Properties

Label 210.2.t.c.89.2
Level $210$
Weight $2$
Character 210.89
Analytic conductor $1.677$
Analytic rank $0$
Dimension $4$
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] = [210,2,Mod(59,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 210.89
Dual form 210.2.t.c.59.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 1.65831i) q^{5} +(1.18614 - 1.26217i) q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 1.65831i) q^{5} +(1.18614 - 1.26217i) q^{6} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 + 1.33591i) q^{9} +(2.18614 - 0.469882i) q^{10} +(3.68614 - 2.12819i) q^{11} +(-0.500000 - 1.65831i) q^{12} -2.00000 q^{13} +(-2.00000 + 1.73205i) q^{14} +(1.87228 + 3.39036i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.74456 + 3.31662i) q^{17} +(2.50000 - 1.65831i) q^{18} +(-3.00000 - 1.73205i) q^{19} +(0.686141 - 2.12819i) q^{20} +(-3.87228 - 2.45060i) q^{21} -4.25639i q^{22} +(2.18614 - 3.78651i) q^{23} +(-1.68614 - 0.396143i) q^{24} +(-0.500000 + 4.97494i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(4.00000 + 3.31662i) q^{27} +(0.500000 + 2.59808i) q^{28} -3.31662i q^{29} +(3.87228 + 0.0737384i) q^{30} +(-2.05842 + 1.18843i) q^{31} +(0.500000 + 0.866025i) q^{32} +(7.05842 - 2.12819i) q^{33} +6.63325i q^{34} +(-2.31386 - 5.44482i) q^{35} +(-0.186141 - 2.99422i) q^{36} +(-10.1168 - 5.84096i) q^{37} +(-3.00000 + 1.73205i) q^{38} +(-3.37228 - 0.792287i) q^{39} +(-1.50000 - 1.65831i) q^{40} +1.62772 q^{41} +(-4.05842 + 2.12819i) q^{42} +11.0371i q^{43} +(-3.68614 - 2.12819i) q^{44} +(1.81386 + 6.45832i) q^{45} +(-2.18614 - 3.78651i) q^{46} +(1.62772 + 0.939764i) q^{47} +(-1.18614 + 1.26217i) q^{48} +(5.50000 + 4.33013i) q^{49} +(4.05842 + 2.92048i) q^{50} +(-11.0000 + 3.31662i) q^{51} +(1.00000 + 1.73205i) q^{52} +(0.686141 + 1.18843i) q^{53} +(4.87228 - 1.80579i) q^{54} +(9.05842 + 2.92048i) q^{55} +(2.50000 + 0.866025i) q^{56} +(-4.37228 - 4.10891i) q^{57} +(-2.87228 - 1.65831i) q^{58} +(2.05842 + 3.56529i) q^{59} +(2.00000 - 3.31662i) q^{60} +(-2.44158 - 1.40965i) q^{61} +2.37686i q^{62} +(-5.55842 - 5.66603i) q^{63} +1.00000 q^{64} +(-3.00000 - 3.31662i) q^{65} +(1.68614 - 7.17687i) q^{66} +(6.55842 - 3.78651i) q^{67} +(5.74456 + 3.31662i) q^{68} +(5.18614 - 5.51856i) q^{69} +(-5.87228 - 0.718549i) q^{70} +1.87953i q^{71} +(-2.68614 - 1.33591i) q^{72} +(1.00000 + 1.73205i) q^{73} +(-10.1168 + 5.84096i) q^{74} +(-2.81386 + 8.19037i) q^{75} +3.46410i q^{76} +(-11.0584 + 2.12819i) q^{77} +(-2.37228 + 2.52434i) q^{78} +(4.05842 - 7.02939i) q^{79} +(-2.18614 + 0.469882i) q^{80} +(5.43070 + 7.17687i) q^{81} +(0.813859 - 1.40965i) q^{82} -1.43710i q^{83} +(-0.186141 + 4.57879i) q^{84} +(-14.1168 - 4.55134i) q^{85} +(9.55842 + 5.51856i) q^{86} +(1.31386 - 5.59230i) q^{87} +(-3.68614 + 2.12819i) q^{88} +(2.18614 - 3.78651i) q^{89} +(6.50000 + 1.65831i) q^{90} +(5.00000 + 1.73205i) q^{91} -4.37228 q^{92} +(-3.94158 + 1.18843i) q^{93} +(1.62772 - 0.939764i) q^{94} +(-1.62772 - 7.57301i) q^{95} +(0.500000 + 1.65831i) q^{96} +2.11684 q^{97} +(6.50000 - 2.59808i) q^{98} +(12.7446 - 0.792287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} - 4 q^{8} + 5 q^{9} + 3 q^{10} + 9 q^{11} - 2 q^{12} - 8 q^{13} - 8 q^{14} - 4 q^{15} - 2 q^{16} + 10 q^{18} - 12 q^{19} - 3 q^{20} - 4 q^{21} + 3 q^{23} - q^{24} - 2 q^{25} - 4 q^{26} + 16 q^{27} + 2 q^{28} + 4 q^{30} + 9 q^{31} + 2 q^{32} + 11 q^{33} - 15 q^{35} + 5 q^{36} - 6 q^{37} - 12 q^{38} - 2 q^{39} - 6 q^{40} + 18 q^{41} + q^{42} - 9 q^{44} + 13 q^{45} - 3 q^{46} + 18 q^{47} + q^{48} + 22 q^{49} - q^{50} - 44 q^{51} + 4 q^{52} - 3 q^{53} + 8 q^{54} + 19 q^{55} + 10 q^{56} - 6 q^{57} - 9 q^{59} + 8 q^{60} - 27 q^{61} - 5 q^{63} + 4 q^{64} - 12 q^{65} + q^{66} + 9 q^{67} + 15 q^{69} - 12 q^{70} - 5 q^{72} + 4 q^{73} - 6 q^{74} - 17 q^{75} - 27 q^{77} + 2 q^{78} - q^{79} - 3 q^{80} - 7 q^{81} + 9 q^{82} + 5 q^{84} - 22 q^{85} + 21 q^{86} + 11 q^{87} - 9 q^{88} + 3 q^{89} + 26 q^{90} + 20 q^{91} - 6 q^{92} - 33 q^{93} + 18 q^{94} - 18 q^{95} + 2 q^{96} - 26 q^{97} + 26 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.68614 + 0.396143i 0.973494 + 0.228714i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.50000 + 1.65831i 0.670820 + 0.741620i
\(6\) 1.18614 1.26217i 0.484240 0.515278i
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 2.68614 + 1.33591i 0.895380 + 0.445302i
\(10\) 2.18614 0.469882i 0.691318 0.148590i
\(11\) 3.68614 2.12819i 1.11141 0.641675i 0.172218 0.985059i \(-0.444907\pi\)
0.939195 + 0.343384i \(0.111573\pi\)
\(12\) −0.500000 1.65831i −0.144338 0.478714i
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 1.87228 + 3.39036i 0.483421 + 0.875388i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −5.74456 + 3.31662i −1.39326 + 0.804400i −0.993675 0.112296i \(-0.964180\pi\)
−0.399586 + 0.916696i \(0.630846\pi\)
\(18\) 2.50000 1.65831i 0.589256 0.390868i
\(19\) −3.00000 1.73205i −0.688247 0.397360i 0.114708 0.993399i \(-0.463407\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0.686141 2.12819i 0.153426 0.475879i
\(21\) −3.87228 2.45060i −0.845001 0.534765i
\(22\) 4.25639i 0.907465i
\(23\) 2.18614 3.78651i 0.455842 0.789541i −0.542894 0.839801i \(-0.682672\pi\)
0.998736 + 0.0502598i \(0.0160049\pi\)
\(24\) −1.68614 0.396143i −0.344182 0.0808625i
\(25\) −0.500000 + 4.97494i −0.100000 + 0.994987i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0.500000 + 2.59808i 0.0944911 + 0.490990i
\(29\) 3.31662i 0.615882i −0.951405 0.307941i \(-0.900360\pi\)
0.951405 0.307941i \(-0.0996399\pi\)
\(30\) 3.87228 + 0.0737384i 0.706979 + 0.0134627i
\(31\) −2.05842 + 1.18843i −0.369704 + 0.213448i −0.673329 0.739343i \(-0.735136\pi\)
0.303625 + 0.952791i \(0.401803\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 7.05842 2.12819i 1.22871 0.370471i
\(34\) 6.63325i 1.13759i
\(35\) −2.31386 5.44482i −0.391114 0.920342i
\(36\) −0.186141 2.99422i −0.0310234 0.499037i
\(37\) −10.1168 5.84096i −1.66320 0.960248i −0.971173 0.238376i \(-0.923385\pi\)
−0.692026 0.721873i \(-0.743282\pi\)
\(38\) −3.00000 + 1.73205i −0.486664 + 0.280976i
\(39\) −3.37228 0.792287i −0.539997 0.126867i
\(40\) −1.50000 1.65831i −0.237171 0.262202i
\(41\) 1.62772 0.254207 0.127103 0.991889i \(-0.459432\pi\)
0.127103 + 0.991889i \(0.459432\pi\)
\(42\) −4.05842 + 2.12819i −0.626228 + 0.328388i
\(43\) 11.0371i 1.68314i 0.540145 + 0.841572i \(0.318369\pi\)
−0.540145 + 0.841572i \(0.681631\pi\)
\(44\) −3.68614 2.12819i −0.555707 0.320837i
\(45\) 1.81386 + 6.45832i 0.270394 + 0.962750i
\(46\) −2.18614 3.78651i −0.322329 0.558290i
\(47\) 1.62772 + 0.939764i 0.237427 + 0.137079i 0.613994 0.789311i \(-0.289562\pi\)
−0.376566 + 0.926390i \(0.622895\pi\)
\(48\) −1.18614 + 1.26217i −0.171205 + 0.182178i
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 4.05842 + 2.92048i 0.573948 + 0.413018i
\(51\) −11.0000 + 3.31662i −1.54031 + 0.464420i
\(52\) 1.00000 + 1.73205i 0.138675 + 0.240192i
\(53\) 0.686141 + 1.18843i 0.0942487 + 0.163243i 0.909295 0.416153i \(-0.136622\pi\)
−0.815046 + 0.579396i \(0.803288\pi\)
\(54\) 4.87228 1.80579i 0.663034 0.245737i
\(55\) 9.05842 + 2.92048i 1.22144 + 0.393798i
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) −4.37228 4.10891i −0.579123 0.544239i
\(58\) −2.87228 1.65831i −0.377149 0.217747i
\(59\) 2.05842 + 3.56529i 0.267984 + 0.464161i 0.968341 0.249631i \(-0.0803093\pi\)
−0.700357 + 0.713792i \(0.746976\pi\)
\(60\) 2.00000 3.31662i 0.258199 0.428174i
\(61\) −2.44158 1.40965i −0.312612 0.180487i 0.335483 0.942046i \(-0.391101\pi\)
−0.648095 + 0.761560i \(0.724434\pi\)
\(62\) 2.37686i 0.301862i
\(63\) −5.55842 5.66603i −0.700295 0.713853i
\(64\) 1.00000 0.125000
\(65\) −3.00000 3.31662i −0.372104 0.411377i
\(66\) 1.68614 7.17687i 0.207550 0.883412i
\(67\) 6.55842 3.78651i 0.801239 0.462595i −0.0426654 0.999089i \(-0.513585\pi\)
0.843904 + 0.536494i \(0.180252\pi\)
\(68\) 5.74456 + 3.31662i 0.696631 + 0.402200i
\(69\) 5.18614 5.51856i 0.624338 0.664356i
\(70\) −5.87228 0.718549i −0.701872 0.0858830i
\(71\) 1.87953i 0.223059i 0.993761 + 0.111529i \(0.0355749\pi\)
−0.993761 + 0.111529i \(0.964425\pi\)
\(72\) −2.68614 1.33591i −0.316565 0.157438i
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) −10.1168 + 5.84096i −1.17606 + 0.678998i
\(75\) −2.81386 + 8.19037i −0.324916 + 0.945743i
\(76\) 3.46410i 0.397360i
\(77\) −11.0584 + 2.12819i −1.26022 + 0.242530i
\(78\) −2.37228 + 2.52434i −0.268608 + 0.285825i
\(79\) 4.05842 7.02939i 0.456608 0.790869i −0.542171 0.840268i \(-0.682397\pi\)
0.998779 + 0.0493997i \(0.0157308\pi\)
\(80\) −2.18614 + 0.469882i −0.244418 + 0.0525344i
\(81\) 5.43070 + 7.17687i 0.603411 + 0.797430i
\(82\) 0.813859 1.40965i 0.0898757 0.155669i
\(83\) 1.43710i 0.157742i −0.996885 0.0788710i \(-0.974868\pi\)
0.996885 0.0788710i \(-0.0251315\pi\)
\(84\) −0.186141 + 4.57879i −0.0203096 + 0.499587i
\(85\) −14.1168 4.55134i −1.53119 0.493662i
\(86\) 9.55842 + 5.51856i 1.03071 + 0.595081i
\(87\) 1.31386 5.59230i 0.140861 0.599557i
\(88\) −3.68614 + 2.12819i −0.392944 + 0.226866i
\(89\) 2.18614 3.78651i 0.231730 0.401369i −0.726587 0.687074i \(-0.758895\pi\)
0.958317 + 0.285706i \(0.0922279\pi\)
\(90\) 6.50000 + 1.65831i 0.685160 + 0.174801i
\(91\) 5.00000 + 1.73205i 0.524142 + 0.181568i
\(92\) −4.37228 −0.455842
\(93\) −3.94158 + 1.18843i −0.408723 + 0.123235i
\(94\) 1.62772 0.939764i 0.167886 0.0969292i
\(95\) −1.62772 7.57301i −0.167000 0.776975i
\(96\) 0.500000 + 1.65831i 0.0510310 + 0.169251i
\(97\) 2.11684 0.214933 0.107466 0.994209i \(-0.465726\pi\)
0.107466 + 0.994209i \(0.465726\pi\)
\(98\) 6.50000 2.59808i 0.656599 0.262445i
\(99\) 12.7446 0.792287i 1.28088 0.0796278i
\(100\) 4.55842 2.05446i 0.455842 0.205446i
\(101\) 8.18614 + 14.1788i 0.814551 + 1.41084i 0.909650 + 0.415377i \(0.136350\pi\)
−0.0950981 + 0.995468i \(0.530316\pi\)
\(102\) −2.62772 + 11.1846i −0.260183 + 1.10744i
\(103\) 7.55842 13.0916i 0.744753 1.28995i −0.205556 0.978645i \(-0.565900\pi\)
0.950310 0.311306i \(-0.100766\pi\)
\(104\) 2.00000 0.196116
\(105\) −1.74456 10.0974i −0.170252 0.985401i
\(106\) 1.37228 0.133288
\(107\) 8.87228 15.3672i 0.857716 1.48561i −0.0163866 0.999866i \(-0.505216\pi\)
0.874102 0.485742i \(-0.161450\pi\)
\(108\) 0.872281 5.12241i 0.0839353 0.492905i
\(109\) −4.55842 7.89542i −0.436618 0.756244i 0.560808 0.827946i \(-0.310490\pi\)
−0.997426 + 0.0717016i \(0.977157\pi\)
\(110\) 7.05842 6.38458i 0.672994 0.608746i
\(111\) −14.7446 13.8564i −1.39949 1.31519i
\(112\) 2.00000 1.73205i 0.188982 0.163663i
\(113\) 3.25544 0.306246 0.153123 0.988207i \(-0.451067\pi\)
0.153123 + 0.988207i \(0.451067\pi\)
\(114\) −5.74456 + 1.73205i −0.538028 + 0.162221i
\(115\) 9.55842 2.05446i 0.891327 0.191579i
\(116\) −2.87228 + 1.65831i −0.266685 + 0.153970i
\(117\) −5.37228 2.67181i −0.496668 0.247009i
\(118\) 4.11684 0.378986
\(119\) 17.2337 3.31662i 1.57981 0.304034i
\(120\) −1.87228 3.39036i −0.170915 0.309496i
\(121\) 3.55842 6.16337i 0.323493 0.560306i
\(122\) −2.44158 + 1.40965i −0.221050 + 0.127623i
\(123\) 2.74456 + 0.644810i 0.247469 + 0.0581406i
\(124\) 2.05842 + 1.18843i 0.184852 + 0.106724i
\(125\) −9.00000 + 6.63325i −0.804984 + 0.593296i
\(126\) −7.68614 + 1.98072i −0.684736 + 0.176456i
\(127\) 2.37686i 0.210912i 0.994424 + 0.105456i \(0.0336303\pi\)
−0.994424 + 0.105456i \(0.966370\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −4.37228 + 18.6101i −0.384958 + 1.63853i
\(130\) −4.37228 + 0.939764i −0.383474 + 0.0824227i
\(131\) 2.31386 4.00772i 0.202163 0.350156i −0.747062 0.664754i \(-0.768536\pi\)
0.949225 + 0.314598i \(0.101870\pi\)
\(132\) −5.37228 5.04868i −0.467597 0.439431i
\(133\) 6.00000 + 6.92820i 0.520266 + 0.600751i
\(134\) 7.57301i 0.654209i
\(135\) 0.500000 + 11.6082i 0.0430331 + 0.999074i
\(136\) 5.74456 3.31662i 0.492592 0.284398i
\(137\) 1.37228 + 2.37686i 0.117242 + 0.203069i 0.918674 0.395017i \(-0.129261\pi\)
−0.801432 + 0.598086i \(0.795928\pi\)
\(138\) −2.18614 7.25061i −0.186097 0.617213i
\(139\) 11.6819i 0.990848i −0.868651 0.495424i \(-0.835013\pi\)
0.868651 0.495424i \(-0.164987\pi\)
\(140\) −3.55842 + 4.72627i −0.300742 + 0.399443i
\(141\) 2.37228 + 2.22938i 0.199782 + 0.187748i
\(142\) 1.62772 + 0.939764i 0.136595 + 0.0788632i
\(143\) −7.37228 + 4.25639i −0.616501 + 0.355937i
\(144\) −2.50000 + 1.65831i −0.208333 + 0.138193i
\(145\) 5.50000 4.97494i 0.456750 0.413146i
\(146\) 2.00000 0.165521
\(147\) 7.55842 + 9.47999i 0.623408 + 0.781897i
\(148\) 11.6819i 0.960248i
\(149\) −12.3030 7.10313i −1.00790 0.581911i −0.0973237 0.995253i \(-0.531028\pi\)
−0.910576 + 0.413342i \(0.864362\pi\)
\(150\) 5.68614 + 6.53206i 0.464271 + 0.533340i
\(151\) 4.05842 + 7.02939i 0.330270 + 0.572044i 0.982565 0.185921i \(-0.0595270\pi\)
−0.652295 + 0.757965i \(0.726194\pi\)
\(152\) 3.00000 + 1.73205i 0.243332 + 0.140488i
\(153\) −19.8614 + 1.23472i −1.60570 + 0.0998210i
\(154\) −3.68614 + 10.6410i −0.297038 + 0.857474i
\(155\) −5.05842 1.63086i −0.406302 0.130994i
\(156\) 1.00000 + 3.31662i 0.0800641 + 0.265543i
\(157\) 4.00000 + 6.92820i 0.319235 + 0.552931i 0.980329 0.197372i \(-0.0632408\pi\)
−0.661094 + 0.750303i \(0.729907\pi\)
\(158\) −4.05842 7.02939i −0.322871 0.559228i
\(159\) 0.686141 + 2.27567i 0.0544145 + 0.180472i
\(160\) −0.686141 + 2.12819i −0.0542442 + 0.168249i
\(161\) −8.74456 + 7.57301i −0.689168 + 0.596837i
\(162\) 8.93070 1.11469i 0.701662 0.0875785i
\(163\) 3.00000 + 1.73205i 0.234978 + 0.135665i 0.612866 0.790186i \(-0.290016\pi\)
−0.377888 + 0.925851i \(0.623350\pi\)
\(164\) −0.813859 1.40965i −0.0635517 0.110075i
\(165\) 14.1168 + 8.51278i 1.09899 + 0.662719i
\(166\) −1.24456 0.718549i −0.0965968 0.0557702i
\(167\) 11.3321i 0.876902i 0.898755 + 0.438451i \(0.144473\pi\)
−0.898755 + 0.438451i \(0.855527\pi\)
\(168\) 3.87228 + 2.45060i 0.298753 + 0.189068i
\(169\) −9.00000 −0.692308
\(170\) −11.0000 + 9.94987i −0.843661 + 0.763121i
\(171\) −5.74456 8.66025i −0.439298 0.662266i
\(172\) 9.55842 5.51856i 0.728823 0.420786i
\(173\) −3.25544 1.87953i −0.247506 0.142898i 0.371116 0.928587i \(-0.378975\pi\)
−0.618622 + 0.785689i \(0.712309\pi\)
\(174\) −4.18614 3.93398i −0.317351 0.298235i
\(175\) 5.55842 12.0043i 0.420177 0.907442i
\(176\) 4.25639i 0.320837i
\(177\) 2.05842 + 6.82701i 0.154720 + 0.513150i
\(178\) −2.18614 3.78651i −0.163858 0.283811i
\(179\) −2.48913 + 1.43710i −0.186046 + 0.107414i −0.590130 0.807308i \(-0.700924\pi\)
0.404084 + 0.914722i \(0.367590\pi\)
\(180\) 4.68614 4.80001i 0.349284 0.357772i
\(181\) 17.9653i 1.33535i 0.744452 + 0.667676i \(0.232711\pi\)
−0.744452 + 0.667676i \(0.767289\pi\)
\(182\) 4.00000 3.46410i 0.296500 0.256776i
\(183\) −3.55842 3.34408i −0.263046 0.247201i
\(184\) −2.18614 + 3.78651i −0.161164 + 0.279145i
\(185\) −5.48913 25.5383i −0.403569 1.87762i
\(186\) −0.941578 + 4.00772i −0.0690398 + 0.293860i
\(187\) −14.1168 + 24.4511i −1.03233 + 1.78804i
\(188\) 1.87953i 0.137079i
\(189\) −7.12772 11.7557i −0.518465 0.855099i
\(190\) −7.37228 2.37686i −0.534842 0.172436i
\(191\) 3.25544 + 1.87953i 0.235555 + 0.135998i 0.613132 0.789980i \(-0.289909\pi\)
−0.377577 + 0.925978i \(0.623243\pi\)
\(192\) 1.68614 + 0.396143i 0.121687 + 0.0285892i
\(193\) 6.94158 4.00772i 0.499666 0.288482i −0.228910 0.973448i \(-0.573516\pi\)
0.728575 + 0.684966i \(0.240183\pi\)
\(194\) 1.05842 1.83324i 0.0759903 0.131619i
\(195\) −3.74456 6.78073i −0.268154 0.485578i
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 20.2337 1.44159 0.720795 0.693148i \(-0.243777\pi\)
0.720795 + 0.693148i \(0.243777\pi\)
\(198\) 5.68614 11.4333i 0.404096 0.812526i
\(199\) −16.1168 + 9.30506i −1.14249 + 0.659619i −0.947047 0.321096i \(-0.895949\pi\)
−0.195446 + 0.980714i \(0.562615\pi\)
\(200\) 0.500000 4.97494i 0.0353553 0.351781i
\(201\) 12.5584 3.78651i 0.885803 0.267080i
\(202\) 16.3723 1.15195
\(203\) −2.87228 + 8.29156i −0.201595 + 0.581954i
\(204\) 8.37228 + 7.86797i 0.586177 + 0.550868i
\(205\) 2.44158 + 2.69927i 0.170527 + 0.188525i
\(206\) −7.55842 13.0916i −0.526620 0.912133i
\(207\) 10.9307 7.25061i 0.759736 0.503952i
\(208\) 1.00000 1.73205i 0.0693375 0.120096i
\(209\) −14.7446 −1.01990
\(210\) −9.61684 3.53784i −0.663625 0.244134i
\(211\) −18.2337 −1.25526 −0.627629 0.778512i \(-0.715975\pi\)
−0.627629 + 0.778512i \(0.715975\pi\)
\(212\) 0.686141 1.18843i 0.0471243 0.0816217i
\(213\) −0.744563 + 3.16915i −0.0510166 + 0.217146i
\(214\) −8.87228 15.3672i −0.606497 1.05048i
\(215\) −18.3030 + 16.5557i −1.24825 + 1.12909i
\(216\) −4.00000 3.31662i −0.272166 0.225668i
\(217\) 6.17527 1.18843i 0.419204 0.0806759i
\(218\) −9.11684 −0.617471
\(219\) 1.00000 + 3.31662i 0.0675737 + 0.224117i
\(220\) −2.00000 9.30506i −0.134840 0.627347i
\(221\) 11.4891 6.63325i 0.772842 0.446201i
\(222\) −19.3723 + 5.84096i −1.30018 + 0.392020i
\(223\) −18.1168 −1.21319 −0.606597 0.795010i \(-0.707466\pi\)
−0.606597 + 0.795010i \(0.707466\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) −7.98913 + 12.6954i −0.532608 + 0.846362i
\(226\) 1.62772 2.81929i 0.108274 0.187536i
\(227\) 13.5475 7.82168i 0.899182 0.519143i 0.0222475 0.999752i \(-0.492918\pi\)
0.876935 + 0.480609i \(0.159584\pi\)
\(228\) −1.37228 + 5.84096i −0.0908816 + 0.386827i
\(229\) 12.0000 + 6.92820i 0.792982 + 0.457829i 0.841011 0.541017i \(-0.181961\pi\)
−0.0480291 + 0.998846i \(0.515294\pi\)
\(230\) 3.00000 9.30506i 0.197814 0.613558i
\(231\) −19.4891 0.792287i −1.28229 0.0521287i
\(232\) 3.31662i 0.217747i
\(233\) −11.7446 + 20.3422i −0.769412 + 1.33266i 0.168470 + 0.985707i \(0.446117\pi\)
−0.937882 + 0.346954i \(0.887216\pi\)
\(234\) −5.00000 + 3.31662i −0.326860 + 0.216815i
\(235\) 0.883156 + 4.10891i 0.0576107 + 0.268036i
\(236\) 2.05842 3.56529i 0.133992 0.232081i
\(237\) 9.62772 10.2448i 0.625388 0.665473i
\(238\) 5.74456 16.5831i 0.372365 1.07492i
\(239\) 2.87419i 0.185916i −0.995670 0.0929581i \(-0.970368\pi\)
0.995670 0.0929581i \(-0.0296323\pi\)
\(240\) −3.87228 0.0737384i −0.249955 0.00475979i
\(241\) 9.17527 5.29734i 0.591031 0.341232i −0.174474 0.984662i \(-0.555823\pi\)
0.765505 + 0.643430i \(0.222489\pi\)
\(242\) −3.55842 6.16337i −0.228744 0.396196i
\(243\) 6.31386 + 14.2525i 0.405034 + 0.914302i
\(244\) 2.81929i 0.180487i
\(245\) 1.06930 + 15.6159i 0.0683149 + 0.997664i
\(246\) 1.93070 2.05446i 0.123097 0.130987i
\(247\) 6.00000 + 3.46410i 0.381771 + 0.220416i
\(248\) 2.05842 1.18843i 0.130710 0.0754654i
\(249\) 0.569297 2.42315i 0.0360777 0.153561i
\(250\) 1.24456 + 11.1109i 0.0787131 + 0.702712i
\(251\) 16.1168 1.01729 0.508643 0.860977i \(-0.330147\pi\)
0.508643 + 0.860977i \(0.330147\pi\)
\(252\) −2.12772 + 7.64675i −0.134034 + 0.481700i
\(253\) 18.6101i 1.17001i
\(254\) 2.05842 + 1.18843i 0.129157 + 0.0745688i
\(255\) −22.0000 13.2665i −1.37769 0.830780i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.37228 4.25639i −0.459870 0.265506i 0.252119 0.967696i \(-0.418872\pi\)
−0.711990 + 0.702190i \(0.752206\pi\)
\(258\) 13.9307 + 13.0916i 0.867288 + 0.815046i
\(259\) 20.2337 + 23.3639i 1.25726 + 1.45176i
\(260\) −1.37228 + 4.25639i −0.0851053 + 0.263970i
\(261\) 4.43070 8.90892i 0.274254 0.551448i
\(262\) −2.31386 4.00772i −0.142951 0.247598i
\(263\) 0.813859 + 1.40965i 0.0501847 + 0.0869225i 0.890027 0.455909i \(-0.150686\pi\)
−0.839842 + 0.542831i \(0.817352\pi\)
\(264\) −7.05842 + 2.12819i −0.434416 + 0.130981i
\(265\) −0.941578 + 2.92048i −0.0578407 + 0.179404i
\(266\) 9.00000 1.73205i 0.551825 0.106199i
\(267\) 5.18614 5.51856i 0.317387 0.337730i
\(268\) −6.55842 3.78651i −0.400619 0.231298i
\(269\) 9.98913 + 17.3017i 0.609048 + 1.05490i 0.991398 + 0.130884i \(0.0417815\pi\)
−0.382350 + 0.924018i \(0.624885\pi\)
\(270\) 10.3030 + 5.37108i 0.627020 + 0.326874i
\(271\) −18.1753 10.4935i −1.10407 0.637434i −0.166782 0.985994i \(-0.553338\pi\)
−0.937287 + 0.348559i \(0.886671\pi\)
\(272\) 6.63325i 0.402200i
\(273\) 7.74456 + 4.90120i 0.468722 + 0.296634i
\(274\) 2.74456 0.165805
\(275\) 8.74456 + 19.4024i 0.527317 + 1.17001i
\(276\) −7.37228 1.73205i −0.443759 0.104257i
\(277\) −25.1168 + 14.5012i −1.50912 + 0.871294i −0.509181 + 0.860659i \(0.670052\pi\)
−0.999943 + 0.0106345i \(0.996615\pi\)
\(278\) −10.1168 5.84096i −0.606768 0.350318i
\(279\) −7.11684 + 0.442430i −0.426074 + 0.0264876i
\(280\) 2.31386 + 5.44482i 0.138280 + 0.325390i
\(281\) 21.7793i 1.29924i 0.760258 + 0.649621i \(0.225073\pi\)
−0.760258 + 0.649621i \(0.774927\pi\)
\(282\) 3.11684 0.939764i 0.185605 0.0559621i
\(283\) −8.00000 13.8564i −0.475551 0.823678i 0.524057 0.851683i \(-0.324418\pi\)
−0.999608 + 0.0280052i \(0.991084\pi\)
\(284\) 1.62772 0.939764i 0.0965873 0.0557647i
\(285\) 0.255437 13.4140i 0.0151308 0.794575i
\(286\) 8.51278i 0.503371i
\(287\) −4.06930 1.40965i −0.240203 0.0832088i
\(288\) 0.186141 + 2.99422i 0.0109684 + 0.176436i
\(289\) 13.5000 23.3827i 0.794118 1.37545i
\(290\) −1.55842 7.25061i −0.0915137 0.425770i
\(291\) 3.56930 + 0.838574i 0.209236 + 0.0491581i
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) 25.0410i 1.46291i −0.681889 0.731455i \(-0.738841\pi\)
0.681889 0.731455i \(-0.261159\pi\)
\(294\) 11.9891 1.80579i 0.699220 0.105316i
\(295\) −2.82473 + 8.76144i −0.164462 + 0.510111i
\(296\) 10.1168 + 5.84096i 0.588030 + 0.339499i
\(297\) 21.8030 + 3.71277i 1.26514 + 0.215437i
\(298\) −12.3030 + 7.10313i −0.712693 + 0.411473i
\(299\) −4.37228 + 7.57301i −0.252856 + 0.437959i
\(300\) 8.50000 1.65831i 0.490748 0.0957427i
\(301\) 9.55842 27.5928i 0.550938 1.59042i
\(302\) 8.11684 0.467072
\(303\) 8.18614 + 27.1504i 0.470281 + 1.55975i
\(304\) 3.00000 1.73205i 0.172062 0.0993399i
\(305\) −1.32473 6.16337i −0.0758541 0.352913i
\(306\) −8.86141 + 17.8178i −0.506573 + 1.01858i
\(307\) −6.88316 −0.392842 −0.196421 0.980520i \(-0.562932\pi\)
−0.196421 + 0.980520i \(0.562932\pi\)
\(308\) 7.37228 + 8.51278i 0.420075 + 0.485060i
\(309\) 17.9307 19.0800i 1.02004 1.08542i
\(310\) −3.94158 + 3.56529i −0.223867 + 0.202495i
\(311\) −7.11684 12.3267i −0.403559 0.698985i 0.590593 0.806969i \(-0.298894\pi\)
−0.994153 + 0.107984i \(0.965560\pi\)
\(312\) 3.37228 + 0.792287i 0.190918 + 0.0448544i
\(313\) −7.05842 + 12.2255i −0.398966 + 0.691029i −0.993599 0.112969i \(-0.963964\pi\)
0.594633 + 0.803997i \(0.297297\pi\)
\(314\) 8.00000 0.451466
\(315\) 1.05842 17.7167i 0.0596353 0.998220i
\(316\) −8.11684 −0.456608
\(317\) 8.05842 13.9576i 0.452606 0.783937i −0.545941 0.837824i \(-0.683828\pi\)
0.998547 + 0.0538869i \(0.0171611\pi\)
\(318\) 2.31386 + 0.543620i 0.129755 + 0.0304847i
\(319\) −7.05842 12.2255i −0.395196 0.684499i
\(320\) 1.50000 + 1.65831i 0.0838525 + 0.0927025i
\(321\) 21.0475 22.3966i 1.17476 1.25006i
\(322\) 2.18614 + 11.3595i 0.121829 + 0.633041i
\(323\) 22.9783 1.27854
\(324\) 3.50000 8.29156i 0.194444 0.460642i
\(325\) 1.00000 9.94987i 0.0554700 0.551920i
\(326\) 3.00000 1.73205i 0.166155 0.0959294i
\(327\) −4.55842 15.1186i −0.252081 0.836059i
\(328\) −1.62772 −0.0898757
\(329\) −3.25544 3.75906i −0.179478 0.207243i
\(330\) 14.4307 7.96916i 0.794384 0.438688i
\(331\) −5.11684 + 8.86263i −0.281247 + 0.487134i −0.971692 0.236250i \(-0.924081\pi\)
0.690445 + 0.723385i \(0.257415\pi\)
\(332\) −1.24456 + 0.718549i −0.0683042 + 0.0394355i
\(333\) −19.3723 29.2048i −1.06159 1.60041i
\(334\) 9.81386 + 5.66603i 0.536990 + 0.310032i
\(335\) 16.1168 + 5.19615i 0.880557 + 0.283896i
\(336\) 4.05842 2.12819i 0.221405 0.116103i
\(337\) 9.30506i 0.506879i 0.967351 + 0.253440i \(0.0815619\pi\)
−0.967351 + 0.253440i \(0.918438\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) 5.48913 + 1.28962i 0.298128 + 0.0700426i
\(340\) 3.11684 + 14.5012i 0.169035 + 0.786439i
\(341\) −5.05842 + 8.76144i −0.273929 + 0.474459i
\(342\) −10.3723 + 0.644810i −0.560869 + 0.0348673i
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 11.0371i 0.595081i
\(345\) 16.9307 + 0.322405i 0.911518 + 0.0173577i
\(346\) −3.25544 + 1.87953i −0.175013 + 0.101044i
\(347\) 9.55842 + 16.5557i 0.513123 + 0.888755i 0.999884 + 0.0152200i \(0.00484486\pi\)
−0.486761 + 0.873535i \(0.661822\pi\)
\(348\) −5.50000 + 1.65831i −0.294831 + 0.0888949i
\(349\) 24.0087i 1.28515i 0.766221 + 0.642577i \(0.222135\pi\)
−0.766221 + 0.642577i \(0.777865\pi\)
\(350\) −7.61684 10.8159i −0.407137 0.578134i
\(351\) −8.00000 6.63325i −0.427008 0.354057i
\(352\) 3.68614 + 2.12819i 0.196472 + 0.113433i
\(353\) 16.3723 9.45254i 0.871409 0.503108i 0.00359253 0.999994i \(-0.498856\pi\)
0.867816 + 0.496886i \(0.165523\pi\)
\(354\) 6.94158 + 1.63086i 0.368941 + 0.0866793i
\(355\) −3.11684 + 2.81929i −0.165425 + 0.149632i
\(356\) −4.37228 −0.231730
\(357\) 30.3723 + 1.23472i 1.60747 + 0.0653482i
\(358\) 2.87419i 0.151906i
\(359\) 12.2554 + 7.07568i 0.646817 + 0.373440i 0.787236 0.616652i \(-0.211511\pi\)
−0.140419 + 0.990092i \(0.544845\pi\)
\(360\) −1.81386 6.45832i −0.0955988 0.340383i
\(361\) −3.50000 6.06218i −0.184211 0.319062i
\(362\) 15.5584 + 8.98266i 0.817733 + 0.472118i
\(363\) 8.44158 8.98266i 0.443068 0.471467i
\(364\) −1.00000 5.19615i −0.0524142 0.272352i
\(365\) −1.37228 + 4.25639i −0.0718285 + 0.222790i
\(366\) −4.67527 + 1.40965i −0.244380 + 0.0736834i
\(367\) −10.6168 18.3889i −0.554195 0.959893i −0.997966 0.0637532i \(-0.979693\pi\)
0.443771 0.896140i \(-0.353640\pi\)
\(368\) 2.18614 + 3.78651i 0.113960 + 0.197385i
\(369\) 4.37228 + 2.17448i 0.227612 + 0.113199i
\(370\) −24.8614 8.01544i −1.29248 0.416703i
\(371\) −0.686141 3.56529i −0.0356226 0.185101i
\(372\) 3.00000 + 2.81929i 0.155543 + 0.146173i
\(373\) 14.2337 + 8.21782i 0.736992 + 0.425503i 0.820975 0.570964i \(-0.193431\pi\)
−0.0839823 + 0.996467i \(0.526764\pi\)
\(374\) 14.1168 + 24.4511i 0.729965 + 1.26434i
\(375\) −17.8030 + 7.61930i −0.919342 + 0.393459i
\(376\) −1.62772 0.939764i −0.0839432 0.0484646i
\(377\) 6.63325i 0.341630i
\(378\) −13.7446 + 0.294954i −0.706944 + 0.0151708i
\(379\) 22.2337 1.14207 0.571034 0.820926i \(-0.306542\pi\)
0.571034 + 0.820926i \(0.306542\pi\)
\(380\) −5.74456 + 5.19615i −0.294690 + 0.266557i
\(381\) −0.941578 + 4.00772i −0.0482385 + 0.205322i
\(382\) 3.25544 1.87953i 0.166563 0.0961650i
\(383\) −18.0475 10.4198i −0.922187 0.532425i −0.0378546 0.999283i \(-0.512052\pi\)
−0.884332 + 0.466859i \(0.845386\pi\)
\(384\) 1.18614 1.26217i 0.0605300 0.0644098i
\(385\) −20.1168 15.1460i −1.02525 0.771913i
\(386\) 8.01544i 0.407975i
\(387\) −14.7446 + 29.6472i −0.749508 + 1.50705i
\(388\) −1.05842 1.83324i −0.0537332 0.0930687i
\(389\) −29.4891 + 17.0256i −1.49516 + 0.863230i −0.999985 0.00556424i \(-0.998229\pi\)
−0.495173 + 0.868794i \(0.664896\pi\)
\(390\) −7.74456 0.147477i −0.392161 0.00746778i
\(391\) 29.0024i 1.46672i
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) 5.48913 5.84096i 0.276890 0.294638i
\(394\) 10.1168 17.5229i 0.509679 0.882790i
\(395\) 17.7446 3.81396i 0.892826 0.191901i
\(396\) −7.05842 10.6410i −0.354699 0.534729i
\(397\) 4.00000 6.92820i 0.200754 0.347717i −0.748017 0.663679i \(-0.768994\pi\)
0.948772 + 0.315963i \(0.102327\pi\)
\(398\) 18.6101i 0.932841i
\(399\) 7.37228 + 14.0588i 0.369076 + 0.703820i
\(400\) −4.05842 2.92048i −0.202921 0.146024i
\(401\) −17.1861 9.92242i −0.858235 0.495502i 0.00518590 0.999987i \(-0.498349\pi\)
−0.863421 + 0.504484i \(0.831683\pi\)
\(402\) 3.00000 12.7692i 0.149626 0.636868i
\(403\) 4.11684 2.37686i 0.205075 0.118400i
\(404\) 8.18614 14.1788i 0.407276 0.705422i
\(405\) −3.75544 + 19.7711i −0.186609 + 0.982434i
\(406\) 5.74456 + 6.63325i 0.285098 + 0.329203i
\(407\) −49.7228 −2.46467
\(408\) 11.0000 3.31662i 0.544581 0.164197i
\(409\) −30.7337 + 17.7441i −1.51968 + 0.877389i −0.519952 + 0.854195i \(0.674050\pi\)
−0.999731 + 0.0231940i \(0.992616\pi\)
\(410\) 3.55842 0.764836i 0.175738 0.0377725i
\(411\) 1.37228 + 4.55134i 0.0676896 + 0.224501i
\(412\) −15.1168 −0.744753
\(413\) −2.05842 10.6959i −0.101288 0.526310i
\(414\) −0.813859 13.0916i −0.0399990 0.643416i
\(415\) 2.38316 2.15565i 0.116985 0.105816i
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 4.62772 19.6974i 0.226620 0.964584i
\(418\) −7.37228 + 12.7692i −0.360590 + 0.624560i
\(419\) −29.4891 −1.44064 −0.720319 0.693643i \(-0.756005\pi\)
−0.720319 + 0.693643i \(0.756005\pi\)
\(420\) −7.87228 + 6.55951i −0.384128 + 0.320071i
\(421\) 15.1168 0.736750 0.368375 0.929677i \(-0.379914\pi\)
0.368375 + 0.929677i \(0.379914\pi\)
\(422\) −9.11684 + 15.7908i −0.443801 + 0.768686i
\(423\) 3.11684 + 4.69882i 0.151546 + 0.228464i
\(424\) −0.686141 1.18843i −0.0333219 0.0577153i
\(425\) −13.6277 30.2372i −0.661041 1.46672i
\(426\) 2.37228 + 2.22938i 0.114937 + 0.108014i
\(427\) 4.88316 + 5.63858i 0.236312 + 0.272870i
\(428\) −17.7446 −0.857716
\(429\) −14.1168 + 4.25639i −0.681568 + 0.205500i
\(430\) 5.18614 + 24.1287i 0.250098 + 1.16359i
\(431\) −3.25544 + 1.87953i −0.156809 + 0.0905337i −0.576351 0.817202i \(-0.695524\pi\)
0.419542 + 0.907736i \(0.362191\pi\)
\(432\) −4.87228 + 1.80579i −0.234418 + 0.0868811i
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 2.05842 5.94215i 0.0988074 0.285232i
\(435\) 11.2446 6.20965i 0.539136 0.297730i
\(436\) −4.55842 + 7.89542i −0.218309 + 0.378122i
\(437\) −13.1168 + 7.57301i −0.627464 + 0.362266i
\(438\) 3.37228 + 0.792287i 0.161134 + 0.0378569i
\(439\) −11.0584 6.38458i −0.527790 0.304720i 0.212326 0.977199i \(-0.431896\pi\)
−0.740116 + 0.672479i \(0.765229\pi\)
\(440\) −9.05842 2.92048i −0.431843 0.139228i
\(441\) 8.98913 + 18.9788i 0.428054 + 0.903753i
\(442\) 13.2665i 0.631023i
\(443\) 4.50000 7.79423i 0.213801 0.370315i −0.739100 0.673596i \(-0.764749\pi\)
0.952901 + 0.303281i \(0.0980821\pi\)
\(444\) −4.62772 + 19.6974i −0.219622 + 0.934796i
\(445\) 9.55842 2.05446i 0.453113 0.0973905i
\(446\) −9.05842 + 15.6896i −0.428929 + 0.742926i
\(447\) −17.9307 16.8506i −0.848093 0.797007i
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) 35.9855i 1.69826i −0.528182 0.849131i \(-0.677126\pi\)
0.528182 0.849131i \(-0.322874\pi\)
\(450\) 7.00000 + 13.2665i 0.329983 + 0.625389i
\(451\) 6.00000 3.46410i 0.282529 0.163118i
\(452\) −1.62772 2.81929i −0.0765614 0.132608i
\(453\) 4.05842 + 13.4603i 0.190681 + 0.632418i
\(454\) 15.6434i 0.734179i
\(455\) 4.62772 + 10.8896i 0.216951 + 0.510514i
\(456\) 4.37228 + 4.10891i 0.204751 + 0.192417i
\(457\) −11.0584 6.38458i −0.517291 0.298658i 0.218534 0.975829i \(-0.429872\pi\)
−0.735826 + 0.677171i \(0.763206\pi\)
\(458\) 12.0000 6.92820i 0.560723 0.323734i
\(459\) −33.9783 5.78606i −1.58597 0.270070i
\(460\) −6.55842 7.25061i −0.305788 0.338061i
\(461\) −0.510875 −0.0237938 −0.0118969 0.999929i \(-0.503787\pi\)
−0.0118969 + 0.999929i \(0.503787\pi\)
\(462\) −10.4307 + 16.4819i −0.485280 + 0.766809i
\(463\) 36.5754i 1.69981i −0.526940 0.849903i \(-0.676661\pi\)
0.526940 0.849903i \(-0.323339\pi\)
\(464\) 2.87228 + 1.65831i 0.133342 + 0.0769852i
\(465\) −7.88316 4.75372i −0.365573 0.220449i
\(466\) 11.7446 + 20.3422i 0.544056 + 0.942333i
\(467\) −0.0475473 0.0274514i −0.00220023 0.00127030i 0.498899 0.866660i \(-0.333738\pi\)
−0.501100 + 0.865390i \(0.667071\pi\)
\(468\) 0.372281 + 5.98844i 0.0172087 + 0.276816i
\(469\) −19.6753 + 3.78651i −0.908519 + 0.174845i
\(470\) 4.00000 + 1.28962i 0.184506 + 0.0594858i
\(471\) 4.00000 + 13.2665i 0.184310 + 0.611288i
\(472\) −2.05842 3.56529i −0.0947466 0.164106i
\(473\) 23.4891 + 40.6844i 1.08003 + 1.87067i
\(474\) −4.05842 13.4603i −0.186409 0.618250i
\(475\) 10.1168 14.0588i 0.464193 0.645061i
\(476\) −11.4891 13.2665i −0.526603 0.608069i
\(477\) 0.255437 + 4.10891i 0.0116957 + 0.188134i
\(478\) −2.48913 1.43710i −0.113850 0.0657313i
\(479\) −4.37228 7.57301i −0.199775 0.346020i 0.748681 0.662931i \(-0.230688\pi\)
−0.948455 + 0.316911i \(0.897354\pi\)
\(480\) −2.00000 + 3.31662i −0.0912871 + 0.151383i
\(481\) 20.2337 + 11.6819i 0.922577 + 0.532650i
\(482\) 10.5947i 0.482575i
\(483\) −17.7446 + 9.30506i −0.807406 + 0.423395i
\(484\) −7.11684 −0.323493
\(485\) 3.17527 + 3.51039i 0.144181 + 0.159399i
\(486\) 15.5000 + 1.65831i 0.703094 + 0.0752226i
\(487\) −3.94158 + 2.27567i −0.178610 + 0.103121i −0.586639 0.809848i \(-0.699549\pi\)
0.408029 + 0.912969i \(0.366216\pi\)
\(488\) 2.44158 + 1.40965i 0.110525 + 0.0638117i
\(489\) 4.37228 + 4.10891i 0.197721 + 0.185811i
\(490\) 14.0584 + 6.88192i 0.635095 + 0.310893i
\(491\) 26.9205i 1.21491i −0.794355 0.607453i \(-0.792191\pi\)
0.794355 0.607453i \(-0.207809\pi\)
\(492\) −0.813859 2.69927i −0.0366916 0.121692i
\(493\) 11.0000 + 19.0526i 0.495415 + 0.858084i
\(494\) 6.00000 3.46410i 0.269953 0.155857i
\(495\) 20.4307 + 19.9460i 0.918292 + 0.896508i
\(496\) 2.37686i 0.106724i
\(497\) 1.62772 4.69882i 0.0730132 0.210771i
\(498\) −1.81386 1.70460i −0.0812810 0.0763849i
\(499\) −14.1168 + 24.4511i −0.631957 + 1.09458i 0.355195 + 0.934792i \(0.384415\pi\)
−0.987151 + 0.159789i \(0.948919\pi\)
\(500\) 10.2446 + 4.47760i 0.458151 + 0.200245i
\(501\) −4.48913 + 19.1075i −0.200559 + 0.853658i
\(502\) 8.05842 13.9576i 0.359665 0.622958i
\(503\) 9.45254i 0.421468i −0.977543 0.210734i \(-0.932415\pi\)
0.977543 0.210734i \(-0.0675854\pi\)
\(504\) 5.55842 + 5.66603i 0.247592 + 0.252385i
\(505\) −11.2337 + 34.8434i −0.499893 + 1.55051i
\(506\) −16.1168 9.30506i −0.716481 0.413661i
\(507\) −15.1753 3.56529i −0.673957 0.158340i
\(508\) 2.05842 1.18843i 0.0913277 0.0527281i
\(509\) −0.127719 + 0.221215i −0.00566103 + 0.00980519i −0.868842 0.495089i \(-0.835135\pi\)
0.863181 + 0.504895i \(0.168469\pi\)
\(510\) −22.4891 + 12.4193i −0.995835 + 0.549936i
\(511\) −1.00000 5.19615i −0.0442374 0.229864i
\(512\) −1.00000 −0.0441942
\(513\) −6.25544 16.8781i −0.276184 0.745185i
\(514\) −7.37228 + 4.25639i −0.325177 + 0.187741i
\(515\) 33.0475 7.10313i 1.45625 0.313001i
\(516\) 18.3030 5.51856i 0.805744 0.242941i
\(517\) 8.00000 0.351840
\(518\) 30.3505 5.84096i 1.33353 0.256637i
\(519\) −4.74456 4.45877i −0.208263 0.195718i
\(520\) 3.00000 + 3.31662i 0.131559 + 0.145444i
\(521\) −1.62772 2.81929i −0.0713116 0.123515i 0.828165 0.560485i \(-0.189385\pi\)
−0.899476 + 0.436969i \(0.856052\pi\)
\(522\) −5.50000 8.29156i −0.240728 0.362912i
\(523\) −12.1168 + 20.9870i −0.529833 + 0.917697i 0.469562 + 0.882900i \(0.344412\pi\)
−0.999394 + 0.0347974i \(0.988921\pi\)
\(524\) −4.62772 −0.202163
\(525\) 14.1277 18.0391i 0.616584 0.787289i
\(526\) 1.62772 0.0709719
\(527\) 7.88316 13.6540i 0.343396 0.594779i
\(528\) −1.68614 + 7.17687i −0.0733799 + 0.312333i
\(529\) 1.94158 + 3.36291i 0.0844164 + 0.146214i
\(530\) 2.05842 + 2.27567i 0.0894121 + 0.0988488i
\(531\) 0.766312 + 12.3267i 0.0332551 + 0.534935i
\(532\) 3.00000 8.66025i 0.130066 0.375470i
\(533\) −3.25544 −0.141009
\(534\) −2.18614 7.25061i −0.0946036 0.313765i
\(535\) 38.7921 8.33785i 1.67713 0.360477i
\(536\) −6.55842 + 3.78651i −0.283281 + 0.163552i
\(537\) −4.76631 + 1.43710i −0.205682 + 0.0620153i
\(538\) 19.9783 0.861324
\(539\) 29.4891 + 4.25639i 1.27019 + 0.183336i
\(540\) 9.80298 6.23711i 0.421853 0.268402i
\(541\) 6.67527 11.5619i 0.286992 0.497085i −0.686098 0.727509i \(-0.740678\pi\)
0.973090 + 0.230424i \(0.0740113\pi\)
\(542\) −18.1753 + 10.4935i −0.780695 + 0.450734i
\(543\) −7.11684 + 30.2921i −0.305413 + 1.29996i
\(544\) −5.74456 3.31662i −0.246296 0.142199i
\(545\) 6.25544 19.4024i 0.267953 0.831108i
\(546\) 8.11684 4.25639i 0.347369 0.182157i
\(547\) 0.644810i 0.0275701i 0.999905 + 0.0137850i \(0.00438806\pi\)
−0.999905 + 0.0137850i \(0.995612\pi\)
\(548\) 1.37228 2.37686i 0.0586210 0.101534i
\(549\) −4.67527 7.04823i −0.199535 0.300811i
\(550\) 21.1753 + 2.12819i 0.902916 + 0.0907465i
\(551\) −5.74456 + 9.94987i −0.244727 + 0.423879i
\(552\) −5.18614 + 5.51856i −0.220737 + 0.234885i
\(553\) −16.2337 + 14.0588i −0.690327 + 0.597840i
\(554\) 29.0024i 1.23220i
\(555\) 0.861407 45.2357i 0.0365647 1.92015i
\(556\) −10.1168 + 5.84096i −0.429050 + 0.247712i
\(557\) −0.430703 0.746000i −0.0182495 0.0316090i 0.856756 0.515721i \(-0.172476\pi\)
−0.875006 + 0.484112i \(0.839143\pi\)
\(558\) −3.17527 + 6.38458i −0.134420 + 0.270281i
\(559\) 22.0742i 0.933640i
\(560\) 5.87228 + 0.718549i 0.248149 + 0.0303642i
\(561\) −33.4891 + 35.6357i −1.41391 + 1.50454i
\(562\) 18.8614 + 10.8896i 0.795620 + 0.459352i
\(563\) −10.2446 + 5.91470i −0.431757 + 0.249275i −0.700095 0.714050i \(-0.746859\pi\)
0.268338 + 0.963325i \(0.413526\pi\)
\(564\) 0.744563 3.16915i 0.0313517 0.133445i
\(565\) 4.88316 + 5.39853i 0.205436 + 0.227118i
\(566\) −16.0000 −0.672530
\(567\) −7.36141 22.6453i −0.309150 0.951013i
\(568\) 1.87953i 0.0788632i
\(569\) −18.8614 10.8896i −0.790711 0.456517i 0.0495016 0.998774i \(-0.484237\pi\)
−0.840213 + 0.542257i \(0.817570\pi\)
\(570\) −11.4891 6.92820i −0.481227 0.290191i
\(571\) −17.1168 29.6472i −0.716318 1.24070i −0.962449 0.271462i \(-0.912493\pi\)
0.246132 0.969236i \(-0.420840\pi\)
\(572\) 7.37228 + 4.25639i 0.308251 + 0.177969i
\(573\) 4.74456 + 4.45877i 0.198207 + 0.186268i
\(574\) −3.25544 + 2.81929i −0.135879 + 0.117675i
\(575\) 17.7446 + 12.7692i 0.739999 + 0.532511i
\(576\) 2.68614 + 1.33591i 0.111923 + 0.0556628i
\(577\) −8.94158 15.4873i −0.372243 0.644743i 0.617667 0.786439i \(-0.288078\pi\)
−0.989910 + 0.141696i \(0.954744\pi\)
\(578\) −13.5000 23.3827i −0.561526 0.972592i
\(579\) 13.2921 4.00772i 0.552401 0.166555i
\(580\) −7.05842 2.27567i −0.293085 0.0944921i
\(581\) −1.24456 + 3.59274i −0.0516332 + 0.149052i
\(582\) 2.51087 2.67181i 0.104079 0.110750i
\(583\) 5.05842 + 2.92048i 0.209498 + 0.120954i
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) −3.62772 12.9166i −0.149988 0.534037i
\(586\) −21.6861 12.5205i −0.895846 0.517217i
\(587\) 36.4280i 1.50354i 0.659424 + 0.751772i \(0.270800\pi\)
−0.659424 + 0.751772i \(0.729200\pi\)
\(588\) 4.43070 11.2858i 0.182719 0.465418i
\(589\) 8.23369 0.339263
\(590\) 6.17527 + 6.82701i 0.254232 + 0.281064i
\(591\) 34.1168 + 8.01544i 1.40338 + 0.329711i
\(592\) 10.1168 5.84096i 0.415800 0.240062i
\(593\) −12.2554 7.07568i −0.503270 0.290563i 0.226793 0.973943i \(-0.427176\pi\)
−0.730063 + 0.683380i \(0.760509\pi\)
\(594\) 14.1168 17.0256i 0.579221 0.698567i
\(595\) 31.3505 + 23.6039i 1.28525 + 0.967666i
\(596\) 14.2063i 0.581911i
\(597\) −30.8614 + 9.30506i −1.26307 + 0.380831i
\(598\) 4.37228 + 7.57301i 0.178796 + 0.309684i
\(599\) −7.37228 + 4.25639i −0.301223 + 0.173911i −0.642992 0.765873i \(-0.722307\pi\)
0.341769 + 0.939784i \(0.388974\pi\)
\(600\) 2.81386 8.19037i 0.114875 0.334371i
\(601\) 10.5947i 0.432166i −0.976375 0.216083i \(-0.930672\pi\)
0.976375 0.216083i \(-0.0693282\pi\)
\(602\) −19.1168 22.0742i −0.779144 0.899678i
\(603\) 22.6753 1.40965i 0.923408 0.0574052i
\(604\) 4.05842 7.02939i 0.165135 0.286022i
\(605\) 15.5584 3.34408i 0.632540 0.135956i
\(606\) 27.6060 + 6.48577i 1.12142 + 0.263467i
\(607\) 13.7337 23.7874i 0.557433 0.965503i −0.440277 0.897862i \(-0.645120\pi\)
0.997710 0.0676404i \(-0.0215471\pi\)
\(608\) 3.46410i 0.140488i
\(609\) −8.12772 + 12.8429i −0.329352 + 0.520421i
\(610\) −6.00000 1.93443i −0.242933 0.0783228i
\(611\) −3.25544 1.87953i −0.131701 0.0760375i
\(612\) 11.0000 + 16.5831i 0.444649 + 0.670333i
\(613\) 11.2337 6.48577i 0.453724 0.261958i −0.255677 0.966762i \(-0.582299\pi\)
0.709402 + 0.704804i \(0.248965\pi\)
\(614\) −3.44158 + 5.96099i −0.138891 + 0.240566i
\(615\) 3.04755 + 5.51856i 0.122889 + 0.222530i
\(616\) 11.0584 2.12819i 0.445557 0.0857474i
\(617\) 1.02175 0.0411341 0.0205670 0.999788i \(-0.493453\pi\)
0.0205670 + 0.999788i \(0.493453\pi\)
\(618\) −7.55842 25.0684i −0.304044 1.00840i
\(619\) 20.2337 11.6819i 0.813261 0.469536i −0.0348263 0.999393i \(-0.511088\pi\)
0.848087 + 0.529857i \(0.177754\pi\)
\(620\) 1.11684 + 5.19615i 0.0448535 + 0.208683i
\(621\) 21.3030 7.89542i 0.854859 0.316832i
\(622\) −14.2337 −0.570719
\(623\) −8.74456 + 7.57301i −0.350344 + 0.303406i
\(624\) 2.37228 2.52434i 0.0949673 0.101054i
\(625\) −24.5000 4.97494i −0.980000 0.198997i
\(626\) 7.05842 + 12.2255i 0.282111 + 0.488631i
\(627\) −24.8614 5.84096i −0.992869 0.233266i
\(628\) 4.00000 6.92820i 0.159617 0.276465i
\(629\) 77.4891 3.08969
\(630\) −14.8139 9.77495i −0.590198 0.389443i
\(631\) 30.1168 1.19893 0.599466 0.800400i \(-0.295380\pi\)
0.599466 + 0.800400i \(0.295380\pi\)
\(632\) −4.05842 + 7.02939i −0.161435 + 0.279614i
\(633\) −30.7446 7.22316i −1.22199 0.287095i
\(634\) −8.05842 13.9576i −0.320041 0.554327i
\(635\) −3.94158 + 3.56529i −0.156417 + 0.141484i
\(636\) 1.62772 1.73205i 0.0645432 0.0686803i
\(637\) −11.0000 8.66025i −0.435836 0.343132i
\(638\) −14.1168 −0.558891
\(639\) −2.51087 + 5.04868i −0.0993287 + 0.199723i
\(640\) 2.18614 0.469882i 0.0864148 0.0185737i
\(641\) 12.3030 7.10313i 0.485939 0.280557i −0.236949 0.971522i \(-0.576148\pi\)
0.722888 + 0.690965i \(0.242814\pi\)
\(642\) −8.87228 29.4260i −0.350161 1.16135i
\(643\) −16.2337 −0.640194 −0.320097 0.947385i \(-0.603716\pi\)
−0.320097 + 0.947385i \(0.603716\pi\)
\(644\) 10.9307 + 3.78651i 0.430730 + 0.149209i
\(645\) −37.4198 + 20.6646i −1.47340 + 0.813667i
\(646\) 11.4891 19.8997i 0.452034 0.782945i
\(647\) −22.0693 + 12.7417i −0.867634 + 0.500928i −0.866561 0.499071i \(-0.833675\pi\)
−0.00107245 + 0.999999i \(0.500341\pi\)
\(648\) −5.43070 7.17687i −0.213338 0.281934i
\(649\) 15.1753 + 8.76144i 0.595681 + 0.343917i
\(650\) −8.11684 5.84096i −0.318369 0.229101i
\(651\) 10.8832 + 0.442430i 0.426545 + 0.0173402i
\(652\) 3.46410i 0.135665i
\(653\) −5.31386 + 9.20387i −0.207947 + 0.360175i −0.951068 0.308982i \(-0.900012\pi\)
0.743120 + 0.669158i \(0.233345\pi\)
\(654\) −15.3723 3.61158i −0.601104 0.141224i
\(655\) 10.1168 2.17448i 0.395298 0.0849640i
\(656\) −0.813859 + 1.40965i −0.0317759 + 0.0550374i
\(657\) 0.372281 + 5.98844i 0.0145241 + 0.233631i
\(658\) −4.88316 + 0.939764i −0.190365 + 0.0366358i
\(659\) 36.9253i 1.43841i 0.694800 + 0.719203i \(0.255493\pi\)
−0.694800 + 0.719203i \(0.744507\pi\)
\(660\) 0.313859 16.4819i 0.0122170 0.641558i
\(661\) 2.44158 1.40965i 0.0949664 0.0548289i −0.451765 0.892137i \(-0.649205\pi\)
0.546731 + 0.837308i \(0.315872\pi\)
\(662\) 5.11684 + 8.86263i 0.198872 + 0.344456i
\(663\) 22.0000 6.63325i 0.854409 0.257614i
\(664\) 1.43710i 0.0557702i
\(665\) −2.48913 + 20.3422i −0.0965241 + 0.788836i
\(666\) −34.9783 + 2.17448i −1.35538 + 0.0842594i
\(667\) −12.5584 7.25061i −0.486264 0.280745i
\(668\) 9.81386 5.66603i 0.379710 0.219225i
\(669\) −30.5475 7.17687i −1.18104 0.277474i
\(670\) 12.5584 11.3595i 0.485174 0.438857i
\(671\) −12.0000 −0.463255
\(672\) 0.186141 4.57879i 0.00718053 0.176631i
\(673\) 17.1181i 0.659855i 0.944006 + 0.329928i \(0.107024\pi\)
−0.944006 + 0.329928i \(0.892976\pi\)
\(674\) 8.05842 + 4.65253i 0.310399 + 0.179209i
\(675\) −18.5000 + 18.2414i −0.712065 + 0.702113i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) 38.9198 + 22.4704i 1.49581 + 0.863607i 0.999988 0.00481749i \(-0.00153346\pi\)
0.495822 + 0.868424i \(0.334867\pi\)
\(678\) 3.86141 4.10891i 0.148296 0.157802i
\(679\) −5.29211 1.83324i −0.203093 0.0703533i
\(680\) 14.1168 + 4.55134i 0.541356 + 0.174536i
\(681\) 25.9416 7.82168i 0.994083 0.299727i
\(682\) 5.05842 + 8.76144i 0.193697 + 0.335493i
\(683\) −6.98913 12.1055i −0.267431 0.463205i 0.700766 0.713391i \(-0.252842\pi\)
−0.968198 + 0.250186i \(0.919508\pi\)
\(684\) −4.62772 + 9.30506i −0.176945 + 0.355788i
\(685\) −1.88316 + 5.84096i −0.0719517 + 0.223172i
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 17.4891 + 16.4356i 0.667252 + 0.627059i
\(688\) −9.55842 5.51856i −0.364411 0.210393i
\(689\) −1.37228 2.37686i −0.0522798 0.0905512i
\(690\) 8.74456 14.5012i 0.332900 0.552052i
\(691\) −26.2337 15.1460i −0.997977 0.576182i −0.0903276 0.995912i \(-0.528791\pi\)
−0.907649 + 0.419730i \(0.862125\pi\)
\(692\) 3.75906i 0.142898i
\(693\) −32.5475 9.05640i −1.23638 0.344024i
\(694\) 19.1168 0.725665
\(695\) 19.3723 17.5229i 0.734833 0.664681i
\(696\) −1.31386 + 5.59230i −0.0498017 + 0.211975i
\(697\) −9.35053 + 5.39853i −0.354177 + 0.204484i
\(698\) 20.7921 + 12.0043i 0.786993 + 0.454371i
\(699\) −27.8614 + 29.6472i −1.05382 + 1.12136i
\(700\) −13.1753 + 1.18843i −0.497978 + 0.0449185i
\(701\) 12.7143i 0.480211i 0.970747 + 0.240106i \(0.0771821\pi\)
−0.970747 + 0.240106i \(0.922818\pi\)
\(702\) −9.74456 + 3.61158i −0.367785 + 0.136310i
\(703\) 20.2337 + 35.0458i 0.763128 + 1.32178i
\(704\) 3.68614 2.12819i 0.138927 0.0802093i
\(705\) −0.138593 + 7.27806i −0.00521973 + 0.274108i
\(706\) 18.9051i 0.711502i
\(707\) −8.18614 42.5364i −0.307872 1.59975i
\(708\) 4.88316 5.19615i 0.183520 0.195283i
\(709\) 2.55842 4.43132i 0.0960836 0.166422i −0.813977 0.580897i \(-0.802702\pi\)
0.910060 + 0.414476i \(0.136035\pi\)
\(710\) 0.883156 + 4.10891i 0.0331443 + 0.154205i
\(711\) 20.2921 13.4603i 0.761014 0.504799i
\(712\) −2.18614 + 3.78651i −0.0819291 + 0.141905i
\(713\) 10.3923i 0.389195i
\(714\) 16.2554 25.6858i 0.608344 0.961267i
\(715\) −18.1168 5.84096i −0.677532 0.218440i
\(716\) 2.48913 + 1.43710i 0.0930230 + 0.0537068i
\(717\) 1.13859 4.84630i 0.0425215 0.180988i
\(718\) 12.2554 7.07568i 0.457369 0.264062i
\(719\) 16.6277 28.8001i 0.620109 1.07406i −0.369356 0.929288i \(-0.620422\pi\)
0.989465 0.144773i \(-0.0462451\pi\)
\(720\) −6.50000 1.65831i −0.242241 0.0618017i
\(721\) −30.2337 + 26.1831i −1.12596 + 0.975111i
\(722\) −7.00000 −0.260513
\(723\) 17.5693 5.29734i 0.653409 0.197010i
\(724\) 15.5584 8.98266i 0.578224 0.333838i
\(725\) 16.5000 + 1.65831i 0.612795 + 0.0615882i
\(726\) −3.55842 11.8020i −0.132065 0.438011i
\(727\) 19.0000 0.704671 0.352335 0.935874i \(-0.385388\pi\)
0.352335 + 0.935874i \(0.385388\pi\)
\(728\) −5.00000 1.73205i −0.185312 0.0641941i
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 3.00000 + 3.31662i 0.111035 + 0.122754i
\(731\) −36.6060 63.4034i −1.35392 2.34506i
\(732\) −1.11684 + 4.75372i −0.0412797 + 0.175703i
\(733\) 18.2337 31.5817i 0.673477 1.16650i −0.303435 0.952852i \(-0.598134\pi\)
0.976912 0.213644i \(-0.0685331\pi\)
\(734\) −21.2337 −0.783750
\(735\) −4.38316 + 26.7542i −0.161675 + 0.986844i
\(736\) 4.37228 0.161164
\(737\) 16.1168 27.9152i 0.593672 1.02827i
\(738\) 4.06930 2.69927i 0.149793 0.0993614i
\(739\) 18.1168 + 31.3793i 0.666439 + 1.15431i 0.978893 + 0.204373i \(0.0655156\pi\)
−0.312454 + 0.949933i \(0.601151\pi\)
\(740\) −19.3723 + 17.5229i −0.712139 + 0.644154i
\(741\) 8.74456 + 8.21782i 0.321240 + 0.301889i
\(742\) −3.43070 1.18843i −0.125945 0.0436287i
\(743\) 18.6060 0.682587 0.341293 0.939957i \(-0.389135\pi\)
0.341293 + 0.939957i \(0.389135\pi\)
\(744\) 3.94158 1.18843i 0.144505 0.0435700i
\(745\) −6.67527 31.0569i −0.244563 1.13784i
\(746\) 14.2337 8.21782i 0.521132 0.300876i
\(747\) 1.91983 3.86025i 0.0702429 0.141239i
\(748\) 28.2337 1.03233
\(749\) −35.4891 + 30.7345i −1.29674 + 1.12301i
\(750\) −2.30298 + 19.2275i −0.0840931 + 0.702089i
\(751\) −21.0584 + 36.4743i −0.768433 + 1.33096i 0.169980 + 0.985448i \(0.445630\pi\)
−0.938412 + 0.345517i \(0.887704\pi\)
\(752\) −1.62772 + 0.939764i −0.0593568 + 0.0342697i
\(753\) 27.1753 + 6.38458i 0.990322 + 0.232667i
\(754\) 5.74456 + 3.31662i 0.209205 + 0.120784i
\(755\) −5.56930 + 17.2742i −0.202687 + 0.628673i
\(756\) −6.61684 + 12.0506i −0.240652 + 0.438277i
\(757\) 5.63858i 0.204938i 0.994736 + 0.102469i \(0.0326742\pi\)
−0.994736 + 0.102469i \(0.967326\pi\)
\(758\) 11.1168 19.2549i 0.403782 0.699371i
\(759\) 7.37228 31.3793i 0.267597 1.13900i
\(760\) 1.62772 + 7.57301i 0.0590436 + 0.274702i
\(761\) 26.4891 45.8805i 0.960230 1.66317i 0.238312 0.971189i \(-0.423406\pi\)
0.721918 0.691979i \(-0.243261\pi\)
\(762\) 3.00000 + 2.81929i 0.108679 + 0.102132i
\(763\) 4.55842 + 23.6863i 0.165026 + 0.857500i
\(764\) 3.75906i 0.135998i
\(765\) −31.8397 31.0843i −1.15117 1.12386i
\(766\) −18.0475 + 10.4198i −0.652084 + 0.376481i
\(767\) −4.11684 7.13058i −0.148651 0.257470i
\(768\) −0.500000 1.65831i −0.0180422 0.0598392i
\(769\) 40.4820i 1.45982i −0.683545 0.729909i \(-0.739563\pi\)
0.683545 0.729909i \(-0.260437\pi\)
\(770\) −23.1753 + 9.84868i −0.835179 + 0.354922i
\(771\) −10.7446 10.0974i −0.386956 0.363647i
\(772\) −6.94158 4.00772i −0.249833 0.144241i
\(773\) −1.62772 + 0.939764i −0.0585450 + 0.0338010i −0.528987 0.848630i \(-0.677428\pi\)
0.470442 + 0.882431i \(0.344095\pi\)
\(774\) 18.3030 + 27.5928i 0.657887 + 0.991802i
\(775\) −4.88316 10.8347i −0.175408 0.389195i
\(776\) −2.11684 −0.0759903
\(777\) 24.8614 + 47.4102i 0.891898 + 1.70083i
\(778\) 34.0511i 1.22079i
\(779\) −4.88316 2.81929i −0.174957 0.101012i
\(780\) −4.00000 + 6.63325i −0.143223 + 0.237508i
\(781\) 4.00000 + 6.92820i 0.143131 + 0.247911i
\(782\) 25.1168 + 14.5012i 0.898177 + 0.518562i
\(783\) 11.0000 13.2665i 0.393108 0.474106i
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) −5.48913 + 17.0256i −0.195915 + 0.607668i
\(786\) −2.31386 7.67420i −0.0825326 0.273730i
\(787\) 13.5584 + 23.4839i 0.483306 + 0.837110i 0.999816 0.0191710i \(-0.00610269\pi\)
−0.516511 + 0.856281i \(0.672769\pi\)
\(788\) −10.1168 17.5229i −0.360398 0.624227i
\(789\) 0.813859 + 2.69927i 0.0289742 + 0.0960964i
\(790\) 5.56930 17.2742i 0.198147 0.614589i
\(791\) −8.13859 2.81929i −0.289375 0.100242i
\(792\) −12.7446 + 0.792287i −0.452858 + 0.0281527i
\(793\) 4.88316 + 2.81929i 0.173406 + 0.100116i
\(794\) −4.00000 6.92820i −0.141955 0.245873i
\(795\) −2.74456 + 4.55134i −0.0973396 + 0.161419i
\(796\) 16.1168 + 9.30506i 0.571246 + 0.329809i
\(797\) 4.25639i 0.150769i −0.997155 0.0753845i \(-0.975982\pi\)
0.997155 0.0753845i \(-0.0240184\pi\)
\(798\) 15.8614 + 0.644810i 0.561488 + 0.0228260i
\(799\) −12.4674 −0.441064
\(800\) −4.55842 + 2.05446i −0.161165 + 0.0726360i
\(801\) 10.9307 7.25061i 0.386217 0.256188i
\(802\) −17.1861 + 9.92242i −0.606864 + 0.350373i
\(803\) 7.37228 + 4.25639i 0.260162 + 0.150205i
\(804\) −9.55842 8.98266i −0.337100 0.316794i
\(805\) −25.6753 3.14170i −0.904934 0.110730i
\(806\) 4.75372i 0.167443i
\(807\) 9.98913 + 33.1302i 0.351634 + 1.16624i
\(808\) −8.18614 14.1788i −0.287987 0.498809i
\(809\) 22.0693 12.7417i 0.775915 0.447975i −0.0590655 0.998254i \(-0.518812\pi\)
0.834981 + 0.550279i \(0.185479\pi\)
\(810\) 15.2446 + 13.1379i 0.535639 + 0.461617i
\(811\) 10.3923i 0.364923i −0.983213 0.182462i \(-0.941593\pi\)
0.983213 0.182462i \(-0.0584065\pi\)
\(812\) 8.61684 1.65831i 0.302392 0.0581954i
\(813\) −26.4891 24.8935i −0.929014 0.873054i
\(814\) −24.8614 + 43.0612i −0.871392 + 1.50929i
\(815\) 1.62772 + 7.57301i 0.0570165 + 0.265271i
\(816\) 2.62772 11.1846i 0.0919886 0.391539i
\(817\) 19.1168 33.1113i 0.668814 1.15842i
\(818\) 35.4882i 1.24082i
\(819\) 11.1168 + 11.3321i 0.388454 + 0.395975i
\(820\) 1.11684 3.46410i 0.0390019 0.120972i
\(821\) 18.4307 + 10.6410i 0.643236 + 0.371372i 0.785860 0.618404i \(-0.212221\pi\)
−0.142624 + 0.989777i \(0.545554\pi\)
\(822\) 4.62772 + 1.08724i 0.161410 + 0.0379219i
\(823\) −37.6753 + 21.7518i −1.31328 + 0.758221i −0.982637 0.185536i \(-0.940598\pi\)
−0.330640 + 0.943757i \(0.607265\pi\)
\(824\) −7.55842 + 13.0916i −0.263310 + 0.456066i
\(825\) 7.05842 + 36.1793i 0.245743 + 1.25960i
\(826\) −10.2921 3.56529i −0.358108 0.124052i
\(827\) −33.0000 −1.14752 −0.573761 0.819023i \(-0.694516\pi\)
−0.573761 + 0.819023i \(0.694516\pi\)
\(828\) −11.7446 5.84096i −0.408152 0.202987i
\(829\) −16.1168 + 9.30506i −0.559761 + 0.323178i −0.753050 0.657964i \(-0.771418\pi\)
0.193288 + 0.981142i \(0.438085\pi\)
\(830\) −0.675266 3.14170i −0.0234388 0.109050i
\(831\) −48.0951 + 14.5012i −1.66840 + 0.503042i
\(832\) −2.00000 −0.0693375
\(833\) −45.9565 6.63325i −1.59230 0.229828i
\(834\) −14.7446 13.8564i −0.510562 0.479808i
\(835\) −18.7921 + 16.9981i −0.650328 + 0.588244i
\(836\) 7.37228 + 12.7692i 0.254976 + 0.441631i
\(837\) −12.1753 2.07329i −0.420839 0.0716634i
\(838\) −14.7446 + 25.5383i −0.509342 + 0.882207i
\(839\) 1.72281 0.0594781 0.0297391 0.999558i \(-0.490532\pi\)
0.0297391 + 0.999558i \(0.490532\pi\)
\(840\) 1.74456 + 10.0974i 0.0601931 + 0.348392i
\(841\) 18.0000 0.620690
\(842\) 7.55842 13.0916i 0.260480 0.451165i
\(843\) −8.62772 + 36.7229i −0.297154 + 1.26480i
\(844\) 9.11684 + 15.7908i 0.313815 + 0.543543i
\(845\) −13.5000 14.9248i −0.464414 0.513429i
\(846\) 5.62772 0.349857i 0.193485 0.0120283i
\(847\) −14.2337 + 12.3267i −0.489075 + 0.423552i
\(848\) −1.37228 −0.0471243
\(849\) −8.00000 26.5330i −0.274559 0.910610i
\(850\) −33.0000 3.31662i −1.13189 0.113759i
\(851\) −44.2337 + 25.5383i −1.51631 + 0.875443i
\(852\) 3.11684 0.939764i 0.106781 0.0321958i
\(853\) −30.4674 −1.04318 −0.521592 0.853195i \(-0.674661\pi\)
−0.521592 + 0.853195i \(0.674661\pi\)
\(854\) 7.32473 1.40965i 0.250647 0.0482371i
\(855\) 5.74456 22.5167i 0.196460 0.770054i
\(856\) −8.87228 + 15.3672i −0.303248 + 0.525242i
\(857\) −32.7446 + 18.9051i −1.11853 + 0.645785i −0.941026 0.338334i \(-0.890137\pi\)
−0.177507 + 0.984120i \(0.556803\pi\)
\(858\) −3.37228 + 14.3537i −0.115128 + 0.490029i
\(859\) 28.4674 + 16.4356i 0.971294 + 0.560777i 0.899631 0.436652i \(-0.143836\pi\)
0.0716637 + 0.997429i \(0.477169\pi\)
\(860\) 23.4891 + 7.57301i 0.800973 + 0.258238i
\(861\) −6.30298 3.98889i −0.214805 0.135941i
\(862\) 3.75906i 0.128034i
\(863\) 3.81386 6.60580i 0.129825 0.224864i −0.793783 0.608200i \(-0.791892\pi\)
0.923609 + 0.383336i \(0.125225\pi\)
\(864\) −0.872281 + 5.12241i −0.0296756 + 0.174268i
\(865\) −1.76631 8.21782i −0.0600564 0.279414i
\(866\) 17.0000 29.4449i 0.577684 1.00058i
\(867\) 32.0258 34.0786i 1.08765 1.15737i
\(868\) −4.11684 4.75372i −0.139735 0.161352i
\(869\) 34.5484i 1.17198i
\(870\) 0.244563 12.8429i 0.00829145 0.435415i
\(871\) −13.1168 + 7.57301i −0.444447 + 0.256602i
\(872\) 4.55842 + 7.89542i 0.154368 + 0.267373i
\(873\) 5.68614 + 2.82791i 0.192447 + 0.0957102i
\(874\) 15.1460i 0.512322i
\(875\) 28.2446 8.78890i 0.954840 0.297119i
\(876\) 2.37228 2.52434i 0.0801520 0.0852895i
\(877\) 27.3505 + 15.7908i 0.923562 + 0.533219i 0.884770 0.466029i \(-0.154316\pi\)
0.0387922 + 0.999247i \(0.487649\pi\)
\(878\) −11.0584 + 6.38458i −0.373204 + 0.215469i
\(879\) 9.91983 42.2226i 0.334588 1.42413i
\(880\) −7.05842 + 6.38458i −0.237939 + 0.215224i
\(881\) −51.3505 −1.73004 −0.865022 0.501734i \(-0.832695\pi\)
−0.865022 + 0.501734i \(0.832695\pi\)
\(882\) 20.9307 + 1.70460i 0.704773 + 0.0573968i
\(883\) 54.9455i 1.84906i −0.381104 0.924532i \(-0.624456\pi\)
0.381104 0.924532i \(-0.375544\pi\)
\(884\) −11.4891 6.63325i −0.386421 0.223100i
\(885\) −8.23369 + 13.6540i −0.276772 + 0.458975i
\(886\) −4.50000 7.79423i −0.151180 0.261852i
\(887\) 47.5367 + 27.4453i 1.59613 + 0.921523i 0.992224 + 0.124464i \(0.0397212\pi\)
0.603901 + 0.797059i \(0.293612\pi\)
\(888\) 14.7446 + 13.8564i 0.494795 + 0.464991i
\(889\) 2.05842 5.94215i 0.0690373 0.199293i
\(890\) 3.00000 9.30506i 0.100560 0.311906i
\(891\) 35.2921 + 14.8974i 1.18233 + 0.499080i
\(892\) 9.05842 + 15.6896i 0.303298 + 0.525328i
\(893\) −3.25544 5.63858i −0.108939 0.188688i
\(894\) −23.5584 + 7.10313i −0.787911 + 0.237564i
\(895\) −6.11684 1.97210i −0.204464 0.0659201i
\(896\) −2.00000 + 1.73205i −0.0668153 + 0.0578638i
\(897\) −10.3723 + 11.0371i −0.346320 + 0.368519i
\(898\) −31.1644 17.9928i −1.03997 0.600427i
\(899\) 3.94158 + 6.82701i 0.131459 + 0.227694i
\(900\) 14.9891 + 0.571072i 0.499638 + 0.0190357i
\(901\) −7.88316 4.55134i −0.262626 0.151627i
\(902\) 6.92820i 0.230684i
\(903\) 27.0475 42.7388i 0.900086 1.42226i
\(904\) −3.25544 −0.108274
\(905\) −29.7921 + 26.9480i −0.990323 + 0.895781i
\(906\) 13.6861 + 3.21543i 0.454692 + 0.106826i
\(907\) 38.7921 22.3966i 1.28807 0.743668i 0.309761 0.950814i \(-0.399751\pi\)
0.978310 + 0.207146i \(0.0664177\pi\)
\(908\) −13.5475 7.82168i −0.449591 0.259572i
\(909\) 3.04755 + 49.0222i 0.101081 + 1.62596i
\(910\) 11.7446 + 1.43710i 0.389328 + 0.0476393i
\(911\) 24.5437i 0.813168i −0.913613 0.406584i \(-0.866720\pi\)
0.913613 0.406584i \(-0.133280\pi\)
\(912\) 5.74456 1.73205i 0.190221 0.0573539i
\(913\) −3.05842 5.29734i −0.101219 0.175316i
\(914\) −11.0584 + 6.38458i −0.365780 + 0.211183i
\(915\) 0.207890 10.9171i 0.00687263 0.360908i
\(916\) 13.8564i 0.457829i
\(917\) −9.25544 + 8.01544i −0.305641 + 0.264693i
\(918\) −22.0000 + 26.5330i −0.726108 + 0.875719i
\(919\) 9.11684 15.7908i 0.300737 0.520892i −0.675566 0.737299i \(-0.736101\pi\)
0.976303 + 0.216408i \(0.0694341\pi\)
\(920\) −9.55842 + 2.05446i −0.315132 + 0.0677334i
\(921\) −11.6060 2.72672i −0.382430 0.0898484i
\(922\) −0.255437 + 0.442430i −0.00841238 + 0.0145707i
\(923\) 3.75906i 0.123731i
\(924\) 9.05842 + 17.2742i 0.298000 + 0.568280i
\(925\) 34.1168 47.4102i 1.12175 1.55884i
\(926\) −31.6753 18.2877i −1.04091 0.600972i
\(927\) 37.7921 25.0684i 1.24126 0.823356i
\(928\) 2.87228 1.65831i 0.0942873 0.0544368i
\(929\) −8.44158 + 14.6212i −0.276959 + 0.479707i −0.970628 0.240587i \(-0.922660\pi\)
0.693668 + 0.720295i \(0.255993\pi\)
\(930\) −8.05842 + 4.45015i −0.264246 + 0.145926i
\(931\) −9.00000 22.5167i −0.294963 0.737954i
\(932\) 23.4891 0.769412
\(933\) −7.11684 23.6039i −0.232995 0.772757i
\(934\) −0.0475473 + 0.0274514i −0.00155579 + 0.000898238i
\(935\) −61.7228 + 13.2665i −2.01855 + 0.433861i
\(936\) 5.37228 + 2.67181i 0.175599 + 0.0873310i
\(937\) −50.3505 −1.64488 −0.822440 0.568852i \(-0.807388\pi\)
−0.822440 + 0.568852i \(0.807388\pi\)
\(938\) −6.55842 + 18.9325i −0.214140 + 0.618169i
\(939\) −16.7446 + 17.8178i −0.546438 + 0.581463i
\(940\) 3.11684 2.81929i 0.101660 0.0919551i
\(941\) 12.1753 + 21.0882i 0.396902 + 0.687455i 0.993342 0.115203i \(-0.0367518\pi\)
−0.596440 + 0.802658i \(0.703418\pi\)
\(942\) 13.4891 + 3.16915i 0.439499 + 0.103256i
\(943\) 3.55842 6.16337i 0.115878 0.200707i
\(944\) −4.11684 −0.133992
\(945\) 8.80298 29.4535i 0.286361 0.958122i
\(946\) 46.9783 1.52739
\(947\) 21.5584 37.3403i 0.700555 1.21340i −0.267717 0.963497i \(-0.586269\pi\)
0.968272 0.249899i \(-0.0803973\pi\)
\(948\) −13.6861 3.21543i −0.444505 0.104432i
\(949\) −2.00000 3.46410i −0.0649227 0.112449i
\(950\) −7.11684 15.7908i −0.230901 0.512322i
\(951\) 19.1168 20.3422i 0.619906 0.659640i
\(952\) −17.2337 + 3.31662i −0.558547 + 0.107492i
\(953\) 48.0000 1.55487 0.777436 0.628962i \(-0.216520\pi\)
0.777436 + 0.628962i \(0.216520\pi\)
\(954\) 3.68614 + 1.83324i 0.119343 + 0.0593534i
\(955\) 1.76631 + 8.21782i 0.0571565 + 0.265923i
\(956\) −2.48913 + 1.43710i −0.0805041 + 0.0464790i
\(957\) −7.05842 23.4101i −0.228166 0.756742i
\(958\) −8.74456 −0.282524
\(959\) −1.37228 7.13058i −0.0443133 0.230259i
\(960\) 1.87228 + 3.39036i 0.0604276 + 0.109424i
\(961\) −12.6753 + 21.9542i −0.408880 + 0.708200i
\(962\) 20.2337 11.6819i 0.652360 0.376640i
\(963\) 44.3614 29.4260i 1.42953 0.948241i
\(964\) −9.17527 5.29734i −0.295515 0.170616i
\(965\) 17.0584 + 5.49972i 0.549130 + 0.177042i
\(966\) −0.813859 + 20.0198i −0.0261855 + 0.644126i
\(967\) 51.9239i 1.66976i 0.550433 + 0.834879i \(0.314463\pi\)
−0.550433 + 0.834879i \(0.685537\pi\)
\(968\) −3.55842 + 6.16337i −0.114372 + 0.198098i
\(969\) 38.7446 + 9.10268i 1.24465 + 0.292420i
\(970\) 4.62772 0.994667i 0.148587 0.0319368i
\(971\) −14.3139 + 24.7923i −0.459354 + 0.795624i −0.998927 0.0463149i \(-0.985252\pi\)
0.539573 + 0.841939i \(0.318586\pi\)
\(972\) 9.18614 12.5942i 0.294646 0.403960i
\(973\) −10.1168 + 29.2048i −0.324331 + 0.936263i
\(974\) 4.55134i 0.145834i
\(975\) 5.62772 16.3807i 0.180231 0.524604i
\(976\) 2.44158 1.40965i 0.0781530 0.0451217i
\(977\) −20.2337 35.0458i −0.647333 1.12121i −0.983757 0.179503i \(-0.942551\pi\)
0.336424 0.941710i \(-0.390782\pi\)
\(978\) 5.74456 1.73205i 0.183691 0.0553849i
\(979\) 18.6101i 0.594782i
\(980\) 12.9891 8.73399i 0.414922 0.278997i
\(981\) −1.69702 27.2978i −0.0541815 0.871553i
\(982\) −23.3139 13.4603i −0.743975 0.429534i
\(983\) 18.8139 10.8622i 0.600069 0.346450i −0.169000 0.985616i \(-0.554054\pi\)
0.769069 + 0.639166i \(0.220720\pi\)
\(984\) −2.74456 0.644810i −0.0874935 0.0205558i
\(985\) 30.3505 + 33.5538i 0.967048 + 1.06911i
\(986\) 22.0000 0.700623
\(987\) −4.00000 7.62792i −0.127321 0.242799i
\(988\) 6.92820i 0.220416i
\(989\) 41.7921 + 24.1287i 1.32891 + 0.767248i
\(990\) 27.4891 7.72049i 0.873662 0.245373i
\(991\) 14.1753 + 24.5523i 0.450292 + 0.779929i 0.998404 0.0564762i \(-0.0179865\pi\)
−0.548112 + 0.836405i \(0.684653\pi\)
\(992\) −2.05842 1.18843i −0.0653550 0.0377327i
\(993\) −12.1386 + 12.9166i −0.385207 + 0.409897i
\(994\) −3.25544 3.75906i −0.103256 0.119230i
\(995\) −39.6060 12.7692i −1.25559 0.404810i
\(996\) −2.38316 + 0.718549i −0.0755132 + 0.0227681i
\(997\) 15.2337 + 26.3855i 0.482456 + 0.835638i 0.999797 0.0201413i \(-0.00641159\pi\)
−0.517341 + 0.855779i \(0.673078\pi\)
\(998\) 14.1168 + 24.4511i 0.446861 + 0.773986i
\(999\) −21.0951 56.9176i −0.667419 1.80079i
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 210.2.t.c.89.2 yes 4
3.2 odd 2 210.2.t.a.89.2 yes 4
5.2 odd 4 1050.2.s.d.551.4 8
5.3 odd 4 1050.2.s.d.551.1 8
5.4 even 2 210.2.t.b.89.1 yes 4
7.2 even 3 1470.2.d.b.1469.2 4
7.3 odd 6 210.2.t.d.59.2 yes 4
7.5 odd 6 1470.2.d.a.1469.3 4
15.2 even 4 1050.2.s.e.551.2 8
15.8 even 4 1050.2.s.e.551.3 8
15.14 odd 2 210.2.t.d.89.1 yes 4
21.2 odd 6 1470.2.d.d.1469.1 4
21.5 even 6 1470.2.d.c.1469.4 4
21.17 even 6 210.2.t.b.59.1 yes 4
35.3 even 12 1050.2.s.e.101.3 8
35.9 even 6 1470.2.d.c.1469.3 4
35.17 even 12 1050.2.s.e.101.2 8
35.19 odd 6 1470.2.d.d.1469.2 4
35.24 odd 6 210.2.t.a.59.1 4
105.17 odd 12 1050.2.s.d.101.4 8
105.38 odd 12 1050.2.s.d.101.1 8
105.44 odd 6 1470.2.d.a.1469.4 4
105.59 even 6 inner 210.2.t.c.59.2 yes 4
105.89 even 6 1470.2.d.b.1469.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.t.a.59.1 4 35.24 odd 6
210.2.t.a.89.2 yes 4 3.2 odd 2
210.2.t.b.59.1 yes 4 21.17 even 6
210.2.t.b.89.1 yes 4 5.4 even 2
210.2.t.c.59.2 yes 4 105.59 even 6 inner
210.2.t.c.89.2 yes 4 1.1 even 1 trivial
210.2.t.d.59.2 yes 4 7.3 odd 6
210.2.t.d.89.1 yes 4 15.14 odd 2
1050.2.s.d.101.1 8 105.38 odd 12
1050.2.s.d.101.4 8 105.17 odd 12
1050.2.s.d.551.1 8 5.3 odd 4
1050.2.s.d.551.4 8 5.2 odd 4
1050.2.s.e.101.2 8 35.17 even 12
1050.2.s.e.101.3 8 35.3 even 12
1050.2.s.e.551.2 8 15.2 even 4
1050.2.s.e.551.3 8 15.8 even 4
1470.2.d.a.1469.3 4 7.5 odd 6
1470.2.d.a.1469.4 4 105.44 odd 6
1470.2.d.b.1469.1 4 105.89 even 6
1470.2.d.b.1469.2 4 7.2 even 3
1470.2.d.c.1469.3 4 35.9 even 6
1470.2.d.c.1469.4 4 21.5 even 6
1470.2.d.d.1469.1 4 21.2 odd 6
1470.2.d.d.1469.2 4 35.19 odd 6