Properties

Label 1380.2.p.b.91.5
Level $1380$
Weight $2$
Character 1380.91
Analytic conductor $11.019$
Analytic rank $0$
Dimension $48$
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] = [1380,2,Mod(91,1380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1380.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.p (of order \(2\), degree \(1\), 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: \(11.0193554789\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.5
Character \(\chi\) \(=\) 1380.91
Dual form 1380.2.p.b.91.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32949 - 0.482147i) q^{2} +1.00000i q^{3} +(1.53507 + 1.28202i) q^{4} -1.00000i q^{5} +(0.482147 - 1.32949i) q^{6} +4.27008 q^{7} +(-1.42273 - 2.44455i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-1.32949 - 0.482147i) q^{2} +1.00000i q^{3} +(1.53507 + 1.28202i) q^{4} -1.00000i q^{5} +(0.482147 - 1.32949i) q^{6} +4.27008 q^{7} +(-1.42273 - 2.44455i) q^{8} -1.00000 q^{9} +(-0.482147 + 1.32949i) q^{10} +6.33992 q^{11} +(-1.28202 + 1.53507i) q^{12} +5.06818 q^{13} +(-5.67701 - 2.05880i) q^{14} +1.00000 q^{15} +(0.712870 + 3.93596i) q^{16} -2.28607i q^{17} +(1.32949 + 0.482147i) q^{18} +2.14696 q^{19} +(1.28202 - 1.53507i) q^{20} +4.27008i q^{21} +(-8.42884 - 3.05678i) q^{22} +(-4.21933 + 2.27976i) q^{23} +(2.44455 - 1.42273i) q^{24} -1.00000 q^{25} +(-6.73807 - 2.44361i) q^{26} -1.00000i q^{27} +(6.55486 + 5.47430i) q^{28} -0.184440 q^{29} +(-1.32949 - 0.482147i) q^{30} -6.08631i q^{31} +(0.949963 - 5.57652i) q^{32} +6.33992i q^{33} +(-1.10222 + 3.03930i) q^{34} -4.27008i q^{35} +(-1.53507 - 1.28202i) q^{36} -0.639401i q^{37} +(-2.85435 - 1.03515i) q^{38} +5.06818i q^{39} +(-2.44455 + 1.42273i) q^{40} -9.20080 q^{41} +(2.05880 - 5.67701i) q^{42} -5.56828 q^{43} +(9.73221 + 8.12788i) q^{44} +1.00000i q^{45} +(6.70871 - 0.996570i) q^{46} -13.4174i q^{47} +(-3.93596 + 0.712870i) q^{48} +11.2335 q^{49} +(1.32949 + 0.482147i) q^{50} +2.28607 q^{51} +(7.78000 + 6.49748i) q^{52} -1.68353i q^{53} +(-0.482147 + 1.32949i) q^{54} -6.33992i q^{55} +(-6.07517 - 10.4384i) q^{56} +2.14696i q^{57} +(0.245211 + 0.0889274i) q^{58} -6.99605i q^{59} +(1.53507 + 1.28202i) q^{60} +10.7249i q^{61} +(-2.93450 + 8.09167i) q^{62} -4.27008 q^{63} +(-3.95167 + 6.95589i) q^{64} -5.06818i q^{65} +(3.05678 - 8.42884i) q^{66} -11.6198 q^{67} +(2.93078 - 3.50928i) q^{68} +(-2.27976 - 4.21933i) q^{69} +(-2.05880 + 5.67701i) q^{70} +14.8246i q^{71} +(1.42273 + 2.44455i) q^{72} +4.06642 q^{73} +(-0.308285 + 0.850075i) q^{74} -1.00000i q^{75} +(3.29573 + 2.75244i) q^{76} +27.0719 q^{77} +(2.44361 - 6.73807i) q^{78} -3.65467 q^{79} +(3.93596 - 0.712870i) q^{80} +1.00000 q^{81} +(12.2323 + 4.43614i) q^{82} -1.98859 q^{83} +(-5.47430 + 6.55486i) q^{84} -2.28607 q^{85} +(7.40296 + 2.68473i) q^{86} -0.184440i q^{87} +(-9.02001 - 15.4983i) q^{88} +13.1874i q^{89} +(0.482147 - 1.32949i) q^{90} +21.6415 q^{91} +(-9.39964 - 1.90966i) q^{92} +6.08631 q^{93} +(-6.46916 + 17.8382i) q^{94} -2.14696i q^{95} +(5.57652 + 0.949963i) q^{96} -8.73755i q^{97} +(-14.9348 - 5.41622i) q^{98} -6.33992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(691\) \(1201\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32949 0.482147i −0.940089 0.340929i
\(3\) 1.00000i 0.577350i
\(4\) 1.53507 + 1.28202i 0.767534 + 0.641008i
\(5\) 1.00000i 0.447214i
\(6\) 0.482147 1.32949i 0.196836 0.542761i
\(7\) 4.27008 1.61394 0.806968 0.590595i \(-0.201107\pi\)
0.806968 + 0.590595i \(0.201107\pi\)
\(8\) −1.42273 2.44455i −0.503012 0.864280i
\(9\) −1.00000 −0.333333
\(10\) −0.482147 + 1.32949i −0.152468 + 0.420421i
\(11\) 6.33992 1.91156 0.955779 0.294085i \(-0.0950148\pi\)
0.955779 + 0.294085i \(0.0950148\pi\)
\(12\) −1.28202 + 1.53507i −0.370086 + 0.443136i
\(13\) 5.06818 1.40566 0.702829 0.711358i \(-0.251920\pi\)
0.702829 + 0.711358i \(0.251920\pi\)
\(14\) −5.67701 2.05880i −1.51724 0.550239i
\(15\) 1.00000 0.258199
\(16\) 0.712870 + 3.93596i 0.178217 + 0.983991i
\(17\) 2.28607i 0.554454i −0.960804 0.277227i \(-0.910585\pi\)
0.960804 0.277227i \(-0.0894153\pi\)
\(18\) 1.32949 + 0.482147i 0.313363 + 0.113643i
\(19\) 2.14696 0.492546 0.246273 0.969200i \(-0.420794\pi\)
0.246273 + 0.969200i \(0.420794\pi\)
\(20\) 1.28202 1.53507i 0.286667 0.343252i
\(21\) 4.27008i 0.931807i
\(22\) −8.42884 3.05678i −1.79704 0.651707i
\(23\) −4.21933 + 2.27976i −0.879790 + 0.475362i
\(24\) 2.44455 1.42273i 0.498992 0.290414i
\(25\) −1.00000 −0.200000
\(26\) −6.73807 2.44361i −1.32144 0.479231i
\(27\) 1.00000i 0.192450i
\(28\) 6.55486 + 5.47430i 1.23875 + 1.03455i
\(29\) −0.184440 −0.0342497 −0.0171249 0.999853i \(-0.505451\pi\)
−0.0171249 + 0.999853i \(0.505451\pi\)
\(30\) −1.32949 0.482147i −0.242730 0.0880276i
\(31\) 6.08631i 1.09313i −0.837415 0.546567i \(-0.815934\pi\)
0.837415 0.546567i \(-0.184066\pi\)
\(32\) 0.949963 5.57652i 0.167931 0.985799i
\(33\) 6.33992i 1.10364i
\(34\) −1.10222 + 3.03930i −0.189030 + 0.521236i
\(35\) 4.27008i 0.721774i
\(36\) −1.53507 1.28202i −0.255845 0.213669i
\(37\) 0.639401i 0.105117i −0.998618 0.0525584i \(-0.983262\pi\)
0.998618 0.0525584i \(-0.0167376\pi\)
\(38\) −2.85435 1.03515i −0.463037 0.167924i
\(39\) 5.06818i 0.811558i
\(40\) −2.44455 + 1.42273i −0.386518 + 0.224954i
\(41\) −9.20080 −1.43692 −0.718462 0.695566i \(-0.755154\pi\)
−0.718462 + 0.695566i \(0.755154\pi\)
\(42\) 2.05880 5.67701i 0.317680 0.875981i
\(43\) −5.56828 −0.849155 −0.424578 0.905392i \(-0.639577\pi\)
−0.424578 + 0.905392i \(0.639577\pi\)
\(44\) 9.73221 + 8.12788i 1.46719 + 1.22532i
\(45\) 1.00000i 0.149071i
\(46\) 6.70871 0.996570i 0.989146 0.146936i
\(47\) 13.4174i 1.95713i −0.205942 0.978564i \(-0.566026\pi\)
0.205942 0.978564i \(-0.433974\pi\)
\(48\) −3.93596 + 0.712870i −0.568108 + 0.102894i
\(49\) 11.2335 1.60479
\(50\) 1.32949 + 0.482147i 0.188018 + 0.0681859i
\(51\) 2.28607 0.320114
\(52\) 7.78000 + 6.49748i 1.07889 + 0.901039i
\(53\) 1.68353i 0.231251i −0.993293 0.115626i \(-0.963113\pi\)
0.993293 0.115626i \(-0.0368873\pi\)
\(54\) −0.482147 + 1.32949i −0.0656119 + 0.180920i
\(55\) 6.33992i 0.854875i
\(56\) −6.07517 10.4384i −0.811829 1.39489i
\(57\) 2.14696i 0.284372i
\(58\) 0.245211 + 0.0889274i 0.0321978 + 0.0116767i
\(59\) 6.99605i 0.910808i −0.890285 0.455404i \(-0.849495\pi\)
0.890285 0.455404i \(-0.150505\pi\)
\(60\) 1.53507 + 1.28202i 0.198176 + 0.165508i
\(61\) 10.7249i 1.37319i 0.727041 + 0.686594i \(0.240895\pi\)
−0.727041 + 0.686594i \(0.759105\pi\)
\(62\) −2.93450 + 8.09167i −0.372682 + 1.02764i
\(63\) −4.27008 −0.537979
\(64\) −3.95167 + 6.95589i −0.493958 + 0.869486i
\(65\) 5.06818i 0.628630i
\(66\) 3.05678 8.42884i 0.376263 1.03752i
\(67\) −11.6198 −1.41959 −0.709795 0.704409i \(-0.751212\pi\)
−0.709795 + 0.704409i \(0.751212\pi\)
\(68\) 2.93078 3.50928i 0.355409 0.425562i
\(69\) −2.27976 4.21933i −0.274450 0.507947i
\(70\) −2.05880 + 5.67701i −0.246074 + 0.678532i
\(71\) 14.8246i 1.75936i 0.475569 + 0.879678i \(0.342242\pi\)
−0.475569 + 0.879678i \(0.657758\pi\)
\(72\) 1.42273 + 2.44455i 0.167671 + 0.288093i
\(73\) 4.06642 0.475938 0.237969 0.971273i \(-0.423518\pi\)
0.237969 + 0.971273i \(0.423518\pi\)
\(74\) −0.308285 + 0.850075i −0.0358374 + 0.0988192i
\(75\) 1.00000i 0.115470i
\(76\) 3.29573 + 2.75244i 0.378046 + 0.315726i
\(77\) 27.0719 3.08513
\(78\) 2.44361 6.73807i 0.276684 0.762936i
\(79\) −3.65467 −0.411182 −0.205591 0.978638i \(-0.565912\pi\)
−0.205591 + 0.978638i \(0.565912\pi\)
\(80\) 3.93596 0.712870i 0.440054 0.0797013i
\(81\) 1.00000 0.111111
\(82\) 12.2323 + 4.43614i 1.35084 + 0.489890i
\(83\) −1.98859 −0.218276 −0.109138 0.994027i \(-0.534809\pi\)
−0.109138 + 0.994027i \(0.534809\pi\)
\(84\) −5.47430 + 6.55486i −0.597296 + 0.715194i
\(85\) −2.28607 −0.247959
\(86\) 7.40296 + 2.68473i 0.798281 + 0.289502i
\(87\) 0.184440i 0.0197741i
\(88\) −9.02001 15.4983i −0.961537 1.65212i
\(89\) 13.1874i 1.39786i 0.715191 + 0.698930i \(0.246340\pi\)
−0.715191 + 0.698930i \(0.753660\pi\)
\(90\) 0.482147 1.32949i 0.0508228 0.140140i
\(91\) 21.6415 2.26864
\(92\) −9.39964 1.90966i −0.979980 0.199096i
\(93\) 6.08631 0.631121
\(94\) −6.46916 + 17.8382i −0.667243 + 1.83987i
\(95\) 2.14696i 0.220273i
\(96\) 5.57652 + 0.949963i 0.569151 + 0.0969552i
\(97\) 8.73755i 0.887164i −0.896234 0.443582i \(-0.853707\pi\)
0.896234 0.443582i \(-0.146293\pi\)
\(98\) −14.9348 5.41622i −1.50865 0.547121i
\(99\) −6.33992 −0.637186
\(100\) −1.53507 1.28202i −0.153507 0.128202i
\(101\) −1.23440 −0.122827 −0.0614135 0.998112i \(-0.519561\pi\)
−0.0614135 + 0.998112i \(0.519561\pi\)
\(102\) −3.03930 1.10222i −0.300936 0.109136i
\(103\) −5.53812 −0.545687 −0.272844 0.962058i \(-0.587964\pi\)
−0.272844 + 0.962058i \(0.587964\pi\)
\(104\) −7.21066 12.3894i −0.707063 1.21488i
\(105\) 4.27008 0.416717
\(106\) −0.811711 + 2.23824i −0.0788403 + 0.217397i
\(107\) 8.82985 0.853614 0.426807 0.904343i \(-0.359638\pi\)
0.426807 + 0.904343i \(0.359638\pi\)
\(108\) 1.28202 1.53507i 0.123362 0.147712i
\(109\) 13.7436i 1.31640i 0.752843 + 0.658200i \(0.228682\pi\)
−0.752843 + 0.658200i \(0.771318\pi\)
\(110\) −3.05678 + 8.42884i −0.291452 + 0.803658i
\(111\) 0.639401 0.0606892
\(112\) 3.04401 + 16.8069i 0.287632 + 1.58810i
\(113\) 9.28660i 0.873610i 0.899556 + 0.436805i \(0.143890\pi\)
−0.899556 + 0.436805i \(0.856110\pi\)
\(114\) 1.03515 2.85435i 0.0969507 0.267335i
\(115\) 2.27976 + 4.21933i 0.212588 + 0.393454i
\(116\) −0.283129 0.236456i −0.0262878 0.0219543i
\(117\) −5.06818 −0.468553
\(118\) −3.37312 + 9.30115i −0.310521 + 0.856240i
\(119\) 9.76170i 0.894853i
\(120\) −1.42273 2.44455i −0.129877 0.223156i
\(121\) 29.1946 2.65406
\(122\) 5.17100 14.2587i 0.468161 1.29092i
\(123\) 9.20080i 0.829609i
\(124\) 7.80275 9.34291i 0.700708 0.839018i
\(125\) 1.00000i 0.0894427i
\(126\) 5.67701 + 2.05880i 0.505748 + 0.183413i
\(127\) 1.34406i 0.119266i −0.998220 0.0596328i \(-0.981007\pi\)
0.998220 0.0596328i \(-0.0189930\pi\)
\(128\) 8.60745 7.34247i 0.760798 0.648989i
\(129\) 5.56828i 0.490260i
\(130\) −2.44361 + 6.73807i −0.214318 + 0.590968i
\(131\) 4.08505i 0.356913i 0.983948 + 0.178456i \(0.0571103\pi\)
−0.983948 + 0.178456i \(0.942890\pi\)
\(132\) −8.12788 + 9.73221i −0.707441 + 0.847081i
\(133\) 9.16768 0.794939
\(134\) 15.4484 + 5.60247i 1.33454 + 0.483980i
\(135\) −1.00000 −0.0860663
\(136\) −5.58842 + 3.25247i −0.479203 + 0.278897i
\(137\) 4.20683i 0.359413i 0.983720 + 0.179707i \(0.0575149\pi\)
−0.983720 + 0.179707i \(0.942485\pi\)
\(138\) 0.996570 + 6.70871i 0.0848337 + 0.571084i
\(139\) 3.26694i 0.277098i −0.990356 0.138549i \(-0.955756\pi\)
0.990356 0.138549i \(-0.0442439\pi\)
\(140\) 5.47430 6.55486i 0.462663 0.553987i
\(141\) 13.4174 1.12995
\(142\) 7.14764 19.7091i 0.599817 1.65395i
\(143\) 32.1318 2.68700
\(144\) −0.712870 3.93596i −0.0594058 0.327997i
\(145\) 0.184440i 0.0153169i
\(146\) −5.40625 1.96061i −0.447424 0.162261i
\(147\) 11.2335i 0.926527i
\(148\) 0.819722 0.981524i 0.0673807 0.0806808i
\(149\) 4.04197i 0.331131i −0.986199 0.165566i \(-0.947055\pi\)
0.986199 0.165566i \(-0.0529450\pi\)
\(150\) −0.482147 + 1.32949i −0.0393671 + 0.108552i
\(151\) 13.1086i 1.06676i 0.845874 + 0.533382i \(0.179079\pi\)
−0.845874 + 0.533382i \(0.820921\pi\)
\(152\) −3.05455 5.24835i −0.247757 0.425698i
\(153\) 2.28607i 0.184818i
\(154\) −35.9918 13.0527i −2.90030 1.05181i
\(155\) −6.08631 −0.488864
\(156\) −6.49748 + 7.78000i −0.520215 + 0.622898i
\(157\) 5.45303i 0.435200i −0.976038 0.217600i \(-0.930177\pi\)
0.976038 0.217600i \(-0.0698228\pi\)
\(158\) 4.85883 + 1.76209i 0.386548 + 0.140184i
\(159\) 1.68353 0.133513
\(160\) −5.57652 0.949963i −0.440863 0.0751012i
\(161\) −18.0168 + 9.73473i −1.41993 + 0.767204i
\(162\) −1.32949 0.482147i −0.104454 0.0378811i
\(163\) 11.4235i 0.894754i −0.894345 0.447377i \(-0.852358\pi\)
0.894345 0.447377i \(-0.147642\pi\)
\(164\) −14.1239 11.7956i −1.10289 0.921080i
\(165\) 6.33992 0.493562
\(166\) 2.64380 + 0.958792i 0.205199 + 0.0744167i
\(167\) 20.6429i 1.59739i −0.601734 0.798697i \(-0.705523\pi\)
0.601734 0.798697i \(-0.294477\pi\)
\(168\) 10.4384 6.07517i 0.805342 0.468710i
\(169\) 12.6864 0.975877
\(170\) 3.03930 + 1.10222i 0.233104 + 0.0845366i
\(171\) −2.14696 −0.164182
\(172\) −8.54769 7.13863i −0.651756 0.544315i
\(173\) −5.69694 −0.433131 −0.216565 0.976268i \(-0.569485\pi\)
−0.216565 + 0.976268i \(0.569485\pi\)
\(174\) −0.0889274 + 0.245211i −0.00674157 + 0.0185894i
\(175\) −4.27008 −0.322787
\(176\) 4.51954 + 24.9537i 0.340673 + 1.88096i
\(177\) 6.99605 0.525855
\(178\) 6.35825 17.5324i 0.476571 1.31411i
\(179\) 4.11047i 0.307231i −0.988131 0.153615i \(-0.950908\pi\)
0.988131 0.153615i \(-0.0490917\pi\)
\(180\) −1.28202 + 1.53507i −0.0955558 + 0.114417i
\(181\) 11.3771i 0.845655i 0.906210 + 0.422827i \(0.138962\pi\)
−0.906210 + 0.422827i \(0.861038\pi\)
\(182\) −28.7721 10.4344i −2.13273 0.773448i
\(183\) −10.7249 −0.792811
\(184\) 11.5760 + 7.07088i 0.853391 + 0.521272i
\(185\) −0.639401 −0.0470097
\(186\) −8.09167 2.93450i −0.593310 0.215168i
\(187\) 14.4935i 1.05987i
\(188\) 17.2013 20.5966i 1.25454 1.50216i
\(189\) 4.27008i 0.310602i
\(190\) −1.03515 + 2.85435i −0.0750977 + 0.207077i
\(191\) 6.76632 0.489593 0.244797 0.969574i \(-0.421279\pi\)
0.244797 + 0.969574i \(0.421279\pi\)
\(192\) −6.95589 3.95167i −0.501998 0.285187i
\(193\) −22.6747 −1.63216 −0.816079 0.577941i \(-0.803857\pi\)
−0.816079 + 0.577941i \(0.803857\pi\)
\(194\) −4.21279 + 11.6165i −0.302460 + 0.834013i
\(195\) 5.06818 0.362940
\(196\) 17.2443 + 14.4016i 1.23173 + 1.02868i
\(197\) −18.6303 −1.32735 −0.663677 0.748019i \(-0.731005\pi\)
−0.663677 + 0.748019i \(0.731005\pi\)
\(198\) 8.42884 + 3.05678i 0.599012 + 0.217236i
\(199\) 8.02404 0.568809 0.284405 0.958704i \(-0.408204\pi\)
0.284405 + 0.958704i \(0.408204\pi\)
\(200\) 1.42273 + 2.44455i 0.100602 + 0.172856i
\(201\) 11.6198i 0.819600i
\(202\) 1.64111 + 0.595160i 0.115468 + 0.0418753i
\(203\) −0.787574 −0.0552769
\(204\) 3.50928 + 2.93078i 0.245698 + 0.205196i
\(205\) 9.20080i 0.642612i
\(206\) 7.36286 + 2.67019i 0.512994 + 0.186041i
\(207\) 4.21933 2.27976i 0.293263 0.158454i
\(208\) 3.61295 + 19.9482i 0.250513 + 1.38316i
\(209\) 13.6116 0.941531
\(210\) −5.67701 2.05880i −0.391751 0.142071i
\(211\) 19.6771i 1.35463i −0.735694 0.677314i \(-0.763144\pi\)
0.735694 0.677314i \(-0.236856\pi\)
\(212\) 2.15832 2.58434i 0.148234 0.177493i
\(213\) −14.8246 −1.01577
\(214\) −11.7392 4.25729i −0.802473 0.291022i
\(215\) 5.56828i 0.379754i
\(216\) −2.44455 + 1.42273i −0.166331 + 0.0968047i
\(217\) 25.9890i 1.76425i
\(218\) 6.62644 18.2719i 0.448799 1.23753i
\(219\) 4.06642i 0.274783i
\(220\) 8.12788 9.73221i 0.547982 0.656146i
\(221\) 11.5862i 0.779373i
\(222\) −0.850075 0.308285i −0.0570533 0.0206908i
\(223\) 21.7302i 1.45516i 0.686022 + 0.727581i \(0.259356\pi\)
−0.686022 + 0.727581i \(0.740644\pi\)
\(224\) 4.05641 23.8122i 0.271031 1.59102i
\(225\) 1.00000 0.0666667
\(226\) 4.47751 12.3464i 0.297839 0.821271i
\(227\) −19.5294 −1.29621 −0.648106 0.761550i \(-0.724438\pi\)
−0.648106 + 0.761550i \(0.724438\pi\)
\(228\) −2.75244 + 3.29573i −0.182285 + 0.218265i
\(229\) 6.03097i 0.398538i −0.979945 0.199269i \(-0.936143\pi\)
0.979945 0.199269i \(-0.0638567\pi\)
\(230\) −0.996570 6.70871i −0.0657119 0.442360i
\(231\) 27.0719i 1.78120i
\(232\) 0.262409 + 0.450874i 0.0172280 + 0.0296013i
\(233\) 15.5780 1.02055 0.510275 0.860011i \(-0.329544\pi\)
0.510275 + 0.860011i \(0.329544\pi\)
\(234\) 6.73807 + 2.44361i 0.440481 + 0.159744i
\(235\) −13.4174 −0.875254
\(236\) 8.96904 10.7394i 0.583835 0.699076i
\(237\) 3.65467i 0.237396i
\(238\) −4.70657 + 12.9780i −0.305082 + 0.841241i
\(239\) 29.6232i 1.91616i 0.286496 + 0.958081i \(0.407509\pi\)
−0.286496 + 0.958081i \(0.592491\pi\)
\(240\) 0.712870 + 3.93596i 0.0460155 + 0.254065i
\(241\) 1.02822i 0.0662336i 0.999451 + 0.0331168i \(0.0105433\pi\)
−0.999451 + 0.0331168i \(0.989457\pi\)
\(242\) −38.8139 14.0761i −2.49505 0.904846i
\(243\) 1.00000i 0.0641500i
\(244\) −13.7496 + 16.4635i −0.880225 + 1.05397i
\(245\) 11.2335i 0.717685i
\(246\) −4.43614 + 12.2323i −0.282838 + 0.779906i
\(247\) 10.8812 0.692352
\(248\) −14.8783 + 8.65919i −0.944773 + 0.549859i
\(249\) 1.98859i 0.126022i
\(250\) 0.482147 1.32949i 0.0304937 0.0840841i
\(251\) 7.72202 0.487410 0.243705 0.969849i \(-0.421637\pi\)
0.243705 + 0.969849i \(0.421637\pi\)
\(252\) −6.55486 5.47430i −0.412917 0.344849i
\(253\) −26.7502 + 14.4535i −1.68177 + 0.908683i
\(254\) −0.648033 + 1.78690i −0.0406612 + 0.112120i
\(255\) 2.28607i 0.143159i
\(256\) −14.9836 + 5.61166i −0.936477 + 0.350729i
\(257\) 15.8364 0.987846 0.493923 0.869506i \(-0.335563\pi\)
0.493923 + 0.869506i \(0.335563\pi\)
\(258\) −2.68473 + 7.40296i −0.167144 + 0.460888i
\(259\) 2.73029i 0.169652i
\(260\) 6.49748 7.78000i 0.402957 0.482495i
\(261\) 0.184440 0.0114166
\(262\) 1.96960 5.43102i 0.121682 0.335530i
\(263\) 18.7282 1.15483 0.577414 0.816452i \(-0.304062\pi\)
0.577414 + 0.816452i \(0.304062\pi\)
\(264\) 15.4983 9.02001i 0.953853 0.555143i
\(265\) −1.68353 −0.103419
\(266\) −12.1883 4.42017i −0.747313 0.271018i
\(267\) −13.1874 −0.807054
\(268\) −17.8372 14.8968i −1.08958 0.909968i
\(269\) −7.39847 −0.451093 −0.225546 0.974232i \(-0.572417\pi\)
−0.225546 + 0.974232i \(0.572417\pi\)
\(270\) 1.32949 + 0.482147i 0.0809100 + 0.0293425i
\(271\) 6.22206i 0.377963i −0.981981 0.188982i \(-0.939481\pi\)
0.981981 0.188982i \(-0.0605186\pi\)
\(272\) 8.99789 1.62967i 0.545577 0.0988133i
\(273\) 21.6415i 1.30980i
\(274\) 2.02831 5.59292i 0.122535 0.337880i
\(275\) −6.33992 −0.382312
\(276\) 1.90966 9.39964i 0.114948 0.565792i
\(277\) −11.9387 −0.717326 −0.358663 0.933467i \(-0.616767\pi\)
−0.358663 + 0.933467i \(0.616767\pi\)
\(278\) −1.57514 + 4.34335i −0.0944709 + 0.260497i
\(279\) 6.08631i 0.364378i
\(280\) −10.4384 + 6.07517i −0.623815 + 0.363061i
\(281\) 28.3633i 1.69201i 0.533174 + 0.846006i \(0.320999\pi\)
−0.533174 + 0.846006i \(0.679001\pi\)
\(282\) −17.8382 6.46916i −1.06225 0.385233i
\(283\) 11.4358 0.679788 0.339894 0.940464i \(-0.389609\pi\)
0.339894 + 0.940464i \(0.389609\pi\)
\(284\) −19.0054 + 22.7568i −1.12776 + 1.35037i
\(285\) 2.14696 0.127175
\(286\) −42.7188 15.4923i −2.52602 0.916077i
\(287\) −39.2881 −2.31910
\(288\) −0.949963 + 5.57652i −0.0559771 + 0.328600i
\(289\) 11.7739 0.692581
\(290\) 0.0889274 0.245211i 0.00522200 0.0143993i
\(291\) 8.73755 0.512205
\(292\) 6.24223 + 5.21322i 0.365299 + 0.305080i
\(293\) 21.5790i 1.26066i 0.776327 + 0.630330i \(0.217080\pi\)
−0.776327 + 0.630330i \(0.782920\pi\)
\(294\) 5.41622 14.9348i 0.315880 0.871018i
\(295\) −6.99605 −0.407326
\(296\) −1.56305 + 0.909696i −0.0908504 + 0.0528750i
\(297\) 6.33992i 0.367880i
\(298\) −1.94882 + 5.37375i −0.112892 + 0.311293i
\(299\) −21.3843 + 11.5542i −1.23668 + 0.668197i
\(300\) 1.28202 1.53507i 0.0740172 0.0886272i
\(301\) −23.7770 −1.37048
\(302\) 6.32029 17.4277i 0.363692 1.00285i
\(303\) 1.23440i 0.0709142i
\(304\) 1.53050 + 8.45036i 0.0877804 + 0.484661i
\(305\) 10.7249 0.614109
\(306\) 1.10222 3.03930i 0.0630099 0.173745i
\(307\) 5.89225i 0.336289i 0.985762 + 0.168144i \(0.0537775\pi\)
−0.985762 + 0.168144i \(0.946223\pi\)
\(308\) 41.5573 + 34.7067i 2.36795 + 1.97760i
\(309\) 5.53812i 0.315053i
\(310\) 8.09167 + 2.93450i 0.459576 + 0.166668i
\(311\) 10.5498i 0.598224i 0.954218 + 0.299112i \(0.0966905\pi\)
−0.954218 + 0.299112i \(0.903310\pi\)
\(312\) 12.3894 7.21066i 0.701413 0.408223i
\(313\) 22.2836i 1.25954i 0.776781 + 0.629771i \(0.216851\pi\)
−0.776781 + 0.629771i \(0.783149\pi\)
\(314\) −2.62916 + 7.24974i −0.148372 + 0.409126i
\(315\) 4.27008i 0.240591i
\(316\) −5.61017 4.68534i −0.315597 0.263571i
\(317\) 4.20644 0.236257 0.118129 0.992998i \(-0.462310\pi\)
0.118129 + 0.992998i \(0.462310\pi\)
\(318\) −2.23824 0.811711i −0.125514 0.0455185i
\(319\) −1.16934 −0.0654703
\(320\) 6.95589 + 3.95167i 0.388846 + 0.220905i
\(321\) 8.82985i 0.492834i
\(322\) 28.6467 4.25543i 1.59642 0.237146i
\(323\) 4.90810i 0.273094i
\(324\) 1.53507 + 1.28202i 0.0852816 + 0.0712231i
\(325\) −5.06818 −0.281132
\(326\) −5.50779 + 15.1873i −0.305048 + 0.841149i
\(327\) −13.7436 −0.760023
\(328\) 13.0903 + 22.4918i 0.722790 + 1.24190i
\(329\) 57.2933i 3.15868i
\(330\) −8.42884 3.05678i −0.463992 0.168270i
\(331\) 16.0620i 0.882847i −0.897299 0.441423i \(-0.854474\pi\)
0.897299 0.441423i \(-0.145526\pi\)
\(332\) −3.05262 2.54940i −0.167534 0.139917i
\(333\) 0.639401i 0.0350390i
\(334\) −9.95290 + 27.4444i −0.544598 + 1.50169i
\(335\) 11.6198i 0.634860i
\(336\) −16.8069 + 3.04401i −0.916890 + 0.166064i
\(337\) 3.96429i 0.215948i −0.994154 0.107974i \(-0.965564\pi\)
0.994154 0.107974i \(-0.0344364\pi\)
\(338\) −16.8664 6.11671i −0.917411 0.332705i
\(339\) −9.28660 −0.504379
\(340\) −3.50928 2.93078i −0.190317 0.158944i
\(341\) 38.5868i 2.08959i
\(342\) 2.85435 + 1.03515i 0.154346 + 0.0559745i
\(343\) 18.0775 0.976096
\(344\) 7.92217 + 13.6120i 0.427135 + 0.733907i
\(345\) −4.21933 + 2.27976i −0.227161 + 0.122738i
\(346\) 7.57401 + 2.74677i 0.407181 + 0.147667i
\(347\) 7.81164i 0.419351i 0.977771 + 0.209675i \(0.0672408\pi\)
−0.977771 + 0.209675i \(0.932759\pi\)
\(348\) 0.236456 0.283129i 0.0126753 0.0151773i
\(349\) −33.4169 −1.78876 −0.894382 0.447305i \(-0.852384\pi\)
−0.894382 + 0.447305i \(0.852384\pi\)
\(350\) 5.67701 + 2.05880i 0.303449 + 0.110048i
\(351\) 5.06818i 0.270519i
\(352\) 6.02269 35.3547i 0.321011 1.88441i
\(353\) −0.0557663 −0.00296814 −0.00148407 0.999999i \(-0.500472\pi\)
−0.00148407 + 0.999999i \(0.500472\pi\)
\(354\) −9.30115 3.37312i −0.494350 0.179279i
\(355\) 14.8246 0.786808
\(356\) −16.9064 + 20.2435i −0.896039 + 1.07290i
\(357\) 9.76170 0.516644
\(358\) −1.98185 + 5.46481i −0.104744 + 0.288824i
\(359\) −10.1353 −0.534923 −0.267462 0.963569i \(-0.586185\pi\)
−0.267462 + 0.963569i \(0.586185\pi\)
\(360\) 2.44455 1.42273i 0.128839 0.0749846i
\(361\) −14.3906 −0.757398
\(362\) 5.48545 15.1257i 0.288309 0.794991i
\(363\) 29.1946i 1.53232i
\(364\) 33.2212 + 27.7447i 1.74126 + 1.45422i
\(365\) 4.06642i 0.212846i
\(366\) 14.2587 + 5.17100i 0.745313 + 0.270293i
\(367\) 26.4828 1.38239 0.691195 0.722668i \(-0.257085\pi\)
0.691195 + 0.722668i \(0.257085\pi\)
\(368\) −11.9809 14.9819i −0.624546 0.780988i
\(369\) 9.20080 0.478975
\(370\) 0.850075 + 0.308285i 0.0441933 + 0.0160270i
\(371\) 7.18881i 0.373225i
\(372\) 9.34291 + 7.80275i 0.484407 + 0.404554i
\(373\) 22.9313i 1.18734i 0.804710 + 0.593668i \(0.202321\pi\)
−0.804710 + 0.593668i \(0.797679\pi\)
\(374\) −6.98801 + 19.2689i −0.361341 + 0.996373i
\(375\) −1.00000 −0.0516398
\(376\) −32.7995 + 19.0894i −1.69151 + 0.984459i
\(377\) −0.934776 −0.0481434
\(378\) −2.05880 + 5.67701i −0.105893 + 0.291994i
\(379\) 17.6902 0.908686 0.454343 0.890827i \(-0.349874\pi\)
0.454343 + 0.890827i \(0.349874\pi\)
\(380\) 2.75244 3.29573i 0.141197 0.169067i
\(381\) 1.34406 0.0688581
\(382\) −8.99572 3.26236i −0.460261 0.166917i
\(383\) −34.2904 −1.75216 −0.876079 0.482167i \(-0.839850\pi\)
−0.876079 + 0.482167i \(0.839850\pi\)
\(384\) 7.34247 + 8.60745i 0.374694 + 0.439247i
\(385\) 27.0719i 1.37971i
\(386\) 30.1457 + 10.9325i 1.53437 + 0.556451i
\(387\) 5.56828 0.283052
\(388\) 11.2017 13.4127i 0.568679 0.680929i
\(389\) 0.380521i 0.0192932i −0.999953 0.00964660i \(-0.996929\pi\)
0.999953 0.00964660i \(-0.00307066\pi\)
\(390\) −6.73807 2.44361i −0.341195 0.123737i
\(391\) 5.21169 + 9.64568i 0.263566 + 0.487803i
\(392\) −15.9823 27.4610i −0.807229 1.38699i
\(393\) −4.08505 −0.206064
\(394\) 24.7687 + 8.98254i 1.24783 + 0.452534i
\(395\) 3.65467i 0.183886i
\(396\) −9.73221 8.12788i −0.489062 0.408441i
\(397\) −13.1522 −0.660089 −0.330045 0.943965i \(-0.607064\pi\)
−0.330045 + 0.943965i \(0.607064\pi\)
\(398\) −10.6679 3.86877i −0.534731 0.193924i
\(399\) 9.16768i 0.458958i
\(400\) −0.712870 3.93596i −0.0356435 0.196798i
\(401\) 7.17569i 0.358337i −0.983818 0.179169i \(-0.942659\pi\)
0.983818 0.179169i \(-0.0573407\pi\)
\(402\) −5.60247 + 15.4484i −0.279426 + 0.770497i
\(403\) 30.8465i 1.53657i
\(404\) −1.89488 1.58252i −0.0942739 0.0787331i
\(405\) 1.00000i 0.0496904i
\(406\) 1.04707 + 0.379727i 0.0519652 + 0.0188455i
\(407\) 4.05375i 0.200937i
\(408\) −3.25247 5.58842i −0.161021 0.276668i
\(409\) 0.900619 0.0445327 0.0222664 0.999752i \(-0.492912\pi\)
0.0222664 + 0.999752i \(0.492912\pi\)
\(410\) 4.43614 12.2323i 0.219085 0.604112i
\(411\) −4.20683 −0.207507
\(412\) −8.50139 7.09996i −0.418834 0.349790i
\(413\) 29.8736i 1.46999i
\(414\) −6.70871 + 0.996570i −0.329715 + 0.0489787i
\(415\) 1.98859i 0.0976160i
\(416\) 4.81458 28.2628i 0.236054 1.38570i
\(417\) 3.26694 0.159983
\(418\) −18.0964 6.56277i −0.885123 0.320996i
\(419\) −3.26664 −0.159586 −0.0797929 0.996811i \(-0.525426\pi\)
−0.0797929 + 0.996811i \(0.525426\pi\)
\(420\) 6.55486 + 5.47430i 0.319844 + 0.267119i
\(421\) 4.17945i 0.203694i −0.994800 0.101847i \(-0.967525\pi\)
0.994800 0.101847i \(-0.0324752\pi\)
\(422\) −9.48726 + 26.1604i −0.461833 + 1.27347i
\(423\) 13.4174i 0.652376i
\(424\) −4.11548 + 2.39522i −0.199866 + 0.116322i
\(425\) 2.28607i 0.110891i
\(426\) 19.7091 + 7.14764i 0.954909 + 0.346304i
\(427\) 45.7963i 2.21624i
\(428\) 13.5544 + 11.3200i 0.655178 + 0.547173i
\(429\) 32.1318i 1.55134i
\(430\) 2.68473 7.40296i 0.129469 0.357002i
\(431\) −17.2005 −0.828520 −0.414260 0.910159i \(-0.635960\pi\)
−0.414260 + 0.910159i \(0.635960\pi\)
\(432\) 3.93596 0.712870i 0.189369 0.0342980i
\(433\) 16.2997i 0.783313i −0.920111 0.391657i \(-0.871902\pi\)
0.920111 0.391657i \(-0.128098\pi\)
\(434\) −12.5305 + 34.5520i −0.601485 + 1.65855i
\(435\) −0.184440 −0.00884324
\(436\) −17.6195 + 21.0974i −0.843822 + 1.01038i
\(437\) −9.05872 + 4.89455i −0.433337 + 0.234138i
\(438\) 1.96061 5.40625i 0.0936817 0.258321i
\(439\) 6.44669i 0.307684i −0.988095 0.153842i \(-0.950835\pi\)
0.988095 0.153842i \(-0.0491647\pi\)
\(440\) −15.4983 + 9.02001i −0.738851 + 0.430012i
\(441\) −11.2335 −0.534931
\(442\) −5.58626 + 15.4037i −0.265711 + 0.732680i
\(443\) 21.1812i 1.00635i 0.864185 + 0.503175i \(0.167835\pi\)
−0.864185 + 0.503175i \(0.832165\pi\)
\(444\) 0.981524 + 0.819722i 0.0465811 + 0.0389023i
\(445\) 13.1874 0.625142
\(446\) 10.4772 28.8900i 0.496108 1.36798i
\(447\) 4.04197 0.191179
\(448\) −16.8739 + 29.7022i −0.797217 + 1.40329i
\(449\) −10.8884 −0.513855 −0.256927 0.966431i \(-0.582710\pi\)
−0.256927 + 0.966431i \(0.582710\pi\)
\(450\) −1.32949 0.482147i −0.0626726 0.0227286i
\(451\) −58.3324 −2.74676
\(452\) −11.9056 + 14.2556i −0.559991 + 0.670526i
\(453\) −13.1086 −0.615897
\(454\) 25.9641 + 9.41604i 1.21855 + 0.441917i
\(455\) 21.6415i 1.01457i
\(456\) 5.24835 3.05455i 0.245777 0.143042i
\(457\) 19.9654i 0.933942i 0.884273 + 0.466971i \(0.154655\pi\)
−0.884273 + 0.466971i \(0.845345\pi\)
\(458\) −2.90782 + 8.01810i −0.135873 + 0.374661i
\(459\) −2.28607 −0.106705
\(460\) −1.90966 + 9.39964i −0.0890384 + 0.438260i
\(461\) −23.0529 −1.07368 −0.536840 0.843684i \(-0.680382\pi\)
−0.536840 + 0.843684i \(0.680382\pi\)
\(462\) 13.0527 35.9918i 0.607265 1.67449i
\(463\) 31.1058i 1.44561i −0.691053 0.722804i \(-0.742853\pi\)
0.691053 0.722804i \(-0.257147\pi\)
\(464\) −0.131482 0.725951i −0.00610390 0.0337014i
\(465\) 6.08631i 0.282246i
\(466\) −20.7108 7.51090i −0.959408 0.347936i
\(467\) −35.4360 −1.63978 −0.819891 0.572520i \(-0.805966\pi\)
−0.819891 + 0.572520i \(0.805966\pi\)
\(468\) −7.78000 6.49748i −0.359630 0.300346i
\(469\) −49.6176 −2.29113
\(470\) 17.8382 + 6.46916i 0.822817 + 0.298400i
\(471\) 5.45303 0.251263
\(472\) −17.1022 + 9.95350i −0.787192 + 0.458147i
\(473\) −35.3025 −1.62321
\(474\) −1.76209 + 4.85883i −0.0809354 + 0.223174i
\(475\) −2.14696 −0.0985093
\(476\) 12.5146 14.9849i 0.573608 0.686830i
\(477\) 1.68353i 0.0770837i
\(478\) 14.2827 39.3836i 0.653276 1.80136i
\(479\) 29.2482 1.33638 0.668192 0.743989i \(-0.267068\pi\)
0.668192 + 0.743989i \(0.267068\pi\)
\(480\) 0.949963 5.57652i 0.0433597 0.254532i
\(481\) 3.24060i 0.147758i
\(482\) 0.495754 1.36701i 0.0225810 0.0622655i
\(483\) −9.73473 18.0168i −0.442946 0.819795i
\(484\) 44.8157 + 37.4280i 2.03708 + 1.70127i
\(485\) −8.73755 −0.396752
\(486\) 0.482147 1.32949i 0.0218706 0.0603067i
\(487\) 13.0759i 0.592526i 0.955106 + 0.296263i \(0.0957405\pi\)
−0.955106 + 0.296263i \(0.904260\pi\)
\(488\) 26.2177 15.2587i 1.18682 0.690730i
\(489\) 11.4235 0.516587
\(490\) −5.41622 + 14.9348i −0.244680 + 0.674687i
\(491\) 16.4461i 0.742203i −0.928592 0.371102i \(-0.878980\pi\)
0.928592 0.371102i \(-0.121020\pi\)
\(492\) 11.7956 14.1239i 0.531786 0.636753i
\(493\) 0.421644i 0.0189899i
\(494\) −14.4664 5.24632i −0.650873 0.236043i
\(495\) 6.33992i 0.284958i
\(496\) 23.9555 4.33875i 1.07563 0.194816i
\(497\) 63.3022i 2.83949i
\(498\) −0.958792 + 2.64380i −0.0429645 + 0.118472i
\(499\) 33.1788i 1.48529i −0.669686 0.742644i \(-0.733571\pi\)
0.669686 0.742644i \(-0.266429\pi\)
\(500\) −1.28202 + 1.53507i −0.0573335 + 0.0686503i
\(501\) 20.6429 0.922255
\(502\) −10.2663 3.72315i −0.458209 0.166172i
\(503\) 5.75291 0.256510 0.128255 0.991741i \(-0.459062\pi\)
0.128255 + 0.991741i \(0.459062\pi\)
\(504\) 6.07517 + 10.4384i 0.270610 + 0.464964i
\(505\) 1.23440i 0.0549299i
\(506\) 42.5327 6.31818i 1.89081 0.280877i
\(507\) 12.6864i 0.563423i
\(508\) 1.72310 2.06322i 0.0764503 0.0915405i
\(509\) 33.4402 1.48221 0.741105 0.671389i \(-0.234302\pi\)
0.741105 + 0.671389i \(0.234302\pi\)
\(510\) −1.10222 + 3.03930i −0.0488072 + 0.134582i
\(511\) 17.3639 0.768134
\(512\) 22.6262 0.236311i 0.999945 0.0104436i
\(513\) 2.14696i 0.0947906i
\(514\) −21.0542 7.63546i −0.928663 0.336786i
\(515\) 5.53812i 0.244039i
\(516\) 7.13863 8.54769i 0.314261 0.376291i
\(517\) 85.0653i 3.74117i
\(518\) −1.31640 + 3.62988i −0.0578394 + 0.159488i
\(519\) 5.69694i 0.250068i
\(520\) −12.3894 + 7.21066i −0.543312 + 0.316208i
\(521\) 42.6418i 1.86817i 0.357050 + 0.934085i \(0.383783\pi\)
−0.357050 + 0.934085i \(0.616217\pi\)
\(522\) −0.245211 0.0889274i −0.0107326 0.00389225i
\(523\) 23.8459 1.04271 0.521353 0.853341i \(-0.325427\pi\)
0.521353 + 0.853341i \(0.325427\pi\)
\(524\) −5.23710 + 6.27083i −0.228784 + 0.273943i
\(525\) 4.27008i 0.186361i
\(526\) −24.8988 9.02972i −1.08564 0.393715i
\(527\) −13.9137 −0.606092
\(528\) −24.9537 + 4.51954i −1.08597 + 0.196688i
\(529\) 12.6054 19.2381i 0.548062 0.836438i
\(530\) 2.23824 + 0.811711i 0.0972227 + 0.0352585i
\(531\) 6.99605i 0.303603i
\(532\) 14.0730 + 11.7531i 0.610143 + 0.509562i
\(533\) −46.6313 −2.01983
\(534\) 17.5324 + 6.35825i 0.758703 + 0.275149i
\(535\) 8.82985i 0.381748i
\(536\) 16.5319 + 28.4053i 0.714070 + 1.22692i
\(537\) 4.11047 0.177380
\(538\) 9.83617 + 3.56715i 0.424067 + 0.153791i
\(539\) 71.2198 3.06765
\(540\) −1.53507 1.28202i −0.0660588 0.0551692i
\(541\) −21.7135 −0.933535 −0.466768 0.884380i \(-0.654582\pi\)
−0.466768 + 0.884380i \(0.654582\pi\)
\(542\) −2.99995 + 8.27214i −0.128859 + 0.355319i
\(543\) −11.3771 −0.488239
\(544\) −12.7483 2.17168i −0.546580 0.0931101i
\(545\) 13.7436 0.588712
\(546\) 10.4344 28.7721i 0.446550 1.23133i
\(547\) 0.483696i 0.0206813i 0.999947 + 0.0103407i \(0.00329159\pi\)
−0.999947 + 0.0103407i \(0.996708\pi\)
\(548\) −5.39322 + 6.45776i −0.230387 + 0.275862i
\(549\) 10.7249i 0.457730i
\(550\) 8.42884 + 3.05678i 0.359407 + 0.130341i
\(551\) −0.395986 −0.0168696
\(552\) −7.07088 + 11.5760i −0.300956 + 0.492705i
\(553\) −15.6057 −0.663622
\(554\) 15.8723 + 5.75620i 0.674350 + 0.244557i
\(555\) 0.639401i 0.0271411i
\(556\) 4.18827 5.01497i 0.177622 0.212682i
\(557\) 44.9485i 1.90453i −0.305272 0.952265i \(-0.598748\pi\)
0.305272 0.952265i \(-0.401252\pi\)
\(558\) 2.93450 8.09167i 0.124227 0.342548i
\(559\) −28.2210 −1.19362
\(560\) 16.8069 3.04401i 0.710220 0.128633i
\(561\) 14.4935 0.611917
\(562\) 13.6753 37.7086i 0.576857 1.59064i
\(563\) 33.9938 1.43267 0.716334 0.697757i \(-0.245819\pi\)
0.716334 + 0.697757i \(0.245819\pi\)
\(564\) 20.5966 + 17.2013i 0.867274 + 0.724306i
\(565\) 9.28660 0.390690
\(566\) −15.2038 5.51374i −0.639061 0.231760i
\(567\) 4.27008 0.179326
\(568\) 36.2395 21.0914i 1.52058 0.884977i
\(569\) 11.3973i 0.477801i 0.971044 + 0.238900i \(0.0767870\pi\)
−0.971044 + 0.238900i \(0.923213\pi\)
\(570\) −2.85435 1.03515i −0.119556 0.0433577i
\(571\) 21.2400 0.888866 0.444433 0.895812i \(-0.353405\pi\)
0.444433 + 0.895812i \(0.353405\pi\)
\(572\) 49.3246 + 41.1935i 2.06236 + 1.72239i
\(573\) 6.76632i 0.282667i
\(574\) 52.2330 + 18.9427i 2.18016 + 0.790651i
\(575\) 4.21933 2.27976i 0.175958 0.0950724i
\(576\) 3.95167 6.95589i 0.164653 0.289829i
\(577\) 31.9987 1.33212 0.666062 0.745896i \(-0.267978\pi\)
0.666062 + 0.745896i \(0.267978\pi\)
\(578\) −15.6532 5.67674i −0.651088 0.236121i
\(579\) 22.6747i 0.942327i
\(580\) −0.236456 + 0.283129i −0.00981828 + 0.0117563i
\(581\) −8.49142 −0.352284
\(582\) −11.6165 4.21279i −0.481518 0.174626i
\(583\) 10.6735i 0.442050i
\(584\) −5.78543 9.94057i −0.239403 0.411344i
\(585\) 5.06818i 0.209543i
\(586\) 10.4043 28.6890i 0.429796 1.18513i
\(587\) 41.5654i 1.71559i 0.513994 + 0.857794i \(0.328165\pi\)
−0.513994 + 0.857794i \(0.671835\pi\)
\(588\) −14.4016 + 17.2443i −0.593911 + 0.711141i
\(589\) 13.0671i 0.538419i
\(590\) 9.30115 + 3.37312i 0.382922 + 0.138869i
\(591\) 18.6303i 0.766348i
\(592\) 2.51666 0.455810i 0.103434 0.0187337i
\(593\) 40.3723 1.65789 0.828945 0.559330i \(-0.188942\pi\)
0.828945 + 0.559330i \(0.188942\pi\)
\(594\) −3.05678 + 8.42884i −0.125421 + 0.345840i
\(595\) −9.76170 −0.400190
\(596\) 5.18187 6.20470i 0.212258 0.254155i
\(597\) 8.02404i 0.328402i
\(598\) 34.0009 5.05079i 1.39040 0.206542i
\(599\) 2.25262i 0.0920395i 0.998941 + 0.0460198i \(0.0146537\pi\)
−0.998941 + 0.0460198i \(0.985346\pi\)
\(600\) −2.44455 + 1.42273i −0.0997984 + 0.0580828i
\(601\) −0.510957 −0.0208424 −0.0104212 0.999946i \(-0.503317\pi\)
−0.0104212 + 0.999946i \(0.503317\pi\)
\(602\) 31.6112 + 11.4640i 1.28838 + 0.467238i
\(603\) 11.6198 0.473196
\(604\) −16.8055 + 20.1226i −0.683805 + 0.818779i
\(605\) 29.1946i 1.18693i
\(606\) −0.595160 + 1.64111i −0.0241767 + 0.0666656i
\(607\) 47.9293i 1.94539i −0.232083 0.972696i \(-0.574554\pi\)
0.232083 0.972696i \(-0.425446\pi\)
\(608\) 2.03953 11.9726i 0.0827140 0.485552i
\(609\) 0.787574i 0.0319141i
\(610\) −14.2587 5.17100i −0.577317 0.209368i
\(611\) 68.0017i 2.75106i
\(612\) −2.93078 + 3.50928i −0.118470 + 0.141854i
\(613\) 13.6334i 0.550649i −0.961351 0.275325i \(-0.911215\pi\)
0.961351 0.275325i \(-0.0887854\pi\)
\(614\) 2.84093 7.83367i 0.114651 0.316141i
\(615\) −9.20080 −0.371012
\(616\) −38.5161 66.1788i −1.55186 2.66642i
\(617\) 44.3044i 1.78363i 0.452402 + 0.891814i \(0.350567\pi\)
−0.452402 + 0.891814i \(0.649433\pi\)
\(618\) −2.67019 + 7.36286i −0.107411 + 0.296177i
\(619\) 26.7059 1.07340 0.536700 0.843773i \(-0.319671\pi\)
0.536700 + 0.843773i \(0.319671\pi\)
\(620\) −9.34291 7.80275i −0.375220 0.313366i
\(621\) 2.27976 + 4.21933i 0.0914835 + 0.169316i
\(622\) 5.08656 14.0258i 0.203952 0.562384i
\(623\) 56.3111i 2.25606i
\(624\) −19.9482 + 3.61295i −0.798565 + 0.144634i
\(625\) 1.00000 0.0400000
\(626\) 10.7440 29.6257i 0.429415 1.18408i
\(627\) 13.6116i 0.543593i
\(628\) 6.99088 8.37078i 0.278966 0.334031i
\(629\) −1.46172 −0.0582824
\(630\) 2.05880 5.67701i 0.0820247 0.226177i
\(631\) −29.7923 −1.18601 −0.593006 0.805198i \(-0.702059\pi\)
−0.593006 + 0.805198i \(0.702059\pi\)
\(632\) 5.19962 + 8.93403i 0.206830 + 0.355377i
\(633\) 19.6771 0.782095
\(634\) −5.59241 2.02812i −0.222103 0.0805471i
\(635\) −1.34406 −0.0533372
\(636\) 2.58434 + 2.15832i 0.102476 + 0.0855828i
\(637\) 56.9336 2.25579
\(638\) 1.55462 + 0.563793i 0.0615479 + 0.0223208i
\(639\) 14.8246i 0.586452i
\(640\) −7.34247 8.60745i −0.290237 0.340239i
\(641\) 16.6470i 0.657517i 0.944414 + 0.328758i \(0.106630\pi\)
−0.944414 + 0.328758i \(0.893370\pi\)
\(642\) 4.25729 11.7392i 0.168022 0.463308i
\(643\) −19.8644 −0.783375 −0.391687 0.920098i \(-0.628109\pi\)
−0.391687 + 0.920098i \(0.628109\pi\)
\(644\) −40.1372 8.15439i −1.58163 0.321328i
\(645\) −5.56828 −0.219251
\(646\) −2.36643 + 6.52526i −0.0931058 + 0.256733i
\(647\) 3.09993i 0.121871i 0.998142 + 0.0609354i \(0.0194083\pi\)
−0.998142 + 0.0609354i \(0.980592\pi\)
\(648\) −1.42273 2.44455i −0.0558902 0.0960311i
\(649\) 44.3544i 1.74106i
\(650\) 6.73807 + 2.44361i 0.264289 + 0.0958461i
\(651\) 25.9890 1.01859
\(652\) 14.6451 17.5358i 0.573545 0.686755i
\(653\) 10.1831 0.398497 0.199249 0.979949i \(-0.436150\pi\)
0.199249 + 0.979949i \(0.436150\pi\)
\(654\) 18.2719 + 6.62644i 0.714490 + 0.259114i
\(655\) 4.08505 0.159616
\(656\) −6.55898 36.2140i −0.256085 1.41392i
\(657\) −4.06642 −0.158646
\(658\) −27.6238 + 76.1707i −1.07689 + 2.96944i
\(659\) 34.4249 1.34100 0.670501 0.741908i \(-0.266079\pi\)
0.670501 + 0.741908i \(0.266079\pi\)
\(660\) 9.73221 + 8.12788i 0.378826 + 0.316377i
\(661\) 36.0651i 1.40277i −0.712783 0.701385i \(-0.752565\pi\)
0.712783 0.701385i \(-0.247435\pi\)
\(662\) −7.74424 + 21.3542i −0.300989 + 0.829955i
\(663\) 11.5862 0.449971
\(664\) 2.82923 + 4.86121i 0.109795 + 0.188651i
\(665\) 9.16768i 0.355507i
\(666\) 0.308285 0.850075i 0.0119458 0.0329397i
\(667\) 0.778214 0.420479i 0.0301326 0.0162810i
\(668\) 26.4645 31.6882i 1.02394 1.22605i
\(669\) −21.7302 −0.840138
\(670\) 5.60247 15.4484i 0.216442 0.596824i
\(671\) 67.9953i 2.62493i
\(672\) 23.8122 + 4.05641i 0.918574 + 0.156480i
\(673\) 17.8360 0.687527 0.343764 0.939056i \(-0.388298\pi\)
0.343764 + 0.939056i \(0.388298\pi\)
\(674\) −1.91137 + 5.27047i −0.0736232 + 0.203011i
\(675\) 1.00000i 0.0384900i
\(676\) 19.4745 + 16.2642i 0.749019 + 0.625545i
\(677\) 31.3870i 1.20630i 0.797627 + 0.603151i \(0.206088\pi\)
−0.797627 + 0.603151i \(0.793912\pi\)
\(678\) 12.3464 + 4.47751i 0.474161 + 0.171958i
\(679\) 37.3100i 1.43183i
\(680\) 3.25247 + 5.58842i 0.124726 + 0.214306i
\(681\) 19.5294i 0.748368i
\(682\) −18.6045 + 51.3006i −0.712403 + 1.96440i
\(683\) 27.7435i 1.06157i −0.847505 0.530787i \(-0.821896\pi\)
0.847505 0.530787i \(-0.178104\pi\)
\(684\) −3.29573 2.75244i −0.126015 0.105242i
\(685\) 4.20683 0.160735
\(686\) −24.0338 8.71603i −0.917617 0.332780i
\(687\) 6.03097 0.230096
\(688\) −3.96946 21.9166i −0.151334 0.835561i
\(689\) 8.53244i 0.325060i
\(690\) 6.70871 0.996570i 0.255396 0.0379388i
\(691\) 0.927373i 0.0352789i −0.999844 0.0176395i \(-0.994385\pi\)
0.999844 0.0176395i \(-0.00561511\pi\)
\(692\) −8.74520 7.30357i −0.332443 0.277640i
\(693\) −27.0719 −1.02838
\(694\) 3.76636 10.3855i 0.142969 0.394227i
\(695\) −3.26694 −0.123922
\(696\) −0.450874 + 0.262409i −0.0170903 + 0.00994660i
\(697\) 21.0337i 0.796708i
\(698\) 44.4273 + 16.1118i 1.68160 + 0.609842i
\(699\) 15.5780i 0.589215i
\(700\) −6.55486 5.47430i −0.247750 0.206909i
\(701\) 11.5413i 0.435910i 0.975959 + 0.217955i \(0.0699385\pi\)
−0.975959 + 0.217955i \(0.930061\pi\)
\(702\) −2.44361 + 6.73807i −0.0922280 + 0.254312i
\(703\) 1.37277i 0.0517749i
\(704\) −25.0533 + 44.0998i −0.944230 + 1.66207i
\(705\) 13.4174i 0.505328i
\(706\) 0.0741406 + 0.0268876i 0.00279032 + 0.00101193i
\(707\) −5.27096 −0.198235
\(708\) 10.7394 + 8.96904i 0.403612 + 0.337077i
\(709\) 46.1072i 1.73159i −0.500398 0.865796i \(-0.666813\pi\)
0.500398 0.865796i \(-0.333187\pi\)
\(710\) −19.7091 7.14764i −0.739670 0.268246i
\(711\) 3.65467 0.137061
\(712\) 32.2372 18.7621i 1.20814 0.703140i
\(713\) 13.8753 + 25.6801i 0.519635 + 0.961729i
\(714\) −12.9780 4.70657i −0.485691 0.176139i
\(715\) 32.1318i 1.20166i
\(716\) 5.26969 6.30985i 0.196938 0.235810i
\(717\) −29.6232 −1.10630
\(718\) 13.4748 + 4.88673i 0.502875 + 0.182371i
\(719\) 11.3976i 0.425058i −0.977155 0.212529i \(-0.931830\pi\)
0.977155 0.212529i \(-0.0681700\pi\)
\(720\) −3.93596 + 0.712870i −0.146685 + 0.0265671i
\(721\) −23.6482 −0.880705
\(722\) 19.1321 + 6.93837i 0.712021 + 0.258219i
\(723\) −1.02822 −0.0382400
\(724\) −14.5857 + 17.4647i −0.542072 + 0.649069i
\(725\) 0.184440 0.00684994
\(726\) 14.0761 38.8139i 0.522413 1.44052i
\(727\) 20.4020 0.756668 0.378334 0.925669i \(-0.376497\pi\)
0.378334 + 0.925669i \(0.376497\pi\)
\(728\) −30.7900 52.9037i −1.14115 1.96074i
\(729\) −1.00000 −0.0370370
\(730\) −1.96061 + 5.40625i −0.0725655 + 0.200094i
\(731\) 12.7295i 0.470817i
\(732\) −16.4635 13.7496i −0.608509 0.508198i
\(733\) 14.1545i 0.522807i 0.965230 + 0.261403i \(0.0841853\pi\)
−0.965230 + 0.261403i \(0.915815\pi\)
\(734\) −35.2085 12.7686i −1.29957 0.471297i
\(735\) 11.2335 0.414355
\(736\) 8.70490 + 25.6948i 0.320867 + 0.947124i
\(737\) −73.6689 −2.71363
\(738\) −12.2323 4.43614i −0.450279 0.163297i
\(739\) 20.9145i 0.769354i 0.923051 + 0.384677i \(0.125687\pi\)
−0.923051 + 0.384677i \(0.874313\pi\)
\(740\) −0.981524 0.819722i −0.0360815 0.0301336i
\(741\) 10.8812i 0.399730i
\(742\) −3.46607 + 9.55743i −0.127243 + 0.350864i
\(743\) −42.2593 −1.55034 −0.775171 0.631752i \(-0.782336\pi\)
−0.775171 + 0.631752i \(0.782336\pi\)
\(744\) −8.65919 14.8783i −0.317461 0.545465i
\(745\) −4.04197 −0.148086
\(746\) 11.0563 30.4868i 0.404798 1.11620i
\(747\) 1.98859 0.0727587
\(748\) 18.5809 22.2485i 0.679386 0.813487i
\(749\) 37.7041 1.37768
\(750\) 1.32949 + 0.482147i 0.0485460 + 0.0176055i
\(751\) −2.04064 −0.0744641 −0.0372320 0.999307i \(-0.511854\pi\)
−0.0372320 + 0.999307i \(0.511854\pi\)
\(752\) 52.8104 9.56486i 1.92580 0.348794i
\(753\) 7.72202i 0.281406i
\(754\) 1.24277 + 0.450700i 0.0452591 + 0.0164135i
\(755\) 13.1086 0.477072
\(756\) 5.47430 6.55486i 0.199099 0.238398i
\(757\) 16.9083i 0.614544i 0.951622 + 0.307272i \(0.0994161\pi\)
−0.951622 + 0.307272i \(0.900584\pi\)
\(758\) −23.5189 8.52930i −0.854246 0.309798i
\(759\) −14.4535 26.7502i −0.524628 0.970971i
\(760\) −5.24835 + 3.05455i −0.190378 + 0.110800i
\(761\) 15.7867 0.572269 0.286134 0.958189i \(-0.407630\pi\)
0.286134 + 0.958189i \(0.407630\pi\)
\(762\) −1.78690 0.648033i −0.0647327 0.0234757i
\(763\) 58.6863i 2.12459i
\(764\) 10.3868 + 8.67452i 0.375780 + 0.313833i
\(765\) 2.28607 0.0826531
\(766\) 45.5886 + 16.5330i 1.64718 + 0.597362i
\(767\) 35.4572i 1.28028i
\(768\) −5.61166 14.9836i −0.202493 0.540675i
\(769\) 2.35009i 0.0847464i 0.999102 + 0.0423732i \(0.0134919\pi\)
−0.999102 + 0.0423732i \(0.986508\pi\)
\(770\) −13.0527 + 35.9918i −0.470385 + 1.29705i
\(771\) 15.8364i 0.570333i
\(772\) −34.8072 29.0693i −1.25274 1.04623i
\(773\) 37.8489i 1.36133i 0.732595 + 0.680665i \(0.238309\pi\)
−0.732595 + 0.680665i \(0.761691\pi\)
\(774\) −7.40296 2.68473i −0.266094 0.0965007i
\(775\) 6.08631i 0.218627i
\(776\) −21.3594 + 12.4312i −0.766758 + 0.446254i
\(777\) 2.73029 0.0979486
\(778\) −0.183467 + 0.505898i −0.00657762 + 0.0181373i
\(779\) −19.7538 −0.707752
\(780\) 7.78000 + 6.49748i 0.278569 + 0.232647i
\(781\) 93.9868i 3.36311i
\(782\) −2.27823 15.3366i −0.0814693 0.548436i
\(783\) 0.184440i 0.00659136i
\(784\) 8.00805 + 44.2148i 0.286002 + 1.57910i
\(785\) −5.45303 −0.194627
\(786\) 5.43102 + 1.96960i 0.193718 + 0.0702532i
\(787\) 7.72930 0.275520 0.137760 0.990466i \(-0.456010\pi\)
0.137760 + 0.990466i \(0.456010\pi\)
\(788\) −28.5988 23.8843i −1.01879 0.850844i
\(789\) 18.7282i 0.666740i
\(790\) 1.76209 4.85883i 0.0626923 0.172870i
\(791\) 39.6545i 1.40995i
\(792\) 9.02001 + 15.4983i 0.320512 + 0.550707i
\(793\) 54.3559i 1.93023i
\(794\) 17.4857 + 6.34129i 0.620543 + 0.225044i
\(795\) 1.68353i 0.0597088i
\(796\) 12.3175 + 10.2870i 0.436581 + 0.364611i
\(797\) 42.3887i 1.50149i −0.660594 0.750743i \(-0.729696\pi\)
0.660594 0.750743i \(-0.270304\pi\)
\(798\) 4.42017 12.1883i 0.156472 0.431461i
\(799\) −30.6731 −1.08514
\(800\) −0.949963 + 5.57652i −0.0335863 + 0.197160i
\(801\) 13.1874i 0.465953i
\(802\) −3.45974 + 9.53999i −0.122168 + 0.336869i
\(803\) 25.7808 0.909784
\(804\) 14.8968 17.8372i 0.525370 0.629071i
\(805\) 9.73473 + 18.0168i 0.343104 + 0.635010i
\(806\) −14.8725 + 41.0100i −0.523863 + 1.44452i
\(807\) 7.39847i 0.260439i
\(808\) 1.75621 + 3.01754i 0.0617834 + 0.106157i
\(809\) 20.6701 0.726720 0.363360 0.931649i \(-0.381629\pi\)
0.363360 + 0.931649i \(0.381629\pi\)
\(810\) −0.482147 + 1.32949i −0.0169409 + 0.0467134i
\(811\) 30.9310i 1.08613i −0.839689 0.543067i \(-0.817263\pi\)
0.839689 0.543067i \(-0.182737\pi\)
\(812\) −1.20898 1.00968i −0.0424269 0.0354329i
\(813\) 6.22206 0.218217
\(814\) −1.95450 + 5.38941i −0.0685054 + 0.188899i
\(815\) −11.4235 −0.400146
\(816\) 1.62967 + 8.99789i 0.0570499 + 0.314989i
\(817\) −11.9549 −0.418248
\(818\) −1.19736 0.434231i −0.0418647 0.0151825i
\(819\) −21.6415 −0.756215
\(820\) −11.7956 + 14.1239i −0.411919 + 0.493227i
\(821\) 2.34307 0.0817735 0.0408868 0.999164i \(-0.486982\pi\)
0.0408868 + 0.999164i \(0.486982\pi\)
\(822\) 5.59292 + 2.02831i 0.195075 + 0.0707454i
\(823\) 38.8494i 1.35420i 0.735889 + 0.677102i \(0.236764\pi\)
−0.735889 + 0.677102i \(0.763236\pi\)
\(824\) 7.87926 + 13.5382i 0.274487 + 0.471626i
\(825\) 6.33992i 0.220728i
\(826\) −14.4035 + 39.7166i −0.501161 + 1.38192i
\(827\) 0.484323 0.0168415 0.00842077 0.999965i \(-0.497320\pi\)
0.00842077 + 0.999965i \(0.497320\pi\)
\(828\) 9.39964 + 1.90966i 0.326660 + 0.0663653i
\(829\) 21.9471 0.762255 0.381128 0.924522i \(-0.375536\pi\)
0.381128 + 0.924522i \(0.375536\pi\)
\(830\) 0.958792 2.64380i 0.0332802 0.0917677i
\(831\) 11.9387i 0.414148i
\(832\) −20.0277 + 35.2536i −0.694337 + 1.22220i
\(833\) 25.6807i 0.889783i
\(834\) −4.34335 1.57514i −0.150398 0.0545428i
\(835\) −20.6429 −0.714376
\(836\) 20.8947 + 17.4502i 0.722657 + 0.603529i
\(837\) −6.08631 −0.210374
\(838\) 4.34295 + 1.57500i 0.150025 + 0.0544075i
\(839\) −41.6416 −1.43763 −0.718813 0.695203i \(-0.755314\pi\)
−0.718813 + 0.695203i \(0.755314\pi\)
\(840\) −6.07517 10.4384i −0.209613 0.360160i
\(841\) −28.9660 −0.998827
\(842\) −2.01511 + 5.55652i −0.0694452 + 0.191490i
\(843\) −28.3633 −0.976883
\(844\) 25.2264 30.2057i 0.868327 1.03972i
\(845\) 12.6864i 0.436425i
\(846\) 6.46916 17.8382i 0.222414 0.613292i
\(847\) 124.663 4.28348
\(848\) 6.62633 1.20014i 0.227549 0.0412130i
\(849\) 11.4358i 0.392476i
\(850\) 1.10222 3.03930i 0.0378059 0.104247i
\(851\) 1.45768 + 2.69784i 0.0499686 + 0.0924808i
\(852\) −22.7568 19.0054i −0.779634 0.651114i
\(853\) −25.8101 −0.883721 −0.441860 0.897084i \(-0.645681\pi\)
−0.441860 + 0.897084i \(0.645681\pi\)
\(854\) 22.0806 60.8856i 0.755581 2.08346i
\(855\) 2.14696i 0.0734245i
\(856\) −12.5625 21.5850i −0.429378 0.737761i
\(857\) −0.817165 −0.0279138 −0.0139569 0.999903i \(-0.504443\pi\)
−0.0139569 + 0.999903i \(0.504443\pi\)
\(858\) 15.4923 42.7188i 0.528897 1.45840i
\(859\) 5.27081i 0.179838i 0.995949 + 0.0899189i \(0.0286608\pi\)
−0.995949 + 0.0899189i \(0.971339\pi\)
\(860\) −7.13863 + 8.54769i −0.243425 + 0.291474i
\(861\) 39.2881i 1.33894i
\(862\) 22.8679 + 8.29318i 0.778882 + 0.282467i
\(863\) 3.58063i 0.121886i 0.998141 + 0.0609430i \(0.0194108\pi\)
−0.998141 + 0.0609430i \(0.980589\pi\)
\(864\) −5.57652 0.949963i −0.189717 0.0323184i
\(865\) 5.69694i 0.193702i
\(866\) −7.85885 + 21.6702i −0.267055 + 0.736384i
\(867\) 11.7739i 0.399862i
\(868\) 33.3183 39.8949i 1.13090 1.35412i
\(869\) −23.1703 −0.785999
\(870\) 0.245211 + 0.0889274i 0.00831343 + 0.00301492i
\(871\) −58.8914 −1.99546
\(872\) 33.5970 19.5535i 1.13774 0.662164i
\(873\) 8.73755i 0.295721i
\(874\) 14.4033 2.13960i 0.487200 0.0723729i
\(875\) 4.27008i 0.144355i
\(876\) −5.21322 + 6.24223i −0.176138 + 0.210905i
\(877\) −43.6993 −1.47562 −0.737810 0.675008i \(-0.764140\pi\)
−0.737810 + 0.675008i \(0.764140\pi\)
\(878\) −3.10825 + 8.57079i −0.104899 + 0.289250i
\(879\) −21.5790 −0.727842
\(880\) 24.9537 4.51954i 0.841189 0.152354i
\(881\) 21.6563i 0.729620i −0.931082 0.364810i \(-0.881134\pi\)
0.931082 0.364810i \(-0.118866\pi\)
\(882\) 14.9348 + 5.41622i 0.502882 + 0.182374i
\(883\) 37.3040i 1.25538i −0.778464 0.627689i \(-0.784001\pi\)
0.778464 0.627689i \(-0.215999\pi\)
\(884\) 14.8537 17.7856i 0.499584 0.598195i
\(885\) 6.99605i 0.235170i
\(886\) 10.2125 28.1601i 0.343094 0.946058i
\(887\) 6.79994i 0.228320i −0.993462 0.114160i \(-0.963582\pi\)
0.993462 0.114160i \(-0.0364176\pi\)
\(888\) −0.909696 1.56305i −0.0305274 0.0524525i
\(889\) 5.73922i 0.192487i
\(890\) −17.5324 6.35825i −0.587689 0.213129i
\(891\) 6.33992 0.212395
\(892\) −27.8585 + 33.3574i −0.932771 + 1.11689i
\(893\) 28.8066i 0.963977i
\(894\) −5.37375 1.94882i −0.179725 0.0651784i
\(895\) −4.11047 −0.137398
\(896\) 36.7544 31.3529i 1.22788 1.04743i
\(897\) −11.5542 21.3843i −0.385784 0.714000i
\(898\) 14.4760 + 5.24980i 0.483069 + 0.175188i
\(899\) 1.12256i 0.0374395i
\(900\) 1.53507 + 1.28202i 0.0511689 + 0.0427339i
\(901\) −3.84868 −0.128218
\(902\) 77.5521 + 28.1248i 2.58220 + 0.936453i
\(903\) 23.7770i 0.791248i
\(904\) 22.7016 13.2124i 0.755043 0.439436i
\(905\) 11.3771 0.378188
\(906\) 17.4277 + 6.32029i 0.578998 + 0.209977i
\(907\) −29.6090 −0.983151 −0.491575 0.870835i \(-0.663579\pi\)
−0.491575 + 0.870835i \(0.663579\pi\)
\(908\) −29.9789 25.0370i −0.994886 0.830882i
\(909\) 1.23440 0.0409423
\(910\) −10.4344 + 28.7721i −0.345896 + 0.953785i
\(911\) −44.4726 −1.47344 −0.736721 0.676196i \(-0.763627\pi\)
−0.736721 + 0.676196i \(0.763627\pi\)
\(912\) −8.45036 + 1.53050i −0.279819 + 0.0506800i
\(913\) −12.6075 −0.417247
\(914\) 9.62626 26.5437i 0.318408 0.877989i
\(915\) 10.7249i 0.354556i
\(916\) 7.73180 9.25795i 0.255466 0.305891i
\(917\) 17.4435i 0.576035i
\(918\) 3.03930 + 1.10222i 0.100312 + 0.0363788i
\(919\) −25.2267 −0.832153 −0.416076 0.909330i \(-0.636595\pi\)
−0.416076 + 0.909330i \(0.636595\pi\)
\(920\) 7.07088 11.5760i 0.233120 0.381648i
\(921\) −5.89225 −0.194156
\(922\) 30.6485 + 11.1149i 1.00935 + 0.366049i
\(923\) 75.1337i 2.47306i
\(924\) −34.7067 + 41.5573i −1.14177 + 1.36713i
\(925\) 0.639401i 0.0210234i
\(926\) −14.9976 + 41.3547i −0.492850 + 1.35900i
\(927\) 5.53812 0.181896
\(928\) −0.175212 + 1.02854i −0.00575160 + 0.0337633i
\(929\) −7.22571 −0.237068 −0.118534 0.992950i \(-0.537819\pi\)
−0.118534 + 0.992950i \(0.537819\pi\)
\(930\) −2.93450 + 8.09167i −0.0962260 + 0.265336i
\(931\) 24.1180 0.790434
\(932\) 23.9133 + 19.9713i 0.783307 + 0.654181i
\(933\) −10.5498 −0.345385
\(934\) 47.1116 + 17.0853i 1.54154 + 0.559050i
\(935\) −14.4935 −0.473989
\(936\) 7.21066 + 12.3894i 0.235688 + 0.404961i
\(937\) 5.18714i 0.169457i −0.996404 0.0847283i \(-0.972998\pi\)
0.996404 0.0847283i \(-0.0270022\pi\)
\(938\) 65.9659 + 23.9230i 2.15386 + 0.781113i
\(939\) −22.2836 −0.727197
\(940\) −20.5966 17.2013i −0.671788 0.561045i
\(941\) 5.57594i 0.181770i 0.995861 + 0.0908852i \(0.0289696\pi\)
−0.995861 + 0.0908852i \(0.971030\pi\)
\(942\) −7.24974 2.62916i −0.236209 0.0856628i
\(943\) 38.8212 20.9756i 1.26419 0.683059i
\(944\) 27.5362 4.98727i 0.896227 0.162322i
\(945\) −4.27008 −0.138906
\(946\) 46.9342 + 17.0210i 1.52596 + 0.553400i
\(947\) 16.3670i 0.531856i −0.963993 0.265928i \(-0.914322\pi\)
0.963993 0.265928i \(-0.0856783\pi\)
\(948\) 4.68534 5.61017i 0.152173 0.182210i
\(949\) 20.6093 0.669007
\(950\) 2.85435 + 1.03515i 0.0926075 + 0.0335847i
\(951\) 4.20644i 0.136403i
\(952\) −23.8630 + 13.8883i −0.773403 + 0.450122i
\(953\) 28.4543i 0.921727i 0.887471 + 0.460863i \(0.152460\pi\)
−0.887471 + 0.460863i \(0.847540\pi\)
\(954\) 0.811711 2.23824i 0.0262801 0.0724655i
\(955\) 6.76632i 0.218953i
\(956\) −37.9774 + 45.4736i −1.22828 + 1.47072i
\(957\) 1.16934i 0.0377993i
\(958\) −38.8851 14.1019i −1.25632 0.455613i
\(959\) 17.9635i 0.580070i
\(960\) −3.95167 + 6.95589i −0.127539 + 0.224500i
\(961\) −6.04320 −0.194942
\(962\) −1.56244 + 4.30833i −0.0503752 + 0.138906i
\(963\) −8.82985 −0.284538
\(964\) −1.31820 + 1.57839i −0.0424563 + 0.0508366i
\(965\) 22.6747i 0.729923i
\(966\) 4.25543 + 28.6467i 0.136916 + 0.921693i
\(967\) 29.3267i 0.943085i −0.881843 0.471542i \(-0.843697\pi\)
0.881843 0.471542i \(-0.156303\pi\)
\(968\) −41.5361 71.3678i −1.33502 2.29385i
\(969\) 4.90810 0.157671
\(970\) 11.6165 + 4.21279i 0.372982 + 0.135264i
\(971\) −23.4011 −0.750977 −0.375488 0.926827i \(-0.622525\pi\)
−0.375488 + 0.926827i \(0.622525\pi\)
\(972\) −1.28202 + 1.53507i −0.0411207 + 0.0492373i
\(973\) 13.9501i 0.447219i
\(974\) 6.30451 17.3842i 0.202010 0.557027i
\(975\) 5.06818i 0.162312i
\(976\) −42.2130 + 7.64549i −1.35121 + 0.244726i
\(977\) 53.5732i 1.71396i −0.515351 0.856979i \(-0.672338\pi\)
0.515351 0.856979i \(-0.327662\pi\)
\(978\) −15.1873 5.50779i −0.485637 0.176120i
\(979\) 83.6069i 2.67209i
\(980\) 14.4016 17.2443i 0.460042 0.550848i
\(981\) 13.7436i 0.438800i
\(982\) −7.92945 + 21.8649i −0.253039 + 0.697737i
\(983\) 31.8612 1.01622 0.508108 0.861294i \(-0.330345\pi\)
0.508108 + 0.861294i \(0.330345\pi\)
\(984\) −22.4918 + 13.0903i −0.717014 + 0.417303i
\(985\) 18.6303i 0.593611i
\(986\) 0.203294 0.560570i 0.00647421 0.0178522i
\(987\) 57.2933 1.82367
\(988\) 16.7033 + 13.9498i 0.531404 + 0.443803i
\(989\) 23.4944 12.6943i 0.747078 0.403656i
\(990\) 3.05678 8.42884i 0.0971507 0.267886i
\(991\) 20.7723i 0.659855i −0.944006 0.329928i \(-0.892976\pi\)
0.944006 0.329928i \(-0.107024\pi\)
\(992\) −33.9404 5.78177i −1.07761 0.183571i
\(993\) 16.0620 0.509712
\(994\) 30.5210 84.1594i 0.968066 2.66937i
\(995\) 8.02404i 0.254379i
\(996\) 2.54940 3.05262i 0.0807809 0.0967259i
\(997\) −23.2860 −0.737475 −0.368737 0.929534i \(-0.620210\pi\)
−0.368737 + 0.929534i \(0.620210\pi\)
\(998\) −15.9971 + 44.1108i −0.506379 + 1.39630i
\(999\) −0.639401 −0.0202297
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 1380.2.p.b.91.5 yes 48
4.3 odd 2 1380.2.p.a.91.6 yes 48
23.22 odd 2 1380.2.p.a.91.5 48
92.91 even 2 inner 1380.2.p.b.91.6 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1380.2.p.a.91.5 48 23.22 odd 2
1380.2.p.a.91.6 yes 48 4.3 odd 2
1380.2.p.b.91.5 yes 48 1.1 even 1 trivial
1380.2.p.b.91.6 yes 48 92.91 even 2 inner