Properties

Label 648.2.bb.b.11.9
Level $648$
Weight $2$
Character 648.11
Analytic conductor $5.174$
Analytic rank $0$
Dimension $1872$
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] = [648,2,Mod(11,648)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(648, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([27, 27, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("648.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.bb (of order \(54\), degree \(18\), 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: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(1872\)
Relative dimension: \(104\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 11.9
Character \(\chi\) \(=\) 648.11
Dual form 648.2.bb.b.59.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36258 + 0.378650i) q^{2} +(1.53556 + 0.801277i) q^{3} +(1.71325 - 1.03188i) q^{4} +(3.32079 + 0.388144i) q^{5} +(-2.39573 - 0.510362i) q^{6} +(-1.72247 - 3.42973i) q^{7} +(-1.94371 + 2.05474i) q^{8} +(1.71591 + 2.46082i) q^{9} +O(q^{10})\) \(q+(-1.36258 + 0.378650i) q^{2} +(1.53556 + 0.801277i) q^{3} +(1.71325 - 1.03188i) q^{4} +(3.32079 + 0.388144i) q^{5} +(-2.39573 - 0.510362i) q^{6} +(-1.72247 - 3.42973i) q^{7} +(-1.94371 + 2.05474i) q^{8} +(1.71591 + 2.46082i) q^{9} +(-4.67181 + 0.728539i) q^{10} +(-0.940294 - 0.405603i) q^{11} +(3.45762 - 0.211735i) q^{12} +(-0.161661 - 0.682099i) q^{13} +(3.64568 + 4.02106i) q^{14} +(4.78827 + 3.25689i) q^{15} +(1.87044 - 3.53574i) q^{16} +(5.93324 - 1.04619i) q^{17} +(-3.26986 - 2.70334i) q^{18} +(-1.27783 + 7.24691i) q^{19} +(6.08985 - 2.76168i) q^{20} +(0.103193 - 6.64674i) q^{21} +(1.43481 + 0.196624i) q^{22} +(3.70572 + 1.86108i) q^{23} +(-4.63112 + 1.59774i) q^{24} +(6.01175 + 1.42481i) q^{25} +(0.478552 + 0.868202i) q^{26} +(0.663090 + 5.15367i) q^{27} +(-6.49010 - 4.09858i) q^{28} +(-2.78929 - 9.31688i) q^{29} +(-7.75762 - 2.62469i) q^{30} +(0.412241 + 0.626783i) q^{31} +(-1.20981 + 5.52597i) q^{32} +(-1.11888 - 1.37627i) q^{33} +(-7.68838 + 3.67214i) q^{34} +(-4.38874 - 12.0580i) q^{35} +(5.47906 + 2.44538i) q^{36} +(0.558209 - 1.53367i) q^{37} +(-1.00290 - 10.3583i) q^{38} +(0.298310 - 1.17694i) q^{39} +(-7.25220 + 6.06893i) q^{40} +(4.81302 - 4.54085i) q^{41} +(2.37618 + 9.09579i) q^{42} +(-2.41655 - 3.24599i) q^{43} +(-2.02949 + 0.275374i) q^{44} +(4.74302 + 8.83789i) q^{45} +(-5.75405 - 1.13270i) q^{46} +(-1.77247 - 1.16577i) q^{47} +(5.70528 - 3.93062i) q^{48} +(-4.61600 + 6.20037i) q^{49} +(-8.73100 + 0.334932i) q^{50} +(9.94916 + 3.14768i) q^{51} +(-0.980811 - 1.00179i) q^{52} +(6.38574 + 11.0604i) q^{53} +(-2.85495 - 6.77121i) q^{54} +(-2.96509 - 1.71189i) q^{55} +(10.3952 + 3.12717i) q^{56} +(-7.76896 + 10.1042i) q^{57} +(7.32847 + 11.6388i) q^{58} +(-11.6365 + 5.01950i) q^{59} +(11.5642 + 0.638930i) q^{60} +(-4.97245 - 0.289612i) q^{61} +(-0.799043 - 0.697946i) q^{62} +(5.48434 - 10.1238i) q^{63} +(-0.443946 - 7.98767i) q^{64} +(-0.272087 - 2.32785i) q^{65} +(2.04569 + 1.45161i) q^{66} +(0.651628 - 2.17659i) q^{67} +(9.08557 - 7.91479i) q^{68} +(4.19913 + 5.82713i) q^{69} +(10.5458 + 14.7681i) q^{70} +(5.76176 - 4.83469i) q^{71} +(-8.39160 - 1.25738i) q^{72} +(2.41918 + 2.02994i) q^{73} +(-0.179881 + 2.30111i) q^{74} +(8.08976 + 7.00497i) q^{75} +(5.28872 + 13.7343i) q^{76} +(0.228523 + 3.92359i) q^{77} +(0.0391775 + 1.71663i) q^{78} +(-2.86107 - 2.69928i) q^{79} +(7.58370 - 11.0154i) q^{80} +(-3.11130 + 8.44511i) q^{81} +(-4.83873 + 8.00973i) q^{82} +(0.655704 + 0.618625i) q^{83} +(-6.68186 - 11.4940i) q^{84} +(20.1091 - 1.17122i) q^{85} +(4.52184 + 3.50790i) q^{86} +(3.18227 - 16.5417i) q^{87} +(2.66108 - 1.14369i) q^{88} +(5.88245 - 7.01043i) q^{89} +(-9.80922 - 10.2464i) q^{90} +(-2.06096 + 1.72935i) q^{91} +(8.26925 - 0.635372i) q^{92} +(0.130796 + 1.29278i) q^{93} +(2.85655 + 0.917310i) q^{94} +(-7.05623 + 23.5695i) q^{95} +(-6.28557 + 7.51609i) q^{96} +(-16.8545 + 1.97001i) q^{97} +(3.94190 - 10.1963i) q^{98} +(-0.615343 - 3.00988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1872 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1872 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 36 q^{11} - 18 q^{12} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 90 q^{18} - 36 q^{19} - 18 q^{20} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 36 q^{27} - 9 q^{28} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 36 q^{35} - 18 q^{36} + 90 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 36 q^{43} + 54 q^{44} - 18 q^{46} + 81 q^{48} - 36 q^{49} - 135 q^{50} - 54 q^{51} - 18 q^{52} - 144 q^{54} + 108 q^{56} - 36 q^{57} - 18 q^{58} + 18 q^{59} + 99 q^{60} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 36 q^{67} + 243 q^{68} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 36 q^{75} - 54 q^{76} - 45 q^{78} - 36 q^{81} - 36 q^{82} - 36 q^{83} + 9 q^{84} - 18 q^{86} + 54 q^{88} - 198 q^{89} - 81 q^{90} - 36 q^{91} - 108 q^{92} - 18 q^{94} - 423 q^{96} - 36 q^{97} - 189 q^{98} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{13}{54}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36258 + 0.378650i −0.963489 + 0.267746i
\(3\) 1.53556 + 0.801277i 0.886558 + 0.462617i
\(4\) 1.71325 1.03188i 0.856624 0.515941i
\(5\) 3.32079 + 0.388144i 1.48510 + 0.173583i 0.819653 0.572860i \(-0.194166\pi\)
0.665449 + 0.746444i \(0.268240\pi\)
\(6\) −2.39573 0.510362i −0.978053 0.208355i
\(7\) −1.72247 3.42973i −0.651034 1.29632i −0.940717 0.339192i \(-0.889846\pi\)
0.289683 0.957123i \(-0.406450\pi\)
\(8\) −1.94371 + 2.05474i −0.687207 + 0.726462i
\(9\) 1.71591 + 2.46082i 0.571970 + 0.820274i
\(10\) −4.67181 + 0.728539i −1.47736 + 0.230384i
\(11\) −0.940294 0.405603i −0.283509 0.122294i 0.249577 0.968355i \(-0.419709\pi\)
−0.533086 + 0.846061i \(0.678968\pi\)
\(12\) 3.45762 0.211735i 0.998130 0.0611227i
\(13\) −0.161661 0.682099i −0.0448366 0.189180i 0.946018 0.324114i \(-0.105066\pi\)
−0.990855 + 0.134933i \(0.956918\pi\)
\(14\) 3.64568 + 4.02106i 0.974348 + 1.07467i
\(15\) 4.78827 + 3.25689i 1.23633 + 0.840926i
\(16\) 1.87044 3.53574i 0.467609 0.883935i
\(17\) 5.93324 1.04619i 1.43902 0.253739i 0.600946 0.799290i \(-0.294791\pi\)
0.838077 + 0.545551i \(0.183680\pi\)
\(18\) −3.26986 2.70334i −0.770713 0.637183i
\(19\) −1.27783 + 7.24691i −0.293153 + 1.66255i 0.381462 + 0.924385i \(0.375421\pi\)
−0.674615 + 0.738170i \(0.735690\pi\)
\(20\) 6.08985 2.76168i 1.36173 0.617529i
\(21\) 0.103193 6.64674i 0.0225186 1.45044i
\(22\) 1.43481 + 0.196624i 0.305902 + 0.0419205i
\(23\) 3.70572 + 1.86108i 0.772697 + 0.388063i 0.791037 0.611769i \(-0.209542\pi\)
−0.0183396 + 0.999832i \(0.505838\pi\)
\(24\) −4.63112 + 1.59774i −0.945323 + 0.326137i
\(25\) 6.01175 + 1.42481i 1.20235 + 0.284962i
\(26\) 0.478552 + 0.868202i 0.0938519 + 0.170268i
\(27\) 0.663090 + 5.15367i 0.127612 + 0.991824i
\(28\) −6.49010 4.09858i −1.22651 0.774559i
\(29\) −2.78929 9.31688i −0.517958 1.73010i −0.670600 0.741819i \(-0.733963\pi\)
0.152642 0.988282i \(-0.451222\pi\)
\(30\) −7.75762 2.62469i −1.41634 0.479202i
\(31\) 0.412241 + 0.626783i 0.0740408 + 0.112573i 0.870610 0.491974i \(-0.163724\pi\)
−0.796569 + 0.604547i \(0.793354\pi\)
\(32\) −1.20981 + 5.52597i −0.213866 + 0.976863i
\(33\) −1.11888 1.37627i −0.194772 0.239577i
\(34\) −7.68838 + 3.67214i −1.31855 + 0.629767i
\(35\) −4.38874 12.0580i −0.741833 2.03817i
\(36\) 5.47906 + 2.44538i 0.913177 + 0.407564i
\(37\) 0.558209 1.53367i 0.0917689 0.252133i −0.885313 0.464995i \(-0.846056\pi\)
0.977082 + 0.212862i \(0.0682784\pi\)
\(38\) −1.00290 10.3583i −0.162693 1.68034i
\(39\) 0.298310 1.17694i 0.0477679 0.188461i
\(40\) −7.25220 + 6.06893i −1.14667 + 0.959582i
\(41\) 4.81302 4.54085i 0.751668 0.709162i −0.211703 0.977334i \(-0.567901\pi\)
0.963371 + 0.268172i \(0.0864195\pi\)
\(42\) 2.37618 + 9.09579i 0.366653 + 1.40351i
\(43\) −2.41655 3.24599i −0.368521 0.495010i 0.578722 0.815525i \(-0.303551\pi\)
−0.947243 + 0.320515i \(0.896144\pi\)
\(44\) −2.02949 + 0.275374i −0.305958 + 0.0415142i
\(45\) 4.74302 + 8.83789i 0.707048 + 1.31748i
\(46\) −5.75405 1.13270i −0.848388 0.167008i
\(47\) −1.77247 1.16577i −0.258541 0.170045i 0.413621 0.910449i \(-0.364264\pi\)
−0.672162 + 0.740404i \(0.734634\pi\)
\(48\) 5.70528 3.93062i 0.823487 0.567336i
\(49\) −4.61600 + 6.20037i −0.659429 + 0.885767i
\(50\) −8.73100 + 0.334932i −1.23475 + 0.0473666i
\(51\) 9.94916 + 3.14768i 1.39316 + 0.440763i
\(52\) −0.980811 1.00179i −0.136014 0.138923i
\(53\) 6.38574 + 11.0604i 0.877149 + 1.51927i 0.854456 + 0.519524i \(0.173891\pi\)
0.0226927 + 0.999742i \(0.492776\pi\)
\(54\) −2.85495 6.77121i −0.388510 0.921445i
\(55\) −2.96509 1.71189i −0.399812 0.230832i
\(56\) 10.3952 + 3.12717i 1.38912 + 0.417885i
\(57\) −7.76896 + 10.1042i −1.02902 + 1.33833i
\(58\) 7.32847 + 11.6388i 0.962275 + 1.52825i
\(59\) −11.6365 + 5.01950i −1.51494 + 0.653483i −0.981345 0.192255i \(-0.938420\pi\)
−0.533599 + 0.845738i \(0.679161\pi\)
\(60\) 11.5642 + 0.638930i 1.49293 + 0.0824856i
\(61\) −4.97245 0.289612i −0.636656 0.0370810i −0.263219 0.964736i \(-0.584784\pi\)
−0.373438 + 0.927655i \(0.621821\pi\)
\(62\) −0.799043 0.697946i −0.101479 0.0886393i
\(63\) 5.48434 10.1238i 0.690962 1.27548i
\(64\) −0.443946 7.98767i −0.0554933 0.998459i
\(65\) −0.272087 2.32785i −0.0337483 0.288735i
\(66\) 2.04569 + 1.45161i 0.251807 + 0.178681i
\(67\) 0.651628 2.17659i 0.0796091 0.265913i −0.908914 0.416984i \(-0.863087\pi\)
0.988523 + 0.151071i \(0.0482723\pi\)
\(68\) 9.08557 7.91479i 1.10179 0.959810i
\(69\) 4.19913 + 5.82713i 0.505516 + 0.701503i
\(70\) 10.5458 + 14.7681i 1.26046 + 1.76513i
\(71\) 5.76176 4.83469i 0.683795 0.573773i −0.233317 0.972401i \(-0.574958\pi\)
0.917113 + 0.398628i \(0.130514\pi\)
\(72\) −8.39160 1.25738i −0.988960 0.148184i
\(73\) 2.41918 + 2.02994i 0.283144 + 0.237586i 0.773287 0.634056i \(-0.218611\pi\)
−0.490143 + 0.871642i \(0.663056\pi\)
\(74\) −0.179881 + 2.30111i −0.0209107 + 0.267498i
\(75\) 8.08976 + 7.00497i 0.934125 + 0.808864i
\(76\) 5.28872 + 13.7343i 0.606658 + 1.57543i
\(77\) 0.228523 + 3.92359i 0.0260427 + 0.447135i
\(78\) 0.0391775 + 1.71663i 0.00443598 + 0.194370i
\(79\) −2.86107 2.69928i −0.321895 0.303692i 0.508284 0.861190i \(-0.330280\pi\)
−0.830179 + 0.557497i \(0.811762\pi\)
\(80\) 7.58370 11.0154i 0.847884 1.23156i
\(81\) −3.11130 + 8.44511i −0.345700 + 0.938345i
\(82\) −4.83873 + 8.00973i −0.534349 + 0.884527i
\(83\) 0.655704 + 0.618625i 0.0719729 + 0.0679029i 0.721388 0.692531i \(-0.243505\pi\)
−0.649415 + 0.760434i \(0.724986\pi\)
\(84\) −6.68186 11.4940i −0.729051 1.25410i
\(85\) 20.1091 1.17122i 2.18114 0.127037i
\(86\) 4.52184 + 3.50790i 0.487603 + 0.378266i
\(87\) 3.18227 16.5417i 0.341175 1.77345i
\(88\) 2.66108 1.14369i 0.283672 0.121917i
\(89\) 5.88245 7.01043i 0.623538 0.743104i −0.358136 0.933669i \(-0.616588\pi\)
0.981674 + 0.190566i \(0.0610322\pi\)
\(90\) −9.80922 10.2464i −1.03398 1.08006i
\(91\) −2.06096 + 1.72935i −0.216047 + 0.181285i
\(92\) 8.26925 0.635372i 0.862128 0.0662421i
\(93\) 0.130796 + 1.29278i 0.0135630 + 0.134055i
\(94\) 2.85655 + 0.917310i 0.294630 + 0.0946133i
\(95\) −7.05623 + 23.5695i −0.723954 + 2.41818i
\(96\) −6.28557 + 7.51609i −0.641519 + 0.767107i
\(97\) −16.8545 + 1.97001i −1.71132 + 0.200024i −0.914608 0.404341i \(-0.867501\pi\)
−0.796707 + 0.604365i \(0.793427\pi\)
\(98\) 3.94190 10.1963i 0.398192 1.02999i
\(99\) −0.615343 3.00988i −0.0618443 0.302504i
\(100\) 11.7699 3.76237i 1.17699 0.376237i
\(101\) −0.471434 + 8.09421i −0.0469095 + 0.805404i 0.890028 + 0.455906i \(0.150685\pi\)
−0.936937 + 0.349498i \(0.886352\pi\)
\(102\) −14.7484 0.521711i −1.46031 0.0516570i
\(103\) −15.8345 + 6.83035i −1.56022 + 0.673014i −0.989018 0.147794i \(-0.952783\pi\)
−0.571204 + 0.820808i \(0.693524\pi\)
\(104\) 1.71576 + 0.993635i 0.168244 + 0.0974340i
\(105\) 2.92258 22.0324i 0.285215 2.15014i
\(106\) −12.8891 12.6528i −1.25190 1.22894i
\(107\) 9.74617 + 5.62695i 0.942198 + 0.543978i 0.890649 0.454692i \(-0.150251\pi\)
0.0515493 + 0.998670i \(0.483584\pi\)
\(108\) 6.45402 + 8.14528i 0.621038 + 0.783780i
\(109\) −12.5778 + 7.26182i −1.20474 + 0.695556i −0.961605 0.274437i \(-0.911509\pi\)
−0.243133 + 0.969993i \(0.578175\pi\)
\(110\) 4.68838 + 1.20986i 0.447019 + 0.115356i
\(111\) 2.08606 1.90776i 0.198000 0.181077i
\(112\) −15.3484 0.324868i −1.45029 0.0306972i
\(113\) 1.07088 + 0.797239i 0.100740 + 0.0749980i 0.646350 0.763041i \(-0.276295\pi\)
−0.545610 + 0.838039i \(0.683702\pi\)
\(114\) 6.75987 16.7095i 0.633120 1.56499i
\(115\) 11.5836 + 7.61863i 1.08017 + 0.710440i
\(116\) −14.3927 13.0839i −1.33633 1.21481i
\(117\) 1.40113 1.56824i 0.129535 0.144984i
\(118\) 13.9550 11.2456i 1.28466 1.03524i
\(119\) −13.8080 18.5474i −1.26578 1.70023i
\(120\) −15.9991 + 3.50820i −1.46051 + 0.320254i
\(121\) −6.82902 7.23834i −0.620820 0.658031i
\(122\) 6.88502 1.48820i 0.623340 0.134735i
\(123\) 11.0292 3.11621i 0.994468 0.280979i
\(124\) 1.35304 + 0.648449i 0.121506 + 0.0582325i
\(125\) 3.70191 + 1.34739i 0.331109 + 0.120514i
\(126\) −3.63947 + 15.8711i −0.324230 + 1.41391i
\(127\) −0.601289 1.65203i −0.0533558 0.146594i 0.910152 0.414275i \(-0.135965\pi\)
−0.963508 + 0.267681i \(0.913743\pi\)
\(128\) 3.62945 + 10.7157i 0.320801 + 0.947147i
\(129\) −1.10983 6.92076i −0.0977152 0.609339i
\(130\) 1.25218 + 3.06886i 0.109824 + 0.269157i
\(131\) −6.75086 10.2642i −0.589825 0.896786i 0.410058 0.912059i \(-0.365508\pi\)
−0.999883 + 0.0152737i \(0.995138\pi\)
\(132\) −3.33707 1.20333i −0.290454 0.104737i
\(133\) 27.0559 8.10001i 2.34605 0.702360i
\(134\) −0.0637293 + 3.21252i −0.00550537 + 0.277519i
\(135\) 0.201611 + 17.3716i 0.0173519 + 1.49511i
\(136\) −9.38288 + 14.2248i −0.804575 + 1.21977i
\(137\) −4.72303 + 19.9280i −0.403516 + 1.70257i 0.269552 + 0.962986i \(0.413124\pi\)
−0.673068 + 0.739581i \(0.735024\pi\)
\(138\) −7.92809 6.34992i −0.674884 0.540541i
\(139\) 0.568107 + 0.285314i 0.0481862 + 0.0242000i 0.472729 0.881208i \(-0.343269\pi\)
−0.424543 + 0.905408i \(0.639565\pi\)
\(140\) −19.9614 16.1296i −1.68705 1.36320i
\(141\) −1.78763 3.21035i −0.150546 0.270360i
\(142\) −6.02020 + 8.76935i −0.505204 + 0.735907i
\(143\) −0.124653 + 0.706944i −0.0104240 + 0.0591176i
\(144\) 11.9103 1.46420i 0.992528 0.122017i
\(145\) −5.64635 32.0220i −0.468904 2.65928i
\(146\) −4.06497 1.84992i −0.336419 0.153101i
\(147\) −12.0564 + 5.82236i −0.994393 + 0.480220i
\(148\) −0.626213 3.20356i −0.0514744 0.263331i
\(149\) −13.9327 + 3.30211i −1.14141 + 0.270519i −0.757490 0.652846i \(-0.773575\pi\)
−0.383921 + 0.923366i \(0.625427\pi\)
\(150\) −13.6754 6.48164i −1.11659 0.529224i
\(151\) −8.02477 3.46155i −0.653046 0.281697i 0.0436673 0.999046i \(-0.486096\pi\)
−0.696714 + 0.717349i \(0.745355\pi\)
\(152\) −12.4068 16.7115i −1.00633 1.35548i
\(153\) 12.7554 + 12.8055i 1.03121 + 1.03526i
\(154\) −1.79705 5.25968i −0.144811 0.423837i
\(155\) 1.12568 + 2.24142i 0.0904171 + 0.180035i
\(156\) −0.703386 2.32421i −0.0563159 0.186086i
\(157\) 1.60652 13.7446i 0.128214 1.09694i −0.763965 0.645258i \(-0.776750\pi\)
0.892179 0.451682i \(-0.149176\pi\)
\(158\) 4.92052 + 2.59464i 0.391455 + 0.206418i
\(159\) 0.943246 + 22.1007i 0.0748043 + 1.75270i
\(160\) −6.16240 + 17.8810i −0.487181 + 1.41362i
\(161\) 15.9153i 1.25430i
\(162\) 1.04165 12.6852i 0.0818400 0.996645i
\(163\) −10.6876 −0.837119 −0.418560 0.908189i \(-0.637465\pi\)
−0.418560 + 0.908189i \(0.637465\pi\)
\(164\) 3.56028 12.7461i 0.278011 0.995302i
\(165\) −3.18138 5.00458i −0.247670 0.389606i
\(166\) −1.12769 0.594643i −0.0875259 0.0461533i
\(167\) −6.45057 0.753963i −0.499160 0.0583434i −0.137212 0.990542i \(-0.543814\pi\)
−0.361948 + 0.932198i \(0.617888\pi\)
\(168\) 13.4568 + 13.1314i 1.03821 + 1.01311i
\(169\) 11.1781 5.61385i 0.859854 0.431835i
\(170\) −26.9568 + 9.21021i −2.06749 + 0.706391i
\(171\) −20.0260 + 9.29054i −1.53143 + 0.710466i
\(172\) −7.48964 3.06759i −0.571080 0.233902i
\(173\) −9.27817 + 21.5092i −0.705406 + 1.63532i 0.0650965 + 0.997879i \(0.479264\pi\)
−0.770503 + 0.637437i \(0.779995\pi\)
\(174\) 1.92741 + 23.7443i 0.146116 + 1.80005i
\(175\) −5.46837 23.0729i −0.413370 1.74415i
\(176\) −3.19287 + 2.56598i −0.240672 + 0.193418i
\(177\) −21.8906 1.61630i −1.64540 0.121489i
\(178\) −5.36080 + 11.7797i −0.401809 + 0.882922i
\(179\) 2.46275 0.434249i 0.184075 0.0324573i −0.0808509 0.996726i \(-0.525764\pi\)
0.264925 + 0.964269i \(0.414653\pi\)
\(180\) 17.2456 + 10.2473i 1.28541 + 0.763786i
\(181\) 7.35828 + 1.29746i 0.546937 + 0.0964397i 0.440287 0.897857i \(-0.354877\pi\)
0.106650 + 0.994297i \(0.465988\pi\)
\(182\) 2.15340 3.13676i 0.159621 0.232512i
\(183\) −7.40345 4.42902i −0.547279 0.327403i
\(184\) −11.0269 + 3.99690i −0.812916 + 0.294655i
\(185\) 2.44898 4.87631i 0.180052 0.358514i
\(186\) −0.667734 1.71200i −0.0489606 0.125530i
\(187\) −6.00333 1.42282i −0.439007 0.104047i
\(188\) −4.23961 0.168275i −0.309206 0.0122727i
\(189\) 16.5335 11.1513i 1.20264 0.811136i
\(190\) 0.690099 34.7871i 0.0500651 2.52372i
\(191\) −0.760510 2.54028i −0.0550286 0.183808i 0.926057 0.377385i \(-0.123176\pi\)
−0.981085 + 0.193576i \(0.937991\pi\)
\(192\) 5.71863 12.6213i 0.412707 0.910864i
\(193\) 5.80740 3.81959i 0.418026 0.274940i −0.323023 0.946391i \(-0.604699\pi\)
0.741049 + 0.671451i \(0.234329\pi\)
\(194\) 22.2197 9.06626i 1.59528 0.650919i
\(195\) 1.44745 3.79259i 0.103654 0.271593i
\(196\) −1.51031 + 15.3859i −0.107879 + 1.09900i
\(197\) −1.46113 + 0.531808i −0.104101 + 0.0378898i −0.393546 0.919305i \(-0.628752\pi\)
0.289444 + 0.957195i \(0.406529\pi\)
\(198\) 1.97815 + 3.86820i 0.140581 + 0.274901i
\(199\) 2.57189 7.06622i 0.182317 0.500911i −0.814543 0.580104i \(-0.803012\pi\)
0.996859 + 0.0791928i \(0.0252343\pi\)
\(200\) −14.6128 + 9.58319i −1.03328 + 0.677634i
\(201\) 2.74467 2.82016i 0.193594 0.198919i
\(202\) −2.42251 11.2075i −0.170447 0.788558i
\(203\) −27.1499 + 25.6146i −1.90555 + 1.79779i
\(204\) 20.2934 4.87361i 1.42082 0.341221i
\(205\) 17.7455 13.2111i 1.23940 0.922701i
\(206\) 18.9895 15.3026i 1.32306 1.06619i
\(207\) 1.77889 + 12.3126i 0.123642 + 0.855784i
\(208\) −2.71410 0.704234i −0.188189 0.0488299i
\(209\) 4.14090 6.29594i 0.286432 0.435499i
\(210\) 4.36032 + 31.1275i 0.300890 + 2.14800i
\(211\) 8.97381 12.0539i 0.617782 0.829826i −0.377585 0.925975i \(-0.623245\pi\)
0.995367 + 0.0961494i \(0.0306527\pi\)
\(212\) 22.3534 + 12.3599i 1.53524 + 0.848883i
\(213\) 12.7215 2.80721i 0.871661 0.192347i
\(214\) −15.4106 3.97679i −1.05345 0.271847i
\(215\) −6.76495 11.7172i −0.461366 0.799109i
\(216\) −11.8783 8.65478i −0.808218 0.588883i
\(217\) 1.43962 2.49349i 0.0977277 0.169269i
\(218\) 14.3886 14.6574i 0.974520 0.992725i
\(219\) 2.08827 + 5.05553i 0.141112 + 0.341621i
\(220\) −6.84640 + 0.126723i −0.461584 + 0.00854364i
\(221\) −1.67278 3.87793i −0.112523 0.260858i
\(222\) −2.12004 + 3.38936i −0.142288 + 0.227479i
\(223\) −2.45016 0.142706i −0.164075 0.00955627i −0.0240892 0.999710i \(-0.507669\pi\)
−0.139986 + 0.990154i \(0.544706\pi\)
\(224\) 21.0364 5.36902i 1.40556 0.358733i
\(225\) 6.80942 + 17.2387i 0.453962 + 1.14925i
\(226\) −1.76103 0.680814i −0.117142 0.0452871i
\(227\) −0.0445765 0.381377i −0.00295865 0.0253129i 0.991678 0.128740i \(-0.0410932\pi\)
−0.994637 + 0.103427i \(0.967019\pi\)
\(228\) −2.88381 + 25.3276i −0.190985 + 1.67736i
\(229\) −6.84545 2.04939i −0.452360 0.135428i 0.0525151 0.998620i \(-0.483276\pi\)
−0.504875 + 0.863192i \(0.668461\pi\)
\(230\) −18.6683 5.99487i −1.23095 0.395290i
\(231\) −2.79297 + 6.20804i −0.183764 + 0.408459i
\(232\) 24.5654 + 12.3781i 1.61280 + 0.812660i
\(233\) −2.88861 3.44251i −0.189239 0.225527i 0.663080 0.748549i \(-0.269249\pi\)
−0.852319 + 0.523022i \(0.824805\pi\)
\(234\) −1.31534 + 2.66739i −0.0859864 + 0.174373i
\(235\) −5.43350 4.55925i −0.354443 0.297413i
\(236\) −14.7567 + 20.6071i −0.960578 + 1.34141i
\(237\) −2.23048 6.43742i −0.144885 0.418155i
\(238\) 25.8375 + 20.0439i 1.67479 + 1.29925i
\(239\) −0.569786 9.78284i −0.0368564 0.632800i −0.965270 0.261252i \(-0.915864\pi\)
0.928414 0.371547i \(-0.121173\pi\)
\(240\) 20.4717 10.8383i 1.32144 0.699607i
\(241\) 9.16786 9.71736i 0.590554 0.625950i −0.361320 0.932442i \(-0.617674\pi\)
0.951873 + 0.306492i \(0.0991551\pi\)
\(242\) 12.0459 + 7.27700i 0.774339 + 0.467783i
\(243\) −11.5445 + 10.4750i −0.740578 + 0.671971i
\(244\) −8.81788 + 4.63480i −0.564507 + 0.296713i
\(245\) −17.7354 + 18.7984i −1.13307 + 1.20099i
\(246\) −13.8482 + 8.42228i −0.882929 + 0.536985i
\(247\) 5.14968 0.299935i 0.327667 0.0190844i
\(248\) −2.08916 0.371236i −0.132662 0.0235735i
\(249\) 0.511186 + 1.47534i 0.0323951 + 0.0934958i
\(250\) −5.55434 0.434191i −0.351287 0.0274606i
\(251\) 10.7892 12.8581i 0.681009 0.811595i −0.309228 0.950988i \(-0.600071\pi\)
0.990237 + 0.139393i \(0.0445150\pi\)
\(252\) −1.05055 23.0038i −0.0661782 1.44910i
\(253\) −2.72961 3.25302i −0.171609 0.204516i
\(254\) 1.44485 + 2.02334i 0.0906577 + 0.126956i
\(255\) 31.8173 + 14.3145i 1.99248 + 0.896408i
\(256\) −9.00293 13.2268i −0.562683 0.826673i
\(257\) −3.91813 1.17301i −0.244406 0.0731705i 0.162257 0.986749i \(-0.448123\pi\)
−0.406663 + 0.913578i \(0.633308\pi\)
\(258\) 4.13278 + 9.00985i 0.257296 + 0.560929i
\(259\) −6.22156 + 0.727196i −0.386589 + 0.0451857i
\(260\) −2.86823 3.70743i −0.177880 0.229925i
\(261\) 18.1410 22.8509i 1.12290 1.41443i
\(262\) 13.0851 + 11.4296i 0.808401 + 0.706120i
\(263\) −0.245523 + 4.21548i −0.0151396 + 0.259937i 0.982242 + 0.187619i \(0.0600769\pi\)
−0.997382 + 0.0723187i \(0.976960\pi\)
\(264\) 5.00266 + 0.376054i 0.307892 + 0.0231445i
\(265\) 16.9126 + 39.2079i 1.03894 + 2.40852i
\(266\) −33.7988 + 21.2817i −2.07234 + 1.30486i
\(267\) 14.6502 6.05149i 0.896575 0.370345i
\(268\) −1.12958 4.40144i −0.0690004 0.268861i
\(269\) 1.60873 2.78640i 0.0980860 0.169890i −0.812806 0.582534i \(-0.802061\pi\)
0.910892 + 0.412644i \(0.135395\pi\)
\(270\) −6.85248 23.5939i −0.417029 1.43588i
\(271\) −10.9717 + 6.33454i −0.666486 + 0.384796i −0.794744 0.606945i \(-0.792395\pi\)
0.128258 + 0.991741i \(0.459062\pi\)
\(272\) 7.39870 22.9352i 0.448612 1.39065i
\(273\) −4.55042 + 1.00413i −0.275404 + 0.0607726i
\(274\) −1.11025 28.9419i −0.0670725 1.74844i
\(275\) −5.07491 3.77813i −0.306029 0.227830i
\(276\) 13.2071 + 5.65030i 0.794972 + 0.340108i
\(277\) −13.3397 + 20.2820i −0.801506 + 1.21863i 0.170890 + 0.985290i \(0.445336\pi\)
−0.972395 + 0.233340i \(0.925035\pi\)
\(278\) −0.882126 0.173649i −0.0529064 0.0104148i
\(279\) −0.835032 + 2.08996i −0.0499920 + 0.125122i
\(280\) 33.3065 + 14.4195i 1.99044 + 0.861730i
\(281\) −18.4788 + 13.7570i −1.10235 + 0.820671i −0.985023 0.172422i \(-0.944841\pi\)
−0.117330 + 0.993093i \(0.537433\pi\)
\(282\) 3.65139 + 3.69747i 0.217437 + 0.220181i
\(283\) 16.9873 + 18.0055i 1.00979 + 1.07032i 0.997519 + 0.0703910i \(0.0224247\pi\)
0.0122713 + 0.999925i \(0.496094\pi\)
\(284\) 4.88249 14.2285i 0.289723 0.844306i
\(285\) −29.7210 + 30.5384i −1.76052 + 1.80894i
\(286\) −0.0978345 1.01047i −0.00578507 0.0597502i
\(287\) −23.8642 8.68586i −1.40866 0.512710i
\(288\) −15.6744 + 6.50494i −0.923621 + 0.383307i
\(289\) 18.1341 6.60027i 1.06671 0.388251i
\(290\) 19.8187 + 41.4946i 1.16380 + 2.43665i
\(291\) −27.4597 10.4801i −1.60972 0.614351i
\(292\) 6.23931 + 0.981470i 0.365128 + 0.0574362i
\(293\) 6.19775 4.07632i 0.362076 0.238141i −0.355415 0.934708i \(-0.615661\pi\)
0.717492 + 0.696567i \(0.245290\pi\)
\(294\) 14.2231 12.4986i 0.829510 0.728932i
\(295\) −40.5907 + 12.1520i −2.36328 + 0.707519i
\(296\) 2.06629 + 4.12798i 0.120101 + 0.239934i
\(297\) 1.46685 5.11492i 0.0851151 0.296798i
\(298\) 17.7341 9.77501i 1.02731 0.566251i
\(299\) 0.670375 2.82854i 0.0387688 0.163578i
\(300\) 21.0881 + 3.65357i 1.21752 + 0.210939i
\(301\) −6.97043 + 13.8793i −0.401769 + 0.799987i
\(302\) 12.2451 + 1.67805i 0.704626 + 0.0965611i
\(303\) −7.20962 + 12.0514i −0.414182 + 0.692337i
\(304\) 23.2331 + 18.0729i 1.33251 + 1.03655i
\(305\) −16.4000 2.89177i −0.939063 0.165582i
\(306\) −22.2291 12.6187i −1.27075 0.721361i
\(307\) 1.40209 + 7.95164i 0.0800214 + 0.453824i 0.998320 + 0.0579362i \(0.0184520\pi\)
−0.918299 + 0.395888i \(0.870437\pi\)
\(308\) 4.44021 + 6.48628i 0.253004 + 0.369590i
\(309\) −29.7879 2.19941i −1.69458 0.125120i
\(310\) −2.38255 2.62788i −0.135320 0.149253i
\(311\) 26.6752 6.32214i 1.51261 0.358496i 0.611206 0.791471i \(-0.290685\pi\)
0.901406 + 0.432976i \(0.142536\pi\)
\(312\) 1.83848 + 2.90059i 0.104084 + 0.164214i
\(313\) 6.35711 14.7374i 0.359325 0.833009i −0.638656 0.769493i \(-0.720509\pi\)
0.997981 0.0635167i \(-0.0202316\pi\)
\(314\) 3.01540 + 19.3365i 0.170169 + 1.09122i
\(315\) 22.1418 31.4903i 1.24755 1.77428i
\(316\) −7.68706 1.67225i −0.432431 0.0940713i
\(317\) −5.26871 + 2.64604i −0.295920 + 0.148617i −0.590565 0.806990i \(-0.701095\pi\)
0.294645 + 0.955607i \(0.404799\pi\)
\(318\) −9.65370 29.7569i −0.541352 1.66868i
\(319\) −1.15620 + 9.89195i −0.0647350 + 0.553843i
\(320\) 1.62612 26.6977i 0.0909028 1.49245i
\(321\) 10.4571 + 16.4499i 0.583659 + 0.918145i
\(322\) 6.02633 + 21.6859i 0.335834 + 1.20851i
\(323\) 44.3345i 2.46684i
\(324\) 3.38393 + 17.6791i 0.187996 + 0.982170i
\(325\) 4.33095i 0.240238i
\(326\) 14.5627 4.04687i 0.806556 0.224135i
\(327\) −25.1328 + 1.07265i −1.38985 + 0.0593178i
\(328\) −0.0248528 + 18.7157i −0.00137227 + 1.03340i
\(329\) −0.945245 + 8.08709i −0.0521131 + 0.445856i
\(330\) 6.22986 + 5.61450i 0.342943 + 0.309068i
\(331\) 14.1147 7.08867i 0.775815 0.389629i −0.0164045 0.999865i \(-0.505222\pi\)
0.792219 + 0.610237i \(0.208926\pi\)
\(332\) 1.76173 + 0.383248i 0.0966876 + 0.0210335i
\(333\) 4.73192 1.25798i 0.259307 0.0689369i
\(334\) 9.07490 1.41517i 0.496557 0.0774349i
\(335\) 3.00875 6.97507i 0.164386 0.381089i
\(336\) −23.3081 12.7972i −1.27156 0.698143i
\(337\) 7.26862 1.72269i 0.395947 0.0938411i −0.0278188 0.999613i \(-0.508856\pi\)
0.423766 + 0.905772i \(0.360708\pi\)
\(338\) −13.1054 + 11.8819i −0.712838 + 0.646291i
\(339\) 1.00559 + 2.08228i 0.0546163 + 0.113094i
\(340\) 33.2433 22.7568i 1.80287 1.23416i
\(341\) −0.133403 0.756567i −0.00722419 0.0409704i
\(342\) 23.7691 20.2420i 1.28529 1.09456i
\(343\) 2.75894 + 0.486476i 0.148969 + 0.0262672i
\(344\) 11.3668 + 1.34389i 0.612856 + 0.0724576i
\(345\) 11.6827 + 20.9805i 0.628973 + 1.12955i
\(346\) 4.49778 32.8212i 0.241802 1.76448i
\(347\) 13.5337 26.9478i 0.726527 1.44663i −0.161515 0.986870i \(-0.551638\pi\)
0.888041 0.459763i \(-0.152066\pi\)
\(348\) −11.6170 31.6237i −0.622738 1.69521i
\(349\) 2.38728 10.0727i 0.127788 0.539182i −0.871059 0.491179i \(-0.836566\pi\)
0.998847 0.0480029i \(-0.0152857\pi\)
\(350\) 16.1876 + 29.3680i 0.865266 + 1.56979i
\(351\) 3.40812 1.28544i 0.181912 0.0686116i
\(352\) 3.37893 4.70534i 0.180098 0.250795i
\(353\) 25.3351 7.58484i 1.34845 0.403700i 0.470480 0.882411i \(-0.344081\pi\)
0.877973 + 0.478711i \(0.158896\pi\)
\(354\) 30.4397 6.08654i 1.61785 0.323496i
\(355\) 21.0102 13.8186i 1.11510 0.733415i
\(356\) 2.84415 18.0806i 0.150740 0.958269i
\(357\) −6.34149 39.5447i −0.335627 2.09293i
\(358\) −3.19126 + 1.52422i −0.168664 + 0.0805575i
\(359\) 14.2521 5.18733i 0.752196 0.273777i 0.0626664 0.998035i \(-0.480040\pi\)
0.689529 + 0.724258i \(0.257817\pi\)
\(360\) −27.3787 7.43265i −1.44298 0.391735i
\(361\) −33.0307 12.0222i −1.73846 0.632746i
\(362\) −10.5175 + 1.01832i −0.552789 + 0.0535216i
\(363\) −4.68648 16.5869i −0.245976 0.870584i
\(364\) −1.74645 + 5.08947i −0.0915387 + 0.266761i
\(365\) 7.24569 + 7.67998i 0.379257 + 0.401988i
\(366\) 11.7648 + 3.23158i 0.614958 + 0.168917i
\(367\) −3.91862 + 2.91730i −0.204550 + 0.152282i −0.694560 0.719435i \(-0.744401\pi\)
0.490009 + 0.871717i \(0.336993\pi\)
\(368\) 13.5116 9.62144i 0.704343 0.501552i
\(369\) 19.4330 + 4.05230i 1.01164 + 0.210954i
\(370\) −1.49051 + 7.57167i −0.0774879 + 0.393633i
\(371\) 26.9350 40.9526i 1.39839 2.12615i
\(372\) 1.55809 + 2.07989i 0.0807831 + 0.107837i
\(373\) −3.08835 2.29919i −0.159909 0.119048i 0.514230 0.857652i \(-0.328078\pi\)
−0.674139 + 0.738605i \(0.735485\pi\)
\(374\) 8.71877 0.334463i 0.450837 0.0172947i
\(375\) 4.60489 + 5.03525i 0.237795 + 0.260019i
\(376\) 5.84053 1.37604i 0.301202 0.0709640i
\(377\) −5.90412 + 3.40874i −0.304078 + 0.175559i
\(378\) −18.3058 + 21.4549i −0.941550 + 1.10352i
\(379\) −6.00463 + 10.4003i −0.308437 + 0.534229i −0.978021 0.208508i \(-0.933139\pi\)
0.669583 + 0.742737i \(0.266473\pi\)
\(380\) 12.2318 + 47.6615i 0.627480 + 2.44499i
\(381\) 0.400415 3.01859i 0.0205139 0.154647i
\(382\) 1.99813 + 3.17337i 0.102233 + 0.162364i
\(383\) 10.4964 + 24.3334i 0.536340 + 1.24338i 0.943910 + 0.330203i \(0.107117\pi\)
−0.407570 + 0.913174i \(0.633624\pi\)
\(384\) −3.01303 + 19.3629i −0.153758 + 0.988109i
\(385\) −0.764044 + 13.1181i −0.0389393 + 0.668562i
\(386\) −6.46676 + 7.40347i −0.329150 + 0.376827i
\(387\) 3.84123 11.5165i 0.195261 0.585419i
\(388\) −26.8431 + 20.7670i −1.36275 + 1.05428i
\(389\) 0.502263 0.0587061i 0.0254657 0.00297652i −0.103351 0.994645i \(-0.532956\pi\)
0.128816 + 0.991668i \(0.458882\pi\)
\(390\) −0.536201 + 5.71578i −0.0271516 + 0.289430i
\(391\) 23.9340 + 7.16537i 1.21040 + 0.362369i
\(392\) −3.76798 21.5365i −0.190312 1.08776i
\(393\) −2.14192 21.1706i −0.108046 1.06792i
\(394\) 1.78954 1.27789i 0.0901557 0.0643791i
\(395\) −8.45329 10.0742i −0.425331 0.506890i
\(396\) −4.16008 4.52170i −0.209052 0.227224i
\(397\) −12.3801 + 14.7540i −0.621337 + 0.740481i −0.981300 0.192486i \(-0.938345\pi\)
0.359963 + 0.932967i \(0.382789\pi\)
\(398\) −0.828784 + 10.6021i −0.0415432 + 0.531437i
\(399\) 48.0365 + 9.24121i 2.40483 + 0.462639i
\(400\) 16.2824 18.5910i 0.814119 0.929549i
\(401\) −19.2951 + 1.12381i −0.963552 + 0.0561205i −0.532702 0.846303i \(-0.678823\pi\)
−0.430850 + 0.902423i \(0.641786\pi\)
\(402\) −2.67198 + 4.88196i −0.133266 + 0.243490i
\(403\) 0.360885 0.382516i 0.0179770 0.0190545i
\(404\) 7.54459 + 14.3539i 0.375358 + 0.714131i
\(405\) −13.6099 + 26.8368i −0.676281 + 1.33353i
\(406\) 27.2949 45.1822i 1.35462 2.24236i
\(407\) −1.14694 + 1.21569i −0.0568517 + 0.0602593i
\(408\) −25.8060 + 14.3248i −1.27759 + 0.709183i
\(409\) −0.788517 13.5383i −0.0389897 0.669427i −0.960019 0.279934i \(-0.909687\pi\)
0.921030 0.389493i \(-0.127350\pi\)
\(410\) −19.1773 + 24.7205i −0.947102 + 1.22086i
\(411\) −23.2204 + 26.8163i −1.14538 + 1.32275i
\(412\) −20.0804 + 28.0415i −0.989288 + 1.38150i
\(413\) 37.2591 + 31.2641i 1.83340 + 1.53840i
\(414\) −7.08605 16.1033i −0.348260 0.791434i
\(415\) 1.93734 + 2.30883i 0.0951002 + 0.113336i
\(416\) 3.96484 0.0681201i 0.194392 0.00333986i
\(417\) 0.643749 + 0.893329i 0.0315245 + 0.0437465i
\(418\) −3.25835 + 10.1467i −0.159371 + 0.496290i
\(419\) −4.55286 1.36304i −0.222422 0.0665887i 0.173653 0.984807i \(-0.444443\pi\)
−0.396075 + 0.918218i \(0.629628\pi\)
\(420\) −17.7277 40.7627i −0.865024 1.98901i
\(421\) 0.0623432 + 0.533380i 0.00303842 + 0.0259954i 0.994673 0.103085i \(-0.0328715\pi\)
−0.991634 + 0.129081i \(0.958797\pi\)
\(422\) −7.66331 + 19.8224i −0.373044 + 0.964937i
\(423\) −0.172642 6.36209i −0.00839414 0.309335i
\(424\) −35.1384 8.37725i −1.70647 0.406835i
\(425\) 37.1598 + 2.16431i 1.80252 + 0.104985i
\(426\) −16.2711 + 8.64204i −0.788337 + 0.418708i
\(427\) 7.57162 + 17.5530i 0.366416 + 0.849448i
\(428\) 22.5040 0.416535i 1.08777 0.0201340i
\(429\) −0.757871 + 0.985676i −0.0365904 + 0.0475889i
\(430\) 13.6545 + 13.4041i 0.658479 + 0.646404i
\(431\) 11.1854 19.3737i 0.538782 0.933199i −0.460187 0.887822i \(-0.652218\pi\)
0.998970 0.0453768i \(-0.0144489\pi\)
\(432\) 19.4623 + 7.29510i 0.936381 + 0.350986i
\(433\) −11.8148 20.4638i −0.567782 0.983427i −0.996785 0.0801240i \(-0.974468\pi\)
0.429003 0.903303i \(-0.358865\pi\)
\(434\) −1.01743 + 3.94269i −0.0488384 + 0.189255i
\(435\) 16.9882 53.6961i 0.814521 2.57453i
\(436\) −14.0556 + 25.4201i −0.673142 + 1.21740i
\(437\) −18.2224 + 24.4769i −0.871694 + 1.17089i
\(438\) −4.75971 6.09784i −0.227428 0.291366i
\(439\) −3.41816 + 5.19706i −0.163140 + 0.248042i −0.907802 0.419400i \(-0.862240\pi\)
0.744662 + 0.667442i \(0.232611\pi\)
\(440\) 9.28078 2.76506i 0.442444 0.131819i
\(441\) −23.1787 0.719888i −1.10375 0.0342804i
\(442\) 3.74767 + 4.65060i 0.178259 + 0.221206i
\(443\) 19.1252 14.2382i 0.908668 0.676478i −0.0377969 0.999285i \(-0.512034\pi\)
0.946465 + 0.322807i \(0.104627\pi\)
\(444\) 1.60535 5.42103i 0.0761863 0.257271i
\(445\) 22.2554 20.9969i 1.05501 0.995349i
\(446\) 3.39257 0.733306i 0.160643 0.0347230i
\(447\) −24.0405 6.09335i −1.13707 0.288206i
\(448\) −26.6309 + 15.2812i −1.25819 + 0.721967i
\(449\) −10.0744 + 27.6792i −0.475441 + 1.30626i 0.437883 + 0.899032i \(0.355728\pi\)
−0.913324 + 0.407233i \(0.866494\pi\)
\(450\) −15.8058 20.9107i −0.745094 0.985741i
\(451\) −6.36745 + 2.31756i −0.299831 + 0.109130i
\(452\) 2.65734 + 0.260848i 0.124991 + 0.0122693i
\(453\) −9.54888 11.7455i −0.448646 0.551851i
\(454\) 0.205147 + 0.502777i 0.00962805 + 0.0235965i
\(455\) −7.51524 + 4.94285i −0.352320 + 0.231725i
\(456\) −5.66089 35.6029i −0.265095 1.66726i
\(457\) 1.52932 + 5.10828i 0.0715384 + 0.238955i 0.986279 0.165086i \(-0.0527903\pi\)
−0.914741 + 0.404041i \(0.867605\pi\)
\(458\) 10.1035 + 0.200430i 0.472104 + 0.00936550i
\(459\) 9.32599 + 29.8843i 0.435300 + 1.39488i
\(460\) 27.7070 + 1.09973i 1.29185 + 0.0512749i
\(461\) −12.7724 3.02711i −0.594868 0.140986i −0.0778565 0.996965i \(-0.524808\pi\)
−0.517012 + 0.855978i \(0.672956\pi\)
\(462\) 1.45497 9.51651i 0.0676915 0.442748i
\(463\) 1.76610 3.51658i 0.0820774 0.163430i −0.848850 0.528634i \(-0.822705\pi\)
0.930927 + 0.365204i \(0.119001\pi\)
\(464\) −38.1593 7.56443i −1.77150 0.351170i
\(465\) −0.0674396 + 4.34383i −0.00312744 + 0.201440i
\(466\) 5.23947 + 3.59693i 0.242714 + 0.166624i
\(467\) −39.3824 6.94418i −1.82240 0.321338i −0.845328 0.534247i \(-0.820595\pi\)
−0.977072 + 0.212909i \(0.931706\pi\)
\(468\) 0.782246 4.13259i 0.0361593 0.191029i
\(469\) −8.58753 + 1.51421i −0.396535 + 0.0699198i
\(470\) 9.12994 + 4.15495i 0.421133 + 0.191653i
\(471\) 13.4802 19.8185i 0.621133 0.913187i
\(472\) 12.3043 33.6665i 0.566349 1.54963i
\(473\) 0.955685 + 4.03235i 0.0439425 + 0.185408i
\(474\) 5.47674 + 7.92693i 0.251555 + 0.364096i
\(475\) −18.0074 + 41.7460i −0.826238 + 1.91544i
\(476\) −42.7952 17.5280i −1.96152 0.803395i
\(477\) −16.2604 + 34.6929i −0.744512 + 1.58848i
\(478\) 4.48065 + 13.1142i 0.204940 + 0.599828i
\(479\) −0.237414 + 0.119234i −0.0108477 + 0.00544793i −0.454215 0.890892i \(-0.650080\pi\)
0.443367 + 0.896340i \(0.353784\pi\)
\(480\) −23.7904 + 22.5196i −1.08588 + 1.02788i
\(481\) −1.13635 0.132821i −0.0518132 0.00605610i
\(482\) −8.81246 + 16.7121i −0.401397 + 0.761215i
\(483\) 12.7526 24.4389i 0.580261 1.11201i
\(484\) −19.1689 5.35432i −0.871314 0.243378i
\(485\) −56.7349 −2.57620
\(486\) 11.7639 18.6443i 0.533621 0.845723i
\(487\) 0.529011i 0.0239718i 0.999928 + 0.0119859i \(0.00381532\pi\)
−0.999928 + 0.0119859i \(0.996185\pi\)
\(488\) 10.2601 9.65418i 0.464453 0.437024i
\(489\) −16.4115 8.56375i −0.742155 0.387266i
\(490\) 17.0479 32.3299i 0.770145 1.46052i
\(491\) −2.99167 + 25.5954i −0.135012 + 1.15510i 0.740551 + 0.672001i \(0.234565\pi\)
−0.875563 + 0.483104i \(0.839509\pi\)
\(492\) 15.6802 16.7197i 0.706917 0.753780i
\(493\) −26.2968 52.3612i −1.18435 2.35823i
\(494\) −6.90328 + 2.35861i −0.310593 + 0.106119i
\(495\) −0.875157 10.2340i −0.0393354 0.459984i
\(496\) 2.98721 0.285221i 0.134130 0.0128068i
\(497\) −26.5062 11.4336i −1.18896 0.512869i
\(498\) −1.25517 1.81671i −0.0562454 0.0814085i
\(499\) 25.0013 5.92542i 1.11921 0.265258i 0.370944 0.928655i \(-0.379034\pi\)
0.748268 + 0.663397i \(0.230886\pi\)
\(500\) 7.73263 1.51153i 0.345814 0.0675977i
\(501\) −9.30112 6.32645i −0.415544 0.282645i
\(502\) −9.83245 + 21.6055i −0.438844 + 0.964301i
\(503\) −6.30436 35.7538i −0.281097 1.59418i −0.718901 0.695112i \(-0.755355\pi\)
0.437804 0.899070i \(-0.355756\pi\)
\(504\) 10.1418 + 30.9467i 0.451754 + 1.37848i
\(505\) −4.70726 + 26.6962i −0.209470 + 1.18796i
\(506\) 4.95107 + 3.39894i 0.220102 + 0.151101i
\(507\) 21.6629 + 0.336325i 0.962085 + 0.0149367i
\(508\) −2.73486 2.20988i −0.121340 0.0980474i
\(509\) 10.0987 + 5.07176i 0.447618 + 0.224802i 0.658305 0.752752i \(-0.271274\pi\)
−0.210687 + 0.977554i \(0.567570\pi\)
\(510\) −48.7738 7.45700i −2.15974 0.330201i
\(511\) 2.79515 11.7936i 0.123650 0.521720i
\(512\) 17.2755 + 14.6136i 0.763478 + 0.645834i
\(513\) −38.1955 1.78014i −1.68637 0.0785951i
\(514\) 5.78293 + 0.114721i 0.255074 + 0.00506011i
\(515\) −55.2343 + 16.5361i −2.43391 + 0.728666i
\(516\) −9.04283 10.7118i −0.398088 0.471559i
\(517\) 1.19380 + 1.81509i 0.0525033 + 0.0798274i
\(518\) 8.20201 3.34666i 0.360376 0.147044i
\(519\) −31.4821 + 25.5944i −1.38191 + 1.12347i
\(520\) 5.31201 + 3.96562i 0.232947 + 0.173904i
\(521\) 2.67266 + 7.34308i 0.117092 + 0.321706i 0.984369 0.176119i \(-0.0563543\pi\)
−0.867277 + 0.497825i \(0.834132\pi\)
\(522\) −16.0661 + 38.0053i −0.703194 + 1.66344i
\(523\) 14.7706 + 5.37606i 0.645874 + 0.235079i 0.644126 0.764920i \(-0.277221\pi\)
0.00174797 + 0.999998i \(0.499444\pi\)
\(524\) −22.1573 10.6190i −0.967947 0.463893i
\(525\) 10.0907 39.8115i 0.440396 1.73752i
\(526\) −1.26165 5.83689i −0.0550104 0.254500i
\(527\) 3.10166 + 3.28757i 0.135111 + 0.143209i
\(528\) −6.95892 + 1.38186i −0.302848 + 0.0601375i
\(529\) −3.46589 4.65550i −0.150691 0.202413i
\(530\) −37.8909 47.0199i −1.64588 2.04242i
\(531\) −32.3193 20.0224i −1.40254 0.868897i
\(532\) 37.9953 41.7959i 1.64730 1.81208i
\(533\) −3.87539 2.54888i −0.167862 0.110404i
\(534\) −17.6706 + 13.7929i −0.764682 + 0.596878i
\(535\) 30.1809 + 22.4688i 1.30483 + 0.971413i
\(536\) 3.20576 + 5.56960i 0.138468 + 0.240570i
\(537\) 4.12966 + 1.30653i 0.178208 + 0.0563808i
\(538\) −1.13695 + 4.40584i −0.0490174 + 0.189949i
\(539\) 6.85529 3.95791i 0.295278 0.170479i
\(540\) 18.2709 + 29.5539i 0.786254 + 1.27180i
\(541\) −6.82627 3.94115i −0.293484 0.169443i 0.346028 0.938224i \(-0.387530\pi\)
−0.639512 + 0.768781i \(0.720864\pi\)
\(542\) 12.5513 12.7858i 0.539125 0.549196i
\(543\) 10.2595 + 7.88836i 0.440277 + 0.338522i
\(544\) −1.39688 + 34.0526i −0.0598908 + 1.45999i
\(545\) −44.5870 + 19.2329i −1.90990 + 0.823849i
\(546\) 5.82010 3.09122i 0.249077 0.132292i
\(547\) −2.49788 + 42.8869i −0.106801 + 1.83371i 0.341562 + 0.939859i \(0.389044\pi\)
−0.448364 + 0.893851i \(0.647993\pi\)
\(548\) 12.4717 + 39.0153i 0.532763 + 1.66665i
\(549\) −7.81959 12.7333i −0.333732 0.543442i
\(550\) 8.34556 + 3.22639i 0.355856 + 0.137574i
\(551\) 71.0828 8.30838i 3.02823 0.353949i
\(552\) −20.1352 2.69813i −0.857010 0.114840i
\(553\) −4.32967 + 14.4621i −0.184116 + 0.614992i
\(554\) 10.4966 32.6870i 0.445959 1.38874i
\(555\) 7.66784 5.52558i 0.325482 0.234548i
\(556\) 1.26772 0.0974060i 0.0537633 0.00413093i
\(557\) 20.4125 17.1281i 0.864904 0.725741i −0.0981146 0.995175i \(-0.531281\pi\)
0.963019 + 0.269434i \(0.0868367\pi\)
\(558\) 0.346435 3.16392i 0.0146658 0.133939i
\(559\) −1.82343 + 2.17308i −0.0771229 + 0.0919114i
\(560\) −50.8427 7.03622i −2.14850 0.297334i
\(561\) −8.07843 6.99516i −0.341072 0.295336i
\(562\) 19.9698 25.7420i 0.842374 1.08586i
\(563\) 17.5193 1.02038i 0.738351 0.0430041i 0.315153 0.949041i \(-0.397944\pi\)
0.423199 + 0.906037i \(0.360907\pi\)
\(564\) −6.37536 3.65550i −0.268451 0.153924i
\(565\) 3.24672 + 3.06312i 0.136590 + 0.128866i
\(566\) −29.9644 18.1017i −1.25950 0.760870i
\(567\) 34.3235 3.87556i 1.44145 0.162758i
\(568\) −1.26517 + 21.2362i −0.0530852 + 0.891052i
\(569\) 28.6565 + 27.0360i 1.20134 + 1.13341i 0.987678 + 0.156499i \(0.0500209\pi\)
0.213663 + 0.976907i \(0.431461\pi\)
\(570\) 28.9338 52.8649i 1.21190 2.21427i
\(571\) 2.71792 + 46.6649i 0.113742 + 1.95287i 0.264709 + 0.964328i \(0.414724\pi\)
−0.150967 + 0.988539i \(0.548239\pi\)
\(572\) 0.515921 + 1.33980i 0.0215718 + 0.0560198i
\(573\) 0.867656 4.51014i 0.0362469 0.188414i
\(574\) 35.8058 + 2.79899i 1.49450 + 0.116828i
\(575\) 19.6262 + 16.4683i 0.818469 + 0.686777i
\(576\) 18.8945 14.7986i 0.787270 0.616609i
\(577\) 9.48274 7.95696i 0.394772 0.331253i −0.423697 0.905804i \(-0.639268\pi\)
0.818469 + 0.574551i \(0.194823\pi\)
\(578\) −22.2099 + 15.8599i −0.923812 + 0.659683i
\(579\) 11.9782 1.21188i 0.497796 0.0503642i
\(580\) −42.7166 49.0353i −1.77371 2.03608i
\(581\) 0.992282 3.31445i 0.0411668 0.137507i
\(582\) 41.3843 + 3.88229i 1.71543 + 0.160926i
\(583\) −1.51833 12.9901i −0.0628828 0.537996i
\(584\) −8.87320 + 1.02519i −0.367176 + 0.0424225i
\(585\) 5.26156 4.66395i 0.217539 0.192831i
\(586\) −6.90142 + 7.90109i −0.285095 + 0.326391i
\(587\) 16.9530 + 0.987402i 0.699727 + 0.0407545i 0.404321 0.914617i \(-0.367508\pi\)
0.295406 + 0.955372i \(0.404545\pi\)
\(588\) −14.6476 + 22.4159i −0.604056 + 0.924417i
\(589\) −5.06901 + 2.18656i −0.208865 + 0.0900955i
\(590\) 50.7066 31.9278i 2.08756 1.31445i
\(591\) −2.66979 0.354145i −0.109820 0.0145676i
\(592\) −4.37855 4.84231i −0.179957 0.199018i
\(593\) 19.2272 + 11.1008i 0.789565 + 0.455856i 0.839809 0.542881i \(-0.182667\pi\)
−0.0502444 + 0.998737i \(0.516000\pi\)
\(594\) −0.0619307 + 7.52491i −0.00254105 + 0.308751i
\(595\) −38.6544 66.9514i −1.58468 2.74474i
\(596\) −20.4628 + 20.0342i −0.838188 + 0.820635i
\(597\) 9.61130 8.78983i 0.393364 0.359744i
\(598\) 0.157586 + 4.10794i 0.00644417 + 0.167986i
\(599\) −20.7051 + 27.8117i −0.845987 + 1.13636i 0.143200 + 0.989694i \(0.454261\pi\)
−0.989186 + 0.146663i \(0.953147\pi\)
\(600\) −30.1176 + 3.00673i −1.22955 + 0.122749i
\(601\) −10.8630 7.14472i −0.443112 0.291439i 0.308280 0.951296i \(-0.400247\pi\)
−0.751392 + 0.659856i \(0.770617\pi\)
\(602\) 4.24238 21.5510i 0.172906 0.878351i
\(603\) 6.47434 2.13129i 0.263656 0.0867930i
\(604\) −17.3203 + 2.35013i −0.704754 + 0.0956254i
\(605\) −19.8682 26.6876i −0.807757 1.08501i
\(606\) 5.26041 19.1510i 0.213690 0.777955i
\(607\) 19.5803 18.4730i 0.794739 0.749798i −0.177416 0.984136i \(-0.556774\pi\)
0.972155 + 0.234338i \(0.0752923\pi\)
\(608\) −38.5003 15.8286i −1.56139 0.641935i
\(609\) −62.2147 + 17.5783i −2.52107 + 0.712307i
\(610\) 23.4413 2.26961i 0.949111 0.0918939i
\(611\) −0.508633 + 1.39746i −0.0205771 + 0.0565351i
\(612\) 35.0669 + 8.77690i 1.41750 + 0.354785i
\(613\) 12.3254 + 33.8638i 0.497819 + 1.36775i 0.893378 + 0.449306i \(0.148329\pi\)
−0.395559 + 0.918441i \(0.629449\pi\)
\(614\) −4.92135 10.3038i −0.198609 0.415829i
\(615\) 37.8351 6.06734i 1.52566 0.244659i
\(616\) −8.50617 7.15679i −0.342723 0.288355i
\(617\) 7.26053 + 11.0391i 0.292298 + 0.444418i 0.951545 0.307509i \(-0.0994953\pi\)
−0.659247 + 0.751926i \(0.729125\pi\)
\(618\) 41.4212 8.28234i 1.66621 0.333165i
\(619\) −7.49477 25.0343i −0.301240 1.00621i −0.965867 0.259038i \(-0.916595\pi\)
0.664627 0.747175i \(-0.268591\pi\)
\(620\) 4.24146 + 2.67854i 0.170341 + 0.107573i
\(621\) −7.13419 + 20.3321i −0.286285 + 0.815901i
\(622\) −33.9532 + 18.7150i −1.36140 + 0.750403i
\(623\) −34.1762 8.09991i −1.36924 0.324516i
\(624\) −3.60339 3.25614i −0.144251 0.130350i
\(625\) −15.8353 7.95280i −0.633413 0.318112i
\(626\) −3.08174 + 22.4881i −0.123171 + 0.898804i
\(627\) 11.4034 6.34980i 0.455408 0.253587i
\(628\) −11.4305 25.2057i −0.456126 1.00582i
\(629\) 1.70748 9.68360i 0.0680817 0.386111i
\(630\) −18.2462 + 51.2921i −0.726946 + 2.04353i
\(631\) −5.27945 + 0.930910i −0.210172 + 0.0370590i −0.277743 0.960656i \(-0.589586\pi\)
0.0675709 + 0.997714i \(0.478475\pi\)
\(632\) 11.1074 0.632135i 0.441830 0.0251450i
\(633\) 23.4384 11.3190i 0.931592 0.449892i
\(634\) 6.17711 5.60044i 0.245324 0.222422i
\(635\) −1.35553 5.71943i −0.0537925 0.226968i
\(636\) 24.4214 + 36.8907i 0.968370 + 1.46281i
\(637\) 4.97549 + 2.14622i 0.197136 + 0.0850363i
\(638\) −2.17017 13.9164i −0.0859179 0.550955i
\(639\) 21.7840 + 5.88278i 0.861762 + 0.232719i
\(640\) 7.89337 + 36.9935i 0.312013 + 1.46229i
\(641\) 8.92277 + 17.7667i 0.352428 + 0.701742i 0.998083 0.0618872i \(-0.0197119\pi\)
−0.645655 + 0.763629i \(0.723416\pi\)
\(642\) −20.4774 18.4548i −0.808180 0.728351i
\(643\) −30.0356 3.51065i −1.18449 0.138447i −0.499046 0.866575i \(-0.666316\pi\)
−0.685440 + 0.728129i \(0.740390\pi\)
\(644\) −16.4227 27.2668i −0.647146 1.07446i
\(645\) −0.999259 23.4132i −0.0393458 0.921892i
\(646\) −16.7873 60.4093i −0.660486 2.37677i
\(647\) 24.2988 0.955283 0.477642 0.878555i \(-0.341492\pi\)
0.477642 + 0.878555i \(0.341492\pi\)
\(648\) −11.3051 22.8078i −0.444104 0.895975i
\(649\) 12.9777 0.509418
\(650\) 1.63991 + 5.90126i 0.0643228 + 0.231467i
\(651\) 4.20860 2.67538i 0.164948 0.104857i
\(652\) −18.3106 + 11.0284i −0.717097 + 0.431904i
\(653\) 23.6867 + 2.76857i 0.926930 + 0.108343i 0.566144 0.824306i \(-0.308434\pi\)
0.360786 + 0.932649i \(0.382509\pi\)
\(654\) 33.8393 10.9781i 1.32322 0.429278i
\(655\) −18.4342 36.7055i −0.720283 1.43420i
\(656\) −7.05283 25.5110i −0.275367 0.996037i
\(657\) −0.844210 + 9.43637i −0.0329358 + 0.368148i
\(658\) −1.77421 11.3772i −0.0691658 0.443530i
\(659\) −16.8215 7.25610i −0.655274 0.282658i 0.0423702 0.999102i \(-0.486509\pi\)
−0.697644 + 0.716444i \(0.745768\pi\)
\(660\) −10.6146 5.29127i −0.413174 0.205962i
\(661\) 1.25206 + 5.28286i 0.0486995 + 0.205479i 0.991956 0.126587i \(-0.0404023\pi\)
−0.943256 + 0.332066i \(0.892254\pi\)
\(662\) −16.5483 + 15.0034i −0.643168 + 0.583125i
\(663\) 0.538643 7.29517i 0.0209191 0.283321i
\(664\) −2.54562 + 0.144874i −0.0987891 + 0.00562219i
\(665\) 92.9910 16.3968i 3.60604 0.635841i
\(666\) −5.97128 + 3.50584i −0.231382 + 0.135849i
\(667\) 7.00316 39.7169i 0.271163 1.53784i
\(668\) −11.8294 + 5.36450i −0.457694 + 0.207559i
\(669\) −3.64803 2.18239i −0.141041 0.0843760i
\(670\) −1.45855 + 10.6434i −0.0563488 + 0.411189i
\(671\) 4.55810 + 2.28916i 0.175963 + 0.0883721i
\(672\) 36.6049 + 8.61154i 1.41206 + 0.332198i
\(673\) 30.0148 + 7.11365i 1.15699 + 0.274211i 0.763927 0.645302i \(-0.223269\pi\)
0.393059 + 0.919513i \(0.371417\pi\)
\(674\) −9.25178 + 5.09957i −0.356365 + 0.196428i
\(675\) −3.35668 + 31.9274i −0.129199 + 1.22889i
\(676\) 13.3580 21.1524i 0.513770 0.813554i
\(677\) 4.19391 + 14.0086i 0.161185 + 0.538395i 0.999982 0.00604958i \(-0.00192565\pi\)
−0.838797 + 0.544445i \(0.816740\pi\)
\(678\) −2.15866 2.45651i −0.0829027 0.0943416i
\(679\) 35.7880 + 54.4131i 1.37342 + 2.08818i
\(680\) −36.6798 + 43.5956i −1.40661 + 1.67182i
\(681\) 0.237138 0.621346i 0.00908716 0.0238100i
\(682\) 0.468247 + 0.980370i 0.0179301 + 0.0375403i
\(683\) 16.6447 + 45.7309i 0.636891 + 1.74984i 0.661277 + 0.750142i \(0.270015\pi\)
−0.0243854 + 0.999703i \(0.507763\pi\)
\(684\) −24.7227 + 36.5815i −0.945297 + 1.39873i
\(685\) −23.4191 + 64.3436i −0.894799 + 2.45844i
\(686\) −3.94348 + 0.381812i −0.150563 + 0.0145776i
\(687\) −8.86949 8.63207i −0.338392 0.329334i
\(688\) −15.9970 + 2.47288i −0.609880 + 0.0942776i
\(689\) 6.51199 6.14374i 0.248087 0.234058i
\(690\) −23.8628 24.1640i −0.908443 0.919907i
\(691\) −21.4705 28.8399i −0.816776 1.09712i −0.993609 0.112879i \(-0.963993\pi\)
0.176833 0.984241i \(-0.443415\pi\)
\(692\) 6.29918 + 46.4246i 0.239459 + 1.76480i
\(693\) −9.26315 + 7.29489i −0.351878 + 0.277110i
\(694\) −8.23695 + 41.8431i −0.312670 + 1.58834i
\(695\) 1.77582 + 1.16798i 0.0673607 + 0.0443038i
\(696\) 27.8034 + 38.6910i 1.05389 + 1.46658i
\(697\) 23.8062 31.9773i 0.901726 1.21123i
\(698\) 0.561182 + 14.6289i 0.0212410 + 0.553711i
\(699\) −1.67724 7.60078i −0.0634391 0.287488i
\(700\) −33.1772 33.8868i −1.25398 1.28080i
\(701\) −15.8230 27.4062i −0.597626 1.03512i −0.993171 0.116672i \(-0.962777\pi\)
0.395544 0.918447i \(-0.370556\pi\)
\(702\) −4.15710 + 3.04200i −0.156900 + 0.114813i
\(703\) 10.4010 + 6.00504i 0.392283 + 0.226484i
\(704\) −2.82239 + 7.69083i −0.106373 + 0.289859i
\(705\) −4.69027 11.3548i −0.176646 0.427645i
\(706\) −31.6491 + 19.9281i −1.19113 + 0.750004i
\(707\) 28.5730 12.3252i 1.07460 0.463536i
\(708\) −39.1719 + 19.8194i −1.47217 + 0.744858i
\(709\) 38.3851 + 2.23568i 1.44158 + 0.0839627i 0.761021 0.648727i \(-0.224698\pi\)
0.680563 + 0.732690i \(0.261735\pi\)
\(710\) −23.3956 + 26.7844i −0.878021 + 1.00520i
\(711\) 1.73311 11.6723i 0.0649967 0.437745i
\(712\) 2.97083 + 25.7132i 0.111337 + 0.963642i
\(713\) 0.361158 + 3.08990i 0.0135255 + 0.115718i
\(714\) 23.6144 + 51.4816i 0.883747 + 1.92665i
\(715\) −0.688344 + 2.29923i −0.0257426 + 0.0859863i
\(716\) 3.77121 3.28524i 0.140937 0.122775i
\(717\) 6.96382 15.4787i 0.260069 0.578064i
\(718\) −17.4554 + 12.4647i −0.651430 + 0.465179i
\(719\) 16.9599 14.2310i 0.632496 0.530727i −0.269207 0.963082i \(-0.586762\pi\)
0.901704 + 0.432355i \(0.142317\pi\)
\(720\) 40.1200 0.239371i 1.49519 0.00892082i
\(721\) 50.7008 + 42.5430i 1.88820 + 1.58438i
\(722\) 49.5591 + 3.87411i 1.84440 + 0.144179i
\(723\) 21.8641 7.57564i 0.813136 0.281741i
\(724\) 13.9454 5.37001i 0.518276 0.199575i
\(725\) −3.49373 59.9850i −0.129754 2.22779i
\(726\) 12.6663 + 20.8264i 0.470091 + 0.772940i
\(727\) 6.17566 + 5.82643i 0.229043 + 0.216090i 0.792204 0.610256i \(-0.208934\pi\)
−0.563161 + 0.826347i \(0.690415\pi\)
\(728\) 0.452545 7.59610i 0.0167724 0.281530i
\(729\) −26.1206 + 6.83469i −0.967431 + 0.253137i
\(730\) −12.7809 7.72100i −0.473041 0.285767i
\(731\) −17.7339 16.7311i −0.655913 0.618822i
\(732\) −17.2542 + 0.0514719i −0.637733 + 0.00190246i
\(733\) 38.1584 2.22247i 1.40941 0.0820888i 0.663521 0.748158i \(-0.269061\pi\)
0.745890 + 0.666069i \(0.232024\pi\)
\(734\) 4.23479 5.45885i 0.156309 0.201490i
\(735\) −42.2966 + 14.6552i −1.56013 + 0.540566i
\(736\) −14.7675 + 18.2262i −0.544338 + 0.671825i
\(737\) −1.49556 + 1.78233i −0.0550895 + 0.0656531i
\(738\) −28.0134 + 1.83671i −1.03119 + 0.0676103i
\(739\) −0.576804 + 0.483996i −0.0212181 + 0.0178041i −0.653335 0.757069i \(-0.726631\pi\)
0.632117 + 0.774873i \(0.282186\pi\)
\(740\) −0.836078 10.8814i −0.0307348 0.400008i
\(741\) 8.14800 + 3.66575i 0.299324 + 0.134665i
\(742\) −21.1943 + 66.0002i −0.778068 + 2.42294i
\(743\) 2.12999 7.11466i 0.0781418 0.261012i −0.909988 0.414635i \(-0.863909\pi\)
0.988129 + 0.153624i \(0.0490943\pi\)
\(744\) −2.91057 2.24405i −0.106707 0.0822709i
\(745\) −47.5492 + 5.55771i −1.74207 + 0.203619i
\(746\) 5.07872 + 1.96343i 0.185945 + 0.0718862i
\(747\) −0.397197 + 2.67508i −0.0145327 + 0.0978760i
\(748\) −11.7534 + 3.75710i −0.429746 + 0.137373i
\(749\) 2.51140 43.1190i 0.0917644 1.57553i
\(750\) −8.18113 5.11729i −0.298733 0.186857i
\(751\) −37.7411 + 16.2799i −1.37719 + 0.594063i −0.950610 0.310387i \(-0.899542\pi\)
−0.426581 + 0.904449i \(0.640282\pi\)
\(752\) −7.43715 + 4.08649i −0.271205 + 0.149019i
\(753\) 26.8704 11.0993i 0.979212 0.404480i
\(754\) 6.75411 6.88028i 0.245970 0.250565i
\(755\) −25.3050 14.6098i −0.920942 0.531706i
\(756\) 16.8192 36.1656i 0.611709 1.31533i
\(757\) 19.4870 11.2508i 0.708267 0.408918i −0.102152 0.994769i \(-0.532573\pi\)
0.810419 + 0.585851i \(0.199239\pi\)
\(758\) 4.24370 16.4449i 0.154138 0.597307i
\(759\) −1.58492 7.18240i −0.0575289 0.260704i
\(760\) −34.7139 60.3111i −1.25921 2.18771i
\(761\) −0.293473 0.218483i −0.0106384 0.00791999i 0.591826 0.806066i \(-0.298407\pi\)
−0.602465 + 0.798146i \(0.705815\pi\)
\(762\) 0.597395 + 4.26469i 0.0216413 + 0.154494i
\(763\) 46.5711 + 30.6303i 1.68599 + 1.10889i
\(764\) −3.92421 3.56737i −0.141973 0.129063i
\(765\) 37.3876 + 47.4753i 1.35175 + 1.71647i
\(766\) −23.5160 29.1817i −0.849668 1.05438i
\(767\) 5.30496 + 7.12580i 0.191551 + 0.257298i
\(768\) −3.22627 27.5244i −0.116418 0.993200i
\(769\) −31.6983 33.5983i −1.14307 1.21158i −0.974137 0.225957i \(-0.927449\pi\)
−0.168933 0.985627i \(-0.554032\pi\)
\(770\) −3.92611 18.1638i −0.141487 0.654578i
\(771\) −5.07663 4.94074i −0.182831 0.177937i
\(772\) 6.00815 12.5365i 0.216238 0.451197i
\(773\) 51.4250 + 18.7172i 1.84963 + 0.673209i 0.985436 + 0.170046i \(0.0543918\pi\)
0.864192 + 0.503163i \(0.167830\pi\)
\(774\) −0.873237 + 17.1467i −0.0313878 + 0.616325i
\(775\) 1.58525 + 4.35543i 0.0569437 + 0.156452i
\(776\) 28.7125 38.4608i 1.03072 1.38066i
\(777\) −10.1363 3.86853i −0.363637 0.138783i
\(778\) −0.662144 + 0.270174i −0.0237390 + 0.00968619i
\(779\) 26.7569 + 40.6820i 0.958667 + 1.45758i
\(780\) −1.43366 7.99124i −0.0513334 0.286132i
\(781\) −7.37872 + 2.20904i −0.264031 + 0.0790458i
\(782\) −35.3252 0.700773i −1.26323 0.0250596i
\(783\) 46.1666 20.5530i 1.64986 0.734504i
\(784\) 13.2890 + 27.9184i 0.474605 + 0.997085i
\(785\) 10.6698 45.0194i 0.380821 1.60681i
\(786\) 10.9348 + 28.0356i 0.390031 + 0.999997i
\(787\) −2.58698 1.29923i −0.0922158 0.0463125i 0.402094 0.915599i \(-0.368283\pi\)
−0.494309 + 0.869286i \(0.664579\pi\)
\(788\) −1.95452 + 2.41884i −0.0696268 + 0.0861675i
\(789\) −3.75478 + 6.27640i −0.133674 + 0.223446i
\(790\) 15.3329 + 10.5261i 0.545520 + 0.374502i
\(791\) 0.889754 5.04605i 0.0316360 0.179417i
\(792\) 7.38058 + 4.58597i 0.262257 + 0.162955i
\(793\) 0.606304 + 3.43852i 0.0215305 + 0.122105i
\(794\) 11.2822 24.7912i 0.400391 0.879806i
\(795\) −5.44596 + 73.7580i −0.193148 + 2.61593i
\(796\) −2.88522 14.7601i −0.102264 0.523157i
\(797\) 33.4185 7.92033i 1.18374 0.280553i 0.408825 0.912613i \(-0.365939\pi\)
0.774919 + 0.632060i \(0.217791\pi\)
\(798\) −68.9527 + 5.59714i −2.44090 + 0.198136i
\(799\) −11.7361 5.06246i −0.415193 0.179097i
\(800\) −15.1466 + 31.4970i −0.535512 + 1.11359i
\(801\) 27.3452 + 2.44639i 0.966194 + 0.0864390i
\(802\) 25.8656 8.83739i 0.913347 0.312059i
\(803\) −1.45140 2.88997i −0.0512186 0.101985i
\(804\) 1.79223 7.66381i 0.0632069 0.270282i
\(805\) 6.17743 52.8513i 0.217726 1.86276i
\(806\) −0.346895 + 0.657857i −0.0122188 + 0.0231720i
\(807\) 4.70299 2.98966i 0.165553 0.105241i
\(808\) −15.7152 16.7015i −0.552859 0.587557i
\(809\) 5.47530i 0.192501i −0.995357 0.0962506i \(-0.969315\pi\)
0.995357 0.0962506i \(-0.0306850\pi\)
\(810\) 8.38281 41.7206i 0.294542 1.46591i
\(811\) 14.7626 0.518386 0.259193 0.965826i \(-0.416543\pi\)
0.259193 + 0.965826i \(0.416543\pi\)
\(812\) −20.0832 + 71.8996i −0.704783 + 2.52318i
\(813\) −21.9235 + 0.935683i −0.768892 + 0.0328158i
\(814\) 1.10248 2.09076i 0.0386418 0.0732811i
\(815\) −35.4913 4.14834i −1.24321 0.145310i
\(816\) 29.7387 29.2901i 1.04106 1.02536i
\(817\) 26.6114 13.3647i 0.931013 0.467572i
\(818\) 6.20070 + 18.1485i 0.216803 + 0.634546i
\(819\) −7.79204 2.10424i −0.272276 0.0735283i
\(820\) 16.7702 40.9451i 0.585642 1.42987i
\(821\) −16.9506 + 39.2958i −0.591579 + 1.37143i 0.314877 + 0.949133i \(0.398037\pi\)
−0.906455 + 0.422301i \(0.861222\pi\)
\(822\) 21.4856 45.3318i 0.749397 1.58113i
\(823\) 7.15050 + 30.1703i 0.249251 + 1.05167i 0.943352 + 0.331794i \(0.107654\pi\)
−0.694101 + 0.719878i \(0.744198\pi\)
\(824\) 16.7432 45.8122i 0.583277 1.59594i
\(825\) −4.76552 9.86797i −0.165914 0.343559i
\(826\) −62.6066 28.4916i −2.17836 0.991351i
\(827\) −23.6512 + 4.17035i −0.822434 + 0.145017i −0.569002 0.822336i \(-0.692670\pi\)
−0.253432 + 0.967353i \(0.581559\pi\)
\(828\) 15.7528 + 19.2589i 0.547449 + 0.669293i
\(829\) 36.2057 + 6.38404i 1.25748 + 0.221727i 0.762390 0.647118i \(-0.224026\pi\)
0.495085 + 0.868844i \(0.335137\pi\)
\(830\) −3.51402 2.41239i −0.121973 0.0837354i
\(831\) −36.7355 + 20.4556i −1.27434 + 0.709596i
\(832\) −5.37662 + 1.59411i −0.186401 + 0.0552657i
\(833\) −20.9011 + 41.6175i −0.724180 + 1.44196i
\(834\) −1.21542 0.973477i −0.0420865 0.0337087i
\(835\) −21.1283 5.00751i −0.731176 0.173292i
\(836\) 0.597726 15.0594i 0.0206728 0.520841i
\(837\) −2.95688 + 2.54017i −0.102205 + 0.0878011i
\(838\) 6.71975 + 0.133305i 0.232130 + 0.00460494i
\(839\) 8.62352 + 28.8046i 0.297717 + 0.994444i 0.967708 + 0.252075i \(0.0811129\pi\)
−0.669991 + 0.742369i \(0.733702\pi\)
\(840\) 39.5902 + 48.8298i 1.36599 + 1.68479i
\(841\) −54.7949 + 36.0392i −1.88948 + 1.24273i
\(842\) −0.286912 0.703167i −0.00988764 0.0242327i
\(843\) −39.3985 + 6.31805i −1.35696 + 0.217605i
\(844\) 2.93613 29.9113i 0.101066 1.02959i
\(845\) 39.2991 14.3037i 1.35193 0.492062i
\(846\) 2.64424 + 8.60348i 0.0909110 + 0.295794i
\(847\) −13.0627 + 35.8895i −0.448840 + 1.23318i
\(848\) 51.0509 1.89049i 1.75310 0.0649197i
\(849\) 11.6577 + 41.2601i 0.400091 + 1.41604i
\(850\) −51.4527 + 11.1215i −1.76481 + 0.381465i
\(851\) 4.92285 4.64447i 0.168753 0.159210i
\(852\) 18.8983 17.9365i 0.647446 0.614495i
\(853\) −14.0604 + 10.4676i −0.481420 + 0.358404i −0.810346 0.585952i \(-0.800721\pi\)
0.328926 + 0.944356i \(0.393313\pi\)
\(854\) −16.9634 21.0503i −0.580475 0.720328i
\(855\) −70.1081 + 23.0790i −2.39765 + 0.789283i
\(856\) −30.5057 + 9.08869i −1.04266 + 0.310645i
\(857\) 15.1592 23.0485i 0.517830 0.787322i −0.478019 0.878350i \(-0.658645\pi\)
0.995848 + 0.0910278i \(0.0290152\pi\)
\(858\) 0.659434 1.63003i 0.0225127 0.0556483i
\(859\) 31.3470 42.1063i 1.06954 1.43665i 0.177823 0.984062i \(-0.443095\pi\)
0.891721 0.452585i \(-0.149498\pi\)
\(860\) −23.6808 13.0939i −0.807510 0.446498i
\(861\) −29.6852 32.4595i −1.01167 1.10622i
\(862\) −7.90516 + 30.6336i −0.269251 + 1.04338i
\(863\) −15.0451 26.0588i −0.512139 0.887052i −0.999901 0.0140746i \(-0.995520\pi\)
0.487761 0.872977i \(-0.337814\pi\)
\(864\) −29.2812 2.57075i −0.996168 0.0874588i
\(865\) −39.1595 + 67.8263i −1.33146 + 2.30616i
\(866\) 23.8472 + 23.4099i 0.810361 + 0.795500i
\(867\) 33.1347 + 4.39529i 1.12531 + 0.149272i
\(868\) −0.106568 5.75749i −0.00361714 0.195422i
\(869\) 1.59541 + 3.69857i 0.0541206 + 0.125466i
\(870\) −2.81570 + 79.5979i −0.0954611 + 2.69862i
\(871\) −1.58999 0.0926066i −0.0538749 0.00313785i
\(872\) 9.52655 39.9591i 0.322610 1.35319i
\(873\) −33.7687 38.0956i −1.14290 1.28934i
\(874\) 15.5613 40.2516i 0.526367 1.36153i
\(875\) −1.75528 15.0174i −0.0593393 0.507680i
\(876\) 8.79443 + 6.50653i 0.297136 + 0.219835i
\(877\) −34.8216 10.4249i −1.17584 0.352024i −0.361479 0.932380i \(-0.617728\pi\)
−0.814363 + 0.580357i \(0.802913\pi\)
\(878\) 2.68965 8.37569i 0.0907712 0.282666i
\(879\) 12.7833 1.29334i 0.431170 0.0436233i
\(880\) −11.5988 + 7.28179i −0.390996 + 0.245469i
\(881\) −20.0763 23.9260i −0.676386 0.806086i 0.313252 0.949670i \(-0.398582\pi\)
−0.989638 + 0.143584i \(0.954137\pi\)
\(882\) 31.8554 7.79570i 1.07263 0.262495i
\(883\) 24.5222 + 20.5765i 0.825237 + 0.692456i 0.954192 0.299194i \(-0.0967179\pi\)
−0.128955 + 0.991650i \(0.541162\pi\)
\(884\) −6.86745 4.91775i −0.230977 0.165402i
\(885\) −72.0667 13.8641i −2.42249 0.466037i
\(886\) −20.6684 + 26.6425i −0.694367 + 0.895072i
\(887\) 0.851849 + 14.6257i 0.0286023 + 0.491082i 0.981942 + 0.189182i \(0.0605837\pi\)
−0.953340 + 0.301900i \(0.902379\pi\)
\(888\) −0.134736 + 7.99445i −0.00452143 + 0.268276i
\(889\) −4.63030 + 4.90784i −0.155295 + 0.164604i
\(890\) −22.3743 + 37.0370i −0.749988 + 1.24148i
\(891\) 6.35090 6.67893i 0.212763 0.223753i
\(892\) −4.34499 + 2.28379i −0.145481 + 0.0764668i
\(893\) 10.7131 11.3553i 0.358501 0.379989i
\(894\) 35.0643 0.800247i 1.17273 0.0267643i
\(895\) 8.34682 0.486147i 0.279003 0.0162501i
\(896\) 30.5004 30.9056i 1.01895 1.03248i
\(897\) 3.29584 3.80624i 0.110045 0.127087i
\(898\) 3.24645 41.5299i 0.108335 1.38587i
\(899\) 4.68980 5.58908i 0.156413 0.186406i
\(900\) 29.4546 + 22.5077i 0.981819 + 0.750255i
\(901\) 49.4595 + 58.9435i 1.64773 + 1.96369i
\(902\) 7.79861 5.56890i 0.259665 0.185424i
\(903\) −21.8247 + 15.7272i −0.726279 + 0.523370i
\(904\) −3.71961 + 0.650775i −0.123712 + 0.0216445i
\(905\) 23.9317 + 7.16468i 0.795516 + 0.238162i
\(906\) 17.4585 + 12.3885i 0.580021 + 0.411580i
\(907\) 44.6277 5.21624i 1.48184 0.173202i 0.663604 0.748084i \(-0.269026\pi\)
0.818236 + 0.574882i \(0.194952\pi\)
\(908\) −0.469907 0.607395i −0.0155944 0.0201571i
\(909\) −20.7274 + 12.7288i −0.687483 + 0.422189i
\(910\) 8.36851 9.58068i 0.277413 0.317597i
\(911\) 2.81869 48.3950i 0.0933872 1.60340i −0.548200 0.836347i \(-0.684687\pi\)
0.641588 0.767050i \(-0.278276\pi\)
\(912\) 21.1945 + 46.3683i 0.701819 + 1.53541i
\(913\) −0.365639 0.847645i −0.0121009 0.0280530i
\(914\) −4.01807 6.38136i −0.132906 0.211077i
\(915\) −22.8662 17.5815i −0.755933 0.581225i
\(916\) −13.8427 + 3.55258i −0.457375 + 0.117381i
\(917\) −23.5752 + 40.8334i −0.778521 + 1.34844i
\(918\) −24.0231 37.1884i −0.792880 1.22740i
\(919\) 26.0410 15.0348i 0.859012 0.495951i −0.00466900 0.999989i \(-0.501486\pi\)
0.863681 + 0.504038i \(0.168153\pi\)
\(920\) −38.1695 + 8.99281i −1.25841 + 0.296484i
\(921\) −4.21847 + 13.3337i −0.139003 + 0.439361i
\(922\) 18.5496 0.711585i 0.610898 0.0234348i
\(923\) −4.22919 3.14852i −0.139205 0.103635i
\(924\) 1.62091 + 13.5179i 0.0533241 + 0.444707i
\(925\) 5.54100 8.42468i 0.182187 0.277002i
\(926\) −1.07489 + 5.46036i −0.0353231 + 0.179439i
\(927\) −43.9789 27.2457i −1.44446 0.894866i
\(928\) 54.8593 4.14188i 1.80085 0.135964i
\(929\) −11.7780 + 8.76836i −0.386422 + 0.287681i −0.772787 0.634665i \(-0.781138\pi\)
0.386365 + 0.922346i \(0.373731\pi\)
\(930\) −1.55290 5.94435i −0.0509216 0.194923i
\(931\) −39.0350 41.3747i −1.27932 1.35600i
\(932\) −8.50118 2.91717i −0.278465 0.0955552i
\(933\) 46.0273 + 11.6662i 1.50686 + 0.381933i
\(934\) 56.2911 5.45016i 1.84190 0.178335i
\(935\) −19.3835 7.05503i −0.633910 0.230724i
\(936\) 0.498932 + 5.92718i 0.0163081 + 0.193736i
\(937\) −33.8414 + 12.3173i −1.10555 + 0.402387i −0.829359 0.558716i \(-0.811294\pi\)
−0.276190 + 0.961103i \(0.589072\pi\)
\(938\) 11.1278 5.31490i 0.363337 0.173538i
\(939\) 21.5705 17.5365i 0.703927 0.572281i
\(940\) −14.0135 2.20439i −0.457071 0.0718993i
\(941\) −23.8689 + 15.6988i −0.778104 + 0.511767i −0.875348 0.483494i \(-0.839368\pi\)
0.0972442 + 0.995261i \(0.468997\pi\)
\(942\) −10.8635 + 32.1085i −0.353952 + 1.04615i
\(943\) 26.2867 7.86971i 0.856011 0.256273i
\(944\) −4.01771 + 50.5323i −0.130765 + 1.64469i
\(945\) 59.2327 30.6136i 1.92684 0.995862i
\(946\) −2.82905 5.13253i −0.0919803 0.166873i
\(947\) 3.53101 14.8985i 0.114743 0.484137i −0.885083 0.465434i \(-0.845898\pi\)
0.999825 0.0187028i \(-0.00595364\pi\)
\(948\) −10.4640 8.72730i −0.339856 0.283450i
\(949\) 0.993531 1.97828i 0.0322514 0.0642178i
\(950\) 8.72947 63.7007i 0.283221 2.06672i
\(951\) −10.2106 0.158524i −0.331103 0.00514050i
\(952\) 64.9489 + 7.67888i 2.10501 + 0.248874i
\(953\) −21.3471 3.76407i −0.691500 0.121930i −0.183156 0.983084i \(-0.558631\pi\)
−0.508344 + 0.861154i \(0.669742\pi\)
\(954\) 9.01961 53.4288i 0.292021 1.72982i
\(955\) −1.53950 8.73092i −0.0498169 0.282526i
\(956\) −11.0709 16.1725i −0.358059 0.523056i
\(957\) −9.70162 + 14.2633i −0.313609 + 0.461067i
\(958\) 0.278347 0.252362i 0.00899300 0.00815346i
\(959\) 76.4830 18.1268i 2.46977 0.585345i
\(960\) 23.8892 39.6930i 0.771022 1.28109i
\(961\) 12.0556 27.9479i 0.388889 0.901546i
\(962\) 1.59866 0.249302i 0.0515430 0.00803781i
\(963\) 2.87662 + 33.6390i 0.0926978 + 1.08400i
\(964\) 5.67964 26.1084i 0.182929 0.840895i
\(965\) 20.7677 10.4299i 0.668536 0.335751i
\(966\) −8.12256 + 38.1288i −0.261339 + 1.22677i
\(967\) 2.07240 17.7305i 0.0666438 0.570174i −0.918123 0.396295i \(-0.870296\pi\)
0.984767 0.173879i \(-0.0556301\pi\)
\(968\) 28.1466 + 0.0373763i 0.904666 + 0.00120132i
\(969\) −35.5242 + 68.0785i −1.14120 + 2.18699i
\(970\) 77.3058 21.4827i 2.48214 0.689767i
\(971\) 28.9390i 0.928698i 0.885652 + 0.464349i \(0.153712\pi\)
−0.885652 + 0.464349i \(0.846288\pi\)
\(972\) −8.96958 + 29.8588i −0.287700 + 0.957721i
\(973\) 2.43990i 0.0782196i
\(974\) −0.200310 0.720820i −0.00641835 0.0230966i
\(975\) 3.47029 6.65045i 0.111138 0.212985i
\(976\) −10.3246 + 17.0396i −0.330484 + 0.545424i
\(977\) 2.45028 20.9635i 0.0783914 0.670681i −0.895721 0.444617i \(-0.853340\pi\)
0.974112 0.226065i \(-0.0725860\pi\)
\(978\) 25.6047 + 5.45456i 0.818747 + 0.174418i
\(979\) −8.37468 + 4.20592i −0.267656 + 0.134422i
\(980\) −10.9874 + 50.5072i −0.350979 + 1.61339i
\(981\) −39.4525 18.4912i −1.25962 0.590379i
\(982\) −5.61531 36.0086i −0.179192 1.14908i
\(983\) −4.00957 + 9.29524i −0.127886 + 0.296472i −0.970114 0.242648i \(-0.921984\pi\)
0.842229 + 0.539120i \(0.181243\pi\)
\(984\) −15.0346 + 28.7192i −0.479285 + 0.915534i
\(985\) −5.05853 + 1.19889i −0.161178 + 0.0381999i
\(986\) 55.6580 + 61.3890i 1.77251 + 1.95502i
\(987\) −7.93148 + 11.6608i −0.252462 + 0.371169i
\(988\) 8.51319 5.82773i 0.270841 0.185405i
\(989\) −2.91401 16.5262i −0.0926601 0.525502i
\(990\) 5.06758 + 13.6133i 0.161058 + 0.432658i
\(991\) −0.763275 0.134586i −0.0242462 0.00427526i 0.161512 0.986871i \(-0.448363\pi\)
−0.185758 + 0.982596i \(0.559474\pi\)
\(992\) −3.96232 + 1.51975i −0.125804 + 0.0482520i
\(993\) 27.3540 + 0.424681i 0.868054 + 0.0134769i
\(994\) 40.4461 + 5.54269i 1.28287 + 0.175803i
\(995\) 11.2834 22.4671i 0.357709 0.712256i
\(996\) 2.39816 + 2.00014i 0.0759887 + 0.0633768i
\(997\) 0.351563 1.48336i 0.0111341 0.0469785i −0.967194 0.254038i \(-0.918241\pi\)
0.978328 + 0.207059i \(0.0663893\pi\)
\(998\) −31.8226 + 17.5406i −1.00733 + 0.555238i
\(999\) 8.27415 + 1.85987i 0.261782 + 0.0588435i
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 648.2.bb.b.11.9 1872
8.3 odd 2 inner 648.2.bb.b.11.59 yes 1872
81.59 odd 54 inner 648.2.bb.b.59.59 yes 1872
648.59 even 54 inner 648.2.bb.b.59.9 yes 1872
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
648.2.bb.b.11.9 1872 1.1 even 1 trivial
648.2.bb.b.11.59 yes 1872 8.3 odd 2 inner
648.2.bb.b.59.9 yes 1872 648.59 even 54 inner
648.2.bb.b.59.59 yes 1872 81.59 odd 54 inner