Properties

Label 930.2.r.b.119.13
Level $930$
Weight $2$
Character 930.119
Analytic conductor $7.426$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(119,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.119");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.r (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 119.13
Character \(\chi\) \(=\) 930.119
Dual form 930.2.r.b.719.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.681795 - 1.59222i) q^{3} +1.00000 q^{4} +(1.27870 + 1.83437i) q^{5} +(-0.681795 - 1.59222i) q^{6} +(1.56394 + 0.902941i) q^{7} +1.00000 q^{8} +(-2.07031 + 2.17113i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.681795 - 1.59222i) q^{3} +1.00000 q^{4} +(1.27870 + 1.83437i) q^{5} +(-0.681795 - 1.59222i) q^{6} +(1.56394 + 0.902941i) q^{7} +1.00000 q^{8} +(-2.07031 + 2.17113i) q^{9} +(1.27870 + 1.83437i) q^{10} +(1.36676 + 2.36730i) q^{11} +(-0.681795 - 1.59222i) q^{12} +(-1.89509 - 3.28240i) q^{13} +(1.56394 + 0.902941i) q^{14} +(2.04891 - 3.28664i) q^{15} +1.00000 q^{16} +(5.50887 + 3.18055i) q^{17} +(-2.07031 + 2.17113i) q^{18} +(0.217690 - 0.377051i) q^{19} +(1.27870 + 1.83437i) q^{20} +(0.371391 - 3.10575i) q^{21} +(1.36676 + 2.36730i) q^{22} +2.68202i q^{23} +(-0.681795 - 1.59222i) q^{24} +(-1.72984 + 4.69123i) q^{25} +(-1.89509 - 3.28240i) q^{26} +(4.86844 + 1.81611i) q^{27} +(1.56394 + 0.902941i) q^{28} -3.54035 q^{29} +(2.04891 - 3.28664i) q^{30} +(-0.925384 + 5.49032i) q^{31} +1.00000 q^{32} +(2.83741 - 3.79020i) q^{33} +(5.50887 + 3.18055i) q^{34} +(0.343482 + 4.02344i) q^{35} +(-2.07031 + 2.17113i) q^{36} +(5.35919 - 9.28239i) q^{37} +(0.217690 - 0.377051i) q^{38} +(-3.93422 + 5.25532i) q^{39} +(1.27870 + 1.83437i) q^{40} +(2.25018 - 1.29914i) q^{41} +(0.371391 - 3.10575i) q^{42} +(0.848315 - 1.46932i) q^{43} +(1.36676 + 2.36730i) q^{44} +(-6.62997 - 1.02149i) q^{45} +2.68202i q^{46} +1.54613 q^{47} +(-0.681795 - 1.59222i) q^{48} +(-1.86940 - 3.23789i) q^{49} +(-1.72984 + 4.69123i) q^{50} +(1.30820 - 10.9398i) q^{51} +(-1.89509 - 3.28240i) q^{52} +(8.31697 - 4.80180i) q^{53} +(4.86844 + 1.81611i) q^{54} +(-2.59483 + 5.53423i) q^{55} +(1.56394 + 0.902941i) q^{56} +(-0.748767 - 0.0895387i) q^{57} -3.54035 q^{58} +(-10.8827 - 6.28315i) q^{59} +(2.04891 - 3.28664i) q^{60} -3.25814i q^{61} +(-0.925384 + 5.49032i) q^{62} +(-5.19824 + 1.52615i) q^{63} +1.00000 q^{64} +(3.59788 - 7.67351i) q^{65} +(2.83741 - 3.79020i) q^{66} +(7.83494 - 4.52350i) q^{67} +(5.50887 + 3.18055i) q^{68} +(4.27036 - 1.82859i) q^{69} +(0.343482 + 4.02344i) q^{70} +(-5.72140 + 3.30325i) q^{71} +(-2.07031 + 2.17113i) q^{72} +(-3.73631 - 6.47149i) q^{73} +(5.35919 - 9.28239i) q^{74} +(8.64886 - 0.444174i) q^{75} +(0.217690 - 0.377051i) q^{76} +4.93642i q^{77} +(-3.93422 + 5.25532i) q^{78} +(0.884726 + 0.510797i) q^{79} +(1.27870 + 1.83437i) q^{80} +(-0.427634 - 8.98983i) q^{81} +(2.25018 - 1.29914i) q^{82} +(-1.00160 + 0.578276i) q^{83} +(0.371391 - 3.10575i) q^{84} +(1.20989 + 14.1723i) q^{85} +(0.848315 - 1.46932i) q^{86} +(2.41379 + 5.63700i) q^{87} +(1.36676 + 2.36730i) q^{88} +2.32751 q^{89} +(-6.62997 - 1.02149i) q^{90} -6.84462i q^{91} +2.68202i q^{92} +(9.37271 - 2.26987i) q^{93} +1.54613 q^{94} +(0.970012 - 0.0828103i) q^{95} +(-0.681795 - 1.59222i) q^{96} +11.8138i q^{97} +(-1.86940 - 3.23789i) q^{98} +(-7.96935 - 1.93363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.681795 1.59222i −0.393635 0.919267i
\(4\) 1.00000 0.500000
\(5\) 1.27870 + 1.83437i 0.571853 + 0.820356i
\(6\) −0.681795 1.59222i −0.278342 0.650020i
\(7\) 1.56394 + 0.902941i 0.591113 + 0.341279i 0.765538 0.643391i \(-0.222473\pi\)
−0.174424 + 0.984671i \(0.555806\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.07031 + 2.17113i −0.690103 + 0.723711i
\(10\) 1.27870 + 1.83437i 0.404361 + 0.580079i
\(11\) 1.36676 + 2.36730i 0.412095 + 0.713769i 0.995119 0.0986861i \(-0.0314640\pi\)
−0.583024 + 0.812455i \(0.698131\pi\)
\(12\) −0.681795 1.59222i −0.196817 0.459633i
\(13\) −1.89509 3.28240i −0.525604 0.910373i −0.999555 0.0298216i \(-0.990506\pi\)
0.473951 0.880551i \(-0.342827\pi\)
\(14\) 1.56394 + 0.902941i 0.417980 + 0.241321i
\(15\) 2.04891 3.28664i 0.529025 0.848606i
\(16\) 1.00000 0.250000
\(17\) 5.50887 + 3.18055i 1.33610 + 0.771397i 0.986226 0.165401i \(-0.0528918\pi\)
0.349872 + 0.936798i \(0.386225\pi\)
\(18\) −2.07031 + 2.17113i −0.487977 + 0.511741i
\(19\) 0.217690 0.377051i 0.0499416 0.0865013i −0.839974 0.542627i \(-0.817430\pi\)
0.889916 + 0.456125i \(0.150763\pi\)
\(20\) 1.27870 + 1.83437i 0.285926 + 0.410178i
\(21\) 0.371391 3.10575i 0.0810441 0.677730i
\(22\) 1.36676 + 2.36730i 0.291395 + 0.504711i
\(23\) 2.68202i 0.559240i 0.960111 + 0.279620i \(0.0902085\pi\)
−0.960111 + 0.279620i \(0.909791\pi\)
\(24\) −0.681795 1.59222i −0.139171 0.325010i
\(25\) −1.72984 + 4.69123i −0.345969 + 0.938246i
\(26\) −1.89509 3.28240i −0.371658 0.643731i
\(27\) 4.86844 + 1.81611i 0.936932 + 0.349511i
\(28\) 1.56394 + 0.902941i 0.295557 + 0.170640i
\(29\) −3.54035 −0.657426 −0.328713 0.944430i \(-0.606615\pi\)
−0.328713 + 0.944430i \(0.606615\pi\)
\(30\) 2.04891 3.28664i 0.374077 0.600055i
\(31\) −0.925384 + 5.49032i −0.166204 + 0.986091i
\(32\) 1.00000 0.176777
\(33\) 2.83741 3.79020i 0.493929 0.659789i
\(34\) 5.50887 + 3.18055i 0.944764 + 0.545460i
\(35\) 0.343482 + 4.02344i 0.0580591 + 0.680085i
\(36\) −2.07031 + 2.17113i −0.345052 + 0.361855i
\(37\) 5.35919 9.28239i 0.881045 1.52602i 0.0308649 0.999524i \(-0.490174\pi\)
0.850180 0.526492i \(-0.176493\pi\)
\(38\) 0.217690 0.377051i 0.0353140 0.0611657i
\(39\) −3.93422 + 5.25532i −0.629979 + 0.841525i
\(40\) 1.27870 + 1.83437i 0.202181 + 0.290040i
\(41\) 2.25018 1.29914i 0.351420 0.202892i −0.313891 0.949459i \(-0.601633\pi\)
0.665310 + 0.746567i \(0.268299\pi\)
\(42\) 0.371391 3.10575i 0.0573068 0.479228i
\(43\) 0.848315 1.46932i 0.129367 0.224070i −0.794065 0.607833i \(-0.792039\pi\)
0.923431 + 0.383763i \(0.125372\pi\)
\(44\) 1.36676 + 2.36730i 0.206047 + 0.356884i
\(45\) −6.62997 1.02149i −0.988338 0.152274i
\(46\) 2.68202i 0.395443i
\(47\) 1.54613 0.225526 0.112763 0.993622i \(-0.464030\pi\)
0.112763 + 0.993622i \(0.464030\pi\)
\(48\) −0.681795 1.59222i −0.0984087 0.229817i
\(49\) −1.86940 3.23789i −0.267057 0.462556i
\(50\) −1.72984 + 4.69123i −0.244637 + 0.663440i
\(51\) 1.30820 10.9398i 0.183185 1.53188i
\(52\) −1.89509 3.28240i −0.262802 0.455186i
\(53\) 8.31697 4.80180i 1.14242 0.659578i 0.195394 0.980725i \(-0.437401\pi\)
0.947030 + 0.321146i \(0.104068\pi\)
\(54\) 4.86844 + 1.81611i 0.662511 + 0.247142i
\(55\) −2.59483 + 5.53423i −0.349887 + 0.746235i
\(56\) 1.56394 + 0.902941i 0.208990 + 0.120661i
\(57\) −0.748767 0.0895387i −0.0991766 0.0118597i
\(58\) −3.54035 −0.464871
\(59\) −10.8827 6.28315i −1.41681 0.817997i −0.420794 0.907156i \(-0.638249\pi\)
−0.996017 + 0.0891593i \(0.971582\pi\)
\(60\) 2.04891 3.28664i 0.264513 0.424303i
\(61\) 3.25814i 0.417163i −0.978005 0.208581i \(-0.933115\pi\)
0.978005 0.208581i \(-0.0668846\pi\)
\(62\) −0.925384 + 5.49032i −0.117524 + 0.697272i
\(63\) −5.19824 + 1.52615i −0.654917 + 0.192277i
\(64\) 1.00000 0.125000
\(65\) 3.59788 7.67351i 0.446262 0.951782i
\(66\) 2.83741 3.79020i 0.349261 0.466541i
\(67\) 7.83494 4.52350i 0.957190 0.552634i 0.0618830 0.998083i \(-0.480289\pi\)
0.895307 + 0.445449i \(0.146956\pi\)
\(68\) 5.50887 + 3.18055i 0.668049 + 0.385698i
\(69\) 4.27036 1.82859i 0.514091 0.220136i
\(70\) 0.343482 + 4.02344i 0.0410540 + 0.480893i
\(71\) −5.72140 + 3.30325i −0.679005 + 0.392024i −0.799480 0.600692i \(-0.794892\pi\)
0.120475 + 0.992716i \(0.461558\pi\)
\(72\) −2.07031 + 2.17113i −0.243988 + 0.255870i
\(73\) −3.73631 6.47149i −0.437302 0.757430i 0.560178 0.828372i \(-0.310733\pi\)
−0.997480 + 0.0709422i \(0.977399\pi\)
\(74\) 5.35919 9.28239i 0.622993 1.07906i
\(75\) 8.64886 0.444174i 0.998684 0.0512888i
\(76\) 0.217690 0.377051i 0.0249708 0.0432507i
\(77\) 4.93642i 0.562558i
\(78\) −3.93422 + 5.25532i −0.445463 + 0.595048i
\(79\) 0.884726 + 0.510797i 0.0995395 + 0.0574692i 0.548943 0.835860i \(-0.315030\pi\)
−0.449404 + 0.893329i \(0.648364\pi\)
\(80\) 1.27870 + 1.83437i 0.142963 + 0.205089i
\(81\) −0.427634 8.98983i −0.0475149 0.998871i
\(82\) 2.25018 1.29914i 0.248491 0.143466i
\(83\) −1.00160 + 0.578276i −0.109940 + 0.0634740i −0.553962 0.832542i \(-0.686885\pi\)
0.444022 + 0.896016i \(0.353551\pi\)
\(84\) 0.371391 3.10575i 0.0405221 0.338865i
\(85\) 1.20989 + 14.1723i 0.131232 + 1.53720i
\(86\) 0.848315 1.46932i 0.0914761 0.158441i
\(87\) 2.41379 + 5.63700i 0.258786 + 0.604350i
\(88\) 1.36676 + 2.36730i 0.145697 + 0.252355i
\(89\) 2.32751 0.246715 0.123358 0.992362i \(-0.460634\pi\)
0.123358 + 0.992362i \(0.460634\pi\)
\(90\) −6.62997 1.02149i −0.698861 0.107674i
\(91\) 6.84462i 0.717511i
\(92\) 2.68202i 0.279620i
\(93\) 9.37271 2.26987i 0.971905 0.235374i
\(94\) 1.54613 0.159471
\(95\) 0.970012 0.0828103i 0.0995211 0.00849616i
\(96\) −0.681795 1.59222i −0.0695855 0.162505i
\(97\) 11.8138i 1.19951i 0.800183 + 0.599755i \(0.204735\pi\)
−0.800183 + 0.599755i \(0.795265\pi\)
\(98\) −1.86940 3.23789i −0.188838 0.327076i
\(99\) −7.96935 1.93363i −0.800950 0.194337i
\(100\) −1.72984 + 4.69123i −0.172984 + 0.469123i
\(101\) 15.5501i 1.54729i 0.633620 + 0.773645i \(0.281568\pi\)
−0.633620 + 0.773645i \(0.718432\pi\)
\(102\) 1.30820 10.9398i 0.129531 1.08320i
\(103\) −14.1597 + 8.17508i −1.39519 + 0.805515i −0.993884 0.110428i \(-0.964778\pi\)
−0.401308 + 0.915943i \(0.631444\pi\)
\(104\) −1.89509 3.28240i −0.185829 0.321865i
\(105\) 6.17200 3.29006i 0.602326 0.321077i
\(106\) 8.31697 4.80180i 0.807815 0.466392i
\(107\) −2.70745 + 4.68944i −0.261739 + 0.453345i −0.966704 0.255897i \(-0.917629\pi\)
0.704965 + 0.709242i \(0.250963\pi\)
\(108\) 4.86844 + 1.81611i 0.468466 + 0.174756i
\(109\) −3.08751 −0.295730 −0.147865 0.989008i \(-0.547240\pi\)
−0.147865 + 0.989008i \(0.547240\pi\)
\(110\) −2.59483 + 5.53423i −0.247408 + 0.527668i
\(111\) −18.4334 2.20430i −1.74963 0.209223i
\(112\) 1.56394 + 0.902941i 0.147778 + 0.0853199i
\(113\) −5.84956 10.1317i −0.550280 0.953113i −0.998254 0.0590664i \(-0.981188\pi\)
0.447974 0.894047i \(-0.352146\pi\)
\(114\) −0.748767 0.0895387i −0.0701284 0.00838607i
\(115\) −4.91983 + 3.42951i −0.458776 + 0.319803i
\(116\) −3.54035 −0.328713
\(117\) 11.0499 + 2.68108i 1.02157 + 0.247866i
\(118\) −10.8827 6.28315i −1.00184 0.578411i
\(119\) 5.74370 + 9.94837i 0.526524 + 0.911966i
\(120\) 2.04891 3.28664i 0.187039 0.300028i
\(121\) 1.76392 3.05519i 0.160356 0.277745i
\(122\) 3.25814i 0.294979i
\(123\) −3.60268 2.69703i −0.324843 0.243183i
\(124\) −0.925384 + 5.49032i −0.0831019 + 0.493046i
\(125\) −10.8174 + 2.82551i −0.967539 + 0.252721i
\(126\) −5.19824 + 1.52615i −0.463096 + 0.135960i
\(127\) 2.92334 5.06337i 0.259404 0.449301i −0.706678 0.707535i \(-0.749807\pi\)
0.966082 + 0.258234i \(0.0831405\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.91786 0.348923i −0.256903 0.0307209i
\(130\) 3.59788 7.67351i 0.315555 0.673011i
\(131\) −13.3521 7.70881i −1.16657 0.673522i −0.213704 0.976899i \(-0.568553\pi\)
−0.952871 + 0.303376i \(0.901886\pi\)
\(132\) 2.83741 3.79020i 0.246965 0.329895i
\(133\) 0.680908 0.393123i 0.0590423 0.0340881i
\(134\) 7.83494 4.52350i 0.676836 0.390771i
\(135\) 2.89386 + 11.2528i 0.249064 + 0.968487i
\(136\) 5.50887 + 3.18055i 0.472382 + 0.272730i
\(137\) −5.75226 + 3.32107i −0.491448 + 0.283738i −0.725175 0.688564i \(-0.758241\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(138\) 4.27036 1.82859i 0.363517 0.155660i
\(139\) 10.0512i 0.852531i 0.904598 + 0.426266i \(0.140171\pi\)
−0.904598 + 0.426266i \(0.859829\pi\)
\(140\) 0.343482 + 4.02344i 0.0290296 + 0.340043i
\(141\) −1.05414 2.46177i −0.0887748 0.207318i
\(142\) −5.72140 + 3.30325i −0.480129 + 0.277203i
\(143\) 5.18028 8.97251i 0.433197 0.750319i
\(144\) −2.07031 + 2.17113i −0.172526 + 0.180928i
\(145\) −4.52705 6.49432i −0.375951 0.539324i
\(146\) −3.73631 6.47149i −0.309220 0.535584i
\(147\) −3.88088 + 5.18406i −0.320089 + 0.427574i
\(148\) 5.35919 9.28239i 0.440523 0.763008i
\(149\) 6.45518 + 3.72690i 0.528829 + 0.305320i 0.740540 0.672013i \(-0.234570\pi\)
−0.211710 + 0.977332i \(0.567903\pi\)
\(150\) 8.64886 0.444174i 0.706176 0.0362667i
\(151\) 18.6368i 1.51664i −0.651880 0.758322i \(-0.726019\pi\)
0.651880 0.758322i \(-0.273981\pi\)
\(152\) 0.217690 0.377051i 0.0176570 0.0305828i
\(153\) −18.3105 + 5.37577i −1.48031 + 0.434605i
\(154\) 4.93642i 0.397788i
\(155\) −11.2546 + 5.32299i −0.903990 + 0.427553i
\(156\) −3.93422 + 5.25532i −0.314990 + 0.420762i
\(157\) 11.8145i 0.942901i −0.881893 0.471450i \(-0.843731\pi\)
0.881893 0.471450i \(-0.156269\pi\)
\(158\) 0.884726 + 0.510797i 0.0703851 + 0.0406368i
\(159\) −13.3160 9.96857i −1.05603 0.790559i
\(160\) 1.27870 + 1.83437i 0.101090 + 0.145020i
\(161\) −2.42171 + 4.19452i −0.190857 + 0.330574i
\(162\) −0.427634 8.98983i −0.0335981 0.706308i
\(163\) 20.5432i 1.60906i 0.593909 + 0.804532i \(0.297584\pi\)
−0.593909 + 0.804532i \(0.702416\pi\)
\(164\) 2.25018 1.29914i 0.175710 0.101446i
\(165\) 10.5808 + 0.358326i 0.823717 + 0.0278956i
\(166\) −1.00160 + 0.578276i −0.0777395 + 0.0448829i
\(167\) −9.55459 5.51635i −0.739356 0.426868i 0.0824789 0.996593i \(-0.473716\pi\)
−0.821835 + 0.569725i \(0.807050\pi\)
\(168\) 0.371391 3.10575i 0.0286534 0.239614i
\(169\) −0.682746 + 1.18255i −0.0525189 + 0.0909654i
\(170\) 1.20989 + 14.1723i 0.0927947 + 1.08697i
\(171\) 0.367941 + 1.25325i 0.0281371 + 0.0958381i
\(172\) 0.848315 1.46932i 0.0646834 0.112035i
\(173\) −13.0225 22.5556i −0.990079 1.71487i −0.616727 0.787177i \(-0.711542\pi\)
−0.373351 0.927690i \(-0.621791\pi\)
\(174\) 2.41379 + 5.63700i 0.182989 + 0.427340i
\(175\) −6.94127 + 5.77485i −0.524711 + 0.436538i
\(176\) 1.36676 + 2.36730i 0.103024 + 0.178442i
\(177\) −2.58434 + 21.6115i −0.194251 + 1.62442i
\(178\) 2.32751 0.174454
\(179\) 2.35224 4.07419i 0.175814 0.304519i −0.764628 0.644471i \(-0.777078\pi\)
0.940443 + 0.339952i \(0.110411\pi\)
\(180\) −6.62997 1.02149i −0.494169 0.0761372i
\(181\) −2.33559 + 1.34845i −0.173603 + 0.100230i −0.584284 0.811549i \(-0.698624\pi\)
0.410681 + 0.911779i \(0.365291\pi\)
\(182\) 6.84462i 0.507357i
\(183\) −5.18767 + 2.22139i −0.383484 + 0.164210i
\(184\) 2.68202i 0.197721i
\(185\) 23.8802 2.03866i 1.75570 0.149885i
\(186\) 9.37271 2.26987i 0.687240 0.166435i
\(187\) 17.3882i 1.27155i
\(188\) 1.54613 0.112763
\(189\) 5.97410 + 7.23621i 0.434552 + 0.526356i
\(190\) 0.970012 0.0828103i 0.0703721 0.00600769i
\(191\) −14.5902 + 8.42368i −1.05571 + 0.609516i −0.924243 0.381804i \(-0.875303\pi\)
−0.131470 + 0.991320i \(0.541970\pi\)
\(192\) −0.681795 1.59222i −0.0492044 0.114908i
\(193\) 14.2645 + 8.23560i 1.02678 + 0.592811i 0.916060 0.401041i \(-0.131351\pi\)
0.110719 + 0.993852i \(0.464685\pi\)
\(194\) 11.8138i 0.848182i
\(195\) −14.6709 0.496838i −1.05061 0.0355793i
\(196\) −1.86940 3.23789i −0.133528 0.231278i
\(197\) −0.508531 + 0.293601i −0.0362313 + 0.0209182i −0.518006 0.855377i \(-0.673326\pi\)
0.481775 + 0.876295i \(0.339992\pi\)
\(198\) −7.96935 1.93363i −0.566357 0.137417i
\(199\) 0.625276 0.361003i 0.0443246 0.0255908i −0.477674 0.878537i \(-0.658520\pi\)
0.521999 + 0.852946i \(0.325187\pi\)
\(200\) −1.72984 + 4.69123i −0.122318 + 0.331720i
\(201\) −12.5442 9.39082i −0.884801 0.662377i
\(202\) 15.5501i 1.09410i
\(203\) −5.53689 3.19672i −0.388613 0.224366i
\(204\) 1.30820 10.9398i 0.0915923 0.765940i
\(205\) 5.26043 + 2.46646i 0.367404 + 0.172265i
\(206\) −14.1597 + 8.17508i −0.986550 + 0.569585i
\(207\) −5.82303 5.55262i −0.404728 0.385934i
\(208\) −1.89509 3.28240i −0.131401 0.227593i
\(209\) 1.19012 0.0823226
\(210\) 6.17200 3.29006i 0.425909 0.227036i
\(211\) −12.8281 + 22.2190i −0.883124 + 1.52962i −0.0352755 + 0.999378i \(0.511231\pi\)
−0.847849 + 0.530238i \(0.822102\pi\)
\(212\) 8.31697 4.80180i 0.571212 0.329789i
\(213\) 9.16032 + 6.85757i 0.627655 + 0.469873i
\(214\) −2.70745 + 4.68944i −0.185077 + 0.320564i
\(215\) 3.78003 0.322703i 0.257796 0.0220081i
\(216\) 4.86844 + 1.81611i 0.331256 + 0.123571i
\(217\) −6.40468 + 7.75097i −0.434778 + 0.526170i
\(218\) −3.08751 −0.209112
\(219\) −7.75661 + 10.3613i −0.524143 + 0.700148i
\(220\) −2.59483 + 5.53423i −0.174944 + 0.373118i
\(221\) 24.1097i 1.62180i
\(222\) −18.4334 2.20430i −1.23717 0.147943i
\(223\) −2.25149 + 3.89969i −0.150771 + 0.261143i −0.931511 0.363713i \(-0.881509\pi\)
0.780740 + 0.624856i \(0.214842\pi\)
\(224\) 1.56394 + 0.902941i 0.104495 + 0.0603303i
\(225\) −6.60397 13.4680i −0.440265 0.897868i
\(226\) −5.84956 10.1317i −0.389107 0.673953i
\(227\) −7.02539 12.1683i −0.466292 0.807641i 0.532967 0.846136i \(-0.321077\pi\)
−0.999259 + 0.0384951i \(0.987744\pi\)
\(228\) −0.748767 0.0895387i −0.0495883 0.00592985i
\(229\) 18.8343 + 10.8740i 1.24461 + 0.718574i 0.970029 0.242990i \(-0.0781283\pi\)
0.274579 + 0.961565i \(0.411462\pi\)
\(230\) −4.91983 + 3.42951i −0.324404 + 0.226135i
\(231\) 7.85986 3.36563i 0.517141 0.221442i
\(232\) −3.54035 −0.232435
\(233\) 8.80114 0.576582 0.288291 0.957543i \(-0.406913\pi\)
0.288291 + 0.957543i \(0.406913\pi\)
\(234\) 11.0499 + 2.68108i 0.722357 + 0.175268i
\(235\) 1.97703 + 2.83617i 0.128968 + 0.185011i
\(236\) −10.8827 6.28315i −0.708406 0.408998i
\(237\) 0.210097 1.75694i 0.0136473 0.114125i
\(238\) 5.74370 + 9.94837i 0.372308 + 0.644857i
\(239\) 7.39846 + 12.8145i 0.478567 + 0.828902i 0.999698 0.0245746i \(-0.00782311\pi\)
−0.521131 + 0.853477i \(0.674490\pi\)
\(240\) 2.04891 3.28664i 0.132256 0.212152i
\(241\) 7.91848 + 4.57174i 0.510074 + 0.294491i 0.732864 0.680375i \(-0.238183\pi\)
−0.222790 + 0.974866i \(0.571516\pi\)
\(242\) 1.76392 3.05519i 0.113389 0.196395i
\(243\) −14.0222 + 6.81012i −0.899525 + 0.436869i
\(244\) 3.25814i 0.208581i
\(245\) 3.54909 7.56947i 0.226743 0.483595i
\(246\) −3.60268 2.69703i −0.229699 0.171956i
\(247\) −1.65017 −0.104998
\(248\) −0.925384 + 5.49032i −0.0587619 + 0.348636i
\(249\) 1.60363 + 1.20050i 0.101626 + 0.0760789i
\(250\) −10.8174 + 2.82551i −0.684153 + 0.178701i
\(251\) 11.7310 20.3187i 0.740454 1.28250i −0.211835 0.977305i \(-0.567944\pi\)
0.952289 0.305198i \(-0.0987226\pi\)
\(252\) −5.19824 + 1.52615i −0.327458 + 0.0961385i
\(253\) −6.34916 + 3.66569i −0.399168 + 0.230460i
\(254\) 2.92334 5.06337i 0.183426 0.317704i
\(255\) 21.7405 11.5890i 1.36144 0.725733i
\(256\) 1.00000 0.0625000
\(257\) −9.45976 16.3848i −0.590084 1.02206i −0.994221 0.107357i \(-0.965761\pi\)
0.404137 0.914699i \(-0.367572\pi\)
\(258\) −2.91786 0.348923i −0.181658 0.0217230i
\(259\) 16.7629 9.67806i 1.04160 0.601365i
\(260\) 3.59788 7.67351i 0.223131 0.475891i
\(261\) 7.32962 7.68657i 0.453692 0.475787i
\(262\) −13.3521 7.70881i −0.824893 0.476252i
\(263\) 9.36711i 0.577600i 0.957389 + 0.288800i \(0.0932563\pi\)
−0.957389 + 0.288800i \(0.906744\pi\)
\(264\) 2.83741 3.79020i 0.174630 0.233271i
\(265\) 19.4432 + 9.11634i 1.19439 + 0.560012i
\(266\) 0.680908 0.393123i 0.0417492 0.0241039i
\(267\) −1.58688 3.70589i −0.0971157 0.226797i
\(268\) 7.83494 4.52350i 0.478595 0.276317i
\(269\) −4.99236 8.64703i −0.304390 0.527219i 0.672735 0.739883i \(-0.265119\pi\)
−0.977125 + 0.212664i \(0.931786\pi\)
\(270\) 2.89386 + 11.2528i 0.176115 + 0.684824i
\(271\) 14.3826i 0.873678i −0.899540 0.436839i \(-0.856098\pi\)
0.899540 0.436839i \(-0.143902\pi\)
\(272\) 5.50887 + 3.18055i 0.334025 + 0.192849i
\(273\) −10.8981 + 4.66663i −0.659584 + 0.282437i
\(274\) −5.75226 + 3.32107i −0.347506 + 0.200633i
\(275\) −13.4699 + 2.31674i −0.812263 + 0.139705i
\(276\) 4.27036 1.82859i 0.257046 0.110068i
\(277\) −10.7709 −0.647163 −0.323581 0.946200i \(-0.604887\pi\)
−0.323581 + 0.946200i \(0.604887\pi\)
\(278\) 10.0512i 0.602831i
\(279\) −10.0044 13.3758i −0.598947 0.800788i
\(280\) 0.343482 + 4.02344i 0.0205270 + 0.240446i
\(281\) 15.1194i 0.901949i −0.892537 0.450975i \(-0.851076\pi\)
0.892537 0.450975i \(-0.148924\pi\)
\(282\) −1.05414 2.46177i −0.0627732 0.146596i
\(283\) 15.4123i 0.916167i −0.888909 0.458083i \(-0.848536\pi\)
0.888909 0.458083i \(-0.151464\pi\)
\(284\) −5.72140 + 3.30325i −0.339503 + 0.196012i
\(285\) −0.793202 1.48801i −0.0469852 0.0881421i
\(286\) 5.18028 8.97251i 0.306317 0.530556i
\(287\) 4.69220 0.276972
\(288\) −2.07031 + 2.17113i −0.121994 + 0.127935i
\(289\) 11.7318 + 20.3201i 0.690106 + 1.19530i
\(290\) −4.52705 6.49432i −0.265838 0.381360i
\(291\) 18.8101 8.05460i 1.10267 0.472169i
\(292\) −3.73631 6.47149i −0.218651 0.378715i
\(293\) 16.8667 29.2139i 0.985361 1.70670i 0.345039 0.938588i \(-0.387866\pi\)
0.640322 0.768107i \(-0.278801\pi\)
\(294\) −3.88088 + 5.18406i −0.226337 + 0.302341i
\(295\) −2.39014 27.9973i −0.139159 1.63006i
\(296\) 5.35919 9.28239i 0.311497 0.539528i
\(297\) 2.35471 + 14.0073i 0.136634 + 0.812785i
\(298\) 6.45518 + 3.72690i 0.373939 + 0.215894i
\(299\) 8.80346 5.08268i 0.509117 0.293939i
\(300\) 8.64886 0.444174i 0.499342 0.0256444i
\(301\) 2.65343 1.53196i 0.152941 0.0883005i
\(302\) 18.6368i 1.07243i
\(303\) 24.7591 10.6020i 1.42237 0.609067i
\(304\) 0.217690 0.377051i 0.0124854 0.0216253i
\(305\) 5.97665 4.16620i 0.342222 0.238556i
\(306\) −18.3105 + 5.37577i −1.04674 + 0.307312i
\(307\) 10.3344 + 5.96659i 0.589818 + 0.340532i 0.765025 0.644000i \(-0.222726\pi\)
−0.175208 + 0.984532i \(0.556060\pi\)
\(308\) 4.93642i 0.281279i
\(309\) 22.6705 + 16.9715i 1.28968 + 0.965475i
\(310\) −11.2546 + 5.32299i −0.639218 + 0.302326i
\(311\) 0.401203i 0.0227501i 0.999935 + 0.0113751i \(0.00362088\pi\)
−0.999935 + 0.0113751i \(0.996379\pi\)
\(312\) −3.93422 + 5.25532i −0.222731 + 0.297524i
\(313\) −10.0123 + 17.3418i −0.565930 + 0.980219i 0.431033 + 0.902336i \(0.358149\pi\)
−0.996963 + 0.0778829i \(0.975184\pi\)
\(314\) 11.8145i 0.666732i
\(315\) −9.44653 7.58402i −0.532252 0.427311i
\(316\) 0.884726 + 0.510797i 0.0497697 + 0.0287346i
\(317\) −14.0966 + 24.4161i −0.791746 + 1.37134i 0.133139 + 0.991097i \(0.457494\pi\)
−0.924885 + 0.380247i \(0.875839\pi\)
\(318\) −13.3160 9.96857i −0.746723 0.559010i
\(319\) −4.83882 8.38108i −0.270922 0.469250i
\(320\) 1.27870 + 1.83437i 0.0714816 + 0.102545i
\(321\) 9.31253 + 1.11361i 0.519775 + 0.0621555i
\(322\) −2.42171 + 4.19452i −0.134956 + 0.233751i
\(323\) 2.39846 1.38475i 0.133454 0.0770495i
\(324\) −0.427634 8.98983i −0.0237575 0.499435i
\(325\) 18.6767 3.21228i 1.03600 0.178185i
\(326\) 20.5432i 1.13778i
\(327\) 2.10505 + 4.91598i 0.116410 + 0.271855i
\(328\) 2.25018 1.29914i 0.124246 0.0717332i
\(329\) 2.41805 + 1.39606i 0.133311 + 0.0769673i
\(330\) 10.5808 + 0.358326i 0.582456 + 0.0197252i
\(331\) 7.83238 4.52202i 0.430506 0.248553i −0.269056 0.963125i \(-0.586712\pi\)
0.699562 + 0.714572i \(0.253378\pi\)
\(332\) −1.00160 + 0.578276i −0.0549701 + 0.0317370i
\(333\) 9.05811 + 30.8529i 0.496382 + 1.69073i
\(334\) −9.55459 5.51635i −0.522804 0.301841i
\(335\) 18.3163 + 8.58798i 1.00073 + 0.469212i
\(336\) 0.371391 3.10575i 0.0202610 0.169433i
\(337\) −24.7796 −1.34983 −0.674916 0.737894i \(-0.735820\pi\)
−0.674916 + 0.737894i \(0.735820\pi\)
\(338\) −0.682746 + 1.18255i −0.0371365 + 0.0643222i
\(339\) −12.1437 + 16.2215i −0.659556 + 0.881033i
\(340\) 1.20989 + 14.1723i 0.0656158 + 0.768601i
\(341\) −14.2620 + 5.31331i −0.772333 + 0.287732i
\(342\) 0.367941 + 1.25325i 0.0198959 + 0.0677678i
\(343\) 19.3930i 1.04712i
\(344\) 0.848315 1.46932i 0.0457381 0.0792207i
\(345\) 8.81483 + 5.49521i 0.474575 + 0.295852i
\(346\) −13.0225 22.5556i −0.700091 1.21259i
\(347\) −1.62104 0.935905i −0.0870217 0.0502420i 0.455858 0.890053i \(-0.349333\pi\)
−0.542879 + 0.839811i \(0.682666\pi\)
\(348\) 2.41379 + 5.63700i 0.129393 + 0.302175i
\(349\) 7.55278 0.404291 0.202146 0.979356i \(-0.435209\pi\)
0.202146 + 0.979356i \(0.435209\pi\)
\(350\) −6.94127 + 5.77485i −0.371027 + 0.308679i
\(351\) −3.26494 19.4219i −0.174270 1.03666i
\(352\) 1.36676 + 2.36730i 0.0728487 + 0.126178i
\(353\) −10.3150 5.95534i −0.549010 0.316971i 0.199713 0.979854i \(-0.435999\pi\)
−0.748722 + 0.662884i \(0.769332\pi\)
\(354\) −2.58434 + 21.6115i −0.137356 + 1.14864i
\(355\) −13.3754 6.27130i −0.709890 0.332846i
\(356\) 2.32751 0.123358
\(357\) 11.9239 15.9280i 0.631082 0.842997i
\(358\) 2.35224 4.07419i 0.124319 0.215328i
\(359\) −30.4010 + 17.5520i −1.60450 + 0.926361i −0.613934 + 0.789357i \(0.710414\pi\)
−0.990570 + 0.137004i \(0.956253\pi\)
\(360\) −6.62997 1.02149i −0.349430 0.0538371i
\(361\) 9.40522 + 16.2903i 0.495012 + 0.857385i
\(362\) −2.33559 + 1.34845i −0.122756 + 0.0708732i
\(363\) −6.06716 0.725521i −0.318443 0.0380800i
\(364\) 6.84462i 0.358756i
\(365\) 7.09348 15.1289i 0.371290 0.791882i
\(366\) −5.18767 + 2.22139i −0.271164 + 0.116114i
\(367\) −10.3863 17.9896i −0.542159 0.939047i −0.998780 0.0493855i \(-0.984274\pi\)
0.456621 0.889661i \(-0.349060\pi\)
\(368\) 2.68202i 0.139810i
\(369\) −1.83796 + 7.57508i −0.0956805 + 0.394343i
\(370\) 23.8802 2.03866i 1.24147 0.105985i
\(371\) 17.3430 0.900402
\(372\) 9.37271 2.26987i 0.485952 0.117687i
\(373\) 17.6858i 0.915738i −0.889020 0.457869i \(-0.848613\pi\)
0.889020 0.457869i \(-0.151387\pi\)
\(374\) 17.3882i 0.899124i
\(375\) 11.8741 + 15.2973i 0.613175 + 0.789947i
\(376\) 1.54613 0.0797354
\(377\) 6.70929 + 11.6208i 0.345546 + 0.598503i
\(378\) 5.97410 + 7.23621i 0.307275 + 0.372190i
\(379\) 4.38746 7.59930i 0.225369 0.390350i −0.731061 0.682312i \(-0.760975\pi\)
0.956430 + 0.291962i \(0.0943081\pi\)
\(380\) 0.970012 0.0828103i 0.0497606 0.00424808i
\(381\) −10.0551 1.20240i −0.515138 0.0616011i
\(382\) −14.5902 + 8.42368i −0.746502 + 0.430993i
\(383\) 32.0004 18.4754i 1.63514 0.944050i 0.652671 0.757642i \(-0.273648\pi\)
0.982472 0.186409i \(-0.0596849\pi\)
\(384\) −0.681795 1.59222i −0.0347927 0.0812525i
\(385\) −9.05524 + 6.31221i −0.461498 + 0.321700i
\(386\) 14.2645 + 8.23560i 0.726042 + 0.419181i
\(387\) 1.43382 + 4.88376i 0.0728854 + 0.248256i
\(388\) 11.8138i 0.599755i
\(389\) 15.0730 26.1072i 0.764232 1.32369i −0.176420 0.984315i \(-0.556452\pi\)
0.940652 0.339374i \(-0.110215\pi\)
\(390\) −14.6709 0.496838i −0.742890 0.0251584i
\(391\) −8.53031 + 14.7749i −0.431396 + 0.747200i
\(392\) −1.86940 3.23789i −0.0944188 0.163538i
\(393\) −3.17073 + 26.5152i −0.159942 + 1.33752i
\(394\) −0.508531 + 0.293601i −0.0256194 + 0.0147914i
\(395\) 0.194309 + 2.27607i 0.00977677 + 0.114522i
\(396\) −7.96935 1.93363i −0.400475 0.0971684i
\(397\) 18.5049 + 10.6838i 0.928732 + 0.536204i 0.886410 0.462900i \(-0.153191\pi\)
0.0423219 + 0.999104i \(0.486525\pi\)
\(398\) 0.625276 0.361003i 0.0313422 0.0180954i
\(399\) −1.09018 0.816125i −0.0545771 0.0408573i
\(400\) −1.72984 + 4.69123i −0.0864922 + 0.234562i
\(401\) −10.2194 −0.510331 −0.255165 0.966897i \(-0.582130\pi\)
−0.255165 + 0.966897i \(0.582130\pi\)
\(402\) −12.5442 9.39082i −0.625649 0.468371i
\(403\) 19.7751 7.36719i 0.985068 0.366986i
\(404\) 15.5501i 0.773645i
\(405\) 15.9439 12.2798i 0.792258 0.610186i
\(406\) −5.53689 3.19672i −0.274791 0.158651i
\(407\) 29.2990 1.45230
\(408\) 1.30820 10.9398i 0.0647656 0.541601i
\(409\) −21.7788 12.5740i −1.07689 0.621744i −0.146836 0.989161i \(-0.546909\pi\)
−0.930056 + 0.367417i \(0.880242\pi\)
\(410\) 5.26043 + 2.46646i 0.259794 + 0.121810i
\(411\) 9.20972 + 6.89455i 0.454282 + 0.340083i
\(412\) −14.1597 + 8.17508i −0.697596 + 0.402757i
\(413\) −11.3466 19.6529i −0.558331 0.967058i
\(414\) −5.82303 5.55262i −0.286186 0.272896i
\(415\) −2.34153 1.09787i −0.114941 0.0538924i
\(416\) −1.89509 3.28240i −0.0929145 0.160933i
\(417\) 16.0037 6.85286i 0.783704 0.335586i
\(418\) 1.19012 0.0582109
\(419\) 21.1866i 1.03503i 0.855673 + 0.517516i \(0.173143\pi\)
−0.855673 + 0.517516i \(0.826857\pi\)
\(420\) 6.17200 3.29006i 0.301163 0.160539i
\(421\) −3.99936 6.92709i −0.194917 0.337606i 0.751956 0.659213i \(-0.229110\pi\)
−0.946873 + 0.321607i \(0.895777\pi\)
\(422\) −12.8281 + 22.2190i −0.624463 + 1.08160i
\(423\) −3.20096 + 3.35685i −0.155636 + 0.163215i
\(424\) 8.31697 4.80180i 0.403908 0.233196i
\(425\) −24.4502 + 20.3415i −1.18601 + 0.986710i
\(426\) 9.16032 + 6.85757i 0.443819 + 0.332250i
\(427\) 2.94191 5.09554i 0.142369 0.246590i
\(428\) −2.70745 + 4.68944i −0.130870 + 0.226673i
\(429\) −17.8181 2.13072i −0.860265 0.102872i
\(430\) 3.78003 0.322703i 0.182289 0.0155621i
\(431\) 20.4694 + 11.8180i 0.985976 + 0.569253i 0.904069 0.427387i \(-0.140566\pi\)
0.0819068 + 0.996640i \(0.473899\pi\)
\(432\) 4.86844 + 1.81611i 0.234233 + 0.0873778i
\(433\) −10.0836 −0.484588 −0.242294 0.970203i \(-0.577900\pi\)
−0.242294 + 0.970203i \(0.577900\pi\)
\(434\) −6.40468 + 7.75097i −0.307434 + 0.372058i
\(435\) −7.25384 + 11.6358i −0.347795 + 0.557896i
\(436\) −3.08751 −0.147865
\(437\) 1.01126 + 0.583850i 0.0483750 + 0.0279293i
\(438\) −7.75661 + 10.3613i −0.370625 + 0.495080i
\(439\) −19.2622 33.3630i −0.919332 1.59233i −0.800432 0.599424i \(-0.795396\pi\)
−0.118901 0.992906i \(-0.537937\pi\)
\(440\) −2.59483 + 5.53423i −0.123704 + 0.263834i
\(441\) 10.9001 + 2.64473i 0.519053 + 0.125939i
\(442\) 24.1097i 1.14678i
\(443\) 11.5516 + 20.0079i 0.548831 + 0.950603i 0.998355 + 0.0573347i \(0.0182602\pi\)
−0.449524 + 0.893268i \(0.648406\pi\)
\(444\) −18.4334 2.20430i −0.874813 0.104612i
\(445\) 2.97619 + 4.26951i 0.141085 + 0.202394i
\(446\) −2.25149 + 3.89969i −0.106611 + 0.184656i
\(447\) 1.53292 12.8190i 0.0725047 0.606320i
\(448\) 1.56394 + 0.902941i 0.0738892 + 0.0426599i
\(449\) 15.1659 0.715722 0.357861 0.933775i \(-0.383506\pi\)
0.357861 + 0.933775i \(0.383506\pi\)
\(450\) −6.60397 13.4680i −0.311314 0.634889i
\(451\) 6.15094 + 3.55124i 0.289636 + 0.167222i
\(452\) −5.84956 10.1317i −0.275140 0.476556i
\(453\) −29.6739 + 12.7065i −1.39420 + 0.597004i
\(454\) −7.02539 12.1683i −0.329718 0.571088i
\(455\) 12.5556 8.75223i 0.588615 0.410311i
\(456\) −0.748767 0.0895387i −0.0350642 0.00419304i
\(457\) 39.7824 1.86094 0.930471 0.366366i \(-0.119398\pi\)
0.930471 + 0.366366i \(0.119398\pi\)
\(458\) 18.8343 + 10.8740i 0.880070 + 0.508109i
\(459\) 21.0434 + 25.4891i 0.982222 + 1.18973i
\(460\) −4.91983 + 3.42951i −0.229388 + 0.159902i
\(461\) −23.1667 −1.07898 −0.539490 0.841992i \(-0.681383\pi\)
−0.539490 + 0.841992i \(0.681383\pi\)
\(462\) 7.85986 3.36563i 0.365674 0.156583i
\(463\) 30.4160 1.41355 0.706775 0.707438i \(-0.250149\pi\)
0.706775 + 0.707438i \(0.250149\pi\)
\(464\) −3.54035 −0.164357
\(465\) 16.1487 + 14.2906i 0.748877 + 0.662709i
\(466\) 8.80114 0.407705
\(467\) 7.94617 0.367705 0.183852 0.982954i \(-0.441143\pi\)
0.183852 + 0.982954i \(0.441143\pi\)
\(468\) 11.0499 + 2.68108i 0.510784 + 0.123933i
\(469\) 16.3378 0.754410
\(470\) 1.97703 + 2.83617i 0.0911938 + 0.130823i
\(471\) −18.8113 + 8.05508i −0.866778 + 0.371159i
\(472\) −10.8827 6.28315i −0.500919 0.289206i
\(473\) 4.63778 0.213245
\(474\) 0.210097 1.75694i 0.00965009 0.0806987i
\(475\) 1.39226 + 1.67347i 0.0638813 + 0.0767842i
\(476\) 5.74370 + 9.94837i 0.263262 + 0.455983i
\(477\) −6.79335 + 27.9985i −0.311046 + 1.28196i
\(478\) 7.39846 + 12.8145i 0.338398 + 0.586122i
\(479\) −24.5119 14.1519i −1.11998 0.646618i −0.178581 0.983925i \(-0.557151\pi\)
−0.941395 + 0.337307i \(0.890484\pi\)
\(480\) 2.04891 3.28664i 0.0935193 0.150014i
\(481\) −40.6246 −1.85232
\(482\) 7.91848 + 4.57174i 0.360677 + 0.208237i
\(483\) 8.32969 + 0.996078i 0.379014 + 0.0453231i
\(484\) 1.76392 3.05519i 0.0801780 0.138872i
\(485\) −21.6709 + 15.1063i −0.984026 + 0.685944i
\(486\) −14.0222 + 6.81012i −0.636060 + 0.308913i
\(487\) −0.193235 0.334692i −0.00875630 0.0151664i 0.861614 0.507564i \(-0.169454\pi\)
−0.870370 + 0.492398i \(0.836121\pi\)
\(488\) 3.25814i 0.147489i
\(489\) 32.7092 14.0062i 1.47916 0.633384i
\(490\) 3.54909 7.56947i 0.160332 0.341954i
\(491\) 10.1542 + 17.5877i 0.458255 + 0.793721i 0.998869 0.0475501i \(-0.0151414\pi\)
−0.540614 + 0.841271i \(0.681808\pi\)
\(492\) −3.60268 2.69703i −0.162422 0.121592i
\(493\) −19.5033 11.2603i −0.878386 0.507137i
\(494\) −1.65017 −0.0742447
\(495\) −6.64343 17.0913i −0.298600 0.768196i
\(496\) −0.925384 + 5.49032i −0.0415509 + 0.246523i
\(497\) −11.9306 −0.535159
\(498\) 1.60363 + 1.20050i 0.0718604 + 0.0537959i
\(499\) −5.94228 3.43078i −0.266013 0.153583i 0.361061 0.932542i \(-0.382414\pi\)
−0.627074 + 0.778959i \(0.715748\pi\)
\(500\) −10.8174 + 2.82551i −0.483770 + 0.126361i
\(501\) −2.26894 + 18.9740i −0.101369 + 0.847696i
\(502\) 11.7310 20.3187i 0.523580 0.906867i
\(503\) −10.3142 + 17.8646i −0.459885 + 0.796545i −0.998954 0.0457166i \(-0.985443\pi\)
0.539069 + 0.842262i \(0.318776\pi\)
\(504\) −5.19824 + 1.52615i −0.231548 + 0.0679802i
\(505\) −28.5246 + 19.8839i −1.26933 + 0.884822i
\(506\) −6.34916 + 3.66569i −0.282255 + 0.162960i
\(507\) 2.34837 + 0.280822i 0.104295 + 0.0124717i
\(508\) 2.92334 5.06337i 0.129702 0.224651i
\(509\) −2.25242 3.90131i −0.0998370 0.172923i 0.811780 0.583963i \(-0.198499\pi\)
−0.911617 + 0.411041i \(0.865165\pi\)
\(510\) 21.7405 11.5890i 0.962685 0.513171i
\(511\) 13.4947i 0.596969i
\(512\) 1.00000 0.0441942
\(513\) 1.74458 1.44030i 0.0770251 0.0635907i
\(514\) −9.45976 16.3848i −0.417252 0.722702i
\(515\) −33.1021 15.5206i −1.45865 0.683919i
\(516\) −2.91786 0.348923i −0.128452 0.0153605i
\(517\) 2.11319 + 3.66015i 0.0929379 + 0.160973i
\(518\) 16.7629 9.67806i 0.736519 0.425229i
\(519\) −27.0347 + 36.1128i −1.18669 + 1.58518i
\(520\) 3.59788 7.67351i 0.157777 0.336506i
\(521\) −4.65889 2.68981i −0.204110 0.117843i 0.394461 0.918913i \(-0.370931\pi\)
−0.598571 + 0.801070i \(0.704265\pi\)
\(522\) 7.32962 7.68657i 0.320809 0.336432i
\(523\) 3.08855 0.135053 0.0675265 0.997717i \(-0.478489\pi\)
0.0675265 + 0.997717i \(0.478489\pi\)
\(524\) −13.3521 7.70881i −0.583287 0.336761i
\(525\) 13.9273 + 7.11474i 0.607839 + 0.310513i
\(526\) 9.36711i 0.408425i
\(527\) −22.5601 + 27.3023i −0.982732 + 1.18931i
\(528\) 2.83741 3.79020i 0.123482 0.164947i
\(529\) 15.8068 0.687250
\(530\) 19.4432 + 9.11634i 0.844559 + 0.395989i
\(531\) 36.1722 10.6198i 1.56974 0.460860i
\(532\) 0.680908 0.393123i 0.0295211 0.0170440i
\(533\) −8.52861 4.92399i −0.369415 0.213282i
\(534\) −1.58688 3.70589i −0.0686711 0.160370i
\(535\) −12.0642 + 1.02993i −0.521581 + 0.0445276i
\(536\) 7.83494 4.52350i 0.338418 0.195386i
\(537\) −8.09074 0.967504i −0.349141 0.0417509i
\(538\) −4.99236 8.64703i −0.215236 0.372800i
\(539\) 5.11005 8.85086i 0.220105 0.381233i
\(540\) 2.89386 + 11.2528i 0.124532 + 0.484244i
\(541\) 7.60401 13.1705i 0.326922 0.566245i −0.654978 0.755648i \(-0.727322\pi\)
0.981899 + 0.189403i \(0.0606553\pi\)
\(542\) 14.3826i 0.617784i
\(543\) 3.73943 + 2.79940i 0.160474 + 0.120134i
\(544\) 5.50887 + 3.18055i 0.236191 + 0.136365i
\(545\) −3.94800 5.66364i −0.169114 0.242604i
\(546\) −10.8981 + 4.66663i −0.466397 + 0.199713i
\(547\) −10.7704 + 6.21829i −0.460509 + 0.265875i −0.712258 0.701917i \(-0.752328\pi\)
0.251749 + 0.967792i \(0.418994\pi\)
\(548\) −5.75226 + 3.32107i −0.245724 + 0.141869i
\(549\) 7.07386 + 6.74537i 0.301905 + 0.287885i
\(550\) −13.4699 + 2.31674i −0.574356 + 0.0987860i
\(551\) −0.770700 + 1.33489i −0.0328329 + 0.0568683i
\(552\) 4.27036 1.82859i 0.181759 0.0778300i
\(553\) 0.922439 + 1.59771i 0.0392261 + 0.0679416i
\(554\) −10.7709 −0.457613
\(555\) −19.5274 36.6324i −0.828891 1.55496i
\(556\) 10.0512i 0.426266i
\(557\) 5.01476i 0.212482i −0.994340 0.106241i \(-0.966118\pi\)
0.994340 0.106241i \(-0.0338815\pi\)
\(558\) −10.0044 13.3758i −0.423520 0.566243i
\(559\) −6.43054 −0.271983
\(560\) 0.343482 + 4.02344i 0.0145148 + 0.170021i
\(561\) 27.6858 11.8552i 1.16890 0.500528i
\(562\) 15.1194i 0.637774i
\(563\) −1.82585 3.16246i −0.0769503 0.133282i 0.824982 0.565158i \(-0.191185\pi\)
−0.901933 + 0.431877i \(0.857852\pi\)
\(564\) −1.05414 2.46177i −0.0443874 0.103659i
\(565\) 11.1055 23.6857i 0.467213 0.996466i
\(566\) 15.4123i 0.647828i
\(567\) 7.44849 14.4457i 0.312807 0.606662i
\(568\) −5.72140 + 3.30325i −0.240065 + 0.138601i
\(569\) 12.6503 + 21.9110i 0.530328 + 0.918555i 0.999374 + 0.0353813i \(0.0112646\pi\)
−0.469046 + 0.883174i \(0.655402\pi\)
\(570\) −0.793202 1.48801i −0.0332236 0.0623259i
\(571\) −13.7614 + 7.94517i −0.575898 + 0.332495i −0.759502 0.650505i \(-0.774557\pi\)
0.183603 + 0.983000i \(0.441224\pi\)
\(572\) 5.18028 8.97251i 0.216599 0.375160i
\(573\) 23.3599 + 17.4876i 0.975874 + 0.730556i
\(574\) 4.69220 0.195849
\(575\) −12.5820 4.63948i −0.524705 0.193480i
\(576\) −2.07031 + 2.17113i −0.0862629 + 0.0904639i
\(577\) 30.6800 + 17.7131i 1.27723 + 0.737406i 0.976337 0.216253i \(-0.0693837\pi\)
0.300888 + 0.953660i \(0.402717\pi\)
\(578\) 11.7318 + 20.3201i 0.487978 + 0.845204i
\(579\) 3.38740 28.3271i 0.140776 1.17724i
\(580\) −4.52705 6.49432i −0.187976 0.269662i
\(581\) −2.08860 −0.0866495
\(582\) 18.8101 8.05460i 0.779706 0.333874i
\(583\) 22.7347 + 13.1259i 0.941573 + 0.543617i
\(584\) −3.73631 6.47149i −0.154610 0.267792i
\(585\) 9.21148 + 23.6980i 0.380848 + 0.979792i
\(586\) 16.8667 29.2139i 0.696755 1.20682i
\(587\) 47.0276i 1.94104i 0.241024 + 0.970519i \(0.422517\pi\)
−0.241024 + 0.970519i \(0.577483\pi\)
\(588\) −3.88088 + 5.18406i −0.160045 + 0.213787i
\(589\) 1.86868 + 1.54411i 0.0769977 + 0.0636238i
\(590\) −2.39014 27.9973i −0.0984004 1.15263i
\(591\) 0.814190 + 0.609516i 0.0334913 + 0.0250722i
\(592\) 5.35919 9.28239i 0.220261 0.381504i
\(593\) 15.5928 0.640320 0.320160 0.947363i \(-0.396263\pi\)
0.320160 + 0.947363i \(0.396263\pi\)
\(594\) 2.35471 + 14.0073i 0.0966151 + 0.574726i
\(595\) −10.9045 + 23.2571i −0.447043 + 0.953447i
\(596\) 6.45518 + 3.72690i 0.264415 + 0.152660i
\(597\) −1.00111 0.749444i −0.0409725 0.0306727i
\(598\) 8.80346 5.08268i 0.360000 0.207846i
\(599\) 19.2164 11.0946i 0.785162 0.453313i −0.0530949 0.998589i \(-0.516909\pi\)
0.838256 + 0.545276i \(0.183575\pi\)
\(600\) 8.64886 0.444174i 0.353088 0.0181333i
\(601\) 17.2042 + 9.93286i 0.701775 + 0.405170i 0.808008 0.589171i \(-0.200546\pi\)
−0.106233 + 0.994341i \(0.533879\pi\)
\(602\) 2.65343 1.53196i 0.108146 0.0624379i
\(603\) −6.39962 + 26.3757i −0.260613 + 1.07410i
\(604\) 18.6368i 0.758322i
\(605\) 7.85989 0.671002i 0.319550 0.0272801i
\(606\) 24.7591 10.6020i 1.00577 0.430675i
\(607\) 9.96246 5.75183i 0.404364 0.233460i −0.284001 0.958824i \(-0.591662\pi\)
0.688365 + 0.725364i \(0.258329\pi\)
\(608\) 0.217690 0.377051i 0.00882851 0.0152914i
\(609\) −1.31485 + 10.9954i −0.0532805 + 0.445558i
\(610\) 5.97665 4.16620i 0.241987 0.168684i
\(611\) −2.93005 5.07500i −0.118537 0.205312i
\(612\) −18.3105 + 5.37577i −0.740157 + 0.217303i
\(613\) 6.19651 10.7327i 0.250275 0.433488i −0.713327 0.700832i \(-0.752812\pi\)
0.963601 + 0.267343i \(0.0861458\pi\)
\(614\) 10.3344 + 5.96659i 0.417064 + 0.240792i
\(615\) 0.340598 10.0574i 0.0137342 0.405552i
\(616\) 4.93642i 0.198894i
\(617\) −2.85076 + 4.93766i −0.114767 + 0.198783i −0.917687 0.397305i \(-0.869946\pi\)
0.802919 + 0.596087i \(0.203279\pi\)
\(618\) 22.6705 + 16.9715i 0.911941 + 0.682694i
\(619\) 31.2487i 1.25599i −0.778217 0.627995i \(-0.783876\pi\)
0.778217 0.627995i \(-0.216124\pi\)
\(620\) −11.2546 + 5.32299i −0.451995 + 0.213776i
\(621\) −4.87086 + 13.0573i −0.195461 + 0.523970i
\(622\) 0.401203i 0.0160868i
\(623\) 3.64008 + 2.10160i 0.145837 + 0.0841988i
\(624\) −3.93422 + 5.25532i −0.157495 + 0.210381i
\(625\) −19.0153 16.2302i −0.760611 0.649207i
\(626\) −10.0123 + 17.3418i −0.400173 + 0.693120i
\(627\) −0.811421 1.89494i −0.0324050 0.0756764i
\(628\) 11.8145i 0.471450i
\(629\) 59.0462 34.0903i 2.35433 1.35927i
\(630\) −9.44653 7.58402i −0.376359 0.302154i
\(631\) −16.5180 + 9.53670i −0.657573 + 0.379650i −0.791352 0.611361i \(-0.790622\pi\)
0.133779 + 0.991011i \(0.457289\pi\)
\(632\) 0.884726 + 0.510797i 0.0351925 + 0.0203184i
\(633\) 44.1236 + 5.27637i 1.75375 + 0.209717i
\(634\) −14.0966 + 24.4161i −0.559849 + 0.969687i
\(635\) 13.0262 1.11205i 0.516928 0.0441303i
\(636\) −13.3160 9.96857i −0.528013 0.395280i
\(637\) −7.08536 + 12.2722i −0.280732 + 0.486242i
\(638\) −4.83882 8.38108i −0.191571 0.331810i
\(639\) 4.67327 19.2607i 0.184872 0.761941i
\(640\) 1.27870 + 1.83437i 0.0505451 + 0.0725099i
\(641\) −12.2113 21.1506i −0.482318 0.835400i 0.517475 0.855698i \(-0.326872\pi\)
−0.999794 + 0.0202979i \(0.993539\pi\)
\(642\) 9.31253 + 1.11361i 0.367536 + 0.0439506i
\(643\) 26.0049 1.02553 0.512767 0.858528i \(-0.328621\pi\)
0.512767 + 0.858528i \(0.328621\pi\)
\(644\) −2.42171 + 4.19452i −0.0954286 + 0.165287i
\(645\) −3.09102 5.79861i −0.121709 0.228320i
\(646\) 2.39846 1.38475i 0.0943660 0.0544822i
\(647\) 40.9565i 1.61016i −0.593163 0.805082i \(-0.702121\pi\)
0.593163 0.805082i \(-0.297879\pi\)
\(648\) −0.427634 8.98983i −0.0167991 0.353154i
\(649\) 34.3503i 1.34837i
\(650\) 18.6767 3.21228i 0.732560 0.125996i
\(651\) 16.7079 + 4.91307i 0.654834 + 0.192558i
\(652\) 20.5432i 0.804532i
\(653\) 47.4222 1.85577 0.927886 0.372863i \(-0.121624\pi\)
0.927886 + 0.372863i \(0.121624\pi\)
\(654\) 2.10505 + 4.91598i 0.0823140 + 0.192230i
\(655\) −2.93247 34.3499i −0.114581 1.34216i
\(656\) 2.25018 1.29914i 0.0878549 0.0507231i
\(657\) 21.7858 + 5.28595i 0.849944 + 0.206224i
\(658\) 2.41805 + 1.39606i 0.0942653 + 0.0544241i
\(659\) 16.2173i 0.631737i 0.948803 + 0.315868i \(0.102296\pi\)
−0.948803 + 0.315868i \(0.897704\pi\)
\(660\) 10.5808 + 0.358326i 0.411858 + 0.0139478i
\(661\) 6.59103 + 11.4160i 0.256361 + 0.444031i 0.965264 0.261275i \(-0.0841430\pi\)
−0.708903 + 0.705306i \(0.750810\pi\)
\(662\) 7.83238 4.52202i 0.304414 0.175753i
\(663\) −38.3879 + 16.4379i −1.49086 + 0.638396i
\(664\) −1.00160 + 0.578276i −0.0388698 + 0.0224415i
\(665\) 1.59181 + 0.746353i 0.0617278 + 0.0289423i
\(666\) 9.05811 + 30.8529i 0.350995 + 1.19553i
\(667\) 9.49530i 0.367659i
\(668\) −9.55459 5.51635i −0.369678 0.213434i
\(669\) 7.74422 + 0.926066i 0.299409 + 0.0358038i
\(670\) 18.3163 + 8.58798i 0.707622 + 0.331783i
\(671\) 7.71302 4.45311i 0.297758 0.171910i
\(672\) 0.371391 3.10575i 0.0143267 0.119807i
\(673\) −9.84175 17.0464i −0.379371 0.657091i 0.611600 0.791168i \(-0.290526\pi\)
−0.990971 + 0.134077i \(0.957193\pi\)
\(674\) −24.7796 −0.954476
\(675\) −16.9415 + 19.6974i −0.652077 + 0.758153i
\(676\) −0.682746 + 1.18255i −0.0262594 + 0.0454827i
\(677\) −8.27505 + 4.77760i −0.318036 + 0.183618i −0.650517 0.759492i \(-0.725448\pi\)
0.332481 + 0.943110i \(0.392114\pi\)
\(678\) −12.1437 + 16.2215i −0.466376 + 0.622984i
\(679\) −10.6672 + 18.4761i −0.409368 + 0.709047i
\(680\) 1.20989 + 14.1723i 0.0463974 + 0.543483i
\(681\) −14.5848 + 19.4823i −0.558889 + 0.746562i
\(682\) −14.2620 + 5.31331i −0.546122 + 0.203457i
\(683\) 4.31865 0.165249 0.0826244 0.996581i \(-0.473670\pi\)
0.0826244 + 0.996581i \(0.473670\pi\)
\(684\) 0.367941 + 1.25325i 0.0140686 + 0.0479191i
\(685\) −13.4475 6.30512i −0.513802 0.240906i
\(686\) 19.3930i 0.740428i
\(687\) 4.47261 37.4022i 0.170641 1.42698i
\(688\) 0.848315 1.46932i 0.0323417 0.0560175i
\(689\) −31.5228 18.1997i −1.20092 0.693354i
\(690\) 8.81483 + 5.49521i 0.335575 + 0.209199i
\(691\) 1.62251 + 2.81027i 0.0617232 + 0.106908i 0.895236 0.445593i \(-0.147007\pi\)
−0.833513 + 0.552501i \(0.813674\pi\)
\(692\) −13.0225 22.5556i −0.495039 0.857433i
\(693\) −10.7176 10.2199i −0.407129 0.388223i
\(694\) −1.62104 0.935905i −0.0615337 0.0355265i
\(695\) −18.4376 + 12.8525i −0.699379 + 0.487522i
\(696\) 2.41379 + 5.63700i 0.0914946 + 0.213670i
\(697\) 16.5280 0.626042
\(698\) 7.55278 0.285877
\(699\) −6.00058 14.0133i −0.226963 0.530033i
\(700\) −6.94127 + 5.77485i −0.262355 + 0.218269i
\(701\) 39.4575 + 22.7808i 1.49029 + 0.860419i 0.999938 0.0111057i \(-0.00353513\pi\)
0.490351 + 0.871525i \(0.336868\pi\)
\(702\) −3.26494 19.4219i −0.123227 0.733031i
\(703\) −2.33329 4.04137i −0.0880016 0.152423i
\(704\) 1.36676 + 2.36730i 0.0515118 + 0.0892211i
\(705\) 3.16787 5.08156i 0.119309 0.191383i
\(706\) −10.3150 5.95534i −0.388208 0.224132i
\(707\) −14.0408 + 24.3193i −0.528058 + 0.914623i
\(708\) −2.58434 + 21.6115i −0.0971254 + 0.812210i
\(709\) 11.3089i 0.424715i −0.977192 0.212357i \(-0.931886\pi\)
0.977192 0.212357i \(-0.0681141\pi\)
\(710\) −13.3754 6.27130i −0.501968 0.235358i
\(711\) −2.94067 + 0.863350i −0.110284 + 0.0323782i
\(712\) 2.32751 0.0872270
\(713\) −14.7252 2.48190i −0.551462 0.0929479i
\(714\) 11.9239 15.9280i 0.446242 0.596089i
\(715\) 23.0830 1.97060i 0.863254 0.0736963i
\(716\) 2.35224 4.07419i 0.0879071 0.152260i
\(717\) 15.3592 20.5168i 0.573602 0.766215i
\(718\) −30.4010 + 17.5520i −1.13456 + 0.655036i
\(719\) −9.66837 + 16.7461i −0.360570 + 0.624525i −0.988055 0.154104i \(-0.950751\pi\)
0.627485 + 0.778629i \(0.284084\pi\)
\(720\) −6.62997 1.02149i −0.247085 0.0380686i
\(721\) −29.5264 −1.09962
\(722\) 9.40522 + 16.2903i 0.350026 + 0.606263i
\(723\) 1.88041 15.7249i 0.0699333 0.584816i
\(724\) −2.33559 + 1.34845i −0.0868016 + 0.0501149i
\(725\) 6.12425 16.6086i 0.227449 0.616828i
\(726\) −6.06716 0.725521i −0.225173 0.0269266i
\(727\) −6.15704 3.55477i −0.228352 0.131839i 0.381460 0.924386i \(-0.375422\pi\)
−0.609812 + 0.792546i \(0.708755\pi\)
\(728\) 6.84462i 0.253679i
\(729\) 20.4035 + 17.6833i 0.755684 + 0.654937i
\(730\) 7.09348 15.1289i 0.262542 0.559945i
\(731\) 9.34652 5.39622i 0.345694 0.199586i
\(732\) −5.18767 + 2.22139i −0.191742 + 0.0821049i
\(733\) −38.5132 + 22.2356i −1.42252 + 0.821290i −0.996513 0.0834322i \(-0.973412\pi\)
−0.426002 + 0.904722i \(0.640078\pi\)
\(734\) −10.3863 17.9896i −0.383364 0.664006i
\(735\) −14.4720 0.490102i −0.533807 0.0180777i
\(736\) 2.68202i 0.0988607i
\(737\) 21.4170 + 12.3651i 0.788906 + 0.455475i
\(738\) −1.83796 + 7.57508i −0.0676564 + 0.278842i
\(739\) 23.8106 13.7470i 0.875886 0.505693i 0.00658608 0.999978i \(-0.497904\pi\)
0.869300 + 0.494285i \(0.164570\pi\)
\(740\) 23.8802 2.03866i 0.877852 0.0749426i
\(741\) 1.12508 + 2.62743i 0.0413308 + 0.0965211i
\(742\) 17.3430 0.636681
\(743\) 21.7557i 0.798138i 0.916921 + 0.399069i \(0.130667\pi\)
−0.916921 + 0.399069i \(0.869333\pi\)
\(744\) 9.37271 2.26987i 0.343620 0.0832174i
\(745\) 1.41773 + 16.6068i 0.0519416 + 0.608426i
\(746\) 17.6858i 0.647524i
\(747\) 0.818116 3.37182i 0.0299333 0.123369i
\(748\) 17.3882i 0.635777i
\(749\) −8.46857 + 4.88933i −0.309435 + 0.178652i
\(750\) 11.8741 + 15.2973i 0.433580 + 0.558577i
\(751\) −6.82872 + 11.8277i −0.249184 + 0.431599i −0.963300 0.268429i \(-0.913496\pi\)
0.714116 + 0.700028i \(0.246829\pi\)
\(752\) 1.54613 0.0563814
\(753\) −40.3499 4.82510i −1.47043 0.175837i
\(754\) 6.70929 + 11.6208i 0.244338 + 0.423206i
\(755\) 34.1869 23.8310i 1.24419 0.867297i
\(756\) 5.97410 + 7.23621i 0.217276 + 0.263178i
\(757\) −23.9396 41.4647i −0.870101 1.50706i −0.861892 0.507093i \(-0.830720\pi\)
−0.00820943 0.999966i \(-0.502613\pi\)
\(758\) 4.38746 7.59930i 0.159360 0.276019i
\(759\) 10.1654 + 7.60999i 0.368981 + 0.276225i
\(760\) 0.970012 0.0828103i 0.0351860 0.00300385i
\(761\) −10.0986 + 17.4912i −0.366073 + 0.634057i −0.988948 0.148265i \(-0.952631\pi\)
0.622875 + 0.782321i \(0.285965\pi\)
\(762\) −10.0551 1.20240i −0.364258 0.0435585i
\(763\) −4.82868 2.78784i −0.174810 0.100926i
\(764\) −14.5902 + 8.42368i −0.527857 + 0.304758i
\(765\) −33.2748 26.7142i −1.20305 0.965854i
\(766\) 32.0004 18.4754i 1.15622 0.667544i
\(767\) 47.6286i 1.71977i
\(768\) −0.681795 1.59222i −0.0246022 0.0574542i
\(769\) −9.43636 + 16.3443i −0.340284 + 0.589389i −0.984485 0.175467i \(-0.943856\pi\)
0.644201 + 0.764856i \(0.277190\pi\)
\(770\) −9.05524 + 6.31221i −0.326328 + 0.227476i
\(771\) −19.6385 + 26.2331i −0.707264 + 0.944761i
\(772\) 14.2645 + 8.23560i 0.513390 + 0.296406i
\(773\) 41.2864i 1.48497i −0.669863 0.742485i \(-0.733647\pi\)
0.669863 0.742485i \(-0.266353\pi\)
\(774\) 1.43382 + 4.88376i 0.0515377 + 0.175543i
\(775\) −24.1556 13.8386i −0.867695 0.497097i
\(776\) 11.8138i 0.424091i
\(777\) −26.8384 20.0917i −0.962823 0.720786i
\(778\) 15.0730 26.1072i 0.540394 0.935989i
\(779\) 1.13124i 0.0405310i
\(780\) −14.6709 0.496838i −0.525303 0.0177897i
\(781\) −15.6396 9.02953i −0.559629 0.323102i
\(782\) −8.53031 + 14.7749i −0.305043 + 0.528350i
\(783\) −17.2360 6.42968i −0.615964 0.229778i
\(784\) −1.86940 3.23789i −0.0667642 0.115639i
\(785\) 21.6722 15.1072i 0.773515 0.539201i
\(786\) −3.17073 + 26.5152i −0.113096 + 0.945766i
\(787\) −27.0761 + 46.8971i −0.965157 + 1.67170i −0.255966 + 0.966686i \(0.582393\pi\)
−0.709192 + 0.705016i \(0.750940\pi\)
\(788\) −0.508531 + 0.293601i −0.0181157 + 0.0104591i
\(789\) 14.9145 6.38645i 0.530969 0.227364i
\(790\) 0.194309 + 2.27607i 0.00691322 + 0.0809791i
\(791\) 21.1272i 0.751197i
\(792\) −7.96935 1.93363i −0.283179 0.0687084i
\(793\) −10.6945 + 6.17448i −0.379773 + 0.219262i
\(794\) 18.5049 + 10.6838i 0.656713 + 0.379153i
\(795\) 1.25889 37.1733i 0.0446484 1.31840i
\(796\) 0.625276 0.361003i 0.0221623 0.0127954i
\(797\) −34.2218 + 19.7580i −1.21220 + 0.699864i −0.963238 0.268649i \(-0.913423\pi\)
−0.248962 + 0.968513i \(0.580089\pi\)
\(798\) −1.09018 0.816125i −0.0385918 0.0288905i
\(799\) 8.51742 + 4.91753i 0.301325 + 0.173970i
\(800\) −1.72984 + 4.69123i −0.0611592 + 0.165860i
\(801\) −4.81866 + 5.05332i −0.170259 + 0.178550i
\(802\) −10.2194 −0.360858
\(803\) 10.2133 17.6900i 0.360420 0.624266i
\(804\) −12.5442 9.39082i −0.442401 0.331189i
\(805\) −10.7909 + 0.921228i −0.380331 + 0.0324690i
\(806\) 19.7751 7.36719i 0.696548 0.259498i
\(807\) −10.3642 + 13.8444i −0.364836 + 0.487347i
\(808\) 15.5501i 0.547049i
\(809\) −15.4256 + 26.7179i −0.542335 + 0.939352i 0.456434 + 0.889757i \(0.349126\pi\)
−0.998769 + 0.0495948i \(0.984207\pi\)
\(810\) 15.9439 12.2798i 0.560211 0.431467i
\(811\) 18.5015 + 32.0456i 0.649676 + 1.12527i 0.983200 + 0.182531i \(0.0584289\pi\)
−0.333524 + 0.942742i \(0.608238\pi\)
\(812\) −5.53689 3.19672i −0.194307 0.112183i
\(813\) −22.9002 + 9.80597i −0.803144 + 0.343910i
\(814\) 29.2990 1.02693
\(815\) −37.6838 + 26.2686i −1.32001 + 0.920148i
\(816\) 1.30820 10.9398i 0.0457962 0.382970i
\(817\) −0.369340 0.639715i −0.0129216 0.0223808i
\(818\) −21.7788 12.5740i −0.761478 0.439639i
\(819\) 14.8606 + 14.1705i 0.519271 + 0.495157i
\(820\) 5.26043 + 2.46646i 0.183702 + 0.0861324i
\(821\) −27.5335 −0.960924 −0.480462 0.877016i \(-0.659531\pi\)
−0.480462 + 0.877016i \(0.659531\pi\)
\(822\) 9.20972 + 6.89455i 0.321226 + 0.240475i
\(823\) −27.1266 + 46.9846i −0.945573 + 1.63778i −0.190972 + 0.981596i \(0.561164\pi\)
−0.754601 + 0.656184i \(0.772169\pi\)
\(824\) −14.1597 + 8.17508i −0.493275 + 0.284792i
\(825\) 12.8724 + 19.8674i 0.448161 + 0.691694i
\(826\) −11.3466 19.6529i −0.394800 0.683813i
\(827\) 28.8678 16.6668i 1.00383 0.579562i 0.0944515 0.995529i \(-0.469890\pi\)
0.909380 + 0.415967i \(0.136557\pi\)
\(828\) −5.82303 5.55262i −0.202364 0.192967i
\(829\) 21.4599i 0.745334i 0.927965 + 0.372667i \(0.121557\pi\)
−0.927965 + 0.372667i \(0.878443\pi\)
\(830\) −2.34153 1.09787i −0.0812755 0.0381077i
\(831\) 7.34358 + 17.1497i 0.254746 + 0.594915i
\(832\) −1.89509 3.28240i −0.0657005 0.113797i
\(833\) 23.7828i 0.824027i
\(834\) 16.0037 6.85286i 0.554162 0.237295i
\(835\) −2.09844 24.5804i −0.0726196 0.850641i
\(836\) 1.19012 0.0411613
\(837\) −14.4762 + 25.0487i −0.500372 + 0.865811i
\(838\) 21.1866i 0.731878i
\(839\) 10.3784i 0.358302i 0.983822 + 0.179151i \(0.0573350\pi\)
−0.983822 + 0.179151i \(0.942665\pi\)
\(840\) 6.17200 3.29006i 0.212954 0.113518i
\(841\) −16.4659 −0.567791
\(842\) −3.99936 6.92709i −0.137827 0.238723i
\(843\) −24.0734 + 10.3084i −0.829132 + 0.355039i
\(844\) −12.8281 + 22.2190i −0.441562 + 0.764808i
\(845\) −3.04226 + 0.259719i −0.104657 + 0.00893462i
\(846\) −3.20096 + 3.35685i −0.110051 + 0.115411i
\(847\) 5.51732 3.18542i 0.189577 0.109452i
\(848\) 8.31697 4.80180i 0.285606 0.164895i
\(849\) −24.5397 + 10.5080i −0.842202 + 0.360635i
\(850\) −24.4502 + 20.3415i −0.838634 + 0.697709i
\(851\) 24.8956 + 14.3735i 0.853409 + 0.492716i
\(852\) 9.16032 + 6.85757i 0.313827 + 0.234936i
\(853\) 31.6014i 1.08201i −0.841019 0.541005i \(-0.818044\pi\)
0.841019 0.541005i \(-0.181956\pi\)
\(854\) 2.94191 5.09554i 0.100670 0.174366i
\(855\) −1.82843 + 2.27747i −0.0625311 + 0.0778878i
\(856\) −2.70745 + 4.68944i −0.0925387 + 0.160282i
\(857\) 8.70164 + 15.0717i 0.297242 + 0.514839i 0.975504 0.219981i \(-0.0705997\pi\)
−0.678262 + 0.734821i \(0.737266\pi\)
\(858\) −17.8181 2.13072i −0.608299 0.0727414i
\(859\) −14.3943 + 8.31055i −0.491127 + 0.283552i −0.725042 0.688705i \(-0.758180\pi\)
0.233915 + 0.972257i \(0.424846\pi\)
\(860\) 3.78003 0.322703i 0.128898 0.0110041i
\(861\) −3.19912 7.47100i −0.109026 0.254611i
\(862\) 20.4694 + 11.8180i 0.697190 + 0.402523i
\(863\) −24.2209 + 13.9839i −0.824488 + 0.476018i −0.851962 0.523604i \(-0.824587\pi\)
0.0274739 + 0.999623i \(0.491254\pi\)
\(864\) 4.86844 + 1.81611i 0.165628 + 0.0617855i
\(865\) 24.7234 52.7299i 0.840622 1.79287i
\(866\) −10.0836 −0.342656
\(867\) 24.3553 32.5337i 0.827148 1.10490i
\(868\) −6.40468 + 7.75097i −0.217389 + 0.263085i
\(869\) 2.79255i 0.0947309i
\(870\) −7.25384 + 11.6358i −0.245928 + 0.394492i
\(871\) −29.6959 17.1449i −1.00621 0.580933i
\(872\) −3.08751 −0.104556
\(873\) −25.6493 24.4582i −0.868099 0.827786i
\(874\) 1.01126 + 0.583850i 0.0342063 + 0.0197490i
\(875\) −19.4690 5.34856i −0.658174 0.180814i
\(876\) −7.75661 + 10.3613i −0.262071 + 0.350074i
\(877\) 38.0665 21.9777i 1.28541 0.742134i 0.307581 0.951522i \(-0.400481\pi\)
0.977833 + 0.209388i \(0.0671472\pi\)
\(878\) −19.2622 33.3630i −0.650066 1.12595i
\(879\) −58.0145 6.93747i −1.95678 0.233995i
\(880\) −2.59483 + 5.53423i −0.0874718 + 0.186559i
\(881\) 13.9628 + 24.1844i 0.470420 + 0.814792i 0.999428 0.0338253i \(-0.0107690\pi\)
−0.529007 + 0.848617i \(0.677436\pi\)
\(882\) 10.9001 + 2.64473i 0.367026 + 0.0890526i
\(883\) 24.3754 0.820297 0.410148 0.912019i \(-0.365477\pi\)
0.410148 + 0.912019i \(0.365477\pi\)
\(884\) 24.1097i 0.810898i
\(885\) −42.9481 + 22.8940i −1.44369 + 0.769574i
\(886\) 11.5516 + 20.0079i 0.388082 + 0.672178i
\(887\) −4.78670 + 8.29081i −0.160722 + 0.278378i −0.935128 0.354311i \(-0.884715\pi\)
0.774406 + 0.632689i \(0.218049\pi\)
\(888\) −18.4334 2.20430i −0.618586 0.0739715i
\(889\) 9.14384 5.27920i 0.306674 0.177059i
\(890\) 2.97619 + 4.26951i 0.0997620 + 0.143114i
\(891\) 20.6972 13.2993i 0.693382 0.445544i
\(892\) −2.25149 + 3.89969i −0.0753855 + 0.130571i
\(893\) 0.336577 0.582968i 0.0112631 0.0195083i
\(894\) 1.53292 12.8190i 0.0512686 0.428733i
\(895\) 10.4814 0.894800i 0.350354 0.0299099i
\(896\) 1.56394 + 0.902941i 0.0522475 + 0.0301651i
\(897\) −14.0949 10.5517i −0.470614 0.352310i
\(898\) 15.1659 0.506092
\(899\) 3.27618 19.4377i 0.109267 0.648283i
\(900\) −6.60397 13.4680i −0.220132 0.448934i
\(901\) 61.0895 2.03519
\(902\) 6.15094 + 3.55124i 0.204804 + 0.118244i
\(903\) −4.24830 3.18035i −0.141375 0.105835i
\(904\) −5.84956 10.1317i −0.194553 0.336976i
\(905\) −5.46009 2.56007i −0.181500 0.0850997i
\(906\) −29.6739 + 12.7065i −0.985849 + 0.422146i
\(907\) 51.8786i 1.72260i −0.508095 0.861301i \(-0.669650\pi\)
0.508095 0.861301i \(-0.330350\pi\)
\(908\) −7.02539 12.1683i −0.233146 0.403820i
\(909\) −33.7613 32.1935i −1.11979 1.06779i
\(910\) 12.5556 8.75223i 0.416214 0.290134i
\(911\) 12.2756 21.2619i 0.406708 0.704439i −0.587810 0.808999i \(-0.700010\pi\)
0.994519 + 0.104559i \(0.0333432\pi\)
\(912\) −0.748767 0.0895387i −0.0247941 0.00296492i
\(913\) −2.73791 1.58073i −0.0906116 0.0523146i
\(914\) 39.7824 1.31588
\(915\) −10.7083 6.67563i −0.354007 0.220690i
\(916\) 18.8343 + 10.8740i 0.622304 + 0.359287i
\(917\) −13.9212 24.1122i −0.459719 0.796256i
\(918\) 21.0434 + 25.4891i 0.694536 + 0.841265i
\(919\) −18.2267 31.5695i −0.601243 1.04138i −0.992633 0.121158i \(-0.961339\pi\)
0.391390 0.920225i \(-0.371994\pi\)
\(920\) −4.91983 + 3.42951i −0.162202 + 0.113067i
\(921\) 2.45414 20.5227i 0.0808665 0.676245i
\(922\) −23.1667 −0.762954
\(923\) 21.6852 + 12.5199i 0.713776 + 0.412099i
\(924\) 7.85986 3.36563i 0.258570 0.110721i
\(925\) 34.2753 + 41.1983i 1.12696 + 1.35459i
\(926\) 30.4160 0.999531
\(927\) 11.5657 47.6674i 0.379867 1.56560i
\(928\) −3.54035 −0.116218
\(929\) −49.3802 −1.62011 −0.810056 0.586353i \(-0.800563\pi\)
−0.810056 + 0.586353i \(0.800563\pi\)
\(930\) 16.1487 + 14.2906i 0.529536 + 0.468606i
\(931\) −1.62780 −0.0533489
\(932\) 8.80114 0.288291
\(933\) 0.638802 0.273538i 0.0209135 0.00895525i
\(934\) 7.94617 0.260007
\(935\) −31.8965 + 22.2344i −1.04313 + 0.727142i
\(936\) 11.0499 + 2.68108i 0.361179 + 0.0876338i
\(937\) 11.3636 + 6.56077i 0.371232 + 0.214331i 0.673997 0.738734i \(-0.264576\pi\)
−0.302764 + 0.953065i \(0.597910\pi\)
\(938\) 16.3378 0.533449
\(939\) 34.4383 + 4.11819i 1.12385 + 0.134392i
\(940\) 1.97703 + 2.83617i 0.0644838 + 0.0925057i
\(941\) 18.2683 + 31.6415i 0.595528 + 1.03148i 0.993472 + 0.114075i \(0.0363905\pi\)
−0.397944 + 0.917410i \(0.630276\pi\)
\(942\) −18.8113 + 8.05508i −0.612904 + 0.262449i
\(943\) 3.48433 + 6.03504i 0.113466 + 0.196528i
\(944\) −10.8827 6.28315i −0.354203 0.204499i
\(945\) −5.63480 + 20.2117i −0.183300 + 0.657486i
\(946\) 4.63778 0.150787
\(947\) −6.64300 3.83534i −0.215868 0.124632i 0.388167 0.921589i \(-0.373108\pi\)
−0.604036 + 0.796957i \(0.706442\pi\)
\(948\) 0.210097 1.75694i 0.00682364 0.0570626i
\(949\) −14.1613 + 24.5281i −0.459696 + 0.796216i
\(950\) 1.39226 + 1.67347i 0.0451709 + 0.0542946i
\(951\) 48.4867 + 5.79812i 1.57229 + 0.188017i
\(952\) 5.74370 + 9.94837i 0.186154 + 0.322429i
\(953\) 35.0031i 1.13386i −0.823765 0.566931i \(-0.808130\pi\)
0.823765 0.566931i \(-0.191870\pi\)
\(954\) −6.79335 + 27.9985i −0.219943 + 0.906484i
\(955\) −34.1088 15.9926i −1.10373 0.517507i
\(956\) 7.39846 + 12.8145i 0.239283 + 0.414451i
\(957\) −10.0454 + 13.4186i −0.324722 + 0.433763i
\(958\) −24.5119 14.1519i −0.791942 0.457228i
\(959\) −11.9949 −0.387336
\(960\) 2.04891 3.28664i 0.0661281 0.106076i
\(961\) −29.2873 10.1613i −0.944753 0.327784i
\(962\) −40.6246 −1.30979
\(963\) −4.57614 15.5868i −0.147464 0.502278i
\(964\) 7.91848 + 4.57174i 0.255037 + 0.147246i
\(965\) 3.13286 + 36.6972i 0.100850 + 1.18133i
\(966\) 8.32969 + 0.996078i 0.268003 + 0.0320483i
\(967\) −21.3722 + 37.0178i −0.687285 + 1.19041i 0.285428 + 0.958400i \(0.407864\pi\)
−0.972713 + 0.232012i \(0.925469\pi\)
\(968\) 1.76392 3.05519i 0.0566944 0.0981976i
\(969\) −3.84008 2.87475i −0.123361 0.0923502i
\(970\) −21.6709 + 15.1063i −0.695811 + 0.485035i
\(971\) −35.6432 + 20.5786i −1.14384 + 0.660398i −0.947379 0.320113i \(-0.896279\pi\)
−0.196464 + 0.980511i \(0.562946\pi\)
\(972\) −14.0222 + 6.81012i −0.449763 + 0.218435i
\(973\) −9.07563 + 15.7195i −0.290951 + 0.503943i
\(974\) −0.193235 0.334692i −0.00619164 0.0107242i
\(975\) −17.8483 27.5472i −0.571604 0.882217i
\(976\) 3.25814i 0.104291i
\(977\) 16.9620 0.542662 0.271331 0.962486i \(-0.412536\pi\)
0.271331 + 0.962486i \(0.412536\pi\)
\(978\) 32.7092 14.0062i 1.04592 0.447870i
\(979\) 3.18115 + 5.50991i 0.101670 + 0.176098i
\(980\) 3.54909 7.56947i 0.113372 0.241798i
\(981\) 6.39210 6.70339i 0.204084 0.214023i
\(982\) 10.1542 + 17.5877i 0.324035 + 0.561245i
\(983\) −22.0203 + 12.7134i −0.702338 + 0.405495i −0.808218 0.588884i \(-0.799568\pi\)
0.105880 + 0.994379i \(0.466234\pi\)
\(984\) −3.60268 2.69703i −0.114849 0.0859782i
\(985\) −1.18883 0.557408i −0.0378794 0.0177605i
\(986\) −19.5033 11.2603i −0.621113 0.358600i
\(987\) 0.574217 4.80188i 0.0182775 0.152846i
\(988\) −1.65017 −0.0524990
\(989\) 3.94076 + 2.27520i 0.125309 + 0.0723471i
\(990\) −6.64343 17.0913i −0.211142 0.543197i
\(991\) 20.4866i 0.650778i −0.945580 0.325389i \(-0.894505\pi\)
0.945580 0.325389i \(-0.105495\pi\)
\(992\) −0.925384 + 5.49032i −0.0293810 + 0.174318i
\(993\) −12.5401 9.38775i −0.397949 0.297911i
\(994\) −11.9306 −0.378414
\(995\) 1.46175 + 0.685373i 0.0463407 + 0.0217278i
\(996\) 1.60363 + 1.20050i 0.0508129 + 0.0380394i
\(997\) 17.1606 9.90769i 0.543482 0.313780i −0.203007 0.979177i \(-0.565071\pi\)
0.746489 + 0.665398i \(0.231738\pi\)
\(998\) −5.94228 3.43078i −0.188100 0.108599i
\(999\) 42.9488 35.4579i 1.35884 1.12184i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 930.2.r.b.119.13 yes 64
3.2 odd 2 930.2.r.a.119.31 yes 64
5.4 even 2 930.2.r.a.119.20 64
15.14 odd 2 inner 930.2.r.b.119.2 yes 64
31.6 odd 6 inner 930.2.r.b.719.2 yes 64
93.68 even 6 930.2.r.a.719.20 yes 64
155.99 odd 6 930.2.r.a.719.31 yes 64
465.254 even 6 inner 930.2.r.b.719.13 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.r.a.119.20 64 5.4 even 2
930.2.r.a.119.31 yes 64 3.2 odd 2
930.2.r.a.719.20 yes 64 93.68 even 6
930.2.r.a.719.31 yes 64 155.99 odd 6
930.2.r.b.119.2 yes 64 15.14 odd 2 inner
930.2.r.b.119.13 yes 64 1.1 even 1 trivial
930.2.r.b.719.2 yes 64 31.6 odd 6 inner
930.2.r.b.719.13 yes 64 465.254 even 6 inner