Properties

Label 560.2.bd.b.141.20
Level $560$
Weight $2$
Character 560.141
Analytic conductor $4.472$
Analytic rank $0$
Dimension $52$
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] = [560,2,Mod(141,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.141");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bd (of order \(4\), 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: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 141.20
Character \(\chi\) \(=\) 560.141
Dual form 560.2.bd.b.421.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.912154 + 1.08073i) q^{2} +(-1.81546 - 1.81546i) q^{3} +(-0.335949 + 1.97158i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.306040 - 3.61800i) q^{6} +1.00000i q^{7} +(-2.43718 + 1.43532i) q^{8} +3.59179i q^{9} +O(q^{10})\) \(q+(0.912154 + 1.08073i) q^{2} +(-1.81546 - 1.81546i) q^{3} +(-0.335949 + 1.97158i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.306040 - 3.61800i) q^{6} +1.00000i q^{7} +(-2.43718 + 1.43532i) q^{8} +3.59179i q^{9} +(-1.40918 - 0.119200i) q^{10} +(2.54671 - 2.54671i) q^{11} +(4.18923 - 2.96943i) q^{12} +(-4.47686 - 4.47686i) q^{13} +(-1.08073 + 0.912154i) q^{14} +2.56745 q^{15} +(-3.77428 - 1.32470i) q^{16} -6.94064 q^{17} +(-3.88175 + 3.27627i) q^{18} +(0.422385 + 0.422385i) q^{19} +(-1.15657 - 1.63167i) q^{20} +(1.81546 - 1.81546i) q^{21} +(5.07530 + 0.429310i) q^{22} +2.52392i q^{23} +(7.03037 + 1.81885i) q^{24} -1.00000i q^{25} +(0.754684 - 8.92187i) q^{26} +(1.07438 - 1.07438i) q^{27} +(-1.97158 - 0.335949i) q^{28} +(-5.14200 - 5.14200i) q^{29} +(2.34191 + 2.77472i) q^{30} -4.19574 q^{31} +(-2.01108 - 5.28730i) q^{32} -9.24692 q^{33} +(-6.33093 - 7.50095i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(-7.08152 - 1.20666i) q^{36} +(-0.793799 + 0.793799i) q^{37} +(-0.0712032 + 0.841763i) q^{38} +16.2551i q^{39} +(0.708425 - 2.73827i) q^{40} -5.99164i q^{41} +(3.61800 + 0.306040i) q^{42} +(2.47186 - 2.47186i) q^{43} +(4.16549 + 5.87662i) q^{44} +(-2.53978 - 2.53978i) q^{45} +(-2.72767 + 2.30220i) q^{46} -1.71220 q^{47} +(4.44711 + 9.25699i) q^{48} -1.00000 q^{49} +(1.08073 - 0.912154i) q^{50} +(12.6005 + 12.6005i) q^{51} +(10.3305 - 7.32251i) q^{52} +(-4.42723 + 4.42723i) q^{53} +(2.14111 + 0.181112i) q^{54} +3.60160i q^{55} +(-1.43532 - 2.43718i) q^{56} -1.53365i q^{57} +(0.866809 - 10.2474i) q^{58} +(5.91194 - 5.91194i) q^{59} +(-0.862531 + 5.06194i) q^{60} +(6.31741 + 6.31741i) q^{61} +(-3.82717 - 4.53446i) q^{62} -3.59179 q^{63} +(3.87972 - 6.99627i) q^{64} +6.33124 q^{65} +(-8.43462 - 9.99341i) q^{66} +(-2.86753 - 2.86753i) q^{67} +(2.33170 - 13.6840i) q^{68} +(4.58207 - 4.58207i) q^{69} +(0.119200 - 1.40918i) q^{70} +6.72492i q^{71} +(-5.15537 - 8.75386i) q^{72} +11.9794i q^{73} +(-1.58195 - 0.133814i) q^{74} +(-1.81546 + 1.81546i) q^{75} +(-0.974666 + 0.690867i) q^{76} +(2.54671 + 2.54671i) q^{77} +(-17.5674 + 14.8272i) q^{78} -2.80562 q^{79} +(3.60552 - 1.73211i) q^{80} +6.87440 q^{81} +(6.47533 - 5.46530i) q^{82} +(10.4832 + 10.4832i) q^{83} +(2.96943 + 4.18923i) q^{84} +(4.90777 - 4.90777i) q^{85} +(4.92612 + 0.416691i) q^{86} +18.6702i q^{87} +(-2.55146 + 9.86215i) q^{88} +2.53289i q^{89} +(0.428142 - 5.06149i) q^{90} +(4.47686 - 4.47686i) q^{91} +(-4.97611 - 0.847907i) q^{92} +(7.61721 + 7.61721i) q^{93} +(-1.56179 - 1.85042i) q^{94} -0.597342 q^{95} +(-5.94785 + 13.2499i) q^{96} +8.10717 q^{97} +(-0.912154 - 1.08073i) q^{98} +(9.14727 + 9.14727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.912154 + 1.08073i 0.644991 + 0.764191i
\(3\) −1.81546 1.81546i −1.04816 1.04816i −0.998780 0.0493763i \(-0.984277\pi\)
−0.0493763 0.998780i \(-0.515723\pi\)
\(4\) −0.335949 + 1.97158i −0.167974 + 0.985791i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) 0.306040 3.61800i 0.124940 1.47704i
\(7\) 1.00000i 0.377964i
\(8\) −2.43718 + 1.43532i −0.861674 + 0.507462i
\(9\) 3.59179i 1.19726i
\(10\) −1.40918 0.119200i −0.445622 0.0376943i
\(11\) 2.54671 2.54671i 0.767863 0.767863i −0.209867 0.977730i \(-0.567303\pi\)
0.977730 + 0.209867i \(0.0673030\pi\)
\(12\) 4.18923 2.96943i 1.20933 0.857200i
\(13\) −4.47686 4.47686i −1.24166 1.24166i −0.959313 0.282346i \(-0.908887\pi\)
−0.282346 0.959313i \(-0.591113\pi\)
\(14\) −1.08073 + 0.912154i −0.288837 + 0.243784i
\(15\) 2.56745 0.662912
\(16\) −3.77428 1.32470i −0.943569 0.331175i
\(17\) −6.94064 −1.68335 −0.841676 0.539983i \(-0.818431\pi\)
−0.841676 + 0.539983i \(0.818431\pi\)
\(18\) −3.88175 + 3.27627i −0.914938 + 0.772224i
\(19\) 0.422385 + 0.422385i 0.0969017 + 0.0969017i 0.753896 0.656994i \(-0.228172\pi\)
−0.656994 + 0.753896i \(0.728172\pi\)
\(20\) −1.15657 1.63167i −0.258616 0.364853i
\(21\) 1.81546 1.81546i 0.396166 0.396166i
\(22\) 5.07530 + 0.429310i 1.08206 + 0.0915293i
\(23\) 2.52392i 0.526273i 0.964759 + 0.263137i \(0.0847570\pi\)
−0.964759 + 0.263137i \(0.915243\pi\)
\(24\) 7.03037 + 1.81885i 1.43507 + 0.371270i
\(25\) 1.00000i 0.200000i
\(26\) 0.754684 8.92187i 0.148006 1.74972i
\(27\) 1.07438 1.07438i 0.206764 0.206764i
\(28\) −1.97158 0.335949i −0.372594 0.0634883i
\(29\) −5.14200 5.14200i −0.954846 0.954846i 0.0441776 0.999024i \(-0.485933\pi\)
−0.999024 + 0.0441776i \(0.985933\pi\)
\(30\) 2.34191 + 2.77472i 0.427572 + 0.506591i
\(31\) −4.19574 −0.753578 −0.376789 0.926299i \(-0.622972\pi\)
−0.376789 + 0.926299i \(0.622972\pi\)
\(32\) −2.01108 5.28730i −0.355512 0.934672i
\(33\) −9.24692 −1.60968
\(34\) −6.33093 7.50095i −1.08575 1.28640i
\(35\) −0.707107 0.707107i −0.119523 0.119523i
\(36\) −7.08152 1.20666i −1.18025 0.201110i
\(37\) −0.793799 + 0.793799i −0.130500 + 0.130500i −0.769340 0.638840i \(-0.779415\pi\)
0.638840 + 0.769340i \(0.279415\pi\)
\(38\) −0.0712032 + 0.841763i −0.0115507 + 0.136552i
\(39\) 16.2551i 2.60291i
\(40\) 0.708425 2.73827i 0.112012 0.432959i
\(41\) 5.99164i 0.935736i −0.883798 0.467868i \(-0.845022\pi\)
0.883798 0.467868i \(-0.154978\pi\)
\(42\) 3.61800 + 0.306040i 0.558270 + 0.0472230i
\(43\) 2.47186 2.47186i 0.376954 0.376954i −0.493048 0.870002i \(-0.664117\pi\)
0.870002 + 0.493048i \(0.164117\pi\)
\(44\) 4.16549 + 5.87662i 0.627972 + 0.885934i
\(45\) −2.53978 2.53978i −0.378608 0.378608i
\(46\) −2.72767 + 2.30220i −0.402173 + 0.339441i
\(47\) −1.71220 −0.249750 −0.124875 0.992173i \(-0.539853\pi\)
−0.124875 + 0.992173i \(0.539853\pi\)
\(48\) 4.44711 + 9.25699i 0.641885 + 1.33613i
\(49\) −1.00000 −0.142857
\(50\) 1.08073 0.912154i 0.152838 0.128998i
\(51\) 12.6005 + 12.6005i 1.76442 + 1.76442i
\(52\) 10.3305 7.32251i 1.43258 1.01545i
\(53\) −4.42723 + 4.42723i −0.608127 + 0.608127i −0.942456 0.334329i \(-0.891490\pi\)
0.334329 + 0.942456i \(0.391490\pi\)
\(54\) 2.14111 + 0.181112i 0.291368 + 0.0246463i
\(55\) 3.60160i 0.485639i
\(56\) −1.43532 2.43718i −0.191803 0.325682i
\(57\) 1.53365i 0.203136i
\(58\) 0.866809 10.2474i 0.113818 1.34555i
\(59\) 5.91194 5.91194i 0.769669 0.769669i −0.208379 0.978048i \(-0.566819\pi\)
0.978048 + 0.208379i \(0.0668189\pi\)
\(60\) −0.862531 + 5.06194i −0.111352 + 0.653493i
\(61\) 6.31741 + 6.31741i 0.808862 + 0.808862i 0.984462 0.175600i \(-0.0561865\pi\)
−0.175600 + 0.984462i \(0.556186\pi\)
\(62\) −3.82717 4.53446i −0.486051 0.575877i
\(63\) −3.59179 −0.452523
\(64\) 3.87972 6.99627i 0.484965 0.874533i
\(65\) 6.33124 0.785294
\(66\) −8.43462 9.99341i −1.03823 1.23010i
\(67\) −2.86753 2.86753i −0.350325 0.350325i 0.509906 0.860230i \(-0.329680\pi\)
−0.860230 + 0.509906i \(0.829680\pi\)
\(68\) 2.33170 13.6840i 0.282760 1.65943i
\(69\) 4.58207 4.58207i 0.551617 0.551617i
\(70\) 0.119200 1.40918i 0.0142471 0.168429i
\(71\) 6.72492i 0.798101i 0.916929 + 0.399050i \(0.130660\pi\)
−0.916929 + 0.399050i \(0.869340\pi\)
\(72\) −5.15537 8.75386i −0.607566 1.03165i
\(73\) 11.9794i 1.40209i 0.713119 + 0.701043i \(0.247282\pi\)
−0.713119 + 0.701043i \(0.752718\pi\)
\(74\) −1.58195 0.133814i −0.183898 0.0155556i
\(75\) −1.81546 + 1.81546i −0.209631 + 0.209631i
\(76\) −0.974666 + 0.690867i −0.111802 + 0.0792479i
\(77\) 2.54671 + 2.54671i 0.290225 + 0.290225i
\(78\) −17.5674 + 14.8272i −1.98912 + 1.67885i
\(79\) −2.80562 −0.315657 −0.157829 0.987467i \(-0.550449\pi\)
−0.157829 + 0.987467i \(0.550449\pi\)
\(80\) 3.60552 1.73211i 0.403110 0.193656i
\(81\) 6.87440 0.763822
\(82\) 6.47533 5.46530i 0.715081 0.603541i
\(83\) 10.4832 + 10.4832i 1.15068 + 1.15068i 0.986417 + 0.164260i \(0.0525236\pi\)
0.164260 + 0.986417i \(0.447476\pi\)
\(84\) 2.96943 + 4.18923i 0.323991 + 0.457083i
\(85\) 4.90777 4.90777i 0.532323 0.532323i
\(86\) 4.92612 + 0.416691i 0.531197 + 0.0449330i
\(87\) 18.6702i 2.00166i
\(88\) −2.55146 + 9.86215i −0.271987 + 1.05131i
\(89\) 2.53289i 0.268486i 0.990948 + 0.134243i \(0.0428602\pi\)
−0.990948 + 0.134243i \(0.957140\pi\)
\(90\) 0.428142 5.06149i 0.0451301 0.533528i
\(91\) 4.47686 4.47686i 0.469303 0.469303i
\(92\) −4.97611 0.847907i −0.518796 0.0884004i
\(93\) 7.61721 + 7.61721i 0.789868 + 0.789868i
\(94\) −1.56179 1.85042i −0.161086 0.190856i
\(95\) −0.597342 −0.0612860
\(96\) −5.94785 + 13.2499i −0.607050 + 1.35231i
\(97\) 8.10717 0.823158 0.411579 0.911374i \(-0.364977\pi\)
0.411579 + 0.911374i \(0.364977\pi\)
\(98\) −0.912154 1.08073i −0.0921415 0.109170i
\(99\) 9.14727 + 9.14727i 0.919335 + 0.919335i
\(100\) 1.97158 + 0.335949i 0.197158 + 0.0335949i
\(101\) −10.8669 + 10.8669i −1.08130 + 1.08130i −0.0849100 + 0.996389i \(0.527060\pi\)
−0.996389 + 0.0849100i \(0.972940\pi\)
\(102\) −2.12411 + 25.1112i −0.210318 + 2.48638i
\(103\) 14.9689i 1.47493i −0.675384 0.737466i \(-0.736022\pi\)
0.675384 0.737466i \(-0.263978\pi\)
\(104\) 17.3367 + 4.48521i 1.70000 + 0.439811i
\(105\) 2.56745i 0.250557i
\(106\) −8.82296 0.746318i −0.856962 0.0724888i
\(107\) 4.24500 4.24500i 0.410379 0.410379i −0.471491 0.881871i \(-0.656284\pi\)
0.881871 + 0.471491i \(0.156284\pi\)
\(108\) 1.75729 + 2.47916i 0.169095 + 0.238557i
\(109\) −3.81859 3.81859i −0.365754 0.365754i 0.500172 0.865926i \(-0.333270\pi\)
−0.865926 + 0.500172i \(0.833270\pi\)
\(110\) −3.89235 + 3.28521i −0.371121 + 0.313233i
\(111\) 2.88222 0.273568
\(112\) 1.32470 3.77428i 0.125172 0.356636i
\(113\) −18.9272 −1.78052 −0.890259 0.455455i \(-0.849476\pi\)
−0.890259 + 0.455455i \(0.849476\pi\)
\(114\) 1.65745 1.39892i 0.155235 0.131021i
\(115\) −1.78468 1.78468i −0.166422 0.166422i
\(116\) 11.8653 8.41044i 1.10167 0.780889i
\(117\) 16.0800 16.0800i 1.48659 1.48659i
\(118\) 11.7818 + 0.996600i 1.08460 + 0.0917445i
\(119\) 6.94064i 0.636247i
\(120\) −6.25734 + 3.68511i −0.571215 + 0.336403i
\(121\) 1.97151i 0.179228i
\(122\) −1.06495 + 12.5899i −0.0964163 + 1.13983i
\(123\) −10.8776 + 10.8776i −0.980798 + 0.980798i
\(124\) 1.40955 8.27226i 0.126582 0.742870i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) −3.27627 3.88175i −0.291873 0.345814i
\(127\) 1.13143 0.100399 0.0501993 0.998739i \(-0.484014\pi\)
0.0501993 + 0.998739i \(0.484014\pi\)
\(128\) 11.1000 2.18875i 0.981108 0.193460i
\(129\) −8.97511 −0.790215
\(130\) 5.77507 + 6.84236i 0.506507 + 0.600114i
\(131\) −1.90954 1.90954i −0.166837 0.166837i 0.618751 0.785588i \(-0.287639\pi\)
−0.785588 + 0.618751i \(0.787639\pi\)
\(132\) 3.10649 18.2311i 0.270385 1.58681i
\(133\) −0.422385 + 0.422385i −0.0366254 + 0.0366254i
\(134\) 0.483392 5.71465i 0.0417587 0.493671i
\(135\) 1.51940i 0.130769i
\(136\) 16.9156 9.96203i 1.45050 0.854237i
\(137\) 17.0771i 1.45900i −0.683983 0.729498i \(-0.739754\pi\)
0.683983 0.729498i \(-0.260246\pi\)
\(138\) 9.13154 + 0.772420i 0.777328 + 0.0657527i
\(139\) 11.0354 11.0354i 0.936008 0.936008i −0.0620644 0.998072i \(-0.519768\pi\)
0.998072 + 0.0620644i \(0.0197684\pi\)
\(140\) 1.63167 1.15657i 0.137901 0.0977478i
\(141\) 3.10843 + 3.10843i 0.261777 + 0.261777i
\(142\) −7.26781 + 6.13416i −0.609901 + 0.514768i
\(143\) −22.8026 −1.90685
\(144\) 4.75805 13.5564i 0.396504 1.12970i
\(145\) 7.27189 0.603898
\(146\) −12.9465 + 10.9271i −1.07146 + 0.904332i
\(147\) 1.81546 + 1.81546i 0.149737 + 0.149737i
\(148\) −1.29836 1.83172i −0.106725 0.150566i
\(149\) −5.52861 + 5.52861i −0.452921 + 0.452921i −0.896323 0.443402i \(-0.853771\pi\)
0.443402 + 0.896323i \(0.353771\pi\)
\(150\) −3.61800 0.306040i −0.295408 0.0249880i
\(151\) 17.6067i 1.43281i 0.697683 + 0.716407i \(0.254214\pi\)
−0.697683 + 0.716407i \(0.745786\pi\)
\(152\) −1.63569 0.423172i −0.132672 0.0343238i
\(153\) 24.9293i 2.01542i
\(154\) −0.429310 + 5.07530i −0.0345948 + 0.408980i
\(155\) 2.96684 2.96684i 0.238302 0.238302i
\(156\) −32.0484 5.46089i −2.56592 0.437221i
\(157\) −2.90009 2.90009i −0.231452 0.231452i 0.581846 0.813299i \(-0.302330\pi\)
−0.813299 + 0.581846i \(0.802330\pi\)
\(158\) −2.55916 3.03212i −0.203596 0.241222i
\(159\) 16.0749 1.27483
\(160\) 5.16074 + 2.31664i 0.407992 + 0.183146i
\(161\) −2.52392 −0.198913
\(162\) 6.27052 + 7.42936i 0.492658 + 0.583706i
\(163\) −7.00743 7.00743i −0.548864 0.548864i 0.377248 0.926112i \(-0.376870\pi\)
−0.926112 + 0.377248i \(0.876870\pi\)
\(164\) 11.8130 + 2.01288i 0.922441 + 0.157180i
\(165\) 6.53856 6.53856i 0.509026 0.509026i
\(166\) −1.76719 + 20.8917i −0.137161 + 1.62151i
\(167\) 16.2345i 1.25627i 0.778106 + 0.628133i \(0.216181\pi\)
−0.778106 + 0.628133i \(0.783819\pi\)
\(168\) −1.81885 + 7.03037i −0.140327 + 0.542405i
\(169\) 27.0846i 2.08343i
\(170\) 9.78062 + 0.827324i 0.750139 + 0.0634528i
\(171\) −1.51712 + 1.51712i −0.116017 + 0.116017i
\(172\) 4.04305 + 5.70388i 0.308280 + 0.434917i
\(173\) −16.5096 16.5096i −1.25520 1.25520i −0.953357 0.301844i \(-0.902398\pi\)
−0.301844 0.953357i \(-0.597602\pi\)
\(174\) −20.1774 + 17.0301i −1.52965 + 1.29105i
\(175\) 1.00000 0.0755929
\(176\) −12.9856 + 6.23837i −0.978829 + 0.470235i
\(177\) −21.4658 −1.61347
\(178\) −2.73737 + 2.31039i −0.205174 + 0.173171i
\(179\) −9.36773 9.36773i −0.700177 0.700177i 0.264271 0.964448i \(-0.414869\pi\)
−0.964448 + 0.264271i \(0.914869\pi\)
\(180\) 5.86063 4.15415i 0.436825 0.309632i
\(181\) 13.1534 13.1534i 0.977684 0.977684i −0.0220723 0.999756i \(-0.507026\pi\)
0.999756 + 0.0220723i \(0.00702639\pi\)
\(182\) 8.92187 + 0.754684i 0.661333 + 0.0559409i
\(183\) 22.9380i 1.69563i
\(184\) −3.62263 6.15125i −0.267064 0.453476i
\(185\) 1.12260i 0.0825353i
\(186\) −1.28406 + 15.1802i −0.0941522 + 1.11307i
\(187\) −17.6758 + 17.6758i −1.29258 + 1.29258i
\(188\) 0.575210 3.37574i 0.0419515 0.246201i
\(189\) 1.07438 + 1.07438i 0.0781494 + 0.0781494i
\(190\) −0.544868 0.645565i −0.0395289 0.0468342i
\(191\) −18.4360 −1.33398 −0.666992 0.745065i \(-0.732418\pi\)
−0.666992 + 0.745065i \(0.732418\pi\)
\(192\) −19.7449 + 5.65797i −1.42497 + 0.408329i
\(193\) 5.73208 0.412604 0.206302 0.978488i \(-0.433857\pi\)
0.206302 + 0.978488i \(0.433857\pi\)
\(194\) 7.39499 + 8.76165i 0.530929 + 0.629050i
\(195\) −11.4941 11.4941i −0.823111 0.823111i
\(196\) 0.335949 1.97158i 0.0239963 0.140827i
\(197\) −1.72742 + 1.72742i −0.123074 + 0.123074i −0.765961 0.642887i \(-0.777736\pi\)
0.642887 + 0.765961i \(0.277736\pi\)
\(198\) −1.54199 + 18.2294i −0.109585 + 1.29551i
\(199\) 17.8793i 1.26743i 0.773565 + 0.633717i \(0.218471\pi\)
−0.773565 + 0.633717i \(0.781529\pi\)
\(200\) 1.43532 + 2.43718i 0.101492 + 0.172335i
\(201\) 10.4118i 0.734390i
\(202\) −21.6565 1.83188i −1.52375 0.128891i
\(203\) 5.14200 5.14200i 0.360898 0.360898i
\(204\) −29.0759 + 20.6097i −2.03572 + 1.44297i
\(205\) 4.23673 + 4.23673i 0.295906 + 0.295906i
\(206\) 16.1773 13.6540i 1.12713 0.951317i
\(207\) −9.06539 −0.630088
\(208\) 10.9664 + 22.8274i 0.760384 + 1.58280i
\(209\) 2.15139 0.148815
\(210\) −2.77472 + 2.34191i −0.191474 + 0.161607i
\(211\) −14.0989 14.0989i −0.970606 0.970606i 0.0289744 0.999580i \(-0.490776\pi\)
−0.999580 + 0.0289744i \(0.990776\pi\)
\(212\) −7.24134 10.2160i −0.497337 0.701637i
\(213\) 12.2088 12.2088i 0.836535 0.836535i
\(214\) 8.45978 + 0.715597i 0.578299 + 0.0489172i
\(215\) 3.49573i 0.238407i
\(216\) −1.07638 + 4.16053i −0.0732384 + 0.283088i
\(217\) 4.19574i 0.284826i
\(218\) 0.643716 7.61000i 0.0435979 0.515414i
\(219\) 21.7482 21.7482i 1.46960 1.46960i
\(220\) −7.10085 1.20995i −0.478739 0.0815749i
\(221\) 31.0723 + 31.0723i 2.09015 + 2.09015i
\(222\) 2.62903 + 3.11490i 0.176449 + 0.209058i
\(223\) 23.1771 1.55205 0.776027 0.630699i \(-0.217232\pi\)
0.776027 + 0.630699i \(0.217232\pi\)
\(224\) 5.28730 2.01108i 0.353273 0.134371i
\(225\) 3.59179 0.239453
\(226\) −17.2645 20.4551i −1.14842 1.36065i
\(227\) −13.0632 13.0632i −0.867033 0.867033i 0.125110 0.992143i \(-0.460072\pi\)
−0.992143 + 0.125110i \(0.960072\pi\)
\(228\) 3.02371 + 0.515226i 0.200250 + 0.0341217i
\(229\) −12.1266 + 12.1266i −0.801349 + 0.801349i −0.983306 0.181957i \(-0.941757\pi\)
0.181957 + 0.983306i \(0.441757\pi\)
\(230\) 0.300851 3.55666i 0.0198375 0.234519i
\(231\) 9.24692i 0.608403i
\(232\) 19.9124 + 5.15159i 1.30731 + 0.338218i
\(233\) 24.8161i 1.62576i −0.582433 0.812879i \(-0.697899\pi\)
0.582433 0.812879i \(-0.302101\pi\)
\(234\) 32.0455 + 2.71067i 2.09488 + 0.177202i
\(235\) 1.21071 1.21071i 0.0789778 0.0789778i
\(236\) 9.66976 + 13.6420i 0.629448 + 0.888017i
\(237\) 5.09350 + 5.09350i 0.330858 + 0.330858i
\(238\) 7.50095 6.33093i 0.486214 0.410373i
\(239\) 16.3724 1.05905 0.529523 0.848296i \(-0.322371\pi\)
0.529523 + 0.848296i \(0.322371\pi\)
\(240\) −9.69026 3.40110i −0.625504 0.219540i
\(241\) −4.15685 −0.267766 −0.133883 0.990997i \(-0.542745\pi\)
−0.133883 + 0.990997i \(0.542745\pi\)
\(242\) 2.13066 1.79832i 0.136964 0.115600i
\(243\) −15.7033 15.7033i −1.00737 1.00737i
\(244\) −14.5776 + 10.3330i −0.933237 + 0.661501i
\(245\) 0.707107 0.707107i 0.0451754 0.0451754i
\(246\) −21.6777 1.83368i −1.38212 0.116911i
\(247\) 3.78192i 0.240638i
\(248\) 10.2258 6.02223i 0.649339 0.382412i
\(249\) 38.0635i 2.41218i
\(250\) −0.119200 + 1.40918i −0.00753887 + 0.0891244i
\(251\) −19.0523 + 19.0523i −1.20257 + 1.20257i −0.229190 + 0.973382i \(0.573608\pi\)
−0.973382 + 0.229190i \(0.926392\pi\)
\(252\) 1.20666 7.08152i 0.0760123 0.446094i
\(253\) 6.42770 + 6.42770i 0.404106 + 0.404106i
\(254\) 1.03204 + 1.22277i 0.0647561 + 0.0767236i
\(255\) −17.8197 −1.11591
\(256\) 12.4903 + 9.99958i 0.780646 + 0.624974i
\(257\) −23.4022 −1.45979 −0.729896 0.683558i \(-0.760432\pi\)
−0.729896 + 0.683558i \(0.760432\pi\)
\(258\) −8.18669 9.69966i −0.509681 0.603875i
\(259\) −0.793799 0.793799i −0.0493243 0.0493243i
\(260\) −2.12697 + 12.4826i −0.131909 + 0.774136i
\(261\) 18.4690 18.4690i 1.14320 1.14320i
\(262\) 0.321899 3.80548i 0.0198870 0.235104i
\(263\) 0.465779i 0.0287212i −0.999897 0.0143606i \(-0.995429\pi\)
0.999897 0.0143606i \(-0.00457127\pi\)
\(264\) 22.5364 13.2723i 1.38702 0.816852i
\(265\) 6.26106i 0.384614i
\(266\) −0.841763 0.0712032i −0.0516118 0.00436575i
\(267\) 4.59836 4.59836i 0.281415 0.281415i
\(268\) 6.61691 4.69023i 0.404192 0.286501i
\(269\) −13.2699 13.2699i −0.809080 0.809080i 0.175415 0.984495i \(-0.443873\pi\)
−0.984495 + 0.175415i \(0.943873\pi\)
\(270\) −1.64206 + 1.38593i −0.0999325 + 0.0843448i
\(271\) 20.8313 1.26541 0.632707 0.774391i \(-0.281944\pi\)
0.632707 + 0.774391i \(0.281944\pi\)
\(272\) 26.1959 + 9.19427i 1.58836 + 0.557485i
\(273\) −16.2551 −0.983806
\(274\) 18.4557 15.5770i 1.11495 0.941038i
\(275\) −2.54671 2.54671i −0.153573 0.153573i
\(276\) 7.49460 + 10.5733i 0.451122 + 0.636437i
\(277\) 17.0034 17.0034i 1.02164 1.02164i 0.0218756 0.999761i \(-0.493036\pi\)
0.999761 0.0218756i \(-0.00696377\pi\)
\(278\) 21.9922 + 1.86028i 1.31900 + 0.111572i
\(279\) 15.0702i 0.902232i
\(280\) 2.73827 + 0.708425i 0.163643 + 0.0423365i
\(281\) 18.2067i 1.08612i 0.839693 + 0.543061i \(0.182735\pi\)
−0.839693 + 0.543061i \(0.817265\pi\)
\(282\) −0.524000 + 6.19473i −0.0312038 + 0.368891i
\(283\) 0.993068 0.993068i 0.0590318 0.0590318i −0.676975 0.736006i \(-0.736709\pi\)
0.736006 + 0.676975i \(0.236709\pi\)
\(284\) −13.2587 2.25923i −0.786761 0.134060i
\(285\) 1.08445 + 1.08445i 0.0642374 + 0.0642374i
\(286\) −20.7995 24.6434i −1.22990 1.45720i
\(287\) 5.99164 0.353675
\(288\) 18.9909 7.22339i 1.11905 0.425642i
\(289\) 31.1725 1.83367
\(290\) 6.63309 + 7.85894i 0.389508 + 0.461493i
\(291\) −14.7182 14.7182i −0.862799 0.862799i
\(292\) −23.6184 4.02447i −1.38216 0.235514i
\(293\) 2.21860 2.21860i 0.129612 0.129612i −0.639325 0.768937i \(-0.720786\pi\)
0.768937 + 0.639325i \(0.220786\pi\)
\(294\) −0.306040 + 3.61800i −0.0178486 + 0.211006i
\(295\) 8.36074i 0.486781i
\(296\) 0.795279 3.07399i 0.0462246 0.178672i
\(297\) 5.47226i 0.317533i
\(298\) −11.0179 0.931981i −0.638248 0.0539882i
\(299\) 11.2992 11.2992i 0.653452 0.653452i
\(300\) −2.96943 4.18923i −0.171440 0.241865i
\(301\) 2.47186 + 2.47186i 0.142475 + 0.142475i
\(302\) −19.0281 + 16.0600i −1.09494 + 0.924151i
\(303\) 39.4569 2.26674
\(304\) −1.03466 2.15373i −0.0593420 0.123525i
\(305\) −8.93417 −0.511569
\(306\) 26.9418 22.7394i 1.54016 1.29993i
\(307\) 21.1972 + 21.1972i 1.20979 + 1.20979i 0.971096 + 0.238690i \(0.0767179\pi\)
0.238690 + 0.971096i \(0.423282\pi\)
\(308\) −5.87662 + 4.16549i −0.334852 + 0.237351i
\(309\) −27.1755 + 27.1755i −1.54596 + 1.54596i
\(310\) 5.91256 + 0.500132i 0.335811 + 0.0284056i
\(311\) 11.3674i 0.644588i −0.946640 0.322294i \(-0.895546\pi\)
0.946640 0.322294i \(-0.104454\pi\)
\(312\) −23.3313 39.6168i −1.32088 2.24286i
\(313\) 2.83021i 0.159973i −0.996796 0.0799865i \(-0.974512\pi\)
0.996796 0.0799865i \(-0.0254877\pi\)
\(314\) 0.488880 5.77954i 0.0275891 0.326158i
\(315\) 2.53978 2.53978i 0.143100 0.143100i
\(316\) 0.942545 5.53152i 0.0530223 0.311172i
\(317\) 20.6711 + 20.6711i 1.16101 + 1.16101i 0.984256 + 0.176751i \(0.0565588\pi\)
0.176751 + 0.984256i \(0.443441\pi\)
\(318\) 14.6628 + 17.3726i 0.822250 + 0.974210i
\(319\) −26.1904 −1.46638
\(320\) 2.20373 + 7.69049i 0.123192 + 0.429911i
\(321\) −15.4132 −0.860283
\(322\) −2.30220 2.72767i −0.128297 0.152007i
\(323\) −2.93162 2.93162i −0.163120 0.163120i
\(324\) −2.30945 + 13.5535i −0.128303 + 0.752969i
\(325\) −4.47686 + 4.47686i −0.248332 + 0.248332i
\(326\) 1.18127 13.9650i 0.0654246 0.773449i
\(327\) 13.8650i 0.766736i
\(328\) 8.59991 + 14.6027i 0.474850 + 0.806300i
\(329\) 1.71220i 0.0943965i
\(330\) 13.0306 + 1.10223i 0.717310 + 0.0606759i
\(331\) 10.2473 10.2473i 0.563241 0.563241i −0.366986 0.930227i \(-0.619610\pi\)
0.930227 + 0.366986i \(0.119610\pi\)
\(332\) −24.1902 + 17.1466i −1.32761 + 0.941043i
\(333\) −2.85116 2.85116i −0.156243 0.156243i
\(334\) −17.5451 + 14.8084i −0.960027 + 0.810280i
\(335\) 4.05530 0.221565
\(336\) −9.25699 + 4.44711i −0.505010 + 0.242610i
\(337\) 18.3870 1.00161 0.500803 0.865561i \(-0.333038\pi\)
0.500803 + 0.865561i \(0.333038\pi\)
\(338\) −29.2711 + 24.7054i −1.59214 + 1.34380i
\(339\) 34.3615 + 34.3615i 1.86626 + 1.86626i
\(340\) 8.02732 + 11.3248i 0.435343 + 0.614176i
\(341\) −10.6854 + 10.6854i −0.578645 + 0.578645i
\(342\) −3.02344 0.255747i −0.163489 0.0138292i
\(343\) 1.00000i 0.0539949i
\(344\) −2.47646 + 9.57227i −0.133522 + 0.516102i
\(345\) 6.48003i 0.348873i
\(346\) 2.78309 32.9017i 0.149620 1.76881i
\(347\) 6.05275 6.05275i 0.324929 0.324929i −0.525726 0.850654i \(-0.676206\pi\)
0.850654 + 0.525726i \(0.176206\pi\)
\(348\) −36.8099 6.27223i −1.97322 0.336227i
\(349\) −12.0786 12.0786i −0.646551 0.646551i 0.305607 0.952158i \(-0.401141\pi\)
−0.952158 + 0.305607i \(0.901141\pi\)
\(350\) 0.912154 + 1.08073i 0.0487567 + 0.0577674i
\(351\) −9.61968 −0.513461
\(352\) −18.5869 8.34360i −0.990685 0.444715i
\(353\) −18.4927 −0.984270 −0.492135 0.870519i \(-0.663783\pi\)
−0.492135 + 0.870519i \(0.663783\pi\)
\(354\) −19.5801 23.1987i −1.04067 1.23300i
\(355\) −4.75523 4.75523i −0.252382 0.252382i
\(356\) −4.99380 0.850921i −0.264671 0.0450987i
\(357\) −12.6005 + 12.6005i −0.666887 + 0.666887i
\(358\) 1.57916 18.6688i 0.0834611 0.986676i
\(359\) 32.1811i 1.69845i −0.528028 0.849227i \(-0.677069\pi\)
0.528028 0.849227i \(-0.322931\pi\)
\(360\) 9.83531 + 2.54452i 0.518366 + 0.134108i
\(361\) 18.6432i 0.981220i
\(362\) 26.2132 + 2.21732i 1.37773 + 0.116540i
\(363\) −3.57919 + 3.57919i −0.187859 + 0.187859i
\(364\) 7.32251 + 10.3305i 0.383804 + 0.541466i
\(365\) −8.47073 8.47073i −0.443378 0.443378i
\(366\) 24.7898 20.9230i 1.29578 1.09366i
\(367\) 28.6858 1.49739 0.748695 0.662915i \(-0.230681\pi\)
0.748695 + 0.662915i \(0.230681\pi\)
\(368\) 3.34344 9.52597i 0.174289 0.496575i
\(369\) 21.5207 1.12032
\(370\) 1.21323 1.02399i 0.0630727 0.0532345i
\(371\) −4.42723 4.42723i −0.229851 0.229851i
\(372\) −17.5769 + 12.4590i −0.911322 + 0.645967i
\(373\) −7.27067 + 7.27067i −0.376461 + 0.376461i −0.869824 0.493363i \(-0.835768\pi\)
0.493363 + 0.869824i \(0.335768\pi\)
\(374\) −35.2258 2.97969i −1.82149 0.154076i
\(375\) 2.56745i 0.132582i
\(376\) 4.17294 2.45755i 0.215203 0.126738i
\(377\) 46.0401i 2.37119i
\(378\) −0.181112 + 2.14111i −0.00931541 + 0.110127i
\(379\) −2.00688 + 2.00688i −0.103086 + 0.103086i −0.756769 0.653683i \(-0.773223\pi\)
0.653683 + 0.756769i \(0.273223\pi\)
\(380\) 0.200676 1.17771i 0.0102945 0.0604152i
\(381\) −2.05407 2.05407i −0.105233 0.105233i
\(382\) −16.8165 19.9243i −0.860406 1.01942i
\(383\) −6.99740 −0.357550 −0.178775 0.983890i \(-0.557213\pi\)
−0.178775 + 0.983890i \(0.557213\pi\)
\(384\) −24.1251 16.1780i −1.23113 0.825579i
\(385\) −3.60160 −0.183554
\(386\) 5.22854 + 6.19482i 0.266126 + 0.315308i
\(387\) 8.87839 + 8.87839i 0.451314 + 0.451314i
\(388\) −2.72359 + 15.9840i −0.138269 + 0.811463i
\(389\) −14.8826 + 14.8826i −0.754577 + 0.754577i −0.975330 0.220753i \(-0.929149\pi\)
0.220753 + 0.975330i \(0.429149\pi\)
\(390\) 1.93761 22.9064i 0.0981148 1.15991i
\(391\) 17.5176i 0.885903i
\(392\) 2.43718 1.43532i 0.123096 0.0724945i
\(393\) 6.93338i 0.349743i
\(394\) −3.44255 0.291199i −0.173433 0.0146704i
\(395\) 1.98387 1.98387i 0.0998196 0.0998196i
\(396\) −21.1076 + 14.9616i −1.06070 + 0.751848i
\(397\) −1.69613 1.69613i −0.0851263 0.0851263i 0.663261 0.748388i \(-0.269172\pi\)
−0.748388 + 0.663261i \(0.769172\pi\)
\(398\) −19.3227 + 16.3087i −0.968560 + 0.817482i
\(399\) 1.53365 0.0767783
\(400\) −1.32470 + 3.77428i −0.0662351 + 0.188714i
\(401\) −3.40156 −0.169866 −0.0849329 0.996387i \(-0.527068\pi\)
−0.0849329 + 0.996387i \(0.527068\pi\)
\(402\) −11.2523 + 9.49714i −0.561214 + 0.473675i
\(403\) 18.7838 + 18.7838i 0.935687 + 0.935687i
\(404\) −17.7743 25.0758i −0.884304 1.24757i
\(405\) −4.86094 + 4.86094i −0.241542 + 0.241542i
\(406\) 10.2474 + 0.866809i 0.508571 + 0.0430190i
\(407\) 4.04316i 0.200412i
\(408\) −48.7953 12.6239i −2.41573 0.624978i
\(409\) 37.5939i 1.85890i −0.368948 0.929450i \(-0.620282\pi\)
0.368948 0.929450i \(-0.379718\pi\)
\(410\) −0.714203 + 8.44330i −0.0352720 + 0.416985i
\(411\) −31.0028 + 31.0028i −1.52926 + 1.52926i
\(412\) 29.5125 + 5.02879i 1.45398 + 0.247751i
\(413\) 5.91194 + 5.91194i 0.290907 + 0.290907i
\(414\) −8.26904 9.79723i −0.406401 0.481508i
\(415\) −14.8254 −0.727752
\(416\) −14.6672 + 32.6739i −0.719118 + 1.60197i
\(417\) −40.0686 −1.96217
\(418\) 1.96240 + 2.32507i 0.0959840 + 0.113723i
\(419\) −4.51286 4.51286i −0.220468 0.220468i 0.588228 0.808695i \(-0.299826\pi\)
−0.808695 + 0.588228i \(0.799826\pi\)
\(420\) −5.06194 0.862531i −0.246997 0.0420872i
\(421\) −4.26147 + 4.26147i −0.207691 + 0.207691i −0.803285 0.595594i \(-0.796917\pi\)
0.595594 + 0.803285i \(0.296917\pi\)
\(422\) 2.37670 28.0974i 0.115696 1.36776i
\(423\) 6.14986i 0.299016i
\(424\) 4.43549 17.1445i 0.215406 0.832609i
\(425\) 6.94064i 0.336670i
\(426\) 24.3308 + 2.05809i 1.17883 + 0.0997149i
\(427\) −6.31741 + 6.31741i −0.305721 + 0.305721i
\(428\) 6.94326 + 9.79546i 0.335615 + 0.473481i
\(429\) 41.3972 + 41.3972i 1.99868 + 1.99868i
\(430\) −3.77794 + 3.18865i −0.182188 + 0.153770i
\(431\) −15.1939 −0.731863 −0.365932 0.930642i \(-0.619250\pi\)
−0.365932 + 0.930642i \(0.619250\pi\)
\(432\) −5.47823 + 2.63177i −0.263571 + 0.126621i
\(433\) −26.3375 −1.26570 −0.632849 0.774275i \(-0.718115\pi\)
−0.632849 + 0.774275i \(0.718115\pi\)
\(434\) 4.53446 3.82717i 0.217661 0.183710i
\(435\) −13.2018 13.2018i −0.632979 0.632979i
\(436\) 8.81151 6.24581i 0.421995 0.299120i
\(437\) −1.06606 + 1.06606i −0.0509968 + 0.0509968i
\(438\) 43.3415 + 3.66618i 2.07094 + 0.175177i
\(439\) 6.11953i 0.292069i −0.989279 0.146035i \(-0.953349\pi\)
0.989279 0.146035i \(-0.0466511\pi\)
\(440\) −5.16944 8.77775i −0.246443 0.418463i
\(441\) 3.59179i 0.171038i
\(442\) −5.23799 + 61.9235i −0.249146 + 2.94540i
\(443\) −14.7639 + 14.7639i −0.701456 + 0.701456i −0.964723 0.263267i \(-0.915200\pi\)
0.263267 + 0.964723i \(0.415200\pi\)
\(444\) −0.968278 + 5.68254i −0.0459525 + 0.269681i
\(445\) −1.79102 1.79102i −0.0849026 0.0849026i
\(446\) 21.1411 + 25.0482i 1.00106 + 1.18607i
\(447\) 20.0739 0.949465
\(448\) 6.99627 + 3.87972i 0.330543 + 0.183300i
\(449\) 12.5904 0.594176 0.297088 0.954850i \(-0.403985\pi\)
0.297088 + 0.954850i \(0.403985\pi\)
\(450\) 3.27627 + 3.88175i 0.154445 + 0.182988i
\(451\) −15.2590 15.2590i −0.718517 0.718517i
\(452\) 6.35855 37.3165i 0.299081 1.75522i
\(453\) 31.9643 31.9643i 1.50181 1.50181i
\(454\) 2.20211 26.0334i 0.103350 1.22181i
\(455\) 6.33124i 0.296813i
\(456\) 2.20127 + 3.73778i 0.103084 + 0.175037i
\(457\) 0.819072i 0.0383146i −0.999816 0.0191573i \(-0.993902\pi\)
0.999816 0.0191573i \(-0.00609833\pi\)
\(458\) −24.1669 2.04423i −1.12925 0.0955208i
\(459\) −7.45686 + 7.45686i −0.348057 + 0.348057i
\(460\) 4.11821 2.91908i 0.192012 0.136103i
\(461\) 15.3987 + 15.3987i 0.717188 + 0.717188i 0.968028 0.250841i \(-0.0807070\pi\)
−0.250841 + 0.968028i \(0.580707\pi\)
\(462\) 9.99341 8.43462i 0.464935 0.392414i
\(463\) −6.23603 −0.289813 −0.144906 0.989445i \(-0.546288\pi\)
−0.144906 + 0.989445i \(0.546288\pi\)
\(464\) 12.5957 + 26.2190i 0.584742 + 1.21718i
\(465\) −10.7724 −0.499556
\(466\) 26.8195 22.6361i 1.24239 1.04860i
\(467\) 1.91550 + 1.91550i 0.0886387 + 0.0886387i 0.750036 0.661397i \(-0.230036\pi\)
−0.661397 + 0.750036i \(0.730036\pi\)
\(468\) 26.3010 + 37.1050i 1.21576 + 1.71518i
\(469\) 2.86753 2.86753i 0.132410 0.132410i
\(470\) 2.41280 + 0.204094i 0.111294 + 0.00941415i
\(471\) 10.5300i 0.485196i
\(472\) −5.92296 + 22.8940i −0.272626 + 1.05378i
\(473\) 12.5902i 0.578899i
\(474\) −0.858632 + 10.1507i −0.0394383 + 0.466239i
\(475\) 0.422385 0.422385i 0.0193803 0.0193803i
\(476\) 13.6840 + 2.33170i 0.627207 + 0.106873i
\(477\) −15.9017 15.9017i −0.728089 0.728089i
\(478\) 14.9342 + 17.6942i 0.683074 + 0.809313i
\(479\) −16.6168 −0.759240 −0.379620 0.925143i \(-0.623945\pi\)
−0.379620 + 0.925143i \(0.623945\pi\)
\(480\) −5.16335 13.5749i −0.235673 0.619605i
\(481\) 7.10746 0.324072
\(482\) −3.79169 4.49243i −0.172707 0.204625i
\(483\) 4.58207 + 4.58207i 0.208492 + 0.208492i
\(484\) 3.88699 + 0.662325i 0.176681 + 0.0301057i
\(485\) −5.73264 + 5.73264i −0.260306 + 0.260306i
\(486\) 2.64718 31.2949i 0.120078 1.41957i
\(487\) 0.537219i 0.0243437i −0.999926 0.0121719i \(-0.996125\pi\)
0.999926 0.0121719i \(-0.00387452\pi\)
\(488\) −24.4642 6.32919i −1.10744 0.286509i
\(489\) 25.4434i 1.15059i
\(490\) 1.40918 + 0.119200i 0.0636603 + 0.00538491i
\(491\) 13.8555 13.8555i 0.625288 0.625288i −0.321591 0.946879i \(-0.604218\pi\)
0.946879 + 0.321591i \(0.104218\pi\)
\(492\) −17.7917 25.1004i −0.802113 1.13161i
\(493\) 35.6888 + 35.6888i 1.60734 + 1.60734i
\(494\) 4.08723 3.44969i 0.183893 0.155209i
\(495\) −12.9362 −0.581439
\(496\) 15.8359 + 5.55811i 0.711053 + 0.249566i
\(497\) −6.72492 −0.301654
\(498\) 41.1364 34.7198i 1.84336 1.55583i
\(499\) −13.9831 13.9831i −0.625967 0.625967i 0.321084 0.947051i \(-0.395953\pi\)
−0.947051 + 0.321084i \(0.895953\pi\)
\(500\) −1.63167 + 1.15657i −0.0729706 + 0.0517233i
\(501\) 29.4732 29.4732i 1.31676 1.31676i
\(502\) −37.9691 3.21173i −1.69464 0.143347i
\(503\) 1.12937i 0.0503561i 0.999683 + 0.0251781i \(0.00801528\pi\)
−0.999683 + 0.0251781i \(0.991985\pi\)
\(504\) 8.75386 5.15537i 0.389928 0.229638i
\(505\) 15.3681i 0.683873i
\(506\) −1.08354 + 12.8097i −0.0481694 + 0.569459i
\(507\) 49.1711 49.1711i 2.18376 2.18376i
\(508\) −0.380104 + 2.23072i −0.0168644 + 0.0989721i
\(509\) −24.2090 24.2090i −1.07305 1.07305i −0.997113 0.0759334i \(-0.975806\pi\)
−0.0759334 0.997113i \(-0.524194\pi\)
\(510\) −16.2543 19.2583i −0.719755 0.852772i
\(511\) −11.9794 −0.529938
\(512\) 0.586282 + 22.6198i 0.0259103 + 0.999664i
\(513\) 0.907601 0.0400716
\(514\) −21.3465 25.2915i −0.941552 1.11556i
\(515\) 10.5846 + 10.5846i 0.466415 + 0.466415i
\(516\) 3.01518 17.6952i 0.132736 0.778987i
\(517\) −4.36048 + 4.36048i −0.191774 + 0.191774i
\(518\) 0.133814 1.58195i 0.00587945 0.0695068i
\(519\) 59.9450i 2.63129i
\(520\) −15.4304 + 9.08735i −0.676668 + 0.398507i
\(521\) 7.96169i 0.348808i 0.984674 + 0.174404i \(0.0557999\pi\)
−0.984674 + 0.174404i \(0.944200\pi\)
\(522\) 36.8066 + 3.11340i 1.61098 + 0.136270i
\(523\) −12.8185 + 12.8185i −0.560516 + 0.560516i −0.929454 0.368938i \(-0.879721\pi\)
0.368938 + 0.929454i \(0.379721\pi\)
\(524\) 4.40632 3.12330i 0.192491 0.136442i
\(525\) −1.81546 1.81546i −0.0792332 0.0792332i
\(526\) 0.503381 0.424862i 0.0219484 0.0185249i
\(527\) 29.1211 1.26854
\(528\) 34.9004 + 12.2494i 1.51885 + 0.533087i
\(529\) 16.6298 0.723036
\(530\) 6.76650 5.71105i 0.293918 0.248072i
\(531\) 21.2345 + 21.2345i 0.921497 + 0.921497i
\(532\) −0.690867 0.974666i −0.0299529 0.0422571i
\(533\) −26.8237 + 26.8237i −1.16187 + 1.16187i
\(534\) 9.16399 + 0.775165i 0.396565 + 0.0335447i
\(535\) 6.00333i 0.259547i
\(536\) 11.1045 + 2.87288i 0.479642 + 0.124089i
\(537\) 34.0135i 1.46779i
\(538\) 2.23696 26.4453i 0.0964423 1.14014i
\(539\) −2.54671 + 2.54671i −0.109695 + 0.109695i
\(540\) −2.99562 0.510440i −0.128911 0.0219658i
\(541\) −2.41665 2.41665i −0.103900 0.103900i 0.653246 0.757146i \(-0.273407\pi\)
−0.757146 + 0.653246i \(0.773407\pi\)
\(542\) 19.0014 + 22.5130i 0.816180 + 0.967018i
\(543\) −47.7589 −2.04953
\(544\) 13.9582 + 36.6972i 0.598452 + 1.57338i
\(545\) 5.40030 0.231323
\(546\) −14.8272 17.5674i −0.634546 0.751815i
\(547\) −24.9172 24.9172i −1.06538 1.06538i −0.997707 0.0676744i \(-0.978442\pi\)
−0.0676744 0.997707i \(-0.521558\pi\)
\(548\) 33.6689 + 5.73703i 1.43826 + 0.245074i
\(549\) −22.6908 + 22.6908i −0.968422 + 0.968422i
\(550\) 0.429310 5.07530i 0.0183059 0.216412i
\(551\) 4.34381i 0.185052i
\(552\) −4.59062 + 17.7441i −0.195390 + 0.755239i
\(553\) 2.80562i 0.119307i
\(554\) 33.8858 + 2.86634i 1.43967 + 0.121779i
\(555\) −2.03804 + 2.03804i −0.0865099 + 0.0865099i
\(556\) 18.0498 + 25.4645i 0.765483 + 1.07993i
\(557\) 12.4881 + 12.4881i 0.529140 + 0.529140i 0.920316 0.391176i \(-0.127932\pi\)
−0.391176 + 0.920316i \(0.627932\pi\)
\(558\) 16.2868 13.7464i 0.689477 0.581931i
\(559\) −22.1323 −0.936098
\(560\) 1.73211 + 3.60552i 0.0731951 + 0.152361i
\(561\) 64.1795 2.70966
\(562\) −19.6765 + 16.6073i −0.830004 + 0.700538i
\(563\) −7.39743 7.39743i −0.311764 0.311764i 0.533828 0.845593i \(-0.320753\pi\)
−0.845593 + 0.533828i \(0.820753\pi\)
\(564\) −7.17279 + 5.08425i −0.302029 + 0.214085i
\(565\) 13.3835 13.3835i 0.563049 0.563049i
\(566\) 1.97907 + 0.167406i 0.0831865 + 0.00703659i
\(567\) 6.87440i 0.288698i
\(568\) −9.65240 16.3899i −0.405006 0.687703i
\(569\) 2.78440i 0.116728i 0.998295 + 0.0583642i \(0.0185885\pi\)
−0.998295 + 0.0583642i \(0.981412\pi\)
\(570\) −0.182811 + 2.16118i −0.00765709 + 0.0905221i
\(571\) −14.6312 + 14.6312i −0.612295 + 0.612295i −0.943544 0.331248i \(-0.892530\pi\)
0.331248 + 0.943544i \(0.392530\pi\)
\(572\) 7.66050 44.9572i 0.320302 1.87975i
\(573\) 33.4699 + 33.4699i 1.39822 + 1.39822i
\(574\) 5.46530 + 6.47533i 0.228117 + 0.270275i
\(575\) 2.52392 0.105255
\(576\) 25.1291 + 13.9352i 1.04705 + 0.580632i
\(577\) 19.9134 0.829006 0.414503 0.910048i \(-0.363955\pi\)
0.414503 + 0.910048i \(0.363955\pi\)
\(578\) 28.4341 + 33.6890i 1.18270 + 1.40128i
\(579\) −10.4064 10.4064i −0.432473 0.432473i
\(580\) −2.44298 + 14.3371i −0.101439 + 0.595317i
\(581\) −10.4832 + 10.4832i −0.434915 + 0.434915i
\(582\) 2.48112 29.3317i 0.102846 1.21584i
\(583\) 22.5498i 0.933917i
\(584\) −17.1943 29.1960i −0.711505 1.20814i
\(585\) 22.7405i 0.940205i
\(586\) 4.42140 + 0.373998i 0.182646 + 0.0154497i
\(587\) 14.8859 14.8859i 0.614409 0.614409i −0.329683 0.944092i \(-0.606942\pi\)
0.944092 + 0.329683i \(0.106942\pi\)
\(588\) −4.18923 + 2.96943i −0.172761 + 0.122457i
\(589\) −1.77222 1.77222i −0.0730230 0.0730230i
\(590\) −9.03569 + 7.62629i −0.371994 + 0.313969i
\(591\) 6.27214 0.258001
\(592\) 4.04756 1.94447i 0.166354 0.0799172i
\(593\) 35.0444 1.43910 0.719551 0.694440i \(-0.244348\pi\)
0.719551 + 0.694440i \(0.244348\pi\)
\(594\) 5.91403 4.99155i 0.242656 0.204806i
\(595\) 4.90777 + 4.90777i 0.201199 + 0.201199i
\(596\) −9.04278 12.7574i −0.370407 0.522565i
\(597\) 32.4592 32.4592i 1.32847 1.32847i
\(598\) 22.5181 + 1.90476i 0.920832 + 0.0778915i
\(599\) 29.5483i 1.20731i 0.797245 + 0.603656i \(0.206290\pi\)
−0.797245 + 0.603656i \(0.793710\pi\)
\(600\) 1.81885 7.03037i 0.0742540 0.287014i
\(601\) 2.61725i 0.106760i −0.998574 0.0533798i \(-0.983001\pi\)
0.998574 0.0533798i \(-0.0169994\pi\)
\(602\) −0.416691 + 4.92612i −0.0169831 + 0.200774i
\(603\) 10.2996 10.2996i 0.419431 0.419431i
\(604\) −34.7131 5.91495i −1.41245 0.240676i
\(605\) 1.39407 + 1.39407i 0.0566768 + 0.0566768i
\(606\) 35.9908 + 42.6422i 1.46203 + 1.73222i
\(607\) 15.4816 0.628380 0.314190 0.949360i \(-0.398267\pi\)
0.314190 + 0.949360i \(0.398267\pi\)
\(608\) 1.38383 3.08273i 0.0561215 0.125021i
\(609\) −18.6702 −0.756555
\(610\) −8.14934 9.65541i −0.329957 0.390936i
\(611\) 7.66528 + 7.66528i 0.310104 + 0.310104i
\(612\) 49.1503 + 8.37498i 1.98678 + 0.338538i
\(613\) −13.7576 + 13.7576i −0.555663 + 0.555663i −0.928070 0.372407i \(-0.878533\pi\)
0.372407 + 0.928070i \(0.378533\pi\)
\(614\) −3.57329 + 42.2435i −0.144206 + 1.70481i
\(615\) 15.3832i 0.620311i
\(616\) −9.86215 2.55146i −0.397358 0.102801i
\(617\) 8.55504i 0.344413i −0.985061 0.172207i \(-0.944910\pi\)
0.985061 0.172207i \(-0.0550896\pi\)
\(618\) −54.1576 4.58109i −2.17854 0.184278i
\(619\) 3.67786 3.67786i 0.147825 0.147825i −0.629320 0.777146i \(-0.716667\pi\)
0.777146 + 0.629320i \(0.216667\pi\)
\(620\) 4.85266 + 6.84607i 0.194888 + 0.274945i
\(621\) 2.71164 + 2.71164i 0.108814 + 0.108814i
\(622\) 12.2851 10.3689i 0.492588 0.415753i
\(623\) −2.53289 −0.101478
\(624\) 21.5332 61.3514i 0.862018 2.45602i
\(625\) −1.00000 −0.0400000
\(626\) 3.05869 2.58159i 0.122250 0.103181i
\(627\) −3.90576 3.90576i −0.155981 0.155981i
\(628\) 6.69204 4.74348i 0.267042 0.189286i
\(629\) 5.50947 5.50947i 0.219677 0.219677i
\(630\) 5.06149 + 0.428142i 0.201654 + 0.0170576i
\(631\) 33.5577i 1.33591i −0.744202 0.667954i \(-0.767170\pi\)
0.744202 0.667954i \(-0.232830\pi\)
\(632\) 6.83782 4.02696i 0.271994 0.160184i
\(633\) 51.1919i 2.03469i
\(634\) −3.48462 + 41.1952i −0.138392 + 1.63607i
\(635\) −0.800045 + 0.800045i −0.0317488 + 0.0317488i
\(636\) −5.40035 + 31.6931i −0.214138 + 1.25671i
\(637\) 4.47686 + 4.47686i 0.177380 + 0.177380i
\(638\) −23.8897 28.3047i −0.945803 1.12060i
\(639\) −24.1545 −0.955538
\(640\) −6.30118 + 9.39655i −0.249076 + 0.371431i
\(641\) 16.6300 0.656844 0.328422 0.944531i \(-0.393483\pi\)
0.328422 + 0.944531i \(0.393483\pi\)
\(642\) −14.0593 16.6575i −0.554875 0.657420i
\(643\) 10.3201 + 10.3201i 0.406984 + 0.406984i 0.880685 0.473702i \(-0.157083\pi\)
−0.473702 + 0.880685i \(0.657083\pi\)
\(644\) 0.847907 4.97611i 0.0334122 0.196086i
\(645\) 6.34636 6.34636i 0.249888 0.249888i
\(646\) 0.494196 5.84238i 0.0194439 0.229865i
\(647\) 38.0570i 1.49617i −0.663601 0.748087i \(-0.730973\pi\)
0.663601 0.748087i \(-0.269027\pi\)
\(648\) −16.7542 + 9.86696i −0.658166 + 0.387611i
\(649\) 30.1120i 1.18200i
\(650\) −8.92187 0.754684i −0.349944 0.0296011i
\(651\) −7.61721 + 7.61721i −0.298542 + 0.298542i
\(652\) 16.1699 11.4616i 0.633261 0.448871i
\(653\) −11.7003 11.7003i −0.457870 0.457870i 0.440086 0.897956i \(-0.354948\pi\)
−0.897956 + 0.440086i \(0.854948\pi\)
\(654\) −14.9843 + 12.6470i −0.585932 + 0.494537i
\(655\) 2.70049 0.105517
\(656\) −7.93713 + 22.6141i −0.309893 + 0.882932i
\(657\) −43.0276 −1.67867
\(658\) 1.85042 1.56179i 0.0721369 0.0608848i
\(659\) −16.8626 16.8626i −0.656873 0.656873i 0.297766 0.954639i \(-0.403759\pi\)
−0.954639 + 0.297766i \(0.903759\pi\)
\(660\) 10.6947 + 15.0879i 0.416290 + 0.587297i
\(661\) −25.8182 + 25.8182i −1.00421 + 1.00421i −0.00422235 + 0.999991i \(0.501344\pi\)
−0.999991 + 0.00422235i \(0.998656\pi\)
\(662\) 20.4216 + 1.72743i 0.793709 + 0.0671383i
\(663\) 112.821i 4.38161i
\(664\) −40.5961 10.5027i −1.57543 0.407584i
\(665\) 0.597342i 0.0231639i
\(666\) 0.480632 5.68203i 0.0186241 0.220174i
\(667\) 12.9780 12.9780i 0.502510 0.502510i
\(668\) −32.0078 5.45397i −1.23842 0.211021i
\(669\) −42.0771 42.0771i −1.62680 1.62680i
\(670\) 3.69906 + 4.38268i 0.142907 + 0.169318i
\(671\) 32.1773 1.24219
\(672\) −13.2499 5.94785i −0.511127 0.229443i
\(673\) 8.99006 0.346541 0.173271 0.984874i \(-0.444566\pi\)
0.173271 + 0.984874i \(0.444566\pi\)
\(674\) 16.7718 + 19.8714i 0.646026 + 0.765417i
\(675\) −1.07438 1.07438i −0.0413528 0.0413528i
\(676\) −53.3996 9.09905i −2.05383 0.349963i
\(677\) −11.5984 + 11.5984i −0.445762 + 0.445762i −0.893943 0.448181i \(-0.852072\pi\)
0.448181 + 0.893943i \(0.352072\pi\)
\(678\) −5.79246 + 68.4785i −0.222458 + 2.62990i
\(679\) 8.10717i 0.311125i
\(680\) −4.91692 + 19.0054i −0.188555 + 0.728822i
\(681\) 47.4313i 1.81757i
\(682\) −21.2947 1.80128i −0.815415 0.0689744i
\(683\) −2.59539 + 2.59539i −0.0993098 + 0.0993098i −0.755016 0.655706i \(-0.772371\pi\)
0.655706 + 0.755016i \(0.272371\pi\)
\(684\) −2.48145 3.50080i −0.0948807 0.133856i
\(685\) 12.0753 + 12.0753i 0.461375 + 0.461375i
\(686\) 1.08073 0.912154i 0.0412624 0.0348262i
\(687\) 44.0308 1.67988
\(688\) −12.6039 + 6.05500i −0.480521 + 0.230845i
\(689\) 39.6403 1.51017
\(690\) −7.00316 + 5.91079i −0.266606 + 0.225020i
\(691\) −19.4028 19.4028i −0.738117 0.738117i 0.234096 0.972213i \(-0.424787\pi\)
−0.972213 + 0.234096i \(0.924787\pi\)
\(692\) 38.0964 27.0037i 1.44821 1.02652i
\(693\) −9.14727 + 9.14727i −0.347476 + 0.347476i
\(694\) 12.0624 + 1.02034i 0.457883 + 0.0387315i
\(695\) 15.6064i 0.591983i
\(696\) −26.7977 45.5027i −1.01576 1.72478i
\(697\) 41.5858i 1.57517i
\(698\) 2.03613 24.0712i 0.0770688 0.911107i
\(699\) −45.0527 + 45.0527i −1.70405 + 1.70405i
\(700\) −0.335949 + 1.97158i −0.0126977 + 0.0745188i
\(701\) −24.0020 24.0020i −0.906545 0.906545i 0.0894470 0.995992i \(-0.471490\pi\)
−0.995992 + 0.0894470i \(0.971490\pi\)
\(702\) −8.77464 10.3963i −0.331177 0.392382i
\(703\) −0.670577 −0.0252913
\(704\) −7.93695 27.6980i −0.299135 1.04391i
\(705\) −4.39598 −0.165562
\(706\) −16.8682 19.9856i −0.634845 0.752170i
\(707\) −10.8669 10.8669i −0.408692 0.408692i
\(708\) 7.21140 42.3215i 0.271021 1.59054i
\(709\) 0.135968 0.135968i 0.00510640 0.00510640i −0.704549 0.709655i \(-0.748851\pi\)
0.709655 + 0.704549i \(0.248851\pi\)
\(710\) 0.801610 9.47663i 0.0300839 0.355651i
\(711\) 10.0772i 0.377925i
\(712\) −3.63550 6.17311i −0.136246 0.231347i
\(713\) 10.5897i 0.396588i
\(714\) −25.1112 2.12411i −0.939764 0.0794929i
\(715\) 16.1239 16.1239i 0.602998 0.602998i
\(716\) 21.6163 15.3222i 0.807840 0.572617i
\(717\) −29.7235 29.7235i −1.11005 1.11005i
\(718\) 34.7790 29.3541i 1.29794 1.09549i
\(719\) −3.06462 −0.114291 −0.0571455 0.998366i \(-0.518200\pi\)
−0.0571455 + 0.998366i \(0.518200\pi\)
\(720\) 6.22139 + 12.9503i 0.231857 + 0.482629i
\(721\) 14.9689 0.557472
\(722\) 20.1482 17.0055i 0.749839 0.632878i
\(723\) 7.54660 + 7.54660i 0.280661 + 0.280661i
\(724\) 21.5141 + 30.3519i 0.799567 + 1.12802i
\(725\) −5.14200 + 5.14200i −0.190969 + 0.190969i
\(726\) −7.13291 0.603359i −0.264727 0.0223928i
\(727\) 7.86232i 0.291597i 0.989314 + 0.145799i \(0.0465752\pi\)
−0.989314 + 0.145799i \(0.953425\pi\)
\(728\) −4.48521 + 17.3367i −0.166233 + 0.642540i
\(729\) 36.3944i 1.34794i
\(730\) 1.42795 16.8812i 0.0528507 0.624800i
\(731\) −17.1563 + 17.1563i −0.634547 + 0.634547i
\(732\) 45.2242 + 7.70600i 1.67154 + 0.284822i
\(733\) −2.68403 2.68403i −0.0991370 0.0991370i 0.655799 0.754936i \(-0.272332\pi\)
−0.754936 + 0.655799i \(0.772332\pi\)
\(734\) 26.1659 + 31.0016i 0.965802 + 1.14429i
\(735\) −2.56745 −0.0947018
\(736\) 13.3447 5.07580i 0.491893 0.187097i
\(737\) −14.6056 −0.538003
\(738\) 19.6302 + 23.2581i 0.722598 + 0.856141i
\(739\) 11.1492 + 11.1492i 0.410132 + 0.410132i 0.881784 0.471653i \(-0.156342\pi\)
−0.471653 + 0.881784i \(0.656342\pi\)
\(740\) 2.21330 + 0.377136i 0.0813626 + 0.0138638i
\(741\) −6.86593 + 6.86593i −0.252226 + 0.252226i
\(742\) 0.746318 8.82296i 0.0273982 0.323901i
\(743\) 49.1110i 1.80171i 0.434123 + 0.900854i \(0.357058\pi\)
−0.434123 + 0.900854i \(0.642942\pi\)
\(744\) −29.4976 7.63141i −1.08144 0.279781i
\(745\) 7.81863i 0.286452i
\(746\) −14.4896 1.22565i −0.530502 0.0448741i
\(747\) −37.6534 + 37.6534i −1.37766 + 1.37766i
\(748\) −28.9112 40.7875i −1.05710 1.49134i
\(749\) 4.24500 + 4.24500i 0.155109 + 0.155109i
\(750\) 2.77472 2.34191i 0.101318 0.0855145i
\(751\) −26.1068 −0.952650 −0.476325 0.879269i \(-0.658031\pi\)
−0.476325 + 0.879269i \(0.658031\pi\)
\(752\) 6.46231 + 2.26815i 0.235656 + 0.0827109i
\(753\) 69.1775 2.52097
\(754\) −49.7569 + 41.9957i −1.81204 + 1.52939i
\(755\) −12.4498 12.4498i −0.453095 0.453095i
\(756\) −2.47916 + 1.75729i −0.0901661 + 0.0639119i
\(757\) 19.1268 19.1268i 0.695177 0.695177i −0.268189 0.963366i \(-0.586425\pi\)
0.963366 + 0.268189i \(0.0864253\pi\)
\(758\) −3.99947 0.338308i −0.145267 0.0122879i
\(759\) 23.3385i 0.847133i
\(760\) 1.45583 0.857377i 0.0528086 0.0311003i
\(761\) 30.1038i 1.09126i 0.838026 + 0.545631i \(0.183710\pi\)
−0.838026 + 0.545631i \(0.816290\pi\)
\(762\) 0.346264 4.09353i 0.0125438 0.148293i
\(763\) 3.81859 3.81859i 0.138242 0.138242i
\(764\) 6.19355 36.3481i 0.224075 1.31503i
\(765\) 17.6277 + 17.6277i 0.637331 + 0.637331i
\(766\) −6.38271 7.56229i −0.230617 0.273237i
\(767\) −52.9339 −1.91133
\(768\) −4.52187 40.8295i −0.163169 1.47331i
\(769\) −9.47275 −0.341596 −0.170798 0.985306i \(-0.554635\pi\)
−0.170798 + 0.985306i \(0.554635\pi\)
\(770\) −3.28521 3.89235i −0.118391 0.140271i
\(771\) 42.4858 + 42.4858i 1.53009 + 1.53009i
\(772\) −1.92568 + 11.3013i −0.0693069 + 0.406741i
\(773\) −7.10418 + 7.10418i −0.255520 + 0.255520i −0.823229 0.567709i \(-0.807830\pi\)
0.567709 + 0.823229i \(0.307830\pi\)
\(774\) −1.49667 + 17.6936i −0.0537966 + 0.635983i
\(775\) 4.19574i 0.150716i
\(776\) −19.7587 + 11.6364i −0.709294 + 0.417721i
\(777\) 2.88222i 0.103399i
\(778\) −29.6593 2.50882i −1.06334 0.0899456i
\(779\) 2.53078 2.53078i 0.0906745 0.0906745i
\(780\) 26.5230 18.8002i 0.949677 0.673154i
\(781\) 17.1264 + 17.1264i 0.612832 + 0.612832i
\(782\) 18.9318 15.9788i 0.676999 0.571399i
\(783\) −11.0489 −0.394856
\(784\) 3.77428 + 1.32470i 0.134796 + 0.0473108i
\(785\) 4.10134 0.146383
\(786\) −7.49310 + 6.32431i −0.267270 + 0.225581i
\(787\) −0.0406865 0.0406865i −0.00145032 0.00145032i 0.706381 0.707832i \(-0.250326\pi\)
−0.707832 + 0.706381i \(0.750326\pi\)
\(788\) −2.82543 3.98608i −0.100652 0.141998i
\(789\) −0.845603 + 0.845603i −0.0301043 + 0.0301043i
\(790\) 3.95363 + 0.334430i 0.140664 + 0.0118985i
\(791\) 18.9272i 0.672972i
\(792\) −35.4228 9.16432i −1.25870 0.325640i
\(793\) 56.5644i 2.00866i
\(794\) 0.285924 3.38019i 0.0101470 0.119958i
\(795\) −11.3667 + 11.3667i −0.403135 + 0.403135i
\(796\) −35.2506 6.00654i −1.24942 0.212896i
\(797\) −21.3500 21.3500i −0.756254 0.756254i 0.219384 0.975639i \(-0.429595\pi\)
−0.975639 + 0.219384i \(0.929595\pi\)
\(798\) 1.39892 + 1.65745i 0.0495213 + 0.0586733i
\(799\) 11.8837 0.420417
\(800\) −5.28730 + 2.01108i −0.186934 + 0.0711024i
\(801\) −9.09761 −0.321448
\(802\) −3.10275 3.67616i −0.109562 0.129810i
\(803\) 30.5082 + 30.5082i 1.07661 + 1.07661i
\(804\) −20.5277 3.49782i −0.723955 0.123359i
\(805\) 1.78468 1.78468i 0.0629017 0.0629017i
\(806\) −3.16646 + 37.4339i −0.111534 + 1.31855i
\(807\) 48.1819i 1.69608i
\(808\) 10.8872 42.0822i 0.383010 1.48044i
\(809\) 25.6345i 0.901261i 0.892710 + 0.450631i \(0.148801\pi\)
−0.892710 + 0.450631i \(0.851199\pi\)
\(810\) −9.68728 0.819428i −0.340376 0.0287918i
\(811\) −11.0332 + 11.0332i −0.387427 + 0.387427i −0.873769 0.486342i \(-0.838331\pi\)
0.486342 + 0.873769i \(0.338331\pi\)
\(812\) 8.41044 + 11.8653i 0.295148 + 0.416392i
\(813\) −37.8185 37.8185i −1.32635 1.32635i
\(814\) −4.36956 + 3.68798i −0.153153 + 0.129264i
\(815\) 9.91000 0.347132
\(816\) −30.8658 64.2494i −1.08052 2.24918i
\(817\) 2.08815 0.0730551
\(818\) 40.6288 34.2915i 1.42055 1.19897i
\(819\) 16.0800 + 16.0800i 0.561880 + 0.561880i
\(820\) −9.77638 + 6.92973i −0.341406 + 0.241997i
\(821\) 14.9801 14.9801i 0.522809 0.522809i −0.395610 0.918419i \(-0.629467\pi\)
0.918419 + 0.395610i \(0.129467\pi\)
\(822\) −61.7850 5.22627i −2.15500 0.182287i
\(823\) 5.21910i 0.181926i 0.995854 + 0.0909632i \(0.0289946\pi\)
−0.995854 + 0.0909632i \(0.971005\pi\)
\(824\) 21.4852 + 36.4820i 0.748472 + 1.27091i
\(825\) 9.24692i 0.321936i
\(826\) −0.996600 + 11.7818i −0.0346761 + 0.409941i
\(827\) 2.30972 2.30972i 0.0803167 0.0803167i −0.665807 0.746124i \(-0.731913\pi\)
0.746124 + 0.665807i \(0.231913\pi\)
\(828\) 3.04551 17.8732i 0.105839 0.621136i
\(829\) −17.3124 17.3124i −0.601286 0.601286i 0.339368 0.940654i \(-0.389787\pi\)
−0.940654 + 0.339368i \(0.889787\pi\)
\(830\) −13.5231 16.0223i −0.469393 0.556141i
\(831\) −61.7381 −2.14167
\(832\) −48.6903 + 13.9524i −1.68803 + 0.483711i
\(833\) 6.94064 0.240479
\(834\) −36.5487 43.3032i −1.26558 1.49947i
\(835\) −11.4796 11.4796i −0.397266 0.397266i
\(836\) −0.722755 + 4.24164i −0.0249970 + 0.146700i
\(837\) −4.50781 + 4.50781i −0.155813 + 0.155813i
\(838\) 0.760752 8.99361i 0.0262798 0.310679i
\(839\) 46.9080i 1.61944i −0.586815 0.809721i \(-0.699618\pi\)
0.586815 0.809721i \(-0.300382\pi\)
\(840\) −3.68511 6.25734i −0.127148 0.215899i
\(841\) 23.8804i 0.823462i
\(842\) −8.49261 0.718374i −0.292675 0.0247568i
\(843\) 33.0536 33.0536i 1.13843 1.13843i
\(844\) 32.5336 23.0606i 1.11985 0.793778i
\(845\) −19.1517 19.1517i −0.658840 0.658840i
\(846\) 6.64633 5.60962i 0.228505 0.192863i
\(847\) 1.97151 0.0677418
\(848\) 22.5744 10.8448i 0.775207 0.372414i
\(849\) −3.60575 −0.123749
\(850\) −7.50095 + 6.33093i −0.257280 + 0.217149i
\(851\) −2.00348 2.00348i −0.0686785 0.0686785i
\(852\) 19.9692 + 28.1722i 0.684132 + 0.965165i
\(853\) 3.76562 3.76562i 0.128932 0.128932i −0.639696 0.768628i \(-0.720940\pi\)
0.768628 + 0.639696i \(0.220940\pi\)
\(854\) −12.5899 1.06495i −0.430816 0.0364419i
\(855\) 2.14553i 0.0733756i
\(856\) −4.25291 + 16.4388i −0.145361 + 0.561865i
\(857\) 21.1558i 0.722668i −0.932436 0.361334i \(-0.882321\pi\)
0.932436 0.361334i \(-0.117679\pi\)
\(858\) −6.97850 + 82.4998i −0.238242 + 2.81650i
\(859\) −35.8965 + 35.8965i −1.22477 + 1.22477i −0.258855 + 0.965916i \(0.583345\pi\)
−0.965916 + 0.258855i \(0.916655\pi\)
\(860\) −6.89212 1.17439i −0.235020 0.0400462i
\(861\) −10.8776 10.8776i −0.370707 0.370707i
\(862\) −13.8592 16.4205i −0.472045 0.559283i
\(863\) −7.60406 −0.258845 −0.129423 0.991590i \(-0.541312\pi\)
−0.129423 + 0.991590i \(0.541312\pi\)
\(864\) −7.84122 3.51990i −0.266764 0.119749i
\(865\) 23.3481 0.793859
\(866\) −24.0238 28.4637i −0.816363 0.967234i
\(867\) −56.5924 56.5924i −1.92198 1.92198i
\(868\) 8.27226 + 1.40955i 0.280779 + 0.0478434i
\(869\) −7.14512 + 7.14512i −0.242382 + 0.242382i
\(870\) 2.22549 26.3097i 0.0754511 0.891983i
\(871\) 25.6751i 0.869967i
\(872\) 14.7875 + 3.82571i 0.500768 + 0.129555i
\(873\) 29.1193i 0.985538i
\(874\) −2.12454 0.179711i −0.0718637 0.00607882i
\(875\) −0.707107 + 0.707107i −0.0239046 + 0.0239046i
\(876\) 35.5720 + 50.1846i 1.20187 + 1.69558i
\(877\) −34.0221 34.0221i −1.14884 1.14884i −0.986780 0.162064i \(-0.948185\pi\)
−0.162064 0.986780i \(-0.551815\pi\)
\(878\) 6.61355 5.58196i 0.223197 0.188382i
\(879\) −8.05555 −0.271707
\(880\) 4.77104 13.5934i 0.160832 0.458234i
\(881\) 52.0702 1.75429 0.877145 0.480226i \(-0.159445\pi\)
0.877145 + 0.480226i \(0.159445\pi\)
\(882\) 3.88175 3.27627i 0.130705 0.110318i
\(883\) 14.8051 + 14.8051i 0.498233 + 0.498233i 0.910888 0.412655i \(-0.135398\pi\)
−0.412655 + 0.910888i \(0.635398\pi\)
\(884\) −71.7003 + 50.8229i −2.41154 + 1.70936i
\(885\) 15.1786 15.1786i 0.510223 0.510223i
\(886\) −29.4228 2.48882i −0.988479 0.0836135i
\(887\) 8.29831i 0.278630i 0.990248 + 0.139315i \(0.0444900\pi\)
−0.990248 + 0.139315i \(0.955510\pi\)
\(888\) −7.02450 + 4.13690i −0.235727 + 0.138825i
\(889\) 1.13143i 0.0379471i
\(890\) 0.301920 3.56930i 0.0101204 0.119643i
\(891\) 17.5071 17.5071i 0.586511 0.586511i
\(892\) −7.78632 + 45.6956i −0.260705 + 1.53000i
\(893\) −0.723206 0.723206i −0.0242012 0.0242012i
\(894\) 18.3105 + 21.6945i 0.612396 + 0.725572i
\(895\) 13.2480 0.442831
\(896\) 2.18875 + 11.1000i 0.0731210 + 0.370824i
\(897\) −41.0267 −1.36984
\(898\) 11.4843 + 13.6068i 0.383238 + 0.454063i
\(899\) 21.5745 + 21.5745i 0.719551 + 0.719551i
\(900\) −1.20666 + 7.08152i −0.0402219 + 0.236051i
\(901\) 30.7278 30.7278i 1.02369 1.02369i
\(902\) 2.57227 30.4094i 0.0856473 1.01252i
\(903\) 8.97511i 0.298673i
\(904\) 46.1289 27.1665i 1.53423 0.903544i
\(905\) 18.6017i 0.618342i
\(906\) 63.7011 + 5.38835i 2.11633 + 0.179016i
\(907\) 26.0800 26.0800i 0.865971 0.865971i −0.126052 0.992024i \(-0.540231\pi\)
0.992024 + 0.126052i \(0.0402308\pi\)
\(908\) 30.1437 21.3666i 1.00035 0.709074i
\(909\) −39.0317 39.0317i −1.29460 1.29460i
\(910\) −6.84236 + 5.77507i −0.226822 + 0.191442i
\(911\) −27.7837 −0.920514 −0.460257 0.887786i \(-0.652243\pi\)
−0.460257 + 0.887786i \(0.652243\pi\)
\(912\) −2.03162 + 5.78840i −0.0672737 + 0.191673i
\(913\) 53.3953 1.76713
\(914\) 0.885195 0.747120i 0.0292796 0.0247125i
\(915\) 16.2196 + 16.2196i 0.536205 + 0.536205i
\(916\) −19.8347 27.9825i −0.655357 0.924569i
\(917\) 1.90954 1.90954i 0.0630585 0.0630585i
\(918\) −14.8607 1.25703i −0.490475 0.0414883i
\(919\) 31.2148i 1.02968i −0.857286 0.514841i \(-0.827851\pi\)
0.857286 0.514841i \(-0.172149\pi\)
\(920\) 6.91118 + 1.78801i 0.227855 + 0.0589489i
\(921\) 76.9652i 2.53609i
\(922\) −2.59582 + 30.6878i −0.0854888 + 1.01065i
\(923\) 30.1065 30.1065i 0.990969 0.990969i
\(924\) 18.2311 + 3.10649i 0.599758 + 0.102196i
\(925\) 0.793799 + 0.793799i 0.0260999 + 0.0260999i
\(926\) −5.68822 6.73945i −0.186927 0.221472i
\(927\) 53.7653 1.76588
\(928\) −16.8463 + 37.5283i −0.553008 + 1.23193i
\(929\) 3.65249 0.119834 0.0599171 0.998203i \(-0.480916\pi\)
0.0599171 + 0.998203i \(0.480916\pi\)
\(930\) −9.82605 11.6420i −0.322209 0.381756i
\(931\) −0.422385 0.422385i −0.0138431 0.0138431i
\(932\) 48.9270 + 8.33694i 1.60266 + 0.273086i
\(933\) −20.6371 + 20.6371i −0.675629 + 0.675629i
\(934\) −0.322904 + 3.81737i −0.0105657 + 0.124908i
\(935\) 24.9974i 0.817502i
\(936\) −16.1100 + 62.2697i −0.526570 + 2.03535i
\(937\) 43.6027i 1.42444i 0.701958 + 0.712218i \(0.252309\pi\)
−0.701958 + 0.712218i \(0.747691\pi\)
\(938\) 5.71465 + 0.483392i 0.186590 + 0.0157833i
\(939\) −5.13814 + 5.13814i −0.167677 + 0.167677i
\(940\) 1.98027 + 2.79374i 0.0645894 + 0.0911218i
\(941\) −13.0694 13.0694i −0.426052 0.426052i 0.461229 0.887281i \(-0.347409\pi\)
−0.887281 + 0.461229i \(0.847409\pi\)
\(942\) −11.3801 + 9.60498i −0.370782 + 0.312947i
\(943\) 15.1224 0.492453
\(944\) −30.1448 + 14.4817i −0.981131 + 0.471340i
\(945\) −1.51940 −0.0494260
\(946\) 13.6066 11.4842i 0.442389 0.373384i
\(947\) 34.6394 + 34.6394i 1.12563 + 1.12563i 0.990880 + 0.134750i \(0.0430232\pi\)
0.134750 + 0.990880i \(0.456977\pi\)
\(948\) −11.7534 + 8.33110i −0.381733 + 0.270581i
\(949\) 53.6302 53.6302i 1.74091 1.74091i
\(950\) 0.841763 + 0.0712032i 0.0273104 + 0.00231014i
\(951\) 75.0553i 2.43383i
\(952\) 9.96203 + 16.9156i 0.322871 + 0.548238i
\(953\) 38.3932i 1.24368i −0.783145 0.621840i \(-0.786386\pi\)
0.783145 0.621840i \(-0.213614\pi\)
\(954\) 2.68062 31.6903i 0.0867882 1.02601i
\(955\) 13.0362 13.0362i 0.421842 0.421842i
\(956\) −5.50030 + 32.2796i −0.177892 + 1.04400i
\(957\) 47.5477 + 47.5477i 1.53700 + 1.53700i
\(958\) −15.1571 17.9582i −0.489703 0.580204i
\(959\) 17.0771 0.551448
\(960\) 9.96099 17.9626i 0.321489 0.579739i
\(961\) −13.3957 −0.432121
\(962\) 6.48310 + 7.68124i 0.209024 + 0.247653i
\(963\) 15.2471 + 15.2471i 0.491332 + 0.491332i
\(964\) 1.39649 8.19558i 0.0449779 0.263962i
\(965\) −4.05319 + 4.05319i −0.130477 + 0.130477i
\(966\) −0.772420 + 9.13154i −0.0248522 + 0.293802i
\(967\) 21.3385i 0.686201i 0.939299 + 0.343100i \(0.111477\pi\)
−0.939299 + 0.343100i \(0.888523\pi\)
\(968\) 2.82974 + 4.80492i 0.0909513 + 0.154436i
\(969\) 10.6445i 0.341950i
\(970\) −11.4245 0.966374i −0.366818 0.0310284i
\(971\) −12.9037 + 12.9037i −0.414099 + 0.414099i −0.883164 0.469065i \(-0.844591\pi\)
0.469065 + 0.883164i \(0.344591\pi\)
\(972\) 36.2359 25.6849i 1.16227 0.823844i
\(973\) 11.0354 + 11.0354i 0.353778 + 0.353778i
\(974\) 0.580588 0.490027i 0.0186032 0.0157015i
\(975\) 16.2551 0.520581
\(976\) −15.4750 32.2124i −0.495342 1.03109i
\(977\) −27.6238 −0.883763 −0.441882 0.897073i \(-0.645689\pi\)
−0.441882 + 0.897073i \(0.645689\pi\)
\(978\) −27.4974 + 23.2083i −0.879271 + 0.742121i
\(979\) 6.45054 + 6.45054i 0.206160 + 0.206160i
\(980\) 1.15657 + 1.63167i 0.0369452 + 0.0521218i
\(981\) 13.7156 13.7156i 0.437905 0.437905i
\(982\) 27.6123 + 2.33567i 0.881144 + 0.0745343i
\(983\) 28.2366i 0.900608i 0.892875 + 0.450304i \(0.148684\pi\)
−0.892875 + 0.450304i \(0.851316\pi\)
\(984\) 10.8979 42.1234i 0.347411 1.34285i
\(985\) 2.44294i 0.0778387i
\(986\) −6.01621 + 71.1236i −0.191595 + 2.26504i
\(987\) −3.10843 + 3.10843i −0.0989423 + 0.0989423i
\(988\) 7.45637 + 1.27053i 0.237219 + 0.0404210i
\(989\) 6.23876 + 6.23876i 0.198381 + 0.198381i
\(990\) −11.7998 13.9805i −0.375022 0.444330i
\(991\) −17.0447 −0.541442 −0.270721 0.962658i \(-0.587262\pi\)
−0.270721 + 0.962658i \(0.587262\pi\)
\(992\) 8.43798 + 22.1842i 0.267906 + 0.704348i
\(993\) −37.2070 −1.18073
\(994\) −6.13416 7.26781i −0.194564 0.230521i
\(995\) −12.6426 12.6426i −0.400798 0.400798i
\(996\) 75.0454 + 12.7874i 2.37791 + 0.405184i
\(997\) −12.6924 + 12.6924i −0.401971 + 0.401971i −0.878927 0.476956i \(-0.841740\pi\)
0.476956 + 0.878927i \(0.341740\pi\)
\(998\) 2.35718 27.8666i 0.0746153 0.882101i
\(999\) 1.70568i 0.0539653i
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 560.2.bd.b.141.20 52
4.3 odd 2 2240.2.bd.b.1681.23 52
16.5 even 4 inner 560.2.bd.b.421.20 yes 52
16.11 odd 4 2240.2.bd.b.561.23 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
560.2.bd.b.141.20 52 1.1 even 1 trivial
560.2.bd.b.421.20 yes 52 16.5 even 4 inner
2240.2.bd.b.561.23 52 16.11 odd 4
2240.2.bd.b.1681.23 52 4.3 odd 2