Properties

Label 462.2.j.g.295.2
Level $462$
Weight $2$
Character 462.295
Analytic conductor $3.689$
Analytic rank $0$
Dimension $8$
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] = [462,2,Mod(169,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 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("462.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.j (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.324000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 295.2
Root \(1.40126 - 1.01807i\) of defining polynomial
Character \(\chi\) \(=\) 462.295
Dual form 462.2.j.g.379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.330792 + 1.01807i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.330792 + 1.01807i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.07047 q^{10} +(-3.25134 - 0.654803i) q^{11} +1.00000 q^{12} +(-2.12387 + 6.53660i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-0.866025 - 0.629204i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.18850 - 6.73551i) q^{17} +(0.809017 + 0.587785i) q^{18} +(-4.70378 + 3.41749i) q^{19} +(0.330792 - 1.01807i) q^{20} +1.00000 q^{21} +(1.62747 - 2.88987i) q^{22} -2.29850 q^{23} +(-0.309017 + 0.951057i) q^{24} +(3.11803 - 2.26538i) q^{25} +(-5.56036 - 4.03984i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.309017 + 0.951057i) q^{28} +(-3.14275 - 2.28334i) q^{29} +(0.866025 - 0.629204i) q^{30} +(1.10570 - 3.40299i) q^{31} -1.00000 q^{32} +(3.01528 - 1.38135i) q^{33} +7.08214 q^{34} +(0.330792 - 1.01807i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-2.63799 - 1.91661i) q^{37} +(-1.79668 - 5.52962i) q^{38} +(-2.12387 - 6.53660i) q^{39} +(0.866025 + 0.629204i) q^{40} +(3.92055 - 2.84845i) q^{41} +(-0.309017 + 0.951057i) q^{42} -5.20419 q^{43} +(2.24551 + 2.44084i) q^{44} +1.07047 q^{45} +(0.710276 - 2.18600i) q^{46} +(-8.22489 + 5.97573i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.19098 + 3.66547i) q^{50} +(5.72957 + 4.16277i) q^{51} +(5.56036 - 4.03984i) q^{52} +(-3.18336 + 9.79737i) q^{53} -1.00000 q^{54} +(-0.408882 - 3.52671i) q^{55} -1.00000 q^{56} +(1.79668 - 5.52962i) q^{57} +(3.14275 - 2.28334i) q^{58} +(-0.410699 - 0.298390i) q^{59} +(0.330792 + 1.01807i) q^{60} +(2.47019 + 7.60246i) q^{61} +(2.89476 + 2.10317i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} -7.35730 q^{65} +(0.381966 + 3.29456i) q^{66} +3.79167 q^{67} +(-2.18850 + 6.73551i) q^{68} +(1.85953 - 1.35102i) q^{69} +(0.866025 + 0.629204i) q^{70} +(-4.39364 - 13.5222i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(10.4174 + 7.56869i) q^{73} +(2.63799 - 1.91661i) q^{74} +(-1.19098 + 3.66547i) q^{75} +5.81419 q^{76} +(2.24551 + 2.44084i) q^{77} +6.87298 q^{78} +(-2.77491 + 8.54029i) q^{79} +(-0.866025 + 0.629204i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.49752 + 4.60888i) q^{82} +(-0.553656 - 1.70398i) q^{83} +(-0.809017 - 0.587785i) q^{84} +(6.13331 - 4.45611i) q^{85} +(1.60818 - 4.94948i) q^{86} +3.88465 q^{87} +(-3.01528 + 1.38135i) q^{88} +6.23110 q^{89} +(-0.330792 + 1.01807i) q^{90} +(5.56036 - 4.03984i) q^{91} +(1.85953 + 1.35102i) q^{92} +(1.10570 + 3.40299i) q^{93} +(-3.14163 - 9.66893i) q^{94} +(-5.03523 - 3.65831i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-5.17839 + 15.9375i) q^{97} -1.00000 q^{98} +(-1.62747 + 2.88987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} + 8 q^{21} + 2 q^{22} + 2 q^{24} + 16 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{29} - 4 q^{31} - 8 q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{36} - 24 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{42} + 8 q^{43} - 2 q^{44} - 10 q^{46} - 2 q^{47} - 2 q^{48} - 2 q^{49} + 14 q^{50} + 10 q^{51} + 6 q^{52} - 22 q^{53} - 8 q^{54} - 8 q^{56} + 6 q^{57} - 2 q^{58} + 10 q^{59} + 26 q^{61} - 6 q^{62} - 2 q^{63} - 2 q^{64} - 60 q^{65} + 12 q^{66} + 4 q^{67} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 2 q^{73} + 24 q^{74} - 14 q^{75} - 4 q^{76} - 2 q^{77} + 24 q^{78} - 12 q^{79} - 2 q^{81} - 10 q^{82} - 38 q^{83} - 2 q^{84} + 24 q^{85} + 22 q^{86} - 28 q^{87} - 8 q^{88} - 12 q^{89} + 6 q^{91} - 10 q^{92} - 4 q^{93} - 8 q^{94} - 36 q^{95} + 2 q^{96} + 6 q^{97} - 8 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) −0.809017 + 0.587785i −0.467086 + 0.339358i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.330792 + 1.01807i 0.147935 + 0.455296i 0.997377 0.0723856i \(-0.0230612\pi\)
−0.849442 + 0.527682i \(0.823061\pi\)
\(6\) −0.309017 0.951057i −0.126156 0.388267i
\(7\) −0.809017 0.587785i −0.305780 0.222162i
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) −1.07047 −0.338511
\(11\) −3.25134 0.654803i −0.980317 0.197430i
\(12\) 1.00000 0.288675
\(13\) −2.12387 + 6.53660i −0.589055 + 1.81293i −0.00671890 + 0.999977i \(0.502139\pi\)
−0.582336 + 0.812948i \(0.697861\pi\)
\(14\) 0.809017 0.587785i 0.216219 0.157092i
\(15\) −0.866025 0.629204i −0.223607 0.162460i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −2.18850 6.73551i −0.530789 1.63360i −0.752575 0.658506i \(-0.771189\pi\)
0.221786 0.975095i \(-0.428811\pi\)
\(18\) 0.809017 + 0.587785i 0.190687 + 0.138542i
\(19\) −4.70378 + 3.41749i −1.07912 + 0.784027i −0.977529 0.210800i \(-0.932393\pi\)
−0.101591 + 0.994826i \(0.532393\pi\)
\(20\) 0.330792 1.01807i 0.0739674 0.227648i
\(21\) 1.00000 0.218218
\(22\) 1.62747 2.88987i 0.346979 0.616122i
\(23\) −2.29850 −0.479270 −0.239635 0.970863i \(-0.577028\pi\)
−0.239635 + 0.970863i \(0.577028\pi\)
\(24\) −0.309017 + 0.951057i −0.0630778 + 0.194134i
\(25\) 3.11803 2.26538i 0.623607 0.453077i
\(26\) −5.56036 4.03984i −1.09048 0.792277i
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) 0.309017 + 0.951057i 0.0583987 + 0.179733i
\(29\) −3.14275 2.28334i −0.583594 0.424006i 0.256424 0.966564i \(-0.417456\pi\)
−0.840018 + 0.542559i \(0.817456\pi\)
\(30\) 0.866025 0.629204i 0.158114 0.114876i
\(31\) 1.10570 3.40299i 0.198589 0.611196i −0.801326 0.598227i \(-0.795872\pi\)
0.999916 0.0129682i \(-0.00412803\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.01528 1.38135i 0.524892 0.240461i
\(34\) 7.08214 1.21458
\(35\) 0.330792 1.01807i 0.0559141 0.172086i
\(36\) −0.809017 + 0.587785i −0.134836 + 0.0979642i
\(37\) −2.63799 1.91661i −0.433683 0.315089i 0.349437 0.936960i \(-0.386373\pi\)
−0.783120 + 0.621871i \(0.786373\pi\)
\(38\) −1.79668 5.52962i −0.291460 0.897023i
\(39\) −2.12387 6.53660i −0.340091 1.04669i
\(40\) 0.866025 + 0.629204i 0.136931 + 0.0994859i
\(41\) 3.92055 2.84845i 0.612287 0.444853i −0.237932 0.971282i \(-0.576469\pi\)
0.850219 + 0.526429i \(0.176469\pi\)
\(42\) −0.309017 + 0.951057i −0.0476824 + 0.146751i
\(43\) −5.20419 −0.793631 −0.396816 0.917898i \(-0.629885\pi\)
−0.396816 + 0.917898i \(0.629885\pi\)
\(44\) 2.24551 + 2.44084i 0.338523 + 0.367970i
\(45\) 1.07047 0.159576
\(46\) 0.710276 2.18600i 0.104724 0.322309i
\(47\) −8.22489 + 5.97573i −1.19972 + 0.871650i −0.994257 0.107015i \(-0.965871\pi\)
−0.205465 + 0.978664i \(0.565871\pi\)
\(48\) −0.809017 0.587785i −0.116772 0.0848395i
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) 1.19098 + 3.66547i 0.168430 + 0.518376i
\(51\) 5.72957 + 4.16277i 0.802300 + 0.582905i
\(52\) 5.56036 4.03984i 0.771083 0.560225i
\(53\) −3.18336 + 9.79737i −0.437268 + 1.34577i 0.453476 + 0.891268i \(0.350184\pi\)
−0.890744 + 0.454505i \(0.849816\pi\)
\(54\) −1.00000 −0.136083
\(55\) −0.408882 3.52671i −0.0551336 0.475542i
\(56\) −1.00000 −0.133631
\(57\) 1.79668 5.52962i 0.237976 0.732416i
\(58\) 3.14275 2.28334i 0.412663 0.299817i
\(59\) −0.410699 0.298390i −0.0534685 0.0388471i 0.560730 0.827999i \(-0.310521\pi\)
−0.614198 + 0.789152i \(0.710521\pi\)
\(60\) 0.330792 + 1.01807i 0.0427051 + 0.131433i
\(61\) 2.47019 + 7.60246i 0.316275 + 0.973396i 0.975226 + 0.221210i \(0.0710005\pi\)
−0.658951 + 0.752186i \(0.728999\pi\)
\(62\) 2.89476 + 2.10317i 0.367635 + 0.267102i
\(63\) −0.809017 + 0.587785i −0.101927 + 0.0740540i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −7.35730 −0.912560
\(66\) 0.381966 + 3.29456i 0.0470168 + 0.405532i
\(67\) 3.79167 0.463226 0.231613 0.972808i \(-0.425600\pi\)
0.231613 + 0.972808i \(0.425600\pi\)
\(68\) −2.18850 + 6.73551i −0.265395 + 0.816801i
\(69\) 1.85953 1.35102i 0.223861 0.162644i
\(70\) 0.866025 + 0.629204i 0.103510 + 0.0752043i
\(71\) −4.39364 13.5222i −0.521429 1.60479i −0.771272 0.636506i \(-0.780379\pi\)
0.249843 0.968286i \(-0.419621\pi\)
\(72\) −0.309017 0.951057i −0.0364180 0.112083i
\(73\) 10.4174 + 7.56869i 1.21926 + 0.885848i 0.996039 0.0889190i \(-0.0283412\pi\)
0.223226 + 0.974767i \(0.428341\pi\)
\(74\) 2.63799 1.91661i 0.306660 0.222802i
\(75\) −1.19098 + 3.66547i −0.137523 + 0.423252i
\(76\) 5.81419 0.666933
\(77\) 2.24551 + 2.44084i 0.255899 + 0.278159i
\(78\) 6.87298 0.778212
\(79\) −2.77491 + 8.54029i −0.312201 + 0.960857i 0.664690 + 0.747120i \(0.268564\pi\)
−0.976891 + 0.213738i \(0.931436\pi\)
\(80\) −0.866025 + 0.629204i −0.0968246 + 0.0703472i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 1.49752 + 4.60888i 0.165373 + 0.508966i
\(83\) −0.553656 1.70398i −0.0607717 0.187036i 0.916062 0.401037i \(-0.131350\pi\)
−0.976833 + 0.214001i \(0.931350\pi\)
\(84\) −0.809017 0.587785i −0.0882710 0.0641326i
\(85\) 6.13331 4.45611i 0.665251 0.483333i
\(86\) 1.60818 4.94948i 0.173415 0.533716i
\(87\) 3.88465 0.416478
\(88\) −3.01528 + 1.38135i −0.321429 + 0.147252i
\(89\) 6.23110 0.660496 0.330248 0.943894i \(-0.392868\pi\)
0.330248 + 0.943894i \(0.392868\pi\)
\(90\) −0.330792 + 1.01807i −0.0348686 + 0.107314i
\(91\) 5.56036 4.03984i 0.582884 0.423490i
\(92\) 1.85953 + 1.35102i 0.193869 + 0.140854i
\(93\) 1.10570 + 3.40299i 0.114656 + 0.352874i
\(94\) −3.14163 9.66893i −0.324034 0.997274i
\(95\) −5.03523 3.65831i −0.516604 0.375335i
\(96\) 0.809017 0.587785i 0.0825700 0.0599906i
\(97\) −5.17839 + 15.9375i −0.525786 + 1.61820i 0.236969 + 0.971517i \(0.423846\pi\)
−0.762756 + 0.646687i \(0.776154\pi\)
\(98\) −1.00000 −0.101015
\(99\) −1.62747 + 2.88987i −0.163567 + 0.290442i
\(100\) −3.85410 −0.385410
\(101\) −4.42096 + 13.6063i −0.439902 + 1.35388i 0.448077 + 0.893995i \(0.352109\pi\)
−0.887979 + 0.459885i \(0.847891\pi\)
\(102\) −5.72957 + 4.16277i −0.567312 + 0.412176i
\(103\) 5.22849 + 3.79872i 0.515179 + 0.374299i 0.814785 0.579764i \(-0.196855\pi\)
−0.299606 + 0.954063i \(0.596855\pi\)
\(104\) 2.12387 + 6.53660i 0.208262 + 0.640966i
\(105\) 0.330792 + 1.01807i 0.0322820 + 0.0993538i
\(106\) −8.33414 6.05511i −0.809484 0.588124i
\(107\) −5.38424 + 3.91188i −0.520514 + 0.378176i −0.816798 0.576924i \(-0.804253\pi\)
0.296283 + 0.955100i \(0.404253\pi\)
\(108\) 0.309017 0.951057i 0.0297352 0.0915155i
\(109\) −13.4250 −1.28588 −0.642941 0.765915i \(-0.722286\pi\)
−0.642941 + 0.765915i \(0.722286\pi\)
\(110\) 3.48045 + 0.700944i 0.331848 + 0.0668324i
\(111\) 3.26074 0.309495
\(112\) 0.309017 0.951057i 0.0291994 0.0898664i
\(113\) 10.5186 7.64223i 0.989509 0.718921i 0.0296957 0.999559i \(-0.490546\pi\)
0.959814 + 0.280638i \(0.0905462\pi\)
\(114\) 4.70378 + 3.41749i 0.440549 + 0.320078i
\(115\) −0.760326 2.34004i −0.0709008 0.218210i
\(116\) 1.20042 + 3.69452i 0.111457 + 0.343028i
\(117\) 5.56036 + 4.03984i 0.514055 + 0.373483i
\(118\) 0.410699 0.298390i 0.0378079 0.0274691i
\(119\) −2.18850 + 6.73551i −0.200619 + 0.617443i
\(120\) −1.07047 −0.0977198
\(121\) 10.1425 + 4.25798i 0.922042 + 0.387089i
\(122\) −7.99370 −0.723716
\(123\) −1.49752 + 4.60888i −0.135027 + 0.415569i
\(124\) −2.89476 + 2.10317i −0.259957 + 0.188870i
\(125\) 7.66788 + 5.57104i 0.685836 + 0.498289i
\(126\) −0.309017 0.951057i −0.0275294 0.0847268i
\(127\) 3.91968 + 12.0635i 0.347816 + 1.07047i 0.960059 + 0.279797i \(0.0902672\pi\)
−0.612244 + 0.790669i \(0.709733\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) 4.21028 3.05894i 0.370694 0.269325i
\(130\) 2.27353 6.99721i 0.199402 0.613695i
\(131\) 0.283254 0.0247480 0.0123740 0.999923i \(-0.496061\pi\)
0.0123740 + 0.999923i \(0.496061\pi\)
\(132\) −3.25134 0.654803i −0.282993 0.0569933i
\(133\) 5.81419 0.504154
\(134\) −1.17169 + 3.60609i −0.101219 + 0.311519i
\(135\) −0.866025 + 0.629204i −0.0745356 + 0.0541533i
\(136\) −5.72957 4.16277i −0.491306 0.356955i
\(137\) 1.64564 + 5.06477i 0.140597 + 0.432713i 0.996419 0.0845584i \(-0.0269479\pi\)
−0.855822 + 0.517271i \(0.826948\pi\)
\(138\) 0.710276 + 2.18600i 0.0604627 + 0.186085i
\(139\) −14.5449 10.5675i −1.23368 0.896321i −0.236520 0.971627i \(-0.576007\pi\)
−0.997161 + 0.0753053i \(0.976007\pi\)
\(140\) −0.866025 + 0.629204i −0.0731925 + 0.0531775i
\(141\) 3.14163 9.66893i 0.264573 0.814271i
\(142\) 14.2181 1.19316
\(143\) 11.1856 19.8620i 0.935387 1.66094i
\(144\) 1.00000 0.0833333
\(145\) 1.28501 3.95486i 0.106715 0.328434i
\(146\) −10.4174 + 7.56869i −0.862150 + 0.626389i
\(147\) −0.809017 0.587785i −0.0667266 0.0484797i
\(148\) 1.00762 + 3.10115i 0.0828261 + 0.254913i
\(149\) −3.23607 9.95959i −0.265109 0.815922i −0.991668 0.128818i \(-0.958882\pi\)
0.726559 0.687104i \(-0.241118\pi\)
\(150\) −3.11803 2.26538i −0.254586 0.184968i
\(151\) −4.14784 + 3.01358i −0.337547 + 0.245242i −0.743626 0.668596i \(-0.766896\pi\)
0.406079 + 0.913838i \(0.366896\pi\)
\(152\) −1.79668 + 5.52962i −0.145730 + 0.448511i
\(153\) −7.08214 −0.572557
\(154\) −3.01528 + 1.38135i −0.242978 + 0.111312i
\(155\) 3.83026 0.307653
\(156\) −2.12387 + 6.53660i −0.170046 + 0.523346i
\(157\) 8.60503 6.25192i 0.686756 0.498958i −0.188836 0.982009i \(-0.560471\pi\)
0.875592 + 0.483051i \(0.160471\pi\)
\(158\) −7.26480 5.27819i −0.577957 0.419910i
\(159\) −3.18336 9.79737i −0.252457 0.776982i
\(160\) −0.330792 1.01807i −0.0261514 0.0804858i
\(161\) 1.85953 + 1.35102i 0.146551 + 0.106476i
\(162\) 0.809017 0.587785i 0.0635624 0.0461808i
\(163\) 0.145898 0.449028i 0.0114276 0.0351706i −0.945180 0.326549i \(-0.894114\pi\)
0.956608 + 0.291379i \(0.0941140\pi\)
\(164\) −4.84607 −0.378414
\(165\) 2.40374 + 2.61283i 0.187131 + 0.203409i
\(166\) 1.79167 0.139061
\(167\) −6.55854 + 20.1851i −0.507515 + 1.56197i 0.288985 + 0.957334i \(0.406682\pi\)
−0.796501 + 0.604638i \(0.793318\pi\)
\(168\) 0.809017 0.587785i 0.0624170 0.0453486i
\(169\) −27.6990 20.1245i −2.13070 1.54804i
\(170\) 2.34272 + 7.21014i 0.179678 + 0.552992i
\(171\) 1.79668 + 5.52962i 0.137396 + 0.422861i
\(172\) 4.21028 + 3.05894i 0.321030 + 0.233242i
\(173\) 14.4774 10.5184i 1.10069 0.799700i 0.119520 0.992832i \(-0.461864\pi\)
0.981173 + 0.193132i \(0.0618645\pi\)
\(174\) −1.20042 + 3.69452i −0.0910039 + 0.280081i
\(175\) −3.85410 −0.291343
\(176\) −0.381966 3.29456i −0.0287918 0.248337i
\(177\) 0.507652 0.0381575
\(178\) −1.92552 + 5.92613i −0.144324 + 0.444182i
\(179\) 10.3429 7.51457i 0.773066 0.561665i −0.129824 0.991537i \(-0.541441\pi\)
0.902890 + 0.429872i \(0.141441\pi\)
\(180\) −0.866025 0.629204i −0.0645497 0.0468981i
\(181\) 0.785453 + 2.41738i 0.0583823 + 0.179682i 0.975995 0.217794i \(-0.0698861\pi\)
−0.917612 + 0.397476i \(0.869886\pi\)
\(182\) 2.12387 + 6.53660i 0.157432 + 0.484525i
\(183\) −6.46704 4.69858i −0.478058 0.347329i
\(184\) −1.85953 + 1.35102i −0.137086 + 0.0995988i
\(185\) 1.07863 3.31967i 0.0793022 0.244067i
\(186\) −3.57812 −0.262360
\(187\) 2.70514 + 23.3325i 0.197819 + 1.70624i
\(188\) 10.1665 0.741470
\(189\) 0.309017 0.951057i 0.0224777 0.0691792i
\(190\) 5.03523 3.65831i 0.365294 0.265402i
\(191\) −6.16138 4.47650i −0.445822 0.323908i 0.342122 0.939655i \(-0.388854\pi\)
−0.787944 + 0.615747i \(0.788854\pi\)
\(192\) 0.309017 + 0.951057i 0.0223014 + 0.0686366i
\(193\) −4.15414 12.7851i −0.299021 0.920293i −0.981841 0.189706i \(-0.939247\pi\)
0.682820 0.730587i \(-0.260753\pi\)
\(194\) −13.5572 9.84989i −0.973351 0.707181i
\(195\) 5.95218 4.32451i 0.426244 0.309685i
\(196\) 0.309017 0.951057i 0.0220726 0.0679326i
\(197\) −6.97391 −0.496870 −0.248435 0.968649i \(-0.579916\pi\)
−0.248435 + 0.968649i \(0.579916\pi\)
\(198\) −2.24551 2.44084i −0.159581 0.173463i
\(199\) 24.6592 1.74804 0.874021 0.485887i \(-0.161503\pi\)
0.874021 + 0.485887i \(0.161503\pi\)
\(200\) 1.19098 3.66547i 0.0842152 0.259188i
\(201\) −3.06753 + 2.22869i −0.216367 + 0.157200i
\(202\) −11.5742 8.40917i −0.814360 0.591667i
\(203\) 1.20042 + 3.69452i 0.0842532 + 0.259305i
\(204\) −2.18850 6.73551i −0.153226 0.471580i
\(205\) 4.19682 + 3.04917i 0.293118 + 0.212963i
\(206\) −5.22849 + 3.79872i −0.364286 + 0.264669i
\(207\) −0.710276 + 2.18600i −0.0493676 + 0.151938i
\(208\) −6.87298 −0.476556
\(209\) 17.5314 8.03140i 1.21267 0.555543i
\(210\) −1.07047 −0.0738692
\(211\) 6.73763 20.7363i 0.463838 1.42755i −0.396601 0.917991i \(-0.629810\pi\)
0.860438 0.509554i \(-0.170190\pi\)
\(212\) 8.33414 6.05511i 0.572391 0.415867i
\(213\) 11.5027 + 8.35719i 0.788151 + 0.572625i
\(214\) −2.05660 6.32956i −0.140586 0.432680i
\(215\) −1.72150 5.29825i −0.117406 0.361337i
\(216\) 0.809017 + 0.587785i 0.0550466 + 0.0399937i
\(217\) −2.89476 + 2.10317i −0.196509 + 0.142772i
\(218\) 4.14856 12.7679i 0.280976 0.864754i
\(219\) −12.8766 −0.870121
\(220\) −1.74216 + 3.09350i −0.117456 + 0.208564i
\(221\) 48.6754 3.27426
\(222\) −1.00762 + 3.10115i −0.0676272 + 0.208135i
\(223\) 6.81009 4.94782i 0.456038 0.331331i −0.335937 0.941884i \(-0.609053\pi\)
0.791975 + 0.610554i \(0.209053\pi\)
\(224\) 0.809017 + 0.587785i 0.0540547 + 0.0392731i
\(225\) −1.19098 3.66547i −0.0793989 0.244365i
\(226\) 4.01776 + 12.3654i 0.267257 + 0.822533i
\(227\) −17.0949 12.4202i −1.13463 0.824357i −0.148268 0.988947i \(-0.547370\pi\)
−0.986362 + 0.164590i \(0.947370\pi\)
\(228\) −4.70378 + 3.41749i −0.311515 + 0.226329i
\(229\) −1.91899 + 5.90604i −0.126810 + 0.390282i −0.994227 0.107301i \(-0.965779\pi\)
0.867416 + 0.497583i \(0.165779\pi\)
\(230\) 2.46047 0.162238
\(231\) −3.25134 0.654803i −0.213923 0.0430829i
\(232\) −3.88465 −0.255040
\(233\) −6.05759 + 18.6434i −0.396846 + 1.22137i 0.530668 + 0.847580i \(0.321941\pi\)
−0.927514 + 0.373787i \(0.878059\pi\)
\(234\) −5.56036 + 4.03984i −0.363492 + 0.264092i
\(235\) −8.80446 6.39682i −0.574340 0.417282i
\(236\) 0.156873 + 0.482806i 0.0102116 + 0.0314280i
\(237\) −2.77491 8.54029i −0.180250 0.554751i
\(238\) −5.72957 4.16277i −0.371393 0.269833i
\(239\) −10.7383 + 7.80183i −0.694603 + 0.504658i −0.878170 0.478349i \(-0.841235\pi\)
0.183567 + 0.983007i \(0.441235\pi\)
\(240\) 0.330792 1.01807i 0.0213525 0.0657164i
\(241\) −23.8051 −1.53342 −0.766710 0.641994i \(-0.778108\pi\)
−0.766710 + 0.641994i \(0.778108\pi\)
\(242\) −7.18377 + 8.33027i −0.461790 + 0.535490i
\(243\) 1.00000 0.0641500
\(244\) 2.47019 7.60246i 0.158138 0.486698i
\(245\) −0.866025 + 0.629204i −0.0553283 + 0.0401984i
\(246\) −3.92055 2.84845i −0.249965 0.181610i
\(247\) −12.3486 38.0050i −0.785721 2.41820i
\(248\) −1.10570 3.40299i −0.0702120 0.216090i
\(249\) 1.44949 + 1.05312i 0.0918578 + 0.0667386i
\(250\) −7.66788 + 5.57104i −0.484959 + 0.352343i
\(251\) 0.0931899 0.286809i 0.00588209 0.0181032i −0.948072 0.318055i \(-0.896970\pi\)
0.953954 + 0.299951i \(0.0969705\pi\)
\(252\) 1.00000 0.0629941
\(253\) 7.47321 + 1.50506i 0.469837 + 0.0946226i
\(254\) −12.6844 −0.795887
\(255\) −2.34272 + 7.21014i −0.146707 + 0.451516i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 10.5015 + 7.62981i 0.655068 + 0.475935i 0.864994 0.501783i \(-0.167322\pi\)
−0.209926 + 0.977717i \(0.567322\pi\)
\(258\) 1.60818 + 4.94948i 0.100121 + 0.308141i
\(259\) 1.00762 + 3.10115i 0.0626107 + 0.192696i
\(260\) 5.95218 + 4.32451i 0.369138 + 0.268195i
\(261\) −3.14275 + 2.28334i −0.194531 + 0.141335i
\(262\) −0.0875302 + 0.269390i −0.00540763 + 0.0166430i
\(263\) −2.73287 −0.168516 −0.0842581 0.996444i \(-0.526852\pi\)
−0.0842581 + 0.996444i \(0.526852\pi\)
\(264\) 1.62747 2.88987i 0.100164 0.177859i
\(265\) −11.0275 −0.677413
\(266\) −1.79668 + 5.52962i −0.110162 + 0.339043i
\(267\) −5.04107 + 3.66255i −0.308508 + 0.224144i
\(268\) −3.06753 2.22869i −0.187379 0.136139i
\(269\) −7.72212 23.7662i −0.470826 1.44905i −0.851505 0.524346i \(-0.824310\pi\)
0.380679 0.924707i \(-0.375690\pi\)
\(270\) −0.330792 1.01807i −0.0201314 0.0619580i
\(271\) 9.51279 + 6.91145i 0.577861 + 0.419841i 0.837952 0.545743i \(-0.183753\pi\)
−0.260091 + 0.965584i \(0.583753\pi\)
\(272\) 5.72957 4.16277i 0.347406 0.252405i
\(273\) −2.12387 + 6.53660i −0.128542 + 0.395613i
\(274\) −5.32542 −0.321720
\(275\) −11.6212 + 5.32385i −0.700783 + 0.321040i
\(276\) −2.29850 −0.138353
\(277\) 6.48406 19.9559i 0.389589 1.19903i −0.543506 0.839405i \(-0.682904\pi\)
0.933096 0.359628i \(-0.117096\pi\)
\(278\) 14.5449 10.5675i 0.872344 0.633795i
\(279\) −2.89476 2.10317i −0.173305 0.125913i
\(280\) −0.330792 1.01807i −0.0197686 0.0608416i
\(281\) −3.63083 11.1745i −0.216597 0.666617i −0.999036 0.0438902i \(-0.986025\pi\)
0.782439 0.622727i \(-0.213975\pi\)
\(282\) 8.22489 + 5.97573i 0.489785 + 0.355849i
\(283\) −11.2499 + 8.17356i −0.668739 + 0.485868i −0.869603 0.493752i \(-0.835625\pi\)
0.200864 + 0.979619i \(0.435625\pi\)
\(284\) −4.39364 + 13.5222i −0.260714 + 0.802396i
\(285\) 6.22389 0.368671
\(286\) 15.4333 + 16.7758i 0.912593 + 0.991976i
\(287\) −4.84607 −0.286054
\(288\) −0.309017 + 0.951057i −0.0182090 + 0.0560415i
\(289\) −26.8243 + 19.4890i −1.57790 + 1.14641i
\(290\) 3.36421 + 2.44424i 0.197553 + 0.143531i
\(291\) −5.17839 15.9375i −0.303563 0.934270i
\(292\) −3.97909 12.2464i −0.232859 0.716666i
\(293\) −1.11642 0.811129i −0.0652222 0.0473867i 0.554696 0.832053i \(-0.312834\pi\)
−0.619919 + 0.784666i \(0.712834\pi\)
\(294\) 0.809017 0.587785i 0.0471828 0.0342803i
\(295\) 0.167927 0.516827i 0.00977711 0.0300909i
\(296\) −3.26074 −0.189526
\(297\) −0.381966 3.29456i −0.0221639 0.191170i
\(298\) 10.4721 0.606635
\(299\) 4.88171 15.0244i 0.282317 0.868881i
\(300\) 3.11803 2.26538i 0.180020 0.130792i
\(301\) 4.21028 + 3.05894i 0.242676 + 0.176315i
\(302\) −1.58434 4.87608i −0.0911683 0.280587i
\(303\) −4.42096 13.6063i −0.253978 0.781663i
\(304\) −4.70378 3.41749i −0.269780 0.196007i
\(305\) −6.92275 + 5.02967i −0.396396 + 0.287998i
\(306\) 2.18850 6.73551i 0.125108 0.385044i
\(307\) −16.0206 −0.914345 −0.457173 0.889378i \(-0.651138\pi\)
−0.457173 + 0.889378i \(0.651138\pi\)
\(308\) −0.381966 3.29456i −0.0217645 0.187725i
\(309\) −6.46277 −0.367654
\(310\) −1.18361 + 3.64279i −0.0672248 + 0.206897i
\(311\) 1.20621 0.876364i 0.0683980 0.0496940i −0.553061 0.833141i \(-0.686540\pi\)
0.621459 + 0.783447i \(0.286540\pi\)
\(312\) −5.56036 4.03984i −0.314793 0.228711i
\(313\) 1.97226 + 6.07000i 0.111479 + 0.343097i 0.991196 0.132400i \(-0.0422684\pi\)
−0.879718 + 0.475497i \(0.842268\pi\)
\(314\) 3.28683 + 10.1158i 0.185487 + 0.570869i
\(315\) −0.866025 0.629204i −0.0487950 0.0354516i
\(316\) 7.26480 5.27819i 0.408677 0.296921i
\(317\) 1.40776 4.33264i 0.0790676 0.243345i −0.903708 0.428150i \(-0.859165\pi\)
0.982775 + 0.184805i \(0.0591654\pi\)
\(318\) 10.3016 0.577683
\(319\) 8.72302 + 9.48181i 0.488395 + 0.530879i
\(320\) 1.07047 0.0598409
\(321\) 2.05660 6.32956i 0.114788 0.353281i
\(322\) −1.85953 + 1.35102i −0.103627 + 0.0752896i
\(323\) 33.3128 + 24.2031i 1.85357 + 1.34670i
\(324\) 0.309017 + 0.951057i 0.0171676 + 0.0528365i
\(325\) 8.18561 + 25.1927i 0.454056 + 1.39744i
\(326\) 0.381966 + 0.277515i 0.0211551 + 0.0153701i
\(327\) 10.8611 7.89102i 0.600618 0.436375i
\(328\) 1.49752 4.60888i 0.0826866 0.254483i
\(329\) 10.1665 0.560498
\(330\) −3.22775 + 1.47868i −0.177682 + 0.0813988i
\(331\) 9.56098 0.525519 0.262759 0.964861i \(-0.415367\pi\)
0.262759 + 0.964861i \(0.415367\pi\)
\(332\) −0.553656 + 1.70398i −0.0303858 + 0.0935180i
\(333\) −2.63799 + 1.91661i −0.144561 + 0.105030i
\(334\) −17.1705 12.4751i −0.939527 0.682607i
\(335\) 1.25426 + 3.86020i 0.0685273 + 0.210905i
\(336\) 0.309017 + 0.951057i 0.0168583 + 0.0518844i
\(337\) −3.88867 2.82528i −0.211829 0.153903i 0.476812 0.879005i \(-0.341792\pi\)
−0.688641 + 0.725102i \(0.741792\pi\)
\(338\) 27.6990 20.1245i 1.50663 1.09463i
\(339\) −4.01776 + 12.3654i −0.218215 + 0.671596i
\(340\) −7.58119 −0.411148
\(341\) −5.82330 + 10.3403i −0.315349 + 0.559958i
\(342\) −5.81419 −0.314395
\(343\) 0.309017 0.951057i 0.0166853 0.0513522i
\(344\) −4.21028 + 3.05894i −0.227003 + 0.164927i
\(345\) 1.99056 + 1.44623i 0.107168 + 0.0778622i
\(346\) 5.52986 + 17.0191i 0.297287 + 0.914955i
\(347\) 10.4322 + 32.1071i 0.560032 + 1.72360i 0.682270 + 0.731100i \(0.260993\pi\)
−0.122238 + 0.992501i \(0.539007\pi\)
\(348\) −3.14275 2.28334i −0.168469 0.122400i
\(349\) −26.0727 + 18.9429i −1.39564 + 1.01399i −0.400419 + 0.916332i \(0.631136\pi\)
−0.995220 + 0.0976592i \(0.968864\pi\)
\(350\) 1.19098 3.66547i 0.0636607 0.195928i
\(351\) −6.87298 −0.366853
\(352\) 3.25134 + 0.654803i 0.173297 + 0.0349011i
\(353\) −8.35904 −0.444907 −0.222453 0.974943i \(-0.571406\pi\)
−0.222453 + 0.974943i \(0.571406\pi\)
\(354\) −0.156873 + 0.482806i −0.00833771 + 0.0256608i
\(355\) 12.3132 8.94609i 0.653519 0.474809i
\(356\) −5.04107 3.66255i −0.267176 0.194115i
\(357\) −2.18850 6.73551i −0.115828 0.356481i
\(358\) 3.95064 + 12.1588i 0.208798 + 0.642614i
\(359\) 10.2223 + 7.42696i 0.539514 + 0.391980i 0.823904 0.566729i \(-0.191791\pi\)
−0.284391 + 0.958708i \(0.591791\pi\)
\(360\) 0.866025 0.629204i 0.0456435 0.0331620i
\(361\) 4.57492 14.0802i 0.240785 0.741061i
\(362\) −2.54178 −0.133593
\(363\) −10.7082 + 2.51682i −0.562035 + 0.132099i
\(364\) −6.87298 −0.360242
\(365\) −4.25949 + 13.1093i −0.222952 + 0.686175i
\(366\) 6.46704 4.69858i 0.338038 0.245599i
\(367\) 4.69728 + 3.41277i 0.245196 + 0.178145i 0.703595 0.710601i \(-0.251577\pi\)
−0.458399 + 0.888746i \(0.651577\pi\)
\(368\) −0.710276 2.18600i −0.0370257 0.113953i
\(369\) −1.49752 4.60888i −0.0779576 0.239929i
\(370\) 2.82388 + 2.05167i 0.146807 + 0.106661i
\(371\) 8.33414 6.05511i 0.432687 0.314366i
\(372\) 1.10570 3.40299i 0.0573278 0.176437i
\(373\) 31.9384 1.65371 0.826853 0.562417i \(-0.190129\pi\)
0.826853 + 0.562417i \(0.190129\pi\)
\(374\) −23.0265 4.63740i −1.19067 0.239794i
\(375\) −9.47802 −0.489443
\(376\) −3.14163 + 9.66893i −0.162017 + 0.498637i
\(377\) 21.6001 15.6934i 1.11246 0.808250i
\(378\) 0.809017 + 0.587785i 0.0416113 + 0.0302324i
\(379\) −0.906889 2.79112i −0.0465838 0.143370i 0.925059 0.379823i \(-0.124015\pi\)
−0.971643 + 0.236453i \(0.924015\pi\)
\(380\) 1.92329 + 5.91927i 0.0986626 + 0.303652i
\(381\) −10.2619 7.45568i −0.525731 0.381966i
\(382\) 6.16138 4.47650i 0.315243 0.229038i
\(383\) −0.304288 + 0.936501i −0.0155484 + 0.0478530i −0.958530 0.284993i \(-0.908009\pi\)
0.942981 + 0.332846i \(0.108009\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −1.74216 + 3.09350i −0.0887885 + 0.157660i
\(386\) 13.4431 0.684234
\(387\) −1.60818 + 4.94948i −0.0817485 + 0.251596i
\(388\) 13.5572 9.84989i 0.688263 0.500052i
\(389\) −2.73533 1.98733i −0.138687 0.100762i 0.516279 0.856421i \(-0.327317\pi\)
−0.654965 + 0.755659i \(0.727317\pi\)
\(390\) 2.27353 + 6.99721i 0.115125 + 0.354317i
\(391\) 5.03027 + 15.4816i 0.254392 + 0.782937i
\(392\) 0.809017 + 0.587785i 0.0408615 + 0.0296876i
\(393\) −0.229157 + 0.166492i −0.0115594 + 0.00839842i
\(394\) 2.15506 6.63258i 0.108570 0.334145i
\(395\) −9.61256 −0.483660
\(396\) 3.01528 1.38135i 0.151523 0.0694152i
\(397\) −14.6427 −0.734896 −0.367448 0.930044i \(-0.619768\pi\)
−0.367448 + 0.930044i \(0.619768\pi\)
\(398\) −7.62011 + 23.4523i −0.381961 + 1.17556i
\(399\) −4.70378 + 3.41749i −0.235483 + 0.171089i
\(400\) 3.11803 + 2.26538i 0.155902 + 0.113269i
\(401\) −6.85968 21.1119i −0.342556 1.05428i −0.962879 0.269933i \(-0.912998\pi\)
0.620323 0.784347i \(-0.287002\pi\)
\(402\) −1.17169 3.60609i −0.0584386 0.179856i
\(403\) 19.8956 + 14.4550i 0.991072 + 0.720056i
\(404\) 11.5742 8.40917i 0.575839 0.418372i
\(405\) 0.330792 1.01807i 0.0164372 0.0505885i
\(406\) −3.88465 −0.192792
\(407\) 7.32201 + 7.95893i 0.362939 + 0.394510i
\(408\) 7.08214 0.350618
\(409\) 6.47659 19.9329i 0.320247 0.985619i −0.653294 0.757105i \(-0.726613\pi\)
0.973541 0.228514i \(-0.0733867\pi\)
\(410\) −4.19682 + 3.04917i −0.207266 + 0.150588i
\(411\) −4.30835 3.13020i −0.212515 0.154401i
\(412\) −1.99711 6.14646i −0.0983904 0.302814i
\(413\) 0.156873 + 0.482806i 0.00771922 + 0.0237573i
\(414\) −1.85953 1.35102i −0.0913907 0.0663992i
\(415\) 1.55163 1.12733i 0.0761666 0.0553383i
\(416\) 2.12387 6.53660i 0.104131 0.320483i
\(417\) 17.9785 0.880409
\(418\) 2.22082 + 19.1552i 0.108624 + 0.936910i
\(419\) −22.3088 −1.08986 −0.544929 0.838482i \(-0.683443\pi\)
−0.544929 + 0.838482i \(0.683443\pi\)
\(420\) 0.330792 1.01807i 0.0161410 0.0496769i
\(421\) −11.9980 + 8.71706i −0.584747 + 0.424844i −0.840432 0.541917i \(-0.817699\pi\)
0.255685 + 0.966760i \(0.417699\pi\)
\(422\) 17.6393 + 12.8157i 0.858670 + 0.623860i
\(423\) 3.14163 + 9.66893i 0.152751 + 0.470120i
\(424\) 3.18336 + 9.79737i 0.154598 + 0.475803i
\(425\) −22.0823 16.0438i −1.07115 0.778237i
\(426\) −11.5027 + 8.35719i −0.557307 + 0.404907i
\(427\) 2.47019 7.60246i 0.119541 0.367909i
\(428\) 6.65529 0.321696
\(429\) 2.62525 + 22.6434i 0.126748 + 1.09324i
\(430\) 5.57091 0.268653
\(431\) 1.77035 5.44859i 0.0852749 0.262449i −0.899323 0.437286i \(-0.855940\pi\)
0.984597 + 0.174837i \(0.0559398\pi\)
\(432\) −0.809017 + 0.587785i −0.0389238 + 0.0282798i
\(433\) 3.76588 + 2.73607i 0.180977 + 0.131487i 0.674585 0.738197i \(-0.264322\pi\)
−0.493609 + 0.869684i \(0.664322\pi\)
\(434\) −1.10570 3.40299i −0.0530753 0.163349i
\(435\) 1.28501 + 3.95486i 0.0616117 + 0.189621i
\(436\) 10.8611 + 7.89102i 0.520150 + 0.377911i
\(437\) 10.8116 7.85511i 0.517190 0.375761i
\(438\) 3.97909 12.2464i 0.190128 0.585155i
\(439\) −3.00895 −0.143609 −0.0718047 0.997419i \(-0.522876\pi\)
−0.0718047 + 0.997419i \(0.522876\pi\)
\(440\) −2.40374 2.61283i −0.114594 0.124562i
\(441\) 1.00000 0.0476190
\(442\) −15.0415 + 46.2931i −0.715452 + 2.20194i
\(443\) −4.15033 + 3.01539i −0.197188 + 0.143265i −0.681998 0.731354i \(-0.738889\pi\)
0.484810 + 0.874619i \(0.338889\pi\)
\(444\) −2.63799 1.91661i −0.125194 0.0909584i
\(445\) 2.06120 + 6.34372i 0.0977103 + 0.300721i
\(446\) 2.60122 + 8.00574i 0.123172 + 0.379083i
\(447\) 8.47214 + 6.15537i 0.400718 + 0.291139i
\(448\) −0.809017 + 0.587785i −0.0382225 + 0.0277702i
\(449\) 1.15959 3.56886i 0.0547245 0.168425i −0.919959 0.392016i \(-0.871778\pi\)
0.974683 + 0.223591i \(0.0717779\pi\)
\(450\) 3.85410 0.181684
\(451\) −14.6122 + 6.69409i −0.688063 + 0.315212i
\(452\) −13.0017 −0.611550
\(453\) 1.58434 4.87608i 0.0744386 0.229098i
\(454\) 17.0949 12.4202i 0.802305 0.582909i
\(455\) 5.95218 + 4.32451i 0.279042 + 0.202736i
\(456\) −1.79668 5.52962i −0.0841374 0.258948i
\(457\) 6.68850 + 20.5851i 0.312875 + 0.962930i 0.976620 + 0.214971i \(0.0689658\pi\)
−0.663746 + 0.747958i \(0.731034\pi\)
\(458\) −5.02397 3.65013i −0.234755 0.170559i
\(459\) 5.72957 4.16277i 0.267433 0.194302i
\(460\) −0.760326 + 2.34004i −0.0354504 + 0.109105i
\(461\) 4.96761 0.231365 0.115682 0.993286i \(-0.463095\pi\)
0.115682 + 0.993286i \(0.463095\pi\)
\(462\) 1.62747 2.88987i 0.0757170 0.134449i
\(463\) −14.3253 −0.665754 −0.332877 0.942970i \(-0.608019\pi\)
−0.332877 + 0.942970i \(0.608019\pi\)
\(464\) 1.20042 3.69452i 0.0557283 0.171514i
\(465\) −3.09874 + 2.25137i −0.143701 + 0.104405i
\(466\) −15.8590 11.5222i −0.734653 0.533757i
\(467\) 1.86879 + 5.75155i 0.0864773 + 0.266150i 0.984939 0.172902i \(-0.0553144\pi\)
−0.898462 + 0.439052i \(0.855314\pi\)
\(468\) −2.12387 6.53660i −0.0981759 0.302154i
\(469\) −3.06753 2.22869i −0.141645 0.102911i
\(470\) 8.80446 6.39682i 0.406120 0.295063i
\(471\) −3.28683 + 10.1158i −0.151449 + 0.466113i
\(472\) −0.507652 −0.0233666
\(473\) 16.9206 + 3.40772i 0.778010 + 0.156687i
\(474\) 8.97979 0.412455
\(475\) −6.92460 + 21.3117i −0.317722 + 0.977849i
\(476\) 5.72957 4.16277i 0.262614 0.190800i
\(477\) 8.33414 + 6.05511i 0.381594 + 0.277244i
\(478\) −4.10166 12.6236i −0.187606 0.577391i
\(479\) 1.39446 + 4.29170i 0.0637144 + 0.196093i 0.977846 0.209324i \(-0.0671264\pi\)
−0.914132 + 0.405417i \(0.867126\pi\)
\(480\) 0.866025 + 0.629204i 0.0395285 + 0.0287191i
\(481\) 18.1309 13.1729i 0.826697 0.600630i
\(482\) 7.35617 22.6400i 0.335065 1.03122i
\(483\) −2.29850 −0.104585
\(484\) −5.70265 9.40637i −0.259211 0.427562i
\(485\) −17.9385 −0.814545
\(486\) −0.309017 + 0.951057i −0.0140173 + 0.0431408i
\(487\) 0.573025 0.416327i 0.0259662 0.0188656i −0.574726 0.818346i \(-0.694892\pi\)
0.600693 + 0.799480i \(0.294892\pi\)
\(488\) 6.46704 + 4.69858i 0.292749 + 0.212695i
\(489\) 0.145898 + 0.449028i 0.00659774 + 0.0203057i
\(490\) −0.330792 1.01807i −0.0149437 0.0459919i
\(491\) 32.8358 + 23.8566i 1.48186 + 1.07663i 0.976953 + 0.213456i \(0.0684722\pi\)
0.504904 + 0.863175i \(0.331528\pi\)
\(492\) 3.92055 2.84845i 0.176752 0.128418i
\(493\) −8.50156 + 26.1651i −0.382891 + 1.17842i
\(494\) 39.9608 1.79792
\(495\) −3.48045 0.700944i −0.156435 0.0315051i
\(496\) 3.57812 0.160662
\(497\) −4.39364 + 13.5222i −0.197081 + 0.606554i
\(498\) −1.44949 + 1.05312i −0.0649533 + 0.0471913i
\(499\) −4.72017 3.42941i −0.211304 0.153521i 0.477099 0.878849i \(-0.341688\pi\)
−0.688404 + 0.725328i \(0.741688\pi\)
\(500\) −2.92887 9.01413i −0.130983 0.403124i
\(501\) −6.55854 20.1851i −0.293014 0.901805i
\(502\) 0.243974 + 0.177258i 0.0108891 + 0.00791140i
\(503\) −17.4126 + 12.6510i −0.776391 + 0.564081i −0.903894 0.427757i \(-0.859304\pi\)
0.127502 + 0.991838i \(0.459304\pi\)
\(504\) −0.309017 + 0.951057i −0.0137647 + 0.0423634i
\(505\) −15.3147 −0.681494
\(506\) −3.74075 + 6.64236i −0.166297 + 0.295289i
\(507\) 34.2379 1.52056
\(508\) 3.91968 12.0635i 0.173908 0.535233i
\(509\) −13.7717 + 10.0057i −0.610420 + 0.443496i −0.849562 0.527488i \(-0.823134\pi\)
0.239142 + 0.970985i \(0.423134\pi\)
\(510\) −6.13331 4.45611i −0.271588 0.197320i
\(511\) −3.97909 12.2464i −0.176025 0.541748i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) −4.70378 3.41749i −0.207677 0.150886i
\(514\) −10.5015 + 7.62981i −0.463203 + 0.336537i
\(515\) −2.13783 + 6.57958i −0.0942043 + 0.289931i
\(516\) −5.20419 −0.229102
\(517\) 30.6549 14.0435i 1.34820 0.617631i
\(518\) −3.26074 −0.143269
\(519\) −5.52986 + 17.0191i −0.242734 + 0.747058i
\(520\) −5.95218 + 4.32451i −0.261020 + 0.189642i
\(521\) −3.55614 2.58368i −0.155797 0.113193i 0.507156 0.861855i \(-0.330697\pi\)
−0.662953 + 0.748661i \(0.730697\pi\)
\(522\) −1.20042 3.69452i −0.0525411 0.161705i
\(523\) −8.16872 25.1407i −0.357193 1.09933i −0.954727 0.297484i \(-0.903853\pi\)
0.597534 0.801844i \(-0.296147\pi\)
\(524\) −0.229157 0.166492i −0.0100108 0.00727325i
\(525\) 3.11803 2.26538i 0.136082 0.0988695i
\(526\) 0.844504 2.59912i 0.0368221 0.113327i
\(527\) −25.3407 −1.10386
\(528\) 2.24551 + 2.44084i 0.0977232 + 0.106224i
\(529\) −17.7169 −0.770300
\(530\) 3.40768 10.4878i 0.148020 0.455559i
\(531\) −0.410699 + 0.298390i −0.0178228 + 0.0129490i
\(532\) −4.70378 3.41749i −0.203935 0.148167i
\(533\) 10.2924 + 31.6768i 0.445814 + 1.37207i
\(534\) −1.92552 5.92613i −0.0833253 0.256449i
\(535\) −5.76365 4.18754i −0.249184 0.181043i
\(536\) 3.06753 2.22869i 0.132497 0.0962646i
\(537\) −3.95064 + 12.1588i −0.170483 + 0.524692i
\(538\) 24.9893 1.07737
\(539\) −0.381966 3.29456i −0.0164524 0.141907i
\(540\) 1.07047 0.0460655
\(541\) 7.13141 21.9482i 0.306603 0.943628i −0.672471 0.740124i \(-0.734767\pi\)
0.979074 0.203504i \(-0.0652331\pi\)
\(542\) −9.51279 + 6.91145i −0.408609 + 0.296872i
\(543\) −2.05634 1.49402i −0.0882461 0.0641146i
\(544\) 2.18850 + 6.73551i 0.0938312 + 0.288783i
\(545\) −4.44089 13.6677i −0.190227 0.585458i
\(546\) −5.56036 4.03984i −0.237961 0.172889i
\(547\) 3.13044 2.27440i 0.133848 0.0972464i −0.518847 0.854867i \(-0.673638\pi\)
0.652695 + 0.757621i \(0.273638\pi\)
\(548\) 1.64564 5.06477i 0.0702984 0.216356i
\(549\) 7.99370 0.341163
\(550\) −1.47214 12.6976i −0.0627721 0.541426i
\(551\) 22.5861 0.962200
\(552\) 0.710276 2.18600i 0.0302313 0.0930425i
\(553\) 7.26480 5.27819i 0.308931 0.224451i
\(554\) 16.9755 + 12.3334i 0.721219 + 0.523997i
\(555\) 1.07863 + 3.31967i 0.0457852 + 0.140912i
\(556\) 5.55565 + 17.0985i 0.235612 + 0.725139i
\(557\) 13.4192 + 9.74963i 0.568591 + 0.413105i 0.834593 0.550867i \(-0.185703\pi\)
−0.266002 + 0.963972i \(0.585703\pi\)
\(558\) 2.89476 2.10317i 0.122545 0.0890341i
\(559\) 11.0530 34.0177i 0.467492 1.43879i
\(560\) 1.07047 0.0452355
\(561\) −15.9030 17.2863i −0.671425 0.729830i
\(562\) 11.7496 0.495627
\(563\) 3.32053 10.2195i 0.139944 0.430702i −0.856383 0.516342i \(-0.827293\pi\)
0.996326 + 0.0856397i \(0.0272934\pi\)
\(564\) −8.22489 + 5.97573i −0.346330 + 0.251624i
\(565\) 11.2598 + 8.18075i 0.473705 + 0.344167i
\(566\) −4.29709 13.2251i −0.180620 0.555892i
\(567\) 0.309017 + 0.951057i 0.0129775 + 0.0399406i
\(568\) −11.5027 8.35719i −0.482642 0.350660i
\(569\) 9.67653 7.03041i 0.405661 0.294730i −0.366182 0.930543i \(-0.619335\pi\)
0.771843 + 0.635813i \(0.219335\pi\)
\(570\) −1.92329 + 5.91927i −0.0805577 + 0.247931i
\(571\) 8.27920 0.346474 0.173237 0.984880i \(-0.444577\pi\)
0.173237 + 0.984880i \(0.444577\pi\)
\(572\) −20.7239 + 9.49396i −0.866511 + 0.396963i
\(573\) 7.61588 0.318158
\(574\) 1.49752 4.60888i 0.0625052 0.192371i
\(575\) −7.16680 + 5.20699i −0.298876 + 0.217146i
\(576\) −0.809017 0.587785i −0.0337090 0.0244911i
\(577\) −0.351208 1.08091i −0.0146210 0.0449988i 0.943480 0.331430i \(-0.107531\pi\)
−0.958101 + 0.286431i \(0.907531\pi\)
\(578\) −10.2460 31.5338i −0.426176 1.31163i
\(579\) 10.8757 + 7.90164i 0.451977 + 0.328381i
\(580\) −3.36421 + 2.44424i −0.139691 + 0.101492i
\(581\) −0.553656 + 1.70398i −0.0229695 + 0.0706930i
\(582\) 16.7576 0.694626
\(583\) 16.7655 29.7702i 0.694358 1.23295i
\(584\) 12.8766 0.532838
\(585\) −2.27353 + 6.99721i −0.0939989 + 0.289299i
\(586\) 1.11642 0.811129i 0.0461190 0.0335074i
\(587\) −9.04007 6.56799i −0.373124 0.271090i 0.385381 0.922757i \(-0.374070\pi\)
−0.758505 + 0.651667i \(0.774070\pi\)
\(588\) 0.309017 + 0.951057i 0.0127436 + 0.0392209i
\(589\) 6.42874 + 19.7856i 0.264892 + 0.815253i
\(590\) 0.439640 + 0.319417i 0.0180997 + 0.0131502i
\(591\) 5.64201 4.09916i 0.232081 0.168617i
\(592\) 1.00762 3.10115i 0.0414131 0.127456i
\(593\) −13.0875 −0.537440 −0.268720 0.963218i \(-0.586601\pi\)
−0.268720 + 0.963218i \(0.586601\pi\)
\(594\) 3.25134 + 0.654803i 0.133404 + 0.0268669i
\(595\) −7.58119 −0.310798
\(596\) −3.23607 + 9.95959i −0.132555 + 0.407961i
\(597\) −19.9497 + 14.4943i −0.816487 + 0.593212i
\(598\) 12.7805 + 9.28557i 0.522633 + 0.379715i
\(599\) −8.57349 26.3865i −0.350303 1.07812i −0.958683 0.284476i \(-0.908180\pi\)
0.608380 0.793646i \(-0.291820\pi\)
\(600\) 1.19098 + 3.66547i 0.0486217 + 0.149642i
\(601\) −21.1077 15.3357i −0.861002 0.625554i 0.0671555 0.997743i \(-0.478608\pi\)
−0.928157 + 0.372188i \(0.878608\pi\)
\(602\) −4.21028 + 3.05894i −0.171598 + 0.124673i
\(603\) 1.17169 3.60609i 0.0477149 0.146851i
\(604\) 5.12702 0.208615
\(605\) −0.979885 + 11.7343i −0.0398380 + 0.477067i
\(606\) 14.3065 0.581163
\(607\) 13.8113 42.5068i 0.560583 1.72530i −0.120141 0.992757i \(-0.538335\pi\)
0.680724 0.732540i \(-0.261665\pi\)
\(608\) 4.70378 3.41749i 0.190763 0.138598i
\(609\) −3.14275 2.28334i −0.127351 0.0925257i
\(610\) −2.64426 8.13818i −0.107063 0.329505i
\(611\) −21.5923 66.4544i −0.873533 2.68846i
\(612\) 5.72957 + 4.16277i 0.231604 + 0.168270i
\(613\) −30.6941 + 22.3006i −1.23972 + 0.900712i −0.997580 0.0695281i \(-0.977851\pi\)
−0.242144 + 0.970240i \(0.577851\pi\)
\(614\) 4.95064 15.2365i 0.199792 0.614896i
\(615\) −5.18755 −0.209182
\(616\) 3.25134 + 0.654803i 0.131000 + 0.0263828i
\(617\) −27.2763 −1.09810 −0.549052 0.835788i \(-0.685011\pi\)
−0.549052 + 0.835788i \(0.685011\pi\)
\(618\) 1.99711 6.14646i 0.0803354 0.247247i
\(619\) 32.4572 23.5815i 1.30456 0.947822i 0.304576 0.952488i \(-0.401485\pi\)
0.999989 + 0.00466642i \(0.00148537\pi\)
\(620\) −3.09874 2.25137i −0.124448 0.0904171i
\(621\) −0.710276 2.18600i −0.0285024 0.0877213i
\(622\) 0.460732 + 1.41799i 0.0184737 + 0.0568561i
\(623\) −5.04107 3.66255i −0.201966 0.146737i
\(624\) 5.56036 4.03984i 0.222593 0.161723i
\(625\) 2.81966 8.67802i 0.112786 0.347121i
\(626\) −6.38237 −0.255091
\(627\) −9.46244 + 16.8022i −0.377893 + 0.671016i
\(628\) −10.6364 −0.424439
\(629\) −7.13612 + 21.9627i −0.284536 + 0.875711i
\(630\) 0.866025 0.629204i 0.0345033 0.0250681i
\(631\) 27.5546 + 20.0196i 1.09693 + 0.796966i 0.980556 0.196240i \(-0.0628731\pi\)
0.116373 + 0.993206i \(0.462873\pi\)
\(632\) 2.77491 + 8.54029i 0.110380 + 0.339714i
\(633\) 6.73763 + 20.7363i 0.267797 + 0.824194i
\(634\) 3.68556 + 2.67772i 0.146372 + 0.106346i
\(635\) −10.9850 + 7.98105i −0.435925 + 0.316718i
\(636\) −3.18336 + 9.79737i −0.126228 + 0.388491i
\(637\) −6.87298 −0.272318
\(638\) −11.7133 + 5.36605i −0.463734 + 0.212444i
\(639\) −14.2181 −0.562459
\(640\) −0.330792 + 1.01807i −0.0130757 + 0.0402429i
\(641\) −40.1489 + 29.1699i −1.58579 + 1.15214i −0.676132 + 0.736781i \(0.736345\pi\)
−0.909656 + 0.415362i \(0.863655\pi\)
\(642\) 5.38424 + 3.91188i 0.212499 + 0.154390i
\(643\) −3.73962 11.5094i −0.147476 0.453886i 0.849845 0.527033i \(-0.176696\pi\)
−0.997321 + 0.0731475i \(0.976696\pi\)
\(644\) −0.710276 2.18600i −0.0279888 0.0861406i
\(645\) 4.50696 + 3.27450i 0.177461 + 0.128933i
\(646\) −33.3128 + 24.2031i −1.31067 + 0.952260i
\(647\) −8.39964 + 25.8514i −0.330224 + 1.01633i 0.638803 + 0.769370i \(0.279430\pi\)
−0.969027 + 0.246955i \(0.920570\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 1.13994 + 1.23910i 0.0447465 + 0.0486388i
\(650\) −26.4892 −1.03899
\(651\) 1.10570 3.40299i 0.0433358 0.133374i
\(652\) −0.381966 + 0.277515i −0.0149589 + 0.0108683i
\(653\) 4.84934 + 3.52325i 0.189769 + 0.137876i 0.678613 0.734496i \(-0.262581\pi\)
−0.488844 + 0.872371i \(0.662581\pi\)
\(654\) 4.14856 + 12.7679i 0.162221 + 0.499266i
\(655\) 0.0936981 + 0.288373i 0.00366109 + 0.0112677i
\(656\) 3.92055 + 2.84845i 0.153072 + 0.111213i
\(657\) 10.4174 7.56869i 0.406422 0.295283i
\(658\) −3.14163 + 9.66893i −0.122473 + 0.376934i
\(659\) −37.0565 −1.44352 −0.721758 0.692146i \(-0.756666\pi\)
−0.721758 + 0.692146i \(0.756666\pi\)
\(660\) −0.408882 3.52671i −0.0159157 0.137277i
\(661\) −0.424601 −0.0165150 −0.00825752 0.999966i \(-0.502628\pi\)
−0.00825752 + 0.999966i \(0.502628\pi\)
\(662\) −2.95450 + 9.09303i −0.114830 + 0.353411i
\(663\) −39.3792 + 28.6107i −1.52936 + 1.11115i
\(664\) −1.44949 1.05312i −0.0562512 0.0408689i
\(665\) 1.92329 + 5.91927i 0.0745819 + 0.229540i
\(666\) −1.00762 3.10115i −0.0390446 0.120167i
\(667\) 7.22361 + 5.24826i 0.279699 + 0.203213i
\(668\) 17.1705 12.4751i 0.664346 0.482676i
\(669\) −2.60122 + 8.00574i −0.100569 + 0.309520i
\(670\) −4.05885 −0.156807
\(671\) −3.05332 26.3357i −0.117872 1.01668i
\(672\) −1.00000 −0.0385758
\(673\) 0.423778 1.30426i 0.0163354 0.0502753i −0.942557 0.334047i \(-0.891586\pi\)
0.958892 + 0.283771i \(0.0915857\pi\)
\(674\) 3.88867 2.82528i 0.149786 0.108826i
\(675\) 3.11803 + 2.26538i 0.120013 + 0.0871947i
\(676\) 10.5801 + 32.5622i 0.406927 + 1.25239i
\(677\) −0.231575 0.712714i −0.00890015 0.0273918i 0.946508 0.322681i \(-0.104584\pi\)
−0.955408 + 0.295289i \(0.904584\pi\)
\(678\) −10.5186 7.64223i −0.403965 0.293498i
\(679\) 13.5572 9.84989i 0.520278 0.378004i
\(680\) 2.34272 7.21014i 0.0898390 0.276496i
\(681\) 21.1305 0.809722
\(682\) −8.03470 8.73361i −0.307664 0.334427i
\(683\) 23.8913 0.914174 0.457087 0.889422i \(-0.348893\pi\)
0.457087 + 0.889422i \(0.348893\pi\)
\(684\) 1.79668 5.52962i 0.0686979 0.211430i
\(685\) −4.61195 + 3.35077i −0.176213 + 0.128027i
\(686\) 0.809017 + 0.587785i 0.0308884 + 0.0224417i
\(687\) −1.91899 5.90604i −0.0732139 0.225329i
\(688\) −1.60818 4.94948i −0.0613114 0.188697i
\(689\) −57.2804 41.6167i −2.18221 1.58547i
\(690\) −1.99056 + 1.44623i −0.0757793 + 0.0550569i
\(691\) −9.95200 + 30.6291i −0.378592 + 1.16519i 0.562431 + 0.826844i \(0.309866\pi\)
−0.941023 + 0.338342i \(0.890134\pi\)
\(692\) −17.8950 −0.680266
\(693\) 3.01528 1.38135i 0.114541 0.0524730i
\(694\) −33.7594 −1.28149
\(695\) 5.94713 18.3034i 0.225588 0.694287i
\(696\) 3.14275 2.28334i 0.119126 0.0865498i
\(697\) −27.7659 20.1731i −1.05171 0.764110i
\(698\) −9.95888 30.6503i −0.376949 1.16013i
\(699\) −6.05759 18.6434i −0.229119 0.705157i
\(700\) 3.11803 + 2.26538i 0.117851 + 0.0856235i
\(701\) −4.10892 + 2.98531i −0.155192 + 0.112754i −0.662671 0.748910i \(-0.730577\pi\)
0.507479 + 0.861664i \(0.330577\pi\)
\(702\) 2.12387 6.53660i 0.0801603 0.246708i
\(703\) 18.9585 0.715035
\(704\) −1.62747 + 2.88987i −0.0613378 + 0.108916i
\(705\) 10.8829 0.409874
\(706\) 2.58308 7.94991i 0.0972156 0.299199i
\(707\) 11.5742 8.40917i 0.435294 0.316259i
\(708\) −0.410699 0.298390i −0.0154350 0.0112142i
\(709\) −3.78680 11.6546i −0.142216 0.437697i 0.854426 0.519573i \(-0.173909\pi\)
−0.996643 + 0.0818759i \(0.973909\pi\)
\(710\) 4.70324 + 14.4751i 0.176509 + 0.543240i
\(711\) 7.26480 + 5.27819i 0.272451 + 0.197947i
\(712\) 5.04107 3.66255i 0.188922 0.137260i
\(713\) −2.54145 + 7.82178i −0.0951780 + 0.292928i
\(714\) 7.08214 0.265042
\(715\) 23.9211 + 4.81758i 0.894598 + 0.180167i
\(716\) −12.7846 −0.477781
\(717\) 4.10166 12.6236i 0.153179 0.471438i
\(718\) −10.2223 + 7.42696i −0.381494 + 0.277172i
\(719\) −17.1987 12.4956i −0.641402 0.466006i 0.218929 0.975741i \(-0.429744\pi\)
−0.860332 + 0.509735i \(0.829744\pi\)
\(720\) 0.330792 + 1.01807i 0.0123279 + 0.0379414i
\(721\) −1.99711 6.14646i −0.0743761 0.228906i
\(722\) 11.9773 + 8.70202i 0.445749 + 0.323856i
\(723\) 19.2587 13.9923i 0.716239 0.520378i
\(724\) 0.785453 2.41738i 0.0291911 0.0898411i
\(725\) −14.9718 −0.556040
\(726\) 0.915382 10.9618i 0.0339730 0.406832i
\(727\) −27.9895 −1.03807 −0.519037 0.854752i \(-0.673709\pi\)
−0.519037 + 0.854752i \(0.673709\pi\)
\(728\) 2.12387 6.53660i 0.0787158 0.242262i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) −11.1515 8.10202i −0.412735 0.299869i
\(731\) 11.3894 + 35.0529i 0.421251 + 1.29648i
\(732\) 2.47019 + 7.60246i 0.0913009 + 0.280995i
\(733\) −27.3088 19.8410i −1.00867 0.732843i −0.0447419 0.998999i \(-0.514247\pi\)
−0.963930 + 0.266155i \(0.914247\pi\)
\(734\) −4.69728 + 3.41277i −0.173380 + 0.125968i
\(735\) 0.330792 1.01807i 0.0122015 0.0375522i
\(736\) 2.29850 0.0847238
\(737\) −12.3280 2.48280i −0.454108 0.0914550i
\(738\) 4.84607 0.178386
\(739\) 5.83522 17.9590i 0.214652 0.660631i −0.784526 0.620096i \(-0.787094\pi\)
0.999178 0.0405352i \(-0.0129063\pi\)
\(740\) −2.82388 + 2.05167i −0.103808 + 0.0754209i
\(741\) 32.3290 + 23.4884i 1.18763 + 0.862867i
\(742\) 3.18336 + 9.79737i 0.116865 + 0.359673i
\(743\) 15.2479 + 46.9281i 0.559390 + 1.72162i 0.684059 + 0.729426i \(0.260213\pi\)
−0.124669 + 0.992198i \(0.539787\pi\)
\(744\) 2.89476 + 2.10317i 0.106127 + 0.0771058i
\(745\) 9.06914 6.58911i 0.332267 0.241406i
\(746\) −9.86950 + 30.3752i −0.361348 + 1.11212i
\(747\) −1.79167 −0.0655538
\(748\) 11.5260 20.4664i 0.421432 0.748327i
\(749\) 6.65529 0.243179
\(750\) 2.92887 9.01413i 0.106947 0.329150i
\(751\) 18.9891 13.7964i 0.692922 0.503437i −0.184697 0.982795i \(-0.559130\pi\)
0.877619 + 0.479358i \(0.159130\pi\)
\(752\) −8.22489 5.97573i −0.299931 0.217912i
\(753\) 0.0931899 + 0.286809i 0.00339603 + 0.0104519i
\(754\) 8.25049 + 25.3924i 0.300465 + 0.924737i
\(755\) −4.44013 3.22594i −0.161593 0.117404i
\(756\) −0.809017 + 0.587785i −0.0294237 + 0.0213775i
\(757\) 11.4730 35.3101i 0.416992 1.28337i −0.493466 0.869765i \(-0.664270\pi\)
0.910457 0.413603i \(-0.135730\pi\)
\(758\) 2.93476 0.106595
\(759\) −6.93061 + 3.17502i −0.251565 + 0.115246i
\(760\) −6.22389 −0.225764
\(761\) 2.65437 8.16932i 0.0962209 0.296138i −0.891349 0.453318i \(-0.850240\pi\)
0.987570 + 0.157180i \(0.0502403\pi\)
\(762\) 10.2619 7.45568i 0.371748 0.270091i
\(763\) 10.8611 + 7.89102i 0.393197 + 0.285674i
\(764\) 2.35344 + 7.24313i 0.0851444 + 0.262047i
\(765\) −2.34272 7.21014i −0.0847011 0.260683i
\(766\) −0.796636 0.578790i −0.0287836 0.0209125i
\(767\) 2.82273 2.05083i 0.101923 0.0740513i
\(768\) 0.309017 0.951057i 0.0111507 0.0343183i
\(769\) −52.0121 −1.87561 −0.937803 0.347168i \(-0.887143\pi\)
−0.937803 + 0.347168i \(0.887143\pi\)
\(770\) −2.40374 2.61283i −0.0866248 0.0941600i
\(771\) −12.9806 −0.467485
\(772\) −4.15414 + 12.7851i −0.149511 + 0.460146i
\(773\) 2.14672 1.55968i 0.0772122 0.0560979i −0.548510 0.836144i \(-0.684805\pi\)
0.625722 + 0.780046i \(0.284805\pi\)
\(774\) −4.21028 3.05894i −0.151335 0.109951i
\(775\) −4.26148 13.1155i −0.153077 0.471122i
\(776\) 5.17839 + 15.9375i 0.185894 + 0.572121i
\(777\) −2.63799 1.91661i −0.0946374 0.0687581i
\(778\) 2.73533 1.98733i 0.0980662 0.0712493i
\(779\) −8.70684 + 26.7969i −0.311955 + 0.960099i
\(780\) −7.35730 −0.263433
\(781\) 5.43083 + 46.8423i 0.194330 + 1.67615i
\(782\) −16.2783 −0.582110
\(783\) 1.20042 3.69452i 0.0428996 0.132032i
\(784\) −0.809017 + 0.587785i −0.0288935 + 0.0209923i
\(785\) 9.21140 + 6.69247i 0.328769 + 0.238865i
\(786\) −0.0875302 0.269390i −0.00312210 0.00960883i
\(787\) 10.3016 + 31.7049i 0.367211 + 1.13016i 0.948585 + 0.316522i \(0.102515\pi\)
−0.581375 + 0.813636i \(0.697485\pi\)
\(788\) 5.64201 + 4.09916i 0.200988 + 0.146027i
\(789\) 2.21094 1.60634i 0.0787116 0.0571873i
\(790\) 2.97044 9.14209i 0.105684 0.325261i
\(791\) −13.0017 −0.462289
\(792\) 0.381966 + 3.29456i 0.0135726 + 0.117067i
\(793\) −54.9406 −1.95100
\(794\) 4.52484 13.9260i 0.160581 0.494217i
\(795\) 8.92142 6.48179i 0.316410 0.229885i
\(796\) −19.9497 14.4943i −0.707098 0.513737i
\(797\) 8.76659 + 26.9808i 0.310529 + 0.955709i 0.977556 + 0.210675i \(0.0675663\pi\)
−0.667028 + 0.745033i \(0.732434\pi\)
\(798\) −1.79668 5.52962i −0.0636019 0.195746i
\(799\) 58.2498 + 42.3209i 2.06073 + 1.49721i
\(800\) −3.11803 + 2.26538i −0.110239 + 0.0800934i
\(801\) 1.92552 5.92613i 0.0680348 0.209390i
\(802\) 22.1984 0.783853
\(803\) −28.9146 31.4297i −1.02037 1.10913i
\(804\) 3.79167 0.133722
\(805\) −0.760326 + 2.34004i −0.0267980 + 0.0824757i
\(806\) −19.8956 + 14.4550i −0.700794 + 0.509156i
\(807\) 20.2168 + 14.6883i 0.711664 + 0.517054i
\(808\) 4.42096 + 13.6063i 0.155529 + 0.478669i
\(809\) −9.33527 28.7310i −0.328211 1.01013i −0.969971 0.243223i \(-0.921795\pi\)
0.641760 0.766906i \(-0.278205\pi\)
\(810\) 0.866025 + 0.629204i 0.0304290 + 0.0221080i
\(811\) 31.4385 22.8414i 1.10396 0.802071i 0.122254 0.992499i \(-0.460988\pi\)
0.981701 + 0.190428i \(0.0609877\pi\)
\(812\) 1.20042 3.69452i 0.0421266 0.129652i
\(813\) −11.7585 −0.412387
\(814\) −9.83202 + 4.50420i −0.344612 + 0.157872i
\(815\) 0.505406 0.0177036
\(816\) −2.18850 + 6.73551i −0.0766128 + 0.235790i
\(817\) 24.4793 17.7853i 0.856423 0.622228i
\(818\) 16.9559 + 12.3192i 0.592851 + 0.430731i
\(819\) −2.12387 6.53660i −0.0742140 0.228407i
\(820\) −1.60304 4.93366i −0.0559806 0.172291i
\(821\) 19.4618 + 14.1398i 0.679221 + 0.493483i 0.873099 0.487543i \(-0.162107\pi\)
−0.193878 + 0.981026i \(0.562107\pi\)
\(822\) 4.30835 3.13020i 0.150271 0.109178i
\(823\) 0.925820 2.84938i 0.0322720 0.0993231i −0.933623 0.358257i \(-0.883371\pi\)
0.965895 + 0.258934i \(0.0833712\pi\)
\(824\) 6.46277 0.225141
\(825\) 6.27245 11.1378i 0.218379 0.387770i
\(826\) −0.507652 −0.0176635
\(827\) −0.0102920 + 0.0316754i −0.000357886 + 0.00110146i −0.951235 0.308466i \(-0.900184\pi\)
0.950877 + 0.309568i \(0.100184\pi\)
\(828\) 1.85953 1.35102i 0.0646230 0.0469513i
\(829\) 7.49283 + 5.44386i 0.260237 + 0.189073i 0.710251 0.703948i \(-0.248581\pi\)
−0.450015 + 0.893021i \(0.648581\pi\)
\(830\) 0.592671 + 1.82405i 0.0205719 + 0.0633138i
\(831\) 6.48406 + 19.9559i 0.224930 + 0.692262i
\(832\) 5.56036 + 4.03984i 0.192771 + 0.140056i
\(833\) 5.72957 4.16277i 0.198518 0.144232i
\(834\) −5.55565 + 17.0985i −0.192376 + 0.592074i
\(835\) −22.7195 −0.786239
\(836\) −18.9039 3.80714i −0.653806 0.131673i
\(837\) 3.57812 0.123678
\(838\) 6.89381 21.2170i 0.238143 0.732928i
\(839\) 2.43698 1.77057i 0.0841338 0.0611268i −0.544923 0.838486i \(-0.683441\pi\)
0.629057 + 0.777359i \(0.283441\pi\)
\(840\) 0.866025 + 0.629204i 0.0298807 + 0.0217096i
\(841\) −4.29826 13.2287i −0.148216 0.456162i
\(842\) −4.58283 14.1045i −0.157935 0.486073i
\(843\) 9.50563 + 6.90624i 0.327391 + 0.237864i
\(844\) −17.6393 + 12.8157i −0.607171 + 0.441136i
\(845\) 11.3256 34.8567i 0.389614 1.19911i
\(846\) −10.1665 −0.349532
\(847\) −5.70265 9.40637i −0.195945 0.323207i
\(848\) −10.3016 −0.353757
\(849\) 4.29709 13.2251i 0.147476 0.453884i
\(850\) 22.0823 16.0438i 0.757418 0.550296i
\(851\) 6.06342 + 4.40534i 0.207851 + 0.151013i
\(852\) −4.39364 13.5222i −0.150523 0.463264i
\(853\) −12.0965 37.2293i −0.414177 1.27471i −0.912985 0.407993i \(-0.866229\pi\)
0.498808 0.866713i \(-0.333771\pi\)
\(854\) 6.46704 + 4.69858i 0.221298 + 0.160782i
\(855\) −5.03523 + 3.65831i −0.172201 + 0.125112i
\(856\) −2.05660 + 6.32956i −0.0702930 + 0.216340i
\(857\) −5.97666 −0.204159 −0.102079 0.994776i \(-0.532550\pi\)
−0.102079 + 0.994776i \(0.532550\pi\)
\(858\) −22.3464 4.50045i −0.762894 0.153643i
\(859\) −4.14359 −0.141378 −0.0706888 0.997498i \(-0.522520\pi\)
−0.0706888 + 0.997498i \(0.522520\pi\)
\(860\) −1.72150 + 5.29825i −0.0587028 + 0.180669i
\(861\) 3.92055 2.84845i 0.133612 0.0970748i
\(862\) 4.63484 + 3.36741i 0.157863 + 0.114694i
\(863\) 0.746156 + 2.29643i 0.0253994 + 0.0781715i 0.962953 0.269670i \(-0.0869147\pi\)
−0.937553 + 0.347842i \(0.886915\pi\)
\(864\) −0.309017 0.951057i −0.0105130 0.0323556i
\(865\) 15.4975 + 11.2596i 0.526931 + 0.382838i
\(866\) −3.76588 + 2.73607i −0.127970 + 0.0929755i
\(867\) 10.2460 31.5338i 0.347971 1.07095i
\(868\) 3.57812 0.121449
\(869\) 14.6144 25.9504i 0.495759 0.880307i
\(870\) −4.15839 −0.140983
\(871\) −8.05301 + 24.7846i −0.272866 + 0.839795i
\(872\) −10.8611 + 7.89102i −0.367802 + 0.267224i
\(873\) 13.5572 + 9.84989i 0.458842 + 0.333368i
\(874\) 4.12967 + 12.7098i 0.139688 + 0.429916i
\(875\) −2.92887 9.01413i −0.0990138 0.304733i
\(876\) 10.4174 + 7.56869i 0.351971 + 0.255722i
\(877\) 16.4440 11.9473i 0.555274 0.403430i −0.274452 0.961601i \(-0.588497\pi\)
0.829726 + 0.558171i \(0.188497\pi\)
\(878\) 0.929817 2.86168i 0.0313798 0.0965771i
\(879\) 1.37998 0.0465454
\(880\) 3.22775 1.47868i 0.108807 0.0498464i
\(881\) 33.4251 1.12612 0.563060 0.826416i \(-0.309624\pi\)
0.563060 + 0.826416i \(0.309624\pi\)
\(882\) −0.309017 + 0.951057i −0.0104051 + 0.0320237i
\(883\) 26.2444 19.0677i 0.883194 0.641678i −0.0509007 0.998704i \(-0.516209\pi\)
0.934094 + 0.357026i \(0.116209\pi\)
\(884\) −39.3792 28.6107i −1.32447 0.962281i
\(885\) 0.167927 + 0.516827i 0.00564482 + 0.0173730i
\(886\) −1.58528 4.87900i −0.0532586 0.163913i
\(887\) 7.37964 + 5.36162i 0.247784 + 0.180026i 0.704744 0.709462i \(-0.251062\pi\)
−0.456960 + 0.889487i \(0.651062\pi\)
\(888\) 2.63799 1.91661i 0.0885252 0.0643173i
\(889\) 3.91968 12.0635i 0.131462 0.404598i
\(890\) −6.67019 −0.223585
\(891\) 2.24551 + 2.44084i 0.0752274 + 0.0817712i
\(892\) −8.41774 −0.281847
\(893\) 18.2660 56.2170i 0.611249 1.88123i
\(894\) −8.47214 + 6.15537i −0.283351 + 0.205866i
\(895\) 11.0717 + 8.04409i 0.370088 + 0.268884i
\(896\) −0.309017 0.951057i −0.0103235 0.0317726i
\(897\) 4.88171 + 15.0244i 0.162996 + 0.501649i
\(898\) 3.03585 + 2.20568i 0.101308 + 0.0736043i
\(899\) −11.2451 + 8.17007i −0.375046 + 0.272487i
\(900\) −1.19098 + 3.66547i −0.0396994 + 0.122182i
\(901\) 72.9571 2.43055
\(902\) −1.85103 15.9656i −0.0616327 0.531598i
\(903\) −5.20419 −0.173184
\(904\) 4.01776 12.3654i 0.133629 0.411267i
\(905\) −2.20125 + 1.59930i −0.0731719 + 0.0531625i
\(906\) 4.14784 + 3.01358i 0.137803 + 0.100120i
\(907\) 0.253053 + 0.778816i 0.00840248 + 0.0258602i 0.955170 0.296058i \(-0.0956723\pi\)
−0.946767 + 0.321919i \(0.895672\pi\)
\(908\) 6.52968 + 20.0963i 0.216695 + 0.666919i
\(909\) 11.5742 + 8.40917i 0.383893 + 0.278915i
\(910\) −5.95218 + 4.32451i −0.197313 + 0.143356i
\(911\) −7.04494 + 21.6821i −0.233409 + 0.718360i 0.763919 + 0.645312i \(0.223273\pi\)
−0.997328 + 0.0730479i \(0.976727\pi\)
\(912\) 5.81419 0.192527
\(913\) 0.684357 + 5.90276i 0.0226489 + 0.195353i
\(914\) −21.6444 −0.715934
\(915\) 2.64426 8.13818i 0.0874164 0.269040i
\(916\) 5.02397 3.65013i 0.165997 0.120604i
\(917\) −0.229157 0.166492i −0.00756743 0.00549806i
\(918\) 2.18850 + 6.73551i 0.0722313 + 0.222305i
\(919\) 17.2494 + 53.0883i 0.569006 + 1.75122i 0.655738 + 0.754989i \(0.272358\pi\)
−0.0867314 + 0.996232i \(0.527642\pi\)
\(920\) −1.99056 1.44623i −0.0656268 0.0476807i
\(921\) 12.9610 9.41668i 0.427078 0.310290i
\(922\) −1.53508 + 4.72448i −0.0505550 + 0.155592i
\(923\) 97.7208 3.21652
\(924\) 2.24551 + 2.44084i 0.0738718 + 0.0802977i
\(925\) −12.5672 −0.413207
\(926\) 4.42677 13.6242i 0.145473 0.447719i
\(927\) 5.22849 3.79872i 0.171726 0.124766i
\(928\) 3.14275 + 2.28334i 0.103166 + 0.0749544i
\(929\) 9.99045 + 30.7474i 0.327776 + 1.00879i 0.970172 + 0.242418i \(0.0779405\pi\)
−0.642396 + 0.766373i \(0.722059\pi\)
\(930\) −1.18361 3.64279i −0.0388122 0.119452i
\(931\) −4.70378 3.41749i −0.154160 0.112004i
\(932\) 15.8590 11.5222i 0.519478 0.377423i
\(933\) −0.460732 + 1.41799i −0.0150837 + 0.0464228i
\(934\) −6.04754 −0.197881
\(935\) −22.8594 + 10.4722i −0.747581 + 0.342479i
\(936\) 6.87298 0.224650
\(937\) 3.69697 11.3781i 0.120775 0.371707i −0.872333 0.488913i \(-0.837394\pi\)
0.993108 + 0.117206i \(0.0373937\pi\)
\(938\) 3.06753 2.22869i 0.100158 0.0727692i
\(939\) −5.16345 3.75147i −0.168503 0.122424i
\(940\) 3.36301 + 10.3503i 0.109689 + 0.337588i
\(941\) −3.75840 11.5672i −0.122520 0.377079i 0.870921 0.491423i \(-0.163523\pi\)
−0.993441 + 0.114345i \(0.963523\pi\)
\(942\) −8.60503 6.25192i −0.280367 0.203699i
\(943\) −9.01139 + 6.54716i −0.293451 + 0.213205i
\(944\) 0.156873 0.482806i 0.00510579 0.0157140i
\(945\) 1.07047 0.0348223
\(946\) −8.46968 + 15.0394i −0.275373 + 0.488973i
\(947\) 0.662536 0.0215295 0.0107648 0.999942i \(-0.496573\pi\)
0.0107648 + 0.999942i \(0.496573\pi\)
\(948\) −2.77491 + 8.54029i −0.0901248 + 0.277376i
\(949\) −71.5986 + 52.0195i −2.32419 + 1.68862i
\(950\) −18.1288 13.1714i −0.588177 0.427336i
\(951\) 1.40776 + 4.33264i 0.0456497 + 0.140495i
\(952\) 2.18850 + 6.73551i 0.0709297 + 0.218299i
\(953\) −43.6292 31.6985i −1.41329 1.02681i −0.992834 0.119501i \(-0.961871\pi\)
−0.420455 0.907314i \(-0.638129\pi\)
\(954\) −8.33414 + 6.05511i −0.269828 + 0.196041i
\(955\) 2.51927 7.75353i 0.0815218 0.250898i
\(956\) 13.2733 0.429288
\(957\) −12.6303 2.54368i −0.408281 0.0822255i
\(958\) −4.51256 −0.145794
\(959\) 1.64564 5.06477i 0.0531406 0.163550i
\(960\) −0.866025 + 0.629204i −0.0279508 + 0.0203075i
\(961\) 14.7217 + 10.6960i 0.474895 + 0.345031i
\(962\) 6.92538 + 21.3141i 0.223283 + 0.687195i
\(963\) 2.05660 + 6.32956i 0.0662729 + 0.203967i
\(964\) 19.2587 + 13.9923i 0.620281 + 0.450661i
\(965\) 11.6420 8.45844i 0.374770 0.272287i
\(966\) 0.710276 2.18600i 0.0228527 0.0703335i
\(967\) 55.7169 1.79173 0.895867 0.444322i \(-0.146555\pi\)
0.895867 + 0.444322i \(0.146555\pi\)
\(968\) 10.7082 2.51682i 0.344175 0.0808936i
\(969\) −41.1769 −1.32279
\(970\) 5.54330 17.0605i 0.177985 0.547780i
\(971\) −22.1000 + 16.0566i −0.709223 + 0.515281i −0.882923 0.469518i \(-0.844428\pi\)
0.173700 + 0.984799i \(0.444428\pi\)
\(972\) −0.809017 0.587785i −0.0259492 0.0188532i
\(973\) 5.55565 + 17.0985i 0.178106 + 0.548154i
\(974\) 0.218876 + 0.673631i 0.00701324 + 0.0215845i
\(975\) −21.4302 15.5699i −0.686316 0.498637i
\(976\) −6.46704 + 4.69858i −0.207005 + 0.150398i
\(977\) −4.78177 + 14.7168i −0.152982 + 0.470831i −0.997951 0.0639848i \(-0.979619\pi\)
0.844969 + 0.534816i \(0.179619\pi\)
\(978\) −0.472136 −0.0150972
\(979\) −20.2595 4.08014i −0.647495 0.130402i
\(980\) 1.07047 0.0341948
\(981\) −4.14856 + 12.7679i −0.132453 + 0.407649i
\(982\) −32.8358 + 23.8566i −1.04783 + 0.761294i
\(983\) 19.7819 + 14.3724i 0.630944 + 0.458408i 0.856727 0.515770i \(-0.172494\pi\)
−0.225783 + 0.974178i \(0.572494\pi\)
\(984\) 1.49752 + 4.60888i 0.0477391 + 0.146926i
\(985\) −2.30691 7.09995i −0.0735044 0.226223i
\(986\) −22.2574 16.1709i −0.708819 0.514987i
\(987\) −8.22489 + 5.97573i −0.261801 + 0.190210i
\(988\) −12.3486 + 38.0050i −0.392860 + 1.20910i
\(989\) 11.9618 0.380364
\(990\) 1.74216 3.09350i 0.0553694 0.0983180i
\(991\) 59.1364 1.87853 0.939264 0.343194i \(-0.111509\pi\)
0.939264 + 0.343194i \(0.111509\pi\)
\(992\) −1.10570 + 3.40299i −0.0351060 + 0.108045i
\(993\) −7.73499 + 5.61980i −0.245463 + 0.178339i
\(994\) −11.5027 8.35719i −0.364843 0.265074i
\(995\) 8.15707 + 25.1049i 0.258596 + 0.795878i
\(996\) −0.553656 1.70398i −0.0175433 0.0539927i
\(997\) 13.5068 + 9.81323i 0.427763 + 0.310788i 0.780754 0.624839i \(-0.214835\pi\)
−0.352991 + 0.935627i \(0.614835\pi\)
\(998\) 4.72017 3.42941i 0.149415 0.108556i
\(999\) 1.00762 3.10115i 0.0318798 0.0981159i
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 462.2.j.g.295.2 8
11.4 even 5 5082.2.a.bz.1.3 4
11.5 even 5 inner 462.2.j.g.379.2 yes 8
11.7 odd 10 5082.2.a.ce.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.j.g.295.2 8 1.1 even 1 trivial
462.2.j.g.379.2 yes 8 11.5 even 5 inner
5082.2.a.bz.1.3 4 11.4 even 5
5082.2.a.ce.1.3 4 11.7 odd 10