Properties

Label 64.2.i.a.53.1
Level $64$
Weight $2$
Character 64.53
Analytic conductor $0.511$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [64,2,Mod(5,64)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(64, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("64.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 64.i (of order \(16\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.511042572936\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 53.1
Character \(\chi\) \(=\) 64.53
Dual form 64.2.i.a.29.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.40388 + 0.170631i) q^{2} +(-2.23702 + 0.444970i) q^{3} +(1.94177 - 0.479090i) q^{4} +(-2.33237 - 3.49064i) q^{5} +(3.06458 - 1.00639i) q^{6} +(-1.63661 - 0.677907i) q^{7} +(-2.64427 + 1.00391i) q^{8} +(2.03460 - 0.842759i) q^{9} +O(q^{10})\) \(q+(-1.40388 + 0.170631i) q^{2} +(-2.23702 + 0.444970i) q^{3} +(1.94177 - 0.479090i) q^{4} +(-2.33237 - 3.49064i) q^{5} +(3.06458 - 1.00639i) q^{6} +(-1.63661 - 0.677907i) q^{7} +(-2.64427 + 1.00391i) q^{8} +(2.03460 - 0.842759i) q^{9} +(3.86998 + 4.50247i) q^{10} +(-0.234463 + 1.17872i) q^{11} +(-4.13059 + 1.93576i) q^{12} +(-0.154344 + 0.230992i) q^{13} +(2.41328 + 0.672446i) q^{14} +(6.77078 + 6.77078i) q^{15} +(3.54094 - 1.86057i) q^{16} +(1.16542 - 1.16542i) q^{17} +(-2.71254 + 1.53030i) q^{18} +(-2.64509 - 1.76739i) q^{19} +(-6.20126 - 5.66061i) q^{20} +(3.96278 + 0.788246i) q^{21} +(0.128032 - 1.69479i) q^{22} +(-1.18934 - 2.87131i) q^{23} +(5.46856 - 3.42239i) q^{24} +(-4.83120 + 11.6635i) q^{25} +(0.177266 - 0.350621i) q^{26} +(1.51292 - 1.01090i) q^{27} +(-3.50271 - 0.532255i) q^{28} +(-0.141213 - 0.709928i) q^{29} +(-10.6607 - 8.35008i) q^{30} -7.01473i q^{31} +(-4.65360 + 3.21621i) q^{32} -2.74115i q^{33} +(-1.43726 + 1.83497i) q^{34} +(1.45086 + 7.29396i) q^{35} +(3.54697 - 2.61120i) q^{36} +(7.22008 - 4.82430i) q^{37} +(4.01496 + 2.02987i) q^{38} +(0.242485 - 0.585411i) q^{39} +(9.67171 + 6.88870i) q^{40} +(-0.152591 - 0.368387i) q^{41} +(-5.69777 - 0.430433i) q^{42} +(-4.98611 - 0.991798i) q^{43} +(0.109442 + 2.40114i) q^{44} +(-7.68722 - 5.13643i) q^{45} +(2.15962 + 3.82804i) q^{46} +(2.16092 - 2.16092i) q^{47} +(-7.09325 + 5.73773i) q^{48} +(-2.73080 - 2.73080i) q^{49} +(4.79227 - 17.1986i) q^{50} +(-2.08849 + 3.12564i) q^{51} +(-0.189034 + 0.522478i) q^{52} +(-1.84431 + 9.27195i) q^{53} +(-1.95147 + 1.67733i) q^{54} +(4.66135 - 1.93079i) q^{55} +(5.00821 + 0.149555i) q^{56} +(6.70353 + 2.77669i) q^{57} +(0.319382 + 0.972559i) q^{58} +(3.85360 + 5.76732i) q^{59} +(16.3911 + 9.90349i) q^{60} +(-9.69397 + 1.92825i) q^{61} +(1.19693 + 9.84785i) q^{62} -3.90117 q^{63} +(5.98432 - 5.30923i) q^{64} +1.16630 q^{65} +(0.467724 + 3.84825i) q^{66} +(7.14707 - 1.42164i) q^{67} +(1.70464 - 2.82132i) q^{68} +(3.93821 + 5.89395i) q^{69} +(-3.28141 - 9.99230i) q^{70} +(-4.28878 - 1.77647i) q^{71} +(-4.53398 + 4.27104i) q^{72} +(-3.39319 + 1.40550i) q^{73} +(-9.31297 + 8.00472i) q^{74} +(5.61753 - 28.2413i) q^{75} +(-5.98289 - 2.16463i) q^{76} +(1.18279 - 1.77017i) q^{77} +(-0.240532 + 0.863224i) q^{78} +(-1.54634 - 1.54634i) q^{79} +(-14.7534 - 8.02063i) q^{80} +(-7.60625 + 7.60625i) q^{81} +(0.277078 + 0.491135i) q^{82} +(-9.93110 - 6.63575i) q^{83} +(8.07245 - 0.367937i) q^{84} +(-6.78626 - 1.34987i) q^{85} +(7.16914 + 0.541586i) q^{86} +(0.631793 + 1.52528i) q^{87} +(-0.563352 - 3.35224i) q^{88} +(3.81437 - 9.20870i) q^{89} +(11.6684 + 5.89927i) q^{90} +(0.409193 - 0.273414i) q^{91} +(-3.68503 - 5.00563i) q^{92} +(3.12134 + 15.6921i) q^{93} +(-2.66496 + 3.40240i) q^{94} +13.3552i q^{95} +(8.97906 - 9.26542i) q^{96} -9.29602i q^{97} +(4.29968 + 3.36777i) q^{98} +(0.516342 + 2.59583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(63\)
\(\chi(n)\) \(e\left(\frac{5}{16}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40388 + 0.170631i −0.992695 + 0.120654i
\(3\) −2.23702 + 0.444970i −1.29154 + 0.256904i −0.792605 0.609735i \(-0.791276\pi\)
−0.498936 + 0.866639i \(0.666276\pi\)
\(4\) 1.94177 0.479090i 0.970885 0.239545i
\(5\) −2.33237 3.49064i −1.04307 1.56106i −0.808088 0.589061i \(-0.799498\pi\)
−0.234980 0.972000i \(-0.575502\pi\)
\(6\) 3.06458 1.00639i 1.25111 0.410856i
\(7\) −1.63661 0.677907i −0.618582 0.256225i 0.0513111 0.998683i \(-0.483660\pi\)
−0.669893 + 0.742458i \(0.733660\pi\)
\(8\) −2.64427 + 1.00391i −0.934890 + 0.354936i
\(9\) 2.03460 0.842759i 0.678200 0.280920i
\(10\) 3.86998 + 4.50247i 1.22380 + 1.42381i
\(11\) −0.234463 + 1.17872i −0.0706931 + 0.355398i −0.999900 0.0141624i \(-0.995492\pi\)
0.929207 + 0.369561i \(0.120492\pi\)
\(12\) −4.13059 + 1.93576i −1.19240 + 0.558806i
\(13\) −0.154344 + 0.230992i −0.0428073 + 0.0640657i −0.852256 0.523125i \(-0.824766\pi\)
0.809449 + 0.587191i \(0.199766\pi\)
\(14\) 2.41328 + 0.672446i 0.644977 + 0.179719i
\(15\) 6.77078 + 6.77078i 1.74821 + 1.74821i
\(16\) 3.54094 1.86057i 0.885236 0.465142i
\(17\) 1.16542 1.16542i 0.282656 0.282656i −0.551511 0.834167i \(-0.685949\pi\)
0.834167 + 0.551511i \(0.185949\pi\)
\(18\) −2.71254 + 1.53030i −0.639352 + 0.360695i
\(19\) −2.64509 1.76739i −0.606824 0.405467i 0.213847 0.976867i \(-0.431400\pi\)
−0.820672 + 0.571400i \(0.806400\pi\)
\(20\) −6.20126 5.66061i −1.38664 1.26575i
\(21\) 3.96278 + 0.788246i 0.864749 + 0.172009i
\(22\) 0.128032 1.69479i 0.0272964 0.361331i
\(23\) −1.18934 2.87131i −0.247994 0.598710i 0.750040 0.661393i \(-0.230034\pi\)
−0.998033 + 0.0626831i \(0.980034\pi\)
\(24\) 5.46856 3.42239i 1.11627 0.698592i
\(25\) −4.83120 + 11.6635i −0.966239 + 2.33271i
\(26\) 0.177266 0.350621i 0.0347648 0.0687625i
\(27\) 1.51292 1.01090i 0.291161 0.194548i
\(28\) −3.50271 0.532255i −0.661949 0.100587i
\(29\) −0.141213 0.709928i −0.0262227 0.131830i 0.965456 0.260564i \(-0.0839086\pi\)
−0.991679 + 0.128734i \(0.958909\pi\)
\(30\) −10.6607 8.35008i −1.94637 1.52451i
\(31\) 7.01473i 1.25988i −0.776643 0.629941i \(-0.783079\pi\)
0.776643 0.629941i \(-0.216921\pi\)
\(32\) −4.65360 + 3.21621i −0.822648 + 0.568551i
\(33\) 2.74115i 0.477173i
\(34\) −1.43726 + 1.83497i −0.246487 + 0.314695i
\(35\) 1.45086 + 7.29396i 0.245240 + 1.23290i
\(36\) 3.54697 2.61120i 0.591162 0.435201i
\(37\) 7.22008 4.82430i 1.18697 0.793111i 0.204383 0.978891i \(-0.434481\pi\)
0.982591 + 0.185780i \(0.0594813\pi\)
\(38\) 4.01496 + 2.02987i 0.651312 + 0.329289i
\(39\) 0.242485 0.585411i 0.0388287 0.0937408i
\(40\) 9.67171 + 6.88870i 1.52923 + 1.08920i
\(41\) −0.152591 0.368387i −0.0238307 0.0575323i 0.911516 0.411264i \(-0.134913\pi\)
−0.935347 + 0.353732i \(0.884913\pi\)
\(42\) −5.69777 0.430433i −0.879185 0.0664172i
\(43\) −4.98611 0.991798i −0.760374 0.151248i −0.200350 0.979724i \(-0.564208\pi\)
−0.560024 + 0.828477i \(0.689208\pi\)
\(44\) 0.109442 + 2.40114i 0.0164990 + 0.361985i
\(45\) −7.68722 5.13643i −1.14594 0.765694i
\(46\) 2.15962 + 3.82804i 0.318419 + 0.564414i
\(47\) 2.16092 2.16092i 0.315203 0.315203i −0.531719 0.846921i \(-0.678454\pi\)
0.846921 + 0.531719i \(0.178454\pi\)
\(48\) −7.09325 + 5.73773i −1.02382 + 0.828170i
\(49\) −2.73080 2.73080i −0.390115 0.390115i
\(50\) 4.79227 17.1986i 0.677730 2.43225i
\(51\) −2.08849 + 3.12564i −0.292447 + 0.437677i
\(52\) −0.189034 + 0.522478i −0.0262144 + 0.0724547i
\(53\) −1.84431 + 9.27195i −0.253335 + 1.27360i 0.619272 + 0.785177i \(0.287428\pi\)
−0.872607 + 0.488423i \(0.837572\pi\)
\(54\) −1.95147 + 1.67733i −0.265561 + 0.228256i
\(55\) 4.66135 1.93079i 0.628536 0.260348i
\(56\) 5.00821 + 0.149555i 0.669250 + 0.0199851i
\(57\) 6.70353 + 2.77669i 0.887905 + 0.367782i
\(58\) 0.319382 + 0.972559i 0.0419370 + 0.127703i
\(59\) 3.85360 + 5.76732i 0.501696 + 0.750840i 0.992738 0.120295i \(-0.0383841\pi\)
−0.491043 + 0.871136i \(0.663384\pi\)
\(60\) 16.3911 + 9.90349i 2.11608 + 1.27853i
\(61\) −9.69397 + 1.92825i −1.24119 + 0.246887i −0.771662 0.636033i \(-0.780574\pi\)
−0.469524 + 0.882920i \(0.655574\pi\)
\(62\) 1.19693 + 9.84785i 0.152010 + 1.25068i
\(63\) −3.90117 −0.491501
\(64\) 5.98432 5.30923i 0.748040 0.663653i
\(65\) 1.16630 0.144661
\(66\) 0.467724 + 3.84825i 0.0575728 + 0.473687i
\(67\) 7.14707 1.42164i 0.873153 0.173681i 0.261880 0.965100i \(-0.415658\pi\)
0.611273 + 0.791420i \(0.290658\pi\)
\(68\) 1.70464 2.82132i 0.206718 0.342135i
\(69\) 3.93821 + 5.89395i 0.474105 + 0.709548i
\(70\) −3.28141 9.99230i −0.392203 1.19431i
\(71\) −4.28878 1.77647i −0.508984 0.210828i 0.113386 0.993551i \(-0.463830\pi\)
−0.622370 + 0.782723i \(0.713830\pi\)
\(72\) −4.53398 + 4.27104i −0.534334 + 0.503347i
\(73\) −3.39319 + 1.40550i −0.397142 + 0.164502i −0.572311 0.820037i \(-0.693953\pi\)
0.175169 + 0.984538i \(0.443953\pi\)
\(74\) −9.31297 + 8.00472i −1.08261 + 0.930530i
\(75\) 5.61753 28.2413i 0.648657 3.26102i
\(76\) −5.98289 2.16463i −0.686284 0.248300i
\(77\) 1.18279 1.77017i 0.134791 0.201730i
\(78\) −0.240532 + 0.863224i −0.0272349 + 0.0977408i
\(79\) −1.54634 1.54634i −0.173977 0.173977i 0.614747 0.788724i \(-0.289258\pi\)
−0.788724 + 0.614747i \(0.789258\pi\)
\(80\) −14.7534 8.02063i −1.64948 0.896734i
\(81\) −7.60625 + 7.60625i −0.845139 + 0.845139i
\(82\) 0.277078 + 0.491135i 0.0305981 + 0.0542368i
\(83\) −9.93110 6.63575i −1.09008 0.728368i −0.125483 0.992096i \(-0.540048\pi\)
−0.964597 + 0.263728i \(0.915048\pi\)
\(84\) 8.07245 0.367937i 0.880776 0.0401452i
\(85\) −6.78626 1.34987i −0.736073 0.146414i
\(86\) 7.16914 + 0.541586i 0.773068 + 0.0584007i
\(87\) 0.631793 + 1.52528i 0.0677353 + 0.163528i
\(88\) −0.563352 3.35224i −0.0600535 0.357350i
\(89\) 3.81437 9.20870i 0.404322 0.976120i −0.582282 0.812987i \(-0.697840\pi\)
0.986604 0.163133i \(-0.0521600\pi\)
\(90\) 11.6684 + 5.89927i 1.22995 + 0.621838i
\(91\) 0.409193 0.273414i 0.0428950 0.0286616i
\(92\) −3.68503 5.00563i −0.384191 0.521873i
\(93\) 3.12134 + 15.6921i 0.323668 + 1.62719i
\(94\) −2.66496 + 3.40240i −0.274869 + 0.350930i
\(95\) 13.3552i 1.37022i
\(96\) 8.97906 9.26542i 0.916421 0.945648i
\(97\) 9.29602i 0.943868i −0.881634 0.471934i \(-0.843556\pi\)
0.881634 0.471934i \(-0.156444\pi\)
\(98\) 4.29968 + 3.36777i 0.434334 + 0.340196i
\(99\) 0.516342 + 2.59583i 0.0518943 + 0.260890i
\(100\) −3.79318 + 24.9625i −0.379318 + 2.49625i
\(101\) 6.78178 4.53144i 0.674813 0.450895i −0.170365 0.985381i \(-0.554495\pi\)
0.845177 + 0.534486i \(0.179495\pi\)
\(102\) 2.39866 4.74439i 0.237503 0.469765i
\(103\) −2.37519 + 5.73422i −0.234035 + 0.565009i −0.996645 0.0818489i \(-0.973917\pi\)
0.762610 + 0.646858i \(0.223917\pi\)
\(104\) 0.176231 0.765753i 0.0172809 0.0750882i
\(105\) −6.49119 15.6711i −0.633475 1.52934i
\(106\) 1.00711 13.3314i 0.0978191 1.29486i
\(107\) 18.1355 + 3.60738i 1.75323 + 0.348738i 0.964110 0.265504i \(-0.0855385\pi\)
0.789117 + 0.614243i \(0.210539\pi\)
\(108\) 2.45343 2.68776i 0.236081 0.258630i
\(109\) −4.97622 3.32500i −0.476636 0.318478i 0.293943 0.955823i \(-0.405032\pi\)
−0.770578 + 0.637345i \(0.780032\pi\)
\(110\) −6.21453 + 3.50598i −0.592533 + 0.334282i
\(111\) −14.0048 + 14.0048i −1.32927 + 1.32927i
\(112\) −7.05645 + 0.644596i −0.666772 + 0.0609086i
\(113\) −2.54136 2.54136i −0.239071 0.239071i 0.577394 0.816465i \(-0.304070\pi\)
−0.816465 + 0.577394i \(0.804070\pi\)
\(114\) −9.88476 2.75432i −0.925792 0.257966i
\(115\) −7.24874 + 10.8485i −0.675948 + 1.01163i
\(116\) −0.614323 1.31086i −0.0570385 0.121711i
\(117\) −0.119358 + 0.600052i −0.0110346 + 0.0554748i
\(118\) −6.39408 7.43909i −0.588622 0.684824i
\(119\) −2.69739 + 1.11730i −0.247269 + 0.102422i
\(120\) −24.7010 11.1065i −2.25489 1.01388i
\(121\) 8.82826 + 3.65679i 0.802569 + 0.332435i
\(122\) 13.2802 4.36113i 1.20233 0.394838i
\(123\) 0.505269 + 0.756189i 0.0455586 + 0.0681832i
\(124\) −3.36069 13.6210i −0.301799 1.22320i
\(125\) 31.3939 6.24464i 2.80796 0.558537i
\(126\) 5.47678 0.665659i 0.487910 0.0593016i
\(127\) 6.27367 0.556698 0.278349 0.960480i \(-0.410213\pi\)
0.278349 + 0.960480i \(0.410213\pi\)
\(128\) −7.49537 + 8.47464i −0.662503 + 0.749059i
\(129\) 11.5953 1.02091
\(130\) −1.63734 + 0.199006i −0.143605 + 0.0174540i
\(131\) 14.9538 2.97450i 1.30652 0.259883i 0.507743 0.861509i \(-0.330480\pi\)
0.798778 + 0.601625i \(0.205480\pi\)
\(132\) −1.31326 5.32268i −0.114304 0.463280i
\(133\) 3.13086 + 4.68566i 0.271480 + 0.406298i
\(134\) −9.79106 + 3.21532i −0.845819 + 0.277762i
\(135\) −7.05737 2.92326i −0.607402 0.251594i
\(136\) −1.91171 + 4.25166i −0.163927 + 0.364577i
\(137\) 3.38200 1.40087i 0.288944 0.119685i −0.233504 0.972356i \(-0.575019\pi\)
0.522448 + 0.852671i \(0.325019\pi\)
\(138\) −6.53447 7.60243i −0.556251 0.647162i
\(139\) −4.19783 + 21.1039i −0.356055 + 1.79001i 0.223102 + 0.974795i \(0.428382\pi\)
−0.579158 + 0.815216i \(0.696618\pi\)
\(140\) 6.31170 + 13.4681i 0.533436 + 1.13826i
\(141\) −3.87247 + 5.79555i −0.326120 + 0.488074i
\(142\) 6.32406 + 1.76216i 0.530703 + 0.147877i
\(143\) −0.236088 0.236088i −0.0197426 0.0197426i
\(144\) 5.63640 6.76968i 0.469700 0.564140i
\(145\) −2.14874 + 2.14874i −0.178443 + 0.178443i
\(146\) 4.52381 2.55214i 0.374393 0.211217i
\(147\) 7.32397 + 4.89372i 0.604071 + 0.403627i
\(148\) 11.7085 12.8268i 0.962430 1.05435i
\(149\) −8.61517 1.71366i −0.705782 0.140389i −0.170867 0.985294i \(-0.554657\pi\)
−0.534916 + 0.844905i \(0.679657\pi\)
\(150\) −3.06754 + 40.6059i −0.250463 + 3.31546i
\(151\) −3.51806 8.49334i −0.286295 0.691178i 0.713661 0.700491i \(-0.247036\pi\)
−0.999957 + 0.00931286i \(0.997036\pi\)
\(152\) 8.76862 + 2.01802i 0.711229 + 0.163683i
\(153\) 1.38900 3.35334i 0.112294 0.271101i
\(154\) −1.35845 + 2.68693i −0.109467 + 0.216519i
\(155\) −24.4859 + 16.3610i −1.96675 + 1.31414i
\(156\) 0.190386 1.25291i 0.0152431 0.100313i
\(157\) −1.02494 5.15272i −0.0817990 0.411232i −0.999890 0.0148608i \(-0.995269\pi\)
0.918091 0.396371i \(-0.129731\pi\)
\(158\) 2.43473 + 1.90703i 0.193697 + 0.151715i
\(159\) 21.5622i 1.70999i
\(160\) 22.0806 + 8.74265i 1.74562 + 0.691167i
\(161\) 5.50548i 0.433893i
\(162\) 9.38042 11.9761i 0.736996 0.940934i
\(163\) −3.54698 17.8319i −0.277821 1.39670i −0.827566 0.561368i \(-0.810275\pi\)
0.549745 0.835333i \(-0.314725\pi\)
\(164\) −0.472787 0.642218i −0.0369184 0.0501488i
\(165\) −9.56837 + 6.39338i −0.744896 + 0.497724i
\(166\) 15.0744 + 7.62126i 1.17000 + 0.591525i
\(167\) −7.42288 + 17.9204i −0.574400 + 1.38672i 0.323376 + 0.946270i \(0.395182\pi\)
−0.897776 + 0.440453i \(0.854818\pi\)
\(168\) −11.2700 + 1.89395i −0.869498 + 0.146121i
\(169\) 4.94535 + 11.9391i 0.380411 + 0.918395i
\(170\) 9.75743 + 0.737116i 0.748361 + 0.0565342i
\(171\) −6.87118 1.36676i −0.525452 0.104519i
\(172\) −10.1570 + 0.462951i −0.774466 + 0.0352997i
\(173\) 4.21489 + 2.81630i 0.320452 + 0.214119i 0.705383 0.708826i \(-0.250775\pi\)
−0.384931 + 0.922945i \(0.625775\pi\)
\(174\) −1.14722 2.03352i −0.0869708 0.154160i
\(175\) 15.8136 15.8136i 1.19540 1.19540i
\(176\) 1.36287 + 4.61003i 0.102730 + 0.347494i
\(177\) −11.1868 11.1868i −0.840854 0.840854i
\(178\) −3.78364 + 13.5788i −0.283596 + 1.01777i
\(179\) 9.57074 14.3236i 0.715351 1.07060i −0.278561 0.960419i \(-0.589857\pi\)
0.993912 0.110180i \(-0.0351426\pi\)
\(180\) −17.3876 6.29090i −1.29600 0.468896i
\(181\) 2.13516 10.7342i 0.158705 0.797865i −0.816634 0.577156i \(-0.804163\pi\)
0.975340 0.220710i \(-0.0708374\pi\)
\(182\) −0.527805 + 0.453661i −0.0391235 + 0.0336276i
\(183\) 20.8276 8.62705i 1.53962 0.637730i
\(184\) 6.02747 + 6.39853i 0.444351 + 0.471706i
\(185\) −33.6798 13.9506i −2.47619 1.02567i
\(186\) −7.05954 21.4972i −0.517631 1.57625i
\(187\) 1.10046 + 1.64696i 0.0804736 + 0.120437i
\(188\) 3.16073 5.23129i 0.230520 0.381531i
\(189\) −3.16136 + 0.628833i −0.229955 + 0.0457409i
\(190\) −2.27881 18.7492i −0.165323 1.36021i
\(191\) −20.6704 −1.49566 −0.747830 0.663890i \(-0.768904\pi\)
−0.747830 + 0.663890i \(0.768904\pi\)
\(192\) −11.0246 + 14.5397i −0.795630 + 1.04931i
\(193\) 19.6483 1.41432 0.707158 0.707056i \(-0.249977\pi\)
0.707158 + 0.707056i \(0.249977\pi\)
\(194\) 1.58619 + 13.0505i 0.113881 + 0.936973i
\(195\) −2.60903 + 0.518967i −0.186836 + 0.0371640i
\(196\) −6.61089 3.99429i −0.472207 0.285306i
\(197\) −11.3923 17.0498i −0.811669 1.21475i −0.973671 0.227959i \(-0.926795\pi\)
0.162001 0.986791i \(-0.448205\pi\)
\(198\) −1.16781 3.55613i −0.0829927 0.252723i
\(199\) 1.25587 + 0.520198i 0.0890262 + 0.0368759i 0.426752 0.904369i \(-0.359658\pi\)
−0.337726 + 0.941245i \(0.609658\pi\)
\(200\) 1.06582 35.6916i 0.0753649 2.52378i
\(201\) −15.3555 + 6.36046i −1.08309 + 0.448632i
\(202\) −8.74762 + 7.51879i −0.615480 + 0.529020i
\(203\) −0.250154 + 1.25761i −0.0175573 + 0.0882667i
\(204\) −2.55790 + 7.06985i −0.179089 + 0.494989i
\(205\) −0.930007 + 1.39185i −0.0649545 + 0.0972113i
\(206\) 2.35606 8.45545i 0.164154 0.589119i
\(207\) −4.83965 4.83965i −0.336379 0.336379i
\(208\) −0.116747 + 1.10510i −0.00809497 + 0.0766247i
\(209\) 2.70344 2.70344i 0.187001 0.187001i
\(210\) 11.7868 + 20.8928i 0.813369 + 1.44174i
\(211\) 9.24556 + 6.17768i 0.636490 + 0.425289i 0.831510 0.555510i \(-0.187477\pi\)
−0.195019 + 0.980799i \(0.562477\pi\)
\(212\) 0.860884 + 18.8876i 0.0591257 + 1.29720i
\(213\) 10.3845 + 2.06561i 0.711537 + 0.141533i
\(214\) −26.0757 1.96986i −1.78250 0.134657i
\(215\) 8.16744 + 19.7179i 0.557015 + 1.34475i
\(216\) −2.98571 + 4.19193i −0.203152 + 0.285225i
\(217\) −4.75534 + 11.4804i −0.322813 + 0.779340i
\(218\) 7.55338 + 3.81882i 0.511579 + 0.258643i
\(219\) 6.96520 4.65400i 0.470665 0.314488i
\(220\) 8.12625 5.98237i 0.547872 0.403331i
\(221\) 0.0893273 + 0.449078i 0.00600880 + 0.0302083i
\(222\) 17.2714 22.0507i 1.15918 1.47994i
\(223\) 0.398929i 0.0267143i −0.999911 0.0133571i \(-0.995748\pi\)
0.999911 0.0133571i \(-0.00425183\pi\)
\(224\) 9.79644 2.10898i 0.654552 0.140912i
\(225\) 27.8022i 1.85348i
\(226\) 4.00140 + 3.13414i 0.266169 + 0.208480i
\(227\) −2.31877 11.6572i −0.153902 0.773718i −0.978217 0.207586i \(-0.933439\pi\)
0.824315 0.566132i \(-0.191561\pi\)
\(228\) 14.3470 + 2.18010i 0.950154 + 0.144381i
\(229\) −5.87305 + 3.92425i −0.388102 + 0.259322i −0.734279 0.678848i \(-0.762480\pi\)
0.346177 + 0.938169i \(0.387480\pi\)
\(230\) 8.32529 16.4669i 0.548953 1.08579i
\(231\) −1.85825 + 4.48620i −0.122264 + 0.295170i
\(232\) 1.08611 + 1.73547i 0.0713067 + 0.113939i
\(233\) −2.63067 6.35099i −0.172341 0.416067i 0.813983 0.580889i \(-0.197295\pi\)
−0.986323 + 0.164822i \(0.947295\pi\)
\(234\) 0.0651770 0.862768i 0.00426075 0.0564009i
\(235\) −12.5831 2.50293i −0.820828 0.163273i
\(236\) 10.2459 + 9.35258i 0.666949 + 0.608801i
\(237\) 4.14727 + 2.77111i 0.269394 + 0.180003i
\(238\) 3.59617 2.02881i 0.233105 0.131508i
\(239\) 2.18529 2.18529i 0.141355 0.141355i −0.632888 0.774243i \(-0.718131\pi\)
0.774243 + 0.632888i \(0.218131\pi\)
\(240\) 36.5725 + 11.3775i 2.36074 + 0.734413i
\(241\) 9.11533 + 9.11533i 0.587170 + 0.587170i 0.936864 0.349694i \(-0.113714\pi\)
−0.349694 + 0.936864i \(0.613714\pi\)
\(242\) −13.0178 3.62732i −0.836816 0.233173i
\(243\) 10.5980 15.8611i 0.679865 1.01749i
\(244\) −17.8997 + 8.38851i −1.14591 + 0.537019i
\(245\) −3.16300 + 15.9015i −0.202077 + 1.01591i
\(246\) −0.838367 0.975385i −0.0534523 0.0621883i
\(247\) 0.816506 0.338208i 0.0519530 0.0215196i
\(248\) 7.04217 + 18.5488i 0.447178 + 1.17785i
\(249\) 25.1687 + 10.4252i 1.59500 + 0.660672i
\(250\) −43.0078 + 14.1235i −2.72005 + 0.893248i
\(251\) −10.9216 16.3453i −0.689364 1.03171i −0.996784 0.0801321i \(-0.974466\pi\)
0.307420 0.951574i \(-0.400534\pi\)
\(252\) −7.57517 + 1.86901i −0.477191 + 0.117737i
\(253\) 3.66333 0.728682i 0.230312 0.0458119i
\(254\) −8.80749 + 1.07048i −0.552631 + 0.0671679i
\(255\) 15.7816 0.988283
\(256\) 9.07658 13.1763i 0.567286 0.823521i
\(257\) −16.2065 −1.01093 −0.505466 0.862846i \(-0.668680\pi\)
−0.505466 + 0.862846i \(0.668680\pi\)
\(258\) −16.2785 + 1.97851i −1.01345 + 0.123177i
\(259\) −15.0869 + 3.00097i −0.937455 + 0.186471i
\(260\) 2.26468 0.558762i 0.140450 0.0346529i
\(261\) −0.885611 1.32541i −0.0548180 0.0820409i
\(262\) −20.4859 + 6.72743i −1.26562 + 0.415622i
\(263\) 22.6730 + 9.39145i 1.39808 + 0.579102i 0.949251 0.314518i \(-0.101843\pi\)
0.448824 + 0.893620i \(0.351843\pi\)
\(264\) 2.75187 + 7.24834i 0.169366 + 0.446104i
\(265\) 36.6666 15.1878i 2.25241 0.932980i
\(266\) −5.19487 6.04389i −0.318518 0.370575i
\(267\) −4.43521 + 22.2973i −0.271430 + 1.36457i
\(268\) 13.1969 6.18459i 0.806127 0.377784i
\(269\) 0.381447 0.570875i 0.0232572 0.0348069i −0.819659 0.572852i \(-0.805837\pi\)
0.842916 + 0.538045i \(0.180837\pi\)
\(270\) 10.4065 + 2.89971i 0.633321 + 0.176471i
\(271\) 10.0189 + 10.0189i 0.608606 + 0.608606i 0.942582 0.333975i \(-0.108390\pi\)
−0.333975 + 0.942582i \(0.608390\pi\)
\(272\) 1.95835 6.29503i 0.118742 0.381692i
\(273\) −0.793709 + 0.793709i −0.0480375 + 0.0480375i
\(274\) −4.50890 + 2.54373i −0.272393 + 0.153672i
\(275\) −12.6153 8.42930i −0.760734 0.508306i
\(276\) 10.4708 + 9.55793i 0.630270 + 0.575320i
\(277\) −22.7599 4.52722i −1.36751 0.272014i −0.543889 0.839157i \(-0.683049\pi\)
−0.823619 + 0.567143i \(0.808049\pi\)
\(278\) 2.29229 30.3437i 0.137482 1.81989i
\(279\) −5.91173 14.2722i −0.353926 0.854453i
\(280\) −11.1590 17.8307i −0.666875 1.06559i
\(281\) 1.29852 3.13490i 0.0774631 0.187012i −0.880404 0.474225i \(-0.842728\pi\)
0.957867 + 0.287212i \(0.0927285\pi\)
\(282\) 4.44759 8.79704i 0.264850 0.523856i
\(283\) 10.2454 6.84576i 0.609026 0.406938i −0.212458 0.977170i \(-0.568147\pi\)
0.821484 + 0.570232i \(0.193147\pi\)
\(284\) −9.17891 1.39478i −0.544668 0.0827652i
\(285\) −5.94269 29.8759i −0.352014 1.76970i
\(286\) 0.371723 + 0.291156i 0.0219804 + 0.0172164i
\(287\) 0.706349i 0.0416945i
\(288\) −6.75773 + 10.4656i −0.398203 + 0.616690i
\(289\) 14.2836i 0.840211i
\(290\) 2.64994 3.38322i 0.155610 0.198669i
\(291\) 4.13645 + 20.7953i 0.242483 + 1.21904i
\(292\) −5.91543 + 4.35481i −0.346174 + 0.254846i
\(293\) −11.3488 + 7.58301i −0.663003 + 0.443004i −0.841006 0.541026i \(-0.818036\pi\)
0.178004 + 0.984030i \(0.443036\pi\)
\(294\) −11.1170 5.62052i −0.648357 0.327795i
\(295\) 11.1436 26.9030i 0.648806 1.56636i
\(296\) −14.2487 + 20.0051i −0.828187 + 1.16277i
\(297\) 0.836848 + 2.02033i 0.0485588 + 0.117231i
\(298\) 12.3871 + 0.935771i 0.717565 + 0.0542078i
\(299\) 0.846817 + 0.168442i 0.0489727 + 0.00974127i
\(300\) −2.62215 57.5293i −0.151390 3.32146i
\(301\) 7.48798 + 5.00331i 0.431600 + 0.288386i
\(302\) 6.38816 + 11.3234i 0.367597 + 0.651586i
\(303\) −13.1546 + 13.1546i −0.755712 + 0.755712i
\(304\) −12.6544 1.33687i −0.725782 0.0766748i
\(305\) 29.3408 + 29.3408i 1.68005 + 1.68005i
\(306\) −1.37781 + 4.94469i −0.0787640 + 0.282669i
\(307\) −14.2506 + 21.3276i −0.813326 + 1.21723i 0.159844 + 0.987142i \(0.448901\pi\)
−0.973170 + 0.230086i \(0.926099\pi\)
\(308\) 1.44863 4.00393i 0.0825436 0.228145i
\(309\) 2.76178 13.8844i 0.157112 0.789857i
\(310\) 31.5836 27.1469i 1.79383 1.54184i
\(311\) 8.17983 3.38820i 0.463835 0.192127i −0.138512 0.990361i \(-0.544232\pi\)
0.602348 + 0.798234i \(0.294232\pi\)
\(312\) −0.0534952 + 1.79142i −0.00302857 + 0.101419i
\(313\) −3.15454 1.30665i −0.178305 0.0738564i 0.291745 0.956496i \(-0.405764\pi\)
−0.470050 + 0.882640i \(0.655764\pi\)
\(314\) 2.31810 + 7.05892i 0.130818 + 0.398358i
\(315\) 9.09897 + 13.6176i 0.512669 + 0.767264i
\(316\) −3.74348 2.26180i −0.210587 0.127236i
\(317\) −17.1528 + 3.41191i −0.963399 + 0.191632i −0.651639 0.758529i \(-0.725918\pi\)
−0.311760 + 0.950161i \(0.600918\pi\)
\(318\) 3.67916 + 30.2707i 0.206317 + 1.69750i
\(319\) 0.869917 0.0487060
\(320\) −32.4903 8.50603i −1.81626 0.475501i
\(321\) −42.1746 −2.35396
\(322\) −0.939404 7.72905i −0.0523509 0.430723i
\(323\) −5.14239 + 1.02288i −0.286130 + 0.0569148i
\(324\) −11.1255 + 18.4137i −0.618084 + 1.02298i
\(325\) −1.94852 2.91616i −0.108084 0.161760i
\(326\) 8.02221 + 24.4286i 0.444309 + 1.35298i
\(327\) 12.6114 + 5.22382i 0.697413 + 0.288878i
\(328\) 0.773319 + 0.820926i 0.0426994 + 0.0453281i
\(329\) −5.00149 + 2.07169i −0.275741 + 0.114216i
\(330\) 12.3420 10.6082i 0.679402 0.583963i
\(331\) 2.90638 14.6113i 0.159749 0.803112i −0.814940 0.579546i \(-0.803230\pi\)
0.974689 0.223566i \(-0.0717699\pi\)
\(332\) −22.4630 8.12721i −1.23282 0.446038i
\(333\) 10.6243 15.9003i 0.582206 0.871332i
\(334\) 7.36308 26.4247i 0.402890 1.44590i
\(335\) −21.6320 21.6320i −1.18188 1.18188i
\(336\) 15.4986 4.58188i 0.845516 0.249962i
\(337\) −4.78263 + 4.78263i −0.260527 + 0.260527i −0.825268 0.564741i \(-0.808976\pi\)
0.564741 + 0.825268i \(0.308976\pi\)
\(338\) −8.97987 15.9173i −0.488440 0.865787i
\(339\) 6.81589 + 4.55423i 0.370188 + 0.247352i
\(340\) −13.8241 + 0.630092i −0.749715 + 0.0341715i
\(341\) 8.26842 + 1.64469i 0.447760 + 0.0890650i
\(342\) 9.87954 + 0.746341i 0.534224 + 0.0403575i
\(343\) 7.36339 + 17.7768i 0.397586 + 0.959857i
\(344\) 14.1803 2.38303i 0.764550 0.128484i
\(345\) 11.3883 27.4937i 0.613124 1.48021i
\(346\) −6.39776 3.23457i −0.343946 0.173891i
\(347\) 9.14973 6.11366i 0.491183 0.328198i −0.285191 0.958471i \(-0.592057\pi\)
0.776374 + 0.630273i \(0.217057\pi\)
\(348\) 1.95755 + 2.65906i 0.104935 + 0.142541i
\(349\) 3.87593 + 19.4856i 0.207474 + 1.04304i 0.934373 + 0.356297i \(0.115961\pi\)
−0.726899 + 0.686744i \(0.759039\pi\)
\(350\) −19.5021 + 24.8987i −1.04243 + 1.33089i
\(351\) 0.505498i 0.0269815i
\(352\) −2.69993 6.23939i −0.143907 0.332560i
\(353\) 22.7162i 1.20906i −0.796583 0.604529i \(-0.793361\pi\)
0.796583 0.604529i \(-0.206639\pi\)
\(354\) 17.6138 + 13.7962i 0.936164 + 0.733259i
\(355\) 3.80200 + 19.1140i 0.201789 + 1.01446i
\(356\) 2.99483 19.7086i 0.158726 1.04455i
\(357\) 5.53694 3.69967i 0.293046 0.195807i
\(358\) −10.9921 + 21.7417i −0.580953 + 1.14909i
\(359\) 14.0062 33.8139i 0.739218 1.78463i 0.130179 0.991490i \(-0.458445\pi\)
0.609039 0.793140i \(-0.291555\pi\)
\(360\) 25.4836 + 5.86483i 1.34310 + 0.309104i
\(361\) −3.39817 8.20392i −0.178851 0.431785i
\(362\) −1.16594 + 15.4338i −0.0612802 + 0.811185i
\(363\) −21.3761 4.25197i −1.12196 0.223171i
\(364\) 0.663568 0.726947i 0.0347804 0.0381024i
\(365\) 12.8203 + 8.56624i 0.671044 + 0.448377i
\(366\) −27.7674 + 15.6652i −1.45142 + 0.818832i
\(367\) 10.6394 10.6394i 0.555373 0.555373i −0.372614 0.927987i \(-0.621538\pi\)
0.927987 + 0.372614i \(0.121538\pi\)
\(368\) −9.55364 7.95431i −0.498018 0.414647i
\(369\) −0.620923 0.620923i −0.0323240 0.0323240i
\(370\) 49.6629 + 13.8382i 2.58185 + 0.719416i
\(371\) 9.30394 13.9243i 0.483036 0.722915i
\(372\) 13.5788 + 28.9750i 0.704030 + 1.50228i
\(373\) 0.946981 4.76079i 0.0490328 0.246505i −0.948494 0.316796i \(-0.897393\pi\)
0.997526 + 0.0702914i \(0.0223929\pi\)
\(374\) −1.82594 2.12436i −0.0944170 0.109848i
\(375\) −67.4500 + 27.9387i −3.48310 + 1.44275i
\(376\) −3.54468 + 7.88343i −0.182803 + 0.406557i
\(377\) 0.185783 + 0.0769539i 0.00956831 + 0.00396333i
\(378\) 4.33088 1.42223i 0.222756 0.0731517i
\(379\) −4.29469 6.42746i −0.220603 0.330156i 0.704616 0.709589i \(-0.251119\pi\)
−0.925219 + 0.379432i \(0.876119\pi\)
\(380\) 6.39837 + 25.9328i 0.328230 + 1.33033i
\(381\) −14.0343 + 2.79160i −0.718999 + 0.143018i
\(382\) 29.0189 3.52701i 1.48473 0.180457i
\(383\) −13.2624 −0.677675 −0.338837 0.940845i \(-0.610034\pi\)
−0.338837 + 0.940845i \(0.610034\pi\)
\(384\) 12.9963 22.2931i 0.663214 1.13764i
\(385\) −8.93773 −0.455509
\(386\) −27.5839 + 3.35260i −1.40398 + 0.170643i
\(387\) −10.9806 + 2.18417i −0.558174 + 0.111028i
\(388\) −4.45363 18.0507i −0.226099 0.916387i
\(389\) 7.11261 + 10.6448i 0.360624 + 0.539711i 0.966772 0.255640i \(-0.0822863\pi\)
−0.606148 + 0.795352i \(0.707286\pi\)
\(390\) 3.57421 1.17375i 0.180987 0.0594351i
\(391\) −4.73236 1.96021i −0.239326 0.0991320i
\(392\) 9.96246 + 4.47949i 0.503180 + 0.226249i
\(393\) −32.1284 + 13.3080i −1.62066 + 0.671300i
\(394\) 18.9027 + 21.9921i 0.952304 + 1.10794i
\(395\) −1.79108 + 9.00437i −0.0901190 + 0.453059i
\(396\) 2.24625 + 4.79312i 0.112878 + 0.240864i
\(397\) 21.7727 32.5851i 1.09274 1.63540i 0.395675 0.918390i \(-0.370511\pi\)
0.697064 0.717009i \(-0.254489\pi\)
\(398\) −1.85185 0.516007i −0.0928251 0.0258651i
\(399\) −9.08875 9.08875i −0.455007 0.455007i
\(400\) 4.59380 + 50.2887i 0.229690 + 2.51444i
\(401\) 1.79901 1.79901i 0.0898380 0.0898380i −0.660760 0.750598i \(-0.729766\pi\)
0.750598 + 0.660760i \(0.229766\pi\)
\(402\) 20.4720 11.5495i 1.02105 0.576035i
\(403\) 1.62035 + 1.08268i 0.0807152 + 0.0539322i
\(404\) 10.9977 12.0481i 0.547156 0.599416i
\(405\) 44.2913 + 8.81008i 2.20085 + 0.437777i
\(406\) 0.136600 1.80822i 0.00677934 0.0897402i
\(407\) 3.99368 + 9.64159i 0.197959 + 0.477916i
\(408\) 2.38465 10.3617i 0.118058 0.512980i
\(409\) −2.64478 + 6.38506i −0.130776 + 0.315721i −0.975681 0.219195i \(-0.929657\pi\)
0.844905 + 0.534916i \(0.179657\pi\)
\(410\) 1.06813 2.11269i 0.0527511 0.104338i
\(411\) −6.94225 + 4.63866i −0.342436 + 0.228808i
\(412\) −1.86487 + 12.2725i −0.0918754 + 0.604621i
\(413\) −2.39714 12.0512i −0.117956 0.593003i
\(414\) 7.62009 + 5.96850i 0.374507 + 0.293336i
\(415\) 50.1429i 2.46142i
\(416\) −0.0246640 1.57135i −0.00120925 0.0770416i
\(417\) 49.0777i 2.40334i
\(418\) −3.33402 + 4.25659i −0.163072 + 0.208197i
\(419\) −1.12208 5.64109i −0.0548173 0.275585i 0.943649 0.330948i \(-0.107368\pi\)
−0.998466 + 0.0553627i \(0.982368\pi\)
\(420\) −20.1123 27.3198i −0.981379 1.33307i
\(421\) 21.9884 14.6922i 1.07165 0.716052i 0.110999 0.993821i \(-0.464595\pi\)
0.960648 + 0.277769i \(0.0895949\pi\)
\(422\) −14.0338 7.09517i −0.683153 0.345387i
\(423\) 2.57547 6.21774i 0.125224 0.302317i
\(424\) −4.43138 26.3690i −0.215207 1.28059i
\(425\) 7.96255 + 19.2233i 0.386241 + 0.932467i
\(426\) −14.9311 1.12796i −0.723415 0.0546497i
\(427\) 17.1725 + 3.41581i 0.831034 + 0.165303i
\(428\) 36.9433 1.68385i 1.78572 0.0813920i
\(429\) 0.633184 + 0.423080i 0.0305704 + 0.0204265i
\(430\) −14.8306 26.2881i −0.715195 1.26772i
\(431\) −5.66697 + 5.66697i −0.272968 + 0.272968i −0.830294 0.557326i \(-0.811828\pi\)
0.557326 + 0.830294i \(0.311828\pi\)
\(432\) 3.47631 6.39443i 0.167254 0.307652i
\(433\) −9.43057 9.43057i −0.453204 0.453204i 0.443212 0.896417i \(-0.353839\pi\)
−0.896417 + 0.443212i \(0.853839\pi\)
\(434\) 4.71703 16.9285i 0.226425 0.812596i
\(435\) 3.85064 5.76289i 0.184624 0.276309i
\(436\) −11.2557 4.07234i −0.539048 0.195030i
\(437\) −1.92883 + 9.69688i −0.0922684 + 0.463865i
\(438\) −8.98421 + 7.72214i −0.429282 + 0.368978i
\(439\) −19.0108 + 7.87451i −0.907334 + 0.375830i −0.787036 0.616908i \(-0.788385\pi\)
−0.120299 + 0.992738i \(0.538385\pi\)
\(440\) −10.3875 + 9.78513i −0.495206 + 0.466488i
\(441\) −7.85750 3.25468i −0.374167 0.154985i
\(442\) −0.202031 0.615211i −0.00960966 0.0292626i
\(443\) 9.86124 + 14.7584i 0.468522 + 0.701193i 0.988200 0.153170i \(-0.0489481\pi\)
−0.519678 + 0.854362i \(0.673948\pi\)
\(444\) −20.4845 + 33.9036i −0.972151 + 1.60899i
\(445\) −41.0408 + 8.16352i −1.94552 + 0.386988i
\(446\) 0.0680695 + 0.560049i 0.00322318 + 0.0265191i
\(447\) 20.0348 0.947614
\(448\) −13.3932 + 4.63233i −0.632769 + 0.218857i
\(449\) 12.8596 0.606883 0.303441 0.952850i \(-0.401864\pi\)
0.303441 + 0.952850i \(0.401864\pi\)
\(450\) −4.74390 39.0310i −0.223630 1.83994i
\(451\) 0.470003 0.0934893i 0.0221316 0.00440224i
\(452\) −6.15228 3.71720i −0.289379 0.174842i
\(453\) 11.6492 + 17.4343i 0.547328 + 0.819135i
\(454\) 5.24436 + 15.9697i 0.246130 + 0.749497i
\(455\) −1.90878 0.790642i −0.0894849 0.0370659i
\(456\) −20.5135 0.612572i −0.960633 0.0286863i
\(457\) 4.61582 1.91193i 0.215919 0.0894365i −0.272102 0.962268i \(-0.587719\pi\)
0.488021 + 0.872832i \(0.337719\pi\)
\(458\) 7.57548 6.51131i 0.353979 0.304253i
\(459\) 0.585063 2.94131i 0.0273084 0.137289i
\(460\) −8.87797 + 24.5381i −0.413938 + 1.14410i
\(461\) −16.4812 + 24.6659i −0.767606 + 1.14880i 0.217366 + 0.976090i \(0.430254\pi\)
−0.984972 + 0.172714i \(0.944746\pi\)
\(462\) 1.84328 6.61517i 0.0857569 0.307766i
\(463\) 14.2150 + 14.2150i 0.660625 + 0.660625i 0.955527 0.294903i \(-0.0952872\pi\)
−0.294903 + 0.955527i \(0.595287\pi\)
\(464\) −1.82090 2.25108i −0.0845330 0.104504i
\(465\) 47.4952 47.4952i 2.20254 2.20254i
\(466\) 4.77682 + 8.46717i 0.221282 + 0.392234i
\(467\) 9.72658 + 6.49909i 0.450093 + 0.300742i 0.759880 0.650064i \(-0.225258\pi\)
−0.309787 + 0.950806i \(0.600258\pi\)
\(468\) 0.0557137 + 1.22235i 0.00257537 + 0.0565029i
\(469\) −12.6607 2.51837i −0.584618 0.116288i
\(470\) 18.0922 + 1.36676i 0.834531 + 0.0630439i
\(471\) 4.58561 + 11.0706i 0.211294 + 0.510108i
\(472\) −15.9798 11.3817i −0.735531 0.523884i
\(473\) 2.33811 5.64470i 0.107506 0.259543i
\(474\) −6.29511 3.18267i −0.289144 0.146185i
\(475\) 33.3929 22.3125i 1.53217 1.02377i
\(476\) −4.70243 + 3.46182i −0.215535 + 0.158672i
\(477\) 4.06160 + 20.4190i 0.185968 + 0.934923i
\(478\) −2.69502 + 3.44077i −0.123267 + 0.157377i
\(479\) 33.3214i 1.52249i −0.648463 0.761246i \(-0.724588\pi\)
0.648463 0.761246i \(-0.275412\pi\)
\(480\) −53.2848 9.73225i −2.43211 0.444214i
\(481\) 2.41238i 0.109995i
\(482\) −14.3522 11.2415i −0.653725 0.512036i
\(483\) −2.44978 12.3159i −0.111469 0.560391i
\(484\) 18.8944 + 2.87110i 0.858836 + 0.130505i
\(485\) −32.4491 + 21.6818i −1.47344 + 0.984519i
\(486\) −12.1720 + 24.0755i −0.552134 + 1.09209i
\(487\) −8.84785 + 21.3606i −0.400934 + 0.967941i 0.586505 + 0.809945i \(0.300503\pi\)
−0.987440 + 0.157996i \(0.949497\pi\)
\(488\) 23.6977 14.8307i 1.07274 0.671355i
\(489\) 15.8693 + 38.3119i 0.717635 + 1.73252i
\(490\) 1.72720 22.8635i 0.0780271 1.03287i
\(491\) −16.4921 3.28049i −0.744280 0.148046i −0.191638 0.981466i \(-0.561380\pi\)
−0.552641 + 0.833419i \(0.686380\pi\)
\(492\) 1.34340 + 1.22628i 0.0605651 + 0.0552847i
\(493\) −0.991937 0.662791i −0.0446746 0.0298506i
\(494\) −1.08857 + 0.614125i −0.0489771 + 0.0276308i
\(495\) 7.85680 7.85680i 0.353137 0.353137i
\(496\) −13.0514 24.8388i −0.586024 1.11529i
\(497\) 5.81479 + 5.81479i 0.260829 + 0.260829i
\(498\) −37.1128 10.3412i −1.66306 0.463402i
\(499\) −8.82586 + 13.2088i −0.395100 + 0.591308i −0.974679 0.223607i \(-0.928217\pi\)
0.579580 + 0.814916i \(0.303217\pi\)
\(500\) 57.9680 27.1662i 2.59241 1.21491i
\(501\) 8.63105 43.3912i 0.385607 1.93858i
\(502\) 18.1216 + 21.0833i 0.808807 + 0.940994i
\(503\) −0.539361 + 0.223411i −0.0240489 + 0.00996138i −0.394675 0.918821i \(-0.629143\pi\)
0.370627 + 0.928782i \(0.379143\pi\)
\(504\) 10.3157 3.91643i 0.459500 0.174452i
\(505\) −31.6353 13.1038i −1.40775 0.583109i
\(506\) −5.01855 + 1.64806i −0.223102 + 0.0732652i
\(507\) −16.3754 24.5075i −0.727256 1.08842i
\(508\) 12.1820 3.00565i 0.540490 0.133354i
\(509\) −7.93668 + 1.57870i −0.351787 + 0.0699748i −0.367821 0.929897i \(-0.619896\pi\)
0.0160338 + 0.999871i \(0.494896\pi\)
\(510\) −22.1555 + 2.69283i −0.981063 + 0.119240i
\(511\) 6.50614 0.287814
\(512\) −10.4942 + 20.0468i −0.463781 + 0.885950i
\(513\) −5.78845 −0.255566
\(514\) 22.7520 2.76532i 1.00355 0.121973i
\(515\) 25.5559 5.08339i 1.12613 0.224001i
\(516\) 22.5154 5.55520i 0.991187 0.244554i
\(517\) 2.04047 + 3.05378i 0.0897398 + 0.134305i
\(518\) 20.6682 6.78730i 0.908108 0.298217i
\(519\) −10.6819 4.42461i −0.468885 0.194219i
\(520\) −3.08400 + 1.17086i −0.135243 + 0.0513456i
\(521\) 0.958515 0.397030i 0.0419933 0.0173942i −0.361588 0.932338i \(-0.617765\pi\)
0.403581 + 0.914944i \(0.367765\pi\)
\(522\) 1.46945 + 1.70961i 0.0643161 + 0.0748275i
\(523\) −0.257581 + 1.29495i −0.0112632 + 0.0566240i −0.986008 0.166697i \(-0.946690\pi\)
0.974745 + 0.223321i \(0.0716898\pi\)
\(524\) 27.6118 12.9400i 1.20623 0.565288i
\(525\) −28.3387 + 42.4118i −1.23680 + 1.85100i
\(526\) −33.4327 9.31579i −1.45773 0.406188i
\(527\) −8.17511 8.17511i −0.356113 0.356113i
\(528\) −5.10009 9.70626i −0.221953 0.422411i
\(529\) 9.43355 9.43355i 0.410154 0.410154i
\(530\) −48.8841 + 27.5784i −2.12339 + 1.19793i
\(531\) 12.7010 + 8.48653i 0.551176 + 0.368284i
\(532\) 8.32426 + 7.59851i 0.360902 + 0.329437i
\(533\) 0.108646 + 0.0216110i 0.00470598 + 0.000936077i
\(534\) 2.42191 32.0595i 0.104806 1.38735i
\(535\) −29.7067 71.7183i −1.28433 3.10065i
\(536\) −17.4716 + 10.9342i −0.754657 + 0.472287i
\(537\) −15.0363 + 36.3009i −0.648865 + 1.56650i
\(538\) −0.438097 + 0.866528i −0.0188877 + 0.0373587i
\(539\) 3.85913 2.57859i 0.166224 0.111068i
\(540\) −15.1043 2.29518i −0.649986 0.0987688i
\(541\) −0.446774 2.24608i −0.0192083 0.0965667i 0.969992 0.243137i \(-0.0781765\pi\)
−0.989200 + 0.146570i \(0.953177\pi\)
\(542\) −15.7749 12.3559i −0.677591 0.530730i
\(543\) 24.9626i 1.07125i
\(544\) −1.67516 + 9.17164i −0.0718220 + 0.393231i
\(545\) 25.1253i 1.07625i
\(546\) 0.978843 1.24971i 0.0418906 0.0534825i
\(547\) −7.07297 35.5582i −0.302418 1.52036i −0.770940 0.636907i \(-0.780213\pi\)
0.468522 0.883452i \(-0.344787\pi\)
\(548\) 5.89593 4.34046i 0.251862 0.185415i
\(549\) −18.0983 + 12.0929i −0.772417 + 0.516113i
\(550\) 19.1488 + 9.68119i 0.816506 + 0.412807i
\(551\) −0.881197 + 2.12740i −0.0375403 + 0.0906302i
\(552\) −16.3307 11.6316i −0.695080 0.495072i
\(553\) 1.48249 + 3.57904i 0.0630418 + 0.152196i
\(554\) 32.7247 + 2.47215i 1.39034 + 0.105032i
\(555\) 81.5499 + 16.2213i 3.46160 + 0.688555i
\(556\) 1.95946 + 42.9901i 0.0830996 + 1.82319i
\(557\) 19.6484 + 13.1287i 0.832531 + 0.556280i 0.897199 0.441627i \(-0.145599\pi\)
−0.0646672 + 0.997907i \(0.520599\pi\)
\(558\) 10.7346 + 19.0277i 0.454434 + 0.805508i
\(559\) 0.998673 0.998673i 0.0422393 0.0422393i
\(560\) 18.7083 + 23.1281i 0.790571 + 0.977340i
\(561\) −3.19459 3.19459i −0.134876 0.134876i
\(562\) −1.28806 + 4.62260i −0.0543334 + 0.194993i
\(563\) 10.2079 15.2772i 0.430212 0.643858i −0.551512 0.834167i \(-0.685949\pi\)
0.981724 + 0.190309i \(0.0609489\pi\)
\(564\) −4.74285 + 13.1089i −0.199710 + 0.551984i
\(565\) −2.94358 + 14.7984i −0.123837 + 0.622572i
\(566\) −13.2152 + 11.3588i −0.555478 + 0.477447i
\(567\) 17.6048 7.29216i 0.739333 0.306242i
\(568\) 13.1241 + 0.391911i 0.550675 + 0.0164442i
\(569\) 32.6965 + 13.5433i 1.37071 + 0.567765i 0.941980 0.335669i \(-0.108962\pi\)
0.428727 + 0.903434i \(0.358962\pi\)
\(570\) 13.4406 + 40.9282i 0.562964 + 1.71430i
\(571\) −9.13934 13.6780i −0.382470 0.572406i 0.589425 0.807823i \(-0.299354\pi\)
−0.971894 + 0.235417i \(0.924354\pi\)
\(572\) −0.571535 0.345321i −0.0238971 0.0144386i
\(573\) 46.2401 9.19773i 1.93171 0.384241i
\(574\) −0.120525 0.991631i −0.00503061 0.0413899i
\(575\) 39.2356 1.63624
\(576\) 7.70131 15.8455i 0.320888 0.660229i
\(577\) −11.7086 −0.487435 −0.243717 0.969846i \(-0.578367\pi\)
−0.243717 + 0.969846i \(0.578367\pi\)
\(578\) −2.43722 20.0525i −0.101375 0.834073i
\(579\) −43.9535 + 8.74290i −1.82665 + 0.363343i
\(580\) −3.14292 + 5.20180i −0.130503 + 0.215993i
\(581\) 11.7549 + 17.5925i 0.487677 + 0.729861i
\(582\) −9.35541 28.4884i −0.387794 1.18088i
\(583\) −10.4966 4.34785i −0.434726 0.180070i
\(584\) 7.56150 7.12299i 0.312897 0.294751i
\(585\) 2.37295 0.982908i 0.0981094 0.0406383i
\(586\) 14.6385 12.5821i 0.604709 0.519762i
\(587\) −6.29094 + 31.6267i −0.259655 + 1.30537i 0.602252 + 0.798306i \(0.294270\pi\)
−0.861906 + 0.507067i \(0.830730\pi\)
\(588\) 16.5660 + 5.99364i 0.683171 + 0.247174i
\(589\) −12.3978 + 18.5546i −0.510841 + 0.764527i
\(590\) −11.0538 + 39.6701i −0.455079 + 1.63319i
\(591\) 33.0715 + 33.0715i 1.36038 + 1.36038i
\(592\) 16.5900 30.5160i 0.681843 1.25420i
\(593\) −25.2454 + 25.2454i −1.03670 + 1.03670i −0.0374032 + 0.999300i \(0.511909\pi\)
−0.999300 + 0.0374032i \(0.988091\pi\)
\(594\) −1.51957 2.69351i −0.0623485 0.110516i
\(595\) 10.1914 + 6.80967i 0.417806 + 0.279169i
\(596\) −17.5497 + 0.799903i −0.718863 + 0.0327653i
\(597\) −3.04087 0.604867i −0.124455 0.0247556i
\(598\) −1.21757 0.0919804i −0.0497902 0.00376136i
\(599\) 1.52504 + 3.68178i 0.0623115 + 0.150433i 0.951968 0.306196i \(-0.0990564\pi\)
−0.889657 + 0.456630i \(0.849056\pi\)
\(600\) 13.4975 + 80.3170i 0.551031 + 3.27893i
\(601\) 11.5852 27.9691i 0.472570 1.14088i −0.490454 0.871467i \(-0.663169\pi\)
0.963024 0.269417i \(-0.0868310\pi\)
\(602\) −11.3660 5.74638i −0.463242 0.234205i
\(603\) 13.3433 8.91573i 0.543382 0.363077i
\(604\) −10.9003 14.8066i −0.443528 0.602474i
\(605\) −7.82626 39.3453i −0.318183 1.59961i
\(606\) 16.2229 20.7121i 0.659011 0.841371i
\(607\) 40.9668i 1.66279i 0.555680 + 0.831396i \(0.312458\pi\)
−0.555680 + 0.831396i \(0.687542\pi\)
\(608\) 17.9935 0.282427i 0.729731 0.0114539i
\(609\) 2.92460i 0.118511i
\(610\) −46.1974 36.1846i −1.87048 1.46507i
\(611\) 0.165630 + 0.832680i 0.00670069 + 0.0336866i
\(612\) 1.09056 7.17686i 0.0440834 0.290107i
\(613\) 13.2362 8.84413i 0.534604 0.357211i −0.258776 0.965937i \(-0.583319\pi\)
0.793380 + 0.608726i \(0.208319\pi\)
\(614\) 16.3671 32.3730i 0.660521 1.30647i
\(615\) 1.46111 3.52742i 0.0589175 0.142239i
\(616\) −1.35052 + 5.86822i −0.0544140 + 0.236437i
\(617\) −9.10950 21.9923i −0.366735 0.885376i −0.994281 0.106796i \(-0.965941\pi\)
0.627546 0.778579i \(-0.284059\pi\)
\(618\) −1.50811 + 19.9633i −0.0606652 + 0.803043i
\(619\) −44.5733 8.86617i −1.79155 0.356362i −0.816328 0.577589i \(-0.803994\pi\)
−0.975222 + 0.221227i \(0.928994\pi\)
\(620\) −39.7076 + 43.5002i −1.59470 + 1.74701i
\(621\) −4.70197 3.14176i −0.188684 0.126074i
\(622\) −10.9054 + 6.15236i −0.437266 + 0.246687i
\(623\) −12.4853 + 12.4853i −0.500213 + 0.500213i
\(624\) −0.230570 2.52407i −0.00923018 0.101044i
\(625\) −50.3856 50.3856i −2.01542 2.01542i
\(626\) 4.65156 + 1.29613i 0.185914 + 0.0518036i
\(627\) −4.84468 + 7.25058i −0.193478 + 0.289560i
\(628\) −4.45881 9.51435i −0.177926 0.379664i
\(629\) 2.79209 14.0368i 0.111328 0.559683i
\(630\) −15.0975 17.5649i −0.601497 0.699803i
\(631\) −5.81286 + 2.40776i −0.231406 + 0.0958516i −0.495374 0.868680i \(-0.664969\pi\)
0.263967 + 0.964532i \(0.414969\pi\)
\(632\) 5.64134 + 2.53655i 0.224400 + 0.100899i
\(633\) −23.4313 9.70558i −0.931312 0.385762i
\(634\) 23.4984 7.71672i 0.933240 0.306470i
\(635\) −14.6325 21.8991i −0.580674 0.869040i
\(636\) −10.3302 41.8687i −0.409620 1.66020i
\(637\) 1.05228 0.209311i 0.0416927 0.00829320i
\(638\) −1.22126 + 0.148434i −0.0483502 + 0.00587658i
\(639\) −10.2231 −0.404419
\(640\) 47.0639 + 6.39763i 1.86036 + 0.252889i
\(641\) 5.83590 0.230504 0.115252 0.993336i \(-0.463232\pi\)
0.115252 + 0.993336i \(0.463232\pi\)
\(642\) 59.2082 7.19628i 2.33676 0.284014i
\(643\) −44.3564 + 8.82303i −1.74924 + 0.347946i −0.962903 0.269846i \(-0.913027\pi\)
−0.786341 + 0.617793i \(0.788027\pi\)
\(644\) 2.63762 + 10.6904i 0.103937 + 0.421260i
\(645\) −27.0446 40.4751i −1.06488 1.59370i
\(646\) 7.04477 2.31346i 0.277173 0.0910218i
\(647\) −39.4132 16.3255i −1.54949 0.641820i −0.566267 0.824222i \(-0.691613\pi\)
−0.983224 + 0.182402i \(0.941613\pi\)
\(648\) 12.4770 27.7490i 0.490142 1.09008i
\(649\) −7.70159 + 3.19010i −0.302314 + 0.125222i
\(650\) 3.23308 + 3.76147i 0.126812 + 0.147537i
\(651\) 5.52933 27.7978i 0.216711 1.08948i
\(652\) −15.4305 32.9261i −0.604305 1.28949i
\(653\) 9.71620 14.5413i 0.380224 0.569046i −0.591161 0.806553i \(-0.701330\pi\)
0.971386 + 0.237507i \(0.0763304\pi\)
\(654\) −18.5963 5.18173i −0.727172 0.202622i
\(655\) −45.2608 45.2608i −1.76848 1.76848i
\(656\) −1.22572 1.02053i −0.0478565 0.0398451i
\(657\) −5.71928 + 5.71928i −0.223130 + 0.223130i
\(658\) 6.66801 3.76181i 0.259946 0.146651i
\(659\) 15.4630 + 10.3321i 0.602354 + 0.402480i 0.819019 0.573766i \(-0.194518\pi\)
−0.216665 + 0.976246i \(0.569518\pi\)
\(660\) −15.5166 + 16.9986i −0.603982 + 0.661669i
\(661\) 35.0453 + 6.97094i 1.36310 + 0.271138i 0.821842 0.569715i \(-0.192947\pi\)
0.541262 + 0.840854i \(0.317947\pi\)
\(662\) −1.58707 + 21.0085i −0.0616832 + 0.816519i
\(663\) −0.399653 0.964847i −0.0155212 0.0374716i
\(664\) 32.9222 + 7.57676i 1.27763 + 0.294035i
\(665\) 9.05362 21.8574i 0.351084 0.847593i
\(666\) −12.2021 + 24.1350i −0.472823 + 0.935213i
\(667\) −1.87047 + 1.24981i −0.0724250 + 0.0483928i
\(668\) −5.82803 + 38.3536i −0.225493 + 1.48394i
\(669\) 0.177511 + 0.892410i 0.00686299 + 0.0345026i
\(670\) 34.0599 + 26.6778i 1.31585 + 1.03065i
\(671\) 11.8786i 0.458569i
\(672\) −20.9763 + 9.07695i −0.809180 + 0.350151i
\(673\) 36.6129i 1.41132i 0.708549 + 0.705662i \(0.249350\pi\)
−0.708549 + 0.705662i \(0.750650\pi\)
\(674\) 5.89819 7.53031i 0.227190 0.290057i
\(675\) 4.48146 + 22.5298i 0.172492 + 0.867174i
\(676\) 15.3227 + 20.8138i 0.589333 + 0.800530i
\(677\) 10.2445 6.84516i 0.393728 0.263081i −0.342909 0.939368i \(-0.611412\pi\)
0.736638 + 0.676288i \(0.236412\pi\)
\(678\) −10.3458 5.23061i −0.397328 0.200880i
\(679\) −6.30184 + 15.2140i −0.241843 + 0.583859i
\(680\) 19.2998 3.24338i 0.740115 0.124378i
\(681\) 10.3742 + 25.0456i 0.397542 + 0.959751i
\(682\) −11.8885 0.898108i −0.455235 0.0343903i
\(683\) 32.2106 + 6.40709i 1.23251 + 0.245161i 0.768023 0.640422i \(-0.221241\pi\)
0.464482 + 0.885583i \(0.346241\pi\)
\(684\) −13.9971 + 0.637977i −0.535191 + 0.0243936i
\(685\) −12.7780 8.53800i −0.488223 0.326220i
\(686\) −13.3706 23.7001i −0.510492 0.904874i
\(687\) 11.3919 11.3919i 0.434630 0.434630i
\(688\) −19.5008 + 5.76508i −0.743462 + 0.219792i
\(689\) −1.85709 1.85709i −0.0707495 0.0707495i
\(690\) −11.2965 + 40.5412i −0.430052 + 1.54338i
\(691\) −12.8884 + 19.2889i −0.490299 + 0.733785i −0.991294 0.131666i \(-0.957967\pi\)
0.500995 + 0.865450i \(0.332967\pi\)
\(692\) 9.53361 + 3.44930i 0.362414 + 0.131123i
\(693\) 0.914678 4.59840i 0.0347457 0.174679i
\(694\) −11.8020 + 10.1441i −0.447997 + 0.385064i
\(695\) 83.4571 34.5690i 3.16571 1.31128i
\(696\) −3.20188 3.39900i −0.121367 0.128839i
\(697\) −0.607158 0.251493i −0.0229977 0.00952598i
\(698\) −8.76619 26.6942i −0.331805 1.01039i
\(699\) 8.71084 + 13.0367i 0.329474 + 0.493093i
\(700\) 23.1302 38.2825i 0.874241 1.44694i
\(701\) 7.52527 1.49687i 0.284226 0.0565360i −0.0509187 0.998703i \(-0.516215\pi\)
0.335144 + 0.942167i \(0.391215\pi\)
\(702\) −0.0862535 0.709660i −0.00325543 0.0267844i
\(703\) −27.6242 −1.04186
\(704\) 4.85501 + 8.29867i 0.182980 + 0.312768i
\(705\) 29.2622 1.10208
\(706\) 3.87607 + 31.8908i 0.145878 + 1.20023i
\(707\) −14.1711 + 2.81880i −0.532957 + 0.106012i
\(708\) −27.0818 16.3628i −1.01780 0.614950i
\(709\) 10.0146 + 14.9879i 0.376106 + 0.562883i 0.970442 0.241334i \(-0.0775850\pi\)
−0.594336 + 0.804217i \(0.702585\pi\)
\(710\) −8.59899 26.1850i −0.322714 0.982706i
\(711\) −4.44938 1.84299i −0.166865 0.0691177i
\(712\) −0.841496 + 28.1796i −0.0315364 + 1.05607i
\(713\) −20.1415 + 8.34287i −0.754304 + 0.312443i
\(714\) −7.14194 + 6.13867i −0.267280 + 0.229734i
\(715\) −0.273453 + 1.37474i −0.0102266 + 0.0514124i
\(716\) 11.7219 32.3984i 0.438067 1.21079i
\(717\) −3.91614 + 5.86092i −0.146251 + 0.218880i
\(718\) −13.8933 + 49.8607i −0.518495 + 1.86078i
\(719\) 10.5187 + 10.5187i 0.392280 + 0.392280i 0.875499 0.483219i \(-0.160533\pi\)
−0.483219 + 0.875499i \(0.660533\pi\)
\(720\) −36.7767 3.88525i −1.37059 0.144795i
\(721\) 7.77454 7.77454i 0.289539 0.289539i
\(722\) 6.17048 + 10.9375i 0.229641 + 0.407052i
\(723\) −24.4472 16.3351i −0.909201 0.607508i
\(724\) −0.996649 21.8662i −0.0370402 0.812653i
\(725\) 8.96250 + 1.78275i 0.332859 + 0.0662097i
\(726\) 30.7351 + 2.32185i 1.14069 + 0.0861720i
\(727\) 12.9735 + 31.3209i 0.481162 + 1.16163i 0.959058 + 0.283211i \(0.0913996\pi\)
−0.477896 + 0.878416i \(0.658600\pi\)
\(728\) −0.807532 + 1.13377i −0.0299291 + 0.0420204i
\(729\) −4.30086 + 10.3832i −0.159291 + 0.384563i
\(730\) −19.4598 9.83845i −0.720240 0.364138i
\(731\) −6.96677 + 4.65505i −0.257675 + 0.172173i
\(732\) 36.3092 26.7300i 1.34203 0.987971i
\(733\) −4.66780 23.4666i −0.172409 0.866759i −0.966047 0.258368i \(-0.916815\pi\)
0.793637 0.608391i \(-0.208185\pi\)
\(734\) −13.1211 + 16.7519i −0.484308 + 0.618324i
\(735\) 36.9793i 1.36400i
\(736\) 14.7694 + 9.53678i 0.544408 + 0.351530i
\(737\) 8.75773i 0.322595i
\(738\) 0.977651 + 0.765754i 0.0359878 + 0.0281878i
\(739\) 4.30057 + 21.6204i 0.158199 + 0.795320i 0.975652 + 0.219325i \(0.0703854\pi\)
−0.817453 + 0.575996i \(0.804615\pi\)
\(740\) −72.0821 10.9533i −2.64979 0.402650i
\(741\) −1.67604 + 1.11990i −0.0615710 + 0.0411404i
\(742\) −10.6857 + 21.1357i −0.392285 + 0.775914i
\(743\) −1.75751 + 4.24301i −0.0644769 + 0.155661i −0.952834 0.303493i \(-0.901847\pi\)
0.888357 + 0.459154i \(0.151847\pi\)
\(744\) −24.0071 38.3605i −0.880144 1.40636i
\(745\) 14.1120 + 34.0694i 0.517024 + 1.24821i
\(746\) −0.517113 + 6.84518i −0.0189328 + 0.250620i
\(747\) −25.7982 5.13158i −0.943906 0.187755i
\(748\) 2.92588 + 2.67079i 0.106981 + 0.0976537i
\(749\) −27.2354 18.1981i −0.995158 0.664944i
\(750\) 89.9246 50.7317i 3.28358 1.85246i
\(751\) 25.9585 25.9585i 0.947238 0.947238i −0.0514384 0.998676i \(-0.516381\pi\)
0.998676 + 0.0514384i \(0.0163806\pi\)
\(752\) 3.63116 11.6722i 0.132415 0.425643i
\(753\) 31.7049 + 31.7049i 1.15539 + 1.15539i
\(754\) −0.273948 0.0763339i −0.00997661 0.00277992i
\(755\) −21.4418 + 32.0899i −0.780346 + 1.16787i
\(756\) −5.83737 + 2.73563i −0.212303 + 0.0994938i
\(757\) −1.73528 + 8.72382i −0.0630697 + 0.317073i −0.999422 0.0339884i \(-0.989179\pi\)
0.936353 + 0.351061i \(0.114179\pi\)
\(758\) 7.12596 + 8.29059i 0.258826 + 0.301128i
\(759\) −7.87069 + 3.26015i −0.285688 + 0.118336i
\(760\) −13.4075 35.3149i −0.486341 1.28101i
\(761\) 27.8964 + 11.5551i 1.01124 + 0.418871i 0.825909 0.563804i \(-0.190663\pi\)
0.185336 + 0.982675i \(0.440663\pi\)
\(762\) 19.2262 6.31375i 0.696491 0.228723i
\(763\) 5.89011 + 8.81517i 0.213236 + 0.319130i
\(764\) −40.1372 + 9.90301i −1.45211 + 0.358278i
\(765\) −14.9449 + 2.97273i −0.540336 + 0.107479i
\(766\) 18.6188 2.26296i 0.672724 0.0817642i
\(767\) −1.92698 −0.0695793
\(768\) −14.4414 + 33.5145i −0.521108 + 1.20935i
\(769\) 17.7614 0.640492 0.320246 0.947334i \(-0.396234\pi\)
0.320246 + 0.947334i \(0.396234\pi\)
\(770\) 12.5475 1.52505i 0.452181 0.0549590i
\(771\) 36.2542 7.21140i 1.30566 0.259712i
\(772\) 38.1525 9.41331i 1.37314 0.338792i
\(773\) 18.1617 + 27.1809i 0.653230 + 0.977627i 0.999224 + 0.0393906i \(0.0125417\pi\)
−0.345994 + 0.938237i \(0.612458\pi\)
\(774\) 15.0428 4.93995i 0.540701 0.177563i
\(775\) 81.8166 + 33.8895i 2.93894 + 1.21735i
\(776\) 9.33238 + 24.5812i 0.335013 + 0.882413i
\(777\) 32.4143 13.4264i 1.16286 0.481671i
\(778\) −11.8016 13.7304i −0.423107 0.492258i
\(779\) −0.247467 + 1.24410i −0.00886643 + 0.0445746i
\(780\) −4.81750 + 2.25767i −0.172494 + 0.0808377i
\(781\) 3.09952 4.63876i 0.110910 0.165988i
\(782\) 6.97815 + 1.94442i 0.249538 + 0.0695322i
\(783\) −0.931310 0.931310i −0.0332823 0.0332823i
\(784\) −14.7505 4.58878i −0.526802 0.163885i
\(785\) −15.5957 + 15.5957i −0.556636 + 0.556636i
\(786\) 42.8337 24.1649i 1.52783 0.861935i
\(787\) 20.5749 + 13.7477i 0.733416 + 0.490053i 0.865326 0.501209i \(-0.167111\pi\)
−0.131911 + 0.991262i \(0.542111\pi\)
\(788\) −30.2897 27.6489i −1.07903 0.984951i
\(789\) −54.8987 10.9200i −1.95445 0.388763i
\(790\) 0.978045 12.9467i 0.0347973 0.460622i
\(791\) 2.43642 + 5.88203i 0.0866290 + 0.209141i
\(792\) −3.97133 6.34570i −0.141115 0.225485i
\(793\) 1.05080 2.53684i 0.0373148 0.0900860i
\(794\) −25.0063 + 49.4607i −0.887439 + 1.75530i
\(795\) −75.2657 + 50.2909i −2.66940 + 1.78364i
\(796\) 2.68783 + 0.408430i 0.0952677 + 0.0144764i
\(797\) 0.0956446 + 0.480838i 0.00338791 + 0.0170322i 0.982442 0.186567i \(-0.0597361\pi\)
−0.979054 + 0.203599i \(0.934736\pi\)
\(798\) 14.3104 + 11.2087i 0.506581 + 0.396784i
\(799\) 5.03676i 0.178188i
\(800\) −15.0299 69.8156i −0.531389 2.46835i
\(801\) 21.9506i 0.775587i
\(802\) −2.21863 + 2.83256i −0.0783424 + 0.100021i
\(803\) −0.861124 4.32916i −0.0303884 0.152773i
\(804\) −26.7696 + 19.7072i −0.944093 + 0.695021i
\(805\) 19.2177 12.8408i 0.677334 0.452580i
\(806\) −2.45951 1.24348i −0.0866327 0.0437996i
\(807\) −0.599279 + 1.44679i −0.0210956 + 0.0509294i
\(808\) −13.3837 + 18.7907i −0.470837 + 0.661053i
\(809\) −20.2707 48.9378i −0.712680 1.72056i −0.693193 0.720752i \(-0.743797\pi\)
−0.0194867 0.999810i \(-0.506203\pi\)
\(810\) −63.6830 4.81087i −2.23759 0.169037i
\(811\) −1.17029 0.232786i −0.0410945 0.00817421i 0.174500 0.984657i \(-0.444169\pi\)
−0.215595 + 0.976483i \(0.569169\pi\)
\(812\) 0.116767 + 2.56183i 0.00409770 + 0.0899026i
\(813\) −26.8706 17.9544i −0.942394 0.629687i
\(814\) −7.25180 12.8542i −0.254176 0.450540i
\(815\) −53.9718 + 53.9718i −1.89055 + 1.89055i
\(816\) −1.57975 + 14.9535i −0.0553024 + 0.523477i
\(817\) 11.4358 + 11.4358i 0.400087 + 0.400087i
\(818\) 2.62347 9.41516i 0.0917276 0.329193i
\(819\) 0.602122 0.901139i 0.0210398 0.0314883i
\(820\) −1.13904 + 3.14822i −0.0397769 + 0.109941i
\(821\) 5.87139 29.5175i 0.204913 1.03017i −0.732187 0.681104i \(-0.761500\pi\)
0.937099 0.349062i \(-0.113500\pi\)
\(822\) 8.95460 7.69669i 0.312328 0.268453i
\(823\) −28.7325 + 11.9014i −1.00155 + 0.414857i −0.822366 0.568958i \(-0.807347\pi\)
−0.179187 + 0.983815i \(0.557347\pi\)
\(824\) 0.523996 17.5473i 0.0182543 0.611289i
\(825\) 31.9715 + 13.2430i 1.11311 + 0.461063i
\(826\) 5.42162 + 16.5095i 0.188642 + 0.574439i
\(827\) −2.10263 3.14680i −0.0731155 0.109425i 0.793110 0.609079i \(-0.208461\pi\)
−0.866225 + 0.499654i \(0.833461\pi\)
\(828\) −11.7161 7.07886i −0.407163 0.246007i
\(829\) 25.7896 5.12986i 0.895709 0.178168i 0.274291 0.961647i \(-0.411557\pi\)
0.621418 + 0.783479i \(0.286557\pi\)
\(830\) −8.55591 70.3948i −0.296980 2.44344i
\(831\) 52.9287 1.83607
\(832\) 0.302745 + 2.20178i 0.0104958 + 0.0763329i
\(833\) −6.36507 −0.220536
\(834\) 8.37415 + 68.8993i 0.289973 + 2.38579i
\(835\) 79.8666 15.8865i 2.76390 0.549774i
\(836\) 3.95426 6.54464i 0.136761 0.226351i
\(837\) −7.09119 10.6127i −0.245107 0.366829i
\(838\) 2.53781 + 7.72796i 0.0876673 + 0.266958i
\(839\) 21.7694 + 9.01718i 0.751563 + 0.311308i 0.725379 0.688349i \(-0.241664\pi\)
0.0261841 + 0.999657i \(0.491664\pi\)
\(840\) 32.8969 + 34.9221i 1.13505 + 1.20493i
\(841\) 26.3085 10.8973i 0.907188 0.375770i
\(842\) −28.3621 + 24.3779i −0.977424 + 0.840119i
\(843\) −1.50987 + 7.59062i −0.0520026 + 0.261435i
\(844\) 20.9124 + 7.56619i 0.719835 + 0.260439i
\(845\) 30.1408 45.1089i 1.03688 1.55179i
\(846\) −2.55473 + 9.16844i −0.0878333 + 0.315217i
\(847\) −11.9695 11.9695i −0.411276 0.411276i
\(848\) 10.7205 + 36.2629i 0.368143 + 1.24527i
\(849\) −19.8730 + 19.8730i −0.682038 + 0.682038i
\(850\) −14.4586 25.6286i −0.495925 0.879054i
\(851\) −22.4392 14.9934i −0.769205 0.513966i
\(852\) 21.1540 0.964186i 0.724724 0.0330325i
\(853\) −13.0606 2.59791i −0.447186 0.0889509i −0.0336401 0.999434i \(-0.510710\pi\)
−0.413546 + 0.910483i \(0.635710\pi\)
\(854\) −24.6910 1.86526i −0.844907 0.0638277i
\(855\) 11.2553 + 27.1726i 0.384922 + 0.929284i
\(856\) −51.5767 + 8.66758i −1.76285 + 0.296252i
\(857\) −13.3651 + 32.2661i −0.456542 + 1.10219i 0.513246 + 0.858241i \(0.328443\pi\)
−0.969788 + 0.243948i \(0.921557\pi\)
\(858\) −0.961106 0.485914i −0.0328116 0.0165888i
\(859\) 3.86744 2.58414i 0.131955 0.0881697i −0.487841 0.872933i \(-0.662215\pi\)
0.619796 + 0.784763i \(0.287215\pi\)
\(860\) 25.3060 + 34.3748i 0.862926 + 1.17217i
\(861\) −0.314304 1.58011i −0.0107115 0.0538501i
\(862\) 6.98880 8.92272i 0.238040 0.303909i
\(863\) 9.50850i 0.323673i −0.986818 0.161837i \(-0.948258\pi\)
0.986818 0.161837i \(-0.0517418\pi\)
\(864\) −3.78925 + 9.57019i −0.128913 + 0.325584i
\(865\) 21.2813i 0.723587i
\(866\) 14.8486 + 11.6303i 0.504574 + 0.395213i
\(867\) −6.35577 31.9526i −0.215853 1.08517i
\(868\) −3.73362 + 24.5705i −0.126727 + 0.833978i
\(869\) 2.18527 1.46015i 0.0741301 0.0495322i
\(870\) −4.42252 + 8.74745i −0.149937 + 0.296566i
\(871\) −0.774719 + 1.87034i −0.0262504 + 0.0633740i
\(872\) 16.4965 + 3.79652i 0.558641 + 0.128566i
\(873\) −7.83431 18.9137i −0.265151 0.640132i
\(874\) 1.05327 13.9424i 0.0356272 0.471609i
\(875\) −55.6130 11.0621i −1.88006 0.373968i
\(876\) 11.2951 12.3740i 0.381627 0.418077i
\(877\) −16.1414 10.7854i −0.545058 0.364196i 0.252351 0.967636i \(-0.418796\pi\)
−0.797408 + 0.603440i \(0.793796\pi\)
\(878\) 25.3452 14.2987i 0.855360 0.482558i
\(879\) 22.0132 22.0132i 0.742486 0.742486i
\(880\) 12.9132 15.5096i 0.435304 0.522828i
\(881\) 18.1256 + 18.1256i 0.610667 + 0.610667i 0.943120 0.332453i \(-0.107876\pi\)
−0.332453 + 0.943120i \(0.607876\pi\)
\(882\) 11.5864 + 3.22846i 0.390133 + 0.108708i
\(883\) 25.2429 37.7787i 0.849491 1.27135i −0.111218 0.993796i \(-0.535475\pi\)
0.960709 0.277557i \(-0.0895249\pi\)
\(884\) 0.388602 + 0.829211i 0.0130701 + 0.0278894i
\(885\) −12.9574 + 65.1411i −0.435557 + 2.18969i
\(886\) −16.3623 19.0364i −0.549701 0.639541i
\(887\) −36.7160 + 15.2083i −1.23280 + 0.510644i −0.901458 0.432866i \(-0.857502\pi\)
−0.331345 + 0.943510i \(0.607502\pi\)
\(888\) 22.9728 51.0919i 0.770917 1.71453i
\(889\) −10.2676 4.25297i −0.344363 0.142640i
\(890\) 56.2235 18.4634i 1.88462 0.618896i
\(891\) −7.18228 10.7490i −0.240615 0.360106i
\(892\) −0.191123 0.774628i −0.00639927 0.0259365i
\(893\) −9.53500 + 1.89663i −0.319077 + 0.0634683i
\(894\) −28.1265 + 3.41855i −0.940691 + 0.114333i
\(895\) −72.3211 −2.41743
\(896\) 18.0120 8.78854i 0.601740 0.293604i
\(897\) −1.96929 −0.0657528
\(898\) −18.0534 + 2.19424i −0.602449 + 0.0732228i
\(899\) −4.97995 + 0.990574i −0.166091 + 0.0330375i
\(900\) 13.3198 + 53.9855i 0.443992 + 1.79952i
\(901\) 8.65633 + 12.9551i 0.288384 + 0.431597i
\(902\) −0.643876 + 0.211445i −0.0214387 + 0.00704034i
\(903\) −18.9770 7.86055i −0.631517 0.261583i
\(904\) 9.27134 + 4.16874i 0.308360 + 0.138650i
\(905\) −42.4491 + 17.5830i −1.41106 + 0.584479i
\(906\) −19.3290 22.4880i −0.642162 0.747113i
\(907\) 5.87925 29.5570i 0.195217 0.981424i −0.751592 0.659628i \(-0.770714\pi\)
0.946809 0.321796i \(-0.104286\pi\)
\(908\) −10.0874 21.5248i −0.334762 0.714325i
\(909\) 9.97931 14.9351i 0.330993 0.495366i
\(910\) 2.81461 + 0.784272i 0.0933033 + 0.0259984i
\(911\) 16.2630 + 16.2630i 0.538818 + 0.538818i 0.923182 0.384364i \(-0.125579\pi\)
−0.384364 + 0.923182i \(0.625579\pi\)
\(912\) 28.9031 2.64025i 0.957076 0.0874274i
\(913\) 10.1502 10.1502i 0.335922 0.335922i
\(914\) −6.15383 + 3.47173i −0.203551 + 0.114835i
\(915\) −78.6915 52.5800i −2.60146 1.73824i
\(916\) −9.52405 + 10.4337i −0.314684 + 0.344740i
\(917\) −26.4901 5.26920i −0.874779 0.174004i
\(918\) −0.319482 + 4.22908i −0.0105445 + 0.139580i
\(919\) −6.05005 14.6061i −0.199573 0.481811i 0.792132 0.610350i \(-0.208971\pi\)
−0.991704 + 0.128539i \(0.958971\pi\)
\(920\) 8.27668 35.9635i 0.272874 1.18568i
\(921\) 22.3887 54.0512i 0.737734 1.78105i
\(922\) 18.9289 37.4402i 0.623391 1.23303i
\(923\) 1.07230 0.716486i 0.0352951 0.0235834i
\(924\) −1.45899 + 9.60144i −0.0479973 + 0.315864i
\(925\) 21.3868 + 107.519i 0.703195 + 3.53520i
\(926\) −22.3816 17.5306i −0.735506 0.576092i
\(927\) 13.6686i 0.448935i
\(928\) 2.94043 + 2.84955i 0.0965243 + 0.0935410i
\(929\) 15.1489i 0.497021i −0.968629 0.248510i \(-0.920059\pi\)
0.968629 0.248510i \(-0.0799410\pi\)
\(930\) −58.5735 + 74.7818i −1.92070 + 2.45219i
\(931\) 2.39681 + 12.0496i 0.0785524 + 0.394910i
\(932\) −8.15085 11.0718i −0.266990 0.362670i
\(933\) −16.7908 + 11.2192i −0.549705 + 0.367301i
\(934\) −14.7639 7.46431i −0.483090 0.244240i
\(935\) 3.18225 7.68262i 0.104071 0.251249i
\(936\) −0.286785 1.70652i −0.00937386 0.0557794i
\(937\) −16.5832 40.0355i −0.541751 1.30790i −0.923487 0.383630i \(-0.874674\pi\)
0.381736 0.924271i \(-0.375326\pi\)
\(938\) 18.2039 + 1.37520i 0.594378 + 0.0449017i
\(939\) 7.63818 + 1.51933i 0.249262 + 0.0495814i
\(940\) −25.6325 + 1.16831i −0.836041 + 0.0381062i
\(941\) 47.9669 + 32.0505i 1.56368 + 1.04481i 0.970911 + 0.239439i \(0.0769636\pi\)
0.592765 + 0.805376i \(0.298036\pi\)
\(942\) −8.32664 14.7594i −0.271297 0.480888i
\(943\) −0.876271 + 0.876271i −0.0285353 + 0.0285353i
\(944\) 24.3758 + 13.2519i 0.793366 + 0.431312i
\(945\) 9.56849 + 9.56849i 0.311263 + 0.311263i
\(946\) −2.31927 + 8.32344i −0.0754061 + 0.270618i
\(947\) −4.70450 + 7.04078i −0.152876 + 0.228794i −0.900000 0.435890i \(-0.856434\pi\)
0.747125 + 0.664684i \(0.231434\pi\)
\(948\) 9.38065 + 3.39395i 0.304669 + 0.110230i
\(949\) 0.199058 1.00073i 0.00646168 0.0324851i
\(950\) −43.0726 + 37.0219i −1.39746 + 1.20115i
\(951\) 36.8530 15.2650i 1.19504 0.495001i
\(952\) 6.01096 5.66237i 0.194816 0.183519i
\(953\) −19.9974 8.28320i −0.647780 0.268319i 0.0345063 0.999404i \(-0.489014\pi\)
−0.682286 + 0.731085i \(0.739014\pi\)
\(954\) −9.18611 27.9729i −0.297411 0.905655i
\(955\) 48.2111 + 72.1531i 1.56008 + 2.33482i
\(956\) 3.19638 5.29029i 0.103378 0.171100i
\(957\) −1.94602 + 0.387087i −0.0629058 + 0.0125127i
\(958\) 5.68565 + 46.7793i 0.183695 + 1.51137i
\(959\) −6.48469 −0.209402
\(960\) 76.4661 + 4.57093i 2.46793 + 0.147526i
\(961\) −18.2064 −0.587304
\(962\) −0.411626 3.38670i −0.0132714 0.109192i
\(963\) 39.9387 7.94430i 1.28701 0.256002i
\(964\) 22.0669 + 13.3328i 0.710729 + 0.429421i
\(965\) −45.8271 68.5851i −1.47523 2.20783i
\(966\) 5.54066 + 16.8720i 0.178268 + 0.542848i
\(967\) −4.47791 1.85481i −0.144000 0.0596467i 0.309520 0.950893i \(-0.399832\pi\)
−0.453519 + 0.891246i \(0.649832\pi\)
\(968\) −27.0154 0.806731i −0.868307 0.0259293i
\(969\) 11.0484 4.57642i 0.354927 0.147016i
\(970\) 41.8551 35.9755i 1.34389 1.15510i
\(971\) 9.90954 49.8186i 0.318012 1.59876i −0.409268 0.912414i \(-0.634216\pi\)
0.727280 0.686341i \(-0.240784\pi\)
\(972\) 12.9801 35.8760i 0.416336 1.15072i
\(973\) 21.1767 31.6932i 0.678895 1.01604i
\(974\) 8.77657 31.4975i 0.281219 1.00924i
\(975\) 5.65647 + 5.65647i 0.181152 + 0.181152i
\(976\) −30.7382 + 24.8641i −0.983905 + 0.795881i
\(977\) −26.9502 + 26.9502i −0.862215 + 0.862215i −0.991595 0.129380i \(-0.958701\pi\)
0.129380 + 0.991595i \(0.458701\pi\)
\(978\) −28.8158 51.0776i −0.921428 1.63328i
\(979\) 9.96018 + 6.65518i 0.318329 + 0.212700i
\(980\) 1.47642 + 32.3924i 0.0471627 + 1.03474i
\(981\) −12.9268 2.57130i −0.412721 0.0820953i
\(982\) 23.7128 + 1.79136i 0.756705 + 0.0571646i
\(983\) 5.35576 + 12.9300i 0.170822 + 0.412402i 0.985986 0.166829i \(-0.0533529\pi\)
−0.815163 + 0.579231i \(0.803353\pi\)
\(984\) −2.09521 1.49232i −0.0667930 0.0475734i
\(985\) −32.9436 + 79.5330i −1.04967 + 2.53413i
\(986\) 1.50566 + 0.761226i 0.0479498 + 0.0242424i
\(987\) 10.2666 6.85991i 0.326789 0.218353i
\(988\) 1.42343 1.04790i 0.0452855 0.0333382i
\(989\) 3.08239 + 15.4962i 0.0980144 + 0.492752i
\(990\) −9.68941 + 12.3706i −0.307950 + 0.393164i
\(991\) 45.6448i 1.44996i −0.688772 0.724978i \(-0.741850\pi\)
0.688772 0.724978i \(-0.258150\pi\)
\(992\) 22.5608 + 32.6437i 0.716307 + 1.03644i
\(993\) 33.9790i 1.07829i
\(994\) −9.15546 7.17110i −0.290394 0.227453i
\(995\) −1.11333 5.59708i −0.0352949 0.177439i
\(996\) 53.8665 + 8.18531i 1.70683 + 0.259361i
\(997\) 25.8151 17.2491i 0.817572 0.546284i −0.0750031 0.997183i \(-0.523897\pi\)
0.892575 + 0.450899i \(0.148897\pi\)
\(998\) 10.1366 20.0496i 0.320869 0.634659i
\(999\) 6.04651 14.5976i 0.191303 0.461846i
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 64.2.i.a.53.1 yes 56
3.2 odd 2 576.2.bd.a.181.7 56
4.3 odd 2 256.2.i.a.49.6 56
8.3 odd 2 512.2.i.a.353.2 56
8.5 even 2 512.2.i.b.353.6 56
64.3 odd 16 512.2.i.a.161.2 56
64.29 even 16 inner 64.2.i.a.29.1 56
64.35 odd 16 256.2.i.a.209.6 56
64.61 even 16 512.2.i.b.161.6 56
192.29 odd 16 576.2.bd.a.541.7 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
64.2.i.a.29.1 56 64.29 even 16 inner
64.2.i.a.53.1 yes 56 1.1 even 1 trivial
256.2.i.a.49.6 56 4.3 odd 2
256.2.i.a.209.6 56 64.35 odd 16
512.2.i.a.161.2 56 64.3 odd 16
512.2.i.a.353.2 56 8.3 odd 2
512.2.i.b.161.6 56 64.61 even 16
512.2.i.b.353.6 56 8.5 even 2
576.2.bd.a.181.7 56 3.2 odd 2
576.2.bd.a.541.7 56 192.29 odd 16