Properties

Label 462.2.y.a.235.2
Level $462$
Weight $2$
Character 462.235
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(25,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 20, 24]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.y (of order \(15\), degree \(8\), 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: \(3\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 235.2
Character \(\chi\) \(=\) 462.235
Dual form 462.2.y.a.289.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.104528 - 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.10227 + 0.490763i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(0.798293 + 2.52244i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\) \(q+(0.104528 - 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.10227 + 0.490763i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(0.798293 + 2.52244i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.603294 - 1.04494i) q^{10} +(3.21216 + 0.825846i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.40301 + 2.47243i) q^{13} +(2.59207 - 0.530253i) q^{14} +(-0.372856 - 1.14753i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.453210 - 4.31200i) q^{17} +(0.978148 + 0.207912i) q^{18} +(0.0256144 - 0.00544450i) q^{19} +(-0.976150 - 0.709214i) q^{20} +(1.34038 - 2.28109i) q^{21} +(1.15708 - 3.10824i) q^{22} +(2.68364 + 4.64819i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-2.37150 - 2.63381i) q^{25} +(2.81460 - 3.12593i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.256403 - 2.63330i) q^{28} +(-0.918447 - 2.82669i) q^{29} +(-1.18022 + 0.250864i) q^{30} +(2.45698 - 1.09392i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.53563 - 2.93970i) q^{33} -4.33575 q^{34} +(-0.357987 + 3.17219i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-4.33319 + 4.81250i) q^{37} +(-0.00273725 - 0.0260432i) q^{38} +(-0.439683 - 4.18331i) q^{39} +(-0.807365 + 0.896669i) q^{40} +(0.792855 - 2.44016i) q^{41} +(-2.12849 - 1.57148i) q^{42} -1.01203 q^{43} +(-2.97026 - 1.47565i) q^{44} +(-0.603294 + 1.04494i) q^{45} +(4.90325 - 2.18307i) q^{46} +(11.1369 - 2.36721i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-5.72546 + 4.02730i) q^{49} +(-2.86728 + 2.08320i) q^{50} +(-2.90119 + 3.22209i) q^{51} +(-2.81460 - 3.12593i) q^{52} +(10.7904 - 4.80419i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(3.13538 + 2.48672i) q^{55} +(-2.64567 - 0.0202566i) q^{56} +(-0.0211854 - 0.0153921i) q^{57} +(-2.90721 + 0.617946i) q^{58} +(2.09757 + 0.445852i) q^{59} +(0.126123 + 1.19998i) q^{60} +(-6.21390 - 2.76661i) q^{61} +(-0.831101 - 2.55786i) q^{62} +(-2.59207 + 0.530253i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.53766 + 4.39536i) q^{65} +(-3.08411 + 1.21994i) q^{66} +(-1.64058 + 2.84156i) q^{67} +(-0.453210 + 4.31200i) q^{68} +(1.65858 - 5.10458i) q^{69} +(3.11740 + 0.687611i) q^{70} +(-7.42060 + 5.39138i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-2.73214 - 0.580733i) q^{73} +(4.33319 + 4.81250i) q^{74} +(-0.370464 + 3.52473i) q^{75} -0.0261866 q^{76} +(0.481094 + 8.76177i) q^{77} -4.20635 q^{78} +(-1.31340 + 12.4962i) q^{79} +(0.807365 + 0.896669i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-2.34391 - 1.04358i) q^{82} +(-1.92453 + 1.39825i) q^{83} +(-1.78535 + 1.95256i) q^{84} +(1.61661 - 4.97542i) q^{85} +(-0.105786 + 1.00649i) q^{86} +(-1.48608 + 2.57396i) q^{87} +(-1.77804 + 2.79975i) q^{88} +(1.52737 + 2.64548i) q^{89} +(0.976150 + 0.709214i) q^{90} +(-3.51997 + 10.5576i) q^{91} +(-1.65858 - 5.10458i) q^{92} +(-2.45698 - 1.09392i) q^{93} +(-1.19012 - 11.3233i) q^{94} +(0.0309060 + 0.00656927i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(-15.2431 - 11.0748i) q^{97} +(3.40677 + 6.11506i) q^{98} +(-1.15708 + 3.10824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} + 11 q^{7} + 6 q^{8} + 3 q^{9} + 10 q^{10} + 6 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{14} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 7 q^{19} - 10 q^{20} - 4 q^{21} + 2 q^{22} + 24 q^{23} + 3 q^{24} + 4 q^{25} + 4 q^{26} + 6 q^{27} + 14 q^{28} - 6 q^{29} - 7 q^{31} + 12 q^{32} - q^{33} - 24 q^{34} + 4 q^{35} - 6 q^{36} - q^{37} + 8 q^{38} - q^{39} + 16 q^{41} - 4 q^{42} + 52 q^{43} - 4 q^{44} - 10 q^{45} - 4 q^{46} + 27 q^{47} + 6 q^{48} - 33 q^{49} - 22 q^{50} - 8 q^{51} - 4 q^{52} + 13 q^{53} - 12 q^{54} + 30 q^{55} + 14 q^{56} - 16 q^{57} - 3 q^{58} + 14 q^{59} - 5 q^{60} + 9 q^{61} - 4 q^{62} + 5 q^{63} - 6 q^{64} - 50 q^{65} - 4 q^{66} - 20 q^{67} - 2 q^{68} - 32 q^{69} - 17 q^{70} - 18 q^{71} - 3 q^{72} + 7 q^{73} + q^{74} + 11 q^{75} - 4 q^{76} - 34 q^{77} - 12 q^{78} + q^{79} + 3 q^{81} - 2 q^{82} - 68 q^{83} - 5 q^{84} - 19 q^{86} - 8 q^{87} - q^{88} - 42 q^{89} + 10 q^{90} - 16 q^{91} + 32 q^{92} + 7 q^{93} + 8 q^{94} + 38 q^{95} + 3 q^{96} - 80 q^{97} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.104528 0.994522i 0.0739128 0.703233i
\(3\) −0.669131 0.743145i −0.386323 0.429055i
\(4\) −0.978148 0.207912i −0.489074 0.103956i
\(5\) 1.10227 + 0.490763i 0.492951 + 0.219476i 0.638129 0.769930i \(-0.279709\pi\)
−0.145178 + 0.989406i \(0.546375\pi\)
\(6\) −0.809017 + 0.587785i −0.330280 + 0.239962i
\(7\) 0.798293 + 2.52244i 0.301726 + 0.953395i
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) −0.104528 + 0.994522i −0.0348428 + 0.331507i
\(10\) 0.603294 1.04494i 0.190778 0.330438i
\(11\) 3.21216 + 0.825846i 0.968503 + 0.249002i
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 3.40301 + 2.47243i 0.943824 + 0.685728i 0.949338 0.314256i \(-0.101755\pi\)
−0.00551388 + 0.999985i \(0.501755\pi\)
\(14\) 2.59207 0.530253i 0.692760 0.141716i
\(15\) −0.372856 1.14753i −0.0962710 0.296292i
\(16\) 0.913545 + 0.406737i 0.228386 + 0.101684i
\(17\) −0.453210 4.31200i −0.109920 1.04581i −0.900916 0.433994i \(-0.857104\pi\)
0.790996 0.611821i \(-0.209563\pi\)
\(18\) 0.978148 + 0.207912i 0.230552 + 0.0490053i
\(19\) 0.0256144 0.00544450i 0.00587634 0.00124905i −0.204973 0.978768i \(-0.565711\pi\)
0.210849 + 0.977519i \(0.432377\pi\)
\(20\) −0.976150 0.709214i −0.218274 0.158585i
\(21\) 1.34038 2.28109i 0.292495 0.497775i
\(22\) 1.15708 3.10824i 0.246691 0.662679i
\(23\) 2.68364 + 4.64819i 0.559577 + 0.969215i 0.997532 + 0.0702183i \(0.0223696\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(24\) 0.913545 0.406737i 0.186477 0.0830248i
\(25\) −2.37150 2.63381i −0.474299 0.526763i
\(26\) 2.81460 3.12593i 0.551988 0.613044i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) −0.256403 2.63330i −0.0484555 0.497647i
\(29\) −0.918447 2.82669i −0.170551 0.524903i 0.828851 0.559469i \(-0.188995\pi\)
−0.999402 + 0.0345664i \(0.988995\pi\)
\(30\) −1.18022 + 0.250864i −0.215478 + 0.0458012i
\(31\) 2.45698 1.09392i 0.441286 0.196473i −0.174052 0.984736i \(-0.555686\pi\)
0.615338 + 0.788263i \(0.289019\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.53563 2.93970i −0.267319 0.511736i
\(34\) −4.33575 −0.743576
\(35\) −0.357987 + 3.17219i −0.0605108 + 0.536199i
\(36\) 0.309017 0.951057i 0.0515028 0.158509i
\(37\) −4.33319 + 4.81250i −0.712372 + 0.791169i −0.985294 0.170867i \(-0.945343\pi\)
0.272922 + 0.962036i \(0.412010\pi\)
\(38\) −0.00273725 0.0260432i −0.000444040 0.00422476i
\(39\) −0.439683 4.18331i −0.0704056 0.669865i
\(40\) −0.807365 + 0.896669i −0.127656 + 0.141776i
\(41\) 0.792855 2.44016i 0.123823 0.381088i −0.869862 0.493296i \(-0.835792\pi\)
0.993685 + 0.112207i \(0.0357921\pi\)
\(42\) −2.12849 1.57148i −0.328433 0.242484i
\(43\) −1.01203 −0.154334 −0.0771668 0.997018i \(-0.524587\pi\)
−0.0771668 + 0.997018i \(0.524587\pi\)
\(44\) −2.97026 1.47565i −0.447784 0.222462i
\(45\) −0.603294 + 1.04494i −0.0899337 + 0.155770i
\(46\) 4.90325 2.18307i 0.722944 0.321875i
\(47\) 11.1369 2.36721i 1.62448 0.345293i 0.696392 0.717662i \(-0.254788\pi\)
0.928085 + 0.372369i \(0.121454\pi\)
\(48\) −0.309017 0.951057i −0.0446028 0.137273i
\(49\) −5.72546 + 4.02730i −0.817922 + 0.575329i
\(50\) −2.86728 + 2.08320i −0.405494 + 0.294609i
\(51\) −2.90119 + 3.22209i −0.406247 + 0.451183i
\(52\) −2.81460 3.12593i −0.390314 0.433488i
\(53\) 10.7904 4.80419i 1.48217 0.659907i 0.503252 0.864140i \(-0.332137\pi\)
0.978922 + 0.204233i \(0.0654700\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 3.13538 + 2.48672i 0.422775 + 0.335309i
\(56\) −2.64567 0.0202566i −0.353543 0.00270690i
\(57\) −0.0211854 0.0153921i −0.00280608 0.00203873i
\(58\) −2.90721 + 0.617946i −0.381735 + 0.0811403i
\(59\) 2.09757 + 0.445852i 0.273080 + 0.0580450i 0.342416 0.939548i \(-0.388755\pi\)
−0.0693359 + 0.997593i \(0.522088\pi\)
\(60\) 0.126123 + 1.19998i 0.0162824 + 0.154916i
\(61\) −6.21390 2.76661i −0.795608 0.354228i −0.0316547 0.999499i \(-0.510078\pi\)
−0.763954 + 0.645271i \(0.776744\pi\)
\(62\) −0.831101 2.55786i −0.105550 0.324849i
\(63\) −2.59207 + 0.530253i −0.326570 + 0.0668055i
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 2.53766 + 4.39536i 0.314758 + 0.545178i
\(66\) −3.08411 + 1.21994i −0.379628 + 0.150164i
\(67\) −1.64058 + 2.84156i −0.200428 + 0.347152i −0.948667 0.316278i \(-0.897567\pi\)
0.748238 + 0.663430i \(0.230900\pi\)
\(68\) −0.453210 + 4.31200i −0.0549598 + 0.522907i
\(69\) 1.65858 5.10458i 0.199669 0.614519i
\(70\) 3.11740 + 0.687611i 0.372600 + 0.0821852i
\(71\) −7.42060 + 5.39138i −0.880663 + 0.639839i −0.933427 0.358768i \(-0.883197\pi\)
0.0527638 + 0.998607i \(0.483197\pi\)
\(72\) −0.913545 0.406737i −0.107662 0.0479344i
\(73\) −2.73214 0.580733i −0.319772 0.0679697i 0.0452292 0.998977i \(-0.485598\pi\)
−0.365001 + 0.931007i \(0.618932\pi\)
\(74\) 4.33319 + 4.81250i 0.503723 + 0.559441i
\(75\) −0.370464 + 3.52473i −0.0427775 + 0.407001i
\(76\) −0.0261866 −0.00300381
\(77\) 0.481094 + 8.76177i 0.0548257 + 0.998496i
\(78\) −4.20635 −0.476275
\(79\) −1.31340 + 12.4962i −0.147769 + 1.40593i 0.629618 + 0.776905i \(0.283211\pi\)
−0.777387 + 0.629023i \(0.783455\pi\)
\(80\) 0.807365 + 0.896669i 0.0902661 + 0.100251i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) −2.34391 1.04358i −0.258842 0.115244i
\(83\) −1.92453 + 1.39825i −0.211244 + 0.153478i −0.688377 0.725354i \(-0.741676\pi\)
0.477132 + 0.878832i \(0.341676\pi\)
\(84\) −1.78535 + 1.95256i −0.194798 + 0.213042i
\(85\) 1.61661 4.97542i 0.175346 0.539660i
\(86\) −0.105786 + 1.00649i −0.0114072 + 0.108532i
\(87\) −1.48608 + 2.57396i −0.159324 + 0.275958i
\(88\) −1.77804 + 2.79975i −0.189540 + 0.298454i
\(89\) 1.52737 + 2.64548i 0.161901 + 0.280421i 0.935550 0.353193i \(-0.114904\pi\)
−0.773649 + 0.633614i \(0.781571\pi\)
\(90\) 0.976150 + 0.709214i 0.102895 + 0.0747577i
\(91\) −3.51997 + 10.5576i −0.368993 + 1.10674i
\(92\) −1.65858 5.10458i −0.172919 0.532189i
\(93\) −2.45698 1.09392i −0.254777 0.113434i
\(94\) −1.19012 11.3233i −0.122752 1.16791i
\(95\) 0.0309060 + 0.00656927i 0.00317089 + 0.000673993i
\(96\) −0.978148 + 0.207912i −0.0998318 + 0.0212199i
\(97\) −15.2431 11.0748i −1.54770 1.12447i −0.945263 0.326310i \(-0.894195\pi\)
−0.602442 0.798163i \(-0.705805\pi\)
\(98\) 3.40677 + 6.11506i 0.344135 + 0.617714i
\(99\) −1.15708 + 3.10824i −0.116291 + 0.312390i
\(100\) 1.77207 + 3.06932i 0.177207 + 0.306932i
\(101\) 1.18784 0.528859i 0.118194 0.0526234i −0.346788 0.937944i \(-0.612728\pi\)
0.464982 + 0.885320i \(0.346061\pi\)
\(102\) 2.90119 + 3.22209i 0.287260 + 0.319035i
\(103\) 10.0355 11.1455i 0.988822 1.09820i −0.00634249 0.999980i \(-0.502019\pi\)
0.995165 0.0982186i \(-0.0313144\pi\)
\(104\) −3.40301 + 2.47243i −0.333692 + 0.242442i
\(105\) 2.59694 1.85658i 0.253435 0.181183i
\(106\) −3.64997 11.2335i −0.354517 1.09109i
\(107\) −4.51213 + 0.959083i −0.436204 + 0.0927181i −0.420779 0.907163i \(-0.638243\pi\)
−0.0154247 + 0.999881i \(0.504910\pi\)
\(108\) −0.913545 + 0.406737i −0.0879060 + 0.0391383i
\(109\) −8.39462 + 14.5399i −0.804059 + 1.39267i 0.112866 + 0.993610i \(0.463997\pi\)
−0.916925 + 0.399060i \(0.869337\pi\)
\(110\) 2.80083 2.85827i 0.267049 0.272526i
\(111\) 6.47585 0.614661
\(112\) −0.296694 + 2.62906i −0.0280349 + 0.248423i
\(113\) 3.48797 10.7349i 0.328121 1.00985i −0.641891 0.766796i \(-0.721850\pi\)
0.970012 0.243056i \(-0.0781500\pi\)
\(114\) −0.0175223 + 0.0194604i −0.00164111 + 0.00182264i
\(115\) 0.676935 + 6.44060i 0.0631245 + 0.600589i
\(116\) 0.310675 + 2.95587i 0.0288454 + 0.274446i
\(117\) −2.81460 + 3.12593i −0.260210 + 0.288992i
\(118\) 0.662666 2.03947i 0.0610033 0.187749i
\(119\) 10.5150 4.58544i 0.963908 0.420346i
\(120\) 1.20659 0.110146
\(121\) 9.63596 + 5.30550i 0.875996 + 0.482318i
\(122\) −3.40098 + 5.89067i −0.307910 + 0.533316i
\(123\) −2.34391 + 1.04358i −0.211343 + 0.0940962i
\(124\) −2.63073 + 0.559178i −0.236246 + 0.0502157i
\(125\) −3.18574 9.80469i −0.284941 0.876958i
\(126\) 0.256403 + 2.63330i 0.0228422 + 0.234593i
\(127\) −10.7947 + 7.84280i −0.957874 + 0.695936i −0.952656 0.304050i \(-0.901661\pi\)
−0.00521779 + 0.999986i \(0.501661\pi\)
\(128\) −0.669131 + 0.743145i −0.0591433 + 0.0656853i
\(129\) 0.677182 + 0.752087i 0.0596225 + 0.0662175i
\(130\) 4.63654 2.06432i 0.406652 0.181053i
\(131\) 0.441349 + 0.764438i 0.0385608 + 0.0667893i 0.884662 0.466233i \(-0.154389\pi\)
−0.846101 + 0.533023i \(0.821056\pi\)
\(132\) 0.890876 + 3.19474i 0.0775408 + 0.278066i
\(133\) 0.0341812 + 0.0602645i 0.00296389 + 0.00522560i
\(134\) 2.65451 + 1.92861i 0.229315 + 0.166607i
\(135\) 1.18022 0.250864i 0.101577 0.0215909i
\(136\) 4.24101 + 0.901454i 0.363663 + 0.0772990i
\(137\) 0.834115 + 7.93608i 0.0712633 + 0.678025i 0.970589 + 0.240745i \(0.0773916\pi\)
−0.899325 + 0.437280i \(0.855942\pi\)
\(138\) −4.90325 2.18307i −0.417392 0.185835i
\(139\) −2.68169 8.25340i −0.227458 0.700044i −0.998033 0.0626945i \(-0.980031\pi\)
0.770575 0.637350i \(-0.219969\pi\)
\(140\) 1.00970 3.02844i 0.0853353 0.255950i
\(141\) −9.21119 6.69232i −0.775722 0.563595i
\(142\) 4.58618 + 7.94350i 0.384864 + 0.666604i
\(143\) 8.88916 + 10.7522i 0.743349 + 0.899144i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 0.374856 3.56652i 0.0311301 0.296183i
\(146\) −0.863138 + 2.65647i −0.0714338 + 0.219851i
\(147\) 6.82395 + 1.56005i 0.562830 + 0.128671i
\(148\) 5.23907 3.80641i 0.430649 0.312885i
\(149\) −19.5695 8.71289i −1.60319 0.713788i −0.606503 0.795081i \(-0.707428\pi\)
−0.996690 + 0.0812934i \(0.974095\pi\)
\(150\) 3.46670 + 0.736870i 0.283055 + 0.0601651i
\(151\) 11.5573 + 12.8357i 0.940522 + 1.04456i 0.998929 + 0.0462623i \(0.0147310\pi\)
−0.0584077 + 0.998293i \(0.518602\pi\)
\(152\) −0.00273725 + 0.0260432i −0.000222020 + 0.00211238i
\(153\) 4.33575 0.350525
\(154\) 8.76406 + 0.437396i 0.706228 + 0.0352464i
\(155\) 3.24511 0.260654
\(156\) −0.439683 + 4.18331i −0.0352028 + 0.334932i
\(157\) −12.0851 13.4219i −0.964497 1.07118i −0.997424 0.0717252i \(-0.977150\pi\)
0.0329269 0.999458i \(-0.489517\pi\)
\(158\) 12.2904 + 2.61241i 0.977773 + 0.207832i
\(159\) −10.7904 4.80419i −0.855734 0.380997i
\(160\) 0.976150 0.709214i 0.0771714 0.0560683i
\(161\) −9.58248 + 10.4799i −0.755205 + 0.825935i
\(162\) −0.309017 + 0.951057i −0.0242787 + 0.0747221i
\(163\) 0.838067 7.97367i 0.0656424 0.624546i −0.911403 0.411515i \(-0.865000\pi\)
0.977045 0.213031i \(-0.0683336\pi\)
\(164\) −1.28287 + 2.22199i −0.100175 + 0.173508i
\(165\) −0.249988 3.99398i −0.0194615 0.310931i
\(166\) 1.18942 + 2.06014i 0.0923172 + 0.159898i
\(167\) −13.8324 10.0499i −1.07039 0.777682i −0.0944051 0.995534i \(-0.530095\pi\)
−0.975982 + 0.217852i \(0.930095\pi\)
\(168\) 1.75525 + 1.97967i 0.135420 + 0.152735i
\(169\) 1.45033 + 4.46365i 0.111564 + 0.343358i
\(170\) −4.77918 2.12783i −0.366547 0.163197i
\(171\) 0.00273725 + 0.0260432i 0.000209322 + 0.00199157i
\(172\) 0.989917 + 0.210413i 0.0754805 + 0.0160439i
\(173\) 5.07531 1.07879i 0.385869 0.0820189i −0.0108927 0.999941i \(-0.503467\pi\)
0.396761 + 0.917922i \(0.370134\pi\)
\(174\) 2.40452 + 1.74699i 0.182287 + 0.132439i
\(175\) 4.75050 8.08453i 0.359104 0.611133i
\(176\) 2.59855 + 2.06095i 0.195873 + 0.155350i
\(177\) −1.07222 1.85713i −0.0805926 0.139591i
\(178\) 2.79065 1.24248i 0.209168 0.0931275i
\(179\) −15.5444 17.2638i −1.16184 1.29036i −0.949715 0.313117i \(-0.898627\pi\)
−0.212129 0.977242i \(-0.568040\pi\)
\(180\) 0.807365 0.896669i 0.0601774 0.0668338i
\(181\) 14.0623 10.2169i 1.04524 0.759414i 0.0739416 0.997263i \(-0.476442\pi\)
0.971302 + 0.237848i \(0.0764421\pi\)
\(182\) 10.1318 + 4.60426i 0.751023 + 0.341290i
\(183\) 2.10192 + 6.46905i 0.155378 + 0.478206i
\(184\) −5.24998 + 1.11592i −0.387034 + 0.0822666i
\(185\) −7.13815 + 3.17811i −0.524807 + 0.233659i
\(186\) −1.34475 + 2.32917i −0.0986018 + 0.170783i
\(187\) 2.10527 14.2251i 0.153953 1.04024i
\(188\) −11.3857 −0.830384
\(189\) 2.12849 + 1.57148i 0.154825 + 0.114308i
\(190\) 0.00976383 0.0300500i 0.000708343 0.00218006i
\(191\) −8.60692 + 9.55895i −0.622775 + 0.691662i −0.969160 0.246431i \(-0.920742\pi\)
0.346386 + 0.938092i \(0.387409\pi\)
\(192\) 0.104528 + 0.994522i 0.00754369 + 0.0717734i
\(193\) −1.58884 15.1168i −0.114367 1.08813i −0.889690 0.456564i \(-0.849080\pi\)
0.775324 0.631564i \(-0.217587\pi\)
\(194\) −12.6074 + 14.0020i −0.905162 + 1.00528i
\(195\) 1.56836 4.82692i 0.112313 0.345663i
\(196\) 6.43766 2.74890i 0.459833 0.196350i
\(197\) 8.53605 0.608168 0.304084 0.952645i \(-0.401650\pi\)
0.304084 + 0.952645i \(0.401650\pi\)
\(198\) 2.97026 + 1.47565i 0.211087 + 0.104870i
\(199\) 0.659603 1.14247i 0.0467580 0.0809873i −0.841699 0.539947i \(-0.818444\pi\)
0.888457 + 0.458959i \(0.151778\pi\)
\(200\) 3.23774 1.44153i 0.228943 0.101932i
\(201\) 3.20945 0.682190i 0.226377 0.0481180i
\(202\) −0.401799 1.23661i −0.0282705 0.0870076i
\(203\) 6.39698 4.57326i 0.448980 0.320980i
\(204\) 3.50770 2.54849i 0.245588 0.178430i
\(205\) 2.07148 2.30061i 0.144679 0.160682i
\(206\) −10.0355 11.1455i −0.699203 0.776544i
\(207\) −4.90325 + 2.18307i −0.340799 + 0.151734i
\(208\) 2.10317 + 3.64280i 0.145829 + 0.252583i
\(209\) 0.0867738 + 0.00366492i 0.00600227 + 0.000253508i
\(210\) −1.57495 2.77678i −0.108682 0.191616i
\(211\) 0.823037 + 0.597971i 0.0566602 + 0.0411660i 0.615755 0.787938i \(-0.288851\pi\)
−0.559095 + 0.829104i \(0.688851\pi\)
\(212\) −11.5534 + 2.45576i −0.793494 + 0.168662i
\(213\) 8.97193 + 1.90704i 0.614746 + 0.130668i
\(214\) 0.482183 + 4.58766i 0.0329613 + 0.313606i
\(215\) −1.11554 0.496668i −0.0760789 0.0338725i
\(216\) 0.309017 + 0.951057i 0.0210259 + 0.0647112i
\(217\) 4.72073 + 5.32433i 0.320464 + 0.361439i
\(218\) 13.5828 + 9.86846i 0.919942 + 0.668377i
\(219\) 1.39659 + 2.41896i 0.0943726 + 0.163458i
\(220\) −2.54985 3.08426i −0.171911 0.207941i
\(221\) 9.11885 15.7943i 0.613400 1.06244i
\(222\) 0.676911 6.44038i 0.0454313 0.432250i
\(223\) −2.87037 + 8.83410i −0.192214 + 0.591575i 0.807783 + 0.589479i \(0.200667\pi\)
−0.999998 + 0.00209559i \(0.999333\pi\)
\(224\) 2.58365 + 0.569880i 0.172627 + 0.0380767i
\(225\) 2.86728 2.08320i 0.191152 0.138880i
\(226\) −10.3115 4.59096i −0.685909 0.305386i
\(227\) −7.84005 1.66645i −0.520362 0.110606i −0.0597596 0.998213i \(-0.519033\pi\)
−0.460603 + 0.887606i \(0.652367\pi\)
\(228\) 0.0175223 + 0.0194604i 0.00116044 + 0.00128880i
\(229\) 0.364279 3.46588i 0.0240722 0.229032i −0.975871 0.218349i \(-0.929933\pi\)
0.999943 0.0106827i \(-0.00340048\pi\)
\(230\) 6.47608 0.427020
\(231\) 6.18935 6.22029i 0.407229 0.409265i
\(232\) 2.97216 0.195132
\(233\) −0.456938 + 4.34748i −0.0299350 + 0.284813i 0.969306 + 0.245858i \(0.0790696\pi\)
−0.999241 + 0.0389550i \(0.987597\pi\)
\(234\) 2.81460 + 3.12593i 0.183996 + 0.204348i
\(235\) 13.4376 + 2.85625i 0.876571 + 0.186321i
\(236\) −1.95904 0.872219i −0.127522 0.0567766i
\(237\) 10.1653 7.38552i 0.660307 0.479741i
\(238\) −3.46120 10.9367i −0.224356 0.708921i
\(239\) −2.20457 + 6.78496i −0.142602 + 0.438882i −0.996695 0.0812375i \(-0.974113\pi\)
0.854093 + 0.520120i \(0.174113\pi\)
\(240\) 0.126123 1.19998i 0.00814119 0.0774582i
\(241\) −9.74338 + 16.8760i −0.627627 + 1.08708i 0.360400 + 0.932798i \(0.382640\pi\)
−0.988027 + 0.154283i \(0.950693\pi\)
\(242\) 6.28367 9.02859i 0.403930 0.580380i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 5.50290 + 3.99809i 0.352287 + 0.255952i
\(245\) −8.28746 + 1.62934i −0.529467 + 0.104095i
\(246\) 0.792855 + 2.44016i 0.0505506 + 0.155579i
\(247\) 0.100627 + 0.0448020i 0.00640274 + 0.00285068i
\(248\) 0.281129 + 2.67476i 0.0178517 + 0.169848i
\(249\) 2.32686 + 0.494590i 0.147459 + 0.0313434i
\(250\) −10.0840 + 2.14342i −0.637767 + 0.135562i
\(251\) −8.40038 6.10323i −0.530227 0.385233i 0.290215 0.956961i \(-0.406273\pi\)
−0.820443 + 0.571729i \(0.806273\pi\)
\(252\) 2.64567 + 0.0202566i 0.166662 + 0.00127604i
\(253\) 4.78158 + 17.1470i 0.300615 + 1.07802i
\(254\) 6.67148 + 11.5554i 0.418606 + 0.725047i
\(255\) −4.77918 + 2.12783i −0.299284 + 0.133250i
\(256\) 0.669131 + 0.743145i 0.0418207 + 0.0464466i
\(257\) 11.8557 13.1671i 0.739541 0.821343i −0.249595 0.968350i \(-0.580297\pi\)
0.989135 + 0.147007i \(0.0469641\pi\)
\(258\) 0.818752 0.594858i 0.0509732 0.0370342i
\(259\) −15.5984 7.08845i −0.969238 0.440455i
\(260\) −1.56836 4.82692i −0.0972657 0.299353i
\(261\) 2.90721 0.617946i 0.179952 0.0382499i
\(262\) 0.806384 0.359025i 0.0498186 0.0221807i
\(263\) 6.34072 10.9825i 0.390986 0.677207i −0.601594 0.798802i \(-0.705468\pi\)
0.992580 + 0.121595i \(0.0388009\pi\)
\(264\) 3.27036 0.552055i 0.201277 0.0339767i
\(265\) 14.2517 0.875473
\(266\) 0.0635073 0.0276946i 0.00389388 0.00169807i
\(267\) 0.943967 2.90523i 0.0577698 0.177797i
\(268\) 2.19552 2.43837i 0.134113 0.148947i
\(269\) −3.29384 31.3388i −0.200829 1.91076i −0.376676 0.926345i \(-0.622933\pi\)
0.175847 0.984418i \(-0.443734\pi\)
\(270\) −0.126123 1.19998i −0.00767558 0.0730283i
\(271\) 8.57997 9.52902i 0.521196 0.578847i −0.423871 0.905722i \(-0.639329\pi\)
0.945067 + 0.326876i \(0.105996\pi\)
\(272\) 1.33982 4.12355i 0.0812386 0.250027i
\(273\) 10.2012 4.44858i 0.617402 0.269240i
\(274\) 7.97979 0.482077
\(275\) −5.44250 10.4187i −0.328195 0.628273i
\(276\) −2.68364 + 4.64819i −0.161536 + 0.279788i
\(277\) 3.76791 1.67758i 0.226392 0.100796i −0.290406 0.956903i \(-0.593791\pi\)
0.516798 + 0.856107i \(0.327124\pi\)
\(278\) −8.48850 + 1.80429i −0.509107 + 0.108214i
\(279\) 0.831101 + 2.55786i 0.0497567 + 0.153135i
\(280\) −2.90631 1.32073i −0.173685 0.0789286i
\(281\) −9.60503 + 6.97846i −0.572988 + 0.416300i −0.836189 0.548441i \(-0.815222\pi\)
0.263201 + 0.964741i \(0.415222\pi\)
\(282\) −7.61849 + 8.46119i −0.453674 + 0.503857i
\(283\) 0.696585 + 0.773637i 0.0414077 + 0.0459879i 0.763493 0.645816i \(-0.223483\pi\)
−0.722085 + 0.691804i \(0.756816\pi\)
\(284\) 8.37937 3.73074i 0.497224 0.221378i
\(285\) −0.0157982 0.0273633i −0.000935805 0.00162086i
\(286\) 11.6225 7.71655i 0.687251 0.456289i
\(287\) 6.78809 + 0.0519729i 0.400688 + 0.00306786i
\(288\) 0.809017 + 0.587785i 0.0476718 + 0.0346356i
\(289\) −1.75946 + 0.373984i −0.103497 + 0.0219991i
\(290\) −3.50780 0.745606i −0.205985 0.0437835i
\(291\) 1.96948 + 18.7383i 0.115453 + 1.09846i
\(292\) 2.55169 + 1.13609i 0.149326 + 0.0664844i
\(293\) −0.353770 1.08879i −0.0206675 0.0636079i 0.940191 0.340648i \(-0.110646\pi\)
−0.960858 + 0.277040i \(0.910646\pi\)
\(294\) 2.26480 6.62349i 0.132086 0.386290i
\(295\) 2.09329 + 1.52086i 0.121876 + 0.0885480i
\(296\) −3.23793 5.60825i −0.188201 0.325973i
\(297\) 3.08411 1.21994i 0.178958 0.0707879i
\(298\) −10.7107 + 18.5515i −0.620456 + 1.07466i
\(299\) −2.35990 + 22.4529i −0.136476 + 1.29849i
\(300\) 1.09520 3.37068i 0.0632315 0.194607i
\(301\) −0.807899 2.55280i −0.0465665 0.147141i
\(302\) 13.9735 10.1523i 0.804082 0.584200i
\(303\) −1.18784 0.528859i −0.0682394 0.0303821i
\(304\) 0.0256144 + 0.00544450i 0.00146908 + 0.000312264i
\(305\) −5.49166 6.09911i −0.314452 0.349234i
\(306\) 0.453210 4.31200i 0.0259083 0.246501i
\(307\) −17.6325 −1.00634 −0.503171 0.864187i \(-0.667833\pi\)
−0.503171 + 0.864187i \(0.667833\pi\)
\(308\) 1.35109 8.67033i 0.0769857 0.494038i
\(309\) −14.9977 −0.853192
\(310\) 0.339207 3.22734i 0.0192657 0.183300i
\(311\) 16.4294 + 18.2467i 0.931625 + 1.03467i 0.999316 + 0.0369683i \(0.0117700\pi\)
−0.0676913 + 0.997706i \(0.521563\pi\)
\(312\) 4.11443 + 0.874549i 0.232934 + 0.0495116i
\(313\) 28.4235 + 12.6549i 1.60659 + 0.715300i 0.996999 0.0774166i \(-0.0246671\pi\)
0.609591 + 0.792716i \(0.291334\pi\)
\(314\) −14.6116 + 10.6159i −0.824580 + 0.599093i
\(315\) −3.11740 0.687611i −0.175645 0.0387425i
\(316\) 3.88280 11.9500i 0.218424 0.672241i
\(317\) 3.26400 31.0549i 0.183324 1.74421i −0.386358 0.922349i \(-0.626267\pi\)
0.569682 0.821865i \(-0.307066\pi\)
\(318\) −5.90578 + 10.2291i −0.331180 + 0.573620i
\(319\) −0.615788 9.83827i −0.0344775 0.550838i
\(320\) −0.603294 1.04494i −0.0337251 0.0584137i
\(321\) 3.73194 + 2.71142i 0.208297 + 0.151336i
\(322\) 9.42089 + 10.6254i 0.525006 + 0.592133i
\(323\) −0.0350854 0.107982i −0.00195220 0.00600826i
\(324\) 0.913545 + 0.406737i 0.0507525 + 0.0225965i
\(325\) −1.55830 14.8262i −0.0864390 0.822412i
\(326\) −7.84239 1.66695i −0.434350 0.0923239i
\(327\) 16.4223 3.49068i 0.908158 0.193035i
\(328\) 2.07572 + 1.50810i 0.114612 + 0.0832709i
\(329\) 14.8616 + 26.2024i 0.819348 + 1.44458i
\(330\) −3.99823 0.168867i −0.220095 0.00929580i
\(331\) 13.3437 + 23.1120i 0.733438 + 1.27035i 0.955405 + 0.295298i \(0.0954189\pi\)
−0.221967 + 0.975054i \(0.571248\pi\)
\(332\) 2.17319 0.967565i 0.119269 0.0531020i
\(333\) −4.33319 4.81250i −0.237457 0.263723i
\(334\) −11.4407 + 12.7062i −0.626007 + 0.695251i
\(335\) −3.20290 + 2.32704i −0.174993 + 0.127140i
\(336\) 2.15230 1.53870i 0.117418 0.0839430i
\(337\) −2.08198 6.40767i −0.113413 0.349048i 0.878200 0.478293i \(-0.158744\pi\)
−0.991613 + 0.129246i \(0.958744\pi\)
\(338\) 4.59080 0.975805i 0.249707 0.0530768i
\(339\) −10.3115 + 4.59096i −0.560042 + 0.249347i
\(340\) −2.61573 + 4.53058i −0.141858 + 0.245705i
\(341\) 8.79562 1.48475i 0.476309 0.0804038i
\(342\) 0.0261866 0.00141601
\(343\) −14.7292 11.2272i −0.795304 0.606211i
\(344\) 0.312735 0.962500i 0.0168616 0.0518945i
\(345\) 4.33334 4.81267i 0.233299 0.259105i
\(346\) −0.542366 5.16027i −0.0291578 0.277418i
\(347\) −2.99209 28.4678i −0.160624 1.52823i −0.716865 0.697212i \(-0.754423\pi\)
0.556241 0.831021i \(-0.312243\pi\)
\(348\) 1.98876 2.20874i 0.106609 0.118401i
\(349\) −9.68888 + 29.8193i −0.518634 + 1.59619i 0.257937 + 0.966162i \(0.416957\pi\)
−0.776571 + 0.630030i \(0.783043\pi\)
\(350\) −7.54368 5.56954i −0.403226 0.297705i
\(351\) 4.20635 0.224518
\(352\) 2.32128 2.36889i 0.123725 0.126262i
\(353\) −4.06857 + 7.04696i −0.216548 + 0.375072i −0.953750 0.300600i \(-0.902813\pi\)
0.737202 + 0.675672i \(0.236146\pi\)
\(354\) −1.95904 + 0.872219i −0.104122 + 0.0463579i
\(355\) −10.8254 + 2.30101i −0.574553 + 0.122125i
\(356\) −0.943967 2.90523i −0.0500302 0.153977i
\(357\) −10.4435 4.74591i −0.552731 0.251180i
\(358\) −18.7941 + 13.6547i −0.993298 + 0.721673i
\(359\) −15.5546 + 17.2751i −0.820938 + 0.911744i −0.997363 0.0725701i \(-0.976880\pi\)
0.176425 + 0.984314i \(0.443547\pi\)
\(360\) −0.807365 0.896669i −0.0425518 0.0472586i
\(361\) −17.3567 + 7.72772i −0.913512 + 0.406722i
\(362\) −8.69099 15.0532i −0.456788 0.791181i
\(363\) −2.50496 10.7110i −0.131476 0.562181i
\(364\) 5.63810 9.59507i 0.295517 0.502918i
\(365\) −2.72656 1.98096i −0.142714 0.103688i
\(366\) 6.65332 1.41421i 0.347775 0.0739218i
\(367\) 18.8806 + 4.01320i 0.985561 + 0.209487i 0.672380 0.740206i \(-0.265272\pi\)
0.313181 + 0.949694i \(0.398605\pi\)
\(368\) 0.561033 + 5.33787i 0.0292458 + 0.278256i
\(369\) 2.34391 + 1.04358i 0.122019 + 0.0543265i
\(370\) 2.41456 + 7.43125i 0.125527 + 0.386332i
\(371\) 20.7322 + 23.3830i 1.07636 + 1.21399i
\(372\) 2.17585 + 1.58085i 0.112813 + 0.0819631i
\(373\) −0.284157 0.492175i −0.0147131 0.0254838i 0.858575 0.512688i \(-0.171350\pi\)
−0.873288 + 0.487204i \(0.838017\pi\)
\(374\) −13.9271 3.58067i −0.720155 0.185152i
\(375\) −5.15463 + 8.92808i −0.266184 + 0.461044i
\(376\) −1.19012 + 11.3233i −0.0613760 + 0.583954i
\(377\) 3.86331 11.8900i 0.198970 0.612368i
\(378\) 1.78535 1.95256i 0.0918287 0.100429i
\(379\) 9.86864 7.16998i 0.506918 0.368297i −0.304735 0.952437i \(-0.598568\pi\)
0.811653 + 0.584140i \(0.198568\pi\)
\(380\) −0.0288648 0.0128514i −0.00148073 0.000659264i
\(381\) 13.0514 + 2.77416i 0.668643 + 0.142124i
\(382\) 8.60692 + 9.55895i 0.440368 + 0.489079i
\(383\) −3.48003 + 33.1102i −0.177821 + 1.69185i 0.434044 + 0.900892i \(0.357086\pi\)
−0.611865 + 0.790962i \(0.709580\pi\)
\(384\) 1.00000 0.0510310
\(385\) −3.76966 + 9.89396i −0.192120 + 0.504243i
\(386\) −15.2000 −0.773661
\(387\) 0.105786 1.00649i 0.00537742 0.0511627i
\(388\) 12.6074 + 14.0020i 0.640046 + 0.710843i
\(389\) −16.1811 3.43939i −0.820412 0.174384i −0.221461 0.975169i \(-0.571082\pi\)
−0.598951 + 0.800785i \(0.704416\pi\)
\(390\) −4.63654 2.06432i −0.234780 0.104531i
\(391\) 18.8268 13.6784i 0.952111 0.691749i
\(392\) −2.06093 6.68974i −0.104093 0.337883i
\(393\) 0.272768 0.839495i 0.0137593 0.0423469i
\(394\) 0.892260 8.48929i 0.0449514 0.427684i
\(395\) −7.58038 + 13.1296i −0.381410 + 0.660622i
\(396\) 1.77804 2.79975i 0.0893498 0.140693i
\(397\) 17.6628 + 30.5929i 0.886472 + 1.53542i 0.844017 + 0.536317i \(0.180185\pi\)
0.0424555 + 0.999098i \(0.486482\pi\)
\(398\) −1.06726 0.775410i −0.0534969 0.0388678i
\(399\) 0.0219136 0.0657264i 0.00109705 0.00329044i
\(400\) −1.09520 3.37068i −0.0547601 0.168534i
\(401\) −28.2495 12.5775i −1.41071 0.628089i −0.446878 0.894595i \(-0.647464\pi\)
−0.963833 + 0.266505i \(0.914131\pi\)
\(402\) −0.342974 3.26318i −0.0171060 0.162753i
\(403\) 11.0657 + 2.35210i 0.551224 + 0.117166i
\(404\) −1.27184 + 0.270337i −0.0632762 + 0.0134498i
\(405\) −0.976150 0.709214i −0.0485053 0.0352411i
\(406\) −3.87954 6.83997i −0.192538 0.339462i
\(407\) −17.8933 + 11.8800i −0.886937 + 0.588868i
\(408\) −2.16788 3.75487i −0.107326 0.185894i
\(409\) −28.8096 + 12.8269i −1.42454 + 0.634248i −0.966962 0.254919i \(-0.917951\pi\)
−0.457582 + 0.889167i \(0.651284\pi\)
\(410\) −2.07148 2.30061i −0.102303 0.113619i
\(411\) 5.33952 5.93014i 0.263379 0.292512i
\(412\) −12.1334 + 8.81545i −0.597771 + 0.434306i
\(413\) 0.549838 + 5.64693i 0.0270557 + 0.277867i
\(414\) 1.65858 + 5.10458i 0.0815147 + 0.250876i
\(415\) −2.80756 + 0.596766i −0.137818 + 0.0292941i
\(416\) 3.84269 1.71088i 0.188403 0.0838826i
\(417\) −4.33907 + 7.51549i −0.212485 + 0.368035i
\(418\) 0.0127152 0.0859153i 0.000621919 0.00420226i
\(419\) −21.1091 −1.03125 −0.515623 0.856816i \(-0.672439\pi\)
−0.515623 + 0.856816i \(0.672439\pi\)
\(420\) −2.92619 + 1.27607i −0.142784 + 0.0622659i
\(421\) −2.77136 + 8.52936i −0.135068 + 0.415696i −0.995601 0.0936992i \(-0.970131\pi\)
0.860533 + 0.509395i \(0.170131\pi\)
\(422\) 0.680726 0.756023i 0.0331372 0.0368026i
\(423\) 1.19012 + 11.3233i 0.0578659 + 0.550557i
\(424\) 1.23464 + 11.7469i 0.0599596 + 0.570478i
\(425\) −10.2822 + 11.4196i −0.498761 + 0.553931i
\(426\) 2.83442 8.72344i 0.137328 0.422652i
\(427\) 2.01810 17.8828i 0.0976627 0.865408i
\(428\) 4.61293 0.222975
\(429\) 2.04243 13.8006i 0.0986097 0.666297i
\(430\) −0.610553 + 1.05751i −0.0294435 + 0.0509976i
\(431\) −22.2341 + 9.89927i −1.07098 + 0.476831i −0.865024 0.501730i \(-0.832697\pi\)
−0.205956 + 0.978561i \(0.566030\pi\)
\(432\) 0.978148 0.207912i 0.0470611 0.0100032i
\(433\) −2.89353 8.90538i −0.139054 0.427965i 0.857144 0.515076i \(-0.172236\pi\)
−0.996199 + 0.0871113i \(0.972236\pi\)
\(434\) 5.78861 4.13833i 0.277862 0.198646i
\(435\) −2.90127 + 2.10790i −0.139105 + 0.101066i
\(436\) 11.2342 12.4768i 0.538020 0.597532i
\(437\) 0.0940467 + 0.104449i 0.00449886 + 0.00499649i
\(438\) 2.55169 1.13609i 0.121924 0.0542843i
\(439\) −20.0366 34.7044i −0.956294 1.65635i −0.731379 0.681971i \(-0.761123\pi\)
−0.224915 0.974378i \(-0.572210\pi\)
\(440\) −3.33390 + 2.21349i −0.158937 + 0.105524i
\(441\) −3.40677 6.11506i −0.162227 0.291193i
\(442\) −14.7546 10.7198i −0.701805 0.509891i
\(443\) 29.6323 6.29853i 1.40787 0.299252i 0.559578 0.828778i \(-0.310963\pi\)
0.848294 + 0.529525i \(0.177630\pi\)
\(444\) −6.33434 1.34641i −0.300614 0.0638976i
\(445\) 0.385272 + 3.66562i 0.0182637 + 0.173767i
\(446\) 8.48567 + 3.77806i 0.401808 + 0.178896i
\(447\) 6.61959 + 20.3730i 0.313096 + 0.963610i
\(448\) 0.836823 2.50993i 0.0395362 0.118583i
\(449\) 32.5829 + 23.6728i 1.53768 + 1.11719i 0.951769 + 0.306815i \(0.0992634\pi\)
0.585911 + 0.810375i \(0.300737\pi\)
\(450\) −1.77207 3.06932i −0.0835363 0.144689i
\(451\) 4.56197 7.18340i 0.214815 0.338253i
\(452\) −5.64366 + 9.77510i −0.265455 + 0.459782i
\(453\) 1.80543 17.1775i 0.0848266 0.807071i
\(454\) −2.47683 + 7.62291i −0.116244 + 0.357761i
\(455\) −9.06126 + 9.90990i −0.424798 + 0.464583i
\(456\) 0.0211854 0.0153921i 0.000992098 0.000720801i
\(457\) 22.8871 + 10.1900i 1.07061 + 0.476668i 0.864900 0.501944i \(-0.167382\pi\)
0.205714 + 0.978612i \(0.434048\pi\)
\(458\) −3.40882 0.724566i −0.159284 0.0338568i
\(459\) −2.90119 3.22209i −0.135416 0.150394i
\(460\) 0.676935 6.44060i 0.0315622 0.300295i
\(461\) −23.5803 −1.09824 −0.549122 0.835742i \(-0.685038\pi\)
−0.549122 + 0.835742i \(0.685038\pi\)
\(462\) −5.53925 6.80564i −0.257709 0.316627i
\(463\) 35.1779 1.63485 0.817427 0.576032i \(-0.195400\pi\)
0.817427 + 0.576032i \(0.195400\pi\)
\(464\) 0.310675 2.95587i 0.0144227 0.137223i
\(465\) −2.17141 2.41159i −0.100697 0.111835i
\(466\) 4.27590 + 0.908870i 0.198077 + 0.0421026i
\(467\) 20.6182 + 9.17980i 0.954095 + 0.424791i 0.823924 0.566701i \(-0.191781\pi\)
0.130172 + 0.991491i \(0.458447\pi\)
\(468\) 3.40301 2.47243i 0.157304 0.114288i
\(469\) −8.47735 1.86987i −0.391448 0.0863424i
\(470\) 4.24521 13.0654i 0.195817 0.602663i
\(471\) −1.88788 + 17.9620i −0.0869890 + 0.827645i
\(472\) −1.07222 + 1.85713i −0.0493527 + 0.0854814i
\(473\) −3.25081 0.835783i −0.149472 0.0384294i
\(474\) −6.28249 10.8816i −0.288565 0.499808i
\(475\) −0.0750842 0.0545519i −0.00344510 0.00250301i
\(476\) −11.2386 + 2.29904i −0.515120 + 0.105377i
\(477\) 3.64997 + 11.2335i 0.167121 + 0.514345i
\(478\) 6.51735 + 2.90171i 0.298097 + 0.132721i
\(479\) −2.77322 26.3854i −0.126712 1.20558i −0.854379 0.519650i \(-0.826062\pi\)
0.727668 0.685930i \(-0.240604\pi\)
\(480\) −1.18022 0.250864i −0.0538695 0.0114503i
\(481\) −26.6444 + 5.66345i −1.21488 + 0.258231i
\(482\) 15.7651 + 11.4540i 0.718082 + 0.521717i
\(483\) 14.2000 + 0.108722i 0.646124 + 0.00494704i
\(484\) −8.32231 7.19299i −0.378287 0.326954i
\(485\) −11.3670 19.6882i −0.516148 0.893994i
\(486\) 0.913545 0.406737i 0.0414393 0.0184499i
\(487\) −19.8675 22.0650i −0.900280 0.999863i −0.999988 0.00484598i \(-0.998457\pi\)
0.0997078 0.995017i \(-0.468209\pi\)
\(488\) 4.55140 5.05484i 0.206032 0.228822i
\(489\) −6.48637 + 4.71262i −0.293324 + 0.213112i
\(490\) 0.754137 + 8.41238i 0.0340684 + 0.380032i
\(491\) −0.895409 2.75579i −0.0404092 0.124367i 0.928817 0.370539i \(-0.120827\pi\)
−0.969226 + 0.246172i \(0.920827\pi\)
\(492\) 2.50966 0.533446i 0.113144 0.0240496i
\(493\) −11.7724 + 5.24143i −0.530204 + 0.236062i
\(494\) 0.0550750 0.0953927i 0.00247794 0.00429192i
\(495\) −2.80083 + 2.85827i −0.125888 + 0.128470i
\(496\) 2.68950 0.120762
\(497\) −19.5233 14.4141i −0.875738 0.646563i
\(498\) 0.735104 2.26242i 0.0329408 0.101381i
\(499\) −13.7194 + 15.2369i −0.614163 + 0.682097i −0.967347 0.253457i \(-0.918432\pi\)
0.353184 + 0.935554i \(0.385099\pi\)
\(500\) 1.07761 + 10.2528i 0.0481922 + 0.458518i
\(501\) 1.78721 + 17.0042i 0.0798467 + 0.759691i
\(502\) −6.94788 + 7.71640i −0.310099 + 0.344400i
\(503\) −6.14130 + 18.9010i −0.273827 + 0.842752i 0.715701 + 0.698407i \(0.246108\pi\)
−0.989527 + 0.144345i \(0.953892\pi\)
\(504\) 0.296694 2.62906i 0.0132158 0.117108i
\(505\) 1.56886 0.0698135
\(506\) 17.5529 2.96303i 0.780321 0.131723i
\(507\) 2.34668 4.06457i 0.104220 0.180514i
\(508\) 12.1894 5.42707i 0.540818 0.240787i
\(509\) −16.3200 + 3.46892i −0.723370 + 0.153757i −0.554861 0.831943i \(-0.687229\pi\)
−0.168509 + 0.985700i \(0.553895\pi\)
\(510\) 1.61661 + 4.97542i 0.0715848 + 0.220315i
\(511\) −0.716177 7.35526i −0.0316818 0.325377i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) 0.0175223 0.0194604i 0.000773627 0.000859199i
\(514\) −11.8557 13.1671i −0.522934 0.580777i
\(515\) 16.5316 7.36034i 0.728469 0.324335i
\(516\) −0.506016 0.876446i −0.0222761 0.0385834i
\(517\) 37.7283 + 1.59347i 1.65929 + 0.0700806i
\(518\) −8.68010 + 14.7720i −0.381382 + 0.649045i
\(519\) −4.19774 3.04984i −0.184260 0.133873i
\(520\) −4.96442 + 1.05522i −0.217704 + 0.0462744i
\(521\) 25.2086 + 5.35826i 1.10441 + 0.234750i 0.723816 0.689993i \(-0.242386\pi\)
0.380594 + 0.924742i \(0.375720\pi\)
\(522\) −0.310675 2.95587i −0.0135979 0.129375i
\(523\) −13.5873 6.04947i −0.594133 0.264525i 0.0875650 0.996159i \(-0.472091\pi\)
−0.681698 + 0.731634i \(0.738758\pi\)
\(524\) −0.272768 0.839495i −0.0119159 0.0366735i
\(525\) −9.18668 + 1.87929i −0.400940 + 0.0820191i
\(526\) −10.2595 7.45396i −0.447336 0.325008i
\(527\) −5.83050 10.0987i −0.253981 0.439907i
\(528\) −0.207186 3.31015i −0.00901660 0.144056i
\(529\) −2.90380 + 5.02952i −0.126252 + 0.218675i
\(530\) 1.48971 14.1736i 0.0647087 0.615662i
\(531\) −0.662666 + 2.03947i −0.0287572 + 0.0885057i
\(532\) −0.0209046 0.0660543i −0.000906329 0.00286382i
\(533\) 8.73120 6.34359i 0.378190 0.274771i
\(534\) −2.79065 1.24248i −0.120763 0.0537672i
\(535\) −5.44428 1.15722i −0.235377 0.0500309i
\(536\) −2.19552 2.43837i −0.0948321 0.105322i
\(537\) −2.42828 + 23.1035i −0.104788 + 0.996989i
\(538\) −31.5115 −1.35856
\(539\) −21.7170 + 8.20799i −0.935418 + 0.353543i
\(540\) −1.20659 −0.0519233
\(541\) 2.11417 20.1150i 0.0908955 0.864813i −0.850152 0.526538i \(-0.823490\pi\)
0.941047 0.338275i \(-0.109843\pi\)
\(542\) −8.57997 9.52902i −0.368541 0.409306i
\(543\) −17.0021 3.61392i −0.729632 0.155088i
\(544\) −3.96091 1.76351i −0.169823 0.0756099i
\(545\) −16.3888 + 11.9072i −0.702019 + 0.510047i
\(546\) −3.35790 10.6103i −0.143705 0.454078i
\(547\) −8.05689 + 24.7966i −0.344488 + 1.06022i 0.617370 + 0.786673i \(0.288198\pi\)
−0.961857 + 0.273551i \(0.911802\pi\)
\(548\) 0.834115 7.93608i 0.0356316 0.339012i
\(549\) 3.40098 5.89067i 0.145150 0.251408i
\(550\) −10.9305 + 4.32364i −0.466080 + 0.184360i
\(551\) −0.0389153 0.0674033i −0.00165785 0.00287148i
\(552\) 4.34221 + 3.15480i 0.184817 + 0.134277i
\(553\) −32.5693 + 6.66262i −1.38499 + 0.283323i
\(554\) −1.27454 3.92262i −0.0541499 0.166656i
\(555\) 7.13815 + 3.17811i 0.302998 + 0.134903i
\(556\) 0.907113 + 8.63060i 0.0384701 + 0.366019i
\(557\) 23.1286 + 4.91613i 0.979989 + 0.208303i 0.669938 0.742417i \(-0.266321\pi\)
0.310051 + 0.950720i \(0.399654\pi\)
\(558\) 2.63073 0.559178i 0.111368 0.0236719i
\(559\) −3.44395 2.50218i −0.145664 0.105831i
\(560\) −1.61729 + 2.75234i −0.0683428 + 0.116307i
\(561\) −11.9800 + 7.95395i −0.505797 + 0.335816i
\(562\) 5.93624 + 10.2819i 0.250405 + 0.433714i
\(563\) 7.22829 3.21824i 0.304636 0.135633i −0.248725 0.968574i \(-0.580012\pi\)
0.553361 + 0.832941i \(0.313345\pi\)
\(564\) 7.61849 + 8.46119i 0.320796 + 0.356280i
\(565\) 9.11298 10.1210i 0.383386 0.425793i
\(566\) 0.842212 0.611902i 0.0354008 0.0257202i
\(567\) −0.256403 2.63330i −0.0107679 0.110588i
\(568\) −2.83442 8.72344i −0.118929 0.366027i
\(569\) 34.3048 7.29171i 1.43813 0.305685i 0.578118 0.815953i \(-0.303787\pi\)
0.860015 + 0.510269i \(0.170454\pi\)
\(570\) −0.0288648 + 0.0128514i −0.00120901 + 0.000538287i
\(571\) 10.5372 18.2509i 0.440967 0.763777i −0.556795 0.830650i \(-0.687969\pi\)
0.997761 + 0.0668731i \(0.0213023\pi\)
\(572\) −6.45940 12.3654i −0.270081 0.517023i
\(573\) 12.8628 0.537353
\(574\) 0.761237 6.74547i 0.0317734 0.281551i
\(575\) 5.87824 18.0914i 0.245140 0.754462i
\(576\) 0.669131 0.743145i 0.0278804 0.0309644i
\(577\) 2.57820 + 24.5299i 0.107332 + 1.02119i 0.907109 + 0.420896i \(0.138284\pi\)
−0.799777 + 0.600297i \(0.795049\pi\)
\(578\) 0.188022 + 1.78891i 0.00782069 + 0.0744088i
\(579\) −10.1708 + 11.2958i −0.422684 + 0.469438i
\(580\) −1.10819 + 3.41065i −0.0460149 + 0.141619i
\(581\) −5.06335 3.73830i −0.210063 0.155091i
\(582\) 18.8415 0.781007
\(583\) 38.6280 6.52063i 1.59981 0.270057i
\(584\) 1.39659 2.41896i 0.0577912 0.100097i
\(585\) −4.63654 + 2.06432i −0.191697 + 0.0853492i
\(586\) −1.11981 + 0.238022i −0.0462588 + 0.00983261i
\(587\) −1.18255 3.63951i −0.0488090 0.150219i 0.923682 0.383161i \(-0.125165\pi\)
−0.972491 + 0.232943i \(0.925165\pi\)
\(588\) −6.35047 2.94474i −0.261889 0.121439i
\(589\) 0.0569781 0.0413970i 0.00234774 0.00170573i
\(590\) 1.73134 1.92285i 0.0712780 0.0791623i
\(591\) −5.71173 6.34352i −0.234949 0.260938i
\(592\) −5.91599 + 2.63397i −0.243146 + 0.108255i
\(593\) 12.8958 + 22.3362i 0.529567 + 0.917236i 0.999405 + 0.0344841i \(0.0109788\pi\)
−0.469839 + 0.882752i \(0.655688\pi\)
\(594\) −0.890876 3.19474i −0.0365531 0.131082i
\(595\) 13.8408 + 0.105971i 0.567416 + 0.00434441i
\(596\) 17.3303 + 12.5912i 0.709877 + 0.515756i
\(597\) −1.29038 + 0.274278i −0.0528117 + 0.0112255i
\(598\) 22.0833 + 4.69394i 0.903051 + 0.191949i
\(599\) −0.667250 6.34846i −0.0272631 0.259391i −0.999660 0.0260596i \(-0.991704\pi\)
0.972397 0.233331i \(-0.0749626\pi\)
\(600\) −3.23774 1.44153i −0.132180 0.0588504i
\(601\) 8.31679 + 25.5965i 0.339249 + 1.04410i 0.964591 + 0.263750i \(0.0849595\pi\)
−0.625342 + 0.780351i \(0.715040\pi\)
\(602\) −2.62326 + 0.536633i −0.106916 + 0.0218715i
\(603\) −2.65451 1.92861i −0.108100 0.0785393i
\(604\) −8.63607 14.9581i −0.351397 0.608637i
\(605\) 8.01770 + 10.5771i 0.325966 + 0.430020i
\(606\) −0.650124 + 1.12605i −0.0264095 + 0.0457426i
\(607\) 2.51687 23.9464i 0.102157 0.971956i −0.816619 0.577177i \(-0.804154\pi\)
0.918776 0.394779i \(-0.129179\pi\)
\(608\) 0.00809211 0.0249049i 0.000328178 0.00101003i
\(609\) −7.67900 1.69377i −0.311169 0.0686352i
\(610\) −6.63973 + 4.82405i −0.268835 + 0.195320i
\(611\) 43.7515 + 19.4794i 1.77000 + 0.788054i
\(612\) −4.24101 0.901454i −0.171433 0.0364391i
\(613\) −14.0582 15.6132i −0.567806 0.630612i 0.389036 0.921223i \(-0.372808\pi\)
−0.956841 + 0.290610i \(0.906142\pi\)
\(614\) −1.84310 + 17.5359i −0.0743815 + 0.707693i
\(615\) −3.09578 −0.124834
\(616\) −8.48160 2.24999i −0.341733 0.0906546i
\(617\) −8.04764 −0.323986 −0.161993 0.986792i \(-0.551792\pi\)
−0.161993 + 0.986792i \(0.551792\pi\)
\(618\) −1.56769 + 14.9156i −0.0630618 + 0.599993i
\(619\) 2.06251 + 2.29065i 0.0828991 + 0.0920688i 0.783167 0.621811i \(-0.213603\pi\)
−0.700268 + 0.713880i \(0.746936\pi\)
\(620\) −3.17420 0.674697i −0.127479 0.0270965i
\(621\) 4.90325 + 2.18307i 0.196760 + 0.0876034i
\(622\) 19.8641 14.4321i 0.796477 0.578674i
\(623\) −5.45380 + 5.96458i −0.218502 + 0.238966i
\(624\) 1.29983 4.00047i 0.0520350 0.160147i
\(625\) −0.552089 + 5.25278i −0.0220836 + 0.210111i
\(626\) 15.5567 26.9450i 0.621770 1.07694i
\(627\) −0.0553394 0.0669378i −0.00221004 0.00267324i
\(628\) 9.03046 + 15.6412i 0.360355 + 0.624153i
\(629\) 22.7153 + 16.5037i 0.905720 + 0.658044i
\(630\) −1.00970 + 3.02844i −0.0402274 + 0.120656i
\(631\) −4.90944 15.1097i −0.195442 0.601508i −0.999971 0.00759504i \(-0.997582\pi\)
0.804529 0.593913i \(-0.202418\pi\)
\(632\) −11.4787 5.11064i −0.456598 0.203290i
\(633\) −0.106340 1.01176i −0.00422663 0.0402137i
\(634\) −30.5436 6.49223i −1.21304 0.257839i
\(635\) −15.7476 + 3.34727i −0.624926 + 0.132832i
\(636\) 9.55575 + 6.94266i 0.378910 + 0.275294i
\(637\) −29.4410 0.450855i −1.16649 0.0178635i
\(638\) −9.84875 0.415965i −0.389916 0.0164682i
\(639\) −4.58618 7.94350i −0.181427 0.314240i
\(640\) −1.10227 + 0.490763i −0.0435711 + 0.0193991i
\(641\) 3.92178 + 4.35558i 0.154901 + 0.172035i 0.815600 0.578616i \(-0.196407\pi\)
−0.660699 + 0.750651i \(0.729740\pi\)
\(642\) 3.08666 3.42808i 0.121821 0.135295i
\(643\) 18.6602 13.5575i 0.735888 0.534654i −0.155532 0.987831i \(-0.549709\pi\)
0.891421 + 0.453177i \(0.149709\pi\)
\(644\) 11.5520 8.25862i 0.455212 0.325435i
\(645\) 0.377342 + 1.16134i 0.0148578 + 0.0457277i
\(646\) −0.111058 + 0.0236060i −0.00436950 + 0.000928766i
\(647\) −5.93111 + 2.64070i −0.233176 + 0.103817i −0.519999 0.854167i \(-0.674068\pi\)
0.286823 + 0.957984i \(0.407401\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 6.36953 + 3.16442i 0.250026 + 0.124214i
\(650\) −14.9079 −0.584737
\(651\) 0.797957 7.07086i 0.0312744 0.277129i
\(652\) −2.47757 + 7.62518i −0.0970292 + 0.298625i
\(653\) 27.9200 31.0083i 1.09259 1.21345i 0.117168 0.993112i \(-0.462618\pi\)
0.975424 0.220335i \(-0.0707151\pi\)
\(654\) −1.75495 16.6973i −0.0686241 0.652915i
\(655\) 0.111328 + 1.05922i 0.00434995 + 0.0413870i
\(656\) 1.71681 1.90671i 0.0670302 0.0744445i
\(657\) 0.863138 2.65647i 0.0336742 0.103639i
\(658\) 27.6123 12.0413i 1.07644 0.469420i
\(659\) 36.9193 1.43817 0.719086 0.694921i \(-0.244561\pi\)
0.719086 + 0.694921i \(0.244561\pi\)
\(660\) −0.585871 + 3.95868i −0.0228050 + 0.154091i
\(661\) 23.8818 41.3645i 0.928895 1.60889i 0.143721 0.989618i \(-0.454093\pi\)
0.785174 0.619275i \(-0.212574\pi\)
\(662\) 24.3802 10.8548i 0.947564 0.421883i
\(663\) −17.8392 + 3.79183i −0.692815 + 0.147262i
\(664\) −0.735104 2.26242i −0.0285276 0.0877989i
\(665\) 0.00810141 + 0.0832028i 0.000314159 + 0.00322647i
\(666\) −5.23907 + 3.80641i −0.203010 + 0.147495i
\(667\) 10.6742 11.8549i 0.413307 0.459024i
\(668\) 11.4407 + 12.7062i 0.442654 + 0.491617i
\(669\) 8.48567 3.77806i 0.328075 0.146068i
\(670\) 1.97950 + 3.42859i 0.0764748 + 0.132458i
\(671\) −17.6753 14.0185i −0.682346 0.541179i
\(672\) −1.30529 2.30135i −0.0503528 0.0887765i
\(673\) 12.0226 + 8.73491i 0.463436 + 0.336706i 0.794878 0.606770i \(-0.207535\pi\)
−0.331442 + 0.943476i \(0.607535\pi\)
\(674\) −6.59019 + 1.40079i −0.253845 + 0.0539563i
\(675\) −3.46670 0.736870i −0.133433 0.0283621i
\(676\) −0.490590 4.66765i −0.0188688 0.179525i
\(677\) 15.1081 + 6.72657i 0.580653 + 0.258523i 0.675977 0.736923i \(-0.263722\pi\)
−0.0953239 + 0.995446i \(0.530389\pi\)
\(678\) 3.48797 + 10.7349i 0.133955 + 0.412270i
\(679\) 15.7670 47.2909i 0.605083 1.81486i
\(680\) 4.23235 + 3.07498i 0.162303 + 0.117920i
\(681\) 4.00760 + 6.94137i 0.153572 + 0.265994i
\(682\) −0.557225 8.90263i −0.0213373 0.340899i
\(683\) 7.88153 13.6512i 0.301578 0.522349i −0.674915 0.737895i \(-0.735820\pi\)
0.976494 + 0.215546i \(0.0691532\pi\)
\(684\) 0.00273725 0.0260432i 0.000104661 0.000995785i
\(685\) −2.97531 + 9.15707i −0.113681 + 0.349874i
\(686\) −12.7053 + 13.4750i −0.485091 + 0.514477i
\(687\) −2.81940 + 2.04842i −0.107567 + 0.0781519i
\(688\) −0.924538 0.411631i −0.0352477 0.0156933i
\(689\) 48.5978 + 10.3298i 1.85143 + 0.393533i
\(690\) −4.33334 4.81267i −0.164968 0.183215i
\(691\) −1.46763 + 13.9636i −0.0558313 + 0.531199i 0.930484 + 0.366331i \(0.119386\pi\)
−0.986316 + 0.164868i \(0.947280\pi\)
\(692\) −5.18870 −0.197245
\(693\) −8.76406 0.437396i −0.332919 0.0166153i
\(694\) −28.6246 −1.08658
\(695\) 1.09451 10.4136i 0.0415172 0.395009i
\(696\) −1.98876 2.20874i −0.0753838 0.0837222i
\(697\) −10.8813 2.31289i −0.412158 0.0876069i
\(698\) 28.6432 + 12.7528i 1.08416 + 0.482700i
\(699\) 3.53656 2.56946i 0.133765 0.0971858i
\(700\) −6.32756 + 6.92018i −0.239159 + 0.261558i
\(701\) 3.35575 10.3279i 0.126745 0.390081i −0.867470 0.497489i \(-0.834255\pi\)
0.994215 + 0.107409i \(0.0342554\pi\)
\(702\) 0.439683 4.18331i 0.0165948 0.157889i
\(703\) −0.0847903 + 0.146861i −0.00319793 + 0.00553897i
\(704\) −2.11327 2.55618i −0.0796470 0.0963398i
\(705\) −6.86889 11.8973i −0.258698 0.448077i
\(706\) 6.58308 + 4.78289i 0.247757 + 0.180006i
\(707\) 2.28226 + 2.57407i 0.0858332 + 0.0968078i
\(708\) 0.662666 + 2.03947i 0.0249045 + 0.0766482i
\(709\) −33.3496 14.8482i −1.25247 0.557635i −0.330101 0.943946i \(-0.607083\pi\)
−0.922369 + 0.386310i \(0.873749\pi\)
\(710\) 1.15684 + 11.0066i 0.0434156 + 0.413072i
\(711\) −12.2904 2.61241i −0.460927 0.0979730i
\(712\) −2.98799 + 0.635116i −0.111980 + 0.0238020i
\(713\) 11.6784 + 8.48483i 0.437358 + 0.317760i
\(714\) −5.81156 + 9.89026i −0.217492 + 0.370134i
\(715\) 4.52149 + 16.2143i 0.169094 + 0.606382i
\(716\) 11.6154 + 20.1184i 0.434087 + 0.751861i
\(717\) 6.51735 2.90171i 0.243395 0.108366i
\(718\) 15.5546 + 17.2751i 0.580491 + 0.644700i
\(719\) −12.1083 + 13.4476i −0.451564 + 0.501512i −0.925343 0.379131i \(-0.876223\pi\)
0.473779 + 0.880644i \(0.342890\pi\)
\(720\) −0.976150 + 0.709214i −0.0363790 + 0.0264309i
\(721\) 36.1251 + 16.4165i 1.34537 + 0.611382i
\(722\) 5.87111 + 18.0694i 0.218500 + 0.672474i
\(723\) 19.0609 4.05153i 0.708884 0.150678i
\(724\) −15.8792 + 7.06989i −0.590147 + 0.262750i
\(725\) −5.26688 + 9.12250i −0.195607 + 0.338801i
\(726\) −10.9141 + 1.37163i −0.405062 + 0.0509060i
\(727\) 27.5893 1.02323 0.511615 0.859215i \(-0.329048\pi\)
0.511615 + 0.859215i \(0.329048\pi\)
\(728\) −8.95316 6.61017i −0.331826 0.244989i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −2.25511 + 2.50455i −0.0834653 + 0.0926976i
\(731\) 0.458663 + 4.36389i 0.0169643 + 0.161404i
\(732\) −0.710998 6.76470i −0.0262793 0.250030i
\(733\) 23.6009 26.2114i 0.871718 0.968141i −0.128003 0.991774i \(-0.540857\pi\)
0.999721 + 0.0236331i \(0.00752335\pi\)
\(734\) 5.96478 18.3577i 0.220164 0.677595i
\(735\) 6.75623 + 5.06855i 0.249207 + 0.186956i
\(736\) 5.36727 0.197840
\(737\) −7.61649 + 7.77269i −0.280557 + 0.286311i
\(738\) 1.28287 2.22199i 0.0472229 0.0817925i
\(739\) 9.88311 4.40024i 0.363556 0.161866i −0.216825 0.976210i \(-0.569570\pi\)
0.580381 + 0.814345i \(0.302904\pi\)
\(740\) 7.64293 1.62456i 0.280960 0.0597199i
\(741\) −0.0340382 0.104759i −0.00125042 0.00384841i
\(742\) 25.4220 18.1744i 0.933272 0.667205i
\(743\) −2.25197 + 1.63615i −0.0826168 + 0.0600246i −0.628327 0.777949i \(-0.716260\pi\)
0.545710 + 0.837974i \(0.316260\pi\)
\(744\) 1.79963 1.99869i 0.0659775 0.0732754i
\(745\) −17.2949 19.2080i −0.633637 0.703725i
\(746\) −0.519181 + 0.231154i −0.0190086 + 0.00846316i
\(747\) −1.18942 2.06014i −0.0435187 0.0753767i
\(748\) −5.01683 + 13.4766i −0.183434 + 0.492752i
\(749\) −6.02124 10.6160i −0.220011 0.387899i
\(750\) 8.34037 + 6.05963i 0.304547 + 0.221266i
\(751\) −0.593477 + 0.126148i −0.0216563 + 0.00460319i −0.218727 0.975786i \(-0.570190\pi\)
0.197071 + 0.980389i \(0.436857\pi\)
\(752\) 11.1369 + 2.36721i 0.406119 + 0.0863233i
\(753\) 1.08537 + 10.3266i 0.0395529 + 0.376321i
\(754\) −11.4211 5.08499i −0.415931 0.185184i
\(755\) 6.44002 + 19.8204i 0.234376 + 0.721337i
\(756\) −1.75525 1.97967i −0.0638377 0.0720000i
\(757\) −10.5666 7.67711i −0.384051 0.279029i 0.378962 0.925412i \(-0.376281\pi\)
−0.763013 + 0.646383i \(0.776281\pi\)
\(758\) −6.09915 10.5640i −0.221531 0.383703i
\(759\) 9.54322 15.0270i 0.346397 0.545445i
\(760\) −0.0157982 + 0.0273633i −0.000573061 + 0.000992572i
\(761\) 0.0854314 0.812825i 0.00309688 0.0294649i −0.992864 0.119249i \(-0.961951\pi\)
0.995961 + 0.0897846i \(0.0286178\pi\)
\(762\) 4.12320 12.6899i 0.149368 0.459707i
\(763\) −43.3775 9.56786i −1.57037 0.346380i
\(764\) 10.4063 7.56059i 0.376485 0.273532i
\(765\) 4.77918 + 2.12783i 0.172792 + 0.0769318i
\(766\) 32.5651 + 6.92192i 1.17662 + 0.250099i
\(767\) 6.03571 + 6.70333i 0.217937 + 0.242043i
\(768\) 0.104528 0.994522i 0.00377185 0.0358867i
\(769\) 25.6336 0.924372 0.462186 0.886783i \(-0.347065\pi\)
0.462186 + 0.886783i \(0.347065\pi\)
\(770\) 9.44572 + 4.78321i 0.340400 + 0.172375i
\(771\) −17.7181 −0.638103
\(772\) −1.58884 + 15.1168i −0.0571835 + 0.544064i
\(773\) 13.8460 + 15.3776i 0.498007 + 0.553092i 0.938776 0.344528i \(-0.111961\pi\)
−0.440769 + 0.897620i \(0.645294\pi\)
\(774\) −0.989917 0.210413i −0.0355818 0.00756315i
\(775\) −8.70789 3.87700i −0.312797 0.139266i
\(776\) 15.2431 11.0748i 0.547196 0.397561i
\(777\) 5.16963 + 16.3350i 0.185459 + 0.586014i
\(778\) −5.11193 + 15.7329i −0.183272 + 0.564052i
\(779\) 0.00702304 0.0668197i 0.000251626 0.00239407i
\(780\) −2.53766 + 4.39536i −0.0908629 + 0.157379i
\(781\) −28.2886 + 11.1897i −1.01225 + 0.400399i
\(782\) −11.6356 20.1534i −0.416088 0.720685i
\(783\) −2.40452 1.74699i −0.0859307 0.0624323i
\(784\) −6.86852 + 1.35037i −0.245304 + 0.0482275i
\(785\) −6.73413 20.7255i −0.240351 0.739725i
\(786\) −0.806384 0.359025i −0.0287628 0.0128060i
\(787\) −1.56199 14.8613i −0.0556789 0.529750i −0.986440 0.164122i \(-0.947521\pi\)
0.930761 0.365628i \(-0.119146\pi\)
\(788\) −8.34952 1.77474i −0.297439 0.0632226i
\(789\) −12.4043 + 2.63662i −0.441606 + 0.0938662i
\(790\) 12.2653 + 8.91127i 0.436380 + 0.317049i
\(791\) 29.8626 + 0.228642i 1.06179 + 0.00812958i
\(792\) −2.59855 2.06095i −0.0923356 0.0732327i
\(793\) −14.3057 24.7782i −0.508010 0.879900i
\(794\) 32.2716 14.3682i 1.14528 0.509910i
\(795\) −9.53623 10.5911i −0.338215 0.375626i
\(796\) −0.882721 + 0.980361i −0.0312872 + 0.0347480i
\(797\) −24.9813 + 18.1500i −0.884884 + 0.642906i −0.934539 0.355861i \(-0.884188\pi\)
0.0496553 + 0.998766i \(0.484188\pi\)
\(798\) −0.0630758 0.0286638i −0.00223286 0.00101469i
\(799\) −15.2547 46.9493i −0.539674 1.66095i
\(800\) −3.46670 + 0.736870i −0.122566 + 0.0260523i
\(801\) −2.79065 + 1.24248i −0.0986026 + 0.0439007i
\(802\) −15.4615 + 26.7800i −0.545963 + 0.945636i
\(803\) −8.29646 4.12173i −0.292776 0.145453i
\(804\) −3.28116 −0.115717
\(805\) −15.7057 + 6.84902i −0.553552 + 0.241396i
\(806\) 3.49590 10.7593i 0.123138 0.378979i
\(807\) −21.0853 + 23.4176i −0.742237 + 0.824338i
\(808\) 0.135913 + 1.29313i 0.00478140 + 0.0454920i
\(809\) 3.42010 + 32.5401i 0.120244 + 1.14405i 0.873671 + 0.486516i \(0.161733\pi\)
−0.753427 + 0.657531i \(0.771601\pi\)
\(810\) −0.807365 + 0.896669i −0.0283679 + 0.0315057i
\(811\) −7.47886 + 23.0175i −0.262618 + 0.808255i 0.729614 + 0.683859i \(0.239700\pi\)
−0.992233 + 0.124397i \(0.960300\pi\)
\(812\) −7.20802 + 3.14331i −0.252952 + 0.110309i
\(813\) −12.8226 −0.449707
\(814\) 9.94452 + 19.0371i 0.348555 + 0.667249i
\(815\) 4.83696 8.37787i 0.169431 0.293464i
\(816\) −3.96091 + 1.76351i −0.138660 + 0.0617352i
\(817\) −0.0259226 + 0.00551001i −0.000906916 + 0.000192771i
\(818\) 9.74518 + 29.9926i 0.340732 + 1.04867i
\(819\) −10.1318 4.60426i −0.354035 0.160886i
\(820\) −2.50454 + 1.81965i −0.0874623 + 0.0635451i
\(821\) −2.43768 + 2.70732i −0.0850756 + 0.0944860i −0.784179 0.620534i \(-0.786916\pi\)
0.699104 + 0.715020i \(0.253583\pi\)
\(822\) −5.33952 5.93014i −0.186237 0.206837i
\(823\) −3.12005 + 1.38914i −0.108758 + 0.0484223i −0.460395 0.887714i \(-0.652292\pi\)
0.351636 + 0.936137i \(0.385625\pi\)
\(824\) 7.49887 + 12.9884i 0.261236 + 0.452473i
\(825\) −4.10088 + 11.0161i −0.142774 + 0.383530i
\(826\) 5.67346 + 0.0434388i 0.197405 + 0.00151143i
\(827\) −23.5604 17.1177i −0.819277 0.595240i 0.0972283 0.995262i \(-0.469002\pi\)
−0.916505 + 0.400023i \(0.869002\pi\)
\(828\) 5.24998 1.11592i 0.182450 0.0387808i
\(829\) 26.6380 + 5.66207i 0.925174 + 0.196652i 0.645779 0.763524i \(-0.276533\pi\)
0.279395 + 0.960176i \(0.409866\pi\)
\(830\) 0.300027 + 2.85456i 0.0104141 + 0.0990834i
\(831\) −3.76791 1.67758i −0.130707 0.0581946i
\(832\) −1.29983 4.00047i −0.0450636 0.138692i
\(833\) 19.9606 + 22.8630i 0.691592 + 0.792155i
\(834\) 7.02076 + 5.10088i 0.243109 + 0.176629i
\(835\) −10.3150 17.8661i −0.356966 0.618283i
\(836\) −0.0841156 0.0216261i −0.00290920 0.000747955i
\(837\) 1.34475 2.32917i 0.0464813 0.0805080i
\(838\) −2.20650 + 20.9934i −0.0762222 + 0.725206i
\(839\) −2.96969 + 9.13976i −0.102525 + 0.315539i −0.989142 0.146966i \(-0.953049\pi\)
0.886617 + 0.462505i \(0.153049\pi\)
\(840\) 0.963210 + 3.04355i 0.0332339 + 0.105012i
\(841\) 16.3149 11.8534i 0.562582 0.408740i
\(842\) 8.19295 + 3.64774i 0.282348 + 0.125709i
\(843\) 11.6130 + 2.46843i 0.399974 + 0.0850171i
\(844\) −0.680726 0.756023i −0.0234316 0.0260234i
\(845\) −0.591940 + 5.63193i −0.0203633 + 0.193744i
\(846\) 11.3857 0.391447
\(847\) −5.69052 + 28.5415i −0.195529 + 0.980698i
\(848\) 11.8116 0.405611
\(849\) 0.108817 1.03533i 0.00373460 0.0355324i
\(850\) 10.2822 + 11.4196i 0.352678 + 0.391688i
\(851\) −33.9981 7.22652i −1.16544 0.247722i
\(852\) −8.37937 3.73074i −0.287073 0.127813i
\(853\) −22.4392 + 16.3030i −0.768304 + 0.558206i −0.901446 0.432891i \(-0.857493\pi\)
0.133142 + 0.991097i \(0.457493\pi\)
\(854\) −17.5739 3.87630i −0.601365 0.132644i
\(855\) −0.00976383 + 0.0300500i −0.000333916 + 0.00102769i
\(856\) 0.482183 4.58766i 0.0164807 0.156803i
\(857\) 1.90716 3.30330i 0.0651473 0.112838i −0.831612 0.555357i \(-0.812582\pi\)
0.896759 + 0.442519i \(0.145915\pi\)
\(858\) −13.5115 3.47380i −0.461274 0.118593i
\(859\) −20.6868 35.8305i −0.705823 1.22252i −0.966394 0.257066i \(-0.917244\pi\)
0.260571 0.965455i \(-0.416089\pi\)
\(860\) 0.987895 + 0.717748i 0.0336870 + 0.0244750i
\(861\) −4.50349 5.07931i −0.153479 0.173102i
\(862\) 7.52094 + 23.1471i 0.256164 + 0.788393i
\(863\) −1.31085 0.583628i −0.0446218 0.0198669i 0.384304 0.923206i \(-0.374441\pi\)
−0.428926 + 0.903340i \(0.641108\pi\)
\(864\) −0.104528 0.994522i −0.00355613 0.0338343i
\(865\) 6.12381 + 1.30166i 0.208216 + 0.0442576i
\(866\) −9.15905 + 1.94682i −0.311237 + 0.0661555i
\(867\) 1.45523 + 1.05729i 0.0494222 + 0.0359073i
\(868\) −3.51059 6.18947i −0.119157 0.210084i
\(869\) −14.5388 + 39.0550i −0.493193 + 1.32485i
\(870\) 1.79308 + 3.10571i 0.0607912 + 0.105293i
\(871\) −12.6085 + 5.61365i −0.427221 + 0.190211i
\(872\) −11.2342 12.4768i −0.380438 0.422519i
\(873\) 12.6074 14.0020i 0.426697 0.473896i
\(874\) 0.113708 0.0826136i 0.00384622 0.00279445i
\(875\) 22.1886 15.8629i 0.750113 0.536263i
\(876\) −0.863138 2.65647i −0.0291627 0.0897536i
\(877\) −39.8645 + 8.47346i −1.34613 + 0.286129i −0.823928 0.566694i \(-0.808222\pi\)
−0.522201 + 0.852823i \(0.674889\pi\)
\(878\) −36.6087 + 16.2992i −1.23548 + 0.550072i
\(879\) −0.572412 + 0.991447i −0.0193070 + 0.0334407i
\(880\) 1.85287 + 3.54700i 0.0624604 + 0.119570i
\(881\) 0.869111 0.0292811 0.0146406 0.999893i \(-0.495340\pi\)
0.0146406 + 0.999893i \(0.495340\pi\)
\(882\) −6.43766 + 2.74890i −0.216767 + 0.0925604i
\(883\) −8.53212 + 26.2592i −0.287129 + 0.883691i 0.698624 + 0.715489i \(0.253796\pi\)
−0.985753 + 0.168202i \(0.946204\pi\)
\(884\) −12.2034 + 13.5532i −0.410445 + 0.455845i
\(885\) −0.270461 2.57327i −0.00909146 0.0864995i
\(886\) −3.16661 30.1283i −0.106384 1.01218i
\(887\) 27.8363 30.9153i 0.934651 1.03803i −0.0645441 0.997915i \(-0.520559\pi\)
0.999195 0.0401200i \(-0.0127740\pi\)
\(888\) −2.00115 + 6.15890i −0.0671541 + 0.206679i
\(889\) −28.4004 20.9682i −0.952517 0.703249i
\(890\) 3.68581 0.123549
\(891\) −2.97026 1.47565i −0.0995076 0.0494360i
\(892\) 4.64436 8.04427i 0.155505 0.269342i
\(893\) 0.272375 0.121269i 0.00911468 0.00405812i
\(894\) 20.9533 4.45377i 0.700785 0.148956i
\(895\) −8.66173 26.6581i −0.289530 0.891081i
\(896\) −2.40870 1.09460i −0.0804692 0.0365679i
\(897\) 18.2649 13.2702i 0.609846 0.443079i
\(898\) 26.9490 29.9299i 0.899300 0.998773i
\(899\) −5.34877 5.94041i −0.178391 0.198124i
\(900\) −3.23774 + 1.44153i −0.107925 + 0.0480511i
\(901\) −25.6060 44.3509i −0.853060 1.47754i
\(902\) −6.66719 5.28785i −0.221993 0.176066i
\(903\) −1.35651 + 2.30854i −0.0451418 + 0.0768234i
\(904\) 9.13163 + 6.63452i 0.303713 + 0.220661i
\(905\) 20.5146 4.36051i 0.681927 0.144948i
\(906\) −16.8947 3.59108i −0.561289 0.119306i
\(907\) 2.55643 + 24.3228i 0.0848848 + 0.807624i 0.951293 + 0.308288i \(0.0997561\pi\)
−0.866408 + 0.499336i \(0.833577\pi\)
\(908\) 7.32225 + 3.26008i 0.242997 + 0.108189i
\(909\) 0.401799 + 1.23661i 0.0133268 + 0.0410158i
\(910\) 8.90846 + 10.0475i 0.295312 + 0.333071i
\(911\) −19.5111 14.1757i −0.646432 0.469661i 0.215622 0.976477i \(-0.430822\pi\)
−0.862054 + 0.506816i \(0.830822\pi\)
\(912\) −0.0130933 0.0226783i −0.000433563 0.000750952i
\(913\) −7.33664 + 2.90204i −0.242807 + 0.0960437i
\(914\) 12.5265 21.6966i 0.414341 0.717659i
\(915\) −0.857882 + 8.16220i −0.0283607 + 0.269834i
\(916\) −1.07692 + 3.31441i −0.0355823 + 0.109511i
\(917\) −1.57593 + 1.72352i −0.0520417 + 0.0569158i
\(918\) −3.50770 + 2.54849i −0.115771 + 0.0841128i
\(919\) 24.0012 + 10.6860i 0.791727 + 0.352500i 0.762430 0.647071i \(-0.224006\pi\)
0.0292976 + 0.999571i \(0.490673\pi\)
\(920\) −6.33456 1.34645i −0.208844 0.0443912i
\(921\) 11.7985 + 13.1035i 0.388773 + 0.431776i
\(922\) −2.46481 + 23.4511i −0.0811743 + 0.772322i
\(923\) −38.5822 −1.26995
\(924\) −7.34737 + 4.79752i −0.241711 + 0.157827i
\(925\) 22.9514 0.754636
\(926\) 3.67709 34.9852i 0.120837 1.14968i
\(927\) 10.0355 + 11.1455i 0.329607 + 0.366066i
\(928\) −2.90721 0.617946i −0.0954338 0.0202851i
\(929\) −24.2426 10.7935i −0.795374 0.354123i −0.0315123 0.999503i \(-0.510032\pi\)
−0.763862 + 0.645380i \(0.776699\pi\)
\(930\) −2.62535 + 1.90743i −0.0860887 + 0.0625471i
\(931\) −0.124727 + 0.134329i −0.00408777 + 0.00440245i
\(932\) 1.35084 4.15747i 0.0442484 0.136182i
\(933\) 2.56652 24.4188i 0.0840242 0.799437i
\(934\) 11.2847 19.5457i 0.369247 0.639554i
\(935\) 9.30175 14.6468i 0.304200 0.479001i
\(936\) −2.10317 3.64280i −0.0687444 0.119069i
\(937\) 33.2472 + 24.1555i 1.08614 + 0.789127i 0.978743 0.205089i \(-0.0657485\pi\)
0.107397 + 0.994216i \(0.465748\pi\)
\(938\) −2.74575 + 8.23546i −0.0896518 + 0.268897i
\(939\) −9.61456 29.5906i −0.313759 0.965652i
\(940\) −12.5501 5.58766i −0.409339 0.182249i
\(941\) −2.80237 26.6628i −0.0913546 0.869181i −0.940219 0.340570i \(-0.889380\pi\)
0.848864 0.528611i \(-0.177287\pi\)
\(942\) 17.6663 + 3.75508i 0.575598 + 0.122347i
\(943\) 13.4700 2.86315i 0.438645 0.0932369i
\(944\) 1.73488 + 1.26046i 0.0564656 + 0.0410246i
\(945\) 1.57495 + 2.77678i 0.0512332 + 0.0903286i
\(946\) −1.17101 + 3.14564i −0.0380727 + 0.102274i
\(947\) −4.07374 7.05593i −0.132379 0.229287i 0.792214 0.610243i \(-0.208928\pi\)
−0.924593 + 0.380956i \(0.875595\pi\)
\(948\) −11.4787 + 5.11064i −0.372810 + 0.165986i
\(949\) −7.86165 8.73125i −0.255200 0.283428i
\(950\) −0.0621015 + 0.0689707i −0.00201484 + 0.00223770i
\(951\) −25.2623 + 18.3541i −0.819186 + 0.595173i
\(952\) 1.11170 + 11.4173i 0.0360304 + 0.370038i
\(953\) −14.8638 45.7460i −0.481484 1.48186i −0.837009 0.547190i \(-0.815698\pi\)
0.355524 0.934667i \(-0.384302\pi\)
\(954\) 11.5534 2.45576i 0.374057 0.0795082i
\(955\) −14.1784 + 6.31261i −0.458801 + 0.204271i
\(956\) 3.56706 6.17833i 0.115367 0.199822i
\(957\) −6.89922 + 7.04071i −0.223020 + 0.227594i
\(958\) −26.5308 −0.857170
\(959\) −19.3525 + 8.43933i −0.624923 + 0.272520i
\(960\) −0.372856 + 1.14753i −0.0120339 + 0.0370365i
\(961\) −15.9030 + 17.6620i −0.512999 + 0.569743i
\(962\) 2.84732 + 27.0905i 0.0918014 + 0.873432i
\(963\) −0.482183 4.58766i −0.0155381 0.147835i
\(964\) 13.0392 14.4815i 0.419964 0.466417i
\(965\) 5.66742 17.4425i 0.182441 0.561495i
\(966\) 1.59244 14.1109i 0.0512358 0.454011i
\(967\) 9.55633 0.307311 0.153655 0.988124i \(-0.450895\pi\)
0.153655 + 0.988124i \(0.450895\pi\)
\(968\) −8.02351 + 7.52485i −0.257885 + 0.241858i
\(969\) −0.0567693 + 0.0983274i −0.00182369 + 0.00315873i
\(970\) −20.7685 + 9.24673i −0.666837 + 0.296895i
\(971\) 36.1544 7.68485i 1.16025 0.246619i 0.412727 0.910855i \(-0.364576\pi\)
0.747523 + 0.664236i \(0.231243\pi\)
\(972\) −0.309017 0.951057i −0.00991172 0.0305052i
\(973\) 18.6780 13.3531i 0.598788 0.428079i
\(974\) −24.0209 + 17.4522i −0.769679 + 0.559204i
\(975\) −9.97534 + 11.0787i −0.319467 + 0.354804i
\(976\) −4.55140 5.05484i −0.145687 0.161802i
\(977\) −15.1200 + 6.73185i −0.483731 + 0.215371i −0.634088 0.773261i \(-0.718624\pi\)
0.150357 + 0.988632i \(0.451958\pi\)
\(978\) 4.00880 + 6.94344i 0.128187 + 0.222027i
\(979\) 2.72140 + 9.75909i 0.0869762 + 0.311902i
\(980\) 8.44512 + 0.129327i 0.269770 + 0.00413121i
\(981\) −13.5828 9.86846i −0.433665 0.315076i
\(982\) −2.83429 + 0.602446i −0.0904457 + 0.0192248i
\(983\) −23.0949 4.90897i −0.736612 0.156572i −0.175696 0.984444i \(-0.556218\pi\)
−0.560916 + 0.827873i \(0.689551\pi\)
\(984\) −0.268192 2.55168i −0.00854965 0.0813445i
\(985\) 9.40905 + 4.18918i 0.299797 + 0.133478i
\(986\) 3.98216 + 12.2558i 0.126818 + 0.390305i
\(987\) 9.52778 28.5771i 0.303273 0.909621i
\(988\) −0.0891132 0.0647445i −0.00283507 0.00205980i
\(989\) −2.71593 4.70412i −0.0863614 0.149582i
\(990\) 2.54985 + 3.08426i 0.0810395 + 0.0980242i
\(991\) 13.5326 23.4392i 0.429878 0.744570i −0.566984 0.823729i \(-0.691890\pi\)
0.996862 + 0.0791584i \(0.0252233\pi\)
\(992\) 0.281129 2.67476i 0.00892586 0.0849239i
\(993\) 8.24688 25.3813i 0.261707 0.805451i
\(994\) −16.3759 + 17.9096i −0.519413 + 0.568059i
\(995\) 1.28774 0.935600i 0.0408242 0.0296605i
\(996\) −2.17319 0.967565i −0.0688600 0.0306585i
\(997\) 8.96336 + 1.90522i 0.283873 + 0.0603390i 0.347647 0.937625i \(-0.386981\pi\)
−0.0637749 + 0.997964i \(0.520314\pi\)
\(998\) 13.7194 + 15.2369i 0.434279 + 0.482315i
\(999\) −0.676911 + 6.44038i −0.0214165 + 0.203765i
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.y.a.235.2 yes 24
7.2 even 3 inner 462.2.y.a.37.2 yes 24
11.3 even 5 inner 462.2.y.a.25.2 24
77.58 even 15 inner 462.2.y.a.289.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.y.a.25.2 24 11.3 even 5 inner
462.2.y.a.37.2 yes 24 7.2 even 3 inner
462.2.y.a.235.2 yes 24 1.1 even 1 trivial
462.2.y.a.289.2 yes 24 77.58 even 15 inner