Properties

Label 462.2.n.a.65.2
Level $462$
Weight $2$
Character 462.65
Analytic conductor $3.689$
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] = [462,2,Mod(65,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.65");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.n (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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.2
Root \(-1.63746 + 1.52274i\) of defining polynomial
Character \(\chi\) \(=\) 462.65
Dual form 462.2.n.a.263.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.63746 + 1.52274i) q^{5} -1.73205i q^{6} +(2.63746 - 0.209313i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.63746 + 1.52274i) q^{5} -1.73205i q^{6} +(2.63746 - 0.209313i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.63746 + 1.52274i) q^{10} +(2.50000 - 2.17945i) q^{11} +(1.50000 + 0.866025i) q^{12} -6.09095i q^{13} +(-1.13746 + 2.38876i) q^{14} -5.27492 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.13746 - 3.70219i) q^{17} +(1.50000 + 2.59808i) q^{18} +(1.86254 + 1.07534i) q^{19} -3.04547i q^{20} +(-3.77492 + 2.59808i) q^{21} +(0.637459 + 3.25479i) q^{22} +(6.41238 + 3.70219i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(2.13746 + 3.70219i) q^{25} +(5.27492 + 3.04547i) q^{26} +5.19615i q^{27} +(-1.50000 - 2.17945i) q^{28} -1.00000 q^{29} +(2.63746 - 4.56821i) q^{30} +(1.36254 + 2.35999i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.86254 + 5.43424i) q^{33} +4.27492 q^{34} +(7.27492 + 3.46410i) q^{35} -3.00000 q^{36} +(-0.137459 + 0.238085i) q^{37} +(-1.86254 + 1.07534i) q^{38} +(5.27492 + 9.13642i) q^{39} +(2.63746 + 1.52274i) q^{40} -8.54983 q^{41} +(-0.362541 - 4.56821i) q^{42} +5.61478i q^{43} +(-3.13746 - 1.07534i) q^{44} +(7.91238 - 4.56821i) q^{45} +(-6.41238 + 3.70219i) q^{46} +(-9.41238 - 5.43424i) q^{47} -1.73205i q^{48} +(6.91238 - 1.10411i) q^{49} -4.27492 q^{50} +(6.41238 + 3.70219i) q^{51} +(-5.27492 + 3.04547i) q^{52} +(-7.18729 + 4.14959i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(9.91238 - 1.94136i) q^{55} +(2.63746 - 0.209313i) q^{56} -3.72508 q^{57} +(0.500000 - 0.866025i) q^{58} +(1.50000 - 0.866025i) q^{59} +(2.63746 + 4.56821i) q^{60} +(6.00000 + 3.46410i) q^{61} -2.72508 q^{62} +(3.41238 - 7.16629i) q^{63} +1.00000 q^{64} +(9.27492 - 16.0646i) q^{65} +(-3.77492 - 4.33013i) q^{66} +(-3.27492 - 5.67232i) q^{67} +(-2.13746 + 3.70219i) q^{68} -12.8248 q^{69} +(-6.63746 + 4.56821i) q^{70} +5.61478i q^{71} +(1.50000 - 2.59808i) q^{72} +(-10.5498 + 6.09095i) q^{73} +(-0.137459 - 0.238085i) q^{74} +(-6.41238 - 3.70219i) q^{75} -2.15068i q^{76} +(6.13746 - 6.27149i) q^{77} -10.5498 q^{78} +(5.63746 + 3.25479i) q^{79} +(-2.63746 + 1.52274i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.27492 - 7.40437i) q^{82} -2.72508 q^{83} +(4.13746 + 1.97014i) q^{84} -13.0192i q^{85} +(-4.86254 - 2.80739i) q^{86} +(1.50000 - 0.866025i) q^{87} +(2.50000 - 2.17945i) q^{88} +(-5.27492 - 3.04547i) q^{89} +9.13642i q^{90} +(-1.27492 - 16.0646i) q^{91} -7.40437i q^{92} +(-4.08762 - 2.35999i) q^{93} +(9.41238 - 5.43424i) q^{94} +(3.27492 + 5.67232i) q^{95} +(1.50000 + 0.866025i) q^{96} +1.54983 q^{97} +(-2.50000 + 6.53835i) q^{98} +(-1.91238 - 9.76436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 3 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 3 q^{7} + 4 q^{8} + 6 q^{9} - 3 q^{10} + 10 q^{11} + 6 q^{12} + 3 q^{14} - 6 q^{15} - 2 q^{16} - q^{17} + 6 q^{18} + 15 q^{19} - 5 q^{22} + 3 q^{23} - 6 q^{24} + q^{25} + 6 q^{26} - 6 q^{28} - 4 q^{29} + 3 q^{30} + 13 q^{31} - 2 q^{32} - 15 q^{33} + 2 q^{34} + 14 q^{35} - 12 q^{36} + 7 q^{37} - 15 q^{38} + 6 q^{39} + 3 q^{40} - 4 q^{41} - 9 q^{42} - 5 q^{44} + 9 q^{45} - 3 q^{46} - 15 q^{47} + 5 q^{49} - 2 q^{50} + 3 q^{51} - 6 q^{52} + 9 q^{53} - 18 q^{54} + 17 q^{55} + 3 q^{56} - 30 q^{57} + 2 q^{58} + 6 q^{59} + 3 q^{60} + 24 q^{61} - 26 q^{62} - 9 q^{63} + 4 q^{64} + 22 q^{65} + 2 q^{67} - q^{68} - 6 q^{69} - 19 q^{70} + 6 q^{72} - 12 q^{73} + 7 q^{74} - 3 q^{75} + 17 q^{77} - 12 q^{78} + 15 q^{79} - 3 q^{80} - 18 q^{81} + 2 q^{82} - 26 q^{83} + 9 q^{84} - 27 q^{86} + 6 q^{87} + 10 q^{88} - 6 q^{89} + 10 q^{91} - 39 q^{93} + 15 q^{94} - 2 q^{95} + 6 q^{96} - 24 q^{97} - 10 q^{98} + 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.63746 + 1.52274i 1.17951 + 0.680989i 0.955901 0.293691i \(-0.0948835\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 2.63746 0.209313i 0.996866 0.0791130i
\(8\) 1.00000 0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −2.63746 + 1.52274i −0.834038 + 0.481532i
\(11\) 2.50000 2.17945i 0.753778 0.657129i
\(12\) 1.50000 + 0.866025i 0.433013 + 0.250000i
\(13\) 6.09095i 1.68933i −0.535299 0.844663i \(-0.679801\pi\)
0.535299 0.844663i \(-0.320199\pi\)
\(14\) −1.13746 + 2.38876i −0.303999 + 0.638424i
\(15\) −5.27492 −1.36198
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.13746 3.70219i −0.518410 0.897912i −0.999771 0.0213900i \(-0.993191\pi\)
0.481361 0.876522i \(-0.340142\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) 1.86254 + 1.07534i 0.427296 + 0.246700i 0.698194 0.715908i \(-0.253987\pi\)
−0.270898 + 0.962608i \(0.587321\pi\)
\(20\) 3.04547i 0.680989i
\(21\) −3.77492 + 2.59808i −0.823754 + 0.566947i
\(22\) 0.637459 + 3.25479i 0.135907 + 0.693923i
\(23\) 6.41238 + 3.70219i 1.33707 + 0.771959i 0.986372 0.164528i \(-0.0526102\pi\)
0.350700 + 0.936488i \(0.385944\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) 2.13746 + 3.70219i 0.427492 + 0.740437i
\(26\) 5.27492 + 3.04547i 1.03450 + 0.597267i
\(27\) 5.19615i 1.00000i
\(28\) −1.50000 2.17945i −0.283473 0.411877i
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 2.63746 4.56821i 0.481532 0.834038i
\(31\) 1.36254 + 2.35999i 0.244720 + 0.423867i 0.962053 0.272863i \(-0.0879707\pi\)
−0.717333 + 0.696730i \(0.754637\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.86254 + 5.43424i −0.324227 + 0.945979i
\(34\) 4.27492 0.733142
\(35\) 7.27492 + 3.46410i 1.22969 + 0.585540i
\(36\) −3.00000 −0.500000
\(37\) −0.137459 + 0.238085i −0.0225981 + 0.0391410i −0.877103 0.480302i \(-0.840527\pi\)
0.854505 + 0.519443i \(0.173860\pi\)
\(38\) −1.86254 + 1.07534i −0.302144 + 0.174443i
\(39\) 5.27492 + 9.13642i 0.844663 + 1.46300i
\(40\) 2.63746 + 1.52274i 0.417019 + 0.240766i
\(41\) −8.54983 −1.33526 −0.667630 0.744493i \(-0.732691\pi\)
−0.667630 + 0.744493i \(0.732691\pi\)
\(42\) −0.362541 4.56821i −0.0559414 0.704890i
\(43\) 5.61478i 0.856246i 0.903721 + 0.428123i \(0.140825\pi\)
−0.903721 + 0.428123i \(0.859175\pi\)
\(44\) −3.13746 1.07534i −0.472990 0.162113i
\(45\) 7.91238 4.56821i 1.17951 0.680989i
\(46\) −6.41238 + 3.70219i −0.945453 + 0.545858i
\(47\) −9.41238 5.43424i −1.37294 0.792665i −0.381639 0.924311i \(-0.624640\pi\)
−0.991297 + 0.131646i \(0.957974\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 6.91238 1.10411i 0.987482 0.157730i
\(50\) −4.27492 −0.604565
\(51\) 6.41238 + 3.70219i 0.897912 + 0.518410i
\(52\) −5.27492 + 3.04547i −0.731499 + 0.422331i
\(53\) −7.18729 + 4.14959i −0.987251 + 0.569989i −0.904451 0.426577i \(-0.859719\pi\)
−0.0827993 + 0.996566i \(0.526386\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 9.91238 1.94136i 1.33658 0.261773i
\(56\) 2.63746 0.209313i 0.352445 0.0279707i
\(57\) −3.72508 −0.493399
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) 1.50000 0.866025i 0.195283 0.112747i −0.399170 0.916877i \(-0.630702\pi\)
0.594454 + 0.804130i \(0.297368\pi\)
\(60\) 2.63746 + 4.56821i 0.340494 + 0.589754i
\(61\) 6.00000 + 3.46410i 0.768221 + 0.443533i 0.832240 0.554416i \(-0.187058\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) −2.72508 −0.346086
\(63\) 3.41238 7.16629i 0.429919 0.902867i
\(64\) 1.00000 0.125000
\(65\) 9.27492 16.0646i 1.15041 1.99257i
\(66\) −3.77492 4.33013i −0.464660 0.533002i
\(67\) −3.27492 5.67232i −0.400095 0.692985i 0.593642 0.804729i \(-0.297689\pi\)
−0.993737 + 0.111745i \(0.964356\pi\)
\(68\) −2.13746 + 3.70219i −0.259205 + 0.448956i
\(69\) −12.8248 −1.54392
\(70\) −6.63746 + 4.56821i −0.793328 + 0.546006i
\(71\) 5.61478i 0.666352i 0.942865 + 0.333176i \(0.108120\pi\)
−0.942865 + 0.333176i \(0.891880\pi\)
\(72\) 1.50000 2.59808i 0.176777 0.306186i
\(73\) −10.5498 + 6.09095i −1.23476 + 0.712892i −0.968019 0.250875i \(-0.919282\pi\)
−0.266745 + 0.963767i \(0.585948\pi\)
\(74\) −0.137459 0.238085i −0.0159792 0.0276769i
\(75\) −6.41238 3.70219i −0.740437 0.427492i
\(76\) 2.15068i 0.246700i
\(77\) 6.13746 6.27149i 0.699428 0.714703i
\(78\) −10.5498 −1.19453
\(79\) 5.63746 + 3.25479i 0.634264 + 0.366192i 0.782401 0.622774i \(-0.213995\pi\)
−0.148138 + 0.988967i \(0.547328\pi\)
\(80\) −2.63746 + 1.52274i −0.294877 + 0.170247i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 4.27492 7.40437i 0.472086 0.817676i
\(83\) −2.72508 −0.299117 −0.149558 0.988753i \(-0.547785\pi\)
−0.149558 + 0.988753i \(0.547785\pi\)
\(84\) 4.13746 + 1.97014i 0.451434 + 0.214959i
\(85\) 13.0192i 1.41213i
\(86\) −4.86254 2.80739i −0.524341 0.302729i
\(87\) 1.50000 0.866025i 0.160817 0.0928477i
\(88\) 2.50000 2.17945i 0.266501 0.232330i
\(89\) −5.27492 3.04547i −0.559140 0.322820i 0.193660 0.981069i \(-0.437964\pi\)
−0.752800 + 0.658249i \(0.771297\pi\)
\(90\) 9.13642i 0.963064i
\(91\) −1.27492 16.0646i −0.133648 1.68403i
\(92\) 7.40437i 0.771959i
\(93\) −4.08762 2.35999i −0.423867 0.244720i
\(94\) 9.41238 5.43424i 0.970812 0.560499i
\(95\) 3.27492 + 5.67232i 0.335999 + 0.581968i
\(96\) 1.50000 + 0.866025i 0.153093 + 0.0883883i
\(97\) 1.54983 0.157362 0.0786809 0.996900i \(-0.474929\pi\)
0.0786809 + 0.996900i \(0.474929\pi\)
\(98\) −2.50000 + 6.53835i −0.252538 + 0.660473i
\(99\) −1.91238 9.76436i −0.192201 0.981356i
\(100\) 2.13746 3.70219i 0.213746 0.370219i
\(101\) 6.41238 + 11.1066i 0.638055 + 1.10514i 0.985859 + 0.167577i \(0.0535942\pi\)
−0.347804 + 0.937567i \(0.613072\pi\)
\(102\) −6.41238 + 3.70219i −0.634920 + 0.366571i
\(103\) −8.54983 + 14.8087i −0.842440 + 1.45915i 0.0453856 + 0.998970i \(0.485548\pi\)
−0.887826 + 0.460180i \(0.847785\pi\)
\(104\) 6.09095i 0.597267i
\(105\) −13.9124 + 1.10411i −1.35771 + 0.107750i
\(106\) 8.29917i 0.806087i
\(107\) 3.36254 5.82409i 0.325069 0.563036i −0.656457 0.754363i \(-0.727946\pi\)
0.981526 + 0.191327i \(0.0612791\pi\)
\(108\) 4.50000 2.59808i 0.433013 0.250000i
\(109\) 11.2749 6.50958i 1.07994 0.623504i 0.149061 0.988828i \(-0.452375\pi\)
0.930881 + 0.365324i \(0.119042\pi\)
\(110\) −3.27492 + 9.55505i −0.312251 + 0.911038i
\(111\) 0.476171i 0.0451961i
\(112\) −1.13746 + 2.38876i −0.107480 + 0.225717i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 1.86254 3.22602i 0.174443 0.302144i
\(115\) 11.2749 + 19.5287i 1.05139 + 1.82106i
\(116\) 0.500000 + 0.866025i 0.0464238 + 0.0804084i
\(117\) −15.8248 9.13642i −1.46300 0.844663i
\(118\) 1.73205i 0.159448i
\(119\) −6.41238 9.31697i −0.587822 0.854085i
\(120\) −5.27492 −0.481532
\(121\) 1.50000 10.8972i 0.136364 0.990659i
\(122\) −6.00000 + 3.46410i −0.543214 + 0.313625i
\(123\) 12.8248 7.40437i 1.15637 0.667630i
\(124\) 1.36254 2.35999i 0.122360 0.211933i
\(125\) 2.20822i 0.197509i
\(126\) 4.50000 + 6.53835i 0.400892 + 0.582482i
\(127\) 13.9140i 1.23466i 0.786703 + 0.617332i \(0.211786\pi\)
−0.786703 + 0.617332i \(0.788214\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −4.86254 8.42217i −0.428123 0.741531i
\(130\) 9.27492 + 16.0646i 0.813464 + 1.40896i
\(131\) −1.36254 + 2.35999i −0.119046 + 0.206193i −0.919390 0.393348i \(-0.871317\pi\)
0.800344 + 0.599541i \(0.204650\pi\)
\(132\) 5.63746 1.10411i 0.490678 0.0961005i
\(133\) 5.13746 + 2.44631i 0.445474 + 0.212122i
\(134\) 6.54983 0.565820
\(135\) −7.91238 + 13.7046i −0.680989 + 1.17951i
\(136\) −2.13746 3.70219i −0.183286 0.317460i
\(137\) 11.2749 6.50958i 0.963281 0.556151i 0.0660998 0.997813i \(-0.478944\pi\)
0.897181 + 0.441662i \(0.145611\pi\)
\(138\) 6.41238 11.1066i 0.545858 0.945453i
\(139\) 4.77753i 0.405224i 0.979259 + 0.202612i \(0.0649431\pi\)
−0.979259 + 0.202612i \(0.935057\pi\)
\(140\) −0.637459 8.03231i −0.0538751 0.678854i
\(141\) 18.8248 1.58533
\(142\) −4.86254 2.80739i −0.408055 0.235591i
\(143\) −13.2749 15.2274i −1.11010 1.27338i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) −2.63746 1.52274i −0.219029 0.126456i
\(146\) 12.1819i 1.00818i
\(147\) −9.41238 + 7.64246i −0.776320 + 0.630339i
\(148\) 0.274917 0.0225981
\(149\) −0.137459 + 0.238085i −0.0112610 + 0.0195047i −0.871601 0.490216i \(-0.836918\pi\)
0.860340 + 0.509721i \(0.170251\pi\)
\(150\) 6.41238 3.70219i 0.523568 0.302282i
\(151\) −10.5000 + 6.06218i −0.854478 + 0.493333i −0.862159 0.506637i \(-0.830888\pi\)
0.00768132 + 0.999970i \(0.497555\pi\)
\(152\) 1.86254 + 1.07534i 0.151072 + 0.0872215i
\(153\) −12.8248 −1.03682
\(154\) 2.36254 + 8.45094i 0.190379 + 0.680996i
\(155\) 8.29917i 0.666605i
\(156\) 5.27492 9.13642i 0.422331 0.731499i
\(157\) −4.86254 8.42217i −0.388073 0.672162i 0.604117 0.796895i \(-0.293526\pi\)
−0.992190 + 0.124733i \(0.960193\pi\)
\(158\) −5.63746 + 3.25479i −0.448492 + 0.258937i
\(159\) 7.18729 12.4488i 0.569989 0.987251i
\(160\) 3.04547i 0.240766i
\(161\) 17.6873 + 8.42217i 1.39395 + 0.663760i
\(162\) 9.00000 0.707107
\(163\) −0.725083 + 1.25588i −0.0567929 + 0.0983681i −0.893024 0.450009i \(-0.851421\pi\)
0.836231 + 0.548377i \(0.184754\pi\)
\(164\) 4.27492 + 7.40437i 0.333815 + 0.578184i
\(165\) −13.1873 + 11.4964i −1.02663 + 0.894995i
\(166\) 1.36254 2.35999i 0.105754 0.183171i
\(167\) −22.5498 −1.74496 −0.872479 0.488651i \(-0.837489\pi\)
−0.872479 + 0.488651i \(0.837489\pi\)
\(168\) −3.77492 + 2.59808i −0.291241 + 0.200446i
\(169\) −24.0997 −1.85382
\(170\) 11.2749 + 6.50958i 0.864747 + 0.499262i
\(171\) 5.58762 3.22602i 0.427296 0.246700i
\(172\) 4.86254 2.80739i 0.370765 0.214061i
\(173\) −7.00000 + 12.1244i −0.532200 + 0.921798i 0.467093 + 0.884208i \(0.345301\pi\)
−0.999293 + 0.0375896i \(0.988032\pi\)
\(174\) 1.73205i 0.131306i
\(175\) 6.41238 + 9.31697i 0.484730 + 0.704296i
\(176\) 0.637459 + 3.25479i 0.0480503 + 0.245339i
\(177\) −1.50000 + 2.59808i −0.112747 + 0.195283i
\(178\) 5.27492 3.04547i 0.395372 0.228268i
\(179\) 16.1375 9.31697i 1.20617 0.696383i 0.244250 0.969712i \(-0.421458\pi\)
0.961920 + 0.273330i \(0.0881250\pi\)
\(180\) −7.91238 4.56821i −0.589754 0.340494i
\(181\) 8.54983 0.635504 0.317752 0.948174i \(-0.397072\pi\)
0.317752 + 0.948174i \(0.397072\pi\)
\(182\) 14.5498 + 6.92820i 1.07851 + 0.513553i
\(183\) −12.0000 −0.887066
\(184\) 6.41238 + 3.70219i 0.472727 + 0.272929i
\(185\) −0.725083 + 0.418627i −0.0533091 + 0.0307781i
\(186\) 4.08762 2.35999i 0.299719 0.173043i
\(187\) −13.4124 4.59698i −0.980810 0.336165i
\(188\) 10.8685i 0.792665i
\(189\) 1.08762 + 13.7046i 0.0791130 + 0.996866i
\(190\) −6.54983 −0.475175
\(191\) 12.8248 + 7.40437i 0.927966 + 0.535762i 0.886168 0.463364i \(-0.153358\pi\)
0.0417986 + 0.999126i \(0.486691\pi\)
\(192\) −1.50000 + 0.866025i −0.108253 + 0.0625000i
\(193\) −15.3625 + 8.86957i −1.10582 + 0.638445i −0.937744 0.347329i \(-0.887089\pi\)
−0.168076 + 0.985774i \(0.553756\pi\)
\(194\) −0.774917 + 1.34220i −0.0556358 + 0.0963641i
\(195\) 32.1293i 2.30082i
\(196\) −4.41238 5.43424i −0.315170 0.388160i
\(197\) 20.2749 1.44453 0.722264 0.691617i \(-0.243102\pi\)
0.722264 + 0.691617i \(0.243102\pi\)
\(198\) 9.41238 + 3.22602i 0.668908 + 0.229263i
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 2.13746 + 3.70219i 0.151141 + 0.261784i
\(201\) 9.82475 + 5.67232i 0.692985 + 0.400095i
\(202\) −12.8248 −0.902346
\(203\) −2.63746 + 0.209313i −0.185113 + 0.0146909i
\(204\) 7.40437i 0.518410i
\(205\) −22.5498 13.0192i −1.57495 0.909297i
\(206\) −8.54983 14.8087i −0.595695 1.03177i
\(207\) 19.2371 11.1066i 1.33707 0.771959i
\(208\) 5.27492 + 3.04547i 0.365750 + 0.211166i
\(209\) 7.00000 1.37097i 0.484200 0.0948318i
\(210\) 6.00000 12.6005i 0.414039 0.869519i
\(211\) 11.2296i 0.773075i −0.922274 0.386537i \(-0.873671\pi\)
0.922274 0.386537i \(-0.126329\pi\)
\(212\) 7.18729 + 4.14959i 0.493625 + 0.284995i
\(213\) −4.86254 8.42217i −0.333176 0.577077i
\(214\) 3.36254 + 5.82409i 0.229859 + 0.398127i
\(215\) −8.54983 + 14.8087i −0.583094 + 1.00995i
\(216\) 5.19615i 0.353553i
\(217\) 4.08762 + 5.93918i 0.277486 + 0.403178i
\(218\) 13.0192i 0.881768i
\(219\) 10.5498 18.2728i 0.712892 1.23476i
\(220\) −6.63746 7.61369i −0.447497 0.513315i
\(221\) −22.5498 + 13.0192i −1.51687 + 0.875763i
\(222\) 0.412376 + 0.238085i 0.0276769 + 0.0159792i
\(223\) −19.8248 −1.32756 −0.663782 0.747926i \(-0.731050\pi\)
−0.663782 + 0.747926i \(0.731050\pi\)
\(224\) −1.50000 2.17945i −0.100223 0.145621i
\(225\) 12.8248 0.854983
\(226\) 0 0
\(227\) −7.18729 12.4488i −0.477037 0.826253i 0.522616 0.852568i \(-0.324956\pi\)
−0.999654 + 0.0263150i \(0.991623\pi\)
\(228\) 1.86254 + 3.22602i 0.123350 + 0.213648i
\(229\) −4.27492 + 7.40437i −0.282494 + 0.489295i −0.971998 0.234987i \(-0.924495\pi\)
0.689504 + 0.724282i \(0.257829\pi\)
\(230\) −22.5498 −1.48689
\(231\) −3.77492 + 14.7224i −0.248371 + 0.968665i
\(232\) −1.00000 −0.0656532
\(233\) 2.41238 4.17836i 0.158040 0.273733i −0.776122 0.630583i \(-0.782816\pi\)
0.934162 + 0.356850i \(0.116149\pi\)
\(234\) 15.8248 9.13642i 1.03450 0.597267i
\(235\) −16.5498 28.6652i −1.07959 1.86991i
\(236\) −1.50000 0.866025i −0.0976417 0.0563735i
\(237\) −11.2749 −0.732385
\(238\) 11.2749 0.894797i 0.730844 0.0580011i
\(239\) −2.54983 −0.164935 −0.0824675 0.996594i \(-0.526280\pi\)
−0.0824675 + 0.996594i \(0.526280\pi\)
\(240\) 2.63746 4.56821i 0.170247 0.294877i
\(241\) 7.91238 4.56821i 0.509681 0.294264i −0.223022 0.974814i \(-0.571592\pi\)
0.732702 + 0.680549i \(0.238259\pi\)
\(242\) 8.68729 + 6.74766i 0.558440 + 0.433756i
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) 6.92820i 0.443533i
\(245\) 19.9124 + 7.61369i 1.27216 + 0.486421i
\(246\) 14.8087i 0.944171i
\(247\) 6.54983 11.3446i 0.416756 0.721843i
\(248\) 1.36254 + 2.35999i 0.0865215 + 0.149860i
\(249\) 4.08762 2.35999i 0.259043 0.149558i
\(250\) 1.91238 + 1.10411i 0.120949 + 0.0698301i
\(251\) 7.82300i 0.493783i 0.969043 + 0.246892i \(0.0794092\pi\)
−0.969043 + 0.246892i \(0.920591\pi\)
\(252\) −7.91238 + 0.627940i −0.498433 + 0.0395565i
\(253\) 24.0997 4.71998i 1.51513 0.296743i
\(254\) −12.0498 6.95698i −0.756074 0.436519i
\(255\) 11.2749 + 19.5287i 0.706063 + 1.22294i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.72508 + 3.88273i 0.419499 + 0.242198i 0.694863 0.719142i \(-0.255465\pi\)
−0.275364 + 0.961340i \(0.588798\pi\)
\(258\) 9.72508 0.605457
\(259\) −0.312707 + 0.656712i −0.0194307 + 0.0408061i
\(260\) −18.5498 −1.15041
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) −1.36254 2.35999i −0.0841781 0.145801i
\(263\) −0.549834 0.952341i −0.0339042 0.0587239i 0.848575 0.529074i \(-0.177461\pi\)
−0.882480 + 0.470351i \(0.844127\pi\)
\(264\) −1.86254 + 5.43424i −0.114631 + 0.334454i
\(265\) −25.2749 −1.55263
\(266\) −4.68729 + 3.22602i −0.287396 + 0.197800i
\(267\) 10.5498 0.645639
\(268\) −3.27492 + 5.67232i −0.200047 + 0.346492i
\(269\) 13.9124 8.03231i 0.848253 0.489739i −0.0118083 0.999930i \(-0.503759\pi\)
0.860061 + 0.510191i \(0.170425\pi\)
\(270\) −7.91238 13.7046i −0.481532 0.834038i
\(271\) 26.7371 + 15.4367i 1.62416 + 0.937712i 0.985789 + 0.167987i \(0.0537267\pi\)
0.638376 + 0.769725i \(0.279607\pi\)
\(272\) 4.27492 0.259205
\(273\) 15.8248 + 22.9928i 0.957758 + 1.39159i
\(274\) 13.0192i 0.786516i
\(275\) 13.4124 + 4.59698i 0.808797 + 0.277209i
\(276\) 6.41238 + 11.1066i 0.385980 + 0.668536i
\(277\) −22.5498 + 13.0192i −1.35489 + 0.782245i −0.988930 0.148386i \(-0.952592\pi\)
−0.365959 + 0.930631i \(0.619259\pi\)
\(278\) −4.13746 2.38876i −0.248148 0.143268i
\(279\) 8.17525 0.489439
\(280\) 7.27492 + 3.46410i 0.434759 + 0.207020i
\(281\) −3.72508 −0.222220 −0.111110 0.993808i \(-0.535441\pi\)
−0.111110 + 0.993808i \(0.535441\pi\)
\(282\) −9.41238 + 16.3027i −0.560499 + 0.970812i
\(283\) 2.27492 1.31342i 0.135230 0.0780750i −0.430859 0.902419i \(-0.641789\pi\)
0.566089 + 0.824344i \(0.308456\pi\)
\(284\) 4.86254 2.80739i 0.288539 0.166588i
\(285\) −9.82475 5.67232i −0.581968 0.335999i
\(286\) 19.8248 3.88273i 1.17226 0.229591i
\(287\) −22.5498 + 1.78959i −1.33107 + 0.105636i
\(288\) −3.00000 −0.176777
\(289\) −0.637459 + 1.10411i −0.0374976 + 0.0649477i
\(290\) 2.63746 1.52274i 0.154877 0.0894182i
\(291\) −2.32475 + 1.34220i −0.136279 + 0.0786809i
\(292\) 10.5498 + 6.09095i 0.617382 + 0.356446i
\(293\) 24.0997 1.40792 0.703959 0.710241i \(-0.251414\pi\)
0.703959 + 0.710241i \(0.251414\pi\)
\(294\) −1.91238 11.9726i −0.111532 0.698255i
\(295\) 5.27492 0.307118
\(296\) −0.137459 + 0.238085i −0.00798962 + 0.0138384i
\(297\) 11.3248 + 12.9904i 0.657129 + 0.753778i
\(298\) −0.137459 0.238085i −0.00796276 0.0137919i
\(299\) 22.5498 39.0575i 1.30409 2.25875i
\(300\) 7.40437i 0.427492i
\(301\) 1.17525 + 14.8087i 0.0677402 + 0.853562i
\(302\) 12.1244i 0.697678i
\(303\) −19.2371 11.1066i −1.10514 0.638055i
\(304\) −1.86254 + 1.07534i −0.106824 + 0.0616749i
\(305\) 10.5498 + 18.2728i 0.604082 + 1.04630i
\(306\) 6.41238 11.1066i 0.366571 0.634920i
\(307\) 15.6460i 0.892964i −0.894793 0.446482i \(-0.852677\pi\)
0.894793 0.446482i \(-0.147323\pi\)
\(308\) −8.50000 2.17945i −0.484332 0.124186i
\(309\) 29.6175i 1.68488i
\(310\) −7.18729 4.14959i −0.408211 0.235681i
\(311\) −19.1375 + 11.0490i −1.08519 + 0.626532i −0.932291 0.361710i \(-0.882193\pi\)
−0.152895 + 0.988242i \(0.548860\pi\)
\(312\) 5.27492 + 9.13642i 0.298633 + 0.517248i
\(313\) −3.50000 + 6.06218i −0.197832 + 0.342655i −0.947825 0.318791i \(-0.896723\pi\)
0.749993 + 0.661445i \(0.230057\pi\)
\(314\) 9.72508 0.548818
\(315\) 19.9124 13.7046i 1.12194 0.772169i
\(316\) 6.50958i 0.366192i
\(317\) 7.18729 + 4.14959i 0.403679 + 0.233064i 0.688070 0.725644i \(-0.258458\pi\)
−0.284391 + 0.958708i \(0.591792\pi\)
\(318\) 7.18729 + 12.4488i 0.403043 + 0.698092i
\(319\) −2.50000 + 2.17945i −0.139973 + 0.122026i
\(320\) 2.63746 + 1.52274i 0.147438 + 0.0851236i
\(321\) 11.6482i 0.650138i
\(322\) −16.1375 + 11.1066i −0.899305 + 0.618944i
\(323\) 9.19397i 0.511566i
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 22.5498 13.0192i 1.25084 0.722173i
\(326\) −0.725083 1.25588i −0.0401586 0.0695568i
\(327\) −11.2749 + 19.5287i −0.623504 + 1.07994i
\(328\) −8.54983 −0.472086
\(329\) −25.9622 12.3624i −1.43134 0.681563i
\(330\) −3.36254 17.1687i −0.185102 0.945108i
\(331\) −12.5498 + 21.7370i −0.689801 + 1.19477i 0.282101 + 0.959385i \(0.408969\pi\)
−0.971902 + 0.235386i \(0.924365\pi\)
\(332\) 1.36254 + 2.35999i 0.0747792 + 0.129521i
\(333\) 0.412376 + 0.714256i 0.0225981 + 0.0391410i
\(334\) 11.2749 19.5287i 0.616936 1.06856i
\(335\) 19.9474i 1.08984i
\(336\) −0.362541 4.56821i −0.0197783 0.249216i
\(337\) 21.3183i 1.16128i 0.814159 + 0.580642i \(0.197198\pi\)
−0.814159 + 0.580642i \(0.802802\pi\)
\(338\) 12.0498 20.8709i 0.655425 1.13523i
\(339\) 0 0
\(340\) −11.2749 + 6.50958i −0.611468 + 0.353031i
\(341\) 8.54983 + 2.93039i 0.462999 + 0.158689i
\(342\) 6.45203i 0.348886i
\(343\) 18.0000 4.35890i 0.971909 0.235358i
\(344\) 5.61478i 0.302729i
\(345\) −33.8248 19.5287i −1.82106 1.05139i
\(346\) −7.00000 12.1244i −0.376322 0.651809i
\(347\) −2.00000 3.46410i −0.107366 0.185963i 0.807337 0.590091i \(-0.200908\pi\)
−0.914702 + 0.404128i \(0.867575\pi\)
\(348\) −1.50000 0.866025i −0.0804084 0.0464238i
\(349\) 35.7084i 1.91143i −0.294295 0.955715i \(-0.595085\pi\)
0.294295 0.955715i \(-0.404915\pi\)
\(350\) −11.2749 + 0.894797i −0.602670 + 0.0478289i
\(351\) 31.6495 1.68933
\(352\) −3.13746 1.07534i −0.167227 0.0573157i
\(353\) −13.6495 + 7.88054i −0.726490 + 0.419439i −0.817137 0.576444i \(-0.804440\pi\)
0.0906469 + 0.995883i \(0.471107\pi\)
\(354\) −1.50000 2.59808i −0.0797241 0.138086i
\(355\) −8.54983 + 14.8087i −0.453778 + 0.785967i
\(356\) 6.09095i 0.322820i
\(357\) 17.6873 + 8.42217i 0.936111 + 0.445748i
\(358\) 18.6339i 0.984834i
\(359\) −9.82475 + 17.0170i −0.518531 + 0.898121i 0.481238 + 0.876590i \(0.340187\pi\)
−0.999768 + 0.0215311i \(0.993146\pi\)
\(360\) 7.91238 4.56821i 0.417019 0.240766i
\(361\) −7.18729 12.4488i −0.378279 0.655198i
\(362\) −4.27492 + 7.40437i −0.224685 + 0.389165i
\(363\) 7.18729 + 17.6449i 0.377235 + 0.926118i
\(364\) −13.2749 + 9.13642i −0.695795 + 0.478879i
\(365\) −37.0997 −1.94189
\(366\) 6.00000 10.3923i 0.313625 0.543214i
\(367\) −12.6375 21.8887i −0.659670 1.14258i −0.980701 0.195513i \(-0.937363\pi\)
0.321031 0.947069i \(-0.395971\pi\)
\(368\) −6.41238 + 3.70219i −0.334268 + 0.192990i
\(369\) −12.8248 + 22.2131i −0.667630 + 1.15637i
\(370\) 0.837253i 0.0435267i
\(371\) −18.0876 + 12.4488i −0.939063 + 0.646307i
\(372\) 4.71998i 0.244720i
\(373\) −22.5498 13.0192i −1.16759 0.674106i −0.214476 0.976729i \(-0.568804\pi\)
−0.953110 + 0.302623i \(0.902138\pi\)
\(374\) 10.6873 9.31697i 0.552627 0.481769i
\(375\) 1.91238 + 3.31233i 0.0987547 + 0.171048i
\(376\) −9.41238 5.43424i −0.485406 0.280249i
\(377\) 6.09095i 0.313700i
\(378\) −12.4124 5.91041i −0.638424 0.303999i
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 3.27492 5.67232i 0.168000 0.290984i
\(381\) −12.0498 20.8709i −0.617332 1.06925i
\(382\) −12.8248 + 7.40437i −0.656171 + 0.378841i
\(383\) 15.5120 + 8.95588i 0.792628 + 0.457624i 0.840887 0.541211i \(-0.182034\pi\)
−0.0482586 + 0.998835i \(0.515367\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 25.7371 7.19506i 1.31169 0.366694i
\(386\) 17.7391i 0.902898i
\(387\) 14.5876 + 8.42217i 0.741531 + 0.428123i
\(388\) −0.774917 1.34220i −0.0393405 0.0681397i
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) −27.8248 16.0646i −1.40896 0.813464i
\(391\) 31.6531i 1.60077i
\(392\) 6.91238 1.10411i 0.349128 0.0557660i
\(393\) 4.71998i 0.238092i
\(394\) −10.1375 + 17.5586i −0.510718 + 0.884589i
\(395\) 9.91238 + 17.1687i 0.498746 + 0.863853i
\(396\) −7.50000 + 6.53835i −0.376889 + 0.328564i
\(397\) 9.13746 15.8265i 0.458596 0.794311i −0.540291 0.841478i \(-0.681686\pi\)
0.998887 + 0.0471668i \(0.0150192\pi\)
\(398\) 0 0
\(399\) −9.82475 + 0.779710i −0.491853 + 0.0390343i
\(400\) −4.27492 −0.213746
\(401\) −25.6495 14.8087i −1.28088 0.739514i −0.303867 0.952715i \(-0.598278\pi\)
−0.977008 + 0.213201i \(0.931611\pi\)
\(402\) −9.82475 + 5.67232i −0.490014 + 0.282910i
\(403\) 14.3746 8.29917i 0.716049 0.413411i
\(404\) 6.41238 11.1066i 0.319028 0.552572i
\(405\) 27.4093i 1.36198i
\(406\) 1.13746 2.38876i 0.0564511 0.118552i
\(407\) 0.175248 + 0.894797i 0.00868674 + 0.0443535i
\(408\) 6.41238 + 3.70219i 0.317460 + 0.183286i
\(409\) −31.1873 + 18.0060i −1.54211 + 0.890339i −0.543407 + 0.839469i \(0.682866\pi\)
−0.998705 + 0.0508697i \(0.983801\pi\)
\(410\) 22.5498 13.0192i 1.11366 0.642970i
\(411\) −11.2749 + 19.5287i −0.556151 + 0.963281i
\(412\) 17.0997 0.842440
\(413\) 3.77492 2.59808i 0.185752 0.127843i
\(414\) 22.2131i 1.09172i
\(415\) −7.18729 4.14959i −0.352810 0.203695i
\(416\) −5.27492 + 3.04547i −0.258624 + 0.149317i
\(417\) −4.13746 7.16629i −0.202612 0.350935i
\(418\) −2.31271 + 6.74766i −0.113118 + 0.330039i
\(419\) 22.9353i 1.12046i −0.828336 0.560231i \(-0.810712\pi\)
0.828336 0.560231i \(-0.189288\pi\)
\(420\) 7.91238 + 11.4964i 0.386084 + 0.560968i
\(421\) −15.3746 −0.749311 −0.374656 0.927164i \(-0.622239\pi\)
−0.374656 + 0.927164i \(0.622239\pi\)
\(422\) 9.72508 + 5.61478i 0.473410 + 0.273323i
\(423\) −28.2371 + 16.3027i −1.37294 + 0.792665i
\(424\) −7.18729 + 4.14959i −0.349046 + 0.201522i
\(425\) 9.13746 15.8265i 0.443232 0.767700i
\(426\) 9.72508 0.471182
\(427\) 16.5498 + 7.88054i 0.800903 + 0.381366i
\(428\) −6.72508 −0.325069
\(429\) 33.0997 + 11.3446i 1.59807 + 0.547725i
\(430\) −8.54983 14.8087i −0.412310 0.714141i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) −4.50000 2.59808i −0.216506 0.125000i
\(433\) 4.27492 0.205439 0.102720 0.994710i \(-0.467246\pi\)
0.102720 + 0.994710i \(0.467246\pi\)
\(434\) −7.18729 + 0.570396i −0.345001 + 0.0273799i
\(435\) 5.27492 0.252913
\(436\) −11.2749 6.50958i −0.539971 0.311752i
\(437\) 7.96221 + 13.7910i 0.380884 + 0.659711i
\(438\) 10.5498 + 18.2728i 0.504091 + 0.873111i
\(439\) 20.3248 + 11.7345i 0.970047 + 0.560057i 0.899251 0.437434i \(-0.144112\pi\)
0.0707968 + 0.997491i \(0.477446\pi\)
\(440\) 9.91238 1.94136i 0.472554 0.0925509i
\(441\) 7.50000 19.6150i 0.357143 0.934050i
\(442\) 26.0383i 1.23852i
\(443\) −12.0498 6.95698i −0.572505 0.330536i 0.185644 0.982617i \(-0.440563\pi\)
−0.758149 + 0.652081i \(0.773896\pi\)
\(444\) −0.412376 + 0.238085i −0.0195705 + 0.0112990i
\(445\) −9.27492 16.0646i −0.439673 0.761536i
\(446\) 9.91238 17.1687i 0.469365 0.812963i
\(447\) 0.476171i 0.0225221i
\(448\) 2.63746 0.209313i 0.124608 0.00988913i
\(449\) 13.0192i 0.614412i −0.951643 0.307206i \(-0.900606\pi\)
0.951643 0.307206i \(-0.0993940\pi\)
\(450\) −6.41238 + 11.1066i −0.302282 + 0.523568i
\(451\) −21.3746 + 18.6339i −1.00649 + 0.877438i
\(452\) 0 0
\(453\) 10.5000 18.1865i 0.493333 0.854478i
\(454\) 14.3746 0.674633
\(455\) 21.0997 44.3112i 0.989168 2.07734i
\(456\) −3.72508 −0.174443
\(457\) 32.8368 + 18.9583i 1.53604 + 0.886833i 0.999065 + 0.0432357i \(0.0137666\pi\)
0.536976 + 0.843598i \(0.319567\pi\)
\(458\) −4.27492 7.40437i −0.199754 0.345984i
\(459\) 19.2371 11.1066i 0.897912 0.518410i
\(460\) 11.2749 19.5287i 0.525696 0.910532i
\(461\) −12.8248 −0.597308 −0.298654 0.954361i \(-0.596538\pi\)
−0.298654 + 0.954361i \(0.596538\pi\)
\(462\) −10.8625 10.6304i −0.505371 0.494571i
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) 0.500000 0.866025i 0.0232119 0.0402042i
\(465\) −7.18729 12.4488i −0.333303 0.577297i
\(466\) 2.41238 + 4.17836i 0.111751 + 0.193559i
\(467\) −20.6873 11.9438i −0.957294 0.552694i −0.0619547 0.998079i \(-0.519733\pi\)
−0.895339 + 0.445385i \(0.853067\pi\)
\(468\) 18.2728i 0.844663i
\(469\) −9.82475 14.2750i −0.453665 0.659160i
\(470\) 33.0997 1.52677
\(471\) 14.5876 + 8.42217i 0.672162 + 0.388073i
\(472\) 1.50000 0.866025i 0.0690431 0.0398621i
\(473\) 12.2371 + 14.0369i 0.562664 + 0.645420i
\(474\) 5.63746 9.76436i 0.258937 0.448492i
\(475\) 9.19397i 0.421848i
\(476\) −4.86254 + 10.2118i −0.222874 + 0.468055i
\(477\) 24.8975i 1.13998i
\(478\) 1.27492 2.20822i 0.0583134 0.101002i
\(479\) −14.0000 24.2487i −0.639676 1.10795i −0.985504 0.169654i \(-0.945735\pi\)
0.345827 0.938298i \(-0.387598\pi\)
\(480\) 2.63746 + 4.56821i 0.120383 + 0.208509i
\(481\) 1.45017 + 0.837253i 0.0661219 + 0.0381755i
\(482\) 9.13642i 0.416153i
\(483\) −33.8248 + 2.68439i −1.53908 + 0.122144i
\(484\) −10.1873 + 4.14959i −0.463059 + 0.188618i
\(485\) 4.08762 + 2.35999i 0.185609 + 0.107162i
\(486\) −13.5000 + 7.79423i −0.612372 + 0.353553i
\(487\) −9.18729 15.9129i −0.416316 0.721080i 0.579250 0.815150i \(-0.303346\pi\)
−0.995566 + 0.0940698i \(0.970012\pi\)
\(488\) 6.00000 + 3.46410i 0.271607 + 0.156813i
\(489\) 2.51176i 0.113586i
\(490\) −16.5498 + 13.4378i −0.747645 + 0.607057i
\(491\) −22.3746 −1.00975 −0.504875 0.863192i \(-0.668462\pi\)
−0.504875 + 0.863192i \(0.668462\pi\)
\(492\) −12.8248 7.40437i −0.578184 0.333815i
\(493\) 2.13746 + 3.70219i 0.0962663 + 0.166738i
\(494\) 6.54983 + 11.3446i 0.294691 + 0.510420i
\(495\) 9.82475 28.6652i 0.441590 1.28840i
\(496\) −2.72508 −0.122360
\(497\) 1.17525 + 14.8087i 0.0527171 + 0.664263i
\(498\) 4.71998i 0.211507i
\(499\) −9.27492 + 16.0646i −0.415202 + 0.719152i −0.995450 0.0952888i \(-0.969623\pi\)
0.580247 + 0.814440i \(0.302956\pi\)
\(500\) −1.91238 + 1.10411i −0.0855240 + 0.0493773i
\(501\) 33.8248 19.5287i 1.51118 0.872479i
\(502\) −6.77492 3.91150i −0.302379 0.174579i
\(503\) 11.6495 0.519426 0.259713 0.965686i \(-0.416372\pi\)
0.259713 + 0.965686i \(0.416372\pi\)
\(504\) 3.41238 7.16629i 0.151999 0.319212i
\(505\) 39.0575i 1.73803i
\(506\) −7.96221 + 23.2309i −0.353963 + 1.03274i
\(507\) 36.1495 20.8709i 1.60546 0.926910i
\(508\) 12.0498 6.95698i 0.534625 0.308666i
\(509\) −31.9124 18.4246i −1.41449 0.816657i −0.418684 0.908132i \(-0.637508\pi\)
−0.995807 + 0.0914752i \(0.970842\pi\)
\(510\) −22.5498 −0.998523
\(511\) −26.5498 + 18.2728i −1.17450 + 0.808343i
\(512\) 1.00000 0.0441942
\(513\) −5.58762 + 9.67805i −0.246700 + 0.427296i
\(514\) −6.72508 + 3.88273i −0.296631 + 0.171260i
\(515\) −45.0997 + 26.0383i −1.98733 + 1.14738i
\(516\) −4.86254 + 8.42217i −0.214061 + 0.370765i
\(517\) −35.3746 + 6.92820i −1.55577 + 0.304702i
\(518\) −0.412376 0.599168i −0.0181188 0.0263259i
\(519\) 24.2487i 1.06440i
\(520\) 9.27492 16.0646i 0.406732 0.704481i
\(521\) 15.0997 8.71780i 0.661529 0.381934i −0.131331 0.991339i \(-0.541925\pi\)
0.792859 + 0.609405i \(0.208592\pi\)
\(522\) −1.50000 2.59808i −0.0656532 0.113715i
\(523\) −6.09967 3.52165i −0.266720 0.153991i 0.360676 0.932691i \(-0.382546\pi\)
−0.627396 + 0.778700i \(0.715879\pi\)
\(524\) 2.72508 0.119046
\(525\) −17.6873 8.42217i −0.771937 0.367574i
\(526\) 1.09967 0.0479478
\(527\) 5.82475 10.0888i 0.253730 0.439474i
\(528\) −3.77492 4.33013i −0.164282 0.188445i
\(529\) 15.9124 + 27.5610i 0.691842 + 1.19831i
\(530\) 12.6375 21.8887i 0.548936 0.950785i
\(531\) 5.19615i 0.225494i
\(532\) −0.450166 5.67232i −0.0195172 0.245926i
\(533\) 52.0766i 2.25569i
\(534\) −5.27492 + 9.13642i −0.228268 + 0.395372i
\(535\) 17.7371 10.2405i 0.766843 0.442737i
\(536\) −3.27492 5.67232i −0.141455 0.245007i
\(537\) −16.1375 + 27.9509i −0.696383 + 1.20617i
\(538\) 16.0646i 0.692595i
\(539\) 14.8746 17.8255i 0.640694 0.767797i
\(540\) 15.8248 0.680989
\(541\) 22.5498 + 13.0192i 0.969493 + 0.559737i 0.899082 0.437781i \(-0.144235\pi\)
0.0704114 + 0.997518i \(0.477569\pi\)
\(542\) −26.7371 + 15.4367i −1.14846 + 0.663063i
\(543\) −12.8248 + 7.40437i −0.550363 + 0.317752i
\(544\) −2.13746 + 3.70219i −0.0916428 + 0.158730i
\(545\) 39.6495 1.69840
\(546\) −27.8248 + 2.20822i −1.19079 + 0.0945032i
\(547\) 22.2131i 0.949764i 0.880049 + 0.474882i \(0.157509\pi\)
−0.880049 + 0.474882i \(0.842491\pi\)
\(548\) −11.2749 6.50958i −0.481641 0.278075i
\(549\) 18.0000 10.3923i 0.768221 0.443533i
\(550\) −10.6873 + 9.31697i −0.455708 + 0.397277i
\(551\) −1.86254 1.07534i −0.0793469 0.0458110i
\(552\) −12.8248 −0.545858
\(553\) 15.5498 + 7.40437i 0.661246 + 0.314866i
\(554\) 26.0383i 1.10626i
\(555\) 0.725083 1.25588i 0.0307781 0.0533091i
\(556\) 4.13746 2.38876i 0.175467 0.101306i
\(557\) −15.3248 26.5432i −0.649331 1.12467i −0.983283 0.182084i \(-0.941716\pi\)
0.333952 0.942590i \(-0.391617\pi\)
\(558\) −4.08762 + 7.07997i −0.173043 + 0.299719i
\(559\) 34.1993 1.44648
\(560\) −6.63746 + 4.56821i −0.280484 + 0.193042i
\(561\) 24.0997 4.71998i 1.01749 0.199278i
\(562\) 1.86254 3.22602i 0.0785666 0.136081i
\(563\) 15.3625 + 26.6087i 0.647454 + 1.12142i 0.983729 + 0.179659i \(0.0574995\pi\)
−0.336275 + 0.941764i \(0.609167\pi\)
\(564\) −9.41238 16.3027i −0.396333 0.686468i
\(565\) 0 0
\(566\) 2.62685i 0.110415i
\(567\) −13.5000 19.6150i −0.566947 0.823754i
\(568\) 5.61478i 0.235591i
\(569\) −14.6873 + 25.4391i −0.615723 + 1.06646i 0.374534 + 0.927213i \(0.377803\pi\)
−0.990257 + 0.139251i \(0.955531\pi\)
\(570\) 9.82475 5.67232i 0.411514 0.237587i
\(571\) 7.96221 4.59698i 0.333208 0.192378i −0.324056 0.946038i \(-0.605047\pi\)
0.657265 + 0.753660i \(0.271713\pi\)
\(572\) −6.54983 + 19.1101i −0.273862 + 0.799034i
\(573\) −25.6495 −1.07152
\(574\) 9.72508 20.4235i 0.405917 0.852462i
\(575\) 31.6531i 1.32002i
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −0.187293 0.324401i −0.00779711 0.0135050i 0.862101 0.506737i \(-0.169149\pi\)
−0.869898 + 0.493232i \(0.835815\pi\)
\(578\) −0.637459 1.10411i −0.0265148 0.0459250i
\(579\) 15.3625 26.6087i 0.638445 1.10582i
\(580\) 3.04547i 0.126456i
\(581\) −7.18729 + 0.570396i −0.298179 + 0.0236640i
\(582\) 2.68439i 0.111272i
\(583\) −8.92442 + 26.0383i −0.369612 + 1.07840i
\(584\) −10.5498 + 6.09095i −0.436555 + 0.252045i
\(585\) −27.8248 48.1939i −1.15041 1.99257i
\(586\) −12.0498 + 20.8709i −0.497774 + 0.862170i
\(587\) 26.4569i 1.09199i 0.837787 + 0.545997i \(0.183849\pi\)
−0.837787 + 0.545997i \(0.816151\pi\)
\(588\) 11.3248 + 4.33013i 0.467025 + 0.178571i
\(589\) 5.86077i 0.241489i
\(590\) −2.63746 + 4.56821i −0.108582 + 0.188070i
\(591\) −30.4124 + 17.5586i −1.25100 + 0.722264i
\(592\) −0.137459 0.238085i −0.00564951 0.00978525i
\(593\) 6.41238 11.1066i 0.263325 0.456092i −0.703799 0.710400i \(-0.748514\pi\)
0.967123 + 0.254308i \(0.0818476\pi\)
\(594\) −16.9124 + 3.31233i −0.693923 + 0.135907i
\(595\) −2.72508 34.3375i −0.111718 1.40770i
\(596\) 0.274917 0.0112610
\(597\) 0 0
\(598\) 22.5498 + 39.0575i 0.922131 + 1.59718i
\(599\) 24.0997 13.9140i 0.984686 0.568509i 0.0810042 0.996714i \(-0.474187\pi\)
0.903682 + 0.428205i \(0.140854\pi\)
\(600\) −6.41238 3.70219i −0.261784 0.151141i
\(601\) 1.37097i 0.0559229i −0.999609 0.0279615i \(-0.991098\pi\)
0.999609 0.0279615i \(-0.00890157\pi\)
\(602\) −13.4124 6.38658i −0.546648 0.260298i
\(603\) −19.6495 −0.800190
\(604\) 10.5000 + 6.06218i 0.427239 + 0.246667i
\(605\) 20.5498 26.4569i 0.835470 1.07563i
\(606\) 19.2371 11.1066i 0.781455 0.451173i
\(607\) −18.3625 10.6016i −0.745313 0.430306i 0.0786852 0.996900i \(-0.474928\pi\)
−0.823998 + 0.566593i \(0.808261\pi\)
\(608\) 2.15068i 0.0872215i
\(609\) 3.77492 2.59808i 0.152967 0.105279i
\(610\) −21.0997 −0.854301
\(611\) −33.0997 + 57.3303i −1.33907 + 2.31934i
\(612\) 6.41238 + 11.1066i 0.259205 + 0.448956i
\(613\) 8.17525 4.71998i 0.330195 0.190638i −0.325733 0.945462i \(-0.605611\pi\)
0.655928 + 0.754824i \(0.272278\pi\)
\(614\) 13.5498 + 7.82300i 0.546827 + 0.315711i
\(615\) 45.0997 1.81859
\(616\) 6.13746 6.27149i 0.247285 0.252686i
\(617\) 3.57919i 0.144093i 0.997401 + 0.0720464i \(0.0229530\pi\)
−0.997401 + 0.0720464i \(0.977047\pi\)
\(618\) 25.6495 + 14.8087i 1.03177 + 0.595695i
\(619\) 8.54983 + 14.8087i 0.343647 + 0.595214i 0.985107 0.171943i \(-0.0550044\pi\)
−0.641460 + 0.767156i \(0.721671\pi\)
\(620\) 7.18729 4.14959i 0.288649 0.166651i
\(621\) −19.2371 + 33.3197i −0.771959 + 1.33707i
\(622\) 22.0980i 0.886050i
\(623\) −14.5498 6.92820i −0.582927 0.277573i
\(624\) −10.5498 −0.422331
\(625\) 14.0498 24.3350i 0.561993 0.973401i
\(626\) −3.50000 6.06218i −0.139888 0.242293i
\(627\) −9.31271 + 8.11863i −0.371914 + 0.324227i
\(628\) −4.86254 + 8.42217i −0.194037 + 0.336081i
\(629\) 1.17525 0.0468602
\(630\) 1.91238 + 24.0969i 0.0761909 + 0.960045i
\(631\) 24.9244 0.992226 0.496113 0.868258i \(-0.334760\pi\)
0.496113 + 0.868258i \(0.334760\pi\)
\(632\) 5.63746 + 3.25479i 0.224246 + 0.129469i
\(633\) 9.72508 + 16.8443i 0.386537 + 0.669502i
\(634\) −7.18729 + 4.14959i −0.285444 + 0.164801i
\(635\) −21.1873 + 36.6975i −0.840792 + 1.45629i
\(636\) −14.3746 −0.569989
\(637\) −6.72508 42.1029i −0.266457 1.66818i
\(638\) −0.637459 3.25479i −0.0252372 0.128858i
\(639\) 14.5876 + 8.42217i 0.577077 + 0.333176i
\(640\) −2.63746 + 1.52274i −0.104255 + 0.0601915i
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) −10.0876 5.82409i −0.398127 0.229859i
\(643\) 11.6495 0.459412 0.229706 0.973260i \(-0.426224\pi\)
0.229706 + 0.973260i \(0.426224\pi\)
\(644\) −1.54983 19.5287i −0.0610720 0.769540i
\(645\) 29.6175i 1.16619i
\(646\) 7.96221 + 4.59698i 0.313269 + 0.180866i
\(647\) −0.824752 + 0.476171i −0.0324243 + 0.0187202i −0.516125 0.856514i \(-0.672626\pi\)
0.483700 + 0.875234i \(0.339293\pi\)
\(648\) −4.50000 7.79423i −0.176777 0.306186i
\(649\) 1.86254 5.43424i 0.0731111 0.213312i
\(650\) 26.0383i 1.02131i
\(651\) −11.2749 5.36878i −0.441899 0.210419i
\(652\) 1.45017 0.0567929
\(653\) 15.3625 + 8.86957i 0.601183 + 0.347093i 0.769507 0.638639i \(-0.220502\pi\)
−0.168324 + 0.985732i \(0.553835\pi\)
\(654\) −11.2749 19.5287i −0.440884 0.763634i
\(655\) −7.18729 + 4.14959i −0.280831 + 0.162138i
\(656\) 4.27492 7.40437i 0.166907 0.289092i
\(657\) 36.5457i 1.42578i
\(658\) 23.6873 16.3027i 0.923427 0.635546i
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 16.5498 + 5.67232i 0.644201 + 0.220795i
\(661\) 9.13746 + 15.8265i 0.355406 + 0.615581i 0.987187 0.159565i \(-0.0510093\pi\)
−0.631781 + 0.775147i \(0.717676\pi\)
\(662\) −12.5498 21.7370i −0.487763 0.844831i
\(663\) 22.5498 39.0575i 0.875763 1.51687i
\(664\) −2.72508 −0.105754
\(665\) 9.82475 + 14.2750i 0.380988 + 0.553562i
\(666\) −0.824752 −0.0319585
\(667\) −6.41238 3.70219i −0.248288 0.143349i
\(668\) 11.2749 + 19.5287i 0.436240 + 0.755589i
\(669\) 29.7371 17.1687i 1.14970 0.663782i
\(670\) 17.2749 + 9.97368i 0.667388 + 0.385317i
\(671\) 22.5498 4.41644i 0.870527 0.170495i
\(672\) 4.13746 + 1.97014i 0.159606 + 0.0759997i
\(673\) 17.7391i 0.683793i −0.939738 0.341897i \(-0.888931\pi\)
0.939738 0.341897i \(-0.111069\pi\)
\(674\) −18.4622 10.6592i −0.711138 0.410576i
\(675\) −19.2371 + 11.1066i −0.740437 + 0.427492i
\(676\) 12.0498 + 20.8709i 0.463455 + 0.802728i
\(677\) 13.5997 23.5553i 0.522678 0.905304i −0.476974 0.878917i \(-0.658266\pi\)
0.999652 0.0263870i \(-0.00840023\pi\)
\(678\) 0 0
\(679\) 4.08762 0.324401i 0.156869 0.0124494i
\(680\) 13.0192i 0.499262i
\(681\) 21.5619 + 12.4488i 0.826253 + 0.477037i
\(682\) −6.81271 + 5.93918i −0.260872 + 0.227423i
\(683\) −18.6752 + 10.7822i −0.714589 + 0.412568i −0.812758 0.582602i \(-0.802035\pi\)
0.0981692 + 0.995170i \(0.468701\pi\)
\(684\) −5.58762 3.22602i −0.213648 0.123350i
\(685\) 39.6495 1.51493
\(686\) −5.22508 + 17.7679i −0.199495 + 0.678382i
\(687\) 14.8087i 0.564989i
\(688\) −4.86254 2.80739i −0.185383 0.107031i
\(689\) 25.2749 + 43.7774i 0.962898 + 1.66779i
\(690\) 33.8248 19.5287i 1.28769 0.743446i
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) 14.0000 0.532200
\(693\) −7.08762 25.3528i −0.269237 0.963074i
\(694\) 4.00000 0.151838
\(695\) −7.27492 + 12.6005i −0.275953 + 0.477965i
\(696\) 1.50000 0.866025i 0.0568574 0.0328266i
\(697\) 18.2749 + 31.6531i 0.692212 + 1.19895i
\(698\) 30.9244 + 17.8542i 1.17051 + 0.675792i
\(699\) 8.35671i 0.316080i
\(700\) 4.86254 10.2118i 0.183787 0.385968i
\(701\) 40.0997 1.51454 0.757272 0.653100i \(-0.226532\pi\)
0.757272 + 0.653100i \(0.226532\pi\)
\(702\) −15.8248 + 27.4093i −0.597267 + 1.03450i
\(703\) −0.512045 + 0.295629i −0.0193121 + 0.0111499i
\(704\) 2.50000 2.17945i 0.0942223 0.0821411i
\(705\) 49.6495 + 28.6652i 1.86991 + 1.07959i
\(706\) 15.7611i 0.593176i
\(707\) 19.2371 + 27.9509i 0.723487 + 1.05120i
\(708\) 3.00000 0.112747
\(709\) 13.8625 24.0106i 0.520619 0.901738i −0.479094 0.877764i \(-0.659035\pi\)
0.999713 0.0239743i \(-0.00763200\pi\)
\(710\) −8.54983 14.8087i −0.320870 0.555762i
\(711\) 16.9124 9.76436i 0.634264 0.366192i
\(712\) −5.27492 3.04547i −0.197686 0.114134i
\(713\) 20.1775i 0.755654i
\(714\) −16.1375 + 11.1066i −0.603929 + 0.415653i
\(715\) −11.8248 60.3758i −0.442221 2.25793i
\(716\) −16.1375 9.31697i −0.603085 0.348191i
\(717\) 3.82475 2.20822i 0.142838 0.0824675i
\(718\) −9.82475 17.0170i −0.366656 0.635068i
\(719\) 24.4124 + 14.0945i 0.910428 + 0.525636i 0.880569 0.473918i \(-0.157161\pi\)
0.0298592 + 0.999554i \(0.490494\pi\)
\(720\) 9.13642i 0.340494i
\(721\) −19.4502 + 40.8471i −0.724362 + 1.52122i
\(722\) 14.3746 0.534967
\(723\) −7.91238 + 13.7046i −0.294264 + 0.509681i
\(724\) −4.27492 7.40437i −0.158876 0.275181i
\(725\) −2.13746 3.70219i −0.0793832 0.137496i
\(726\) −18.8746 2.59808i −0.700502 0.0964237i
\(727\) 2.72508 0.101068 0.0505339 0.998722i \(-0.483908\pi\)
0.0505339 + 0.998722i \(0.483908\pi\)
\(728\) −1.27492 16.0646i −0.0472516 0.595395i
\(729\) −27.0000 −1.00000
\(730\) 18.5498 32.1293i 0.686560 1.18916i
\(731\) 20.7870 12.0014i 0.768834 0.443886i
\(732\) 6.00000 + 10.3923i 0.221766 + 0.384111i
\(733\) 2.90033 + 1.67451i 0.107126 + 0.0618493i 0.552606 0.833443i \(-0.313634\pi\)
−0.445480 + 0.895292i \(0.646967\pi\)
\(734\) 25.2749 0.932914
\(735\) −36.4622 + 5.82409i −1.34493 + 0.214825i
\(736\) 7.40437i 0.272929i
\(737\) −20.5498 7.04329i −0.756963 0.259443i
\(738\) −12.8248 22.2131i −0.472086 0.817676i
\(739\) −24.0997 + 13.9140i −0.886521 + 0.511833i −0.872803 0.488073i \(-0.837700\pi\)
−0.0137178 + 0.999906i \(0.504367\pi\)
\(740\) 0.725083 + 0.418627i 0.0266546 + 0.0153890i
\(741\) 22.6893i 0.833512i
\(742\) −1.73713 21.8887i −0.0637720 0.803560i
\(743\) −47.6495 −1.74809 −0.874045 0.485844i \(-0.838512\pi\)
−0.874045 + 0.485844i \(0.838512\pi\)
\(744\) −4.08762 2.35999i −0.149860 0.0865215i
\(745\) −0.725083 + 0.418627i −0.0265650 + 0.0153373i
\(746\) 22.5498 13.0192i 0.825608 0.476665i
\(747\) −4.08762 + 7.07997i −0.149558 + 0.259043i
\(748\) 2.72508 + 13.9140i 0.0996389 + 0.508744i
\(749\) 7.64950 16.0646i 0.279507 0.586989i
\(750\) −3.82475 −0.139660
\(751\) −13.3625 + 23.1446i −0.487606 + 0.844558i −0.999898 0.0142526i \(-0.995463\pi\)
0.512292 + 0.858811i \(0.328796\pi\)
\(752\) 9.41238 5.43424i 0.343234 0.198166i
\(753\) −6.77492 11.7345i −0.246892 0.427629i
\(754\) −5.27492 3.04547i −0.192101 0.110910i
\(755\) −36.9244 −1.34382
\(756\) 11.3248 7.79423i 0.411877 0.283473i
\(757\) −32.4743 −1.18030 −0.590148 0.807295i \(-0.700931\pi\)
−0.590148 + 0.807295i \(0.700931\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) −32.0619 + 27.9509i −1.16377 + 1.01455i
\(760\) 3.27492 + 5.67232i 0.118794 + 0.205757i
\(761\) −10.0997 + 17.4931i −0.366113 + 0.634126i −0.988954 0.148222i \(-0.952645\pi\)
0.622841 + 0.782348i \(0.285978\pi\)
\(762\) 24.0997 0.873039
\(763\) 28.3746 19.5287i 1.02723 0.706987i
\(764\) 14.8087i 0.535762i
\(765\) −33.8248 19.5287i −1.22294 0.706063i
\(766\) −15.5120 + 8.95588i −0.560473 + 0.323589i
\(767\) −5.27492 9.13642i −0.190466 0.329897i
\(768\) 1.50000 + 0.866025i 0.0541266 + 0.0312500i
\(769\) 18.8066i 0.678182i 0.940754 + 0.339091i \(0.110119\pi\)
−0.940754 + 0.339091i \(0.889881\pi\)
\(770\) −6.63746 + 25.8865i −0.239197 + 0.932886i
\(771\) −13.4502 −0.484396
\(772\) 15.3625 + 8.86957i 0.552910 + 0.319223i
\(773\) 12.0000 6.92820i 0.431610 0.249190i −0.268422 0.963301i \(-0.586502\pi\)
0.700032 + 0.714111i \(0.253169\pi\)
\(774\) −14.5876 + 8.42217i −0.524341 + 0.302729i
\(775\) −5.82475 + 10.0888i −0.209231 + 0.362399i
\(776\) 1.54983 0.0556358
\(777\) −0.0996689 1.25588i −0.00357560 0.0450545i
\(778\) 0 0
\(779\) −15.9244 9.19397i −0.570552 0.329408i
\(780\) 27.8248 16.0646i 0.996286 0.575206i
\(781\) 12.2371 + 14.0369i 0.437879 + 0.502281i
\(782\) 27.4124 + 15.8265i 0.980265 + 0.565956i
\(783\) 5.19615i 0.185695i
\(784\) −2.50000 + 6.53835i −0.0892857 + 0.233512i
\(785\) 29.6175i 1.05709i
\(786\) 4.08762 + 2.35999i 0.145801 + 0.0841781i
\(787\) 13.7629 7.94600i 0.490593 0.283244i −0.234227 0.972182i \(-0.575256\pi\)
0.724821 + 0.688938i \(0.241923\pi\)
\(788\) −10.1375 17.5586i −0.361132 0.625499i
\(789\) 1.64950 + 0.952341i 0.0587239 + 0.0339042i
\(790\) −19.8248 −0.705333
\(791\) 0 0
\(792\) −1.91238 9.76436i −0.0679533 0.346962i
\(793\) 21.0997 36.5457i 0.749271 1.29778i
\(794\) 9.13746 + 15.8265i 0.324276 + 0.561663i
\(795\) 37.9124 21.8887i 1.34461 0.776313i
\(796\) 0 0
\(797\) 11.6482i 0.412600i 0.978489 + 0.206300i \(0.0661423\pi\)
−0.978489 + 0.206300i \(0.933858\pi\)
\(798\) 4.23713 8.89834i 0.149993 0.314998i
\(799\) 46.4618i 1.64370i
\(800\) 2.13746 3.70219i 0.0755706 0.130892i
\(801\) −15.8248 + 9.13642i −0.559140 + 0.322820i
\(802\) 25.6495 14.8087i 0.905715 0.522915i
\(803\) −13.0997 + 38.2202i −0.462277 + 1.34876i
\(804\) 11.3446i 0.400095i
\(805\) 33.8248 + 49.1462i 1.19217 + 1.73218i
\(806\) 16.5983i 0.584652i
\(807\) −13.9124 + 24.0969i −0.489739 + 0.848253i
\(808\) 6.41238 + 11.1066i 0.225587 + 0.390727i
\(809\) 6.82475 + 11.8208i 0.239945 + 0.415598i 0.960698 0.277594i \(-0.0895371\pi\)
−0.720753 + 0.693192i \(0.756204\pi\)
\(810\) 23.7371 + 13.7046i 0.834038 + 0.481532i
\(811\) 17.3205i 0.608205i −0.952639 0.304103i \(-0.901643\pi\)
0.952639 0.304103i \(-0.0983566\pi\)
\(812\) 1.50000 + 2.17945i 0.0526397 + 0.0764837i
\(813\) −53.4743 −1.87542
\(814\) −0.862541 0.295629i −0.0302321 0.0103618i
\(815\) −3.82475 + 2.20822i −0.133975 + 0.0773506i
\(816\) −6.41238 + 3.70219i −0.224478 + 0.129602i
\(817\) −6.03779 + 10.4578i −0.211236 + 0.365871i
\(818\) 36.0120i 1.25913i
\(819\) −43.6495 20.7846i −1.52524 0.726273i
\(820\) 26.0383i 0.909297i
\(821\) 13.4622 23.3172i 0.469834 0.813777i −0.529571 0.848266i \(-0.677647\pi\)
0.999405 + 0.0344888i \(0.0109803\pi\)
\(822\) −11.2749 19.5287i −0.393258 0.681143i
\(823\) −28.5498 49.4498i −0.995185 1.72371i −0.582478 0.812846i \(-0.697917\pi\)
−0.412706 0.910864i \(-0.635416\pi\)
\(824\) −8.54983 + 14.8087i −0.297848 + 0.515887i
\(825\) −24.0997 + 4.71998i −0.839043 + 0.164329i
\(826\) 0.362541 + 4.56821i 0.0126144 + 0.158948i
\(827\) 23.4743 0.816280 0.408140 0.912919i \(-0.366178\pi\)
0.408140 + 0.912919i \(0.366178\pi\)
\(828\) −19.2371 11.1066i −0.668536 0.385980i
\(829\) −10.6873 18.5109i −0.371185 0.642911i 0.618563 0.785735i \(-0.287715\pi\)
−0.989748 + 0.142824i \(0.954382\pi\)
\(830\) 7.18729 4.14959i 0.249475 0.144034i
\(831\) 22.5498 39.0575i 0.782245 1.35489i
\(832\) 6.09095i 0.211166i
\(833\) −18.8625 23.2309i −0.653548 0.804904i
\(834\) 8.27492 0.286537
\(835\) −59.4743 34.3375i −2.05819 1.18830i
\(836\) −4.68729 5.37669i −0.162113 0.185957i
\(837\) −12.2629 + 7.07997i −0.423867 + 0.244720i
\(838\) 19.8625 + 11.4676i 0.686140 + 0.396143i
\(839\) 39.7796i 1.37335i −0.726967 0.686673i \(-0.759071\pi\)
0.726967 0.686673i \(-0.240929\pi\)
\(840\) −13.9124 + 1.10411i −0.480023 + 0.0380954i
\(841\) −28.0000 −0.965517
\(842\) 7.68729 13.3148i 0.264922 0.458858i
\(843\) 5.58762 3.22602i 0.192448 0.111110i
\(844\) −9.72508 + 5.61478i −0.334751 + 0.193269i
\(845\) −63.5619 36.6975i −2.18660 1.26243i
\(846\) 32.6054i 1.12100i
\(847\) 1.67525 29.0550i 0.0575622 0.998342i
\(848\) 8.29917i 0.284995i
\(849\) −2.27492 + 3.94027i −0.0780750 + 0.135230i
\(850\) 9.13746 + 15.8265i 0.313412 + 0.542846i
\(851\) −1.76287 + 1.01779i −0.0604305 + 0.0348896i
\(852\) −4.86254 + 8.42217i −0.166588 + 0.288539i
\(853\) 30.4547i 1.04275i −0.853327 0.521375i \(-0.825419\pi\)
0.853327 0.521375i \(-0.174581\pi\)
\(854\) −15.0997 + 10.3923i −0.516700 + 0.355617i
\(855\) 19.6495 0.671999
\(856\) 3.36254 5.82409i 0.114929 0.199063i
\(857\) −4.86254 8.42217i −0.166101 0.287696i 0.770945 0.636902i \(-0.219785\pi\)
−0.937046 + 0.349206i \(0.886451\pi\)
\(858\) −26.3746 + 22.9928i −0.900414 + 0.784962i
\(859\) −14.0000 + 24.2487i −0.477674 + 0.827355i −0.999672 0.0255910i \(-0.991853\pi\)
0.521999 + 0.852946i \(0.325187\pi\)
\(860\) 17.0997 0.583094
\(861\) 32.2749 22.2131i 1.09993 0.757021i
\(862\) 12.0000 0.408722
\(863\) 27.1993 + 15.7035i 0.925876 + 0.534555i 0.885505 0.464630i \(-0.153813\pi\)
0.0403712 + 0.999185i \(0.487146\pi\)
\(864\) 4.50000 2.59808i 0.153093 0.0883883i
\(865\) −36.9244 + 21.3183i −1.25547 + 0.724845i
\(866\) −2.13746 + 3.70219i −0.0726338 + 0.125805i
\(867\) 2.20822i 0.0749951i
\(868\) 3.09967 6.50958i 0.105210 0.220949i
\(869\) 21.1873 4.14959i 0.718730 0.140765i
\(870\) −2.63746 + 4.56821i −0.0894182 + 0.154877i
\(871\) −34.5498 + 19.9474i −1.17068 + 0.675890i
\(872\) 11.2749 6.50958i 0.381817 0.220442i
\(873\) 2.32475 4.02659i 0.0786809 0.136279i
\(874\) −15.9244 −0.538652
\(875\) −0.462210 5.82409i −0.0156256 0.196890i
\(876\) −21.0997 −0.712892
\(877\) 25.6495 + 14.8087i 0.866122 + 0.500056i 0.866058 0.499944i \(-0.166646\pi\)
6.45221e−5 1.00000i \(0.499979\pi\)
\(878\) −20.3248 + 11.7345i −0.685927 + 0.396020i
\(879\) −36.1495 + 20.8709i −1.21929 + 0.703959i
\(880\) −3.27492 + 9.55505i −0.110397 + 0.322101i
\(881\) 49.5649i 1.66988i 0.550339 + 0.834941i \(0.314498\pi\)
−0.550339 + 0.834941i \(0.685502\pi\)
\(882\) 13.2371 + 16.3027i 0.445717 + 0.548941i
\(883\) 26.1993 0.881678 0.440839 0.897586i \(-0.354681\pi\)
0.440839 + 0.897586i \(0.354681\pi\)
\(884\) 22.5498 + 13.0192i 0.758433 + 0.437882i
\(885\) −7.91238 + 4.56821i −0.265972 + 0.153559i
\(886\) 12.0498 6.95698i 0.404822 0.233724i
\(887\) 11.2749 19.5287i 0.378575 0.655711i −0.612280 0.790641i \(-0.709748\pi\)
0.990855 + 0.134930i \(0.0430810\pi\)
\(888\) 0.476171i 0.0159792i
\(889\) 2.91238 + 36.6975i 0.0976780 + 1.23079i
\(890\) 18.5498 0.621792
\(891\) −28.2371 9.67805i −0.945979 0.324227i
\(892\) 9.91238 + 17.1687i 0.331891 + 0.574852i
\(893\) −11.6873 20.2430i −0.391100 0.677406i
\(894\) 0.412376 + 0.238085i 0.0137919 + 0.00796276i
\(895\) 56.7492 1.89692
\(896\) −1.13746 + 2.38876i −0.0379998 + 0.0798030i
\(897\) 78.1149i 2.60818i
\(898\) 11.2749 + 6.50958i 0.376249 + 0.217227i
\(899\) −1.36254 2.35999i −0.0454433 0.0787101i
\(900\) −6.41238 11.1066i −0.213746 0.370219i
\(901\) 30.7251 + 17.7391i 1.02360 + 0.590976i
\(902\) −5.45017 27.8279i −0.181471 0.926568i
\(903\) −14.5876 21.1953i −0.485446 0.705336i
\(904\) 0 0
\(905\) 22.5498 + 13.0192i 0.749582 + 0.432771i
\(906\) 10.5000 + 18.1865i 0.348839 + 0.604207i
\(907\) −13.2749 22.9928i −0.440786 0.763464i 0.556962 0.830538i \(-0.311967\pi\)
−0.997748 + 0.0670738i \(0.978634\pi\)
\(908\) −7.18729 + 12.4488i −0.238519 + 0.413127i
\(909\) 38.4743 1.27611
\(910\) 27.8248 + 40.4284i 0.922382 + 1.34019i
\(911\) 12.7732i 0.423194i 0.977357 + 0.211597i \(0.0678664\pi\)
−0.977357 + 0.211597i \(0.932134\pi\)
\(912\) 1.86254 3.22602i 0.0616749 0.106824i
\(913\) −6.81271 + 5.93918i −0.225468 + 0.196558i
\(914\) −32.8368 + 18.9583i −1.08614 + 0.627086i
\(915\) −31.6495 18.2728i −1.04630 0.604082i
\(916\) 8.54983 0.282494
\(917\) −3.09967 + 6.50958i −0.102360 + 0.214965i
\(918\) 22.2131i 0.733142i
\(919\) −38.6873 22.3361i −1.27618 0.736801i −0.300033 0.953929i \(-0.596998\pi\)
−0.976143 + 0.217128i \(0.930331\pi\)
\(920\) 11.2749 + 19.5287i 0.371723 + 0.643843i
\(921\) 13.5498 + 23.4690i 0.446482 + 0.773330i
\(922\) 6.41238 11.1066i 0.211180 0.365775i
\(923\) 34.1993 1.12568
\(924\) 14.6375 4.09204i 0.481537 0.134618i
\(925\) −1.17525 −0.0386419
\(926\) −10.0000 + 17.3205i −0.328620 + 0.569187i
\(927\) 25.6495 + 44.4262i 0.842440 + 1.45915i
\(928\) 0.500000 + 0.866025i 0.0164133 + 0.0284287i
\(929\) −1.45017 0.837253i −0.0475784 0.0274694i 0.476022 0.879433i \(-0.342078\pi\)
−0.523601 + 0.851964i \(0.675412\pi\)
\(930\) 14.3746 0.471361
\(931\) 14.0619 + 5.37669i 0.460859 + 0.176214i
\(932\) −4.82475 −0.158040
\(933\) 19.1375 33.1471i 0.626532 1.08519i
\(934\) 20.6873 11.9438i 0.676909 0.390814i
\(935\) −28.3746 32.5479i −0.927948 1.06443i
\(936\) −15.8248 9.13642i −0.517248 0.298633i
\(937\) 16.9019i 0.552160i 0.961135 + 0.276080i \(0.0890355\pi\)
−0.961135 + 0.276080i \(0.910964\pi\)
\(938\) 17.2749 1.37097i 0.564046 0.0447637i
\(939\) 12.1244i 0.395663i
\(940\) −16.5498 + 28.6652i −0.539796 + 0.934954i
\(941\) 13.5997 + 23.5553i 0.443337 + 0.767881i 0.997935 0.0642369i \(-0.0204613\pi\)
−0.554598 + 0.832118i \(0.687128\pi\)
\(942\) −14.5876 + 8.42217i −0.475290 + 0.274409i
\(943\) −54.8248 31.6531i −1.78534 1.03077i
\(944\) 1.73205i 0.0563735i
\(945\) −18.0000 + 37.8016i −0.585540 + 1.22969i
\(946\) −18.2749 + 3.57919i −0.594169 + 0.116369i
\(947\) −19.2371 11.1066i −0.625123 0.360915i 0.153738 0.988112i \(-0.450869\pi\)
−0.778861 + 0.627197i \(0.784202\pi\)
\(948\) 5.63746 + 9.76436i 0.183096 + 0.317132i
\(949\) 37.0997 + 64.2585i 1.20431 + 2.08592i
\(950\) −7.96221 4.59698i −0.258328 0.149146i
\(951\) −14.3746 −0.466128
\(952\) −6.41238 9.31697i −0.207826 0.301965i
\(953\) 17.6495 0.571723 0.285862 0.958271i \(-0.407720\pi\)
0.285862 + 0.958271i \(0.407720\pi\)
\(954\) −21.5619 12.4488i −0.698092 0.403043i
\(955\) 22.5498 + 39.0575i 0.729696 + 1.26387i
\(956\) 1.27492 + 2.20822i 0.0412338 + 0.0714190i
\(957\) 1.86254 5.43424i 0.0602074 0.175664i
\(958\) 28.0000 0.904639
\(959\) 28.3746 19.5287i 0.916263 0.630616i
\(960\) −5.27492 −0.170247
\(961\) 11.7870 20.4156i 0.380225 0.658568i
\(962\) −1.45017 + 0.837253i −0.0467552 + 0.0269941i
\(963\) −10.0876 17.4723i −0.325069 0.563036i
\(964\) −7.91238 4.56821i −0.254840 0.147132i
\(965\) −54.0241 −1.73910
\(966\) 14.5876 30.6353i 0.469349 0.985674i
\(967\) 10.3348i 0.332344i 0.986097 + 0.166172i \(0.0531406\pi\)
−0.986097 + 0.166172i \(0.946859\pi\)
\(968\) 1.50000 10.8972i 0.0482118 0.350251i
\(969\) 7.96221 + 13.7910i 0.255783 + 0.443029i
\(970\) −4.08762 + 2.35999i −0.131246 + 0.0757747i
\(971\) −15.2629 8.81202i −0.489809 0.282791i 0.234686 0.972071i \(-0.424594\pi\)
−0.724495 + 0.689280i \(0.757927\pi\)
\(972\) 15.5885i 0.500000i
\(973\) 1.00000 + 12.6005i 0.0320585 + 0.403954i
\(974\) 18.3746 0.588760
\(975\) −22.5498 + 39.0575i −0.722173 + 1.25084i
\(976\) −6.00000 + 3.46410i −0.192055 + 0.110883i
\(977\) −3.09967 + 1.78959i −0.0991672 + 0.0572542i −0.548763 0.835978i \(-0.684901\pi\)
0.449596 + 0.893232i \(0.351568\pi\)
\(978\) 2.17525 + 1.25588i 0.0695568 + 0.0401586i
\(979\) −19.8248 + 3.88273i −0.633602 + 0.124093i
\(980\) −3.36254 21.0515i −0.107412 0.672464i
\(981\) 39.0575i 1.24701i
\(982\) 11.1873 19.3770i 0.357001 0.618344i
\(983\) 0.312707 0.180541i 0.00997380 0.00575838i −0.495005 0.868890i \(-0.664834\pi\)
0.504979 + 0.863132i \(0.331500\pi\)
\(984\) 12.8248 7.40437i 0.408838 0.236043i
\(985\) 53.4743 + 30.8734i 1.70383 + 0.983708i
\(986\) −4.27492 −0.136141
\(987\) 49.6495 3.94027i 1.58036 0.125420i
\(988\) −13.0997 −0.416756
\(989\) −20.7870 + 36.0041i −0.660987 + 1.14486i
\(990\) 19.9124 + 22.8411i 0.632857 + 0.725937i
\(991\) 3.91238 + 6.77643i 0.124281 + 0.215261i 0.921452 0.388493i \(-0.127004\pi\)
−0.797171 + 0.603754i \(0.793671\pi\)
\(992\) 1.36254 2.35999i 0.0432607 0.0749298i
\(993\) 43.4739i 1.37960i
\(994\) −13.4124 6.38658i −0.425415 0.202570i
\(995\) 0 0
\(996\) −4.08762 2.35999i −0.129521 0.0747792i
\(997\) 32.3746 18.6915i 1.02531 0.591965i 0.109675 0.993968i \(-0.465019\pi\)
0.915639 + 0.402003i \(0.131686\pi\)
\(998\) −9.27492 16.0646i −0.293592 0.508517i
\(999\) −1.23713 0.714256i −0.0391410 0.0225981i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 462.2.n.a.65.2 4
3.2 odd 2 462.2.n.d.65.1 yes 4
7.4 even 3 462.2.n.b.263.1 yes 4
11.10 odd 2 462.2.n.c.65.2 yes 4
21.11 odd 6 462.2.n.c.263.2 yes 4
33.32 even 2 462.2.n.b.65.1 yes 4
77.32 odd 6 462.2.n.d.263.1 yes 4
231.32 even 6 inner 462.2.n.a.263.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.n.a.65.2 4 1.1 even 1 trivial
462.2.n.a.263.2 yes 4 231.32 even 6 inner
462.2.n.b.65.1 yes 4 33.32 even 2
462.2.n.b.263.1 yes 4 7.4 even 3
462.2.n.c.65.2 yes 4 11.10 odd 2
462.2.n.c.263.2 yes 4 21.11 odd 6
462.2.n.d.65.1 yes 4 3.2 odd 2
462.2.n.d.263.1 yes 4 77.32 odd 6