Properties

Label 304.2.bg.a.203.23
Level $304$
Weight $2$
Character 304.203
Analytic conductor $2.427$
Analytic rank $0$
Dimension $456$
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] = [304,2,Mod(3,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 27, 26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.bg (of order \(36\), degree \(12\), 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: \(2.42745222145\)
Analytic rank: \(0\)
Dimension: \(456\)
Relative dimension: \(38\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 203.23
Character \(\chi\) \(=\) 304.203
Dual form 304.2.bg.a.3.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.278524 - 1.38652i) q^{2} +(-1.52751 + 0.712288i) q^{3} +(-1.84485 - 0.772356i) q^{4} +(-0.0344794 + 0.0492417i) q^{5} +(0.562151 + 2.31630i) q^{6} +(2.22167 - 3.84804i) q^{7} +(-1.58472 + 2.34279i) q^{8} +(-0.102440 + 0.122083i) q^{9} +O(q^{10})\) \(q+(0.278524 - 1.38652i) q^{2} +(-1.52751 + 0.712288i) q^{3} +(-1.84485 - 0.772356i) q^{4} +(-0.0344794 + 0.0492417i) q^{5} +(0.562151 + 2.31630i) q^{6} +(2.22167 - 3.84804i) q^{7} +(-1.58472 + 2.34279i) q^{8} +(-0.102440 + 0.122083i) q^{9} +(0.0586710 + 0.0615212i) q^{10} +(-2.72589 - 0.730400i) q^{11} +(3.36816 - 0.134285i) q^{12} +(-5.08503 - 2.37119i) q^{13} +(-4.71658 - 4.15215i) q^{14} +(0.0175933 - 0.0997763i) q^{15} +(2.80693 + 2.84976i) q^{16} +(-3.77112 + 3.16435i) q^{17} +(0.140738 + 0.176037i) q^{18} +(-3.94311 - 1.85792i) q^{19} +(0.101641 - 0.0642131i) q^{20} +(-0.652698 + 7.46037i) q^{21} +(-1.77194 + 3.57605i) q^{22} +(-0.348312 + 1.97538i) q^{23} +(0.751925 - 4.70741i) q^{24} +(1.70886 + 4.69507i) q^{25} +(-4.70399 + 6.39004i) q^{26} +(1.37817 - 5.14341i) q^{27} +(-7.07069 + 5.38313i) q^{28} +(-0.631332 - 7.21616i) q^{29} +(-0.133441 - 0.0521834i) q^{30} +(5.51586 - 9.55374i) q^{31} +(4.73303 - 3.09813i) q^{32} +(4.68407 - 0.825928i) q^{33} +(3.33707 + 6.11006i) q^{34} +(0.112882 + 0.242077i) q^{35} +(0.283277 - 0.146104i) q^{36} +(-1.81779 + 1.81779i) q^{37} +(-3.67429 + 4.94971i) q^{38} +9.45639 q^{39} +(-0.0607229 - 0.158812i) q^{40} +(0.822845 + 0.299491i) q^{41} +(10.1621 + 2.98287i) q^{42} +(-1.99291 - 1.39545i) q^{43} +(4.46473 + 3.45283i) q^{44} +(-0.00247950 - 0.00925364i) q^{45} +(2.64188 + 1.03313i) q^{46} +(1.07854 - 1.28536i) q^{47} +(-6.31746 - 2.35368i) q^{48} +(-6.37161 - 11.0359i) q^{49} +(6.98574 - 1.06168i) q^{50} +(3.50649 - 7.51969i) q^{51} +(7.54971 + 8.30194i) q^{52} +(3.12148 + 4.45793i) q^{53} +(-6.74757 - 3.34342i) q^{54} +(0.129953 - 0.109044i) q^{55} +(5.49444 + 11.3030i) q^{56} +(7.34651 + 0.0293553i) q^{57} +(-10.1811 - 1.13452i) q^{58} +(13.6217 + 1.19174i) q^{59} +(-0.109520 + 0.170484i) q^{60} +(3.59923 + 5.14023i) q^{61} +(-11.7101 - 10.3088i) q^{62} +(0.242193 + 0.665419i) q^{63} +(-2.97734 - 7.42533i) q^{64} +(0.292090 - 0.168638i) q^{65} +(0.159465 - 6.72458i) q^{66} +(-5.76877 + 0.504702i) q^{67} +(9.40115 - 2.92509i) q^{68} +(-0.874988 - 3.26550i) q^{69} +(0.367083 - 0.0890887i) q^{70} +(-9.27455 + 1.63535i) q^{71} +(-0.123676 - 0.433461i) q^{72} +(1.10787 - 3.04386i) q^{73} +(2.01410 + 3.02670i) q^{74} +(-5.95454 - 5.95454i) q^{75} +(5.83947 + 6.47307i) q^{76} +(-8.86663 + 8.86663i) q^{77} +(2.63383 - 13.1114i) q^{78} +(-10.1134 - 3.68096i) q^{79} +(-0.237108 + 0.0399601i) q^{80} +(1.47540 + 8.36742i) q^{81} +(0.644431 - 1.05747i) q^{82} +(2.09061 - 0.560178i) q^{83} +(6.96619 - 13.2591i) q^{84} +(-0.0257918 - 0.294801i) q^{85} +(-2.48989 + 2.37454i) q^{86} +(6.10435 + 10.5730i) q^{87} +(6.03094 - 5.22871i) q^{88} +(13.8084 - 5.02584i) q^{89} +(-0.0135209 + 0.000860510i) q^{90} +(-20.4217 + 14.2994i) q^{91} +(2.16828 - 3.37525i) q^{92} +(-1.62049 + 18.5223i) q^{93} +(-1.48177 - 1.85342i) q^{94} +(0.227443 - 0.130105i) q^{95} +(-5.02298 + 8.10370i) q^{96} +(-8.75890 - 10.4385i) q^{97} +(-17.0761 + 5.76055i) q^{98} +(0.368408 - 0.257962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8} - 42 q^{10} - 6 q^{11} - 18 q^{12} - 12 q^{13} - 24 q^{16} - 24 q^{17} - 12 q^{19} - 24 q^{20} + 6 q^{21} - 12 q^{22} - 24 q^{23} - 12 q^{24} - 54 q^{26} - 18 q^{27} + 12 q^{28} - 12 q^{29} - 48 q^{30} + 18 q^{32} - 24 q^{33} + 48 q^{34} + 18 q^{35} - 60 q^{36} - 66 q^{38} - 48 q^{39} - 42 q^{40} + 144 q^{42} - 12 q^{43} + 54 q^{44} - 6 q^{45} - 108 q^{46} - 12 q^{48} - 168 q^{49} + 36 q^{50} + 12 q^{51} - 60 q^{52} - 12 q^{53} - 126 q^{54} - 24 q^{55} - 24 q^{58} - 12 q^{59} + 30 q^{60} - 12 q^{61} - 6 q^{64} - 36 q^{65} - 72 q^{66} - 12 q^{67} - 42 q^{68} + 126 q^{69} + 102 q^{70} - 24 q^{71} - 48 q^{72} + 72 q^{74} + 36 q^{76} + 60 q^{77} - 108 q^{78} + 48 q^{80} - 24 q^{81} - 72 q^{82} - 6 q^{83} - 18 q^{84} - 108 q^{85} - 12 q^{86} - 12 q^{87} - 18 q^{88} + 96 q^{90} + 30 q^{91} - 12 q^{92} + 6 q^{93} - 132 q^{96} - 24 q^{97} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.278524 1.38652i 0.196946 0.980414i
\(3\) −1.52751 + 0.712288i −0.881907 + 0.411240i −0.810178 0.586184i \(-0.800629\pi\)
−0.0717289 + 0.997424i \(0.522852\pi\)
\(4\) −1.84485 0.772356i −0.922424 0.386178i
\(5\) −0.0344794 + 0.0492417i −0.0154197 + 0.0220216i −0.826788 0.562514i \(-0.809834\pi\)
0.811368 + 0.584535i \(0.198723\pi\)
\(6\) 0.562151 + 2.31630i 0.229497 + 0.945626i
\(7\) 2.22167 3.84804i 0.839711 1.45442i −0.0504253 0.998728i \(-0.516058\pi\)
0.890136 0.455694i \(-0.150609\pi\)
\(8\) −1.58472 + 2.34279i −0.560282 + 0.828302i
\(9\) −0.102440 + 0.122083i −0.0341465 + 0.0406942i
\(10\) 0.0586710 + 0.0615212i 0.0185534 + 0.0194547i
\(11\) −2.72589 0.730400i −0.821887 0.220224i −0.176716 0.984262i \(-0.556547\pi\)
−0.645171 + 0.764038i \(0.723214\pi\)
\(12\) 3.36816 0.134285i 0.972304 0.0387648i
\(13\) −5.08503 2.37119i −1.41033 0.657650i −0.439685 0.898152i \(-0.644910\pi\)
−0.970649 + 0.240502i \(0.922688\pi\)
\(14\) −4.71658 4.15215i −1.26056 1.10971i
\(15\) 0.0175933 0.0997763i 0.00454256 0.0257621i
\(16\) 2.80693 + 2.84976i 0.701733 + 0.712440i
\(17\) −3.77112 + 3.16435i −0.914631 + 0.767467i −0.972994 0.230829i \(-0.925856\pi\)
0.0583630 + 0.998295i \(0.481412\pi\)
\(18\) 0.140738 + 0.176037i 0.0331722 + 0.0414923i
\(19\) −3.94311 1.85792i −0.904612 0.426236i
\(20\) 0.101641 0.0642131i 0.0227277 0.0143585i
\(21\) −0.652698 + 7.46037i −0.142430 + 1.62799i
\(22\) −1.77194 + 3.57605i −0.377778 + 0.762417i
\(23\) −0.348312 + 1.97538i −0.0726281 + 0.411894i 0.926719 + 0.375756i \(0.122617\pi\)
−0.999347 + 0.0361385i \(0.988494\pi\)
\(24\) 0.751925 4.70741i 0.153486 0.960895i
\(25\) 1.70886 + 4.69507i 0.341773 + 0.939013i
\(26\) −4.70399 + 6.39004i −0.922529 + 1.25319i
\(27\) 1.37817 5.14341i 0.265230 0.989850i
\(28\) −7.07069 + 5.38313i −1.33624 + 1.01732i
\(29\) −0.631332 7.21616i −0.117235 1.34001i −0.795842 0.605504i \(-0.792971\pi\)
0.678607 0.734502i \(-0.262584\pi\)
\(30\) −0.133441 0.0521834i −0.0243629 0.00952734i
\(31\) 5.51586 9.55374i 0.990677 1.71590i 0.377357 0.926068i \(-0.376833\pi\)
0.613320 0.789835i \(-0.289834\pi\)
\(32\) 4.73303 3.09813i 0.836690 0.547677i
\(33\) 4.68407 0.825928i 0.815392 0.143776i
\(34\) 3.33707 + 6.11006i 0.572302 + 1.04787i
\(35\) 0.112882 + 0.242077i 0.0190806 + 0.0409184i
\(36\) 0.283277 0.146104i 0.0472128 0.0243507i
\(37\) −1.81779 + 1.81779i −0.298843 + 0.298843i −0.840561 0.541717i \(-0.817774\pi\)
0.541717 + 0.840561i \(0.317774\pi\)
\(38\) −3.67429 + 4.94971i −0.596048 + 0.802949i
\(39\) 9.45639 1.51423
\(40\) −0.0607229 0.158812i −0.00960113 0.0251104i
\(41\) 0.822845 + 0.299491i 0.128507 + 0.0467726i 0.405473 0.914107i \(-0.367107\pi\)
−0.276966 + 0.960880i \(0.589329\pi\)
\(42\) 10.1621 + 2.98287i 1.56805 + 0.460267i
\(43\) −1.99291 1.39545i −0.303916 0.212805i 0.411663 0.911336i \(-0.364948\pi\)
−0.715579 + 0.698532i \(0.753837\pi\)
\(44\) 4.46473 + 3.45283i 0.673083 + 0.520534i
\(45\) −0.00247950 0.00925364i −0.000369623 0.00137945i
\(46\) 2.64188 + 1.03313i 0.389523 + 0.152327i
\(47\) 1.07854 1.28536i 0.157321 0.187488i −0.681626 0.731701i \(-0.738727\pi\)
0.838948 + 0.544212i \(0.183171\pi\)
\(48\) −6.31746 2.35368i −0.911847 0.339725i
\(49\) −6.37161 11.0359i −0.910229 1.57656i
\(50\) 6.98574 1.06168i 0.987933 0.150144i
\(51\) 3.50649 7.51969i 0.491007 1.05297i
\(52\) 7.54971 + 8.30194i 1.04696 + 1.15127i
\(53\) 3.12148 + 4.45793i 0.428768 + 0.612344i 0.974166 0.225833i \(-0.0725104\pi\)
−0.545398 + 0.838177i \(0.683621\pi\)
\(54\) −6.74757 3.34342i −0.918228 0.454982i
\(55\) 0.129953 0.109044i 0.0175229 0.0147034i
\(56\) 5.49444 + 11.3030i 0.734225 + 1.51042i
\(57\) 7.34651 + 0.0293553i 0.973069 + 0.00388820i
\(58\) −10.1811 1.13452i −1.33685 0.148970i
\(59\) 13.6217 + 1.19174i 1.77340 + 0.155152i 0.926423 0.376485i \(-0.122867\pi\)
0.846972 + 0.531637i \(0.178423\pi\)
\(60\) −0.109520 + 0.170484i −0.0141389 + 0.0220094i
\(61\) 3.59923 + 5.14023i 0.460834 + 0.658140i 0.980566 0.196190i \(-0.0628569\pi\)
−0.519732 + 0.854330i \(0.673968\pi\)
\(62\) −11.7101 10.3088i −1.48719 1.30921i
\(63\) 0.242193 + 0.665419i 0.0305134 + 0.0838349i
\(64\) −2.97734 7.42533i −0.372167 0.928166i
\(65\) 0.292090 0.168638i 0.0362293 0.0209170i
\(66\) 0.159465 6.72458i 0.0196288 0.827738i
\(67\) −5.76877 + 0.504702i −0.704768 + 0.0616592i −0.433905 0.900959i \(-0.642865\pi\)
−0.270863 + 0.962618i \(0.587309\pi\)
\(68\) 9.40115 2.92509i 1.14006 0.354720i
\(69\) −0.874988 3.26550i −0.105336 0.393120i
\(70\) 0.367083 0.0890887i 0.0438749 0.0106481i
\(71\) −9.27455 + 1.63535i −1.10069 + 0.194081i −0.694346 0.719641i \(-0.744306\pi\)
−0.406341 + 0.913722i \(0.633195\pi\)
\(72\) −0.123676 0.433461i −0.0145754 0.0510839i
\(73\) 1.10787 3.04386i 0.129667 0.356256i −0.857822 0.513947i \(-0.828183\pi\)
0.987489 + 0.157691i \(0.0504049\pi\)
\(74\) 2.01410 + 3.02670i 0.234134 + 0.351847i
\(75\) −5.95454 5.95454i −0.687572 0.687572i
\(76\) 5.83947 + 6.47307i 0.669833 + 0.742512i
\(77\) −8.86663 + 8.86663i −1.01045 + 1.01045i
\(78\) 2.63383 13.1114i 0.298223 1.48458i
\(79\) −10.1134 3.68096i −1.13784 0.414140i −0.296708 0.954968i \(-0.595889\pi\)
−0.841133 + 0.540828i \(0.818111\pi\)
\(80\) −0.237108 + 0.0399601i −0.0265095 + 0.00446768i
\(81\) 1.47540 + 8.36742i 0.163934 + 0.929713i
\(82\) 0.644431 1.05747i 0.0711655 0.116778i
\(83\) 2.09061 0.560178i 0.229475 0.0614875i −0.142249 0.989831i \(-0.545433\pi\)
0.371724 + 0.928343i \(0.378767\pi\)
\(84\) 6.96619 13.2591i 0.760074 1.44669i
\(85\) −0.0257918 0.294801i −0.00279751 0.0319757i
\(86\) −2.48989 + 2.37454i −0.268492 + 0.256053i
\(87\) 6.10435 + 10.5730i 0.654455 + 1.13355i
\(88\) 6.03094 5.22871i 0.642901 0.557383i
\(89\) 13.8084 5.02584i 1.46369 0.532738i 0.517308 0.855799i \(-0.326934\pi\)
0.946378 + 0.323061i \(0.104712\pi\)
\(90\) −0.0135209 0.000860510i −0.00142523 9.07057e-5i
\(91\) −20.4217 + 14.2994i −2.14077 + 1.49899i
\(92\) 2.16828 3.37525i 0.226058 0.351894i
\(93\) −1.62049 + 18.5223i −0.168037 + 1.92067i
\(94\) −1.48177 1.85342i −0.152832 0.191165i
\(95\) 0.227443 0.130105i 0.0233352 0.0133485i
\(96\) −5.02298 + 8.10370i −0.512656 + 0.827080i
\(97\) −8.75890 10.4385i −0.889332 1.05986i −0.997835 0.0657680i \(-0.979050\pi\)
0.108503 0.994096i \(-0.465394\pi\)
\(98\) −17.0761 + 5.76055i −1.72495 + 0.581904i
\(99\) 0.368408 0.257962i 0.0370264 0.0259262i
\(100\) 0.473666 9.98154i 0.0473666 0.998154i
\(101\) 10.8442 + 5.05675i 1.07904 + 0.503166i 0.879098 0.476641i \(-0.158146\pi\)
0.199945 + 0.979807i \(0.435924\pi\)
\(102\) −9.44952 6.95621i −0.935642 0.688768i
\(103\) 9.58971 5.53662i 0.944903 0.545540i 0.0534089 0.998573i \(-0.482991\pi\)
0.891494 + 0.453033i \(0.149658\pi\)
\(104\) 13.6135 8.15550i 1.33492 0.799713i
\(105\) −0.344857 0.289369i −0.0336546 0.0282395i
\(106\) 7.05040 3.08633i 0.684795 0.299771i
\(107\) −7.23473 + 1.93854i −0.699407 + 0.187406i −0.590965 0.806697i \(-0.701253\pi\)
−0.108442 + 0.994103i \(0.534586\pi\)
\(108\) −6.51507 + 8.42438i −0.626913 + 0.810636i
\(109\) 6.87841 9.82339i 0.658832 0.940910i −0.341167 0.940003i \(-0.610822\pi\)
1.00000 0.000907235i \(-0.000288782\pi\)
\(110\) −0.114996 0.210553i −0.0109644 0.0200755i
\(111\) 1.48190 4.07149i 0.140656 0.386448i
\(112\) 17.2021 4.46997i 1.62544 0.422373i
\(113\) 5.45811i 0.513456i −0.966484 0.256728i \(-0.917356\pi\)
0.966484 0.256728i \(-0.0826444\pi\)
\(114\) 2.08688 10.1779i 0.195454 0.953244i
\(115\) −0.0852612 0.0852612i −0.00795065 0.00795065i
\(116\) −4.40873 + 13.8003i −0.409340 + 1.28133i
\(117\) 0.810390 0.377891i 0.0749205 0.0349360i
\(118\) 5.44635 18.5548i 0.501377 1.70811i
\(119\) 3.79836 + 21.5415i 0.348195 + 1.97471i
\(120\) 0.205875 + 0.199335i 0.0187937 + 0.0181967i
\(121\) −2.62929 1.51802i −0.239026 0.138002i
\(122\) 8.12949 3.55871i 0.736009 0.322190i
\(123\) −1.47022 + 0.128628i −0.132566 + 0.0115980i
\(124\) −17.5548 + 13.3650i −1.57647 + 1.20021i
\(125\) −0.580437 0.155528i −0.0519159 0.0139108i
\(126\) 0.990069 0.150469i 0.0882024 0.0134048i
\(127\) 1.39961 0.509418i 0.124196 0.0452035i −0.279175 0.960240i \(-0.590061\pi\)
0.403370 + 0.915037i \(0.367839\pi\)
\(128\) −11.1246 + 2.05999i −0.983284 + 0.182079i
\(129\) 4.03815 + 0.712036i 0.355540 + 0.0626912i
\(130\) −0.152465 0.451957i −0.0133721 0.0396393i
\(131\) −3.76918 0.329761i −0.329315 0.0288113i −0.0787005 0.996898i \(-0.525077\pi\)
−0.250614 + 0.968087i \(0.580633\pi\)
\(132\) −9.27931 2.09406i −0.807661 0.182264i
\(133\) −15.9096 + 11.0456i −1.37954 + 0.957772i
\(134\) −0.906965 + 8.13906i −0.0783499 + 0.703108i
\(135\) 0.205752 + 0.245205i 0.0177083 + 0.0211039i
\(136\) −1.43724 13.8495i −0.123242 1.18759i
\(137\) −14.1045 2.48700i −1.20503 0.212479i −0.465157 0.885228i \(-0.654002\pi\)
−0.739870 + 0.672750i \(0.765113\pi\)
\(138\) −4.77137 + 0.303664i −0.406166 + 0.0258496i
\(139\) 2.28209 4.89396i 0.193564 0.415100i −0.785440 0.618937i \(-0.787564\pi\)
0.979005 + 0.203837i \(0.0653413\pi\)
\(140\) −0.0212813 0.533780i −0.00179860 0.0451127i
\(141\) −0.731936 + 2.73162i −0.0616401 + 0.230044i
\(142\) −0.315744 + 13.3148i −0.0264966 + 1.11735i
\(143\) 12.1293 + 10.1777i 1.01430 + 0.851103i
\(144\) −0.635447 + 0.0507499i −0.0529539 + 0.00422916i
\(145\) 0.377104 + 0.217721i 0.0313168 + 0.0180807i
\(146\) −3.91178 2.38387i −0.323741 0.197290i
\(147\) 17.5934 + 12.3191i 1.45108 + 1.01606i
\(148\) 4.75754 1.94957i 0.391067 0.160254i
\(149\) 5.15880 + 11.0631i 0.422626 + 0.906323i 0.996194 + 0.0871656i \(0.0277809\pi\)
−0.573568 + 0.819158i \(0.694441\pi\)
\(150\) −9.91455 + 6.59758i −0.809520 + 0.538690i
\(151\) 11.3968i 0.927458i 0.885977 + 0.463729i \(0.153489\pi\)
−0.885977 + 0.463729i \(0.846511\pi\)
\(152\) 10.6014 6.29361i 0.859890 0.510479i
\(153\) 0.784543i 0.0634266i
\(154\) 9.82414 + 14.7633i 0.791652 + 1.18966i
\(155\) 0.280259 + 0.601017i 0.0225109 + 0.0482749i
\(156\) −17.4456 7.30370i −1.39677 0.584764i
\(157\) 2.64217 + 1.85007i 0.210868 + 0.147651i 0.674239 0.738513i \(-0.264472\pi\)
−0.463372 + 0.886164i \(0.653360\pi\)
\(158\) −7.92052 + 12.9971i −0.630123 + 1.03399i
\(159\) −7.94341 4.58613i −0.629954 0.363704i
\(160\) −0.0106351 + 0.339884i −0.000840775 + 0.0268702i
\(161\) 6.82749 + 5.72894i 0.538082 + 0.451504i
\(162\) 12.0125 + 0.284861i 0.943790 + 0.0223808i
\(163\) 2.03217 7.58416i 0.159172 0.594037i −0.839540 0.543298i \(-0.817176\pi\)
0.998712 0.0507395i \(-0.0161578\pi\)
\(164\) −1.28671 1.18804i −0.100475 0.0927707i
\(165\) −0.120834 + 0.259129i −0.00940691 + 0.0201732i
\(166\) −0.194409 3.05469i −0.0150891 0.237090i
\(167\) −16.4447 2.89965i −1.27253 0.224382i −0.503726 0.863864i \(-0.668038\pi\)
−0.768806 + 0.639482i \(0.779149\pi\)
\(168\) −16.4438 13.3517i −1.26866 1.03011i
\(169\) 11.8788 + 14.1566i 0.913751 + 1.08897i
\(170\) −0.415930 0.0463486i −0.0319004 0.00355477i
\(171\) 0.630751 0.291061i 0.0482347 0.0222580i
\(172\) 2.59884 + 4.11364i 0.198160 + 0.313662i
\(173\) −11.9399 1.04461i −0.907775 0.0794200i −0.376304 0.926496i \(-0.622805\pi\)
−0.531471 + 0.847076i \(0.678361\pi\)
\(174\) 16.3599 5.51892i 1.24024 0.418388i
\(175\) 21.8633 + 3.85510i 1.65271 + 0.291418i
\(176\) −5.56993 9.81831i −0.419849 0.740083i
\(177\) −21.6561 + 7.88218i −1.62777 + 0.592461i
\(178\) −3.12244 20.5454i −0.234037 1.53994i
\(179\) −11.8070 3.16369i −0.882500 0.236465i −0.211014 0.977483i \(-0.567677\pi\)
−0.671485 + 0.741018i \(0.734343\pi\)
\(180\) −0.00257279 + 0.0189866i −0.000191764 + 0.00141518i
\(181\) −1.46519 + 0.128187i −0.108906 + 0.00952807i −0.141479 0.989941i \(-0.545186\pi\)
0.0325722 + 0.999469i \(0.489630\pi\)
\(182\) 14.1384 + 32.2977i 1.04801 + 2.39406i
\(183\) −9.15918 5.28805i −0.677066 0.390904i
\(184\) −4.07592 3.94644i −0.300481 0.290935i
\(185\) −0.0268348 0.152188i −0.00197293 0.0111891i
\(186\) 25.2301 + 7.40574i 1.84996 + 0.543015i
\(187\) 12.5909 5.87123i 0.920738 0.429347i
\(188\) −2.98250 + 1.53827i −0.217521 + 0.112190i
\(189\) −16.7302 16.7302i −1.21694 1.21694i
\(190\) −0.117045 0.351591i −0.00849132 0.0255071i
\(191\) 1.76306i 0.127570i 0.997964 + 0.0637851i \(0.0203172\pi\)
−0.997964 + 0.0637851i \(0.979683\pi\)
\(192\) 9.83688 + 9.22151i 0.709915 + 0.665505i
\(193\) −2.41762 + 6.64234i −0.174024 + 0.478126i −0.995786 0.0917037i \(-0.970769\pi\)
0.821763 + 0.569830i \(0.192991\pi\)
\(194\) −16.9126 + 9.23699i −1.21426 + 0.663177i
\(195\) −0.326051 + 0.465649i −0.0233490 + 0.0333458i
\(196\) 3.23097 + 25.2808i 0.230784 + 1.80577i
\(197\) −6.51968 + 1.74694i −0.464508 + 0.124464i −0.483480 0.875356i \(-0.660627\pi\)
0.0189720 + 0.999820i \(0.493961\pi\)
\(198\) −0.255058 0.582652i −0.0181262 0.0414073i
\(199\) −0.902676 0.757435i −0.0639890 0.0536932i 0.610232 0.792223i \(-0.291076\pi\)
−0.674221 + 0.738529i \(0.735521\pi\)
\(200\) −13.7076 3.43684i −0.969276 0.243022i
\(201\) 8.45235 4.87997i 0.596183 0.344206i
\(202\) 10.0316 13.6273i 0.705824 0.958812i
\(203\) −29.1707 13.6025i −2.04738 0.954708i
\(204\) −12.2768 + 11.1644i −0.859549 + 0.781666i
\(205\) −0.0431186 + 0.0301920i −0.00301154 + 0.00210870i
\(206\) −5.00565 14.8384i −0.348760 1.03384i
\(207\) −0.205478 0.244880i −0.0142817 0.0170203i
\(208\) −7.51602 21.1469i −0.521143 1.46627i
\(209\) 9.39146 + 7.94454i 0.649621 + 0.549535i
\(210\) −0.497266 + 0.397553i −0.0343146 + 0.0274338i
\(211\) 0.248960 2.84563i 0.0171391 0.195901i −0.982798 0.184684i \(-0.940874\pi\)
0.999937 0.0112171i \(-0.00357060\pi\)
\(212\) −2.31554 10.6351i −0.159032 0.730422i
\(213\) 13.0021 9.10417i 0.890889 0.623807i
\(214\) 0.672768 + 10.5710i 0.0459895 + 0.722618i
\(215\) 0.137429 0.0500200i 0.00937258 0.00341134i
\(216\) 9.86593 + 11.3796i 0.671291 + 0.774286i
\(217\) −24.5088 42.4505i −1.66376 2.88172i
\(218\) −11.7045 12.2731i −0.792727 0.831237i
\(219\) 0.475819 + 5.43864i 0.0321529 + 0.367509i
\(220\) −0.323964 + 0.100799i −0.0218417 + 0.00679587i
\(221\) 26.6795 7.14876i 1.79466 0.480878i
\(222\) −5.23243 3.18868i −0.351178 0.214010i
\(223\) 0.946855 + 5.36988i 0.0634061 + 0.359594i 0.999959 + 0.00906731i \(0.00288625\pi\)
−0.936553 + 0.350527i \(0.886003\pi\)
\(224\) −1.40650 25.0959i −0.0939758 1.67679i
\(225\) −0.748242 0.272338i −0.0498828 0.0181559i
\(226\) −7.56775 1.52022i −0.503399 0.101123i
\(227\) 8.86854 8.86854i 0.588626 0.588626i −0.348633 0.937259i \(-0.613354\pi\)
0.937259 + 0.348633i \(0.113354\pi\)
\(228\) −13.5305 5.72827i −0.896081 0.379364i
\(229\) −10.3962 10.3962i −0.687002 0.687002i 0.274566 0.961568i \(-0.411466\pi\)
−0.961568 + 0.274566i \(0.911466\pi\)
\(230\) −0.141963 + 0.0944687i −0.00936078 + 0.00622908i
\(231\) 7.22824 19.8594i 0.475583 1.30665i
\(232\) 17.9064 + 9.95649i 1.17561 + 0.653676i
\(233\) 3.87634 0.683504i 0.253948 0.0447778i −0.0452250 0.998977i \(-0.514400\pi\)
0.299173 + 0.954199i \(0.403289\pi\)
\(234\) −0.298238 1.22887i −0.0194965 0.0803337i
\(235\) 0.0261056 + 0.0974275i 0.00170294 + 0.00635547i
\(236\) −24.2095 12.7194i −1.57591 0.827962i
\(237\) 18.0701 1.58093i 1.17378 0.102693i
\(238\) 30.9256 + 0.733362i 2.00461 + 0.0475368i
\(239\) −10.6978 + 6.17636i −0.691981 + 0.399515i −0.804354 0.594151i \(-0.797488\pi\)
0.112373 + 0.993666i \(0.464155\pi\)
\(240\) 0.333722 0.229929i 0.0215416 0.0148418i
\(241\) −1.24706 3.42626i −0.0803301 0.220705i 0.893025 0.450006i \(-0.148578\pi\)
−0.973356 + 0.229301i \(0.926356\pi\)
\(242\) −2.83708 + 3.22274i −0.182374 + 0.207166i
\(243\) 0.948932 + 1.35522i 0.0608740 + 0.0869371i
\(244\) −2.66995 12.2628i −0.170926 0.785048i
\(245\) 0.763118 + 0.0667641i 0.0487538 + 0.00426540i
\(246\) −0.231148 + 2.07432i −0.0147375 + 0.132254i
\(247\) 15.6454 + 18.7974i 0.995491 + 1.19605i
\(248\) 13.6413 + 28.0625i 0.866226 + 1.78197i
\(249\) −2.79442 + 2.34480i −0.177089 + 0.148595i
\(250\) −0.377307 + 0.761467i −0.0238630 + 0.0481594i
\(251\) 11.7473 + 16.7769i 0.741485 + 1.05895i 0.995775 + 0.0918229i \(0.0292694\pi\)
−0.254290 + 0.967128i \(0.581842\pi\)
\(252\) 0.0671313 1.41466i 0.00422887 0.0891149i
\(253\) 2.39228 5.13025i 0.150401 0.322536i
\(254\) −0.316489 2.08247i −0.0198583 0.130666i
\(255\) 0.249381 + 0.431940i 0.0156168 + 0.0270491i
\(256\) −0.242254 + 15.9982i −0.0151409 + 0.999885i
\(257\) −4.61167 + 5.49598i −0.287668 + 0.342830i −0.890454 0.455074i \(-0.849613\pi\)
0.602786 + 0.797903i \(0.294057\pi\)
\(258\) 2.11197 5.40064i 0.131486 0.336229i
\(259\) 2.95641 + 11.0335i 0.183702 + 0.685587i
\(260\) −0.669111 + 0.0855147i −0.0414965 + 0.00530340i
\(261\) 0.945641 + 0.662145i 0.0585337 + 0.0409858i
\(262\) −1.50703 + 5.13418i −0.0931044 + 0.317191i
\(263\) −9.97112 3.62919i −0.614845 0.223785i 0.0157767 0.999876i \(-0.494978\pi\)
−0.630622 + 0.776090i \(0.717200\pi\)
\(264\) −5.48796 + 12.2827i −0.337760 + 0.755946i
\(265\) −0.327143 −0.0200962
\(266\) 10.8836 + 25.1354i 0.667318 + 1.54115i
\(267\) −17.5126 + 17.5126i −1.07175 + 1.07175i
\(268\) 11.0323 + 3.52445i 0.673907 + 0.215290i
\(269\) 6.37945 + 13.6808i 0.388962 + 0.834132i 0.999124 + 0.0418551i \(0.0133268\pi\)
−0.610161 + 0.792277i \(0.708895\pi\)
\(270\) 0.397288 0.216982i 0.0241782 0.0132051i
\(271\) 4.62422 0.815375i 0.280902 0.0495305i −0.0314224 0.999506i \(-0.510004\pi\)
0.312324 + 0.949976i \(0.398893\pi\)
\(272\) −19.6029 1.86468i −1.18860 0.113063i
\(273\) 21.0089 36.3886i 1.27152 2.20234i
\(274\) −7.37670 + 18.8634i −0.445643 + 1.13958i
\(275\) −1.22890 14.0464i −0.0741055 0.847029i
\(276\) −0.907907 + 6.70015i −0.0546496 + 0.403302i
\(277\) 2.02907 7.57259i 0.121915 0.454993i −0.877796 0.479035i \(-0.840987\pi\)
0.999711 + 0.0240420i \(0.00765353\pi\)
\(278\) −6.14993 4.52724i −0.368848 0.271526i
\(279\) 0.601305 + 1.65207i 0.0359992 + 0.0989069i
\(280\) −0.746022 0.119164i −0.0445833 0.00712140i
\(281\) 2.71099 15.3748i 0.161724 0.917184i −0.790654 0.612264i \(-0.790259\pi\)
0.952378 0.304920i \(-0.0986298\pi\)
\(282\) 3.58357 + 1.77566i 0.213399 + 0.105739i
\(283\) 0.251709 2.87705i 0.0149626 0.171023i −0.985037 0.172345i \(-0.944865\pi\)
0.999999 + 0.00132268i \(0.000421022\pi\)
\(284\) 18.3732 + 4.14627i 1.09025 + 0.246036i
\(285\) −0.254749 + 0.360742i −0.0150900 + 0.0213685i
\(286\) 17.4899 13.9827i 1.03420 0.826817i
\(287\) 2.98054 2.50097i 0.175936 0.147628i
\(288\) −0.106622 + 0.895192i −0.00628275 + 0.0527497i
\(289\) 1.25625 7.12454i 0.0738970 0.419091i
\(290\) 0.406906 0.462219i 0.0238943 0.0271425i
\(291\) 20.8145 + 9.70595i 1.22017 + 0.568973i
\(292\) −4.39480 + 4.75978i −0.257186 + 0.278545i
\(293\) 19.3661 + 5.18913i 1.13138 + 0.303152i 0.775480 0.631372i \(-0.217508\pi\)
0.355900 + 0.934524i \(0.384174\pi\)
\(294\) 21.9808 20.9624i 1.28194 1.22255i
\(295\) −0.528352 + 0.629665i −0.0307618 + 0.0366605i
\(296\) −1.37802 7.13940i −0.0800958 0.414969i
\(297\) −7.51350 + 13.0138i −0.435977 + 0.755135i
\(298\) 16.7760 4.07142i 0.971807 0.235851i
\(299\) 6.45517 9.21893i 0.373312 0.533145i
\(300\) 6.38621 + 15.5843i 0.368708 + 0.899758i
\(301\) −9.79735 + 4.56858i −0.564710 + 0.263328i
\(302\) 15.8018 + 3.17428i 0.909293 + 0.182659i
\(303\) −20.1665 −1.15854
\(304\) −5.77342 16.4520i −0.331129 0.943586i
\(305\) −0.377213 −0.0215992
\(306\) −1.08778 0.218514i −0.0621843 0.0124916i
\(307\) −23.3730 + 10.8990i −1.33397 + 0.622039i −0.953118 0.302599i \(-0.902146\pi\)
−0.380848 + 0.924638i \(0.624368\pi\)
\(308\) 23.2058 9.50939i 1.32227 0.541848i
\(309\) −10.7047 + 15.2879i −0.608968 + 0.869697i
\(310\) 0.911379 0.221186i 0.0517628 0.0125625i
\(311\) 14.4802 25.0805i 0.821098 1.42218i −0.0837678 0.996485i \(-0.526695\pi\)
0.904865 0.425698i \(-0.139971\pi\)
\(312\) −14.9857 + 22.1543i −0.848399 + 1.25424i
\(313\) 6.70379 7.98926i 0.378920 0.451580i −0.542553 0.840022i \(-0.682542\pi\)
0.921473 + 0.388442i \(0.126987\pi\)
\(314\) 3.30105 3.14812i 0.186289 0.177659i
\(315\) −0.0411170 0.0110173i −0.00231668 0.000620753i
\(316\) 15.8146 + 14.6019i 0.889641 + 0.821422i
\(317\) −1.32871 0.619586i −0.0746276 0.0347994i 0.384946 0.922939i \(-0.374220\pi\)
−0.459574 + 0.888140i \(0.651998\pi\)
\(318\) −8.57117 + 9.73631i −0.480647 + 0.545985i
\(319\) −3.54974 + 20.1316i −0.198747 + 1.12715i
\(320\) 0.468292 + 0.109412i 0.0261783 + 0.00611629i
\(321\) 9.67030 8.11434i 0.539743 0.452898i
\(322\) 9.84489 7.87077i 0.548634 0.438621i
\(323\) 20.7491 5.47093i 1.15451 0.304411i
\(324\) 3.74073 16.5762i 0.207818 0.920897i
\(325\) 2.44326 27.9266i 0.135528 1.54909i
\(326\) −9.94954 4.93000i −0.551054 0.273048i
\(327\) −3.50974 + 19.9047i −0.194089 + 1.10073i
\(328\) −2.00562 + 1.45314i −0.110742 + 0.0802365i
\(329\) −2.54994 7.00590i −0.140583 0.386248i
\(330\) 0.325631 + 0.239712i 0.0179254 + 0.0131957i
\(331\) 1.66231 6.20383i 0.0913689 0.340993i −0.905075 0.425252i \(-0.860185\pi\)
0.996444 + 0.0842585i \(0.0268522\pi\)
\(332\) −4.28952 0.581253i −0.235418 0.0319004i
\(333\) −0.0357072 0.408135i −0.00195674 0.0223657i
\(334\) −8.60067 + 21.9933i −0.470607 + 1.20342i
\(335\) 0.174051 0.301466i 0.00950945 0.0164708i
\(336\) −23.0923 + 19.0807i −1.25979 + 1.04094i
\(337\) 8.07297 1.42348i 0.439762 0.0775420i 0.0506166 0.998718i \(-0.483881\pi\)
0.389146 + 0.921176i \(0.372770\pi\)
\(338\) 22.9368 12.5271i 1.24760 0.681387i
\(339\) 3.88775 + 8.33730i 0.211153 + 0.452820i
\(340\) −0.180110 + 0.563784i −0.00976781 + 0.0305755i
\(341\) −22.0137 + 22.0137i −1.19211 + 1.19211i
\(342\) −0.227881 0.955613i −0.0123224 0.0516736i
\(343\) −25.5190 −1.37790
\(344\) 6.42746 2.45758i 0.346545 0.132504i
\(345\) 0.190968 + 0.0695066i 0.0102814 + 0.00374211i
\(346\) −4.77392 + 16.2639i −0.256647 + 0.874354i
\(347\) −14.4949 10.1494i −0.778126 0.544849i 0.115689 0.993285i \(-0.463092\pi\)
−0.893815 + 0.448436i \(0.851981\pi\)
\(348\) −3.09545 24.2204i −0.165933 1.29835i
\(349\) −1.71401 6.39677i −0.0917488 0.342411i 0.904758 0.425927i \(-0.140052\pi\)
−0.996506 + 0.0835154i \(0.973385\pi\)
\(350\) 11.4346 29.2401i 0.611206 1.56295i
\(351\) −19.2041 + 22.8865i −1.02504 + 1.22159i
\(352\) −15.1646 + 4.98815i −0.808276 + 0.265869i
\(353\) 14.0900 + 24.4046i 0.749935 + 1.29893i 0.947853 + 0.318707i \(0.103249\pi\)
−0.197919 + 0.980218i \(0.563418\pi\)
\(354\) 4.89701 + 32.2219i 0.260273 + 1.71258i
\(355\) 0.239253 0.513081i 0.0126983 0.0272315i
\(356\) −29.3561 1.39307i −1.55587 0.0738326i
\(357\) −21.1458 30.1993i −1.11915 1.59832i
\(358\) −7.67505 + 15.4895i −0.405639 + 0.818645i
\(359\) 18.0222 15.1225i 0.951177 0.798132i −0.0283182 0.999599i \(-0.509015\pi\)
0.979495 + 0.201466i \(0.0645707\pi\)
\(360\) 0.0256087 + 0.00885544i 0.00134969 + 0.000466723i
\(361\) 12.0963 + 14.6520i 0.636645 + 0.771157i
\(362\) −0.230356 + 2.06721i −0.0121072 + 0.108650i
\(363\) 5.09752 + 0.445975i 0.267550 + 0.0234076i
\(364\) 48.7191 10.6074i 2.55358 0.555981i
\(365\) 0.111686 + 0.159504i 0.00584590 + 0.00834881i
\(366\) −9.88302 + 11.2265i −0.516594 + 0.586818i
\(367\) −6.35425 17.4582i −0.331689 0.911308i −0.987673 0.156533i \(-0.949968\pi\)
0.655984 0.754775i \(-0.272254\pi\)
\(368\) −6.60703 + 4.55214i −0.344415 + 0.237297i
\(369\) −0.120855 + 0.0697754i −0.00629143 + 0.00363236i
\(370\) −0.218485 0.00518109i −0.0113585 0.000269352i
\(371\) 24.0892 2.10753i 1.25065 0.109418i
\(372\) 17.2954 32.9192i 0.896722 1.70678i
\(373\) −4.47127 16.6870i −0.231514 0.864021i −0.979689 0.200521i \(-0.935737\pi\)
0.748176 0.663501i \(-0.230930\pi\)
\(374\) −4.63369 19.0928i −0.239602 0.987263i
\(375\) 0.997402 0.175869i 0.0515056 0.00908183i
\(376\) 1.30214 + 4.56372i 0.0671525 + 0.235356i
\(377\) −13.9005 + 38.1914i −0.715914 + 1.96696i
\(378\) −27.8565 + 18.5369i −1.43278 + 0.953437i
\(379\) 21.0226 + 21.0226i 1.07986 + 1.07986i 0.996522 + 0.0833354i \(0.0265573\pi\)
0.0833354 + 0.996522i \(0.473443\pi\)
\(380\) −0.520086 + 0.0643578i −0.0266799 + 0.00330148i
\(381\) −1.77507 + 1.77507i −0.0909395 + 0.0909395i
\(382\) 2.44450 + 0.491054i 0.125072 + 0.0251245i
\(383\) −1.78657 0.650260i −0.0912897 0.0332267i 0.295972 0.955197i \(-0.404357\pi\)
−0.387261 + 0.921970i \(0.626579\pi\)
\(384\) 15.5256 11.0706i 0.792286 0.564942i
\(385\) −0.130892 0.742324i −0.00667086 0.0378323i
\(386\) 8.53635 + 5.20211i 0.434489 + 0.264781i
\(387\) 0.374514 0.100351i 0.0190376 0.00510111i
\(388\) 8.09665 + 26.0223i 0.411045 + 1.32108i
\(389\) 0.435743 + 4.98056i 0.0220930 + 0.252524i 0.999207 + 0.0398094i \(0.0126751\pi\)
−0.977114 + 0.212715i \(0.931769\pi\)
\(390\) 0.554816 + 0.581769i 0.0280942 + 0.0294590i
\(391\) −4.93725 8.55156i −0.249687 0.432471i
\(392\) 35.9521 + 2.56152i 1.81586 + 0.129376i
\(393\) 5.99234 2.18103i 0.302273 0.110019i
\(394\) 0.606275 + 9.52620i 0.0305437 + 0.479923i
\(395\) 0.529959 0.371081i 0.0266651 0.0186711i
\(396\) −0.878896 + 0.191359i −0.0441662 + 0.00961615i
\(397\) 0.394639 4.51075i 0.0198064 0.226388i −0.979840 0.199785i \(-0.935976\pi\)
0.999646 0.0266026i \(-0.00846888\pi\)
\(398\) −1.30161 + 1.04061i −0.0652439 + 0.0521611i
\(399\) 16.4344 28.2044i 0.822751 1.41199i
\(400\) −8.58314 + 18.0486i −0.429157 + 0.902430i
\(401\) −6.35004 7.56768i −0.317106 0.377912i 0.583821 0.811882i \(-0.301557\pi\)
−0.900927 + 0.433970i \(0.857112\pi\)
\(402\) −4.41196 13.0785i −0.220049 0.652296i
\(403\) −50.7020 + 35.5019i −2.52565 + 1.76848i
\(404\) −16.1004 17.7046i −0.801024 0.880835i
\(405\) −0.462897 0.215852i −0.0230015 0.0107258i
\(406\) −26.9848 + 36.6569i −1.33923 + 1.81925i
\(407\) 6.28282 3.62739i 0.311428 0.179803i
\(408\) 12.0603 + 20.1316i 0.597072 + 0.996660i
\(409\) −3.12747 2.62426i −0.154643 0.129761i 0.562183 0.827013i \(-0.309962\pi\)
−0.716826 + 0.697252i \(0.754406\pi\)
\(410\) 0.0298521 + 0.0681938i 0.00147429 + 0.00336785i
\(411\) 23.3161 6.24754i 1.15010 0.308169i
\(412\) −21.9678 + 2.80756i −1.08228 + 0.138319i
\(413\) 34.8488 49.7692i 1.71480 2.44898i
\(414\) −0.396760 + 0.216694i −0.0194997 + 0.0106499i
\(415\) −0.0444990 + 0.122260i −0.00218437 + 0.00600150i
\(416\) −31.4139 + 4.53117i −1.54019 + 0.222159i
\(417\) 9.10106i 0.445681i
\(418\) 13.6310 10.8087i 0.666713 0.528669i
\(419\) −16.2731 16.2731i −0.794994 0.794994i 0.187307 0.982301i \(-0.440024\pi\)
−0.982301 + 0.187307i \(0.940024\pi\)
\(420\) 0.412713 + 0.800195i 0.0201383 + 0.0390455i
\(421\) 32.2785 15.0517i 1.57316 0.733575i 0.576642 0.816997i \(-0.304363\pi\)
0.996514 + 0.0834220i \(0.0265849\pi\)
\(422\) −3.87616 1.13776i −0.188689 0.0553854i
\(423\) 0.0464344 + 0.263343i 0.00225772 + 0.0128042i
\(424\) −15.3907 + 0.248405i −0.747437 + 0.0120636i
\(425\) −21.3012 12.2982i −1.03326 0.596552i
\(426\) −9.00167 20.5633i −0.436132 0.996297i
\(427\) 27.7761 2.43010i 1.34418 0.117601i
\(428\) 14.8442 + 2.01147i 0.717522 + 0.0972281i
\(429\) −25.7771 6.90695i −1.24453 0.333471i
\(430\) −0.0310763 0.204479i −0.00149863 0.00986086i
\(431\) −22.3533 + 8.13595i −1.07672 + 0.391895i −0.818687 0.574241i \(-0.805297\pi\)
−0.258035 + 0.966135i \(0.583075\pi\)
\(432\) 18.5259 10.5098i 0.891329 0.505651i
\(433\) −38.6678 6.81817i −1.85825 0.327660i −0.871565 0.490280i \(-0.836894\pi\)
−0.986689 + 0.162620i \(0.948006\pi\)
\(434\) −65.6845 + 22.1583i −3.15296 + 1.06363i
\(435\) −0.731108 0.0639637i −0.0350540 0.00306682i
\(436\) −20.2768 + 12.8101i −0.971081 + 0.613492i
\(437\) 5.04353 7.14199i 0.241265 0.341648i
\(438\) 7.67328 + 0.855061i 0.366643 + 0.0408564i
\(439\) −19.4412 23.1691i −0.927876 1.10580i −0.994151 0.107999i \(-0.965556\pi\)
0.0662746 0.997801i \(-0.478889\pi\)
\(440\) 0.0495274 + 0.477257i 0.00236113 + 0.0227523i
\(441\) 2.00000 + 0.352654i 0.0952382 + 0.0167931i
\(442\) −2.48097 38.9827i −0.118008 1.85422i
\(443\) −5.92838 + 12.7134i −0.281666 + 0.604034i −0.995338 0.0964455i \(-0.969253\pi\)
0.713673 + 0.700479i \(0.247030\pi\)
\(444\) −5.87852 + 6.36672i −0.278982 + 0.302151i
\(445\) −0.228624 + 0.853236i −0.0108378 + 0.0404473i
\(446\) 7.70914 + 0.182813i 0.365039 + 0.00865643i
\(447\) −15.7602 13.2244i −0.745432 0.625492i
\(448\) −35.1876 5.03968i −1.66246 0.238103i
\(449\) 7.79555 + 4.50076i 0.367895 + 0.212404i 0.672538 0.740062i \(-0.265204\pi\)
−0.304644 + 0.952466i \(0.598537\pi\)
\(450\) −0.586004 + 0.961596i −0.0276245 + 0.0453301i
\(451\) −2.02424 1.41739i −0.0953175 0.0667421i
\(452\) −4.21560 + 10.0694i −0.198285 + 0.473624i
\(453\) −8.11781 17.4087i −0.381408 0.817932i
\(454\) −9.82626 14.7665i −0.461169 0.693025i
\(455\) 1.49863i 0.0702570i
\(456\) −11.7109 + 17.1648i −0.548414 + 0.803816i
\(457\) 4.39882i 0.205768i 0.994693 + 0.102884i \(0.0328071\pi\)
−0.994693 + 0.102884i \(0.967193\pi\)
\(458\) −17.3101 + 11.5189i −0.808849 + 0.538244i
\(459\) 11.0783 + 23.7575i 0.517090 + 1.10890i
\(460\) 0.0914421 + 0.223146i 0.00426351 + 0.0104042i
\(461\) −8.55853 5.99275i −0.398610 0.279110i 0.357035 0.934091i \(-0.383788\pi\)
−0.755645 + 0.654981i \(0.772677\pi\)
\(462\) −25.5222 15.5534i −1.18740 0.723610i
\(463\) 32.7050 + 18.8822i 1.51993 + 0.877531i 0.999724 + 0.0234889i \(0.00747743\pi\)
0.520204 + 0.854042i \(0.325856\pi\)
\(464\) 18.7922 22.0544i 0.872406 1.02385i
\(465\) −0.856195 0.718433i −0.0397051 0.0333165i
\(466\) 0.131966 5.56498i 0.00611323 0.257793i
\(467\) −5.33507 + 19.9108i −0.246878 + 0.921360i 0.725553 + 0.688167i \(0.241584\pi\)
−0.972430 + 0.233194i \(0.925082\pi\)
\(468\) −1.78691 + 0.0712424i −0.0826001 + 0.00329318i
\(469\) −10.8742 + 23.3198i −0.502123 + 1.07681i
\(470\) 0.142356 0.00905993i 0.00656638 0.000417903i
\(471\) −5.35371 0.944004i −0.246686 0.0434974i
\(472\) −24.3786 + 30.0242i −1.12211 + 1.38198i
\(473\) 4.41322 + 5.25948i 0.202920 + 0.241831i
\(474\) 2.84098 25.4948i 0.130491 1.17102i
\(475\) 1.98482 21.6881i 0.0910698 0.995119i
\(476\) 9.63035 42.6746i 0.441406 1.95599i
\(477\) −0.863999 0.0755901i −0.0395598 0.00346104i
\(478\) 5.58403 + 16.5529i 0.255407 + 0.757111i
\(479\) 7.05172 + 1.24341i 0.322201 + 0.0568128i 0.332410 0.943135i \(-0.392138\pi\)
−0.0102084 + 0.999948i \(0.503249\pi\)
\(480\) −0.225850 0.526751i −0.0103086 0.0240428i
\(481\) 13.5539 4.93321i 0.618003 0.224935i
\(482\) −5.09790 + 0.774768i −0.232203 + 0.0352897i
\(483\) −14.5097 3.88786i −0.660214 0.176904i
\(484\) 3.67818 + 4.83126i 0.167190 + 0.219603i
\(485\) 0.816009 0.0713915i 0.0370530 0.00324172i
\(486\) 2.14333 0.938249i 0.0972233 0.0425598i
\(487\) 0.134615 + 0.0777199i 0.00609998 + 0.00352182i 0.503047 0.864259i \(-0.332212\pi\)
−0.496947 + 0.867781i \(0.665546\pi\)
\(488\) −17.7463 + 0.286424i −0.803336 + 0.0129658i
\(489\) 2.29795 + 13.0323i 0.103917 + 0.589343i
\(490\) 0.305116 1.03948i 0.0137837 0.0469589i
\(491\) 11.3334 5.28487i 0.511471 0.238503i −0.149709 0.988730i \(-0.547834\pi\)
0.661180 + 0.750227i \(0.270056\pi\)
\(492\) 2.81169 + 0.898238i 0.126761 + 0.0404957i
\(493\) 25.2152 + 25.2152i 1.13564 + 1.13564i
\(494\) 30.4206 16.4570i 1.36869 0.740435i
\(495\) 0.0270354i 0.00121515i
\(496\) 42.7085 11.0979i 1.91767 0.498308i
\(497\) −14.3121 + 39.3221i −0.641984 + 1.76384i
\(498\) 2.47278 + 4.52759i 0.110808 + 0.202886i
\(499\) −3.04642 + 4.35075i −0.136377 + 0.194766i −0.881531 0.472126i \(-0.843487\pi\)
0.745155 + 0.666892i \(0.232376\pi\)
\(500\) 0.950696 + 0.735229i 0.0425164 + 0.0328804i
\(501\) 27.1848 7.28416i 1.21453 0.325432i
\(502\) 26.5334 11.6151i 1.18424 0.518406i
\(503\) −33.4928 28.1038i −1.49337 1.25309i −0.890282 0.455409i \(-0.849493\pi\)
−0.603086 0.797676i \(-0.706063\pi\)
\(504\) −1.94274 0.487094i −0.0865367 0.0216969i
\(505\) −0.622906 + 0.359635i −0.0277190 + 0.0160035i
\(506\) −6.44686 4.74582i −0.286598 0.210978i
\(507\) −28.2285 13.1631i −1.25367 0.584596i
\(508\) −2.97553 0.141201i −0.132018 0.00626479i
\(509\) −3.60896 + 2.52702i −0.159964 + 0.112008i −0.650818 0.759234i \(-0.725574\pi\)
0.490854 + 0.871242i \(0.336685\pi\)
\(510\) 0.668349 0.225464i 0.0295950 0.00998372i
\(511\) −9.25155 11.0256i −0.409265 0.487743i
\(512\) 22.1142 + 4.79176i 0.977320 + 0.211768i
\(513\) −14.9903 + 17.7205i −0.661840 + 0.782380i
\(514\) 6.33579 + 7.92491i 0.279460 + 0.349553i
\(515\) −0.0580149 + 0.663113i −0.00255644 + 0.0292203i
\(516\) −6.89984 4.43249i −0.303748 0.195129i
\(517\) −3.87881 + 2.71597i −0.170590 + 0.119448i
\(518\) 16.1215 1.02602i 0.708339 0.0450807i
\(519\) 18.9824 6.90901i 0.833233 0.303272i
\(520\) −0.0677961 + 0.951550i −0.00297306 + 0.0417282i
\(521\) 15.9890 + 27.6938i 0.700491 + 1.21329i 0.968294 + 0.249812i \(0.0803688\pi\)
−0.267804 + 0.963473i \(0.586298\pi\)
\(522\) 1.18146 1.12672i 0.0517110 0.0493153i
\(523\) −1.92408 21.9923i −0.0841341 0.961657i −0.914539 0.404497i \(-0.867447\pi\)
0.830405 0.557160i \(-0.188109\pi\)
\(524\) 6.69888 + 3.51951i 0.292642 + 0.153750i
\(525\) −36.1423 + 9.68431i −1.57738 + 0.422658i
\(526\) −7.80912 + 12.8143i −0.340494 + 0.558729i
\(527\) 9.43039 + 53.4824i 0.410794 + 2.32973i
\(528\) 15.5016 + 11.0302i 0.674619 + 0.480026i
\(529\) 17.8321 + 6.49037i 0.775311 + 0.282190i
\(530\) −0.0911172 + 0.453588i −0.00395788 + 0.0197026i
\(531\) −1.54089 + 1.54089i −0.0668691 + 0.0668691i
\(532\) 37.8820 8.08950i 1.64239 0.350725i
\(533\) −3.47404 3.47404i −0.150477 0.150477i
\(534\) 19.4038 + 29.1591i 0.839683 + 1.26184i
\(535\) 0.153992 0.423090i 0.00665766 0.0182918i
\(536\) 7.95947 14.3148i 0.343797 0.618307i
\(537\) 20.2888 3.57746i 0.875526 0.154379i
\(538\) 20.7454 5.03478i 0.894400 0.217065i
\(539\) 9.30764 + 34.7366i 0.400909 + 1.49621i
\(540\) −0.190195 0.611280i −0.00818469 0.0263053i
\(541\) 29.2664 2.56048i 1.25826 0.110083i 0.561554 0.827440i \(-0.310204\pi\)
0.696706 + 0.717357i \(0.254648\pi\)
\(542\) 0.157427 6.63866i 0.00676209 0.285155i
\(543\) 2.14678 1.23944i 0.0921269 0.0531895i
\(544\) −8.04529 + 26.6604i −0.344939 + 1.14305i
\(545\) 0.246557 + 0.677409i 0.0105613 + 0.0290170i
\(546\) −44.6018 39.2643i −1.90878 1.68036i
\(547\) −3.81124 5.44302i −0.162957 0.232727i 0.729367 0.684123i \(-0.239815\pi\)
−0.892323 + 0.451396i \(0.850926\pi\)
\(548\) 24.0998 + 15.4818i 1.02949 + 0.661350i
\(549\) −0.996238 0.0871595i −0.0425184 0.00371988i
\(550\) −19.8178 2.20837i −0.845035 0.0941652i
\(551\) −10.9176 + 29.6271i −0.465107 + 1.26216i
\(552\) 9.03699 + 3.12498i 0.384640 + 0.133008i
\(553\) −36.6330 + 30.7387i −1.55779 + 1.30714i
\(554\) −9.93436 4.92248i −0.422071 0.209136i
\(555\) 0.149392 + 0.213354i 0.00634133 + 0.00905636i
\(556\) −7.98999 + 7.26603i −0.338851 + 0.308148i
\(557\) −7.09642 + 15.2183i −0.300685 + 0.644821i −0.997364 0.0725623i \(-0.976882\pi\)
0.696679 + 0.717383i \(0.254660\pi\)
\(558\) 2.45810 0.373577i 0.104060 0.0158148i
\(559\) 6.82514 + 11.8215i 0.288673 + 0.499996i
\(560\) −0.373007 + 1.00118i −0.0157624 + 0.0423076i
\(561\) −15.0507 + 17.9367i −0.635440 + 0.757288i
\(562\) −20.5623 8.04109i −0.867369 0.339193i
\(563\) −3.77278 14.0802i −0.159004 0.593409i −0.998729 0.0503984i \(-0.983951\pi\)
0.839726 0.543011i \(-0.182716\pi\)
\(564\) 3.46010 4.47412i 0.145696 0.188394i
\(565\) 0.268767 + 0.188192i 0.0113071 + 0.00791731i
\(566\) −3.91896 1.15033i −0.164726 0.0483518i
\(567\) 35.4760 + 12.9122i 1.48985 + 0.542262i
\(568\) 10.8663 24.3199i 0.455938 1.02044i
\(569\) 23.3364 0.978313 0.489156 0.872196i \(-0.337305\pi\)
0.489156 + 0.872196i \(0.337305\pi\)
\(570\) 0.429221 + 0.453688i 0.0179781 + 0.0190029i
\(571\) −2.90566 + 2.90566i −0.121598 + 0.121598i −0.765287 0.643689i \(-0.777403\pi\)
0.643689 + 0.765287i \(0.277403\pi\)
\(572\) −14.5159 28.1445i −0.606942 1.17678i
\(573\) −1.25580 2.69308i −0.0524620 0.112505i
\(574\) −2.63748 4.82914i −0.110086 0.201565i
\(575\) −9.86974 + 1.74030i −0.411597 + 0.0725756i
\(576\) 1.21150 + 0.397165i 0.0504792 + 0.0165486i
\(577\) 5.12486 8.87651i 0.213351 0.369534i −0.739410 0.673255i \(-0.764896\pi\)
0.952761 + 0.303721i \(0.0982290\pi\)
\(578\) −9.52839 3.72617i −0.396329 0.154988i
\(579\) −1.03834 11.8683i −0.0431519 0.493228i
\(580\) −0.527541 0.692920i −0.0219050 0.0287719i
\(581\) 2.48906 9.28929i 0.103264 0.385385i
\(582\) 19.2548 26.1562i 0.798136 1.08421i
\(583\) −5.25273 14.4318i −0.217546 0.597703i
\(584\) 5.37545 + 7.41917i 0.222438 + 0.307007i
\(585\) −0.00933376 + 0.0529344i −0.000385904 + 0.00218857i
\(586\) 12.5887 25.4061i 0.520036 1.04952i
\(587\) 2.72010 31.0909i 0.112271 1.28326i −0.705912 0.708300i \(-0.749462\pi\)
0.818182 0.574959i \(-0.194982\pi\)
\(588\) −22.9425 36.3152i −0.946135 1.49761i
\(589\) −39.4997 + 27.4234i −1.62756 + 1.12996i
\(590\) 0.725882 + 0.907945i 0.0298841 + 0.0373795i
\(591\) 8.71453 7.31235i 0.358468 0.300790i
\(592\) −10.2827 0.0778489i −0.422616 0.00319957i
\(593\) −2.42984 + 13.7803i −0.0997814 + 0.565889i 0.893395 + 0.449271i \(0.148316\pi\)
−0.993177 + 0.116618i \(0.962795\pi\)
\(594\) 15.9511 + 14.0422i 0.654481 + 0.576160i
\(595\) −1.19171 0.555702i −0.0488552 0.0227816i
\(596\) −0.972570 24.3942i −0.0398380 0.999223i
\(597\) 1.91836 + 0.514022i 0.0785131 + 0.0210375i
\(598\) −10.9843 11.5179i −0.449180 0.471001i
\(599\) 20.9655 24.9857i 0.856625 1.02089i −0.142890 0.989739i \(-0.545639\pi\)
0.999515 0.0311476i \(-0.00991618\pi\)
\(600\) 23.3865 4.51398i 0.954751 0.184282i
\(601\) −4.27504 + 7.40458i −0.174382 + 0.302039i −0.939947 0.341319i \(-0.889126\pi\)
0.765565 + 0.643359i \(0.222460\pi\)
\(602\) 3.60561 + 14.8566i 0.146954 + 0.605511i
\(603\) 0.529335 0.755969i 0.0215562 0.0307854i
\(604\) 8.80238 21.0254i 0.358164 0.855510i
\(605\) 0.165406 0.0771301i 0.00672471 0.00313578i
\(606\) −5.61686 + 27.9612i −0.228169 + 1.13585i
\(607\) 1.32911 0.0539469 0.0269734 0.999636i \(-0.491413\pi\)
0.0269734 + 0.999636i \(0.491413\pi\)
\(608\) −24.4190 + 3.42267i −0.990319 + 0.138807i
\(609\) 54.2473 2.19821
\(610\) −0.105063 + 0.523012i −0.00425388 + 0.0211761i
\(611\) −8.53224 + 3.97865i −0.345177 + 0.160959i
\(612\) −0.605946 + 1.44736i −0.0244939 + 0.0585062i
\(613\) −5.31812 + 7.59507i −0.214797 + 0.306762i −0.912063 0.410051i \(-0.865511\pi\)
0.697266 + 0.716813i \(0.254400\pi\)
\(614\) 8.60169 + 35.4426i 0.347136 + 1.43035i
\(615\) 0.0443586 0.0768314i 0.00178871 0.00309814i
\(616\) −6.72155 34.8238i −0.270819 1.40309i
\(617\) −27.0827 + 32.2759i −1.09031 + 1.29938i −0.139289 + 0.990252i \(0.544482\pi\)
−0.951020 + 0.309129i \(0.899963\pi\)
\(618\) 18.2154 + 19.1002i 0.732729 + 0.768325i
\(619\) 30.7359 + 8.23565i 1.23538 + 0.331019i 0.816672 0.577102i \(-0.195817\pi\)
0.418707 + 0.908121i \(0.362483\pi\)
\(620\) −0.0528362 1.32525i −0.00212195 0.0532231i
\(621\) 9.68014 + 4.51392i 0.388451 + 0.181138i
\(622\) −30.7414 27.0626i −1.23262 1.08511i
\(623\) 11.3380 64.3010i 0.454247 2.57616i
\(624\) 26.5435 + 26.9484i 1.06259 + 1.07880i
\(625\) −19.1096 + 16.0349i −0.764384 + 0.641394i
\(626\) −9.21007 11.5201i −0.368108 0.460436i
\(627\) −20.0043 5.44591i −0.798896 0.217489i
\(628\) −3.44549 5.45379i −0.137490 0.217630i
\(629\) 1.10299 12.6073i 0.0439792 0.502684i
\(630\) −0.0267277 + 0.0539408i −0.00106486 + 0.00214905i
\(631\) 4.90764 27.8326i 0.195370 1.10800i −0.716521 0.697565i \(-0.754267\pi\)
0.911891 0.410432i \(-0.134622\pi\)
\(632\) 24.6505 17.8602i 0.980546 0.710440i
\(633\) 1.64662 + 4.52405i 0.0654472 + 0.179815i
\(634\) −1.22914 + 1.66970i −0.0488155 + 0.0663123i
\(635\) −0.0231733 + 0.0864838i −0.000919603 + 0.00343200i
\(636\) 11.1123 + 14.5959i 0.440630 + 0.578763i
\(637\) 6.23150 + 71.2264i 0.246901 + 2.82209i
\(638\) 26.9240 + 10.5289i 1.06593 + 0.416843i
\(639\) 0.750433 1.29979i 0.0296867 0.0514188i
\(640\) 0.282132 0.618821i 0.0111522 0.0244610i
\(641\) 24.0389 4.23872i 0.949481 0.167419i 0.322601 0.946535i \(-0.395443\pi\)
0.626880 + 0.779116i \(0.284332\pi\)
\(642\) −8.55725 15.6681i −0.337728 0.618369i
\(643\) 8.09862 + 17.3675i 0.319378 + 0.684909i 0.998807 0.0488326i \(-0.0155501\pi\)
−0.679429 + 0.733742i \(0.737772\pi\)
\(644\) −8.17090 15.8423i −0.321979 0.624274i
\(645\) −0.174295 + 0.174295i −0.00686286 + 0.00686286i
\(646\) −1.80641 30.2927i −0.0710722 1.19185i
\(647\) −22.3543 −0.878837 −0.439419 0.898282i \(-0.644815\pi\)
−0.439419 + 0.898282i \(0.644815\pi\)
\(648\) −21.9412 9.80344i −0.861932 0.385115i
\(649\) −36.2608 13.1979i −1.42336 0.518061i
\(650\) −38.0402 11.1659i −1.49206 0.437961i
\(651\) 67.6743 + 47.3861i 2.65236 + 1.85721i
\(652\) −9.60671 + 12.4221i −0.376228 + 0.486486i
\(653\) −9.63375 35.9536i −0.376998 1.40697i −0.850404 0.526130i \(-0.823642\pi\)
0.473407 0.880844i \(-0.343024\pi\)
\(654\) 26.6206 + 10.4102i 1.04095 + 0.407073i
\(655\) 0.146197 0.174231i 0.00571239 0.00680777i
\(656\) 1.45619 + 3.18556i 0.0568548 + 0.124375i
\(657\) 0.258112 + 0.447063i 0.0100699 + 0.0174416i
\(658\) −10.4240 + 1.58422i −0.406370 + 0.0617592i
\(659\) 6.38195 13.6861i 0.248606 0.533137i −0.741916 0.670493i \(-0.766083\pi\)
0.990522 + 0.137356i \(0.0438605\pi\)
\(660\) 0.423060 0.384727i 0.0164676 0.0149755i
\(661\) 21.2644 + 30.3688i 0.827091 + 1.18121i 0.981169 + 0.193150i \(0.0618703\pi\)
−0.154078 + 0.988059i \(0.549241\pi\)
\(662\) −8.13871 4.03274i −0.316320 0.156737i
\(663\) −35.6612 + 29.9233i −1.38497 + 1.16212i
\(664\) −2.00065 + 5.78559i −0.0776404 + 0.224525i
\(665\) 0.00465217 1.16426i 0.000180404 0.0451481i
\(666\) −0.575831 0.0641669i −0.0223130 0.00248642i
\(667\) 14.4745 + 1.26636i 0.560456 + 0.0490335i
\(668\) 28.0985 + 18.0506i 1.08716 + 0.698399i
\(669\) −5.27123 7.52810i −0.203798 0.291053i
\(670\) −0.369510 0.325291i −0.0142754 0.0125671i
\(671\) −6.05668 16.6406i −0.233816 0.642403i
\(672\) 20.0240 + 37.3323i 0.772441 + 1.44013i
\(673\) −24.0047 + 13.8591i −0.925315 + 0.534231i −0.885327 0.464969i \(-0.846065\pi\)
−0.0399882 + 0.999200i \(0.512732\pi\)
\(674\) 0.274837 11.5898i 0.0105863 0.446421i
\(675\) 26.5038 2.31878i 1.02013 0.0892499i
\(676\) −10.9806 35.2913i −0.422332 1.35736i
\(677\) 1.85910 + 6.93825i 0.0714510 + 0.266659i 0.992405 0.123012i \(-0.0392554\pi\)
−0.920954 + 0.389671i \(0.872589\pi\)
\(678\) 12.6426 3.06828i 0.485537 0.117837i
\(679\) −59.6269 + 10.5138i −2.28827 + 0.403484i
\(680\) 0.731530 + 0.406752i 0.0280529 + 0.0155982i
\(681\) −7.22980 + 19.8637i −0.277047 + 0.761179i
\(682\) 24.3909 + 36.6536i 0.933978 + 1.40354i
\(683\) 0.350373 + 0.350373i 0.0134067 + 0.0134067i 0.713778 0.700372i \(-0.246982\pi\)
−0.700372 + 0.713778i \(0.746982\pi\)
\(684\) −1.38844 + 0.0497999i −0.0530884 + 0.00190415i
\(685\) 0.608778 0.608778i 0.0232602 0.0232602i
\(686\) −7.10766 + 35.3825i −0.271372 + 1.35091i
\(687\) 23.2854 + 8.47520i 0.888394 + 0.323349i
\(688\) −1.61727 9.59627i −0.0616578 0.365854i
\(689\) −5.30221 30.0703i −0.201998 1.14559i
\(690\) 0.149561 0.245420i 0.00569369 0.00934300i
\(691\) 33.7829 9.05210i 1.28516 0.344358i 0.449341 0.893360i \(-0.351659\pi\)
0.835821 + 0.549002i \(0.184992\pi\)
\(692\) 21.2205 + 11.1490i 0.806683 + 0.423821i
\(693\) −0.174169 1.99076i −0.00661612 0.0756225i
\(694\) −18.1095 + 17.2705i −0.687427 + 0.655579i
\(695\) 0.162302 + 0.281115i 0.00615645 + 0.0106633i
\(696\) −34.4441 2.45407i −1.30560 0.0930215i
\(697\) −4.05074 + 1.47435i −0.153433 + 0.0558450i
\(698\) −9.34661 + 0.594845i −0.353775 + 0.0225152i
\(699\) −5.43429 + 3.80513i −0.205544 + 0.143923i
\(700\) −37.3570 23.9983i −1.41196 0.907052i
\(701\) −0.735500 + 8.40680i −0.0277794 + 0.317520i 0.969573 + 0.244802i \(0.0787230\pi\)
−0.997353 + 0.0727184i \(0.976833\pi\)
\(702\) 26.3837 + 33.0012i 0.995789 + 1.24555i
\(703\) 10.5451 3.79045i 0.397715 0.142959i
\(704\) 2.69244 + 22.4153i 0.101475 + 0.844807i
\(705\) −0.109273 0.130226i −0.00411546 0.00490461i
\(706\) 37.7617 12.7387i 1.42118 0.479428i
\(707\) 43.5509 30.4947i 1.63790 1.14687i
\(708\) 46.0401 + 2.18479i 1.73029 + 0.0821096i
\(709\) −13.1179 6.11699i −0.492654 0.229728i 0.160382 0.987055i \(-0.448727\pi\)
−0.653036 + 0.757327i \(0.726505\pi\)
\(710\) −0.644756 0.474634i −0.0241973 0.0178127i
\(711\) 1.48539 0.857590i 0.0557065 0.0321621i
\(712\) −10.1079 + 40.3147i −0.378810 + 1.51086i
\(713\) 16.9510 + 14.2236i 0.634820 + 0.532677i
\(714\) −47.7615 + 20.9077i −1.78743 + 0.782452i
\(715\) −0.919379 + 0.246347i −0.0343828 + 0.00921285i
\(716\) 19.3387 + 14.9558i 0.722722 + 0.558923i
\(717\) 11.9416 17.0543i 0.445966 0.636905i
\(718\) −15.9479 29.2001i −0.595170 1.08974i
\(719\) 3.50940 9.64201i 0.130879 0.359586i −0.856893 0.515495i \(-0.827608\pi\)
0.987772 + 0.155908i \(0.0498305\pi\)
\(720\) 0.0194108 0.0330403i 0.000723399 0.00123134i
\(721\) 49.2021i 1.83238i
\(722\) 23.6843 12.6907i 0.881438 0.472300i
\(723\) 4.34538 + 4.34538i 0.161606 + 0.161606i
\(724\) 2.80205 + 0.895159i 0.104137 + 0.0332683i
\(725\) 32.8015 15.2956i 1.21822 0.568064i
\(726\) 2.03813 6.94357i 0.0756422 0.257700i
\(727\) 4.16703 + 23.6324i 0.154546 + 0.876476i 0.959199 + 0.282731i \(0.0912403\pi\)
−0.804653 + 0.593746i \(0.797649\pi\)
\(728\) −1.13794 70.5042i −0.0421747 2.61306i
\(729\) −24.4894 14.1389i −0.907013 0.523664i
\(730\) 0.252262 0.110428i 0.00933662 0.00408714i
\(731\) 11.9312 1.04385i 0.441292 0.0386080i
\(732\) 12.8130 + 16.8298i 0.473584 + 0.622048i
\(733\) 29.1010 + 7.79759i 1.07487 + 0.288010i 0.752492 0.658601i \(-0.228851\pi\)
0.322377 + 0.946611i \(0.395518\pi\)
\(734\) −25.9758 + 3.94775i −0.958785 + 0.145714i
\(735\) −1.21322 + 0.441577i −0.0447504 + 0.0162878i
\(736\) 4.47140 + 10.4286i 0.164818 + 0.384405i
\(737\) 16.0937 + 2.83775i 0.592818 + 0.104530i
\(738\) 0.0630837 + 0.187001i 0.00232214 + 0.00688359i
\(739\) −9.86377 0.862968i −0.362845 0.0317448i −0.0957242 0.995408i \(-0.530517\pi\)
−0.267121 + 0.963663i \(0.586072\pi\)
\(740\) −0.0680369 + 0.301489i −0.00250109 + 0.0110830i
\(741\) −37.2876 17.5692i −1.36979 0.645422i
\(742\) 3.78730 33.9870i 0.139036 1.24770i
\(743\) 9.78016 + 11.6555i 0.358799 + 0.427600i 0.915004 0.403445i \(-0.132187\pi\)
−0.556205 + 0.831045i \(0.687743\pi\)
\(744\) −40.8258 33.1491i −1.49675 1.21530i
\(745\) −0.722637 0.127420i −0.0264754 0.00466833i
\(746\) −24.3822 + 1.55175i −0.892695 + 0.0568137i
\(747\) −0.145773 + 0.312612i −0.00533357 + 0.0114379i
\(748\) −27.7630 + 1.10688i −1.01512 + 0.0404716i
\(749\) −8.61357 + 32.1463i −0.314733 + 1.17460i
\(750\) 0.0339556 1.43190i 0.00123988 0.0522855i
\(751\) −5.22709 4.38605i −0.190739 0.160049i 0.542417 0.840109i \(-0.317509\pi\)
−0.733156 + 0.680060i \(0.761954\pi\)
\(752\) 6.69035 0.534324i 0.243972 0.0194848i
\(753\) −29.8942 17.2594i −1.08940 0.628967i
\(754\) 49.0813 + 29.9105i 1.78744 + 1.08928i
\(755\) −0.561198 0.392955i −0.0204241 0.0143011i
\(756\) 17.9430 + 43.7864i 0.652582 + 1.59250i
\(757\) 6.68201 + 14.3296i 0.242862 + 0.520818i 0.989521 0.144388i \(-0.0461213\pi\)
−0.746660 + 0.665206i \(0.768344\pi\)
\(758\) 35.0034 23.2928i 1.27138 0.846033i
\(759\) 9.54048i 0.346298i
\(760\) −0.0556235 + 0.739033i −0.00201768 + 0.0268075i
\(761\) 5.73553i 0.207913i 0.994582 + 0.103956i \(0.0331502\pi\)
−0.994582 + 0.103956i \(0.966850\pi\)
\(762\) 1.96676 + 2.95556i 0.0712482 + 0.107069i
\(763\) −22.5192 48.2927i −0.815251 1.74831i
\(764\) 1.36171 3.25257i 0.0492648 0.117674i
\(765\) 0.0386322 + 0.0270506i 0.00139675 + 0.000978016i
\(766\) −1.39920 + 2.29600i −0.0505551 + 0.0829578i
\(767\) −66.4409 38.3597i −2.39904 1.38509i
\(768\) −11.0253 24.6099i −0.397840 0.888032i
\(769\) −20.1718 16.9261i −0.727413 0.610372i 0.202012 0.979383i \(-0.435252\pi\)
−0.929425 + 0.369011i \(0.879697\pi\)
\(770\) −1.06570 0.0252717i −0.0384051 0.000910730i
\(771\) 3.12964 11.6800i 0.112711 0.420644i
\(772\) 9.59039 10.3869i 0.345166 0.373831i
\(773\) 16.5644 35.5226i 0.595782 1.27766i −0.344987 0.938608i \(-0.612117\pi\)
0.940768 0.339050i \(-0.110106\pi\)
\(774\) −0.0348266 0.547219i −0.00125182 0.0196694i
\(775\) 54.2813 + 9.57126i 1.94984 + 0.343810i
\(776\) 38.3355 3.97827i 1.37616 0.142812i
\(777\) −12.3750 14.7479i −0.443949 0.529078i
\(778\) 7.02699 + 0.783042i 0.251930 + 0.0280734i
\(779\) −2.68814 2.70971i −0.0963125 0.0970853i
\(780\) 0.961161 0.607224i 0.0344151 0.0217421i
\(781\) 26.4759 + 2.31634i 0.947381 + 0.0828851i
\(782\) −13.2320 + 4.46375i −0.473176 + 0.159623i
\(783\) −37.9858 6.69791i −1.35750 0.239364i
\(784\) 13.5651 49.1347i 0.484468 1.75481i
\(785\) −0.182201 + 0.0663156i −0.00650302 + 0.00236691i
\(786\) −1.35502 8.91593i −0.0483321 0.318021i
\(787\) 14.6277 + 3.91948i 0.521421 + 0.139714i 0.509924 0.860220i \(-0.329674\pi\)
0.0114972 + 0.999934i \(0.496340\pi\)
\(788\) 13.3771 + 1.81267i 0.476539 + 0.0645736i
\(789\) 17.8160 1.55870i 0.634266 0.0554910i
\(790\) −0.366904 0.838152i −0.0130538 0.0298201i
\(791\) −21.0030 12.1261i −0.746782 0.431155i
\(792\) 0.0205285 + 1.27190i 0.000729447 + 0.0451950i
\(793\) −6.11373 34.6727i −0.217105 1.23126i
\(794\) −6.14430 1.80352i −0.218053 0.0640047i
\(795\) 0.499713 0.233020i 0.0177230 0.00826437i
\(796\) 1.08029 + 2.09454i 0.0382899 + 0.0742390i
\(797\) 11.3653 + 11.3653i 0.402578 + 0.402578i 0.879141 0.476562i \(-0.158117\pi\)
−0.476562 + 0.879141i \(0.658117\pi\)
\(798\) −34.5285 30.6422i −1.22229 1.08472i
\(799\) 8.26011i 0.292222i
\(800\) 22.6340 + 16.9276i 0.800234 + 0.598482i
\(801\) −0.800957 + 2.20061i −0.0283004 + 0.0777547i
\(802\) −12.2613 + 6.69664i −0.432963 + 0.236467i
\(803\) −5.24317 + 7.48803i −0.185028 + 0.264247i
\(804\) −19.3624 + 2.47458i −0.682858 + 0.0872716i
\(805\) −0.517511 + 0.138667i −0.0182399 + 0.00488735i
\(806\) 35.1022 + 80.1873i 1.23642 + 2.82448i
\(807\) −19.4893 16.3535i −0.686057 0.575670i
\(808\) −29.0320 + 17.3923i −1.02134 + 0.611858i
\(809\) −0.156917 + 0.0905958i −0.00551689 + 0.00318518i −0.502756 0.864428i \(-0.667681\pi\)
0.497239 + 0.867614i \(0.334347\pi\)
\(810\) −0.428210 + 0.581693i −0.0150458 + 0.0204386i
\(811\) −43.1148 20.1047i −1.51396 0.705973i −0.524589 0.851356i \(-0.675781\pi\)
−0.989376 + 0.145382i \(0.953559\pi\)
\(812\) 43.3095 + 47.6247i 1.51986 + 1.67130i
\(813\) −6.48275 + 4.53927i −0.227360 + 0.159199i
\(814\) −3.27951 9.72155i −0.114947 0.340740i
\(815\) 0.303389 + 0.361565i 0.0106272 + 0.0126651i
\(816\) 31.2718 11.1146i 1.09473 0.389089i
\(817\) 5.26564 + 9.20510i 0.184221 + 0.322046i
\(818\) −4.50965 + 3.60536i −0.157676 + 0.126059i
\(819\) 0.346277 3.95796i 0.0120999 0.138302i
\(820\) 0.102866 0.0223967i 0.00359225 0.000782128i
\(821\) −19.8108 + 13.8717i −0.691401 + 0.484124i −0.865697 0.500569i \(-0.833124\pi\)
0.174295 + 0.984693i \(0.444235\pi\)
\(822\) −2.16820 34.0683i −0.0756248 1.18827i
\(823\) 12.6849 4.61691i 0.442167 0.160935i −0.111336 0.993783i \(-0.535513\pi\)
0.553503 + 0.832847i \(0.313291\pi\)
\(824\) −2.22584 + 31.2407i −0.0775408 + 1.08832i
\(825\) 11.8822 + 20.5806i 0.413686 + 0.716526i
\(826\) −59.2995 62.1803i −2.06329 2.16353i
\(827\) −2.89148 33.0497i −0.100546 1.14925i −0.864035 0.503431i \(-0.832071\pi\)
0.763489 0.645821i \(-0.223485\pi\)
\(828\) 0.189942 + 0.610468i 0.00660095 + 0.0212152i
\(829\) 6.14481 1.64650i 0.213418 0.0571852i −0.150526 0.988606i \(-0.548097\pi\)
0.363944 + 0.931421i \(0.381430\pi\)
\(830\) 0.157121 + 0.0957508i 0.00545376 + 0.00332356i
\(831\) 2.29445 + 13.0125i 0.0795935 + 0.451397i
\(832\) −2.46699 + 44.8178i −0.0855275 + 1.55378i
\(833\) 58.9497 + 21.4559i 2.04248 + 0.743404i
\(834\) 12.6188 + 2.53487i 0.436952 + 0.0877752i
\(835\) 0.709788 0.709788i 0.0245632 0.0245632i
\(836\) −11.1898 21.9100i −0.387008 0.757774i
\(837\) −41.5370 41.5370i −1.43573 1.43573i
\(838\) −27.0954 + 18.0305i −0.935994 + 0.622852i
\(839\) −14.0525 + 38.6090i −0.485147 + 1.33293i 0.419882 + 0.907579i \(0.362072\pi\)
−0.905028 + 0.425351i \(0.860151\pi\)
\(840\) 1.22443 0.349359i 0.0422469 0.0120540i
\(841\) −23.1149 + 4.07578i −0.797065 + 0.140544i
\(842\) −11.8791 48.9469i −0.409380 1.68682i
\(843\) 6.81023 + 25.4161i 0.234557 + 0.875378i
\(844\) −2.65713 + 5.05747i −0.0914622 + 0.174085i
\(845\) −1.10667 + 0.0968207i −0.0380705 + 0.00333073i
\(846\) 0.378062 + 0.00896525i 0.0129980 + 0.000308232i
\(847\) −11.6828 + 6.74506i −0.401426 + 0.231763i
\(848\) −3.94225 + 21.4086i −0.135378 + 0.735174i
\(849\) 1.66480 + 4.57400i 0.0571358 + 0.156979i
\(850\) −22.9846 + 26.1090i −0.788364 + 0.895532i
\(851\) −2.95767 4.22399i −0.101388 0.144796i
\(852\) −31.0186 + 6.75357i −1.06268 + 0.231373i
\(853\) 52.4235 + 4.58646i 1.79495 + 0.157037i 0.935301 0.353853i \(-0.115129\pi\)
0.859646 + 0.510891i \(0.170684\pi\)
\(854\) 4.36695 39.1888i 0.149434 1.34101i
\(855\) −0.00741556 + 0.0410948i −0.000253607 + 0.00140541i
\(856\) 6.92341 20.0215i 0.236637 0.684320i
\(857\) 42.9218 36.0157i 1.46618 1.23027i 0.546585 0.837403i \(-0.315927\pi\)
0.919595 0.392868i \(-0.128517\pi\)
\(858\) −16.7561 + 33.8166i −0.572045 + 1.15448i
\(859\) −31.4835 44.9631i −1.07420 1.53412i −0.824553 0.565785i \(-0.808573\pi\)
−0.249650 0.968336i \(-0.580316\pi\)
\(860\) −0.292169 0.0138646i −0.00996288 0.000472780i
\(861\) −2.77138 + 5.94325i −0.0944485 + 0.202545i
\(862\) 5.05467 + 33.2593i 0.172163 + 1.13282i
\(863\) 10.5732 + 18.3134i 0.359917 + 0.623395i 0.987947 0.154795i \(-0.0494716\pi\)
−0.628029 + 0.778190i \(0.716138\pi\)
\(864\) −9.41202 28.6137i −0.320203 0.973458i
\(865\) 0.463119 0.551924i 0.0157465 0.0187660i
\(866\) −20.2234 + 51.7144i −0.687219 + 1.75733i
\(867\) 3.15580 + 11.7776i 0.107177 + 0.399988i
\(868\) 12.4281 + 97.2442i 0.421838 + 3.30068i
\(869\) 24.8793 + 17.4207i 0.843973 + 0.590956i
\(870\) −0.292318 + 0.995878i −0.00991051 + 0.0337634i
\(871\) 30.5311 + 11.1124i 1.03451 + 0.376530i
\(872\) 12.1138 + 31.6820i 0.410225 + 1.07289i
\(873\) 2.17161 0.0734979
\(874\) −8.49774 8.98214i −0.287440 0.303825i
\(875\) −1.88801 + 1.88801i −0.0638265 + 0.0638265i
\(876\) 3.32275 10.4010i 0.112265 0.351416i
\(877\) −3.12083 6.69264i −0.105383 0.225995i 0.846545 0.532318i \(-0.178679\pi\)
−0.951928 + 0.306323i \(0.900901\pi\)
\(878\) −37.5391 + 20.5023i −1.26688 + 0.691920i
\(879\) −33.2780 + 5.86781i −1.12244 + 0.197916i
\(880\) 0.675518 + 0.0642570i 0.0227717 + 0.00216610i
\(881\) 20.0875 34.7926i 0.676766 1.17219i −0.299183 0.954196i \(-0.596714\pi\)
0.975949 0.217998i \(-0.0699526\pi\)
\(882\) 1.04601 2.67481i 0.0352210 0.0900656i
\(883\) 2.82761 + 32.3198i 0.0951567 + 1.08765i 0.882240 + 0.470800i \(0.156035\pi\)
−0.787083 + 0.616847i \(0.788410\pi\)
\(884\) −54.7411 7.41771i −1.84114 0.249485i
\(885\) 0.358558 1.33816i 0.0120528 0.0449816i
\(886\) 15.9762 + 11.7608i 0.536730 + 0.395111i
\(887\) −6.71950 18.4617i −0.225619 0.619883i 0.774297 0.632822i \(-0.218103\pi\)
−0.999916 + 0.0129392i \(0.995881\pi\)
\(888\) 7.19025 + 9.92394i 0.241289 + 0.333026i
\(889\) 1.14922 6.51753i 0.0385435 0.218591i
\(890\) 1.11935 + 0.554637i 0.0375206 + 0.0185915i
\(891\) 2.08978 23.8863i 0.0700103 0.800221i
\(892\) 2.40066 10.6379i 0.0803799 0.356184i
\(893\) −6.64090 + 3.06446i −0.222229 + 0.102548i
\(894\) −22.7254 + 18.1685i −0.760052 + 0.607644i
\(895\) 0.562885 0.472317i 0.0188152 0.0157878i
\(896\) −16.7882 + 47.3845i −0.560854 + 1.58300i
\(897\) −3.29377 + 18.6799i −0.109976 + 0.623705i
\(898\) 8.41162 9.55507i 0.280699 0.318857i
\(899\) −72.4236 33.7717i −2.41546 1.12635i
\(900\) 1.17005 + 1.08033i 0.0390017 + 0.0360110i
\(901\) −25.8779 6.93397i −0.862118 0.231004i
\(902\) −2.52902 + 2.41186i −0.0842073 + 0.0803061i
\(903\) 11.7114 13.9571i 0.389730 0.464462i
\(904\) 12.7872 + 8.64957i 0.425296 + 0.287680i
\(905\) 0.0442066 0.0765680i 0.00146948 0.00254521i
\(906\) −26.3984 + 6.40672i −0.877029 + 0.212849i
\(907\) 5.40668 7.72154i 0.179526 0.256390i −0.719296 0.694704i \(-0.755535\pi\)
0.898822 + 0.438314i \(0.144424\pi\)
\(908\) −23.2108 + 9.51145i −0.770277 + 0.315648i
\(909\) −1.72822 + 0.805883i −0.0573215 + 0.0267295i
\(910\) −2.07788 0.417405i −0.0688810 0.0138369i
\(911\) 21.4338 0.710134 0.355067 0.934841i \(-0.384458\pi\)
0.355067 + 0.934841i \(0.384458\pi\)
\(912\) 20.5375 + 21.0182i 0.680064 + 0.695981i
\(913\) −6.10794 −0.202143
\(914\) 6.09903 + 1.22518i 0.201738 + 0.0405253i
\(915\) 0.576196 0.268685i 0.0190484 0.00888244i
\(916\) 11.1499 + 27.2090i 0.368402 + 0.899012i
\(917\) −9.64280 + 13.7713i −0.318433 + 0.454770i
\(918\) 36.0256 8.74319i 1.18902 0.288568i
\(919\) −11.3231 + 19.6121i −0.373513 + 0.646944i −0.990103 0.140340i \(-0.955180\pi\)
0.616590 + 0.787284i \(0.288514\pi\)
\(920\) 0.334864 0.0646343i 0.0110401 0.00213093i
\(921\) 27.9392 33.2966i 0.920626 1.09716i
\(922\) −10.6928 + 10.1974i −0.352148 + 0.335834i
\(923\) 51.0391 + 13.6759i 1.67997 + 0.450148i
\(924\) −28.6736 + 31.0549i −0.943291 + 1.02163i
\(925\) −11.6410 5.42830i −0.382755 0.178481i
\(926\) 35.2896 40.0868i 1.15969 1.31733i
\(927\) −0.306440 + 1.73791i −0.0100648 + 0.0570804i
\(928\) −25.3447 32.1984i −0.831980 1.05696i
\(929\) 2.09355 1.75670i 0.0686872 0.0576354i −0.607798 0.794092i \(-0.707947\pi\)
0.676485 + 0.736457i \(0.263502\pi\)
\(930\) −1.23459 + 0.987027i −0.0404838 + 0.0323659i
\(931\) 4.62004 + 55.3539i 0.151416 + 1.81415i
\(932\) −7.67917 1.73295i −0.251540 0.0567648i
\(933\) −4.25411 + 48.6247i −0.139273 + 1.59190i
\(934\) 26.1206 + 12.9428i 0.854693 + 0.423501i
\(935\) −0.145017 + 0.822434i −0.00474257 + 0.0268965i
\(936\) −0.398920 + 2.49742i −0.0130391 + 0.0816309i
\(937\) −15.8628 43.5828i −0.518217 1.42379i −0.872483 0.488644i \(-0.837492\pi\)
0.354267 0.935144i \(-0.384730\pi\)
\(938\) 29.3045 + 21.5723i 0.956825 + 0.704361i
\(939\) −4.54942 + 16.9787i −0.148465 + 0.554078i
\(940\) 0.0270878 0.199902i 0.000883506 0.00652008i
\(941\) −4.89383 55.9367i −0.159534 1.82349i −0.481176 0.876624i \(-0.659790\pi\)
0.321641 0.946862i \(-0.395766\pi\)
\(942\) −2.80001 + 7.16007i −0.0912293 + 0.233288i
\(943\) −0.878214 + 1.52111i −0.0285986 + 0.0495342i
\(944\) 34.8390 + 42.1637i 1.13391 + 1.37231i
\(945\) 1.40067 0.246976i 0.0455639 0.00803414i
\(946\) 8.52153 4.65411i 0.277059 0.151318i
\(947\) 2.51255 + 5.38818i 0.0816470 + 0.175092i 0.942893 0.333096i \(-0.108093\pi\)
−0.861246 + 0.508188i \(0.830315\pi\)
\(948\) −34.5577 11.0400i −1.12238 0.358562i
\(949\) −12.8511 + 12.8511i −0.417165 + 0.417165i
\(950\) −29.5181 8.79264i −0.957693 0.285271i
\(951\) 2.47093 0.0801255
\(952\) −56.4867 25.2385i −1.83074 0.817985i
\(953\) −56.2976 20.4906i −1.82366 0.663757i −0.994499 0.104742i \(-0.966598\pi\)
−0.829158 0.559015i \(-0.811179\pi\)
\(954\) −0.345452 + 1.17689i −0.0111844 + 0.0381034i
\(955\) −0.0868159 0.0607891i −0.00280930 0.00196709i
\(956\) 24.5061 3.13196i 0.792584 0.101295i
\(957\) −8.91723 33.2796i −0.288253 1.07578i
\(958\) 3.68808 9.43099i 0.119156 0.304702i
\(959\) −40.9055 + 48.7493i −1.32091 + 1.57420i
\(960\) −0.793253 + 0.166432i −0.0256021 + 0.00537158i
\(961\) −45.3493 78.5473i −1.46288 2.53378i
\(962\) −3.06488 20.1667i −0.0988158 0.650199i
\(963\) 0.504460 1.08182i 0.0162560 0.0348611i
\(964\) −0.345661 + 7.28411i −0.0111330 + 0.234605i
\(965\) −0.243722 0.348072i −0.00784570 0.0112048i
\(966\) −9.43188 + 19.0351i −0.303466 + 0.612443i
\(967\) 30.9631 25.9811i 0.995705 0.835496i 0.00932157 0.999957i \(-0.497033\pi\)
0.986384 + 0.164461i \(0.0525884\pi\)
\(968\) 7.72308 3.75424i 0.248229 0.120666i
\(969\) −27.7975 + 23.1362i −0.892983 + 0.743242i
\(970\) 0.128293 1.15129i 0.00411923 0.0369658i
\(971\) −55.6755 4.87098i −1.78671 0.156317i −0.854790 0.518975i \(-0.826314\pi\)
−0.931922 + 0.362657i \(0.881869\pi\)
\(972\) −0.703928 3.23308i −0.0225785 0.103701i
\(973\) −13.7621 19.6543i −0.441193 0.630089i
\(974\) 0.145253 0.164999i 0.00465421 0.00528689i
\(975\) 16.1597 + 44.3984i 0.517524 + 1.42189i
\(976\) −4.54563 + 24.6852i −0.145502 + 0.790155i
\(977\) −45.1145 + 26.0468i −1.44334 + 0.833312i −0.998071 0.0620849i \(-0.980225\pi\)
−0.445268 + 0.895397i \(0.646892\pi\)
\(978\) 18.7096 + 0.443674i 0.598266 + 0.0141871i
\(979\) −41.3110 + 3.61425i −1.32031 + 0.115512i
\(980\) −1.35627 0.712568i −0.0433245 0.0227622i
\(981\) 0.494644 + 1.84604i 0.0157928 + 0.0589395i
\(982\) −4.17092 17.1860i −0.133099 0.548426i
\(983\) 29.7919 5.25312i 0.950215 0.167549i 0.323004 0.946398i \(-0.395307\pi\)
0.627211 + 0.778849i \(0.284196\pi\)
\(984\) 2.02854 3.64827i 0.0646676 0.116303i
\(985\) 0.138772 0.381273i 0.00442165 0.0121484i
\(986\) 41.9844 27.9383i 1.33705 0.889736i
\(987\) 8.88527 + 8.88527i 0.282821 + 0.282821i
\(988\) −14.3450 46.7622i −0.456376 1.48770i
\(989\) 3.45070 3.45070i 0.109726 0.109726i
\(990\) 0.0374850 + 0.00753002i 0.00119135 + 0.000239320i
\(991\) 33.9679 + 12.3633i 1.07902 + 0.392733i 0.819545 0.573015i \(-0.194226\pi\)
0.259480 + 0.965748i \(0.416449\pi\)
\(992\) −3.49200 62.3070i −0.110871 1.97825i
\(993\) 1.87972 + 10.6604i 0.0596512 + 0.338299i
\(994\) 50.5344 + 30.7960i 1.60285 + 0.976791i
\(995\) 0.0684211 0.0183334i 0.00216910 0.000581207i
\(996\) 6.96630 2.16751i 0.220736 0.0686801i
\(997\) 3.12776 + 35.7505i 0.0990572 + 1.13223i 0.869235 + 0.494400i \(0.164612\pi\)
−0.770178 + 0.637830i \(0.779832\pi\)
\(998\) 5.18387 + 5.43570i 0.164093 + 0.172064i
\(999\) 6.84443 + 11.8549i 0.216548 + 0.375072i
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 304.2.bg.a.203.23 yes 456
16.3 odd 4 inner 304.2.bg.a.51.2 yes 456
19.3 odd 18 inner 304.2.bg.a.155.2 yes 456
304.3 even 36 inner 304.2.bg.a.3.23 456
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
304.2.bg.a.3.23 456 304.3 even 36 inner
304.2.bg.a.51.2 yes 456 16.3 odd 4 inner
304.2.bg.a.155.2 yes 456 19.3 odd 18 inner
304.2.bg.a.203.23 yes 456 1.1 even 1 trivial