Properties

Label 430.2.l.a.7.4
Level $430$
Weight $2$
Character 430.7
Analytic conductor $3.434$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [430,2,Mod(7,430)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(430, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("430.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 430.l (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: \(3.43356728692\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 7.4
Character \(\chi\) \(=\) 430.7
Dual form 430.2.l.a.123.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.388695 + 1.45063i) q^{3} -1.00000i q^{4} +(-0.951195 + 2.02367i) q^{5} +(-0.750902 - 1.30060i) q^{6} +(0.957274 + 3.57260i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.644831 + 0.372294i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.388695 + 1.45063i) q^{3} -1.00000i q^{4} +(-0.951195 + 2.02367i) q^{5} +(-0.750902 - 1.30060i) q^{6} +(0.957274 + 3.57260i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.644831 + 0.372294i) q^{9} +(-0.758352 - 2.10355i) q^{10} +5.85835 q^{11} +(1.45063 + 0.388695i) q^{12} +(-0.325074 - 1.21319i) q^{13} +(-3.20310 - 1.84931i) q^{14} +(-2.56587 - 2.16642i) q^{15} -1.00000 q^{16} +(-5.89376 + 1.57923i) q^{17} +(-0.719216 + 0.192713i) q^{18} +(-1.28855 - 2.23183i) q^{19} +(2.02367 + 0.951195i) q^{20} -5.55460 q^{21} +(-4.14248 + 4.14248i) q^{22} +(1.73706 + 0.465444i) q^{23} +(-1.30060 + 0.750902i) q^{24} +(-3.19046 - 3.84980i) q^{25} +(1.08772 + 0.627995i) q^{26} +(-3.97651 + 3.97651i) q^{27} +(3.57260 - 0.957274i) q^{28} +(-1.89925 + 3.28961i) q^{29} +(3.34623 - 0.282451i) q^{30} +(-2.54770 - 4.41274i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.27711 + 8.49830i) q^{33} +(3.05083 - 5.28420i) q^{34} +(-8.14030 - 1.46103i) q^{35} +(0.372294 - 0.644831i) q^{36} +(7.90170 + 2.11725i) q^{37} +(2.48928 + 0.667000i) q^{38} +1.88625 q^{39} +(-2.10355 + 0.758352i) q^{40} +11.4087 q^{41} +(3.92770 - 3.92770i) q^{42} +(-6.44809 - 1.19252i) q^{43} -5.85835i q^{44} +(-1.36676 + 0.950800i) q^{45} +(-1.55740 + 0.899168i) q^{46} +(-6.64908 - 6.64908i) q^{47} +(0.388695 - 1.45063i) q^{48} +(-5.78489 + 3.33991i) q^{49} +(4.97822 + 0.466228i) q^{50} -9.16350i q^{51} +(-1.21319 + 0.325074i) q^{52} +(4.82436 + 1.29268i) q^{53} -5.62363i q^{54} +(-5.57243 + 11.8553i) q^{55} +(-1.84931 + 3.20310i) q^{56} +(3.73841 - 1.00170i) q^{57} +(-0.983127 - 3.66908i) q^{58} +6.77889i q^{59} +(-2.16642 + 2.56587i) q^{60} +(-10.1476 - 5.85874i) q^{61} +(4.92178 + 1.31879i) q^{62} +(-0.712774 + 2.66011i) q^{63} +1.00000i q^{64} +(2.76431 + 0.496141i) q^{65} +(-4.39904 - 7.61937i) q^{66} +(3.47065 - 12.9526i) q^{67} +(1.57923 + 5.89376i) q^{68} +(-1.35037 + 2.33891i) q^{69} +(6.78916 - 4.72296i) q^{70} +(4.34431 + 2.50819i) q^{71} +(0.192713 + 0.719216i) q^{72} +(13.3372 - 3.57369i) q^{73} +(-7.08447 + 4.09022i) q^{74} +(6.82476 - 3.13177i) q^{75} +(-2.23183 + 1.28855i) q^{76} +(5.60804 + 20.9295i) q^{77} +(-1.33378 + 1.33378i) q^{78} +(-3.69801 - 2.13505i) q^{79} +(0.951195 - 2.02367i) q^{80} +(-3.10591 - 5.37960i) q^{81} +(-8.06719 + 8.06719i) q^{82} +(13.6163 + 3.64847i) q^{83} +5.55460i q^{84} +(2.41028 - 13.4292i) q^{85} +(5.40273 - 3.71625i) q^{86} +(-4.03377 - 4.03377i) q^{87} +(4.14248 + 4.14248i) q^{88} +(4.93483 + 8.54737i) q^{89} +(0.294127 - 1.63876i) q^{90} +(4.02306 - 2.32272i) q^{91} +(0.465444 - 1.73706i) q^{92} +(7.39154 - 1.98056i) q^{93} +9.40322 q^{94} +(5.74213 - 0.484685i) q^{95} +(0.750902 + 1.30060i) q^{96} +(0.604877 + 0.604877i) q^{97} +(1.72886 - 6.45221i) q^{98} +(3.77765 + 2.18103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/430\mathbb{Z}\right)^\times\).

\(n\) \(87\) \(261\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.388695 + 1.45063i −0.224413 + 0.837522i 0.758225 + 0.651993i \(0.226067\pi\)
−0.982639 + 0.185529i \(0.940600\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −0.951195 + 2.02367i −0.425387 + 0.905011i
\(6\) −0.750902 1.30060i −0.306554 0.530968i
\(7\) 0.957274 + 3.57260i 0.361816 + 1.35031i 0.871687 + 0.490063i \(0.163026\pi\)
−0.509871 + 0.860251i \(0.670307\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0.644831 + 0.372294i 0.214944 + 0.124098i
\(10\) −0.758352 2.10355i −0.239812 0.665199i
\(11\) 5.85835 1.76636 0.883179 0.469036i \(-0.155398\pi\)
0.883179 + 0.469036i \(0.155398\pi\)
\(12\) 1.45063 + 0.388695i 0.418761 + 0.112207i
\(13\) −0.325074 1.21319i −0.0901593 0.336479i 0.906082 0.423102i \(-0.139059\pi\)
−0.996241 + 0.0866234i \(0.972392\pi\)
\(14\) −3.20310 1.84931i −0.856065 0.494249i
\(15\) −2.56587 2.16642i −0.662504 0.559368i
\(16\) −1.00000 −0.250000
\(17\) −5.89376 + 1.57923i −1.42945 + 0.383019i −0.888825 0.458247i \(-0.848477\pi\)
−0.540621 + 0.841266i \(0.681811\pi\)
\(18\) −0.719216 + 0.192713i −0.169521 + 0.0454230i
\(19\) −1.28855 2.23183i −0.295613 0.512016i 0.679515 0.733662i \(-0.262190\pi\)
−0.975127 + 0.221646i \(0.928857\pi\)
\(20\) 2.02367 + 0.951195i 0.452506 + 0.212694i
\(21\) −5.55460 −1.21211
\(22\) −4.14248 + 4.14248i −0.883179 + 0.883179i
\(23\) 1.73706 + 0.465444i 0.362202 + 0.0970517i 0.435330 0.900271i \(-0.356632\pi\)
−0.0731284 + 0.997323i \(0.523298\pi\)
\(24\) −1.30060 + 0.750902i −0.265484 + 0.153277i
\(25\) −3.19046 3.84980i −0.638091 0.769961i
\(26\) 1.08772 + 0.627995i 0.213319 + 0.123160i
\(27\) −3.97651 + 3.97651i −0.765280 + 0.765280i
\(28\) 3.57260 0.957274i 0.675157 0.180908i
\(29\) −1.89925 + 3.28961i −0.352683 + 0.610865i −0.986719 0.162439i \(-0.948064\pi\)
0.634036 + 0.773304i \(0.281397\pi\)
\(30\) 3.34623 0.282451i 0.610936 0.0515683i
\(31\) −2.54770 4.41274i −0.457580 0.792552i 0.541252 0.840860i \(-0.317950\pi\)
−0.998832 + 0.0483082i \(0.984617\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −2.27711 + 8.49830i −0.396394 + 1.47936i
\(34\) 3.05083 5.28420i 0.523214 0.906232i
\(35\) −8.14030 1.46103i −1.37596 0.246959i
\(36\) 0.372294 0.644831i 0.0620489 0.107472i
\(37\) 7.90170 + 2.11725i 1.29903 + 0.348074i 0.841084 0.540905i \(-0.181918\pi\)
0.457947 + 0.888979i \(0.348585\pi\)
\(38\) 2.48928 + 0.667000i 0.403814 + 0.108202i
\(39\) 1.88625 0.302042
\(40\) −2.10355 + 0.758352i −0.332600 + 0.119906i
\(41\) 11.4087 1.78174 0.890872 0.454255i \(-0.150094\pi\)
0.890872 + 0.454255i \(0.150094\pi\)
\(42\) 3.92770 3.92770i 0.606057 0.606057i
\(43\) −6.44809 1.19252i −0.983325 0.181858i
\(44\) 5.85835i 0.883179i
\(45\) −1.36676 + 0.950800i −0.203744 + 0.141737i
\(46\) −1.55740 + 0.899168i −0.229627 + 0.132575i
\(47\) −6.64908 6.64908i −0.969868 0.969868i 0.0296910 0.999559i \(-0.490548\pi\)
−0.999559 + 0.0296910i \(0.990548\pi\)
\(48\) 0.388695 1.45063i 0.0561033 0.209380i
\(49\) −5.78489 + 3.33991i −0.826413 + 0.477130i
\(50\) 4.97822 + 0.466228i 0.704026 + 0.0659346i
\(51\) 9.16350i 1.28315i
\(52\) −1.21319 + 0.325074i −0.168240 + 0.0450796i
\(53\) 4.82436 + 1.29268i 0.662677 + 0.177564i 0.574454 0.818537i \(-0.305215\pi\)
0.0882231 + 0.996101i \(0.471881\pi\)
\(54\) 5.62363i 0.765280i
\(55\) −5.57243 + 11.8553i −0.751386 + 1.59857i
\(56\) −1.84931 + 3.20310i −0.247125 + 0.428032i
\(57\) 3.73841 1.00170i 0.495164 0.132679i
\(58\) −0.983127 3.66908i −0.129091 0.481774i
\(59\) 6.77889i 0.882537i 0.897375 + 0.441268i \(0.145471\pi\)
−0.897375 + 0.441268i \(0.854529\pi\)
\(60\) −2.16642 + 2.56587i −0.279684 + 0.331252i
\(61\) −10.1476 5.85874i −1.29927 0.750135i −0.318993 0.947757i \(-0.603345\pi\)
−0.980278 + 0.197622i \(0.936678\pi\)
\(62\) 4.92178 + 1.31879i 0.625066 + 0.167486i
\(63\) −0.712774 + 2.66011i −0.0898011 + 0.335142i
\(64\) 1.00000i 0.125000i
\(65\) 2.76431 + 0.496141i 0.342870 + 0.0615387i
\(66\) −4.39904 7.61937i −0.541485 0.937879i
\(67\) 3.47065 12.9526i 0.424007 1.58242i −0.342074 0.939673i \(-0.611129\pi\)
0.766081 0.642744i \(-0.222204\pi\)
\(68\) 1.57923 + 5.89376i 0.191509 + 0.714723i
\(69\) −1.35037 + 2.33891i −0.162566 + 0.281572i
\(70\) 6.78916 4.72296i 0.811460 0.564501i
\(71\) 4.34431 + 2.50819i 0.515574 + 0.297667i 0.735122 0.677935i \(-0.237125\pi\)
−0.219548 + 0.975602i \(0.570458\pi\)
\(72\) 0.192713 + 0.719216i 0.0227115 + 0.0847604i
\(73\) 13.3372 3.57369i 1.56100 0.418269i 0.628021 0.778196i \(-0.283865\pi\)
0.932980 + 0.359927i \(0.117199\pi\)
\(74\) −7.08447 + 4.09022i −0.823553 + 0.475478i
\(75\) 6.82476 3.13177i 0.788055 0.361626i
\(76\) −2.23183 + 1.28855i −0.256008 + 0.147806i
\(77\) 5.60804 + 20.9295i 0.639096 + 2.38514i
\(78\) −1.33378 + 1.33378i −0.151021 + 0.151021i
\(79\) −3.69801 2.13505i −0.416058 0.240211i 0.277331 0.960774i \(-0.410550\pi\)
−0.693389 + 0.720563i \(0.743883\pi\)
\(80\) 0.951195 2.02367i 0.106347 0.226253i
\(81\) −3.10591 5.37960i −0.345102 0.597733i
\(82\) −8.06719 + 8.06719i −0.890872 + 0.890872i
\(83\) 13.6163 + 3.64847i 1.49458 + 0.400472i 0.911281 0.411785i \(-0.135095\pi\)
0.583300 + 0.812257i \(0.301761\pi\)
\(84\) 5.55460i 0.606057i
\(85\) 2.41028 13.4292i 0.261432 1.45660i
\(86\) 5.40273 3.71625i 0.582592 0.400733i
\(87\) −4.03377 4.03377i −0.432466 0.432466i
\(88\) 4.14248 + 4.14248i 0.441590 + 0.441590i
\(89\) 4.93483 + 8.54737i 0.523091 + 0.906020i 0.999639 + 0.0268713i \(0.00855442\pi\)
−0.476548 + 0.879148i \(0.658112\pi\)
\(90\) 0.294127 1.63876i 0.0310037 0.172741i
\(91\) 4.02306 2.32272i 0.421731 0.243487i
\(92\) 0.465444 1.73706i 0.0485258 0.181101i
\(93\) 7.39154 1.98056i 0.766467 0.205374i
\(94\) 9.40322 0.969868
\(95\) 5.74213 0.484685i 0.589130 0.0497277i
\(96\) 0.750902 + 1.30060i 0.0766386 + 0.132742i
\(97\) 0.604877 + 0.604877i 0.0614160 + 0.0614160i 0.737148 0.675732i \(-0.236172\pi\)
−0.675732 + 0.737148i \(0.736172\pi\)
\(98\) 1.72886 6.45221i 0.174642 0.651771i
\(99\) 3.77765 + 2.18103i 0.379668 + 0.219201i
\(100\) −3.84980 + 3.19046i −0.384980 + 0.319046i
\(101\) −5.40532 + 9.36229i −0.537849 + 0.931582i 0.461170 + 0.887312i \(0.347430\pi\)
−0.999020 + 0.0442706i \(0.985904\pi\)
\(102\) 6.47957 + 6.47957i 0.641573 + 0.641573i
\(103\) 1.53443 + 5.72658i 0.151192 + 0.564257i 0.999401 + 0.0345957i \(0.0110143\pi\)
−0.848209 + 0.529661i \(0.822319\pi\)
\(104\) 0.627995 1.08772i 0.0615799 0.106660i
\(105\) 5.28351 11.2407i 0.515618 1.09698i
\(106\) −4.32540 + 2.49727i −0.420120 + 0.242557i
\(107\) −5.82762 5.82762i −0.563377 0.563377i 0.366888 0.930265i \(-0.380423\pi\)
−0.930265 + 0.366888i \(0.880423\pi\)
\(108\) 3.97651 + 3.97651i 0.382640 + 0.382640i
\(109\) −13.7305 + 7.92731i −1.31514 + 0.759299i −0.982943 0.183910i \(-0.941125\pi\)
−0.332201 + 0.943209i \(0.607791\pi\)
\(110\) −4.44269 12.3233i −0.423594 1.17498i
\(111\) −6.14271 + 10.6395i −0.583040 + 1.00985i
\(112\) −0.957274 3.57260i −0.0904539 0.337579i
\(113\) 4.21257 + 4.21257i 0.396285 + 0.396285i 0.876921 0.480635i \(-0.159594\pi\)
−0.480635 + 0.876921i \(0.659594\pi\)
\(114\) −1.93514 + 3.35176i −0.181243 + 0.313921i
\(115\) −2.59418 + 3.07250i −0.241909 + 0.286512i
\(116\) 3.28961 + 1.89925i 0.305432 + 0.176341i
\(117\) 0.242046 0.903328i 0.0223772 0.0835127i
\(118\) −4.79340 4.79340i −0.441268 0.441268i
\(119\) −11.2839 19.5443i −1.03439 1.79162i
\(120\) −0.282451 3.34623i −0.0257841 0.305468i
\(121\) 23.3202 2.12002
\(122\) 11.3182 3.03271i 1.02470 0.274568i
\(123\) −4.43452 + 16.5498i −0.399847 + 1.49225i
\(124\) −4.41274 + 2.54770i −0.396276 + 0.228790i
\(125\) 10.8255 2.79451i 0.968259 0.249949i
\(126\) −1.37697 2.38499i −0.122671 0.212472i
\(127\) 1.92210 + 1.92210i 0.170559 + 0.170559i 0.787225 0.616666i \(-0.211517\pi\)
−0.616666 + 0.787225i \(0.711517\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 4.23626 8.89027i 0.372981 0.782745i
\(130\) −2.30548 + 1.60384i −0.202204 + 0.140666i
\(131\) 9.53894i 0.833421i −0.909039 0.416711i \(-0.863183\pi\)
0.909039 0.416711i \(-0.136817\pi\)
\(132\) 8.49830 + 2.27711i 0.739682 + 0.198197i
\(133\) 6.73992 6.73992i 0.584425 0.584425i
\(134\) 6.70478 + 11.6130i 0.579205 + 1.00321i
\(135\) −4.26470 11.8296i −0.367047 1.01813i
\(136\) −5.28420 3.05083i −0.453116 0.261607i
\(137\) 1.48924 1.48924i 0.127234 0.127234i −0.640622 0.767856i \(-0.721323\pi\)
0.767856 + 0.640622i \(0.221323\pi\)
\(138\) −0.699005 2.60872i −0.0595032 0.222069i
\(139\) 2.50765 1.44779i 0.212696 0.122800i −0.389868 0.920871i \(-0.627479\pi\)
0.602564 + 0.798071i \(0.294146\pi\)
\(140\) −1.46103 + 8.14030i −0.123480 + 0.687981i
\(141\) 12.2298 7.06089i 1.02994 0.594634i
\(142\) −4.84544 + 1.29833i −0.406621 + 0.108954i
\(143\) −1.90440 7.10730i −0.159254 0.594343i
\(144\) −0.644831 0.372294i −0.0537360 0.0310245i
\(145\) −4.85051 6.97252i −0.402813 0.579036i
\(146\) −6.90384 + 11.9578i −0.571366 + 0.989635i
\(147\) −2.59641 9.68994i −0.214148 0.799213i
\(148\) 2.11725 7.90170i 0.174037 0.649516i
\(149\) 6.10509 + 10.5743i 0.500149 + 0.866283i 1.00000 0.000171762i \(5.46735e-5\pi\)
−0.499851 + 0.866111i \(0.666612\pi\)
\(150\) −2.61133 + 7.04033i −0.213215 + 0.574841i
\(151\) 7.45280i 0.606500i 0.952911 + 0.303250i \(0.0980717\pi\)
−0.952911 + 0.303250i \(0.901928\pi\)
\(152\) 0.667000 2.48928i 0.0541009 0.201907i
\(153\) −4.38842 1.17587i −0.354782 0.0950637i
\(154\) −18.7649 10.8339i −1.51212 0.873021i
\(155\) 11.3533 0.958315i 0.911917 0.0769737i
\(156\) 1.88625i 0.151021i
\(157\) 3.23061 + 12.0568i 0.257831 + 0.962237i 0.966494 + 0.256690i \(0.0826320\pi\)
−0.708663 + 0.705547i \(0.750701\pi\)
\(158\) 4.12459 1.10518i 0.328135 0.0879234i
\(159\) −3.75041 + 6.49590i −0.297427 + 0.515159i
\(160\) 0.758352 + 2.10355i 0.0599530 + 0.166300i
\(161\) 6.65137i 0.524201i
\(162\) 6.00017 + 1.60774i 0.471417 + 0.126316i
\(163\) −14.2561 + 3.81991i −1.11663 + 0.299199i −0.769517 0.638626i \(-0.779503\pi\)
−0.347108 + 0.937825i \(0.612836\pi\)
\(164\) 11.4087i 0.890872i
\(165\) −15.0317 12.6917i −1.17022 0.988044i
\(166\) −12.2080 + 7.04830i −0.947526 + 0.547054i
\(167\) −0.296153 + 1.10526i −0.0229170 + 0.0855274i −0.976437 0.215802i \(-0.930764\pi\)
0.953520 + 0.301329i \(0.0974302\pi\)
\(168\) −3.92770 3.92770i −0.303029 0.303029i
\(169\) 9.89217 5.71125i 0.760936 0.439327i
\(170\) 7.79152 + 11.2002i 0.597582 + 0.859014i
\(171\) 1.91887i 0.146740i
\(172\) −1.19252 + 6.44809i −0.0909292 + 0.491662i
\(173\) −13.2428 + 13.2428i −1.00683 + 1.00683i −0.00685416 + 0.999977i \(0.502182\pi\)
−0.999977 + 0.00685416i \(0.997818\pi\)
\(174\) 5.70461 0.432466
\(175\) 10.6996 15.0835i 0.808817 1.14021i
\(176\) −5.85835 −0.441590
\(177\) −9.83367 2.63492i −0.739144 0.198053i
\(178\) −9.53335 2.55445i −0.714555 0.191464i
\(179\) −0.117211 + 0.203016i −0.00876079 + 0.0151741i −0.870373 0.492394i \(-0.836122\pi\)
0.861612 + 0.507568i \(0.169455\pi\)
\(180\) 0.950800 + 1.36676i 0.0708685 + 0.101872i
\(181\) −0.256825 + 0.444833i −0.0190896 + 0.0330642i −0.875412 0.483377i \(-0.839410\pi\)
0.856323 + 0.516441i \(0.172743\pi\)
\(182\) −1.20233 + 4.48714i −0.0891223 + 0.332609i
\(183\) 12.4432 12.4432i 0.919828 0.919828i
\(184\) 0.899168 + 1.55740i 0.0662875 + 0.114813i
\(185\) −11.8007 + 13.9765i −0.867603 + 1.02757i
\(186\) −3.82614 + 6.62707i −0.280546 + 0.485920i
\(187\) −34.5277 + 9.25166i −2.52491 + 0.676549i
\(188\) −6.64908 + 6.64908i −0.484934 + 0.484934i
\(189\) −18.0131 10.3999i −1.31026 0.756478i
\(190\) −3.71758 + 4.40302i −0.269701 + 0.319429i
\(191\) 6.00285 3.46575i 0.434351 0.250773i −0.266848 0.963739i \(-0.585982\pi\)
0.701198 + 0.712966i \(0.252649\pi\)
\(192\) −1.45063 0.388695i −0.104690 0.0280517i
\(193\) 4.34418 4.34418i 0.312701 0.312701i −0.533254 0.845955i \(-0.679031\pi\)
0.845955 + 0.533254i \(0.179031\pi\)
\(194\) −0.855426 −0.0614160
\(195\) −1.79419 + 3.81714i −0.128485 + 0.273351i
\(196\) 3.33991 + 5.78489i 0.238565 + 0.413206i
\(197\) 2.27640 0.609958i 0.162186 0.0434577i −0.176812 0.984245i \(-0.556578\pi\)
0.338999 + 0.940787i \(0.389912\pi\)
\(198\) −4.21342 + 1.12898i −0.299435 + 0.0802332i
\(199\) 16.6372 1.17938 0.589688 0.807631i \(-0.299251\pi\)
0.589688 + 0.807631i \(0.299251\pi\)
\(200\) 0.466228 4.97822i 0.0329673 0.352013i
\(201\) 17.4405 + 10.0693i 1.23016 + 0.710231i
\(202\) −2.79800 10.4423i −0.196866 0.734716i
\(203\) −13.5705 3.63622i −0.952465 0.255212i
\(204\) −9.16350 −0.641573
\(205\) −10.8519 + 23.0875i −0.757931 + 1.61250i
\(206\) −5.13431 2.96430i −0.357725 0.206532i
\(207\) 0.946829 + 0.946829i 0.0658091 + 0.0658091i
\(208\) 0.325074 + 1.21319i 0.0225398 + 0.0841198i
\(209\) −7.54875 13.0748i −0.522158 0.904404i
\(210\) 4.21235 + 11.6844i 0.290680 + 0.806297i
\(211\) 9.79097i 0.674038i −0.941498 0.337019i \(-0.890581\pi\)
0.941498 0.337019i \(-0.109419\pi\)
\(212\) 1.29268 4.82436i 0.0887819 0.331338i
\(213\) −5.32706 + 5.32706i −0.365004 + 0.365004i
\(214\) 8.24150 0.563377
\(215\) 8.54666 11.9145i 0.582878 0.812560i
\(216\) −5.62363 −0.382640
\(217\) 13.3261 13.3261i 0.904635 0.904635i
\(218\) 4.10348 15.3144i 0.277923 1.03722i
\(219\) 20.7364i 1.40124i
\(220\) 11.8553 + 5.57243i 0.799287 + 0.375693i
\(221\) 3.83181 + 6.63690i 0.257756 + 0.446446i
\(222\) −3.17970 11.8668i −0.213407 0.796447i
\(223\) 5.54239 + 5.54239i 0.371146 + 0.371146i 0.867895 0.496749i \(-0.165473\pi\)
−0.496749 + 0.867895i \(0.665473\pi\)
\(224\) 3.20310 + 1.84931i 0.214016 + 0.123562i
\(225\) −0.624050 3.67026i −0.0416033 0.244684i
\(226\) −5.95747 −0.396285
\(227\) −19.3485 5.18440i −1.28420 0.344101i −0.448747 0.893659i \(-0.648129\pi\)
−0.835455 + 0.549558i \(0.814796\pi\)
\(228\) −1.00170 3.73841i −0.0663394 0.247582i
\(229\) −8.31230 4.79911i −0.549292 0.317134i 0.199544 0.979889i \(-0.436054\pi\)
−0.748837 + 0.662755i \(0.769387\pi\)
\(230\) −0.338221 4.00695i −0.0223017 0.264211i
\(231\) −32.5408 −2.14103
\(232\) −3.66908 + 0.983127i −0.240887 + 0.0645454i
\(233\) 1.51192 0.405117i 0.0990490 0.0265401i −0.208954 0.977925i \(-0.567006\pi\)
0.308003 + 0.951385i \(0.400339\pi\)
\(234\) 0.467597 + 0.809901i 0.0305678 + 0.0529449i
\(235\) 19.7801 7.13095i 1.29031 0.465172i
\(236\) 6.77889 0.441268
\(237\) 4.53456 4.53456i 0.294551 0.294551i
\(238\) 21.7988 + 5.84097i 1.41301 + 0.378614i
\(239\) 13.7842 7.95829i 0.891623 0.514779i 0.0171500 0.999853i \(-0.494541\pi\)
0.874473 + 0.485074i \(0.161207\pi\)
\(240\) 2.56587 + 2.16642i 0.165626 + 0.139842i
\(241\) −4.13497 2.38733i −0.266357 0.153781i 0.360874 0.932615i \(-0.382478\pi\)
−0.627231 + 0.778833i \(0.715812\pi\)
\(242\) −16.4899 + 16.4899i −1.06001 + 1.06001i
\(243\) −7.28497 + 1.95200i −0.467331 + 0.125221i
\(244\) −5.85874 + 10.1476i −0.375067 + 0.649636i
\(245\) −1.25630 14.8836i −0.0802623 0.950878i
\(246\) −8.56683 14.8382i −0.546201 0.946048i
\(247\) −2.28876 + 2.28876i −0.145630 + 0.145630i
\(248\) 1.31879 4.92178i 0.0837430 0.312533i
\(249\) −10.5852 + 18.3340i −0.670808 + 1.16187i
\(250\) −5.67874 + 9.63078i −0.359155 + 0.609104i
\(251\) −2.24164 + 3.88263i −0.141491 + 0.245069i −0.928058 0.372435i \(-0.878523\pi\)
0.786567 + 0.617504i \(0.211856\pi\)
\(252\) 2.66011 + 0.712774i 0.167571 + 0.0449005i
\(253\) 10.1763 + 2.72673i 0.639778 + 0.171428i
\(254\) −2.71826 −0.170559
\(255\) 18.5439 + 8.71627i 1.16126 + 0.545834i
\(256\) 1.00000 0.0625000
\(257\) 8.40996 8.40996i 0.524599 0.524599i −0.394358 0.918957i \(-0.629033\pi\)
0.918957 + 0.394358i \(0.129033\pi\)
\(258\) 3.29088 + 9.28185i 0.204882 + 0.577863i
\(259\) 30.2564i 1.88004i
\(260\) 0.496141 2.76431i 0.0307694 0.171435i
\(261\) −2.44940 + 1.41416i −0.151614 + 0.0875344i
\(262\) 6.74505 + 6.74505i 0.416711 + 0.416711i
\(263\) 5.15600 19.2424i 0.317933 1.18654i −0.603296 0.797518i \(-0.706146\pi\)
0.921228 0.389023i \(-0.127187\pi\)
\(264\) −7.61937 + 4.39904i −0.468940 + 0.270742i
\(265\) −7.20487 + 8.53331i −0.442591 + 0.524197i
\(266\) 9.53169i 0.584425i
\(267\) −14.3172 + 3.83629i −0.876200 + 0.234777i
\(268\) −12.9526 3.47065i −0.791209 0.212004i
\(269\) 0.453147i 0.0276288i 0.999905 + 0.0138144i \(0.00439741\pi\)
−0.999905 + 0.0138144i \(0.995603\pi\)
\(270\) 11.3804 + 5.34917i 0.692587 + 0.325540i
\(271\) −4.31181 + 7.46827i −0.261924 + 0.453665i −0.966753 0.255712i \(-0.917690\pi\)
0.704829 + 0.709377i \(0.251024\pi\)
\(272\) 5.89376 1.57923i 0.357361 0.0957547i
\(273\) 1.80566 + 6.73880i 0.109283 + 0.407851i
\(274\) 2.10610i 0.127234i
\(275\) −18.6908 22.5535i −1.12710 1.36003i
\(276\) 2.33891 + 1.35037i 0.140786 + 0.0812829i
\(277\) −0.190909 0.0511540i −0.0114706 0.00307355i 0.253079 0.967446i \(-0.418557\pi\)
−0.264550 + 0.964372i \(0.585223\pi\)
\(278\) −0.749433 + 2.79692i −0.0449480 + 0.167748i
\(279\) 3.79397i 0.227139i
\(280\) −4.72296 6.78916i −0.282251 0.405730i
\(281\) 4.80170 + 8.31678i 0.286445 + 0.496138i 0.972959 0.230979i \(-0.0741930\pi\)
−0.686513 + 0.727117i \(0.740860\pi\)
\(282\) −3.65499 + 13.6406i −0.217651 + 0.812286i
\(283\) −3.23477 12.0723i −0.192287 0.717624i −0.992953 0.118513i \(-0.962187\pi\)
0.800666 0.599111i \(-0.204479\pi\)
\(284\) 2.50819 4.34431i 0.148833 0.257787i
\(285\) −1.52884 + 8.51810i −0.0905606 + 0.504569i
\(286\) 6.37223 + 3.67901i 0.376798 + 0.217544i
\(287\) 10.9213 + 40.7588i 0.644663 + 2.40591i
\(288\) 0.719216 0.192713i 0.0423802 0.0113557i
\(289\) 17.5200 10.1152i 1.03059 0.595010i
\(290\) 8.36014 + 1.50049i 0.490924 + 0.0881117i
\(291\) −1.11257 + 0.642341i −0.0652198 + 0.0376547i
\(292\) −3.57369 13.3372i −0.209135 0.780501i
\(293\) −5.41287 + 5.41287i −0.316223 + 0.316223i −0.847314 0.531091i \(-0.821782\pi\)
0.531091 + 0.847314i \(0.321782\pi\)
\(294\) 8.68776 + 5.01588i 0.506681 + 0.292532i
\(295\) −13.7182 6.44805i −0.798706 0.375420i
\(296\) 4.09022 + 7.08447i 0.237739 + 0.411776i
\(297\) −23.2958 + 23.2958i −1.35176 + 1.35176i
\(298\) −11.7941 3.16023i −0.683216 0.183067i
\(299\) 2.25869i 0.130623i
\(300\) −3.13177 6.82476i −0.180813 0.394028i
\(301\) −1.91218 24.1780i −0.110216 1.39360i
\(302\) −5.26992 5.26992i −0.303250 0.303250i
\(303\) −11.4802 11.4802i −0.659520 0.659520i
\(304\) 1.28855 + 2.23183i 0.0739031 + 0.128004i
\(305\) 21.5085 14.9626i 1.23157 0.856758i
\(306\) 3.93455 2.27161i 0.224923 0.129859i
\(307\) 2.05993 7.68778i 0.117567 0.438765i −0.881899 0.471438i \(-0.843735\pi\)
0.999466 + 0.0326728i \(0.0104019\pi\)
\(308\) 20.9295 5.60804i 1.19257 0.319548i
\(309\) −8.90358 −0.506507
\(310\) −7.35035 + 8.70561i −0.417472 + 0.494446i
\(311\) −5.13592 8.89567i −0.291231 0.504427i 0.682870 0.730540i \(-0.260732\pi\)
−0.974101 + 0.226113i \(0.927398\pi\)
\(312\) 1.33378 + 1.33378i 0.0755104 + 0.0755104i
\(313\) 5.83491 21.7762i 0.329809 1.23086i −0.579580 0.814916i \(-0.696783\pi\)
0.909389 0.415948i \(-0.136550\pi\)
\(314\) −10.8098 6.24106i −0.610034 0.352203i
\(315\) −4.70519 3.97270i −0.265107 0.223836i
\(316\) −2.13505 + 3.69801i −0.120106 + 0.208029i
\(317\) −1.37821 1.37821i −0.0774082 0.0774082i 0.667343 0.744751i \(-0.267432\pi\)
−0.744751 + 0.667343i \(0.767432\pi\)
\(318\) −1.94136 7.24524i −0.108866 0.406293i
\(319\) −11.1265 + 19.2717i −0.622964 + 1.07901i
\(320\) −2.02367 0.951195i −0.113126 0.0531734i
\(321\) 10.7189 6.18855i 0.598270 0.345411i
\(322\) −4.70323 4.70323i −0.262101 0.262101i
\(323\) 11.1189 + 11.1189i 0.618674 + 0.618674i
\(324\) −5.37960 + 3.10591i −0.298867 + 0.172551i
\(325\) −3.63342 + 5.12211i −0.201546 + 0.284123i
\(326\) 7.37951 12.7817i 0.408713 0.707912i
\(327\) −6.16262 22.9992i −0.340793 1.27186i
\(328\) 8.06719 + 8.06719i 0.445436 + 0.445436i
\(329\) 17.3895 30.1195i 0.958713 1.66054i
\(330\) 19.6034 1.65470i 1.07913 0.0910881i
\(331\) −6.66828 3.84993i −0.366522 0.211611i 0.305416 0.952219i \(-0.401204\pi\)
−0.671938 + 0.740608i \(0.734538\pi\)
\(332\) 3.64847 13.6163i 0.200236 0.747290i
\(333\) 4.30702 + 4.30702i 0.236023 + 0.236023i
\(334\) −0.572123 0.990947i −0.0313052 0.0542222i
\(335\) 22.9106 + 19.3439i 1.25174 + 1.05687i
\(336\) 5.55460 0.303029
\(337\) 17.9758 4.81659i 0.979203 0.262377i 0.266494 0.963837i \(-0.414135\pi\)
0.712709 + 0.701460i \(0.247468\pi\)
\(338\) −2.95636 + 11.0333i −0.160805 + 0.600131i
\(339\) −7.74829 + 4.47348i −0.420829 + 0.242966i
\(340\) −13.4292 2.41028i −0.728298 0.130716i
\(341\) −14.9253 25.8514i −0.808250 1.39993i
\(342\) 1.35685 + 1.35685i 0.0733698 + 0.0733698i
\(343\) 0.837388 + 0.837388i 0.0452147 + 0.0452147i
\(344\) −3.71625 5.40273i −0.200367 0.291296i
\(345\) −3.44872 4.95747i −0.185673 0.266901i
\(346\) 18.7281i 1.00683i
\(347\) 17.5630 + 4.70600i 0.942833 + 0.252631i 0.697318 0.716762i \(-0.254376\pi\)
0.245515 + 0.969393i \(0.421043\pi\)
\(348\) −4.03377 + 4.03377i −0.216233 + 0.216233i
\(349\) 14.9656 + 25.9211i 0.801088 + 1.38753i 0.918900 + 0.394490i \(0.129079\pi\)
−0.117812 + 0.993036i \(0.537588\pi\)
\(350\) 3.09987 + 18.2315i 0.165695 + 0.974513i
\(351\) 6.11693 + 3.53161i 0.326498 + 0.188503i
\(352\) 4.14248 4.14248i 0.220795 0.220795i
\(353\) −4.18258 15.6096i −0.222616 0.830815i −0.983346 0.181746i \(-0.941825\pi\)
0.760729 0.649069i \(-0.224841\pi\)
\(354\) 8.81663 5.09028i 0.468598 0.270545i
\(355\) −9.20802 + 6.40566i −0.488711 + 0.339977i
\(356\) 8.54737 4.93483i 0.453010 0.261545i
\(357\) 32.7375 8.77198i 1.73265 0.464263i
\(358\) −0.0606731 0.226435i −0.00320667 0.0119675i
\(359\) 23.8164 + 13.7504i 1.25698 + 0.725719i 0.972487 0.232959i \(-0.0748408\pi\)
0.284495 + 0.958678i \(0.408174\pi\)
\(360\) −1.63876 0.294127i −0.0863703 0.0155018i
\(361\) 6.17930 10.7029i 0.325226 0.563309i
\(362\) −0.132942 0.496147i −0.00698729 0.0260769i
\(363\) −9.06447 + 33.8290i −0.475761 + 1.77556i
\(364\) −2.32272 4.02306i −0.121743 0.210866i
\(365\) −5.45431 + 30.3893i −0.285492 + 1.59065i
\(366\) 17.5974i 0.919828i
\(367\) 7.08146 26.4284i 0.369649 1.37955i −0.491358 0.870958i \(-0.663499\pi\)
0.861008 0.508592i \(-0.169834\pi\)
\(368\) −1.73706 0.465444i −0.0905505 0.0242629i
\(369\) 7.35671 + 4.24740i 0.382975 + 0.221111i
\(370\) −1.53853 18.2272i −0.0799845 0.947587i
\(371\) 18.4729i 0.959067i
\(372\) −1.98056 7.39154i −0.102687 0.383233i
\(373\) −9.93714 + 2.66265i −0.514526 + 0.137867i −0.506733 0.862103i \(-0.669147\pi\)
−0.00779248 + 0.999970i \(0.502480\pi\)
\(374\) 17.8728 30.9567i 0.924183 1.60073i
\(375\) −0.154007 + 16.7900i −0.00795288 + 0.867030i
\(376\) 9.40322i 0.484934i
\(377\) 4.60832 + 1.23480i 0.237341 + 0.0635953i
\(378\) 20.0910 5.38336i 1.03337 0.276890i
\(379\) 21.7270i 1.11604i −0.829827 0.558020i \(-0.811561\pi\)
0.829827 0.558020i \(-0.188439\pi\)
\(380\) −0.484685 5.74213i −0.0248638 0.294565i
\(381\) −3.53537 + 2.04114i −0.181122 + 0.104571i
\(382\) −1.79400 + 6.69531i −0.0917891 + 0.342562i
\(383\) −21.7891 21.7891i −1.11337 1.11337i −0.992691 0.120680i \(-0.961493\pi\)
−0.120680 0.992691i \(-0.538507\pi\)
\(384\) 1.30060 0.750902i 0.0663710 0.0383193i
\(385\) −47.6887 8.55922i −2.43044 0.436218i
\(386\) 6.14360i 0.312701i
\(387\) −3.71396 3.16956i −0.188791 0.161118i
\(388\) 0.604877 0.604877i 0.0307080 0.0307080i
\(389\) 9.60057 0.486768 0.243384 0.969930i \(-0.421742\pi\)
0.243384 + 0.969930i \(0.421742\pi\)
\(390\) −1.43044 3.96781i −0.0724332 0.200918i
\(391\) −10.9728 −0.554921
\(392\) −6.45221 1.72886i −0.325886 0.0873208i
\(393\) 13.8375 + 3.70774i 0.698008 + 0.187031i
\(394\) −1.17835 + 2.04096i −0.0593644 + 0.102822i
\(395\) 7.83814 5.45269i 0.394380 0.274355i
\(396\) 2.18103 3.77765i 0.109601 0.189834i
\(397\) −4.44076 + 16.5731i −0.222875 + 0.831782i 0.760369 + 0.649491i \(0.225018\pi\)
−0.983245 + 0.182291i \(0.941649\pi\)
\(398\) −11.7642 + 11.7642i −0.589688 + 0.589688i
\(399\) 7.15736 + 12.3969i 0.358316 + 0.620622i
\(400\) 3.19046 + 3.84980i 0.159523 + 0.192490i
\(401\) −12.6033 + 21.8295i −0.629377 + 1.09011i 0.358300 + 0.933606i \(0.383356\pi\)
−0.987677 + 0.156506i \(0.949977\pi\)
\(402\) −19.4523 + 5.21223i −0.970194 + 0.259963i
\(403\) −4.52532 + 4.52532i −0.225422 + 0.225422i
\(404\) 9.36229 + 5.40532i 0.465791 + 0.268925i
\(405\) 13.8409 1.16829i 0.687757 0.0580527i
\(406\) 12.1670 7.02463i 0.603839 0.348626i
\(407\) 46.2909 + 12.4036i 2.29455 + 0.614824i
\(408\) 6.47957 6.47957i 0.320787 0.320787i
\(409\) −9.19045 −0.454438 −0.227219 0.973844i \(-0.572963\pi\)
−0.227219 + 0.973844i \(0.572963\pi\)
\(410\) −8.65184 23.9988i −0.427284 1.18521i
\(411\) 1.58148 + 2.73920i 0.0780085 + 0.135115i
\(412\) 5.72658 1.53443i 0.282129 0.0755961i
\(413\) −24.2182 + 6.48926i −1.19170 + 0.319316i
\(414\) −1.33902 −0.0658091
\(415\) −20.3350 + 24.0844i −0.998207 + 1.18226i
\(416\) −1.08772 0.627995i −0.0533298 0.0307900i
\(417\) 1.12550 + 4.20043i 0.0551160 + 0.205696i
\(418\) 14.5831 + 3.90752i 0.713281 + 0.191123i
\(419\) 4.94794 0.241723 0.120861 0.992669i \(-0.461434\pi\)
0.120861 + 0.992669i \(0.461434\pi\)
\(420\) −11.2407 5.28351i −0.548489 0.257809i
\(421\) 23.8893 + 13.7925i 1.16430 + 0.672206i 0.952330 0.305071i \(-0.0986802\pi\)
0.211966 + 0.977277i \(0.432014\pi\)
\(422\) 6.92326 + 6.92326i 0.337019 + 0.337019i
\(423\) −1.81213 6.76295i −0.0881086 0.328826i
\(424\) 2.49727 + 4.32540i 0.121278 + 0.210060i
\(425\) 24.8835 + 17.6513i 1.20703 + 0.856216i
\(426\) 7.53361i 0.365004i
\(427\) 11.2168 41.8618i 0.542821 2.02584i
\(428\) −5.82762 + 5.82762i −0.281689 + 0.281689i
\(429\) 11.0503 0.533514
\(430\) 2.38140 + 14.4682i 0.114841 + 0.697719i
\(431\) 3.40036 0.163790 0.0818948 0.996641i \(-0.473903\pi\)
0.0818948 + 0.996641i \(0.473903\pi\)
\(432\) 3.97651 3.97651i 0.191320 0.191320i
\(433\) −8.35525 + 31.1822i −0.401527 + 1.49852i 0.408844 + 0.912604i \(0.365932\pi\)
−0.810371 + 0.585917i \(0.800735\pi\)
\(434\) 18.8460i 0.904635i
\(435\) 11.9999 4.32611i 0.575352 0.207421i
\(436\) 7.92731 + 13.7305i 0.379649 + 0.657572i
\(437\) −1.19949 4.47656i −0.0573794 0.214143i
\(438\) −14.6629 14.6629i −0.700619 0.700619i
\(439\) 28.9042 + 16.6878i 1.37952 + 0.796467i 0.992102 0.125436i \(-0.0400330\pi\)
0.387420 + 0.921903i \(0.373366\pi\)
\(440\) −12.3233 + 4.44269i −0.587490 + 0.211797i
\(441\) −4.97370 −0.236843
\(442\) −7.40250 1.98349i −0.352101 0.0943451i
\(443\) 6.86297 + 25.6129i 0.326069 + 1.21691i 0.913232 + 0.407439i \(0.133578\pi\)
−0.587163 + 0.809469i \(0.699755\pi\)
\(444\) 10.6395 + 6.14271i 0.504927 + 0.291520i
\(445\) −21.9910 + 1.85623i −1.04247 + 0.0879938i
\(446\) −7.83812 −0.371146
\(447\) −17.7125 + 4.74604i −0.837771 + 0.224480i
\(448\) −3.57260 + 0.957274i −0.168789 + 0.0452270i
\(449\) −15.3320 26.5558i −0.723561 1.25324i −0.959563 0.281492i \(-0.909171\pi\)
0.236002 0.971753i \(-0.424163\pi\)
\(450\) 3.03654 + 2.15400i 0.143144 + 0.101540i
\(451\) 66.8363 3.14720
\(452\) 4.21257 4.21257i 0.198143 0.198143i
\(453\) −10.8113 2.89687i −0.507957 0.136107i
\(454\) 17.3473 10.0155i 0.814151 0.470051i
\(455\) 0.873688 + 10.3507i 0.0409591 + 0.485248i
\(456\) 3.35176 + 1.93514i 0.156961 + 0.0906213i
\(457\) 9.93087 9.93087i 0.464546 0.464546i −0.435596 0.900142i \(-0.643462\pi\)
0.900142 + 0.435596i \(0.143462\pi\)
\(458\) 9.27117 2.48420i 0.433213 0.116079i
\(459\) 17.1568 29.7164i 0.800809 1.38704i
\(460\) 3.07250 + 2.59418i 0.143256 + 0.120954i
\(461\) 0.233783 + 0.404924i 0.0108883 + 0.0188592i 0.871418 0.490541i \(-0.163201\pi\)
−0.860530 + 0.509400i \(0.829867\pi\)
\(462\) 23.0098 23.0098i 1.07051 1.07051i
\(463\) −2.20016 + 8.21109i −0.102250 + 0.381602i −0.998019 0.0629185i \(-0.979959\pi\)
0.895769 + 0.444520i \(0.146626\pi\)
\(464\) 1.89925 3.28961i 0.0881707 0.152716i
\(465\) −3.02281 + 16.8419i −0.140179 + 0.781025i
\(466\) −0.782626 + 1.35555i −0.0362545 + 0.0627946i
\(467\) −29.5224 7.91049i −1.36613 0.366054i −0.500068 0.865986i \(-0.666692\pi\)
−0.866065 + 0.499932i \(0.833358\pi\)
\(468\) −0.903328 0.242046i −0.0417563 0.0111886i
\(469\) 49.5969 2.29017
\(470\) −8.94429 + 19.0290i −0.412570 + 0.877742i
\(471\) −18.7457 −0.863755
\(472\) −4.79340 + 4.79340i −0.220634 + 0.220634i
\(473\) −37.7752 6.98622i −1.73690 0.321227i
\(474\) 6.41283i 0.294551i
\(475\) −4.48104 + 12.0812i −0.205604 + 0.554323i
\(476\) −19.5443 + 11.2839i −0.895810 + 0.517196i
\(477\) 2.62964 + 2.62964i 0.120403 + 0.120403i
\(478\) −4.11951 + 15.3742i −0.188422 + 0.703201i
\(479\) 12.0014 6.92904i 0.548360 0.316596i −0.200100 0.979775i \(-0.564127\pi\)
0.748460 + 0.663180i \(0.230793\pi\)
\(480\) −3.34623 + 0.282451i −0.152734 + 0.0128921i
\(481\) 10.2745i 0.468479i
\(482\) 4.61196 1.23577i 0.210069 0.0562879i
\(483\) −9.64867 2.58535i −0.439030 0.117638i
\(484\) 23.3202i 1.06001i
\(485\) −1.79943 + 0.648714i −0.0817078 + 0.0294566i
\(486\) 3.77098 6.53153i 0.171055 0.296276i
\(487\) −8.80058 + 2.35811i −0.398792 + 0.106856i −0.452641 0.891693i \(-0.649518\pi\)
0.0538482 + 0.998549i \(0.482851\pi\)
\(488\) −3.03271 11.3182i −0.137284 0.512352i
\(489\) 22.1651i 1.00234i
\(490\) 11.4126 + 9.63595i 0.515570 + 0.435308i
\(491\) −30.2587 17.4699i −1.36556 0.788404i −0.375199 0.926944i \(-0.622426\pi\)
−0.990357 + 0.138540i \(0.955759\pi\)
\(492\) 16.5498 + 4.43452i 0.746125 + 0.199924i
\(493\) 5.99871 22.3875i 0.270168 1.00828i
\(494\) 3.23680i 0.145630i
\(495\) −8.00695 + 5.57012i −0.359886 + 0.250358i
\(496\) 2.54770 + 4.41274i 0.114395 + 0.198138i
\(497\) −4.80204 + 17.9215i −0.215401 + 0.803888i
\(498\) −5.47928 20.4490i −0.245533 0.916340i
\(499\) 0.476911 0.826034i 0.0213495 0.0369784i −0.855153 0.518375i \(-0.826537\pi\)
0.876503 + 0.481397i \(0.159870\pi\)
\(500\) −2.79451 10.8255i −0.124974 0.484130i
\(501\) −1.48821 0.859217i −0.0664882 0.0383870i
\(502\) −1.16036 4.33051i −0.0517893 0.193280i
\(503\) −20.8866 + 5.59656i −0.931289 + 0.249538i −0.692404 0.721510i \(-0.743449\pi\)
−0.238885 + 0.971048i \(0.576782\pi\)
\(504\) −2.38499 + 1.37697i −0.106236 + 0.0613353i
\(505\) −13.8046 19.8439i −0.614298 0.883043i
\(506\) −9.12382 + 5.26764i −0.405603 + 0.234175i
\(507\) 4.43987 + 16.5698i 0.197181 + 0.735891i
\(508\) 1.92210 1.92210i 0.0852794 0.0852794i
\(509\) −11.1861 6.45828i −0.495814 0.286258i 0.231169 0.972914i \(-0.425745\pi\)
−0.726983 + 0.686655i \(0.759078\pi\)
\(510\) −19.2758 + 6.94916i −0.853548 + 0.307714i
\(511\) 25.5347 + 44.2274i 1.12959 + 1.95651i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 13.9988 + 3.75096i 0.618062 + 0.165609i
\(514\) 11.8935i 0.524599i
\(515\) −13.0482 2.34191i −0.574974 0.103197i
\(516\) −8.89027 4.23626i −0.391372 0.186491i
\(517\) −38.9526 38.9526i −1.71313 1.71313i
\(518\) −21.3945 21.3945i −0.940020 0.940020i
\(519\) −14.0630 24.3578i −0.617297 1.06919i
\(520\) 1.60384 + 2.30548i 0.0703328 + 0.101102i
\(521\) −1.15892 + 0.669106i −0.0507734 + 0.0293141i −0.525172 0.850996i \(-0.675999\pi\)
0.474398 + 0.880310i \(0.342666\pi\)
\(522\) 0.732024 2.73195i 0.0320398 0.119574i
\(523\) −0.109939 + 0.0294581i −0.00480731 + 0.00128811i −0.261222 0.965279i \(-0.584125\pi\)
0.256415 + 0.966567i \(0.417459\pi\)
\(524\) −9.53894 −0.416711
\(525\) 17.7217 + 21.3841i 0.773439 + 0.933280i
\(526\) 9.96062 + 17.2523i 0.434304 + 0.752236i
\(527\) 21.9842 + 21.9842i 0.957648 + 0.957648i
\(528\) 2.27711 8.49830i 0.0990986 0.369841i
\(529\) −17.1178 9.88299i −0.744254 0.429695i
\(530\) −0.939347 11.1286i −0.0408026 0.483394i
\(531\) −2.52374 + 4.37124i −0.109521 + 0.189696i
\(532\) −6.73992 6.73992i −0.292213 0.292213i
\(533\) −3.70868 13.8410i −0.160641 0.599520i
\(534\) 7.41114 12.8365i 0.320711 0.555488i
\(535\) 17.3364 6.24996i 0.749516 0.270209i
\(536\) 11.6130 6.70478i 0.501606 0.289602i
\(537\) −0.248942 0.248942i −0.0107426 0.0107426i
\(538\) −0.320423 0.320423i −0.0138144 0.0138144i
\(539\) −33.8899 + 19.5663i −1.45974 + 0.842782i
\(540\) −11.8296 + 4.26470i −0.509063 + 0.183523i
\(541\) 9.80121 16.9762i 0.421387 0.729864i −0.574688 0.818372i \(-0.694877\pi\)
0.996075 + 0.0885085i \(0.0282100\pi\)
\(542\) −2.23196 8.32978i −0.0958708 0.357795i
\(543\) −0.545462 0.545462i −0.0234080 0.0234080i
\(544\) −3.05083 + 5.28420i −0.130803 + 0.226558i
\(545\) −2.98185 35.3264i −0.127729 1.51322i
\(546\) −6.04185 3.48826i −0.258567 0.149284i
\(547\) 2.73733 10.2158i 0.117040 0.436798i −0.882392 0.470516i \(-0.844068\pi\)
0.999431 + 0.0337175i \(0.0107346\pi\)
\(548\) −1.48924 1.48924i −0.0636172 0.0636172i
\(549\) −4.36234 7.55580i −0.186180 0.322474i
\(550\) 29.1641 + 2.73133i 1.24356 + 0.116464i
\(551\) 9.78911 0.417030
\(552\) −2.60872 + 0.699005i −0.111035 + 0.0297516i
\(553\) 4.08765 15.2553i 0.173824 0.648722i
\(554\) 0.171165 0.0988220i 0.00727209 0.00419854i
\(555\) −15.6879 22.5510i −0.665912 0.957237i
\(556\) −1.44779 2.50765i −0.0614001 0.106348i
\(557\) 7.65086 + 7.65086i 0.324178 + 0.324178i 0.850367 0.526190i \(-0.176380\pi\)
−0.526190 + 0.850367i \(0.676380\pi\)
\(558\) 2.68274 + 2.68274i 0.113569 + 0.113569i
\(559\) 0.649345 + 8.21044i 0.0274643 + 0.347264i
\(560\) 8.14030 + 1.46103i 0.343990 + 0.0617398i
\(561\) 53.6830i 2.26650i
\(562\) −9.27617 2.48554i −0.391291 0.104846i
\(563\) 18.5027 18.5027i 0.779796 0.779796i −0.200000 0.979796i \(-0.564094\pi\)
0.979796 + 0.200000i \(0.0640942\pi\)
\(564\) −7.06089 12.2298i −0.297317 0.514969i
\(565\) −12.5318 + 4.51786i −0.527217 + 0.190068i
\(566\) 10.8237 + 6.24909i 0.454956 + 0.262669i
\(567\) 16.2459 16.2459i 0.682265 0.682265i
\(568\) 1.29833 + 4.84544i 0.0544768 + 0.203310i
\(569\) −27.6735 + 15.9773i −1.16013 + 0.669804i −0.951336 0.308155i \(-0.900288\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(570\) −4.94216 7.10426i −0.207004 0.297565i
\(571\) −18.5906 + 10.7333i −0.777993 + 0.449174i −0.835718 0.549158i \(-0.814948\pi\)
0.0577257 + 0.998332i \(0.481615\pi\)
\(572\) −7.10730 + 1.90440i −0.297171 + 0.0796268i
\(573\) 2.69424 + 10.0550i 0.112553 + 0.420055i
\(574\) −36.5433 21.0983i −1.52529 0.880626i
\(575\) −3.75015 8.17231i −0.156392 0.340809i
\(576\) −0.372294 + 0.644831i −0.0155122 + 0.0268680i
\(577\) 8.18303 + 30.5395i 0.340664 + 1.27137i 0.897597 + 0.440817i \(0.145311\pi\)
−0.556933 + 0.830557i \(0.688022\pi\)
\(578\) −5.23599 + 19.5410i −0.217789 + 0.812798i
\(579\) 4.61324 + 7.99036i 0.191720 + 0.332068i
\(580\) −6.97252 + 4.85051i −0.289518 + 0.201406i
\(581\) 52.1380i 2.16305i
\(582\) 0.332500 1.24091i 0.0137826 0.0514372i
\(583\) 28.2628 + 7.57299i 1.17052 + 0.313641i
\(584\) 11.9578 + 6.90384i 0.494818 + 0.285683i
\(585\) 1.59780 + 1.34906i 0.0660610 + 0.0557768i
\(586\) 7.65495i 0.316223i
\(587\) −4.50362 16.8077i −0.185884 0.693730i −0.994439 0.105310i \(-0.966417\pi\)
0.808555 0.588420i \(-0.200250\pi\)
\(588\) −9.68994 + 2.59641i −0.399606 + 0.107074i
\(589\) −6.56565 + 11.3720i −0.270533 + 0.468577i
\(590\) 14.2597 5.14079i 0.587063 0.211643i
\(591\) 3.53930i 0.145587i
\(592\) −7.90170 2.11725i −0.324758 0.0870186i
\(593\) −34.7381 + 9.30804i −1.42652 + 0.382235i −0.887793 0.460244i \(-0.847762\pi\)
−0.538729 + 0.842479i \(0.681095\pi\)
\(594\) 32.9452i 1.35176i
\(595\) 50.2842 4.24442i 2.06145 0.174004i
\(596\) 10.5743 6.10509i 0.433142 0.250074i
\(597\) −6.46678 + 24.1344i −0.264668 + 0.987754i
\(598\) 1.59714 + 1.59714i 0.0653117 + 0.0653117i
\(599\) −13.1034 + 7.56528i −0.535392 + 0.309109i −0.743209 0.669059i \(-0.766697\pi\)
0.207817 + 0.978168i \(0.433364\pi\)
\(600\) 7.04033 + 2.61133i 0.287420 + 0.106607i
\(601\) 9.71694i 0.396362i −0.980165 0.198181i \(-0.936497\pi\)
0.980165 0.198181i \(-0.0635035\pi\)
\(602\) 18.4485 + 15.7443i 0.751906 + 0.641690i
\(603\) 7.06017 7.06017i 0.287512 0.287512i
\(604\) 7.45280 0.303250
\(605\) −22.1821 + 47.1924i −0.901830 + 1.91864i
\(606\) 16.2354 0.659520
\(607\) −27.7814 7.44400i −1.12761 0.302143i −0.353652 0.935377i \(-0.615060\pi\)
−0.773960 + 0.633235i \(0.781727\pi\)
\(608\) −2.48928 0.667000i −0.100954 0.0270504i
\(609\) 10.5496 18.2725i 0.427492 0.740437i
\(610\) −4.62864 + 25.7890i −0.187408 + 1.04417i
\(611\) −5.90517 + 10.2281i −0.238898 + 0.413783i
\(612\) −1.17587 + 4.38842i −0.0475318 + 0.177391i
\(613\) −7.32011 + 7.32011i −0.295657 + 0.295657i −0.839310 0.543653i \(-0.817041\pi\)
0.543653 + 0.839310i \(0.317041\pi\)
\(614\) 3.97949 + 6.89267i 0.160599 + 0.278166i
\(615\) −29.2733 24.7161i −1.18041 0.996650i
\(616\) −10.8339 + 18.7649i −0.436511 + 0.756059i
\(617\) 18.6713 5.00297i 0.751680 0.201412i 0.137417 0.990513i \(-0.456120\pi\)
0.614263 + 0.789101i \(0.289453\pi\)
\(618\) 6.29578 6.29578i 0.253254 0.253254i
\(619\) −25.6943 14.8346i −1.03274 0.596253i −0.114971 0.993369i \(-0.536678\pi\)
−0.917768 + 0.397116i \(0.870011\pi\)
\(620\) −0.958315 11.3533i −0.0384869 0.455959i
\(621\) −8.75827 + 5.05659i −0.351457 + 0.202914i
\(622\) 9.92183 + 2.65855i 0.397829 + 0.106598i
\(623\) −25.8123 + 25.8123i −1.03415 + 1.03415i
\(624\) −1.88625 −0.0755104
\(625\) −4.64197 + 24.5653i −0.185679 + 0.982610i
\(626\) 11.2722 + 19.5240i 0.450527 + 0.780336i
\(627\) 21.9009 5.86832i 0.874637 0.234358i
\(628\) 12.0568 3.23061i 0.481119 0.128915i
\(629\) −49.9143 −1.99021
\(630\) 6.13619 0.517948i 0.244472 0.0206355i
\(631\) 5.91743 + 3.41643i 0.235569 + 0.136006i 0.613139 0.789975i \(-0.289907\pi\)
−0.377569 + 0.925981i \(0.623240\pi\)
\(632\) −1.10518 4.12459i −0.0439617 0.164067i
\(633\) 14.2031 + 3.80570i 0.564522 + 0.151263i
\(634\) 1.94909 0.0774082
\(635\) −5.71798 + 2.06140i −0.226911 + 0.0818041i
\(636\) 6.49590 + 3.75041i 0.257579 + 0.148714i
\(637\) 5.93247 + 5.93247i 0.235053 + 0.235053i
\(638\) −5.75950 21.4947i −0.228021 0.850985i
\(639\) 1.86756 + 3.23472i 0.0738797 + 0.127963i
\(640\) 2.10355 0.758352i 0.0831499 0.0299765i
\(641\) 14.5962i 0.576517i 0.957553 + 0.288258i \(0.0930762\pi\)
−0.957553 + 0.288258i \(0.906924\pi\)
\(642\) −3.20343 + 11.9554i −0.126429 + 0.471841i
\(643\) 26.5550 26.5550i 1.04723 1.04723i 0.0483976 0.998828i \(-0.484589\pi\)
0.998828 0.0483976i \(-0.0154115\pi\)
\(644\) 6.65137 0.262101
\(645\) 13.9614 + 17.0291i 0.549731 + 0.670522i
\(646\) −15.7245 −0.618674
\(647\) 4.78805 4.78805i 0.188238 0.188238i −0.606696 0.794934i \(-0.707506\pi\)
0.794934 + 0.606696i \(0.207506\pi\)
\(648\) 1.60774 6.00017i 0.0631580 0.235709i
\(649\) 39.7131i 1.55888i
\(650\) −1.05266 6.19109i −0.0412889 0.242835i
\(651\) 14.1515 + 24.5110i 0.554639 + 0.960663i
\(652\) 3.81991 + 14.2561i 0.149599 + 0.558313i
\(653\) 4.64808 + 4.64808i 0.181893 + 0.181893i 0.792180 0.610287i \(-0.208946\pi\)
−0.610287 + 0.792180i \(0.708946\pi\)
\(654\) 20.6205 + 11.9053i 0.806326 + 0.465533i
\(655\) 19.3036 + 9.07339i 0.754256 + 0.354527i
\(656\) −11.4087 −0.445436
\(657\) 9.93071 + 2.66093i 0.387434 + 0.103813i
\(658\) 9.00146 + 33.5939i 0.350913 + 1.30963i
\(659\) −20.0969 11.6029i −0.782864 0.451987i 0.0545805 0.998509i \(-0.482618\pi\)
−0.837444 + 0.546523i \(0.815951\pi\)
\(660\) −12.6917 + 15.0317i −0.494022 + 0.585110i
\(661\) 41.4783 1.61332 0.806660 0.591016i \(-0.201273\pi\)
0.806660 + 0.591016i \(0.201273\pi\)
\(662\) 7.43749 1.99287i 0.289066 0.0774551i
\(663\) −11.1171 + 2.97882i −0.431752 + 0.115688i
\(664\) 7.04830 + 12.2080i 0.273527 + 0.473763i
\(665\) 7.22838 + 20.0503i 0.280305 + 0.777519i
\(666\) −6.09105 −0.236023
\(667\) −4.83024 + 4.83024i −0.187028 + 0.187028i
\(668\) 1.10526 + 0.296153i 0.0427637 + 0.0114585i
\(669\) −10.1943 + 5.88566i −0.394133 + 0.227553i
\(670\) −29.8784 + 2.52200i −1.15431 + 0.0974333i
\(671\) −59.4484 34.3225i −2.29498 1.32501i
\(672\) −3.92770 + 3.92770i −0.151514 + 0.151514i
\(673\) 9.24162 2.47628i 0.356238 0.0954537i −0.0762615 0.997088i \(-0.524298\pi\)
0.432500 + 0.901634i \(0.357632\pi\)
\(674\) −9.30495 + 16.1166i −0.358413 + 0.620790i
\(675\) 27.9957 + 2.62190i 1.07755 + 0.100917i
\(676\) −5.71125 9.89217i −0.219663 0.380468i
\(677\) −2.14535 + 2.14535i −0.0824525 + 0.0824525i −0.747130 0.664678i \(-0.768569\pi\)
0.664678 + 0.747130i \(0.268569\pi\)
\(678\) 2.31564 8.64209i 0.0889317 0.331898i
\(679\) −1.58195 + 2.74002i −0.0607096 + 0.105152i
\(680\) 11.2002 7.79152i 0.429507 0.298791i
\(681\) 15.0413 26.0523i 0.576384 0.998326i
\(682\) 28.8335 + 7.72590i 1.10409 + 0.295840i
\(683\) 30.2787 + 8.11316i 1.15858 + 0.310441i 0.786400 0.617718i \(-0.211943\pi\)
0.372183 + 0.928159i \(0.378609\pi\)
\(684\) −1.91887 −0.0733698
\(685\) 1.59717 + 4.43028i 0.0610247 + 0.169272i
\(686\) −1.18425 −0.0452147
\(687\) 10.1927 10.1927i 0.388875 0.388875i
\(688\) 6.44809 + 1.19252i 0.245831 + 0.0454646i
\(689\) 6.27310i 0.238986i
\(690\) 5.94407 + 1.06685i 0.226287 + 0.0406142i
\(691\) −2.40300 + 1.38737i −0.0914145 + 0.0527782i −0.545010 0.838429i \(-0.683474\pi\)
0.453596 + 0.891207i \(0.350141\pi\)
\(692\) 13.2428 + 13.2428i 0.503415 + 0.503415i
\(693\) −4.17568 + 15.5838i −0.158621 + 0.591981i
\(694\) −15.7466 + 9.09129i −0.597732 + 0.345101i
\(695\) 0.544587 + 6.45179i 0.0206573 + 0.244730i
\(696\) 5.70461i 0.216233i
\(697\) −67.2403 + 18.0170i −2.54691 + 0.682442i
\(698\) −28.9113 7.74675i −1.09431 0.293219i
\(699\) 2.35070i 0.0889117i
\(700\) −15.0835 10.6996i −0.570104 0.404409i
\(701\) −20.6304 + 35.7329i −0.779199 + 1.34961i 0.153205 + 0.988194i \(0.451041\pi\)
−0.932404 + 0.361418i \(0.882293\pi\)
\(702\) −6.82255 + 1.82810i −0.257501 + 0.0689971i
\(703\) −5.45635 20.3634i −0.205790 0.768020i
\(704\) 5.85835i 0.220795i
\(705\) 2.65595 + 31.4654i 0.100029 + 1.18505i
\(706\) 13.9952 + 8.08012i 0.526715 + 0.304099i
\(707\) −38.6220 10.3487i −1.45253 0.389205i
\(708\) −2.63492 + 9.83367i −0.0990265 + 0.369572i
\(709\) 37.1283i 1.39438i −0.716885 0.697192i \(-0.754433\pi\)
0.716885 0.697192i \(-0.245567\pi\)
\(710\) 1.98157 11.0405i 0.0743669 0.414344i
\(711\) −1.58973 2.75349i −0.0596194 0.103264i
\(712\) −2.55445 + 9.53335i −0.0957322 + 0.357278i
\(713\) −2.37162 8.85100i −0.0888178 0.331473i
\(714\) −16.9462 + 29.3516i −0.634194 + 1.09846i
\(715\) 16.1943 + 2.90657i 0.605631 + 0.108699i
\(716\) 0.203016 + 0.117211i 0.00758707 + 0.00438039i
\(717\) 6.18670 + 23.0891i 0.231046 + 0.862277i
\(718\) −26.5637 + 7.11773i −0.991350 + 0.265631i
\(719\) 6.99456 4.03831i 0.260853 0.150604i −0.363871 0.931450i \(-0.618545\pi\)
0.624724 + 0.780846i \(0.285212\pi\)
\(720\) 1.36676 0.950800i 0.0509361 0.0354342i
\(721\) −18.9899 + 10.9638i −0.707221 + 0.408314i
\(722\) 3.19864 + 11.9375i 0.119041 + 0.444268i
\(723\) 5.07038 5.07038i 0.188569 0.188569i
\(724\) 0.444833 + 0.256825i 0.0165321 + 0.00954481i
\(725\) 18.7238 3.18359i 0.695385 0.118235i
\(726\) −17.5112 30.3303i −0.649902 1.12566i
\(727\) 30.9315 30.9315i 1.14718 1.14718i 0.160080 0.987104i \(-0.448825\pi\)
0.987104 0.160080i \(-0.0511754\pi\)
\(728\) 4.48714 + 1.20233i 0.166305 + 0.0445612i
\(729\) 29.9620i 1.10970i
\(730\) −17.6317 25.3453i −0.652579 0.938071i
\(731\) 39.8867 3.15455i 1.47526 0.116675i
\(732\) −12.4432 12.4432i −0.459914 0.459914i
\(733\) −35.2205 35.2205i −1.30090 1.30090i −0.927785 0.373115i \(-0.878290\pi\)
−0.373115 0.927785i \(-0.621710\pi\)
\(734\) 13.6803 + 23.6950i 0.504950 + 0.874599i
\(735\) 22.0789 + 3.96275i 0.814393 + 0.146168i
\(736\) 1.55740 0.899168i 0.0574067 0.0331438i
\(737\) 20.3323 75.8811i 0.748949 2.79512i
\(738\) −8.20534 + 2.19861i −0.302043 + 0.0809321i
\(739\) 16.4923 0.606678 0.303339 0.952883i \(-0.401898\pi\)
0.303339 + 0.952883i \(0.401898\pi\)
\(740\) 13.9765 + 11.8007i 0.513786 + 0.433801i
\(741\) −2.43052 4.20978i −0.0892873 0.154650i
\(742\) −13.0623 13.0623i −0.479534 0.479534i
\(743\) 2.49698 9.31885i 0.0916053 0.341876i −0.904878 0.425672i \(-0.860038\pi\)
0.996483 + 0.0837963i \(0.0267045\pi\)
\(744\) 6.62707 + 3.82614i 0.242960 + 0.140273i
\(745\) −27.2061 + 2.29643i −0.996753 + 0.0841346i
\(746\) 5.14384 8.90940i 0.188330 0.326196i
\(747\) 7.42190 + 7.42190i 0.271553 + 0.271553i
\(748\) 9.25166 + 34.5277i 0.338274 + 1.26246i
\(749\) 15.2411 26.3984i 0.556898 0.964575i
\(750\) −11.7634 11.9812i −0.429539 0.437491i
\(751\) −11.2279 + 6.48244i −0.409712 + 0.236547i −0.690666 0.723174i \(-0.742683\pi\)
0.280954 + 0.959721i \(0.409349\pi\)
\(752\) 6.64908 + 6.64908i 0.242467 + 0.242467i
\(753\) −4.76095 4.76095i −0.173499 0.173499i
\(754\) −4.13171 + 2.38544i −0.150468 + 0.0868727i
\(755\) −15.0820 7.08906i −0.548890 0.257997i
\(756\) −10.3999 + 18.0131i −0.378239 + 0.655129i
\(757\) −2.36375 8.82163i −0.0859119 0.320627i 0.909573 0.415543i \(-0.136408\pi\)
−0.995485 + 0.0949157i \(0.969742\pi\)
\(758\) 15.3633 + 15.3633i 0.558020 + 0.558020i
\(759\) −7.91095 + 13.7022i −0.287149 + 0.497357i
\(760\) 4.40302 + 3.71758i 0.159714 + 0.134851i
\(761\) −18.2685 10.5473i −0.662233 0.382341i 0.130894 0.991396i \(-0.458215\pi\)
−0.793127 + 0.609056i \(0.791549\pi\)
\(762\) 1.05657 3.94319i 0.0382756 0.142847i
\(763\) −41.4649 41.4649i −1.50113 1.50113i
\(764\) −3.46575 6.00285i −0.125386 0.217175i
\(765\) 6.55381 7.76221i 0.236954 0.280643i
\(766\) 30.8144 1.11337
\(767\) 8.22410 2.20364i 0.296955 0.0795689i
\(768\) −0.388695 + 1.45063i −0.0140258 + 0.0523451i
\(769\) 17.0212 9.82721i 0.613801 0.354378i −0.160650 0.987011i \(-0.551359\pi\)
0.774452 + 0.632633i \(0.218026\pi\)
\(770\) 39.7733 27.6687i 1.43333 0.997111i
\(771\) 8.93083 + 15.4687i 0.321636 + 0.557090i
\(772\) −4.34418 4.34418i −0.156350 0.156350i
\(773\) −11.5040 11.5040i −0.413769 0.413769i 0.469280 0.883049i \(-0.344513\pi\)
−0.883049 + 0.469280i \(0.844513\pi\)
\(774\) 4.86739 0.384950i 0.174955 0.0138368i
\(775\) −8.85987 + 23.8868i −0.318256 + 0.858039i
\(776\) 0.855426i 0.0307080i
\(777\) −43.8908 11.7605i −1.57457 0.421906i
\(778\) −6.78863 + 6.78863i −0.243384 + 0.243384i
\(779\) −14.7007 25.4623i −0.526706 0.912281i
\(780\) 3.81714 + 1.79419i 0.136676 + 0.0642423i
\(781\) 25.4505 + 14.6938i 0.910689 + 0.525787i
\(782\) 7.75897 7.75897i 0.277460 0.277460i
\(783\) −5.52874 20.6336i −0.197581 0.737383i
\(784\) 5.78489 3.33991i 0.206603 0.119282i
\(785\) −27.4719 4.93069i −0.980513 0.175984i
\(786\) −12.4063 + 7.16280i −0.442520 + 0.255489i
\(787\) −3.41060 + 0.913869i −0.121575 + 0.0325759i −0.319093 0.947723i \(-0.603378\pi\)
0.197519 + 0.980299i \(0.436712\pi\)
\(788\) −0.609958 2.27640i −0.0217289 0.0810932i
\(789\) 25.9096 + 14.9589i 0.922405 + 0.532551i
\(790\) −1.68677 + 9.39804i −0.0600126 + 0.334367i
\(791\) −11.0172 + 19.0824i −0.391727 + 0.678492i
\(792\) 1.12898 + 4.21342i 0.0401166 + 0.149717i
\(793\) −3.80905 + 14.2156i −0.135263 + 0.504809i
\(794\) −8.57889 14.8591i −0.304453 0.527329i
\(795\) −9.57817 13.7685i −0.339703 0.488317i
\(796\) 16.6372i 0.589688i
\(797\) 5.80684 21.6714i 0.205689 0.767641i −0.783550 0.621329i \(-0.786593\pi\)
0.989238 0.146312i \(-0.0467404\pi\)
\(798\) −13.8270 3.70492i −0.489469 0.131153i
\(799\) 49.6885 + 28.6877i 1.75785 + 1.01490i
\(800\) −4.97822 0.466228i −0.176007 0.0164837i
\(801\) 7.34882i 0.259658i
\(802\) −6.52393 24.3476i −0.230368 0.859744i
\(803\) 78.1340 20.9359i 2.75729 0.738813i
\(804\) 10.0693 17.4405i 0.355115 0.615078i
\(805\) −13.4602 6.32674i −0.474408 0.222988i
\(806\) 6.39976i 0.225422i
\(807\) −0.657348 0.176136i −0.0231398 0.00620028i
\(808\) −10.4423 + 2.79800i −0.367358 + 0.0984332i
\(809\) 22.4240i 0.788387i 0.919027 + 0.394194i \(0.128976\pi\)
−0.919027 + 0.394194i \(0.871024\pi\)
\(810\) −8.96086 + 10.6131i −0.314852 + 0.372905i
\(811\) 13.0798 7.55164i 0.459295 0.265174i −0.252453 0.967609i \(-0.581237\pi\)
0.711748 + 0.702435i \(0.247904\pi\)
\(812\) −3.63622 + 13.5705i −0.127606 + 0.476233i
\(813\) −9.15773 9.15773i −0.321175 0.321175i
\(814\) −41.5033 + 23.9619i −1.45469 + 0.839865i
\(815\) 5.83011 32.4831i 0.204220 1.13783i
\(816\) 9.16350i 0.320787i
\(817\) 5.64715 + 15.9276i 0.197569 + 0.557238i
\(818\) 6.49863 6.49863i 0.227219 0.227219i
\(819\) 3.45893 0.120865
\(820\) 23.0875 + 10.8519i 0.806249 + 0.378966i
\(821\) −30.8412 −1.07636 −0.538182 0.842828i \(-0.680889\pi\)
−0.538182 + 0.842828i \(0.680889\pi\)
\(822\) −3.05518 0.818633i −0.106562 0.0285531i
\(823\) −13.7552 3.68570i −0.479477 0.128476i 0.0109818 0.999940i \(-0.496504\pi\)
−0.490459 + 0.871464i \(0.663171\pi\)
\(824\) −2.96430 + 5.13431i −0.103266 + 0.178862i
\(825\) 39.9818 18.3470i 1.39199 0.638761i
\(826\) 12.5363 21.7135i 0.436193 0.755509i
\(827\) −3.59010 + 13.3984i −0.124840 + 0.465910i −0.999834 0.0182244i \(-0.994199\pi\)
0.874994 + 0.484134i \(0.160865\pi\)
\(828\) 0.946829 0.946829i 0.0329046 0.0329046i
\(829\) −4.37182 7.57221i −0.151839 0.262994i 0.780064 0.625699i \(-0.215186\pi\)
−0.931904 + 0.362706i \(0.881853\pi\)
\(830\) −2.65121 31.4093i −0.0920250 1.09023i
\(831\) 0.148411 0.257056i 0.00514833 0.00891716i
\(832\) 1.21319 0.325074i 0.0420599 0.0112699i
\(833\) 28.8203 28.8203i 0.998563 0.998563i
\(834\) −3.76600 2.17430i −0.130406 0.0752899i
\(835\) −1.95497 1.65063i −0.0676547 0.0571224i
\(836\) −13.0748 + 7.54875i −0.452202 + 0.261079i
\(837\) 27.6783 + 7.41637i 0.956700 + 0.256347i
\(838\) −3.49872 + 3.49872i −0.120861 + 0.120861i
\(839\) −25.5552 −0.882265 −0.441132 0.897442i \(-0.645423\pi\)
−0.441132 + 0.897442i \(0.645423\pi\)
\(840\) 11.6844 4.21235i 0.403149 0.145340i
\(841\) 7.28566 + 12.6191i 0.251230 + 0.435143i
\(842\) −26.6451 + 7.13953i −0.918251 + 0.246045i
\(843\) −13.9310 + 3.73279i −0.479808 + 0.128564i
\(844\) −9.79097 −0.337019
\(845\) 2.14828 + 25.4510i 0.0739031 + 0.875540i
\(846\) 6.06349 + 3.50076i 0.208467 + 0.120359i
\(847\) 22.3239 + 83.3138i 0.767057 + 2.86270i
\(848\) −4.82436 1.29268i −0.165669 0.0443909i
\(849\) 18.7698 0.644178
\(850\) −30.0767 + 5.11390i −1.03162 + 0.175405i
\(851\) 12.7403 + 7.35559i 0.436730 + 0.252146i
\(852\) 5.32706 + 5.32706i 0.182502 + 0.182502i
\(853\) 10.3042 + 38.4557i 0.352808 + 1.31670i 0.883220 + 0.468958i \(0.155370\pi\)
−0.530412 + 0.847740i \(0.677963\pi\)
\(854\) 21.6693 + 37.5323i 0.741507 + 1.28433i
\(855\) 3.88315 + 1.82522i 0.132801 + 0.0624211i
\(856\) 8.24150i 0.281689i
\(857\) 6.91466 25.8059i 0.236200 0.881512i −0.741404 0.671059i \(-0.765840\pi\)
0.977604 0.210453i \(-0.0674938\pi\)
\(858\) −7.81374 + 7.81374i −0.266757 + 0.266757i
\(859\) 18.3832 0.627227 0.313613 0.949551i \(-0.398460\pi\)
0.313613 + 0.949551i \(0.398460\pi\)
\(860\) −11.9145 8.54666i −0.406280 0.291439i
\(861\) −63.3710 −2.15968
\(862\) −2.40442 + 2.40442i −0.0818948 + 0.0818948i
\(863\) 10.9613 40.9083i 0.373129 1.39254i −0.482931 0.875658i \(-0.660428\pi\)
0.856060 0.516877i \(-0.172905\pi\)
\(864\) 5.62363i 0.191320i
\(865\) −14.2025 39.3955i −0.482900 1.33949i
\(866\) −16.1411 27.9572i −0.548497 0.950024i
\(867\) 7.86343 + 29.3467i 0.267056 + 0.996667i
\(868\) −13.3261 13.3261i −0.452317 0.452317i
\(869\) −21.6642 12.5078i −0.734908 0.424299i
\(870\) −5.42620 + 11.5442i −0.183965 + 0.391386i
\(871\) −16.8423 −0.570678
\(872\) −15.3144 4.10348i −0.518611 0.138961i
\(873\) 0.164852 + 0.615236i 0.00557939 + 0.0208226i
\(874\) 4.01357 + 2.31724i 0.135761 + 0.0783817i
\(875\) 20.3466 + 35.9999i 0.687840 + 1.21702i
\(876\) 20.7364 0.700619
\(877\) −41.8296 + 11.2082i −1.41249 + 0.378474i −0.882812 0.469727i \(-0.844352\pi\)
−0.529674 + 0.848201i \(0.677686\pi\)
\(878\) −32.2384 + 8.63826i −1.08799 + 0.291527i
\(879\) −5.74811 9.95602i −0.193879 0.335808i
\(880\) 5.57243 11.8553i 0.187847 0.399644i
\(881\) 40.5724 1.36692 0.683459 0.729989i \(-0.260475\pi\)
0.683459 + 0.729989i \(0.260475\pi\)
\(882\) 3.51694 3.51694i 0.118422 0.118422i
\(883\) 40.7559 + 10.9205i 1.37154 + 0.367504i 0.868043 0.496490i \(-0.165378\pi\)
0.503502 + 0.863994i \(0.332045\pi\)
\(884\) 6.63690 3.83181i 0.223223 0.128878i
\(885\) 14.6859 17.3937i 0.493663 0.584684i
\(886\) −22.9639 13.2582i −0.771489 0.445419i
\(887\) −29.8472 + 29.8472i −1.00217 + 1.00217i −0.00217452 + 0.999998i \(0.500692\pi\)
−0.999998 + 0.00217452i \(0.999308\pi\)
\(888\) −11.8668 + 3.17970i −0.398224 + 0.106704i
\(889\) −5.02691 + 8.70686i −0.168597 + 0.292019i
\(890\) 14.2374 16.8626i 0.477240 0.565234i
\(891\) −18.1955 31.5156i −0.609573 1.05581i
\(892\) 5.54239 5.54239i 0.185573 0.185573i
\(893\) −6.27195 + 23.4072i −0.209883 + 0.783293i
\(894\) 9.16865 15.8806i 0.306645 0.531126i
\(895\) −0.299346 0.430305i −0.0100060 0.0143835i
\(896\) 1.84931 3.20310i 0.0617812 0.107008i
\(897\) 3.27653 + 0.877942i 0.109400 + 0.0293136i
\(898\) 29.6191 + 7.93642i 0.988403 + 0.264842i
\(899\) 19.3549 0.645523
\(900\) −3.67026 + 0.624050i −0.122342 + 0.0208017i
\(901\) −30.4750 −1.01527
\(902\) −47.2604 + 47.2604i −1.57360 + 1.57360i
\(903\) 35.8166 + 6.62400i 1.19190 + 0.220433i
\(904\) 5.95747i 0.198143i
\(905\) −0.655904 0.942851i −0.0218030 0.0313414i
\(906\) 9.69311 5.59632i 0.322032 0.185925i
\(907\) 23.8273 + 23.8273i 0.791173 + 0.791173i 0.981685 0.190512i \(-0.0610146\pi\)
−0.190512 + 0.981685i \(0.561015\pi\)
\(908\) −5.18440 + 19.3485i −0.172050 + 0.642101i
\(909\) −6.97104 + 4.02473i −0.231215 + 0.133492i
\(910\) −7.93684 6.70125i −0.263104 0.222144i
\(911\) 54.5673i 1.80790i −0.427643 0.903948i \(-0.640656\pi\)
0.427643 0.903948i \(-0.359344\pi\)
\(912\) −3.73841 + 1.00170i −0.123791 + 0.0331697i
\(913\) 79.7689 + 21.3740i 2.63996 + 0.707376i
\(914\) 14.0444i 0.464546i
\(915\) 13.3450 + 37.0168i 0.441172 + 1.22374i
\(916\) −4.79911 + 8.31230i −0.158567 + 0.274646i
\(917\) 34.0788 9.13138i 1.12538 0.301545i
\(918\) 8.88099 + 33.1443i 0.293117 + 1.09393i
\(919\) 32.4698i 1.07108i −0.844510 0.535540i \(-0.820108\pi\)
0.844510 0.535540i \(-0.179892\pi\)
\(920\) −4.00695 + 0.338221i −0.132105 + 0.0111508i
\(921\) 10.3514 + 5.97641i 0.341092 + 0.196929i
\(922\) −0.451634 0.121015i −0.0148738 0.00398541i
\(923\) 1.63069 6.08583i 0.0536749 0.200317i
\(924\) 32.5408i 1.07051i
\(925\) −17.0590 37.1750i −0.560897 1.22231i
\(926\) −4.25037 7.36186i −0.139676 0.241926i
\(927\) −1.14252 + 4.26394i −0.0375253 + 0.140046i
\(928\) 0.983127 + 3.66908i 0.0322727 + 0.120443i
\(929\) 20.1016 34.8170i 0.659513 1.14231i −0.321229 0.947001i \(-0.604096\pi\)
0.980742 0.195308i \(-0.0625707\pi\)
\(930\) −9.77158 14.0465i −0.320423 0.460602i
\(931\) 14.9082 + 8.60724i 0.488596 + 0.282091i
\(932\) −0.405117 1.51192i −0.0132701 0.0495245i
\(933\) 14.9006 3.99261i 0.487825 0.130712i
\(934\) 26.4690 15.2819i 0.866093 0.500039i
\(935\) 14.1203 78.6727i 0.461782 2.57287i
\(936\) 0.809901 0.467597i 0.0264725 0.0152839i
\(937\) −6.60420 24.6472i −0.215750 0.805189i −0.985901 0.167328i \(-0.946486\pi\)
0.770151 0.637861i \(-0.220181\pi\)
\(938\) −35.0703 + 35.0703i −1.14509 + 1.14509i
\(939\) 29.3212 + 16.9286i 0.956862 + 0.552444i
\(940\) −7.13095 19.7801i −0.232586 0.645156i
\(941\) −23.6018 40.8795i −0.769397 1.33264i −0.937890 0.346932i \(-0.887223\pi\)
0.168493 0.985703i \(-0.446110\pi\)
\(942\) 13.2552 13.2552i 0.431878 0.431878i
\(943\) 19.8176 + 5.31012i 0.645351 + 0.172921i
\(944\) 6.77889i 0.220634i
\(945\) 38.1798 26.5602i 1.24199 0.864002i
\(946\) 31.6511 21.7711i 1.02907 0.707838i
\(947\) 3.28189 + 3.28189i 0.106647 + 0.106647i 0.758417 0.651770i \(-0.225973\pi\)
−0.651770 + 0.758417i \(0.725973\pi\)
\(948\) −4.53456 4.53456i −0.147276 0.147276i
\(949\) −8.67115 15.0189i −0.281478 0.487533i
\(950\) −5.37412 11.7113i −0.174359 0.379964i
\(951\) 2.53498 1.46357i 0.0822025 0.0474596i
\(952\) 5.84097 21.7988i 0.189307 0.706503i
\(953\) 8.31471 2.22792i 0.269340 0.0721694i −0.121621 0.992577i \(-0.538809\pi\)
0.390961 + 0.920407i \(0.372143\pi\)
\(954\) −3.71887 −0.120403
\(955\) 1.30364 + 15.4444i 0.0421847 + 0.499768i
\(956\) −7.95829 13.7842i −0.257389 0.445812i
\(957\) −23.6312 23.6312i −0.763889 0.763889i
\(958\) −3.58673 + 13.3859i −0.115882 + 0.432478i
\(959\) 6.74606 + 3.89484i 0.217842 + 0.125771i
\(960\) 2.16642 2.56587i 0.0699210 0.0828130i
\(961\) 2.51847 4.36211i 0.0812409 0.140713i
\(962\) 7.26520 + 7.26520i 0.234239 + 0.234239i
\(963\) −1.58825 5.92742i −0.0511805 0.191008i
\(964\) −2.38733 + 4.13497i −0.0768907 + 0.133179i
\(965\) 4.65901 + 12.9233i 0.149979 + 0.416017i
\(966\) 8.65076 4.99452i 0.278334 0.160696i
\(967\) −19.5722 19.5722i −0.629401 0.629401i 0.318517 0.947917i \(-0.396815\pi\)
−0.947917 + 0.318517i \(0.896815\pi\)
\(968\) 16.4899 + 16.4899i 0.530005 + 0.530005i
\(969\) −20.4513 + 11.8076i −0.656992 + 0.379314i
\(970\) 0.813677 1.73110i 0.0261256 0.0555822i
\(971\) −11.4154 + 19.7720i −0.366337 + 0.634515i −0.988990 0.147983i \(-0.952722\pi\)
0.622652 + 0.782499i \(0.286055\pi\)
\(972\) 1.95200 + 7.28497i 0.0626105 + 0.233666i
\(973\) 7.57289 + 7.57289i 0.242776 + 0.242776i
\(974\) 4.55552 7.89039i 0.145968 0.252824i
\(975\) −6.01800 7.26169i −0.192730 0.232560i
\(976\) 10.1476 + 5.85874i 0.324818 + 0.187534i
\(977\) 9.56069 35.6810i 0.305874 1.14154i −0.626317 0.779568i \(-0.715438\pi\)
0.932191 0.361968i \(-0.117895\pi\)
\(978\) 15.6731 + 15.6731i 0.501171 + 0.501171i
\(979\) 28.9099 + 50.0735i 0.923965 + 1.60036i
\(980\) −14.8836 + 1.25630i −0.475439 + 0.0401312i
\(981\) −11.8051 −0.376909
\(982\) 33.7492 9.04307i 1.07698 0.288576i
\(983\) −12.4888 + 46.6090i −0.398332 + 1.48660i 0.417698 + 0.908586i \(0.362837\pi\)
−0.816030 + 0.578010i \(0.803830\pi\)
\(984\) −14.8382 + 8.56683i −0.473024 + 0.273101i
\(985\) −0.930943 + 5.18686i −0.0296623 + 0.165267i
\(986\) 11.5886 + 20.0721i 0.369057 + 0.639225i
\(987\) 36.9330 + 36.9330i 1.17559 + 1.17559i
\(988\) 2.28876 + 2.28876i 0.0728152 + 0.0728152i
\(989\) −10.6457 5.07271i −0.338512 0.161303i
\(990\) 1.72310 9.60044i 0.0547636 0.305122i
\(991\) 41.2538i 1.31047i 0.755424 + 0.655236i \(0.227431\pi\)
−0.755424 + 0.655236i \(0.772569\pi\)
\(992\) −4.92178 1.31879i −0.156267 0.0418715i
\(993\) 8.17675 8.17675i 0.259481 0.259481i
\(994\) −9.27684 16.0680i −0.294243 0.509645i
\(995\) −15.8252 + 33.6681i −0.501692 + 1.06735i
\(996\) 18.3340 + 10.5852i 0.580936 + 0.335404i
\(997\) 29.2304 29.2304i 0.925737 0.925737i −0.0716896 0.997427i \(-0.522839\pi\)
0.997427 + 0.0716896i \(0.0228391\pi\)
\(998\) 0.246867 + 0.921321i 0.00781445 + 0.0291639i
\(999\) −39.8405 + 23.0019i −1.26050 + 0.727748i
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 430.2.l.a.7.4 88
5.3 odd 4 inner 430.2.l.a.93.15 yes 88
43.37 odd 6 inner 430.2.l.a.37.15 yes 88
215.123 even 12 inner 430.2.l.a.123.4 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
430.2.l.a.7.4 88 1.1 even 1 trivial
430.2.l.a.37.15 yes 88 43.37 odd 6 inner
430.2.l.a.93.15 yes 88 5.3 odd 4 inner
430.2.l.a.123.4 yes 88 215.123 even 12 inner