Properties

Label 187.2.r.a.15.1
Level $187$
Weight $2$
Character 187.15
Analytic conductor $1.493$
Analytic rank $0$
Dimension $256$
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] = [187,2,Mod(9,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(40))
 
chi = DirichletCharacter(H, H._module([24, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.r (of order \(40\), degree \(16\), 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: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(16\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label 15.1
Character \(\chi\) \(=\) 187.15
Dual form 187.2.r.a.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.404781 - 2.55569i) q^{2} +(-0.751908 + 0.0591764i) q^{3} +(-4.46558 + 1.45095i) q^{4} +(-0.925538 + 1.51034i) q^{5} +(0.455595 + 1.89769i) q^{6} +(-0.251290 + 3.19294i) q^{7} +(3.16633 + 6.21427i) q^{8} +(-2.40120 + 0.380313i) q^{9} +O(q^{10})\) \(q+(-0.404781 - 2.55569i) q^{2} +(-0.751908 + 0.0591764i) q^{3} +(-4.46558 + 1.45095i) q^{4} +(-0.925538 + 1.51034i) q^{5} +(0.455595 + 1.89769i) q^{6} +(-0.251290 + 3.19294i) q^{7} +(3.16633 + 6.21427i) q^{8} +(-2.40120 + 0.380313i) q^{9} +(4.23460 + 1.75403i) q^{10} +(-2.38953 - 2.30003i) q^{11} +(3.27184 - 1.35524i) q^{12} +(1.09393 - 1.50567i) q^{13} +(8.26189 - 0.650225i) q^{14} +(0.606543 - 1.19041i) q^{15} +(7.00276 - 5.08780i) q^{16} +(-4.10547 + 0.380902i) q^{17} +(1.94392 + 5.98278i) q^{18} +(-5.53345 + 2.81943i) q^{19} +(1.94163 - 8.08746i) q^{20} -2.41567i q^{21} +(-4.91092 + 7.03791i) q^{22} +(1.97881 - 4.77728i) q^{23} +(-2.74852 - 4.48518i) q^{24} +(0.845444 + 1.65928i) q^{25} +(-4.29081 - 2.18628i) q^{26} +(3.98316 - 0.956271i) q^{27} +(-3.51066 - 14.6230i) q^{28} +(2.74902 + 3.21869i) q^{29} +(-3.28783 - 1.06828i) q^{30} +(0.193789 - 0.807190i) q^{31} +(-5.97408 - 5.97408i) q^{32} +(1.93282 + 1.58801i) q^{33} +(2.63528 + 10.3381i) q^{34} +(-4.58986 - 3.33473i) q^{35} +(10.1709 - 5.18235i) q^{36} +(-3.61782 + 3.08991i) q^{37} +(9.44542 + 13.0005i) q^{38} +(-0.733434 + 1.19686i) q^{39} +(-12.3162 - 0.969308i) q^{40} +(4.61418 - 5.40251i) q^{41} +(-6.17370 + 0.977818i) q^{42} +(-7.63500 + 7.63500i) q^{43} +(14.0079 + 6.80386i) q^{44} +(1.64800 - 3.97863i) q^{45} +(-13.0102 - 3.12348i) q^{46} +(-9.45772 - 3.07300i) q^{47} +(-4.96435 + 4.23996i) q^{48} +(-3.21793 - 0.509670i) q^{49} +(3.89837 - 2.83233i) q^{50} +(3.06440 - 0.529350i) q^{51} +(-2.70038 + 8.31091i) q^{52} +(0.473712 + 2.99090i) q^{53} +(-4.05624 - 9.79262i) q^{54} +(5.68543 - 1.48024i) q^{55} +(-20.6375 + 8.54832i) q^{56} +(3.99380 - 2.44740i) q^{57} +(7.11322 - 8.32851i) q^{58} +(-0.190444 - 0.0970359i) q^{59} +(-0.981338 + 6.19592i) q^{60} +(3.48883 - 0.837595i) q^{61} +(-2.14137 - 0.168529i) q^{62} +(-0.610920 - 7.76247i) q^{63} +(-2.67409 + 3.68057i) q^{64} +(1.26159 + 3.04576i) q^{65} +(3.27608 - 5.58247i) q^{66} -2.88368 q^{67} +(17.7806 - 7.65780i) q^{68} +(-1.20518 + 3.70917i) q^{69} +(-6.66463 + 13.0801i) q^{70} +(7.68701 + 4.71061i) q^{71} +(-9.96636 - 13.7175i) q^{72} +(-6.81765 - 7.98245i) q^{73} +(9.36127 + 7.99528i) q^{74} +(-0.733886 - 1.19759i) q^{75} +(20.6192 - 20.6192i) q^{76} +(7.94433 - 7.05167i) q^{77} +(3.35567 + 1.38996i) q^{78} +(-2.68838 + 1.64744i) q^{79} +(1.20300 + 15.2855i) q^{80} +(3.99806 - 1.29905i) q^{81} +(-15.6749 - 9.60556i) q^{82} +(-11.4485 - 1.81326i) q^{83} +(3.50503 + 10.7874i) q^{84} +(3.22448 - 6.55320i) q^{85} +(22.6032 + 16.4222i) q^{86} +(-2.25748 - 2.25748i) q^{87} +(6.72695 - 22.1318i) q^{88} +8.74598i q^{89} +(-10.8352 - 2.60130i) q^{90} +(4.53261 + 3.87122i) q^{91} +(-1.90493 + 24.2045i) q^{92} +(-0.0979449 + 0.618400i) q^{93} +(-4.02532 + 25.4149i) q^{94} +(0.863112 - 10.9669i) q^{95} +(4.84549 + 4.13844i) q^{96} +(13.4335 + 3.22509i) q^{97} +8.43033i q^{98} +(6.61248 + 4.61406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q - 12 q^{2} - 12 q^{3} - 20 q^{5} - 12 q^{6} - 12 q^{7} - 28 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 256 q - 12 q^{2} - 12 q^{3} - 20 q^{5} - 12 q^{6} - 12 q^{7} - 28 q^{8} - 36 q^{9} - 32 q^{10} - 16 q^{11} - 32 q^{12} - 12 q^{14} + 12 q^{15} + 16 q^{16} + 12 q^{17} - 16 q^{18} - 12 q^{19} - 44 q^{20} + 88 q^{22} - 48 q^{23} - 80 q^{24} - 4 q^{25} - 12 q^{26} - 48 q^{27} - 28 q^{28} - 12 q^{29} + 44 q^{31} - 8 q^{32} - 56 q^{33} - 64 q^{34} - 88 q^{35} + 56 q^{36} - 28 q^{37} + 12 q^{39} + 120 q^{40} - 48 q^{41} + 44 q^{42} + 8 q^{43} - 16 q^{44} - 32 q^{45} - 44 q^{46} + 60 q^{48} + 64 q^{49} + 32 q^{50} - 28 q^{51} - 232 q^{52} - 20 q^{53} + 48 q^{54} - 64 q^{56} + 128 q^{57} + 124 q^{58} + 104 q^{59} + 4 q^{60} + 64 q^{61} - 52 q^{62} - 12 q^{63} - 88 q^{65} - 208 q^{66} - 96 q^{67} + 44 q^{68} + 48 q^{69} + 92 q^{70} - 44 q^{71} + 28 q^{73} - 12 q^{74} + 104 q^{75} + 176 q^{76} - 148 q^{77} - 12 q^{79} + 32 q^{80} - 72 q^{82} - 16 q^{83} + 216 q^{84} + 80 q^{85} - 24 q^{86} - 128 q^{87} - 32 q^{88} - 28 q^{90} - 108 q^{91} + 76 q^{92} + 164 q^{93} - 88 q^{94} - 32 q^{95} - 44 q^{96} + 128 q^{97} + 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.404781 2.55569i −0.286224 1.80714i −0.541967 0.840400i \(-0.682320\pi\)
0.255744 0.966745i \(-0.417680\pi\)
\(3\) −0.751908 + 0.0591764i −0.434114 + 0.0341655i −0.293634 0.955918i \(-0.594865\pi\)
−0.140480 + 0.990083i \(0.544865\pi\)
\(4\) −4.46558 + 1.45095i −2.23279 + 0.725477i
\(5\) −0.925538 + 1.51034i −0.413913 + 0.675445i −0.989861 0.142042i \(-0.954633\pi\)
0.575947 + 0.817487i \(0.304633\pi\)
\(6\) 0.455595 + 1.89769i 0.185996 + 0.774728i
\(7\) −0.251290 + 3.19294i −0.0949788 + 1.20682i 0.746073 + 0.665864i \(0.231937\pi\)
−0.841051 + 0.540955i \(0.818063\pi\)
\(8\) 3.16633 + 6.21427i 1.11947 + 2.19708i
\(9\) −2.40120 + 0.380313i −0.800401 + 0.126771i
\(10\) 4.23460 + 1.75403i 1.33910 + 0.554673i
\(11\) −2.38953 2.30003i −0.720471 0.693485i
\(12\) 3.27184 1.35524i 0.944499 0.391224i
\(13\) 1.09393 1.50567i 0.303402 0.417596i −0.629908 0.776670i \(-0.716907\pi\)
0.933309 + 0.359074i \(0.116907\pi\)
\(14\) 8.26189 0.650225i 2.20808 0.173780i
\(15\) 0.606543 1.19041i 0.156609 0.307362i
\(16\) 7.00276 5.08780i 1.75069 1.27195i
\(17\) −4.10547 + 0.380902i −0.995724 + 0.0923823i
\(18\) 1.94392 + 5.98278i 0.458187 + 1.41015i
\(19\) −5.53345 + 2.81943i −1.26946 + 0.646822i −0.953340 0.301897i \(-0.902380\pi\)
−0.316119 + 0.948719i \(0.602380\pi\)
\(20\) 1.94163 8.08746i 0.434161 1.80841i
\(21\) 2.41567i 0.527142i
\(22\) −4.91092 + 7.03791i −1.04701 + 1.50049i
\(23\) 1.97881 4.77728i 0.412611 0.996132i −0.571823 0.820377i \(-0.693764\pi\)
0.984434 0.175754i \(-0.0562365\pi\)
\(24\) −2.74852 4.48518i −0.561040 0.915535i
\(25\) 0.845444 + 1.65928i 0.169089 + 0.331855i
\(26\) −4.29081 2.18628i −0.841497 0.428764i
\(27\) 3.98316 0.956271i 0.766559 0.184034i
\(28\) −3.51066 14.6230i −0.663453 2.76348i
\(29\) 2.74902 + 3.21869i 0.510481 + 0.597696i 0.954459 0.298341i \(-0.0964333\pi\)
−0.443978 + 0.896037i \(0.646433\pi\)
\(30\) −3.28783 1.06828i −0.600272 0.195040i
\(31\) 0.193789 0.807190i 0.0348055 0.144976i −0.952261 0.305284i \(-0.901249\pi\)
0.987067 + 0.160308i \(0.0512488\pi\)
\(32\) −5.97408 5.97408i −1.05608 1.05608i
\(33\) 1.93282 + 1.58801i 0.336460 + 0.276436i
\(34\) 2.63528 + 10.3381i 0.451948 + 1.77297i
\(35\) −4.58986 3.33473i −0.775827 0.563671i
\(36\) 10.1709 5.18235i 1.69516 0.863725i
\(37\) −3.61782 + 3.08991i −0.594766 + 0.507978i −0.895106 0.445854i \(-0.852900\pi\)
0.300340 + 0.953832i \(0.402900\pi\)
\(38\) 9.44542 + 13.0005i 1.53225 + 2.10896i
\(39\) −0.733434 + 1.19686i −0.117443 + 0.191650i
\(40\) −12.3162 0.969308i −1.94737 0.153261i
\(41\) 4.61418 5.40251i 0.720613 0.843730i −0.272344 0.962200i \(-0.587799\pi\)
0.992958 + 0.118470i \(0.0377989\pi\)
\(42\) −6.17370 + 0.977818i −0.952622 + 0.150881i
\(43\) −7.63500 + 7.63500i −1.16433 + 1.16433i −0.180807 + 0.983519i \(0.557871\pi\)
−0.983519 + 0.180807i \(0.942129\pi\)
\(44\) 14.0079 + 6.80386i 2.11177 + 1.02572i
\(45\) 1.64800 3.97863i 0.245670 0.593099i
\(46\) −13.0102 3.12348i −1.91825 0.460532i
\(47\) −9.45772 3.07300i −1.37955 0.448243i −0.477029 0.878888i \(-0.658286\pi\)
−0.902522 + 0.430645i \(0.858286\pi\)
\(48\) −4.96435 + 4.23996i −0.716543 + 0.611985i
\(49\) −3.21793 0.509670i −0.459704 0.0728100i
\(50\) 3.89837 2.83233i 0.551313 0.400553i
\(51\) 3.06440 0.529350i 0.429101 0.0741239i
\(52\) −2.70038 + 8.31091i −0.374475 + 1.15252i
\(53\) 0.473712 + 2.99090i 0.0650693 + 0.410832i 0.998626 + 0.0524019i \(0.0166877\pi\)
−0.933557 + 0.358430i \(0.883312\pi\)
\(54\) −4.05624 9.79262i −0.551984 1.33261i
\(55\) 5.68543 1.48024i 0.766623 0.199596i
\(56\) −20.6375 + 8.54832i −2.75780 + 1.14232i
\(57\) 3.99380 2.44740i 0.528991 0.324166i
\(58\) 7.11322 8.32851i 0.934012 1.09359i
\(59\) −0.190444 0.0970359i −0.0247936 0.0126330i 0.441550 0.897237i \(-0.354429\pi\)
−0.466343 + 0.884604i \(0.654429\pi\)
\(60\) −0.981338 + 6.19592i −0.126690 + 0.799890i
\(61\) 3.48883 0.837595i 0.446699 0.107243i −0.00385398 0.999993i \(-0.501227\pi\)
0.450553 + 0.892750i \(0.351227\pi\)
\(62\) −2.14137 0.168529i −0.271954 0.0214032i
\(63\) −0.610920 7.76247i −0.0769687 0.977980i
\(64\) −2.67409 + 3.68057i −0.334261 + 0.460071i
\(65\) 1.26159 + 3.04576i 0.156481 + 0.377780i
\(66\) 3.27608 5.58247i 0.403257 0.687154i
\(67\) −2.88368 −0.352297 −0.176149 0.984364i \(-0.556364\pi\)
−0.176149 + 0.984364i \(0.556364\pi\)
\(68\) 17.7806 7.65780i 2.15622 0.928645i
\(69\) −1.20518 + 3.70917i −0.145087 + 0.446532i
\(70\) −6.66463 + 13.0801i −0.796576 + 1.56337i
\(71\) 7.68701 + 4.71061i 0.912280 + 0.559046i 0.897583 0.440846i \(-0.145321\pi\)
0.0146975 + 0.999892i \(0.495321\pi\)
\(72\) −9.96636 13.7175i −1.17455 1.61662i
\(73\) −6.81765 7.98245i −0.797946 0.934275i 0.201027 0.979586i \(-0.435572\pi\)
−0.998973 + 0.0453108i \(0.985572\pi\)
\(74\) 9.36127 + 7.99528i 1.08823 + 0.929433i
\(75\) −0.733886 1.19759i −0.0847418 0.138286i
\(76\) 20.6192 20.6192i 2.36518 2.36518i
\(77\) 7.94433 7.05167i 0.905341 0.803612i
\(78\) 3.35567 + 1.38996i 0.379955 + 0.157382i
\(79\) −2.68838 + 1.64744i −0.302467 + 0.185352i −0.665447 0.746445i \(-0.731759\pi\)
0.362981 + 0.931797i \(0.381759\pi\)
\(80\) 1.20300 + 15.2855i 0.134499 + 1.70897i
\(81\) 3.99806 1.29905i 0.444228 0.144339i
\(82\) −15.6749 9.60556i −1.73100 1.06076i
\(83\) −11.4485 1.81326i −1.25664 0.199031i −0.507618 0.861582i \(-0.669474\pi\)
−0.749017 + 0.662551i \(0.769474\pi\)
\(84\) 3.50503 + 10.7874i 0.382430 + 1.17700i
\(85\) 3.22448 6.55320i 0.349744 0.710795i
\(86\) 22.6032 + 16.4222i 2.43736 + 1.77085i
\(87\) −2.25748 2.25748i −0.242028 0.242028i
\(88\) 6.72695 22.1318i 0.717096 2.35926i
\(89\) 8.74598i 0.927072i 0.886078 + 0.463536i \(0.153420\pi\)
−0.886078 + 0.463536i \(0.846580\pi\)
\(90\) −10.8352 2.60130i −1.14213 0.274201i
\(91\) 4.53261 + 3.87122i 0.475147 + 0.405814i
\(92\) −1.90493 + 24.2045i −0.198603 + 2.52349i
\(93\) −0.0979449 + 0.618400i −0.0101564 + 0.0641251i
\(94\) −4.02532 + 25.4149i −0.415180 + 2.62134i
\(95\) 0.863112 10.9669i 0.0885535 1.12518i
\(96\) 4.84549 + 4.13844i 0.494540 + 0.422377i
\(97\) 13.4335 + 3.22509i 1.36396 + 0.327459i 0.848383 0.529382i \(-0.177576\pi\)
0.515580 + 0.856841i \(0.327576\pi\)
\(98\) 8.43033i 0.851592i
\(99\) 6.61248 + 4.61406i 0.664579 + 0.463731i
\(100\) −6.18293 6.18293i −0.618293 0.618293i
\(101\) 6.68815 + 4.85922i 0.665496 + 0.483511i 0.868514 0.495664i \(-0.165075\pi\)
−0.203019 + 0.979175i \(0.565075\pi\)
\(102\) −2.59326 7.61737i −0.256771 0.754232i
\(103\) −4.17041 12.8352i −0.410922 1.26469i −0.915848 0.401526i \(-0.868480\pi\)
0.504925 0.863163i \(-0.331520\pi\)
\(104\) 12.8203 + 2.03054i 1.25714 + 0.199111i
\(105\) 3.64849 + 2.23579i 0.356056 + 0.218191i
\(106\) 7.45205 2.42132i 0.723807 0.235179i
\(107\) −0.757574 9.62589i −0.0732374 0.930570i −0.918296 0.395895i \(-0.870434\pi\)
0.845058 0.534674i \(-0.179566\pi\)
\(108\) −16.3996 + 10.0497i −1.57805 + 0.967031i
\(109\) 2.78510 + 1.15362i 0.266764 + 0.110497i 0.512056 0.858952i \(-0.328884\pi\)
−0.245292 + 0.969449i \(0.578884\pi\)
\(110\) −6.08440 13.9310i −0.580125 1.32827i
\(111\) 2.53742 2.53742i 0.240841 0.240841i
\(112\) 14.4854 + 23.6379i 1.36874 + 2.23358i
\(113\) 13.9688 + 11.9305i 1.31408 + 1.12233i 0.983960 + 0.178389i \(0.0570887\pi\)
0.330118 + 0.943940i \(0.392911\pi\)
\(114\) −7.87141 9.21624i −0.737225 0.863180i
\(115\) 5.38385 + 7.41024i 0.502047 + 0.691008i
\(116\) −16.9462 10.3846i −1.57341 0.964188i
\(117\) −2.05412 + 4.03144i −0.189904 + 0.372707i
\(118\) −0.170905 + 0.525993i −0.0157331 + 0.0484216i
\(119\) −0.184534 13.2043i −0.0169162 1.21043i
\(120\) 9.31802 0.850615
\(121\) 0.419733 + 10.9920i 0.0381576 + 0.999272i
\(122\) −3.55284 8.57732i −0.321659 0.776554i
\(123\) −3.14973 + 4.33524i −0.284002 + 0.390895i
\(124\) 0.305815 + 3.88575i 0.0274630 + 0.348950i
\(125\) −12.1181 0.953716i −1.08388 0.0853029i
\(126\) −19.5912 + 4.70342i −1.74532 + 0.419014i
\(127\) −2.91049 + 18.3761i −0.258264 + 1.63062i 0.428364 + 0.903606i \(0.359090\pi\)
−0.686628 + 0.727009i \(0.740910\pi\)
\(128\) −4.56677 2.32689i −0.403649 0.205670i
\(129\) 5.28900 6.19262i 0.465671 0.545230i
\(130\) 7.27333 4.45711i 0.637914 0.390914i
\(131\) −7.88386 + 3.26560i −0.688816 + 0.285317i −0.699507 0.714626i \(-0.746597\pi\)
0.0106910 + 0.999943i \(0.496597\pi\)
\(132\) −10.9353 4.28694i −0.951793 0.373130i
\(133\) −7.61179 18.3765i −0.660026 1.59344i
\(134\) 1.16726 + 7.36978i 0.100836 + 0.636652i
\(135\) −2.24227 + 6.90099i −0.192984 + 0.593943i
\(136\) −15.3663 24.3065i −1.31765 2.08426i
\(137\) 4.02094 2.92138i 0.343532 0.249591i −0.402618 0.915368i \(-0.631900\pi\)
0.746151 + 0.665777i \(0.231900\pi\)
\(138\) 9.96732 + 1.57867i 0.848475 + 0.134385i
\(139\) −6.81833 + 5.82341i −0.578323 + 0.493935i −0.889820 0.456313i \(-0.849170\pi\)
0.311496 + 0.950247i \(0.399170\pi\)
\(140\) 25.3349 + 8.23181i 2.14119 + 0.695715i
\(141\) 7.29318 + 1.75094i 0.614197 + 0.147456i
\(142\) 8.92728 21.5524i 0.749161 1.80863i
\(143\) −6.07705 + 1.08177i −0.508189 + 0.0904618i
\(144\) −14.8801 + 14.8801i −1.24001 + 1.24001i
\(145\) −7.40565 + 1.17294i −0.615006 + 0.0974073i
\(146\) −17.6410 + 20.6549i −1.45998 + 1.70942i
\(147\) 2.44975 + 0.192799i 0.202052 + 0.0159018i
\(148\) 11.6723 19.0475i 0.959461 1.56570i
\(149\) 1.83322 + 2.52322i 0.150184 + 0.206710i 0.877480 0.479614i \(-0.159223\pi\)
−0.727296 + 0.686324i \(0.759223\pi\)
\(150\) −2.76361 + 2.36035i −0.225648 + 0.192721i
\(151\) −4.95563 + 2.52502i −0.403284 + 0.205483i −0.643854 0.765148i \(-0.722666\pi\)
0.240570 + 0.970632i \(0.422666\pi\)
\(152\) −35.0414 25.4591i −2.84223 2.06500i
\(153\) 9.71321 2.47599i 0.785266 0.200172i
\(154\) −21.2376 17.4488i −1.71137 1.40607i
\(155\) 1.03977 + 1.03977i 0.0835165 + 0.0835165i
\(156\) 1.53863 6.40884i 0.123189 0.513118i
\(157\) −14.7121 4.78026i −1.17416 0.381506i −0.343963 0.938983i \(-0.611770\pi\)
−0.830193 + 0.557477i \(0.811770\pi\)
\(158\) 5.29856 + 6.20381i 0.421530 + 0.493549i
\(159\) −0.533178 2.22085i −0.0422838 0.176125i
\(160\) 14.5521 3.49366i 1.15045 0.276198i
\(161\) 14.7563 + 7.51873i 1.16296 + 0.592559i
\(162\) −4.93830 9.69195i −0.387989 0.761472i
\(163\) 4.45078 + 7.26301i 0.348612 + 0.568883i 0.978102 0.208126i \(-0.0667363\pi\)
−0.629490 + 0.777008i \(0.716736\pi\)
\(164\) −12.7662 + 30.8203i −0.996871 + 2.40666i
\(165\) −4.18732 + 1.44945i −0.325983 + 0.112840i
\(166\) 29.9927i 2.32789i
\(167\) −2.40641 + 10.0234i −0.186214 + 0.775636i 0.798577 + 0.601892i \(0.205586\pi\)
−0.984791 + 0.173744i \(0.944414\pi\)
\(168\) 15.0116 7.64880i 1.15817 0.590118i
\(169\) 2.94688 + 9.06955i 0.226683 + 0.697658i
\(170\) −18.0532 5.58815i −1.38461 0.428592i
\(171\) 12.2147 8.87447i 0.934078 0.678647i
\(172\) 23.0166 45.1727i 1.75500 3.44439i
\(173\) −9.82949 + 0.773597i −0.747322 + 0.0588155i −0.446400 0.894833i \(-0.647294\pi\)
−0.300922 + 0.953649i \(0.597294\pi\)
\(174\) −4.85563 + 6.68321i −0.368105 + 0.506653i
\(175\) −5.51043 + 2.28250i −0.416549 + 0.172540i
\(176\) −28.4354 3.94908i −2.14340 0.297673i
\(177\) 0.148938 + 0.0616923i 0.0111949 + 0.00463707i
\(178\) 22.3520 3.54021i 1.67535 0.265350i
\(179\) −9.00176 17.6670i −0.672823 1.32049i −0.934717 0.355394i \(-0.884347\pi\)
0.261893 0.965097i \(-0.415653\pi\)
\(180\) −1.58647 + 20.1580i −0.118249 + 1.50249i
\(181\) 0.943544 + 3.93014i 0.0701331 + 0.292125i 0.996404 0.0847340i \(-0.0270040\pi\)
−0.926271 + 0.376859i \(0.877004\pi\)
\(182\) 8.05890 13.1509i 0.597366 0.974812i
\(183\) −2.57371 + 0.836251i −0.190254 + 0.0618174i
\(184\) 35.9529 2.82955i 2.65048 0.208597i
\(185\) −1.31839 8.32397i −0.0969298 0.611991i
\(186\) 1.62008 0.118790
\(187\) 10.6862 + 8.53253i 0.781456 + 0.623960i
\(188\) 46.6930 3.40544
\(189\) 2.05239 + 12.9583i 0.149290 + 0.942578i
\(190\) −28.3773 + 2.23334i −2.05871 + 0.162024i
\(191\) 11.1709 3.62963i 0.808296 0.262631i 0.124420 0.992230i \(-0.460293\pi\)
0.683876 + 0.729599i \(0.260293\pi\)
\(192\) 1.79286 2.92569i 0.129389 0.211143i
\(193\) 6.10878 + 25.4449i 0.439719 + 1.83156i 0.546736 + 0.837305i \(0.315870\pi\)
−0.107016 + 0.994257i \(0.534130\pi\)
\(194\) 2.80471 35.6373i 0.201367 2.55861i
\(195\) −1.12884 2.21547i −0.0808379 0.158653i
\(196\) 15.1094 2.39310i 1.07924 0.170936i
\(197\) −21.2890 8.81818i −1.51678 0.628270i −0.539834 0.841771i \(-0.681513\pi\)
−0.976943 + 0.213502i \(0.931513\pi\)
\(198\) 9.11550 18.7671i 0.647810 1.33372i
\(199\) 0.0921382 0.0381649i 0.00653150 0.00270544i −0.379415 0.925226i \(-0.623875\pi\)
0.385947 + 0.922521i \(0.373875\pi\)
\(200\) −7.63424 + 10.5076i −0.539822 + 0.743002i
\(201\) 2.16826 0.170646i 0.152937 0.0120364i
\(202\) 9.71142 19.0597i 0.683293 1.34104i
\(203\) −10.9679 + 7.96865i −0.769796 + 0.559290i
\(204\) −12.9162 + 6.81016i −0.904318 + 0.476806i
\(205\) 3.88903 + 11.9692i 0.271622 + 0.835966i
\(206\) −31.1146 + 15.8537i −2.16786 + 1.10458i
\(207\) −2.93467 + 12.2238i −0.203974 + 0.849611i
\(208\) 16.1095i 1.11699i
\(209\) 19.7071 + 5.98996i 1.36317 + 0.414334i
\(210\) 4.23716 10.2294i 0.292391 0.705895i
\(211\) −5.10223 8.32608i −0.351252 0.573191i 0.627405 0.778693i \(-0.284117\pi\)
−0.978657 + 0.205502i \(0.934117\pi\)
\(212\) −6.45506 12.6688i −0.443335 0.870094i
\(213\) −6.05868 3.08705i −0.415134 0.211521i
\(214\) −24.2941 + 5.83250i −1.66071 + 0.398702i
\(215\) −4.46497 18.5979i −0.304508 1.26837i
\(216\) 18.5545 + 21.7245i 1.26247 + 1.47817i
\(217\) 2.52861 + 0.821597i 0.171654 + 0.0557736i
\(218\) 1.82095 7.58480i 0.123330 0.513707i
\(219\) 5.59862 + 5.59862i 0.378320 + 0.378320i
\(220\) −23.2410 + 14.8595i −1.56691 + 1.00182i
\(221\) −3.91759 + 6.59815i −0.263526 + 0.443839i
\(222\) −7.51195 5.45775i −0.504169 0.366300i
\(223\) 16.9027 8.61238i 1.13189 0.576727i 0.215298 0.976548i \(-0.430928\pi\)
0.916593 + 0.399821i \(0.130928\pi\)
\(224\) 20.5761 17.5737i 1.37480 1.17419i
\(225\) −2.66113 3.66272i −0.177408 0.244182i
\(226\) 24.8364 40.5293i 1.65209 2.69597i
\(227\) 6.85428 + 0.539444i 0.454935 + 0.0358042i 0.303857 0.952718i \(-0.401726\pi\)
0.151078 + 0.988522i \(0.451726\pi\)
\(228\) −14.2836 + 16.7239i −0.945951 + 1.10757i
\(229\) 13.8695 2.19672i 0.916524 0.145163i 0.319685 0.947524i \(-0.396423\pi\)
0.596839 + 0.802361i \(0.296423\pi\)
\(230\) 16.7590 16.7590i 1.10505 1.10505i
\(231\) −5.55611 + 5.77232i −0.365565 + 0.379791i
\(232\) −11.2975 + 27.2746i −0.741718 + 1.79067i
\(233\) −22.1248 5.31169i −1.44944 0.347981i −0.569081 0.822282i \(-0.692701\pi\)
−0.880363 + 0.474301i \(0.842701\pi\)
\(234\) 11.1346 + 3.61784i 0.727890 + 0.236506i
\(235\) 13.3948 11.4402i 0.873777 0.746276i
\(236\) 0.991236 + 0.156996i 0.0645239 + 0.0102196i
\(237\) 1.92393 1.39781i 0.124972 0.0907978i
\(238\) −33.6713 + 5.81645i −2.18259 + 0.377024i
\(239\) 7.57840 23.3239i 0.490206 1.50870i −0.334091 0.942541i \(-0.608429\pi\)
0.824297 0.566158i \(-0.191571\pi\)
\(240\) −1.80908 11.4221i −0.116776 0.737294i
\(241\) −0.0805740 0.194523i −0.00519023 0.0125303i 0.921263 0.388940i \(-0.127159\pi\)
−0.926453 + 0.376409i \(0.877159\pi\)
\(242\) 27.9222 5.52206i 1.79491 0.354971i
\(243\) −14.2829 + 5.91616i −0.916246 + 0.379522i
\(244\) −14.3643 + 8.80248i −0.919583 + 0.563521i
\(245\) 3.74809 4.38845i 0.239457 0.280368i
\(246\) 12.3545 + 6.29492i 0.787692 + 0.401349i
\(247\) −1.80808 + 11.4158i −0.115045 + 0.726369i
\(248\) 5.62969 1.35157i 0.357486 0.0858247i
\(249\) 8.71551 + 0.685926i 0.552323 + 0.0434688i
\(250\) 2.46778 + 31.3561i 0.156076 + 1.98314i
\(251\) −3.57688 + 4.92315i −0.225770 + 0.310746i −0.906842 0.421470i \(-0.861514\pi\)
0.681072 + 0.732217i \(0.261514\pi\)
\(252\) 13.9911 + 33.7775i 0.881357 + 2.12778i
\(253\) −15.7163 + 6.86414i −0.988077 + 0.431545i
\(254\) 48.1417 3.02068
\(255\) −2.03672 + 5.11822i −0.127544 + 0.320515i
\(256\) −6.90995 + 21.2667i −0.431872 + 1.32917i
\(257\) −1.62554 + 3.19030i −0.101398 + 0.199005i −0.936132 0.351648i \(-0.885621\pi\)
0.834734 + 0.550653i \(0.185621\pi\)
\(258\) −17.9673 11.0104i −1.11860 0.685476i
\(259\) −8.95679 12.3280i −0.556548 0.766022i
\(260\) −10.0530 11.7706i −0.623461 0.729979i
\(261\) −7.82507 6.68324i −0.484360 0.413682i
\(262\) 11.5371 + 18.8268i 0.712764 + 1.16312i
\(263\) −10.5219 + 10.5219i −0.648809 + 0.648809i −0.952705 0.303896i \(-0.901712\pi\)
0.303896 + 0.952705i \(0.401712\pi\)
\(264\) −3.74837 + 17.0392i −0.230696 + 1.04869i
\(265\) −4.95571 2.05272i −0.304427 0.126098i
\(266\) −43.8834 + 26.8918i −2.69067 + 1.64884i
\(267\) −0.517556 6.57617i −0.0316739 0.402455i
\(268\) 12.8773 4.18409i 0.786606 0.255584i
\(269\) −2.24699 1.37696i −0.137002 0.0839547i 0.452309 0.891861i \(-0.350600\pi\)
−0.589310 + 0.807907i \(0.700600\pi\)
\(270\) 18.5444 + 2.93714i 1.12858 + 0.178749i
\(271\) 7.67442 + 23.6194i 0.466188 + 1.43478i 0.857482 + 0.514514i \(0.172028\pi\)
−0.391294 + 0.920266i \(0.627972\pi\)
\(272\) −26.8117 + 23.5552i −1.62570 + 1.42824i
\(273\) −3.63719 2.64257i −0.220133 0.159936i
\(274\) −9.09375 9.09375i −0.549373 0.549373i
\(275\) 1.79617 5.90944i 0.108313 0.356353i
\(276\) 18.3123i 1.10227i
\(277\) 9.14409 + 2.19530i 0.549415 + 0.131903i 0.498643 0.866807i \(-0.333832\pi\)
0.0507720 + 0.998710i \(0.483832\pi\)
\(278\) 17.6427 + 15.0683i 1.05814 + 0.903738i
\(279\) −0.158342 + 2.01193i −0.00947968 + 0.120451i
\(280\) 6.18989 39.0814i 0.369917 2.33556i
\(281\) 0.554708 3.50229i 0.0330911 0.208929i −0.965603 0.260021i \(-0.916270\pi\)
0.998694 + 0.0510926i \(0.0162704\pi\)
\(282\) 1.52271 19.3478i 0.0906760 1.15215i
\(283\) −1.39613 1.19240i −0.0829911 0.0708811i 0.606985 0.794713i \(-0.292379\pi\)
−0.689976 + 0.723832i \(0.742379\pi\)
\(284\) −41.1618 9.88208i −2.44251 0.586394i
\(285\) 8.29716i 0.491481i
\(286\) 5.22453 + 15.0932i 0.308933 + 0.892478i
\(287\) 16.0904 + 16.0904i 0.949787 + 0.949787i
\(288\) 16.6170 + 12.0730i 0.979166 + 0.711406i
\(289\) 16.7098 3.12757i 0.982931 0.183974i
\(290\) 5.99533 + 18.4517i 0.352058 + 1.08352i
\(291\) −10.2916 1.63003i −0.603304 0.0955539i
\(292\) 42.0269 + 25.7541i 2.45944 + 1.50715i
\(293\) −18.6897 + 6.07266i −1.09187 + 0.354769i −0.798967 0.601375i \(-0.794620\pi\)
−0.292899 + 0.956143i \(0.594620\pi\)
\(294\) −0.498877 6.33883i −0.0290951 0.369688i
\(295\) 0.322820 0.197824i 0.0187953 0.0115178i
\(296\) −30.6567 12.6984i −1.78189 0.738082i
\(297\) −11.7173 6.87633i −0.679909 0.399005i
\(298\) 5.70650 5.70650i 0.330568 0.330568i
\(299\) −5.02830 8.20544i −0.290794 0.474533i
\(300\) 5.01488 + 4.28311i 0.289534 + 0.247286i
\(301\) −22.4595 26.2967i −1.29455 1.51572i
\(302\) 8.45911 + 11.6430i 0.486767 + 0.669978i
\(303\) −5.31642 3.25791i −0.305421 0.187162i
\(304\) −24.4047 + 47.8969i −1.39971 + 2.74708i
\(305\) −1.96399 + 6.04455i −0.112458 + 0.346110i
\(306\) −10.2596 23.8217i −0.586501 1.36180i
\(307\) −20.1998 −1.15286 −0.576431 0.817146i \(-0.695555\pi\)
−0.576431 + 0.817146i \(0.695555\pi\)
\(308\) −25.2444 + 43.0167i −1.43843 + 2.45110i
\(309\) 3.89530 + 9.40409i 0.221596 + 0.534980i
\(310\) 2.23645 3.07821i 0.127022 0.174831i
\(311\) 0.727945 + 9.24942i 0.0412780 + 0.524486i 0.982446 + 0.186547i \(0.0597298\pi\)
−0.941168 + 0.337939i \(0.890270\pi\)
\(312\) −9.75988 0.768119i −0.552544 0.0434862i
\(313\) 13.6653 3.28075i 0.772410 0.185439i 0.171962 0.985104i \(-0.444989\pi\)
0.600447 + 0.799664i \(0.294989\pi\)
\(314\) −6.26166 + 39.5346i −0.353366 + 2.23106i
\(315\) 12.2894 + 6.26177i 0.692430 + 0.352811i
\(316\) 9.61482 11.2575i 0.540876 0.633284i
\(317\) 0.976409 0.598344i 0.0548406 0.0336064i −0.494808 0.869002i \(-0.664762\pi\)
0.549649 + 0.835396i \(0.314762\pi\)
\(318\) −5.45997 + 2.26159i −0.306180 + 0.126824i
\(319\) 0.834205 14.0140i 0.0467065 0.784634i
\(320\) −3.08394 7.44529i −0.172397 0.416204i
\(321\) 1.13925 + 7.19295i 0.0635868 + 0.401471i
\(322\) 13.2424 40.7560i 0.737972 2.27124i
\(323\) 21.6435 13.6828i 1.20428 0.761332i
\(324\) −15.9688 + 11.6020i −0.887154 + 0.644555i
\(325\) 3.42317 + 0.542177i 0.189883 + 0.0300746i
\(326\) 16.7604 14.3147i 0.928272 0.792819i
\(327\) −2.16240 0.702607i −0.119581 0.0388543i
\(328\) 48.1826 + 11.5676i 2.66044 + 0.638715i
\(329\) 12.1885 29.4258i 0.671976 1.62229i
\(330\) 5.39929 + 10.1148i 0.297221 + 0.556800i
\(331\) 17.5647 17.5647i 0.965442 0.965442i −0.0339803 0.999423i \(-0.510818\pi\)
0.999423 + 0.0339803i \(0.0108183\pi\)
\(332\) 53.7551 8.51397i 2.95019 0.467265i
\(333\) 7.51198 8.79540i 0.411654 0.481985i
\(334\) 26.5908 + 2.09274i 1.45498 + 0.114510i
\(335\) 2.66895 4.35534i 0.145821 0.237958i
\(336\) −12.2905 16.9164i −0.670500 0.922863i
\(337\) 8.84016 7.55021i 0.481554 0.411286i −0.375253 0.926922i \(-0.622444\pi\)
0.856808 + 0.515636i \(0.172444\pi\)
\(338\) 21.9861 11.2025i 1.19589 0.609334i
\(339\) −11.2093 8.14402i −0.608805 0.442323i
\(340\) −4.89077 + 33.9424i −0.265239 + 1.84079i
\(341\) −2.31962 + 1.48309i −0.125615 + 0.0803136i
\(342\) −27.6246 27.6246i −1.49377 1.49377i
\(343\) −2.79780 + 11.6537i −0.151067 + 0.629239i
\(344\) −71.6208 23.2710i −3.86154 1.25469i
\(345\) −4.48667 5.25322i −0.241554 0.282824i
\(346\) 5.95586 + 24.8080i 0.320189 + 1.33368i
\(347\) 16.1572 3.87901i 0.867366 0.208236i 0.224742 0.974418i \(-0.427846\pi\)
0.642623 + 0.766182i \(0.277846\pi\)
\(348\) 13.3565 + 6.80546i 0.715982 + 0.364811i
\(349\) −9.95790 19.5435i −0.533034 1.04614i −0.987829 0.155542i \(-0.950288\pi\)
0.454795 0.890596i \(-0.349712\pi\)
\(350\) 8.06386 + 13.1590i 0.431032 + 0.703380i
\(351\) 2.91747 7.04339i 0.155723 0.375949i
\(352\) 0.534703 + 28.0158i 0.0284998 + 1.49325i
\(353\) 22.7997i 1.21350i −0.794892 0.606752i \(-0.792472\pi\)
0.794892 0.606752i \(-0.207528\pi\)
\(354\) 0.0973787 0.405612i 0.00517562 0.0215580i
\(355\) −14.2292 + 7.25016i −0.755210 + 0.384799i
\(356\) −12.6900 39.0559i −0.672570 2.06996i
\(357\) 0.920134 + 9.91747i 0.0486986 + 0.524888i
\(358\) −41.5075 + 30.1570i −2.19374 + 1.59384i
\(359\) −10.4233 + 20.4568i −0.550119 + 1.07967i 0.433793 + 0.901013i \(0.357175\pi\)
−0.983912 + 0.178656i \(0.942825\pi\)
\(360\) 29.9424 2.35652i 1.57810 0.124199i
\(361\) 11.5019 15.8310i 0.605364 0.833212i
\(362\) 9.66229 4.00225i 0.507839 0.210354i
\(363\) −0.966067 8.24012i −0.0507054 0.432494i
\(364\) −25.8577 10.7106i −1.35531 0.561388i
\(365\) 18.3662 2.90892i 0.961332 0.152260i
\(366\) 3.17899 + 6.23911i 0.166168 + 0.326124i
\(367\) −0.542389 + 6.89171i −0.0283125 + 0.359744i 0.966400 + 0.257044i \(0.0827484\pi\)
−0.994712 + 0.102701i \(0.967252\pi\)
\(368\) −10.4487 43.5220i −0.544676 2.26874i
\(369\) −9.02493 + 14.7273i −0.469819 + 0.766675i
\(370\) −20.7398 + 6.73877i −1.07821 + 0.350332i
\(371\) −9.66881 + 0.760952i −0.501980 + 0.0395067i
\(372\) −0.459889 2.90363i −0.0238442 0.150546i
\(373\) 12.0003 0.621355 0.310677 0.950515i \(-0.399444\pi\)
0.310677 + 0.950515i \(0.399444\pi\)
\(374\) 17.4809 30.7645i 0.903915 1.59080i
\(375\) 9.16814 0.473441
\(376\) −10.8498 68.5029i −0.559536 3.53277i
\(377\) 7.85351 0.618085i 0.404476 0.0318330i
\(378\) 32.2866 10.4906i 1.66064 0.539576i
\(379\) 6.50112 10.6089i 0.333940 0.544941i −0.640962 0.767572i \(-0.721465\pi\)
0.974903 + 0.222631i \(0.0714646\pi\)
\(380\) 12.0582 + 50.2258i 0.618570 + 2.57653i
\(381\) 1.10099 13.9894i 0.0564053 0.716697i
\(382\) −13.7980 27.0800i −0.705966 1.38554i
\(383\) −27.4045 + 4.34045i −1.40031 + 0.221787i −0.810491 0.585752i \(-0.800799\pi\)
−0.589815 + 0.807538i \(0.700799\pi\)
\(384\) 3.57149 + 1.47936i 0.182257 + 0.0754932i
\(385\) 3.29765 + 18.5252i 0.168064 + 0.944133i
\(386\) 62.5565 25.9117i 3.18404 1.31887i
\(387\) 15.4295 21.2369i 0.784324 1.07953i
\(388\) −64.6678 + 5.08946i −3.28301 + 0.258378i
\(389\) −3.41913 + 6.71042i −0.173357 + 0.340232i −0.961294 0.275523i \(-0.911149\pi\)
0.787938 + 0.615755i \(0.211149\pi\)
\(390\) −5.20512 + 3.78174i −0.263572 + 0.191496i
\(391\) −6.30429 + 20.3667i −0.318822 + 1.02999i
\(392\) −7.02179 21.6109i −0.354654 1.09151i
\(393\) 5.73469 2.92197i 0.289277 0.147394i
\(394\) −13.9191 + 57.9774i −0.701236 + 2.92086i
\(395\) 5.58514i 0.281019i
\(396\) −36.2234 11.0101i −1.82029 0.553276i
\(397\) −2.57674 + 6.22080i −0.129323 + 0.312213i −0.975257 0.221074i \(-0.929044\pi\)
0.845934 + 0.533288i \(0.179044\pi\)
\(398\) −0.134833 0.220028i −0.00675859 0.0110290i
\(399\) 6.81082 + 13.3670i 0.340967 + 0.669186i
\(400\) 14.3625 + 7.31807i 0.718126 + 0.365903i
\(401\) 15.0077 3.60302i 0.749448 0.179926i 0.159309 0.987229i \(-0.449073\pi\)
0.590138 + 0.807302i \(0.299073\pi\)
\(402\) −1.31379 5.47232i −0.0655258 0.272935i
\(403\) −1.00337 1.17479i −0.0499812 0.0585205i
\(404\) −36.9170 11.9951i −1.83669 0.596776i
\(405\) −1.73835 + 7.24075i −0.0863793 + 0.359796i
\(406\) 24.8050 + 24.8050i 1.23105 + 1.23105i
\(407\) 15.7518 + 0.937650i 0.780787 + 0.0464776i
\(408\) 12.9924 + 17.3669i 0.643220 + 0.859789i
\(409\) −2.70999 1.96892i −0.134000 0.0973570i 0.518766 0.854916i \(-0.326392\pi\)
−0.652766 + 0.757559i \(0.726392\pi\)
\(410\) 29.0153 14.7841i 1.43297 0.730133i
\(411\) −2.85050 + 2.43456i −0.140605 + 0.120088i
\(412\) 37.2466 + 51.2655i 1.83501 + 2.52567i
\(413\) 0.357687 0.583692i 0.0176006 0.0287216i
\(414\) 32.4281 + 2.55214i 1.59375 + 0.125431i
\(415\) 13.3347 15.6129i 0.654573 0.766406i
\(416\) −15.5302 + 2.45974i −0.761431 + 0.120599i
\(417\) 4.78215 4.78215i 0.234183 0.234183i
\(418\) 7.33140 52.7899i 0.358591 2.58204i
\(419\) −7.94221 + 19.1742i −0.388002 + 0.936720i 0.602361 + 0.798224i \(0.294227\pi\)
−0.990363 + 0.138496i \(0.955773\pi\)
\(420\) −19.5366 4.69033i −0.953290 0.228865i
\(421\) −14.2405 4.62703i −0.694041 0.225508i −0.0593086 0.998240i \(-0.518890\pi\)
−0.634732 + 0.772732i \(0.718890\pi\)
\(422\) −19.2136 + 16.4100i −0.935303 + 0.798824i
\(423\) 23.8786 + 3.78200i 1.16102 + 0.183887i
\(424\) −17.0863 + 12.4139i −0.829785 + 0.602874i
\(425\) −4.10297 6.49009i −0.199023 0.314815i
\(426\) −5.43710 + 16.7337i −0.263428 + 0.810749i
\(427\) 1.79768 + 11.3501i 0.0869960 + 0.549271i
\(428\) 17.3497 + 41.8860i 0.838631 + 2.02463i
\(429\) 4.50537 1.17301i 0.217521 0.0566333i
\(430\) −45.7232 + 18.9392i −2.20497 + 0.913327i
\(431\) 7.21702 4.42260i 0.347632 0.213029i −0.337711 0.941250i \(-0.609653\pi\)
0.685342 + 0.728221i \(0.259653\pi\)
\(432\) 23.0278 26.9621i 1.10792 1.29721i
\(433\) −21.8081 11.1118i −1.04803 0.533997i −0.156837 0.987625i \(-0.550130\pi\)
−0.891191 + 0.453628i \(0.850130\pi\)
\(434\) 1.07621 6.79492i 0.0516597 0.326166i
\(435\) 5.49895 1.32018i 0.263655 0.0632979i
\(436\) −14.1109 1.11055i −0.675791 0.0531859i
\(437\) 2.51955 + 32.0140i 0.120527 + 1.53144i
\(438\) 12.0421 16.5745i 0.575394 0.791962i
\(439\) 2.87071 + 6.93050i 0.137011 + 0.330775i 0.977461 0.211114i \(-0.0677092\pi\)
−0.840450 + 0.541889i \(0.817709\pi\)
\(440\) 27.2006 + 30.6439i 1.29674 + 1.46089i
\(441\) 7.92073 0.377178
\(442\) 18.4486 + 7.34133i 0.877509 + 0.349191i
\(443\) −10.6586 + 32.8037i −0.506404 + 1.55855i 0.291994 + 0.956420i \(0.405681\pi\)
−0.798398 + 0.602130i \(0.794319\pi\)
\(444\) −7.64936 + 15.0127i −0.363023 + 0.712472i
\(445\) −13.2094 8.09474i −0.626186 0.383727i
\(446\) −28.8525 39.7120i −1.36620 1.88042i
\(447\) −1.52773 1.78874i −0.0722591 0.0846046i
\(448\) −11.0799 9.46311i −0.523475 0.447090i
\(449\) −9.43183 15.3913i −0.445116 0.726362i 0.548866 0.835910i \(-0.315060\pi\)
−0.993982 + 0.109548i \(0.965060\pi\)
\(450\) −8.28361 + 8.28361i −0.390493 + 0.390493i
\(451\) −23.4517 + 2.29673i −1.10430 + 0.108149i
\(452\) −79.6896 33.0085i −3.74828 1.55259i
\(453\) 3.57676 2.19184i 0.168051 0.102982i
\(454\) −1.39584 17.7358i −0.0655098 0.832381i
\(455\) −10.0420 + 3.26283i −0.470774 + 0.152964i
\(456\) 27.8545 + 17.0693i 1.30441 + 0.799341i
\(457\) −16.8592 2.67023i −0.788639 0.124908i −0.250893 0.968015i \(-0.580724\pi\)
−0.537746 + 0.843107i \(0.680724\pi\)
\(458\) −11.2282 34.5570i −0.524661 1.61474i
\(459\) −15.9885 + 5.44314i −0.746279 + 0.254064i
\(460\) −34.7939 25.2793i −1.62228 1.17865i
\(461\) −20.6232 20.6232i −0.960520 0.960520i 0.0387296 0.999250i \(-0.487669\pi\)
−0.999250 + 0.0387296i \(0.987669\pi\)
\(462\) 17.0013 + 11.8632i 0.790970 + 0.551924i
\(463\) 30.6325i 1.42362i −0.702375 0.711808i \(-0.747877\pi\)
0.702375 0.711808i \(-0.252123\pi\)
\(464\) 35.6268 + 8.55325i 1.65393 + 0.397075i
\(465\) −0.843343 0.720283i −0.0391091 0.0334023i
\(466\) −4.61933 + 58.6941i −0.213986 + 2.71895i
\(467\) 0.0849765 0.536520i 0.00393224 0.0248272i −0.985644 0.168836i \(-0.945999\pi\)
0.989576 + 0.144009i \(0.0459993\pi\)
\(468\) 3.32341 20.9832i 0.153624 0.969947i
\(469\) 0.724640 9.20743i 0.0334608 0.425159i
\(470\) −34.6595 29.6020i −1.59872 1.36544i
\(471\) 11.3450 + 2.72370i 0.522752 + 0.125502i
\(472\) 1.49072i 0.0686157i
\(473\) 35.8048 0.683361i 1.64631 0.0314210i
\(474\) −4.35114 4.35114i −0.199855 0.199855i
\(475\) −9.35644 6.79785i −0.429303 0.311907i
\(476\) 19.9828 + 58.6969i 0.915912 + 2.69037i
\(477\) −2.27496 7.00159i −0.104163 0.320581i
\(478\) −62.6762 9.92694i −2.86674 0.454048i
\(479\) −21.9961 13.4793i −1.00503 0.615883i −0.0804049 0.996762i \(-0.525621\pi\)
−0.924625 + 0.380879i \(0.875621\pi\)
\(480\) −10.7351 + 3.48806i −0.489989 + 0.159207i
\(481\) 0.694729 + 8.82737i 0.0316769 + 0.402493i
\(482\) −0.464525 + 0.284661i −0.0211585 + 0.0129660i
\(483\) −11.5403 4.78016i −0.525103 0.217505i
\(484\) −17.8232 48.4766i −0.810147 2.20348i
\(485\) −17.3042 + 17.3042i −0.785743 + 0.785743i
\(486\) 20.9013 + 34.1078i 0.948102 + 1.54716i
\(487\) −16.6421 14.2137i −0.754124 0.644083i 0.186917 0.982376i \(-0.440150\pi\)
−0.941041 + 0.338293i \(0.890150\pi\)
\(488\) 16.2518 + 19.0284i 0.735686 + 0.861377i
\(489\) −3.77637 5.19773i −0.170774 0.235050i
\(490\) −12.7327 7.80259i −0.575203 0.352485i
\(491\) −2.68426 + 5.26817i −0.121139 + 0.237749i −0.943611 0.331057i \(-0.892595\pi\)
0.822471 + 0.568806i \(0.192595\pi\)
\(492\) 7.77516 23.9295i 0.350531 1.07882i
\(493\) −12.5120 12.1671i −0.563514 0.547981i
\(494\) 29.9070 1.34558
\(495\) −13.0889 + 5.71661i −0.588303 + 0.256942i
\(496\) −2.74976 6.63852i −0.123468 0.298078i
\(497\) −16.9724 + 23.3605i −0.761315 + 1.04786i
\(498\) −1.77486 22.5518i −0.0795335 1.01057i
\(499\) −13.0907 1.03026i −0.586018 0.0461207i −0.218016 0.975945i \(-0.569958\pi\)
−0.368003 + 0.929825i \(0.619958\pi\)
\(500\) 55.4982 13.3239i 2.48195 0.595864i
\(501\) 1.21625 7.67910i 0.0543380 0.343077i
\(502\) 14.0299 + 7.14858i 0.626184 + 0.319057i
\(503\) 1.56454 1.83184i 0.0697594 0.0816778i −0.724429 0.689350i \(-0.757896\pi\)
0.794188 + 0.607672i \(0.207896\pi\)
\(504\) 46.3037 28.3750i 2.06253 1.26392i
\(505\) −13.5292 + 5.60399i −0.602042 + 0.249374i
\(506\) 23.9043 + 37.3875i 1.06267 + 1.66208i
\(507\) −2.75248 6.64508i −0.122242 0.295118i
\(508\) −13.6659 86.2829i −0.606325 3.82819i
\(509\) −10.0111 + 30.8110i −0.443734 + 1.36567i 0.440133 + 0.897933i \(0.354931\pi\)
−0.883866 + 0.467739i \(0.845069\pi\)
\(510\) 13.9050 + 3.13345i 0.615723 + 0.138752i
\(511\) 27.2007 19.7625i 1.20329 0.874241i
\(512\) 47.0233 + 7.44776i 2.07816 + 0.329148i
\(513\) −19.3444 + 16.5217i −0.854078 + 0.729452i
\(514\) 8.81139 + 2.86299i 0.388654 + 0.126281i
\(515\) 23.2454 + 5.58072i 1.02431 + 0.245916i
\(516\) −14.6332 + 35.3278i −0.644192 + 1.55522i
\(517\) 15.5315 + 29.0961i 0.683076 + 1.27964i
\(518\) −27.8809 + 27.8809i −1.22502 + 1.22502i
\(519\) 7.34509 1.16335i 0.322414 0.0510653i
\(520\) −14.9325 + 17.4837i −0.654835 + 0.766713i
\(521\) 23.6223 + 1.85912i 1.03491 + 0.0814493i 0.584518 0.811381i \(-0.301284\pi\)
0.450394 + 0.892830i \(0.351284\pi\)
\(522\) −13.9128 + 22.7037i −0.608948 + 0.993713i
\(523\) 5.03940 + 6.93614i 0.220358 + 0.303296i 0.904856 0.425718i \(-0.139979\pi\)
−0.684498 + 0.729015i \(0.739979\pi\)
\(524\) 30.4677 26.0219i 1.33099 1.13677i
\(525\) 4.00827 2.04231i 0.174935 0.0891339i
\(526\) 31.1498 + 22.6316i 1.35820 + 0.986787i
\(527\) −0.488136 + 3.38771i −0.0212635 + 0.147571i
\(528\) 21.6145 + 1.28664i 0.940651 + 0.0559937i
\(529\) −2.64324 2.64324i −0.114923 0.114923i
\(530\) −3.24014 + 13.4962i −0.140743 + 0.586236i
\(531\) 0.494197 + 0.160574i 0.0214463 + 0.00696834i
\(532\) 60.6545 + 71.0173i 2.62971 + 3.07899i
\(533\) −3.08678 12.8574i −0.133703 0.556914i
\(534\) −16.5971 + 3.98462i −0.718228 + 0.172431i
\(535\) 15.2395 + 7.76493i 0.658863 + 0.335707i
\(536\) −9.13067 17.9200i −0.394385 0.774024i
\(537\) 7.81396 + 12.7512i 0.337197 + 0.550256i
\(538\) −2.60954 + 6.29998i −0.112505 + 0.271612i
\(539\) 6.51709 + 8.61920i 0.280711 + 0.371255i
\(540\) 34.0703i 1.46615i
\(541\) −1.42445 + 5.93328i −0.0612421 + 0.255092i −0.994590 0.103883i \(-0.966873\pi\)
0.933347 + 0.358974i \(0.116873\pi\)
\(542\) 57.2575 29.1741i 2.45942 1.25314i
\(543\) −0.942030 2.89927i −0.0404264 0.124420i
\(544\) 26.8020 + 22.2509i 1.14913 + 0.954000i
\(545\) −4.32008 + 3.13872i −0.185052 + 0.134448i
\(546\) −5.28133 + 10.3652i −0.226020 + 0.443589i
\(547\) 18.3951 1.44773i 0.786520 0.0619004i 0.321163 0.947024i \(-0.395926\pi\)
0.465356 + 0.885123i \(0.345926\pi\)
\(548\) −13.7170 + 18.8799i −0.585963 + 0.806508i
\(549\) −8.05884 + 3.33808i −0.343943 + 0.142466i
\(550\) −15.8297 2.19842i −0.674983 0.0937408i
\(551\) −24.2865 10.0598i −1.03464 0.428561i
\(552\) −26.8658 + 4.25512i −1.14348 + 0.181110i
\(553\) −4.58463 8.99784i −0.194958 0.382627i
\(554\) 1.90915 24.2581i 0.0811120 1.03063i
\(555\) 1.48389 + 6.18084i 0.0629876 + 0.262362i
\(556\) 21.9983 35.8980i 0.932936 1.52241i
\(557\) −32.0402 + 10.4105i −1.35758 + 0.441106i −0.895236 0.445592i \(-0.852993\pi\)
−0.462349 + 0.886698i \(0.652993\pi\)
\(558\) 5.20595 0.409717i 0.220385 0.0173447i
\(559\) 3.14360 + 19.8479i 0.132960 + 0.839477i
\(560\) −49.1081 −2.07520
\(561\) −8.54000 5.78330i −0.360559 0.244171i
\(562\) −9.17528 −0.387036
\(563\) 0.937879 + 5.92153i 0.0395269 + 0.249563i 0.999538 0.0303996i \(-0.00967797\pi\)
−0.960011 + 0.279962i \(0.909678\pi\)
\(564\) −35.1088 + 2.76312i −1.47835 + 0.116348i
\(565\) −30.9478 + 10.0556i −1.30199 + 0.423041i
\(566\) −2.48229 + 4.05073i −0.104338 + 0.170265i
\(567\) 3.14311 + 13.0920i 0.131998 + 0.549813i
\(568\) −4.93338 + 62.6845i −0.207000 + 2.63018i
\(569\) 10.0897 + 19.8022i 0.422983 + 0.830151i 0.999911 + 0.0133561i \(0.00425149\pi\)
−0.576928 + 0.816795i \(0.695749\pi\)
\(570\) 21.2049 3.35853i 0.888178 0.140674i
\(571\) 41.9424 + 17.3731i 1.75523 + 0.727042i 0.997196 + 0.0748315i \(0.0238419\pi\)
0.758038 + 0.652210i \(0.226158\pi\)
\(572\) 25.5680 13.6482i 1.06905 0.570662i
\(573\) −8.18467 + 3.39020i −0.341920 + 0.141628i
\(574\) 34.6090 47.6352i 1.44455 1.98825i
\(575\) 9.59981 0.755521i 0.400340 0.0315074i
\(576\) 5.02126 9.85477i 0.209219 0.410616i
\(577\) 5.06723 3.68156i 0.210952 0.153265i −0.477293 0.878744i \(-0.658382\pi\)
0.688244 + 0.725479i \(0.258382\pi\)
\(578\) −14.7569 41.4391i −0.613806 1.72364i
\(579\) −6.09897 18.7707i −0.253465 0.780084i
\(580\) 31.3686 15.9831i 1.30251 0.663663i
\(581\) 8.66654 36.0987i 0.359549 1.49763i
\(582\) 26.9619i 1.11761i
\(583\) 5.74720 8.23640i 0.238025 0.341117i
\(584\) 28.0181 67.6418i 1.15940 2.79904i
\(585\) −4.18768 6.83368i −0.173139 0.282538i
\(586\) 23.0851 + 45.3070i 0.953636 + 1.87162i
\(587\) 28.2568 + 14.3976i 1.16628 + 0.594252i 0.926397 0.376549i \(-0.122889\pi\)
0.239888 + 0.970801i \(0.422889\pi\)
\(588\) −11.2193 + 2.69351i −0.462675 + 0.111079i
\(589\) 1.20349 + 5.01292i 0.0495891 + 0.206554i
\(590\) −0.636249 0.744952i −0.0261939 0.0306692i
\(591\) 16.5292 + 5.37066i 0.679920 + 0.220919i
\(592\) −9.61388 + 40.0447i −0.395128 + 1.64583i
\(593\) −12.3655 12.3655i −0.507792 0.507792i 0.406056 0.913848i \(-0.366904\pi\)
−0.913848 + 0.406056i \(0.866904\pi\)
\(594\) −12.8308 + 32.7293i −0.526454 + 1.34290i
\(595\) 20.1137 + 11.9423i 0.824583 + 0.489588i
\(596\) −11.8475 8.60769i −0.485292 0.352585i
\(597\) −0.0670210 + 0.0341489i −0.00274299 + 0.00139762i
\(598\) −18.9352 + 16.1722i −0.774317 + 0.661329i
\(599\) −8.36252 11.5100i −0.341683 0.470287i 0.603249 0.797553i \(-0.293873\pi\)
−0.944932 + 0.327266i \(0.893873\pi\)
\(600\) 5.11844 8.35254i 0.208959 0.340991i
\(601\) −4.45744 0.350808i −0.181823 0.0143098i −0.0127793 0.999918i \(-0.504068\pi\)
−0.169044 + 0.985609i \(0.554068\pi\)
\(602\) −58.1150 + 68.0439i −2.36859 + 2.77326i
\(603\) 6.92429 1.09670i 0.281979 0.0446611i
\(604\) 18.4661 18.4661i 0.751374 0.751374i
\(605\) −16.9901 9.53956i −0.690747 0.387838i
\(606\) −6.17421 + 14.9059i −0.250810 + 0.605509i
\(607\) 47.5089 + 11.4059i 1.92833 + 0.462950i 0.994429 + 0.105405i \(0.0336139\pi\)
0.933896 + 0.357545i \(0.116386\pi\)
\(608\) 49.9008 + 16.2138i 2.02374 + 0.657555i
\(609\) 7.77530 6.64073i 0.315071 0.269096i
\(610\) 16.2430 + 2.57263i 0.657659 + 0.104163i
\(611\) −14.9730 + 10.8785i −0.605742 + 0.440097i
\(612\) −39.7826 + 25.1501i −1.60811 + 1.01663i
\(613\) −2.45763 + 7.56380i −0.0992626 + 0.305499i −0.988341 0.152256i \(-0.951346\pi\)
0.889078 + 0.457755i \(0.151346\pi\)
\(614\) 8.17648 + 51.6243i 0.329976 + 2.08339i
\(615\) −3.63249 8.76960i −0.146476 0.353624i
\(616\) 68.9753 + 27.0403i 2.77910 + 1.08948i
\(617\) −29.3165 + 12.1433i −1.18024 + 0.488871i −0.884564 0.466418i \(-0.845544\pi\)
−0.295674 + 0.955289i \(0.595544\pi\)
\(618\) 22.4572 13.7618i 0.903360 0.553580i
\(619\) 11.0542 12.9428i 0.444307 0.520216i −0.492382 0.870379i \(-0.663874\pi\)
0.936689 + 0.350163i \(0.113874\pi\)
\(620\) −6.15185 3.13452i −0.247064 0.125885i
\(621\) 3.31355 20.9209i 0.132968 0.839528i
\(622\) 23.3440 5.60439i 0.936008 0.224716i
\(623\) −27.9254 2.19778i −1.11881 0.0880521i
\(624\) 0.953304 + 12.1129i 0.0381627 + 0.484903i
\(625\) 7.18319 9.88681i 0.287328 0.395473i
\(626\) −13.9160 33.5963i −0.556197 1.34278i
\(627\) −15.1724 3.33770i −0.605928 0.133295i
\(628\) 72.6341 2.89842
\(629\) 13.6759 14.0636i 0.545294 0.560752i
\(630\) 11.0286 33.9425i 0.439390 1.35230i
\(631\) 0.0781904 0.153457i 0.00311271 0.00610904i −0.889445 0.457042i \(-0.848909\pi\)
0.892558 + 0.450933i \(0.148909\pi\)
\(632\) −18.7500 11.4900i −0.745833 0.457047i
\(633\) 4.32911 + 5.95852i 0.172067 + 0.236830i
\(634\) −1.92441 2.25320i −0.0764282 0.0894860i
\(635\) −25.0604 21.4036i −0.994492 0.849376i
\(636\) 5.60330 + 9.14375i 0.222185 + 0.362573i
\(637\) −4.28758 + 4.28758i −0.169880 + 0.169880i
\(638\) −36.1531 + 3.54064i −1.43131 + 0.140175i
\(639\) −20.2496 8.38765i −0.801061 0.331810i
\(640\) 7.74111 4.74376i 0.305994 0.187514i
\(641\) −2.09048 26.5620i −0.0825689 1.04914i −0.889030 0.457849i \(-0.848620\pi\)
0.806461 0.591287i \(-0.201380\pi\)
\(642\) 17.9218 5.82314i 0.707316 0.229821i
\(643\) 17.5992 + 10.7848i 0.694046 + 0.425312i 0.824288 0.566171i \(-0.191576\pi\)
−0.130243 + 0.991482i \(0.541576\pi\)
\(644\) −76.8049 12.1647i −3.02654 0.479356i
\(645\) 4.45780 + 13.7197i 0.175526 + 0.540213i
\(646\) −43.7299 49.7755i −1.72053 1.95839i
\(647\) −22.0460 16.0174i −0.866719 0.629708i 0.0629858 0.998014i \(-0.479938\pi\)
−0.929704 + 0.368306i \(0.879938\pi\)
\(648\) 20.7318 + 20.7318i 0.814421 + 0.814421i
\(649\) 0.231886 + 0.669896i 0.00910232 + 0.0262957i
\(650\) 8.96802i 0.351755i
\(651\) −1.94990 0.468130i −0.0764228 0.0183475i
\(652\) −30.4136 25.9757i −1.19109 1.01729i
\(653\) −0.915291 + 11.6299i −0.0358181 + 0.455112i 0.952690 + 0.303944i \(0.0983035\pi\)
−0.988508 + 0.151168i \(0.951696\pi\)
\(654\) −0.920345 + 5.81083i −0.0359883 + 0.227221i
\(655\) 2.36464 14.9297i 0.0923941 0.583353i
\(656\) 4.82508 61.3085i 0.188388 2.39370i
\(657\) 19.4064 + 16.5746i 0.757115 + 0.646638i
\(658\) −80.1367 19.2391i −3.12406 0.750019i
\(659\) 17.2678i 0.672659i 0.941744 + 0.336330i \(0.109186\pi\)
−0.941744 + 0.336330i \(0.890814\pi\)
\(660\) 16.5957 12.5483i 0.645988 0.488440i
\(661\) 9.10883 + 9.10883i 0.354293 + 0.354293i 0.861704 0.507411i \(-0.169398\pi\)
−0.507411 + 0.861704i \(0.669398\pi\)
\(662\) −51.9997 37.7800i −2.02103 1.46836i
\(663\) 2.55521 5.19303i 0.0992362 0.201680i
\(664\) −24.9816 76.8854i −0.969473 2.98373i
\(665\) 34.7998 + 5.51174i 1.34948 + 0.213736i
\(666\) −25.5190 15.6381i −0.988842 0.605963i
\(667\) 20.8164 6.76366i 0.806014 0.261890i
\(668\) −3.79751 48.2520i −0.146930 1.86693i
\(669\) −12.1997 + 7.47596i −0.471666 + 0.289037i
\(670\) −12.2112 5.05806i −0.471761 0.195410i
\(671\) −10.2632 6.02296i −0.396205 0.232514i
\(672\) −14.4314 + 14.4314i −0.556704 + 0.556704i
\(673\) −11.8894 19.4017i −0.458303 0.747882i 0.537114 0.843509i \(-0.319514\pi\)
−0.995417 + 0.0956273i \(0.969514\pi\)
\(674\) −22.8743 19.5365i −0.881086 0.752518i
\(675\) 4.95425 + 5.80069i 0.190689 + 0.223269i
\(676\) −26.3190 36.2250i −1.01227 1.39327i
\(677\) 7.45798 + 4.57026i 0.286633 + 0.175649i 0.658381 0.752684i \(-0.271241\pi\)
−0.371748 + 0.928334i \(0.621241\pi\)
\(678\) −16.2763 + 31.9440i −0.625087 + 1.22680i
\(679\) −13.6733 + 42.0819i −0.524731 + 1.61496i
\(680\) 50.9331 0.711806i 1.95320 0.0272965i
\(681\) −5.18571 −0.198717
\(682\) 4.72924 + 5.32791i 0.181092 + 0.204016i
\(683\) 3.61897 + 8.73698i 0.138476 + 0.334311i 0.977870 0.209212i \(-0.0670899\pi\)
−0.839394 + 0.543523i \(0.817090\pi\)
\(684\) −41.6691 + 57.3525i −1.59326 + 2.19293i
\(685\) 0.690753 + 8.77684i 0.0263923 + 0.335346i
\(686\) 30.9156 + 2.43311i 1.18036 + 0.0928967i
\(687\) −10.2986 + 2.47248i −0.392916 + 0.0943309i
\(688\) −14.6207 + 92.3114i −0.557409 + 3.51934i
\(689\) 5.02150 + 2.55858i 0.191304 + 0.0974742i
\(690\) −11.6095 + 13.5929i −0.441965 + 0.517474i
\(691\) −7.34591 + 4.50158i −0.279451 + 0.171248i −0.655161 0.755489i \(-0.727399\pi\)
0.375709 + 0.926738i \(0.377399\pi\)
\(692\) 42.7719 17.7167i 1.62594 0.673488i
\(693\) −16.3941 + 19.9538i −0.622760 + 0.757983i
\(694\) −16.4537 39.7227i −0.624573 1.50785i
\(695\) −2.48470 15.6878i −0.0942501 0.595072i
\(696\) 6.88067 21.1765i 0.260811 0.802694i
\(697\) −16.8856 + 23.9374i −0.639586 + 0.906694i
\(698\) −45.9162 + 33.3601i −1.73796 + 1.26270i
\(699\) 16.9501 + 2.68464i 0.641113 + 0.101542i
\(700\) 21.2955 18.1880i 0.804893 0.687444i
\(701\) 41.5072 + 13.4865i 1.56770 + 0.509378i 0.958852 0.283906i \(-0.0916303\pi\)
0.608852 + 0.793284i \(0.291630\pi\)
\(702\) −19.1817 4.60511i −0.723965 0.173809i
\(703\) 11.3072 27.2981i 0.426460 1.02957i
\(704\) 14.8552 2.64435i 0.559878 0.0996628i
\(705\) −9.39463 + 9.39463i −0.353822 + 0.353822i
\(706\) −58.2688 + 9.22887i −2.19298 + 0.347333i
\(707\) −17.1959 + 20.1338i −0.646718 + 0.757210i
\(708\) −0.754608 0.0593890i −0.0283599 0.00223197i
\(709\) −14.1731 + 23.1285i −0.532284 + 0.868608i −0.999882 0.0153327i \(-0.995119\pi\)
0.467599 + 0.883941i \(0.345119\pi\)
\(710\) 24.2889 + 33.4308i 0.911545 + 1.25463i
\(711\) 5.82880 4.97827i 0.218597 0.186700i
\(712\) −54.3499 + 27.6926i −2.03685 + 1.03783i
\(713\) −3.47270 2.52306i −0.130054 0.0944894i
\(714\) 24.9735 6.36598i 0.934610 0.238241i
\(715\) 3.99071 10.1796i 0.149244 0.380697i
\(716\) 65.8320 + 65.8320i 2.46026 + 2.46026i
\(717\) −4.31803 + 17.9859i −0.161260 + 0.671696i
\(718\) 56.5004 + 18.3581i 2.10857 + 0.685117i
\(719\) −8.48733 9.93738i −0.316524 0.370602i 0.579221 0.815171i \(-0.303357\pi\)
−0.895745 + 0.444569i \(0.853357\pi\)
\(720\) −8.70192 36.2461i −0.324301 1.35081i
\(721\) 42.0300 10.0905i 1.56528 0.375791i
\(722\) −45.1149 22.9872i −1.67900 0.855495i
\(723\) 0.0720954 + 0.141495i 0.00268126 + 0.00526226i
\(724\) −9.91593 16.1813i −0.368523 0.601374i
\(725\) −3.01656 + 7.28261i −0.112032 + 0.270470i
\(726\) −20.6681 + 5.80441i −0.767067 + 0.215422i
\(727\) 6.59541i 0.244610i 0.992493 + 0.122305i \(0.0390286\pi\)
−0.992493 + 0.122305i \(0.960971\pi\)
\(728\) −9.70504 + 40.4244i −0.359693 + 1.49823i
\(729\) −0.847552 + 0.431849i −0.0313908 + 0.0159944i
\(730\) −14.8686 45.7608i −0.550311 1.69368i
\(731\) 28.4371 34.2535i 1.05178 1.26691i
\(732\) 10.2798 7.46869i 0.379951 0.276051i
\(733\) 2.71773 5.33385i 0.100382 0.197010i −0.835354 0.549713i \(-0.814737\pi\)
0.935736 + 0.352702i \(0.114737\pi\)
\(734\) 17.8326 1.40346i 0.658213 0.0518025i
\(735\) −2.55853 + 3.52151i −0.0943727 + 0.129893i
\(736\) −40.3615 + 16.7183i −1.48774 + 0.616244i
\(737\) 6.89065 + 6.63255i 0.253820 + 0.244313i
\(738\) 41.2916 + 17.1035i 1.51996 + 0.629590i
\(739\) 6.09439 0.965257i 0.224186 0.0355075i −0.0433309 0.999061i \(-0.513797\pi\)
0.267517 + 0.963553i \(0.413797\pi\)
\(740\) 17.9651 + 35.2584i 0.660409 + 1.29613i
\(741\) 0.683966 8.69061i 0.0251261 0.319257i
\(742\) 5.85851 + 24.4024i 0.215073 + 0.895842i
\(743\) 8.23857 13.4441i 0.302244 0.493217i −0.665076 0.746775i \(-0.731601\pi\)
0.967320 + 0.253558i \(0.0816010\pi\)
\(744\) −4.15303 + 1.34940i −0.152257 + 0.0494714i
\(745\) −5.50763 + 0.433460i −0.201784 + 0.0158808i
\(746\) −4.85752 30.6691i −0.177846 1.12288i
\(747\) 28.1797 1.03104
\(748\) −60.1006 22.5974i −2.19750 0.826244i
\(749\) 30.9253 1.12999
\(750\) −3.71109 23.4309i −0.135510 0.855575i
\(751\) 41.4817 3.26468i 1.51369 0.119130i 0.705777 0.708434i \(-0.250598\pi\)
0.807911 + 0.589305i \(0.200598\pi\)
\(752\) −81.8650 + 26.5995i −2.98531 + 0.969986i
\(753\) 2.39815 3.91342i 0.0873933 0.142613i
\(754\) −4.75859 19.8209i −0.173297 0.721836i
\(755\) 0.772984 9.82170i 0.0281318 0.357448i
\(756\) −27.9670 54.8884i −1.01715 1.99627i
\(757\) 9.66607 1.53095i 0.351319 0.0556435i 0.0217191 0.999764i \(-0.493086\pi\)
0.329600 + 0.944121i \(0.393086\pi\)
\(758\) −29.7445 12.3206i −1.08037 0.447503i
\(759\) 11.4110 6.09123i 0.414194 0.221098i
\(760\) 70.8840 29.3611i 2.57123 1.06504i
\(761\) −11.1665 + 15.3694i −0.404786 + 0.557140i −0.961937 0.273271i \(-0.911894\pi\)
0.557151 + 0.830411i \(0.311894\pi\)
\(762\) −36.1981 + 2.84885i −1.31132 + 0.103203i
\(763\) −4.38333 + 8.60276i −0.158687 + 0.311441i
\(764\) −44.6180 + 32.4168i −1.61422 + 1.17280i
\(765\) −5.25036 + 16.9619i −0.189827 + 0.613258i
\(766\) 22.1857 + 68.2805i 0.801601 + 2.46707i
\(767\) −0.354435 + 0.180594i −0.0127979 + 0.00652087i
\(768\) 3.93716 16.3995i 0.142070 0.591765i
\(769\) 39.1191i 1.41067i 0.708875 + 0.705335i \(0.249203\pi\)
−0.708875 + 0.705335i \(0.750797\pi\)
\(770\) 46.0099 15.9264i 1.65808 0.573948i
\(771\) 1.03346 2.49500i 0.0372193 0.0898553i
\(772\) −64.1986 104.763i −2.31056 3.77049i
\(773\) −0.194707 0.382134i −0.00700313 0.0137444i 0.887478 0.460849i \(-0.152455\pi\)
−0.894482 + 0.447105i \(0.852455\pi\)
\(774\) −60.5203 30.8366i −2.17536 1.10840i
\(775\) 1.50319 0.360884i 0.0539961 0.0129633i
\(776\) 22.4932 + 93.6910i 0.807459 + 3.36331i
\(777\) 7.46421 + 8.73946i 0.267777 + 0.313526i
\(778\) 18.5337 + 6.02198i 0.664467 + 0.215898i
\(779\) −10.3003 + 42.9038i −0.369047 + 1.53719i
\(780\) 8.25547 + 8.25547i 0.295593 + 0.295593i
\(781\) −7.53383 28.9365i −0.269582 1.03543i
\(782\) 54.6029 + 7.86774i 1.95259 + 0.281350i
\(783\) 14.0277 + 10.1917i 0.501310 + 0.364223i
\(784\) −25.1275 + 12.8031i −0.897411 + 0.457254i
\(785\) 20.8365 17.7960i 0.743685 0.635167i
\(786\) −9.78893 13.4733i −0.349160 0.480577i
\(787\) 18.1669 29.6456i 0.647579 1.05675i −0.345399 0.938456i \(-0.612256\pi\)
0.992978 0.118297i \(-0.0377435\pi\)
\(788\) 107.862 + 8.48896i 3.84244 + 0.302407i
\(789\) 7.28886 8.53416i 0.259490 0.303824i
\(790\) −14.2739 + 2.26076i −0.507842 + 0.0804343i
\(791\) −41.6037 + 41.6037i −1.47926 + 1.47926i
\(792\) −7.73574 + 55.7014i −0.274878 + 1.97926i
\(793\) 2.55540 6.16928i 0.0907449 0.219078i
\(794\) 16.9414 + 4.06728i 0.601229 + 0.144342i
\(795\) 3.84771 + 1.25020i 0.136464 + 0.0443399i
\(796\) −0.356075 + 0.304117i −0.0126207 + 0.0107791i
\(797\) −24.8929 3.94265i −0.881752 0.139656i −0.300891 0.953659i \(-0.597284\pi\)
−0.580861 + 0.814003i \(0.697284\pi\)
\(798\) 31.4049 22.8170i 1.11172 0.807714i
\(799\) 39.9989 + 9.01365i 1.41506 + 0.318880i
\(800\) 4.86191 14.9634i 0.171894 0.529037i
\(801\) −3.32621 21.0009i −0.117526 0.742029i
\(802\) −15.2830 36.8965i −0.539663 1.30286i
\(803\) −2.06885 + 34.7551i −0.0730082 + 1.22648i
\(804\) −9.43494 + 3.90808i −0.332745 + 0.137827i
\(805\) −25.0134 + 15.3282i −0.881606 + 0.540249i
\(806\) −2.59625 + 3.03982i −0.0914491 + 0.107073i
\(807\) 1.77102 + 0.902378i 0.0623427 + 0.0317652i
\(808\) −9.01965 + 56.9478i −0.317310 + 2.00342i
\(809\) −12.2889 + 2.95031i −0.432056 + 0.103727i −0.443639 0.896206i \(-0.646313\pi\)
0.0115834 + 0.999933i \(0.496313\pi\)
\(810\) 19.2087 + 1.51176i 0.674926 + 0.0531178i
\(811\) 2.04303 + 25.9591i 0.0717404 + 0.911548i 0.922501 + 0.385994i \(0.126142\pi\)
−0.850761 + 0.525553i \(0.823858\pi\)
\(812\) 37.4159 51.4986i 1.31304 1.80725i
\(813\) −7.16817 17.3055i −0.251399 0.606930i
\(814\) −3.97969 40.6362i −0.139488 1.42430i
\(815\) −15.0890 −0.528544
\(816\) 18.7660 19.2980i 0.656942 0.675564i
\(817\) 20.7215 63.7742i 0.724953 2.23118i
\(818\) −3.93500 + 7.72287i −0.137584 + 0.270024i
\(819\) −12.3560 7.57176i −0.431753 0.264579i
\(820\) −34.7335 47.8066i −1.21295 1.66948i
\(821\) −17.0689 19.9852i −0.595710 0.697487i 0.377863 0.925861i \(-0.376659\pi\)
−0.973573 + 0.228374i \(0.926659\pi\)
\(822\) 7.37579 + 6.29952i 0.257260 + 0.219721i
\(823\) −9.88835 16.1363i −0.344686 0.562477i 0.632579 0.774495i \(-0.281996\pi\)
−0.977266 + 0.212019i \(0.931996\pi\)
\(824\) 66.5564 66.5564i 2.31860 2.31860i
\(825\) −1.00085 + 4.54965i −0.0348453 + 0.158398i
\(826\) −1.63652 0.677868i −0.0569418 0.0235861i
\(827\) 16.2103 9.93371i 0.563689 0.345429i −0.211283 0.977425i \(-0.567764\pi\)
0.774972 + 0.631996i \(0.217764\pi\)
\(828\) −4.63115 58.8443i −0.160944 2.04498i
\(829\) 42.0281 13.6558i 1.45970 0.474284i 0.531719 0.846921i \(-0.321546\pi\)
0.927977 + 0.372636i \(0.121546\pi\)
\(830\) −45.2993 27.7594i −1.57236 0.963544i
\(831\) −7.00542 1.10955i −0.243015 0.0384899i
\(832\) 2.61644 + 8.05256i 0.0907086 + 0.279172i
\(833\) 13.4053 + 0.866721i 0.464465 + 0.0300301i
\(834\) −14.1574 10.2860i −0.490231 0.356174i
\(835\) −12.9116 12.9116i −0.446823 0.446823i
\(836\) −96.6949 + 1.84549i −3.34426 + 0.0638277i
\(837\) 3.40048i 0.117538i
\(838\) 52.2181 + 12.5364i 1.80384 + 0.433064i
\(839\) −10.0761 8.60580i −0.347866 0.297105i 0.458297 0.888799i \(-0.348460\pi\)
−0.806163 + 0.591694i \(0.798460\pi\)
\(840\) −2.34153 + 29.7519i −0.0807904 + 1.02654i
\(841\) 1.73375 10.9464i 0.0597843 0.377463i
\(842\) −6.06094 + 38.2673i −0.208874 + 1.31878i
\(843\) −0.209836 + 2.66622i −0.00722714 + 0.0918296i
\(844\) 34.8652 + 29.7777i 1.20011 + 1.02499i
\(845\) −16.4256 3.94343i −0.565056 0.135658i
\(846\) 62.5571i 2.15076i
\(847\) −35.2023 1.42199i −1.20956 0.0488603i
\(848\) 18.5344 + 18.5344i 0.636474 + 0.636474i
\(849\) 1.12032 + 0.813960i 0.0384493 + 0.0279350i
\(850\) −14.9258 + 13.1130i −0.511952 + 0.449771i
\(851\) 7.60237 + 23.3977i 0.260606 + 0.802063i
\(852\) 31.5347 + 4.99460i 1.08036 + 0.171112i
\(853\) −35.6457 21.8437i −1.22049 0.747914i −0.245331 0.969439i \(-0.578897\pi\)
−0.975155 + 0.221525i \(0.928897\pi\)
\(854\) 28.2797 9.18864i 0.967712 0.314429i
\(855\) 2.09834 + 26.6619i 0.0717617 + 0.911819i
\(856\) 57.4191 35.1865i 1.96255 1.20265i
\(857\) 36.1576 + 14.9770i 1.23512 + 0.511603i 0.902186 0.431347i \(-0.141962\pi\)
0.332933 + 0.942950i \(0.391962\pi\)
\(858\) −4.82153 11.0395i −0.164604 0.376883i
\(859\) 10.9287 10.9287i 0.372883 0.372883i −0.495643 0.868526i \(-0.665068\pi\)
0.868526 + 0.495643i \(0.165068\pi\)
\(860\) 46.9234 + 76.5720i 1.60007 + 2.61109i
\(861\) −13.0507 11.1463i −0.444766 0.379866i
\(862\) −14.2241 16.6543i −0.484474 0.567247i
\(863\) 27.0666 + 37.2540i 0.921358 + 1.26814i 0.963137 + 0.269013i \(0.0866975\pi\)
−0.0417789 + 0.999127i \(0.513303\pi\)
\(864\) −29.5086 18.0829i −1.00390 0.615192i
\(865\) 7.92917 15.5619i 0.269600 0.529119i
\(866\) −19.5707 + 60.2324i −0.665039 + 2.04678i
\(867\) −12.3792 + 3.34047i −0.420419 + 0.113448i
\(868\) −12.4838 −0.423729
\(869\) 10.2131 + 2.24674i 0.346457 + 0.0762154i
\(870\) −5.59985 13.5192i −0.189853 0.458345i
\(871\) −3.15454 + 4.34185i −0.106888 + 0.147118i
\(872\) 1.64959 + 20.9601i 0.0558623 + 0.709798i
\(873\) −33.4831 2.63517i −1.13323 0.0891871i
\(874\) 80.7978 19.3978i 2.73303 0.656142i
\(875\) 6.09032 38.4528i 0.205891 1.29994i
\(876\) −33.1244 16.8777i −1.11917 0.570246i
\(877\) 16.5792 19.4117i 0.559839 0.655487i −0.406230 0.913771i \(-0.633157\pi\)
0.966069 + 0.258284i \(0.0831570\pi\)
\(878\) 16.5502 10.1420i 0.558542 0.342275i
\(879\) 13.6936 5.67207i 0.461874 0.191314i
\(880\) 32.2825 39.2922i 1.08824 1.32454i
\(881\) −5.55550 13.4122i −0.187170 0.451867i 0.802243 0.596998i \(-0.203640\pi\)
−0.989413 + 0.145130i \(0.953640\pi\)
\(882\) −3.20616 20.2429i −0.107957 0.681614i
\(883\) −9.43193 + 29.0285i −0.317410 + 0.976887i 0.657341 + 0.753593i \(0.271681\pi\)
−0.974751 + 0.223294i \(0.928319\pi\)
\(884\) 7.92069 35.1488i 0.266402 1.18218i
\(885\) −0.231024 + 0.167849i −0.00776580 + 0.00564218i
\(886\) 88.1504 + 13.9616i 2.96147 + 0.469051i
\(887\) 32.0345 27.3600i 1.07561 0.918659i 0.0786772 0.996900i \(-0.474930\pi\)
0.996934 + 0.0782410i \(0.0249304\pi\)
\(888\) 23.8025 + 7.73390i 0.798759 + 0.259533i
\(889\) −57.9425 13.9108i −1.94333 0.466552i
\(890\) −15.3407 + 37.0357i −0.514221 + 1.24144i
\(891\) −12.5413 6.09153i −0.420150 0.204074i
\(892\) −62.9844 + 62.9844i −2.10887 + 2.10887i
\(893\) 60.9979 9.66112i 2.04122 0.323297i
\(894\) −3.95307 + 4.62845i −0.132210 + 0.154799i
\(895\) 35.0146 + 2.75571i 1.17041 + 0.0921132i
\(896\) 8.57720 13.9967i 0.286544 0.467598i
\(897\) 4.26639 + 5.87218i 0.142450 + 0.196066i
\(898\) −35.5176 + 30.3349i −1.18524 + 1.01229i
\(899\) 3.13083 1.59524i 0.104419 0.0532041i
\(900\) 17.1979 + 12.4950i 0.573264 + 0.416501i
\(901\) −3.08405 12.0986i −0.102745 0.403063i
\(902\) 15.3625 + 59.0054i 0.511515 + 1.96467i
\(903\) 18.4436 + 18.4436i 0.613766 + 0.613766i
\(904\) −29.9095 + 124.582i −0.994776 + 4.14354i
\(905\) −6.80914 2.21242i −0.226344 0.0735435i
\(906\) −7.04946 8.25386i −0.234203 0.274216i
\(907\) 2.14029 + 8.91494i 0.0710671 + 0.296016i 0.996573 0.0827173i \(-0.0263599\pi\)
−0.925506 + 0.378733i \(0.876360\pi\)
\(908\) −31.3911 + 7.53633i −1.04175 + 0.250102i
\(909\) −17.9076 9.12439i −0.593958 0.302637i
\(910\) 12.4036 + 24.3434i 0.411174 + 0.806975i
\(911\) 13.1223 + 21.4136i 0.434761 + 0.709465i 0.992726 0.120399i \(-0.0384175\pi\)
−0.557965 + 0.829865i \(0.688417\pi\)
\(912\) 15.5157 37.4582i 0.513777 1.24037i
\(913\) 23.1860 + 30.6647i 0.767344 + 1.01485i
\(914\) 44.1676i 1.46094i
\(915\) 1.11905 4.66117i 0.0369946 0.154093i
\(916\) −58.7481 + 29.9337i −1.94109 + 0.989036i
\(917\) −8.44574 25.9933i −0.278903 0.858375i
\(918\) 20.3828 + 38.6583i 0.672733 + 1.27592i
\(919\) 7.06358 5.13199i 0.233006 0.169289i −0.465156 0.885229i \(-0.654002\pi\)
0.698162 + 0.715940i \(0.254002\pi\)
\(920\) −29.0022 + 56.9199i −0.956173 + 1.87660i
\(921\) 15.1884 1.19535i 0.500473 0.0393881i
\(922\) −44.3587 + 61.0545i −1.46087 + 2.01072i
\(923\) 15.5016 6.42099i 0.510243 0.211350i
\(924\) 16.4359 33.8384i 0.540701 1.11320i
\(925\) −8.18568 3.39062i −0.269144 0.111483i
\(926\) −78.2872 + 12.3995i −2.57268 + 0.407472i
\(927\) 14.8954 + 29.2338i 0.489228 + 0.960165i
\(928\) 2.80584 35.6516i 0.0921064 1.17032i
\(929\) −9.25503 38.5500i −0.303648 1.26478i −0.890460 0.455061i \(-0.849617\pi\)
0.586812 0.809723i \(-0.300383\pi\)
\(930\) −1.49945 + 2.44688i −0.0491689 + 0.0802363i
\(931\) 19.2432 6.25250i 0.630671 0.204917i
\(932\) 106.507 8.38229i 3.48875 0.274571i
\(933\) −1.09470 6.91163i −0.0358387 0.226277i
\(934\) −1.40558 −0.0459918
\(935\) −22.7776 + 8.24270i −0.744906 + 0.269565i
\(936\) −31.5565 −1.03146
\(937\) −1.82654 11.5323i −0.0596706 0.376745i −0.999394 0.0348097i \(-0.988917\pi\)
0.939723 0.341936i \(-0.111083\pi\)
\(938\) −23.8246 + 1.87504i −0.777902 + 0.0612222i
\(939\) −10.0809 + 3.27549i −0.328978 + 0.106892i
\(940\) −43.2161 + 70.5223i −1.40955 + 2.30018i
\(941\) −8.16794 34.0219i −0.266267 1.10908i −0.931875 0.362780i \(-0.881827\pi\)
0.665607 0.746302i \(-0.268173\pi\)
\(942\) 2.36868 30.0969i 0.0771757 0.980610i
\(943\) −16.6787 32.7338i −0.543133 1.06596i
\(944\) −1.82733 + 0.289421i −0.0594746 + 0.00941984i
\(945\) −21.4710 8.89359i −0.698452 0.289308i
\(946\) −16.2396 91.2292i −0.527994 2.96612i
\(947\) −18.6377 + 7.72000i −0.605644 + 0.250866i −0.664365 0.747408i \(-0.731298\pi\)
0.0587205 + 0.998274i \(0.481298\pi\)
\(948\) −6.56328 + 9.03358i −0.213165 + 0.293397i
\(949\) −19.4769 + 1.53287i −0.632248 + 0.0497590i
\(950\) −13.5859 + 26.6638i −0.440784 + 0.865087i
\(951\) −0.698762 + 0.507680i −0.0226589 + 0.0164627i
\(952\) 81.4706 42.9558i 2.64048 1.39220i
\(953\) 4.00682 + 12.3317i 0.129794 + 0.399464i 0.994744 0.102394i \(-0.0326502\pi\)
−0.864950 + 0.501858i \(0.832650\pi\)
\(954\) −16.9730 + 8.64819i −0.549522 + 0.279995i
\(955\) −4.85708 + 20.2312i −0.157171 + 0.654666i
\(956\) 115.151i 3.72424i
\(957\) 0.202053 + 10.5866i 0.00653145 + 0.342216i
\(958\) −25.5451 + 61.6714i −0.825326 + 1.99251i
\(959\) 8.31740 + 13.5728i 0.268583 + 0.438287i
\(960\) 2.75942 + 5.41567i 0.0890600 + 0.174790i
\(961\) 27.0072 + 13.7609i 0.871200 + 0.443899i
\(962\) 22.2788 5.34866i 0.718297 0.172448i
\(963\) 5.47994 + 22.8256i 0.176589 + 0.735544i
\(964\) 0.642053 + 0.751748i 0.0206791 + 0.0242122i
\(965\) −44.0843 14.3239i −1.41913 0.461102i
\(966\) −7.54529 + 31.4284i −0.242766 + 1.01119i
\(967\) −20.5132 20.5132i −0.659661 0.659661i 0.295639 0.955300i \(-0.404467\pi\)
−0.955300 + 0.295639i \(0.904467\pi\)
\(968\) −66.9782 + 37.4126i −2.15276 + 1.20249i
\(969\) −15.4642 + 11.5690i −0.496782 + 0.371650i
\(970\) 51.2285 + 37.2197i 1.64485 + 1.19505i
\(971\) −11.6068 + 5.91395i −0.372479 + 0.189788i −0.630202 0.776431i \(-0.717028\pi\)
0.257723 + 0.966219i \(0.417028\pi\)
\(972\) 55.1972 47.1429i 1.77045 1.51211i
\(973\) −16.8804 23.2339i −0.541162 0.744845i
\(974\) −29.5893 + 48.2853i −0.948102 + 1.54716i
\(975\) −2.60599 0.205096i −0.0834586 0.00656833i
\(976\) 20.1699 23.6160i 0.645624 0.755929i
\(977\) 29.0094 4.59464i 0.928093 0.146995i 0.325953 0.945386i \(-0.394315\pi\)
0.602140 + 0.798391i \(0.294315\pi\)
\(978\) −11.7552 + 11.7552i −0.375889 + 0.375889i
\(979\) 20.1160 20.8988i 0.642910 0.667929i
\(980\) −10.3700 + 25.0353i −0.331256 + 0.799723i
\(981\) −7.12631 1.71088i −0.227526 0.0546241i
\(982\) 14.5503 + 4.72769i 0.464320 + 0.150867i
\(983\) 27.1045 23.1495i 0.864501 0.738353i −0.102064 0.994778i \(-0.532545\pi\)
0.966564 + 0.256425i \(0.0825445\pi\)
\(984\) −36.9134 5.84651i −1.17676 0.186380i
\(985\) 33.0222 23.9920i 1.05218 0.764450i
\(986\) −26.0308 + 36.9019i −0.828989 + 1.17520i
\(987\) −7.42335 + 22.8467i −0.236288 + 0.727219i
\(988\) −8.48964 53.6015i −0.270092 1.70529i
\(989\) 21.3663 + 51.5827i 0.679408 + 1.64024i
\(990\) 19.9080 + 31.1372i 0.632718 + 0.989605i
\(991\) −27.9090 + 11.5603i −0.886557 + 0.367224i −0.779036 0.626979i \(-0.784291\pi\)
−0.107521 + 0.994203i \(0.534291\pi\)
\(992\) −5.97993 + 3.66451i −0.189863 + 0.116348i
\(993\) −12.1676 + 14.2464i −0.386127 + 0.452097i
\(994\) 66.5722 + 33.9202i 2.11154 + 1.07588i
\(995\) −0.0276354 + 0.174483i −0.000876102 + 0.00553149i
\(996\) −39.9151 + 9.58276i −1.26476 + 0.303641i
\(997\) −61.0256 4.80282i −1.93270 0.152107i −0.947071 0.321025i \(-0.895973\pi\)
−0.985630 + 0.168918i \(0.945973\pi\)
\(998\) 2.66584 + 33.8727i 0.0843856 + 1.07222i
\(999\) −11.4556 + 15.7672i −0.362438 + 0.498853i
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 187.2.r.a.15.1 256
11.3 even 5 inner 187.2.r.a.168.1 yes 256
17.8 even 8 inner 187.2.r.a.59.1 yes 256
187.25 even 40 inner 187.2.r.a.25.1 yes 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.r.a.15.1 256 1.1 even 1 trivial
187.2.r.a.25.1 yes 256 187.25 even 40 inner
187.2.r.a.59.1 yes 256 17.8 even 8 inner
187.2.r.a.168.1 yes 256 11.3 even 5 inner