Properties

Label 462.2.n.e.263.6
Level $462$
Weight $2$
Character 462.263
Analytic conductor $3.689$
Analytic rank $0$
Dimension $24$
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] = [462,2,Mod(65,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.65");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.n (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 263.6
Character \(\chi\) \(=\) 462.263
Dual form 462.2.n.e.65.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.125098 - 1.72753i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.72427 - 2.15021i) q^{5} +(-1.55863 + 0.755426i) q^{6} +(-2.62857 + 0.301041i) q^{7} +1.00000 q^{8} +(-2.96870 - 0.432220i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.125098 - 1.72753i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.72427 - 2.15021i) q^{5} +(-1.55863 + 0.755426i) q^{6} +(-2.62857 + 0.301041i) q^{7} +1.00000 q^{8} +(-2.96870 - 0.432220i) q^{9} +(-3.72427 - 2.15021i) q^{10} +(0.167821 - 3.31238i) q^{11} +(1.43353 + 0.972102i) q^{12} +2.22468i q^{13} +(1.57499 + 2.12589i) q^{14} +(-3.24864 - 6.70276i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.17622 - 3.76933i) q^{17} +(1.11004 + 2.78708i) q^{18} +(-1.35056 + 0.779747i) q^{19} +4.30042i q^{20} +(0.191229 + 4.57858i) q^{21} +(-2.95251 + 1.51085i) q^{22} +(-1.48946 + 0.859942i) q^{23} +(0.125098 - 1.72753i) q^{24} +(6.74679 - 11.6858i) q^{25} +(1.92663 - 1.11234i) q^{26} +(-1.11805 + 5.07444i) q^{27} +(1.05357 - 2.42693i) q^{28} +4.52500 q^{29} +(-4.18044 + 6.16479i) q^{30} +(-1.83135 + 3.17199i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.70123 - 0.704286i) q^{33} -4.35245 q^{34} +(-9.14220 + 6.77313i) q^{35} +(1.85866 - 2.35486i) q^{36} +(3.36669 + 5.83129i) q^{37} +(1.35056 + 0.779747i) q^{38} +(3.84320 + 0.278303i) q^{39} +(3.72427 - 2.15021i) q^{40} -10.0223 q^{41} +(3.86956 - 2.45490i) q^{42} -4.66108i q^{43} +(2.78469 + 1.80152i) q^{44} +(-11.9856 + 4.77362i) q^{45} +(1.48946 + 0.859942i) q^{46} +(3.24960 - 1.87616i) q^{47} +(-1.55863 + 0.755426i) q^{48} +(6.81875 - 1.58262i) q^{49} -13.4936 q^{50} +(-6.23938 - 4.23102i) q^{51} +(-1.92663 - 1.11234i) q^{52} +(-2.14220 - 1.23680i) q^{53} +(4.95362 - 1.56896i) q^{54} +(-6.49729 - 12.6970i) q^{55} +(-2.62857 + 0.301041i) q^{56} +(1.17808 + 2.43068i) q^{57} +(-2.26250 - 3.91876i) q^{58} +(-3.19636 - 1.84542i) q^{59} +(7.42908 + 0.537973i) q^{60} +(-4.02253 + 2.32241i) q^{61} +3.66270 q^{62} +(7.93355 + 0.242419i) q^{63} +1.00000 q^{64} +(4.78353 + 8.28532i) q^{65} +(2.24068 + 5.28955i) q^{66} +(-2.08595 + 3.61297i) q^{67} +(2.17622 + 3.76933i) q^{68} +(1.29925 + 2.68067i) q^{69} +(10.4368 + 4.53081i) q^{70} +7.07802i q^{71} +(-2.96870 - 0.432220i) q^{72} +(12.7024 + 7.33373i) q^{73} +(3.36669 - 5.83129i) q^{74} +(-19.3435 - 13.1171i) q^{75} -1.55949i q^{76} +(0.556035 + 8.75733i) q^{77} +(-1.68058 - 3.46746i) q^{78} +(8.48475 - 4.89868i) q^{79} +(-3.72427 - 2.15021i) q^{80} +(8.62637 + 2.56627i) q^{81} +(5.01114 + 8.67956i) q^{82} +17.6583 q^{83} +(-4.06078 - 2.12368i) q^{84} -18.7173i q^{85} +(-4.03661 + 2.33054i) q^{86} +(0.566068 - 7.81706i) q^{87} +(0.167821 - 3.31238i) q^{88} +(10.8244 - 6.24946i) q^{89} +(10.1269 + 7.99303i) q^{90} +(-0.669722 - 5.84773i) q^{91} -1.71988i q^{92} +(5.25060 + 3.56051i) q^{93} +(-3.24960 - 1.87616i) q^{94} +(-3.35323 + 5.80797i) q^{95} +(1.43353 + 0.972102i) q^{96} -0.541718 q^{97} +(-4.77996 - 5.11390i) q^{98} +(-1.92988 + 9.76092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.125098 1.72753i 0.0722253 0.997388i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 3.72427 2.15021i 1.66554 0.961602i 0.695548 0.718479i \(-0.255162\pi\)
0.969996 0.243123i \(-0.0781717\pi\)
\(6\) −1.55863 + 0.755426i −0.636309 + 0.308401i
\(7\) −2.62857 + 0.301041i −0.993506 + 0.113783i
\(8\) 1.00000 0.353553
\(9\) −2.96870 0.432220i −0.989567 0.144073i
\(10\) −3.72427 2.15021i −1.17772 0.679955i
\(11\) 0.167821 3.31238i 0.0505998 0.998719i
\(12\) 1.43353 + 0.972102i 0.413825 + 0.280622i
\(13\) 2.22468i 0.617016i 0.951222 + 0.308508i \(0.0998297\pi\)
−0.951222 + 0.308508i \(0.900170\pi\)
\(14\) 1.57499 + 2.12589i 0.420935 + 0.568167i
\(15\) −3.24864 6.70276i −0.838796 1.73065i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.17622 3.76933i 0.527812 0.914197i −0.471663 0.881779i \(-0.656346\pi\)
0.999474 0.0324176i \(-0.0103207\pi\)
\(18\) 1.11004 + 2.78708i 0.261638 + 0.656921i
\(19\) −1.35056 + 0.779747i −0.309840 + 0.178886i −0.646855 0.762613i \(-0.723916\pi\)
0.337015 + 0.941499i \(0.390583\pi\)
\(20\) 4.30042i 0.961602i
\(21\) 0.191229 + 4.57858i 0.0417295 + 0.999129i
\(22\) −2.95251 + 1.51085i −0.629478 + 0.322115i
\(23\) −1.48946 + 0.859942i −0.310575 + 0.179310i −0.647184 0.762334i \(-0.724053\pi\)
0.336609 + 0.941645i \(0.390720\pi\)
\(24\) 0.125098 1.72753i 0.0255355 0.352630i
\(25\) 6.74679 11.6858i 1.34936 2.33716i
\(26\) 1.92663 1.11234i 0.377844 0.218148i
\(27\) −1.11805 + 5.07444i −0.215169 + 0.976577i
\(28\) 1.05357 2.42693i 0.199107 0.458646i
\(29\) 4.52500 0.840271 0.420136 0.907461i \(-0.361982\pi\)
0.420136 + 0.907461i \(0.361982\pi\)
\(30\) −4.18044 + 6.16479i −0.763241 + 1.12553i
\(31\) −1.83135 + 3.17199i −0.328920 + 0.569706i −0.982298 0.187326i \(-0.940018\pi\)
0.653378 + 0.757032i \(0.273351\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −5.70123 0.704286i −0.992456 0.122600i
\(34\) −4.35245 −0.746438
\(35\) −9.14220 + 6.77313i −1.54531 + 1.14487i
\(36\) 1.85866 2.35486i 0.309777 0.392477i
\(37\) 3.36669 + 5.83129i 0.553481 + 0.958658i 0.998020 + 0.0628979i \(0.0200343\pi\)
−0.444539 + 0.895760i \(0.646632\pi\)
\(38\) 1.35056 + 0.779747i 0.219090 + 0.126492i
\(39\) 3.84320 + 0.278303i 0.615405 + 0.0445642i
\(40\) 3.72427 2.15021i 0.588859 0.339978i
\(41\) −10.0223 −1.56522 −0.782609 0.622513i \(-0.786112\pi\)
−0.782609 + 0.622513i \(0.786112\pi\)
\(42\) 3.86956 2.45490i 0.597085 0.378799i
\(43\) 4.66108i 0.710808i −0.934713 0.355404i \(-0.884343\pi\)
0.934713 0.355404i \(-0.115657\pi\)
\(44\) 2.78469 + 1.80152i 0.419808 + 0.271590i
\(45\) −11.9856 + 4.77362i −1.78671 + 0.711609i
\(46\) 1.48946 + 0.859942i 0.219609 + 0.126792i
\(47\) 3.24960 1.87616i 0.474002 0.273665i −0.243911 0.969798i \(-0.578431\pi\)
0.717914 + 0.696132i \(0.245097\pi\)
\(48\) −1.55863 + 0.755426i −0.224969 + 0.109036i
\(49\) 6.81875 1.58262i 0.974107 0.226088i
\(50\) −13.4936 −1.90828
\(51\) −6.23938 4.23102i −0.873688 0.592461i
\(52\) −1.92663 1.11234i −0.267176 0.154254i
\(53\) −2.14220 1.23680i −0.294254 0.169887i 0.345605 0.938380i \(-0.387674\pi\)
−0.639859 + 0.768493i \(0.721007\pi\)
\(54\) 4.95362 1.56896i 0.674102 0.213509i
\(55\) −6.49729 12.6970i −0.876094 1.71207i
\(56\) −2.62857 + 0.301041i −0.351257 + 0.0402283i
\(57\) 1.17808 + 2.43068i 0.156041 + 0.321951i
\(58\) −2.26250 3.91876i −0.297081 0.514559i
\(59\) −3.19636 1.84542i −0.416131 0.240253i 0.277290 0.960786i \(-0.410564\pi\)
−0.693420 + 0.720533i \(0.743897\pi\)
\(60\) 7.42908 + 0.537973i 0.959091 + 0.0694520i
\(61\) −4.02253 + 2.32241i −0.515033 + 0.297354i −0.734900 0.678176i \(-0.762771\pi\)
0.219867 + 0.975530i \(0.429438\pi\)
\(62\) 3.66270 0.465163
\(63\) 7.93355 + 0.242419i 0.999533 + 0.0305419i
\(64\) 1.00000 0.125000
\(65\) 4.78353 + 8.28532i 0.593324 + 1.02767i
\(66\) 2.24068 + 5.28955i 0.275809 + 0.651099i
\(67\) −2.08595 + 3.61297i −0.254839 + 0.441394i −0.964852 0.262795i \(-0.915356\pi\)
0.710013 + 0.704189i \(0.248689\pi\)
\(68\) 2.17622 + 3.76933i 0.263906 + 0.457098i
\(69\) 1.29925 + 2.68067i 0.156411 + 0.322714i
\(70\) 10.4368 + 4.53081i 1.24744 + 0.541535i
\(71\) 7.07802i 0.840006i 0.907523 + 0.420003i \(0.137971\pi\)
−0.907523 + 0.420003i \(0.862029\pi\)
\(72\) −2.96870 0.432220i −0.349865 0.0509376i
\(73\) 12.7024 + 7.33373i 1.48670 + 0.858348i 0.999885 0.0151552i \(-0.00482423\pi\)
0.486818 + 0.873504i \(0.338158\pi\)
\(74\) 3.36669 5.83129i 0.391370 0.677873i
\(75\) −19.3435 13.1171i −2.23359 1.51464i
\(76\) 1.55949i 0.178886i
\(77\) 0.556035 + 8.75733i 0.0633660 + 0.997990i
\(78\) −1.68058 3.46746i −0.190289 0.392613i
\(79\) 8.48475 4.89868i 0.954609 0.551144i 0.0600997 0.998192i \(-0.480858\pi\)
0.894510 + 0.447048i \(0.147525\pi\)
\(80\) −3.72427 2.15021i −0.416386 0.240401i
\(81\) 8.62637 + 2.56627i 0.958486 + 0.285141i
\(82\) 5.01114 + 8.67956i 0.553388 + 0.958497i
\(83\) 17.6583 1.93825 0.969126 0.246564i \(-0.0793017\pi\)
0.969126 + 0.246564i \(0.0793017\pi\)
\(84\) −4.06078 2.12368i −0.443068 0.231713i
\(85\) 18.7173i 2.03018i
\(86\) −4.03661 + 2.33054i −0.435279 + 0.251309i
\(87\) 0.566068 7.81706i 0.0606889 0.838077i
\(88\) 0.167821 3.31238i 0.0178897 0.353100i
\(89\) 10.8244 6.24946i 1.14738 0.662441i 0.199134 0.979972i \(-0.436187\pi\)
0.948248 + 0.317531i \(0.102854\pi\)
\(90\) 10.1269 + 7.99303i 1.06747 + 0.842539i
\(91\) −0.669722 5.84773i −0.0702059 0.613009i
\(92\) 1.71988i 0.179310i
\(93\) 5.25060 + 3.56051i 0.544462 + 0.369208i
\(94\) −3.24960 1.87616i −0.335170 0.193511i
\(95\) −3.35323 + 5.80797i −0.344035 + 0.595885i
\(96\) 1.43353 + 0.972102i 0.146309 + 0.0992147i
\(97\) −0.541718 −0.0550031 −0.0275016 0.999622i \(-0.508755\pi\)
−0.0275016 + 0.999622i \(0.508755\pi\)
\(98\) −4.77996 5.11390i −0.482849 0.516582i
\(99\) −1.92988 + 9.76092i −0.193961 + 0.981009i
\(100\) 6.74679 + 11.6858i 0.674679 + 1.16858i
\(101\) 3.92520 6.79864i 0.390572 0.676490i −0.601953 0.798531i \(-0.705611\pi\)
0.992525 + 0.122041i \(0.0389440\pi\)
\(102\) −0.544482 + 7.51897i −0.0539118 + 0.744489i
\(103\) 4.84871 + 8.39821i 0.477758 + 0.827500i 0.999675 0.0254957i \(-0.00811641\pi\)
−0.521917 + 0.852996i \(0.674783\pi\)
\(104\) 2.22468i 0.218148i
\(105\) 10.5571 + 16.6407i 1.03027 + 1.62397i
\(106\) 2.47360i 0.240257i
\(107\) −1.75893 3.04655i −0.170042 0.294521i 0.768392 0.639979i \(-0.221057\pi\)
−0.938434 + 0.345458i \(0.887724\pi\)
\(108\) −3.83557 3.50548i −0.369078 0.337315i
\(109\) 2.06323 + 1.19121i 0.197622 + 0.114097i 0.595546 0.803321i \(-0.296936\pi\)
−0.397924 + 0.917418i \(0.630269\pi\)
\(110\) −7.74731 + 11.9753i −0.738677 + 1.14180i
\(111\) 10.4949 5.08657i 0.996129 0.482796i
\(112\) 1.57499 + 2.12589i 0.148823 + 0.200877i
\(113\) 10.4210i 0.980328i −0.871630 0.490164i \(-0.836937\pi\)
0.871630 0.490164i \(-0.163063\pi\)
\(114\) 1.51599 2.23559i 0.141985 0.209382i
\(115\) −3.69811 + 6.40531i −0.344850 + 0.597299i
\(116\) −2.26250 + 3.91876i −0.210068 + 0.363848i
\(117\) 0.961553 6.60442i 0.0888956 0.610579i
\(118\) 3.69084i 0.339769i
\(119\) −4.58563 + 10.5631i −0.420364 + 0.968316i
\(120\) −3.24864 6.70276i −0.296559 0.611876i
\(121\) −10.9437 1.11177i −0.994879 0.101070i
\(122\) 4.02253 + 2.32241i 0.364183 + 0.210261i
\(123\) −1.25377 + 17.3138i −0.113048 + 1.56113i
\(124\) −1.83135 3.17199i −0.164460 0.284853i
\(125\) 36.5259i 3.26697i
\(126\) −3.75683 6.99187i −0.334685 0.622885i
\(127\) 2.29923i 0.204024i 0.994783 + 0.102012i \(0.0325280\pi\)
−0.994783 + 0.102012i \(0.967472\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −8.05214 0.583091i −0.708951 0.0513383i
\(130\) 4.78353 8.28532i 0.419543 0.726671i
\(131\) −3.88858 6.73522i −0.339747 0.588459i 0.644638 0.764488i \(-0.277008\pi\)
−0.984385 + 0.176029i \(0.943675\pi\)
\(132\) 3.46054 4.58526i 0.301202 0.399096i
\(133\) 3.31531 2.45619i 0.287473 0.212979i
\(134\) 4.17189 0.360397
\(135\) 6.74718 + 21.3026i 0.580705 + 1.83344i
\(136\) 2.17622 3.76933i 0.186610 0.323217i
\(137\) 8.00701 + 4.62285i 0.684085 + 0.394957i 0.801392 0.598139i \(-0.204093\pi\)
−0.117307 + 0.993096i \(0.537426\pi\)
\(138\) 1.67190 2.46551i 0.142322 0.209878i
\(139\) 17.9867i 1.52561i −0.646626 0.762807i \(-0.723821\pi\)
0.646626 0.762807i \(-0.276179\pi\)
\(140\) −1.29460 11.3039i −0.109414 0.955357i
\(141\) −2.83459 5.84847i −0.238716 0.492530i
\(142\) 6.12975 3.53901i 0.514397 0.296987i
\(143\) 7.36899 + 0.373348i 0.616226 + 0.0312209i
\(144\) 1.11004 + 2.78708i 0.0925031 + 0.232257i
\(145\) 16.8523 9.72969i 1.39951 0.808007i
\(146\) 14.6675i 1.21389i
\(147\) −1.88100 11.9776i −0.155142 0.987892i
\(148\) −6.73339 −0.553481
\(149\) 2.47440 + 4.28578i 0.202711 + 0.351105i 0.949401 0.314067i \(-0.101692\pi\)
−0.746690 + 0.665172i \(0.768358\pi\)
\(150\) −1.68802 + 23.3105i −0.137826 + 1.90330i
\(151\) 6.71375 + 3.87618i 0.546357 + 0.315439i 0.747651 0.664091i \(-0.231181\pi\)
−0.201294 + 0.979531i \(0.564515\pi\)
\(152\) −1.35056 + 0.779747i −0.109545 + 0.0632458i
\(153\) −8.08974 + 10.2494i −0.654016 + 0.828615i
\(154\) 7.30605 4.86020i 0.588739 0.391646i
\(155\) 15.7511i 1.26516i
\(156\) −2.16262 + 3.18916i −0.173148 + 0.255337i
\(157\) −7.06587 + 12.2385i −0.563918 + 0.976735i 0.433231 + 0.901283i \(0.357373\pi\)
−0.997149 + 0.0754521i \(0.975960\pi\)
\(158\) −8.48475 4.89868i −0.675011 0.389718i
\(159\) −2.40459 + 3.54598i −0.190696 + 0.281215i
\(160\) 4.30042i 0.339978i
\(161\) 3.65628 2.70881i 0.288155 0.213484i
\(162\) −2.09073 8.75379i −0.164264 0.687763i
\(163\) 8.63677 + 14.9593i 0.676484 + 1.17170i 0.976033 + 0.217623i \(0.0698304\pi\)
−0.299549 + 0.954081i \(0.596836\pi\)
\(164\) 5.01114 8.67956i 0.391305 0.677759i
\(165\) −22.7473 + 9.63587i −1.77087 + 0.750151i
\(166\) −8.82916 15.2926i −0.685276 1.18693i
\(167\) −14.3557 −1.11088 −0.555440 0.831556i \(-0.687450\pi\)
−0.555440 + 0.831556i \(0.687450\pi\)
\(168\) 0.191229 + 4.57858i 0.0147536 + 0.353245i
\(169\) 8.05078 0.619291
\(170\) −16.2097 + 9.35866i −1.24323 + 0.717777i
\(171\) 4.34643 1.73109i 0.332380 0.132380i
\(172\) 4.03661 + 2.33054i 0.307789 + 0.177702i
\(173\) 8.69404 + 15.0585i 0.660996 + 1.14488i 0.980354 + 0.197244i \(0.0631993\pi\)
−0.319358 + 0.947634i \(0.603467\pi\)
\(174\) −7.05281 + 3.41830i −0.534672 + 0.259141i
\(175\) −14.2165 + 32.7479i −1.07467 + 2.47551i
\(176\) −2.95251 + 1.51085i −0.222554 + 0.113885i
\(177\) −3.58787 + 5.29094i −0.269681 + 0.397691i
\(178\) −10.8244 6.24946i −0.811321 0.468417i
\(179\) −12.6301 7.29196i −0.944014 0.545027i −0.0527980 0.998605i \(-0.516814\pi\)
−0.891216 + 0.453578i \(0.850147\pi\)
\(180\) 1.85873 12.7666i 0.138541 0.951570i
\(181\) −23.8500 −1.77275 −0.886377 0.462964i \(-0.846786\pi\)
−0.886377 + 0.462964i \(0.846786\pi\)
\(182\) −4.72943 + 3.50386i −0.350568 + 0.259724i
\(183\) 3.50882 + 7.23957i 0.259379 + 0.535164i
\(184\) −1.48946 + 0.859942i −0.109805 + 0.0633958i
\(185\) 25.0770 + 14.4782i 1.84369 + 1.06446i
\(186\) 0.458196 6.32741i 0.0335965 0.463948i
\(187\) −12.1202 7.84104i −0.886318 0.573394i
\(188\) 3.75231i 0.273665i
\(189\) 1.41126 13.6751i 0.102654 0.994717i
\(190\) 6.70647 0.486538
\(191\) 1.01941 0.588558i 0.0737620 0.0425865i −0.462665 0.886533i \(-0.653107\pi\)
0.536427 + 0.843946i \(0.319774\pi\)
\(192\) 0.125098 1.72753i 0.00902817 0.124674i
\(193\) −1.67930 0.969543i −0.120879 0.0697893i 0.438342 0.898808i \(-0.355566\pi\)
−0.559220 + 0.829019i \(0.688899\pi\)
\(194\) 0.270859 + 0.469142i 0.0194465 + 0.0336824i
\(195\) 14.9115 7.22720i 1.06784 0.517551i
\(196\) −2.03879 + 6.69652i −0.145628 + 0.478323i
\(197\) 1.04430 0.0744031 0.0372015 0.999308i \(-0.488156\pi\)
0.0372015 + 0.999308i \(0.488156\pi\)
\(198\) 9.41815 3.20913i 0.669319 0.228063i
\(199\) 12.1261 21.0030i 0.859596 1.48886i −0.0127192 0.999919i \(-0.504049\pi\)
0.872315 0.488944i \(-0.162618\pi\)
\(200\) 6.74679 11.6858i 0.477070 0.826309i
\(201\) 5.98055 + 4.05551i 0.421836 + 0.286053i
\(202\) −7.85039 −0.552352
\(203\) −11.8943 + 1.36221i −0.834814 + 0.0956085i
\(204\) 6.78386 3.28795i 0.474965 0.230203i
\(205\) −37.3257 + 21.5500i −2.60694 + 1.50512i
\(206\) 4.84871 8.39821i 0.337826 0.585131i
\(207\) 4.79346 1.90914i 0.333168 0.132694i
\(208\) 1.92663 1.11234i 0.133588 0.0771270i
\(209\) 2.35616 + 4.60442i 0.162979 + 0.318495i
\(210\) 9.13272 17.4631i 0.630218 1.20507i
\(211\) 19.8659i 1.36762i 0.729658 + 0.683812i \(0.239679\pi\)
−0.729658 + 0.683812i \(0.760321\pi\)
\(212\) 2.14220 1.23680i 0.147127 0.0849437i
\(213\) 12.2275 + 0.885446i 0.837813 + 0.0606697i
\(214\) −1.75893 + 3.04655i −0.120238 + 0.208258i
\(215\) −10.0223 17.3591i −0.683514 1.18388i
\(216\) −1.11805 + 5.07444i −0.0760737 + 0.345272i
\(217\) 3.85893 8.88910i 0.261961 0.603432i
\(218\) 2.38242i 0.161358i
\(219\) 14.2583 21.0263i 0.963484 1.42083i
\(220\) 14.2446 + 0.721698i 0.960370 + 0.0486569i
\(221\) 8.38557 + 4.84141i 0.564074 + 0.325668i
\(222\) −9.65254 6.54554i −0.647836 0.439308i
\(223\) −17.1150 −1.14611 −0.573053 0.819518i \(-0.694241\pi\)
−0.573053 + 0.819518i \(0.694241\pi\)
\(224\) 1.05357 2.42693i 0.0703949 0.162156i
\(225\) −25.0800 + 31.7755i −1.67200 + 2.11837i
\(226\) −9.02487 + 5.21051i −0.600326 + 0.346598i
\(227\) −9.55949 + 16.5575i −0.634486 + 1.09896i 0.352138 + 0.935948i \(0.385455\pi\)
−0.986624 + 0.163013i \(0.947879\pi\)
\(228\) −2.69407 0.195089i −0.178419 0.0129201i
\(229\) 6.76018 + 11.7090i 0.446725 + 0.773751i 0.998171 0.0604599i \(-0.0192567\pi\)
−0.551445 + 0.834211i \(0.685923\pi\)
\(230\) 7.39622 0.487692
\(231\) 15.1981 + 0.134959i 0.999961 + 0.00887966i
\(232\) 4.52500 0.297081
\(233\) 3.87397 + 6.70992i 0.253792 + 0.439581i 0.964567 0.263839i \(-0.0849887\pi\)
−0.710774 + 0.703420i \(0.751655\pi\)
\(234\) −6.20037 + 2.46948i −0.405331 + 0.161435i
\(235\) 8.06825 13.9746i 0.526314 0.911603i
\(236\) 3.19636 1.84542i 0.208065 0.120127i
\(237\) −7.40117 15.2705i −0.480758 0.991923i
\(238\) 11.4407 1.31027i 0.741591 0.0849320i
\(239\) 11.9552 0.773319 0.386659 0.922223i \(-0.373629\pi\)
0.386659 + 0.922223i \(0.373629\pi\)
\(240\) −4.18044 + 6.16479i −0.269846 + 0.397935i
\(241\) −24.4654 14.1251i −1.57595 0.909876i −0.995416 0.0956417i \(-0.969510\pi\)
−0.580536 0.814235i \(-0.697157\pi\)
\(242\) 4.50902 + 10.0334i 0.289851 + 0.644970i
\(243\) 5.51243 14.5813i 0.353623 0.935388i
\(244\) 4.64482i 0.297354i
\(245\) 21.9919 20.5558i 1.40501 1.31326i
\(246\) 15.6211 7.57109i 0.995962 0.482715i
\(247\) −1.73469 3.00457i −0.110376 0.191176i
\(248\) −1.83135 + 3.17199i −0.116291 + 0.201421i
\(249\) 2.20902 30.5052i 0.139991 1.93319i
\(250\) −31.6323 + 18.2629i −2.00061 + 1.15505i
\(251\) 1.79928i 0.113569i 0.998386 + 0.0567847i \(0.0180849\pi\)
−0.998386 + 0.0567847i \(0.981915\pi\)
\(252\) −4.17672 + 6.74945i −0.263108 + 0.425175i
\(253\) 2.59849 + 5.07798i 0.163366 + 0.319250i
\(254\) 1.99119 1.14962i 0.124939 0.0721333i
\(255\) −32.3347 2.34150i −2.02488 0.146630i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.30536 + 1.90835i −0.206183 + 0.119040i −0.599536 0.800348i \(-0.704648\pi\)
0.393353 + 0.919387i \(0.371315\pi\)
\(258\) 3.52110 + 7.26490i 0.219214 + 0.452293i
\(259\) −10.6050 14.3144i −0.658966 0.889455i
\(260\) −9.56706 −0.593324
\(261\) −13.4334 1.95580i −0.831505 0.121061i
\(262\) −3.88858 + 6.73522i −0.240237 + 0.416103i
\(263\) −7.81378 + 13.5339i −0.481818 + 0.834533i −0.999782 0.0208689i \(-0.993357\pi\)
0.517964 + 0.855402i \(0.326690\pi\)
\(264\) −5.70123 0.704286i −0.350886 0.0433458i
\(265\) −10.6375 −0.653456
\(266\) −3.78478 1.64304i −0.232060 0.100741i
\(267\) −9.44200 19.4812i −0.577841 1.19223i
\(268\) −2.08595 3.61297i −0.127420 0.220697i
\(269\) −10.1509 5.86060i −0.618909 0.357327i 0.157535 0.987513i \(-0.449645\pi\)
−0.776444 + 0.630186i \(0.782979\pi\)
\(270\) 15.0750 16.4945i 0.917437 1.00383i
\(271\) 9.87548 5.70161i 0.599893 0.346348i −0.169107 0.985598i \(-0.554088\pi\)
0.768999 + 0.639249i \(0.220755\pi\)
\(272\) −4.35245 −0.263906
\(273\) −10.1859 + 0.425423i −0.616479 + 0.0257478i
\(274\) 9.24570i 0.558553i
\(275\) −37.5754 24.3090i −2.26588 1.46589i
\(276\) −2.97115 0.215154i −0.178842 0.0129508i
\(277\) 19.9310 + 11.5072i 1.19754 + 0.691398i 0.960005 0.279982i \(-0.0903284\pi\)
0.237531 + 0.971380i \(0.423662\pi\)
\(278\) −15.5770 + 8.99336i −0.934244 + 0.539386i
\(279\) 6.80772 8.62514i 0.407568 0.516374i
\(280\) −9.14220 + 6.77313i −0.546351 + 0.404772i
\(281\) −10.8023 −0.644409 −0.322205 0.946670i \(-0.604424\pi\)
−0.322205 + 0.946670i \(0.604424\pi\)
\(282\) −3.64763 + 5.37906i −0.217213 + 0.320319i
\(283\) 13.2070 + 7.62507i 0.785075 + 0.453263i 0.838226 0.545323i \(-0.183593\pi\)
−0.0531507 + 0.998587i \(0.516926\pi\)
\(284\) −6.12975 3.53901i −0.363733 0.210002i
\(285\) 9.61395 + 6.51937i 0.569481 + 0.386174i
\(286\) −3.36117 6.56841i −0.198750 0.388398i
\(287\) 26.3443 3.01712i 1.55505 0.178095i
\(288\) 1.85866 2.35486i 0.109523 0.138761i
\(289\) −0.971897 1.68337i −0.0571704 0.0990220i
\(290\) −16.8523 9.72969i −0.989602 0.571347i
\(291\) −0.0677678 + 0.935833i −0.00397262 + 0.0548595i
\(292\) −12.7024 + 7.33373i −0.743351 + 0.429174i
\(293\) −10.6037 −0.619474 −0.309737 0.950822i \(-0.600241\pi\)
−0.309737 + 0.950822i \(0.600241\pi\)
\(294\) −9.43237 + 7.61777i −0.550107 + 0.444278i
\(295\) −15.8721 −0.924112
\(296\) 3.36669 + 5.83129i 0.195685 + 0.338937i
\(297\) 16.6208 + 4.55500i 0.964438 + 0.264308i
\(298\) 2.47440 4.28578i 0.143338 0.248269i
\(299\) −1.91310 3.31359i −0.110637 0.191630i
\(300\) 21.0315 10.1934i 1.21425 0.588516i
\(301\) 1.40318 + 12.2520i 0.0808778 + 0.706192i
\(302\) 7.75237i 0.446099i
\(303\) −11.2538 7.63138i −0.646514 0.438411i
\(304\) 1.35056 + 0.779747i 0.0774600 + 0.0447215i
\(305\) −9.98733 + 17.2986i −0.571873 + 0.990513i
\(306\) 12.9211 + 1.88122i 0.738651 + 0.107542i
\(307\) 6.44519i 0.367846i 0.982941 + 0.183923i \(0.0588797\pi\)
−0.982941 + 0.183923i \(0.941120\pi\)
\(308\) −7.86209 3.89712i −0.447984 0.222059i
\(309\) 15.1147 7.32568i 0.859845 0.416743i
\(310\) 13.6409 7.87556i 0.774749 0.447302i
\(311\) −8.01305 4.62634i −0.454378 0.262335i 0.255299 0.966862i \(-0.417826\pi\)
−0.709678 + 0.704527i \(0.751159\pi\)
\(312\) 3.84320 + 0.278303i 0.217578 + 0.0157558i
\(313\) −0.408129 0.706900i −0.0230688 0.0399563i 0.854261 0.519845i \(-0.174010\pi\)
−0.877329 + 0.479889i \(0.840677\pi\)
\(314\) 14.1317 0.797501
\(315\) 30.0679 16.1559i 1.69414 0.910285i
\(316\) 9.79735i 0.551144i
\(317\) 7.19272 4.15272i 0.403983 0.233240i −0.284218 0.958760i \(-0.591734\pi\)
0.688201 + 0.725520i \(0.258401\pi\)
\(318\) 4.27321 + 0.309442i 0.239630 + 0.0173526i
\(319\) 0.759388 14.9885i 0.0425175 0.839195i
\(320\) 3.72427 2.15021i 0.208193 0.120200i
\(321\) −5.48304 + 2.65748i −0.306033 + 0.148326i
\(322\) −4.17404 1.81203i −0.232610 0.100980i
\(323\) 6.78761i 0.377673i
\(324\) −6.53564 + 6.18752i −0.363091 + 0.343751i
\(325\) 25.9972 + 15.0095i 1.44206 + 0.832575i
\(326\) 8.63677 14.9593i 0.478346 0.828520i
\(327\) 2.31595 3.41528i 0.128072 0.188865i
\(328\) −10.0223 −0.553388
\(329\) −7.97699 + 5.90987i −0.439785 + 0.325821i
\(330\) 19.7185 + 14.8818i 1.08547 + 0.819215i
\(331\) −11.4714 19.8690i −0.630523 1.09210i −0.987445 0.157963i \(-0.949507\pi\)
0.356922 0.934134i \(-0.383826\pi\)
\(332\) −8.82916 + 15.2926i −0.484563 + 0.839288i
\(333\) −7.47431 18.7665i −0.409590 1.02840i
\(334\) 7.17787 + 12.4324i 0.392756 + 0.680273i
\(335\) 17.9409i 0.980215i
\(336\) 3.86956 2.45490i 0.211102 0.133926i
\(337\) 33.7202i 1.83686i 0.395587 + 0.918429i \(0.370541\pi\)
−0.395587 + 0.918429i \(0.629459\pi\)
\(338\) −4.02539 6.97218i −0.218952 0.379237i
\(339\) −18.0026 1.30365i −0.977767 0.0708045i
\(340\) 16.2097 + 9.35866i 0.879093 + 0.507545i
\(341\) 10.1995 + 6.59844i 0.552333 + 0.357326i
\(342\) −3.67239 2.89857i −0.198580 0.156737i
\(343\) −17.4471 + 6.21274i −0.942056 + 0.335456i
\(344\) 4.66108i 0.251309i
\(345\) 10.6027 + 7.18988i 0.570832 + 0.387090i
\(346\) 8.69404 15.0585i 0.467395 0.809551i
\(347\) −3.83938 + 6.65000i −0.206109 + 0.356991i −0.950485 0.310769i \(-0.899413\pi\)
0.744377 + 0.667760i \(0.232747\pi\)
\(348\) 6.48674 + 4.39876i 0.347726 + 0.235798i
\(349\) 3.88135i 0.207764i 0.994590 + 0.103882i \(0.0331265\pi\)
−0.994590 + 0.103882i \(0.966874\pi\)
\(350\) 35.4688 4.06212i 1.89589 0.217130i
\(351\) −11.2890 2.48731i −0.602564 0.132763i
\(352\) 2.78469 + 1.80152i 0.148425 + 0.0960216i
\(353\) −2.97893 1.71988i −0.158552 0.0915402i 0.418625 0.908159i \(-0.362512\pi\)
−0.577177 + 0.816619i \(0.695846\pi\)
\(354\) 6.37602 + 0.461716i 0.338882 + 0.0245399i
\(355\) 15.2192 + 26.3605i 0.807752 + 1.39907i
\(356\) 12.4989i 0.662441i
\(357\) 17.6743 + 9.24322i 0.935426 + 0.489203i
\(358\) 14.5839i 0.770785i
\(359\) 11.0163 + 19.0808i 0.581419 + 1.00705i 0.995312 + 0.0967211i \(0.0308355\pi\)
−0.413893 + 0.910326i \(0.635831\pi\)
\(360\) −11.9856 + 4.77362i −0.631697 + 0.251592i
\(361\) −8.28399 + 14.3483i −0.435999 + 0.755173i
\(362\) 11.9250 + 20.6547i 0.626763 + 1.08559i
\(363\) −3.28964 + 18.7664i −0.172661 + 0.984981i
\(364\) 5.39915 + 2.34387i 0.282992 + 0.122852i
\(365\) 63.0762 3.30156
\(366\) 4.51524 6.65851i 0.236015 0.348046i
\(367\) 5.41730 9.38303i 0.282781 0.489790i −0.689288 0.724487i \(-0.742077\pi\)
0.972069 + 0.234697i \(0.0754099\pi\)
\(368\) 1.48946 + 0.859942i 0.0776437 + 0.0448276i
\(369\) 29.7532 + 4.33184i 1.54889 + 0.225506i
\(370\) 28.9564i 1.50537i
\(371\) 6.00324 + 2.60612i 0.311673 + 0.135303i
\(372\) −5.70879 + 2.76690i −0.295987 + 0.143457i
\(373\) −5.25214 + 3.03232i −0.271945 + 0.157008i −0.629771 0.776781i \(-0.716851\pi\)
0.357826 + 0.933788i \(0.383518\pi\)
\(374\) −0.730430 + 14.4169i −0.0377696 + 0.745482i
\(375\) −63.0995 4.56931i −3.25844 0.235958i
\(376\) 3.24960 1.87616i 0.167585 0.0967553i
\(377\) 10.0667i 0.518461i
\(378\) −12.5486 + 5.61537i −0.645431 + 0.288823i
\(379\) −1.95715 −0.100532 −0.0502659 0.998736i \(-0.516007\pi\)
−0.0502659 + 0.998736i \(0.516007\pi\)
\(380\) −3.35323 5.80797i −0.172017 0.297943i
\(381\) 3.97198 + 0.287629i 0.203491 + 0.0147357i
\(382\) −1.01941 0.588558i −0.0521576 0.0301132i
\(383\) 9.20867 5.31663i 0.470541 0.271667i −0.245925 0.969289i \(-0.579092\pi\)
0.716466 + 0.697622i \(0.245758\pi\)
\(384\) −1.55863 + 0.755426i −0.0795386 + 0.0385502i
\(385\) 20.9009 + 31.4191i 1.06521 + 1.60126i
\(386\) 1.93909i 0.0986969i
\(387\) −2.01461 + 13.8373i −0.102409 + 0.703392i
\(388\) 0.270859 0.469142i 0.0137508 0.0238171i
\(389\) −17.3287 10.0047i −0.878601 0.507261i −0.00840444 0.999965i \(-0.502675\pi\)
−0.870197 + 0.492704i \(0.836009\pi\)
\(390\) −13.7147 9.30016i −0.694471 0.470932i
\(391\) 7.48571i 0.378568i
\(392\) 6.81875 1.58262i 0.344399 0.0799342i
\(393\) −12.1217 + 5.87507i −0.611460 + 0.296358i
\(394\) −0.522149 0.904388i −0.0263055 0.0455624i
\(395\) 21.0663 36.4880i 1.05996 1.83591i
\(396\) −7.48826 6.55179i −0.376299 0.329240i
\(397\) 8.09039 + 14.0130i 0.406045 + 0.703291i 0.994443 0.105281i \(-0.0335742\pi\)
−0.588397 + 0.808572i \(0.700241\pi\)
\(398\) −24.2522 −1.21565
\(399\) −3.82840 6.03455i −0.191660 0.302105i
\(400\) −13.4936 −0.674679
\(401\) −20.3865 + 11.7702i −1.01805 + 0.587774i −0.913540 0.406750i \(-0.866662\pi\)
−0.104514 + 0.994523i \(0.533329\pi\)
\(402\) 0.521895 7.20706i 0.0260298 0.359456i
\(403\) −7.05667 4.07417i −0.351518 0.202949i
\(404\) 3.92520 + 6.79864i 0.195286 + 0.338245i
\(405\) 37.6449 8.99103i 1.87059 0.446768i
\(406\) 7.12685 + 9.61964i 0.353699 + 0.477415i
\(407\) 19.8804 10.1731i 0.985436 0.504264i
\(408\) −6.23938 4.23102i −0.308895 0.209467i
\(409\) −29.6972 17.1457i −1.46843 0.847800i −0.469059 0.883167i \(-0.655407\pi\)
−0.999374 + 0.0353664i \(0.988740\pi\)
\(410\) 37.3257 + 21.5500i 1.84338 + 1.06428i
\(411\) 8.98776 13.2540i 0.443334 0.653773i
\(412\) −9.69742 −0.477758
\(413\) 8.95740 + 3.88857i 0.440765 + 0.191344i
\(414\) −4.05009 3.19669i −0.199051 0.157109i
\(415\) 65.7643 37.9691i 3.22824 1.86383i
\(416\) −1.92663 1.11234i −0.0944609 0.0545370i
\(417\) −31.0726 2.25010i −1.52163 0.110188i
\(418\) 2.80947 4.34271i 0.137415 0.212409i
\(419\) 23.8983i 1.16751i 0.811930 + 0.583755i \(0.198417\pi\)
−0.811930 + 0.583755i \(0.801583\pi\)
\(420\) −19.6898 + 0.822363i −0.960765 + 0.0401272i
\(421\) 21.3778 1.04189 0.520944 0.853591i \(-0.325580\pi\)
0.520944 + 0.853591i \(0.325580\pi\)
\(422\) 17.2044 9.93294i 0.837495 0.483528i
\(423\) −10.4580 + 4.16520i −0.508485 + 0.202519i
\(424\) −2.14220 1.23680i −0.104034 0.0600643i
\(425\) −29.3650 50.8617i −1.42441 2.46716i
\(426\) −5.34692 11.0320i −0.259059 0.534503i
\(427\) 9.87437 7.31557i 0.477854 0.354025i
\(428\) 3.51786 0.170042
\(429\) 1.56681 12.6834i 0.0756465 0.612361i
\(430\) −10.0223 + 17.3591i −0.483318 + 0.837131i
\(431\) −1.14236 + 1.97863i −0.0550256 + 0.0953071i −0.892226 0.451589i \(-0.850857\pi\)
0.837201 + 0.546896i \(0.184191\pi\)
\(432\) 4.95362 1.56896i 0.238331 0.0754867i
\(433\) −10.0236 −0.481702 −0.240851 0.970562i \(-0.577427\pi\)
−0.240851 + 0.970562i \(0.577427\pi\)
\(434\) −9.62765 + 1.10262i −0.462142 + 0.0529276i
\(435\) −14.7001 30.3300i −0.704816 1.45421i
\(436\) −2.06323 + 1.19121i −0.0988110 + 0.0570486i
\(437\) 1.34107 2.32281i 0.0641523 0.111115i
\(438\) −25.3384 1.83487i −1.21072 0.0876735i
\(439\) −5.95435 + 3.43774i −0.284185 + 0.164075i −0.635317 0.772252i \(-0.719130\pi\)
0.351131 + 0.936326i \(0.385797\pi\)
\(440\) −6.49729 12.6970i −0.309746 0.605307i
\(441\) −20.9269 + 1.75111i −0.996517 + 0.0833863i
\(442\) 9.68282i 0.460565i
\(443\) 18.4525 10.6536i 0.876706 0.506166i 0.00713504 0.999975i \(-0.497729\pi\)
0.869571 + 0.493808i \(0.164395\pi\)
\(444\) −0.842333 + 11.6321i −0.0399754 + 0.552036i
\(445\) 26.8753 46.5493i 1.27401 2.20665i
\(446\) 8.55750 + 14.8220i 0.405210 + 0.701844i
\(447\) 7.71335 3.73845i 0.364829 0.176823i
\(448\) −2.62857 + 0.301041i −0.124188 + 0.0142229i
\(449\) 11.3648i 0.536340i 0.963372 + 0.268170i \(0.0864189\pi\)
−0.963372 + 0.268170i \(0.913581\pi\)
\(450\) 40.0584 + 5.83219i 1.88837 + 0.274932i
\(451\) −1.68195 + 33.1976i −0.0791997 + 1.56321i
\(452\) 9.02487 + 5.21051i 0.424494 + 0.245082i
\(453\) 7.53609 11.1133i 0.354076 0.522148i
\(454\) 19.1190 0.897298
\(455\) −15.0681 20.3385i −0.706402 0.953483i
\(456\) 1.17808 + 2.43068i 0.0551687 + 0.113827i
\(457\) 0.879305 0.507667i 0.0411321 0.0237476i −0.479293 0.877655i \(-0.659107\pi\)
0.520425 + 0.853907i \(0.325774\pi\)
\(458\) 6.76018 11.7090i 0.315883 0.547125i
\(459\) 16.6941 + 15.2574i 0.779215 + 0.712155i
\(460\) −3.69811 6.40531i −0.172425 0.298649i
\(461\) −29.8887 −1.39206 −0.696029 0.718014i \(-0.745051\pi\)
−0.696029 + 0.718014i \(0.745051\pi\)
\(462\) −7.48216 13.2294i −0.348102 0.615488i
\(463\) −8.61123 −0.400198 −0.200099 0.979776i \(-0.564126\pi\)
−0.200099 + 0.979776i \(0.564126\pi\)
\(464\) −2.26250 3.91876i −0.105034 0.181924i
\(465\) 27.2105 + 1.97043i 1.26186 + 0.0913766i
\(466\) 3.87397 6.70992i 0.179458 0.310831i
\(467\) −31.5910 + 18.2391i −1.46186 + 0.844003i −0.999097 0.0424805i \(-0.986474\pi\)
−0.462759 + 0.886484i \(0.653141\pi\)
\(468\) 5.23882 + 4.13494i 0.242164 + 0.191138i
\(469\) 4.39540 10.1249i 0.202961 0.467524i
\(470\) −16.1365 −0.744321
\(471\) 20.2583 + 13.7375i 0.933455 + 0.632990i
\(472\) −3.19636 1.84542i −0.147124 0.0849423i
\(473\) −15.4392 0.782225i −0.709897 0.0359667i
\(474\) −9.52402 + 14.0448i −0.437453 + 0.645100i
\(475\) 21.0431i 0.965525i
\(476\) −6.85508 9.25281i −0.314202 0.424102i
\(477\) 5.82498 + 4.59759i 0.266707 + 0.210509i
\(478\) −5.97761 10.3535i −0.273410 0.473559i
\(479\) −2.94400 + 5.09916i −0.134515 + 0.232987i −0.925412 0.378962i \(-0.876281\pi\)
0.790897 + 0.611949i \(0.209614\pi\)
\(480\) 7.42908 + 0.537973i 0.339090 + 0.0245550i
\(481\) −12.9728 + 7.48983i −0.591507 + 0.341507i
\(482\) 28.2502i 1.28676i
\(483\) −4.22215 6.65519i −0.192114 0.302822i
\(484\) 6.43466 8.92161i 0.292484 0.405528i
\(485\) −2.01750 + 1.16481i −0.0916101 + 0.0528911i
\(486\) −15.3840 + 2.51672i −0.697830 + 0.114161i
\(487\) 13.0643 22.6280i 0.592000 1.02537i −0.401963 0.915656i \(-0.631672\pi\)
0.993963 0.109718i \(-0.0349948\pi\)
\(488\) −4.02253 + 2.32241i −0.182092 + 0.105131i
\(489\) 26.9231 13.0489i 1.21750 0.590090i
\(490\) −28.7978 8.76764i −1.30095 0.396081i
\(491\) −3.67030 −0.165639 −0.0828193 0.996565i \(-0.526392\pi\)
−0.0828193 + 0.996565i \(0.526392\pi\)
\(492\) −14.3673 9.74268i −0.647727 0.439234i
\(493\) 9.84741 17.0562i 0.443505 0.768173i
\(494\) −1.73469 + 3.00457i −0.0780474 + 0.135182i
\(495\) 13.8006 + 40.5019i 0.620291 + 1.82043i
\(496\) 3.66270 0.164460
\(497\) −2.13078 18.6051i −0.0955784 0.834551i
\(498\) −27.5228 + 13.3396i −1.23333 + 0.597760i
\(499\) 0.575545 + 0.996873i 0.0257649 + 0.0446262i 0.878620 0.477521i \(-0.158465\pi\)
−0.852855 + 0.522147i \(0.825131\pi\)
\(500\) 31.6323 + 18.2629i 1.41464 + 0.816744i
\(501\) −1.79587 + 24.7999i −0.0802337 + 1.10798i
\(502\) 1.55822 0.899639i 0.0695468 0.0401528i
\(503\) −10.1687 −0.453401 −0.226701 0.973965i \(-0.572794\pi\)
−0.226701 + 0.973965i \(0.572794\pi\)
\(504\) 7.93355 + 0.242419i 0.353388 + 0.0107982i
\(505\) 33.7599i 1.50230i
\(506\) 3.09842 4.78935i 0.137741 0.212913i
\(507\) 1.00714 13.9079i 0.0447285 0.617674i
\(508\) −1.99119 1.14962i −0.0883449 0.0510059i
\(509\) −0.280452 + 0.161919i −0.0124308 + 0.00717692i −0.506203 0.862415i \(-0.668951\pi\)
0.493772 + 0.869592i \(0.335618\pi\)
\(510\) 14.1396 + 29.1734i 0.626110 + 1.29182i
\(511\) −35.5969 15.4533i −1.57471 0.683612i
\(512\) 1.00000 0.0441942
\(513\) −2.44678 7.72514i −0.108028 0.341073i
\(514\) 3.30536 + 1.90835i 0.145793 + 0.0841738i
\(515\) 36.1158 + 20.8515i 1.59145 + 0.918825i
\(516\) 4.53104 6.68181i 0.199468 0.294150i
\(517\) −5.66918 11.0787i −0.249330 0.487243i
\(518\) −7.09413 + 16.3415i −0.311698 + 0.718002i
\(519\) 27.1016 13.1354i 1.18963 0.576580i
\(520\) 4.78353 + 8.28532i 0.209772 + 0.363335i
\(521\) −30.0787 17.3659i −1.31777 0.760815i −0.334400 0.942431i \(-0.608534\pi\)
−0.983369 + 0.181616i \(0.941867\pi\)
\(522\) 5.02292 + 12.6115i 0.219847 + 0.551992i
\(523\) −0.209525 + 0.120969i −0.00916189 + 0.00528962i −0.504574 0.863368i \(-0.668350\pi\)
0.495412 + 0.868658i \(0.335017\pi\)
\(524\) 7.77716 0.339747
\(525\) 54.7945 + 28.6561i 2.39143 + 1.25065i
\(526\) 15.6276 0.681394
\(527\) 7.97085 + 13.8059i 0.347216 + 0.601395i
\(528\) 2.24068 + 5.28955i 0.0975132 + 0.230198i
\(529\) −10.0210 + 17.3569i −0.435696 + 0.754647i
\(530\) 5.31875 + 9.21234i 0.231032 + 0.400159i
\(531\) 8.69141 + 6.86003i 0.377175 + 0.297700i
\(532\) 0.469472 + 4.09924i 0.0203542 + 0.177724i
\(533\) 22.2964i 0.965765i
\(534\) −12.1502 + 17.9176i −0.525791 + 0.775371i
\(535\) −13.1014 7.56412i −0.566425 0.327025i
\(536\) −2.08595 + 3.61297i −0.0900992 + 0.156056i
\(537\) −14.1771 + 20.9066i −0.611785 + 0.902184i
\(538\) 11.7212i 0.505337i
\(539\) −4.09789 22.8519i −0.176509 0.984299i
\(540\) −21.8222 4.80808i −0.939078 0.206907i
\(541\) 26.1669 15.1074i 1.12500 0.649520i 0.182328 0.983238i \(-0.441637\pi\)
0.942673 + 0.333718i \(0.108303\pi\)
\(542\) −9.87548 5.70161i −0.424188 0.244905i
\(543\) −2.98358 + 41.2015i −0.128038 + 1.76812i
\(544\) 2.17622 + 3.76933i 0.0933048 + 0.161609i
\(545\) 10.2454 0.438864
\(546\) 5.46138 + 8.60854i 0.233725 + 0.368411i
\(547\) 6.15235i 0.263056i 0.991312 + 0.131528i \(0.0419883\pi\)
−0.991312 + 0.131528i \(0.958012\pi\)
\(548\) −8.00701 + 4.62285i −0.342043 + 0.197478i
\(549\) 12.9455 5.15592i 0.552500 0.220049i
\(550\) −2.26450 + 44.6958i −0.0965585 + 1.90583i
\(551\) −6.11129 + 3.52835i −0.260350 + 0.150313i
\(552\) 1.29925 + 2.68067i 0.0552995 + 0.114097i
\(553\) −20.8281 + 15.4308i −0.885699 + 0.656183i
\(554\) 23.0143i 0.977785i
\(555\) 28.1485 41.5099i 1.19484 1.76200i
\(556\) 15.5770 + 8.99336i 0.660610 + 0.381403i
\(557\) 2.94874 5.10737i 0.124942 0.216406i −0.796768 0.604285i \(-0.793459\pi\)
0.921710 + 0.387879i \(0.126792\pi\)
\(558\) −10.8735 1.58309i −0.460310 0.0670176i
\(559\) 10.3694 0.438580
\(560\) 10.4368 + 4.53081i 0.441035 + 0.191462i
\(561\) −15.0618 + 19.9571i −0.635911 + 0.842590i
\(562\) 5.40113 + 9.35504i 0.227833 + 0.394619i
\(563\) −11.6358 + 20.1537i −0.490389 + 0.849378i −0.999939 0.0110627i \(-0.996479\pi\)
0.509550 + 0.860441i \(0.329812\pi\)
\(564\) 6.48222 + 0.469406i 0.272951 + 0.0197656i
\(565\) −22.4074 38.8107i −0.942685 1.63278i
\(566\) 15.2501i 0.641011i
\(567\) −23.4476 4.14871i −0.984705 0.174229i
\(568\) 7.07802i 0.296987i
\(569\) 19.2703 + 33.3771i 0.807853 + 1.39924i 0.914348 + 0.404929i \(0.132704\pi\)
−0.106496 + 0.994313i \(0.533963\pi\)
\(570\) 0.838965 11.5856i 0.0351404 0.485268i
\(571\) 11.4730 + 6.62396i 0.480131 + 0.277204i 0.720471 0.693485i \(-0.243926\pi\)
−0.240340 + 0.970689i \(0.577259\pi\)
\(572\) −4.00782 + 6.19506i −0.167575 + 0.259028i
\(573\) −0.889223 1.83469i −0.0371478 0.0766452i
\(574\) −15.7850 21.3062i −0.658855 0.889306i
\(575\) 23.2074i 0.967815i
\(576\) −2.96870 0.432220i −0.123696 0.0180092i
\(577\) −11.6105 + 20.1099i −0.483351 + 0.837188i −0.999817 0.0191193i \(-0.993914\pi\)
0.516466 + 0.856307i \(0.327247\pi\)
\(578\) −0.971897 + 1.68337i −0.0404256 + 0.0700191i
\(579\) −1.88499 + 2.77975i −0.0783375 + 0.115522i
\(580\) 19.4594i 0.808007i
\(581\) −46.4161 + 5.31589i −1.92567 + 0.220540i
\(582\) 0.844339 0.409228i 0.0349990 0.0169630i
\(583\) −4.45625 + 6.88821i −0.184559 + 0.285280i
\(584\) 12.7024 + 7.33373i 0.525629 + 0.303472i
\(585\) −10.6198 26.6642i −0.439074 1.10243i
\(586\) 5.30185 + 9.18307i 0.219017 + 0.379349i
\(587\) 26.3040i 1.08568i −0.839836 0.542841i \(-0.817349\pi\)
0.839836 0.542841i \(-0.182651\pi\)
\(588\) 11.3134 + 4.35978i 0.466555 + 0.179794i
\(589\) 5.71195i 0.235357i
\(590\) 7.93607 + 13.7457i 0.326723 + 0.565900i
\(591\) 0.130639 1.80405i 0.00537379 0.0742088i
\(592\) 3.36669 5.83129i 0.138370 0.239664i
\(593\) −15.9757 27.6707i −0.656043 1.13630i −0.981631 0.190788i \(-0.938896\pi\)
0.325588 0.945512i \(-0.394438\pi\)
\(594\) −4.36567 16.6716i −0.179126 0.684042i
\(595\) 5.63469 + 49.1998i 0.231000 + 2.01699i
\(596\) −4.94880 −0.202711
\(597\) −34.7663 23.5756i −1.42289 0.964884i
\(598\) −1.91310 + 3.31359i −0.0782325 + 0.135503i
\(599\) 23.9985 + 13.8555i 0.980552 + 0.566122i 0.902437 0.430822i \(-0.141776\pi\)
0.0781155 + 0.996944i \(0.475110\pi\)
\(600\) −19.3435 13.1171i −0.789695 0.535504i
\(601\) 4.24301i 0.173076i −0.996249 0.0865380i \(-0.972420\pi\)
0.996249 0.0865380i \(-0.0275804\pi\)
\(602\) 9.90893 7.34117i 0.403858 0.299204i
\(603\) 7.75415 9.82423i 0.315773 0.400074i
\(604\) −6.71375 + 3.87618i −0.273179 + 0.157720i
\(605\) −43.1477 + 19.3906i −1.75420 + 0.788342i
\(606\) −0.982068 + 13.5618i −0.0398938 + 0.550909i
\(607\) 8.07423 4.66166i 0.327723 0.189211i −0.327107 0.944987i \(-0.606074\pi\)
0.654830 + 0.755776i \(0.272740\pi\)
\(608\) 1.55949i 0.0632458i
\(609\) 0.865309 + 20.7181i 0.0350641 + 0.839539i
\(610\) 19.9747 0.808751
\(611\) 4.17385 + 7.22932i 0.168856 + 0.292467i
\(612\) −4.83138 12.1306i −0.195297 0.490351i
\(613\) −34.3925 19.8565i −1.38910 0.801996i −0.395885 0.918300i \(-0.629562\pi\)
−0.993214 + 0.116304i \(0.962895\pi\)
\(614\) 5.58170 3.22259i 0.225259 0.130053i
\(615\) 32.5588 + 67.1770i 1.31290 + 2.70884i
\(616\) 0.556035 + 8.75733i 0.0224033 + 0.352843i
\(617\) 16.5103i 0.664679i −0.943160 0.332339i \(-0.892162\pi\)
0.943160 0.332339i \(-0.107838\pi\)
\(618\) −13.9016 9.42688i −0.559203 0.379205i
\(619\) 7.63994 13.2328i 0.307075 0.531870i −0.670646 0.741778i \(-0.733983\pi\)
0.977721 + 0.209908i \(0.0673163\pi\)
\(620\) −13.6409 7.87556i −0.547830 0.316290i
\(621\) −2.69843 8.51966i −0.108284 0.341882i
\(622\) 9.25267i 0.370998i
\(623\) −26.5713 + 19.6857i −1.06456 + 0.788692i
\(624\) −1.68058 3.46746i −0.0672772 0.138810i
\(625\) −44.8043 77.6034i −1.79217 3.10413i
\(626\) −0.408129 + 0.706900i −0.0163121 + 0.0282534i
\(627\) 8.24902 3.49433i 0.329434 0.139550i
\(628\) −7.06587 12.2385i −0.281959 0.488367i
\(629\) 29.3067 1.16854
\(630\) −29.0254 17.9616i −1.15640 0.715608i
\(631\) 31.1076 1.23837 0.619187 0.785244i \(-0.287462\pi\)
0.619187 + 0.785244i \(0.287462\pi\)
\(632\) 8.48475 4.89868i 0.337505 0.194859i
\(633\) 34.3189 + 2.48518i 1.36405 + 0.0987771i
\(634\) −7.19272 4.15272i −0.285659 0.164925i
\(635\) 4.94382 + 8.56295i 0.196190 + 0.339810i
\(636\) −1.86862 3.85543i −0.0740956 0.152878i
\(637\) 3.52082 + 15.1696i 0.139500 + 0.601040i
\(638\) −13.3601 + 6.83660i −0.528932 + 0.270664i
\(639\) 3.05926 21.0125i 0.121023 0.831243i
\(640\) −3.72427 2.15021i −0.147215 0.0849944i
\(641\) −1.86879 1.07895i −0.0738129 0.0426159i 0.462639 0.886547i \(-0.346902\pi\)
−0.536452 + 0.843931i \(0.680236\pi\)
\(642\) 5.04296 + 3.41971i 0.199030 + 0.134965i
\(643\) 36.5368 1.44087 0.720435 0.693522i \(-0.243942\pi\)
0.720435 + 0.693522i \(0.243942\pi\)
\(644\) 0.517756 + 4.52084i 0.0204025 + 0.178146i
\(645\) −31.2421 + 15.1422i −1.23016 + 0.596223i
\(646\) 5.87824 3.39381i 0.231276 0.133528i
\(647\) −7.86424 4.54042i −0.309175 0.178502i 0.337382 0.941368i \(-0.390459\pi\)
−0.646557 + 0.762865i \(0.723792\pi\)
\(648\) 8.62637 + 2.56627i 0.338876 + 0.100812i
\(649\) −6.64914 + 10.2778i −0.261001 + 0.403441i
\(650\) 30.0189i 1.17744i
\(651\) −14.8734 7.77841i −0.582935 0.304860i
\(652\) −17.2735 −0.676484
\(653\) 11.3768 6.56840i 0.445209 0.257041i −0.260596 0.965448i \(-0.583919\pi\)
0.705805 + 0.708407i \(0.250586\pi\)
\(654\) −4.11569 0.298036i −0.160936 0.0116541i
\(655\) −28.9642 16.7225i −1.13173 0.653403i
\(656\) 5.01114 + 8.67956i 0.195652 + 0.338880i
\(657\) −34.5398 27.2619i −1.34753 1.06359i
\(658\) 9.10659 + 3.95334i 0.355012 + 0.154117i
\(659\) −40.4232 −1.57466 −0.787332 0.616530i \(-0.788538\pi\)
−0.787332 + 0.616530i \(0.788538\pi\)
\(660\) 3.02872 24.5176i 0.117893 0.954348i
\(661\) 0.305691 0.529473i 0.0118900 0.0205941i −0.860019 0.510262i \(-0.829549\pi\)
0.871909 + 0.489668i \(0.162882\pi\)
\(662\) −11.4714 + 19.8690i −0.445847 + 0.772230i
\(663\) 9.41268 13.8806i 0.365558 0.539079i
\(664\) 17.6583 0.685276
\(665\) 7.06577 16.2761i 0.273999 0.631161i
\(666\) −12.5151 + 15.8562i −0.484951 + 0.614415i
\(667\) −6.73982 + 3.89124i −0.260967 + 0.150669i
\(668\) 7.17787 12.4324i 0.277720 0.481025i
\(669\) −2.14105 + 29.5666i −0.0827779 + 1.14311i
\(670\) 15.5373 8.97044i 0.600257 0.346558i
\(671\) 7.01764 + 13.7139i 0.270913 + 0.529419i
\(672\) −4.06078 2.12368i −0.156648 0.0819229i
\(673\) 24.7930i 0.955700i 0.878441 + 0.477850i \(0.158584\pi\)
−0.878441 + 0.477850i \(0.841416\pi\)
\(674\) 29.2026 16.8601i 1.12484 0.649427i
\(675\) 51.7555 + 47.3015i 1.99207 + 1.82063i
\(676\) −4.02539 + 6.97218i −0.154823 + 0.268161i
\(677\) −13.3012 23.0383i −0.511206 0.885435i −0.999916 0.0129885i \(-0.995866\pi\)
0.488709 0.872447i \(-0.337468\pi\)
\(678\) 7.87231 + 16.2425i 0.302334 + 0.623791i
\(679\) 1.42394 0.163080i 0.0546459 0.00625842i
\(680\) 18.7173i 0.717777i
\(681\) 27.4077 + 18.5856i 1.05027 + 0.712202i
\(682\) 0.614676 12.1322i 0.0235371 0.464567i
\(683\) −20.7868 12.0013i −0.795386 0.459216i 0.0464694 0.998920i \(-0.485203\pi\)
−0.841855 + 0.539704i \(0.818536\pi\)
\(684\) −0.674045 + 4.62967i −0.0257727 + 0.177020i
\(685\) 39.7604 1.51917
\(686\) 14.1039 + 12.0033i 0.538491 + 0.458287i
\(687\) 21.0733 10.2136i 0.803995 0.389674i
\(688\) −4.03661 + 2.33054i −0.153894 + 0.0888510i
\(689\) 2.75149 4.76571i 0.104823 0.181559i
\(690\) 0.925252 12.7772i 0.0352237 0.486419i
\(691\) 1.78912 + 3.09884i 0.0680612 + 0.117886i 0.898048 0.439898i \(-0.144985\pi\)
−0.829987 + 0.557783i \(0.811652\pi\)
\(692\) −17.3881 −0.660996
\(693\) 2.13439 26.2382i 0.0810790 0.996708i
\(694\) 7.67876 0.291482
\(695\) −38.6752 66.9874i −1.46703 2.54098i
\(696\) 0.566068 7.81706i 0.0214568 0.296305i
\(697\) −21.8107 + 37.7773i −0.826141 + 1.43092i
\(698\) 3.36135 1.94068i 0.127229 0.0734557i
\(699\) 12.0762 5.85299i 0.456763 0.221381i
\(700\) −21.2523 28.6858i −0.803261 1.08422i
\(701\) −9.33214 −0.352470 −0.176235 0.984348i \(-0.556392\pi\)
−0.176235 + 0.984348i \(0.556392\pi\)
\(702\) 3.49044 + 11.0202i 0.131738 + 0.415932i
\(703\) −9.09385 5.25034i −0.342981 0.198020i
\(704\) 0.167821 3.31238i 0.00632497 0.124840i
\(705\) −23.1322 15.6863i −0.871209 0.590781i
\(706\) 3.43977i 0.129457i
\(707\) −8.27098 + 19.0523i −0.311062 + 0.716537i
\(708\) −2.78815 5.75266i −0.104785 0.216198i
\(709\) 8.01982 + 13.8907i 0.301191 + 0.521677i 0.976406 0.215943i \(-0.0692826\pi\)
−0.675215 + 0.737621i \(0.735949\pi\)
\(710\) 15.2192 26.3605i 0.571167 0.989290i
\(711\) −27.3060 + 10.8754i −1.02406 + 0.407860i
\(712\) 10.8244 6.24946i 0.405661 0.234208i
\(713\) 6.29942i 0.235915i
\(714\) −0.832312 19.9280i −0.0311485 0.745788i
\(715\) 28.2469 14.4544i 1.05637 0.540564i
\(716\) 12.6301 7.29196i 0.472007 0.272514i
\(717\) 1.49557 20.6530i 0.0558532 0.771299i
\(718\) 11.0163 19.0808i 0.411125 0.712090i
\(719\) −24.4747 + 14.1305i −0.912753 + 0.526978i −0.881316 0.472528i \(-0.843342\pi\)
−0.0314371 + 0.999506i \(0.510008\pi\)
\(720\) 10.1269 + 7.99303i 0.377406 + 0.297883i
\(721\) −15.2734 20.6156i −0.568810 0.767766i
\(722\) 16.5680 0.616596
\(723\) −27.4620 + 40.4975i −1.02132 + 1.50612i
\(724\) 11.9250 20.6547i 0.443189 0.767625i
\(725\) 30.5292 52.8781i 1.13383 1.96384i
\(726\) 17.8970 6.53429i 0.664220 0.242510i
\(727\) 5.45714 0.202394 0.101197 0.994866i \(-0.467733\pi\)
0.101197 + 0.994866i \(0.467733\pi\)
\(728\) −0.669722 5.84773i −0.0248215 0.216731i
\(729\) −24.4999 11.3470i −0.907405 0.420258i
\(730\) −31.5381 54.6256i −1.16728 2.02178i
\(731\) −17.5691 10.1435i −0.649818 0.375173i
\(732\) −8.02406 0.581058i −0.296578 0.0214765i
\(733\) −23.3511 + 13.4818i −0.862494 + 0.497961i −0.864847 0.502036i \(-0.832584\pi\)
0.00235259 + 0.999997i \(0.499251\pi\)
\(734\) −10.8346 −0.399912
\(735\) −32.7596 40.5631i −1.20836 1.49619i
\(736\) 1.71988i 0.0633958i
\(737\) 11.6174 + 7.51577i 0.427934 + 0.276847i
\(738\) −11.1251 27.9329i −0.409521 1.02823i
\(739\) −28.7950 16.6248i −1.05924 0.611553i −0.134018 0.990979i \(-0.542788\pi\)
−0.925222 + 0.379426i \(0.876121\pi\)
\(740\) −25.0770 + 14.4782i −0.921847 + 0.532229i
\(741\) −5.40748 + 2.62086i −0.198649 + 0.0962796i
\(742\) −0.744655 6.50202i −0.0273372 0.238697i
\(743\) −6.13190 −0.224958 −0.112479 0.993654i \(-0.535879\pi\)
−0.112479 + 0.993654i \(0.535879\pi\)
\(744\) 5.25060 + 3.56051i 0.192496 + 0.130535i
\(745\) 18.4306 + 10.6409i 0.675247 + 0.389854i
\(746\) 5.25214 + 3.03232i 0.192294 + 0.111021i
\(747\) −52.4223 7.63228i −1.91803 0.279251i
\(748\) 12.8507 6.57590i 0.469866 0.240439i
\(749\) 5.54060 + 7.47856i 0.202449 + 0.273261i
\(750\) 27.5926 + 56.9304i 1.00754 + 2.07880i
\(751\) 4.62693 + 8.01408i 0.168839 + 0.292438i 0.938012 0.346603i \(-0.112665\pi\)
−0.769173 + 0.639041i \(0.779331\pi\)
\(752\) −3.24960 1.87616i −0.118501 0.0684163i
\(753\) 3.10830 + 0.225086i 0.113273 + 0.00820259i
\(754\) 8.71801 5.03335i 0.317491 0.183304i
\(755\) 33.3384 1.21331
\(756\) 11.1374 + 8.05973i 0.405062 + 0.293130i
\(757\) −33.0544 −1.20138 −0.600691 0.799481i \(-0.705108\pi\)
−0.600691 + 0.799481i \(0.705108\pi\)
\(758\) 0.978573 + 1.69494i 0.0355434 + 0.0615629i
\(759\) 9.09742 3.85372i 0.330215 0.139881i
\(760\) −3.35323 + 5.80797i −0.121635 + 0.210677i
\(761\) −3.66311 6.34470i −0.132788 0.229995i 0.791962 0.610570i \(-0.209060\pi\)
−0.924750 + 0.380575i \(0.875726\pi\)
\(762\) −1.73690 3.58365i −0.0629212 0.129822i
\(763\) −5.78196 2.51006i −0.209321 0.0908701i
\(764\) 1.17712i 0.0425865i
\(765\) −8.09001 + 55.5662i −0.292495 + 2.00900i
\(766\) −9.20867 5.31663i −0.332723 0.192098i
\(767\) 4.10547 7.11089i 0.148240 0.256759i
\(768\) 1.43353 + 0.972102i 0.0517282 + 0.0350777i
\(769\) 44.3335i 1.59871i −0.600861 0.799353i \(-0.705176\pi\)
0.600861 0.799353i \(-0.294824\pi\)
\(770\) 16.7593 33.8102i 0.603962 1.21844i
\(771\) 2.88324 + 5.94884i 0.103837 + 0.214242i
\(772\) 1.67930 0.969543i 0.0604393 0.0348946i
\(773\) 11.7168 + 6.76468i 0.421423 + 0.243309i 0.695686 0.718346i \(-0.255101\pi\)
−0.274263 + 0.961655i \(0.588434\pi\)
\(774\) 12.9908 5.17397i 0.466945 0.185974i
\(775\) 24.7114 + 42.8015i 0.887661 + 1.53747i
\(776\) −0.541718 −0.0194465
\(777\) −26.0552 + 16.5298i −0.934726 + 0.593003i
\(778\) 20.0095i 0.717375i
\(779\) 13.5357 7.81484i 0.484967 0.279996i
\(780\) −1.19682 + 16.5274i −0.0428530 + 0.591775i
\(781\) 23.4451 + 1.18784i 0.838930 + 0.0425042i
\(782\) 6.48281 3.74285i 0.231825 0.133844i
\(783\) −5.05918 + 22.9618i −0.180800 + 0.820589i
\(784\) −4.77996 5.11390i −0.170713 0.182639i
\(785\) 60.7724i 2.16906i
\(786\) 11.1488 + 7.56019i 0.397665 + 0.269663i
\(787\) 24.1825 + 13.9618i 0.862013 + 0.497683i 0.864686 0.502313i \(-0.167517\pi\)
−0.00267284 + 0.999996i \(0.500851\pi\)
\(788\) −0.522149 + 0.904388i −0.0186008 + 0.0322175i
\(789\) 22.4026 + 15.1916i 0.797555 + 0.540834i
\(790\) −42.1327 −1.49901
\(791\) 3.13716 + 27.3924i 0.111545 + 0.973961i
\(792\) −1.92988 + 9.76092i −0.0685755 + 0.346839i
\(793\) −5.16663 8.94887i −0.183472 0.317784i
\(794\) 8.09039 14.0130i 0.287117 0.497302i
\(795\) −1.33073 + 18.3766i −0.0471961 + 0.651750i
\(796\) 12.1261 + 21.0030i 0.429798 + 0.744432i
\(797\) 18.8457i 0.667549i −0.942653 0.333774i \(-0.891678\pi\)
0.942653 0.333774i \(-0.108322\pi\)
\(798\) −3.31187 + 6.33277i −0.117239 + 0.224177i
\(799\) 16.3317i 0.577775i
\(800\) 6.74679 + 11.6858i 0.238535 + 0.413155i
\(801\) −34.8355 + 13.8743i −1.23085 + 0.490223i
\(802\) 20.3865 + 11.7702i 0.719873 + 0.415619i
\(803\) 26.4238 40.8444i 0.932476 1.44137i
\(804\) −6.50245 + 3.15156i −0.229324 + 0.111147i
\(805\) 7.79247 17.9501i 0.274649 0.632658i
\(806\) 8.14834i 0.287013i
\(807\) −11.3942 + 16.8027i −0.401095 + 0.591485i
\(808\) 3.92520 6.79864i 0.138088 0.239175i
\(809\) 21.4556 37.1622i 0.754339 1.30655i −0.191363 0.981519i \(-0.561291\pi\)
0.945702 0.325034i \(-0.105376\pi\)
\(810\) −26.6089 28.1060i −0.934942 0.987542i
\(811\) 7.13276i 0.250465i −0.992127 0.125233i \(-0.960032\pi\)
0.992127 0.125233i \(-0.0399677\pi\)
\(812\) 4.76743 10.9818i 0.167304 0.385387i
\(813\) −8.61429 17.7734i −0.302116 0.623341i
\(814\) −18.7504 12.1304i −0.657202 0.425169i
\(815\) 64.3313 + 37.1417i 2.25343 + 1.30102i
\(816\) −0.544482 + 7.51897i −0.0190607 + 0.263217i
\(817\) 3.63446 + 6.29507i 0.127154 + 0.220237i
\(818\) 34.2914i 1.19897i
\(819\) −0.539305 + 17.6496i −0.0188448 + 0.616728i
\(820\) 43.1000i 1.50512i
\(821\) 12.3220 + 21.3424i 0.430041 + 0.744854i 0.996876 0.0789778i \(-0.0251656\pi\)
−0.566835 + 0.823831i \(0.691832\pi\)
\(822\) −15.9722 1.15662i −0.557094 0.0403417i
\(823\) 6.36507 11.0246i 0.221872 0.384294i −0.733504 0.679685i \(-0.762117\pi\)
0.955376 + 0.295391i \(0.0954499\pi\)
\(824\) 4.84871 + 8.39821i 0.168913 + 0.292566i
\(825\) −46.6951 + 61.8716i −1.62571 + 2.15409i
\(826\) −1.11109 9.70162i −0.0386599 0.337563i
\(827\) 13.6994 0.476376 0.238188 0.971219i \(-0.423447\pi\)
0.238188 + 0.971219i \(0.423447\pi\)
\(828\) −0.743369 + 5.10582i −0.0258339 + 0.177440i
\(829\) 18.7070 32.4015i 0.649722 1.12535i −0.333467 0.942762i \(-0.608219\pi\)
0.983189 0.182590i \(-0.0584481\pi\)
\(830\) −65.7643 37.9691i −2.28271 1.31793i
\(831\) 22.3723 32.9918i 0.776085 1.14447i
\(832\) 2.22468i 0.0771270i
\(833\) 8.87372 29.1462i 0.307456 1.00986i
\(834\) 13.5876 + 28.0347i 0.470501 + 0.970761i
\(835\) −53.4646 + 30.8678i −1.85022 + 1.06823i
\(836\) −5.16563 0.261715i −0.178657 0.00905160i
\(837\) −14.0485 12.8395i −0.485588 0.443799i
\(838\) 20.6966 11.9492i 0.714951 0.412777i
\(839\) 41.6482i 1.43786i 0.695085 + 0.718928i \(0.255367\pi\)
−0.695085 + 0.718928i \(0.744633\pi\)
\(840\) 10.5571 + 16.6407i 0.364254 + 0.574159i
\(841\) −8.52438 −0.293944
\(842\) −10.6889 18.5137i −0.368363 0.638024i
\(843\) −1.35134 + 18.6612i −0.0465427 + 0.642726i
\(844\) −17.2044 9.93294i −0.592198 0.341906i
\(845\) 29.9833 17.3109i 1.03146 0.595512i
\(846\) 8.83617 + 6.97428i 0.303794 + 0.239781i
\(847\) 29.1009 0.372136i 0.999918 0.0127867i
\(848\) 2.47360i 0.0849437i
\(849\) 14.8247 21.8616i 0.508782 0.750288i
\(850\) −29.3650 + 50.8617i −1.00721 + 1.74454i
\(851\) −10.0291 5.79033i −0.343795 0.198490i
\(852\) −6.88056 + 10.1466i −0.235724 + 0.347616i
\(853\) 20.2141i 0.692117i 0.938213 + 0.346059i \(0.112480\pi\)
−0.938213 + 0.346059i \(0.887520\pi\)
\(854\) −11.2727 4.89367i −0.385742 0.167458i
\(855\) 12.4651 15.7928i 0.426297 0.540102i
\(856\) −1.75893 3.04655i −0.0601189 0.104129i
\(857\) 11.5198 19.9529i 0.393510 0.681579i −0.599400 0.800450i \(-0.704594\pi\)
0.992910 + 0.118871i \(0.0379274\pi\)
\(858\) −11.7676 + 4.98481i −0.401738 + 0.170179i
\(859\) −3.17916 5.50647i −0.108472 0.187878i 0.806680 0.590989i \(-0.201262\pi\)
−0.915151 + 0.403111i \(0.867929\pi\)
\(860\) 20.0446 0.683514
\(861\) −1.91655 45.8879i −0.0653158 1.56385i
\(862\) 2.28472 0.0778180
\(863\) 43.7656 25.2681i 1.48980 0.860135i 0.489866 0.871798i \(-0.337046\pi\)
0.999932 + 0.0116621i \(0.00371226\pi\)
\(864\) −3.83557 3.50548i −0.130489 0.119259i
\(865\) 64.7579 + 37.3880i 2.20184 + 1.27123i
\(866\) 5.01179 + 8.68067i 0.170307 + 0.294981i
\(867\) −3.02966 + 1.46839i −0.102893 + 0.0498692i
\(868\) 5.76873 + 7.78648i 0.195803 + 0.264290i
\(869\) −14.8023 28.9268i −0.502135 0.981274i
\(870\) −18.9165 + 27.8957i −0.641329 + 0.945752i
\(871\) −8.03771 4.64057i −0.272347 0.157240i
\(872\) 2.06323 + 1.19121i 0.0698699 + 0.0403394i
\(873\) 1.60820 + 0.234142i 0.0544293 + 0.00792449i
\(874\) −2.68215 −0.0907250
\(875\) 10.9958 + 96.0108i 0.371726 + 3.24576i
\(876\) 11.0802 + 22.8612i 0.374365 + 0.772407i
\(877\) 44.1014 25.4620i 1.48920 0.859789i 0.489275 0.872130i \(-0.337261\pi\)
0.999924 + 0.0123404i \(0.00392816\pi\)
\(878\) 5.95435 + 3.43774i 0.200949 + 0.116018i
\(879\) −1.32650 + 18.3182i −0.0447417 + 0.617856i
\(880\) −7.74731 + 11.9753i −0.261162 + 0.403688i
\(881\) 43.9018i 1.47909i 0.673107 + 0.739545i \(0.264959\pi\)
−0.673107 + 0.739545i \(0.735041\pi\)
\(882\) 11.9799 + 17.2476i 0.403386 + 0.580758i
\(883\) −22.1919 −0.746816 −0.373408 0.927667i \(-0.621811\pi\)
−0.373408 + 0.927667i \(0.621811\pi\)
\(884\) −8.38557 + 4.84141i −0.282037 + 0.162834i
\(885\) −1.98557 + 27.4195i −0.0667443 + 0.921698i
\(886\) −18.4525 10.6536i −0.619925 0.357914i
\(887\) 19.9074 + 34.4807i 0.668426 + 1.15775i 0.978344 + 0.206984i \(0.0663648\pi\)
−0.309919 + 0.950763i \(0.600302\pi\)
\(888\) 10.4949 5.08657i 0.352185 0.170694i
\(889\) −0.692164 6.04369i −0.0232144 0.202699i
\(890\) −53.7505 −1.80172
\(891\) 9.94812 28.1431i 0.333274 0.942830i
\(892\) 8.55750 14.8220i 0.286526 0.496278i
\(893\) −2.92585 + 5.06772i −0.0979099 + 0.169585i
\(894\) −7.09427 4.81073i −0.237268 0.160895i
\(895\) −62.7170 −2.09640
\(896\) 1.57499 + 2.12589i 0.0526169 + 0.0710209i
\(897\) −5.96363 + 2.89041i −0.199120 + 0.0965080i
\(898\) 9.84224 5.68242i 0.328440 0.189625i
\(899\) −8.28685 + 14.3532i −0.276382 + 0.478708i
\(900\) −14.9784 37.6077i −0.499279 1.25359i
\(901\) −9.32380 + 5.38310i −0.310621 + 0.179337i
\(902\) 29.5909 15.1422i 0.985270 0.504180i
\(903\) 21.3411 0.891332i 0.710189 0.0296617i
\(904\) 10.4210i 0.346598i
\(905\) −88.8237 + 51.2824i −2.95260 + 1.70468i
\(906\) −13.3924 0.969805i −0.444934 0.0322196i
\(907\) −18.2837 + 31.6682i −0.607099 + 1.05153i 0.384617 + 0.923076i \(0.374333\pi\)
−0.991716 + 0.128450i \(0.959000\pi\)
\(908\) −9.55949 16.5575i −0.317243 0.549481i
\(909\) −14.5912 + 18.4866i −0.483961 + 0.613161i
\(910\) −10.0796 + 23.2186i −0.334136 + 0.769688i
\(911\) 55.8387i 1.85002i 0.379944 + 0.925010i \(0.375943\pi\)
−0.379944 + 0.925010i \(0.624057\pi\)
\(912\) 1.51599 2.23559i 0.0501993 0.0740276i
\(913\) 2.96343 58.4910i 0.0980752 1.93577i
\(914\) −0.879305 0.507667i −0.0290848 0.0167921i
\(915\) 28.6344 + 19.4174i 0.946623 + 0.641920i
\(916\) −13.5204 −0.446725
\(917\) 12.2490 + 16.5334i 0.404497 + 0.545980i
\(918\) 4.86626 22.0862i 0.160610 0.728955i
\(919\) 45.8037 26.4448i 1.51092 0.872332i 0.511005 0.859578i \(-0.329274\pi\)
0.999919 0.0127539i \(-0.00405981\pi\)
\(920\) −3.69811 + 6.40531i −0.121923 + 0.211177i
\(921\) 11.1342 + 0.806280i 0.366886 + 0.0265678i
\(922\) 14.9444 + 25.8844i 0.492167 + 0.852458i
\(923\) −15.7464 −0.518298
\(924\) −7.71592 + 13.0944i −0.253835 + 0.430776i
\(925\) 90.8575 2.98738
\(926\) 4.30562 + 7.45755i 0.141491 + 0.245070i
\(927\) −10.7645 27.0275i −0.353552 0.887699i
\(928\) −2.26250 + 3.91876i −0.0742702 + 0.128640i
\(929\) 0.312131 0.180209i 0.0102407 0.00591247i −0.494871 0.868967i \(-0.664785\pi\)
0.505112 + 0.863054i \(0.331451\pi\)
\(930\) −11.8988 24.5502i −0.390177 0.805032i
\(931\) −7.97509 + 7.45432i −0.261373 + 0.244305i
\(932\) −7.74794 −0.253792
\(933\) −8.99454 + 13.2640i −0.294468 + 0.434244i
\(934\) 31.5910 + 18.2391i 1.03369 + 0.596801i
\(935\) −61.9988 3.14115i −2.02758 0.102727i
\(936\) 0.961553 6.60442i 0.0314294 0.215872i
\(937\) 23.8255i 0.778346i −0.921165 0.389173i \(-0.872761\pi\)
0.921165 0.389173i \(-0.127239\pi\)
\(938\) −10.9661 + 1.25591i −0.358056 + 0.0410070i
\(939\) −1.27224 + 0.616622i −0.0415181 + 0.0201227i
\(940\) 8.06825 + 13.9746i 0.263157 + 0.455802i
\(941\) 7.01514 12.1506i 0.228687 0.396098i −0.728732 0.684799i \(-0.759890\pi\)
0.957419 + 0.288701i \(0.0932234\pi\)
\(942\) 1.76785 24.4130i 0.0575998 0.795418i
\(943\) 14.9278 8.61859i 0.486117 0.280660i
\(944\) 3.69084i 0.120127i
\(945\) −24.1484 53.9642i −0.785548 1.75546i
\(946\) 7.04220 + 13.7619i 0.228962 + 0.447438i
\(947\) 42.2760 24.4081i 1.37379 0.793156i 0.382384 0.924003i \(-0.375103\pi\)
0.991403 + 0.130847i \(0.0417697\pi\)
\(948\) 16.9252 + 1.22563i 0.549705 + 0.0398066i
\(949\) −16.3152 + 28.2588i −0.529615 + 0.917320i
\(950\) 18.2239 10.5216i 0.591261 0.341365i
\(951\) −6.27414 12.9451i −0.203453 0.419774i
\(952\) −4.58563 + 10.5631i −0.148621 + 0.342351i
\(953\) −1.92134 −0.0622385 −0.0311192 0.999516i \(-0.509907\pi\)
−0.0311192 + 0.999516i \(0.509907\pi\)
\(954\) 1.06914 7.34337i 0.0346146 0.237750i
\(955\) 2.53104 4.38389i 0.0819026 0.141859i
\(956\) −5.97761 + 10.3535i −0.193330 + 0.334857i
\(957\) −25.7980 3.18689i −0.833932 0.103018i
\(958\) 5.88801 0.190233
\(959\) −22.4387 9.74104i −0.724582 0.314555i
\(960\) −3.24864 6.70276i −0.104850 0.216331i
\(961\) 8.79233 + 15.2288i 0.283623 + 0.491250i
\(962\) 12.9728 + 7.48983i 0.418259 + 0.241482i
\(963\) 3.90495 + 9.80455i 0.125835 + 0.315947i
\(964\) 24.4654 14.1251i 0.787976 0.454938i
\(965\) −8.33888 −0.268438
\(966\) −3.65249 + 6.98408i −0.117517 + 0.224709i
\(967\) 1.76597i 0.0567899i −0.999597 0.0283949i \(-0.990960\pi\)
0.999597 0.0283949i \(-0.00903960\pi\)
\(968\) −10.9437 1.11177i −0.351743 0.0357336i
\(969\) 11.7258 + 0.849116i 0.376686 + 0.0272775i
\(970\) 2.01750 + 1.16481i 0.0647782 + 0.0373997i
\(971\) 21.2217 12.2523i 0.681036 0.393197i −0.119209 0.992869i \(-0.538036\pi\)
0.800245 + 0.599673i \(0.204703\pi\)
\(972\) 9.87152 + 12.0645i 0.316629 + 0.386970i
\(973\) 5.41475 + 47.2793i 0.173589 + 1.51571i
\(974\) −26.1286 −0.837214
\(975\) 29.1814 43.0331i 0.934554 1.37816i
\(976\) 4.02253 + 2.32241i 0.128758 + 0.0743386i
\(977\) −26.1114 15.0755i −0.835379 0.482306i 0.0203117 0.999794i \(-0.493534\pi\)
−0.855691 + 0.517487i \(0.826867\pi\)
\(978\) −24.7622 16.7916i −0.791807 0.536937i
\(979\) −18.8840 36.9032i −0.603535 1.17943i
\(980\) 6.80591 + 29.3234i 0.217407 + 0.936703i
\(981\) −5.61026 4.42811i −0.179122 0.141379i
\(982\) 1.83515 + 3.17858i 0.0585621 + 0.101432i
\(983\) 30.3289 + 17.5104i 0.967341 + 0.558494i 0.898425 0.439128i \(-0.144713\pi\)
0.0689163 + 0.997622i \(0.478046\pi\)
\(984\) −1.25377 + 17.3138i −0.0399686 + 0.551943i
\(985\) 3.88924 2.24546i 0.123922 0.0715462i
\(986\) −19.6948 −0.627211
\(987\) 9.21155 + 14.5198i 0.293207 + 0.462169i
\(988\) 3.46938 0.110376
\(989\) 4.00826 + 6.94251i 0.127455 + 0.220759i
\(990\) 28.1754 32.2026i 0.895473 1.02347i
\(991\) 2.32827 4.03268i 0.0739599 0.128102i −0.826674 0.562682i \(-0.809770\pi\)
0.900633 + 0.434579i \(0.143103\pi\)
\(992\) −1.83135 3.17199i −0.0581454 0.100711i
\(993\) −35.7592 + 17.3315i −1.13479 + 0.549999i
\(994\) −15.0471 + 11.1478i −0.477264 + 0.353588i
\(995\) 104.294i 3.30636i
\(996\) 25.3138 + 17.1657i 0.802098 + 0.543916i
\(997\) −8.75466 5.05450i −0.277263 0.160078i 0.354921 0.934896i \(-0.384508\pi\)
−0.632184 + 0.774819i \(0.717841\pi\)
\(998\) 0.575545 0.996873i 0.0182186 0.0315555i
\(999\) −33.3547 + 10.5644i −1.05529 + 0.334244i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 462.2.n.e.263.6 yes 24
3.2 odd 2 462.2.n.f.263.11 yes 24
7.2 even 3 inner 462.2.n.e.65.11 yes 24
11.10 odd 2 462.2.n.f.263.6 yes 24
21.2 odd 6 462.2.n.f.65.6 yes 24
33.32 even 2 inner 462.2.n.e.263.11 yes 24
77.65 odd 6 462.2.n.f.65.11 yes 24
231.65 even 6 inner 462.2.n.e.65.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.n.e.65.6 24 231.65 even 6 inner
462.2.n.e.65.11 yes 24 7.2 even 3 inner
462.2.n.e.263.6 yes 24 1.1 even 1 trivial
462.2.n.e.263.11 yes 24 33.32 even 2 inner
462.2.n.f.65.6 yes 24 21.2 odd 6
462.2.n.f.65.11 yes 24 77.65 odd 6
462.2.n.f.263.6 yes 24 11.10 odd 2
462.2.n.f.263.11 yes 24 3.2 odd 2