Properties

Label 74.3.g.b.51.3
Level $74$
Weight $3$
Character 74.51
Analytic conductor $2.016$
Analytic rank $0$
Dimension $12$
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] = [74,3,Mod(23,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.23");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 74.g (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.01635395627\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 82x^{10} + 2505x^{8} + 34456x^{6} + 196096x^{4} + 262464x^{2} + 69696 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 51.3
Root \(4.53867i\) of defining polynomial
Character \(\chi\) \(=\) 74.51
Dual form 74.3.g.b.45.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36603 + 0.366025i) q^{2} +(3.93060 - 2.26933i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.866025 + 0.232051i) q^{5} +(-4.53867 + 4.53867i) q^{6} +(-2.63849 - 4.57000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(5.79976 - 10.0455i) q^{9} +O(q^{10})\) \(q+(-1.36603 + 0.366025i) q^{2} +(3.93060 - 2.26933i) q^{3} +(1.73205 - 1.00000i) q^{4} +(0.866025 + 0.232051i) q^{5} +(-4.53867 + 4.53867i) q^{6} +(-2.63849 - 4.57000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(5.79976 - 10.0455i) q^{9} -1.26795 q^{10} +2.58423i q^{11} +(4.53867 - 7.86120i) q^{12} +(14.9302 + 4.00055i) q^{13} +(5.27698 + 5.27698i) q^{14} +(3.93060 - 1.05320i) q^{15} +(2.00000 - 3.46410i) q^{16} +(0.861003 + 3.21331i) q^{17} +(-4.24572 + 15.8452i) q^{18} +(-6.00993 - 1.61036i) q^{19} +(1.73205 - 0.464102i) q^{20} +(-20.7417 - 11.9752i) q^{21} +(-0.945893 - 3.53012i) q^{22} +(-31.8083 + 31.8083i) q^{23} +(-3.32254 + 12.3999i) q^{24} +(-20.9545 - 12.0981i) q^{25} -21.8594 q^{26} -11.7983i q^{27} +(-9.13999 - 5.27698i) q^{28} +(35.8477 + 35.8477i) q^{29} +(-4.98380 + 2.87740i) q^{30} +(-17.4160 - 17.4160i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(5.86448 + 10.1576i) q^{33} +(-2.35230 - 4.07431i) q^{34} +(-1.22453 - 4.57000i) q^{35} -23.1990i q^{36} +(-22.3381 + 29.4959i) q^{37} +8.79915 q^{38} +(67.7634 - 18.1572i) q^{39} +(-2.19615 + 1.26795i) q^{40} +(-21.0885 + 12.1755i) q^{41} +(32.7169 + 8.76647i) q^{42} +(40.1678 - 40.1678i) q^{43} +(2.58423 + 4.47601i) q^{44} +(7.35380 - 7.35380i) q^{45} +(31.8083 - 55.0936i) q^{46} +14.1710 q^{47} -18.1547i q^{48} +(10.5768 - 18.3195i) q^{49} +(33.0526 + 8.85641i) q^{50} +(10.6763 + 10.6763i) q^{51} +(29.8605 - 8.00109i) q^{52} +(-26.9625 + 46.7005i) q^{53} +(4.31849 + 16.1168i) q^{54} +(-0.599672 + 2.23801i) q^{55} +(14.4170 + 3.86302i) q^{56} +(-27.2771 + 7.30888i) q^{57} +(-62.0901 - 35.8477i) q^{58} +(-21.5652 - 80.4823i) q^{59} +(5.75480 - 5.75480i) q^{60} +(-13.1162 + 48.9504i) q^{61} +(30.1654 + 17.4160i) q^{62} -61.2104 q^{63} -8.00000i q^{64} +(12.0016 + 6.92915i) q^{65} +(-11.7290 - 11.7290i) q^{66} +(23.8908 - 13.7933i) q^{67} +(4.70461 + 4.70461i) q^{68} +(-52.8421 + 197.209i) q^{69} +(3.34547 + 5.79452i) q^{70} +(-45.4136 - 78.6586i) q^{71} +(8.49143 + 31.6905i) q^{72} -111.089i q^{73} +(19.7181 - 48.4685i) q^{74} -109.818 q^{75} +(-12.0199 + 3.22071i) q^{76} +(11.8099 - 6.81845i) q^{77} +(-85.9206 + 49.6063i) q^{78} +(108.969 + 29.1982i) q^{79} +(2.53590 - 2.53590i) q^{80} +(25.4235 + 44.0347i) q^{81} +(24.3509 - 24.3509i) q^{82} +(1.27819 - 2.21389i) q^{83} -47.9009 q^{84} +2.98260i q^{85} +(-40.1678 + 69.5727i) q^{86} +(222.254 + 59.5527i) q^{87} +(-5.16845 - 5.16845i) q^{88} +(129.892 - 34.8046i) q^{89} +(-7.35380 + 12.7372i) q^{90} +(-21.1108 - 78.7866i) q^{91} +(-23.2853 + 86.9019i) q^{92} +(-107.978 - 28.9326i) q^{93} +(-19.3579 + 5.18694i) q^{94} +(-4.83107 - 2.78922i) q^{95} +(6.64507 + 24.7997i) q^{96} +(-50.8869 + 50.8869i) q^{97} +(-7.74272 + 28.8962i) q^{98} +(25.9598 + 14.9879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9} - 36 q^{10} - 4 q^{12} + 16 q^{13} + 16 q^{14} + 24 q^{16} + 40 q^{17} + 28 q^{18} - 26 q^{19} + 66 q^{21} + 4 q^{22} - 80 q^{23} - 4 q^{24} - 54 q^{25} - 124 q^{26} - 12 q^{28} + 16 q^{29} - 6 q^{30} - 32 q^{31} + 24 q^{32} - 20 q^{33} - 10 q^{34} + 12 q^{35} - 148 q^{37} + 92 q^{38} + 216 q^{39} + 36 q^{40} + 66 q^{41} - 46 q^{42} + 152 q^{43} - 16 q^{44} + 84 q^{45} + 80 q^{46} - 112 q^{47} - 160 q^{49} + 168 q^{50} - 446 q^{51} + 32 q^{52} + 74 q^{53} + 230 q^{54} + 28 q^{56} + 50 q^{57} + 84 q^{58} - 114 q^{59} - 12 q^{60} + 448 q^{61} - 204 q^{62} - 784 q^{63} - 138 q^{65} + 40 q^{66} + 468 q^{67} + 20 q^{68} - 278 q^{69} + 18 q^{70} + 116 q^{71} - 56 q^{72} - 2 q^{74} + 76 q^{75} - 52 q^{76} + 60 q^{77} - 366 q^{78} + 114 q^{79} + 72 q^{80} + 14 q^{81} + 128 q^{82} - 20 q^{83} - 80 q^{84} - 152 q^{86} + 770 q^{87} + 32 q^{88} + 340 q^{89} - 84 q^{90} + 792 q^{91} + 68 q^{92} - 498 q^{93} + 20 q^{94} + 60 q^{95} + 8 q^{96} - 356 q^{97} - 160 q^{98} - 348 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 0.366025i −0.683013 + 0.183013i
\(3\) 3.93060 2.26933i 1.31020 0.756445i 0.328072 0.944653i \(-0.393601\pi\)
0.982129 + 0.188208i \(0.0602679\pi\)
\(4\) 1.73205 1.00000i 0.433013 0.250000i
\(5\) 0.866025 + 0.232051i 0.173205 + 0.0464102i 0.344379 0.938831i \(-0.388089\pi\)
−0.171174 + 0.985241i \(0.554756\pi\)
\(6\) −4.53867 + 4.53867i −0.756445 + 0.756445i
\(7\) −2.63849 4.57000i −0.376927 0.652857i 0.613686 0.789550i \(-0.289686\pi\)
−0.990613 + 0.136693i \(0.956353\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 5.79976 10.0455i 0.644417 1.11616i
\(10\) −1.26795 −0.126795
\(11\) 2.58423i 0.234930i 0.993077 + 0.117465i \(0.0374768\pi\)
−0.993077 + 0.117465i \(0.962523\pi\)
\(12\) 4.53867 7.86120i 0.378222 0.655100i
\(13\) 14.9302 + 4.00055i 1.14848 + 0.307734i 0.782356 0.622832i \(-0.214018\pi\)
0.366124 + 0.930566i \(0.380684\pi\)
\(14\) 5.27698 + 5.27698i 0.376927 + 0.376927i
\(15\) 3.93060 1.05320i 0.262040 0.0702134i
\(16\) 2.00000 3.46410i 0.125000 0.216506i
\(17\) 0.861003 + 3.21331i 0.0506472 + 0.189018i 0.986615 0.163068i \(-0.0521391\pi\)
−0.935968 + 0.352086i \(0.885472\pi\)
\(18\) −4.24572 + 15.8452i −0.235873 + 0.880291i
\(19\) −6.00993 1.61036i −0.316312 0.0847556i 0.0971699 0.995268i \(-0.469021\pi\)
−0.413482 + 0.910512i \(0.635688\pi\)
\(20\) 1.73205 0.464102i 0.0866025 0.0232051i
\(21\) −20.7417 11.9752i −0.987700 0.570249i
\(22\) −0.945893 3.53012i −0.0429951 0.160460i
\(23\) −31.8083 + 31.8083i −1.38297 + 1.38297i −0.543671 + 0.839298i \(0.682966\pi\)
−0.839298 + 0.543671i \(0.817034\pi\)
\(24\) −3.32254 + 12.3999i −0.138439 + 0.516661i
\(25\) −20.9545 12.0981i −0.838179 0.483923i
\(26\) −21.8594 −0.840746
\(27\) 11.7983i 0.436975i
\(28\) −9.13999 5.27698i −0.326428 0.188463i
\(29\) 35.8477 + 35.8477i 1.23613 + 1.23613i 0.961570 + 0.274559i \(0.0885317\pi\)
0.274559 + 0.961570i \(0.411468\pi\)
\(30\) −4.98380 + 2.87740i −0.166127 + 0.0959134i
\(31\) −17.4160 17.4160i −0.561806 0.561806i 0.368014 0.929820i \(-0.380038\pi\)
−0.929820 + 0.368014i \(0.880038\pi\)
\(32\) −1.46410 + 5.46410i −0.0457532 + 0.170753i
\(33\) 5.86448 + 10.1576i 0.177711 + 0.307805i
\(34\) −2.35230 4.07431i −0.0691854 0.119833i
\(35\) −1.22453 4.57000i −0.0349865 0.130571i
\(36\) 23.1990i 0.644417i
\(37\) −22.3381 + 29.4959i −0.603732 + 0.797187i
\(38\) 8.79915 0.231557
\(39\) 67.7634 18.1572i 1.73752 0.465568i
\(40\) −2.19615 + 1.26795i −0.0549038 + 0.0316987i
\(41\) −21.0885 + 12.1755i −0.514354 + 0.296963i −0.734622 0.678477i \(-0.762640\pi\)
0.220267 + 0.975440i \(0.429307\pi\)
\(42\) 32.7169 + 8.76647i 0.778974 + 0.208726i
\(43\) 40.1678 40.1678i 0.934136 0.934136i −0.0638252 0.997961i \(-0.520330\pi\)
0.997961 + 0.0638252i \(0.0203300\pi\)
\(44\) 2.58423 + 4.47601i 0.0587324 + 0.101728i
\(45\) 7.35380 7.35380i 0.163418 0.163418i
\(46\) 31.8083 55.0936i 0.691485 1.19769i
\(47\) 14.1710 0.301510 0.150755 0.988571i \(-0.451830\pi\)
0.150755 + 0.988571i \(0.451830\pi\)
\(48\) 18.1547i 0.378222i
\(49\) 10.5768 18.3195i 0.215852 0.373867i
\(50\) 33.0526 + 8.85641i 0.661051 + 0.177128i
\(51\) 10.6763 + 10.6763i 0.209340 + 0.209340i
\(52\) 29.8605 8.00109i 0.574240 0.153867i
\(53\) −26.9625 + 46.7005i −0.508727 + 0.881141i 0.491222 + 0.871034i \(0.336550\pi\)
−0.999949 + 0.0101063i \(0.996783\pi\)
\(54\) 4.31849 + 16.1168i 0.0799720 + 0.298460i
\(55\) −0.599672 + 2.23801i −0.0109031 + 0.0406910i
\(56\) 14.4170 + 3.86302i 0.257446 + 0.0689824i
\(57\) −27.2771 + 7.30888i −0.478546 + 0.128226i
\(58\) −62.0901 35.8477i −1.07052 0.618064i
\(59\) −21.5652 80.4823i −0.365511 1.36411i −0.866727 0.498783i \(-0.833780\pi\)
0.501216 0.865322i \(-0.332886\pi\)
\(60\) 5.75480 5.75480i 0.0959134 0.0959134i
\(61\) −13.1162 + 48.9504i −0.215020 + 0.802465i 0.771140 + 0.636666i \(0.219687\pi\)
−0.986160 + 0.165799i \(0.946980\pi\)
\(62\) 30.1654 + 17.4160i 0.486538 + 0.280903i
\(63\) −61.2104 −0.971593
\(64\) 8.00000i 0.125000i
\(65\) 12.0016 + 6.92915i 0.184641 + 0.106602i
\(66\) −11.7290 11.7290i −0.177711 0.177711i
\(67\) 23.8908 13.7933i 0.356579 0.205871i −0.311000 0.950410i \(-0.600664\pi\)
0.667579 + 0.744539i \(0.267331\pi\)
\(68\) 4.70461 + 4.70461i 0.0691854 + 0.0691854i
\(69\) −52.8421 + 197.209i −0.765828 + 2.85811i
\(70\) 3.34547 + 5.79452i 0.0477924 + 0.0827789i
\(71\) −45.4136 78.6586i −0.639628 1.10787i −0.985514 0.169591i \(-0.945755\pi\)
0.345887 0.938276i \(-0.387578\pi\)
\(72\) 8.49143 + 31.6905i 0.117937 + 0.440145i
\(73\) 111.089i 1.52177i −0.648888 0.760884i \(-0.724766\pi\)
0.648888 0.760884i \(-0.275234\pi\)
\(74\) 19.7181 48.4685i 0.266461 0.654980i
\(75\) −109.818 −1.46424
\(76\) −12.0199 + 3.22071i −0.158156 + 0.0423778i
\(77\) 11.8099 6.81845i 0.153375 0.0885514i
\(78\) −85.9206 + 49.6063i −1.10155 + 0.635978i
\(79\) 108.969 + 29.1982i 1.37936 + 0.369597i 0.870887 0.491483i \(-0.163545\pi\)
0.508469 + 0.861080i \(0.330212\pi\)
\(80\) 2.53590 2.53590i 0.0316987 0.0316987i
\(81\) 25.4235 + 44.0347i 0.313870 + 0.543638i
\(82\) 24.3509 24.3509i 0.296963 0.296963i
\(83\) 1.27819 2.21389i 0.0153998 0.0266733i −0.858223 0.513277i \(-0.828431\pi\)
0.873623 + 0.486604i \(0.161765\pi\)
\(84\) −47.9009 −0.570249
\(85\) 2.98260i 0.0350894i
\(86\) −40.1678 + 69.5727i −0.467068 + 0.808985i
\(87\) 222.254 + 59.5527i 2.55464 + 0.684514i
\(88\) −5.16845 5.16845i −0.0587324 0.0587324i
\(89\) 129.892 34.8046i 1.45947 0.391063i 0.560161 0.828384i \(-0.310739\pi\)
0.899305 + 0.437321i \(0.144073\pi\)
\(90\) −7.35380 + 12.7372i −0.0817089 + 0.141524i
\(91\) −21.1108 78.7866i −0.231987 0.865786i
\(92\) −23.2853 + 86.9019i −0.253101 + 0.944586i
\(93\) −107.978 28.9326i −1.16105 0.311104i
\(94\) −19.3579 + 5.18694i −0.205935 + 0.0551802i
\(95\) −4.83107 2.78922i −0.0508534 0.0293602i
\(96\) 6.64507 + 24.7997i 0.0692195 + 0.258331i
\(97\) −50.8869 + 50.8869i −0.524607 + 0.524607i −0.918959 0.394352i \(-0.870969\pi\)
0.394352 + 0.918959i \(0.370969\pi\)
\(98\) −7.74272 + 28.8962i −0.0790074 + 0.294859i
\(99\) 25.9598 + 14.9879i 0.262220 + 0.151393i
\(100\) −48.3923 −0.483923
\(101\) 111.442i 1.10339i −0.834046 0.551695i \(-0.813981\pi\)
0.834046 0.551695i \(-0.186019\pi\)
\(102\) −18.4919 10.6763i −0.181294 0.104670i
\(103\) −93.0692 93.0692i −0.903584 0.903584i 0.0921599 0.995744i \(-0.470623\pi\)
−0.995744 + 0.0921599i \(0.970623\pi\)
\(104\) −37.8616 + 21.8594i −0.364054 + 0.210186i
\(105\) −15.1840 15.1840i −0.144609 0.144609i
\(106\) 19.7379 73.6630i 0.186207 0.694934i
\(107\) −24.5884 42.5883i −0.229798 0.398022i 0.727950 0.685630i \(-0.240473\pi\)
−0.957748 + 0.287608i \(0.907140\pi\)
\(108\) −11.7983 20.4353i −0.109244 0.189216i
\(109\) 15.9102 + 59.3778i 0.145966 + 0.544751i 0.999711 + 0.0240595i \(0.00765911\pi\)
−0.853745 + 0.520691i \(0.825674\pi\)
\(110\) 3.27667i 0.0297879i
\(111\) −20.8660 + 166.629i −0.187982 + 1.50117i
\(112\) −21.1079 −0.188463
\(113\) −97.3431 + 26.0830i −0.861443 + 0.230823i −0.662384 0.749164i \(-0.730455\pi\)
−0.199059 + 0.979987i \(0.563789\pi\)
\(114\) 34.5860 19.9682i 0.303386 0.175160i
\(115\) −34.9279 + 20.1657i −0.303721 + 0.175353i
\(116\) 97.9378 + 26.2424i 0.844292 + 0.226227i
\(117\) 126.779 126.779i 1.08358 1.08358i
\(118\) 58.9171 + 102.047i 0.499297 + 0.864809i
\(119\) 12.4131 12.4131i 0.104311 0.104311i
\(120\) −5.75480 + 9.96761i −0.0479567 + 0.0830634i
\(121\) 114.322 0.944808
\(122\) 71.6683i 0.587445i
\(123\) −55.2604 + 95.7139i −0.449272 + 0.778161i
\(124\) −47.5814 12.7494i −0.383721 0.102818i
\(125\) −31.1891 31.1891i −0.249513 0.249513i
\(126\) 83.6149 22.4046i 0.663611 0.177814i
\(127\) −52.9016 + 91.6282i −0.416548 + 0.721482i −0.995590 0.0938161i \(-0.970093\pi\)
0.579042 + 0.815298i \(0.303427\pi\)
\(128\) 2.92820 + 10.9282i 0.0228766 + 0.0853766i
\(129\) 66.7296 249.038i 0.517283 1.93053i
\(130\) −18.9308 5.07249i −0.145621 0.0390192i
\(131\) 136.790 36.6528i 1.04420 0.279792i 0.304346 0.952561i \(-0.401562\pi\)
0.739852 + 0.672769i \(0.234895\pi\)
\(132\) 20.3151 + 11.7290i 0.153903 + 0.0888557i
\(133\) 8.49782 + 31.7143i 0.0638934 + 0.238453i
\(134\) −27.5867 + 27.5867i −0.205871 + 0.205871i
\(135\) 2.73781 10.2177i 0.0202801 0.0756863i
\(136\) −8.14862 4.70461i −0.0599163 0.0345927i
\(137\) −76.4553 −0.558068 −0.279034 0.960281i \(-0.590014\pi\)
−0.279034 + 0.960281i \(0.590014\pi\)
\(138\) 288.735i 2.09228i
\(139\) 39.4004 + 22.7479i 0.283456 + 0.163654i 0.634987 0.772523i \(-0.281005\pi\)
−0.351531 + 0.936176i \(0.614339\pi\)
\(140\) −6.69094 6.69094i −0.0477924 0.0477924i
\(141\) 55.7005 32.1587i 0.395039 0.228076i
\(142\) 90.8271 + 90.8271i 0.639628 + 0.639628i
\(143\) −10.3383 + 38.5831i −0.0722960 + 0.269812i
\(144\) −23.1990 40.1819i −0.161104 0.279041i
\(145\) 22.7266 + 39.3635i 0.156735 + 0.271473i
\(146\) 40.6614 + 151.750i 0.278503 + 1.03939i
\(147\) 96.0088i 0.653121i
\(148\) −9.19478 + 73.4265i −0.0621269 + 0.496125i
\(149\) 43.2363 0.290177 0.145088 0.989419i \(-0.453653\pi\)
0.145088 + 0.989419i \(0.453653\pi\)
\(150\) 150.015 40.1963i 1.00010 0.267975i
\(151\) −35.9045 + 20.7295i −0.237778 + 0.137281i −0.614155 0.789185i \(-0.710503\pi\)
0.376377 + 0.926467i \(0.377170\pi\)
\(152\) 15.2406 8.79915i 0.100267 0.0578892i
\(153\) 37.2728 + 9.98721i 0.243613 + 0.0652759i
\(154\) −13.6369 + 13.6369i −0.0885514 + 0.0885514i
\(155\) −11.0413 19.1241i −0.0712342 0.123381i
\(156\) 99.2125 99.2125i 0.635978 0.635978i
\(157\) 65.0007 112.585i 0.414017 0.717099i −0.581307 0.813684i \(-0.697459\pi\)
0.995325 + 0.0965850i \(0.0307920\pi\)
\(158\) −159.542 −1.00976
\(159\) 244.748i 1.53929i
\(160\) −2.53590 + 4.39230i −0.0158494 + 0.0274519i
\(161\) 229.290 + 61.4380i 1.42416 + 0.381602i
\(162\) −50.8469 50.8469i −0.313870 0.313870i
\(163\) −137.502 + 36.8436i −0.843572 + 0.226035i −0.654626 0.755953i \(-0.727174\pi\)
−0.188946 + 0.981987i \(0.560507\pi\)
\(164\) −24.3509 + 42.1771i −0.148481 + 0.257177i
\(165\) 2.72171 + 10.1576i 0.0164952 + 0.0615610i
\(166\) −0.935698 + 3.49207i −0.00563674 + 0.0210366i
\(167\) −272.664 73.0601i −1.63272 0.437486i −0.678016 0.735047i \(-0.737160\pi\)
−0.954703 + 0.297561i \(0.903827\pi\)
\(168\) 65.4339 17.5329i 0.389487 0.104363i
\(169\) 60.5495 + 34.9583i 0.358281 + 0.206854i
\(170\) −1.09171 4.07431i −0.00642181 0.0239665i
\(171\) −51.0330 + 51.0330i −0.298438 + 0.298438i
\(172\) 29.4049 109.741i 0.170959 0.638027i
\(173\) −130.152 75.1434i −0.752325 0.434355i 0.0742087 0.997243i \(-0.476357\pi\)
−0.826533 + 0.562888i \(0.809690\pi\)
\(174\) −325.402 −1.87013
\(175\) 127.683i 0.729615i
\(176\) 8.95203 + 5.16845i 0.0508638 + 0.0293662i
\(177\) −267.405 267.405i −1.51076 1.51076i
\(178\) −164.697 + 95.0879i −0.925264 + 0.534202i
\(179\) −47.9819 47.9819i −0.268055 0.268055i 0.560261 0.828316i \(-0.310701\pi\)
−0.828316 + 0.560261i \(0.810701\pi\)
\(180\) 5.38335 20.0909i 0.0299075 0.111616i
\(181\) 102.624 + 177.749i 0.566981 + 0.982040i 0.996862 + 0.0791548i \(0.0252221\pi\)
−0.429881 + 0.902886i \(0.641445\pi\)
\(182\) 57.6758 + 99.8974i 0.316900 + 0.548887i
\(183\) 59.5302 + 222.170i 0.325301 + 1.21404i
\(184\) 127.233i 0.691485i
\(185\) −26.1899 + 20.3607i −0.141567 + 0.110058i
\(186\) 158.091 0.849951
\(187\) −8.30391 + 2.22503i −0.0444060 + 0.0118985i
\(188\) 24.5449 14.1710i 0.130558 0.0753775i
\(189\) −53.9183 + 31.1298i −0.285282 + 0.164708i
\(190\) 7.62029 + 2.04185i 0.0401068 + 0.0107466i
\(191\) −63.0903 + 63.0903i −0.330316 + 0.330316i −0.852706 0.522391i \(-0.825040\pi\)
0.522391 + 0.852706i \(0.325040\pi\)
\(192\) −18.1547 31.4448i −0.0945556 0.163775i
\(193\) −222.820 + 222.820i −1.15451 + 1.15451i −0.168866 + 0.985639i \(0.554011\pi\)
−0.985639 + 0.168866i \(0.945989\pi\)
\(194\) 50.8869 88.1387i 0.262304 0.454323i
\(195\) 62.8982 0.322555
\(196\) 42.3070i 0.215852i
\(197\) 38.6001 66.8573i 0.195940 0.339377i −0.751269 0.659997i \(-0.770558\pi\)
0.947208 + 0.320619i \(0.103891\pi\)
\(198\) −40.9477 10.9719i −0.206806 0.0554136i
\(199\) 119.311 + 119.311i 0.599552 + 0.599552i 0.940193 0.340641i \(-0.110644\pi\)
−0.340641 + 0.940193i \(0.610644\pi\)
\(200\) 66.1051 17.7128i 0.330526 0.0885641i
\(201\) 62.6034 108.432i 0.311460 0.539464i
\(202\) 40.7907 + 152.233i 0.201934 + 0.753629i
\(203\) 69.2402 258.408i 0.341085 1.27295i
\(204\) 29.1683 + 7.81561i 0.142982 + 0.0383118i
\(205\) −21.0885 + 5.65066i −0.102871 + 0.0275642i
\(206\) 161.201 + 93.0692i 0.782527 + 0.451792i
\(207\) 135.049 + 504.010i 0.652411 + 2.43483i
\(208\) 43.7188 43.7188i 0.210186 0.210186i
\(209\) 4.16153 15.5310i 0.0199116 0.0743112i
\(210\) 26.2994 + 15.1840i 0.125235 + 0.0723047i
\(211\) −137.533 −0.651815 −0.325907 0.945402i \(-0.605670\pi\)
−0.325907 + 0.945402i \(0.605670\pi\)
\(212\) 107.850i 0.508727i
\(213\) −357.005 206.117i −1.67608 0.967686i
\(214\) 49.1768 + 49.1768i 0.229798 + 0.229798i
\(215\) 44.1074 25.4654i 0.205150 0.118444i
\(216\) 23.5967 + 23.5967i 0.109244 + 0.109244i
\(217\) −33.6391 + 125.543i −0.155019 + 0.578539i
\(218\) −43.4676 75.2881i −0.199393 0.345358i
\(219\) −252.098 436.647i −1.15113 1.99382i
\(220\) 1.19934 + 4.47601i 0.00545156 + 0.0203455i
\(221\) 51.4199i 0.232669i
\(222\) −32.4871 235.257i −0.146338 1.05972i
\(223\) 413.121 1.85256 0.926280 0.376835i \(-0.122988\pi\)
0.926280 + 0.376835i \(0.122988\pi\)
\(224\) 28.8339 7.72603i 0.128723 0.0344912i
\(225\) −243.062 + 140.332i −1.08027 + 0.623697i
\(226\) 123.426 71.2601i 0.546133 0.315310i
\(227\) −58.6106 15.7047i −0.258196 0.0691835i 0.127399 0.991852i \(-0.459337\pi\)
−0.385595 + 0.922668i \(0.626004\pi\)
\(228\) −39.9364 + 39.9364i −0.175160 + 0.175160i
\(229\) −193.773 335.624i −0.846169 1.46561i −0.884602 0.466346i \(-0.845570\pi\)
0.0384334 0.999261i \(-0.487763\pi\)
\(230\) 40.3313 40.3313i 0.175353 0.175353i
\(231\) 30.9467 53.6013i 0.133968 0.232040i
\(232\) −143.391 −0.618064
\(233\) 300.991i 1.29181i 0.763420 + 0.645903i \(0.223519\pi\)
−0.763420 + 0.645903i \(0.776481\pi\)
\(234\) −126.779 + 219.588i −0.541791 + 0.938410i
\(235\) 12.2724 + 3.28839i 0.0522231 + 0.0139931i
\(236\) −117.834 117.834i −0.499297 0.499297i
\(237\) 494.575 132.521i 2.08681 0.559160i
\(238\) −12.4131 + 21.5000i −0.0521557 + 0.0903363i
\(239\) −27.4484 102.439i −0.114847 0.428614i 0.884429 0.466676i \(-0.154548\pi\)
−0.999275 + 0.0380612i \(0.987882\pi\)
\(240\) 4.21281 15.7224i 0.0175534 0.0655100i
\(241\) 154.225 + 41.3245i 0.639938 + 0.171471i 0.564175 0.825655i \(-0.309194\pi\)
0.0757627 + 0.997126i \(0.475861\pi\)
\(242\) −156.166 + 41.8447i −0.645316 + 0.172912i
\(243\) 291.818 + 168.481i 1.20090 + 0.693338i
\(244\) 26.2324 + 97.9008i 0.107510 + 0.401233i
\(245\) 13.4108 13.4108i 0.0547379 0.0547379i
\(246\) 40.4534 150.974i 0.164445 0.613717i
\(247\) −83.2875 48.0860i −0.337196 0.194680i
\(248\) 69.6640 0.280903
\(249\) 11.6025i 0.0465965i
\(250\) 54.0211 + 31.1891i 0.216084 + 0.124756i
\(251\) −171.928 171.928i −0.684970 0.684970i 0.276145 0.961116i \(-0.410943\pi\)
−0.961116 + 0.276145i \(0.910943\pi\)
\(252\) −106.019 + 61.2104i −0.420712 + 0.242898i
\(253\) −82.1999 82.1999i −0.324901 0.324901i
\(254\) 38.7266 144.530i 0.152467 0.569015i
\(255\) 6.76852 + 11.7234i 0.0265432 + 0.0459742i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 1.31699 + 4.91508i 0.00512448 + 0.0191248i 0.968441 0.249244i \(-0.0801821\pi\)
−0.963316 + 0.268369i \(0.913515\pi\)
\(258\) 364.617i 1.41324i
\(259\) 193.735 + 24.2603i 0.748012 + 0.0936692i
\(260\) 27.7166 0.106602
\(261\) 568.016 152.199i 2.17631 0.583139i
\(262\) −173.443 + 100.137i −0.661995 + 0.382203i
\(263\) 349.916 202.024i 1.33048 0.768153i 0.345107 0.938563i \(-0.387843\pi\)
0.985373 + 0.170410i \(0.0545093\pi\)
\(264\) −32.0441 8.58619i −0.121379 0.0325234i
\(265\) −34.1871 + 34.1871i −0.129008 + 0.129008i
\(266\) −23.2165 40.2121i −0.0872800 0.151173i
\(267\) 431.572 431.572i 1.61638 1.61638i
\(268\) 27.5867 47.7816i 0.102935 0.178289i
\(269\) 318.390 1.18361 0.591803 0.806083i \(-0.298416\pi\)
0.591803 + 0.806083i \(0.298416\pi\)
\(270\) 14.9597i 0.0554062i
\(271\) 11.4462 19.8254i 0.0422369 0.0731564i −0.844134 0.536132i \(-0.819885\pi\)
0.886371 + 0.462976i \(0.153218\pi\)
\(272\) 12.8532 + 3.44401i 0.0472545 + 0.0126618i
\(273\) −261.771 261.771i −0.958869 0.958869i
\(274\) 104.440 27.9846i 0.381167 0.102133i
\(275\) 31.2642 54.1511i 0.113688 0.196913i
\(276\) 105.684 + 394.419i 0.382914 + 1.42905i
\(277\) 17.6380 65.8257i 0.0636749 0.237638i −0.926753 0.375672i \(-0.877412\pi\)
0.990427 + 0.138034i \(0.0440784\pi\)
\(278\) −62.1483 16.6526i −0.223555 0.0599014i
\(279\) −275.960 + 73.9434i −0.989105 + 0.265030i
\(280\) 11.5890 + 6.69094i 0.0413895 + 0.0238962i
\(281\) 81.9314 + 305.772i 0.291571 + 1.08816i 0.943903 + 0.330224i \(0.107124\pi\)
−0.652332 + 0.757933i \(0.726209\pi\)
\(282\) −64.3174 + 64.3174i −0.228076 + 0.228076i
\(283\) 15.3061 57.1232i 0.0540852 0.201849i −0.933596 0.358327i \(-0.883347\pi\)
0.987681 + 0.156478i \(0.0500140\pi\)
\(284\) −157.317 90.8271i −0.553934 0.319814i
\(285\) −25.3187 −0.0888375
\(286\) 56.4896i 0.197516i
\(287\) 111.284 + 64.2497i 0.387748 + 0.223866i
\(288\) 46.3981 + 46.3981i 0.161104 + 0.161104i
\(289\) 240.697 138.967i 0.832863 0.480854i
\(290\) −45.4531 45.4531i −0.156735 0.156735i
\(291\) −84.5368 + 315.496i −0.290504 + 1.08418i
\(292\) −111.089 192.412i −0.380442 0.658945i
\(293\) 120.598 + 208.882i 0.411598 + 0.712909i 0.995065 0.0992280i \(-0.0316373\pi\)
−0.583466 + 0.812137i \(0.698304\pi\)
\(294\) 35.1416 + 131.150i 0.119529 + 0.446090i
\(295\) 74.7039i 0.253234i
\(296\) −14.3157 103.668i −0.0483638 0.350230i
\(297\) 30.4896 0.102658
\(298\) −59.0619 + 15.8256i −0.198194 + 0.0531060i
\(299\) −602.156 + 347.655i −2.01390 + 1.16273i
\(300\) −190.211 + 109.818i −0.634036 + 0.366061i
\(301\) −289.549 77.5845i −0.961958 0.257756i
\(302\) 41.4590 41.4590i 0.137281 0.137281i
\(303\) −252.900 438.036i −0.834653 1.44566i
\(304\) −17.5983 + 17.5983i −0.0578892 + 0.0578892i
\(305\) −22.7179 + 39.3486i −0.0744851 + 0.129012i
\(306\) −54.5711 −0.178337
\(307\) 341.236i 1.11152i 0.831344 + 0.555759i \(0.187572\pi\)
−0.831344 + 0.555759i \(0.812428\pi\)
\(308\) 13.6369 23.6198i 0.0442757 0.0766877i
\(309\) −577.023 154.613i −1.86739 0.500365i
\(310\) 22.0826 + 22.0826i 0.0712342 + 0.0712342i
\(311\) −334.280 + 89.5700i −1.07485 + 0.288006i −0.752486 0.658608i \(-0.771146\pi\)
−0.322368 + 0.946614i \(0.604479\pi\)
\(312\) −99.2125 + 171.841i −0.317989 + 0.550773i
\(313\) 127.067 + 474.220i 0.405964 + 1.51508i 0.802271 + 0.596960i \(0.203625\pi\)
−0.396307 + 0.918118i \(0.629708\pi\)
\(314\) −47.5838 + 177.585i −0.151541 + 0.565558i
\(315\) −53.0097 14.2039i −0.168285 0.0450918i
\(316\) 217.938 58.3964i 0.689678 0.184799i
\(317\) −26.1348 15.0889i −0.0824441 0.0475991i 0.458211 0.888843i \(-0.348490\pi\)
−0.540655 + 0.841244i \(0.681824\pi\)
\(318\) −89.5839 334.332i −0.281711 1.05136i
\(319\) −92.6387 + 92.6387i −0.290403 + 0.290403i
\(320\) 1.85641 6.92820i 0.00580127 0.0216506i
\(321\) −193.294 111.599i −0.602163 0.347659i
\(322\) −335.703 −1.04256
\(323\) 20.6983i 0.0640814i
\(324\) 88.0694 + 50.8469i 0.271819 + 0.156935i
\(325\) −264.457 264.457i −0.813713 0.813713i
\(326\) 174.346 100.659i 0.534803 0.308769i
\(327\) 197.285 + 197.285i 0.603318 + 0.603318i
\(328\) 17.8261 66.5280i 0.0543479 0.202829i
\(329\) −37.3900 64.7613i −0.113647 0.196843i
\(330\) −7.43586 12.8793i −0.0225329 0.0390281i
\(331\) 66.7338 + 249.054i 0.201613 + 0.752429i 0.990455 + 0.137834i \(0.0440139\pi\)
−0.788843 + 0.614595i \(0.789319\pi\)
\(332\) 5.11275i 0.0153998i
\(333\) 166.745 + 395.466i 0.500736 + 1.18759i
\(334\) 399.208 1.19523
\(335\) 23.8908 6.40151i 0.0713157 0.0191090i
\(336\) −82.9668 + 47.9009i −0.246925 + 0.142562i
\(337\) 375.722 216.923i 1.11490 0.643689i 0.174808 0.984603i \(-0.444070\pi\)
0.940095 + 0.340913i \(0.110736\pi\)
\(338\) −95.5078 25.5912i −0.282567 0.0757137i
\(339\) −323.426 + 323.426i −0.954059 + 0.954059i
\(340\) 2.98260 + 5.16602i 0.00877236 + 0.0151942i
\(341\) 45.0069 45.0069i 0.131985 0.131985i
\(342\) 51.0330 88.3917i 0.149219 0.258455i
\(343\) −370.198 −1.07930
\(344\) 160.671i 0.467068i
\(345\) −91.5252 + 158.526i −0.265290 + 0.459497i
\(346\) 205.296 + 55.0088i 0.593340 + 0.158985i
\(347\) −338.398 338.398i −0.975211 0.975211i 0.0244886 0.999700i \(-0.492204\pi\)
−0.999700 + 0.0244886i \(0.992204\pi\)
\(348\) 444.507 119.105i 1.27732 0.342257i
\(349\) −28.1189 + 48.7033i −0.0805698 + 0.139551i −0.903495 0.428599i \(-0.859007\pi\)
0.822925 + 0.568150i \(0.192341\pi\)
\(350\) −46.7351 174.418i −0.133529 0.498336i
\(351\) 47.1998 176.152i 0.134472 0.501857i
\(352\) −14.1205 3.78357i −0.0401150 0.0107488i
\(353\) −196.878 + 52.7533i −0.557729 + 0.149443i −0.526663 0.850074i \(-0.676557\pi\)
−0.0310660 + 0.999517i \(0.509890\pi\)
\(354\) 463.159 + 267.405i 1.30836 + 0.755382i
\(355\) −21.0765 78.6586i −0.0593705 0.221574i
\(356\) 190.176 190.176i 0.534202 0.534202i
\(357\) 20.6214 76.9601i 0.0577630 0.215575i
\(358\) 83.1071 + 47.9819i 0.232143 + 0.134028i
\(359\) 523.169 1.45730 0.728648 0.684889i \(-0.240149\pi\)
0.728648 + 0.684889i \(0.240149\pi\)
\(360\) 29.4152i 0.0817089i
\(361\) −279.109 161.144i −0.773155 0.446382i
\(362\) −205.247 205.247i −0.566981 0.566981i
\(363\) 449.353 259.434i 1.23789 0.714695i
\(364\) −115.352 115.352i −0.316900 0.316900i
\(365\) 25.7783 96.2059i 0.0706255 0.263578i
\(366\) −162.639 281.700i −0.444370 0.769671i
\(367\) 235.671 + 408.195i 0.642156 + 1.11225i 0.984950 + 0.172837i \(0.0552933\pi\)
−0.342794 + 0.939411i \(0.611373\pi\)
\(368\) 46.5706 + 173.804i 0.126550 + 0.472293i
\(369\) 282.459i 0.765472i
\(370\) 28.3236 37.3993i 0.0765502 0.101079i
\(371\) 284.561 0.767011
\(372\) −215.956 + 57.8653i −0.580527 + 0.155552i
\(373\) −51.7992 + 29.9063i −0.138872 + 0.0801776i −0.567826 0.823148i \(-0.692215\pi\)
0.428954 + 0.903326i \(0.358882\pi\)
\(374\) 10.5289 6.07889i 0.0281522 0.0162537i
\(375\) −193.371 51.8135i −0.515655 0.138169i
\(376\) −28.3420 + 28.3420i −0.0753775 + 0.0753775i
\(377\) 391.805 + 678.626i 1.03927 + 1.80007i
\(378\) 62.2595 62.2595i 0.164708 0.164708i
\(379\) 212.159 367.470i 0.559787 0.969579i −0.437727 0.899108i \(-0.644216\pi\)
0.997514 0.0704710i \(-0.0224502\pi\)
\(380\) −11.1569 −0.0293602
\(381\) 480.205i 1.26038i
\(382\) 63.0903 109.276i 0.165158 0.286062i
\(383\) 207.328 + 55.5535i 0.541327 + 0.145048i 0.519114 0.854705i \(-0.326262\pi\)
0.0222134 + 0.999753i \(0.492929\pi\)
\(384\) 36.3093 + 36.3093i 0.0945556 + 0.0945556i
\(385\) 11.8099 3.16446i 0.0306751 0.00821937i
\(386\) 222.820 385.935i 0.577253 0.999831i
\(387\) −170.541 636.469i −0.440675 1.64462i
\(388\) −37.2518 + 139.026i −0.0960098 + 0.358313i
\(389\) 428.270 + 114.755i 1.10095 + 0.294999i 0.763152 0.646219i \(-0.223651\pi\)
0.337800 + 0.941218i \(0.390317\pi\)
\(390\) −85.9206 + 23.0224i −0.220309 + 0.0590317i
\(391\) −129.597 74.8228i −0.331450 0.191363i
\(392\) 15.4854 + 57.7925i 0.0395037 + 0.147430i
\(393\) 454.490 454.490i 1.15646 1.15646i
\(394\) −28.2572 + 105.457i −0.0717189 + 0.267658i
\(395\) 87.5945 + 50.5727i 0.221758 + 0.128032i
\(396\) 59.9516 0.151393
\(397\) 104.624i 0.263536i 0.991281 + 0.131768i \(0.0420655\pi\)
−0.991281 + 0.131768i \(0.957935\pi\)
\(398\) −206.652 119.311i −0.519227 0.299776i
\(399\) 105.372 + 105.372i 0.264090 + 0.264090i
\(400\) −83.8179 + 48.3923i −0.209545 + 0.120981i
\(401\) −466.509 466.509i −1.16336 1.16336i −0.983735 0.179629i \(-0.942510\pi\)
−0.179629 0.983735i \(-0.557490\pi\)
\(402\) −45.8289 + 171.036i −0.114002 + 0.425462i
\(403\) −190.352 329.698i −0.472336 0.818110i
\(404\) −111.442 193.024i −0.275847 0.477782i
\(405\) 11.7991 + 44.0347i 0.0291335 + 0.108728i
\(406\) 378.335i 0.931861i
\(407\) −76.2242 57.7267i −0.187283 0.141835i
\(408\) −42.7053 −0.104670
\(409\) −133.745 + 35.8368i −0.327004 + 0.0876205i −0.418586 0.908177i \(-0.637474\pi\)
0.0915821 + 0.995798i \(0.470808\pi\)
\(410\) 26.7392 15.4379i 0.0652175 0.0376534i
\(411\) −300.515 + 173.503i −0.731181 + 0.422147i
\(412\) −254.270 68.1314i −0.617160 0.165367i
\(413\) −310.904 + 310.904i −0.752795 + 0.752795i
\(414\) −368.961 639.059i −0.891210 1.54362i
\(415\) 1.62068 1.62068i 0.00390524 0.00390524i
\(416\) −43.7188 + 75.7232i −0.105093 + 0.182027i
\(417\) 206.490 0.495180
\(418\) 22.7390i 0.0543996i
\(419\) −316.954 + 548.981i −0.756454 + 1.31022i 0.188195 + 0.982132i \(0.439736\pi\)
−0.944648 + 0.328084i \(0.893597\pi\)
\(420\) −41.4834 11.1154i −0.0987700 0.0264653i
\(421\) −383.928 383.928i −0.911942 0.911942i 0.0844826 0.996425i \(-0.473076\pi\)
−0.996425 + 0.0844826i \(0.973076\pi\)
\(422\) 187.873 50.3405i 0.445198 0.119290i
\(423\) 82.1882 142.354i 0.194298 0.336535i
\(424\) −39.4759 147.326i −0.0931035 0.347467i
\(425\) 20.8330 77.7496i 0.0490187 0.182940i
\(426\) 563.123 + 150.888i 1.32188 + 0.354198i
\(427\) 258.310 69.2140i 0.604942 0.162094i
\(428\) −85.1767 49.1768i −0.199011 0.114899i
\(429\) 46.9222 + 175.116i 0.109376 + 0.408196i
\(430\) −50.9308 + 50.9308i −0.118444 + 0.118444i
\(431\) −182.634 + 681.599i −0.423744 + 1.58144i 0.342905 + 0.939370i \(0.388589\pi\)
−0.766650 + 0.642066i \(0.778078\pi\)
\(432\) −40.8706 23.5967i −0.0946079 0.0546219i
\(433\) −260.578 −0.601797 −0.300898 0.953656i \(-0.597286\pi\)
−0.300898 + 0.953656i \(0.597286\pi\)
\(434\) 183.808i 0.423520i
\(435\) 178.658 + 103.148i 0.410708 + 0.237123i
\(436\) 86.9352 + 86.9352i 0.199393 + 0.199393i
\(437\) 242.388 139.943i 0.554665 0.320236i
\(438\) 504.196 + 504.196i 1.15113 + 1.15113i
\(439\) 170.599 636.684i 0.388608 1.45031i −0.443792 0.896130i \(-0.646367\pi\)
0.832400 0.554175i \(-0.186966\pi\)
\(440\) −3.27667 5.67536i −0.00744697 0.0128985i
\(441\) −122.685 212.497i −0.278198 0.481853i
\(442\) −18.8210 70.2409i −0.0425814 0.158916i
\(443\) 472.541i 1.06668i −0.845900 0.533342i \(-0.820936\pi\)
0.845900 0.533342i \(-0.179064\pi\)
\(444\) 130.488 + 309.477i 0.293893 + 0.697019i
\(445\) 120.567 0.270936
\(446\) −564.334 + 151.213i −1.26532 + 0.339042i
\(447\) 169.945 98.1177i 0.380190 0.219503i
\(448\) −36.5600 + 21.1079i −0.0816071 + 0.0471159i
\(449\) 733.716 + 196.599i 1.63411 + 0.437859i 0.955104 0.296272i \(-0.0957435\pi\)
0.679008 + 0.734131i \(0.262410\pi\)
\(450\) 280.664 280.664i 0.623697 0.623697i
\(451\) −31.4642 54.4976i −0.0697654 0.120837i
\(452\) −142.520 + 142.520i −0.315310 + 0.315310i
\(453\) −94.0843 + 162.959i −0.207692 + 0.359732i
\(454\) 85.8118 0.189013
\(455\) 73.1299i 0.160725i
\(456\) 39.9364 69.1720i 0.0875799 0.151693i
\(457\) 355.673 + 95.3022i 0.778277 + 0.208539i 0.626025 0.779803i \(-0.284681\pi\)
0.152252 + 0.988342i \(0.451347\pi\)
\(458\) 387.545 + 387.545i 0.846169 + 0.846169i
\(459\) 37.9117 10.1584i 0.0825962 0.0221316i
\(460\) −40.3313 + 69.8559i −0.0876767 + 0.151861i
\(461\) 45.9133 + 171.351i 0.0995950 + 0.371694i 0.997676 0.0681364i \(-0.0217053\pi\)
−0.898081 + 0.439830i \(0.855039\pi\)
\(462\) −22.6546 + 84.5480i −0.0490358 + 0.183004i
\(463\) −286.206 76.6887i −0.618156 0.165634i −0.0638667 0.997958i \(-0.520343\pi\)
−0.554289 + 0.832324i \(0.687010\pi\)
\(464\) 195.876 52.4847i 0.422146 0.113114i
\(465\) −86.7979 50.1128i −0.186662 0.107769i
\(466\) −110.170 411.161i −0.236417 0.882320i
\(467\) −55.7642 + 55.7642i −0.119409 + 0.119409i −0.764286 0.644877i \(-0.776909\pi\)
0.644877 + 0.764286i \(0.276909\pi\)
\(468\) 92.8088 346.367i 0.198309 0.740101i
\(469\) −126.071 72.7872i −0.268808 0.155197i
\(470\) −17.9681 −0.0382300
\(471\) 590.033i 1.25272i
\(472\) 204.095 + 117.834i 0.432404 + 0.249649i
\(473\) 103.803 + 103.803i 0.219456 + 0.219456i
\(474\) −627.096 + 362.054i −1.32299 + 0.763827i
\(475\) 106.453 + 106.453i 0.224111 + 0.224111i
\(476\) 9.08698 33.9131i 0.0190903 0.0712460i
\(477\) 312.752 + 541.703i 0.655665 + 1.13564i
\(478\) 74.9904 + 129.887i 0.156884 + 0.271731i
\(479\) −83.2380 310.648i −0.173774 0.648535i −0.996757 0.0804687i \(-0.974358\pi\)
0.822983 0.568067i \(-0.192308\pi\)
\(480\) 23.0192i 0.0479567i
\(481\) −451.513 + 351.017i −0.938696 + 0.729765i
\(482\) −225.801 −0.468467
\(483\) 1040.67 278.847i 2.15460 0.577322i
\(484\) 198.011 114.322i 0.409114 0.236202i
\(485\) −55.8777 + 32.2610i −0.115212 + 0.0665175i
\(486\) −460.299 123.337i −0.947117 0.253779i
\(487\) −89.8601 + 89.8601i −0.184518 + 0.184518i −0.793321 0.608803i \(-0.791650\pi\)
0.608803 + 0.793321i \(0.291650\pi\)
\(488\) −71.6683 124.133i −0.146861 0.254371i
\(489\) −456.856 + 456.856i −0.934267 + 0.934267i
\(490\) −13.4108 + 23.2282i −0.0273690 + 0.0474044i
\(491\) −503.090 −1.02462 −0.512312 0.858799i \(-0.671211\pi\)
−0.512312 + 0.858799i \(0.671211\pi\)
\(492\) 221.042i 0.449272i
\(493\) −84.3248 + 146.055i −0.171044 + 0.296257i
\(494\) 131.374 + 35.2014i 0.265938 + 0.0712579i
\(495\) 19.0039 + 19.0039i 0.0383917 + 0.0383917i
\(496\) −95.1627 + 25.4988i −0.191860 + 0.0514088i
\(497\) −239.646 + 415.080i −0.482186 + 0.835170i
\(498\) 4.24682 + 15.8494i 0.00852776 + 0.0318260i
\(499\) 233.400 871.060i 0.467735 1.74561i −0.179923 0.983681i \(-0.557585\pi\)
0.647658 0.761931i \(-0.275749\pi\)
\(500\) −85.2102 22.8320i −0.170420 0.0456640i
\(501\) −1237.53 + 331.596i −2.47012 + 0.661868i
\(502\) 297.787 + 171.928i 0.593202 + 0.342485i
\(503\) 56.0079 + 209.024i 0.111348 + 0.415555i 0.998988 0.0449826i \(-0.0143232\pi\)
−0.887640 + 0.460538i \(0.847657\pi\)
\(504\) 122.421 122.421i 0.242898 0.242898i
\(505\) 25.8603 96.5119i 0.0512085 0.191113i
\(506\) 142.374 + 82.1999i 0.281372 + 0.162450i
\(507\) 317.328 0.625894
\(508\) 211.606i 0.416548i
\(509\) −120.914 69.8096i −0.237552 0.137151i 0.376499 0.926417i \(-0.377128\pi\)
−0.614051 + 0.789266i \(0.710461\pi\)
\(510\) −13.5370 13.5370i −0.0265432 0.0265432i
\(511\) −507.676 + 293.107i −0.993496 + 0.573595i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −18.9995 + 70.9072i −0.0370361 + 0.138221i
\(514\) −3.59809 6.23208i −0.00700018 0.0121247i
\(515\) −59.0035 102.197i −0.114570 0.198441i
\(516\) −133.459 498.076i −0.258642 0.965264i
\(517\) 36.6210i 0.0708337i
\(518\) −273.527 + 37.7718i −0.528044 + 0.0729185i
\(519\) −682.102 −1.31426
\(520\) −37.8616 + 10.1450i −0.0728107 + 0.0195096i
\(521\) 364.584 210.493i 0.699778 0.404017i −0.107487 0.994206i \(-0.534280\pi\)
0.807265 + 0.590190i \(0.200947\pi\)
\(522\) −720.215 + 415.816i −1.37972 + 0.796583i
\(523\) 963.060 + 258.051i 1.84142 + 0.493406i 0.998970 0.0453753i \(-0.0144484\pi\)
0.842446 + 0.538781i \(0.181115\pi\)
\(524\) 200.274 200.274i 0.382203 0.382203i
\(525\) 289.754 + 501.869i 0.551913 + 0.955942i
\(526\) −404.049 + 404.049i −0.768153 + 0.768153i
\(527\) 40.9677 70.9581i 0.0777376 0.134645i
\(528\) 46.9158 0.0888557
\(529\) 1494.54i 2.82521i
\(530\) 34.1871 59.2138i 0.0645040 0.111724i
\(531\) −933.555 250.145i −1.75811 0.471083i
\(532\) 46.4329 + 46.4329i 0.0872800 + 0.0872800i
\(533\) −363.565 + 97.4171i −0.682112 + 0.182771i
\(534\) −431.572 + 747.505i −0.808188 + 1.39982i
\(535\) −11.4115 42.5883i −0.0213299 0.0796044i
\(536\) −20.1949 + 75.3682i −0.0376770 + 0.140612i
\(537\) −297.485 79.7108i −0.553975 0.148437i
\(538\) −434.929 + 116.539i −0.808417 + 0.216615i
\(539\) 47.3417 + 27.3327i 0.0878324 + 0.0507101i
\(540\) −5.47562 20.4353i −0.0101400 0.0378432i
\(541\) 475.702 475.702i 0.879301 0.879301i −0.114161 0.993462i \(-0.536418\pi\)
0.993462 + 0.114161i \(0.0364180\pi\)
\(542\) −8.37920 + 31.2716i −0.0154598 + 0.0576967i
\(543\) 806.745 + 465.775i 1.48572 + 0.857780i
\(544\) −18.8184 −0.0345927
\(545\) 55.1147i 0.101128i
\(546\) 453.401 + 261.771i 0.830405 + 0.479434i
\(547\) 381.426 + 381.426i 0.697304 + 0.697304i 0.963828 0.266524i \(-0.0858751\pi\)
−0.266524 + 0.963828i \(0.585875\pi\)
\(548\) −132.424 + 76.4553i −0.241650 + 0.139517i
\(549\) 415.659 + 415.659i 0.757120 + 0.757120i
\(550\) −22.8870 + 85.4153i −0.0416127 + 0.155301i
\(551\) −157.715 273.170i −0.286234 0.495772i
\(552\) −288.735 500.103i −0.523070 0.905984i
\(553\) −154.078 575.028i −0.278622 1.03983i
\(554\) 96.3756i 0.173963i
\(555\) −56.7370 + 139.463i −0.102229 + 0.251285i
\(556\) 90.9914 0.163654
\(557\) −91.2573 + 24.4523i −0.163837 + 0.0439000i −0.339805 0.940496i \(-0.610361\pi\)
0.175968 + 0.984396i \(0.443694\pi\)
\(558\) 349.904 202.017i 0.627068 0.362038i
\(559\) 760.409 439.022i 1.36030 0.785371i
\(560\) −18.2800 4.89811i −0.0326428 0.00874662i
\(561\) −27.5901 + 27.5901i −0.0491801 + 0.0491801i
\(562\) −223.841 387.703i −0.398293 0.689864i
\(563\) −346.836 + 346.836i −0.616049 + 0.616049i −0.944516 0.328467i \(-0.893468\pi\)
0.328467 + 0.944516i \(0.393468\pi\)
\(564\) 64.3174 111.401i 0.114038 0.197519i
\(565\) −90.3542 −0.159919
\(566\) 83.6342i 0.147764i
\(567\) 134.159 232.370i 0.236612 0.409824i
\(568\) 248.144 + 66.4901i 0.436874 + 0.117060i
\(569\) 100.632 + 100.632i 0.176858 + 0.176858i 0.789985 0.613127i \(-0.210089\pi\)
−0.613127 + 0.789985i \(0.710089\pi\)
\(570\) 34.5860 9.26728i 0.0606772 0.0162584i
\(571\) 67.9181 117.638i 0.118946 0.206020i −0.800404 0.599461i \(-0.795382\pi\)
0.919350 + 0.393440i \(0.128715\pi\)
\(572\) 20.6766 + 77.1663i 0.0361480 + 0.134906i
\(573\) −104.810 + 391.156i −0.182914 + 0.682645i
\(574\) −175.533 47.0340i −0.305807 0.0819408i
\(575\) 1051.35 281.707i 1.82843 0.489926i
\(576\) −80.3638 46.3981i −0.139520 0.0805522i
\(577\) −181.182 676.182i −0.314008 1.17189i −0.924910 0.380186i \(-0.875860\pi\)
0.610902 0.791706i \(-0.290807\pi\)
\(578\) −277.933 + 277.933i −0.480854 + 0.480854i
\(579\) −370.163 + 1381.47i −0.639314 + 2.38595i
\(580\) 78.7271 + 45.4531i 0.135736 + 0.0783674i
\(581\) −13.4899 −0.0232185
\(582\) 461.918i 0.793673i
\(583\) −120.685 69.6773i −0.207006 0.119515i
\(584\) 222.178 + 222.178i 0.380442 + 0.380442i
\(585\) 139.213 80.3748i 0.237971 0.137393i
\(586\) −241.197 241.197i −0.411598 0.411598i
\(587\) 24.2262 90.4132i 0.0412711 0.154026i −0.942215 0.335008i \(-0.891261\pi\)
0.983486 + 0.180982i \(0.0579276\pi\)
\(588\) −96.0088 166.292i −0.163280 0.282810i
\(589\) 76.6230 + 132.715i 0.130090 + 0.225322i
\(590\) 27.3435 + 102.047i 0.0463449 + 0.172962i
\(591\) 350.386i 0.592870i
\(592\) 57.5007 + 136.373i 0.0971296 + 0.230360i
\(593\) 951.626 1.60477 0.802383 0.596810i \(-0.203565\pi\)
0.802383 + 0.596810i \(0.203565\pi\)
\(594\) −41.6495 + 11.1600i −0.0701170 + 0.0187878i
\(595\) 13.6305 7.86956i 0.0229084 0.0132262i
\(596\) 74.8875 43.2363i 0.125650 0.0725442i
\(597\) 739.720 + 198.207i 1.23906 + 0.332005i
\(598\) 695.310 695.310i 1.16273 1.16273i
\(599\) 123.946 + 214.681i 0.206922 + 0.358399i 0.950743 0.309979i \(-0.100322\pi\)
−0.743822 + 0.668378i \(0.766989\pi\)
\(600\) 219.637 219.637i 0.366061 0.366061i
\(601\) 383.142 663.622i 0.637508 1.10420i −0.348470 0.937320i \(-0.613299\pi\)
0.985978 0.166876i \(-0.0533680\pi\)
\(602\) 423.930 0.704202
\(603\) 319.992i 0.530667i
\(604\) −41.4590 + 71.8090i −0.0686407 + 0.118889i
\(605\) 99.0056 + 26.5285i 0.163646 + 0.0438487i
\(606\) 505.800 + 505.800i 0.834653 + 0.834653i
\(607\) −574.672 + 153.983i −0.946741 + 0.253678i −0.698979 0.715142i \(-0.746362\pi\)
−0.247762 + 0.968821i \(0.579695\pi\)
\(608\) 17.5983 30.4812i 0.0289446 0.0501335i
\(609\) −314.258 1172.83i −0.516023 1.92583i
\(610\) 16.6307 62.0666i 0.0272634 0.101749i
\(611\) 211.576 + 56.6917i 0.346278 + 0.0927850i
\(612\) 74.5456 19.9744i 0.121806 0.0326380i
\(613\) −855.706 494.042i −1.39593 0.805941i −0.401968 0.915654i \(-0.631674\pi\)
−0.993963 + 0.109712i \(0.965007\pi\)
\(614\) −124.901 466.137i −0.203422 0.759181i
\(615\) −70.0674 + 70.0674i −0.113931 + 0.113931i
\(616\) −9.98291 + 37.2567i −0.0162060 + 0.0604817i
\(617\) 162.062 + 93.5667i 0.262662 + 0.151648i 0.625548 0.780186i \(-0.284875\pi\)
−0.362886 + 0.931833i \(0.618209\pi\)
\(618\) 844.820 1.36702
\(619\) 1130.11i 1.82570i 0.408296 + 0.912850i \(0.366123\pi\)
−0.408296 + 0.912850i \(0.633877\pi\)
\(620\) −38.2482 22.0826i −0.0616906 0.0356171i
\(621\) 375.285 + 375.285i 0.604323 + 0.604323i
\(622\) 423.850 244.710i 0.681431 0.393424i
\(623\) −501.777 501.777i −0.805420 0.805420i
\(624\) 72.6286 271.054i 0.116392 0.434381i
\(625\) 282.679 + 489.614i 0.452286 + 0.783382i
\(626\) −347.153 601.286i −0.554557 0.960521i
\(627\) −18.8878 70.4902i −0.0301241 0.112425i
\(628\) 260.003i 0.414017i
\(629\) −114.013 46.3830i −0.181260 0.0737409i
\(630\) 77.6116 0.123193
\(631\) −355.653 + 95.2968i −0.563633 + 0.151025i −0.529375 0.848388i \(-0.677574\pi\)
−0.0342582 + 0.999413i \(0.510907\pi\)
\(632\) −276.335 + 159.542i −0.437238 + 0.252440i
\(633\) −540.587 + 312.108i −0.854008 + 0.493062i
\(634\) 41.2237 + 11.0459i 0.0650216 + 0.0174225i
\(635\) −67.0765 + 67.0765i −0.105632 + 0.105632i
\(636\) 244.748 + 423.916i 0.384824 + 0.666534i
\(637\) 231.201 231.201i 0.362954 0.362954i
\(638\) 92.6387 160.455i 0.145202 0.251497i
\(639\) −1053.55 −1.64875
\(640\) 10.1436i 0.0158494i
\(641\) 53.5878 92.8168i 0.0836003 0.144800i −0.821194 0.570650i \(-0.806691\pi\)
0.904794 + 0.425850i \(0.140025\pi\)
\(642\) 304.893 + 81.6958i 0.474911 + 0.127252i
\(643\) 582.588 + 582.588i 0.906046 + 0.906046i 0.995950 0.0899044i \(-0.0286562\pi\)
−0.0899044 + 0.995950i \(0.528656\pi\)
\(644\) 458.579 122.876i 0.712080 0.190801i
\(645\) 115.579 200.189i 0.179192 0.310370i
\(646\) 7.57610 + 28.2744i 0.0117277 + 0.0437684i
\(647\) −189.200 + 706.104i −0.292427 + 1.09135i 0.650813 + 0.759238i \(0.274428\pi\)
−0.943240 + 0.332113i \(0.892238\pi\)
\(648\) −138.916 37.2225i −0.214377 0.0574422i
\(649\) 207.984 55.7293i 0.320469 0.0858694i
\(650\) 458.052 + 264.457i 0.704696 + 0.406856i
\(651\) 152.677 + 569.798i 0.234527 + 0.875265i
\(652\) −201.317 + 201.317i −0.308769 + 0.308769i
\(653\) 39.6903 148.126i 0.0607814 0.226839i −0.928853 0.370448i \(-0.879204\pi\)
0.989635 + 0.143609i \(0.0458708\pi\)
\(654\) −341.708 197.285i −0.522489 0.301659i
\(655\) 126.969 0.193846
\(656\) 97.4038i 0.148481i
\(657\) −1115.94 644.289i −1.69854 0.980653i
\(658\) 74.7799 + 74.7799i 0.113647 + 0.113647i
\(659\) −730.438 + 421.719i −1.10840 + 0.639937i −0.938416 0.345509i \(-0.887706\pi\)
−0.169989 + 0.985446i \(0.554373\pi\)
\(660\) 14.8717 + 14.8717i 0.0225329 + 0.0225329i
\(661\) −192.641 + 718.947i −0.291439 + 1.08767i 0.652565 + 0.757732i \(0.273693\pi\)
−0.944004 + 0.329933i \(0.892974\pi\)
\(662\) −182.320 315.788i −0.275408 0.477021i
\(663\) 116.689 + 202.111i 0.176002 + 0.304844i
\(664\) 1.87140 + 6.98415i 0.00281837 + 0.0105183i
\(665\) 29.4373i 0.0442666i
\(666\) −372.529 479.184i −0.559352 0.719495i
\(667\) −2280.51 −3.41906
\(668\) −545.328 + 146.120i −0.816360 + 0.218743i
\(669\) 1623.81 937.510i 2.42723 1.40136i
\(670\) −30.2923 + 17.4893i −0.0452124 + 0.0261034i
\(671\) −126.499 33.8953i −0.188523 0.0505146i
\(672\) 95.8018 95.8018i 0.142562 0.142562i
\(673\) 269.525 + 466.831i 0.400483 + 0.693656i 0.993784 0.111324i \(-0.0355091\pi\)
−0.593301 + 0.804980i \(0.702176\pi\)
\(674\) −433.847 + 433.847i −0.643689 + 0.643689i
\(675\) −142.737 + 247.228i −0.211462 + 0.366264i
\(676\) 139.833 0.206854
\(677\) 733.532i 1.08350i −0.840538 0.541752i \(-0.817761\pi\)
0.840538 0.541752i \(-0.182239\pi\)
\(678\) 323.426 560.190i 0.477029 0.826239i
\(679\) 366.818 + 98.2885i 0.540232 + 0.144755i
\(680\) −5.96520 5.96520i −0.00877236 0.00877236i
\(681\) −266.014 + 71.2782i −0.390623 + 0.104667i
\(682\) −45.0069 + 77.9542i −0.0659925 + 0.114302i
\(683\) 5.60855 + 20.9314i 0.00821164 + 0.0306463i 0.969910 0.243463i \(-0.0782836\pi\)
−0.961698 + 0.274110i \(0.911617\pi\)
\(684\) −37.3587 + 139.425i −0.0546180 + 0.203837i
\(685\) −66.2122 17.7415i −0.0966602 0.0259000i
\(686\) 505.701 135.502i 0.737173 0.197525i
\(687\) −1523.29 879.470i −2.21730 1.28016i
\(688\) −58.8098 219.481i −0.0854794 0.319013i
\(689\) −589.384 + 589.384i −0.855420 + 0.855420i
\(690\) 67.0011 250.052i 0.0971031 0.362394i
\(691\) 681.718 + 393.590i 0.986568 + 0.569595i 0.904247 0.427011i \(-0.140433\pi\)
0.0823212 + 0.996606i \(0.473767\pi\)
\(692\) −300.573 −0.434355
\(693\) 158.182i 0.228256i
\(694\) 586.123 + 338.398i 0.844558 + 0.487606i
\(695\) 28.8431 + 28.8431i 0.0415009 + 0.0415009i
\(696\) −563.613 + 325.402i −0.809789 + 0.467532i
\(697\) −57.2808 57.2808i −0.0821819 0.0821819i
\(698\) 20.5844 76.8221i 0.0294906 0.110060i
\(699\) 683.049 + 1183.08i 0.977180 + 1.69253i
\(700\) 127.683 + 221.153i 0.182404 + 0.315932i
\(701\) 65.5540 + 244.651i 0.0935150 + 0.349003i 0.996790 0.0800591i \(-0.0255109\pi\)
−0.903275 + 0.429062i \(0.858844\pi\)
\(702\) 257.904i 0.367385i
\(703\) 181.749 141.296i 0.258534 0.200990i
\(704\) 20.6738 0.0293662
\(705\) 55.7005 14.9249i 0.0790078 0.0211701i
\(706\) 249.632 144.125i 0.353586 0.204143i
\(707\) −509.291 + 294.039i −0.720355 + 0.415897i
\(708\) −730.565 195.754i −1.03187 0.276489i
\(709\) −560.020 + 560.020i −0.789873 + 0.789873i −0.981473 0.191600i \(-0.938632\pi\)
0.191600 + 0.981473i \(0.438632\pi\)
\(710\) 57.5821 + 99.7351i 0.0811015 + 0.140472i
\(711\) 925.304 925.304i 1.30141 1.30141i
\(712\) −190.176 + 329.394i −0.267101 + 0.462632i
\(713\) 1107.95 1.55392
\(714\) 112.677i 0.157812i
\(715\) −17.9065 + 31.0150i −0.0250441 + 0.0433776i
\(716\) −131.089 35.1252i −0.183085 0.0490575i
\(717\) −340.357 340.357i −0.474696 0.474696i
\(718\) −714.662 + 191.493i −0.995352 + 0.266704i
\(719\) 10.6725 18.4853i 0.0148435 0.0257097i −0.858508 0.512800i \(-0.828608\pi\)
0.873352 + 0.487090i \(0.161942\pi\)
\(720\) −10.7667 40.1819i −0.0149538 0.0558082i
\(721\) −179.764 + 670.888i −0.249326 + 0.930496i
\(722\) 440.253 + 117.965i 0.609768 + 0.163387i
\(723\) 699.977 187.558i 0.968156 0.259417i
\(724\) 355.499 + 205.247i 0.491020 + 0.283491i
\(725\) −317.482 1184.86i −0.437906 1.63429i
\(726\) −518.869 + 518.869i −0.714695 + 0.714695i
\(727\) −230.014 + 858.425i −0.316388 + 1.18078i 0.606302 + 0.795235i \(0.292652\pi\)
−0.922690 + 0.385543i \(0.874014\pi\)
\(728\) 199.795 + 115.352i 0.274443 + 0.158450i
\(729\) 1071.74 1.47015
\(730\) 140.855i 0.192952i
\(731\) 163.656 + 94.4869i 0.223880 + 0.129257i
\(732\) 325.279 + 325.279i 0.444370 + 0.444370i
\(733\) 234.846 135.588i 0.320390 0.184977i −0.331176 0.943569i \(-0.607446\pi\)
0.651566 + 0.758592i \(0.274112\pi\)
\(734\) −471.343 471.343i −0.642156 0.642156i
\(735\) 22.2789 83.1460i 0.0303114 0.113124i
\(736\) −127.233 220.374i −0.172871 0.299422i
\(737\) 35.6451 + 61.7392i 0.0483652 + 0.0837709i
\(738\) −103.387 385.846i −0.140091 0.522827i
\(739\) 126.877i 0.171688i 0.996309 + 0.0858439i \(0.0273586\pi\)
−0.996309 + 0.0858439i \(0.972641\pi\)
\(740\) −25.0016 + 61.4556i −0.0337859 + 0.0830481i
\(741\) −436.493 −0.589060
\(742\) −388.718 + 104.157i −0.523879 + 0.140373i
\(743\) −196.167 + 113.257i −0.264020 + 0.152432i −0.626167 0.779689i \(-0.715377\pi\)
0.362147 + 0.932121i \(0.382044\pi\)
\(744\) 273.821 158.091i 0.368039 0.212488i
\(745\) 37.4437 + 10.0330i 0.0502601 + 0.0134671i
\(746\) 59.8125 59.8125i 0.0801776 0.0801776i
\(747\) −14.8264 25.6800i −0.0198479 0.0343775i
\(748\) −12.1578 + 12.1578i −0.0162537 + 0.0162537i
\(749\) −129.752 + 224.738i −0.173234 + 0.300050i
\(750\) 283.114 0.377485
\(751\) 844.287i 1.12422i 0.827064 + 0.562108i \(0.190010\pi\)
−0.827064 + 0.562108i \(0.809990\pi\)
\(752\) 28.3420 49.0897i 0.0376888 0.0652789i
\(753\) −1065.94 285.618i −1.41559 0.379307i
\(754\) −783.610 783.610i −1.03927 1.03927i
\(755\) −35.9045 + 9.62059i −0.0475557 + 0.0127425i
\(756\) −62.2595 + 107.837i −0.0823539 + 0.142641i
\(757\) 121.331 + 452.814i 0.160279 + 0.598169i 0.998595 + 0.0529848i \(0.0168735\pi\)
−0.838317 + 0.545184i \(0.816460\pi\)
\(758\) −155.311 + 579.629i −0.204896 + 0.764683i
\(759\) −509.634 136.556i −0.671454 0.179916i
\(760\) 15.2406 4.08370i 0.0200534 0.00537329i
\(761\) −482.112 278.348i −0.633524 0.365765i 0.148591 0.988899i \(-0.452526\pi\)
−0.782116 + 0.623133i \(0.785859\pi\)
\(762\) −175.767 655.973i −0.230666 0.860856i
\(763\) 229.378 229.378i 0.300626 0.300626i
\(764\) −46.1853 + 172.366i −0.0604519 + 0.225610i
\(765\) 29.9616 + 17.2984i 0.0391655 + 0.0226122i
\(766\) −303.550 −0.396279
\(767\) 1287.89i 1.67913i
\(768\) −62.8896 36.3093i −0.0818876 0.0472778i
\(769\) 101.249 + 101.249i 0.131664 + 0.131664i 0.769867 0.638204i \(-0.220322\pi\)
−0.638204 + 0.769867i \(0.720322\pi\)
\(770\) −14.9744 + 8.64545i −0.0194472 + 0.0112279i
\(771\) 16.3305 + 16.3305i 0.0211810 + 0.0211810i
\(772\) −163.115 + 608.754i −0.211289 + 0.788542i
\(773\) −430.845 746.245i −0.557367 0.965388i −0.997715 0.0675609i \(-0.978478\pi\)
0.440348 0.897827i \(-0.354855\pi\)
\(774\) 465.927 + 807.010i 0.601973 + 1.04265i
\(775\) 154.243 + 575.643i 0.199023 + 0.742765i
\(776\) 203.548i 0.262304i
\(777\) 816.550 344.292i 1.05090 0.443104i
\(778\) −627.031 −0.805953
\(779\) 146.348 39.2137i 0.187866 0.0503385i
\(780\) 108.943 62.8982i 0.139670 0.0806388i
\(781\) 203.272 117.359i 0.260271 0.150268i
\(782\) 204.420 + 54.7741i 0.261406 + 0.0700436i
\(783\) 422.944 422.944i 0.540158 0.540158i
\(784\) −42.3070 73.2779i −0.0539630 0.0934667i
\(785\) 82.4176 82.4176i 0.104991 0.104991i
\(786\) −454.490 + 787.199i −0.578231 + 1.00153i
\(787\) 445.900 0.566582 0.283291 0.959034i \(-0.408574\pi\)
0.283291 + 0.959034i \(0.408574\pi\)
\(788\) 154.400i 0.195940i
\(789\) 916.921 1588.15i 1.16213 2.01287i
\(790\) −138.167 37.0218i −0.174895 0.0468631i
\(791\) 376.038 + 376.038i 0.475396 + 0.475396i
\(792\) −81.8954 + 21.9438i −0.103403 + 0.0277068i
\(793\) −391.657 + 678.369i −0.493892 + 0.855446i
\(794\) −38.2950 142.919i −0.0482305 0.179999i
\(795\) −56.7939 + 211.958i −0.0714389 + 0.266614i
\(796\) 325.963 + 87.3416i 0.409502 + 0.109726i
\(797\) −864.985 + 231.772i −1.08530 + 0.290806i −0.756766 0.653686i \(-0.773222\pi\)
−0.328535 + 0.944492i \(0.606555\pi\)
\(798\) −182.509 105.372i −0.228709 0.132045i
\(799\) 12.2013 + 45.5357i 0.0152707 + 0.0569909i
\(800\) 96.7846 96.7846i 0.120981 0.120981i
\(801\) 403.716 1506.69i 0.504015 1.88101i
\(802\) 808.017 + 466.509i 1.00750 + 0.581682i
\(803\) 287.079 0.357508
\(804\) 250.414i 0.311460i
\(805\) 184.314 + 106.414i 0.228961 + 0.132191i
\(806\) 380.703 + 380.703i 0.472336 + 0.472336i
\(807\) 1251.46 722.533i 1.55076 0.895332i
\(808\) 222.885 + 222.885i 0.275847 + 0.275847i
\(809\) 207.204 773.295i 0.256123 0.955865i −0.711339 0.702849i \(-0.751911\pi\)
0.967462 0.253016i \(-0.0814224\pi\)
\(810\) −32.2356 55.8338i −0.0397971 0.0689306i
\(811\) 523.200 + 906.209i 0.645130 + 1.11740i 0.984272 + 0.176662i \(0.0565301\pi\)
−0.339142 + 0.940735i \(0.610137\pi\)
\(812\) −138.480 516.816i −0.170542 0.636473i
\(813\) 103.901i 0.127800i
\(814\) 125.254 + 50.9561i 0.153874 + 0.0625997i
\(815\) −127.630 −0.156601
\(816\) 58.3365 15.6312i 0.0714908 0.0191559i
\(817\) −306.091 + 176.722i −0.374652 + 0.216305i
\(818\) 169.582 97.9079i 0.207312 0.119692i
\(819\) −913.886 244.875i −1.11586 0.298993i
\(820\) −30.8758 + 30.8758i −0.0376534 + 0.0376534i
\(821\) 584.120 + 1011.73i 0.711474 + 1.23231i 0.964304 + 0.264798i \(0.0853054\pi\)
−0.252830 + 0.967511i \(0.581361\pi\)
\(822\) 347.005 347.005i 0.422147 0.422147i
\(823\) 12.5640 21.7615i 0.0152661 0.0264417i −0.858291 0.513163i \(-0.828474\pi\)
0.873558 + 0.486721i \(0.161807\pi\)
\(824\) 372.277 0.451792
\(825\) 283.795i 0.343995i
\(826\) 310.904 538.502i 0.376397 0.651939i
\(827\) 113.895 + 30.5180i 0.137720 + 0.0369021i 0.327021 0.945017i \(-0.393955\pi\)
−0.189300 + 0.981919i \(0.560622\pi\)
\(828\) 737.922 + 737.922i 0.891210 + 0.891210i
\(829\) −150.428 + 40.3071i −0.181457 + 0.0486214i −0.348403 0.937345i \(-0.613276\pi\)
0.166946 + 0.985966i \(0.446609\pi\)
\(830\) −1.62068 + 2.80709i −0.00195262 + 0.00338204i
\(831\) −80.0528 298.761i −0.0963331 0.359520i
\(832\) 32.0044 119.442i 0.0384668 0.143560i
\(833\) 67.9727 + 18.2132i 0.0815999 + 0.0218646i
\(834\) −282.071 + 75.5806i −0.338214 + 0.0906242i
\(835\) −219.180 126.544i −0.262491 0.151550i
\(836\) −8.32306 31.0621i −0.00995581 0.0371556i
\(837\) −205.480 + 205.480i −0.245495 + 0.245495i
\(838\) 232.027 865.935i 0.276881 1.03333i
\(839\) −716.872 413.886i −0.854436 0.493309i 0.00770908 0.999970i \(-0.497546\pi\)
−0.862145 + 0.506661i \(0.830879\pi\)
\(840\) 60.7359 0.0723047
\(841\) 1729.12i 2.05603i
\(842\) 664.982 + 383.928i 0.789765 + 0.455971i
\(843\) 1015.94 + 1015.94i 1.20515 + 1.20515i
\(844\) −238.214 + 137.533i −0.282244 + 0.162954i
\(845\) 44.3253 + 44.3253i 0.0524560 + 0.0524560i
\(846\) −60.1660 + 224.542i −0.0711182 + 0.265417i
\(847\) −301.637 522.450i −0.356124 0.616824i
\(848\) 107.850 + 186.802i 0.127182 + 0.220285i
\(849\) −69.4694 259.263i −0.0818250 0.305375i
\(850\) 113.833i 0.133922i
\(851\) −227.679 1648.75i −0.267542 1.93743i
\(852\) −824.469 −0.967686
\(853\) 156.425 41.9140i 0.183382 0.0491371i −0.165959 0.986133i \(-0.553072\pi\)
0.349341 + 0.936996i \(0.386405\pi\)
\(854\) −327.524 + 189.096i −0.383518 + 0.221424i
\(855\) −56.0381 + 32.3536i −0.0655416 + 0.0378405i
\(856\) 134.353 + 35.9999i 0.156955 + 0.0420560i
\(857\) 284.490 284.490i 0.331961 0.331961i −0.521370 0.853331i \(-0.674579\pi\)
0.853331 + 0.521370i \(0.174579\pi\)
\(858\) −128.194 222.038i −0.149410 0.258786i
\(859\) 71.6633 71.6633i 0.0834265 0.0834265i −0.664162 0.747589i \(-0.731212\pi\)
0.747589 + 0.664162i \(0.231212\pi\)
\(860\) 50.9308 88.2147i 0.0592218 0.102575i
\(861\) 583.216 0.677371
\(862\) 997.930i 1.15769i
\(863\) 306.166 530.295i 0.354770 0.614479i −0.632309 0.774716i \(-0.717893\pi\)
0.987079 + 0.160237i \(0.0512260\pi\)
\(864\) 64.4673 + 17.2740i 0.0746149 + 0.0199930i
\(865\) −95.2780 95.2780i −0.110148 0.110148i
\(866\) 355.956 95.3781i 0.411035 0.110136i
\(867\) 630.724 1092.45i 0.727478 1.26003i
\(868\) 67.2782 + 251.086i 0.0775095 + 0.289269i
\(869\) −75.4547 + 281.601i −0.0868294 + 0.324052i
\(870\) −281.806 75.5098i −0.323915 0.0867929i
\(871\) 411.876 110.362i 0.472877 0.126707i
\(872\) −150.576 86.9352i −0.172679 0.0996963i
\(873\) 216.051 + 806.315i 0.247482 + 0.923614i
\(874\) −279.886 + 279.886i −0.320236 + 0.320236i
\(875\) −60.2420 + 224.826i −0.0688480 + 0.256944i
\(876\) −873.294 504.196i −0.996910 0.575566i
\(877\) −360.322 −0.410857 −0.205429 0.978672i \(-0.565859\pi\)
−0.205429 + 0.978672i \(0.565859\pi\)
\(878\) 932.170i 1.06170i
\(879\) 948.048 + 547.356i 1.07855 + 0.622703i
\(880\) 6.55334 + 6.55334i 0.00744697 + 0.00744697i
\(881\) 173.512 100.177i 0.196949 0.113709i −0.398282 0.917263i \(-0.630394\pi\)
0.595232 + 0.803554i \(0.297060\pi\)
\(882\) 245.370 + 245.370i 0.278198 + 0.278198i
\(883\) 10.7749 40.2125i 0.0122026 0.0455407i −0.959556 0.281517i \(-0.909162\pi\)
0.971759 + 0.235977i \(0.0758289\pi\)
\(884\) 51.4199 + 89.0619i 0.0581673 + 0.100749i
\(885\) −169.528 293.631i −0.191557 0.331787i
\(886\) 172.962 + 645.502i 0.195217 + 0.728558i
\(887\) 299.625i 0.337796i −0.985634 0.168898i \(-0.945979\pi\)
0.985634 0.168898i \(-0.0540209\pi\)
\(888\) −291.527 374.991i −0.328296 0.422287i
\(889\) 558.321 0.628032
\(890\) −164.697 + 44.1304i −0.185053 + 0.0495848i
\(891\) −113.796 + 65.7000i −0.127717 + 0.0737373i
\(892\) 715.547 413.121i 0.802182 0.463140i
\(893\) −85.1666 22.8203i −0.0953714 0.0255547i
\(894\) −196.235 + 196.235i −0.219503 + 0.219503i
\(895\) −30.4193 52.6878i −0.0339880 0.0588690i
\(896\) 42.2158 42.2158i 0.0471159 0.0471159i
\(897\) −1577.89 + 2732.99i −1.75908 + 3.04681i
\(898\) −1074.24 −1.19625
\(899\) 1248.65i 1.38893i
\(900\) −280.664 + 486.124i −0.311848 + 0.540137i
\(901\) −173.278 46.4296i −0.192317 0.0515312i
\(902\) 62.9284 + 62.9284i 0.0697654 + 0.0697654i
\(903\) −1314.17 + 352.130i −1.45534 + 0.389956i
\(904\) 142.520 246.852i 0.157655 0.273067i
\(905\) 47.6278 + 177.749i 0.0526274 + 0.196408i
\(906\) 68.8745 257.043i 0.0760204 0.283712i
\(907\) 403.168 + 108.028i 0.444507 + 0.119105i 0.474128 0.880456i \(-0.342763\pi\)
−0.0296211 + 0.999561i \(0.509430\pi\)
\(908\) −117.221 + 31.4093i −0.129098 + 0.0345918i
\(909\) −1119.49 646.339i −1.23156 0.711044i
\(910\) 26.7674 + 99.8974i 0.0294147 + 0.109777i
\(911\) −90.2042 + 90.2042i −0.0990167 + 0.0990167i −0.754880 0.655863i \(-0.772305\pi\)
0.655863 + 0.754880i \(0.272305\pi\)
\(912\) −29.2355 + 109.108i −0.0320565 + 0.119636i
\(913\) 5.72118 + 3.30313i 0.00626636 + 0.00361788i
\(914\) −520.741 −0.569738
\(915\) 206.218i 0.225375i
\(916\) −671.248 387.545i −0.732804 0.423084i
\(917\) −528.422 528.422i −0.576251 0.576251i
\(918\) −48.0700 + 27.7533i −0.0523639 + 0.0302323i
\(919\) −416.984 416.984i −0.453737 0.453737i 0.442856 0.896593i \(-0.353965\pi\)
−0.896593 + 0.442856i \(0.853965\pi\)
\(920\) 29.5246 110.187i 0.0320919 0.119769i
\(921\) 774.378 + 1341.26i 0.840802 + 1.45631i
\(922\) −125.437 217.264i −0.136049 0.235644i
\(923\) −363.358 1356.07i −0.393671 1.46920i
\(924\) 123.787i 0.133968i
\(925\) 824.927 347.824i 0.891813 0.376026i
\(926\) 419.035 0.452522
\(927\) −1474.70 + 395.145i −1.59083 + 0.426263i
\(928\) −248.360 + 143.391i −0.267630 + 0.154516i
\(929\) −225.210 + 130.025i −0.242422 + 0.139962i −0.616289 0.787520i \(-0.711365\pi\)
0.373868 + 0.927482i \(0.378031\pi\)
\(930\) 136.911 + 36.6851i 0.147216 + 0.0394463i
\(931\) −93.0665 + 93.0665i −0.0999640 + 0.0999640i
\(932\) 300.991 + 521.331i 0.322951 + 0.559368i
\(933\) −1110.66 + 1110.66i −1.19041 + 1.19041i
\(934\) 55.7642 96.5864i 0.0597047 0.103412i
\(935\) −7.70772 −0.00824355
\(936\) 507.117i 0.541791i
\(937\) −886.119 + 1534.80i −0.945698 + 1.63800i −0.191350 + 0.981522i \(0.561287\pi\)
−0.754348 + 0.656475i \(0.772047\pi\)
\(938\) 198.858 + 53.2839i 0.212002 + 0.0568059i
\(939\) 1575.61 + 1575.61i 1.67797 + 1.67797i
\(940\) 24.5449 6.57677i 0.0261115 0.00699657i
\(941\) 827.078 1432.54i 0.878935 1.52236i 0.0264237 0.999651i \(-0.491588\pi\)
0.852511 0.522709i \(-0.175079\pi\)
\(942\) 215.967 + 806.001i 0.229265 + 0.855627i
\(943\) 283.509 1058.07i 0.300646 1.12203i
\(944\) −321.929 86.2606i −0.341026 0.0913778i
\(945\) −53.9183 + 14.4474i −0.0570564 + 0.0152882i
\(946\) −179.792 103.803i −0.190055 0.109728i
\(947\) 312.818 + 1167.45i 0.330325 + 1.23279i 0.908849 + 0.417125i \(0.136962\pi\)
−0.578524 + 0.815666i \(0.696371\pi\)
\(948\) 724.108 724.108i 0.763827 0.763827i
\(949\) 444.417 1658.59i 0.468300 1.74772i
\(950\) −184.382 106.453i −0.194086 0.112056i
\(951\) −136.967 −0.144024
\(952\) 49.6522i 0.0521557i
\(953\) −654.673 377.976i −0.686960 0.396616i 0.115512 0.993306i \(-0.463149\pi\)
−0.802472 + 0.596690i \(0.796482\pi\)
\(954\) −625.504 625.504i −0.655665 0.655665i
\(955\) −69.2779 + 39.9976i −0.0725423 + 0.0418823i
\(956\) −149.981 149.981i −0.156884 0.156884i
\(957\) −153.898 + 574.354i −0.160813 + 0.600161i
\(958\) 227.410 + 393.886i 0.237380 + 0.411155i
\(959\) 201.726 + 349.400i 0.210351 + 0.364338i
\(960\) −8.42561 31.4448i −0.00877668 0.0327550i
\(961\) 354.367i 0.368748i
\(962\) 488.297 644.763i 0.507585 0.670232i
\(963\) −570.427 −0.592344
\(964\) 308.450 82.6490i 0.319969 0.0857354i
\(965\) −244.673 + 141.262i −0.253547 + 0.146385i
\(966\) −1319.52 + 761.823i −1.36596 + 0.788637i
\(967\) −49.8356 13.3534i −0.0515363 0.0138091i 0.232959 0.972487i \(-0.425159\pi\)
−0.284495 + 0.958677i \(0.591826\pi\)
\(968\) −228.644 + 228.644i −0.236202 + 0.236202i
\(969\) −46.9713 81.3567i −0.0484740 0.0839594i
\(970\) 64.5220 64.5220i 0.0665175 0.0665175i
\(971\) −238.604 + 413.274i −0.245730 + 0.425617i −0.962337 0.271861i \(-0.912361\pi\)
0.716607 + 0.697477i \(0.245694\pi\)
\(972\) 673.924 0.693338
\(973\) 240.080i 0.246742i
\(974\) 89.8601 155.642i 0.0922588 0.159797i
\(975\) −1639.61 439.333i −1.68166 0.450598i
\(976\) 143.337 + 143.337i 0.146861 + 0.146861i
\(977\) −137.157 + 36.7511i −0.140386 + 0.0376163i −0.328328 0.944564i \(-0.606485\pi\)
0.187942 + 0.982180i \(0.439818\pi\)
\(978\) 456.856 791.298i 0.467133 0.809099i
\(979\) 89.9430 + 335.672i 0.0918723 + 0.342872i
\(980\) 9.81738 36.6389i 0.0100177 0.0373867i
\(981\) 688.754 + 184.551i 0.702094 + 0.188125i
\(982\) 687.234 184.144i 0.699831 0.187519i
\(983\) 1683.97 + 972.239i 1.71309 + 0.989053i 0.930325 + 0.366737i \(0.119525\pi\)
0.782766 + 0.622316i \(0.213808\pi\)
\(984\) −80.9069 301.949i −0.0822224 0.306858i
\(985\) 48.9430 48.9430i 0.0496883 0.0496883i
\(986\) 61.7300 230.380i 0.0626065 0.233651i
\(987\) −293.930 169.701i −0.297802 0.171936i
\(988\) −192.344 −0.194680
\(989\) 2555.34i 2.58376i
\(990\) −32.9157 19.0039i −0.0332482 0.0191958i
\(991\) −795.632 795.632i −0.802857 0.802857i 0.180684 0.983541i \(-0.442169\pi\)
−0.983541 + 0.180684i \(0.942169\pi\)
\(992\) 120.662 69.6640i 0.121635 0.0702258i
\(993\) 827.490 + 827.490i 0.833324 + 0.833324i
\(994\) 175.433 654.726i 0.176492 0.658678i
\(995\) 75.6400 + 131.012i 0.0760201 + 0.131671i
\(996\) −11.6025 20.0962i −0.0116491 0.0201769i
\(997\) −171.784 641.107i −0.172301 0.643036i −0.996996 0.0774580i \(-0.975320\pi\)
0.824695 0.565578i \(-0.191347\pi\)
\(998\) 1275.32i 1.27788i
\(999\) 348.003 + 263.552i 0.348351 + 0.263816i
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 74.3.g.b.51.3 yes 12
37.8 odd 12 inner 74.3.g.b.45.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.3.g.b.45.3 12 37.8 odd 12 inner
74.3.g.b.51.3 yes 12 1.1 even 1 trivial