Properties

Label 62.2.d.b.35.1
Level $62$
Weight $2$
Character 62.35
Analytic conductor $0.495$
Analytic rank $0$
Dimension $8$
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] = [62,2,Mod(33,62)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(62, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("62.33");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 62 = 2 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 62.d (of order \(5\), degree \(4\), 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: \(0.495072492532\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.1903140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 6x^{6} + x^{5} + 29x^{4} + 43x^{3} + 194x^{2} + 209x + 361 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 35.1
Root \(2.68070 - 1.94764i\) of defining polynomial
Character \(\chi\) \(=\) 62.35
Dual form 62.2.d.b.39.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(-1.02393 + 3.15135i) q^{3} +(-0.809017 + 0.587785i) q^{4} +2.66590 q^{5} +3.31352 q^{6} +(-0.500000 + 0.363271i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-6.45549 - 4.69019i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(-1.02393 + 3.15135i) q^{3} +(-0.809017 + 0.587785i) q^{4} +2.66590 q^{5} +3.31352 q^{6} +(-0.500000 + 0.363271i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-6.45549 - 4.69019i) q^{9} +(-0.823809 - 2.53542i) q^{10} +(1.09410 - 0.794910i) q^{11} +(-1.02393 - 3.15135i) q^{12} +(0.729710 - 2.24582i) q^{13} +(0.500000 + 0.363271i) q^{14} +(-2.72971 + 8.40118i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.15676 + 1.56698i) q^{17} +(-2.46578 + 7.58888i) q^{18} +(-1.98057 - 6.09557i) q^{19} +(-2.15676 + 1.56698i) q^{20} +(-0.632826 - 1.94764i) q^{21} +(-1.09410 - 0.794910i) q^{22} +(2.37618 + 1.72640i) q^{23} +(-2.68070 + 1.94764i) q^{24} +2.10704 q^{25} -2.36139 q^{26} +(13.3483 - 9.69812i) q^{27} +(0.190983 - 0.587785i) q^{28} +(1.17791 + 3.62524i) q^{29} +8.83353 q^{30} +(-5.42127 - 1.26880i) q^{31} -1.00000 q^{32} +(1.38475 + 4.26182i) q^{33} +(0.823809 - 2.53542i) q^{34} +(-1.33295 + 0.968446i) q^{35} +7.97942 q^{36} -4.57017 q^{37} +(-5.18520 + 3.76727i) q^{38} +(6.33017 + 4.59914i) q^{39} +(2.15676 + 1.56698i) q^{40} +(-0.676191 - 2.08110i) q^{41} +(-1.65676 + 1.20371i) q^{42} +(1.92983 + 5.93942i) q^{43} +(-0.417909 + 1.28619i) q^{44} +(-17.2097 - 12.5036i) q^{45} +(0.907621 - 2.79337i) q^{46} +(-1.50000 + 4.61653i) q^{47} +(2.68070 + 1.94764i) q^{48} +(-2.04508 + 6.29412i) q^{49} +(-0.651111 - 2.00391i) q^{50} +(-7.14647 + 5.19222i) q^{51} +(0.729710 + 2.24582i) q^{52} +(-2.78208 - 2.02130i) q^{53} +(-13.3483 - 9.69812i) q^{54} +(2.91676 - 2.11915i) q^{55} -0.618034 q^{56} +21.2372 q^{57} +(3.08381 - 2.24052i) q^{58} +(3.42591 - 10.5439i) q^{59} +(-2.72971 - 8.40118i) q^{60} -2.39097 q^{61} +(0.468562 + 5.54801i) q^{62} +4.93156 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.94534 - 5.98713i) q^{65} +(3.62532 - 2.63395i) q^{66} -9.40926 q^{67} -2.66590 q^{68} +(-7.87353 + 5.72046i) q^{69} +(1.33295 + 0.968446i) q^{70} +(-6.62439 - 4.81290i) q^{71} +(-2.46578 - 7.58888i) q^{72} +(3.47792 - 2.52686i) q^{73} +(1.41226 + 4.34649i) q^{74} +(-2.15747 + 6.64001i) q^{75} +(5.18520 + 3.76727i) q^{76} +(-0.258282 + 0.794910i) q^{77} +(2.41791 - 7.44156i) q^{78} +(2.64197 + 1.91950i) q^{79} +(0.823809 - 2.53542i) q^{80} +(9.49700 + 29.2288i) q^{81} +(-1.77029 + 1.28619i) q^{82} +(-0.354102 - 1.08981i) q^{83} +(1.65676 + 1.20371i) q^{84} +(5.74971 + 4.17741i) q^{85} +(5.05237 - 3.67076i) q^{86} -12.6305 q^{87} +1.35238 q^{88} +(-6.85675 + 4.98172i) q^{89} +(-6.57352 + 20.2312i) q^{90} +(0.450985 + 1.38799i) q^{91} -2.93712 q^{92} +(9.54946 - 15.7851i) q^{93} +4.85410 q^{94} +(-5.28001 - 16.2502i) q^{95} +(1.02393 - 3.15135i) q^{96} +(2.42255 - 1.76008i) q^{97} +6.61803 q^{98} -10.7912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 4 q^{7} + 2 q^{8} - 12 q^{9} - 5 q^{10} + 6 q^{11} - 2 q^{12} + 7 q^{13} + 4 q^{14} - 23 q^{15} - 2 q^{16} + 5 q^{17} - 3 q^{18} - 2 q^{19} - 5 q^{20} + q^{21} - 6 q^{22} - 15 q^{23} - 3 q^{24} + 16 q^{25} + 18 q^{26} + 37 q^{27} + 6 q^{28} - 19 q^{29} - 2 q^{30} + 13 q^{31} - 8 q^{32} + 30 q^{33} + 5 q^{34} + 18 q^{36} - 40 q^{37} - 3 q^{38} + 30 q^{39} + 5 q^{40} - 7 q^{41} - q^{42} + 12 q^{43} + q^{44} - 31 q^{45} - 20 q^{46} - 12 q^{47} + 3 q^{48} + 6 q^{49} + 19 q^{50} - 22 q^{51} + 7 q^{52} + 9 q^{53} - 37 q^{54} - 13 q^{55} + 4 q^{56} + 28 q^{57} - q^{58} - 18 q^{59} - 23 q^{60} + 12 q^{61} - 3 q^{62} + 6 q^{63} - 2 q^{64} - 16 q^{65} + 10 q^{66} - 26 q^{67} - 50 q^{69} - 25 q^{71} - 3 q^{72} + 35 q^{73} - 5 q^{74} + 26 q^{75} + 3 q^{76} - 8 q^{77} + 15 q^{78} + 6 q^{79} + 5 q^{80} + 43 q^{81} - 13 q^{82} + 24 q^{83} + q^{84} - q^{85} + 8 q^{86} + 8 q^{87} + 14 q^{88} - 7 q^{89} - 4 q^{90} - 16 q^{91} - 10 q^{92} + 3 q^{93} + 12 q^{94} + 30 q^{95} + 2 q^{96} + 26 q^{97} + 44 q^{98} - 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/62\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.951057i −0.218508 0.672499i
\(3\) −1.02393 + 3.15135i −0.591169 + 1.81943i −0.0182279 + 0.999834i \(0.505802\pi\)
−0.572941 + 0.819597i \(0.694198\pi\)
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) 2.66590 1.19223 0.596114 0.802900i \(-0.296711\pi\)
0.596114 + 0.802900i \(0.296711\pi\)
\(6\) 3.31352 1.35274
\(7\) −0.500000 + 0.363271i −0.188982 + 0.137304i −0.678253 0.734828i \(-0.737263\pi\)
0.489271 + 0.872132i \(0.337263\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) −6.45549 4.69019i −2.15183 1.56340i
\(10\) −0.823809 2.53542i −0.260511 0.801772i
\(11\) 1.09410 0.794910i 0.329883 0.239674i −0.410498 0.911862i \(-0.634645\pi\)
0.740381 + 0.672187i \(0.234645\pi\)
\(12\) −1.02393 3.15135i −0.295584 0.909715i
\(13\) 0.729710 2.24582i 0.202385 0.622877i −0.797426 0.603417i \(-0.793805\pi\)
0.999811 0.0194599i \(-0.00619466\pi\)
\(14\) 0.500000 + 0.363271i 0.133631 + 0.0970883i
\(15\) −2.72971 + 8.40118i −0.704808 + 2.16918i
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 2.15676 + 1.56698i 0.523091 + 0.380048i 0.817767 0.575549i \(-0.195212\pi\)
−0.294676 + 0.955597i \(0.595212\pi\)
\(18\) −2.46578 + 7.58888i −0.581189 + 1.78872i
\(19\) −1.98057 6.09557i −0.454374 1.39842i −0.871869 0.489740i \(-0.837092\pi\)
0.417495 0.908679i \(-0.362908\pi\)
\(20\) −2.15676 + 1.56698i −0.482266 + 0.350387i
\(21\) −0.632826 1.94764i −0.138094 0.425010i
\(22\) −1.09410 0.794910i −0.233263 0.169475i
\(23\) 2.37618 + 1.72640i 0.495468 + 0.359979i 0.807283 0.590164i \(-0.200937\pi\)
−0.311815 + 0.950143i \(0.600937\pi\)
\(24\) −2.68070 + 1.94764i −0.547195 + 0.397560i
\(25\) 2.10704 0.421408
\(26\) −2.36139 −0.463107
\(27\) 13.3483 9.69812i 2.56889 1.86640i
\(28\) 0.190983 0.587785i 0.0360924 0.111081i
\(29\) 1.17791 + 3.62524i 0.218733 + 0.673190i 0.998868 + 0.0475784i \(0.0151504\pi\)
−0.780135 + 0.625611i \(0.784850\pi\)
\(30\) 8.83353 1.61277
\(31\) −5.42127 1.26880i −0.973688 0.227884i
\(32\) −1.00000 −0.176777
\(33\) 1.38475 + 4.26182i 0.241054 + 0.741888i
\(34\) 0.823809 2.53542i 0.141282 0.434822i
\(35\) −1.33295 + 0.968446i −0.225310 + 0.163697i
\(36\) 7.97942 1.32990
\(37\) −4.57017 −0.751331 −0.375665 0.926755i \(-0.622586\pi\)
−0.375665 + 0.926755i \(0.622586\pi\)
\(38\) −5.18520 + 3.76727i −0.841150 + 0.611132i
\(39\) 6.33017 + 4.59914i 1.01364 + 0.736451i
\(40\) 2.15676 + 1.56698i 0.341014 + 0.247761i
\(41\) −0.676191 2.08110i −0.105603 0.325013i 0.884268 0.466979i \(-0.154658\pi\)
−0.989872 + 0.141966i \(0.954658\pi\)
\(42\) −1.65676 + 1.20371i −0.255644 + 0.185736i
\(43\) 1.92983 + 5.93942i 0.294297 + 0.905753i 0.983457 + 0.181144i \(0.0579799\pi\)
−0.689160 + 0.724610i \(0.742020\pi\)
\(44\) −0.417909 + 1.28619i −0.0630021 + 0.193901i
\(45\) −17.2097 12.5036i −2.56547 1.86392i
\(46\) 0.907621 2.79337i 0.133821 0.411860i
\(47\) −1.50000 + 4.61653i −0.218797 + 0.673389i 0.780065 + 0.625699i \(0.215186\pi\)
−0.998862 + 0.0476905i \(0.984814\pi\)
\(48\) 2.68070 + 1.94764i 0.386925 + 0.281117i
\(49\) −2.04508 + 6.29412i −0.292155 + 0.899161i
\(50\) −0.651111 2.00391i −0.0920809 0.283396i
\(51\) −7.14647 + 5.19222i −1.00071 + 0.727056i
\(52\) 0.729710 + 2.24582i 0.101193 + 0.311439i
\(53\) −2.78208 2.02130i −0.382148 0.277647i 0.380082 0.924953i \(-0.375896\pi\)
−0.762231 + 0.647306i \(0.775896\pi\)
\(54\) −13.3483 9.69812i −1.81648 1.31975i
\(55\) 2.91676 2.11915i 0.393296 0.285746i
\(56\) −0.618034 −0.0825883
\(57\) 21.2372 2.81294
\(58\) 3.08381 2.24052i 0.404924 0.294195i
\(59\) 3.42591 10.5439i 0.446015 1.37269i −0.435352 0.900260i \(-0.643376\pi\)
0.881367 0.472432i \(-0.156624\pi\)
\(60\) −2.72971 8.40118i −0.352404 1.08459i
\(61\) −2.39097 −0.306133 −0.153066 0.988216i \(-0.548915\pi\)
−0.153066 + 0.988216i \(0.548915\pi\)
\(62\) 0.468562 + 5.54801i 0.0595074 + 0.704598i
\(63\) 4.93156 0.621318
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 1.94534 5.98713i 0.241289 0.742612i
\(66\) 3.62532 2.63395i 0.446246 0.324217i
\(67\) −9.40926 −1.14952 −0.574762 0.818321i \(-0.694905\pi\)
−0.574762 + 0.818321i \(0.694905\pi\)
\(68\) −2.66590 −0.323288
\(69\) −7.87353 + 5.72046i −0.947862 + 0.688662i
\(70\) 1.33295 + 0.968446i 0.159318 + 0.115751i
\(71\) −6.62439 4.81290i −0.786171 0.571186i 0.120654 0.992695i \(-0.461501\pi\)
−0.906825 + 0.421508i \(0.861501\pi\)
\(72\) −2.46578 7.58888i −0.290595 0.894358i
\(73\) 3.47792 2.52686i 0.407060 0.295746i −0.365351 0.930870i \(-0.619051\pi\)
0.772410 + 0.635124i \(0.219051\pi\)
\(74\) 1.41226 + 4.34649i 0.164172 + 0.505269i
\(75\) −2.15747 + 6.64001i −0.249123 + 0.766722i
\(76\) 5.18520 + 3.76727i 0.594783 + 0.432135i
\(77\) −0.258282 + 0.794910i −0.0294340 + 0.0905884i
\(78\) 2.41791 7.44156i 0.273774 0.842591i
\(79\) 2.64197 + 1.91950i 0.297245 + 0.215961i 0.726404 0.687268i \(-0.241190\pi\)
−0.429159 + 0.903229i \(0.641190\pi\)
\(80\) 0.823809 2.53542i 0.0921047 0.283469i
\(81\) 9.49700 + 29.2288i 1.05522 + 3.24764i
\(82\) −1.77029 + 1.28619i −0.195496 + 0.142036i
\(83\) −0.354102 1.08981i −0.0388677 0.119623i 0.929740 0.368217i \(-0.120032\pi\)
−0.968608 + 0.248594i \(0.920032\pi\)
\(84\) 1.65676 + 1.20371i 0.180767 + 0.131335i
\(85\) 5.74971 + 4.17741i 0.623644 + 0.453104i
\(86\) 5.05237 3.67076i 0.544811 0.395829i
\(87\) −12.6305 −1.35413
\(88\) 1.35238 0.144164
\(89\) −6.85675 + 4.98172i −0.726814 + 0.528062i −0.888554 0.458772i \(-0.848289\pi\)
0.161740 + 0.986833i \(0.448289\pi\)
\(90\) −6.57352 + 20.2312i −0.692910 + 2.13256i
\(91\) 0.450985 + 1.38799i 0.0472761 + 0.145501i
\(92\) −2.93712 −0.306216
\(93\) 9.54946 15.7851i 0.990232 1.63684i
\(94\) 4.85410 0.500662
\(95\) −5.28001 16.2502i −0.541717 1.66723i
\(96\) 1.02393 3.15135i 0.104505 0.321633i
\(97\) 2.42255 1.76008i 0.245972 0.178709i −0.457968 0.888969i \(-0.651422\pi\)
0.703940 + 0.710260i \(0.251422\pi\)
\(98\) 6.61803 0.668522
\(99\) −10.7912 −1.08456
\(100\) −1.70463 + 1.23849i −0.170463 + 0.123849i
\(101\) 14.3438 + 10.4214i 1.42726 + 1.03697i 0.990518 + 0.137382i \(0.0438687\pi\)
0.436745 + 0.899586i \(0.356131\pi\)
\(102\) 7.14647 + 5.19222i 0.707606 + 0.514106i
\(103\) −0.170541 0.524870i −0.0168039 0.0517170i 0.942303 0.334761i \(-0.108656\pi\)
−0.959107 + 0.283044i \(0.908656\pi\)
\(104\) 1.91040 1.38799i 0.187331 0.136104i
\(105\) −1.68705 5.19222i −0.164640 0.506708i
\(106\) −1.06266 + 3.27053i −0.103215 + 0.317662i
\(107\) 7.50150 + 5.45016i 0.725198 + 0.526887i 0.888041 0.459765i \(-0.152066\pi\)
−0.162843 + 0.986652i \(0.552066\pi\)
\(108\) −5.09860 + 15.6919i −0.490613 + 1.50995i
\(109\) 5.94070 18.2836i 0.569016 1.75125i −0.0866920 0.996235i \(-0.527630\pi\)
0.655708 0.755015i \(-0.272370\pi\)
\(110\) −2.91676 2.11915i −0.278102 0.202053i
\(111\) 4.67955 14.4022i 0.444163 1.36699i
\(112\) 0.190983 + 0.587785i 0.0180462 + 0.0555405i
\(113\) 10.9718 7.97147i 1.03214 0.749893i 0.0634032 0.997988i \(-0.479805\pi\)
0.968736 + 0.248095i \(0.0798046\pi\)
\(114\) −6.56266 20.1978i −0.614650 1.89170i
\(115\) 6.33467 + 4.60241i 0.590711 + 0.429177i
\(116\) −3.08381 2.24052i −0.286325 0.208027i
\(117\) −15.2439 + 11.0754i −1.40930 + 1.02392i
\(118\) −11.0865 −1.02059
\(119\) −1.64762 −0.151037
\(120\) −7.14647 + 5.19222i −0.652381 + 0.473982i
\(121\) −2.83401 + 8.72220i −0.257638 + 0.792927i
\(122\) 0.738852 + 2.27395i 0.0668925 + 0.205874i
\(123\) 7.25064 0.653769
\(124\) 5.13168 2.16006i 0.460839 0.193979i
\(125\) −7.71236 −0.689814
\(126\) −1.52393 4.69019i −0.135763 0.417835i
\(127\) −4.36324 + 13.4287i −0.387175 + 1.19160i 0.547715 + 0.836665i \(0.315498\pi\)
−0.934890 + 0.354938i \(0.884502\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) −20.6932 −1.82193
\(130\) −6.29524 −0.552129
\(131\) 1.92684 1.39993i 0.168348 0.122312i −0.500421 0.865782i \(-0.666821\pi\)
0.668769 + 0.743470i \(0.266821\pi\)
\(132\) −3.62532 2.63395i −0.315544 0.229256i
\(133\) 3.20463 + 2.32830i 0.277877 + 0.201889i
\(134\) 2.90762 + 8.94874i 0.251180 + 0.773053i
\(135\) 35.5853 25.8542i 3.06270 2.22518i
\(136\) 0.823809 + 2.53542i 0.0706411 + 0.217411i
\(137\) −3.97200 + 12.2246i −0.339351 + 1.04442i 0.625188 + 0.780474i \(0.285022\pi\)
−0.964539 + 0.263941i \(0.914978\pi\)
\(138\) 7.87353 + 5.72046i 0.670240 + 0.486958i
\(139\) 1.71841 5.28872i 0.145754 0.448583i −0.851354 0.524592i \(-0.824218\pi\)
0.997107 + 0.0760089i \(0.0242178\pi\)
\(140\) 0.509142 1.56698i 0.0430304 0.132434i
\(141\) −13.0124 9.45404i −1.09584 0.796174i
\(142\) −2.53029 + 7.78744i −0.212337 + 0.653507i
\(143\) −0.986846 3.03720i −0.0825242 0.253983i
\(144\) −6.45549 + 4.69019i −0.537957 + 0.390849i
\(145\) 3.14020 + 9.66453i 0.260779 + 0.802596i
\(146\) −3.47792 2.52686i −0.287835 0.209124i
\(147\) −17.7409 12.8895i −1.46325 1.06311i
\(148\) 3.69734 2.68628i 0.303920 0.220810i
\(149\) 6.23236 0.510575 0.255287 0.966865i \(-0.417830\pi\)
0.255287 + 0.966865i \(0.417830\pi\)
\(150\) 6.98172 0.570055
\(151\) −12.8765 + 9.35536i −1.04788 + 0.761328i −0.971808 0.235774i \(-0.924237\pi\)
−0.0760703 + 0.997102i \(0.524237\pi\)
\(152\) 1.98057 6.09557i 0.160645 0.494416i
\(153\) −6.57352 20.2312i −0.531438 1.63560i
\(154\) 0.835818 0.0673521
\(155\) −14.4526 3.38250i −1.16086 0.271689i
\(156\) −7.82452 −0.626463
\(157\) −1.96856 6.05861i −0.157108 0.483530i 0.841260 0.540631i \(-0.181814\pi\)
−0.998368 + 0.0571009i \(0.981814\pi\)
\(158\) 1.00914 3.10582i 0.0802830 0.247086i
\(159\) 9.21849 6.69763i 0.731074 0.531156i
\(160\) −2.66590 −0.210758
\(161\) −1.81524 −0.143061
\(162\) 24.8635 18.0644i 1.95346 1.41927i
\(163\) 2.30151 + 1.67215i 0.180268 + 0.130973i 0.674260 0.738494i \(-0.264463\pi\)
−0.493992 + 0.869467i \(0.664463\pi\)
\(164\) 1.77029 + 1.28619i 0.138236 + 0.100435i
\(165\) 3.69161 + 11.3616i 0.287391 + 0.884500i
\(166\) −0.927051 + 0.673542i −0.0719531 + 0.0522770i
\(167\) −0.779432 2.39885i −0.0603143 0.185628i 0.916360 0.400356i \(-0.131114\pi\)
−0.976674 + 0.214728i \(0.931114\pi\)
\(168\) 0.632826 1.94764i 0.0488236 0.150264i
\(169\) 6.00601 + 4.36362i 0.462001 + 0.335663i
\(170\) 2.19620 6.75919i 0.168441 0.518407i
\(171\) −15.8038 + 48.6391i −1.20855 + 3.71953i
\(172\) −5.05237 3.67076i −0.385240 0.279893i
\(173\) −3.56152 + 10.9612i −0.270777 + 0.833366i 0.719529 + 0.694462i \(0.244358\pi\)
−0.990306 + 0.138903i \(0.955642\pi\)
\(174\) 3.90303 + 12.0123i 0.295888 + 0.910650i
\(175\) −1.05352 + 0.765426i −0.0796386 + 0.0578608i
\(176\) −0.417909 1.28619i −0.0315011 0.0969503i
\(177\) 29.7194 + 21.5924i 2.23385 + 1.62299i
\(178\) 6.85675 + 4.98172i 0.513935 + 0.373396i
\(179\) 14.9497 10.8616i 1.11739 0.811834i 0.133582 0.991038i \(-0.457352\pi\)
0.983812 + 0.179204i \(0.0573522\pi\)
\(180\) 21.2724 1.58555
\(181\) −2.75492 −0.204772 −0.102386 0.994745i \(-0.532648\pi\)
−0.102386 + 0.994745i \(0.532648\pi\)
\(182\) 1.18070 0.857825i 0.0875189 0.0635862i
\(183\) 2.44820 7.53479i 0.180976 0.556988i
\(184\) 0.907621 + 2.79337i 0.0669107 + 0.205930i
\(185\) −12.1836 −0.895757
\(186\) −17.9635 4.20420i −1.31715 0.308267i
\(187\) 3.60532 0.263647
\(188\) −1.50000 4.61653i −0.109399 0.336695i
\(189\) −3.15111 + 9.69812i −0.229210 + 0.705435i
\(190\) −13.8232 + 10.0432i −1.00284 + 0.728608i
\(191\) 15.8370 1.14592 0.572961 0.819582i \(-0.305794\pi\)
0.572961 + 0.819582i \(0.305794\pi\)
\(192\) −3.31352 −0.239133
\(193\) −2.49536 + 1.81299i −0.179620 + 0.130502i −0.673962 0.738766i \(-0.735409\pi\)
0.494342 + 0.869267i \(0.335409\pi\)
\(194\) −2.42255 1.76008i −0.173929 0.126367i
\(195\) 16.8756 + 12.2608i 1.20849 + 0.878018i
\(196\) −2.04508 6.29412i −0.146077 0.449580i
\(197\) −18.2409 + 13.2528i −1.29961 + 0.944224i −0.999952 0.00982201i \(-0.996874\pi\)
−0.299661 + 0.954046i \(0.596874\pi\)
\(198\) 3.33467 + 10.2631i 0.236985 + 0.729364i
\(199\) −2.80160 + 8.62242i −0.198600 + 0.611227i 0.801316 + 0.598242i \(0.204134\pi\)
−0.999916 + 0.0129859i \(0.995866\pi\)
\(200\) 1.70463 + 1.23849i 0.120536 + 0.0875742i
\(201\) 9.63446 29.6518i 0.679563 2.09148i
\(202\) 5.47885 16.8622i 0.385491 1.18642i
\(203\) −1.90590 1.38472i −0.133768 0.0971881i
\(204\) 2.72971 8.40118i 0.191118 0.588200i
\(205\) −1.80266 5.54801i −0.125903 0.387490i
\(206\) −0.446481 + 0.324387i −0.0311078 + 0.0226011i
\(207\) −7.24229 22.2895i −0.503374 1.54923i
\(208\) −1.91040 1.38799i −0.132463 0.0962398i
\(209\) −7.01237 5.09478i −0.485056 0.352414i
\(210\) −4.41676 + 3.20897i −0.304786 + 0.221440i
\(211\) 10.9297 0.752431 0.376216 0.926532i \(-0.377225\pi\)
0.376216 + 0.926532i \(0.377225\pi\)
\(212\) 3.43884 0.236181
\(213\) 21.9501 15.9477i 1.50399 1.09272i
\(214\) 2.86532 8.81855i 0.195869 0.602824i
\(215\) 5.14475 + 15.8339i 0.350869 + 1.07986i
\(216\) 16.4994 1.12264
\(217\) 3.17155 1.33499i 0.215299 0.0906250i
\(218\) −19.2245 −1.30205
\(219\) 4.40184 + 13.5475i 0.297449 + 0.915453i
\(220\) −1.11410 + 3.42886i −0.0751129 + 0.231174i
\(221\) 5.09295 3.70025i 0.342589 0.248906i
\(222\) −15.1433 −1.01635
\(223\) −12.2416 −0.819761 −0.409880 0.912139i \(-0.634430\pi\)
−0.409880 + 0.912139i \(0.634430\pi\)
\(224\) 0.500000 0.363271i 0.0334077 0.0242721i
\(225\) −13.6020 9.88240i −0.906798 0.658827i
\(226\) −10.9718 7.97147i −0.729832 0.530254i
\(227\) 2.45849 + 7.56645i 0.163176 + 0.502203i 0.998897 0.0469503i \(-0.0149503\pi\)
−0.835722 + 0.549153i \(0.814950\pi\)
\(228\) −17.1813 + 12.4829i −1.13786 + 0.826702i
\(229\) −6.66820 20.5226i −0.440647 1.35617i −0.887188 0.461409i \(-0.847344\pi\)
0.446541 0.894763i \(-0.352656\pi\)
\(230\) 2.41963 7.44685i 0.159546 0.491031i
\(231\) −2.24057 1.62787i −0.147419 0.107106i
\(232\) −1.17791 + 3.62524i −0.0773337 + 0.238009i
\(233\) −1.59525 + 4.90966i −0.104508 + 0.321643i −0.989615 0.143746i \(-0.954085\pi\)
0.885107 + 0.465388i \(0.154085\pi\)
\(234\) 15.2439 + 11.0754i 0.996527 + 0.724019i
\(235\) −3.99885 + 12.3072i −0.260856 + 0.802834i
\(236\) 3.42591 + 10.5439i 0.223007 + 0.686346i
\(237\) −8.75422 + 6.36031i −0.568648 + 0.413147i
\(238\) 0.509142 + 1.56698i 0.0330028 + 0.101572i
\(239\) −5.15676 3.74661i −0.333563 0.242348i 0.408378 0.912813i \(-0.366095\pi\)
−0.741941 + 0.670465i \(0.766095\pi\)
\(240\) 7.14647 + 5.19222i 0.461303 + 0.335156i
\(241\) 22.5517 16.3847i 1.45268 1.05543i 0.467485 0.884001i \(-0.345160\pi\)
0.985196 0.171433i \(-0.0548398\pi\)
\(242\) 9.17106 0.589538
\(243\) −52.3360 −3.35735
\(244\) 1.93434 1.40538i 0.123833 0.0899702i
\(245\) −5.45200 + 16.7795i −0.348315 + 1.07200i
\(246\) −2.24057 6.89577i −0.142854 0.439658i
\(247\) −15.1348 −0.963002
\(248\) −3.64011 4.21302i −0.231148 0.267527i
\(249\) 3.79696 0.240622
\(250\) 2.38325 + 7.33489i 0.150730 + 0.463899i
\(251\) 8.46401 26.0495i 0.534243 1.64423i −0.211035 0.977478i \(-0.567683\pi\)
0.745278 0.666753i \(-0.232317\pi\)
\(252\) −3.98971 + 2.89870i −0.251328 + 0.182601i
\(253\) 3.97211 0.249724
\(254\) 14.1198 0.885952
\(255\) −19.0518 + 13.8419i −1.19307 + 0.866816i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −8.96914 6.51646i −0.559479 0.406486i 0.271789 0.962357i \(-0.412385\pi\)
−0.831268 + 0.555871i \(0.812385\pi\)
\(258\) 6.39455 + 19.6804i 0.398107 + 1.22525i
\(259\) 2.28508 1.66021i 0.141988 0.103160i
\(260\) 1.94534 + 5.98713i 0.120645 + 0.371306i
\(261\) 9.39905 28.9273i 0.581787 1.79056i
\(262\) −1.92684 1.39993i −0.119040 0.0864878i
\(263\) −7.74685 + 23.8423i −0.477691 + 1.47018i 0.364603 + 0.931163i \(0.381205\pi\)
−0.842294 + 0.539019i \(0.818795\pi\)
\(264\) −1.38475 + 4.26182i −0.0852255 + 0.262297i
\(265\) −7.41676 5.38859i −0.455608 0.331019i
\(266\) 1.22406 3.76727i 0.0750519 0.230986i
\(267\) −8.67827 26.7090i −0.531101 1.63456i
\(268\) 7.61225 5.53062i 0.464992 0.337837i
\(269\) 8.14533 + 25.0687i 0.496629 + 1.52847i 0.814402 + 0.580301i \(0.197065\pi\)
−0.317773 + 0.948167i \(0.602935\pi\)
\(270\) −35.5853 25.8542i −2.16565 1.57344i
\(271\) 21.4162 + 15.5598i 1.30094 + 0.945189i 0.999964 0.00844252i \(-0.00268737\pi\)
0.300977 + 0.953632i \(0.402687\pi\)
\(272\) 2.15676 1.56698i 0.130773 0.0950120i
\(273\) −4.83582 −0.292677
\(274\) 12.8537 0.776519
\(275\) 2.30531 1.67491i 0.139015 0.101001i
\(276\) 3.00742 9.25589i 0.181026 0.557139i
\(277\) −7.80959 24.0355i −0.469233 1.44415i −0.853580 0.520962i \(-0.825573\pi\)
0.384347 0.923189i \(-0.374427\pi\)
\(278\) −5.56089 −0.333520
\(279\) 29.0460 + 33.6175i 1.73894 + 2.01263i
\(280\) −1.64762 −0.0984640
\(281\) −2.94171 9.05365i −0.175488 0.540096i 0.824168 0.566346i \(-0.191643\pi\)
−0.999655 + 0.0262502i \(0.991643\pi\)
\(282\) −4.97028 + 15.2970i −0.295976 + 0.910920i
\(283\) 26.0144 18.9006i 1.54640 1.12352i 0.600240 0.799820i \(-0.295072\pi\)
0.946158 0.323704i \(-0.104928\pi\)
\(284\) 8.18820 0.485880
\(285\) 56.6164 3.35366
\(286\) −2.58360 + 1.87709i −0.152771 + 0.110995i
\(287\) 1.09410 + 0.794910i 0.0645827 + 0.0469220i
\(288\) 6.45549 + 4.69019i 0.380393 + 0.276372i
\(289\) −3.05709 9.40877i −0.179829 0.553457i
\(290\) 8.22114 5.97301i 0.482762 0.350747i
\(291\) 3.06610 + 9.43649i 0.179738 + 0.553177i
\(292\) −1.32845 + 4.08854i −0.0777415 + 0.239264i
\(293\) 3.03051 + 2.20179i 0.177044 + 0.128630i 0.672778 0.739844i \(-0.265101\pi\)
−0.495734 + 0.868474i \(0.665101\pi\)
\(294\) −6.77643 + 20.8557i −0.395210 + 1.21633i
\(295\) 9.13313 28.1089i 0.531751 1.63656i
\(296\) −3.69734 2.68628i −0.214904 0.156137i
\(297\) 6.89526 21.2214i 0.400103 1.23139i
\(298\) −1.92591 5.92733i −0.111565 0.343361i
\(299\) 5.61109 4.07670i 0.324498 0.235762i
\(300\) −2.15747 6.64001i −0.124562 0.383361i
\(301\) −3.12254 2.26866i −0.179980 0.130763i
\(302\) 12.8765 + 9.35536i 0.740962 + 0.538340i
\(303\) −47.5285 + 34.5315i −2.73044 + 1.98378i
\(304\) −6.40926 −0.367596
\(305\) −6.37411 −0.364980
\(306\) −17.2097 + 12.5036i −0.983814 + 0.714782i
\(307\) 5.85446 18.0182i 0.334132 1.02835i −0.633017 0.774138i \(-0.718184\pi\)
0.967148 0.254213i \(-0.0818164\pi\)
\(308\) −0.258282 0.794910i −0.0147170 0.0452942i
\(309\) 1.82867 0.104029
\(310\) 1.24914 + 14.7905i 0.0709464 + 0.840042i
\(311\) 3.89253 0.220725 0.110363 0.993891i \(-0.464799\pi\)
0.110363 + 0.993891i \(0.464799\pi\)
\(312\) 2.41791 + 7.44156i 0.136887 + 0.421295i
\(313\) −4.96979 + 15.2954i −0.280909 + 0.864549i 0.706686 + 0.707527i \(0.250189\pi\)
−0.987595 + 0.157022i \(0.949811\pi\)
\(314\) −5.15376 + 3.74443i −0.290844 + 0.211310i
\(315\) 13.1470 0.740752
\(316\) −3.26565 −0.183707
\(317\) −27.8354 + 20.2236i −1.56339 + 1.13587i −0.630232 + 0.776407i \(0.717040\pi\)
−0.933159 + 0.359463i \(0.882960\pi\)
\(318\) −9.21849 6.69763i −0.516947 0.375584i
\(319\) 4.17049 + 3.03004i 0.233503 + 0.169650i
\(320\) 0.823809 + 2.53542i 0.0460523 + 0.141735i
\(321\) −24.8564 + 18.0592i −1.38735 + 1.00797i
\(322\) 0.560941 + 1.72640i 0.0312600 + 0.0962084i
\(323\) 5.28001 16.2502i 0.293787 0.904185i
\(324\) −24.8635 18.0644i −1.38130 1.00358i
\(325\) 1.53753 4.73202i 0.0852866 0.262485i
\(326\) 0.879100 2.70559i 0.0486888 0.149849i
\(327\) 51.5350 + 37.4424i 2.84989 + 2.07057i
\(328\) 0.676191 2.08110i 0.0373364 0.114910i
\(329\) −0.927051 2.85317i −0.0511100 0.157300i
\(330\) 9.66476 7.02186i 0.532027 0.386541i
\(331\) 6.66489 + 20.5124i 0.366336 + 1.12746i 0.949141 + 0.314853i \(0.101955\pi\)
−0.582805 + 0.812612i \(0.698045\pi\)
\(332\) 0.927051 + 0.673542i 0.0508785 + 0.0369654i
\(333\) 29.5027 + 21.4349i 1.61674 + 1.17463i
\(334\) −2.04058 + 1.48257i −0.111656 + 0.0811225i
\(335\) −25.0842 −1.37049
\(336\) −2.04787 −0.111720
\(337\) −6.29422 + 4.57302i −0.342868 + 0.249108i −0.745871 0.666090i \(-0.767966\pi\)
0.403003 + 0.915199i \(0.367966\pi\)
\(338\) 2.29409 7.06049i 0.124782 0.384040i
\(339\) 13.8865 + 42.7382i 0.754210 + 2.32122i
\(340\) −7.10704 −0.385433
\(341\) −6.93999 + 2.92122i −0.375822 + 0.158193i
\(342\) 51.1422 2.76545
\(343\) −2.60081 8.00448i −0.140431 0.432201i
\(344\) −1.92983 + 5.93942i −0.104050 + 0.320232i
\(345\) −20.9901 + 15.2502i −1.13007 + 0.821042i
\(346\) 11.5253 0.619604
\(347\) 8.97598 0.481856 0.240928 0.970543i \(-0.422548\pi\)
0.240928 + 0.970543i \(0.422548\pi\)
\(348\) 10.2183 7.42401i 0.547757 0.397969i
\(349\) −14.6444 10.6398i −0.783897 0.569534i 0.122249 0.992499i \(-0.460989\pi\)
−0.906146 + 0.422965i \(0.860989\pi\)
\(350\) 1.05352 + 0.765426i 0.0563130 + 0.0409138i
\(351\) −12.0398 37.0547i −0.642637 1.97783i
\(352\) −1.09410 + 0.794910i −0.0583157 + 0.0423688i
\(353\) −8.65884 26.6492i −0.460863 1.41839i −0.864111 0.503301i \(-0.832119\pi\)
0.403248 0.915091i \(-0.367881\pi\)
\(354\) 11.3518 34.9373i 0.603342 1.85690i
\(355\) −17.6600 12.8307i −0.937295 0.680984i
\(356\) 2.61905 8.06060i 0.138809 0.427211i
\(357\) 1.68705 5.19222i 0.0892883 0.274801i
\(358\) −14.9497 10.8616i −0.790117 0.574053i
\(359\) 2.85238 8.77873i 0.150543 0.463324i −0.847139 0.531371i \(-0.821677\pi\)
0.997682 + 0.0680476i \(0.0216770\pi\)
\(360\) −6.57352 20.2312i −0.346455 1.06628i
\(361\) −17.8620 + 12.9775i −0.940103 + 0.683025i
\(362\) 0.851318 + 2.62009i 0.0447443 + 0.137709i
\(363\) −24.5848 17.8619i −1.29037 0.937508i
\(364\) −1.18070 0.857825i −0.0618852 0.0449623i
\(365\) 9.27180 6.73635i 0.485308 0.352597i
\(366\) −7.92255 −0.414118
\(367\) −11.1699 −0.583065 −0.291532 0.956561i \(-0.594165\pi\)
−0.291532 + 0.956561i \(0.594165\pi\)
\(368\) 2.37618 1.72640i 0.123867 0.0899947i
\(369\) −5.39561 + 16.6060i −0.280884 + 0.864473i
\(370\) 3.76494 + 11.5873i 0.195730 + 0.602395i
\(371\) 2.12532 0.110341
\(372\) 1.55259 + 18.3835i 0.0804980 + 0.953138i
\(373\) −1.84237 −0.0953943 −0.0476972 0.998862i \(-0.515188\pi\)
−0.0476972 + 0.998862i \(0.515188\pi\)
\(374\) −1.11410 3.42886i −0.0576090 0.177302i
\(375\) 7.89695 24.3043i 0.407797 1.25507i
\(376\) −3.92705 + 2.85317i −0.202522 + 0.147141i
\(377\) 9.00115 0.463583
\(378\) 10.1972 0.524488
\(379\) 14.5892 10.5997i 0.749399 0.544470i −0.146242 0.989249i \(-0.546718\pi\)
0.895640 + 0.444779i \(0.146718\pi\)
\(380\) 13.8232 + 10.0432i 0.709117 + 0.515204i
\(381\) −37.8508 27.5002i −1.93915 1.40888i
\(382\) −4.89389 15.0619i −0.250393 0.770631i
\(383\) −8.15676 + 5.92623i −0.416791 + 0.302816i −0.776345 0.630308i \(-0.782929\pi\)
0.359554 + 0.933124i \(0.382929\pi\)
\(384\) 1.02393 + 3.15135i 0.0522524 + 0.160816i
\(385\) −0.688554 + 2.11915i −0.0350920 + 0.108002i
\(386\) 2.49536 + 1.81299i 0.127011 + 0.0922786i
\(387\) 15.3990 47.3932i 0.782774 2.40913i
\(388\) −0.925330 + 2.84787i −0.0469765 + 0.144579i
\(389\) 9.44035 + 6.85881i 0.478645 + 0.347756i 0.800801 0.598931i \(-0.204408\pi\)
−0.322156 + 0.946687i \(0.604408\pi\)
\(390\) 6.44591 19.8385i 0.326401 1.00456i
\(391\) 2.41963 + 7.44685i 0.122366 + 0.376604i
\(392\) −5.35410 + 3.88998i −0.270423 + 0.196474i
\(393\) 2.43870 + 7.50556i 0.123016 + 0.378605i
\(394\) 18.2409 + 13.2528i 0.918965 + 0.667667i
\(395\) 7.04323 + 5.11721i 0.354383 + 0.257475i
\(396\) 8.73028 6.34292i 0.438713 0.318744i
\(397\) 21.0966 1.05881 0.529405 0.848370i \(-0.322415\pi\)
0.529405 + 0.848370i \(0.322415\pi\)
\(398\) 9.06615 0.454445
\(399\) −10.6186 + 7.71487i −0.531595 + 0.386227i
\(400\) 0.651111 2.00391i 0.0325555 0.100196i
\(401\) 3.40590 + 10.4823i 0.170083 + 0.523460i 0.999375 0.0353548i \(-0.0112561\pi\)
−0.829292 + 0.558815i \(0.811256\pi\)
\(402\) −31.1778 −1.55501
\(403\) −6.80545 + 11.2493i −0.339003 + 0.560368i
\(404\) −17.7299 −0.882097
\(405\) 25.3181 + 77.9210i 1.25807 + 3.87193i
\(406\) −0.727989 + 2.24052i −0.0361295 + 0.111195i
\(407\) −5.00022 + 3.63287i −0.247851 + 0.180075i
\(408\) −8.83353 −0.437325
\(409\) −27.6133 −1.36539 −0.682696 0.730702i \(-0.739193\pi\)
−0.682696 + 0.730702i \(0.739193\pi\)
\(410\) −4.71942 + 3.42886i −0.233076 + 0.169339i
\(411\) −34.4568 25.0343i −1.69963 1.23485i
\(412\) 0.446481 + 0.324387i 0.0219965 + 0.0159814i
\(413\) 2.11733 + 6.51646i 0.104187 + 0.320654i
\(414\) −18.9606 + 13.7757i −0.931861 + 0.677037i
\(415\) −0.944001 2.90534i −0.0463392 0.142617i
\(416\) −0.729710 + 2.24582i −0.0357770 + 0.110110i
\(417\) 14.9071 + 10.8306i 0.730001 + 0.530377i
\(418\) −2.67849 + 8.24353i −0.131009 + 0.403204i
\(419\) −1.32037 + 4.06368i −0.0645042 + 0.198524i −0.978114 0.208068i \(-0.933283\pi\)
0.913610 + 0.406591i \(0.133283\pi\)
\(420\) 4.41676 + 3.20897i 0.215516 + 0.156582i
\(421\) −11.5717 + 35.6139i −0.563969 + 1.73572i 0.107027 + 0.994256i \(0.465867\pi\)
−0.670996 + 0.741461i \(0.734133\pi\)
\(422\) −3.37746 10.3948i −0.164412 0.506009i
\(423\) 31.3356 22.7667i 1.52359 1.10695i
\(424\) −1.06266 3.27053i −0.0516074 0.158831i
\(425\) 4.54438 + 3.30168i 0.220435 + 0.160155i
\(426\) −21.9501 15.9477i −1.06348 0.772666i
\(427\) 1.19549 0.868572i 0.0578537 0.0420332i
\(428\) −9.27237 −0.448197
\(429\) 10.5817 0.510891
\(430\) 13.4691 9.78590i 0.649539 0.471918i
\(431\) −0.799437 + 2.46041i −0.0385075 + 0.118514i −0.968462 0.249160i \(-0.919846\pi\)
0.929955 + 0.367674i \(0.119846\pi\)
\(432\) −5.09860 15.6919i −0.245307 0.754976i
\(433\) 25.5179 1.22631 0.613155 0.789962i \(-0.289900\pi\)
0.613155 + 0.789962i \(0.289900\pi\)
\(434\) −2.24971 2.60379i −0.107990 0.124986i
\(435\) −33.6716 −1.61443
\(436\) 5.94070 + 18.2836i 0.284508 + 0.875625i
\(437\) 5.81718 17.9034i 0.278273 0.856437i
\(438\) 11.5242 8.37279i 0.550646 0.400068i
\(439\) −24.1961 −1.15482 −0.577408 0.816456i \(-0.695936\pi\)
−0.577408 + 0.816456i \(0.695936\pi\)
\(440\) 3.60532 0.171877
\(441\) 42.7227 31.0398i 2.03441 1.47809i
\(442\) −5.09295 3.70025i −0.242247 0.176003i
\(443\) 14.2301 + 10.3388i 0.676091 + 0.491209i 0.872059 0.489402i \(-0.162785\pi\)
−0.195968 + 0.980610i \(0.562785\pi\)
\(444\) 4.67955 + 14.4022i 0.222082 + 0.683497i
\(445\) −18.2794 + 13.2808i −0.866528 + 0.629570i
\(446\) 3.78287 + 11.6425i 0.179124 + 0.551288i
\(447\) −6.38153 + 19.6403i −0.301836 + 0.928955i
\(448\) −0.500000 0.363271i −0.0236228 0.0171630i
\(449\) 2.57008 7.90990i 0.121290 0.373291i −0.871917 0.489653i \(-0.837123\pi\)
0.993207 + 0.116362i \(0.0371233\pi\)
\(450\) −5.19549 + 15.9901i −0.244918 + 0.753779i
\(451\) −2.39411 1.73942i −0.112734 0.0819061i
\(452\) −4.19085 + 12.8981i −0.197121 + 0.606676i
\(453\) −16.2972 50.1577i −0.765711 2.35661i
\(454\) 6.43641 4.67632i 0.302076 0.219471i
\(455\) 1.20228 + 3.70025i 0.0563639 + 0.173470i
\(456\) 17.1813 + 12.4829i 0.804587 + 0.584566i
\(457\) −1.56810 1.13929i −0.0733524 0.0532937i 0.550505 0.834832i \(-0.314435\pi\)
−0.623857 + 0.781538i \(0.714435\pi\)
\(458\) −17.4576 + 12.6837i −0.815739 + 0.592669i
\(459\) 43.9859 2.05308
\(460\) −7.83009 −0.365080
\(461\) −6.23792 + 4.53212i −0.290529 + 0.211082i −0.723497 0.690328i \(-0.757466\pi\)
0.432968 + 0.901409i \(0.357466\pi\)
\(462\) −0.855823 + 2.63395i −0.0398165 + 0.122542i
\(463\) 6.38077 + 19.6380i 0.296540 + 0.912655i 0.982700 + 0.185205i \(0.0592948\pi\)
−0.686160 + 0.727450i \(0.740705\pi\)
\(464\) 3.81180 0.176958
\(465\) 25.4579 42.0816i 1.18058 1.95149i
\(466\) 5.16232 0.239140
\(467\) 1.02230 + 3.14630i 0.0473062 + 0.145594i 0.971919 0.235314i \(-0.0756117\pi\)
−0.924613 + 0.380907i \(0.875612\pi\)
\(468\) 5.82266 17.9203i 0.269153 0.828367i
\(469\) 4.70463 3.41811i 0.217240 0.157834i
\(470\) 12.9406 0.596904
\(471\) 21.1085 0.972626
\(472\) 8.96914 6.51646i 0.412838 0.299944i
\(473\) 6.83274 + 4.96427i 0.314170 + 0.228258i
\(474\) 8.75422 + 6.36031i 0.402095 + 0.292139i
\(475\) −4.17314 12.8436i −0.191477 0.589304i
\(476\) 1.33295 0.968446i 0.0610957 0.0443886i
\(477\) 8.47942 + 26.0970i 0.388246 + 1.19490i
\(478\) −1.96971 + 6.06214i −0.0900923 + 0.277276i
\(479\) −7.58381 5.50996i −0.346513 0.251757i 0.400892 0.916125i \(-0.368700\pi\)
−0.747405 + 0.664369i \(0.768700\pi\)
\(480\) 2.72971 8.40118i 0.124594 0.383460i
\(481\) −3.33489 + 10.2637i −0.152058 + 0.467987i
\(482\) −22.5517 16.3847i −1.02720 0.746305i
\(483\) 1.85869 5.72046i 0.0845733 0.260290i
\(484\) −2.83401 8.72220i −0.128819 0.396464i
\(485\) 6.45827 4.69221i 0.293255 0.213062i
\(486\) 16.1727 + 49.7745i 0.733609 + 2.25782i
\(487\) −6.20383 4.50735i −0.281122 0.204247i 0.438284 0.898836i \(-0.355586\pi\)
−0.719407 + 0.694589i \(0.755586\pi\)
\(488\) −1.93434 1.40538i −0.0875634 0.0636186i
\(489\) −7.62611 + 5.54070i −0.344865 + 0.250559i
\(490\) 17.6430 0.797031
\(491\) 15.8167 0.713796 0.356898 0.934143i \(-0.383834\pi\)
0.356898 + 0.934143i \(0.383834\pi\)
\(492\) −5.86589 + 4.26182i −0.264455 + 0.192138i
\(493\) −3.14020 + 9.66453i −0.141427 + 0.435269i
\(494\) 4.67690 + 14.3940i 0.210424 + 0.647617i
\(495\) −28.7684 −1.29304
\(496\) −2.88197 + 4.76385i −0.129404 + 0.213903i
\(497\) 5.06059 0.226998
\(498\) −1.17332 3.61112i −0.0525779 0.161818i
\(499\) −4.47448 + 13.7710i −0.200305 + 0.616476i 0.799568 + 0.600575i \(0.205062\pi\)
−0.999874 + 0.0159012i \(0.994938\pi\)
\(500\) 6.23943 4.53321i 0.279036 0.202731i
\(501\) 8.35768 0.373394
\(502\) −27.3901 −1.22248
\(503\) 20.8674 15.1611i 0.930431 0.675998i −0.0156670 0.999877i \(-0.504987\pi\)
0.946098 + 0.323879i \(0.104987\pi\)
\(504\) 3.98971 + 2.89870i 0.177716 + 0.129118i
\(505\) 38.2392 + 27.7824i 1.70162 + 1.23630i
\(506\) −1.22745 3.77770i −0.0545668 0.167939i
\(507\) −19.9010 + 14.4590i −0.883836 + 0.642145i
\(508\) −4.36324 13.4287i −0.193588 0.595802i
\(509\) 9.81202 30.1983i 0.434910 1.33852i −0.458268 0.888814i \(-0.651530\pi\)
0.893179 0.449702i \(-0.148470\pi\)
\(510\) 19.0518 + 13.8419i 0.843628 + 0.612932i
\(511\) −0.821025 + 2.52686i −0.0363200 + 0.111782i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) −85.5528 62.1578i −3.77725 2.74433i
\(514\) −3.42591 + 10.5439i −0.151110 + 0.465069i
\(515\) −0.454645 1.39925i −0.0200340 0.0616584i
\(516\) 16.7411 12.1632i 0.736988 0.535453i
\(517\) 2.02857 + 6.24330i 0.0892165 + 0.274580i
\(518\) −2.28508 1.66021i −0.100401 0.0729454i
\(519\) −30.8958 22.4471i −1.35618 0.985320i
\(520\) 5.09295 3.70025i 0.223341 0.162267i
\(521\) −37.6339 −1.64877 −0.824386 0.566028i \(-0.808479\pi\)
−0.824386 + 0.566028i \(0.808479\pi\)
\(522\) −30.4160 −1.33127
\(523\) 13.2783 9.64724i 0.580619 0.421844i −0.258328 0.966057i \(-0.583172\pi\)
0.838947 + 0.544213i \(0.183172\pi\)
\(524\) −0.735986 + 2.26513i −0.0321517 + 0.0989527i
\(525\) −1.33339 4.10375i −0.0581939 0.179102i
\(526\) 25.0693 1.09307
\(527\) −9.70419 11.2315i −0.422721 0.489252i
\(528\) 4.48114 0.195017
\(529\) −4.44160 13.6698i −0.193113 0.594340i
\(530\) −2.83295 + 8.71893i −0.123056 + 0.378726i
\(531\) −71.5685 + 51.9976i −3.10581 + 2.25650i
\(532\) −3.96114 −0.171737
\(533\) −5.16719 −0.223816
\(534\) −22.7200 + 16.5070i −0.983190 + 0.714330i
\(535\) 19.9983 + 14.5296i 0.864601 + 0.628170i
\(536\) −7.61225 5.53062i −0.328799 0.238887i
\(537\) 18.9211 + 58.2333i 0.816507 + 2.51295i
\(538\) 21.3247 15.4933i 0.919375 0.667965i
\(539\) 2.76573 + 8.51206i 0.119129 + 0.366640i
\(540\) −13.5924 + 41.8331i −0.584923 + 1.80021i
\(541\) 8.57074 + 6.22701i 0.368485 + 0.267720i 0.756582 0.653898i \(-0.226868\pi\)
−0.388097 + 0.921618i \(0.626868\pi\)
\(542\) 8.18026 25.1762i 0.351372 1.08141i
\(543\) 2.82086 8.68172i 0.121055 0.372568i
\(544\) −2.15676 1.56698i −0.0924704 0.0671836i
\(545\) 15.8373 48.7423i 0.678396 2.08789i
\(546\) 1.49435 + 4.59914i 0.0639523 + 0.196825i
\(547\) 6.15663 4.47305i 0.263238 0.191254i −0.448335 0.893866i \(-0.647983\pi\)
0.711573 + 0.702612i \(0.247983\pi\)
\(548\) −3.97200 12.2246i −0.169676 0.522208i
\(549\) 15.4349 + 11.2141i 0.658746 + 0.478607i
\(550\) −2.30531 1.67491i −0.0982987 0.0714182i
\(551\) 19.7649 14.3601i 0.842015 0.611760i
\(552\) −9.73222 −0.414231
\(553\) −2.01828 −0.0858262
\(554\) −20.4458 + 14.8547i −0.868658 + 0.631117i
\(555\) 12.4752 38.3948i 0.529544 1.62977i
\(556\) 1.71841 + 5.28872i 0.0728768 + 0.224292i
\(557\) 21.5577 0.913430 0.456715 0.889613i \(-0.349026\pi\)
0.456715 + 0.889613i \(0.349026\pi\)
\(558\) 22.9964 38.0128i 0.973516 1.60921i
\(559\) 14.7471 0.623734
\(560\) 0.509142 + 1.56698i 0.0215152 + 0.0662169i
\(561\) −3.69161 + 11.3616i −0.155860 + 0.479687i
\(562\) −7.70150 + 5.59546i −0.324868 + 0.236030i
\(563\) −28.2647 −1.19121 −0.595607 0.803276i \(-0.703089\pi\)
−0.595607 + 0.803276i \(0.703089\pi\)
\(564\) 16.0842 0.677266
\(565\) 29.2497 21.2512i 1.23054 0.894043i
\(566\) −26.0144 18.9006i −1.09347 0.794452i
\(567\) −15.3665 11.1644i −0.645331 0.468860i
\(568\) −2.53029 7.78744i −0.106169 0.326754i
\(569\) 21.0763 15.3128i 0.883565 0.641948i −0.0506271 0.998718i \(-0.516122\pi\)
0.934192 + 0.356770i \(0.116122\pi\)
\(570\) −17.4954 53.8454i −0.732802 2.25533i
\(571\) −12.2779 + 37.7876i −0.513816 + 1.58136i 0.271611 + 0.962407i \(0.412444\pi\)
−0.785427 + 0.618955i \(0.787556\pi\)
\(572\) 2.58360 + 1.87709i 0.108026 + 0.0784852i
\(573\) −16.2160 + 49.9078i −0.677434 + 2.08493i
\(574\) 0.417909 1.28619i 0.0174432 0.0536846i
\(575\) 5.00671 + 3.63759i 0.208794 + 0.151698i
\(576\) 2.46578 7.58888i 0.102741 0.316203i
\(577\) −0.186561 0.574175i −0.00776663 0.0239032i 0.947098 0.320944i \(-0.104000\pi\)
−0.954865 + 0.297041i \(0.904000\pi\)
\(578\) −8.00357 + 5.81494i −0.332905 + 0.241869i
\(579\) −3.15826 9.72013i −0.131253 0.403955i
\(580\) −8.22114 5.97301i −0.341364 0.248016i
\(581\) 0.572949 + 0.416272i 0.0237699 + 0.0172699i
\(582\) 8.02716 5.83207i 0.332736 0.241747i
\(583\) −4.65063 −0.192609
\(584\) 4.29894 0.177892
\(585\) −40.6388 + 29.5258i −1.68021 + 1.22074i
\(586\) 1.15755 3.56258i 0.0478180 0.147169i
\(587\) −5.56288 17.1208i −0.229605 0.706650i −0.997791 0.0664247i \(-0.978841\pi\)
0.768187 0.640226i \(-0.221159\pi\)
\(588\) 21.9290 0.904337
\(589\) 3.00313 + 35.5587i 0.123742 + 1.46517i
\(590\) −29.5554 −1.21678
\(591\) −23.0867 71.0535i −0.949659 2.92275i
\(592\) −1.41226 + 4.34649i −0.0580435 + 0.178639i
\(593\) 5.54474 4.02849i 0.227695 0.165430i −0.468089 0.883682i \(-0.655057\pi\)
0.695784 + 0.718251i \(0.255057\pi\)
\(594\) −22.3135 −0.915535
\(595\) −4.39239 −0.180070
\(596\) −5.04209 + 3.66329i −0.206532 + 0.150054i
\(597\) −24.3036 17.6576i −0.994680 0.722677i
\(598\) −5.61109 4.07670i −0.229455 0.166709i
\(599\) 1.44935 + 4.46064i 0.0592189 + 0.182257i 0.976290 0.216467i \(-0.0694533\pi\)
−0.917071 + 0.398724i \(0.869453\pi\)
\(600\) −5.64833 + 4.10375i −0.230592 + 0.167535i
\(601\) 4.84412 + 14.9087i 0.197596 + 0.608137i 0.999936 + 0.0112708i \(0.00358770\pi\)
−0.802341 + 0.596866i \(0.796412\pi\)
\(602\) −1.19270 + 3.67076i −0.0486110 + 0.149609i
\(603\) 60.7414 + 44.1312i 2.47358 + 1.79716i
\(604\) 4.91840 15.1373i 0.200127 0.615927i
\(605\) −7.55521 + 23.2525i −0.307163 + 0.945350i
\(606\) 47.5285 + 34.5315i 1.93071 + 1.40275i
\(607\) 8.63712 26.5823i 0.350570 1.07894i −0.607964 0.793964i \(-0.708014\pi\)
0.958534 0.284978i \(-0.0919864\pi\)
\(608\) 1.98057 + 6.09557i 0.0803227 + 0.247208i
\(609\) 6.31524 4.58829i 0.255907 0.185927i
\(610\) 1.96971 + 6.06214i 0.0797511 + 0.245449i
\(611\) 9.27330 + 6.73745i 0.375158 + 0.272568i
\(612\) 17.2097 + 12.5036i 0.695661 + 0.505427i
\(613\) 6.67133 4.84701i 0.269453 0.195769i −0.444851 0.895604i \(-0.646743\pi\)
0.714304 + 0.699836i \(0.246743\pi\)
\(614\) −18.9454 −0.764575
\(615\) 19.3295 0.779441
\(616\) −0.676191 + 0.491281i −0.0272445 + 0.0197943i
\(617\) −5.73678 + 17.6560i −0.230954 + 0.710803i 0.766679 + 0.642031i \(0.221908\pi\)
−0.997632 + 0.0687718i \(0.978092\pi\)
\(618\) −0.565090 1.73917i −0.0227312 0.0699596i
\(619\) −21.2657 −0.854739 −0.427369 0.904077i \(-0.640560\pi\)
−0.427369 + 0.904077i \(0.640560\pi\)
\(620\) 13.6806 5.75851i 0.549425 0.231267i
\(621\) 48.4609 1.94467
\(622\) −1.20286 3.70202i −0.0482302 0.148437i
\(623\) 1.61866 4.98172i 0.0648502 0.199588i
\(624\) 6.33017 4.59914i 0.253410 0.184113i
\(625\) −31.0956 −1.24382
\(626\) 16.0826 0.642789
\(627\) 23.2356 16.8817i 0.927942 0.674189i
\(628\) 5.15376 + 3.74443i 0.205657 + 0.149419i
\(629\) −9.85675 7.16135i −0.393014 0.285542i
\(630\) −4.06266 12.5036i −0.161860 0.498155i
\(631\) 23.9119 17.3730i 0.951918 0.691609i 0.000658154 1.00000i \(-0.499791\pi\)
0.951260 + 0.308391i \(0.0997905\pi\)
\(632\) 1.00914 + 3.10582i 0.0401415 + 0.123543i
\(633\) −11.1913 + 34.4433i −0.444814 + 1.36900i
\(634\) 27.8354 + 20.2236i 1.10548 + 0.803182i
\(635\) −11.6320 + 35.7996i −0.461601 + 1.42066i
\(636\) −3.52115 + 10.8370i −0.139623 + 0.429714i
\(637\) 12.6431 + 9.18577i 0.500939 + 0.363953i
\(638\) 1.59299 4.90270i 0.0630669 0.194100i
\(639\) 20.1903 + 62.1393i 0.798715 + 2.45819i
\(640\) 2.15676 1.56698i 0.0852535 0.0619403i
\(641\) −5.80858 17.8770i −0.229425 0.706098i −0.997812 0.0661124i \(-0.978940\pi\)
0.768387 0.639985i \(-0.221060\pi\)
\(642\) 24.8564 + 18.0592i 0.981004 + 0.712741i
\(643\) 10.4063 + 7.56065i 0.410386 + 0.298163i 0.773758 0.633481i \(-0.218375\pi\)
−0.363372 + 0.931644i \(0.618375\pi\)
\(644\) 1.46856 1.06697i 0.0578694 0.0420446i
\(645\) −55.1661 −2.17216
\(646\) −17.0865 −0.672258
\(647\) −12.3701 + 8.98737i −0.486317 + 0.353330i −0.803766 0.594945i \(-0.797174\pi\)
0.317449 + 0.948275i \(0.397174\pi\)
\(648\) −9.49700 + 29.2288i −0.373077 + 1.14821i
\(649\) −4.63313 14.2593i −0.181866 0.559727i
\(650\) −4.97554 −0.195157
\(651\) 0.959553 + 11.3616i 0.0376078 + 0.445296i
\(652\) −2.84483 −0.111412
\(653\) 6.90855 + 21.2623i 0.270352 + 0.832059i 0.990412 + 0.138147i \(0.0441146\pi\)
−0.720059 + 0.693913i \(0.755885\pi\)
\(654\) 19.6846 60.5831i 0.769730 2.36899i
\(655\) 5.13676 3.73207i 0.200710 0.145824i
\(656\) −2.18820 −0.0854348
\(657\) −34.3031 −1.33829
\(658\) −2.42705 + 1.76336i −0.0946163 + 0.0687428i
\(659\) −6.85525 4.98063i −0.267043 0.194018i 0.446203 0.894932i \(-0.352776\pi\)
−0.713246 + 0.700914i \(0.752776\pi\)
\(660\) −9.66476 7.02186i −0.376200 0.273325i
\(661\) −8.00862 24.6480i −0.311499 0.958696i −0.977172 0.212452i \(-0.931855\pi\)
0.665672 0.746244i \(-0.268145\pi\)
\(662\) 17.4489 12.6774i 0.678171 0.492720i
\(663\) 6.44591 + 19.8385i 0.250338 + 0.770462i
\(664\) 0.354102 1.08981i 0.0137418 0.0422930i
\(665\) 8.54323 + 6.20702i 0.331292 + 0.240698i
\(666\) 11.2690 34.6825i 0.436665 1.34392i
\(667\) −3.45967 + 10.6478i −0.133959 + 0.412283i
\(668\) 2.04058 + 1.48257i 0.0789524 + 0.0573623i
\(669\) 12.5346 38.5776i 0.484617 1.49150i
\(670\) 7.75144 + 23.8565i 0.299464 + 0.921656i
\(671\) −2.61596 + 1.90061i −0.100988 + 0.0733722i
\(672\) 0.632826 + 1.94764i 0.0244118 + 0.0751318i
\(673\) −37.7404 27.4200i −1.45478 1.05696i −0.984684 0.174349i \(-0.944218\pi\)
−0.470100 0.882613i \(-0.655782\pi\)
\(674\) 6.29422 + 4.57302i 0.242444 + 0.176146i
\(675\) 28.1254 20.4343i 1.08255 0.786517i
\(676\) −7.42384 −0.285532
\(677\) 40.1322 1.54241 0.771203 0.636589i \(-0.219655\pi\)
0.771203 + 0.636589i \(0.219655\pi\)
\(678\) 36.3553 26.4136i 1.39622 1.01441i
\(679\) −0.571886 + 1.76008i −0.0219470 + 0.0675458i
\(680\) 2.19620 + 6.75919i 0.0842203 + 0.259203i
\(681\) −26.3618 −1.01019
\(682\) 4.92282 + 5.69761i 0.188505 + 0.218173i
\(683\) −5.73560 −0.219467 −0.109733 0.993961i \(-0.535000\pi\)
−0.109733 + 0.993961i \(0.535000\pi\)
\(684\) −15.8038 48.6391i −0.604274 1.85976i
\(685\) −10.5890 + 32.5895i −0.404584 + 1.24518i
\(686\) −6.80902 + 4.94704i −0.259969 + 0.188879i
\(687\) 71.5016 2.72796
\(688\) 6.24508 0.238091
\(689\) −6.56958 + 4.77308i −0.250281 + 0.181840i
\(690\) 20.9901 + 15.2502i 0.799078 + 0.580564i
\(691\) −4.33839 3.15202i −0.165040 0.119909i 0.502200 0.864752i \(-0.332524\pi\)
−0.667240 + 0.744843i \(0.732524\pi\)
\(692\) −3.56152 10.9612i −0.135389 0.416683i
\(693\) 5.39561 3.92014i 0.204962 0.148914i
\(694\) −2.77373 8.53667i −0.105289 0.324047i
\(695\) 4.58111 14.0992i 0.173772 0.534814i
\(696\) −10.2183 7.42401i −0.387323 0.281406i
\(697\) 1.80266 5.54801i 0.0682806 0.210146i
\(698\) −5.59366 + 17.2155i −0.211723 + 0.651617i
\(699\) −13.8386 10.0543i −0.523424 0.380290i
\(700\) 0.402408 1.23849i 0.0152096 0.0468104i
\(701\) −0.295457 0.909322i −0.0111592 0.0343446i 0.945322 0.326139i \(-0.105748\pi\)
−0.956481 + 0.291794i \(0.905748\pi\)
\(702\) −31.5206 + 22.9010i −1.18967 + 0.864344i
\(703\) 9.05153 + 27.8578i 0.341385 + 1.05067i
\(704\) 1.09410 + 0.794910i 0.0412354 + 0.0299593i
\(705\) −34.6897 25.2035i −1.30649 0.949221i
\(706\) −22.6691 + 16.4701i −0.853164 + 0.619860i
\(707\) −10.9577 −0.412107
\(708\) −36.7352 −1.38059
\(709\) −2.09273 + 1.52046i −0.0785940 + 0.0571019i −0.626388 0.779511i \(-0.715468\pi\)
0.547794 + 0.836613i \(0.315468\pi\)
\(710\) −6.74551 + 20.7606i −0.253155 + 0.779130i
\(711\) −8.05237 24.7827i −0.301988 0.929422i
\(712\) −8.47541 −0.317630
\(713\) −10.6915 12.3742i −0.400399 0.463416i
\(714\) −5.45942 −0.204314
\(715\) −2.63084 8.09688i −0.0983877 0.302806i
\(716\) −5.71028 + 17.5744i −0.213403 + 0.656787i
\(717\) 17.0870 12.4145i 0.638127 0.463626i
\(718\) −9.23050 −0.344479
\(719\) −13.9417 −0.519938 −0.259969 0.965617i \(-0.583712\pi\)
−0.259969 + 0.965617i \(0.583712\pi\)
\(720\) −17.2097 + 12.5036i −0.641368 + 0.465981i
\(721\) 0.275940 + 0.200482i 0.0102766 + 0.00746636i
\(722\) 17.8620 + 12.9775i 0.664754 + 0.482972i
\(723\) 28.5426 + 87.8450i 1.06151 + 3.26699i
\(724\) 2.22878 1.61930i 0.0828319 0.0601809i
\(725\) 2.48190 + 7.63851i 0.0921756 + 0.283687i
\(726\) −9.39057 + 28.9012i −0.348517 + 1.07262i
\(727\) −21.5984 15.6922i −0.801040 0.581990i 0.110179 0.993912i \(-0.464858\pi\)
−0.911219 + 0.411922i \(0.864858\pi\)
\(728\) −0.450985 + 1.38799i −0.0167146 + 0.0514423i
\(729\) 25.0976 77.2425i 0.929541 2.86083i
\(730\) −9.27180 6.73635i −0.343165 0.249324i
\(731\) −5.14475 + 15.8339i −0.190286 + 0.585639i
\(732\) 2.44820 + 7.53479i 0.0904881 + 0.278494i
\(733\) −3.33903 + 2.42595i −0.123330 + 0.0896045i −0.647740 0.761861i \(-0.724286\pi\)
0.524410 + 0.851466i \(0.324286\pi\)
\(734\) 3.45169 + 10.6232i 0.127404 + 0.392110i
\(735\) −47.2956 34.3623i −1.74452 1.26747i
\(736\) −2.37618 1.72640i −0.0875873 0.0636359i
\(737\) −10.2947 + 7.47951i −0.379209 + 0.275511i
\(738\) 17.4606 0.642732
\(739\) −28.0676 −1.03248 −0.516241 0.856443i \(-0.672669\pi\)
−0.516241 + 0.856443i \(0.672669\pi\)
\(740\) 9.85675 7.16135i 0.362341 0.263256i
\(741\) 15.4970 47.6949i 0.569297 1.75212i
\(742\) −0.656761 2.02130i −0.0241104 0.0742043i
\(743\) 30.8271 1.13094 0.565468 0.824770i \(-0.308696\pi\)
0.565468 + 0.824770i \(0.308696\pi\)
\(744\) 17.0039 7.15740i 0.623394 0.262403i
\(745\) 16.6149 0.608722
\(746\) 0.569324 + 1.75220i 0.0208444 + 0.0641525i
\(747\) −2.82553 + 8.69609i −0.103381 + 0.318173i
\(748\) −2.91676 + 2.11915i −0.106647 + 0.0774839i
\(749\) −5.73064 −0.209393
\(750\) −25.5551 −0.933139
\(751\) 2.65512 1.92906i 0.0968868 0.0703924i −0.538287 0.842762i \(-0.680928\pi\)
0.635174 + 0.772369i \(0.280928\pi\)
\(752\) 3.92705 + 2.85317i 0.143205 + 0.104044i
\(753\) 73.4245 + 53.3460i 2.67574 + 1.94404i
\(754\) −2.78151 8.56060i −0.101297 0.311759i
\(755\) −34.3276 + 24.9405i −1.24931 + 0.907677i
\(756\) −3.15111 9.69812i −0.114605 0.352717i
\(757\) 5.95885 18.3395i 0.216578 0.666559i −0.782460 0.622701i \(-0.786035\pi\)
0.999038 0.0438575i \(-0.0139648\pi\)
\(758\) −14.5892 10.5997i −0.529905 0.384999i
\(759\) −4.06718 + 12.5175i −0.147629 + 0.454356i
\(760\) 5.28001 16.2502i 0.191526 0.589456i
\(761\) 26.8430 + 19.5026i 0.973059 + 0.706969i 0.956147 0.292888i \(-0.0946164\pi\)
0.0169123 + 0.999857i \(0.494616\pi\)
\(762\) −14.4577 + 44.4962i −0.523747 + 1.61193i
\(763\) 3.67155 + 11.2999i 0.132919 + 0.409083i
\(764\) −12.8124 + 9.30874i −0.463535 + 0.336778i
\(765\) −17.5244 53.9345i −0.633595 1.95001i
\(766\) 8.15676 + 5.92623i 0.294716 + 0.214124i
\(767\) −21.1796 15.3879i −0.764752 0.555625i
\(768\) 2.68070 1.94764i 0.0967313 0.0702794i
\(769\) 32.5658 1.17435 0.587177 0.809458i \(-0.300239\pi\)
0.587177 + 0.809458i \(0.300239\pi\)
\(770\) 2.22821 0.0802991
\(771\) 29.7194 21.5924i 1.07032 0.777632i
\(772\) 0.953144 2.93347i 0.0343044 0.105578i
\(773\) −4.27905 13.1695i −0.153907 0.473676i 0.844142 0.536120i \(-0.180110\pi\)
−0.998048 + 0.0624441i \(0.980110\pi\)
\(774\) −49.8321 −1.79118
\(775\) −11.4228 2.67341i −0.410320 0.0960319i
\(776\) 2.99443 0.107494
\(777\) 2.89212 + 8.90103i 0.103754 + 0.319323i
\(778\) 3.60589 11.0978i 0.129278 0.397875i
\(779\) −11.3462 + 8.24353i −0.406522 + 0.295355i
\(780\) −20.8594 −0.746886
\(781\) −11.0736 −0.396243
\(782\) 6.33467 4.60241i 0.226527 0.164582i
\(783\) 50.8811 + 36.9673i 1.81834 + 1.32110i
\(784\) 5.35410 + 3.88998i 0.191218 + 0.138928i
\(785\) −5.24799 16.1517i −0.187309 0.576478i
\(786\) 6.38461 4.63869i 0.227732 0.165457i
\(787\) −14.3147 44.0562i −0.510265 1.57043i −0.791736 0.610864i \(-0.790822\pi\)
0.281471 0.959570i \(-0.409178\pi\)
\(788\) 6.96742 21.4435i 0.248204 0.763893i
\(789\) −67.2032 48.8260i −2.39250 1.73825i
\(790\) 2.69027 8.27981i 0.0957157 0.294583i
\(791\) −2.59009 + 7.97147i −0.0920929 + 0.283433i
\(792\) −8.73028 6.34292i −0.310217 0.225386i
\(793\) −1.74472 + 5.36969i −0.0619567 + 0.190683i
\(794\) −6.51921 20.0641i −0.231358 0.712048i
\(795\) 24.5756 17.8552i 0.871607 0.633259i
\(796\) −2.80160 8.62242i −0.0992999 0.305614i
\(797\) 15.9326 + 11.5757i 0.564362 + 0.410033i 0.833053 0.553193i \(-0.186591\pi\)
−0.268691 + 0.963226i \(0.586591\pi\)
\(798\) 10.6186 + 7.71487i 0.375895 + 0.273103i
\(799\) −10.4691 + 7.60627i −0.370371 + 0.269091i
\(800\) −2.10704 −0.0744950
\(801\) 67.6289 2.38955
\(802\) 8.91676 6.47841i 0.314862 0.228761i
\(803\) 1.79657 5.52926i 0.0633995 0.195124i
\(804\) 9.63446 + 29.6518i 0.339781 + 1.04574i
\(805\) −4.83926 −0.170561
\(806\) 12.8017 + 2.99614i 0.450922 + 0.105534i
\(807\) −87.3406 −3.07453
\(808\) 5.47885 + 16.8622i 0.192745 + 0.593209i
\(809\) 13.3847 41.1940i 0.470583 1.44830i −0.381241 0.924476i \(-0.624503\pi\)
0.851823 0.523829i \(-0.175497\pi\)
\(810\) 66.2836 48.1579i 2.32897 1.69209i
\(811\) −4.91283 −0.172513 −0.0862563 0.996273i \(-0.527490\pi\)
−0.0862563 + 0.996273i \(0.527490\pi\)
\(812\) 2.35582 0.0826732
\(813\) −70.9630 + 51.5576i −2.48878 + 1.80821i
\(814\) 5.00022 + 3.63287i 0.175257 + 0.127332i
\(815\) 6.13561 + 4.45778i 0.214921 + 0.156149i
\(816\) 2.72971 + 8.40118i 0.0955590 + 0.294100i
\(817\) 32.3820 23.5269i 1.13290 0.823101i
\(818\) 8.53299 + 26.2619i 0.298349 + 0.918224i
\(819\) 3.59860 11.0754i 0.125745 0.387005i
\(820\) 4.71942 + 3.42886i 0.164809 + 0.119741i
\(821\) 12.2400 37.6709i 0.427179 1.31472i −0.473713 0.880679i \(-0.657087\pi\)
0.900892 0.434043i \(-0.142913\pi\)
\(822\) −13.1613 + 40.5064i −0.459054 + 1.41282i
\(823\) −40.8661 29.6910i −1.42450 1.03496i −0.991007 0.133807i \(-0.957280\pi\)
−0.433496 0.901156i \(-0.642720\pi\)
\(824\) 0.170541 0.524870i 0.00594106 0.0182847i
\(825\) 2.91772 + 8.97982i 0.101582 + 0.312637i
\(826\) 5.54323 4.02739i 0.192874 0.140131i
\(827\) −0.456414 1.40470i −0.0158711 0.0488461i 0.942807 0.333338i \(-0.108175\pi\)
−0.958678 + 0.284492i \(0.908175\pi\)
\(828\) 18.9606 + 13.7757i 0.658925 + 0.478737i
\(829\) −1.59481 1.15870i −0.0553900 0.0402432i 0.559746 0.828664i \(-0.310899\pi\)
−0.615136 + 0.788421i \(0.710899\pi\)
\(830\) −2.47143 + 1.79560i −0.0857845 + 0.0623261i
\(831\) 83.7405 2.90493
\(832\) 2.36139 0.0818665
\(833\) −14.2735 + 10.3703i −0.494548 + 0.359310i
\(834\) 5.69399 17.5243i 0.197167 0.606816i
\(835\) −2.07789 6.39509i −0.0719084 0.221311i
\(836\) 8.66776 0.299781
\(837\) −84.6698 + 35.6397i −2.92662 + 1.23189i
\(838\) 4.27280 0.147601
\(839\) 13.1434 + 40.4512i 0.453760 + 1.39653i 0.872585 + 0.488463i \(0.162442\pi\)
−0.418824 + 0.908067i \(0.637558\pi\)
\(840\) 1.68705 5.19222i 0.0582089 0.179148i
\(841\) 11.7066 8.50535i 0.403676 0.293288i
\(842\) 37.4467 1.29050
\(843\) 31.5433 1.08641
\(844\) −8.84231 + 6.42431i −0.304365 + 0.221134i
\(845\) 16.0114 + 11.6330i 0.550810 + 0.400187i
\(846\) −31.3356 22.7667i −1.07734 0.782734i
\(847\) −1.75152 5.39062i −0.0601829 0.185224i
\(848\) −2.78208 + 2.02130i −0.0955371 + 0.0694118i
\(849\) 32.9253 + 101.334i 1.12999 + 3.47776i
\(850\) 1.73580 5.34224i 0.0595374 0.183237i
\(851\) −10.8595 7.88992i −0.372260 0.270463i
\(852\) −8.38418 + 25.8038i −0.287237 + 0.884025i
\(853\) 7.88412 24.2648i 0.269947 0.830812i −0.720565 0.693387i \(-0.756117\pi\)
0.990512 0.137425i \(-0.0438825\pi\)
\(854\) −1.19549 0.868572i −0.0409087 0.0297219i
\(855\) −42.1314 + 129.667i −1.44086 + 4.43452i
\(856\) 2.86532 + 8.81855i 0.0979346 + 0.301412i
\(857\) 5.73864 4.16936i 0.196028 0.142423i −0.485442 0.874269i \(-0.661341\pi\)
0.681470 + 0.731846i \(0.261341\pi\)
\(858\) −3.26994 10.0638i −0.111634 0.343573i
\(859\) −31.9802 23.2350i −1.09115 0.792767i −0.111558 0.993758i \(-0.535584\pi\)
−0.979593 + 0.200990i \(0.935584\pi\)
\(860\) −13.4691 9.78590i −0.459294 0.333696i
\(861\) −3.62532 + 2.63395i −0.123551 + 0.0897648i
\(862\) 2.58703 0.0881147
\(863\) −14.3669 −0.489053 −0.244527 0.969643i \(-0.578633\pi\)
−0.244527 + 0.969643i \(0.578633\pi\)
\(864\) −13.3483 + 9.69812i −0.454119 + 0.329937i
\(865\) −9.49465 + 29.2215i −0.322828 + 0.993562i
\(866\) −7.88546 24.2689i −0.267959 0.824692i
\(867\) 32.7805 1.11329
\(868\) −1.78115 + 2.94422i −0.0604563 + 0.0999334i
\(869\) 4.41641 0.149816
\(870\) 10.4051 + 32.0236i 0.352766 + 1.08570i
\(871\) −6.86603 + 21.1315i −0.232646 + 0.716012i
\(872\) 15.5529 11.2999i 0.526689 0.382662i
\(873\) −23.8938 −0.808684
\(874\) −18.8248 −0.636758
\(875\) 3.85618 2.80168i 0.130363 0.0947140i
\(876\) −11.5242 8.37279i −0.389365 0.282890i
\(877\) −34.0462 24.7360i −1.14966 0.835275i −0.161222 0.986918i \(-0.551543\pi\)
−0.988435 + 0.151643i \(0.951543\pi\)
\(878\) 7.47700 + 23.0118i 0.252336 + 0.776612i
\(879\) −10.0417 + 7.29569i −0.338697 + 0.246077i
\(880\) −1.11410 3.42886i −0.0375565 0.115587i
\(881\) 8.66342 26.6633i 0.291878 0.898309i −0.692374 0.721539i \(-0.743435\pi\)
0.984252 0.176770i \(-0.0565648\pi\)
\(882\) −42.7227 31.0398i −1.43855 1.04517i
\(883\) −7.15796 + 22.0299i −0.240885 + 0.741366i 0.755402 + 0.655262i \(0.227442\pi\)
−0.996286 + 0.0861043i \(0.972558\pi\)
\(884\) −1.94534 + 5.98713i −0.0654287 + 0.201369i
\(885\) 79.2291 + 57.5633i 2.66326 + 1.93497i
\(886\) 5.43540 16.7284i 0.182606 0.562003i
\(887\) 14.7695 + 45.4558i 0.495911 + 1.52626i 0.815532 + 0.578712i \(0.196445\pi\)
−0.319620 + 0.947546i \(0.603555\pi\)
\(888\) 12.2512 8.90103i 0.411124 0.298699i
\(889\) −2.69663 8.29938i −0.0904422 0.278352i
\(890\) 18.2794 + 13.2808i 0.612728 + 0.445173i
\(891\) 33.6249 + 24.4299i 1.12648 + 0.818433i
\(892\) 9.90369 7.19545i 0.331600 0.240922i
\(893\) 31.1112 1.04110
\(894\) 20.6511 0.690675
\(895\) 39.8545 28.9560i 1.33219 0.967891i
\(896\) −0.190983 + 0.587785i −0.00638029 + 0.0196365i
\(897\) 7.10170 + 21.8568i 0.237119 + 0.729776i
\(898\) −8.31696 −0.277541
\(899\) −1.78606 21.1479i −0.0595686 0.705323i
\(900\) 16.8130 0.560432
\(901\) −2.83295 8.71893i −0.0943793 0.290470i
\(902\) −0.914468 + 2.81444i −0.0304484 + 0.0937107i
\(903\) 10.3466 7.51724i 0.344313 0.250158i
\(904\) 13.5619 0.451061
\(905\) −7.34436 −0.244135
\(906\) −42.6667 + 30.9992i −1.41751 + 1.02988i
\(907\) −22.9987 16.7096i −0.763660 0.554832i 0.136371 0.990658i \(-0.456456\pi\)
−0.900031 + 0.435826i \(0.856456\pi\)
\(908\) −6.43641 4.67632i −0.213600 0.155189i
\(909\) −43.7181 134.550i −1.45004 4.46275i
\(910\) 3.14762 2.28688i 0.104343 0.0758093i
\(911\) −11.4331 35.1876i −0.378797 1.16582i −0.940881 0.338737i \(-0.890000\pi\)
0.562084 0.827080i \(-0.310000\pi\)
\(912\) 6.56266 20.1978i 0.217311 0.668816i
\(913\) −1.25373 0.910886i −0.0414923 0.0301459i
\(914\) −0.598959 + 1.84341i −0.0198118 + 0.0609745i
\(915\) 6.52667 20.0870i 0.215765 0.664056i
\(916\) 17.4576 + 12.6837i 0.576814 + 0.419080i
\(917\) −0.454864 + 1.39993i −0.0150209 + 0.0462297i
\(918\) −13.5924 41.8331i −0.448615 1.38070i
\(919\) −22.9803 + 16.6962i −0.758052 + 0.550757i −0.898312 0.439358i \(-0.855206\pi\)
0.140260 + 0.990115i \(0.455206\pi\)
\(920\) 2.41963 + 7.44685i 0.0797728 + 0.245515i
\(921\) 50.7869 + 36.8988i 1.67349 + 1.21586i
\(922\) 6.23792 + 4.53212i 0.205435 + 0.149257i
\(923\) −15.6428 + 11.3651i −0.514888 + 0.374088i
\(924\) 2.76950 0.0911099
\(925\) −9.62951 −0.316616
\(926\) 16.7051 12.1369i 0.548963 0.398845i
\(927\) −1.36082 + 4.18816i −0.0446950 + 0.137557i
\(928\) −1.17791 3.62524i −0.0386668 0.119004i
\(929\) 31.9767 1.04912 0.524561 0.851373i \(-0.324230\pi\)
0.524561 + 0.851373i \(0.324230\pi\)
\(930\) −47.8889 11.2080i −1.57034 0.367525i
\(931\) 42.4167 1.39015
\(932\) −1.59525 4.90966i −0.0522540 0.160821i
\(933\) −3.98570 + 12.2667i −0.130486 + 0.401594i
\(934\) 2.67641 1.94452i 0.0875747 0.0636267i
\(935\) 9.61143 0.314327
\(936\) −18.8425 −0.615888
\(937\) 31.8893 23.1690i 1.04178 0.756897i 0.0711473 0.997466i \(-0.477334\pi\)
0.970632 + 0.240569i \(0.0773340\pi\)
\(938\) −4.70463 3.41811i −0.153612 0.111605i
\(939\) −43.1125 31.3231i −1.40692 1.02219i
\(940\) −3.99885 12.3072i −0.130428 0.401417i
\(941\) −44.9074 + 32.6271i −1.46394 + 1.06361i −0.481625 + 0.876377i \(0.659953\pi\)
−0.982315 + 0.187237i \(0.940047\pi\)
\(942\) −6.52287 20.0753i −0.212527 0.654090i
\(943\) 1.98606 6.11245i 0.0646749 0.199049i
\(944\) −8.96914 6.51646i −0.291921 0.212093i
\(945\) −8.40055 + 25.8542i −0.273270 + 0.841039i
\(946\) 2.60987 8.03236i 0.0848543 0.261155i
\(947\) 8.43755 + 6.13024i 0.274184 + 0.199206i 0.716377 0.697714i \(-0.245799\pi\)
−0.442193 + 0.896920i \(0.645799\pi\)
\(948\) 3.34381 10.2912i 0.108602 0.334243i
\(949\) −3.13698 9.65464i −0.101831 0.313403i
\(950\) −10.9254 + 7.93778i −0.354467 + 0.257535i
\(951\) −35.2299 108.427i −1.14241 3.51597i
\(952\) −1.33295 0.968446i −0.0432012 0.0313875i
\(953\) 9.39998 + 6.82949i 0.304495 + 0.221229i 0.729531 0.683948i \(-0.239738\pi\)
−0.425036 + 0.905177i \(0.639738\pi\)
\(954\) 22.1994 16.1288i 0.718733 0.522190i
\(955\) 42.2198 1.36620
\(956\) 6.37411 0.206153
\(957\) −13.8190 + 10.0401i −0.446705 + 0.324550i
\(958\) −2.89676 + 8.91531i −0.0935900 + 0.288040i
\(959\) −2.45483 7.55520i −0.0792707 0.243970i
\(960\) −8.83353 −0.285101
\(961\) 27.7803 + 13.7570i 0.896138 + 0.443775i
\(962\) 10.7919 0.347946
\(963\) −22.8636 70.3669i −0.736769 2.26754i
\(964\) −8.61397 + 26.5111i −0.277437 + 0.853864i
\(965\) −6.65239 + 4.83325i −0.214148 + 0.155588i
\(966\) −6.01484 −0.193524
\(967\) 20.5330 0.660297 0.330149 0.943929i \(-0.392901\pi\)
0.330149 + 0.943929i \(0.392901\pi\)
\(968\) −7.41955 + 5.39062i −0.238473 + 0.173261i
\(969\) 45.8036 + 33.2783i 1.47142 + 1.06905i
\(970\) −6.45827 4.69221i −0.207363 0.150658i
\(971\) 2.40953 + 7.41576i 0.0773254 + 0.237983i 0.982246 0.187597i \(-0.0600700\pi\)
−0.904921 + 0.425580i \(0.860070\pi\)
\(972\) 42.3407 30.7623i 1.35808 0.986702i
\(973\) 1.06204 + 3.26861i 0.0340473 + 0.104787i
\(974\) −2.36965 + 7.29304i −0.0759286 + 0.233684i
\(975\) 13.3379 + 9.69055i 0.427155 + 0.310346i
\(976\) −0.738852 + 2.27395i −0.0236501 + 0.0727874i
\(977\) −6.49806 + 19.9990i −0.207891 + 0.639824i 0.791691 + 0.610922i \(0.209201\pi\)
−0.999582 + 0.0289022i \(0.990799\pi\)
\(978\) 7.62611 + 5.54070i 0.243856 + 0.177172i
\(979\) −3.54195 + 10.9010i −0.113201 + 0.348397i
\(980\) −5.45200 16.7795i −0.174158 0.536002i
\(981\) −124.104 + 90.1665i −3.96232 + 2.87880i
\(982\) −4.88762 15.0425i −0.155970 0.480027i
\(983\) 23.0597 + 16.7538i 0.735489 + 0.534364i 0.891295 0.453424i \(-0.149798\pi\)
−0.155806 + 0.987788i \(0.549798\pi\)
\(984\) 5.86589 + 4.26182i 0.186998 + 0.135862i
\(985\) −48.6286 + 35.3307i −1.54943 + 1.12573i
\(986\) 10.1619 0.323621
\(987\) 9.94056 0.316412
\(988\) 12.2443 8.89599i 0.389542 0.283019i
\(989\) −5.66816 + 17.4448i −0.180237 + 0.554713i
\(990\) 8.88991 + 27.3603i 0.282540 + 0.869569i
\(991\) −0.0388727 −0.00123483 −0.000617417 1.00000i \(-0.500197\pi\)
−0.000617417 1.00000i \(0.500197\pi\)
\(992\) 5.42127 + 1.26880i 0.172125 + 0.0402845i
\(993\) −71.4662 −2.26791
\(994\) −1.56381 4.81290i −0.0496009 0.152656i
\(995\) −7.46878 + 22.9865i −0.236776 + 0.728722i
\(996\) −3.07180 + 2.23180i −0.0973338 + 0.0707172i
\(997\) 61.6176 1.95145 0.975725 0.219001i \(-0.0702798\pi\)
0.975725 + 0.219001i \(0.0702798\pi\)
\(998\) 14.4797 0.458348
\(999\) −61.0040 + 44.3220i −1.93008 + 1.40229i
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 62.2.d.b.35.1 8
3.2 odd 2 558.2.i.g.469.1 8
4.3 odd 2 496.2.n.d.97.2 8
31.8 even 5 inner 62.2.d.b.39.1 yes 8
31.15 odd 10 1922.2.a.l.1.4 4
31.16 even 5 1922.2.a.i.1.1 4
93.8 odd 10 558.2.i.g.163.1 8
124.39 odd 10 496.2.n.d.225.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
62.2.d.b.35.1 8 1.1 even 1 trivial
62.2.d.b.39.1 yes 8 31.8 even 5 inner
496.2.n.d.97.2 8 4.3 odd 2
496.2.n.d.225.2 8 124.39 odd 10
558.2.i.g.163.1 8 93.8 odd 10
558.2.i.g.469.1 8 3.2 odd 2
1922.2.a.i.1.1 4 31.16 even 5
1922.2.a.l.1.4 4 31.15 odd 10