Properties

Label 930.2.i.j.211.1
Level $930$
Weight $2$
Character 930.211
Analytic conductor $7.426$
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] = [930,2,Mod(211,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.211");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.i (of order \(3\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(-1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 930.211
Dual form 930.2.i.j.811.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-1.64575 - 2.85052i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.64575 + 2.85052i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{21} +(-0.500000 + 0.866025i) q^{22} -3.29150 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} -6.29150 q^{29} -1.00000 q^{30} +(1.14575 + 5.44860i) q^{31} -1.00000 q^{32} -1.00000 q^{33} +(1.64575 + 2.85052i) q^{34} +1.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.645751 - 1.11847i) q^{37} +(-1.64575 - 2.85052i) q^{38} +2.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(-2.64575 + 4.58258i) q^{41} +(0.500000 - 0.866025i) q^{42} +(2.00000 + 3.46410i) q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} +3.29150 q^{46} -11.2915 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.64575 + 2.85052i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.50000 + 2.59808i) q^{53} -1.00000 q^{54} +(0.500000 + 0.866025i) q^{55} +(0.500000 + 0.866025i) q^{56} +(1.64575 - 2.85052i) q^{57} +6.29150 q^{58} +(3.50000 + 6.06218i) q^{59} +1.00000 q^{60} -3.29150 q^{61} +(-1.14575 - 5.44860i) q^{62} +1.00000 q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +1.00000 q^{66} +(-0.645751 + 1.11847i) q^{67} +(-1.64575 - 2.85052i) q^{68} +(1.64575 + 2.85052i) q^{69} -1.00000 q^{70} +(-7.29150 + 12.6293i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.29150 + 3.96900i) q^{73} +(0.645751 + 1.11847i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(1.64575 + 2.85052i) q^{76} -1.00000 q^{77} -2.00000 q^{78} +(4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.64575 - 4.58258i) q^{82} +(-4.14575 + 7.18065i) q^{83} +(-0.500000 + 0.866025i) q^{84} +3.29150 q^{85} +(-2.00000 - 3.46410i) q^{86} +(3.14575 + 5.44860i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(0.500000 + 0.866025i) q^{90} +2.00000 q^{91} -3.29150 q^{92} +(4.14575 - 3.71655i) q^{93} +11.2915 q^{94} -3.29150 q^{95} +(0.500000 + 0.866025i) q^{96} -10.2915 q^{97} +(-3.00000 + 5.19615i) q^{98} +(0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} - 2 q^{21} - 2 q^{22} + 8 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 2 q^{28} - 4 q^{29} - 4 q^{30} - 6 q^{31} - 4 q^{32} - 4 q^{33} - 4 q^{34} + 4 q^{35} - 2 q^{36} + 8 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} + 2 q^{42} + 8 q^{43} + 2 q^{44} - 2 q^{45} - 8 q^{46} - 24 q^{47} - 2 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{51} - 4 q^{52} - 6 q^{53} - 4 q^{54} + 2 q^{55} + 2 q^{56} - 4 q^{57} + 4 q^{58} + 14 q^{59} + 4 q^{60} + 8 q^{61} + 6 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} + 4 q^{66} + 8 q^{67} + 4 q^{68} - 4 q^{69} - 4 q^{70} - 8 q^{71} + 2 q^{72} + 12 q^{73} - 8 q^{74} - 2 q^{75} - 4 q^{76} - 4 q^{77} - 8 q^{78} + 16 q^{79} - 2 q^{80} - 2 q^{81} - 6 q^{83} - 2 q^{84} - 8 q^{85} - 8 q^{86} + 2 q^{87} - 2 q^{88} + 2 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} + 24 q^{94} + 8 q^{95} + 2 q^{96} - 20 q^{97} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 1.00000 0.500000
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −0.500000 0.866025i −0.188982 0.327327i 0.755929 0.654654i \(-0.227186\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0.500000 + 0.866025i 0.133631 + 0.231455i
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −1.64575 2.85052i −0.399153 0.691354i 0.594468 0.804119i \(-0.297363\pi\)
−0.993622 + 0.112765i \(0.964029\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 1.64575 + 2.85052i 0.377561 + 0.653955i 0.990707 0.136015i \(-0.0434294\pi\)
−0.613146 + 0.789970i \(0.710096\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) −0.500000 + 0.866025i −0.109109 + 0.188982i
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) −3.29150 −0.686326 −0.343163 0.939276i \(-0.611498\pi\)
−0.343163 + 0.939276i \(0.611498\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 1.00000 0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) −6.29150 −1.16830 −0.584151 0.811645i \(-0.698573\pi\)
−0.584151 + 0.811645i \(0.698573\pi\)
\(30\) −1.00000 −0.182574
\(31\) 1.14575 + 5.44860i 0.205783 + 0.978598i
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) 1.64575 + 2.85052i 0.282244 + 0.488861i
\(35\) 1.00000 0.169031
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −0.645751 1.11847i −0.106161 0.183876i 0.808051 0.589112i \(-0.200523\pi\)
−0.914212 + 0.405236i \(0.867189\pi\)
\(38\) −1.64575 2.85052i −0.266976 0.462416i
\(39\) 2.00000 0.320256
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −2.64575 + 4.58258i −0.413197 + 0.715678i −0.995237 0.0974818i \(-0.968921\pi\)
0.582040 + 0.813160i \(0.302255\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) 3.29150 0.485306
\(47\) −11.2915 −1.64703 −0.823517 0.567291i \(-0.807992\pi\)
−0.823517 + 0.567291i \(0.807992\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) −1.64575 + 2.85052i −0.230451 + 0.399153i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0.500000 + 0.866025i 0.0674200 + 0.116775i
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 1.64575 2.85052i 0.217985 0.377561i
\(58\) 6.29150 0.826115
\(59\) 3.50000 + 6.06218i 0.455661 + 0.789228i 0.998726 0.0504625i \(-0.0160695\pi\)
−0.543065 + 0.839691i \(0.682736\pi\)
\(60\) 1.00000 0.129099
\(61\) −3.29150 −0.421434 −0.210717 0.977547i \(-0.567580\pi\)
−0.210717 + 0.977547i \(0.567580\pi\)
\(62\) −1.14575 5.44860i −0.145511 0.691973i
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) 1.00000 0.123091
\(67\) −0.645751 + 1.11847i −0.0788911 + 0.136643i −0.902772 0.430120i \(-0.858471\pi\)
0.823881 + 0.566763i \(0.191805\pi\)
\(68\) −1.64575 2.85052i −0.199577 0.345677i
\(69\) 1.64575 + 2.85052i 0.198125 + 0.343163i
\(70\) −1.00000 −0.119523
\(71\) −7.29150 + 12.6293i −0.865342 + 1.49882i 0.00136488 + 0.999999i \(0.499566\pi\)
−0.866707 + 0.498818i \(0.833768\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −2.29150 + 3.96900i −0.268200 + 0.464536i −0.968397 0.249414i \(-0.919762\pi\)
0.700197 + 0.713950i \(0.253096\pi\)
\(74\) 0.645751 + 1.11847i 0.0750671 + 0.130020i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 1.64575 + 2.85052i 0.188781 + 0.326978i
\(77\) −1.00000 −0.113961
\(78\) −2.00000 −0.226455
\(79\) 4.00000 + 6.92820i 0.450035 + 0.779484i 0.998388 0.0567635i \(-0.0180781\pi\)
−0.548352 + 0.836247i \(0.684745\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.64575 4.58258i 0.292174 0.506061i
\(83\) −4.14575 + 7.18065i −0.455055 + 0.788179i −0.998691 0.0511421i \(-0.983714\pi\)
0.543636 + 0.839321i \(0.317047\pi\)
\(84\) −0.500000 + 0.866025i −0.0545545 + 0.0944911i
\(85\) 3.29150 0.357014
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 3.14575 + 5.44860i 0.337260 + 0.584151i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) 2.00000 0.209657
\(92\) −3.29150 −0.343163
\(93\) 4.14575 3.71655i 0.429894 0.385388i
\(94\) 11.2915 1.16463
\(95\) −3.29150 −0.337701
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) −10.2915 −1.04494 −0.522472 0.852657i \(-0.674990\pi\)
−0.522472 + 0.852657i \(0.674990\pi\)
\(98\) −3.00000 + 5.19615i −0.303046 + 0.524891i
\(99\) 0.500000 + 0.866025i 0.0502519 + 0.0870388i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 1.70850 0.170002 0.0850009 0.996381i \(-0.472911\pi\)
0.0850009 + 0.996381i \(0.472911\pi\)
\(102\) 1.64575 2.85052i 0.162954 0.282244i
\(103\) −1.79150 + 3.10297i −0.176522 + 0.305745i −0.940687 0.339276i \(-0.889818\pi\)
0.764165 + 0.645021i \(0.223151\pi\)
\(104\) 1.00000 1.73205i 0.0980581 0.169842i
\(105\) −0.500000 0.866025i −0.0487950 0.0845154i
\(106\) 1.50000 2.59808i 0.145693 0.252347i
\(107\) −0.145751 0.252449i −0.0140903 0.0244051i 0.858894 0.512153i \(-0.171152\pi\)
−0.872985 + 0.487748i \(0.837819\pi\)
\(108\) 1.00000 0.0962250
\(109\) −4.70850 −0.450992 −0.225496 0.974244i \(-0.572400\pi\)
−0.225496 + 0.974244i \(0.572400\pi\)
\(110\) −0.500000 0.866025i −0.0476731 0.0825723i
\(111\) −0.645751 + 1.11847i −0.0612920 + 0.106161i
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) −4.29150 + 7.43310i −0.403711 + 0.699247i −0.994170 0.107820i \(-0.965613\pi\)
0.590460 + 0.807067i \(0.298946\pi\)
\(114\) −1.64575 + 2.85052i −0.154139 + 0.266976i
\(115\) 1.64575 2.85052i 0.153467 0.265813i
\(116\) −6.29150 −0.584151
\(117\) −1.00000 1.73205i −0.0924500 0.160128i
\(118\) −3.50000 6.06218i −0.322201 0.558069i
\(119\) −1.64575 + 2.85052i −0.150866 + 0.261307i
\(120\) −1.00000 −0.0912871
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 3.29150 0.297999
\(123\) 5.29150 0.477119
\(124\) 1.14575 + 5.44860i 0.102892 + 0.489299i
\(125\) 1.00000 0.0894427
\(126\) −1.00000 −0.0890871
\(127\) −4.79150 8.29913i −0.425177 0.736428i 0.571260 0.820769i \(-0.306455\pi\)
−0.996437 + 0.0843409i \(0.973122\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 1.00000 + 1.73205i 0.0877058 + 0.151911i
\(131\) 4.00000 + 6.92820i 0.349482 + 0.605320i 0.986157 0.165812i \(-0.0530244\pi\)
−0.636676 + 0.771132i \(0.719691\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 1.64575 2.85052i 0.142705 0.247172i
\(134\) 0.645751 1.11847i 0.0557844 0.0966214i
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 1.64575 + 2.85052i 0.141122 + 0.244430i
\(137\) 7.93725 13.7477i 0.678125 1.17455i −0.297419 0.954747i \(-0.596126\pi\)
0.975545 0.219801i \(-0.0705407\pi\)
\(138\) −1.64575 2.85052i −0.140096 0.242653i
\(139\) −9.29150 −0.788095 −0.394047 0.919090i \(-0.628925\pi\)
−0.394047 + 0.919090i \(0.628925\pi\)
\(140\) 1.00000 0.0845154
\(141\) 5.64575 + 9.77873i 0.475458 + 0.823517i
\(142\) 7.29150 12.6293i 0.611889 1.05982i
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 3.14575 5.44860i 0.261240 0.452482i
\(146\) 2.29150 3.96900i 0.189646 0.328477i
\(147\) −6.00000 −0.494872
\(148\) −0.645751 1.11847i −0.0530804 0.0919380i
\(149\) −5.14575 8.91270i −0.421556 0.730157i 0.574536 0.818480i \(-0.305183\pi\)
−0.996092 + 0.0883226i \(0.971849\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −8.29150 −0.674753 −0.337376 0.941370i \(-0.609540\pi\)
−0.337376 + 0.941370i \(0.609540\pi\)
\(152\) −1.64575 2.85052i −0.133488 0.231208i
\(153\) 3.29150 0.266102
\(154\) 1.00000 0.0805823
\(155\) −5.29150 1.73205i −0.425024 0.139122i
\(156\) 2.00000 0.160128
\(157\) −8.70850 −0.695014 −0.347507 0.937677i \(-0.612972\pi\)
−0.347507 + 0.937677i \(0.612972\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) 3.00000 0.237915
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 1.64575 + 2.85052i 0.129703 + 0.224653i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) 9.87451 0.773431 0.386716 0.922199i \(-0.373610\pi\)
0.386716 + 0.922199i \(0.373610\pi\)
\(164\) −2.64575 + 4.58258i −0.206598 + 0.357839i
\(165\) 0.500000 0.866025i 0.0389249 0.0674200i
\(166\) 4.14575 7.18065i 0.321773 0.557327i
\(167\) −8.64575 14.9749i −0.669028 1.15879i −0.978176 0.207777i \(-0.933377\pi\)
0.309148 0.951014i \(-0.399956\pi\)
\(168\) 0.500000 0.866025i 0.0385758 0.0668153i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) −3.29150 −0.252447
\(171\) −3.29150 −0.251707
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) 5.50000 9.52628i 0.418157 0.724270i −0.577597 0.816322i \(-0.696009\pi\)
0.995754 + 0.0920525i \(0.0293428\pi\)
\(174\) −3.14575 5.44860i −0.238479 0.413057i
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) 0.500000 0.866025i 0.0376889 0.0652791i
\(177\) 3.50000 6.06218i 0.263076 0.455661i
\(178\) 0 0
\(179\) −0.500000 0.866025i −0.0373718 0.0647298i 0.846735 0.532016i \(-0.178565\pi\)
−0.884106 + 0.467286i \(0.845232\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 7.29150 12.6293i 0.541973 0.938725i −0.456818 0.889560i \(-0.651011\pi\)
0.998791 0.0491646i \(-0.0156559\pi\)
\(182\) −2.00000 −0.148250
\(183\) 1.64575 + 2.85052i 0.121657 + 0.210717i
\(184\) 3.29150 0.242653
\(185\) 1.29150 0.0949532
\(186\) −4.14575 + 3.71655i −0.303981 + 0.272511i
\(187\) −3.29150 −0.240699
\(188\) −11.2915 −0.823517
\(189\) −0.500000 0.866025i −0.0363696 0.0629941i
\(190\) 3.29150 0.238791
\(191\) 7.93725 13.7477i 0.574320 0.994751i −0.421796 0.906691i \(-0.638600\pi\)
0.996115 0.0880597i \(-0.0280666\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −1.14575 1.98450i −0.0824730 0.142847i 0.821839 0.569720i \(-0.192948\pi\)
−0.904312 + 0.426873i \(0.859615\pi\)
\(194\) 10.2915 0.738887
\(195\) −1.00000 + 1.73205i −0.0716115 + 0.124035i
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) 9.58301 16.5983i 0.682761 1.18258i −0.291374 0.956609i \(-0.594112\pi\)
0.974135 0.225967i \(-0.0725542\pi\)
\(198\) −0.500000 0.866025i −0.0355335 0.0615457i
\(199\) 4.85425 8.40781i 0.344109 0.596014i −0.641083 0.767472i \(-0.721515\pi\)
0.985191 + 0.171458i \(0.0548478\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 1.29150 0.0910956
\(202\) −1.70850 −0.120209
\(203\) 3.14575 + 5.44860i 0.220788 + 0.382417i
\(204\) −1.64575 + 2.85052i −0.115226 + 0.199577i
\(205\) −2.64575 4.58258i −0.184787 0.320061i
\(206\) 1.79150 3.10297i 0.124820 0.216194i
\(207\) 1.64575 2.85052i 0.114388 0.198125i
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 3.29150 0.227678
\(210\) 0.500000 + 0.866025i 0.0345033 + 0.0597614i
\(211\) −2.35425 4.07768i −0.162073 0.280719i 0.773539 0.633749i \(-0.218485\pi\)
−0.935612 + 0.353030i \(0.885151\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 14.5830 0.999211
\(214\) 0.145751 + 0.252449i 0.00996335 + 0.0172570i
\(215\) −4.00000 −0.272798
\(216\) −1.00000 −0.0680414
\(217\) 4.14575 3.71655i 0.281432 0.252296i
\(218\) 4.70850 0.318900
\(219\) 4.58301 0.309691
\(220\) 0.500000 + 0.866025i 0.0337100 + 0.0583874i
\(221\) 6.58301 0.442821
\(222\) 0.645751 1.11847i 0.0433400 0.0750671i
\(223\) 12.7915 + 22.1555i 0.856582 + 1.48364i 0.875169 + 0.483817i \(0.160750\pi\)
−0.0185869 + 0.999827i \(0.505917\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 1.00000 0.0666667
\(226\) 4.29150 7.43310i 0.285467 0.494442i
\(227\) 4.43725 7.68555i 0.294511 0.510108i −0.680360 0.732878i \(-0.738177\pi\)
0.974871 + 0.222770i \(0.0715099\pi\)
\(228\) 1.64575 2.85052i 0.108993 0.188781i
\(229\) −3.93725 6.81952i −0.260181 0.450647i 0.706109 0.708103i \(-0.250449\pi\)
−0.966290 + 0.257457i \(0.917116\pi\)
\(230\) −1.64575 + 2.85052i −0.108518 + 0.187958i
\(231\) 0.500000 + 0.866025i 0.0328976 + 0.0569803i
\(232\) 6.29150 0.413057
\(233\) 11.8745 0.777925 0.388962 0.921254i \(-0.372834\pi\)
0.388962 + 0.921254i \(0.372834\pi\)
\(234\) 1.00000 + 1.73205i 0.0653720 + 0.113228i
\(235\) 5.64575 9.77873i 0.368288 0.637894i
\(236\) 3.50000 + 6.06218i 0.227831 + 0.394614i
\(237\) 4.00000 6.92820i 0.259828 0.450035i
\(238\) 1.64575 2.85052i 0.106678 0.184772i
\(239\) −8.29150 + 14.3613i −0.536333 + 0.928956i 0.462765 + 0.886481i \(0.346857\pi\)
−0.999098 + 0.0424744i \(0.986476\pi\)
\(240\) 1.00000 0.0645497
\(241\) −2.20850 3.82523i −0.142262 0.246405i 0.786086 0.618117i \(-0.212104\pi\)
−0.928348 + 0.371712i \(0.878771\pi\)
\(242\) −5.00000 8.66025i −0.321412 0.556702i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −3.29150 −0.210717
\(245\) 3.00000 + 5.19615i 0.191663 + 0.331970i
\(246\) −5.29150 −0.337374
\(247\) −6.58301 −0.418867
\(248\) −1.14575 5.44860i −0.0727553 0.345987i
\(249\) 8.29150 0.525453
\(250\) −1.00000 −0.0632456
\(251\) −10.0000 17.3205i −0.631194 1.09326i −0.987308 0.158818i \(-0.949232\pi\)
0.356113 0.934443i \(-0.384102\pi\)
\(252\) 1.00000 0.0629941
\(253\) −1.64575 + 2.85052i −0.103467 + 0.179211i
\(254\) 4.79150 + 8.29913i 0.300646 + 0.520733i
\(255\) −1.64575 2.85052i −0.103061 0.178507i
\(256\) 1.00000 0.0625000
\(257\) 4.93725 8.55157i 0.307977 0.533433i −0.669942 0.742413i \(-0.733681\pi\)
0.977920 + 0.208981i \(0.0670145\pi\)
\(258\) −2.00000 + 3.46410i −0.124515 + 0.215666i
\(259\) −0.645751 + 1.11847i −0.0401250 + 0.0694986i
\(260\) −1.00000 1.73205i −0.0620174 0.107417i
\(261\) 3.14575 5.44860i 0.194717 0.337260i
\(262\) −4.00000 6.92820i −0.247121 0.428026i
\(263\) −8.58301 −0.529251 −0.264625 0.964351i \(-0.585248\pi\)
−0.264625 + 0.964351i \(0.585248\pi\)
\(264\) 1.00000 0.0615457
\(265\) −1.50000 2.59808i −0.0921443 0.159599i
\(266\) −1.64575 + 2.85052i −0.100907 + 0.174777i
\(267\) 0 0
\(268\) −0.645751 + 1.11847i −0.0394455 + 0.0683217i
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) −5.70850 −0.346767 −0.173383 0.984854i \(-0.555470\pi\)
−0.173383 + 0.984854i \(0.555470\pi\)
\(272\) −1.64575 2.85052i −0.0997883 0.172838i
\(273\) −1.00000 1.73205i −0.0605228 0.104828i
\(274\) −7.93725 + 13.7477i −0.479507 + 0.830531i
\(275\) −1.00000 −0.0603023
\(276\) 1.64575 + 2.85052i 0.0990626 + 0.171581i
\(277\) 0.708497 0.0425695 0.0212847 0.999773i \(-0.493224\pi\)
0.0212847 + 0.999773i \(0.493224\pi\)
\(278\) 9.29150 0.557267
\(279\) −5.29150 1.73205i −0.316794 0.103695i
\(280\) −1.00000 −0.0597614
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) −5.64575 9.77873i −0.336200 0.582315i
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −7.29150 + 12.6293i −0.432671 + 0.749408i
\(285\) 1.64575 + 2.85052i 0.0974859 + 0.168851i
\(286\) −1.00000 1.73205i −0.0591312 0.102418i
\(287\) 5.29150 0.312348
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 3.08301 5.33992i 0.181353 0.314113i
\(290\) −3.14575 + 5.44860i −0.184725 + 0.319953i
\(291\) 5.14575 + 8.91270i 0.301649 + 0.522472i
\(292\) −2.29150 + 3.96900i −0.134100 + 0.232268i
\(293\) 11.7915 + 20.4235i 0.688867 + 1.19315i 0.972205 + 0.234132i \(0.0752249\pi\)
−0.283338 + 0.959020i \(0.591442\pi\)
\(294\) 6.00000 0.349927
\(295\) −7.00000 −0.407556
\(296\) 0.645751 + 1.11847i 0.0375335 + 0.0650100i
\(297\) 0.500000 0.866025i 0.0290129 0.0502519i
\(298\) 5.14575 + 8.91270i 0.298085 + 0.516299i
\(299\) 3.29150 5.70105i 0.190353 0.329700i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) 2.00000 3.46410i 0.115278 0.199667i
\(302\) 8.29150 0.477122
\(303\) −0.854249 1.47960i −0.0490753 0.0850009i
\(304\) 1.64575 + 2.85052i 0.0943903 + 0.163489i
\(305\) 1.64575 2.85052i 0.0942354 0.163221i
\(306\) −3.29150 −0.188163
\(307\) 9.35425 + 16.2020i 0.533875 + 0.924699i 0.999217 + 0.0395678i \(0.0125981\pi\)
−0.465342 + 0.885131i \(0.654069\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 3.58301 0.203830
\(310\) 5.29150 + 1.73205i 0.300537 + 0.0983739i
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) −2.00000 −0.113228
\(313\) −7.85425 13.6040i −0.443948 0.768941i 0.554030 0.832497i \(-0.313089\pi\)
−0.997978 + 0.0635556i \(0.979756\pi\)
\(314\) 8.70850 0.491449
\(315\) −0.500000 + 0.866025i −0.0281718 + 0.0487950i
\(316\) 4.00000 + 6.92820i 0.225018 + 0.389742i
\(317\) −4.20850 7.28933i −0.236373 0.409410i 0.723298 0.690536i \(-0.242625\pi\)
−0.959671 + 0.281126i \(0.909292\pi\)
\(318\) −3.00000 −0.168232
\(319\) −3.14575 + 5.44860i −0.176128 + 0.305063i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −0.145751 + 0.252449i −0.00813504 + 0.0140903i
\(322\) −1.64575 2.85052i −0.0917141 0.158854i
\(323\) 5.41699 9.38251i 0.301410 0.522057i
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 2.00000 0.110940
\(326\) −9.87451 −0.546898
\(327\) 2.35425 + 4.07768i 0.130190 + 0.225496i
\(328\) 2.64575 4.58258i 0.146087 0.253030i
\(329\) 5.64575 + 9.77873i 0.311260 + 0.539119i
\(330\) −0.500000 + 0.866025i −0.0275241 + 0.0476731i
\(331\) 4.93725 8.55157i 0.271376 0.470037i −0.697838 0.716255i \(-0.745855\pi\)
0.969214 + 0.246218i \(0.0791880\pi\)
\(332\) −4.14575 + 7.18065i −0.227528 + 0.394089i
\(333\) 1.29150 0.0707739
\(334\) 8.64575 + 14.9749i 0.473074 + 0.819389i
\(335\) −0.645751 1.11847i −0.0352812 0.0611088i
\(336\) −0.500000 + 0.866025i −0.0272772 + 0.0472456i
\(337\) −14.8745 −0.810266 −0.405133 0.914258i \(-0.632775\pi\)
−0.405133 + 0.914258i \(0.632775\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 8.58301 0.466165
\(340\) 3.29150 0.178507
\(341\) 5.29150 + 1.73205i 0.286551 + 0.0937958i
\(342\) 3.29150 0.177984
\(343\) −13.0000 −0.701934
\(344\) −2.00000 3.46410i −0.107833 0.186772i
\(345\) −3.29150 −0.177209
\(346\) −5.50000 + 9.52628i −0.295682 + 0.512136i
\(347\) −3.14575 5.44860i −0.168873 0.292496i 0.769151 0.639067i \(-0.220679\pi\)
−0.938024 + 0.346571i \(0.887346\pi\)
\(348\) 3.14575 + 5.44860i 0.168630 + 0.292076i
\(349\) −24.4575 −1.30918 −0.654590 0.755984i \(-0.727159\pi\)
−0.654590 + 0.755984i \(0.727159\pi\)
\(350\) 0.500000 0.866025i 0.0267261 0.0462910i
\(351\) −1.00000 + 1.73205i −0.0533761 + 0.0924500i
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 15.5830 + 26.9906i 0.829400 + 1.43656i 0.898510 + 0.438953i \(0.144651\pi\)
−0.0691102 + 0.997609i \(0.522016\pi\)
\(354\) −3.50000 + 6.06218i −0.186023 + 0.322201i
\(355\) −7.29150 12.6293i −0.386993 0.670291i
\(356\) 0 0
\(357\) 3.29150 0.174205
\(358\) 0.500000 + 0.866025i 0.0264258 + 0.0457709i
\(359\) 7.64575 13.2428i 0.403527 0.698930i −0.590622 0.806949i \(-0.701117\pi\)
0.994149 + 0.108019i \(0.0344507\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 4.08301 7.07197i 0.214895 0.372209i
\(362\) −7.29150 + 12.6293i −0.383233 + 0.663779i
\(363\) 5.00000 8.66025i 0.262432 0.454545i
\(364\) 2.00000 0.104828
\(365\) −2.29150 3.96900i −0.119943 0.207747i
\(366\) −1.64575 2.85052i −0.0860248 0.148999i
\(367\) −16.5830 + 28.7226i −0.865626 + 1.49931i 0.000798600 1.00000i \(0.499746\pi\)
−0.866424 + 0.499308i \(0.833588\pi\)
\(368\) −3.29150 −0.171581
\(369\) −2.64575 4.58258i −0.137732 0.238559i
\(370\) −1.29150 −0.0671420
\(371\) 3.00000 0.155752
\(372\) 4.14575 3.71655i 0.214947 0.192694i
\(373\) −27.2915 −1.41310 −0.706550 0.707663i \(-0.749750\pi\)
−0.706550 + 0.707663i \(0.749750\pi\)
\(374\) 3.29150 0.170200
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 11.2915 0.582315
\(377\) 6.29150 10.8972i 0.324029 0.561234i
\(378\) 0.500000 + 0.866025i 0.0257172 + 0.0445435i
\(379\) −6.70850 11.6195i −0.344592 0.596851i 0.640687 0.767802i \(-0.278650\pi\)
−0.985280 + 0.170950i \(0.945316\pi\)
\(380\) −3.29150 −0.168851
\(381\) −4.79150 + 8.29913i −0.245476 + 0.425177i
\(382\) −7.93725 + 13.7477i −0.406105 + 0.703395i
\(383\) −16.6458 + 28.8313i −0.850558 + 1.47321i 0.0301472 + 0.999545i \(0.490402\pi\)
−0.880705 + 0.473664i \(0.842931\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0.500000 0.866025i 0.0254824 0.0441367i
\(386\) 1.14575 + 1.98450i 0.0583172 + 0.101008i
\(387\) −4.00000 −0.203331
\(388\) −10.2915 −0.522472
\(389\) −1.00000 1.73205i −0.0507020 0.0878185i 0.839561 0.543266i \(-0.182813\pi\)
−0.890263 + 0.455448i \(0.849479\pi\)
\(390\) 1.00000 1.73205i 0.0506370 0.0877058i
\(391\) 5.41699 + 9.38251i 0.273949 + 0.474494i
\(392\) −3.00000 + 5.19615i −0.151523 + 0.262445i
\(393\) 4.00000 6.92820i 0.201773 0.349482i
\(394\) −9.58301 + 16.5983i −0.482785 + 0.836208i
\(395\) −8.00000 −0.402524
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) −6.58301 11.4021i −0.330392 0.572255i 0.652197 0.758049i \(-0.273847\pi\)
−0.982589 + 0.185794i \(0.940514\pi\)
\(398\) −4.85425 + 8.40781i −0.243322 + 0.421445i
\(399\) −3.29150 −0.164781
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −7.16601 −0.357853 −0.178927 0.983862i \(-0.557263\pi\)
−0.178927 + 0.983862i \(0.557263\pi\)
\(402\) −1.29150 −0.0644143
\(403\) −10.5830 3.46410i −0.527177 0.172559i
\(404\) 1.70850 0.0850009
\(405\) 1.00000 0.0496904
\(406\) −3.14575 5.44860i −0.156121 0.270410i
\(407\) −1.29150 −0.0640174
\(408\) 1.64575 2.85052i 0.0814768 0.141122i
\(409\) 4.50000 + 7.79423i 0.222511 + 0.385400i 0.955570 0.294765i \(-0.0952414\pi\)
−0.733059 + 0.680165i \(0.761908\pi\)
\(410\) 2.64575 + 4.58258i 0.130664 + 0.226317i
\(411\) −15.8745 −0.783032
\(412\) −1.79150 + 3.10297i −0.0882610 + 0.152873i
\(413\) 3.50000 6.06218i 0.172224 0.298300i
\(414\) −1.64575 + 2.85052i −0.0808843 + 0.140096i
\(415\) −4.14575 7.18065i −0.203507 0.352484i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) 4.64575 + 8.04668i 0.227503 + 0.394047i
\(418\) −3.29150 −0.160993
\(419\) −15.5830 −0.761280 −0.380640 0.924723i \(-0.624296\pi\)
−0.380640 + 0.924723i \(0.624296\pi\)
\(420\) −0.500000 0.866025i −0.0243975 0.0422577i
\(421\) 10.3542 17.9341i 0.504635 0.874054i −0.495350 0.868693i \(-0.664960\pi\)
0.999986 0.00536057i \(-0.00170633\pi\)
\(422\) 2.35425 + 4.07768i 0.114603 + 0.198498i
\(423\) 5.64575 9.77873i 0.274506 0.475458i
\(424\) 1.50000 2.59808i 0.0728464 0.126174i
\(425\) −1.64575 + 2.85052i −0.0798307 + 0.138271i
\(426\) −14.5830 −0.706549
\(427\) 1.64575 + 2.85052i 0.0796435 + 0.137947i
\(428\) −0.145751 0.252449i −0.00704516 0.0122026i
\(429\) 1.00000 1.73205i 0.0482805 0.0836242i
\(430\) 4.00000 0.192897
\(431\) −0.645751 1.11847i −0.0311047 0.0538750i 0.850054 0.526696i \(-0.176569\pi\)
−0.881159 + 0.472821i \(0.843236\pi\)
\(432\) 1.00000 0.0481125
\(433\) 22.0000 1.05725 0.528626 0.848855i \(-0.322707\pi\)
0.528626 + 0.848855i \(0.322707\pi\)
\(434\) −4.14575 + 3.71655i −0.199002 + 0.178400i
\(435\) −6.29150 −0.301654
\(436\) −4.70850 −0.225496
\(437\) −5.41699 9.38251i −0.259130 0.448826i
\(438\) −4.58301 −0.218984
\(439\) −3.14575 + 5.44860i −0.150139 + 0.260048i −0.931278 0.364309i \(-0.881305\pi\)
0.781140 + 0.624356i \(0.214639\pi\)
\(440\) −0.500000 0.866025i −0.0238366 0.0412861i
\(441\) 3.00000 + 5.19615i 0.142857 + 0.247436i
\(442\) −6.58301 −0.313122
\(443\) −15.2915 + 26.4857i −0.726521 + 1.25837i 0.231824 + 0.972758i \(0.425531\pi\)
−0.958345 + 0.285614i \(0.907803\pi\)
\(444\) −0.645751 + 1.11847i −0.0306460 + 0.0530804i
\(445\) 0 0
\(446\) −12.7915 22.1555i −0.605695 1.04909i
\(447\) −5.14575 + 8.91270i −0.243386 + 0.421556i
\(448\) −0.500000 0.866025i −0.0236228 0.0409159i
\(449\) −5.41699 −0.255644 −0.127822 0.991797i \(-0.540799\pi\)
−0.127822 + 0.991797i \(0.540799\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 2.64575 + 4.58258i 0.124584 + 0.215785i
\(452\) −4.29150 + 7.43310i −0.201855 + 0.349624i
\(453\) 4.14575 + 7.18065i 0.194784 + 0.337376i
\(454\) −4.43725 + 7.68555i −0.208251 + 0.360701i
\(455\) −1.00000 + 1.73205i −0.0468807 + 0.0811998i
\(456\) −1.64575 + 2.85052i −0.0770694 + 0.133488i
\(457\) −35.1660 −1.64500 −0.822498 0.568768i \(-0.807420\pi\)
−0.822498 + 0.568768i \(0.807420\pi\)
\(458\) 3.93725 + 6.81952i 0.183976 + 0.318655i
\(459\) −1.64575 2.85052i −0.0768171 0.133051i
\(460\) 1.64575 2.85052i 0.0767336 0.132906i
\(461\) 6.29150 0.293024 0.146512 0.989209i \(-0.453195\pi\)
0.146512 + 0.989209i \(0.453195\pi\)
\(462\) −0.500000 0.866025i −0.0232621 0.0402911i
\(463\) 15.0000 0.697109 0.348555 0.937288i \(-0.386673\pi\)
0.348555 + 0.937288i \(0.386673\pi\)
\(464\) −6.29150 −0.292076
\(465\) 1.14575 + 5.44860i 0.0531329 + 0.252673i
\(466\) −11.8745 −0.550076
\(467\) 4.29150 0.198587 0.0992935 0.995058i \(-0.468342\pi\)
0.0992935 + 0.995058i \(0.468342\pi\)
\(468\) −1.00000 1.73205i −0.0462250 0.0800641i
\(469\) 1.29150 0.0596361
\(470\) −5.64575 + 9.77873i −0.260419 + 0.451059i
\(471\) 4.35425 + 7.54178i 0.200633 + 0.347507i
\(472\) −3.50000 6.06218i −0.161101 0.279034i
\(473\) 4.00000 0.183920
\(474\) −4.00000 + 6.92820i −0.183726 + 0.318223i
\(475\) 1.64575 2.85052i 0.0755122 0.130791i
\(476\) −1.64575 + 2.85052i −0.0754329 + 0.130654i
\(477\) −1.50000 2.59808i −0.0686803 0.118958i
\(478\) 8.29150 14.3613i 0.379245 0.656871i
\(479\) 17.6458 + 30.5633i 0.806255 + 1.39647i 0.915441 + 0.402453i \(0.131842\pi\)
−0.109186 + 0.994021i \(0.534824\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 2.58301 0.117775
\(482\) 2.20850 + 3.82523i 0.100594 + 0.174234i
\(483\) 1.64575 2.85052i 0.0748843 0.129703i
\(484\) 5.00000 + 8.66025i 0.227273 + 0.393648i
\(485\) 5.14575 8.91270i 0.233657 0.404705i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −13.0830 + 22.6604i −0.592848 + 1.02684i 0.400999 + 0.916078i \(0.368663\pi\)
−0.993847 + 0.110764i \(0.964670\pi\)
\(488\) 3.29150 0.148999
\(489\) −4.93725 8.55157i −0.223270 0.386716i
\(490\) −3.00000 5.19615i −0.135526 0.234738i
\(491\) −16.7915 + 29.0837i −0.757790 + 1.31253i 0.186185 + 0.982515i \(0.440387\pi\)
−0.943975 + 0.330016i \(0.892946\pi\)
\(492\) 5.29150 0.238559
\(493\) 10.3542 + 17.9341i 0.466332 + 0.807711i
\(494\) 6.58301 0.296183
\(495\) −1.00000 −0.0449467
\(496\) 1.14575 + 5.44860i 0.0514458 + 0.244649i
\(497\) 14.5830 0.654137
\(498\) −8.29150 −0.371551
\(499\) −0.645751 1.11847i −0.0289078 0.0500698i 0.851210 0.524826i \(-0.175870\pi\)
−0.880117 + 0.474756i \(0.842536\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.64575 + 14.9749i −0.386264 + 0.669028i
\(502\) 10.0000 + 17.3205i 0.446322 + 0.773052i
\(503\) 5.35425 + 9.27383i 0.238734 + 0.413500i 0.960351 0.278793i \(-0.0899342\pi\)
−0.721617 + 0.692292i \(0.756601\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −0.854249 + 1.47960i −0.0380136 + 0.0658414i
\(506\) 1.64575 2.85052i 0.0731626 0.126721i
\(507\) 4.50000 7.79423i 0.199852 0.346154i
\(508\) −4.79150 8.29913i −0.212589 0.368214i
\(509\) 13.8542 23.9963i 0.614079 1.06362i −0.376467 0.926430i \(-0.622861\pi\)
0.990545 0.137185i \(-0.0438056\pi\)
\(510\) 1.64575 + 2.85052i 0.0728751 + 0.126223i
\(511\) 4.58301 0.202740
\(512\) −1.00000 −0.0441942
\(513\) 1.64575 + 2.85052i 0.0726617 + 0.125854i
\(514\) −4.93725 + 8.55157i −0.217773 + 0.377194i
\(515\) −1.79150 3.10297i −0.0789430 0.136733i
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) −5.64575 + 9.77873i −0.248300 + 0.430068i
\(518\) 0.645751 1.11847i 0.0283727 0.0491429i
\(519\) −11.0000 −0.482846
\(520\) 1.00000 + 1.73205i 0.0438529 + 0.0759555i
\(521\) 12.8745 + 22.2993i 0.564042 + 0.976950i 0.997138 + 0.0756022i \(0.0240879\pi\)
−0.433096 + 0.901348i \(0.642579\pi\)
\(522\) −3.14575 + 5.44860i −0.137686 + 0.238479i
\(523\) 5.16601 0.225894 0.112947 0.993601i \(-0.463971\pi\)
0.112947 + 0.993601i \(0.463971\pi\)
\(524\) 4.00000 + 6.92820i 0.174741 + 0.302660i
\(525\) 1.00000 0.0436436
\(526\) 8.58301 0.374237
\(527\) 13.6458 12.2330i 0.594418 0.532879i
\(528\) −1.00000 −0.0435194
\(529\) −12.1660 −0.528957
\(530\) 1.50000 + 2.59808i 0.0651558 + 0.112853i
\(531\) −7.00000 −0.303774
\(532\) 1.64575 2.85052i 0.0713524 0.123586i
\(533\) −5.29150 9.16515i −0.229200 0.396987i
\(534\) 0 0
\(535\) 0.291503 0.0126028
\(536\) 0.645751 1.11847i 0.0278922 0.0483107i
\(537\) −0.500000 + 0.866025i −0.0215766 + 0.0373718i
\(538\) −3.00000 + 5.19615i −0.129339 + 0.224022i
\(539\) −3.00000 5.19615i −0.129219 0.223814i
\(540\) −0.500000 + 0.866025i −0.0215166 + 0.0372678i
\(541\) −13.6458 23.6351i −0.586677 1.01615i −0.994664 0.103166i \(-0.967103\pi\)
0.407987 0.912988i \(-0.366231\pi\)
\(542\) 5.70850 0.245201
\(543\) −14.5830 −0.625817
\(544\) 1.64575 + 2.85052i 0.0705610 + 0.122215i
\(545\) 2.35425 4.07768i 0.100845 0.174669i
\(546\) 1.00000 + 1.73205i 0.0427960 + 0.0741249i
\(547\) −6.58301 + 11.4021i −0.281469 + 0.487519i −0.971747 0.236026i \(-0.924155\pi\)
0.690278 + 0.723544i \(0.257488\pi\)
\(548\) 7.93725 13.7477i 0.339063 0.587274i
\(549\) 1.64575 2.85052i 0.0702390 0.121657i
\(550\) 1.00000 0.0426401
\(551\) −10.3542 17.9341i −0.441106 0.764018i
\(552\) −1.64575 2.85052i −0.0700478 0.121326i
\(553\) 4.00000 6.92820i 0.170097 0.294617i
\(554\) −0.708497 −0.0301012
\(555\) −0.645751 1.11847i −0.0274106 0.0474766i
\(556\) −9.29150 −0.394047
\(557\) 40.7490 1.72659 0.863296 0.504699i \(-0.168396\pi\)
0.863296 + 0.504699i \(0.168396\pi\)
\(558\) 5.29150 + 1.73205i 0.224007 + 0.0733236i
\(559\) −8.00000 −0.338364
\(560\) 1.00000 0.0422577
\(561\) 1.64575 + 2.85052i 0.0694837 + 0.120349i
\(562\) 12.0000 0.506189
\(563\) 5.56275 9.63496i 0.234442 0.406065i −0.724669 0.689098i \(-0.758007\pi\)
0.959110 + 0.283033i \(0.0913404\pi\)
\(564\) 5.64575 + 9.77873i 0.237729 + 0.411759i
\(565\) −4.29150 7.43310i −0.180545 0.312713i
\(566\) −14.0000 −0.588464
\(567\) −0.500000 + 0.866025i −0.0209980 + 0.0363696i
\(568\) 7.29150 12.6293i 0.305945 0.529912i
\(569\) 12.2915 21.2895i 0.515287 0.892503i −0.484556 0.874760i \(-0.661019\pi\)
0.999843 0.0177423i \(-0.00564785\pi\)
\(570\) −1.64575 2.85052i −0.0689329 0.119395i
\(571\) 19.2915 33.4139i 0.807324 1.39833i −0.107386 0.994217i \(-0.534248\pi\)
0.914711 0.404109i \(-0.132418\pi\)
\(572\) 1.00000 + 1.73205i 0.0418121 + 0.0724207i
\(573\) −15.8745 −0.663167
\(574\) −5.29150 −0.220863
\(575\) 1.64575 + 2.85052i 0.0686326 + 0.118875i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 12.8745 + 22.2993i 0.535973 + 0.928332i 0.999116 + 0.0420484i \(0.0133884\pi\)
−0.463143 + 0.886284i \(0.653278\pi\)
\(578\) −3.08301 + 5.33992i −0.128236 + 0.222111i
\(579\) −1.14575 + 1.98450i −0.0476158 + 0.0824730i
\(580\) 3.14575 5.44860i 0.130620 0.226241i
\(581\) 8.29150 0.343989
\(582\) −5.14575 8.91270i −0.213298 0.369443i
\(583\) 1.50000 + 2.59808i 0.0621237 + 0.107601i
\(584\) 2.29150 3.96900i 0.0948231 0.164238i
\(585\) 2.00000 0.0826898
\(586\) −11.7915 20.4235i −0.487102 0.843686i
\(587\) 43.4575 1.79368 0.896842 0.442352i \(-0.145856\pi\)
0.896842 + 0.442352i \(0.145856\pi\)
\(588\) −6.00000 −0.247436
\(589\) −13.6458 + 12.2330i −0.562263 + 0.504053i
\(590\) 7.00000 0.288185
\(591\) −19.1660 −0.788384
\(592\) −0.645751 1.11847i −0.0265402 0.0459690i
\(593\) −1.29150 −0.0530357 −0.0265178 0.999648i \(-0.508442\pi\)
−0.0265178 + 0.999648i \(0.508442\pi\)
\(594\) −0.500000 + 0.866025i −0.0205152 + 0.0355335i
\(595\) −1.64575 2.85052i −0.0674692 0.116860i
\(596\) −5.14575 8.91270i −0.210778 0.365079i
\(597\) −9.70850 −0.397342
\(598\) −3.29150 + 5.70105i −0.134600 + 0.233133i
\(599\) −15.8745 + 27.4955i −0.648615 + 1.12343i 0.334839 + 0.942275i \(0.391318\pi\)
−0.983454 + 0.181158i \(0.942015\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) 8.29150 + 14.3613i 0.338217 + 0.585810i 0.984098 0.177629i \(-0.0568427\pi\)
−0.645880 + 0.763439i \(0.723509\pi\)
\(602\) −2.00000 + 3.46410i −0.0815139 + 0.141186i
\(603\) −0.645751 1.11847i −0.0262970 0.0455478i
\(604\) −8.29150 −0.337376
\(605\) −10.0000 −0.406558
\(606\) 0.854249 + 1.47960i 0.0347015 + 0.0601047i
\(607\) −10.5830 + 18.3303i −0.429551 + 0.744004i −0.996833 0.0795193i \(-0.974661\pi\)
0.567282 + 0.823523i \(0.307995\pi\)
\(608\) −1.64575 2.85052i −0.0667440 0.115604i
\(609\) 3.14575 5.44860i 0.127472 0.220788i
\(610\) −1.64575 + 2.85052i −0.0666345 + 0.115414i
\(611\) 11.2915 19.5575i 0.456805 0.791210i
\(612\) 3.29150 0.133051
\(613\) −12.5830 21.7944i −0.508223 0.880268i −0.999955 0.00952103i \(-0.996969\pi\)
0.491732 0.870747i \(-0.336364\pi\)
\(614\) −9.35425 16.2020i −0.377507 0.653861i
\(615\) −2.64575 + 4.58258i −0.106687 + 0.184787i
\(616\) 1.00000 0.0402911
\(617\) 22.9373 + 39.7285i 0.923419 + 1.59941i 0.794084 + 0.607808i \(0.207951\pi\)
0.129335 + 0.991601i \(0.458716\pi\)
\(618\) −3.58301 −0.144130
\(619\) 16.0000 0.643094 0.321547 0.946894i \(-0.395797\pi\)
0.321547 + 0.946894i \(0.395797\pi\)
\(620\) −5.29150 1.73205i −0.212512 0.0695608i
\(621\) −3.29150 −0.132083
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 7.85425 + 13.6040i 0.313919 + 0.543724i
\(627\) −1.64575 2.85052i −0.0657250 0.113839i
\(628\) −8.70850 −0.347507
\(629\) −2.12549 + 3.68146i −0.0847489 + 0.146789i
\(630\) 0.500000 0.866025i 0.0199205 0.0345033i
\(631\) 11.4373 19.8099i 0.455310 0.788620i −0.543396 0.839476i \(-0.682862\pi\)
0.998706 + 0.0508566i \(0.0161951\pi\)
\(632\) −4.00000 6.92820i −0.159111 0.275589i
\(633\) −2.35425 + 4.07768i −0.0935730 + 0.162073i
\(634\) 4.20850 + 7.28933i 0.167141 + 0.289496i
\(635\) 9.58301 0.380290
\(636\) 3.00000 0.118958
\(637\) 6.00000 + 10.3923i 0.237729 + 0.411758i
\(638\) 3.14575 5.44860i 0.124541 0.215712i
\(639\) −7.29150 12.6293i −0.288447 0.499606i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −16.2288 + 28.1090i −0.640997 + 1.11024i 0.344213 + 0.938892i \(0.388146\pi\)
−0.985210 + 0.171348i \(0.945188\pi\)
\(642\) 0.145751 0.252449i 0.00575235 0.00996335i
\(643\) −24.7085 −0.974408 −0.487204 0.873288i \(-0.661983\pi\)
−0.487204 + 0.873288i \(0.661983\pi\)
\(644\) 1.64575 + 2.85052i 0.0648517 + 0.112326i
\(645\) 2.00000 + 3.46410i 0.0787499 + 0.136399i
\(646\) −5.41699 + 9.38251i −0.213129 + 0.369150i
\(647\) −8.70850 −0.342366 −0.171183 0.985239i \(-0.554759\pi\)
−0.171183 + 0.985239i \(0.554759\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 7.00000 0.274774
\(650\) −2.00000 −0.0784465
\(651\) −5.29150 1.73205i −0.207390 0.0678844i
\(652\) 9.87451 0.386716
\(653\) −15.0000 −0.586995 −0.293498 0.955960i \(-0.594819\pi\)
−0.293498 + 0.955960i \(0.594819\pi\)
\(654\) −2.35425 4.07768i −0.0920584 0.159450i
\(655\) −8.00000 −0.312586
\(656\) −2.64575 + 4.58258i −0.103299 + 0.178920i
\(657\) −2.29150 3.96900i −0.0894000 0.154845i
\(658\) −5.64575 9.77873i −0.220094 0.381215i
\(659\) 18.1660 0.707647 0.353824 0.935312i \(-0.384881\pi\)
0.353824 + 0.935312i \(0.384881\pi\)
\(660\) 0.500000 0.866025i 0.0194625 0.0337100i
\(661\) −5.64575 + 9.77873i −0.219594 + 0.380348i −0.954684 0.297621i \(-0.903807\pi\)
0.735090 + 0.677970i \(0.237140\pi\)
\(662\) −4.93725 + 8.55157i −0.191892 + 0.332366i
\(663\) −3.29150 5.70105i −0.127831 0.221410i
\(664\) 4.14575 7.18065i 0.160886 0.278663i
\(665\) 1.64575 + 2.85052i 0.0638195 + 0.110539i
\(666\) −1.29150 −0.0500447
\(667\) 20.7085 0.801836
\(668\) −8.64575 14.9749i −0.334514 0.579396i
\(669\) 12.7915 22.1555i 0.494548 0.856582i
\(670\) 0.645751 + 1.11847i 0.0249475 + 0.0432104i
\(671\) −1.64575 + 2.85052i −0.0635335 + 0.110043i
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) 5.43725 9.41760i 0.209591 0.363022i −0.741995 0.670406i \(-0.766120\pi\)
0.951586 + 0.307384i \(0.0994535\pi\)
\(674\) 14.8745 0.572945
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −4.50000 + 7.79423i −0.172949 + 0.299557i −0.939450 0.342687i \(-0.888663\pi\)
0.766501 + 0.642244i \(0.221996\pi\)
\(678\) −8.58301 −0.329628
\(679\) 5.14575 + 8.91270i 0.197476 + 0.342038i
\(680\) −3.29150 −0.126223
\(681\) −8.87451 −0.340072
\(682\) −5.29150 1.73205i −0.202622 0.0663237i
\(683\) 16.8745 0.645685 0.322843 0.946453i \(-0.395362\pi\)
0.322843 + 0.946453i \(0.395362\pi\)
\(684\) −3.29150 −0.125854
\(685\) 7.93725 + 13.7477i 0.303267 + 0.525274i
\(686\) 13.0000 0.496342
\(687\) −3.93725 + 6.81952i −0.150216 + 0.260181i
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 3.29150 0.125305
\(691\) −8.64575 + 14.9749i −0.328900 + 0.569671i −0.982294 0.187347i \(-0.940011\pi\)
0.653394 + 0.757018i \(0.273345\pi\)
\(692\) 5.50000 9.52628i 0.209079 0.362135i
\(693\) 0.500000 0.866025i 0.0189934 0.0328976i
\(694\) 3.14575 + 5.44860i 0.119411 + 0.206826i
\(695\) 4.64575 8.04668i 0.176223 0.305228i
\(696\) −3.14575 5.44860i −0.119239 0.206529i
\(697\) 17.4170 0.659716
\(698\) 24.4575 0.925731
\(699\) −5.93725 10.2836i −0.224568 0.388962i
\(700\) −0.500000 + 0.866025i −0.0188982 + 0.0327327i
\(701\) 19.1458 + 33.1614i 0.723125 + 1.25249i 0.959741 + 0.280886i \(0.0906283\pi\)
−0.236616 + 0.971603i \(0.576038\pi\)
\(702\) 1.00000 1.73205i 0.0377426 0.0653720i
\(703\) 2.12549 3.68146i 0.0801645 0.138849i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −11.2915 −0.425263
\(706\) −15.5830 26.9906i −0.586474 1.01580i
\(707\) −0.854249 1.47960i −0.0321273 0.0556462i
\(708\) 3.50000 6.06218i 0.131538 0.227831i
\(709\) 1.29150 0.0485034 0.0242517 0.999706i \(-0.492280\pi\)
0.0242517 + 0.999706i \(0.492280\pi\)
\(710\) 7.29150 + 12.6293i 0.273645 + 0.473967i
\(711\) −8.00000 −0.300023
\(712\) 0 0
\(713\) −3.77124 17.9341i −0.141234 0.671637i
\(714\) −3.29150 −0.123181
\(715\) −2.00000 −0.0747958
\(716\) −0.500000 0.866025i −0.0186859 0.0323649i
\(717\) 16.5830 0.619304
\(718\) −7.64575 + 13.2428i −0.285337 + 0.494218i
\(719\) −1.93725 3.35542i −0.0722474 0.125136i 0.827639 0.561261i \(-0.189684\pi\)
−0.899886 + 0.436125i \(0.856350\pi\)
\(720\) −0.500000 0.866025i −0.0186339 0.0322749i
\(721\) 3.58301 0.133438
\(722\) −4.08301 + 7.07197i −0.151954 + 0.263192i
\(723\) −2.20850 + 3.82523i −0.0821349 + 0.142262i
\(724\) 7.29150 12.6293i 0.270987 0.469362i
\(725\) 3.14575 + 5.44860i 0.116830 + 0.202356i
\(726\) −5.00000 + 8.66025i −0.185567 + 0.321412i
\(727\) 11.0830 + 19.1963i 0.411046 + 0.711952i 0.995004 0.0998311i \(-0.0318303\pi\)
−0.583958 + 0.811784i \(0.698497\pi\)
\(728\) −2.00000 −0.0741249
\(729\) 1.00000 0.0370370
\(730\) 2.29150 + 3.96900i 0.0848123 + 0.146899i
\(731\) 6.58301 11.4021i 0.243481 0.421722i
\(732\) 1.64575 + 2.85052i 0.0608287 + 0.105358i
\(733\) −1.70850 + 2.95920i −0.0631048 + 0.109301i −0.895852 0.444353i \(-0.853434\pi\)
0.832747 + 0.553654i \(0.186767\pi\)
\(734\) 16.5830 28.7226i 0.612090 1.06017i
\(735\) 3.00000 5.19615i 0.110657 0.191663i
\(736\) 3.29150 0.121326
\(737\) 0.645751 + 1.11847i 0.0237866 + 0.0411995i
\(738\) 2.64575 + 4.58258i 0.0973915 + 0.168687i
\(739\) 9.93725 17.2118i 0.365548 0.633147i −0.623316 0.781970i \(-0.714215\pi\)
0.988864 + 0.148823i \(0.0475483\pi\)
\(740\) 1.29150 0.0474766
\(741\) 3.29150 + 5.70105i 0.120916 + 0.209433i
\(742\) −3.00000 −0.110133
\(743\) −23.7490 −0.871267 −0.435633 0.900124i \(-0.643476\pi\)
−0.435633 + 0.900124i \(0.643476\pi\)
\(744\) −4.14575 + 3.71655i −0.151991 + 0.136255i
\(745\) 10.2915 0.377051
\(746\) 27.2915 0.999213
\(747\) −4.14575 7.18065i −0.151685 0.262726i
\(748\) −3.29150 −0.120349
\(749\) −0.145751 + 0.252449i −0.00532564 + 0.00922427i
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) −20.4373 35.3984i −0.745766 1.29170i −0.949836 0.312748i \(-0.898750\pi\)
0.204070 0.978956i \(-0.434583\pi\)
\(752\) −11.2915 −0.411759
\(753\) −10.0000 + 17.3205i −0.364420 + 0.631194i
\(754\) −6.29150 + 10.8972i −0.229123 + 0.396853i
\(755\) 4.14575 7.18065i 0.150879 0.261331i
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) 12.0000 20.7846i 0.436147 0.755429i −0.561241 0.827652i \(-0.689676\pi\)
0.997389 + 0.0722229i \(0.0230093\pi\)
\(758\) 6.70850 + 11.6195i 0.243664 + 0.422038i
\(759\) 3.29150 0.119474
\(760\) 3.29150 0.119395
\(761\) −9.93725 17.2118i −0.360225 0.623928i 0.627773 0.778397i \(-0.283967\pi\)
−0.987998 + 0.154469i \(0.950633\pi\)
\(762\) 4.79150 8.29913i 0.173578 0.300646i
\(763\) 2.35425 + 4.07768i 0.0852295 + 0.147622i
\(764\) 7.93725 13.7477i 0.287160 0.497375i
\(765\) −1.64575 + 2.85052i −0.0595023 + 0.103061i
\(766\) 16.6458 28.8313i 0.601435 1.04172i
\(767\) −14.0000 −0.505511
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −20.5000 35.5070i −0.739249 1.28042i −0.952834 0.303492i \(-0.901847\pi\)
0.213585 0.976924i \(-0.431486\pi\)
\(770\) −0.500000 + 0.866025i −0.0180187 + 0.0312094i
\(771\) −9.87451 −0.355622
\(772\) −1.14575 1.98450i −0.0412365 0.0714237i
\(773\) 16.5830 0.596449 0.298225 0.954496i \(-0.403606\pi\)
0.298225 + 0.954496i \(0.403606\pi\)
\(774\) 4.00000 0.143777
\(775\) 4.14575 3.71655i 0.148920 0.133502i
\(776\) 10.2915 0.369443
\(777\) 1.29150 0.0463324
\(778\) 1.00000 + 1.73205i 0.0358517 + 0.0620970i
\(779\) −17.4170 −0.624029
\(780\) −1.00000 + 1.73205i −0.0358057 + 0.0620174i
\(781\) 7.29150 + 12.6293i 0.260910 + 0.451910i
\(782\) −5.41699 9.38251i −0.193711 0.335518i
\(783\) −6.29150 −0.224840
\(784\) 3.00000 5.19615i 0.107143 0.185577i
\(785\) 4.35425 7.54178i 0.155410 0.269178i
\(786\) −4.00000 + 6.92820i −0.142675 + 0.247121i
\(787\) 16.2288 + 28.1090i 0.578493 + 1.00198i 0.995652 + 0.0931456i \(0.0296922\pi\)
−0.417160 + 0.908833i \(0.636974\pi\)
\(788\) 9.58301 16.5983i 0.341380 0.591288i
\(789\) 4.29150 + 7.43310i 0.152782 + 0.264625i
\(790\) 8.00000 0.284627
\(791\) 8.58301 0.305177
\(792\) −0.500000 0.866025i −0.0177667 0.0307729i
\(793\) 3.29150 5.70105i 0.116885 0.202450i
\(794\) 6.58301 + 11.4021i 0.233622 + 0.404645i
\(795\) −1.50000 + 2.59808i −0.0531995 + 0.0921443i
\(796\) 4.85425 8.40781i 0.172054 0.298007i
\(797\) 10.0830 17.4643i 0.357158 0.618616i −0.630327 0.776330i \(-0.717079\pi\)
0.987485 + 0.157714i \(0.0504123\pi\)
\(798\) 3.29150 0.116518
\(799\) 18.5830 + 32.1867i 0.657419 + 1.13868i
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) 0 0
\(802\) 7.16601 0.253041
\(803\) 2.29150 + 3.96900i 0.0808654 + 0.140063i
\(804\) 1.29150 0.0455478
\(805\) −3.29150 −0.116010
\(806\) 10.5830 + 3.46410i 0.372770 + 0.122018i
\(807\) −6.00000 −0.211210
\(808\) −1.70850 −0.0601047
\(809\) −20.2288 35.0372i −0.711205 1.23184i −0.964405 0.264430i \(-0.914816\pi\)
0.253200 0.967414i \(-0.418517\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 14.8745 25.7634i 0.522315 0.904675i −0.477348 0.878714i \(-0.658402\pi\)
0.999663 0.0259613i \(-0.00826467\pi\)
\(812\) 3.14575 + 5.44860i 0.110394 + 0.191208i
\(813\) 2.85425 + 4.94370i 0.100103 + 0.173383i
\(814\) 1.29150 0.0452671
\(815\) −4.93725 + 8.55157i −0.172944 + 0.299549i
\(816\) −1.64575 + 2.85052i −0.0576128 + 0.0997883i
\(817\) −6.58301 + 11.4021i −0.230310 + 0.398909i
\(818\) −4.50000 7.79423i −0.157339 0.272519i
\(819\) −1.00000 + 1.73205i −0.0349428 + 0.0605228i
\(820\) −2.64575 4.58258i −0.0923936 0.160030i
\(821\) 0.291503 0.0101735 0.00508676 0.999987i \(-0.498381\pi\)
0.00508676 + 0.999987i \(0.498381\pi\)
\(822\) 15.8745 0.553687
\(823\) −4.79150 8.29913i −0.167021 0.289289i 0.770350 0.637621i \(-0.220082\pi\)
−0.937371 + 0.348332i \(0.886748\pi\)
\(824\) 1.79150 3.10297i 0.0624100 0.108097i
\(825\) 0.500000 + 0.866025i 0.0174078 + 0.0301511i
\(826\) −3.50000 + 6.06218i −0.121781 + 0.210930i
\(827\) 1.29150 2.23695i 0.0449099 0.0777863i −0.842697 0.538389i \(-0.819033\pi\)
0.887607 + 0.460602i \(0.152367\pi\)
\(828\) 1.64575 2.85052i 0.0571938 0.0990626i
\(829\) −35.2915 −1.22572 −0.612862 0.790190i \(-0.709982\pi\)
−0.612862 + 0.790190i \(0.709982\pi\)
\(830\) 4.14575 + 7.18065i 0.143901 + 0.249244i
\(831\) −0.354249 0.613577i −0.0122888 0.0212847i
\(832\) −1.00000 + 1.73205i −0.0346688 + 0.0600481i
\(833\) −19.7490 −0.684263
\(834\) −4.64575 8.04668i −0.160869 0.278634i
\(835\) 17.2915 0.598397
\(836\) 3.29150 0.113839
\(837\) 1.14575 + 5.44860i 0.0396030 + 0.188331i
\(838\) 15.5830 0.538306
\(839\) 19.2915 0.666017 0.333008 0.942924i \(-0.391936\pi\)
0.333008 + 0.942924i \(0.391936\pi\)
\(840\) 0.500000 + 0.866025i 0.0172516 + 0.0298807i
\(841\) 10.5830 0.364931
\(842\) −10.3542 + 17.9341i −0.356831 + 0.618049i
\(843\) 6.00000 + 10.3923i 0.206651 + 0.357930i
\(844\) −2.35425 4.07768i −0.0810366 0.140359i
\(845\) −9.00000 −0.309609
\(846\) −5.64575 + 9.77873i −0.194105 + 0.336200i
\(847\) 5.00000 8.66025i 0.171802 0.297570i
\(848\) −1.50000 + 2.59808i −0.0515102 + 0.0892183i
\(849\) −7.00000 12.1244i −0.240239 0.416107i
\(850\) 1.64575 2.85052i 0.0564488 0.0977722i
\(851\) 2.12549 + 3.68146i 0.0728609 + 0.126199i
\(852\) 14.5830 0.499606
\(853\) −38.3320 −1.31246 −0.656232 0.754559i \(-0.727851\pi\)
−0.656232 + 0.754559i \(0.727851\pi\)
\(854\) −1.64575 2.85052i −0.0563165 0.0975430i
\(855\) 1.64575 2.85052i 0.0562835 0.0974859i
\(856\) 0.145751 + 0.252449i 0.00498168 + 0.00862852i
\(857\) 5.29150 9.16515i 0.180754 0.313076i −0.761383 0.648302i \(-0.775479\pi\)
0.942138 + 0.335226i \(0.108813\pi\)
\(858\) −1.00000 + 1.73205i −0.0341394 + 0.0591312i
\(859\) 27.8118 48.1714i 0.948925 1.64359i 0.201230 0.979544i \(-0.435506\pi\)
0.747695 0.664042i \(-0.231161\pi\)
\(860\) −4.00000 −0.136399
\(861\) −2.64575 4.58258i −0.0901670 0.156174i
\(862\) 0.645751 + 1.11847i 0.0219944 + 0.0380954i
\(863\) −5.41699 + 9.38251i −0.184397 + 0.319384i −0.943373 0.331734i \(-0.892366\pi\)
0.758976 + 0.651118i \(0.225700\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 5.50000 + 9.52628i 0.187006 + 0.323903i
\(866\) −22.0000 −0.747590
\(867\) −6.16601 −0.209409
\(868\) 4.14575 3.71655i 0.140716 0.126148i
\(869\) 8.00000 0.271381
\(870\) 6.29150 0.213302
\(871\) −1.29150 2.23695i −0.0437609 0.0757961i
\(872\) 4.70850 0.159450
\(873\) 5.14575 8.91270i 0.174157 0.301649i
\(874\) 5.41699 + 9.38251i 0.183233 + 0.317368i
\(875\) −0.500000 0.866025i −0.0169031 0.0292770i
\(876\) 4.58301 0.154845
\(877\) −4.35425 + 7.54178i −0.147033 + 0.254668i −0.930129 0.367232i \(-0.880306\pi\)
0.783097 + 0.621900i \(0.213639\pi\)
\(878\) 3.14575 5.44860i 0.106164 0.183881i
\(879\) 11.7915 20.4235i 0.397718 0.688867i
\(880\) 0.500000 + 0.866025i 0.0168550 + 0.0291937i
\(881\) 11.3542 19.6661i 0.382534 0.662569i −0.608889 0.793255i \(-0.708385\pi\)
0.991424 + 0.130686i \(0.0417180\pi\)
\(882\) −3.00000 5.19615i −0.101015 0.174964i
\(883\) 29.0405 0.977291 0.488646 0.872482i \(-0.337491\pi\)
0.488646 + 0.872482i \(0.337491\pi\)
\(884\) 6.58301 0.221410
\(885\) 3.50000 + 6.06218i 0.117651 + 0.203778i
\(886\) 15.2915 26.4857i 0.513728 0.889803i
\(887\) 11.2915 + 19.5575i 0.379132 + 0.656675i 0.990936 0.134334i \(-0.0428894\pi\)
−0.611805 + 0.791009i \(0.709556\pi\)
\(888\) 0.645751 1.11847i 0.0216700 0.0375335i
\(889\) −4.79150 + 8.29913i −0.160702 + 0.278344i
\(890\) 0 0
\(891\) −1.00000 −0.0335013
\(892\) 12.7915 + 22.1555i 0.428291 + 0.741822i
\(893\) −18.5830 32.1867i −0.621857 1.07709i
\(894\) 5.14575 8.91270i 0.172100 0.298085i
\(895\) 1.00000 0.0334263
\(896\) 0.500000 + 0.866025i 0.0167038 + 0.0289319i
\(897\) −6.58301 −0.219800
\(898\) 5.41699 0.180767
\(899\) −7.20850 34.2799i −0.240417 1.14330i
\(900\) 1.00000 0.0333333
\(901\) 9.87451 0.328968
\(902\) −2.64575 4.58258i −0.0880939 0.152583i
\(903\) −4.00000 −0.133112
\(904\) 4.29150 7.43310i 0.142733 0.247221i
\(905\) 7.29150 + 12.6293i 0.242378 + 0.419811i
\(906\) −4.14575 7.18065i −0.137733 0.238561i
\(907\) −19.4170 −0.644731 −0.322365 0.946615i \(-0.604478\pi\)
−0.322365 + 0.946615i \(0.604478\pi\)
\(908\) 4.43725 7.68555i 0.147255 0.255054i
\(909\) −0.854249 + 1.47960i −0.0283336 + 0.0490753i
\(910\) 1.00000 1.73205i 0.0331497 0.0574169i
\(911\) −21.2288 36.7693i −0.703340 1.21822i −0.967287 0.253684i \(-0.918358\pi\)
0.263947 0.964537i \(-0.414976\pi\)
\(912\) 1.64575 2.85052i 0.0544963 0.0943903i
\(913\) 4.14575 + 7.18065i 0.137204 + 0.237645i
\(914\) 35.1660 1.16319
\(915\) −3.29150 −0.108814
\(916\) −3.93725 6.81952i −0.130091 0.225323i
\(917\) 4.00000 6.92820i 0.132092 0.228789i
\(918\) 1.64575 + 2.85052i 0.0543179 + 0.0940813i
\(919\) −17.4373 + 30.2022i −0.575202 + 0.996279i 0.420818 + 0.907145i \(0.361743\pi\)
−0.996020 + 0.0891338i \(0.971590\pi\)
\(920\) −1.64575 + 2.85052i −0.0542588 + 0.0939790i
\(921\) 9.35425 16.2020i 0.308233 0.533875i
\(922\) −6.29150 −0.207200
\(923\) −14.5830 25.2585i −0.480005 0.831394i
\(924\) 0.500000 + 0.866025i 0.0164488 + 0.0284901i
\(925\) −0.645751 + 1.11847i −0.0212322 + 0.0367752i
\(926\) −15.0000 −0.492931
\(927\) −1.79150 3.10297i −0.0588407 0.101915i
\(928\) 6.29150 0.206529
\(929\) −4.45751 −0.146246 −0.0731231 0.997323i \(-0.523297\pi\)
−0.0731231 + 0.997323i \(0.523297\pi\)
\(930\) −1.14575 5.44860i −0.0375707 0.178667i
\(931\) 19.7490 0.647248
\(932\) 11.8745 0.388962
\(933\) −9.00000 15.5885i −0.294647 0.510343i
\(934\) −4.29150 −0.140422
\(935\) 1.64575 2.85052i 0.0538218 0.0932221i
\(936\) 1.00000 + 1.73205i 0.0326860 + 0.0566139i
\(937\) −12.2915 21.2895i −0.401546 0.695498i 0.592367 0.805668i \(-0.298194\pi\)
−0.993913 + 0.110171i \(0.964860\pi\)
\(938\) −1.29150 −0.0421691
\(939\) −7.85425 + 13.6040i −0.256314 + 0.443948i
\(940\) 5.64575 9.77873i 0.184144 0.318947i
\(941\) −21.0203 + 36.4082i −0.685241 + 1.18687i 0.288120 + 0.957594i \(0.406970\pi\)
−0.973361 + 0.229278i \(0.926364\pi\)
\(942\) −4.35425 7.54178i −0.141869 0.245724i
\(943\) 8.70850 15.0836i 0.283588 0.491188i
\(944\) 3.50000 + 6.06218i 0.113915 + 0.197307i
\(945\) 1.00000 0.0325300
\(946\) −4.00000 −0.130051
\(947\) 12.5830 + 21.7944i 0.408893 + 0.708223i 0.994766 0.102180i \(-0.0325817\pi\)
−0.585873 + 0.810403i \(0.699248\pi\)
\(948\) 4.00000 6.92820i 0.129914 0.225018i
\(949\) −4.58301 7.93800i −0.148771 0.257678i
\(950\) −1.64575 + 2.85052i −0.0533952 + 0.0924832i
\(951\) −4.20850 + 7.28933i −0.136470 + 0.236373i
\(952\) 1.64575 2.85052i 0.0533391 0.0923860i
\(953\) −15.2915 −0.495340 −0.247670 0.968844i \(-0.579665\pi\)
−0.247670 + 0.968844i \(0.579665\pi\)
\(954\) 1.50000 + 2.59808i 0.0485643 + 0.0841158i
\(955\) 7.93725 + 13.7477i 0.256844 + 0.444866i
\(956\) −8.29150 + 14.3613i −0.268166 + 0.464478i
\(957\) 6.29150 0.203375
\(958\) −17.6458 30.5633i −0.570108 0.987457i
\(959\) −15.8745 −0.512615
\(960\) 1.00000 0.0322749
\(961\) −28.3745 + 12.4855i −0.915307 + 0.402758i
\(962\) −2.58301 −0.0832794
\(963\) 0.291503 0.00939354
\(964\) −2.20850 3.82523i −0.0711309 0.123202i
\(965\) 2.29150 0.0737661
\(966\) −1.64575 + 2.85052i −0.0529512 + 0.0917141i
\(967\) 14.5830 + 25.2585i 0.468958 + 0.812259i 0.999370 0.0354809i \(-0.0112963\pi\)
−0.530413 + 0.847740i \(0.677963\pi\)
\(968\) −5.00000 8.66025i −0.160706 0.278351i
\(969\) −10.8340 −0.348038
\(970\) −5.14575 + 8.91270i −0.165220 + 0.286170i
\(971\) −13.7915 + 23.8876i −0.442590 + 0.766589i −0.997881 0.0650674i \(-0.979274\pi\)
0.555290 + 0.831656i \(0.312607\pi\)
\(972\) −0.500000 + 0.866025i −0.0160375 + 0.0277778i
\(973\) 4.64575 + 8.04668i 0.148936 + 0.257965i
\(974\) 13.0830 22.6604i 0.419207 0.726087i
\(975\) −1.00000 1.73205i −0.0320256 0.0554700i
\(976\) −3.29150 −0.105358
\(977\) −6.58301 −0.210609 −0.105304 0.994440i \(-0.533582\pi\)
−0.105304 + 0.994440i \(0.533582\pi\)
\(978\) 4.93725 + 8.55157i 0.157876 + 0.273449i
\(979\) 0 0
\(980\) 3.00000 + 5.19615i 0.0958315 + 0.165985i
\(981\) 2.35425 4.07768i 0.0751654 0.130190i
\(982\) 16.7915 29.0837i 0.535838 0.928099i
\(983\) 3.41699 5.91841i 0.108985 0.188768i −0.806374 0.591406i \(-0.798573\pi\)
0.915359 + 0.402638i \(0.131907\pi\)
\(984\) −5.29150 −0.168687
\(985\) 9.58301 + 16.5983i 0.305340 + 0.528864i
\(986\) −10.3542 17.9341i −0.329746 0.571138i
\(987\) 5.64575 9.77873i 0.179706 0.311260i
\(988\) −6.58301 −0.209433
\(989\) −6.58301 11.4021i −0.209327 0.362566i
\(990\) 1.00000 0.0317821
\(991\) 35.7490 1.13560 0.567802 0.823165i \(-0.307794\pi\)
0.567802 + 0.823165i \(0.307794\pi\)
\(992\) −1.14575 5.44860i −0.0363776 0.172993i
\(993\) −9.87451 −0.313358
\(994\) −14.5830 −0.462545
\(995\) 4.85425 + 8.40781i 0.153890 + 0.266545i
\(996\) 8.29150 0.262726
\(997\) −1.93725 + 3.35542i −0.0613534 + 0.106267i −0.895071 0.445924i \(-0.852875\pi\)
0.833717 + 0.552192i \(0.186208\pi\)
\(998\) 0.645751 + 1.11847i 0.0204409 + 0.0354047i
\(999\) −0.645751 1.11847i −0.0204307 0.0353870i
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 930.2.i.j.211.1 4
31.5 even 3 inner 930.2.i.j.811.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.i.j.211.1 4 1.1 even 1 trivial
930.2.i.j.811.1 yes 4 31.5 even 3 inner