Properties

Label 304.2.bg.a.155.36
Level $304$
Weight $2$
Character 304.155
Analytic conductor $2.427$
Analytic rank $0$
Dimension $456$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [304,2,Mod(3,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 27, 26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.bg (of order \(36\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.42745222145\)
Analytic rank: \(0\)
Dimension: \(456\)
Relative dimension: \(38\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 155.36
Character \(\chi\) \(=\) 304.155
Dual form 304.2.bg.a.51.36

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.39630 + 0.224382i) q^{2} +(-1.37269 + 2.94375i) q^{3} +(1.89931 + 0.626609i) q^{4} +(1.97288 - 1.38143i) q^{5} +(-2.57722 + 3.80235i) q^{6} +(1.46995 + 2.54603i) q^{7} +(2.51140 + 1.30110i) q^{8} +(-4.85302 - 5.78360i) q^{9} +O(q^{10})\) \(q+(1.39630 + 0.224382i) q^{2} +(-1.37269 + 2.94375i) q^{3} +(1.89931 + 0.626609i) q^{4} +(1.97288 - 1.38143i) q^{5} +(-2.57722 + 3.80235i) q^{6} +(1.46995 + 2.54603i) q^{7} +(2.51140 + 1.30110i) q^{8} +(-4.85302 - 5.78360i) q^{9} +(3.06470 - 1.48621i) q^{10} +(-0.908546 - 3.39074i) q^{11} +(-4.45175 + 4.73094i) q^{12} +(0.958964 + 2.05651i) q^{13} +(1.48121 + 3.88485i) q^{14} +(1.35841 + 7.70395i) q^{15} +(3.21472 + 2.38024i) q^{16} +(-5.21968 - 4.37983i) q^{17} +(-5.47853 - 9.16458i) q^{18} +(-2.72076 + 3.40551i) q^{19} +(4.61272 - 1.38752i) q^{20} +(-9.51267 + 0.832251i) q^{21} +(-0.507781 - 4.93835i) q^{22} +(-0.997546 - 5.65736i) q^{23} +(-7.27751 + 5.60692i) q^{24} +(0.273821 - 0.752316i) q^{25} +(0.877558 + 3.08667i) q^{26} +(14.2750 - 3.82498i) q^{27} +(1.19652 + 5.75677i) q^{28} +(2.43725 + 0.213231i) q^{29} +(0.168125 + 11.0618i) q^{30} +(-0.381793 - 0.661284i) q^{31} +(3.95463 + 4.04486i) q^{32} +(11.2287 + 1.97991i) q^{33} +(-6.30548 - 7.28675i) q^{34} +(6.41719 + 2.99238i) q^{35} +(-5.59331 - 14.0258i) q^{36} +(5.50108 - 5.50108i) q^{37} +(-4.56313 + 4.14462i) q^{38} -7.37020 q^{39} +(6.75207 - 0.902389i) q^{40} +(0.138065 - 0.0502516i) q^{41} +(-13.4693 - 0.972401i) q^{42} +(2.92637 + 4.17928i) q^{43} +(0.399063 - 7.00936i) q^{44} +(-17.5641 - 4.70627i) q^{45} +(-0.123462 - 8.12321i) q^{46} +(-2.52575 - 3.01007i) q^{47} +(-11.4197 + 6.19599i) q^{48} +(-0.821508 + 1.42289i) q^{49} +(0.551142 - 0.989018i) q^{50} +(20.0581 - 9.35327i) q^{51} +(0.532741 + 4.50683i) q^{52} +(0.675331 + 0.472872i) q^{53} +(20.7905 - 2.13776i) q^{54} +(-6.47651 - 5.43444i) q^{55} +(0.378983 + 8.30665i) q^{56} +(-6.29020 - 12.6839i) q^{57} +(3.35528 + 0.844609i) q^{58} +(0.710079 + 8.11625i) q^{59} +(-2.24732 + 15.4833i) q^{60} +(4.22429 + 2.95788i) q^{61} +(-0.384717 - 1.00902i) q^{62} +(7.59152 - 20.8575i) q^{63} +(4.61425 + 6.53519i) q^{64} +(4.73283 + 2.73250i) q^{65} +(15.2343 + 5.28406i) q^{66} +(1.07866 - 12.3292i) q^{67} +(-7.16932 - 11.5893i) q^{68} +(18.0232 + 4.82930i) q^{69} +(8.28888 + 5.61817i) q^{70} +(-9.87473 - 1.74118i) q^{71} +(-4.66280 - 20.8392i) q^{72} +(1.98302 + 5.44830i) q^{73} +(8.91550 - 6.44681i) q^{74} +(1.83876 + 1.83876i) q^{75} +(-7.30147 + 4.76325i) q^{76} +(7.29741 - 7.29741i) q^{77} +(-10.2910 - 1.65374i) q^{78} +(-7.90454 + 2.87702i) q^{79} +(9.63040 + 0.255039i) q^{80} +(-4.40233 + 24.9669i) q^{81} +(0.204056 - 0.0391870i) q^{82} +(0.248315 - 0.926722i) q^{83} +(-18.5890 - 4.38003i) q^{84} +(-16.3482 - 1.43028i) q^{85} +(3.14833 + 6.49216i) q^{86} +(-3.97329 + 6.88195i) q^{87} +(2.12999 - 9.69762i) q^{88} +(-9.66380 - 3.51734i) q^{89} +(-23.4687 - 10.5124i) q^{90} +(-3.82629 + 5.46451i) q^{91} +(1.65031 - 11.3701i) q^{92} +(2.47074 - 0.216162i) q^{93} +(-2.85129 - 4.76969i) q^{94} +(-0.663270 + 10.4772i) q^{95} +(-17.3356 + 6.08909i) q^{96} +(1.67248 - 1.99318i) q^{97} +(-1.46634 + 1.80245i) q^{98} +(-15.2015 + 21.7100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8} - 42 q^{10} - 6 q^{11} - 18 q^{12} - 12 q^{13} - 24 q^{16} - 24 q^{17} - 12 q^{19} - 24 q^{20} + 6 q^{21} - 12 q^{22} - 24 q^{23} - 12 q^{24} - 54 q^{26} - 18 q^{27} + 12 q^{28} - 12 q^{29} - 48 q^{30} + 18 q^{32} - 24 q^{33} + 48 q^{34} + 18 q^{35} - 60 q^{36} - 66 q^{38} - 48 q^{39} - 42 q^{40} + 144 q^{42} - 12 q^{43} + 54 q^{44} - 6 q^{45} - 108 q^{46} - 12 q^{48} - 168 q^{49} + 36 q^{50} + 12 q^{51} - 60 q^{52} - 12 q^{53} - 126 q^{54} - 24 q^{55} - 24 q^{58} - 12 q^{59} + 30 q^{60} - 12 q^{61} - 6 q^{64} - 36 q^{65} - 72 q^{66} - 12 q^{67} - 42 q^{68} + 126 q^{69} + 102 q^{70} - 24 q^{71} - 48 q^{72} + 72 q^{74} + 36 q^{76} + 60 q^{77} - 108 q^{78} + 48 q^{80} - 24 q^{81} - 72 q^{82} - 6 q^{83} - 18 q^{84} - 108 q^{85} - 12 q^{86} - 12 q^{87} - 18 q^{88} + 96 q^{90} + 30 q^{91} - 12 q^{92} + 6 q^{93} - 132 q^{96} - 24 q^{97} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39630 + 0.224382i 0.987333 + 0.158662i
\(3\) −1.37269 + 2.94375i −0.792525 + 1.69958i −0.0812157 + 0.996697i \(0.525880\pi\)
−0.711309 + 0.702879i \(0.751898\pi\)
\(4\) 1.89931 + 0.626609i 0.949653 + 0.313305i
\(5\) 1.97288 1.38143i 0.882299 0.617793i −0.0421443 0.999112i \(-0.513419\pi\)
0.924444 + 0.381319i \(0.124530\pi\)
\(6\) −2.57722 + 3.80235i −1.05214 + 1.55230i
\(7\) 1.46995 + 2.54603i 0.555589 + 0.962308i 0.997857 + 0.0654257i \(0.0208405\pi\)
−0.442268 + 0.896883i \(0.645826\pi\)
\(8\) 2.51140 + 1.30110i 0.887914 + 0.460010i
\(9\) −4.85302 5.78360i −1.61767 1.92787i
\(10\) 3.06470 1.48621i 0.969143 0.469980i
\(11\) −0.908546 3.39074i −0.273937 1.02235i −0.956550 0.291567i \(-0.905823\pi\)
0.682613 0.730780i \(-0.260843\pi\)
\(12\) −4.45175 + 4.73094i −1.28511 + 1.36570i
\(13\) 0.958964 + 2.05651i 0.265969 + 0.570372i 0.993253 0.115964i \(-0.0369957\pi\)
−0.727285 + 0.686336i \(0.759218\pi\)
\(14\) 1.48121 + 3.88485i 0.395869 + 1.03827i
\(15\) 1.35841 + 7.70395i 0.350741 + 1.98915i
\(16\) 3.21472 + 2.38024i 0.803680 + 0.595061i
\(17\) −5.21968 4.37983i −1.26596 1.06226i −0.995021 0.0996672i \(-0.968222\pi\)
−0.270937 0.962597i \(-0.587333\pi\)
\(18\) −5.47853 9.16458i −1.29130 2.16011i
\(19\) −2.72076 + 3.40551i −0.624184 + 0.781277i
\(20\) 4.61272 1.38752i 1.03144 0.310260i
\(21\) −9.51267 + 0.832251i −2.07583 + 0.181612i
\(22\) −0.507781 4.93835i −0.108259 1.05286i
\(23\) −0.997546 5.65736i −0.208003 1.17964i −0.892644 0.450762i \(-0.851152\pi\)
0.684642 0.728880i \(-0.259959\pi\)
\(24\) −7.27751 + 5.60692i −1.48552 + 1.14451i
\(25\) 0.273821 0.752316i 0.0547641 0.150463i
\(26\) 0.877558 + 3.08667i 0.172103 + 0.605346i
\(27\) 14.2750 3.82498i 2.74723 0.736118i
\(28\) 1.19652 + 5.75677i 0.226121 + 1.08793i
\(29\) 2.43725 + 0.213231i 0.452585 + 0.0395961i 0.311170 0.950354i \(-0.399279\pi\)
0.141415 + 0.989950i \(0.454835\pi\)
\(30\) 0.168125 + 11.0618i 0.0306953 + 2.01960i
\(31\) −0.381793 0.661284i −0.0685720 0.118770i 0.829701 0.558208i \(-0.188511\pi\)
−0.898273 + 0.439438i \(0.855178\pi\)
\(32\) 3.95463 + 4.04486i 0.699087 + 0.715037i
\(33\) 11.2287 + 1.97991i 1.95466 + 0.344659i
\(34\) −6.30548 7.28675i −1.08138 1.24967i
\(35\) 6.41719 + 2.99238i 1.08470 + 0.505805i
\(36\) −5.59331 14.0258i −0.932218 2.33763i
\(37\) 5.50108 5.50108i 0.904372 0.904372i −0.0914384 0.995811i \(-0.529146\pi\)
0.995811 + 0.0914384i \(0.0291465\pi\)
\(38\) −4.56313 + 4.14462i −0.740237 + 0.672346i
\(39\) −7.37020 −1.18018
\(40\) 6.75207 0.902389i 1.06760 0.142680i
\(41\) 0.138065 0.0502516i 0.0215622 0.00784798i −0.331217 0.943555i \(-0.607459\pi\)
0.352779 + 0.935707i \(0.385237\pi\)
\(42\) −13.4693 0.972401i −2.07835 0.150045i
\(43\) 2.92637 + 4.17928i 0.446267 + 0.637335i 0.977760 0.209728i \(-0.0672578\pi\)
−0.531493 + 0.847063i \(0.678369\pi\)
\(44\) 0.399063 7.00936i 0.0601610 1.05670i
\(45\) −17.5641 4.70627i −2.61829 0.701570i
\(46\) −0.123462 8.12321i −0.0182035 1.19770i
\(47\) −2.52575 3.01007i −0.368418 0.439063i 0.549705 0.835359i \(-0.314740\pi\)
−0.918123 + 0.396295i \(0.870296\pi\)
\(48\) −11.4197 + 6.19599i −1.64829 + 0.894315i
\(49\) −0.821508 + 1.42289i −0.117358 + 0.203271i
\(50\) 0.551142 0.989018i 0.0779432 0.139868i
\(51\) 20.0581 9.35327i 2.80870 1.30972i
\(52\) 0.532741 + 4.50683i 0.0738778 + 0.624985i
\(53\) 0.675331 + 0.472872i 0.0927638 + 0.0649539i 0.619038 0.785361i \(-0.287523\pi\)
−0.526274 + 0.850315i \(0.676412\pi\)
\(54\) 20.7905 2.13776i 2.82922 0.290912i
\(55\) −6.47651 5.43444i −0.873293 0.732780i
\(56\) 0.378983 + 8.30665i 0.0506438 + 1.11002i
\(57\) −6.29020 12.6839i −0.833158 1.68003i
\(58\) 3.35528 + 0.844609i 0.440570 + 0.110903i
\(59\) 0.710079 + 8.11625i 0.0924445 + 1.05665i 0.890781 + 0.454433i \(0.150158\pi\)
−0.798336 + 0.602212i \(0.794286\pi\)
\(60\) −2.24732 + 15.4833i −0.290128 + 1.99889i
\(61\) 4.22429 + 2.95788i 0.540864 + 0.378717i 0.811850 0.583866i \(-0.198461\pi\)
−0.270986 + 0.962583i \(0.587350\pi\)
\(62\) −0.384717 1.00902i −0.0488591 0.128145i
\(63\) 7.59152 20.8575i 0.956442 2.62780i
\(64\) 4.61425 + 6.53519i 0.576782 + 0.816898i
\(65\) 4.73283 + 2.73250i 0.587036 + 0.338925i
\(66\) 15.2343 + 5.28406i 1.87521 + 0.650423i
\(67\) 1.07866 12.3292i 0.131779 1.50625i −0.586191 0.810173i \(-0.699373\pi\)
0.717971 0.696073i \(-0.245071\pi\)
\(68\) −7.16932 11.5893i −0.869407 1.40541i
\(69\) 18.0232 + 4.82930i 2.16974 + 0.581380i
\(70\) 8.28888 + 5.61817i 0.990711 + 0.671499i
\(71\) −9.87473 1.74118i −1.17191 0.206640i −0.446391 0.894838i \(-0.647291\pi\)
−0.725523 + 0.688198i \(0.758402\pi\)
\(72\) −4.66280 20.8392i −0.549516 2.45593i
\(73\) 1.98302 + 5.44830i 0.232095 + 0.637675i 0.999996 0.00289327i \(-0.000920959\pi\)
−0.767901 + 0.640569i \(0.778699\pi\)
\(74\) 8.91550 6.44681i 1.03641 0.749427i
\(75\) 1.83876 + 1.83876i 0.212322 + 0.212322i
\(76\) −7.30147 + 4.76325i −0.837536 + 0.546382i
\(77\) 7.29741 7.29741i 0.831617 0.831617i
\(78\) −10.2910 1.65374i −1.16523 0.187249i
\(79\) −7.90454 + 2.87702i −0.889330 + 0.323690i −0.745969 0.665981i \(-0.768013\pi\)
−0.143361 + 0.989670i \(0.545791\pi\)
\(80\) 9.63040 + 0.255039i 1.07671 + 0.0285142i
\(81\) −4.40233 + 24.9669i −0.489148 + 2.77410i
\(82\) 0.204056 0.0391870i 0.0225342 0.00432748i
\(83\) 0.248315 0.926722i 0.0272561 0.101721i −0.950958 0.309321i \(-0.899898\pi\)
0.978214 + 0.207600i \(0.0665651\pi\)
\(84\) −18.5890 4.38003i −2.02822 0.477900i
\(85\) −16.3482 1.43028i −1.77321 0.155136i
\(86\) 3.14833 + 6.49216i 0.339493 + 0.700067i
\(87\) −3.97329 + 6.88195i −0.425982 + 0.737822i
\(88\) 2.12999 9.69762i 0.227057 1.03377i
\(89\) −9.66380 3.51734i −1.02436 0.372837i −0.225430 0.974259i \(-0.572379\pi\)
−0.798931 + 0.601423i \(0.794601\pi\)
\(90\) −23.4687 10.5124i −2.47382 1.10811i
\(91\) −3.82629 + 5.46451i −0.401104 + 0.572836i
\(92\) 1.65031 11.3701i 0.172057 1.18542i
\(93\) 2.47074 0.216162i 0.256204 0.0224149i
\(94\) −2.85129 4.76969i −0.294088 0.491956i
\(95\) −0.663270 + 10.4772i −0.0680500 + 1.07494i
\(96\) −17.3356 + 6.08909i −1.76930 + 0.621465i
\(97\) 1.67248 1.99318i 0.169814 0.202377i −0.674425 0.738344i \(-0.735608\pi\)
0.844239 + 0.535967i \(0.180053\pi\)
\(98\) −1.46634 + 1.80245i −0.148123 + 0.182075i
\(99\) −15.2015 + 21.7100i −1.52781 + 2.18194i
\(100\) 0.991477 1.25730i 0.0991477 0.125730i
\(101\) 2.15166 + 4.61424i 0.214098 + 0.459134i 0.983800 0.179269i \(-0.0573732\pi\)
−0.769702 + 0.638403i \(0.779595\pi\)
\(102\) 30.1059 8.55927i 2.98093 0.847494i
\(103\) 5.28852 + 3.05333i 0.521093 + 0.300853i 0.737382 0.675476i \(-0.236062\pi\)
−0.216289 + 0.976329i \(0.569395\pi\)
\(104\) −0.267386 + 6.41242i −0.0262193 + 0.628789i
\(105\) −17.6177 + 14.7830i −1.71931 + 1.44267i
\(106\) 0.836860 + 0.811802i 0.0812830 + 0.0788492i
\(107\) −1.23700 + 4.61657i −0.119586 + 0.446300i −0.999589 0.0286675i \(-0.990874\pi\)
0.880003 + 0.474968i \(0.157540\pi\)
\(108\) 29.5094 + 1.68005i 2.83954 + 0.161663i
\(109\) −7.20439 + 5.04457i −0.690055 + 0.483182i −0.865243 0.501353i \(-0.832836\pi\)
0.175188 + 0.984535i \(0.443947\pi\)
\(110\) −7.82376 9.04132i −0.745966 0.862056i
\(111\) 8.64252 + 23.7451i 0.820311 + 2.25379i
\(112\) −1.33469 + 11.6836i −0.126116 + 1.10400i
\(113\) 2.48888i 0.234134i −0.993124 0.117067i \(-0.962651\pi\)
0.993124 0.117067i \(-0.0373492\pi\)
\(114\) −5.93696 19.1220i −0.556047 1.79094i
\(115\) −9.78327 9.78327i −0.912295 0.912295i
\(116\) 4.49546 + 1.93219i 0.417393 + 0.179400i
\(117\) 7.24014 15.5265i 0.669351 1.43543i
\(118\) −0.829656 + 11.4920i −0.0763761 + 1.05793i
\(119\) 3.47850 19.7276i 0.318874 1.80842i
\(120\) −6.61212 + 21.1151i −0.603601 + 1.92754i
\(121\) −1.14539 + 0.661292i −0.104127 + 0.0601175i
\(122\) 5.23467 + 5.07794i 0.473925 + 0.459735i
\(123\) −0.0415930 + 0.475410i −0.00375031 + 0.0428662i
\(124\) −0.310774 1.49522i −0.0279083 0.134274i
\(125\) 2.61770 + 9.76939i 0.234134 + 0.873801i
\(126\) 15.2801 27.4200i 1.36126 2.44277i
\(127\) −13.9648 5.08277i −1.23917 0.451023i −0.362445 0.932005i \(-0.618058\pi\)
−0.876730 + 0.480982i \(0.840280\pi\)
\(128\) 4.97650 + 10.1604i 0.439865 + 0.898064i
\(129\) −16.3198 + 2.87762i −1.43688 + 0.253360i
\(130\) 5.99533 + 4.87735i 0.525825 + 0.427772i
\(131\) 1.36191 + 15.5667i 0.118991 + 1.36007i 0.787477 + 0.616344i \(0.211387\pi\)
−0.668486 + 0.743725i \(0.733057\pi\)
\(132\) 20.0860 + 10.7964i 1.74826 + 0.939710i
\(133\) −12.6699 1.92119i −1.09862 0.166589i
\(134\) 4.27257 16.9732i 0.369094 1.46626i
\(135\) 22.8790 27.2661i 1.96911 2.34669i
\(136\) −7.41008 17.7908i −0.635409 1.52555i
\(137\) −3.12787 + 0.551529i −0.267232 + 0.0471203i −0.305659 0.952141i \(-0.598877\pi\)
0.0384263 + 0.999261i \(0.487766\pi\)
\(138\) 24.0822 + 10.7872i 2.05001 + 0.918270i
\(139\) −2.91443 + 1.35902i −0.247199 + 0.115271i −0.542269 0.840205i \(-0.682435\pi\)
0.295070 + 0.955476i \(0.404657\pi\)
\(140\) 10.3131 + 9.70452i 0.871620 + 0.820182i
\(141\) 12.3280 3.30327i 1.03820 0.278185i
\(142\) −13.3974 4.64692i −1.12428 0.389961i
\(143\) 6.10181 5.12003i 0.510259 0.428158i
\(144\) −1.83472 30.1441i −0.152893 2.51200i
\(145\) 5.10296 2.94620i 0.423778 0.244668i
\(146\) 1.54639 + 8.05241i 0.127980 + 0.666422i
\(147\) −3.06097 4.37151i −0.252464 0.360556i
\(148\) 13.8953 7.00121i 1.14218 0.575496i
\(149\) −10.7567 5.01591i −0.881220 0.410920i −0.0712964 0.997455i \(-0.522714\pi\)
−0.809923 + 0.586536i \(0.800491\pi\)
\(150\) 2.15487 + 2.98004i 0.175945 + 0.243319i
\(151\) 12.8778i 1.04798i 0.851725 + 0.523988i \(0.175556\pi\)
−0.851725 + 0.523988i \(0.824444\pi\)
\(152\) −11.2638 + 5.01260i −0.913617 + 0.406576i
\(153\) 51.4439i 4.15900i
\(154\) 11.8268 8.55196i 0.953029 0.689137i
\(155\) −1.66675 0.777217i −0.133876 0.0624276i
\(156\) −13.9983 4.61824i −1.12076 0.369755i
\(157\) −11.0631 15.7998i −0.882934 1.26096i −0.964444 0.264288i \(-0.914863\pi\)
0.0815094 0.996673i \(-0.474026\pi\)
\(158\) −11.6827 + 2.24354i −0.929422 + 0.178486i
\(159\) −2.31904 + 1.33890i −0.183912 + 0.106181i
\(160\) 13.3897 + 2.51700i 1.05855 + 0.198986i
\(161\) 12.9375 10.8558i 1.01962 0.855559i
\(162\) −11.7491 + 33.8734i −0.923096 + 2.66135i
\(163\) 12.4411 3.33357i 0.974460 0.261106i 0.263750 0.964591i \(-0.415041\pi\)
0.710710 + 0.703485i \(0.248374\pi\)
\(164\) 0.293716 0.00893024i 0.0229354 0.000697335i
\(165\) 24.8879 11.6054i 1.93752 0.903481i
\(166\) 0.554661 1.23826i 0.0430501 0.0961080i
\(167\) 15.1766 2.67604i 1.17440 0.207078i 0.447795 0.894136i \(-0.352209\pi\)
0.726602 + 0.687058i \(0.241098\pi\)
\(168\) −24.9730 10.2869i −1.92671 0.793648i
\(169\) 5.04664 6.01435i 0.388203 0.462642i
\(170\) −22.5061 5.66535i −1.72614 0.434512i
\(171\) 32.9000 0.791224i 2.51593 0.0605064i
\(172\) 2.93928 + 9.77142i 0.224118 + 0.745064i
\(173\) −0.420643 4.80797i −0.0319809 0.365543i −0.995275 0.0970952i \(-0.969045\pi\)
0.963294 0.268448i \(-0.0865107\pi\)
\(174\) −7.09209 + 8.71772i −0.537650 + 0.660889i
\(175\) 2.31792 0.408712i 0.175218 0.0308957i
\(176\) 5.15007 13.0629i 0.388201 0.984650i
\(177\) −24.8669 9.05082i −1.86911 0.680301i
\(178\) −12.7043 7.07964i −0.952230 0.530641i
\(179\) −4.80842 17.9453i −0.359398 1.34129i −0.874858 0.484379i \(-0.839045\pi\)
0.515460 0.856914i \(-0.327621\pi\)
\(180\) −30.4105 19.9445i −2.26667 1.48657i
\(181\) −1.20003 + 13.7164i −0.0891975 + 1.01953i 0.811288 + 0.584647i \(0.198767\pi\)
−0.900486 + 0.434886i \(0.856789\pi\)
\(182\) −6.56879 + 6.77154i −0.486911 + 0.501940i
\(183\) −14.5059 + 8.37499i −1.07231 + 0.619097i
\(184\) 4.85558 15.5058i 0.357958 1.14310i
\(185\) 3.25364 18.4523i 0.239213 1.35664i
\(186\) 3.49840 + 0.252563i 0.256515 + 0.0185188i
\(187\) −10.1085 + 21.6778i −0.739210 + 1.58524i
\(188\) −2.91103 7.29969i −0.212309 0.532385i
\(189\) 30.7221 + 30.7221i 2.23470 + 2.23470i
\(190\) −3.27702 + 14.4805i −0.237740 + 1.05052i
\(191\) 3.50558i 0.253655i 0.991925 + 0.126827i \(0.0404794\pi\)
−0.991925 + 0.126827i \(0.959521\pi\)
\(192\) −25.5719 + 4.61241i −1.84549 + 0.332872i
\(193\) 0.457303 + 1.25643i 0.0329174 + 0.0904398i 0.955063 0.296404i \(-0.0957875\pi\)
−0.922145 + 0.386844i \(0.873565\pi\)
\(194\) 2.78251 2.40780i 0.199773 0.172870i
\(195\) −14.5405 + 10.1814i −1.04127 + 0.729105i
\(196\) −2.45189 + 2.18775i −0.175135 + 0.156268i
\(197\) −0.615389 + 2.29666i −0.0438447 + 0.163631i −0.984377 0.176074i \(-0.943660\pi\)
0.940532 + 0.339704i \(0.110327\pi\)
\(198\) −26.0972 + 26.9027i −1.85465 + 1.91189i
\(199\) 0.181659 0.152430i 0.0128774 0.0108054i −0.636326 0.771420i \(-0.719547\pi\)
0.649204 + 0.760615i \(0.275102\pi\)
\(200\) 1.66651 1.53310i 0.117840 0.108406i
\(201\) 34.8133 + 20.0995i 2.45554 + 1.41771i
\(202\) 1.96900 + 6.92565i 0.138539 + 0.487287i
\(203\) 3.03974 + 6.51874i 0.213348 + 0.457526i
\(204\) 43.9574 5.19609i 3.07763 0.363799i
\(205\) 0.202967 0.289867i 0.0141758 0.0202452i
\(206\) 6.69925 + 5.45001i 0.466759 + 0.379720i
\(207\) −27.8788 + 33.2247i −1.93771 + 2.30928i
\(208\) −1.81218 + 8.89366i −0.125652 + 0.616665i
\(209\) 14.0191 + 6.13132i 0.969724 + 0.424112i
\(210\) −27.9166 + 16.6884i −1.92643 + 1.15161i
\(211\) −9.89856 + 0.866011i −0.681445 + 0.0596187i −0.422622 0.906306i \(-0.638890\pi\)
−0.258823 + 0.965925i \(0.583335\pi\)
\(212\) 0.986353 + 1.32130i 0.0677430 + 0.0907470i
\(213\) 18.6806 26.6786i 1.27997 1.82799i
\(214\) −2.76310 + 6.16855i −0.188882 + 0.421673i
\(215\) 11.5467 + 4.20267i 0.787481 + 0.286620i
\(216\) 40.8270 + 8.96724i 2.77792 + 0.610143i
\(217\) 1.12243 1.94411i 0.0761957 0.131975i
\(218\) −11.1914 + 5.42719i −0.757977 + 0.367576i
\(219\) −18.7605 1.64133i −1.26772 0.110911i
\(220\) −8.89561 14.3799i −0.599742 0.969493i
\(221\) 4.00166 14.9344i 0.269181 1.00460i
\(222\) 6.73956 + 35.0945i 0.452330 + 2.35539i
\(223\) −0.752295 + 4.26648i −0.0503774 + 0.285704i −0.999581 0.0289593i \(-0.990781\pi\)
0.949203 + 0.314664i \(0.101892\pi\)
\(224\) −4.48522 + 16.0143i −0.299681 + 1.07000i
\(225\) −5.67995 + 2.06733i −0.378664 + 0.137822i
\(226\) 0.558459 3.47522i 0.0371482 0.231168i
\(227\) −3.49244 + 3.49244i −0.231801 + 0.231801i −0.813444 0.581643i \(-0.802410\pi\)
0.581643 + 0.813444i \(0.302410\pi\)
\(228\) −3.99914 28.0322i −0.264849 1.85648i
\(229\) −15.4408 15.4408i −1.02035 1.02035i −0.999788 0.0205659i \(-0.993453\pi\)
−0.0205659 0.999788i \(-0.506547\pi\)
\(230\) −11.4652 15.8556i −0.755992 1.04549i
\(231\) 11.4646 + 31.4989i 0.754318 + 2.07247i
\(232\) 5.84346 + 3.70662i 0.383642 + 0.243352i
\(233\) 1.46131 + 0.257668i 0.0957334 + 0.0168804i 0.221310 0.975204i \(-0.428967\pi\)
−0.125576 + 0.992084i \(0.540078\pi\)
\(234\) 13.5933 20.0551i 0.888621 1.31105i
\(235\) −9.14118 2.44937i −0.596305 0.159779i
\(236\) −3.73706 + 15.8602i −0.243262 + 1.03241i
\(237\) 2.38129 27.2182i 0.154681 1.76802i
\(238\) 9.28355 26.7651i 0.601763 1.73492i
\(239\) −12.8962 7.44561i −0.834184 0.481616i 0.0210992 0.999777i \(-0.493283\pi\)
−0.855283 + 0.518161i \(0.826617\pi\)
\(240\) −13.9704 + 27.9994i −0.901783 + 1.80735i
\(241\) 5.60804 15.4080i 0.361245 0.992513i −0.617344 0.786693i \(-0.711791\pi\)
0.978590 0.205820i \(-0.0659863\pi\)
\(242\) −1.74769 + 0.666357i −0.112346 + 0.0428350i
\(243\) −31.1354 21.8013i −1.99734 1.39855i
\(244\) 6.16978 + 8.26489i 0.394979 + 0.529105i
\(245\) 0.344885 + 3.94205i 0.0220339 + 0.251849i
\(246\) −0.164750 + 0.654482i −0.0105041 + 0.0417282i
\(247\) −9.61255 2.32949i −0.611632 0.148222i
\(248\) −0.0984340 2.15750i −0.00625057 0.137001i
\(249\) 2.38718 + 2.00308i 0.151281 + 0.126940i
\(250\) 1.46302 + 14.2284i 0.0925294 + 0.899881i
\(251\) −24.1068 16.8798i −1.52161 1.06544i −0.973403 0.229099i \(-0.926422\pi\)
−0.548206 0.836344i \(-0.684689\pi\)
\(252\) 27.4882 34.8579i 1.73159 2.19584i
\(253\) −18.2763 + 8.52240i −1.14902 + 0.535799i
\(254\) −18.3586 10.2305i −1.15192 0.641920i
\(255\) 26.6515 46.1617i 1.66898 2.89076i
\(256\) 4.66887 + 15.3036i 0.291804 + 0.956478i
\(257\) 14.4881 + 17.2663i 0.903744 + 1.07704i 0.996684 + 0.0813686i \(0.0259291\pi\)
−0.0929399 + 0.995672i \(0.529626\pi\)
\(258\) −23.4330 + 0.356150i −1.45887 + 0.0221729i
\(259\) 22.0922 + 5.91960i 1.37274 + 0.367826i
\(260\) 7.27688 + 8.15549i 0.451293 + 0.505782i
\(261\) −10.5948 15.1309i −0.655799 0.936578i
\(262\) −1.59125 + 22.0414i −0.0983080 + 1.36172i
\(263\) −0.274673 + 0.0999729i −0.0169371 + 0.00616459i −0.350475 0.936572i \(-0.613980\pi\)
0.333538 + 0.942737i \(0.391758\pi\)
\(264\) 25.6236 + 19.5820i 1.57702 + 1.20519i
\(265\) 1.98558 0.121973
\(266\) −17.2599 5.52546i −1.05827 0.338788i
\(267\) 23.6196 23.6196i 1.44550 1.44550i
\(268\) 9.77427 22.7409i 0.597058 1.38912i
\(269\) 24.8407 + 11.5834i 1.51457 + 0.706254i 0.989463 0.144784i \(-0.0462487\pi\)
0.525104 + 0.851038i \(0.324026\pi\)
\(270\) 38.0640 32.9380i 2.31650 2.00454i
\(271\) −16.4138 2.89419i −0.997065 0.175810i −0.348778 0.937205i \(-0.613403\pi\)
−0.648287 + 0.761396i \(0.724514\pi\)
\(272\) −6.35474 26.5040i −0.385313 1.60704i
\(273\) −10.8338 18.7648i −0.655694 1.13569i
\(274\) −4.49120 + 0.0682603i −0.271323 + 0.00412375i
\(275\) −2.79969 0.244941i −0.168827 0.0147705i
\(276\) 31.2055 + 20.4658i 1.87835 + 1.23190i
\(277\) −0.125976 + 0.0337552i −0.00756916 + 0.00202815i −0.262602 0.964904i \(-0.584581\pi\)
0.255032 + 0.966932i \(0.417914\pi\)
\(278\) −4.37436 + 1.24365i −0.262357 + 0.0745895i
\(279\) −1.97176 + 5.41737i −0.118046 + 0.324329i
\(280\) 12.2227 + 15.8645i 0.730447 + 0.948085i
\(281\) 2.43756 + 13.8241i 0.145412 + 0.824675i 0.967035 + 0.254643i \(0.0819579\pi\)
−0.821623 + 0.570032i \(0.806931\pi\)
\(282\) 17.9547 1.84618i 1.06919 0.109938i
\(283\) −1.82930 + 0.160043i −0.108741 + 0.00951358i −0.141396 0.989953i \(-0.545159\pi\)
0.0326555 + 0.999467i \(0.489604\pi\)
\(284\) −17.6641 9.49463i −1.04817 0.563403i
\(285\) −29.9318 16.3345i −1.77300 0.967570i
\(286\) 9.66881 5.77996i 0.571728 0.341776i
\(287\) 0.330891 + 0.277651i 0.0195319 + 0.0163892i
\(288\) 4.20197 42.5018i 0.247604 2.50444i
\(289\) 5.11010 + 28.9808i 0.300594 + 1.70476i
\(290\) 7.78634 2.96876i 0.457229 0.174332i
\(291\) 3.57163 + 7.65938i 0.209373 + 0.449001i
\(292\) 0.352403 + 11.5906i 0.0206229 + 0.678286i
\(293\) 1.50895 + 5.63148i 0.0881538 + 0.328994i 0.995893 0.0905411i \(-0.0288597\pi\)
−0.907739 + 0.419535i \(0.862193\pi\)
\(294\) −3.29314 6.79077i −0.192060 0.396046i
\(295\) 12.6129 + 15.0315i 0.734351 + 0.875166i
\(296\) 20.9729 6.65793i 1.21902 0.386984i
\(297\) −25.9390 44.9277i −1.50514 2.60697i
\(298\) −13.8940 9.41732i −0.804860 0.545531i
\(299\) 10.6778 7.47667i 0.617512 0.432387i
\(300\) 2.34018 + 4.64455i 0.135110 + 0.268153i
\(301\) −6.33896 + 13.5940i −0.365372 + 0.783542i
\(302\) −2.88954 + 17.9812i −0.166274 + 1.03470i
\(303\) −16.5367 −0.950011
\(304\) −16.8524 + 4.47170i −0.966552 + 0.256469i
\(305\) 12.4201 0.711173
\(306\) −11.5431 + 71.8312i −0.659875 + 4.10631i
\(307\) −9.10542 + 19.5266i −0.519673 + 1.11444i 0.454934 + 0.890525i \(0.349663\pi\)
−0.974608 + 0.223918i \(0.928115\pi\)
\(308\) 18.4326 9.28738i 1.05030 0.529198i
\(309\) −16.2478 + 11.3768i −0.924303 + 0.647204i
\(310\) −2.15288 1.45922i −0.122276 0.0828779i
\(311\) −16.3384 28.2990i −0.926468 1.60469i −0.789184 0.614157i \(-0.789496\pi\)
−0.137284 0.990532i \(-0.543837\pi\)
\(312\) −18.5095 9.58941i −1.04790 0.542893i
\(313\) 8.84356 + 10.5393i 0.499868 + 0.595719i 0.955699 0.294347i \(-0.0951022\pi\)
−0.455831 + 0.890066i \(0.650658\pi\)
\(314\) −11.9023 24.5436i −0.671683 1.38508i
\(315\) −13.8360 51.6366i −0.779569 2.90939i
\(316\) −16.8159 + 0.511276i −0.945968 + 0.0287615i
\(317\) 12.8090 + 27.4689i 0.719422 + 1.54281i 0.835454 + 0.549561i \(0.185205\pi\)
−0.116031 + 0.993246i \(0.537017\pi\)
\(318\) −3.53850 + 1.34915i −0.198429 + 0.0756566i
\(319\) −1.49134 8.45780i −0.0834989 0.473546i
\(320\) 18.1313 + 6.51889i 1.01357 + 0.364417i
\(321\) −11.8920 9.97857i −0.663746 0.556949i
\(322\) 20.5004 12.2550i 1.14244 0.682947i
\(323\) 29.1170 5.85921i 1.62011 0.326015i
\(324\) −24.0058 + 44.6611i −1.33366 + 2.48117i
\(325\) 1.80973 0.158330i 0.100386 0.00878260i
\(326\) 18.1195 1.86312i 1.00354 0.103188i
\(327\) −4.96053 28.1326i −0.274318 1.55573i
\(328\) 0.412119 + 0.0534353i 0.0227555 + 0.00295047i
\(329\) 3.95100 10.8553i 0.217825 0.598471i
\(330\) 37.3550 10.6202i 2.05633 0.584625i
\(331\) 16.3772 4.38825i 0.900170 0.241200i 0.221081 0.975256i \(-0.429042\pi\)
0.679089 + 0.734056i \(0.262375\pi\)
\(332\) 1.05232 1.60453i 0.0577534 0.0880602i
\(333\) −58.5129 5.11922i −3.20649 0.280532i
\(334\) 21.7915 0.331201i 1.19238 0.0181225i
\(335\) −14.9037 25.8140i −0.814279 1.41037i
\(336\) −32.5615 19.9670i −1.77638 1.08929i
\(337\) 2.11952 + 0.373728i 0.115457 + 0.0203582i 0.231078 0.972935i \(-0.425775\pi\)
−0.115621 + 0.993293i \(0.536886\pi\)
\(338\) 8.39613 7.26546i 0.456689 0.395189i
\(339\) 7.32663 + 3.41646i 0.397928 + 0.185557i
\(340\) −30.1540 12.9605i −1.63533 0.702881i
\(341\) −1.89537 + 1.89537i −0.102640 + 0.102640i
\(342\) 46.1158 + 6.27738i 2.49366 + 0.339442i
\(343\) 15.7490 0.850366
\(344\) 1.91159 + 14.3034i 0.103066 + 0.771185i
\(345\) 42.2289 15.3701i 2.27353 0.827497i
\(346\) 0.491479 6.80775i 0.0264221 0.365987i
\(347\) 11.2132 + 16.0141i 0.601955 + 0.859681i 0.998292 0.0584245i \(-0.0186077\pi\)
−0.396337 + 0.918105i \(0.629719\pi\)
\(348\) −11.8588 + 10.5812i −0.635698 + 0.567213i
\(349\) 30.2001 + 8.09209i 1.61657 + 0.433160i 0.949993 0.312272i \(-0.101090\pi\)
0.666582 + 0.745432i \(0.267757\pi\)
\(350\) 3.32822 0.0505845i 0.177901 0.00270385i
\(351\) 21.5553 + 25.6886i 1.15054 + 1.37116i
\(352\) 10.1221 17.0841i 0.539510 0.910584i
\(353\) −2.39544 + 4.14902i −0.127496 + 0.220830i −0.922706 0.385505i \(-0.874027\pi\)
0.795210 + 0.606334i \(0.207361\pi\)
\(354\) −32.6908 18.2174i −1.73750 0.968241i
\(355\) −21.8870 + 10.2061i −1.16164 + 0.541682i
\(356\) −16.1505 12.7359i −0.855975 0.675002i
\(357\) 53.2982 + 37.3198i 2.82084 + 1.97517i
\(358\) −2.68740 26.1359i −0.142034 1.38133i
\(359\) −12.7574 10.7047i −0.673308 0.564973i 0.240734 0.970591i \(-0.422612\pi\)
−0.914043 + 0.405618i \(0.867056\pi\)
\(360\) −37.9870 34.6720i −2.00209 1.82738i
\(361\) −4.19497 18.5311i −0.220788 0.975322i
\(362\) −4.75332 + 18.8829i −0.249829 + 0.992465i
\(363\) −0.374408 4.27950i −0.0196513 0.224616i
\(364\) −10.6914 + 7.98119i −0.560382 + 0.418328i
\(365\) 11.4387 + 8.00945i 0.598728 + 0.419234i
\(366\) −22.1338 + 8.43913i −1.15695 + 0.441120i
\(367\) −3.53873 + 9.72257i −0.184720 + 0.507514i −0.997142 0.0755566i \(-0.975927\pi\)
0.812422 + 0.583071i \(0.198149\pi\)
\(368\) 10.2591 20.5613i 0.534791 1.07183i
\(369\) −0.960669 0.554642i −0.0500104 0.0288735i
\(370\) 8.68343 25.0349i 0.451430 1.30150i
\(371\) −0.211242 + 2.41451i −0.0109671 + 0.125355i
\(372\) 4.82814 + 1.13763i 0.250327 + 0.0589835i
\(373\) −32.1010 8.60143i −1.66213 0.445365i −0.699155 0.714970i \(-0.746440\pi\)
−0.962971 + 0.269605i \(0.913107\pi\)
\(374\) −18.9787 + 28.0006i −0.981364 + 1.44788i
\(375\) −32.3520 5.70452i −1.67065 0.294580i
\(376\) −2.42675 10.8457i −0.125150 0.559326i
\(377\) 1.89872 + 5.21669i 0.0977891 + 0.268673i
\(378\) 36.0037 + 49.7907i 1.85183 + 2.56096i
\(379\) 18.9067 + 18.9067i 0.971174 + 0.971174i 0.999596 0.0284219i \(-0.00904819\pi\)
−0.0284219 + 0.999596i \(0.509048\pi\)
\(380\) −7.82485 + 19.4838i −0.401407 + 0.999496i
\(381\) 34.1318 34.1318i 1.74862 1.74862i
\(382\) −0.786589 + 4.89484i −0.0402454 + 0.250442i
\(383\) 22.0522 8.02636i 1.12682 0.410128i 0.289681 0.957123i \(-0.406451\pi\)
0.837136 + 0.546995i \(0.184228\pi\)
\(384\) −36.7410 + 0.702425i −1.87493 + 0.0358455i
\(385\) 4.31609 24.4777i 0.219968 1.24750i
\(386\) 0.356612 + 1.85696i 0.0181511 + 0.0945170i
\(387\) 9.96961 37.2071i 0.506784 1.89134i
\(388\) 4.42549 2.73767i 0.224670 0.138984i
\(389\) 3.17272 + 0.277577i 0.160863 + 0.0140737i 0.167303 0.985906i \(-0.446494\pi\)
−0.00643947 + 0.999979i \(0.502050\pi\)
\(390\) −22.5875 + 10.9536i −1.14376 + 0.554659i
\(391\) −19.5714 + 33.8987i −0.989769 + 1.71433i
\(392\) −3.91447 + 2.50459i −0.197710 + 0.126501i
\(393\) −47.6940 17.3592i −2.40584 0.875655i
\(394\) −1.37460 + 3.06875i −0.0692513 + 0.154601i
\(395\) −11.6203 + 16.5955i −0.584682 + 0.835012i
\(396\) −42.4760 + 31.7085i −2.13450 + 1.59341i
\(397\) −18.2824 + 1.59950i −0.917567 + 0.0802767i −0.536146 0.844125i \(-0.680120\pi\)
−0.381420 + 0.924402i \(0.624565\pi\)
\(398\) 0.287852 0.172076i 0.0144287 0.00862542i
\(399\) 23.0474 34.6598i 1.15381 1.73516i
\(400\) 2.67095 1.76673i 0.133548 0.0883363i
\(401\) 7.62905 9.09195i 0.380977 0.454030i −0.541146 0.840929i \(-0.682009\pi\)
0.922122 + 0.386899i \(0.126454\pi\)
\(402\) 44.0998 + 35.8763i 2.19950 + 1.78935i
\(403\) 0.993809 1.41931i 0.0495052 0.0707007i
\(404\) 1.19533 + 10.1121i 0.0594696 + 0.503096i
\(405\) 25.8046 + 55.3381i 1.28224 + 2.74977i
\(406\) 2.78170 + 9.78418i 0.138053 + 0.485580i
\(407\) −23.6507 13.6548i −1.17232 0.676841i
\(408\) 62.5436 + 2.60795i 3.09637 + 0.129113i
\(409\) 3.57221 2.99744i 0.176634 0.148214i −0.550184 0.835043i \(-0.685443\pi\)
0.726819 + 0.686830i \(0.240998\pi\)
\(410\) 0.348444 0.359199i 0.0172084 0.0177396i
\(411\) 2.67005 9.96476i 0.131704 0.491525i
\(412\) 8.13127 + 9.11304i 0.400599 + 0.448967i
\(413\) −19.6204 + 13.7384i −0.965457 + 0.676020i
\(414\) −46.3822 + 40.1361i −2.27956 + 1.97258i
\(415\) −0.790304 2.17134i −0.0387945 0.106587i
\(416\) −4.52593 + 12.0116i −0.221902 + 0.588917i
\(417\) 10.4449i 0.511488i
\(418\) 18.1992 + 11.7068i 0.890150 + 0.572598i
\(419\) −1.54542 1.54542i −0.0754989 0.0754989i 0.668349 0.743848i \(-0.267001\pi\)
−0.743848 + 0.668349i \(0.767001\pi\)
\(420\) −42.7245 + 17.0380i −2.08474 + 0.831369i
\(421\) −15.7635 + 33.8049i −0.768265 + 1.64755i −0.00625844 + 0.999980i \(0.501992\pi\)
−0.762007 + 0.647569i \(0.775786\pi\)
\(422\) −14.0157 1.01185i −0.682272 0.0492559i
\(423\) −5.15154 + 29.2158i −0.250476 + 1.42052i
\(424\) 1.08077 + 2.06624i 0.0524868 + 0.100346i
\(425\) −4.72427 + 2.72756i −0.229161 + 0.132306i
\(426\) 32.0699 33.0598i 1.55379 1.60175i
\(427\) −1.32135 + 15.1031i −0.0639446 + 0.730890i
\(428\) −5.24223 + 7.99315i −0.253393 + 0.386363i
\(429\) 6.69617 + 24.9905i 0.323294 + 1.20655i
\(430\) 15.1797 + 8.45907i 0.732031 + 0.407933i
\(431\) 19.8878 + 7.23858i 0.957963 + 0.348670i 0.773235 0.634120i \(-0.218637\pi\)
0.184728 + 0.982790i \(0.440860\pi\)
\(432\) 54.9946 + 21.6818i 2.64593 + 1.04317i
\(433\) 23.7933 4.19539i 1.14343 0.201618i 0.430325 0.902674i \(-0.358399\pi\)
0.713106 + 0.701056i \(0.247288\pi\)
\(434\) 2.00348 2.46271i 0.0961699 0.118214i
\(435\) 1.66807 + 19.0661i 0.0799776 + 0.914148i
\(436\) −16.8443 + 5.06684i −0.806696 + 0.242657i
\(437\) 21.9803 + 11.9952i 1.05146 + 0.573806i
\(438\) −25.8270 6.50132i −1.23406 0.310645i
\(439\) −14.1033 + 16.8076i −0.673113 + 0.802185i −0.989204 0.146544i \(-0.953185\pi\)
0.316091 + 0.948729i \(0.397629\pi\)
\(440\) −9.19434 22.0747i −0.438323 1.05237i
\(441\) 12.2162 2.15405i 0.581726 0.102574i
\(442\) 8.93852 19.9550i 0.425162 0.949162i
\(443\) −31.7254 + 14.7938i −1.50732 + 0.702875i −0.988390 0.151940i \(-0.951448\pi\)
−0.518932 + 0.854816i \(0.673670\pi\)
\(444\) 1.53587 + 50.5147i 0.0728890 + 2.39732i
\(445\) −23.9245 + 6.41054i −1.13413 + 0.303889i
\(446\) −2.00775 + 5.78848i −0.0950698 + 0.274092i
\(447\) 29.5312 24.7796i 1.39678 1.17204i
\(448\) −9.85604 + 21.3544i −0.465654 + 1.00890i
\(449\) −19.9377 + 11.5110i −0.940917 + 0.543239i −0.890248 0.455477i \(-0.849469\pi\)
−0.0506695 + 0.998715i \(0.516136\pi\)
\(450\) −8.39479 + 1.61214i −0.395734 + 0.0759969i
\(451\) −0.295829 0.422487i −0.0139300 0.0198942i
\(452\) 1.55955 4.72714i 0.0733552 0.222346i
\(453\) −37.9089 17.6772i −1.78112 0.830548i
\(454\) −5.66013 + 4.09285i −0.265643 + 0.192087i
\(455\) 16.0666i 0.753212i
\(456\) 0.705925 40.0387i 0.0330580 1.87498i
\(457\) 33.5629i 1.57001i −0.619492 0.785003i \(-0.712661\pi\)
0.619492 0.785003i \(-0.287339\pi\)
\(458\) −18.0953 25.0246i −0.845538 1.16932i
\(459\) −91.2637 42.5570i −4.25983 1.98639i
\(460\) −12.4511 24.7117i −0.580537 1.15219i
\(461\) 18.2647 + 26.0846i 0.850670 + 1.21488i 0.974903 + 0.222630i \(0.0714640\pi\)
−0.124233 + 0.992253i \(0.539647\pi\)
\(462\) 8.94030 + 46.5543i 0.415940 + 2.16590i
\(463\) 20.1982 11.6615i 0.938692 0.541954i 0.0491418 0.998792i \(-0.484351\pi\)
0.889550 + 0.456838i \(0.151018\pi\)
\(464\) 7.32753 + 6.48672i 0.340172 + 0.301139i
\(465\) 4.57587 3.83961i 0.212201 0.178058i
\(466\) 1.98261 + 0.687673i 0.0918425 + 0.0318558i
\(467\) 9.16703 2.45630i 0.424200 0.113664i −0.0404025 0.999183i \(-0.512864\pi\)
0.464602 + 0.885520i \(0.346197\pi\)
\(468\) 23.4803 24.9529i 1.08538 1.15345i
\(469\) 32.9760 15.3769i 1.52269 0.710041i
\(470\) −12.2142 5.47118i −0.563401 0.252367i
\(471\) 61.6970 10.8788i 2.84285 0.501270i
\(472\) −8.77679 + 21.3070i −0.403984 + 0.980735i
\(473\) 11.5121 13.7196i 0.529328 0.630829i
\(474\) 9.43228 37.4705i 0.433239 1.72108i
\(475\) 1.81702 + 2.97937i 0.0833705 + 0.136703i
\(476\) 18.9682 35.2890i 0.869407 1.61747i
\(477\) −0.542491 6.20070i −0.0248390 0.283911i
\(478\) −16.3363 13.2900i −0.747203 0.607869i
\(479\) −22.6869 + 4.00032i −1.03659 + 0.182779i −0.665950 0.745997i \(-0.731974\pi\)
−0.370642 + 0.928776i \(0.620862\pi\)
\(480\) −25.7894 + 35.9609i −1.17712 + 1.64138i
\(481\) 16.5883 + 6.03766i 0.756364 + 0.275294i
\(482\) 11.2878 20.2558i 0.514144 0.922625i
\(483\) 14.1977 + 52.9864i 0.646016 + 2.41097i
\(484\) −2.58982 + 0.538283i −0.117719 + 0.0244674i
\(485\) 0.546167 6.24271i 0.0248001 0.283467i
\(486\) −38.5826 37.4273i −1.75014 1.69774i
\(487\) 29.6633 17.1261i 1.34417 0.776058i 0.356755 0.934198i \(-0.383883\pi\)
0.987417 + 0.158140i \(0.0505497\pi\)
\(488\) 6.76036 + 12.9246i 0.306027 + 0.585071i
\(489\) −7.26456 + 41.1994i −0.328515 + 1.86310i
\(490\) −0.402963 + 5.58167i −0.0182040 + 0.252154i
\(491\) 14.4070 30.8960i 0.650180 1.39432i −0.254016 0.967200i \(-0.581752\pi\)
0.904197 0.427116i \(-0.140471\pi\)
\(492\) −0.376894 + 0.876886i −0.0169917 + 0.0395331i
\(493\) −11.7877 11.7877i −0.530892 0.530892i
\(494\) −12.8993 5.40955i −0.580367 0.243387i
\(495\) 63.8310i 2.86899i
\(496\) 0.346661 3.03461i 0.0155656 0.136258i
\(497\) −10.0823 27.7008i −0.452251 1.24255i
\(498\) 2.88376 + 3.33254i 0.129225 + 0.149335i
\(499\) 0.478540 0.335077i 0.0214224 0.0150001i −0.562816 0.826582i \(-0.690282\pi\)
0.584239 + 0.811582i \(0.301393\pi\)
\(500\) −1.14978 + 20.1953i −0.0514197 + 0.903163i
\(501\) −12.9552 + 48.3494i −0.578795 + 2.16009i
\(502\) −29.8728 28.9784i −1.33329 1.29337i
\(503\) 4.79800 4.02600i 0.213932 0.179510i −0.529524 0.848295i \(-0.677630\pi\)
0.743456 + 0.668784i \(0.233185\pi\)
\(504\) 46.2032 42.5043i 2.05805 1.89329i
\(505\) 10.6192 + 6.13099i 0.472548 + 0.272826i
\(506\) −27.4315 + 7.79894i −1.21948 + 0.346705i
\(507\) 10.7773 + 23.1119i 0.478635 + 1.02644i
\(508\) −23.3385 18.4042i −1.03548 0.816554i
\(509\) 11.6247 16.6018i 0.515257 0.735863i −0.474244 0.880394i \(-0.657278\pi\)
0.989500 + 0.144531i \(0.0461673\pi\)
\(510\) 47.5713 58.4755i 2.10649 2.58934i
\(511\) −10.9566 + 13.0576i −0.484691 + 0.577632i
\(512\) 3.08528 + 22.4161i 0.136351 + 0.990661i
\(513\) −25.8128 + 59.0205i −1.13966 + 2.60582i
\(514\) 16.3555 + 27.3598i 0.721411 + 1.20679i
\(515\) 14.6516 1.28185i 0.645625 0.0564849i
\(516\) −32.7994 4.76065i −1.44391 0.209576i
\(517\) −7.91160 + 11.2989i −0.347952 + 0.496927i
\(518\) 29.5191 + 13.2226i 1.29700 + 0.580969i
\(519\) 14.7309 + 5.36160i 0.646614 + 0.235348i
\(520\) 8.33076 + 13.0203i 0.365328 + 0.570979i
\(521\) −13.4672 + 23.3259i −0.590009 + 1.02193i 0.404221 + 0.914661i \(0.367543\pi\)
−0.994230 + 0.107265i \(0.965791\pi\)
\(522\) −11.3984 23.5045i −0.498893 1.02877i
\(523\) 27.8877 + 2.43986i 1.21945 + 0.106688i 0.678647 0.734464i \(-0.262567\pi\)
0.540799 + 0.841152i \(0.318122\pi\)
\(524\) −7.16756 + 30.4193i −0.313116 + 1.32887i
\(525\) −1.97865 + 7.38442i −0.0863553 + 0.322282i
\(526\) −0.405958 + 0.0779604i −0.0177006 + 0.00339923i
\(527\) −0.903478 + 5.12388i −0.0393561 + 0.223200i
\(528\) 31.3843 + 33.0918i 1.36583 + 1.44014i
\(529\) −9.39774 + 3.42050i −0.408597 + 0.148717i
\(530\) 2.77247 + 0.445529i 0.120428 + 0.0193526i
\(531\) 43.4951 43.4951i 1.88753 1.88753i
\(532\) −22.8602 11.5880i −0.991114 0.502404i
\(533\) 0.235742 + 0.235742i 0.0102111 + 0.0102111i
\(534\) 38.2799 27.6802i 1.65653 1.19784i
\(535\) 3.93698 + 10.8168i 0.170211 + 0.467650i
\(536\) 18.7505 29.5600i 0.809897 1.27680i
\(537\) 59.4269 + 10.4786i 2.56446 + 0.452184i
\(538\) 32.0860 + 21.7478i 1.38333 + 0.937613i
\(539\) 5.57104 + 1.49276i 0.239962 + 0.0642976i
\(540\) 60.5394 37.4505i 2.60520 1.61161i
\(541\) 1.47554 16.8655i 0.0634384 0.725104i −0.896160 0.443731i \(-0.853655\pi\)
0.959598 0.281373i \(-0.0907899\pi\)
\(542\) −22.2691 7.72411i −0.956541 0.331779i
\(543\) −38.7304 22.3610i −1.66208 0.959603i
\(544\) −2.92609 38.4335i −0.125455 1.64782i
\(545\) −7.24470 + 19.9047i −0.310329 + 0.852622i
\(546\) −10.9168 28.6321i −0.467196 1.22534i
\(547\) 9.77489 + 6.84445i 0.417944 + 0.292647i 0.763570 0.645725i \(-0.223445\pi\)
−0.345626 + 0.938372i \(0.612334\pi\)
\(548\) −6.28638 0.912434i −0.268541 0.0389772i
\(549\) −3.39336 38.7862i −0.144825 1.65536i
\(550\) −3.85424 0.970211i −0.164345 0.0413699i
\(551\) −7.35731 + 7.71991i −0.313432 + 0.328879i
\(552\) 38.9800 + 35.5784i 1.65910 + 1.51432i
\(553\) −18.9442 15.8961i −0.805591 0.675971i
\(554\) −0.183474 + 0.0188656i −0.00779507 + 0.000801521i
\(555\) 49.8528 + 34.9073i 2.11613 + 1.48173i
\(556\) −6.38697 + 0.754987i −0.270868 + 0.0320186i
\(557\) −8.57131 + 3.99687i −0.363178 + 0.169353i −0.595638 0.803253i \(-0.703101\pi\)
0.232459 + 0.972606i \(0.425323\pi\)
\(558\) −3.96873 + 7.12184i −0.168010 + 0.301491i
\(559\) −5.78844 + 10.0259i −0.244825 + 0.424049i
\(560\) 13.5069 + 24.8942i 0.570769 + 1.05197i
\(561\) −49.9383 59.5141i −2.10839 2.51269i
\(562\) 0.301685 + 19.8495i 0.0127258 + 0.837300i
\(563\) 17.8089 + 4.77189i 0.750557 + 0.201111i 0.613765 0.789488i \(-0.289654\pi\)
0.136792 + 0.990600i \(0.456321\pi\)
\(564\) 25.4844 + 1.45090i 1.07309 + 0.0610940i
\(565\) −3.43820 4.91026i −0.144646 0.206576i
\(566\) −2.59016 0.186994i −0.108873 0.00785996i
\(567\) −70.0375 + 25.4916i −2.94130 + 1.07055i
\(568\) −22.5339 17.2208i −0.945502 0.722571i
\(569\) −27.3628 −1.14711 −0.573554 0.819168i \(-0.694436\pi\)
−0.573554 + 0.819168i \(0.694436\pi\)
\(570\) −38.1285 29.5240i −1.59703 1.23662i
\(571\) 17.8779 17.8779i 0.748167 0.748167i −0.225968 0.974135i \(-0.572554\pi\)
0.974135 + 0.225968i \(0.0725543\pi\)
\(572\) 14.7975 5.90105i 0.618713 0.246735i
\(573\) −10.3196 4.81209i −0.431105 0.201028i
\(574\) 0.399723 + 0.461929i 0.0166841 + 0.0192806i
\(575\) −4.52927 0.798633i −0.188884 0.0333053i
\(576\) 15.4039 58.4024i 0.641827 2.43343i
\(577\) −7.25660 12.5688i −0.302096 0.523246i 0.674514 0.738262i \(-0.264353\pi\)
−0.976611 + 0.215016i \(0.931020\pi\)
\(578\) 0.632455 + 41.6125i 0.0263067 + 1.73085i
\(579\) −4.32635 0.378507i −0.179797 0.0157302i
\(580\) 11.5382 2.39816i 0.479097 0.0995783i
\(581\) 2.72447 0.730020i 0.113030 0.0302863i
\(582\) 3.26844 + 11.4962i 0.135481 + 0.476533i
\(583\) 0.989816 2.71950i 0.0409940 0.112630i
\(584\) −2.10865 + 16.2630i −0.0872567 + 0.672967i
\(585\) −7.16482 40.6337i −0.296229 1.68000i
\(586\) 0.843343 + 8.20181i 0.0348382 + 0.338814i
\(587\) −18.1166 + 1.58500i −0.747753 + 0.0654199i −0.454661 0.890665i \(-0.650240\pi\)
−0.293091 + 0.956084i \(0.594684\pi\)
\(588\) −3.07448 10.2209i −0.126789 0.421501i
\(589\) 3.29077 + 0.498995i 0.135594 + 0.0205607i
\(590\) 14.2386 + 23.8185i 0.586193 + 0.980594i
\(591\) −5.91607 4.96417i −0.243354 0.204199i
\(592\) 30.7784 4.59053i 1.26498 0.188669i
\(593\) 2.93743 + 16.6590i 0.120626 + 0.684104i 0.983810 + 0.179214i \(0.0573556\pi\)
−0.863184 + 0.504889i \(0.831533\pi\)
\(594\) −26.1377 68.5528i −1.07244 2.81276i
\(595\) −20.3895 43.7255i −0.835889 1.79257i
\(596\) −17.2872 16.2670i −0.708110 0.666321i
\(597\) 0.199353 + 0.743997i 0.00815899 + 0.0304498i
\(598\) 16.5870 8.04376i 0.678294 0.328934i
\(599\) 14.1755 + 16.8937i 0.579196 + 0.690259i 0.973491 0.228725i \(-0.0734555\pi\)
−0.394295 + 0.918984i \(0.629011\pi\)
\(600\) 2.22544 + 7.01028i 0.0908532 + 0.286193i
\(601\) 2.52714 + 4.37713i 0.103084 + 0.178547i 0.912954 0.408063i \(-0.133796\pi\)
−0.809870 + 0.586610i \(0.800462\pi\)
\(602\) −11.9013 + 17.5589i −0.485062 + 0.715647i
\(603\) −76.5417 + 53.5951i −3.11702 + 2.18256i
\(604\) −8.06932 + 24.4588i −0.328336 + 0.995214i
\(605\) −1.34620 + 2.88693i −0.0547306 + 0.117370i
\(606\) −23.0902 3.71055i −0.937977 0.150731i
\(607\) −9.17720 −0.372491 −0.186246 0.982503i \(-0.559632\pi\)
−0.186246 + 0.982503i \(0.559632\pi\)
\(608\) −24.5344 + 2.46245i −0.995001 + 0.0998654i
\(609\) −23.3622 −0.946683
\(610\) 17.3422 + 2.78685i 0.702165 + 0.112836i
\(611\) 3.76812 8.08076i 0.152442 0.326912i
\(612\) −32.2352 + 97.7077i −1.30303 + 3.94960i
\(613\) 35.1887 24.6394i 1.42126 0.995175i 0.425327 0.905040i \(-0.360159\pi\)
0.995930 0.0901352i \(-0.0287299\pi\)
\(614\) −17.0953 + 25.2219i −0.689911 + 1.01787i
\(615\) 0.574685 + 0.995384i 0.0231736 + 0.0401378i
\(616\) 27.8214 8.83202i 1.12096 0.355852i
\(617\) 30.8304 + 36.7423i 1.24119 + 1.47919i 0.820154 + 0.572142i \(0.193888\pi\)
0.421032 + 0.907046i \(0.361668\pi\)
\(618\) −25.2395 + 12.2397i −1.01528 + 0.492354i
\(619\) −5.61859 20.9689i −0.225830 0.842810i −0.982070 0.188516i \(-0.939632\pi\)
0.756240 0.654294i \(-0.227034\pi\)
\(620\) −2.67865 2.52057i −0.107577 0.101229i
\(621\) −35.8793 76.9434i −1.43979 3.08763i
\(622\) −16.4636 43.1799i −0.660129 1.73136i
\(623\) −5.25007 29.7746i −0.210340 1.19289i
\(624\) −23.6932 17.5429i −0.948485 0.702278i
\(625\) 21.7266 + 18.2308i 0.869063 + 0.729231i
\(626\) 9.98342 + 16.7004i 0.399018 + 0.667483i
\(627\) −37.2930 + 32.8524i −1.48934 + 1.31200i
\(628\) −11.1120 36.9409i −0.443416 1.47410i
\(629\) −52.8077 + 4.62007i −2.10558 + 0.184214i
\(630\) −7.73285 75.2047i −0.308084 2.99623i
\(631\) −1.22223 6.93160i −0.0486561 0.275943i 0.950767 0.309907i \(-0.100298\pi\)
−0.999423 + 0.0339642i \(0.989187\pi\)
\(632\) −23.5947 3.05929i −0.938549 0.121692i
\(633\) 11.0384 30.3277i 0.438736 1.20542i
\(634\) 11.7216 + 41.2289i 0.465525 + 1.63741i
\(635\) −34.5723 + 9.26363i −1.37196 + 0.367616i
\(636\) −5.24353 + 1.08984i −0.207919 + 0.0432151i
\(637\) −3.71399 0.324932i −0.147153 0.0128743i
\(638\) −0.184576 12.1443i −0.00730745 0.480796i
\(639\) 37.8519 + 65.5615i 1.49740 + 2.59357i
\(640\) 23.8539 + 13.1707i 0.942910 + 0.520616i
\(641\) −15.5447 2.74096i −0.613981 0.108261i −0.141995 0.989867i \(-0.545352\pi\)
−0.471986 + 0.881606i \(0.656463\pi\)
\(642\) −14.3658 16.6014i −0.566972 0.655206i
\(643\) −21.0182 9.80093i −0.828875 0.386511i −0.0385940 0.999255i \(-0.512288\pi\)
−0.790281 + 0.612744i \(0.790066\pi\)
\(644\) 31.3746 12.5118i 1.23633 0.493034i
\(645\) −28.2218 + 28.2218i −1.11123 + 1.11123i
\(646\) 41.9708 1.64787i 1.65132 0.0648347i
\(647\) −7.31978 −0.287770 −0.143885 0.989594i \(-0.545960\pi\)
−0.143885 + 0.989594i \(0.545960\pi\)
\(648\) −43.5405 + 56.9739i −1.71043 + 2.23814i
\(649\) 26.8749 9.78168i 1.05493 0.383965i
\(650\) 2.56245 + 0.184993i 0.100507 + 0.00725603i
\(651\) 4.18222 + 5.97283i 0.163914 + 0.234094i
\(652\) 25.7182 + 1.46421i 1.00720 + 0.0573430i
\(653\) −11.4446 3.06657i −0.447861 0.120004i 0.0278372 0.999612i \(-0.491138\pi\)
−0.475698 + 0.879608i \(0.657805\pi\)
\(654\) −0.613943 40.3945i −0.0240071 1.57955i
\(655\) 24.1911 + 28.8299i 0.945226 + 1.12648i
\(656\) 0.563452 + 0.167084i 0.0219991 + 0.00652353i
\(657\) 21.8872 37.9097i 0.853900 1.47900i
\(658\) 7.95250 14.2707i 0.310021 0.556329i
\(659\) −3.74621 + 1.74689i −0.145932 + 0.0680490i −0.494212 0.869341i \(-0.664543\pi\)
0.348281 + 0.937390i \(0.386766\pi\)
\(660\) 54.5418 6.44725i 2.12304 0.250959i
\(661\) 32.2902 + 22.6098i 1.25594 + 0.879421i 0.996271 0.0862756i \(-0.0274966\pi\)
0.259672 + 0.965697i \(0.416385\pi\)
\(662\) 23.8521 2.45257i 0.927037 0.0953217i
\(663\) 38.4701 + 32.2802i 1.49405 + 1.25366i
\(664\) 1.82938 2.00429i 0.0709937 0.0777814i
\(665\) −27.6502 + 13.7122i −1.07223 + 0.531738i
\(666\) −80.5529 20.2772i −3.12136 0.785726i
\(667\) −1.22494 14.0011i −0.0474298 0.542125i
\(668\) 30.5017 + 4.42716i 1.18015 + 0.171292i
\(669\) −11.5268 8.07114i −0.445651 0.312048i
\(670\) −15.0179 39.3883i −0.580191 1.52170i
\(671\) 6.19144 17.0108i 0.239018 0.656696i
\(672\) −40.9854 35.1862i −1.58105 1.35734i
\(673\) −2.49438 1.44013i −0.0961511 0.0555129i 0.451153 0.892446i \(-0.351013\pi\)
−0.547305 + 0.836934i \(0.684346\pi\)
\(674\) 2.87562 + 0.997417i 0.110765 + 0.0384191i
\(675\) 1.03120 11.7867i 0.0396909 0.453670i
\(676\) 13.3537 8.26081i 0.513606 0.317724i
\(677\) −40.8315 10.9408i −1.56928 0.420488i −0.633694 0.773583i \(-0.718462\pi\)
−0.935587 + 0.353096i \(0.885129\pi\)
\(678\) 9.46358 + 6.41437i 0.363447 + 0.246343i
\(679\) 7.53315 + 1.32830i 0.289096 + 0.0509754i
\(680\) −39.1959 24.8627i −1.50310 0.953443i
\(681\) −5.48682 15.0749i −0.210255 0.577672i
\(682\) −3.07179 + 2.22122i −0.117625 + 0.0850547i
\(683\) 20.0124 + 20.0124i 0.765754 + 0.765754i 0.977356 0.211602i \(-0.0678680\pi\)
−0.211602 + 0.977356i \(0.567868\pi\)
\(684\) 62.9829 + 19.1127i 2.40821 + 0.730791i
\(685\) −5.40903 + 5.40903i −0.206668 + 0.206668i
\(686\) 21.9903 + 3.53379i 0.839594 + 0.134921i
\(687\) 66.6492 24.2583i 2.54283 0.925513i
\(688\) −0.540266 + 20.4007i −0.0205974 + 0.777769i
\(689\) −0.324845 + 1.84229i −0.0123756 + 0.0701856i
\(690\) 62.4130 11.9858i 2.37602 0.456292i
\(691\) 0.951275 3.55021i 0.0361882 0.135056i −0.945468 0.325714i \(-0.894395\pi\)
0.981657 + 0.190658i \(0.0610620\pi\)
\(692\) 2.21379 9.39538i 0.0841556 0.357159i
\(693\) −77.6198 6.79085i −2.94853 0.257963i
\(694\) 12.0637 + 24.8765i 0.457931 + 0.944298i
\(695\) −3.87244 + 6.70726i −0.146890 + 0.254421i
\(696\) −18.9327 + 12.1136i −0.717640 + 0.459167i
\(697\) −0.940749 0.342405i −0.0356334 0.0129695i
\(698\) 40.3527 + 18.0753i 1.52737 + 0.684162i
\(699\) −2.76444 + 3.94803i −0.104561 + 0.149328i
\(700\) 4.65854 + 0.676162i 0.176076 + 0.0255565i
\(701\) 12.9100 1.12948i 0.487605 0.0426599i 0.159297 0.987231i \(-0.449077\pi\)
0.328308 + 0.944571i \(0.393522\pi\)
\(702\) 24.3336 + 40.7057i 0.918413 + 1.53634i
\(703\) 3.76688 + 33.7011i 0.142071 + 1.27106i
\(704\) 17.9669 21.5833i 0.677152 0.813450i
\(705\) 19.7584 23.5471i 0.744144 0.886836i
\(706\) −4.27571 + 5.25578i −0.160919 + 0.197804i
\(707\) −8.58516 + 12.2609i −0.322878 + 0.461118i
\(708\) −41.5586 32.7721i −1.56187 1.23165i
\(709\) −3.72655 7.99162i −0.139954 0.300132i 0.823821 0.566850i \(-0.191838\pi\)
−0.963774 + 0.266719i \(0.914060\pi\)
\(710\) −32.8508 + 9.33968i −1.23287 + 0.350512i
\(711\) 55.0004 + 31.7545i 2.06268 + 1.19089i
\(712\) −19.6932 21.4070i −0.738035 0.802263i
\(713\) −3.36027 + 2.81960i −0.125843 + 0.105595i
\(714\) 66.0463 + 64.0687i 2.47172 + 2.39771i
\(715\) 4.96521 18.5304i 0.185688 0.692998i
\(716\) 2.11201 37.0966i 0.0789297 1.38636i
\(717\) 39.6205 27.7426i 1.47965 1.03607i
\(718\) −15.4112 17.8095i −0.575140 0.664645i
\(719\) 2.08172 + 5.71949i 0.0776352 + 0.213301i 0.972438 0.233160i \(-0.0749065\pi\)
−0.894803 + 0.446461i \(0.852684\pi\)
\(720\) −45.2615 56.9361i −1.68680 2.12188i
\(721\) 17.9530i 0.668603i
\(722\) −1.69939 26.8163i −0.0632447 0.997998i
\(723\) 37.6591 + 37.6591i 1.40056 + 1.40056i
\(724\) −10.8740 + 25.2997i −0.404131 + 0.940256i
\(725\) 0.827786 1.77519i 0.0307432 0.0659290i
\(726\) 0.437458 6.05948i 0.0162356 0.224888i
\(727\) 2.34928 13.3234i 0.0871298 0.494138i −0.909747 0.415163i \(-0.863724\pi\)
0.996877 0.0789743i \(-0.0251645\pi\)
\(728\) −16.7192 + 8.74517i −0.619657 + 0.324117i
\(729\) 41.0505 23.7005i 1.52039 0.877796i
\(730\) 14.1747 + 13.7502i 0.524627 + 0.508919i
\(731\) 3.02986 34.6315i 0.112064 1.28089i
\(732\) −32.7990 + 6.81713i −1.21229 + 0.251968i
\(733\) −1.59814 5.96435i −0.0590288 0.220298i 0.930110 0.367280i \(-0.119711\pi\)
−0.989139 + 0.146982i \(0.953044\pi\)
\(734\) −7.12269 + 12.7816i −0.262903 + 0.471777i
\(735\) −12.0778 4.39598i −0.445498 0.162148i
\(736\) 18.9383 26.4077i 0.698076 0.973401i
\(737\) −42.7850 + 7.54415i −1.57601 + 0.277892i
\(738\) −1.21693 0.990004i −0.0447958 0.0364425i
\(739\) −3.27719 37.4584i −0.120553 1.37793i −0.779812 0.626014i \(-0.784685\pi\)
0.659259 0.751916i \(-0.270870\pi\)
\(740\) 17.7421 33.0078i 0.652211 1.21339i
\(741\) 20.0525 25.0993i 0.736648 0.922046i
\(742\) −0.836730 + 3.32398i −0.0307173 + 0.122027i
\(743\) 25.2941 30.1443i 0.927949 1.10589i −0.0661931 0.997807i \(-0.521085\pi\)
0.994142 0.108080i \(-0.0344702\pi\)
\(744\) 6.48627 + 2.67182i 0.237798 + 0.0979538i
\(745\) −28.1507 + 4.96373i −1.03136 + 0.181857i
\(746\) −42.8926 19.2131i −1.57041 0.703440i
\(747\) −6.56487 + 3.06125i −0.240196 + 0.112005i
\(748\) −32.7828 + 34.8387i −1.19866 + 1.27383i
\(749\) −13.5722 + 3.63667i −0.495919 + 0.132881i
\(750\) −43.8930 15.2244i −1.60275 0.555918i
\(751\) 29.2768 24.5662i 1.06833 0.896433i 0.0734270 0.997301i \(-0.476606\pi\)
0.994900 + 0.100868i \(0.0321620\pi\)
\(752\) −0.954875 15.6884i −0.0348207 0.572098i
\(753\) 82.7811 47.7937i 3.01671 1.74170i
\(754\) 1.48065 + 7.71010i 0.0539221 + 0.280785i
\(755\) 17.7897 + 25.4063i 0.647432 + 0.924629i
\(756\) 39.0999 + 77.6013i 1.42205 + 2.82233i
\(757\) 26.4405 + 12.3294i 0.960997 + 0.448120i 0.838833 0.544389i \(-0.183239\pi\)
0.122165 + 0.992510i \(0.461016\pi\)
\(758\) 22.1571 + 30.6418i 0.804784 + 1.11296i
\(759\) 65.4996i 2.37749i
\(760\) −15.2976 + 25.4494i −0.554904 + 0.923147i
\(761\) 36.3352i 1.31715i 0.752515 + 0.658575i \(0.228841\pi\)
−0.752515 + 0.658575i \(0.771159\pi\)
\(762\) 55.3168 39.9996i 2.00392 1.44903i
\(763\) −23.4337 10.9273i −0.848357 0.395595i
\(764\) −2.19663 + 6.65816i −0.0794712 + 0.240884i
\(765\) 71.0660 + 101.493i 2.56940 + 3.66948i
\(766\) 32.5925 6.25908i 1.17762 0.226150i
\(767\) −16.0102 + 9.24347i −0.578093 + 0.333762i
\(768\) −51.4591 7.26323i −1.85687 0.262089i
\(769\) 27.5505 23.1176i 0.993498 0.833644i 0.00742743 0.999972i \(-0.497636\pi\)
0.986070 + 0.166329i \(0.0531913\pi\)
\(770\) 11.5189 33.2098i 0.415113 1.19680i
\(771\) −70.7154 + 18.9481i −2.54675 + 0.682400i
\(772\) 0.0812676 + 2.67289i 0.00292489 + 0.0961996i
\(773\) −22.4368 + 10.4625i −0.806997 + 0.376309i −0.781922 0.623377i \(-0.785760\pi\)
−0.0250755 + 0.999686i \(0.507983\pi\)
\(774\) 22.2692 49.7153i 0.800449 1.78698i
\(775\) −0.602037 + 0.106155i −0.0216258 + 0.00381322i
\(776\) 6.79360 2.82961i 0.243876 0.101577i
\(777\) −47.7517 + 56.9082i −1.71308 + 2.04157i
\(778\) 4.36779 + 1.09948i 0.156593 + 0.0394184i
\(779\) −0.204509 + 0.606905i −0.00732731 + 0.0217446i
\(780\) −33.9967 + 10.2263i −1.21728 + 0.366162i
\(781\) 3.06775 + 35.0646i 0.109773 + 1.25471i
\(782\) −34.9338 + 42.9412i −1.24923 + 1.53558i
\(783\) 35.6073 6.27854i 1.27250 0.224377i
\(784\) −6.02775 + 2.61882i −0.215277 + 0.0935292i
\(785\) −43.6525 15.8882i −1.55802 0.567075i
\(786\) −62.7000 34.9403i −2.23644 1.24628i
\(787\) −9.83043 36.6877i −0.350417 1.30777i −0.886155 0.463390i \(-0.846633\pi\)
0.535738 0.844385i \(-0.320034\pi\)
\(788\) −2.60792 + 3.97646i −0.0929034 + 0.141655i
\(789\) 0.0827470 0.945802i 0.00294587 0.0336715i
\(790\) −19.9492 + 20.5650i −0.709761 + 0.731668i
\(791\) 6.33675 3.65852i 0.225309 0.130082i
\(792\) −66.4241 + 34.7438i −2.36028 + 1.23457i
\(793\) −2.03195 + 11.5238i −0.0721567 + 0.409221i
\(794\) −25.8866 1.86886i −0.918681 0.0663232i
\(795\) −2.72560 + 5.84507i −0.0966670 + 0.207303i
\(796\) 0.440539 0.175681i 0.0156145 0.00622686i
\(797\) −3.31043 3.31043i −0.117261 0.117261i 0.646041 0.763303i \(-0.276423\pi\)
−0.763303 + 0.646041i \(0.776423\pi\)
\(798\) 39.9581 43.2241i 1.41450 1.53012i
\(799\) 26.7739i 0.947193i
\(800\) 4.12587 1.86757i 0.145872 0.0660284i
\(801\) 26.5557 + 72.9613i 0.938301 + 2.57796i
\(802\) 12.6925 10.9833i 0.448188 0.387833i
\(803\) 16.6721 11.6739i 0.588346 0.411964i
\(804\) 53.5266 + 59.9893i 1.88774 + 2.11566i
\(805\) 10.5276 39.2894i 0.371048 1.38477i
\(806\) 1.70612 1.75878i 0.0600956 0.0619506i
\(807\) −68.1975 + 57.2245i −2.40067 + 2.01440i
\(808\) −0.599941 + 14.3877i −0.0211059 + 0.506158i
\(809\) 33.6701 + 19.4395i 1.18378 + 0.683455i 0.956886 0.290465i \(-0.0938099\pi\)
0.226893 + 0.973920i \(0.427143\pi\)
\(810\) 23.6141 + 83.0587i 0.829714 + 2.91839i
\(811\) 21.7197 + 46.5780i 0.762680 + 1.63557i 0.772005 + 0.635617i \(0.219254\pi\)
−0.00932455 + 0.999957i \(0.502968\pi\)
\(812\) 1.68869 + 14.2858i 0.0592613 + 0.501333i
\(813\) 31.0509 44.3452i 1.08900 1.55525i
\(814\) −29.9596 24.3729i −1.05008 0.854271i
\(815\) 19.9397 23.7632i 0.698456 0.832387i
\(816\) 86.7444 + 17.6751i 3.03666 + 0.618754i
\(817\) −22.1945 1.40505i −0.776488 0.0491564i
\(818\) 5.66044 3.38378i 0.197913 0.118311i
\(819\) 50.1736 4.38963i 1.75321 0.153386i
\(820\) 0.567130 0.423365i 0.0198051 0.0147846i
\(821\) −1.91446 + 2.73414i −0.0668152 + 0.0954221i −0.851169 0.524892i \(-0.824106\pi\)
0.784354 + 0.620314i \(0.212995\pi\)
\(822\) 5.96410 13.3147i 0.208022 0.464403i
\(823\) 37.4796 + 13.6414i 1.30646 + 0.475511i 0.899094 0.437756i \(-0.144227\pi\)
0.407362 + 0.913267i \(0.366449\pi\)
\(824\) 9.30889 + 14.5490i 0.324290 + 0.506840i
\(825\) 4.56416 7.90535i 0.158904 0.275229i
\(826\) −30.4786 + 14.7804i −1.06049 + 0.514276i
\(827\) 27.8651 + 2.43788i 0.968963 + 0.0847733i 0.560636 0.828062i \(-0.310557\pi\)
0.408327 + 0.912836i \(0.366112\pi\)
\(828\) −73.7693 + 45.6347i −2.56366 + 1.58592i
\(829\) −8.61213 + 32.1409i −0.299112 + 1.11630i 0.638785 + 0.769385i \(0.279437\pi\)
−0.937897 + 0.346914i \(0.887229\pi\)
\(830\) −0.616290 3.20917i −0.0213918 0.111392i
\(831\) 0.0735596 0.417177i 0.00255176 0.0144717i
\(832\) −9.01474 + 15.7562i −0.312530 + 0.546250i
\(833\) 10.5200 3.82898i 0.364498 0.132666i
\(834\) 2.34364 14.5842i 0.0811537 0.505009i
\(835\) 26.2448 26.2448i 0.908239 0.908239i
\(836\) 22.7847 + 20.4298i 0.788024 + 0.706578i
\(837\) −7.97950 7.97950i −0.275812 0.275812i
\(838\) −1.81111 2.50464i −0.0625637 0.0865214i
\(839\) −9.01758 24.7756i −0.311322 0.855349i −0.992391 0.123130i \(-0.960707\pi\)
0.681069 0.732219i \(-0.261515\pi\)
\(840\) −63.4792 + 14.2035i −2.19024 + 0.490069i
\(841\) −22.6647 3.99640i −0.781542 0.137807i
\(842\) −29.5958 + 43.6647i −1.01994 + 1.50479i
\(843\) −44.0406 11.8006i −1.51684 0.406436i
\(844\) −19.3430 4.55771i −0.665815 0.156883i
\(845\) 1.64804 18.8371i 0.0566942 0.648018i
\(846\) −13.7486 + 39.6381i −0.472687 + 1.36279i
\(847\) −3.36734 1.94413i −0.115703 0.0668012i
\(848\) 1.04545 + 3.12760i 0.0359009 + 0.107402i
\(849\) 2.03994 5.60470i 0.0700107 0.192353i
\(850\) −7.20851 + 2.74845i −0.247250 + 0.0942709i
\(851\) −36.6092 25.6340i −1.25495 0.878724i
\(852\) 52.1972 38.9654i 1.78825 1.33493i
\(853\) −2.47863 28.3308i −0.0848666 0.970030i −0.912585 0.408886i \(-0.865917\pi\)
0.827719 0.561143i \(-0.189638\pi\)
\(854\) −5.23386 + 20.7919i −0.179099 + 0.711486i
\(855\) 63.8148 47.0099i 2.18242 1.60770i
\(856\) −9.11325 + 9.98457i −0.311484 + 0.341265i
\(857\) −7.07131 5.93353i −0.241551 0.202686i 0.513973 0.857806i \(-0.328173\pi\)
−0.755524 + 0.655121i \(0.772618\pi\)
\(858\) 3.74245 + 36.3967i 0.127765 + 1.24256i
\(859\) −16.0096 11.2101i −0.546241 0.382482i 0.267635 0.963520i \(-0.413758\pi\)
−0.813876 + 0.581038i \(0.802647\pi\)
\(860\) 19.2974 + 15.2175i 0.658035 + 0.518911i
\(861\) −1.27155 + 0.592932i −0.0433342 + 0.0202071i
\(862\) 26.1452 + 14.5697i 0.890507 + 0.496246i
\(863\) −3.48223 + 6.03139i −0.118536 + 0.205311i −0.919188 0.393819i \(-0.871154\pi\)
0.800651 + 0.599130i \(0.204487\pi\)
\(864\) 71.9239 + 42.6141i 2.44690 + 1.44976i
\(865\) −7.47173 8.90446i −0.254046 0.302761i
\(866\) 34.1639 0.519245i 1.16094 0.0176447i
\(867\) −92.3270 24.7389i −3.13559 0.840179i
\(868\) 3.35004 2.98913i 0.113708 0.101458i
\(869\) 16.9369 + 24.1883i 0.574543 + 0.820533i
\(870\) −1.94897 + 26.9962i −0.0660761 + 0.915258i
\(871\) 26.3894 9.60494i 0.894170 0.325451i
\(872\) −24.6566 + 3.29526i −0.834978 + 0.111592i
\(873\) −19.6443 −0.664860
\(874\) 27.9996 + 21.6808i 0.947099 + 0.733364i
\(875\) −21.0253 + 21.0253i −0.710784 + 0.710784i
\(876\) −34.6035 14.8729i −1.16914 0.502509i
\(877\) −40.3041 18.7941i −1.36097 0.634632i −0.401351 0.915924i \(-0.631459\pi\)
−0.959622 + 0.281292i \(0.909237\pi\)
\(878\) −23.4637 + 20.3040i −0.791863 + 0.685226i
\(879\) −18.6490 3.28832i −0.629015 0.110912i
\(880\) −7.88489 32.8859i −0.265800 1.10858i
\(881\) 7.54238 + 13.0638i 0.254109 + 0.440130i 0.964653 0.263523i \(-0.0848844\pi\)
−0.710544 + 0.703653i \(0.751551\pi\)
\(882\) 17.5409 0.266598i 0.590632 0.00897682i
\(883\) 14.6307 + 1.28002i 0.492362 + 0.0430761i 0.330634 0.943759i \(-0.392738\pi\)
0.161728 + 0.986835i \(0.448293\pi\)
\(884\) 16.9584 25.8575i 0.570373 0.869682i
\(885\) −61.5625 + 16.4956i −2.06940 + 0.554495i
\(886\) −47.6177 + 13.5380i −1.59975 + 0.454817i
\(887\) 8.26135 22.6979i 0.277389 0.762120i −0.720267 0.693696i \(-0.755981\pi\)
0.997656 0.0684234i \(-0.0217969\pi\)
\(888\) −9.19007 + 70.8783i −0.308398 + 2.37852i
\(889\) −7.58668 43.0262i −0.254449 1.44305i
\(890\) −34.8441 + 3.58282i −1.16798 + 0.120096i
\(891\) 88.6559 7.75638i 2.97008 0.259849i
\(892\) −4.10225 + 7.63195i −0.137354 + 0.255537i
\(893\) 17.1227 0.411791i 0.572991 0.0137801i
\(894\) 46.7945 27.9735i 1.56504 0.935574i
\(895\) −34.2765 28.7614i −1.14574 0.961388i
\(896\) −18.5535 + 27.6057i −0.619830 + 0.922240i
\(897\) 7.35212 + 41.6959i 0.245480 + 1.39219i
\(898\) −30.4218 + 11.5992i −1.01519 + 0.387070i
\(899\) −0.789516 1.69312i −0.0263318 0.0564688i
\(900\) −12.0834 + 0.367387i −0.402779 + 0.0122462i
\(901\) −1.45391 5.42607i −0.0484368 0.180769i
\(902\) −0.318267 0.656298i −0.0105971 0.0218523i
\(903\) −31.3158 37.3207i −1.04212 1.24195i
\(904\) 3.23829 6.25056i 0.107704 0.207891i
\(905\) 16.5807 + 28.7186i 0.551161 + 0.954638i
\(906\) −48.9657 33.1888i −1.62678 1.10262i
\(907\) 7.84536 5.49338i 0.260501 0.182405i −0.436029 0.899933i \(-0.643615\pi\)
0.696530 + 0.717528i \(0.254726\pi\)
\(908\) −8.82160 + 4.44481i −0.292755 + 0.147506i
\(909\) 16.2449 34.8373i 0.538810 1.15548i
\(910\) −3.60505 + 22.4337i −0.119506 + 0.743671i
\(911\) −30.3312 −1.00492 −0.502458 0.864602i \(-0.667571\pi\)
−0.502458 + 0.864602i \(0.667571\pi\)
\(912\) 9.96964 55.7476i 0.330128 1.84599i
\(913\) −3.36788 −0.111461
\(914\) 7.53091 46.8639i 0.249100 1.55012i
\(915\) −17.0490 + 36.5617i −0.563622 + 1.20869i
\(916\) −19.6514 39.0021i −0.649301 1.28866i
\(917\) −37.6313 + 26.3497i −1.24270 + 0.870145i
\(918\) −117.882 79.9002i −3.89070 2.63710i
\(919\) 3.90061 + 6.75605i 0.128669 + 0.222862i 0.923161 0.384413i \(-0.125596\pi\)
−0.794492 + 0.607275i \(0.792263\pi\)
\(920\) −11.8406 37.2988i −0.390374 1.22970i
\(921\) −44.9826 53.6082i −1.48223 1.76645i
\(922\) 19.6500 + 40.5202i 0.647139 + 1.33446i
\(923\) −5.88876 21.9772i −0.193831 0.723387i
\(924\) 2.03739 + 67.0098i 0.0670252 + 2.20446i
\(925\) −2.63224 5.64486i −0.0865476 0.185602i
\(926\) 30.8194 11.7508i 1.01279 0.386154i
\(927\) −8.00605 45.4046i −0.262953 1.49128i
\(928\) 8.77592 + 10.7016i 0.288084 + 0.351296i
\(929\) −29.4779 24.7349i −0.967140 0.811527i 0.0149598 0.999888i \(-0.495238\pi\)
−0.982100 + 0.188361i \(0.939682\pi\)
\(930\) 7.25082 4.33450i 0.237764 0.142134i
\(931\) −2.61055 6.66900i −0.0855574 0.218568i
\(932\) 2.61401 + 1.40506i 0.0856248 + 0.0460242i
\(933\) 105.733 9.25043i 3.46154 0.302845i
\(934\) 13.3511 1.37281i 0.436860 0.0449198i
\(935\) 10.0034 + 56.7320i 0.327146 + 1.85534i
\(936\) 38.3845 29.5731i 1.25464 0.966629i
\(937\) −10.0040 + 27.4858i −0.326816 + 0.897920i 0.662096 + 0.749419i \(0.269667\pi\)
−0.988912 + 0.148501i \(0.952555\pi\)
\(938\) 49.4946 14.0716i 1.61606 0.459454i
\(939\) −43.1647 + 11.5660i −1.40863 + 0.377441i
\(940\) −15.8271 10.3801i −0.516223 0.338560i
\(941\) −36.0290 3.15213i −1.17451 0.102757i −0.516855 0.856073i \(-0.672897\pi\)
−0.657658 + 0.753317i \(0.728453\pi\)
\(942\) 88.5885 1.34643i 2.88637 0.0438689i
\(943\) −0.422018 0.730957i −0.0137428 0.0238032i
\(944\) −17.0359 + 27.7816i −0.554473 + 0.904215i
\(945\) 103.051 + 18.1707i 3.35226 + 0.591094i
\(946\) 19.1528 16.5736i 0.622712 0.538854i
\(947\) 10.0838 + 4.70216i 0.327680 + 0.152800i 0.579495 0.814976i \(-0.303250\pi\)
−0.251815 + 0.967775i \(0.581028\pi\)
\(948\) 21.5780 50.2036i 0.700821 1.63054i
\(949\) −9.30281 + 9.30281i −0.301982 + 0.301982i
\(950\) 1.86859 + 4.56779i 0.0606249 + 0.148199i
\(951\) −98.4443 −3.19228
\(952\) 34.4035 45.0179i 1.11503 1.45904i
\(953\) 15.3023 5.56957i 0.495689 0.180416i −0.0820650 0.996627i \(-0.526152\pi\)
0.577754 + 0.816211i \(0.303929\pi\)
\(954\) 0.633846 8.77976i 0.0205215 0.284255i
\(955\) 4.84270 + 6.91609i 0.156706 + 0.223799i
\(956\) −19.8283 22.2223i −0.641292 0.718722i
\(957\) 26.9448 + 7.21984i 0.871002 + 0.233384i
\(958\) −32.5753 + 0.495102i −1.05246 + 0.0159960i
\(959\) −6.00203 7.15294i −0.193816 0.230980i
\(960\) −44.0787 + 44.4255i −1.42263 + 1.43383i
\(961\) 15.2085 26.3418i 0.490596 0.849737i
\(962\) 21.8076 + 12.1525i 0.703104 + 0.391813i
\(963\) 32.7036 15.2499i 1.05386 0.491422i
\(964\) 20.3061 25.7504i 0.654017 0.829363i
\(965\) 2.63787 + 1.84706i 0.0849160 + 0.0594589i
\(966\) 7.93499 + 77.1706i 0.255304 + 2.48292i
\(967\) 0.867101 + 0.727584i 0.0278841 + 0.0233975i 0.656623 0.754219i \(-0.271984\pi\)
−0.628739 + 0.777616i \(0.716429\pi\)
\(968\) −3.73695 + 0.170495i −0.120110 + 0.00547991i
\(969\) −22.7207 + 93.7561i −0.729894 + 3.01188i
\(970\) 2.16337 8.59415i 0.0694615 0.275941i
\(971\) −4.25704 48.6582i −0.136615 1.56152i −0.687033 0.726626i \(-0.741087\pi\)
0.550418 0.834889i \(-0.314468\pi\)
\(972\) −45.4748 60.9170i −1.45861 1.95391i
\(973\) −7.74418 5.42253i −0.248267 0.173838i
\(974\) 45.2616 17.2573i 1.45028 0.552959i
\(975\) −2.01811 + 5.54472i −0.0646314 + 0.177573i
\(976\) 6.53943 + 19.5636i 0.209322 + 0.626215i
\(977\) 13.9787 + 8.07061i 0.447218 + 0.258202i 0.706655 0.707559i \(-0.250203\pi\)
−0.259436 + 0.965760i \(0.583537\pi\)
\(978\) −19.3879 + 55.8966i −0.619957 + 1.78738i
\(979\) −3.14636 + 35.9631i −0.100558 + 1.14939i
\(980\) −1.81508 + 7.70327i −0.0579808 + 0.246072i
\(981\) 64.1388 + 17.1859i 2.04779 + 0.548705i
\(982\) 27.0490 39.9074i 0.863170 1.27350i
\(983\) −42.9800 7.57853i −1.37085 0.241717i −0.560737 0.827994i \(-0.689482\pi\)
−0.810111 + 0.586276i \(0.800593\pi\)
\(984\) −0.723014 + 1.13983i −0.0230488 + 0.0363363i
\(985\) 1.95858 + 5.38116i 0.0624056 + 0.171458i
\(986\) −13.8142 19.1041i −0.439935 0.608400i
\(987\) 26.5317 + 26.5317i 0.844514 + 0.844514i
\(988\) −16.7975 10.4477i −0.534400 0.332386i
\(989\) 20.7245 20.7245i 0.659002 0.659002i
\(990\) −14.3225 + 89.1273i −0.455200 + 2.83265i
\(991\) −10.3978 + 3.78449i −0.330297 + 0.120218i −0.501845 0.864958i \(-0.667345\pi\)
0.171548 + 0.985176i \(0.445123\pi\)
\(992\) 1.16495 4.15943i 0.0369873 0.132062i
\(993\) −9.56292 + 54.2340i −0.303470 + 1.72106i
\(994\) −7.86230 40.9409i −0.249377 1.29857i
\(995\) 0.147820 0.551673i 0.00468622 0.0174892i
\(996\) 3.27883 + 5.30029i 0.103894 + 0.167946i
\(997\) −36.8963 3.22801i −1.16852 0.102232i −0.513667 0.857990i \(-0.671713\pi\)
−0.654851 + 0.755758i \(0.727269\pi\)
\(998\) 0.743370 0.360492i 0.0235310 0.0114112i
\(999\) 57.4865 99.5696i 1.81879 3.15024i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 304.2.bg.a.155.36 yes 456
16.3 odd 4 inner 304.2.bg.a.3.15 456
19.13 odd 18 inner 304.2.bg.a.203.15 yes 456
304.51 even 36 inner 304.2.bg.a.51.36 yes 456
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
304.2.bg.a.3.15 456 16.3 odd 4 inner
304.2.bg.a.51.36 yes 456 304.51 even 36 inner
304.2.bg.a.155.36 yes 456 1.1 even 1 trivial
304.2.bg.a.203.15 yes 456 19.13 odd 18 inner