.870479i 0.994098 0.108489i \(-0.0346011\pi\)
0.204014 + 0.978968i \(0.434601\pi\)
\(62\) −2.59549 3.57238i −0.329627 0.453693i
\(63\) −1.73853 2.39288i −0.219034 0.301475i
\(64\) 0.809017 + 0.587785i 0.101127 + 0.0734732i
\(65\) 4.85016 3.66487i 0.601588 0.454571i
\(66\) −0.0993408 + 0.0721753i −0.0122280 + 0.00888417i
\(67\) −3.66555 1.19101i −0.447818 0.145505i 0.0764220 0.997076i \(-0.475650\pi\)
−0.524240 + 0.851571i \(0.675650\pi\)
\(68\) 1.80985i 0.219477i
\(69\) −0.0558361 + 0.171846i −0.00672188 + 0.0206878i
\(70\) 1.28015 1.83337i 0.153007 0.219129i
\(71\) −0.329896 1.01532i −0.0391514 0.120496i 0.929571 0.368644i \(-0.120178\pi\)
−0.968722 + 0.248148i \(0.920178\pi\)
\(72\) −2.81300 + 0.914000i −0.331516 + 0.107716i
\(73\) 4.35351 5.99209i 0.509540 0.701322i −0.474302 0.880362i \(-0.657299\pi\)
0.983842 + 0.179041i \(0.0572994\pi\)
\(74\) 3.87565 0.450535
\(75\) −0.964633 + 0.353974i −0.111386 + 0.0408734i
\(76\) 7.24050 0.830542
\(77\) −0.351209 + 0.483397i −0.0400239 + 0.0550882i
\(78\) 0.531353 0.172647i 0.0601639 0.0195484i
\(79\) 1.32550 + 4.07947i 0.149130 + 0.458976i 0.997519 0.0703978i \(-0.0224269\pi\)
−0.848389 + 0.529374i \(0.822427\pi\)
\(80\) −1.34805 1.78403i −0.150716 0.199461i
\(81\) 2.66425 8.19972i 0.296028 0.911079i
\(82\) 6.09468i 0.673045i
\(83\) 0.811986 + 0.263830i 0.0891271 + 0.0289591i 0.353241 0.935532i \(-0.385080\pi\)
−0.264114 + 0.964491i \(0.585080\pi\)
\(84\) 0.166258 0.120793i 0.0181402 0.0131796i
\(85\) −1.17812 + 3.87167i −0.127785 + 0.419941i
\(86\) 0.638821 + 0.464130i 0.0688858 + 0.0500485i
\(87\) 0.489824 + 0.674185i 0.0525146 + 0.0722802i
\(88\) 0.351209 + 0.483397i 0.0374390 + 0.0515303i
\(89\) 9.67930 + 7.03242i 1.02600 + 0.745435i 0.967505 0.252853i \(-0.0813687\pi\)
0.0584984 + 0.998288i \(0.481369\pi\)
\(90\) 6.61260 0.124124i 0.697030 0.0130838i
\(91\) 2.19943 1.59798i 0.230563 0.167514i
\(92\) 0.836210 + 0.271701i 0.0871810 + 0.0283268i
\(93\) 0.907452i 0.0940984i
\(94\) −0.139889 + 0.430533i −0.0144284 + 0.0444061i
\(95\) −15.4890 4.71320i −1.58914 0.483564i
\(96\) −0.0635047 0.195447i −0.00648142 0.0199478i
\(97\) 3.27298 1.06346i 0.332321 0.107978i −0.138104 0.990418i \(-0.544101\pi\)
0.470425 + 0.882440i \(0.344101\pi\)
\(98\) 0.587785 0.809017i 0.0593753 0.0817231i
\(99\) −1.76730 −0.177620
\(100\) 1.72246 + 4.69395i 0.172246 + 0.469395i
\(101\) 13.8998 1.38308 0.691539 0.722339i \(-0.256933\pi\)
0.691539 + 0.722339i \(0.256933\pi\)
\(102\) −0.218617 + 0.300901i −0.0216464 + 0.0297937i
\(103\) 17.8160 5.78877i 1.75546 0.570384i 0.758749 0.651384i \(-0.225811\pi\)
0.996714 + 0.0809992i \(0.0258111\pi\)
\(104\) −0.840109 2.58559i −0.0823795 0.253538i
\(105\) −0.434292 + 0.150178i −0.0423825 + 0.0146559i
\(106\) −3.16658 + 9.74573i −0.307565 + 0.946589i
\(107\) 15.4645i 1.49501i −0.664255 0.747506i \(-0.731251\pi\)
0.664255 0.747506i \(-0.268749\pi\)
\(108\) 1.16443 + 0.378346i 0.112047 + 0.0364064i
\(109\) −5.75790 + 4.18336i −0.551507 + 0.400693i −0.828341 0.560225i \(-0.810715\pi\)
0.276834 + 0.960918i \(0.410715\pi\)
\(110\) −0.436645 1.26271i −0.0416325 0.120395i
\(111\) −0.644355 0.468152i −0.0611595 0.0444350i
\(112\) −0.587785 0.809017i −0.0555405 0.0764449i
\(113\) 5.71385 + 7.86444i 0.537514 + 0.739824i 0.988252 0.152832i \(-0.0488393\pi\)
−0.450739 + 0.892656i \(0.648839\pi\)
\(114\) −1.20379 0.874603i −0.112745 0.0819140i
\(115\) −1.61197 1.12556i −0.150317 0.104959i
\(116\) 3.28061 2.38351i 0.304597 0.221303i
\(117\) 7.64757 + 2.48485i 0.707019 + 0.229724i
\(118\) 1.50257i 0.138322i
\(119\) −0.559274 + 1.72127i −0.0512686 + 0.157789i
\(120\) 0.00862414 + 0.459444i 0.000787273 + 0.0419413i
\(121\) −3.28886 10.1221i −0.298987 0.920189i
\(122\) −11.0005 + 3.57427i −0.995935 + 0.323599i
\(123\) 0.736195 1.01329i 0.0663805 0.0913649i
\(124\) 4.41571 0.396542
\(125\) −0.629187 11.1626i −0.0562762 0.998415i
\(126\) 2.95777 0.263499
\(127\) −12.8753 + 17.7213i −1.14250 + 1.57251i −0.380695 + 0.924701i \(0.624315\pi\)
−0.761802 + 0.647810i \(0.775685\pi\)
\(128\) −0.951057 + 0.309017i −0.0840623 + 0.0273135i
\(129\) −0.0501450 0.154330i −0.00441502 0.0135880i
\(130\) 0.114090 + 6.07802i 0.0100063 + 0.533077i
\(131\) −0.562324 + 1.73065i −0.0491305 + 0.151208i −0.972612 0.232435i \(-0.925331\pi\)
0.923481 + 0.383643i \(0.125331\pi\)
\(132\) 0.122792i 0.0106877i
\(133\) −6.88612 2.23744i −0.597103 0.194010i
\(134\) 3.11810 2.26543i 0.269363 0.195704i
\(135\) −2.24469 1.56735i −0.193192 0.134896i
\(136\) 1.46420 + 1.06380i 0.125554 + 0.0912204i
\(137\) −10.7406 14.7831i −0.917630 1.26301i −0.964493 0.264108i \(-0.914923\pi\)
0.0468633 0.998901i \(-0.485077\pi\)
\(138\) −0.106207 0.146181i −0.00904091 0.0124437i
\(139\) −0.431646 0.313609i −0.0366117 0.0266000i 0.569329 0.822110i \(-0.307203\pi\)
−0.605941 + 0.795510i \(0.707203\pi\)
\(140\) 0.730773 + 2.11328i 0.0617616 + 0.178605i
\(141\) 0.0752631 0.0546818i 0.00633829 0.00460504i
\(142\) 1.01532 + 0.329896i 0.0852033 + 0.0276842i
\(143\) 1.62443i 0.135841i
\(144\) 0.914000 2.81300i 0.0761667 0.234417i
\(145\) −8.56950 + 2.96333i −0.711658 + 0.246091i
\(146\) 2.28878 + 7.04413i 0.189420 + 0.582976i
\(147\) −0.195447 + 0.0635047i −0.0161202 + 0.00523778i
\(148\) −2.27805 + 3.13546i −0.187254 + 0.257734i
\(149\) −6.57541 −0.538679 −0.269339 0.963045i \(-0.586805\pi\)
−0.269339 + 0.963045i \(0.586805\pi\)
\(150\) 0.280626 0.988465i 0.0229130 0.0807078i
\(151\) −21.8023 −1.77424 −0.887122 0.461535i \(-0.847299\pi\)
−0.887122 + 0.461535i \(0.847299\pi\)
\(152\) −4.25586 + 5.85769i −0.345196 + 0.475121i
\(153\) −5.09112 + 1.65420i −0.411592 + 0.133734i
\(154\) −0.184641 0.568268i −0.0148788 0.0457923i
\(155\) −9.44617 2.87440i −0.758735 0.230878i
\(156\) −0.172647 + 0.531353i −0.0138228 + 0.0425423i
\(157\) 5.49190i 0.438301i 0.975691 + 0.219151i \(0.0703286\pi\)
−0.975691 + 0.219151i \(0.929671\pi\)
\(158\) −4.07947 1.32550i −0.324545 0.105451i
\(159\) 1.70368 1.23780i 0.135111 0.0981639i
\(160\) 2.23567 0.0419655i 0.176746 0.00331766i
\(161\) −0.711323 0.516806i −0.0560601 0.0407301i
\(162\) 5.06770 + 6.97509i 0.398156 + 0.548015i
\(163\) 4.08905 + 5.62809i 0.320279 + 0.440826i 0.938552 0.345137i \(-0.112168\pi\)
−0.618273 + 0.785963i \(0.712168\pi\)
\(164\) −4.93070 3.58236i −0.385023 0.279735i
\(165\) −0.0799314 + 0.262679i −0.00622265 + 0.0204496i
\(166\) −0.690717 + 0.501835i −0.0536100 + 0.0389500i
\(167\) 3.03951 + 0.987596i 0.235204 + 0.0764224i 0.424247 0.905546i \(-0.360539\pi\)
−0.189043 + 0.981969i \(0.560539\pi\)
\(168\) 0.205506i 0.0158551i
\(169\) 1.73326 5.33442i 0.133328 0.410340i
\(170\) −2.43976 3.22883i −0.187121 0.247640i
\(171\) −6.61782 20.3675i −0.506077 1.55755i
\(172\) −0.750979 + 0.244008i −0.0572616 + 0.0186054i
\(173\) −5.78976 + 7.96892i −0.440187 + 0.605866i −0.970254 0.242090i \(-0.922167\pi\)
0.530067 + 0.847956i \(0.322167\pi\)
\(174\) −0.833338 −0.0631752
\(175\) −0.187642 4.99648i −0.0141844 0.377698i
\(176\) −0.597512 −0.0450391
\(177\) 0.181500 0.249813i 0.0136424 0.0187771i
\(178\) −11.3787 + 3.69716i −0.852869 + 0.277114i
\(179\) 6.83054 + 21.0222i 0.510538 + 1.57127i 0.791256 + 0.611485i \(0.209427\pi\)
−0.280718 + 0.959790i \(0.590573\pi\)
\(180\) −3.78637 + 5.42267i −0.282220 + 0.404182i
\(181\) −6.56272 + 20.1980i −0.487803 + 1.50130i 0.340076 + 0.940398i \(0.389547\pi\)
−0.827879 + 0.560907i \(0.810453\pi\)
\(182\) 2.71865i 0.201520i
\(183\) 2.26066 + 0.734532i 0.167113 + 0.0542982i
\(184\) −0.711323 + 0.516806i −0.0524394 + 0.0380995i
\(185\) 6.91428 5.22455i 0.508348 0.384117i
\(186\) −0.734144 0.533387i −0.0538301 0.0391098i
\(187\) 0.635635 + 0.874876i 0.0464822 + 0.0639773i
\(188\) −0.266084 0.366234i −0.0194062 0.0267103i
\(189\) −0.990524 0.719658i −0.0720500 0.0523474i
\(190\) 12.9173 9.76053i 0.937118 0.708103i
\(191\) −7.68045 + 5.58017i −0.555738 + 0.403767i −0.829897 0.557917i \(-0.811601\pi\)
0.274159 + 0.961684i \(0.411601\pi\)
\(192\) 0.195447 + 0.0635047i 0.0141052 + 0.00458306i
\(193\) 13.2568i 0.954245i −0.878837 0.477122i \(-0.841680\pi\)
0.878837 0.477122i \(-0.158320\pi\)
\(194\) −1.06346 + 3.27298i −0.0763517 + 0.234986i
\(195\) 0.715215 1.02430i 0.0512176 0.0733514i
\(196\) 0.309017 + 0.951057i 0.0220726 + 0.0679326i
\(197\) 12.6702 4.11680i 0.902714 0.293310i 0.179357 0.983784i \(-0.442598\pi\)
0.723357 + 0.690474i \(0.242598\pi\)
\(198\) 1.03879 1.42978i 0.0738238 0.101610i
\(199\) 10.0050 0.709234 0.354617 0.935012i \(-0.384611\pi\)
0.354617 + 0.935012i \(0.384611\pi\)
\(200\) −4.80992 1.36554i −0.340113 0.0965581i
\(201\) −0.792056 −0.0558673
\(202\) −8.17008 + 11.2451i −0.574845 + 0.791206i
\(203\) −3.85659 + 1.25308i −0.270680 + 0.0879492i
\(204\) −0.114934 0.353731i −0.00804699 0.0247661i
\(205\) 8.21591 + 10.8731i 0.573824 + 0.759410i
\(206\) −5.78877 + 17.8160i −0.403323 + 1.24130i
\(207\) 2.60060i 0.180754i
\(208\) 2.58559 + 0.840109i 0.179278 + 0.0582511i
\(209\) −3.50004 + 2.54293i −0.242103 + 0.175898i
\(210\) 0.133774 0.439622i 0.00923127 0.0303368i
\(211\) −7.03318 5.10990i −0.484184 0.351780i 0.318759 0.947836i \(-0.396734\pi\)
−0.802943 + 0.596056i \(0.796734\pi\)
\(212\) −6.02319 8.29021i −0.413674 0.569374i
\(213\) −0.128955 0.177491i −0.00883582 0.0121615i
\(214\) 12.5111 + 9.08982i 0.855239 + 0.621368i
\(215\) 1.76535 0.0331370i 0.120396 0.00225993i
\(216\) −0.990524 + 0.719658i −0.0673966 + 0.0489665i
\(217\) −4.19959 1.36453i −0.285086 0.0926302i
\(218\) 7.11716i 0.482035i
\(219\) 0.470356 1.44761i 0.0317837 0.0978203i
\(220\) 1.27821 + 0.388950i 0.0861769 + 0.0262230i
\(221\) −1.52047 4.67953i −0.102278 0.314779i
\(222\) 0.757485 0.246122i 0.0508391 0.0165186i
\(223\) −12.5177 + 17.2291i −0.838247 + 1.15375i 0.148084 + 0.988975i \(0.452689\pi\)
−0.986331 + 0.164773i \(0.947311\pi\)
\(224\) 1.00000 0.0668153
\(225\) 11.6298 9.13554i 0.775318 0.609036i
\(226\) −9.72098 −0.646630
\(227\) −15.7747 + 21.7121i −1.04701 + 1.44108i −0.155630 + 0.987815i \(0.549741\pi\)
−0.891376 + 0.453264i \(0.850259\pi\)
\(228\) 1.41514 0.459806i 0.0937197 0.0304514i
\(229\) 6.51678 + 20.0566i 0.430641 + 1.32538i 0.897488 + 0.441038i \(0.145390\pi\)
−0.466848 + 0.884338i \(0.654610\pi\)
\(230\) 1.85809 0.642527i 0.122519 0.0423670i
\(231\) −0.0379448 + 0.116782i −0.00249659 + 0.00768370i
\(232\) 4.05506i 0.266228i
\(233\) 7.55691 + 2.45539i 0.495069 + 0.160858i 0.545901 0.837849i \(-0.316187\pi\)
−0.0508320 + 0.998707i \(0.516187\pi\)
\(234\) −6.50542 + 4.72646i −0.425272 + 0.308978i
\(235\) 0.330813 + 0.956662i 0.0215799 + 0.0624057i
\(236\) −1.21560 0.883186i −0.0791289 0.0574905i
\(237\) 0.518131 + 0.713146i 0.0336562 + 0.0463238i
\(238\) −1.06380 1.46420i −0.0689561 0.0949099i
\(239\) −14.5058 10.5391i −0.938303 0.681717i 0.00970836 0.999953i \(-0.496910\pi\)
−0.948012 + 0.318236i \(0.896910\pi\)
\(240\) −0.376767 0.263077i −0.0243202 0.0169816i
\(241\) 15.7279 11.4270i 1.01312 0.736076i 0.0482605 0.998835i \(-0.484632\pi\)
0.964862 + 0.262758i \(0.0846322\pi\)
\(242\) 10.1221 + 3.28886i 0.650672 + 0.211416i
\(243\) 5.44487i 0.349289i
\(244\) 3.57427 11.0005i 0.228819 0.704233i
\(245\) −0.0419655 2.23567i −0.00268108 0.142832i
\(246\) 0.387041 + 1.19119i 0.0246768 + 0.0759474i
\(247\) 18.7210 6.08281i 1.19119 0.387040i
\(248\) −2.59549 + 3.57238i −0.164814 + 0.226846i
\(249\) 0.175455 0.0111190
\(250\) 9.40058 + 6.05220i 0.594545 + 0.382775i
\(251\) 1.64512 0.103839 0.0519195 0.998651i \(-0.483466\pi\)
0.0519195 + 0.998651i \(0.483466\pi\)
\(252\) −1.73853 + 2.39288i −0.109517 + 0.150738i
\(253\) −0.499646 + 0.162345i −0.0314124 + 0.0102065i
\(254\) −6.76893 20.8326i −0.424721 1.30716i
\(255\) 0.0156084 + 0.831524i 0.000977436 + 0.0520720i
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 23.4942i 1.46553i −0.680482 0.732765i \(-0.738230\pi\)
0.680482 0.732765i \(-0.261770\pi\)
\(258\) 0.154330 + 0.0501450i 0.00960819 + 0.00312189i
\(259\) 3.13546 2.27805i 0.194828 0.141551i
\(260\) −4.98428 3.48027i −0.309112 0.215837i
\(261\) −9.70329 7.04986i −0.600619 0.436375i
\(262\) −1.06960 1.47218i −0.0660803 0.0909517i
\(263\) 15.6267 + 21.5083i 0.963582 + 1.32626i 0.945223 + 0.326425i \(0.105844\pi\)
0.0183590 + 0.999831i \(0.494156\pi\)
\(264\) 0.0993408 + 0.0721753i 0.00611401 + 0.00444209i
\(265\) 7.48842 + 21.6554i 0.460010 + 1.33028i
\(266\) 5.85769 4.25586i 0.359158 0.260943i
\(267\) 2.33839 + 0.759787i 0.143107 + 0.0464982i
\(268\) 3.85418i 0.235432i
\(269\) 5.31572 16.3601i 0.324105 0.997493i −0.647738 0.761863i \(-0.724285\pi\)
0.971843 0.235630i \(-0.0757153\pi\)
\(270\) 2.58741 0.894725i 0.157465 0.0544512i
\(271\) −9.68797 29.8165i −0.588502 1.81122i −0.584725 0.811231i \(-0.698798\pi\)
−0.00377722 0.999993i \(-0.501202\pi\)
\(272\) −1.72127 + 0.559274i −0.104367 + 0.0339110i
\(273\) 0.328394 0.451996i 0.0198753 0.0273560i
\(274\) 18.2730 1.10391
\(275\) −2.48119 1.66410i −0.149621 0.100349i
\(276\) 0.180689 0.0108762
\(277\) 5.27274 7.25730i 0.316808 0.436049i −0.620681 0.784063i \(-0.713144\pi\)
0.937489 + 0.348014i \(0.113144\pi\)
\(278\) 0.507430 0.164874i 0.0304336 0.00988849i
\(279\) −4.03596 12.4214i −0.241626 0.743650i
\(280\) −2.13922 0.650950i −0.127843 0.0389017i
\(281\) 0.668526 2.05751i 0.0398809 0.122741i −0.929134 0.369743i \(-0.879446\pi\)
0.969015 + 0.247003i \(0.0794456\pi\)
\(282\) 0.0930302i 0.00553987i
\(283\) 7.11838 + 2.31290i 0.423144 + 0.137488i 0.512846 0.858481i \(-0.328591\pi\)
−0.0897017 + 0.995969i \(0.528591\pi\)
\(284\) −0.863679 + 0.627499i −0.0512499 + 0.0372352i
\(285\) −3.32660 + 0.0624431i −0.197051 + 0.00369881i
\(286\) 1.31419 + 0.954814i 0.0777096 + 0.0564593i
\(287\) 3.58236 + 4.93070i 0.211460 + 0.291050i
\(288\) 1.73853 + 2.39288i 0.102444 + 0.141002i
\(289\) −11.1033 8.06703i −0.653136 0.474531i
\(290\) 2.63964 8.67467i 0.155005 0.509394i
\(291\) 0.572162 0.415700i 0.0335407 0.0243687i
\(292\) −7.04413 2.28878i −0.412226 0.133941i
\(293\) 8.18246i 0.478025i 0.971017 + 0.239012i \(0.0768236\pi\)
−0.971017 + 0.239012i \(0.923176\pi\)
\(294\) 0.0635047 0.195447i 0.00370367 0.0113987i
\(295\) 2.02553 + 2.68063i 0.117931 + 0.156072i
\(296\) −1.19764 3.68596i −0.0696115 0.214242i
\(297\) −0.695761 + 0.226066i −0.0403721 + 0.0131177i
\(298\) 3.86493 5.31962i 0.223889 0.308157i
\(299\) 2.39036 0.138238
\(300\) 0.634737 + 0.808036i 0.0366466 + 0.0466520i
\(301\) 0.789626 0.0455133
\(302\) 12.8151 17.6384i 0.737424 1.01498i
\(303\) 2.71667 0.882701i 0.156069 0.0507098i
\(304\) −2.23744 6.88612i −0.128326 0.394946i
\(305\) −14.8069 + 21.2057i −0.847840 + 1.21424i
\(306\) 1.65420 5.09112i 0.0945645 0.291040i
\(307\) 10.8094i 0.616925i 0.951237 + 0.308462i \(0.0998144\pi\)
−0.951237 + 0.308462i \(0.900186\pi\)
\(308\) 0.568268 + 0.184641i 0.0323800 + 0.0105209i
\(309\) 3.11448 2.26280i 0.177176 0.128726i
\(310\) 7.87776 5.95258i 0.447427 0.338084i
\(311\) 18.9746 + 13.7858i 1.07595 + 0.781722i 0.976972 0.213368i \(-0.0684432\pi\)
0.0989763 + 0.995090i \(0.468443\pi\)
\(312\) −0.328394 0.451996i −0.0185917 0.0255892i
\(313\) −3.91222 5.38470i −0.221132 0.304361i 0.684009 0.729473i \(-0.260235\pi\)
−0.905141 + 0.425112i \(0.860235\pi\)
\(314\) −4.44304 3.22806i −0.250735 0.182170i
\(315\) 5.27675 3.98721i 0.297311 0.224654i
\(316\) 3.47020 2.52125i 0.195214 0.141831i
\(317\) 25.5430 + 8.29941i 1.43464 + 0.466141i 0.920221 0.391400i \(-0.128009\pi\)
0.514415 + 0.857541i \(0.328009\pi\)
\(318\) 2.10587i 0.118091i
\(319\) −0.748732 + 2.30436i −0.0419209 + 0.129019i
\(320\) −1.28015 + 1.83337i −0.0715623 + 0.102488i
\(321\) −0.982071 3.02250i −0.0548138 0.168700i
\(322\) 0.836210 0.271701i 0.0466002 0.0151413i
\(323\) −7.70246 + 10.6015i −0.428577 + 0.589885i
\(324\) −8.62169 −0.478983
\(325\) 8.39699 + 10.6896i 0.465781 + 0.592951i
\(326\) −6.95670 −0.385296
\(327\) −0.859704 + 1.18328i −0.0475417 + 0.0654356i
\(328\) 5.79638 1.88336i 0.320052 0.103991i
\(329\) 0.139889 + 0.430533i 0.00771232 + 0.0237361i
\(330\) −0.165529 0.219065i −0.00911210 0.0120591i
\(331\) −10.4285 + 32.0956i −0.573202 + 1.76413i 0.0690191 + 0.997615i \(0.478013\pi\)
−0.642221 + 0.766519i \(0.721987\pi\)
\(332\) 0.853773i 0.0468569i
\(333\) 10.9022 + 3.54234i 0.597437 + 0.194119i
\(334\) −2.58556 + 1.87852i −0.141475 + 0.102788i
\(335\) 2.50888 8.24495i 0.137075 0.450470i
\(336\) −0.166258 0.120793i −0.00907009 0.00658981i
\(337\) −10.9512 15.0730i −0.596547 0.821077i 0.398839 0.917021i \(-0.369413\pi\)
−0.995387 + 0.0959438i \(0.969413\pi\)
\(338\) 3.29685 + 4.53773i 0.179325 + 0.246820i
\(339\) 1.61619 + 1.17423i 0.0877792 + 0.0637753i
\(340\) 4.04623 0.0759513i 0.219438 0.00411904i
\(341\) −2.13454 + 1.55083i −0.115592 + 0.0839824i
\(342\) 20.3675 + 6.61782i 1.10135 + 0.357851i
\(343\) 1.00000i 0.0539949i
\(344\) 0.244008 0.750979i 0.0131560 0.0404901i
\(345\) −0.386535 0.117620i −0.0208103 0.00633244i
\(346\) −3.04386 9.36802i −0.163639 0.503628i
\(347\) 18.4628 5.99892i 0.991134 0.322039i 0.231817 0.972759i \(-0.425533\pi\)
0.759317 + 0.650721i \(0.225533\pi\)
\(348\) 0.489824 0.674185i 0.0262573 0.0361401i
\(349\) −22.2937 −1.19336 −0.596678 0.802481i \(-0.703513\pi\)
−0.596678 + 0.802481i \(0.703513\pi\)
\(350\) 4.15253 + 2.78505i 0.221962 + 0.148867i
\(351\) 3.32859 0.177667
\(352\) 0.351209 0.483397i 0.0187195 0.0257652i
\(353\) −24.3446 + 7.91003i −1.29573 + 0.421008i −0.874094 0.485756i \(-0.838544\pi\)
−0.421637 + 0.906765i \(0.638544\pi\)
\(354\) 0.0954201 + 0.293673i 0.00507152 + 0.0156085i
\(355\) 2.25607 0.780148i 0.119740 0.0414059i
\(356\) 3.69716 11.3787i 0.195949 0.603070i
\(357\) 0.371934i 0.0196849i
\(358\) −21.0222 6.83054i −1.11106 0.361005i
\(359\) 22.0744 16.0380i 1.16504 0.846452i 0.174634 0.984633i \(-0.444126\pi\)
0.990407 + 0.138182i \(0.0441258\pi\)
\(360\) −2.16146 6.25060i −0.113919 0.329436i
\(361\) −27.0412 19.6466i −1.42322 1.03403i
\(362\) −12.4830 17.1814i −0.656094 0.903036i
\(363\) −1.28560 1.76948i −0.0674765 0.0928734i
\(364\) −2.19943 1.59798i −0.115282 0.0837570i
\(365\) 13.5791 + 9.48157i 0.710761 + 0.496288i
\(366\) −1.92303 + 1.39716i −0.100518 + 0.0730309i
\(367\) 21.9376 + 7.12795i 1.14513 + 0.372076i 0.819307 0.573355i \(-0.194358\pi\)
0.325824 + 0.945430i \(0.394358\pi\)
\(368\) 0.879244i 0.0458337i
\(369\) −5.57054 + 17.1444i −0.289991 + 0.892499i
\(370\) 0.162643 + 8.66468i 0.00845543 + 0.450455i
\(371\) 3.16658 + 9.74573i 0.164401 + 0.505973i
\(372\) 0.863038 0.280418i 0.0447465 0.0145390i
\(373\) 9.99802 13.7611i 0.517678 0.712522i −0.467513 0.883986i \(-0.654850\pi\)
0.985190 + 0.171464i \(0.0548498\pi\)
\(374\) −1.08141 −0.0559182
\(375\) −0.831852 2.14175i −0.0429567 0.110599i
\(376\) 0.452690 0.0233457
\(377\) 6.47992 8.91884i 0.333733 0.459344i
\(378\) 1.16443 0.378346i 0.0598918 0.0194600i
\(379\) −10.7117 32.9671i −0.550221 1.69341i −0.708242 0.705970i \(-0.750512\pi\)
0.158022 0.987436i \(-0.449488\pi\)
\(380\) 0.303851 + 16.1874i 0.0155872 + 0.830396i
\(381\) −1.39105 + 4.28122i −0.0712659 + 0.219334i
\(382\) 9.49356i 0.485733i
\(383\) −14.5295 4.72092i −0.742422 0.241228i −0.0867049 0.996234i \(-0.527634\pi\)
−0.655717 + 0.755006i \(0.727634\pi\)
\(384\) −0.166258 + 0.120793i −0.00848429 + 0.00616420i
\(385\) −1.09546 0.764902i −0.0558297 0.0389830i
\(386\) 10.7250 + 7.79215i 0.545887 + 0.396610i
\(387\) 1.37279 + 1.88948i 0.0697828 + 0.0960478i
\(388\) −2.02281 2.78417i −0.102693 0.141345i
\(389\) 19.5191 + 14.1815i 0.989658 + 0.719029i 0.959846 0.280527i \(-0.0905091\pi\)
0.0298121 + 0.999556i \(0.490509\pi\)
\(390\) 0.408281 + 1.18069i 0.0206741 + 0.0597864i
\(391\) −1.28739 + 0.935342i −0.0651060 + 0.0473023i
\(392\) −0.951057 0.309017i −0.0480356 0.0156077i
\(393\) 0.373962i 0.0188639i
\(394\) −4.11680 + 12.6702i −0.207401 + 0.638315i
\(395\) −9.06474 + 3.13458i −0.456097 + 0.157718i
\(396\) 0.546126 + 1.68080i 0.0274439 + 0.0844635i
\(397\) 16.0557 5.21680i 0.805811 0.261824i 0.122988 0.992408i \(-0.460752\pi\)
0.682823 + 0.730584i \(0.260752\pi\)
\(398\) −5.88078 + 8.09420i −0.294777 + 0.405726i
\(399\) −1.48796 −0.0744913
\(400\) 3.93194 3.08866i 0.196597 0.154433i
\(401\) −16.1334 −0.805665 −0.402832 0.915274i \(-0.631974\pi\)
−0.402832 + 0.915274i \(0.631974\pi\)
\(402\) 0.465559 0.640787i 0.0232200 0.0319595i
\(403\) 11.4172 3.70968i 0.568732 0.184792i
\(404\) −4.29526 13.2195i −0.213697 0.657693i
\(405\) 18.4437 + 5.61229i 0.916475 + 0.278877i
\(406\) 1.25308 3.85659i 0.0621895 0.191400i
\(407\) 2.31575i 0.114787i
\(408\) 0.353731 + 0.114934i 0.0175123 + 0.00569008i
\(409\) −3.24392 + 2.35685i −0.160402 + 0.116539i −0.665091 0.746763i \(-0.731607\pi\)
0.504689 + 0.863301i \(0.331607\pi\)
\(410\) −13.6257 + 0.255766i −0.672926 + 0.0126314i
\(411\) −3.03802 2.20725i −0.149854 0.108876i
\(412\) −11.0109 15.1552i −0.542468 0.746643i
\(413\) 0.883186 + 1.21560i 0.0434588 + 0.0598159i
\(414\) 2.10393 + 1.52859i 0.103402 + 0.0751263i
\(415\) −0.555763 + 1.82641i −0.0272813 + 0.0896549i
\(416\) −2.19943 + 1.59798i −0.107836 + 0.0783475i
\(417\) −0.104280 0.0338825i −0.00510660 0.00165924i
\(418\) 4.32628i 0.211605i
\(419\) 9.44691 29.0746i 0.461512 1.42039i −0.401805 0.915725i \(-0.631617\pi\)
0.863317 0.504662i \(-0.168383\pi\)
\(420\) 0.277031 + 0.366629i 0.0135177 + 0.0178896i
\(421\) 3.63978 + 11.2021i 0.177392 + 0.545957i 0.999735 0.0230361i \(-0.00733325\pi\)
−0.822343 + 0.568993i \(0.807333\pi\)
\(422\) 8.26799 2.68643i 0.402480 0.130774i
\(423\) −0.787015 + 1.08323i −0.0382660 + 0.0526686i
\(424\) 10.2473 0.497651
\(425\) −8.70523 2.47142i −0.422266 0.119881i
\(426\) 0.219391 0.0106295
\(427\) −6.79866 + 9.35755i −0.329010 + 0.452844i
\(428\) −14.7076 + 4.77880i −0.710921 + 0.230992i
\(429\) −0.103159 0.317490i −0.00498055 0.0153286i
\(430\) −1.01084 + 1.44767i −0.0487468 + 0.0698129i
\(431\) −2.65854 + 8.18215i −0.128057 + 0.394120i −0.994446 0.105251i \(-0.966436\pi\)
0.866388 + 0.499371i \(0.166436\pi\)
\(432\) 1.22435i 0.0589068i
\(433\) −28.7516 9.34196i −1.38171 0.448946i −0.478481 0.878098i \(-0.658813\pi\)
−0.903232 + 0.429152i \(0.858813\pi\)
\(434\) 3.57238 2.59549i 0.171480 0.124587i
\(435\) −1.48670 + 1.12338i −0.0712819 + 0.0538619i
\(436\) 5.75790 + 4.18336i 0.275753 + 0.200347i
\(437\) −3.74194 5.15033i −0.179001 0.246374i
\(438\) 0.894671 + 1.23141i 0.0427490 + 0.0588390i
\(439\) −6.96389 5.05957i −0.332369 0.241480i 0.409066 0.912505i \(-0.365854\pi\)
−0.741435 + 0.671025i \(0.765854\pi\)
\(440\) −1.06598 + 0.805474i −0.0508186 + 0.0383995i
\(441\) 2.39288 1.73853i 0.113947 0.0827872i
\(442\) 4.67953 + 1.52047i 0.222583 + 0.0723215i
\(443\) 39.6209i 1.88245i 0.337786 + 0.941223i \(0.390322\pi\)
−0.337786 + 0.941223i \(0.609678\pi\)
\(444\) −0.246122 + 0.757485i −0.0116804 + 0.0359487i
\(445\) −15.3160 + 21.9349i −0.726048 + 1.03981i
\(446\) −6.58094 20.2541i −0.311617 0.959058i
\(447\) −1.28515 + 0.417570i −0.0607854 + 0.0197504i
\(448\) −0.587785 + 0.809017i −0.0277702 + 0.0382225i
\(449\) −33.7067 −1.59072 −0.795360 0.606138i \(-0.792718\pi\)
−0.795360 + 0.606138i \(0.792718\pi\)
\(450\) 0.555002 + 14.7784i 0.0261631 + 0.696661i
\(451\) 3.64164 0.171478
\(452\) 5.71385 7.86444i 0.268757 0.369912i
\(453\) −4.26120 + 1.38455i −0.200209 + 0.0650517i
\(454\) −8.29327 25.5241i −0.389222 1.19790i
\(455\) 3.66487 + 4.85016i 0.171812 + 0.227379i
\(456\) −0.459806 + 1.41514i −0.0215324 + 0.0662698i
\(457\) 30.2989i 1.41732i −0.705548 0.708662i \(-0.749299\pi\)
0.705548 0.708662i \(-0.250701\pi\)
\(458\) −20.0566 6.51678i −0.937182 0.304509i
\(459\) −1.79270 + 1.30247i −0.0836760 + 0.0607942i
\(460\) −0.572343 + 1.88090i −0.0266856 + 0.0876972i
\(461\) 23.7399 + 17.2481i 1.10568 + 0.803322i 0.981978 0.188998i \(-0.0605239\pi\)
0.123700 + 0.992320i \(0.460524\pi\)
\(462\) −0.0721753 0.0993408i −0.00335790 0.00462175i
\(463\) 1.96033 + 2.69816i 0.0911043 + 0.125394i 0.852136 0.523320i \(-0.175307\pi\)
−0.761032 + 0.648715i \(0.775307\pi\)
\(464\) −3.28061 2.38351i −0.152299 0.110651i
\(465\) −2.02877 + 0.0380817i −0.0940819 + 0.00176600i
\(466\) −6.42829 + 4.67043i −0.297785 + 0.216353i
\(467\) 2.83618 + 0.921529i 0.131243 + 0.0426433i 0.373902 0.927468i \(-0.378020\pi\)
−0.242659 + 0.970112i \(0.578020\pi\)
\(468\) 8.04114i 0.371702i
\(469\) 1.19101 3.66555i 0.0549956 0.169259i
\(470\) −0.968403 0.294678i −0.0446691 0.0135925i
\(471\) 0.348762 + 1.07338i 0.0160701 + 0.0494586i
\(472\) 1.42903 0.464319i 0.0657762 0.0213720i
\(473\) 0.277323 0.381703i 0.0127513 0.0175507i
\(474\) −0.881497 −0.0404885
\(475\) 9.88718 34.8262i 0.453655 1.59794i
\(476\) 1.80985 0.0829543
\(477\) −17.8152 + 24.5205i −0.815702 + 1.12272i
\(478\) 17.0526 5.54073i 0.779968 0.253427i
\(479\) 0.952326 + 2.93096i 0.0435129 + 0.133919i 0.970453 0.241291i \(-0.0775707\pi\)
−0.926940 + 0.375210i \(0.877571\pi\)
\(480\) 0.434292 0.150178i 0.0198226 0.00685465i
\(481\) −3.25597 + 10.0208i −0.148459 + 0.456911i
\(482\) 19.4407i 0.885501i
\(483\) −0.171846 0.0558361i −0.00781926 0.00254063i
\(484\) −8.61035 + 6.25579i −0.391380 + 0.284354i
\(485\) 2.51489 + 7.27269i 0.114195 + 0.330236i
\(486\) 4.40499 + 3.20041i 0.199814 + 0.145174i
\(487\) −5.20244 7.16055i −0.235745 0.324475i 0.674710 0.738083i \(-0.264269\pi\)
−0.910455 + 0.413607i \(0.864269\pi\)
\(488\) 6.79866 + 9.35755i 0.307761 + 0.423597i
\(489\) 1.15660 + 0.840322i 0.0523034 + 0.0380007i
\(490\) 1.83337 + 1.28015i 0.0828230 + 0.0578311i
\(491\) 3.53757 2.57019i 0.159648 0.115991i −0.505093 0.863065i \(-0.668542\pi\)
0.664741 + 0.747074i \(0.268542\pi\)
\(492\) −1.19119 0.387041i −0.0537030 0.0174491i
\(493\) 7.33905i 0.330534i
\(494\) −6.08281 + 18.7210i −0.273679 + 0.842296i
\(495\) −0.0741657 3.95111i −0.00333350 0.177589i
\(496\) −1.36453 4.19959i −0.0612691 0.188567i
\(497\) 1.01532 0.329896i 0.0455431 0.0147979i
\(498\) −0.103130 + 0.141946i −0.00462136 + 0.00636076i
\(499\) 10.6594 0.477182 0.238591 0.971120i \(-0.423315\pi\)
0.238591 + 0.971120i \(0.423315\pi\)
\(500\) −10.4219 + 4.04783i −0.466080 + 0.181025i
\(501\) 0.656781 0.0293428
\(502\) −0.966976 + 1.33093i −0.0431583 + 0.0594022i
\(503\) −15.8259 + 5.14215i −0.705643 + 0.229277i −0.639787 0.768552i \(-0.720978\pi\)
−0.0658553 + 0.997829i \(0.520978\pi\)
\(504\) −0.914000 2.81300i −0.0407128 0.125301i
\(505\) 0.583311 + 31.0754i 0.0259570 + 1.38284i
\(506\) 0.162345 0.499646i 0.00721710 0.0222120i
\(507\) 1.15267i 0.0511918i
\(508\) 20.8326 + 6.76893i 0.924299 + 0.300323i
\(509\) 23.0243 16.7281i 1.02053 0.741462i 0.0541422 0.998533i \(-0.482758\pi\)
0.966392 + 0.257071i \(0.0827576\pi\)
\(510\) −0.681891 0.476130i −0.0301947 0.0210834i
\(511\) 5.99209 + 4.35351i 0.265075 + 0.192588i
\(512\) 0.587785 + 0.809017i 0.0259767 + 0.0357538i
\(513\) −5.21068 7.17188i −0.230057 0.316646i
\(514\) 19.0072 + 13.8096i 0.838373 + 0.609114i
\(515\) 13.6895 + 39.5878i 0.603230 + 1.74445i
\(516\) −0.131281 + 0.0953814i −0.00577933 + 0.00419893i
\(517\) 0.257249 + 0.0835852i 0.0113138 + 0.00367607i
\(518\) 3.87565i 0.170286i
\(519\) −0.625529 + 1.92518i −0.0274577 + 0.0845061i
\(520\) 5.74528 1.98672i 0.251947 0.0871233i
\(521\) 3.68129 + 11.3298i 0.161280 + 0.496369i 0.998743 0.0501250i \(-0.0159620\pi\)
−0.837463 + 0.546494i \(0.815962\pi\)
\(522\) 11.4069 3.70633i 0.499267 0.162222i
\(523\) 16.1834 22.2745i 0.707649 0.973995i −0.292196 0.956359i \(-0.594386\pi\)
0.999844 0.0176365i \(-0.00561416\pi\)
\(524\) 1.81972 0.0794947
\(525\) −0.353974 0.964633i −0.0154487 0.0421000i
\(526\) −26.5857 −1.15919
\(527\) −4.69744 + 6.46547i −0.204624 + 0.281640i
\(528\) −0.116782 + 0.0379448i −0.00508229 + 0.00165134i
\(529\) 6.86850 + 21.1391i 0.298630 + 0.919090i
\(530\) −21.9212 6.67045i −0.952194 0.289746i
\(531\) −1.37335 + 4.22673i −0.0595982 + 0.183424i
\(532\) 7.24050i 0.313915i
\(533\) −15.7583 5.12019i −0.682569 0.221780i
\(534\) −1.98915 + 1.44520i −0.0860789 + 0.0625400i
\(535\) 34.5737 0.648977i 1.49475 0.0280577i
\(536\) −3.11810 2.26543i −0.134681 0.0978518i
\(537\) 2.67002 + 3.67497i 0.115220 + 0.158587i
\(538\) 10.1111 + 13.9167i 0.435921 + 0.599993i
\(539\) −0.483397 0.351209i −0.0208214 0.0151276i
\(540\) −0.796993 + 2.61916i −0.0342971 + 0.112711i
\(541\) 14.8582 10.7951i 0.638805 0.464119i −0.220634 0.975357i \(-0.570813\pi\)
0.859440 + 0.511237i \(0.170813\pi\)
\(542\) 29.8165 + 9.68797i 1.28073 + 0.416134i
\(543\) 4.36441i 0.187295i
\(544\) 0.559274 1.72127i 0.0239787 0.0737988i
\(545\) −9.59426 12.6972i −0.410973 0.543890i
\(546\) 0.172647 + 0.531353i 0.00738862 + 0.0227398i
\(547\) −0.799842 + 0.259884i −0.0341988 + 0.0111119i −0.326066 0.945347i \(-0.605723\pi\)
0.291868 + 0.956459i \(0.405723\pi\)
\(548\) −10.7406 + 14.7831i −0.458815 + 0.631505i
\(549\) −34.2112 −1.46010
\(550\) 2.80469 1.02919i 0.119592 0.0438847i
\(551\) −29.3607 −1.25081
\(552\) −0.106207 + 0.146181i −0.00452045 + 0.00622187i
\(553\) −4.07947 + 1.32550i −0.173477 + 0.0563660i
\(554\) 2.77204 + 8.53146i 0.117773 + 0.362467i
\(555\) 1.01959 1.46022i 0.0432794 0.0619827i
\(556\) −0.164874 + 0.507430i −0.00699222 + 0.0215198i
\(557\) 8.98757i 0.380816i −0.981705 0.190408i \(-0.939019\pi\)
0.981705 0.190408i \(-0.0609810\pi\)
\(558\) 12.4214 + 4.03596i 0.525840 + 0.170856i
\(559\) −1.73673 + 1.26181i −0.0734558 + 0.0533688i
\(560\) 1.78403 1.34805i 0.0753891 0.0569654i
\(561\) 0.179792 + 0.130627i 0.00759082 + 0.00551506i
\(562\) 1.27161 + 1.75022i 0.0536397 + 0.0738287i
\(563\) −7.70184 10.6007i −0.324594 0.446765i 0.615269 0.788317i \(-0.289047\pi\)
−0.939863 + 0.341552i \(0.889047\pi\)
\(564\) −0.0752631 0.0546818i −0.00316915 0.00230252i
\(565\) −17.3425 + 13.1043i −0.729606 + 0.551304i
\(566\) −6.05526 + 4.39940i −0.254521 + 0.184921i
\(567\) 8.19972 + 2.66425i 0.344356 + 0.111888i
\(568\) 1.06757i 0.0447941i
\(569\) −10.8277 + 33.3243i −0.453922 + 1.39703i 0.418474 + 0.908229i \(0.362565\pi\)
−0.872396 + 0.488799i \(0.837435\pi\)
\(570\) 1.90481 2.72798i 0.0797837 0.114262i
\(571\) −5.34991 16.4653i −0.223887 0.689053i −0.998403 0.0564986i \(-0.982006\pi\)
0.774516 0.632555i \(-0.217994\pi\)
\(572\) −1.54492 + 0.501975i −0.0645964 + 0.0209886i
\(573\) −1.14676 + 1.57838i −0.0479065 + 0.0659376i
\(574\) −6.09468 −0.254387
\(575\) 2.44874 3.65108i 0.102119 0.152261i
\(576\) −2.95777 −0.123240
\(577\) −8.05116 + 11.0815i −0.335174 + 0.461327i −0.943024 0.332724i \(-0.892032\pi\)
0.607850 + 0.794052i \(0.292032\pi\)
\(578\) 13.0527 4.24109i 0.542922 0.176406i
\(579\) −0.841869 2.59101i −0.0349869 0.107679i
\(580\) 5.46641 + 7.23436i 0.226981 + 0.300390i
\(581\) −0.263830 + 0.811986i −0.0109455 + 0.0336869i
\(582\) 0.707231i 0.0293157i
\(583\) 5.82319 + 1.89207i 0.241172 + 0.0783614i
\(584\) 5.99209 4.35351i 0.247955 0.180150i
\(585\) −5.23438 + 17.2018i −0.216415 + 0.711205i
\(586\) −6.61975 4.80953i −0.273459 0.198680i
\(587\) −4.29522 5.91187i −0.177283 0.244009i 0.711123 0.703067i \(-0.248187\pi\)
−0.888406 + 0.459059i \(0.848187\pi\)
\(588\) 0.120793 + 0.166258i 0.00498143 + 0.00685634i
\(589\) −25.8658 18.7926i −1.06578 0.774336i
\(590\) −3.35925 + 0.0630560i −0.138298 + 0.00259597i
\(591\) 2.21492 1.60924i 0.0911097 0.0661951i
\(592\) 3.68596 + 1.19764i 0.151492 + 0.0492227i
\(593\) 1.85774i 0.0762883i 0.999272 + 0.0381442i \(0.0121446\pi\)
−0.999272 + 0.0381442i \(0.987855\pi\)
\(594\) 0.226066 0.695761i 0.00927562 0.0285474i
\(595\) −3.87167 1.17812i −0.158723 0.0482983i
\(596\) 2.03191 + 6.25359i 0.0832305 + 0.256157i
\(597\) 1.95545 0.635364i 0.0800312 0.0260037i
\(598\) −1.40502 + 1.93384i −0.0574554 + 0.0790805i
\(599\) 9.82175 0.401306 0.200653 0.979662i \(-0.435694\pi\)
0.200653 + 0.979662i \(0.435694\pi\)
\(600\) −1.02680 + 0.0385616i −0.0419191 + 0.00157427i
\(601\) −18.6184 −0.759461 −0.379731 0.925097i \(-0.623983\pi\)
−0.379731 + 0.925097i \(0.623983\pi\)
\(602\) −0.464130 + 0.638821i −0.0189165 + 0.0260364i
\(603\) 10.8418 3.52272i 0.441514 0.143456i
\(604\) 6.73727 + 20.7352i 0.274136 + 0.843703i
\(605\) 22.4916 7.77760i 0.914415 0.316204i
\(606\) −0.882701 + 2.71667i −0.0358573 + 0.110357i
\(607\) 25.4476i 1.03289i −0.856322 0.516443i \(-0.827256\pi\)
0.856322 0.516443i \(-0.172744\pi\)
\(608\) 6.88612 + 2.23744i 0.279269 + 0.0907400i
\(609\) −0.674185 + 0.489824i −0.0273193 + 0.0198487i
\(610\) −8.45254 24.4435i −0.342233 0.989687i
\(611\) −0.995661 0.723390i −0.0402801 0.0292652i
\(612\) 3.14648 + 4.33076i 0.127189 + 0.175061i
\(613\) −21.9475 30.2081i −0.886450 1.22009i −0.974592 0.223986i \(-0.928093\pi\)
0.0881418 0.996108i \(-0.471907\pi\)
\(614\) −8.74498 6.35360i −0.352919 0.256411i
\(615\) 2.29627 + 1.60337i 0.0925946 + 0.0646541i
\(616\) −0.483397 + 0.351209i −0.0194766 + 0.0141506i
\(617\) −26.6903 8.67220i −1.07451 0.349129i −0.282267 0.959336i \(-0.591087\pi\)
−0.792243 + 0.610206i \(0.791087\pi\)
\(618\) 3.84971i 0.154858i
\(619\) 6.94800 21.3838i 0.279264 0.859486i −0.708796 0.705414i \(-0.750761\pi\)
0.988060 0.154072i \(-0.0492388\pi\)
\(620\) 0.185307 + 9.87208i 0.00744212 + 0.396472i
\(621\) −0.332659 1.02382i −0.0133491 0.0410844i
\(622\) −22.3059 + 7.24763i −0.894386 + 0.290604i
\(623\) −7.03242 + 9.67930i −0.281748 + 0.387793i
\(624\) 0.558698 0.0223658
\(625\) 24.9296 1.87510i 0.997183 0.0750041i
\(626\) 6.65586 0.266022
\(627\) −0.522585 + 0.719277i −0.0208701 + 0.0287252i
\(628\) 5.22311 1.69709i 0.208425 0.0677213i
\(629\) −2.16755 6.67103i −0.0864259 0.265992i
\(630\) 0.124124 + 6.61260i 0.00494523 + 0.263452i
\(631\) 10.9001 33.5471i 0.433927 1.33549i −0.460255 0.887787i \(-0.652242\pi\)
0.894182 0.447703i \(-0.147758\pi\)
\(632\) 4.28941i 0.170624i
\(633\) −1.69912 0.552077i −0.0675339 0.0219431i
\(634\) −21.7281 + 15.7864i −0.862935 + 0.626959i
\(635\) −40.1594 28.0412i −1.59368 1.11278i
\(636\) −1.70368 1.23780i −0.0675555 0.0490819i
\(637\) 1.59798 + 2.19943i 0.0633144 + 0.0871448i
\(638\) −1.42417 1.96021i −0.0563835 0.0776053i
\(639\) 2.55456 + 1.85600i 0.101057 + 0.0734221i
\(640\) −0.730773 2.11328i −0.0288863 0.0835349i
\(641\) 23.5630 17.1195i 0.930684 0.676181i −0.0154765 0.999880i \(-0.504927\pi\)
0.946160 + 0.323699i \(0.104927\pi\)
\(642\) 3.02250 + 0.982071i 0.119289 + 0.0387592i
\(643\) 25.7756i 1.01649i −0.861212 0.508245i \(-0.830294\pi\)
0.861212 0.508245i \(-0.169706\pi\)
\(644\) −0.271701 + 0.836210i −0.0107065 + 0.0329513i
\(645\) 0.342928 0.118584i 0.0135028 0.00466925i
\(646\) −4.04942 12.4628i −0.159322 0.490344i
\(647\) −25.8145 + 8.38764i −1.01487 + 0.329752i −0.768793 0.639497i \(-0.779143\pi\)
−0.246080 + 0.969250i \(0.579143\pi\)
\(648\) 5.06770 6.97509i 0.199078 0.274008i
\(649\) 0.897801 0.0352418
\(650\) −13.5837 + 0.510134i −0.532796 + 0.0200091i
\(651\) −0.907452 −0.0355659
\(652\) 4.08905 5.62809i 0.160139 0.220413i
\(653\) −42.2646 + 13.7326i −1.65394 + 0.537398i −0.979589 0.201011i \(-0.935577\pi\)
−0.674353 + 0.738409i \(0.735577\pi\)
\(654\) −0.451973 1.39103i −0.0176735 0.0543936i
\(655\) −3.89278 1.18454i −0.152103 0.0462840i
\(656\) −1.88336 + 5.79638i −0.0735328 + 0.226311i
\(657\) 21.9071i 0.854678i
\(658\) −0.430533 0.139889i −0.0167839 0.00545343i
\(659\) 28.9491 21.0328i 1.12770 0.819320i 0.142339 0.989818i \(-0.454538\pi\)
0.985358 + 0.170498i \(0.0545375\pi\)
\(660\) 0.274523 0.00515303i 0.0106858 0.000200581i
\(661\) 34.4791 + 25.0505i 1.34108 + 0.974351i 0.999404 + 0.0345336i \(0.0109946\pi\)
0.341676 + 0.939818i \(0.389005\pi\)
\(662\) −19.8362 27.3022i −0.770955 1.06113i
\(663\) −0.594345 0.818045i −0.0230824 0.0317702i
\(664\) 0.690717 + 0.501835i 0.0268050 + 0.0194750i
\(665\) 4.71320 15.4890i 0.182770 0.600638i
\(666\) −9.27397 + 6.73794i −0.359359 + 0.261090i
\(667\) −3.39089 1.10177i −0.131296 0.0426605i
\(668\) 3.19593i 0.123654i
\(669\) −1.35242 + 4.16232i −0.0522876 + 0.160925i
\(670\) 5.19562 + 6.87598i 0.200724 + 0.265642i
\(671\) 2.13567 + 6.57291i 0.0824465 + 0.253744i
\(672\) 0.195447 0.0635047i 0.00753955 0.00244975i
\(673\) 6.89644 9.49213i 0.265838 0.365895i −0.655141 0.755507i \(-0.727391\pi\)
0.920979 + 0.389612i \(0.127391\pi\)
\(674\) 18.6312 0.717648
\(675\) 3.40989 5.08417i 0.131247 0.195690i
\(676\) −5.60894 −0.215728
\(677\) −12.7545 + 17.5551i −0.490196 + 0.674696i −0.980424 0.196898i \(-0.936913\pi\)
0.490228 + 0.871594i \(0.336913\pi\)
\(678\) −1.89994 + 0.617328i −0.0729668 + 0.0237083i
\(679\) 1.06346 + 3.27298i 0.0408117 + 0.125606i
\(680\) −2.31687 + 3.31812i −0.0888480 + 0.127244i
\(681\) −1.70431 + 5.24534i −0.0653094 + 0.201002i
\(682\) 2.63844i 0.101031i
\(683\) 46.9711 + 15.2618i 1.79730 + 0.583978i 0.999813 0.0193572i \(-0.00616199\pi\)
0.797488 + 0.603335i \(0.206162\pi\)
\(684\) −17.3257 + 12.5878i −0.662464 + 0.481308i
\(685\) 32.5996 24.6328i 1.24557 0.941172i
\(686\) 0.809017 + 0.587785i 0.0308884 + 0.0224417i
\(687\) 2.54738 + 3.50616i 0.0971884 + 0.133768i
\(688\) 0.464130 + 0.638821i 0.0176948 + 0.0243548i
\(689\) −22.5382 16.3749i −0.858636 0.623836i
\(690\) 0.322356 0.243578i 0.0122719 0.00927285i
\(691\) −32.0004 + 23.2496i −1.21735 + 0.884457i −0.995877 0.0907091i \(-0.971087\pi\)
−0.221474 + 0.975166i \(0.571087\pi\)
\(692\) 9.36802 + 3.04386i 0.356119 + 0.115710i
\(693\) 1.76730i 0.0671342i
\(694\) −5.99892 + 18.4628i −0.227716 + 0.700838i
\(695\) 0.683014 0.978180i 0.0259082 0.0371045i
\(696\) 0.257516 + 0.792552i 0.00976110 + 0.0300416i
\(697\) 10.4906 3.40860i 0.397359 0.129110i
\(698\) 13.1039 18.0360i 0.495991 0.682673i
\(699\) 1.63291 0.0617622
\(700\) −4.69395 + 1.72246i −0.177415 + 0.0651027i
\(701\) 37.2403 1.40655 0.703273 0.710920i \(-0.251721\pi\)
0.703273 + 0.710920i \(0.251721\pi\)
\(702\) −1.95650 + 2.69289i −0.0738432 + 0.101636i
\(703\) 26.6882 8.67152i 1.00656 0.327052i
\(704\) 0.184641 + 0.568268i 0.00695893 + 0.0214174i
\(705\) 0.125409 + 0.165969i 0.00472318 + 0.00625075i
\(706\) 7.91003 24.3446i 0.297698 0.916220i
\(707\) 13.8998i 0.522755i
\(708\) −0.293673 0.0954201i −0.0110369 0.00358611i
\(709\) 12.4344 9.03409i 0.466982 0.339282i −0.329282 0.944232i \(-0.606807\pi\)
0.796264 + 0.604949i \(0.206807\pi\)
\(710\) −0.694931 + 2.28376i −0.0260803 + 0.0857079i
\(711\) −10.2641 7.45727i −0.384932 0.279670i
\(712\) 7.03242 + 9.67930i 0.263551 + 0.362747i
\(713\) −2.28207 3.14099i −0.0854640 0.117631i
\(714\) −0.300901 0.218617i −0.0112609 0.00818155i
\(715\) 3.63169 0.0681698i 0.135817 0.00254941i
\(716\) 17.8826 12.9925i 0.668303 0.485551i
\(717\) −3.50441 1.13865i −0.130874 0.0425237i
\(718\) 27.2854i 1.01828i
\(719\) 4.74104 14.5914i 0.176811 0.544168i −0.822901 0.568185i \(-0.807646\pi\)
0.999712 + 0.0240172i \(0.00764565\pi\)
\(720\) 6.32732 + 1.92536i 0.235805 + 0.0717539i
\(721\) 5.78877 + 17.8160i 0.215585 + 0.663503i
\(722\) 31.7889 10.3288i 1.18306 0.384399i
\(723\) 2.34831 3.23217i 0.0873345 0.120206i
\(724\) 21.2374 0.789283
\(725\) −6.98466 19.0343i −0.259404 0.706914i
\(726\) 2.18719 0.0811743
\(727\) −1.17714 + 1.62019i −0.0436576 + 0.0600896i −0.830288 0.557335i \(-0.811824\pi\)
0.786630 + 0.617425i \(0.211824\pi\)
\(728\) 2.58559 0.840109i 0.0958284 0.0311365i
\(729\) 7.64697 + 23.5350i 0.283221 + 0.871665i
\(730\) −15.6523 + 5.41257i −0.579319 + 0.200328i
\(731\) 0.441617 1.35916i 0.0163338 0.0502703i
\(732\) 2.37700i 0.0878563i
\(733\) −8.55268 2.77893i −0.315900 0.102642i 0.146775 0.989170i \(-0.453111\pi\)
−0.462676 + 0.886528i \(0.653111\pi\)
\(734\) −18.6612 + 13.5582i −0.688798 + 0.500441i
\(735\) −0.150178 0.434292i −0.00553940 0.0160191i
\(736\) 0.711323 + 0.516806i 0.0262197 + 0.0190497i
\(737\) −1.35362 1.86310i −0.0498613 0.0686282i
\(738\) −10.5958 14.5839i −0.390036 0.536839i
\(739\) 10.2900 + 7.47610i 0.378523 + 0.275013i 0.760736 0.649061i \(-0.224838\pi\)
−0.382214 + 0.924074i \(0.624838\pi\)
\(740\) −7.10548 4.96139i −0.261202 0.182384i
\(741\) 3.27268 2.37774i 0.120225 0.0873484i
\(742\) −9.74573 3.16658i −0.357777 0.116249i
\(743\) 11.6518i 0.427462i −0.976893 0.213731i \(-0.931438\pi\)
0.976893 0.213731i \(-0.0685616\pi\)
\(744\) −0.280418 + 0.863038i −0.0102806 + 0.0316405i
\(745\) −0.275940 14.7005i −0.0101097 0.538584i
\(746\) 5.25627 + 16.1771i 0.192446 + 0.592287i
\(747\) −2.40167 + 0.780349i −0.0878724 + 0.0285515i
\(748\) 0.635635 0.874876i 0.0232411 0.0319887i
\(749\) 15.4645 0.565062
\(750\) 2.22166 + 0.585906i 0.0811236 + 0.0213943i
\(751\) −6.28867 −0.229477 −0.114738 0.993396i \(-0.536603\pi\)
−0.114738 + 0.993396i \(0.536603\pi\)
\(752\) −0.266084 + 0.366234i −0.00970310 + 0.0133552i
\(753\) 0.321534 0.104473i 0.0117174 0.00380720i
\(754\) 3.40670 + 10.4847i 0.124065 + 0.381831i
\(755\) −0.914943 48.7428i −0.0332982 1.77393i
\(756\) −0.378346 + 1.16443i −0.0137603 + 0.0423499i
\(757\) 18.9570i 0.689003i 0.938786 + 0.344502i \(0.111952\pi\)
−0.938786 + 0.344502i \(0.888048\pi\)
\(758\) 32.9671 + 10.7117i 1.19742 + 0.389065i
\(759\) −0.0873448 + 0.0634597i −0.00317042 + 0.00230344i
\(760\) −13.2745 9.26889i −0.481516 0.336218i
\(761\) −0.844541 0.613595i −0.0306146 0.0222428i 0.572373 0.819994i \(-0.306023\pi\)
−0.602987 + 0.797751i \(0.706023\pi\)
\(762\) −2.64594 3.64183i −0.0958524 0.131929i
\(763\) −4.18336 5.75790i −0.151448 0.208450i
\(764\) 7.68045 + 5.58017i 0.277869 + 0.201884i
\(765\) −3.91191 11.3127i −0.141435 0.409010i
\(766\) 12.3595 8.97972i 0.446568 0.324450i
\(767\) −3.88502 1.26232i −0.140280 0.0455797i
\(768\) 0.205506i 0.00741554i
\(769\) 9.34609 28.7643i 0.337028 1.03727i −0.628686 0.777659i \(-0.716407\pi\)
0.965714 0.259608i \(-0.0835932\pi\)
\(770\) 1.26271 0.436645i 0.0455050 0.0157356i
\(771\) −1.49199 4.59189i −0.0537329 0.165373i
\(772\) −12.6080 + 4.09657i −0.453770 + 0.147439i
\(773\) −5.38935 + 7.41780i −0.193841 + 0.266800i −0.894864 0.446340i \(-0.852727\pi\)
0.701022 + 0.713139i \(0.252727\pi\)
\(774\) −2.33553 −0.0839489
\(775\) 6.02981 21.2392i 0.216597 0.762934i
\(776\) 3.44142 0.123540
\(777\) 0.468152 0.644355i 0.0167948 0.0231161i
\(778\) −22.9461 + 7.45564i −0.822657 + 0.267298i
\(779\) 13.6365 + 41.9687i 0.488577 + 1.50368i
\(780\) −1.19518 0.363684i −0.0427942 0.0130220i
\(781\) 0.197117 0.606663i 0.00705339 0.0217081i
\(782\) 1.59130i 0.0569047i
\(783\) −4.72184 1.53422i −0.168745 0.0548285i
\(784\) 0.809017 0.587785i 0.0288935 0.0209923i
\(785\) −12.2781 + 0.230470i −0.438224 + 0.00822584i
\(786\) −0.302542 0.219809i −0.0107913 0.00784034i
\(787\) 17.4778 + 24.0562i 0.623018 + 0.857510i 0.997568 0.0696962i \(-0.0222030\pi\)
−0.374551 + 0.927206i \(0.622203\pi\)
\(788\) −7.83061 10.7779i −0.278954 0.383947i
\(789\) 4.42007 + 3.21137i 0.157359 + 0.114328i
\(790\) 2.79219 9.17599i 0.0993416 0.326467i
\(791\) −7.86444 + 5.71385i −0.279627 + 0.203161i
\(792\) −1.68080 0.546126i −0.0597247 0.0194057i
\(793\) 31.4455i 1.11666i
\(794\) −5.21680 + 16.0557i −0.185137 + 0.569794i
\(795\) 2.83881 + 3.75694i 0.100682 + 0.133245i
\(796\) −3.09171 9.51530i −0.109583 0.337261i
\(797\) −8.42383 + 2.73707i −0.298387 + 0.0969520i −0.454385 0.890806i \(-0.650141\pi\)
0.155997 + 0.987757i \(0.450141\pi\)
\(798\) 0.874603 1.20379i 0.0309606 0.0426136i
\(799\) 0.819300 0.0289848
\(800\) 0.187642 + 4.99648i 0.00663416 + 0.176652i
\(801\) −35.3875 −1.25036
\(802\) 9.48299 13.0522i 0.334856 0.460890i
\(803\) 4.20895 1.36757i 0.148531 0.0482605i
\(804\) 0.244759 + 0.753290i 0.00863198 + 0.0265665i
\(805\) 1.12556 1.61197i 0.0396708 0.0568146i
\(806\) −3.70968 + 11.4172i −0.130668 + 0.402154i
\(807\) 3.53511i 0.124442i
\(808\) 13.2195 + 4.29526i 0.465059 + 0.151107i
\(809\) 23.5136 17.0837i 0.826695 0.600629i −0.0919272 0.995766i \(-0.529303\pi\)
0.918622 + 0.395136i \(0.129303\pi\)
\(810\) −15.3814 + 11.6224i −0.540446 + 0.408371i
\(811\) 19.7179 + 14.3259i 0.692388 + 0.503049i 0.877444 0.479679i \(-0.159247\pi\)
−0.185056 + 0.982728i \(0.559247\pi\)
\(812\) 2.38351 + 3.28061i 0.0836447 + 0.115127i
\(813\) −3.78698 5.21233i −0.132815 0.182804i
\(814\) 1.87348 + 1.36116i 0.0656653 + 0.0477087i
\(815\) −12.4110 + 9.37796i −0.434738 + 0.328496i
\(816\) −0.300901 + 0.218617i −0.0105336 + 0.00765314i
\(817\) 5.43746 + 1.76674i 0.190233 + 0.0618103i
\(818\) 4.00971i 0.140196i
\(819\) −2.48485 + 7.64757i −0.0868276 + 0.267228i
\(820\) 7.80207 11.1738i 0.272460 0.390205i
\(821\) 0.946848 + 2.91410i 0.0330452 + 0.101703i 0.966219 0.257724i \(-0.0829724\pi\)
−0.933173 + 0.359426i \(0.882972\pi\)
\(822\) 3.57141 1.16042i 0.124567 0.0404743i
\(823\) 30.0822 41.4045i 1.04860 1.44327i 0.158580 0.987346i \(-0.449308\pi\)
0.890018 0.455925i \(-0.150692\pi\)
\(824\) 18.7329 0.652590
\(825\) −0.590620 0.167677i −0.0205627 0.00583777i
\(826\) −1.50257 −0.0522810
\(827\) −12.7684 + 17.5742i −0.444000 + 0.611114i −0.971095 0.238693i \(-0.923281\pi\)
0.527095 + 0.849806i \(0.323281\pi\)
\(828\) −2.47332 + 0.803629i −0.0859537 + 0.0279280i
\(829\) −5.99653 18.4554i −0.208268 0.640983i −0.999563 0.0295490i \(-0.990593\pi\)
0.791295 0.611434i \(-0.209407\pi\)
\(830\) −1.15093 1.52316i −0.0399492 0.0528696i
\(831\) 0.569670 1.75326i 0.0197616 0.0608200i
\(832\) 2.71865i 0.0942522i
\(833\) −1.72127 0.559274i −0.0596385 0.0193777i
\(834\) 0.0887057 0.0644484i 0.00307163 0.00223167i
\(835\) −2.08039 + 6.83679i −0.0719948 + 0.236597i
\(836\) 3.50004 + 2.54293i 0.121051 + 0.0879489i
\(837\) −3.17780 4.37386i −0.109841 0.151183i
\(838\) 17.9691 + 24.7323i 0.620732 + 0.854364i
\(839\) 44.8182 + 32.5623i 1.54730 + 1.12418i 0.945544 + 0.325495i \(0.105531\pi\)
0.601753 + 0.798682i \(0.294469\pi\)
\(840\) −0.459444 + 0.00862414i −0.0158523 + 0.000297561i
\(841\) 10.1584 7.38051i 0.350290 0.254500i
\(842\) −11.2021 3.63978i −0.386050 0.125435i
\(843\) 0.444590i 0.0153125i
\(844\) −2.68643 + 8.26799i −0.0924709 + 0.284596i
\(845\) 11.9988 + 3.65114i 0.412770 + 0.125603i
\(846\) −0.413758 1.27342i −0.0142253 0.0437810i
\(847\) 10.1221 3.28886i 0.347799 0.113007i
\(848\) −6.02319 + 8.29021i −0.206837 + 0.284687i
\(849\) 1.53815 0.0527892
\(850\) 7.11623 5.59001i 0.244085 0.191736i
\(851\) 3.40764 0.116812
\(852\) −0.128955 + 0.177491i −0.00441791 + 0.00608073i
\(853\) −6.28413 + 2.04184i −0.215164 + 0.0699111i −0.414616 0.909997i \(-0.636084\pi\)
0.199451 + 0.979908i \(0.436084\pi\)
\(854\) −3.57427 11.0005i −0.122309 0.376428i
\(855\) 45.2575 15.6500i 1.54777 0.535219i
\(856\) 4.77880 14.7076i 0.163336 0.502697i
\(857\) 41.4918i 1.41733i −0.705544 0.708666i \(-0.749297\pi\)
0.705544 0.708666i \(-0.250703\pi\)
\(858\) 0.317490 + 0.103159i 0.0108389 + 0.00352178i
\(859\) 2.95601 2.14767i 0.100858 0.0732774i −0.536213 0.844082i \(-0.680146\pi\)
0.637071 + 0.770805i \(0.280146\pi\)
\(860\) −0.577037 1.66870i −0.0196768 0.0569023i
\(861\) 1.01329 + 0.736195i 0.0345327 + 0.0250895i
\(862\) −5.05685 6.96015i −0.172237 0.237064i
\(863\) 15.7847 + 21.7257i 0.537316 + 0.739552i 0.988223 0.153019i \(-0.0488995\pi\)
−0.450907 + 0.892571i \(0.648899\pi\)
\(864\) 0.990524 + 0.719658i 0.0336983 + 0.0244832i
\(865\) −18.0589 12.6096i −0.614020 0.428739i
\(866\) 24.4576 17.7695i 0.831102 0.603831i
\(867\) −2.68241 0.871567i −0.0910993 0.0296000i
\(868\) 4.41571i 0.149879i
\(869\) −0.792002 + 2.43753i −0.0268668 + 0.0826876i
\(870\) −0.0349714 1.86307i −0.00118564 0.0631641i
\(871\) 3.23793 + 9.96534i 0.109713 + 0.337663i
\(872\) −6.76882 + 2.19932i −0.229221 + 0.0744784i
\(873\) −5.98302 + 8.23491i −0.202494 + 0.278710i
\(874\) 6.36616 0.215339
\(875\) 11.1626 0.629187i 0.377365 0.0212704i
\(876\) −1.52211 −0.0514272
\(877\) −29.1169 + 40.0759i −0.983206 + 1.35327i −0.0481225 + 0.998841i \(0.515324\pi\)
−0.935084 + 0.354426i \(0.884676\pi\)
\(878\) 8.18655 2.65997i 0.276283 0.0897697i
\(879\) 0.519625 + 1.59924i 0.0175265 + 0.0539411i
\(880\) −0.0250749 1.33584i −0.000845274 0.0450312i
\(881\) 3.04297 9.36530i 0.102520 0.315525i −0.886620 0.462498i \(-0.846953\pi\)
0.989140 + 0.146973i \(0.0469532\pi\)
\(882\) 2.95777i 0.0995932i
\(883\) −7.57933 2.46267i −0.255065 0.0828756i 0.178694 0.983905i \(-0.442813\pi\)
−0.433758 + 0.901029i \(0.642813\pi\)
\(884\) −3.98065 + 2.89211i −0.133884 + 0.0972721i
\(885\) 0.566117 + 0.395291i 0.0190298 + 0.0132876i
\(886\) −32.0540 23.2886i −1.07687 0.782395i
\(887\) −23.5866 32.4642i −0.791962 1.09004i −0.993861 0.110635i \(-0.964711\pi\)
0.201900 0.979406i \(-0.435289\pi\)
\(888\) −0.468152 0.644355i −0.0157101 0.0216232i
\(889\) −17.7213 12.8753i −0.594353 0.431823i
\(890\) −8.74316 25.2839i −0.293071 0.847518i
\(891\) 4.16770 3.02801i 0.139623 0.101442i
\(892\) 20.2541 + 6.58094i 0.678156 + 0.220346i
\(893\) 3.27770i 0.109684i
\(894\) 0.417570 1.28515i 0.0139656 0.0429818i
\(895\) −46.7122 + 16.1531i −1.56142 + 0.539937i
\(896\) −0.309017 0.951057i −0.0103235 0.0317726i
\(897\) 0.467189 0.151799i 0.0155990 0.00506842i
\(898\) 19.8123 27.2693i 0.661146 0.909989i
\(899\) −17.9060 −0.597197
\(900\) −12.2822 8.23753i −0.409407 0.274584i
\(901\) 18.5460 0.617857
\(902\) −2.14050 + 2.94615i −0.0712710 + 0.0980961i
\(903\) 0.154330 0.0501450i 0.00513579 0.00166872i
\(904\) 3.00395 + 9.24520i 0.0999098 + 0.307491i
\(905\) −45.4315 13.8245i −1.51020 0.459542i
\(906\) 1.38455 4.26120i 0.0459985 0.141569i
\(907\) 23.5477i 0.781888i 0.920414 + 0.390944i \(0.127851\pi\)
−0.920414 + 0.390944i \(0.872149\pi\)
\(908\) 25.5241 + 8.29327i 0.847045 + 0.275222i
\(909\) −33.2605 + 24.1652i −1.10318 + 0.801509i
\(910\) −6.07802 + 0.114090i −0.201484 + 0.00378203i
\(911\) 44.1085 + 32.0467i 1.46138 + 1.06176i 0.983001 + 0.183602i \(0.0587758\pi\)
0.478380 + 0.878153i \(0.341224\pi\)
\(912\) −0.874603 1.20379i −0.0289610 0.0398614i
\(913\) 0.299852 + 0.412711i 0.00992367 + 0.0136588i
\(914\) 24.5123 + 17.8093i 0.810796 + 0.589078i
\(915\) −1.54730 + 5.08492i −0.0511523 + 0.168102i
\(916\) 17.0611 12.3956i 0.563716 0.409564i
\(917\) −1.73065 0.562324i −0.0571512 0.0185696i
\(918\) 2.21590i 0.0731355i
\(919\) 3.75109 11.5447i 0.123737 0.380824i −0.869932 0.493172i \(-0.835837\pi\)
0.993669 + 0.112348i \(0.0358372\pi\)
\(920\) −1.18526 1.56860i −0.0390769 0.0517152i
\(921\) 0.686448 + 2.11267i 0.0226192 + 0.0696148i
\(922\) −27.9079 + 9.06784i −0.919099 + 0.298633i
\(923\) −1.70595 + 2.34804i −0.0561521 + 0.0772867i
\(924\) 0.122792 0.00403956
\(925\) 11.9706 + 15.2388i 0.393590 + 0.501049i
\(926\) −3.33511 −0.109599
\(927\) −32.5677 + 44.8255i −1.06966 + 1.47226i
\(928\) 3.85659 1.25308i 0.126599 0.0411345i
\(929\) 10.5876 + 32.5854i 0.347369 + 1.06909i 0.960303 + 0.278957i \(0.0899888\pi\)
−0.612935 + 0.790133i \(0.710011\pi\)
\(930\) 1.16167 1.66369i 0.0380927 0.0545546i
\(931\) 2.23744 6.88612i 0.0733290 0.225684i
\(932\) 7.94580i 0.260273i
\(933\) 4.58399 + 1.48943i 0.150073 + 0.0487617i
\(934\) −2.41260 + 1.75285i −0.0789425 + 0.0573551i
\(935\) −1.92926 + 1.45779i −0.0630937 + 0.0476747i
\(936\) 6.50542 + 4.72646i 0.212636 + 0.154489i
\(937\) 1.78871 + 2.46195i 0.0584348 + 0.0804285i 0.837234 0.546844i \(-0.184171\pi\)
−0.778800 + 0.627273i \(0.784171\pi\)
\(938\) 2.26543 + 3.11810i 0.0739690 + 0.101810i
\(939\) −1.10659 0.803982i −0.0361121 0.0262370i
\(940\) 0.807613 0.610247i 0.0263414 0.0199041i
\(941\) 20.3221 14.7649i 0.662482 0.481322i −0.205018 0.978758i \(-0.565725\pi\)
0.867500 + 0.497437i \(0.165725\pi\)
\(942\) −1.07338 0.348762i −0.0349725 0.0113633i
\(943\) 5.35871i 0.174503i
\(944\) −0.464319 + 1.42903i −0.0151123 + 0.0465108i
\(945\) 1.56735 2.24469i 0.0509860 0.0730197i
\(946\) 0.145798 + 0.448719i 0.00474029 + 0.0145891i
\(947\) −32.3340 + 10.5060i −1.05071 + 0.341398i −0.782949 0.622086i \(-0.786285\pi\)
−0.267766 + 0.963484i \(0.586285\pi\)
\(948\) 0.518131 0.713146i 0.0168281 0.0231619i
\(949\) −20.1361 −0.653644
\(950\) 22.3634 + 28.4692i 0.725566 + 0.923663i
\(951\) 5.51936 0.178977
\(952\) −1.06380 + 1.46420i −0.0344781 + 0.0474550i
\(953\) 17.8597 5.80296i 0.578532 0.187976i −0.00511108 0.999987i \(-0.501627\pi\)
0.583643 + 0.812011i \(0.301627\pi\)
\(954\) −9.36600 28.8256i −0.303236 0.933263i
\(955\) −12.7978 16.9368i −0.414126 0.548062i
\(956\) −5.54073 + 17.0526i −0.179200 + 0.551521i
\(957\) 0.497929i 0.0160958i
\(958\) −2.93096 0.952326i −0.0946950 0.0307683i
\(959\) 14.7831 10.7406i 0.477373 0.346831i
\(960\) −0.133774 + 0.439622i −0.00431753 + 0.0141887i
\(961\) 9.30494 + 6.76044i 0.300159 + 0.218079i
\(962\) −6.19322 8.52423i −0.199677 0.274832i
\(963\) 26.8856 + 37.0048i 0.866376 + 1.19246i
\(964\) −15.7279 11.4270i −0.506561 0.368038i
\(965\) 29.6379 0.556328i 0.954077 0.0179088i
\(966\) 0.146181 0.106207i 0.00470329 0.00341714i
\(967\) −41.0932 13.3520i −1.32147 0.429371i −0.438469 0.898746i \(-0.644479\pi\)
−0.882999 + 0.469376i \(0.844479\pi\)
\(968\) 10.6430i 0.342078i
\(969\) −0.832179 + 2.56119i −0.0267335 + 0.0822771i
\(970\) −7.36195 2.24019i −0.236378 0.0719282i
\(971\) 3.39734 + 10.4560i 0.109026 + 0.335547i 0.990654 0.136397i \(-0.0435523\pi\)
−0.881628 + 0.471944i \(0.843552\pi\)
\(972\) −5.17838 + 1.68256i −0.166097 + 0.0539680i
\(973\) 0.313609 0.431646i 0.0100538 0.0138379i
\(974\) 8.85093 0.283602
\(975\) 2.32001 + 1.55600i 0.0742998 + 0.0498319i
\(976\) −11.5666 −0.370237
\(977\) 16.8687 23.2178i 0.539678 0.742802i −0.448889 0.893588i \(-0.648180\pi\)
0.988567 + 0.150785i \(0.0481801\pi\)
\(978\) −1.35967 + 0.441783i −0.0434774 + 0.0141267i
\(979\) 2.20910 + 6.79890i 0.0706031 + 0.217294i
\(980\) −2.11328 + 0.730773i −0.0675064 + 0.0233437i
\(981\) 6.50508 20.0206i 0.207691 0.639208i
\(982\) 4.37268i 0.139538i
\(983\) −18.4987 6.01061i −0.590018 0.191709i −0.00123459 0.999999i \(-0.500393\pi\)
−0.588784 + 0.808291i \(0.700393\pi\)
\(984\) 1.01329 0.736195i 0.0323024 0.0234691i
\(985\) 9.73553 + 28.1537i 0.310200 + 0.897051i
\(986\) −5.93742 4.31379i −0.189086 0.137379i
\(987\) 0.0546818 + 0.0752631i 0.00174054 + 0.00239565i
\(988\) −11.5702 15.9250i −0.368097 0.506642i
\(989\) 0.561679 + 0.408084i 0.0178604 + 0.0129763i
\(990\) 3.24011 + 2.26240i 0.102977 + 0.0719039i
\(991\) −25.8093 + 18.7516i −0.819861 + 0.595664i −0.916673 0.399639i \(-0.869135\pi\)
0.0968120 + 0.995303i \(0.469135\pi\)
\(992\) 4.19959 + 1.36453i 0.133337 + 0.0433238i
\(993\) 6.93527i 0.220084i
\(994\) −0.329896 + 1.01532i −0.0104637 + 0.0322038i
\(995\) 0.419864 + 22.3679i 0.0133106 + 0.709110i
\(996\) −0.0542186 0.166868i −0.00171798 0.00528741i
\(997\) −53.6265 + 17.4243i −1.69837 + 0.551833i −0.988330 0.152330i \(-0.951322\pi\)
−0.710038 + 0.704163i \(0.751322\pi\)
\(998\) −6.26546 + 8.62366i −0.198330 + 0.272977i
\(999\) 4.74517 0.150130
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 350.2.m.a.309.2 yes 24
25.8 odd 20 8750.2.a.z.1.6 12
25.14 even 10 inner 350.2.m.a.239.2 24
25.17 odd 20 8750.2.a.bb.1.7 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.m.a.239.2 24 25.14 even 10 inner
350.2.m.a.309.2 yes 24 1.1 even 1 trivial
8750.2.a.z.1.6 12 25.8 odd 20
8750.2.a.bb.1.7 12 25.17 odd 20